Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,3,Mod(14,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.14");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.h (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.04360198270\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 14.10 | ||
Character | \(\chi\) | \(=\) | 75.14 |
Dual form | 75.3.h.a.59.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.624639 | − | 0.453826i | 0.312319 | − | 0.226913i | −0.420572 | − | 0.907259i | \(-0.638171\pi\) |
0.732891 | + | 0.680346i | \(0.238171\pi\) | |||||||
\(3\) | 2.28023 | + | 1.94950i | 0.760076 | + | 0.649834i | ||||
\(4\) | −1.05185 | + | 3.23727i | −0.262963 | + | 0.809318i | ||||
\(5\) | 2.07515 | − | 4.54904i | 0.415030 | − | 0.909808i | ||||
\(6\) | 2.30905 | + | 0.182906i | 0.384842 | + | 0.0304843i | ||||
\(7\) | 1.71117i | 0.244453i | 0.992502 | + | 0.122227i | \(0.0390035\pi\) | ||||
−0.992502 | + | 0.122227i | \(0.960997\pi\) | |||||||
\(8\) | 1.76649 | + | 5.43671i | 0.220812 | + | 0.679589i | ||||
\(9\) | 1.39889 | + | 8.89062i | 0.155432 | + | 0.987847i | ||||
\(10\) | −0.768257 | − | 3.78326i | −0.0768257 | − | 0.378326i | ||||
\(11\) | −3.68799 | − | 5.07609i | −0.335272 | − | 0.461462i | 0.607781 | − | 0.794105i | \(-0.292060\pi\) |
−0.943053 | + | 0.332642i | \(0.892060\pi\) | |||||||
\(12\) | −8.70953 | + | 5.33113i | −0.725794 | + | 0.444261i | ||||
\(13\) | 7.16998 | − | 9.86863i | 0.551537 | − | 0.759126i | −0.438683 | − | 0.898642i | \(-0.644555\pi\) |
0.990220 | + | 0.139516i | \(0.0445548\pi\) | |||||||
\(14\) | 0.776575 | + | 1.06886i | 0.0554697 | + | 0.0763474i | ||||
\(15\) | 13.6002 | − | 6.32735i | 0.906678 | − | 0.421823i | ||||
\(16\) | −7.44441 | − | 5.40868i | −0.465275 | − | 0.338042i | ||||
\(17\) | −4.51198 | − | 13.8864i | −0.265411 | − | 0.816850i | −0.991599 | − | 0.129353i | \(-0.958710\pi\) |
0.726188 | − | 0.687496i | \(-0.241290\pi\) | |||||||
\(18\) | 4.90860 | + | 4.91857i | 0.272700 | + | 0.273254i | ||||
\(19\) | −4.19666 | − | 12.9160i | −0.220877 | − | 0.679790i | −0.998684 | − | 0.0512863i | \(-0.983668\pi\) |
0.777807 | − | 0.628503i | \(-0.216332\pi\) | |||||||
\(20\) | 12.5437 | + | 11.5027i | 0.627186 | + | 0.575137i | ||||
\(21\) | −3.33593 | + | 3.90186i | −0.158854 | + | 0.185803i | ||||
\(22\) | −4.60733 | − | 1.49701i | −0.209424 | − | 0.0680459i | ||||
\(23\) | −31.0498 | + | 22.5590i | −1.34999 | + | 0.980826i | −0.350979 | + | 0.936383i | \(0.614151\pi\) |
−0.999012 | + | 0.0444426i | \(0.985849\pi\) | |||||||
\(24\) | −6.57086 | + | 15.8407i | −0.273786 | + | 0.660030i | ||||
\(25\) | −16.3875 | − | 18.8799i | −0.655501 | − | 0.755194i | ||||
\(26\) | − | 9.41826i | − | 0.362241i | ||||||
\(27\) | −14.1425 | + | 22.9998i | −0.523796 | + | 0.851844i | ||||
\(28\) | −5.53953 | − | 1.79990i | −0.197840 | − | 0.0642822i | ||||
\(29\) | 38.1684 | + | 12.4017i | 1.31615 | + | 0.427643i | 0.881171 | − | 0.472797i | \(-0.156756\pi\) |
0.434980 | + | 0.900440i | \(0.356756\pi\) | |||||||
\(30\) | 5.62367 | − | 10.1244i | 0.187456 | − | 0.337481i | ||||
\(31\) | −8.30364 | − | 25.5560i | −0.267859 | − | 0.824386i | −0.991021 | − | 0.133707i | \(-0.957312\pi\) |
0.723162 | − | 0.690679i | \(-0.242688\pi\) | |||||||
\(32\) | −29.9706 | −0.936583 | ||||||||
\(33\) | 1.48637 | − | 18.7644i | 0.0450416 | − | 0.568618i | ||||
\(34\) | −9.12039 | − | 6.62635i | −0.268247 | − | 0.194893i | ||||
\(35\) | 7.78419 | + | 3.55093i | 0.222405 | + | 0.101455i | ||||
\(36\) | −30.2528 | − | 4.82305i | −0.840355 | − | 0.133974i | ||||
\(37\) | −1.16967 | + | 1.60991i | −0.0316126 | + | 0.0435110i | −0.824531 | − | 0.565817i | \(-0.808561\pi\) |
0.792918 | + | 0.609328i | \(0.208561\pi\) | |||||||
\(38\) | −8.48302 | − | 6.16327i | −0.223237 | − | 0.162191i | ||||
\(39\) | 35.5881 | − | 8.52485i | 0.912516 | − | 0.218586i | ||||
\(40\) | 28.3975 | + | 3.24612i | 0.709939 | + | 0.0811531i | ||||
\(41\) | 20.7006 | − | 28.4920i | 0.504893 | − | 0.694926i | −0.478155 | − | 0.878276i | \(-0.658694\pi\) |
0.983048 | + | 0.183350i | \(0.0586942\pi\) | |||||||
\(42\) | −0.312983 | + | 3.95119i | −0.00745199 | + | 0.0940759i | ||||
\(43\) | 73.2513i | 1.70352i | 0.523934 | + | 0.851759i | \(0.324464\pi\) | ||||
−0.523934 | + | 0.851759i | \(0.675536\pi\) | |||||||
\(44\) | 20.3119 | − | 6.59974i | 0.461634 | − | 0.149994i | ||||
\(45\) | 43.3467 | + | 12.0858i | 0.963259 | + | 0.268572i | ||||
\(46\) | −9.15703 | + | 28.1824i | −0.199066 | + | 0.612662i | ||||
\(47\) | 5.42185 | − | 16.6867i | 0.115359 | − | 0.355037i | −0.876663 | − | 0.481105i | \(-0.840236\pi\) |
0.992022 | + | 0.126068i | \(0.0402356\pi\) | |||||||
\(48\) | −6.43072 | − | 26.8459i | −0.133973 | − | 0.559290i | ||||
\(49\) | 46.0719 | 0.940243 | ||||||||
\(50\) | −18.8045 | − | 4.35599i | −0.376089 | − | 0.0871199i | ||||
\(51\) | 16.7833 | − | 40.4604i | 0.329084 | − | 0.793341i | ||||
\(52\) | 24.4057 | + | 33.5915i | 0.469340 | + | 0.645991i | ||||
\(53\) | −25.7997 | + | 79.4032i | −0.486786 | + | 1.49817i | 0.342591 | + | 0.939485i | \(0.388696\pi\) |
−0.829377 | + | 0.558689i | \(0.811304\pi\) | |||||||
\(54\) | 1.60396 | + | 20.7848i | 0.0297029 | + | 0.384903i | ||||
\(55\) | −30.7445 | + | 6.24320i | −0.558990 | + | 0.113513i | ||||
\(56\) | −9.30315 | + | 3.02278i | −0.166128 | + | 0.0539781i | ||||
\(57\) | 15.6104 | − | 37.6328i | 0.273867 | − | 0.660225i | ||||
\(58\) | 29.4696 | − | 9.57527i | 0.508097 | − | 0.165091i | ||||
\(59\) | 5.62764 | − | 7.74578i | 0.0953837 | − | 0.131284i | −0.758658 | − | 0.651489i | \(-0.774144\pi\) |
0.854041 | + | 0.520205i | \(0.174144\pi\) | |||||||
\(60\) | 6.17795 | + | 50.6829i | 0.102966 | + | 0.844715i | ||||
\(61\) | −1.66280 | + | 1.20810i | −0.0272591 | + | 0.0198049i | −0.601331 | − | 0.799000i | \(-0.705363\pi\) |
0.574072 | + | 0.818805i | \(0.305363\pi\) | |||||||
\(62\) | −16.7847 | − | 12.1948i | −0.270722 | − | 0.196691i | ||||
\(63\) | −15.2134 | + | 2.39373i | −0.241482 | + | 0.0379958i | ||||
\(64\) | 11.0568 | − | 8.03324i | 0.172763 | − | 0.125519i | ||||
\(65\) | −30.0140 | − | 53.0954i | −0.461754 | − | 0.816852i | ||||
\(66\) | −7.58733 | − | 12.3955i | −0.114960 | − | 0.187811i | ||||
\(67\) | 25.3218 | − | 8.22755i | 0.377937 | − | 0.122799i | −0.113887 | − | 0.993494i | \(-0.536330\pi\) |
0.491824 | + | 0.870694i | \(0.336330\pi\) | |||||||
\(68\) | 49.7001 | 0.730884 | ||||||||
\(69\) | −114.779 | − | 9.09196i | −1.66347 | − | 0.131768i | ||||
\(70\) | 6.47381 | − | 1.31462i | 0.0924830 | − | 0.0187803i | ||||
\(71\) | 81.8447 | + | 26.5930i | 1.15274 | + | 0.374549i | 0.822176 | − | 0.569234i | \(-0.192760\pi\) |
0.330567 | + | 0.943783i | \(0.392760\pi\) | |||||||
\(72\) | −45.8646 | + | 23.3106i | −0.637008 | + | 0.323758i | ||||
\(73\) | −5.68457 | − | 7.82414i | −0.0778709 | − | 0.107180i | 0.768305 | − | 0.640084i | \(-0.221101\pi\) |
−0.846176 | + | 0.532904i | \(0.821101\pi\) | |||||||
\(74\) | 1.53644i | 0.0207626i | ||||||||
\(75\) | −0.560990 | − | 74.9979i | −0.00747986 | − | 0.999972i | ||||
\(76\) | 46.2269 | 0.608248 | ||||||||
\(77\) | 8.68606 | − | 6.31079i | 0.112806 | − | 0.0819583i | ||||
\(78\) | 18.3609 | − | 21.4758i | 0.235396 | − | 0.275330i | ||||
\(79\) | −41.5338 | + | 127.828i | −0.525744 | + | 1.61807i | 0.237096 | + | 0.971486i | \(0.423805\pi\) |
−0.762840 | + | 0.646588i | \(0.776195\pi\) | |||||||
\(80\) | −40.0525 | + | 22.6411i | −0.500657 | + | 0.283014i | ||||
\(81\) | −77.0862 | + | 24.8739i | −0.951682 | + | 0.307085i | ||||
\(82\) | − | 27.1917i | − | 0.331606i | ||||||
\(83\) | −0.618811 | − | 1.90451i | −0.00745556 | − | 0.0229459i | 0.947260 | − | 0.320467i | \(-0.103840\pi\) |
−0.954715 | + | 0.297522i | \(0.903840\pi\) | |||||||
\(84\) | −9.12248 | − | 14.9035i | −0.108601 | − | 0.177423i | ||||
\(85\) | −72.5330 | − | 8.29125i | −0.853329 | − | 0.0975441i | ||||
\(86\) | 33.2434 | + | 45.7556i | 0.386551 | + | 0.532041i | ||||
\(87\) | 62.8556 | + | 102.688i | 0.722478 | + | 1.18032i | ||||
\(88\) | 21.0824 | − | 29.0174i | 0.239573 | − | 0.329743i | ||||
\(89\) | −62.4318 | − | 85.9300i | −0.701481 | − | 0.965505i | −0.999939 | − | 0.0110825i | \(-0.996472\pi\) |
0.298458 | − | 0.954423i | \(-0.403528\pi\) | |||||||
\(90\) | 32.5608 | − | 12.1226i | 0.361787 | − | 0.134696i | ||||
\(91\) | 16.8869 | + | 12.2691i | 0.185571 | + | 0.134825i | ||||
\(92\) | −40.3698 | − | 124.245i | −0.438802 | − | 1.35049i | ||||
\(93\) | 30.8872 | − | 74.4614i | 0.332121 | − | 0.800660i | ||||
\(94\) | −4.18619 | − | 12.8838i | −0.0445339 | − | 0.137061i | ||||
\(95\) | −67.4641 | − | 7.71182i | −0.710148 | − | 0.0811771i | ||||
\(96\) | −68.3399 | − | 58.4278i | −0.711874 | − | 0.608623i | ||||
\(97\) | −85.9955 | − | 27.9416i | −0.886552 | − | 0.288058i | −0.169877 | − | 0.985465i | \(-0.554337\pi\) |
−0.716675 | + | 0.697407i | \(0.754337\pi\) | |||||||
\(98\) | 28.7783 | − | 20.9086i | 0.293656 | − | 0.213353i | ||||
\(99\) | 39.9705 | − | 39.8894i | 0.403742 | − | 0.402923i | ||||
\(100\) | 78.3565 | − | 33.1920i | 0.783565 | − | 0.331920i | ||||
\(101\) | 157.223i | 1.55666i | 0.627856 | + | 0.778329i | \(0.283933\pi\) | ||||
−0.627856 | + | 0.778329i | \(0.716067\pi\) | |||||||
\(102\) | −7.87849 | − | 32.8898i | −0.0772401 | − | 0.322449i | ||||
\(103\) | −87.8915 | − | 28.5577i | −0.853315 | − | 0.277259i | −0.150481 | − | 0.988613i | \(-0.548082\pi\) |
−0.702834 | + | 0.711354i | \(0.748082\pi\) | |||||||
\(104\) | 66.3186 | + | 21.5482i | 0.637679 | + | 0.207194i | ||||
\(105\) | 10.8272 | + | 23.2722i | 0.103116 | + | 0.221640i | ||||
\(106\) | 19.9198 | + | 61.3069i | 0.187923 | + | 0.578367i | ||||
\(107\) | 4.26071 | 0.0398198 | 0.0199099 | − | 0.999802i | \(-0.493662\pi\) | ||||
0.0199099 | + | 0.999802i | \(0.493662\pi\) | |||||||
\(108\) | −59.5807 | − | 69.9755i | −0.551673 | − | 0.647921i | ||||
\(109\) | −124.599 | − | 90.5264i | −1.14311 | − | 0.830518i | −0.155560 | − | 0.987826i | \(-0.549718\pi\) |
−0.987550 | + | 0.157309i | \(0.949718\pi\) | |||||||
\(110\) | −16.3708 | + | 17.8524i | −0.148826 | + | 0.162294i | ||||
\(111\) | −5.80562 | + | 1.39069i | −0.0523029 | + | 0.0125287i | ||||
\(112\) | 9.25518 | − | 12.7387i | 0.0826355 | − | 0.113738i | ||||
\(113\) | 18.2003 | + | 13.2233i | 0.161064 | + | 0.117020i | 0.665398 | − | 0.746489i | \(-0.268262\pi\) |
−0.504334 | + | 0.863509i | \(0.668262\pi\) | |||||||
\(114\) | −7.32791 | − | 30.5913i | −0.0642799 | − | 0.268345i | ||||
