Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(7,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.g (of order \(6\), degree \(2\), 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: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.9 | ||
Character | \(\chi\) | \(=\) | 76.11 |
Dual form | 76.3.g.c.7.9 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.545551 | + | 1.92416i | 0.272776 | + | 0.962078i | ||||
\(3\) | 3.88623 | + | 2.24371i | 1.29541 | + | 0.747905i | 0.979608 | − | 0.200920i | \(-0.0643932\pi\) |
0.315802 | + | 0.948825i | \(0.397727\pi\) | |||||||
\(4\) | −3.40475 | + | 2.09945i | −0.851187 | + | 0.524863i | ||||
\(5\) | −0.133773 | + | 0.231701i | −0.0267546 | + | 0.0463403i | −0.879093 | − | 0.476651i | \(-0.841851\pi\) |
0.852338 | + | 0.522991i | \(0.175184\pi\) | |||||||
\(6\) | −2.19712 | + | 8.70177i | −0.366186 | + | 1.45029i | ||||
\(7\) | − | 7.24937i | − | 1.03562i | −0.855495 | − | 0.517812i | \(-0.826747\pi\) | ||
0.855495 | − | 0.517812i | \(-0.173253\pi\) | |||||||
\(8\) | −5.89713 | − | 5.40590i | −0.737142 | − | 0.675738i | ||||
\(9\) | 5.56851 | + | 9.64495i | 0.618724 | + | 1.07166i | ||||
\(10\) | −0.518810 | − | 0.130995i | −0.0518810 | − | 0.0130995i | ||||
\(11\) | − | 11.7422i | − | 1.06748i | −0.845650 | − | 0.533738i | \(-0.820787\pi\) | ||
0.845650 | − | 0.533738i | \(-0.179213\pi\) | |||||||
\(12\) | −17.9422 | + | 0.519664i | −1.49518 | + | 0.0433053i | ||||
\(13\) | 4.17006 | + | 7.22276i | 0.320774 | + | 0.555597i | 0.980648 | − | 0.195780i | \(-0.0627237\pi\) |
−0.659874 | + | 0.751376i | \(0.729390\pi\) | |||||||
\(14\) | 13.9489 | − | 3.95490i | 0.996350 | − | 0.282493i | ||||
\(15\) | −1.03974 | + | 0.600297i | −0.0693163 | + | 0.0400198i | ||||
\(16\) | 7.18461 | − | 14.2962i | 0.449038 | − | 0.893513i | ||||
\(17\) | −7.11880 | + | 12.3301i | −0.418753 | + | 0.725301i | −0.995814 | − | 0.0913994i | \(-0.970866\pi\) |
0.577061 | + | 0.816701i | \(0.304199\pi\) | |||||||
\(18\) | −15.5205 | + | 15.9765i | −0.862248 | + | 0.887583i | ||||
\(19\) | −11.9609 | + | 14.7627i | −0.629522 | + | 0.776983i | ||||
\(20\) | −0.0309829 | − | 1.06973i | −0.00154915 | − | 0.0534867i | ||||
\(21\) | 16.2655 | − | 28.1727i | 0.774548 | − | 1.34156i | ||||
\(22\) | 22.5939 | − | 6.40599i | 1.02699 | − | 0.291181i | ||||
\(23\) | 21.4900 | − | 12.4073i | 0.934349 | − | 0.539447i | 0.0461649 | − | 0.998934i | \(-0.485300\pi\) |
0.888185 | + | 0.459487i | \(0.151967\pi\) | |||||||
\(24\) | −10.7883 | − | 34.2401i | −0.449513 | − | 1.42667i | ||||
\(25\) | 12.4642 | + | 21.5886i | 0.498568 | + | 0.863546i | ||||
\(26\) | −11.6227 | + | 11.9642i | −0.447028 | + | 0.460163i | ||||
\(27\) | 9.58976i | 0.355176i | ||||||||