\(115\) | 38.1889 | + | 188.060i | 0.332077 | + | 1.63530i | ||||
\(116\) | −80.2951 | + | 110.517i | −0.692199 | + | 0.952730i | ||||
\(117\) | 97.7682 | + | 49.9405i | 0.835626 | + | 0.426842i | ||||
\(118\) | − | 7.39228i | − | 0.0626464i | ||||||
\(119\) | 23.7621 | − | 7.72077i | 0.199681 | − | 0.0648804i | ||||
\(120\) | 58.4246 | + | 62.7630i | 0.486871 | + | 0.523025i | ||||
\(121\) | 25.2257 | − | 77.6367i | 0.208477 | − | 0.641626i | ||||
\(122\) | −0.490384 | + | 1.50925i | −0.00401954 | + | 0.0123709i | ||||
\(123\) | 102.747 | − | 24.6123i | 0.835344 | − | 0.200100i | ||||
\(124\) | 91.4658 | 0.737627 | ||||||||
\(125\) | −119.892 | + | 35.3690i | −0.959134 | + | 0.282952i | ||||
\(126\) | −8.41652 | + | 8.39945i | −0.0667978 | + | 0.0666623i | ||||
\(127\) | 90.4421 | + | 124.483i | 0.712143 | + | 0.980180i | 0.999748 | + | 0.0224315i | \(0.00714076\pi\) |
−0.287606 | + | 0.957749i | \(0.592859\pi\) | |||||||
\(128\) | 40.3066 | − | 124.051i | 0.314895 | − | 0.969147i | ||||
\(129\) | −142.803 | + | 167.030i | −1.10700 | + | 1.29480i | ||||
\(130\) | −42.8440 | − | 19.5443i | −0.329569 | − | 0.150341i | ||||
\(131\) | 159.091 | − | 51.6917i | 1.21443 | − | 0.394593i | 0.369381 | − | 0.929278i | \(-0.379570\pi\) |
0.845052 | + | 0.534685i | \(0.179570\pi\) | |||||||
\(132\) | 59.1820 | + | 24.5492i | 0.448348 | + | 0.185979i | ||||
\(133\) | 22.1015 | − | 7.18121i | 0.166177 | − | 0.0539941i | ||||
\(134\) | 12.0831 | − | 16.6310i | 0.0901724 | − | 0.124112i | ||||
\(135\) | 75.2791 | + | 112.063i | 0.557623 | + | 0.830094i | ||||
\(136\) | 67.5262 | − | 49.0606i | 0.496516 | − | 0.360740i | ||||
\(137\) | 154.827 | + | 112.488i | 1.13012 | + | 0.821081i | 0.985712 | − | 0.168437i | \(-0.0538719\pi\) |
0.144409 | + | 0.989518i | \(0.453872\pi\) | |||||||
\(138\) | −75.8218 | + | 46.4108i | −0.549434 | + | 0.336310i | ||||
\(139\) | −6.70525 | + | 4.87165i | −0.0482392 | + | 0.0350478i | −0.611644 | − | 0.791133i | \(-0.709491\pi\) |
0.563404 | + | 0.826181i | \(0.309491\pi\) | |||||||
\(140\) | −19.6832 | + | 21.4645i | −0.140594 | + | 0.153318i | ||||
\(141\) | 44.8939 | − | 27.4797i | 0.318397 | − | 0.194891i | ||||
\(142\) | 63.1920 | − | 20.5323i | 0.445014 | − | 0.144594i | ||||
\(143\) | −76.5369 | −0.535223 | ||||||||
\(144\) | 37.6726 | − | 73.7515i | 0.261615 | − | 0.512163i | ||||
\(145\) | 135.621 | − | 147.894i | 0.935315 | − | 1.01996i | ||||
\(146\) | −7.10161 | − | 2.30745i | −0.0486411 | − | 0.0158045i | ||||
\(147\) | 105.054 | + | 89.8172i | 0.714656 | + | 0.611002i | ||||
\(148\) | −3.98139 | − | 5.47991i | −0.0269013 | − | 0.0370264i | ||||
\(149\) | − | 266.284i | − | 1.78714i | −0.448921 | − | 0.893571i | \(-0.648192\pi\) | ||
0.448921 | − | 0.893571i | \(-0.351808\pi\) | |||||||
\(150\) | −34.3864 | − | 46.5920i | −0.229243 | − | 0.310613i | ||||
\(151\) | −209.240 | −1.38570 | −0.692849 | − | 0.721083i | \(-0.743645\pi\) | ||||
−0.692849 | + | 0.721083i | \(0.743645\pi\) | |||||||
\(152\) | 62.8072 | − | 45.6321i | 0.413205 | − | 0.300211i | ||||
\(153\) | 117.147 | − | 59.5398i | 0.765669 | − | 0.389149i | ||||
\(154\) | 2.56164 | − | 7.88393i | 0.0166340 | − | 0.0511943i | ||||
\(155\) | −133.486 | − | 15.2588i | −0.861202 | − | 0.0984440i | ||||
\(156\) | −9.83623 | + | 124.175i | −0.0630527 | + | 0.795995i | ||||
\(157\) | − | 216.981i | − | 1.38204i | −0.722835 | − | 0.691021i | \(-0.757161\pi\) | ||
0.722835 | − | 0.691021i | \(-0.242839\pi\) | |||||||
\(158\) | 32.0681 | + | 98.6953i | 0.202962 | + | 0.624654i | ||||
\(159\) | −213.626 | + | 130.761i | −1.34356 | + | 0.822396i | ||||
\(160\) | −62.1935 | + | 136.338i | −0.388709 | + | 0.852110i | ||||
\(161\) | −38.6023 | − | 53.1315i | −0.239766 | − | 0.330010i | ||||
\(162\) | −36.8626 | + | 50.5210i | −0.227547 | + | 0.311858i | ||||
\(163\) | 8.35407 | − | 11.4984i | 0.0512519 | − | 0.0705422i | −0.782622 | − | 0.622497i | \(-0.786118\pi\) |
0.833874 | + | 0.551955i | \(0.186118\pi\) | |||||||
\(164\) | 70.4622 | + | 96.9829i | 0.429647 | + | 0.591359i | ||||
\(165\) | −82.2755 | − | 45.7004i | −0.498639 | − | 0.276972i | ||||
\(166\) | −1.25085 | − | 0.908795i | −0.00753523 | − | 0.00547467i | ||||
\(167\) | 4.56813 | + | 14.0593i | 0.0273541 | + | 0.0841871i | 0.963802 | − | 0.266621i | \(-0.0859071\pi\) |
−0.936448 | + | 0.350808i | \(0.885907\pi\) | |||||||
\(168\) | −27.1062 | − | 11.2439i | −0.161346 | − | 0.0669279i | ||||
\(169\) | 6.24259 | + | 19.2127i | 0.0369384 | + | 0.113685i | ||||
\(170\) | −49.0697 | + | 27.7384i | −0.288645 | + | 0.163167i | ||||
\(171\) | 108.961 | − | 55.3789i | 0.637196 | − | 0.323853i | ||||
\(172\) | −237.134 | − | 77.0496i | −1.37869 | − | 0.447963i | ||||
\(173\) | −114.125 | + | 82.9168i | −0.659683 | + | 0.479288i | −0.866556 | − | 0.499080i | \(-0.833671\pi\) |
0.206873 | + | 0.978368i | \(0.433671\pi\) | |||||||
\(174\) | 85.8645 | + | 35.6173i | 0.493474 | + | 0.204697i | ||||
\(175\) | 32.3067 | − | 28.0419i | 0.184610 | − | 0.160239i | ||||
\(176\) | 57.7356i | 0.328043i | ||||||||
\(177\) | 27.9327 | − | 6.69106i | 0.157812 | − | 0.0378026i | ||||
\(178\) | −77.9946 | − | 25.3420i | −0.438172 | − | 0.142371i | ||||
\(179\) | −18.8274 | − | 6.11739i | −0.105181 | − | 0.0341754i | 0.255954 | − | 0.966689i | \(-0.417611\pi\) |
−0.361135 | + | 0.932514i | \(0.617611\pi\) | |||||||
\(180\) | −84.7192 | + | 127.612i | −0.470662 | + | 0.708958i | ||||
\(181\) | −24.7103 | − | 76.0504i | −0.136521 | − | 0.420168i | 0.859303 | − | 0.511467i | \(-0.170898\pi\) |
−0.995823 | + | 0.0912996i | \(0.970898\pi\) | |||||||
\(182\) | 16.1163 | 0.0885509 | ||||||||
\(183\) | −6.14676 | − | 0.486900i | −0.0335888 | − | 0.00266065i | ||||
\(184\) | −177.496 | − | 128.958i | −0.964652 | − | 0.700861i | ||||
\(185\) | 4.89630 | + | 8.66165i | 0.0264665 | + | 0.0468197i | ||||
\(186\) | −14.4992 | − | 60.5289i | −0.0779527 | − | 0.325424i | ||||
\(187\) | −53.8486 | + | 74.1163i | −0.287961 | + | 0.396344i | ||||
\(188\) | 48.3165 | + | 35.1040i | 0.257003 | + | 0.186723i | ||||
\(189\) | −39.3566 | − | 24.2003i | −0.208236 | − | 0.128044i | ||||
\(190\) | −45.6405 | + | 25.7999i | −0.240213 | + | 0.135789i | ||||
\(191\) | 82.2359 | − | 113.188i | 0.430554 | − | 0.592607i | −0.537526 | − | 0.843247i | \(-0.680641\pi\) |
0.968080 | + | 0.250640i | \(0.0806410\pi\) | |||||||
\(192\) | 40.8729 | + | 3.23764i | 0.212880 | + | 0.0168627i | ||||
\(193\) | − | 179.383i | − | 0.929445i | −0.885456 | − | 0.464723i | \(-0.846154\pi\) | ||
0.885456 | − | 0.464723i | \(-0.153846\pi\) | |||||||
\(194\) | −66.3968 | + | 21.5736i | −0.342251 | + | 0.111204i | ||||
\(195\) | 35.0707 | − | 179.582i | 0.179850 | − | 0.920934i | ||||
\(196\) | −48.4609 | + | 149.147i | −0.247249 | + | 0.760955i | ||||
\(197\) | 4.98853 | − | 15.3531i | 0.0253225 | − | 0.0779346i | −0.937597 | − | 0.347725i | \(-0.886954\pi\) |
0.962919 | + | 0.269790i | \(0.0869544\pi\) | |||||||
\(198\) | 6.86423 | − | 43.0561i | 0.0346678 | − | 0.217455i | ||||
\(199\) | 344.397 | 1.73064 | 0.865318 | − | 0.501223i | \(-0.167116\pi\) | ||||
0.865318 | + | 0.501223i | \(0.167116\pi\) | |||||||
\(200\) | 73.6958 | − | 122.445i | 0.368479 | − | 0.612227i | ||||
\(201\) | 73.7791 | + | 30.6042i | 0.367060 | + | 0.152260i | ||||
\(202\) | 71.3517 | + | 98.2072i | 0.353226 | + | 0.486174i | ||||
\(203\) | −21.2214 | + | 65.3127i | −0.104539 | + | 0.321737i | ||||
\(204\) | 113.328 | + | 96.8905i | 0.555528 | + | 0.474953i | ||||
\(205\) | −86.6542 | − | 153.293i | −0.422703 | − | 0.747770i | ||||
\(206\) | −67.8606 | + | 22.0493i | −0.329421 | + | 0.107035i | ||||
\(207\) | −243.999 | − | 244.494i | −1.17874 | − | 1.18113i | ||||
\(208\) | −106.753 | + | 34.6860i | −0.513233 | + | 0.166760i | ||||
\(209\) | −50.0855 | + | 68.9367i | −0.239643 | + | 0.329841i | ||||
\(210\) | 17.3246 | + | 9.62307i | 0.0824982 | + | 0.0458242i | ||||
\(211\) | 30.9857 | − | 22.5124i | 0.146852 | − | 0.106694i | −0.511934 | − | 0.859025i | \(-0.671071\pi\) |
0.658785 | + | 0.752331i | \(0.271071\pi\) | |||||||
\(212\) | −229.912 | − | 167.041i | −1.08449 | − | 0.787930i | ||||
\(213\) | 134.782 | + | 220.194i | 0.632778 | + | 1.03378i | ||||
\(214\) | 2.66141 | − | 1.93362i | 0.0124365 | − | 0.00903563i | ||||
\(215\) | 333.223 | + | 152.007i | 1.54987 | + | 0.707010i | ||||
\(216\) | −150.026 | − | 36.2597i | −0.694564 | − | 0.167869i | ||||
\(217\) | 43.7307 | − | 14.2090i | 0.201524 | − | 0.0654790i | ||||
\(218\) | −118.913 | −0.545471 | ||||||||
\(219\) | 2.29106 | − | 28.9229i | 0.0104614 | − | 0.132068i | ||||
\(220\) | 12.1277 | − | 106.095i | 0.0551260 | − | 0.482250i | ||||
\(221\) | −169.391 | − | 55.0385i | −0.766475 | − | 0.249043i | ||||
\(222\) | −2.99528 | + | 3.50342i | −0.0134923 | + | 0.0157812i | ||||
\(223\) | 147.749 | + | 203.359i | 0.662550 | + | 0.911922i | 0.999562 | − | 0.0295784i | \(-0.00941647\pi\) |
−0.337013 | + | 0.941500i | \(0.609416\pi\) | |||||||
\(224\) | − | 51.2849i | − | 0.228951i | ||||||
\(225\) | 144.929 | − | 172.106i | 0.644130 | − | 0.764916i | ||||
\(226\) | 17.3697 | 0.0768570 | ||||||||
\(227\) | −28.4124 | + | 20.6428i | −0.125165 | + | 0.0909376i | −0.648606 | − | 0.761124i | \(-0.724648\pi\) |
0.523442 | + | 0.852062i | \(0.324648\pi\) | |||||||
\(228\) | 105.408 | + | 90.1194i | 0.462315 | + | 0.395260i | ||||
\(229\) | −45.0741 | + | 138.724i | −0.196830 | + | 0.605781i | 0.803120 | + | 0.595817i | \(0.203172\pi\) |
−0.999950 | + | 0.00996408i | \(0.996828\pi\) | |||||||
\(230\) | 109.201 | + | 100.138i | 0.474786 | + | 0.435384i | ||||
\(231\) | 32.1091 | + | 2.54344i | 0.139000 | + | 0.0110106i | ||||
\(232\) | 229.418i | 0.988870i | ||||||||
\(233\) | 40.5672 | + | 124.853i | 0.174108 | + | 0.535849i | 0.999592 | − | 0.0285768i | \(-0.00909751\pi\) |
−0.825484 | + | 0.564426i | \(0.809098\pi\) | |||||||
\(234\) | 83.7341 | − | 13.1751i | 0.357838 | − | 0.0563037i | ||||
\(235\) | −64.6575 | − | 59.2917i | −0.275138 | − | 0.252305i | ||||
\(236\) | 19.1557 | + | 26.3656i | 0.0811684 | + | 0.111719i | ||||
\(237\) | −343.907 | + | 210.507i | −1.45109 | + | 0.888213i | ||||
\(238\) | 11.3388 | − | 15.6066i | 0.0476421 | − | 0.0655738i | ||||
\(239\) | 100.919 | + | 138.903i | 0.422255 | + | 0.581185i | 0.966154 | − | 0.257966i | \(-0.0830524\pi\) |
−0.543899 | + | 0.839151i | \(0.683052\pi\) | |||||||
\(240\) | −135.468 | − | 26.4556i | −0.564449 | − | 0.110232i | ||||
\(241\) | 324.422 | + | 235.706i | 1.34615 | + | 0.978034i | 0.999194 | + | 0.0401521i | \(0.0127843\pi\) |