\(28\) | 15.2197 | + | 24.6823i | 0.543560 | + | 0.881509i | ||||
\(29\) | −25.7911 | − | 44.6716i | −0.889350 | − | 1.54040i | −0.840645 | − | 0.541586i | \(-0.817824\pi\) |
−0.0487047 | − | 0.998813i | \(-0.515509\pi\) | |||||||
\(30\) | −1.72230 | − | 1.67314i | −0.0574099 | − | 0.0557712i | ||||
\(31\) | − | 26.3372i | − | 0.849587i | −0.905290 | − | 0.424793i | \(-0.860347\pi\) | ||
0.905290 | − | 0.424793i | \(-0.139653\pi\) | |||||||
\(32\) | 31.4277 | + | 6.02499i | 0.982115 | + | 0.188281i | ||||
\(33\) | 26.3462 | − | 45.6330i | 0.798371 | − | 1.38282i | ||||
\(34\) | −27.6087 | − | 6.97096i | −0.812022 | − | 0.205028i | ||||
\(35\) | 1.67969 | + | 0.969769i | 0.0479911 | + | 0.0277077i | ||||
\(36\) | −39.2085 | − | 21.1478i | −1.08912 | − | 0.587439i | ||||
\(37\) | −20.1243 | −0.543901 | −0.271950 | − | 0.962311i | \(-0.587669\pi\) | ||||
−0.271950 | + | 0.962311i | \(0.587669\pi\) | |||||||
\(38\) | −34.9310 | − | 14.9608i | −0.919236 | − | 0.393707i | ||||
\(39\) | 37.4257i | 0.959634i | ||||||||
\(40\) | 2.04143 | − | 0.643211i | 0.0510358 | − | 0.0160803i | ||||
\(41\) | −38.5881 | + | 66.8366i | −0.941174 | + | 1.63016i | −0.177937 | + | 0.984042i | \(0.556942\pi\) |
−0.763237 | + | 0.646119i | \(0.776391\pi\) | |||||||
\(42\) | 63.0823 | + | 15.9277i | 1.50196 | + | 0.379231i | ||||
\(43\) | 30.0199 | + | 17.3320i | 0.698138 | + | 0.403070i | 0.806654 | − | 0.591024i | \(-0.201276\pi\) |
−0.108515 | + | 0.994095i | \(0.534610\pi\) | |||||||
\(44\) | 24.6522 | + | 39.9793i | 0.560278 | + | 0.908621i | ||||
\(45\) | −2.97967 | −0.0662148 | ||||||||
\(46\) | 35.5975 | + | 34.5814i | 0.773858 | + | 0.751769i | ||||
\(47\) | −31.9968 | + | 18.4733i | −0.680782 | + | 0.393050i | −0.800150 | − | 0.599800i | \(-0.795247\pi\) |
0.119367 | + | 0.992850i | \(0.461913\pi\) | |||||||
\(48\) | 59.9976 | − | 39.4381i | 1.24995 | − | 0.821627i | ||||
\(49\) | −3.55331 | −0.0725166 | ||||||||
\(50\) | −34.7400 | + | 35.7608i | −0.694801 | + | 0.715216i | ||||
\(51\) | −55.3306 | + | 31.9451i | −1.08491 | + | 0.626375i | ||||
\(52\) | −29.3618 | − | 15.8368i | −0.564651 | − | 0.304554i | ||||
\(53\) | −8.75934 | − | 15.1716i | −0.165271 | − | 0.286257i | 0.771481 | − | 0.636253i | \(-0.219516\pi\) |
−0.936751 | + | 0.349996i | \(0.886183\pi\) | |||||||
\(54\) | −18.4522 | + | 5.23171i | −0.341707 | + | 0.0968835i | ||||
\(55\) | 2.72069 | + | 1.57079i | 0.0494672 | + | 0.0285599i | ||||
\(56\) | −39.1894 | + | 42.7505i | −0.699810 | + | 0.763402i | ||||
\(57\) | −79.6061 | + | 30.5343i | −1.39660 | + | 0.535689i | ||||
\(58\) | 71.8847 | − | 73.9968i | 1.23939 | − | 1.27581i | ||||
\(59\) | −82.8741 | − | 47.8474i | −1.40465 | − | 0.810973i | −0.409781 | − | 0.912184i | \(-0.634395\pi\) |
−0.994865 | + | 0.101211i | \(0.967728\pi\) | |||||||
\(60\) | 2.27977 | − | 4.22675i | 0.0379962 | − | 0.0704458i | ||||
\(61\) | 26.2074 | + | 45.3926i | 0.429630 | + | 0.744141i | 0.996840 | − | 0.0794323i | \(-0.0253107\pi\) |
−0.567210 | + | 0.823573i | \(0.691977\pi\) | |||||||
\(62\) | 50.6769 | − | 14.3683i | 0.817369 | − | 0.231747i | ||||
\(63\) | 69.9198 | − | 40.3682i | 1.10984 | − | 0.640765i | ||||
\(64\) | 5.55239 | + | 63.7587i | 0.0867561 | + | 0.996230i | ||||
\(65\) | −2.23136 | −0.0343287 | ||||||||
\(66\) | 102.178 | + | 25.7991i | 1.54815 | + | 0.390895i | ||||
\(67\) | −11.8862 | + | 6.86248i | −0.177405 | + | 0.102425i | −0.586073 | − | 0.810258i | \(-0.699327\pi\) |
0.408668 | + | 0.912683i | \(0.365994\pi\) | |||||||
\(68\) | −1.64877 | − | 56.9265i | −0.0242467 | − | 0.837155i | ||||
\(69\) | 111.354 | 1.61382 | ||||||||
\(70\) | −0.949629 | + | 3.76104i | −0.0135661 | + | 0.0537292i | ||||
\(71\) | −39.7717 | − | 22.9622i | −0.560164 | − | 0.323411i | 0.193047 | − | 0.981189i | \(-0.438163\pi\) |
−0.753211 | + | 0.657778i | \(0.771496\pi\) | |||||||
\(72\) | 19.3014 | − | 86.9804i | 0.268075 | − | 1.20806i | ||||
\(73\) | 20.0638 | − | 34.7515i | 0.274846 | − | 0.476048i | −0.695250 | − | 0.718768i | \(-0.744706\pi\) |
0.970096 | + | 0.242720i | \(0.0780397\pi\) | |||||||
\(74\) | −10.9789 | − | 38.7223i | −0.148363 | − | 0.523275i | ||||
\(75\) | 111.865i | 1.49153i | ||||||||
\(76\) | 9.73035 | − | 75.3745i | 0.128031 | − | 0.991770i | ||||
\(77\) | −85.1238 | −1.10550 | ||||||||
\(78\) | −72.0129 | + | 20.4176i | −0.923242 | + | 0.261765i | ||||
\(79\) | 106.053 | + | 61.2298i | 1.34245 | + | 0.775061i | 0.987166 | − | 0.159699i | \(-0.0510524\pi\) |
0.355279 | + | 0.934760i | \(0.384386\pi\) | |||||||
\(80\) | 2.35134 | + | 3.57713i | 0.0293918 | + | 0.0447141i | ||||
\(81\) | 28.5999 | − | 49.5365i | 0.353086 | − | 0.611562i | ||||
\(82\) | −149.656 | − | 37.7868i | −1.82507 | − | 0.460814i | ||||
\(83\) | 108.436i | 1.30645i | 0.757163 | + | 0.653226i | \(0.226585\pi\) | ||||
−0.757163 | + | 0.653226i | \(0.773415\pi\) | |||||||
\(84\) | 3.76723 | + | 130.070i | 0.0448480 | + | 1.54845i | ||||
\(85\) | −1.90461 | − | 3.29887i | −0.0224071 | − | 0.0388103i | ||||
\(86\) | −16.9721 | + | 67.2186i | −0.197350 | + | 0.781611i | ||||
\(87\) | − | 231.472i | − | 2.66060i | ||||||
\(88\) | −63.4774 | + | 69.2455i | −0.721334 | + | 0.786881i | ||||
\(89\) | −26.2347 | − | 45.4398i | −0.294772 | − | 0.510559i | 0.680160 | − | 0.733064i | \(-0.261910\pi\) |
−0.974932 | + | 0.222504i | \(0.928577\pi\) | |||||||
\(90\) | −1.62556 | − | 5.73334i | −0.0180618 | − | 0.0637038i | ||||
\(91\) | 52.3604 | − | 30.2303i | 0.575389 | − | 0.332201i | ||||
\(92\) | −47.1197 | + | 87.3609i | −0.512170 | + | 0.949575i | ||||