0.346955 | + | 0.937882i | \(0.387216\pi\) | |||||||
\(242\) | −19.4766 | − | 59.9430i | −0.0804820 | − | 0.247698i | ||||
\(243\) | −224.266 | − | 93.5615i | −0.922905 | − | 0.385027i | ||||
\(244\) | −2.16191 | − | 6.65368i | −0.00886030 | − | 0.0272692i | ||||
\(245\) | 95.6060 | − | 209.583i | 0.390228 | − | 0.855440i | ||||
\(246\) | 53.0102 | − | 62.0032i | 0.215489 | − | 0.252046i | ||||
\(247\) | −157.553 | − | 51.1922i | −0.637867 | − | 0.207256i | ||||
\(248\) | 124.272 | − | 90.2889i | 0.501097 | − | 0.364068i | ||||
\(249\) | 2.30181 | − | 5.54908i | 0.00924420 | − | 0.0222855i | ||||
\(250\) | −58.8376 | + | 76.5029i | −0.235350 | + | 0.306012i | ||||
\(251\) | − | 365.146i | − | 1.45476i | −0.686233 | − | 0.727382i | \(-0.740737\pi\) | ||
0.686233 | − | 0.727382i | \(-0.259263\pi\) | |||||||
\(252\) | 8.25308 | − | 51.7677i | 0.0327503 | − | 0.205427i | ||||
\(253\) | 229.023 | + | 74.4140i | 0.905229 | + | 0.294127i | ||||
\(254\) | 112.987 | + | 36.7118i | 0.444832 | + | 0.144535i | ||||
\(255\) | −149.228 | − | 160.309i | −0.585208 | − | 0.628663i | ||||
\(256\) | −14.2272 | − | 43.7869i | −0.0555751 | − | 0.171043i | ||||
\(257\) | −142.469 | −0.554354 | −0.277177 | − | 0.960819i | \(-0.589399\pi\) | ||||
−0.277177 | + | 0.960819i | \(0.589399\pi\) | |||||||
\(258\) | −13.3981 | + | 169.141i | −0.0519306 | + | 0.655586i | ||||
\(259\) | −2.75483 | − | 2.00150i | −0.0106364 | − | 0.00772780i | ||||
\(260\) | 203.455 | − | 41.3150i | 0.782518 | − | 0.158904i | ||||
\(261\) | −56.8652 | + | 356.689i | −0.217874 | + | 1.36662i | ||||
\(262\) | 75.9151 | − | 104.488i | 0.289752 | − | 0.398810i | ||||
\(263\) | −198.261 | − | 144.045i | −0.753843 | − | 0.547699i | 0.143172 | − | 0.989698i | \(-0.454270\pi\) |
−0.897016 | + | 0.441998i | \(0.854270\pi\) | |||||||
\(264\) | 104.642 | − | 25.0662i | 0.396372 | − | 0.0949477i | ||||
\(265\) | 307.670 | + | 282.137i | 1.16102 | + | 1.06467i | ||||
\(266\) | 10.5464 | − | 14.5159i | 0.0396482 | − | 0.0545711i | ||||
\(267\) | 25.1619 | − | 317.651i | 0.0942393 | − | 1.18970i | ||||
\(268\) | 90.6277i | 0.338163i | ||||||||
\(269\) | 110.951 | − | 36.0503i | 0.412459 | − | 0.134016i | −0.0954349 | − | 0.995436i | \(-0.530424\pi\) |
0.507894 | + | 0.861420i | \(0.330424\pi\) | |||||||
\(270\) | 97.8793 | + | 35.8350i | 0.362516 | + | 0.132722i | ||||
\(271\) | −53.8737 | + | 165.806i | −0.198796 | + | 0.611831i | 0.801115 | + | 0.598510i | \(0.204240\pi\) |
−0.999911 | + | 0.0133212i | \(0.995760\pi\) | |||||||
\(272\) | −41.5183 | + | 127.780i | −0.152641 | + | 0.469780i | ||||
\(273\) | 14.5875 | + | 60.8974i | 0.0534340 | + | 0.223067i | ||||
\(274\) | 147.761 | 0.539273 | ||||||||
\(275\) | −35.3987 | + | 152.813i | −0.128723 | + | 0.555685i | ||||
\(276\) | 150.164 | − | 362.009i | 0.544073 | − | 1.31163i | ||||
\(277\) | 107.330 | + | 147.728i | 0.387475 | + | 0.533313i | 0.957545 | − | 0.288282i | \(-0.0930842\pi\) |
−0.570071 | + | 0.821596i | \(0.693084\pi\) | |||||||
\(278\) | −1.97747 | + | 6.08604i | −0.00711322 | + | 0.0218922i | ||||
\(279\) | 215.593 | − | 109.574i | 0.772733 | − | 0.392740i | ||||
\(280\) | −5.55468 | + | 48.5931i | −0.0198381 | + | 0.173547i | ||||
\(281\) | −17.1449 | + | 5.57070i | −0.0610137 | + | 0.0198246i | −0.339365 | − | 0.940655i | \(-0.610212\pi\) |
0.278351 | + | 0.960479i | \(0.410212\pi\) | |||||||
\(282\) | 15.5715 | − | 37.5389i | 0.0552179 | − | 0.133117i | ||||
\(283\) | 19.2974 | − | 6.27010i | 0.0681887 | − | 0.0221558i | −0.274724 | − | 0.961523i | \(-0.588586\pi\) |
0.342913 | + | 0.939367i | \(0.388586\pi\) | |||||||
\(284\) | −172.177 | + | 236.982i | −0.606258 | + | 0.834443i | ||||
\(285\) | −138.799 | − | 149.106i | −0.487015 | − | 0.523179i | ||||
\(286\) | −47.8079 | + | 34.7345i | −0.167160 | + | 0.121449i | ||||
\(287\) | 48.7546 | + | 35.4223i | 0.169877 | + | 0.123423i | ||||
\(288\) | −41.9255 | − | 266.458i | −0.145575 | − | 0.925200i | ||||
\(289\) | 61.3306 | − | 44.5593i | 0.212217 | − | 0.154184i | ||||
\(290\) | 17.5956 | − | 153.929i | 0.0606744 | − | 0.530788i | ||||
\(291\) | −141.617 | − | 231.362i | −0.486657 | − | 0.795058i | ||||
\(292\) | 31.3082 | − | 10.1727i | 0.107220 | − | 0.0348379i | ||||
\(293\) | 121.001 | 0.412971 | 0.206486 | − | 0.978450i | \(-0.433797\pi\) | ||||
0.206486 | + | 0.978450i | \(0.433797\pi\) | |||||||
\(294\) | 106.382 | + | 8.42682i | 0.361845 | + | 0.0286626i | ||||
\(295\) | −23.5577 | − | 41.6740i | −0.0798565 | − | 0.141268i | ||||
\(296\) | −10.8188 | − | 3.51524i | −0.0365500 | − | 0.0118758i | ||||
\(297\) | 168.906 | − | 13.0345i | 0.568708 | − | 0.0438870i | ||||
\(298\) | −120.847 | − | 166.331i | −0.405526 | − | 0.558159i | ||||
\(299\) | 468.167i | 1.56577i | ||||||||
\(300\) | 243.379 | + | 77.0707i | 0.811262 | + | 0.256902i | ||||
\(301\) | −125.346 | −0.416430 | ||||||||
\(302\) | −130.700 | + | 94.9588i | −0.432780 | + | 0.314433i | ||||
\(303\) | −306.506 | + | 358.503i | −1.01157 | + | 1.18318i | ||||
\(304\) | −38.6168 | + | 118.850i | −0.127029 | + | 0.390955i | ||||
\(305\) | 2.04512 | + | 10.0711i | 0.00670531 | + | 0.0330201i | ||||
\(306\) | 46.1540 | − | 90.3554i | 0.150830 | − | 0.295279i | ||||
\(307\) | 186.483i | 0.607435i | 0.952762 | + | 0.303718i | \(0.0982279\pi\) | ||||
−0.952762 | + | 0.303718i | \(0.901772\pi\) | |||||||
\(308\) | 11.2933 | + | 34.7572i | 0.0366665 | + | 0.112848i | ||||
\(309\) | −144.739 | − | 236.463i | −0.468412 | − | 0.765251i | ||||
\(310\) | −90.3056 | + | 51.0484i | −0.291308 | + | 0.164672i | ||||
\(311\) | −188.941 | − | 260.055i | −0.607526 | − | 0.836188i | 0.388845 | − | 0.921303i | \(-0.372874\pi\) |
−0.996371 | + | 0.0851150i | \(0.972874\pi\) | |||||||
\(312\) | 109.213 | + | 178.423i | 0.350043 | + | 0.571869i | ||||
\(313\) | −117.969 | + | 162.371i | −0.376899 | + | 0.518757i | −0.954760 | − | 0.297378i | \(-0.903888\pi\) |
0.577861 | + | 0.816135i | \(0.303888\pi\) | |||||||
\(314\) | −98.4715 | − | 135.534i | −0.313603 | − | 0.431638i | ||||
\(315\) | −20.6808 | + | 74.1736i | −0.0656534 | + | 0.235472i | ||||
\(316\) | −370.126 | − | 268.912i | −1.17128 | − | 0.850988i | ||||
\(317\) | 124.913 | + | 384.444i | 0.394048 | + | 1.21276i | 0.929700 | + | 0.368317i | \(0.120066\pi\) |
−0.535652 | + | 0.844439i | \(0.679934\pi\) | |||||||
\(318\) | −74.0962 | + | 178.627i | −0.233007 | + | 0.561721i | ||||
\(319\) | −77.8128 | − | 239.483i | −0.243927 | − | 0.750731i | ||||
\(320\) | −13.5990 | − | 66.9680i | −0.0424970 | − | 0.209275i | ||||
\(321\) | 9.71540 | + | 8.30627i | 0.0302660 | + | 0.0258762i | ||||
\(322\) | −48.2250 | − | 15.6693i | −0.149767 | − | 0.0486623i | ||||
\(323\) | −160.422 | + | 116.553i | −0.496663 | + | 0.360847i | ||||
\(324\) | 0.559787 | − | 275.713i | 0.00172774 | − | 0.850965i | ||||
\(325\) | −303.817 | + | 26.3542i | −0.934820 | + | 0.0810900i | ||||
\(326\) | − | 10.9736i | − | 0.0336614i | ||||||
\(327\) | −107.633 | − | 449.327i | −0.329152 | − | 1.37409i | ||||
\(328\) | 191.470 | + | 62.2124i | 0.583750 | + | 0.189672i | ||||
\(329\) | 28.5539 | + | 9.27772i | 0.0867900 | + | 0.0281998i | ||||
\(330\) | −72.1325 | + | 8.79254i | −0.218583 | + | 0.0266441i | ||||
\(331\) | −162.219 | − | 499.260i | −0.490089 | − | 1.50834i | −0.824473 | − | 0.565902i | \(-0.808528\pi\) |
0.334384 | − | 0.942437i | \(-0.391472\pi\) | |||||||
\(332\) | 6.81630 | 0.0205310 | ||||||||
\(333\) | −15.9493 | − | 8.14698i | −0.0478958 | − | 0.0244654i | ||||
\(334\) | 9.23389 | + | 6.70881i | 0.0276464 | + | 0.0200863i | ||||
\(335\) | 15.1190 | − | 132.263i | 0.0451314 | − | 0.394816i | ||||
\(336\) | 45.9380 | − | 11.0041i | 0.136720 | − | 0.0327502i | ||||
\(337\) | 216.442 | − | 297.907i | 0.642261 | − | 0.883996i | −0.356473 | − | 0.934306i | \(-0.616021\pi\) |
0.998734 | + | 0.0503096i | \(0.0160208\pi\) | |||||||
\(338\) | 12.6186 | + | 9.16795i | 0.0373331 | + | 0.0271241i | ||||
\(339\) | 15.7220 | + | 65.6336i | 0.0463776 | + | 0.193609i | ||||
\(340\) | 103.135 | − | 226.088i | 0.303338 | − | 0.664964i | ||||
\(341\) | −99.1005 | + | 136.400i | −0.290617 | + | 0.400001i | ||||
\(342\) | 42.9286 | − | 84.0410i | 0.125522 | − | 0.245734i | ||||
\(343\) | 162.684i | 0.474298i | ||||||||
\(344\) | −398.246 | + | 129.398i | −1.15769 | + | 0.376157i | ||||
\(345\) | −279.544 | + | 503.269i | −0.810272 | + | 1.45875i | ||||
\(346\) | −33.6571 | + | 103.586i | −0.0972750 | + | 0.299382i | ||||
\(347\) | −59.4858 | + | 183.079i | −0.171429 | + | 0.527604i | −0.999452 | − | 0.0330896i | \(-0.989465\pi\) |
0.828024 | + | 0.560693i | \(0.189465\pi\) | |||||||
\(348\) | −398.544 | + | 95.4679i | −1.14524 | + | 0.274333i | ||||
\(349\) | −293.490 | −0.840945 | −0.420473 | − | 0.907305i | \(-0.638136\pi\) | ||||
−0.420473 | + | 0.907305i | \(0.638136\pi\) | |||||||
\(350\) | 7.45386 | − | 32.1777i | 0.0212967 | − | 0.0919362i | ||||
\(351\) | 125.575 | + | 304.475i | 0.357763 | + | 0.867450i | ||||
\(352\) | 110.532 | + | 152.134i | 0.314010 | + | 0.432198i | ||||
\(353\) | 171.108 | − | 526.617i | 0.484726 | − | 1.49183i | −0.347652 | − | 0.937624i | \(-0.613021\pi\) |
0.832378 | − | 0.554209i | \(-0.186979\pi\) | |||||||
\(354\) | 14.4113 | − | 16.8561i | 0.0407098 | − | 0.0476161i | ||||
\(355\) | 290.812 | − | 317.131i | 0.819190 | − | 0.893326i | ||||
\(356\) | 343.848 | − | 111.723i | 0.965864 | − | 0.313828i | ||||
\(357\) | 69.2347 | + | 28.7191i | 0.193935 | + | 0.0804457i | ||||
\(358\) | −14.5366 | + | 4.72321i | −0.0406049 | + | 0.0131933i | ||||
\(359\) | 85.3501 | − | 117.474i | 0.237744 | − | 0.327227i | −0.673428 | − | 0.739253i | \(-0.735179\pi\) |
0.911172 | + | 0.412026i | \(0.135179\pi\) | |||||||
\(360\) | 10.8649 | + | 257.013i | 0.0301802 | + | 0.713924i | ||||
\(361\) | 142.844 | − | 103.782i | 0.395690 | − | 0.287486i | ||||
\(362\) | −49.9487 | − | 36.2898i | −0.137980 | − | 0.100248i | ||||
\(363\) | 208.873 | − | 127.852i | 0.575408 | − | 0.352209i | ||||
\(364\) | −57.4809 | + | 41.7623i | −0.157915 | + | 0.114732i | ||||
\(365\) | −47.3887 | + | 9.62310i | −0.129832 | + | 0.0263646i | ||||
\(366\) | −4.06047 | + | 2.48543i | −0.0110942 | + | 0.00679078i | ||||
\(367\) | −224.988 | + | 73.1032i | −0.613047 | + | 0.199191i | −0.599051 | − | 0.800711i | \(-0.704455\pi\) |
−0.0139964 | + | 0.999902i | \(0.504455\pi\) | |||||||
\(368\) | 353.162 | 0.959678 | ||||||||
\(369\) | 282.269 | + | 144.184i | 0.764956 | + | 0.390743i | ||||
\(370\) | 6.98931 | + | 3.18833i | 0.0188900 | + | 0.00861711i | ||||
\(371\) | −135.873 | − | 44.1477i | −0.366233 | − | 0.118996i | ||||
\(372\) | 208.563 | + | 178.313i | 0.560653 | + | 0.479335i | ||||
\(373\) | −168.516 | − | 231.942i | −0.451784 | − | 0.621828i | 0.520995 | − | 0.853559i | \(-0.325561\pi\) |
−0.972780 | + | 0.231732i | \(0.925561\pi\) | |||||||
\(374\) | 70.7338i | 0.189128i | ||||||||
\(375\) | −342.333 | − | 153.080i | −0.912887 | − | 0.408213i | ||||
\(376\) | 100.299 | 0.266752 | ||||||||
\(377\) | 396.054 | − | 287.750i | 1.05054 | − | 0.763263i | ||||
\(378\) | −35.5663 | + | 2.74464i | −0.0940909 | + | 0.00726097i | ||||
\(379\) | −38.5235 | + | 118.563i | −0.101645 | + | 0.312831i | −0.988928 | − | 0.148393i | \(-0.952590\pi\) |
0.887283 | + | 0.461225i | \(0.152590\pi\) | |||||||
\(380\) | 95.9276 | − | 210.288i | 0.252441 | − | 0.553389i | ||||
\(381\) | −36.4509 | + | 460.167i | −0.0956717 | + | 1.20779i | ||||
\(382\) | − | 108.022i | − | 0.282781i | ||||||
\(383\) | −210.811 | − | 648.811i | −0.550422 | − | 1.69402i | −0.707738 | − | 0.706475i | \(-0.750284\pi\) |
0.157316 | − | 0.987548i | \(-0.449716\pi\) | |||||||
\(384\) | 333.746 | − | 204.287i | 0.869129 | − | 0.531996i | ||||
\(385\) | −10.6832 | − | 52.6090i | −0.0277485 | − | 0.136647i | ||||
\(386\) | −81.4087 | − | 112.050i | −0.210903 | − | 0.290284i | ||||
\(387\) | −651.249 | + | 102.470i | −1.68281 | + | 0.264781i | ||||
\(388\) | 180.909 | − | 249.000i | 0.466261 | − | 0.641753i | ||||
\(389\) | 16.7972 | + | 23.1194i | 0.0431805 | + | 0.0594329i | 0.830061 | − | 0.557672i | \(-0.188305\pi\) |
−0.786881 | + | 0.617105i | \(0.788305\pi\) | |||||||
\(390\) | −59.5926 | − | 128.090i | −0.152801 | − | 0.328436i | ||||
\(391\) | 453.360 | + | 329.385i | 1.15949 | + | 0.842418i | ||||
\(392\) | 81.3857 | + | 250.479i | 0.207617 | + | 0.638978i | ||||
\(393\) | 463.536 | + | 192.279i | 1.17948 | + | 0.489259i | ||||
\(394\) | −3.85162 | − | 11.8541i | −0.00977569 | − | 0.0300865i | ||||
\(395\) | 495.305 | + | 454.200i | 1.25394 | + | 1.14987i | ||||
\(396\) | 87.0898 | + | 171.353i | 0.219924 | + | 0.432710i | ||||
\(397\) | −195.376 | − | 63.4815i | −0.492131 | − | 0.159903i | 0.0524297 | − | 0.998625i | \(-0.483303\pi\) |
−0.544560 | + | 0.838722i | \(0.683303\pi\) | |||||||
\(398\) | 215.123 | − | 156.296i | 0.540511 | − | 0.392704i | ||||
\(399\) | 64.3963 | + | 26.7121i | 0.161394 | + | 0.0669476i | ||||
\(400\) | 19.8803 | + | 229.184i | 0.0497008 | + | 0.572960i | ||||
\(401\) | 396.678i | 0.989222i | 0.869115 | + | 0.494611i | \(0.164689\pi\) | ||||
−0.869115 | + | 0.494611i | \(0.835311\pi\) | |||||||
\(402\) | 59.9743 | − | 14.3664i | 0.149190 | − | 0.0357372i | ||||
\(403\) | −311.739 | − | 101.290i | −0.773547 | − | 0.251341i | ||||
\(404\) | −508.972 | − | 165.375i | −1.25983 | − | 0.409344i | ||||
\(405\) | −46.8129 | + | 402.285i | −0.115587 | + | 0.993297i | ||||
\(406\) | 16.3849 | + | 50.4276i | 0.0403570 | + | 0.124206i | ||||
\(407\) | 12.4858 | 0.0306775 | ||||||||
\(408\) | 249.619 | + | 19.7729i | 0.611811 | + | 0.0484631i | ||||
\(409\) | 279.949 | + | 203.395i | 0.684472 | + | 0.497298i | 0.874838 | − | 0.484415i | \(-0.160968\pi\) |
−0.190366 | + | 0.981713i | \(0.560968\pi\) | |||||||
\(410\) | −123.696 | − | 56.4267i | −0.301697 | − | 0.137626i | ||||
\(411\) | 133.744 | + | 558.333i | 0.325412 | + | 1.35848i | ||||
\(412\) | 184.898 | − | 254.490i | 0.448781 | − | 0.617694i | ||||
\(413\) | 13.2544 | + | 9.62985i | 0.0320929 | + | 0.0233168i | ||||
\(414\) | −263.369 | − | 41.9877i | −0.636157 | − | 0.101419i | ||||
\(415\) | −9.94780 | − | 1.13713i | −0.0239706 | − | 0.00274008i | ||||
\(416\) | −214.889 | + | 295.769i | −0.516560 | + | 0.710984i | ||||
\(417\) | −24.7868 | − | 1.96342i | −0.0594408 | − | 0.00470845i | ||||
\(418\) | 65.7907i | 0.157394i | ||||||||
\(419\) | −158.769 | + | 51.5871i | −0.378923 | + | 0.123120i | −0.492285 | − | 0.870434i | \(-0.663838\pi\) |
0.113362 | + | 0.993554i | \(0.463838\pi\) | |||||||
\(420\) | −86.7271 | + | 10.5715i | −0.206493 | + | 0.0251703i | ||||
\(421\) | 10.2098 | − | 31.4226i | 0.0242514 | − | 0.0746380i | −0.938198 | − | 0.346098i | \(-0.887506\pi\) |
0.962450 | + | 0.271460i | \(0.0875065\pi\) | |||||||
\(422\) | 9.13812 | − | 28.1242i | 0.0216543 | − | 0.0666451i | ||||
\(423\) | 155.940 | + | 24.8608i | 0.368653 | + | 0.0587725i | ||||
\(424\) | −477.267 | −1.12563 | ||||||||
\(425\) | −188.234 | + | 312.750i | −0.442903 | + | 0.735882i | ||||
\(426\) | 184.120 | + | 76.3745i | 0.432206 | + | 0.179283i | ||||
\(427\) | −2.06726 | − | 2.84534i | −0.00484136 | − | 0.00666356i | ||||
\(428\) | −4.48165 | + | 13.7931i | −0.0104711 | + | 0.0322268i | ||||
\(429\) | −174.522 | − | 149.209i | −0.406810 | − | 0.347806i | ||||
\(430\) | 277.129 | − | 56.2758i | 0.644485 | − | 0.130874i | ||||
\(431\) | −570.239 | + | 185.282i | −1.32306 | + | 0.429888i | −0.883545 | − | 0.468347i | \(-0.844850\pi\) |
−0.439516 | + | 0.898235i | \(0.644850\pi\) | |||||||
\(432\) | 229.681 | − | 94.7274i | 0.531669 | − | 0.219277i | ||||
\(433\) | 265.335 | − | 86.2124i | 0.612782 | − | 0.199105i | 0.0138489 | − | 0.999904i | \(-0.495592\pi\) |
0.598933 | + | 0.800799i | \(0.295592\pi\) | |||||||
\(434\) | 20.8675 | − | 28.7216i | 0.0480817 | − | 0.0661788i | ||||
\(435\) | 597.566 | − | 72.8399i | 1.37372 | − | 0.167448i | ||||
\(436\) | 424.118 | − | 308.140i | 0.972749 | − | 0.706743i | ||||
\(437\) | 421.678 | + | 306.367i | 0.964937 | + | 0.701068i | ||||
\(438\) | −11.6949 | − | 19.1061i | −0.0267007 | − | 0.0436213i | ||||
\(439\) | 243.371 | − | 176.819i | 0.554376 | − | 0.402778i | −0.275020 | − | 0.961438i | \(-0.588685\pi\) |
0.829396 | + | 0.558661i | \(0.188685\pi\) | |||||||
\(440\) | −88.2523 | − | 156.120i | −0.200574 | − | 0.354818i | ||||
\(441\) | 64.4493 | + | 409.608i | 0.146144 | + | 0.928816i | ||||
\(442\) | −130.786 | + | 42.4950i | −0.295896 | + | 0.0961425i | ||||
\(443\) | 225.255 | 0.508477 | 0.254239 | − | 0.967142i | \(-0.418175\pi\) | ||||
0.254239 | + | 0.967142i | \(0.418175\pi\) | |||||||
\(444\) | 1.60462 | − | 20.2572i | 0.00361401 | − | 0.0456243i | ||||
\(445\) | −520.454 | + | 105.687i | −1.16956 | + | 0.237500i | ||||
\(446\) | 184.579 | + | 59.9733i | 0.413854 | + | 0.134469i | ||||
\(447\) | 519.122 | − | 607.189i | 1.16135 | − | 1.35836i | ||||
\(448\) | 13.7463 | + | 18.9201i | 0.0306836 | + | 0.0422324i | ||||
\(449\) | − | 544.155i | − | 1.21193i | −0.795493 | − | 0.605963i | \(-0.792788\pi\) | ||
0.795493 | − | 0.605963i | \(-0.207212\pi\) | |||||||
\(450\) | 12.4222 | − | 173.277i | 0.0276049 | − | 0.385060i | ||||
\(451\) | −220.971 | −0.489959 | ||||||||
\(452\) | −61.9514 | + | 45.0103i | −0.137061 | + | 0.0995803i | ||||
\(453\) | −477.116 | − | 407.914i | −1.05324 | − | 0.900473i | ||||
\(454\) | −8.37923 | + | 25.7886i | −0.0184565 | + | 0.0568031i | ||||
\(455\) | 90.8554 | − | 51.3592i | 0.199682 | − | 0.112877i | ||||
\(456\) | 232.175 | + | 18.3911i | 0.509155 | + | 0.0403314i | ||||
\(457\) | 166.755i | 0.364890i | 0.983216 | + | 0.182445i | \(0.0584012\pi\) | ||||
−0.983216 | + | 0.182445i | \(0.941599\pi\) | |||||||
\(458\) | 34.8015 | + | 107.108i | 0.0759859 | + | 0.233861i | ||||
\(459\) | 383.196 | + | 92.6145i | 0.834849 | + | 0.201775i | ||||
\(460\) | −648.970 | − | 74.1838i | −1.41080 | − | 0.161269i | ||||
\(461\) | 82.9803 | + | 114.213i | 0.180001 | + | 0.247750i | 0.889477 | − | 0.456979i | \(-0.151069\pi\) |
−0.709477 | + | 0.704729i | \(0.751069\pi\) | |||||||
\(462\) | 21.2109 | − | 12.9832i | 0.0459110 | − | 0.0281022i | ||||
\(463\) | −275.071 | + | 378.603i | −0.594106 | + | 0.817717i | −0.995153 | − | 0.0983404i | \(-0.968647\pi\) |
0.401046 | + | 0.916058i | \(0.368647\pi\) | |||||||
\(464\) | −217.064 | − | 298.763i | −0.467811 | − | 0.643887i | ||||
\(465\) | −274.632 | − | 295.026i | −0.590607 | − | 0.634464i | ||||
\(466\) | 82.0014 | + | 59.5775i | 0.175969 | + | 0.127849i | ||||
\(467\) | −36.4887 | − | 112.301i | −0.0781342 | − | 0.240472i | 0.904358 | − | 0.426774i | \(-0.140350\pi\) |
−0.982493 | + | 0.186301i | \(0.940350\pi\) | |||||||
\(468\) | −264.509 | + | 263.972i | −0.565190 | + | 0.564043i | ||||
\(469\) | 14.0788 | + | 43.3300i | 0.0300187 | + | 0.0923880i | ||||
\(470\) | −67.2957 | − | 7.69257i | −0.143182 | − | 0.0163672i | ||||
\(471\) | 423.004 | − | 494.765i | 0.898097 | − | 1.05046i | ||||
\(472\) | 52.0527 | + | 16.9130i | 0.110281 | + | 0.0358325i | ||||
\(473\) | 371.830 | − | 270.150i | 0.786110 | − | 0.571142i | ||||
\(474\) | −119.284 | + | 287.565i | −0.251654 | + | 0.606676i | ||||
\(475\) | −175.079 | + | 290.894i | −0.368588 | + | 0.612408i | ||||
\(476\) | 85.0455i | 0.178667i | ||||||||
\(477\) | −742.035 | − | 118.299i | −1.55563 | − | 0.248006i | ||||
\(478\) | 126.076 | + | 40.9645i | 0.263757 | + | 0.0856998i | ||||
\(479\) | −3.93806 | − | 1.27955i | −0.00822141 | − | 0.00267130i | 0.304903 | − | 0.952383i | \(-0.401376\pi\) |
−0.313125 | + | 0.949712i | \(0.601376\pi\) | |||||||
\(480\) | −407.606 | + | 189.635i | −0.849179 | + | 0.395072i | ||||
\(481\) | 7.50110 | + | 23.0860i | 0.0155948 | + | 0.0479959i | ||||
\(482\) | 309.616 | 0.642357 | ||||||||
\(483\) | 15.5579 | − | 196.407i | 0.0322110 | − | 0.406641i | ||||
\(484\) | 224.797 | + | 163.325i | 0.464457 | + | 0.337448i | ||||
\(485\) | −305.561 | + | 333.214i | −0.630023 | + | 0.687039i | ||||
\(486\) | −182.546 | + | 43.3357i | −0.375609 | + | 0.0891681i | ||||
\(487\) | 481.749 | − | 663.071i | 0.989218 | − | 1.36154i | 0.0575051 | − | 0.998345i | \(-0.481685\pi\) |
0.931713 | − | 0.363196i | \(-0.118315\pi\) | |||||||
\(488\) | −9.50540 | − | 6.90608i | −0.0194783 | − | 0.0141518i | ||||
\(489\) | 41.4653 | − | 9.93268i | 0.0847961 | − | 0.0203122i | ||||
\(490\) | −35.3951 | − | 174.302i | −0.0722348 | − | 0.355718i | ||||
\(491\) | 229.669 | − | 316.113i | 0.467758 | − | 0.643814i | −0.508337 | − | 0.861158i | \(-0.669739\pi\) |
0.976095 | + | 0.217344i | \(0.0697394\pi\) | |||||||
\(492\) | −28.3984 | + | 358.509i | −0.0577203 | + | 0.728677i | ||||
\(493\) | − | 585.979i | − | 1.18860i | ||||||
\(494\) | −121.646 | + | 39.5252i | −0.246247 | + | 0.0800106i | ||||
\(495\) | −98.5139 | − | 264.604i | −0.199018 | − | 0.534553i | ||||
\(496\) | −76.4083 | + | 235.161i | −0.154049 | + | 0.474114i | ||||
\(497\) | −45.5051 | + | 140.050i | −0.0915596 | + | 0.281792i | ||||