\(93\) | 59.0932 | − | 102.352i | 0.635410 | − | 1.10056i | ||||
\(94\) | −53.0015 | − | 51.4886i | −0.563845 | − | 0.547751i | ||||
\(95\) | −1.82049 | − | 4.74621i | −0.0191630 | − | 0.0499601i | ||||
\(96\) | 108.617 | + | 93.9293i | 1.13142 | + | 0.978430i | ||||
\(97\) | 29.9055 | − | 51.7979i | 0.308304 | − | 0.533999i | −0.669687 | − | 0.742643i | \(-0.733572\pi\) |
0.977992 | + | 0.208644i | \(0.0669051\pi\) | |||||||
\(98\) | −1.93851 | − | 6.83712i | −0.0197808 | − | 0.0697666i | ||||
\(99\) | 113.253 | − | 65.3868i | 1.14397 | − | 0.660473i | ||||
\(100\) | −87.7618 | − | 47.3359i | −0.877618 | − | 0.473359i | ||||
\(101\) | 29.2672 | + | 50.6923i | 0.289774 | + | 0.501904i | 0.973756 | − | 0.227596i | \(-0.0730864\pi\) |
−0.683981 | + | 0.729499i | \(0.739753\pi\) | |||||||
\(102\) | −91.6530 | − | 89.0369i | −0.898559 | − | 0.872911i | ||||
\(103\) | − | 102.670i | − | 0.996798i | −0.866948 | − | 0.498399i | \(-0.833922\pi\) | ||
0.866948 | − | 0.498399i | \(-0.166078\pi\) | |||||||
\(104\) | 14.4541 | − | 65.1365i | 0.138982 | − | 0.626313i | ||||
\(105\) | 4.35177 | + | 7.53749i | 0.0414454 | + | 0.0717856i | ||||
\(106\) | 24.4139 | − | 25.1312i | 0.230320 | − | 0.237087i | ||||
\(107\) | − | 17.8502i | − | 0.166825i | −0.996515 | − | 0.0834123i | \(-0.973418\pi\) | ||
0.996515 | − | 0.0834123i | \(-0.0265818\pi\) | |||||||
\(108\) | −20.1332 | − | 32.6507i | −0.186419 | − | 0.302321i | ||||
\(109\) | −96.3984 | + | 166.967i | −0.884389 | + | 1.53181i | −0.0379776 | + | 0.999279i | \(0.512092\pi\) |
−0.846412 | + | 0.532529i | \(0.821242\pi\) | |||||||
\(110\) | −1.53817 | + | 6.09199i | −0.0139834 | + | 0.0553817i | ||||
\(111\) | −78.2077 | − | 45.1533i | −0.704574 | − | 0.406786i | ||||
\(112\) | −103.638 | − | 52.0839i | −0.925343 | − | 0.465035i | ||||
\(113\) | 191.548 | 1.69512 | 0.847558 | − | 0.530702i | \(-0.178072\pi\) | ||||
0.847558 | + | 0.530702i | \(0.178072\pi\) | |||||||
\(114\) | −102.182 | − | 136.516i | −0.896332 | − | 1.19751i | ||||
\(115\) | 6.63903i | 0.0577307i | ||||||||
\(116\) | 181.598 | + | 97.9482i | 1.56550 | + | 0.844381i | ||||
\(117\) | −46.4421 | + | 80.4400i | −0.396941 | + | 0.687522i | ||||
\(118\) | 46.8537 | − | 185.566i | 0.397066 | − | 1.57259i | ||||
\(119\) | 89.3856 | + | 51.6068i | 0.751139 | + | 0.433670i | ||||
\(120\) | 9.37666 | + | 2.08073i | 0.0781388 | + | 0.0173394i | ||||
\(121\) | −16.8801 | −0.139505 | ||||||||
\(122\) | −73.0449 | + | 75.1911i | −0.598728 | + | 0.616321i | ||||
\(123\) | −299.925 | + | 173.162i | −2.43841 | + | 1.40782i | ||||
\(124\) | 55.2937 | + | 89.6715i | 0.445917 | + | 0.723157i | ||||
\(125\) | −13.3581 | −0.106865 | ||||||||
\(126\) | 115.820 | + | 112.514i | 0.919202 | + | 0.892965i | ||||