\(498\) | −1.08052 | − | 4.51079i | −0.00216973 | − | 0.00905781i | ||||
\(499\) | −901.118 | −1.80585 | −0.902923 | − | 0.429801i | \(-0.858584\pi\) | ||||
−0.902923 | + | 0.429801i | \(0.858584\pi\) | |||||||
\(500\) | 11.6094 | − | 425.325i | 0.0232189 | − | 0.850650i | ||||
\(501\) | −16.9922 | + | 40.9639i | −0.0339165 | + | 0.0817642i | ||||
\(502\) | −165.713 | − | 228.084i | −0.330105 | − | 0.454351i | ||||
\(503\) | −158.993 | + | 489.331i | −0.316090 | + | 0.972825i | 0.659213 | + | 0.751956i | \(0.270889\pi\) |
−0.975303 | + | 0.220869i | \(0.929111\pi\) | |||||||
\(504\) | −39.8884 | − | 78.4822i | −0.0791436 | − | 0.155719i | ||||
\(505\) | 715.212 | + | 326.260i | 1.41626 | + | 0.646059i | ||||
\(506\) | 176.828 | − | 57.4548i | 0.349462 | − | 0.113547i | ||||
\(507\) | −23.2207 | + | 55.9793i | −0.0458002 | + | 0.110413i | ||||
\(508\) | −498.117 | + | 161.848i | −0.980545 | + | 0.318598i | ||||
\(509\) | 91.7524 | − | 126.286i | 0.180260 | − | 0.248107i | −0.709319 | − | 0.704887i | \(-0.750998\pi\) |
0.889579 | + | 0.456781i | \(0.150998\pi\) | |||||||
\(510\) | −165.966 | − | 32.4116i | −0.325424 | − | 0.0635522i | ||||
\(511\) | 13.3885 | − | 9.72728i | 0.0262005 | − | 0.0190358i | ||||
\(512\) | 393.337 | + | 285.776i | 0.768237 | + | 0.558157i | ||||
\(513\) | 356.416 | + | 86.1422i | 0.694769 | + | 0.167919i | ||||
\(514\) | −88.9917 | + | 64.6562i | −0.173136 | + | 0.125790i | ||||
\(515\) | −312.298 | + | 340.560i | −0.606403 | + | 0.661282i | ||||
\(516\) | −390.512 | − | 637.984i | −0.756806 | − | 1.23640i | ||||
\(517\) | −104.699 | + | 34.0188i | −0.202513 | + | 0.0658004i | ||||
\(518\) | −2.62911 | −0.00507549 | ||||||||
\(519\) | −421.878 | − | 33.4180i | −0.812867 | − | 0.0643892i | ||||
\(520\) | 235.645 | − | 256.970i | 0.453163 | − | 0.494174i | ||||
\(521\) | −749.697 | − | 243.591i | −1.43896 | − | 0.467546i | −0.517386 | − | 0.855752i | \(-0.673095\pi\) |
−0.921573 | + | 0.388206i | \(0.873095\pi\) | |||||||
\(522\) | 126.355 | + | 248.609i | 0.242059 | + | 0.476262i | ||||
\(523\) | 106.206 | + | 146.180i | 0.203070 | + | 0.279503i | 0.898390 | − | 0.439198i | \(-0.144737\pi\) |
−0.695320 | + | 0.718700i | \(0.744737\pi\) | |||||||
\(524\) | 569.392i | 1.08663i | ||||||||
\(525\) | 128.334 | − | 0.959950i | 0.244446 | − | 0.00182848i | ||||
\(526\) | −189.213 | −0.359720 | ||||||||
\(527\) | −317.416 | + | 230.616i | −0.602307 | + | 0.437601i | ||||
\(528\) | −112.556 | + | 131.650i | −0.213174 | + | 0.249338i | ||||
\(529\) | 291.711 | − | 897.795i | 0.551439 | − | 1.69716i | ||||
\(530\) | 320.224 | + | 36.6048i | 0.604196 | + | 0.0690657i | ||||
\(531\) | 76.7372 | + | 39.1977i | 0.144514 | + | 0.0738187i | ||||
\(532\) | 79.1021i | 0.148688i | ||||||||
\(533\) | −132.754 | − | 408.574i | −0.249069 | − | 0.766555i | ||||
\(534\) | −128.441 | − | 209.836i | −0.240527 | − | 0.392951i | ||||
\(535\) | 8.84161 | − | 19.3822i | 0.0165264 | − | 0.0362283i | ||||
\(536\) | 89.4616 | + | 123.133i | 0.166906 | + | 0.229726i | ||||
\(537\) | −31.0049 | − | 50.6531i | −0.0577373 | − | 0.0943261i | ||||
\(538\) | 52.9440 | − | 72.8711i | 0.0984089 | − | 0.135448i | ||||
\(539\) | −169.913 | − | 233.865i | −0.315237 | − | 0.433887i | ||||
\(540\) | −441.960 | + | 125.825i | −0.818444 | + | 0.233010i | ||||
\(541\) | 107.419 | + | 78.0448i | 0.198557 | + | 0.144260i | 0.682621 | − | 0.730772i | \(-0.260840\pi\) |
−0.484064 | + | 0.875033i | \(0.660840\pi\) | |||||||
\(542\) | 41.5957 | + | 128.018i | 0.0767448 | + | 0.236196i | ||||
\(543\) | 91.9153 | − | 221.585i | 0.169273 | − | 0.408075i | ||||
\(544\) | 135.227 | + | 416.186i | 0.248579 | + | 0.765047i | ||||
\(545\) | −670.370 | + | 378.950i | −1.23004 | + | 0.695321i | ||||
\(546\) | 36.7488 | + | 31.4187i | 0.0673054 | + | 0.0575434i | ||||
\(547\) | −113.633 | − | 36.9217i | −0.207739 | − | 0.0674986i | 0.203299 | − | 0.979117i | \(-0.434834\pi\) |
−0.411038 | + | 0.911618i | \(0.634834\pi\) | |||||||
\(548\) | −527.009 | + | 382.895i | −0.961696 | + | 0.698713i | ||||
\(549\) | −13.0668 | − | 13.0934i | −0.0238011 | − | 0.0238495i | ||||
\(550\) | 47.2393 | + | 111.518i | 0.0858897 | + | 0.202760i | ||||
\(551\) | − | 545.028i | − | 0.989162i | ||||||
\(552\) | −153.327 | − | 640.083i | −0.277766 | − | 1.15957i | ||||
\(553\) | −218.735 | − | 71.0715i | −0.395543 | − | 0.128520i | ||||
\(554\) | 134.086 | + | 43.5670i | 0.242032 | + | 0.0786408i | ||||
\(555\) | −5.72122 | + | 29.2959i | −0.0103085 | + | 0.0527854i | ||||
\(556\) | −8.71791 | − | 26.8310i | −0.0156797 | − | 0.0482571i | ||||
\(557\) | 619.206 | 1.11168 | 0.555841 | − | 0.831289i | \(-0.312397\pi\) | ||||
0.555841 | + | 0.831289i | \(0.312397\pi\) | |||||||
\(558\) | 84.9397 | − | 166.286i | 0.152222 | − | 0.298003i | ||||
\(559\) | 722.890 | + | 525.210i | 1.29318 | + | 0.939553i | ||||
\(560\) | −38.7428 | − | 68.5368i | −0.0691836 | − | 0.122387i | ||||
\(561\) | −267.277 | + | 64.0241i | −0.476430 | + | 0.114125i | ||||
\(562\) | −8.18121 | + | 11.2605i | −0.0145573 | + | 0.0200364i | ||||
\(563\) | −102.281 | − | 74.3113i | −0.181671 | − | 0.131992i | 0.493233 | − | 0.869897i | \(-0.335815\pi\) |
−0.674904 | + | 0.737906i | \(0.735815\pi\) | |||||||
\(564\) | 41.7374 | + | 174.238i | 0.0740025 | + | 0.308933i | ||||
\(565\) | 97.9215 | − | 55.3536i | 0.173312 | − | 0.0979709i | ||||
\(566\) | 9.20836 | − | 12.6742i | 0.0162692 | − | 0.0223926i | ||||
\(567\) | −42.5636 | − | 131.908i | −0.0750680 | − | 0.232642i | ||||
\(568\) | 491.942i | 0.866096i | ||||||||
\(569\) | 937.859 | − | 304.729i | 1.64826 | − | 0.535552i | 0.669897 | − | 0.742454i | \(-0.266338\pi\) |
0.978362 | + | 0.206903i | \(0.0663383\pi\) | |||||||
\(570\) | −154.368 | − | 30.1466i | −0.270821 | − | 0.0528887i | ||||
\(571\) | −12.9513 | + | 39.8601i | −0.0226819 | + | 0.0698076i | −0.961757 | − | 0.273905i | \(-0.911685\pi\) |
0.939075 | + | 0.343713i | \(0.111685\pi\) | |||||||
\(572\) | 80.5056 | − | 247.771i | 0.140744 | − | 0.433165i | ||||
\(573\) | 408.177 | − | 97.7755i | 0.712351 | − | 0.170638i | ||||
\(574\) | 46.5296 | 0.0810620 | ||||||||
\(575\) | 934.740 | + | 216.530i | 1.62563 | + | 0.376573i | ||||
\(576\) | 86.8877 | + | 87.0643i | 0.150847 | + | 0.151153i | ||||
\(577\) | 520.698 | + | 716.679i | 0.902423 | + | 1.24208i | 0.969689 | + | 0.244343i | \(0.0785723\pi\) |
−0.0672662 | + | 0.997735i | \(0.521428\pi\) | |||||||
\(578\) | 18.0873 | − | 55.6669i | 0.0312928 | − | 0.0963095i | ||||
\(579\) | 349.707 | − | 409.034i | 0.603985 | − | 0.706449i | ||||
\(580\) | 336.121 | + | 594.604i | 0.579518 | + | 1.02518i | ||||
\(581\) | 3.25894 | − | 1.05889i | 0.00560919 | − | 0.00182254i | ||||
\(582\) | −193.458 | − | 80.2479i | −0.332401 | − | 0.137883i | ||||
\(583\) | 498.207 | − | 161.877i | 0.854557 | − | 0.277662i | ||||
\(584\) | 32.4958 | − | 44.7267i | 0.0556435 | − | 0.0765868i | ||||
\(585\) | 430.065 | − | 341.118i | 0.735154 | − | 0.583107i | ||||
\(586\) | 75.5817 | − | 54.9133i | 0.128979 | − | 0.0937087i | ||||
\(587\) | −806.259 | − | 585.781i | −1.37352 | − | 0.997924i | −0.997453 | − | 0.0713330i | \(-0.977275\pi\) |
−0.376071 | − | 0.926591i | \(-0.622725\pi\) | |||||||
\(588\) | −401.265 | + | 245.615i | −0.682423 | + | 0.417713i | ||||
\(589\) | −295.233 | + | 214.500i | −0.501245 | + | 0.364176i | ||||
\(590\) | −33.6278 | − | 15.3401i | −0.0569962 | − | 0.0260001i | ||||
\(591\) | 41.3059 | − | 25.2835i | 0.0698915 | − | 0.0427808i | ||||
\(592\) | 17.4149 | − | 5.65846i | 0.0294171 | − | 0.00955820i | ||||
\(593\) | −507.055 | −0.855068 | −0.427534 | − | 0.903999i | \(-0.640618\pi\) | ||||
−0.427534 | + | 0.903999i | \(0.640618\pi\) | |||||||
\(594\) | 99.5900 | − | 84.7960i | 0.167660 | − | 0.142754i | ||||
\(595\) | 14.1878 | − | 124.116i | 0.0238450 | − | 0.208599i | ||||
\(596\) | 862.034 | + | 280.092i | 1.44637 | + | 0.469953i | ||||
\(597\) | 785.303 | + | 671.402i | 1.31542 | + | 1.12463i | ||||
\(598\) | 212.466 | + | 292.435i | 0.355295 | + | 0.489022i | ||||
\(599\) | 675.422i | 1.12758i | 0.825917 | + | 0.563791i | \(0.190658\pi\) | ||||
−0.825917 | + | 0.563791i | \(0.809342\pi\) | |||||||
\(600\) | 406.751 | − | 135.533i | 0.677918 | − | 0.225889i | ||||
\(601\) | −659.654 | −1.09759 | −0.548797 | − | 0.835956i | \(-0.684914\pi\) | ||||
−0.548797 | + | 0.835956i | \(0.684914\pi\) | |||||||
\(602\) | −78.2956 | + | 56.8851i | −0.130059 | + | 0.0944935i | ||||
\(603\) | 108.570 | + | 213.617i | 0.180050 | + | 0.354257i | ||||
\(604\) | 220.090 | − | 677.368i | 0.364388 | − | 1.12147i | ||||
\(605\) | −300.825 | − | 275.860i | −0.497232 | − | 0.455967i | ||||
\(606\) | −28.7569 | + | 363.035i | −0.0474537 | + | 0.599068i | ||||
\(607\) | 1147.75i | 1.89085i | 0.325837 | + | 0.945426i | \(0.394354\pi\) | ||||
−0.325837 | + | 0.945426i | \(0.605646\pi\) | |||||||
\(608\) | 125.777 | + | 387.101i | 0.206870 | + | 0.636679i | ||||
\(609\) | −175.717 | + | 107.557i | −0.288533 | + | 0.176612i | ||||
\(610\) | 5.84801 | + | 5.36269i | 0.00958690 | + | 0.00879129i | ||||
\(611\) | −125.801 | − | 173.150i | −0.205893 | − | 0.283388i | ||||
\(612\) | 69.5248 | + | 441.865i | 0.113603 | + | 0.722001i | ||||
\(613\) | −346.355 | + | 476.717i | −0.565016 | + | 0.777678i | −0.991953 | − | 0.126603i | \(-0.959593\pi\) |
0.426937 | + | 0.904281i | \(0.359593\pi\) | |||||||
\(614\) | 84.6307 | + | 116.484i | 0.137835 | + | 0.189714i | ||||
\(615\) | 101.253 | − | 518.475i | 0.164640 | − | 0.843050i | ||||
\(616\) | 49.6538 | + | 36.0756i | 0.0806068 | + | 0.0585643i | ||||
\(617\) | −160.785 | − | 494.845i | −0.260591 | − | 0.802017i | −0.992676 | − | 0.120804i | \(-0.961453\pi\) |
0.732085 | − | 0.681213i | \(-0.238547\pi\) | |||||||
\(618\) | −197.723 | − | 82.0171i | −0.319940 | − | 0.132714i | ||||
\(619\) | 25.3157 | + | 77.9139i | 0.0408978 | + | 0.125871i | 0.969421 | − | 0.245404i | \(-0.0789207\pi\) |
−0.928523 | + | 0.371275i | \(0.878921\pi\) | |||||||
\(620\) | 189.805 | − | 416.082i | 0.306137 | − | 0.671099i | ||||
\(621\) | −79.7301 | − | 1033.18i | −0.128390 | − | 1.66373i | ||||
\(622\) | −236.039 | − | 76.6938i | −0.379484 | − | 0.123302i | ||||
\(623\) | 147.041 | − | 106.832i | 0.236021 | − | 0.171479i | ||||
\(624\) | −311.041 | − | 129.022i | −0.498462 | − | 0.206766i | ||||
\(625\) | −87.8980 | + | 618.788i | −0.140637 | + | 0.990061i | ||||
\(626\) | 154.961i | 0.247541i | ||||||||
\(627\) | −248.599 | + | 59.5498i | −0.396489 | + | 0.0949758i | ||||
\(628\) | 702.425 | + | 228.232i | 1.11851 | + | 0.363426i | ||||
\(629\) | 27.6334 | + | 8.97863i | 0.0439323 | + | 0.0142745i | ||||
\(630\) | 20.7439 | + | 55.7172i | 0.0329269 | + | 0.0884400i | ||||
\(631\) | 80.8343 | + | 248.782i | 0.128105 | + | 0.394267i | 0.994454 | − | 0.105172i | \(-0.0335394\pi\) |
−0.866349 | + | 0.499439i | \(0.833539\pi\) | |||||||
\(632\) | −768.332 | −1.21572 | ||||||||
\(633\) | 114.542 | + | 9.07319i | 0.180952 | + | 0.0143336i | ||||
\(634\) | 252.496 | + | 183.449i | 0.398259 | + | 0.289352i | ||||
\(635\) | 753.958 | − | 153.104i | 1.18734 | − | 0.241109i | ||||
\(636\) | −198.606 | − | 829.106i | −0.312273 | − | 1.30363i | ||||
\(637\) | 330.335 | − | 454.667i | 0.518579 | − | 0.713762i | ||||
\(638\) | −157.289 | − | 114.277i | −0.246534 | − | 0.179117i | ||||
\(639\) | −121.937 | + | 764.851i | −0.190824 | + | 1.19695i | ||||
\(640\) | −480.670 | − | 440.780i | −0.751047 | − | 0.688719i | ||||
\(641\) | 225.134 | − | 309.870i | 0.351222 | − | 0.483416i | −0.596455 | − | 0.802647i | \(-0.703424\pi\) |
0.947677 | + | 0.319231i | \(0.103424\pi\) | |||||||
\(642\) | 9.83822 | + | 0.779309i | 0.0153243 | + | 0.00121388i | ||||
\(643\) | − | 657.068i | − | 1.02188i | −0.859617 | − | 0.510940i | \(-0.829298\pi\) | ||
0.859617 | − | 0.510940i | \(-0.170702\pi\) | |||||||
\(644\) | 212.605 | − | 69.0796i | 0.330132 | − | 0.107266i | ||||
\(645\) | 463.486 | + | 996.230i | 0.718583 | + | 1.54454i | ||||
\(646\) | −47.3108 | + | 145.608i | −0.0732365 | + | 0.225399i | ||||
\(647\) | 228.875 | − | 704.403i | 0.353747 | − | 1.08872i | −0.602985 | − | 0.797753i | \(-0.706022\pi\) |
0.956732 | − | 0.290970i | \(-0.0939779\pi\) | |||||||
\(648\) | −271.405 | − | 375.156i | −0.418834 | − | 0.578944i | ||||
\(649\) | −60.0729 | −0.0925623 | ||||||||
\(650\) | −177.815 | + | 154.342i | −0.273562 | + | 0.237449i | ||||
\(651\) | 127.416 | + | 52.8533i | 0.195724 | + | 0.0811879i | ||||
\(652\) | 28.4361 | + | 39.1390i | 0.0436137 | + | 0.0600291i | ||||
\(653\) | −51.5318 | + | 158.599i | −0.0789155 | + | 0.242877i | −0.982729 | − | 0.185049i | \(-0.940756\pi\) |
0.903814 | + | 0.427926i | \(0.140756\pi\) | |||||||
\(654\) | −271.148 | − | 231.820i | −0.414599 | − | 0.354465i | ||||
\(655\) | 94.9891 | − | 830.978i | 0.145022 | − | 1.26867i | ||||
\(656\) | −308.208 | + | 100.143i | −0.469829 | + | 0.152657i | ||||
\(657\) | 61.6094 | − | 61.4845i | 0.0937739 | − | 0.0935837i | ||||
\(658\) | 22.0463 | − | 7.16329i | 0.0335051 | − | 0.0108865i | ||||
\(659\) | 93.6473 | − | 128.894i | 0.142105 | − | 0.195591i | −0.732032 | − | 0.681270i | \(-0.761428\pi\) |
0.874137 | + | 0.485679i | \(0.161428\pi\) | |||||||
\(660\) | 234.486 | − | 218.278i | 0.355283 | − | 0.330724i | ||||
\(661\) | −302.488 | + | 219.770i | −0.457621 | + | 0.332481i | −0.792597 | − | 0.609745i | \(-0.791272\pi\) |
0.334976 | + | 0.942227i | \(0.391272\pi\) | |||||||
\(662\) | −327.906 | − | 238.238i | −0.495326 | − | 0.359876i | ||||
\(663\) | −278.953 | − | 455.728i | −0.420743 | − | 0.687373i | ||||
\(664\) | 9.26112 | − | 6.72860i | 0.0139475 | − | 0.0101334i | ||||
\(665\) | 13.1963 | − | 115.443i | 0.0198440 | − | 0.173598i | ||||
\(666\) | −13.6599 | + | 2.14930i | −0.0205103 | + | 0.00322717i | ||||
\(667\) | −1464.89 | + | 475.971i | −2.19624 | + | 0.713600i | ||||
\(668\) | −50.3186 | −0.0753273 | ||||||||
\(669\) | −59.5472 | + | 751.740i | −0.0890093 | + | 1.12368i | ||||
\(670\) | −50.5807 | − | 89.4782i | −0.0754935 | − | 0.133549i | ||||
\(671\) | 12.2648 | + | 3.98508i | 0.0182784 | + | 0.00593901i | ||||
\(672\) | 99.9801 | − | 116.941i | 0.148780 | − | 0.174020i | ||||
\(673\) | −238.217 | − | 327.877i | −0.353962 | − | 0.487187i | 0.594492 | − | 0.804102i | \(-0.297353\pi\) |
−0.948454 | + | 0.316914i | \(0.897353\pi\) | |||||||
\(674\) | − | 284.311i | − | 0.421826i | ||||||
\(675\) | 665.993 | − | 109.901i | 0.986656 | − | 0.162816i | ||||
\(676\) | −68.7631 | −0.101721 | ||||||||
\(677\) | −707.402 | + | 513.958i | −1.04491 | + | 0.759169i | −0.971237 | − | 0.238114i | \(-0.923471\pi\) |
−0.0736694 | + | 0.997283i | \(0.523471\pi\) | |||||||
\(678\) | 39.6068 | + | 33.8622i | 0.0584172 | + | 0.0499443i | ||||
\(679\) | 47.8130 | − | 147.153i | 0.0704167 | − | 0.216720i | ||||
\(680\) | −83.0520 | − | 408.987i | −0.122135 | − | 0.601452i | ||||
\(681\) | −105.030 | − | 8.31969i | −0.154229 | − | 0.0122169i | ||||
\(682\) | 130.175i | 0.190873i | ||||||||
\(683\) | 409.220 | + | 1259.45i | 0.599150 | + | 1.84399i | 0.532876 | + | 0.846193i | \(0.321111\pi\) |
0.0662740 | + | 0.997801i | \(0.478889\pi\) | |||||||
\(684\) | 64.6661 | + | 410.986i | 0.0945411 | + | 0.600856i | ||||
\(685\) | 833.001 | − | 470.883i | 1.21606 | − | 0.687420i | ||||
\(686\) | 73.8305 | + | 101.619i | 0.107625 | + | 0.148133i | ||||
\(687\) | −373.222 | + | 228.450i | −0.543263 | + | 0.332533i | ||||
\(688\) | 396.193 | − | 545.312i | 0.575861 | − | 0.792605i | ||||
\(689\) | 598.618 | + | 823.927i | 0.868822 | + | 1.19583i | ||||
\(690\) | 53.7829 | + | 441.226i | 0.0779462 | + | 0.639457i | ||||
\(691\) | 131.537 | + | 95.5669i | 0.190357 | + | 0.138302i | 0.678882 | − | 0.734248i | \(-0.262465\pi\) |
−0.488525 | + | 0.872550i | \(0.662465\pi\) | |||||||
\(692\) | −148.381 | − | 456.670i | −0.214424 | − | 0.659928i | ||||
\(693\) | 68.2576 | + | 68.3964i | 0.0984959 | + | 0.0986961i | ||||
\(694\) | 45.9287 | + | 141.354i | 0.0661797 | + | 0.203680i | ||||
\(695\) | 8.24694 | + | 40.6118i | 0.0118661 | + | 0.0584343i | ||||
\(696\) | −447.251 | + | 523.125i | −0.642601 | + | 0.751617i | ||||
\(697\) | −489.053 | − | 158.903i | −0.701654 | − | 0.227981i | ||||
\(698\) | −183.325 | + | 133.193i | −0.262643 | + | 0.190822i | ||||
\(699\) | −150.899 | + | 363.779i | −0.215878 | + | 0.520428i | ||||
\(700\) | 56.7973 | + | 134.081i | 0.0811390 | + | 0.191545i | ||||
\(701\) | 556.658i | 0.794091i | 0.917799 | + | 0.397046i | \(0.129965\pi\) | ||||
−0.917799 | + | 0.397046i | \(0.870035\pi\) | |||||||
\(702\) | 216.618 | + | 133.198i | 0.308572 | + | 0.189740i | ||||
\(703\) | 25.7023 | + | 8.35117i | 0.0365608 | + | 0.0118793i | ||||
\(704\) | −81.5549 | − | 26.4988i | −0.115845 | − | 0.0376403i | ||||
\(705\) | −31.8447 | − | 261.249i | −0.0451698 | − | 0.370565i | ||||
\(706\) | −132.112 | − | 406.599i | −0.187127 | − | 0.575919i | ||||
\(707\) | −269.035 | −0.380530 | ||||||||
\(708\) | −7.72034 | + | 97.4637i | −0.0109044 | + | 0.137661i | ||||
\(709\) | −427.692 | − | 310.736i | −0.603233 | − | 0.438274i | 0.243792 | − | 0.969828i | \(-0.421609\pi\) |
−0.847025 | + | 0.531553i | \(0.821609\pi\) | |||||||
\(710\) | 37.7303 | − | 330.070i | 0.0531413 | − | 0.464888i | ||||
\(711\) | −1194.57 | − | 190.445i | −1.68013 | − | 0.267855i | ||||
\(712\) | 356.891 | − | 491.218i | 0.501251 | − | 0.689913i | ||||
\(713\) | 834.343 | + | 606.186i | 1.17019 | + | 0.850190i | ||||
\(714\) | 56.2801 | − | 13.4815i | 0.0788237 | − | 0.0188816i | ||||
\(715\) | −158.825 | + | 348.169i | −0.222133 | + | 0.486950i | ||||
\(716\) | 39.6073 | − | 54.5148i | 0.0553175 | − | 0.0761380i | ||||
\(717\) | −40.6734 | + | 513.473i | −0.0567273 | + | 0.716141i | ||||
\(718\) | − | 112.113i | − | 0.156146i | ||||||
\(719\) | −41.8379 | + | 13.5940i | −0.0581890 | + | 0.0189068i | −0.337967 | − | 0.941158i | \(-0.609739\pi\) |
0.279778 | + | 0.960065i | \(0.409739\pi\) | |||||||
\(720\) | −257.322 | − | 324.420i | −0.357392 | − | 0.450583i | ||||
\(721\) | 48.8671 | − | 150.397i | 0.0677768 | − | 0.208596i | ||||
\(722\) | 42.1268 | − | 129.653i | 0.0583473 | − | 0.179575i | ||||
\(723\) | 280.246 | + | 1169.92i | 0.387616 | + | 1.61815i | ||||
\(724\) | 272.187 | 0.375949 | ||||||||
\(725\) | −391.344 | − | 923.846i | −0.539784 | − | 1.27427i | ||||
\(726\) | 72.4477 | − | 174.653i | 0.0997902 | − | 0.240569i | ||||
\(727\) | −498.452 | − | 686.060i | −0.685628 | − | 0.943686i | 0.314356 | − | 0.949305i | \(-0.398211\pi\) |
−0.999984 | + | 0.00561920i | \(0.998211\pi\) | |||||||
\(728\) | −36.8727 | + | 113.483i | −0.0506493 | + | 0.155883i | ||||
\(729\) | −328.979 | − | 650.549i | −0.451275 | − | 0.892385i | ||||
\(730\) | −25.2336 | + | 27.5172i | −0.0345665 | + | 0.0376948i | ||||
\(731\) | 1017.20 | − | 330.508i | 1.39152 | − | 0.452132i | ||||
\(732\) | 8.04171 | − | 19.3866i | 0.0109859 | − | 0.0264844i | ||||
\(733\) | −447.807 | + | 145.501i | −0.610924 | + | 0.198501i | −0.598107 | − | 0.801417i | \(-0.704080\pi\) |
−0.0128176 | + | 0.999918i | \(0.504080\pi\) | |||||||
\(734\) | −107.360 | + | 147.769i | −0.146267 | + | 0.201320i | ||||
\(735\) | 626.586 | − | 291.513i | 0.852497 | − | 0.396616i | ||||
\(736\) | 930.582 | − | 676.108i | 1.26438 | − | 0.918624i | ||||
\(737\) | −135.150 | − | 98.1925i | −0.183379 | − | 0.133233i | ||||
\(738\) | 241.751 | − | 38.0380i | 0.327575 | − | 0.0515420i | ||||
\(739\) | 30.1447 | − | 21.9014i | 0.0407912 | − | 0.0296366i | −0.567203 | − | 0.823578i | \(-0.691974\pi\) |
0.607994 | + | 0.793942i | \(0.291974\pi\) | |||||||
\(740\) | −33.1903 | + | 6.73987i | −0.0448518 | + | 0.00910794i | ||||
\(741\) | −259.458 | − | 423.880i | −0.350146 | − | 0.572038i | ||||
\(742\) | −104.907 | + | 34.0862i | −0.141384 | + | 0.0459383i | ||||
\(743\) | −977.642 | −1.31580 | −0.657902 | − | 0.753104i | \(-0.728556\pi\) | ||||
−0.657902 | + | 0.753104i | \(0.728556\pi\) | |||||||
\(744\) | 459.387 | + | 36.3892i | 0.617456 | + | 0.0489102i | ||||
\(745\) | −1211.34 | − | 552.579i | −1.62596 | − | 0.741717i | ||||
\(746\) | −210.523 | − | 68.4029i | −0.282202 | − | 0.0916930i | ||||
\(747\) | 16.0666 | − | 8.16580i | 0.0215082 | − | 0.0109315i | ||||
\(748\) | −183.294 | − | 252.282i | −0.245045 | − | 0.337276i | ||||
\(749\) | 7.29081i | 0.00973407i | ||||||||
\(750\) | −283.306 | + | 59.7401i | −0.377741 | + | 0.0796534i | ||||
\(751\) | 110.601 | 0.147271 | 0.0736355 | − | 0.997285i | \(-0.476540\pi\) | ||||
0.0736355 | + | 0.997285i | \(0.476540\pi\) | |||||||
\(752\) | −130.616 | + | 94.8979i | −0.173691 | + | 0.126194i | ||||
\(753\) | 711.852 | − | 832.616i | 0.945355 | − | 1.10573i | ||||
\(754\) | 116.802 | − | 359.480i | 0.154910 | − | 0.476763i | ||||
\(755\) | −434.205 | + | 951.843i | −0.575105 | + | 1.26072i | ||||
\(756\) | 119.740 | − | 101.953i | 0.158386 | − | 0.134858i | ||||
\(757\) | 193.534i | 0.255659i | 0.991796 | + | 0.127830i | \(0.0408010\pi\) | ||||
−0.991796 | + | 0.127830i | \(0.959199\pi\) | |||||||