\(127\) | 51.3632 | − | 29.6546i | 0.404435 | − | 0.233501i | −0.283961 | − | 0.958836i | \(-0.591649\pi\) |
0.688396 | + | 0.725335i | \(0.258315\pi\) | |||||||
\(128\) | −119.653 | + | 45.4673i | −0.934785 | + | 0.355213i | ||||
\(129\) | 77.7763 | + | 134.712i | 0.602917 | + | 1.04428i | ||||
\(130\) | −1.21732 | − | 4.29349i | −0.00936403 | − | 0.0330269i | ||||
\(131\) | 25.3061 | + | 14.6105i | 0.193177 | + | 0.111531i | 0.593469 | − | 0.804857i | \(-0.297758\pi\) |
−0.400292 | + | 0.916388i | \(0.631091\pi\) | |||||||
\(132\) | 6.10201 | + | 210.681i | 0.0462274 | + | 1.59607i | ||||
\(133\) | 107.020 | + | 86.7090i | 0.804662 | + | 0.651947i | ||||
\(134\) | −19.6890 | − | 19.1270i | −0.146933 | − | 0.142739i | ||||
\(135\) | −2.22196 | − | 1.28285i | −0.0164590 | − | 0.00950260i | ||||
\(136\) | 108.636 | − | 34.2288i | 0.798794 | − | 0.251683i | ||||
\(137\) | 2.83485 | + | 4.91011i | 0.0206924 | + | 0.0358402i | 0.876186 | − | 0.481973i | \(-0.160080\pi\) |
−0.855494 | + | 0.517813i | \(0.826746\pi\) | |||||||
\(138\) | 60.7491 | + | 214.262i | 0.440211 | + | 1.55262i | ||||
\(139\) | 43.5024 | − | 25.1161i | 0.312967 | − | 0.180692i | −0.335286 | − | 0.942116i | \(-0.608833\pi\) |
0.648253 | + | 0.761425i | \(0.275500\pi\) | |||||||
\(140\) | −7.75490 | + | 0.224607i | −0.0553921 | + | 0.00160433i | ||||
\(141\) | −165.796 | −1.17586 | ||||||||
\(142\) | 22.4853 | − | 89.0539i | 0.158347 | − | 0.627140i | ||||
\(143\) | 84.8113 | − | 48.9658i | 0.593086 | − | 0.342418i | ||||
\(144\) | 177.894 | − | 10.3134i | 1.23537 | − | 0.0716208i | ||||
\(145\) | 13.8006 | 0.0951768 | ||||||||
\(146\) | 77.8131 | + | 19.6471i | 0.532966 | + | 0.134569i | ||||
\(147\) | −13.8090 | − | 7.97262i | −0.0939387 | − | 0.0542355i | ||||
\(148\) | 68.5183 | − | 42.2500i | 0.462961 | − | 0.285473i | ||||
\(149\) | 81.0049 | − | 140.305i | 0.543657 | − | 0.941642i | −0.455033 | − | 0.890475i | \(-0.650373\pi\) |
0.998690 | − | 0.0511672i | \(-0.0162941\pi\) | |||||||
\(150\) | −215.245 | + | 61.0278i | −1.43496 | + | 0.406852i | ||||
\(151\) | 123.556i | 0.818250i | 0.912478 | + | 0.409125i | \(0.134166\pi\) | ||||
−0.912478 | + | 0.409125i | \(0.865834\pi\) | |||||||
\(152\) | 150.341 | − | 22.3980i | 0.989084 | − | 0.147355i | ||||
\(153\) | −158.565 | −1.03637 | ||||||||
\(154\) | −46.4394 | − | 163.791i | −0.301554 | − | 1.06358i | ||||
\(155\) | 6.10237 | + | 3.52320i | 0.0393701 | + | 0.0227303i | ||||
\(156\) | −78.5734 | − | 127.425i | −0.503676 | − | 0.816828i | ||||
\(157\) | −115.986 | + | 200.893i | −0.738763 | + | 1.27958i | 0.214289 | + | 0.976770i | \(0.431257\pi\) |
−0.953052 | + | 0.302806i | \(0.902077\pi\) | |||||||
\(158\) | −59.9582 | + | 237.467i | −0.379483 | + | 1.50295i | ||||