\(758\) | 29.7438 | + | 91.5421i | 0.0392399 | + | 0.120768i | ||||
\(759\) | 377.154 | + | 616.161i | 0.496909 | + | 0.811807i | ||||
\(760\) | −77.2480 | − | 380.406i | −0.101642 | − | 0.500534i | ||||
\(761\) | 369.468 | + | 508.529i | 0.485503 | + | 0.668238i | 0.979551 | − | 0.201197i | \(-0.0644831\pi\) |
−0.494047 | + | 0.869435i | \(0.664483\pi\) | |||||||
\(762\) | 186.067 | + | 303.980i | 0.244183 | + | 0.398924i | ||||
\(763\) | 154.906 | − | 213.210i | 0.203023 | − | 0.279437i | ||||
\(764\) | 279.920 | + | 385.277i | 0.366388 | + | 0.504289i | ||||
\(765\) | −27.7510 | − | 656.462i | −0.0362759 | − | 0.858120i | ||||
\(766\) | −426.129 | − | 309.601i | −0.556304 | − | 0.404178i | ||||
\(767\) | −36.0902 | − | 111.074i | −0.0470537 | − | 0.144816i | ||||
\(768\) | 52.9213 | − | 127.580i | 0.0689079 | − | 0.166120i | ||||
\(769\) | −17.4647 | − | 53.7507i | −0.0227109 | − | 0.0698969i | 0.939059 | − | 0.343757i | \(-0.111700\pi\) |
−0.961770 | + | 0.273860i | \(0.911700\pi\) | |||||||
\(770\) | −30.5485 | − | 28.0133i | −0.0396734 | − | 0.0363809i | ||||
\(771\) | −324.862 | − | 277.744i | −0.421352 | − | 0.360238i | ||||
\(772\) | 580.711 | + | 188.685i | 0.752217 | + | 0.244410i | ||||
\(773\) | −714.283 | + | 518.957i | −0.924040 | + | 0.671354i | −0.944526 | − | 0.328436i | \(-0.893478\pi\) |
0.0204865 | + | 0.999790i | \(0.493478\pi\) | |||||||
\(774\) | −360.292 | + | 359.561i | −0.465493 | + | 0.464549i | ||||
\(775\) | −346.417 | + | 575.570i | −0.446990 | + | 0.742672i | ||||
\(776\) | − | 516.891i | − | 0.666097i | ||||||
\(777\) | −2.37971 | − | 9.93442i | −0.00306269 | − | 0.0127856i | ||||
\(778\) | 20.9844 | + | 6.81824i | 0.0269722 | + | 0.00876381i | ||||
\(779\) | −454.876 | − | 147.798i | −0.583922 | − | 0.189728i | ||||
\(780\) | 544.467 | + | 302.427i | 0.698034 | + | 0.387727i | ||||
\(781\) | −166.855 | − | 513.526i | −0.213642 | − | 0.657523i | ||||
\(782\) | 432.670 | 0.553287 | ||||||||
\(783\) | −825.032 | + | 702.474i | −1.05368 | + | 0.897157i | ||||
\(784\) | −342.978 | − | 249.188i | −0.437472 | − | 0.317842i | ||||
\(785\) | −987.053 | − | 450.267i | −1.25739 | − | 0.573588i | ||||
\(786\) | 376.804 | − | 90.2603i | 0.479394 | − | 0.114835i | ||||
\(787\) | 476.013 | − | 655.176i | 0.604845 | − | 0.832498i | −0.391296 | − | 0.920265i | \(-0.627973\pi\) |
0.996141 | + | 0.0877672i | \(0.0279732\pi\) | |||||||
\(788\) | 44.4550 | + | 32.2984i | 0.0564149 | + | 0.0409879i | ||||
\(789\) | −171.264 | − | 714.965i | −0.217065 | − | 0.906166i | ||||
\(790\) | 515.515 | + | 58.9285i | 0.652551 | + | 0.0745930i | ||||
\(791\) | −22.6273 | + | 31.1438i | −0.0286060 | + | 0.0393727i | ||||
\(792\) | 287.475 | + | 146.843i | 0.362973 | + | 0.185408i | ||||
\(793\) | 25.0716i | 0.0316162i | ||||||||
\(794\) | −150.849 | + | 49.0138i | −0.189986 | + | 0.0617302i | ||||
\(795\) | 151.532 | + | 1243.14i | 0.190606 | + | 1.56370i | ||||
\(796\) | −362.255 | + | 1114.91i | −0.455094 | + | 1.40063i | ||||
\(797\) | −71.4536 | + | 219.912i | −0.0896532 | + | 0.275924i | −0.985823 | − | 0.167786i | \(-0.946338\pi\) |
0.896170 | + | 0.443710i | \(0.146338\pi\) | |||||||
\(798\) | 52.3470 | − | 12.5393i | 0.0655978 | − | 0.0157134i | ||||
\(799\) | −256.183 | −0.320629 | ||||||||
\(800\) | 491.145 | + | 565.841i | 0.613931 | + | 0.707302i | ||||
\(801\) | 676.636 | − | 675.263i | 0.844739 | − | 0.843025i | ||||
\(802\) | 180.023 | + | 247.780i | 0.224468 | + | 0.308953i | ||||
\(803\) | −18.7514 | + | 57.7108i | −0.0233516 | + | 0.0718690i | ||||
\(804\) | −176.679 | + | 206.652i | −0.219750 | + | 0.257030i | ||||
\(805\) | −321.803 | + | 65.3477i | −0.399755 | + | 0.0811773i | ||||
\(806\) | −240.693 | + | 78.2058i | −0.298626 | + | 0.0970295i | ||||
\(807\) | 323.275 | + | 134.097i | 0.400588 | + | 0.166167i | ||||
\(808\) | −854.773 | + | 277.733i | −1.05789 | + | 0.343729i | ||||
\(809\) | 607.858 | − | 836.645i | 0.751370 | − | 1.03417i | −0.246513 | − | 0.969139i | \(-0.579285\pi\) |
0.997883 | − | 0.0650327i | \(-0.0207152\pi\) | |||||||
\(810\) | 153.327 | + | 272.528i | 0.189292 | + | 0.336454i | ||||
\(811\) | −946.582 | + | 687.732i | −1.16718 | + | 0.848005i | −0.990669 | − | 0.136293i | \(-0.956481\pi\) |
−0.176511 | + | 0.984299i | \(0.556481\pi\) | |||||||
\(812\) | −189.113 | − | 137.399i | −0.232898 | − | 0.169210i | ||||
\(813\) | −446.084 | + | 273.049i | −0.548689 | + | 0.335854i | ||||
\(814\) | 7.79908 | − | 5.66636i | 0.00958118 | − | 0.00696113i | ||||
\(815\) | −34.9707 | − | 61.8638i | −0.0429088 | − | 0.0759065i | ||||
\(816\) | −343.779 | + | 210.428i | −0.421298 | + | 0.257877i | ||||
\(817\) | 946.113 | − | 307.411i | 1.15803 | − | 0.376268i | ||||
\(818\) | 267.173 | 0.326617 | ||||||||
\(819\) | −85.4568 | + | 167.298i | −0.104343 | + | 0.204271i | ||||
\(820\) | 587.398 | − | 119.281i | 0.716339 | − | 0.145465i | ||||
\(821\) | 1378.21 | + | 447.806i | 1.67869 | + | 0.545440i | 0.984657 | − | 0.174501i | \(-0.0558311\pi\) |
0.694035 | + | 0.719941i | \(0.255831\pi\) | |||||||
\(822\) | 336.928 | + | 288.060i | 0.409888 | + | 0.350438i | ||||
\(823\) | 413.581 | + | 569.246i | 0.502529 | + | 0.691672i | 0.982637 | − | 0.185537i | \(-0.0594026\pi\) |
−0.480108 | + | 0.877209i | \(0.659403\pi\) | |||||||
\(824\) | − | 528.287i | − | 0.641126i | ||||||
\(825\) | −378.627 | + | 279.439i | −0.458942 | + | 0.338714i | ||||
\(826\) | 12.6495 | 0.0153141 | ||||||||
\(827\) | 701.706 | − | 509.820i | 0.848496 | − | 0.616469i | −0.0762348 | − | 0.997090i | \(-0.524290\pi\) |
0.924731 | + | 0.380621i | \(0.124290\pi\) | |||||||
\(828\) | 1048.15 | − | 532.717i | 1.26588 | − | 0.643378i | ||||
\(829\) | 59.4524 | − | 182.976i | 0.0717158 | − | 0.220718i | −0.908774 | − | 0.417289i | \(-0.862980\pi\) |
0.980490 | + | 0.196570i | \(0.0629804\pi\) | |||||||
\(830\) | −6.72984 | + | 3.80428i | −0.00810824 | + | 0.00458347i | ||||
\(831\) | −43.2574 | + | 546.094i | −0.0520547 | + | 0.657153i | ||||
\(832\) | − | 166.714i | − | 0.200377i | ||||||
\(833\) | −207.875 | − | 639.775i | −0.249550 | − | 0.768037i | ||||
\(834\) | −16.3738 | + | 10.0225i | −0.0196329 | + | 0.0120174i | ||||
\(835\) | 73.4356 | + | 8.39443i | 0.0879469 | + | 0.0100532i | ||||
\(836\) | −170.484 | − | 234.652i | −0.203929 | − | 0.280684i | ||||
\(837\) | 705.216 | + | 170.443i | 0.842552 | + | 0.203636i | ||||
\(838\) | −75.7615 | + | 104.277i | −0.0904075 | + | 0.124435i | ||||
\(839\) | 218.610 | + | 300.892i | 0.260561 | + | 0.358631i | 0.919175 | − | 0.393850i | \(-0.128857\pi\) |
−0.658614 | + | 0.752481i | \(0.728857\pi\) | |||||||
\(840\) | −107.398 | + | 99.9745i | −0.127855 | + | 0.119017i | ||||
\(841\) | 622.641 | + | 452.375i | 0.740358 | + | 0.537901i | ||||
\(842\) | −7.88296 | − | 24.2613i | −0.00936219 | − | 0.0288138i | ||||
\(843\) | −49.9543 | − | 20.7215i | −0.0592578 | − | 0.0245806i | ||||
\(844\) | 40.2864 | + | 123.989i | 0.0477327 | + | 0.146906i | ||||
\(845\) | 100.354 | + | 11.4714i | 0.118762 | + | 0.0135757i | ||||
\(846\) | 108.689 | − | 55.2407i | 0.128474 | − | 0.0652964i | ||||
\(847\) | 132.850 | + | 43.1655i | 0.156847 | + | 0.0509628i | ||||
\(848\) | 621.530 | − | 451.568i | 0.732936 | − | 0.532509i | ||||
\(849\) | 56.2261 | + | 23.3230i | 0.0662262 | + | 0.0274712i | ||||
\(850\) | 24.3561 | + | 280.781i | 0.0286542 | + | 0.330331i | ||||
\(851\) | − | 76.3738i | − | 0.0897459i | ||||||
\(852\) | −854.600 | + | 204.713i | −1.00305 | + | 0.240273i | ||||
\(853\) | −0.0190880 | − | 0.00620206i | −2.23775e−5 | − | 7.27088e-6i | 0.309006 | − | 0.951060i | \(-0.400004\pi\) |
−0.309028 | + | 0.951053i | \(0.600004\pi\) | |||||||
\(854\) | −2.58258 | − | 0.839132i | −0.00302410 | − | 0.000982590i | ||||
\(855\) | −25.8117 | − | 610.586i | −0.0301891 | − | 0.714135i | ||||
\(856\) | 7.52653 | + | 23.1643i | 0.00879267 | + | 0.0270611i | ||||
\(857\) | 56.5546 | 0.0659913 | 0.0329957 | − | 0.999455i | \(-0.489495\pi\) | ||||
0.0329957 | + | 0.999455i | \(0.489495\pi\) | |||||||
\(858\) | −176.728 | − | 13.9990i | −0.205976 | − | 0.0163159i | ||||
\(859\) | 482.719 | + | 350.716i | 0.561955 | + | 0.408284i | 0.832174 | − | 0.554515i | \(-0.187096\pi\) |
−0.270219 | + | 0.962799i | \(0.587096\pi\) | |||||||
\(860\) | −842.590 | + | 918.844i | −0.979756 | + | 1.06842i | ||||
\(861\) | 42.1159 | + | 175.818i | 0.0489150 | + | 0.204202i | ||||
\(862\) | −272.107 | + | 374.524i | −0.315670 | + | 0.434482i | ||||
\(863\) | −206.837 | − | 150.276i | −0.239672 | − | 0.174132i | 0.461465 | − | 0.887158i | \(-0.347324\pi\) |
−0.701137 | + | 0.713027i | \(0.747324\pi\) | |||||||
\(864\) | 423.860 | − | 689.318i | 0.490579 | − | 0.797822i | ||||
\(865\) | 140.365 | + | 691.224i | 0.162272 | + | 0.799103i | ||||
\(866\) | 126.613 | − | 174.267i | 0.146204 | − | 0.201233i | ||||
\(867\) | 226.716 | + | 17.9587i | 0.261495 | + | 0.0207137i | ||||
\(868\) | 156.514i | 0.180315i | ||||||||
\(869\) | 802.042 | − | 260.599i | 0.922948 | − | 0.299884i | ||||
\(870\) | 340.206 | − | 316.690i | 0.391042 | − | 0.364011i | ||||
\(871\) | 100.362 | − | 308.883i | 0.115226 | − | 0.354630i | ||||
\(872\) | 272.063 | − | 837.323i | 0.311998 | − | 0.960233i | ||||
\(873\) | 128.121 | − | 803.641i | 0.146759 | − | 0.920551i | ||||
\(874\) | 402.433 | 0.460450 | ||||||||
\(875\) | −60.5225 | − | 205.155i | −0.0691685 | − | 0.234463i | ||||
\(876\) | 91.2215 | + | 37.8394i | 0.104134 | + | 0.0431957i | ||||
\(877\) | −146.721 | − | 201.945i | −0.167299 | − | 0.230267i | 0.717133 | − | 0.696936i | \(-0.245454\pi\) |
−0.884432 | + | 0.466669i | \(0.845454\pi\) | |||||||
\(878\) | 71.7736 | − | 220.897i | 0.0817467 | − | 0.251591i | ||||
\(879\) | 275.909 | + | 235.891i | 0.313890 | + | 0.268363i | ||||
\(880\) | 262.642 | + | 119.810i | 0.298456 | + | 0.136148i | ||||
\(881\) | −1039.28 | + | 337.681i | −1.17966 | + | 0.383293i | −0.832239 | − | 0.554418i | \(-0.812941\pi\) |
−0.347417 | + | 0.937711i | \(0.612941\pi\) | |||||||
\(882\) | 226.148 | + | 226.608i | 0.256404 | + | 0.256925i | ||||
\(883\) | 598.455 | − | 194.450i | 0.677752 | − | 0.220215i | 0.0501409 | − | 0.998742i | \(-0.484033\pi\) |
0.627611 | + | 0.778527i | \(0.284033\pi\) | |||||||
\(884\) | 356.349 | − | 490.472i | 0.403110 | − | 0.554833i | ||||
\(885\) | 27.5266 | − | 140.952i | 0.0311035 | − | 0.159268i | ||||
\(886\) | 140.703 | − | 102.227i | 0.158807 | − | 0.115380i | ||||
\(887\) | 436.537 | + | 317.163i | 0.492150 | + | 0.357568i | 0.806010 | − | 0.591901i | \(-0.201623\pi\) |
−0.313861 | + | 0.949469i | \(0.601623\pi\) | |||||||
\(888\) | −17.8164 | − | 29.1068i | −0.0200635 | − | 0.0327780i | ||||
\(889\) | −213.012 | + | 154.762i | −0.239608 | + | 0.174086i | ||||
\(890\) | −277.132 | + | 302.212i | −0.311384 | + | 0.339564i | ||||
\(891\) | 410.556 | + | 299.562i | 0.460781 | + | 0.336208i | ||||
\(892\) | −813.737 | + | 264.399i | −0.912261 | + | 0.296412i | ||||
\(893\) | −238.280 | −0.266831 | ||||||||
\(894\) | 48.7049 | − | 614.865i | 0.0544798 | − | 0.687768i | ||||
\(895\) | −66.8979 | + | 72.9521i | −0.0747463 | + | 0.0815107i | ||||
\(896\) | 212.272 | + | 68.9715i | 0.236911 | + | 0.0769771i | ||||
\(897\) | −912.692 | + | 1067.53i | −1.01749 | + | 1.19011i | ||||
\(898\) | −246.952 | − | 339.900i | −0.275002 | − | 0.378508i | ||||
\(899\) | − | 1078.41i | − | 1.19956i | ||||||
\(900\) | 404.709 | + | 650.206i | 0.449677 | + | 0.722451i | ||||
\(901\) | 1219.04 | 1.35298 | ||||||||
\(902\) | −138.027 | + | 100.283i | −0.153024 | + | 0.111178i | ||||
\(903\) | −285.816 | − | 244.361i | −0.316519 | − | 0.270611i | ||||
\(904\) | −39.7404 | + | 122.309i | −0.0439607 | + | 0.135297i | ||||
\(905\) | −397.234 | − | 45.4078i | −0.438932 | − | 0.0501743i | ||||
\(906\) | −483.147 | − | 38.2713i | −0.533275 | − | 0.0422420i | ||||
\(907\) | − | 286.442i | − | 0.315812i | −0.987454 | − | 0.157906i | \(-0.949526\pi\) | ||
0.987454 | − | 0.157906i | \(-0.0504744\pi\) | |||||||
\(908\) | −36.9408 | − | 113.692i | −0.0406837 | − | 0.125211i | ||||
\(909\) | −1397.81 | + | 219.936i | −1.53774 | + | 0.241954i | ||||
\(910\) | 33.4436 | − | 73.3135i | 0.0367512 | − | 0.0805643i | ||||
\(911\) | 828.429 | + | 1140.23i | 0.909362 | + | 1.25163i | 0.967384 | + | 0.253314i | \(0.0815207\pi\) |
−0.0580217 | + | 0.998315i | \(0.518479\pi\) | |||||||
\(912\) | −319.754 | + | 195.722i | −0.350608 | + | 0.214608i | ||||
\(913\) | −7.38526 | + | 10.1649i | −0.00808901 | + | 0.0111336i | ||||
\(914\) | 75.6777 | + | 104.161i | 0.0827984 | + | 0.113962i | ||||
\(915\) | −14.9704 | + | 26.9515i | −0.0163610 | + | 0.0294551i | ||||
\(916\) | −401.676 | − | 291.834i | −0.438510 | − | 0.318596i | ||||
\(917\) | 88.4534 | + | 272.232i | 0.0964596 | + | 0.296872i | ||||
\(918\) | 281.390 | − | 116.054i | 0.306525 | − | 0.126420i | ||||
\(919\) | −9.97272 | − | 30.6929i | −0.0108517 | − | 0.0333981i | 0.945484 | − | 0.325668i | \(-0.105589\pi\) |
−0.956336 | + | 0.292270i | \(0.905589\pi\) | |||||||
\(920\) | −954.967 | + | 539.829i | −1.03801 | + | 0.586770i | ||||
\(921\) | −363.548 | + | 425.223i | −0.394732 | + | 0.461697i | ||||
\(922\) | 103.665 | + | 33.6829i | 0.112435 | + | 0.0365325i | ||||
\(923\) | 849.261 | − | 617.025i | 0.920110 | − | 0.668499i | ||||
\(924\) | −42.0079 | + | 101.271i | −0.0454631 | + | 0.109600i | ||||
\(925\) | 49.5628 | − | 4.29927i | 0.0535814 | − | 0.00464786i | ||||
\(926\) | 361.325i | 0.390199i | ||||||||
\(927\) | 130.945 | − | 821.359i | 0.141257 | − | 0.886040i | ||||
\(928\) | −1143.93 | − | 371.686i | −1.23268 | − | 0.400523i | ||||
\(929\) | −477.883 | − | 155.274i | −0.514406 | − | 0.167141i | 0.0402991 | − | 0.999188i | \(-0.487169\pi\) |
−0.554705 | + | 0.832047i | \(0.687169\pi\) | |||||||
\(930\) | −305.436 | − | 59.6489i | −0.328426 | − | 0.0641386i | ||||
\(931\) | −193.348 | − | 595.065i | −0.207678 | − | 0.639167i | ||||
\(932\) | −446.853 | −0.479456 | ||||||||
\(933\) | 76.1488 | − | 961.324i | 0.0816172 | − | 1.03036i | ||||
\(934\) | −73.7572 | − | 53.5878i | −0.0789692 | − | 0.0573745i | ||||
\(935\) | 225.414 | + | 398.762i | 0.241085 | + | 0.426483i | ||||
\(936\) | −98.8049 | + | 619.757i | −0.105561 | + | 0.662134i | ||||
\(937\) | 40.3942 | − | 55.5978i | 0.0431101 | − | 0.0593360i | −0.786918 | − | 0.617058i | \(-0.788324\pi\) |
0.830028 | + | 0.557722i | \(0.188324\pi\) | |||||||
\(938\) | 28.4584 | + | 20.6763i | 0.0303395 | + | 0.0220429i | ||||
\(939\) | −585.540 | + | 140.261i | −0.623578 | + | 0.149373i | ||||
\(940\) | 259.954 | − | 146.948i | 0.276546 | − | 0.156327i | ||||
\(941\) | −503.452 | + | 692.942i | −0.535018 | + | 0.736389i | −0.987885 | − | 0.155189i | \(-0.950401\pi\) |
0.452867 | + | 0.891578i | \(0.350401\pi\) | |||||||
\(942\) | 39.6870 | − | 501.020i | 0.0421306 | − | 0.531868i | ||||
\(943\) | 1351.65i | 1.43336i | ||||||||
\(944\) | −83.7888 | + | 27.2246i | −0.0887593 | + | 0.0288397i | ||||
\(945\) | −191.759 | + | 128.816i | −0.202919 | + | 0.136313i | ||||
\(946\) | 109.658 | − | 337.492i | 0.115917 | − | 0.356757i | ||||
\(947\) | −220.744 | + | 679.381i | −0.233098 | + | 0.717403i | 0.764270 | + | 0.644897i | \(0.223100\pi\) |
−0.997368 | + | 0.0725062i | \(0.976900\pi\) | |||||||
\(948\) | −319.727 | − | 1334.74i | −0.337265 | − | 1.40796i | ||||
\(949\) | −117.972 | −0.124312 | ||||||||
\(950\) | 22.6540 | + | 261.159i | 0.0238463 | + | 0.274904i | ||||
\(951\) | −464.643 | + | 1120.14i | −0.488583 | + | 1.17785i | ||||
\(952\) | 83.9512 | + | 115.549i | 0.0881840 | + | 0.121375i | ||||
\(953\) | −319.010 | + | 981.811i | −0.334743 | + | 1.03023i | 0.632106 | + | 0.774882i | \(0.282191\pi\) |
−0.966849 | + | 0.255350i | \(0.917809\pi\) | |||||||
\(954\) | −517.191 | + | 262.861i | −0.542129 | + | 0.275535i | ||||
\(955\) | −344.245 | − | 608.976i | −0.360466 | − | 0.637671i | ||||
\(956\) | −555.819 | + | 180.597i | −0.581401 | + | 0.188909i | ||||
\(957\) | 289.442 | − | 697.773i | 0.302447 | − | 0.729125i | ||||
\(958\) | −3.04056 | + | 0.987937i | −0.00317386 | + | 0.00103125i | ||||
\(959\) | −192.487 | + | 264.935i | −0.200716 | + | 0.276262i | ||||
\(960\) | 99.5454 | − | 179.214i | 0.103693 | − | 0.186681i | ||||
\(961\) | 193.308 | − | 140.447i | 0.201153 | − | 0.146146i | ||||
\(962\) | 15.1625 | + | 11.0162i | 0.0157615 | + | 0.0114514i | ||||
\(963\) | 5.96025 | + | 37.8804i | 0.00618925 | + | 0.0393358i | ||||
\(964\) | −1104.29 | + | 802.313i | −1.14553 | + | 0.832275i | ||||
\(965\) | −816.020 | − | 372.246i | −0.845617 | − | 0.385747i | ||||
\(966\) | −79.4168 | − | 129.744i | −0.0822120 | − | 0.134311i | ||||
\(967\) | 956.592 | − | 310.815i | 0.989236 | − | 0.321422i | 0.230680 | − | 0.973030i | \(-0.425905\pi\) |
0.758556 | + | 0.651607i | \(0.225905\pi\) | |||||||
\(968\) | 466.649 | 0.482076 | ||||||||
\(969\) | −593.020 | − | 46.9746i | −0.611992 | − | 0.0484774i | ||||
\(970\) | −39.6439 | + | 346.810i | −0.0408700 | + | 0.357536i | ||||
\(971\) | −756.006 | − | 245.641i | −0.778585 | − | 0.252977i | −0.107349 | − | 0.994221i | \(-0.534236\pi\) |
−0.671236 | + | 0.741244i | \(0.734236\pi\) | |||||||
\(972\) | 538.779 | − | 627.597i | 0.554299 | − | 0.645676i | ||||
\(973\) | −8.33623 | − | 11.4738i | −0.00856756 | − | 0.0117922i | ||||
\(974\) | − | 632.810i | − | 0.649702i | ||||||
\(975\) | −744.149 | − | 532.197i | −0.763230 | − | 0.545843i | ||||
\(976\) | 18.9128 | 0.0193779 | ||||||||
\(977\) | 1195.65 | − | 868.690i | 1.22380 | − | 0.889140i | 0.227387 | − | 0.973805i | \(-0.426982\pi\) |
0.996410 | + | 0.0846646i | \(0.0269819\pi\) | |||||||
\(978\) | 21.3931 | − | 25.0224i | 0.0218743 | − | 0.0255853i | ||||
\(979\) | −205.940 | + | 633.818i | −0.210358 | + | 0.647414i | ||||
\(980\) | 577.913 | + | 529.953i | 0.589707 | + | 0.540768i | ||||
\(981\) | 630.537 | − | 1234.40i | 0.642749 | − | 1.25831i | ||||
\(982\) | − | 301.686i | − | 0.307216i | ||||||
\(983\) | −32.7514 | − | 100.798i | −0.0333178 | − | 0.102542i | 0.933015 | − | 0.359838i | \(-0.117168\pi\) |
−0.966332 | + | 0.257297i | \(0.917168\pi\) | |||||||
\(984\) | 315.312 | + | 515.130i | 0.320439 | + | 0.523506i | ||||
\(985\) | −59.4900 | − | 54.5530i | −0.0603959 | − | 0.0553837i | ||||
\(986\) | −265.933 | − | 366.025i | −0.269709 | − | 0.371222i | ||||
\(987\) | 47.0225 | + | 76.8212i | 0.0476418 | + | 0.0778330i | ||||
\(988\) | 331.446 | − | 456.196i | 0.335471 | − | 0.461737i | ||||
\(989\) | −1652.47 | − | 2274.44i | −1.67085 | − | 2.29973i | ||||
\(990\) | −181.620 | − | 120.573i | −0.183454 | − | 0.121791i | ||||
\(991\) | 763.591 | + | 554.781i | 0.770525 | + | 0.559819i | 0.902121 | − | 0.431484i | \(-0.142010\pi\) |
−0.131595 | + | 0.991304i | \(0.542010\pi\) | |||||||
\(992\) | 248.865 | + | 765.929i | 0.250872 | + | 0.772106i | ||||
\(993\) | 603.411 | − | 1454.67i | 0.607665 | − | 1.46493i | ||||
\(994\) | 35.1343 | + | 108.132i | 0.0353464 | + | 0.108785i | ||||
\(995\) | 714.674 | − | 1566.67i | 0.718265 | − | 1.57455i | ||||
\(996\) | 15.5427 | + | 13.2884i | 0.0156051 | + | 0.0133418i | ||||
\(997\) | −560.352 | − | 182.069i | −0.562038 | − | 0.182617i | 0.0142002 | − | 0.999899i | \(-0.495480\pi\) |
−0.576238 | + | 0.817282i | \(0.695480\pi\) | |||||||
\(998\) | −562.873 | + | 408.951i | −0.564001 | + | 0.409771i | ||||
\(999\) | −20.4855 | − | 49.6702i | −0.0205060 | − | 0.0497199i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 75.3.h.a.14.10 | yes | 72 | |
3.2 | odd | 2 | inner | 75.3.h.a.14.9 | ✓ | 72 | |
5.2 | odd | 4 | 375.3.j.b.176.20 | 144 | |||
5.3 | odd | 4 | 375.3.j.b.176.17 | 144 | |||
5.4 | even | 2 | 375.3.h.a.74.9 | 72 | |||
15.2 | even | 4 | 375.3.j.b.176.18 | 144 | |||
15.8 | even | 4 | 375.3.j.b.176.19 | 144 | |||
15.14 | odd | 2 | 375.3.h.a.74.10 | 72 | |||
25.9 | even | 10 | inner | 75.3.h.a.59.9 | yes | 72 | |
25.12 | odd | 20 | 375.3.j.b.326.18 | 144 | |||
25.13 | odd | 20 | 375.3.j.b.326.19 | 144 | |||
25.16 | even | 5 | 375.3.h.a.299.10 | 72 | |||
75.38 | even | 20 | 375.3.j.b.326.17 | 144 | |||
75.41 | odd | 10 | 375.3.h.a.299.9 | 72 | |||
75.59 | odd | 10 | inner | 75.3.h.a.59.10 | yes | 72 | |
75.62 | even | 20 | 375.3.j.b.326.20 | 144 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.h.a.14.9 | ✓ | 72 | 3.2 | odd | 2 | inner | |
75.3.h.a.14.10 | yes | 72 | 1.1 | even | 1 | trivial | |
75.3.h.a.59.9 | yes | 72 | 25.9 | even | 10 | inner | |
75.3.h.a.59.10 | yes | 72 | 75.59 | odd | 10 | inner | |
375.3.h.a.74.9 | 72 | 5.4 | even | 2 | |||
375.3.h.a.74.10 | 72 | 15.14 | odd | 2 | |||
375.3.h.a.299.9 | 72 | 75.41 | odd | 10 | |||
375.3.h.a.299.10 | 72 | 25.16 | even | 5 | |||
375.3.j.b.176.17 | 144 | 5.3 | odd | 4 | |||
375.3.j.b.176.18 | 144 | 15.2 | even | 4 | |||
375.3.j.b.176.19 | 144 | 15.8 | even | 4 | |||
375.3.j.b.176.20 | 144 | 5.2 | odd | 4 | |||
375.3.j.b.326.17 | 144 | 75.38 | even | 20 | |||
375.3.j.b.326.18 | 144 | 25.12 | odd | 20 | |||
375.3.j.b.326.19 | 144 | 25.13 | odd | 20 | |||
375.3.j.b.326.20 | 144 | 75.62 | even | 20 |