\(159\) | − | 78.6138i | − | 0.494427i | ||||||
\(160\) | −5.60017 | + | 6.47586i | −0.0350011 | + | 0.0404741i | ||||
\(161\) | −89.9449 | − | 155.789i | −0.558664 | − | 0.967635i | ||||
\(162\) | 110.919 | + | 28.0060i | 0.684683 | + | 0.172876i | ||||
\(163\) | 72.2434i | 0.443211i | 0.975136 | + | 0.221606i | \(0.0711298\pi\) | ||||
−0.975136 | + | 0.221606i | \(0.928870\pi\) | |||||||
\(164\) | −8.93734 | − | 308.576i | −0.0544960 | − | 1.88156i | ||||
\(165\) | 7.04882 | + | 12.2089i | 0.0427201 | + | 0.0739935i | ||||
\(166\) | −208.647 | + | 59.1572i | −1.25691 | + | 0.356369i | ||||
\(167\) | −101.024 | + | 58.3264i | −0.604936 | + | 0.349260i | −0.770981 | − | 0.636858i | \(-0.780234\pi\) |
0.166045 | + | 0.986118i | \(0.446900\pi\) | |||||||
\(168\) | −248.219 | + | 78.2084i | −1.47749 | + | 0.465526i | ||||
\(169\) | 49.7212 | − | 86.1196i | 0.294208 | − | 0.509584i | ||||
\(170\) | 5.30848 | − | 5.46446i | 0.0312264 | − | 0.0321439i | ||||
\(171\) | −208.990 | − | 33.1562i | −1.22216 | − | 0.193896i | ||||
\(172\) | −138.598 | + | 4.01425i | −0.805803 | + | 0.0233386i | ||||
\(173\) | 66.5048 | − | 115.190i | 0.384421 | − | 0.665836i | −0.607268 | − | 0.794497i | \(-0.707735\pi\) |
0.991689 | + | 0.128661i | \(0.0410679\pi\) | |||||||
\(174\) | 445.388 | − | 126.280i | 2.55970 | − | 0.725746i | ||||
\(175\) | 156.504 | − | 90.3576i | 0.894309 | − | 0.516329i | ||||
\(176\) | −167.869 | − | 84.3634i | −0.953803 | − | 0.479337i | ||||
\(177\) | −214.712 | − | 371.892i | −1.21306 | − | 2.10108i | ||||
\(178\) | 73.1208 | − | 75.2693i | 0.410791 | − | 0.422861i | ||||
\(179\) | − | 99.3625i | − | 0.555098i | −0.960711 | − | 0.277549i | \(-0.910478\pi\) | ||
0.960711 | − | 0.277549i | \(-0.0895221\pi\) | |||||||
\(180\) | 10.1450 | − | 6.25566i | 0.0563612 | − | 0.0347537i | ||||
\(181\) | −21.9433 | − | 38.0069i | −0.121234 | − | 0.209983i | 0.799021 | − | 0.601303i | \(-0.205352\pi\) |
−0.920254 | + | 0.391321i | \(0.872018\pi\) | |||||||
\(182\) | 86.7331 | + | 84.2574i | 0.476555 | + | 0.462953i | ||||
\(183\) | 235.208i | 1.28529i | ||||||||
\(184\) | −193.802 | − | 43.0057i | −1.05327 | − | 0.233727i | ||||
\(185\) | 2.69209 | − | 4.66284i | 0.0145518 | − | 0.0252045i | ||||
\(186\) | 229.180 | + | 57.8659i | 1.23215 | + | 0.311107i | ||||
\(187\) | 144.783 | + | 83.5906i | 0.774242 | + | 0.447009i | ||||
\(188\) | 70.1570 | − | 130.073i | 0.373176 | − | 0.691876i | ||||
\(189\) | 69.5197 | 0.367829 | ||||||||
\(190\) | 8.13927 | − | 6.09220i | 0.0428383 | − | 0.0320642i | ||||
\(191\) | − | 63.2363i | − | 0.331080i | −0.986203 | − | 0.165540i | \(-0.947063\pi\) | ||
0.986203 | − | 0.165540i | \(-0.0529367\pi\) | |||||||
\(192\) | −121.478 | + | 260.239i | −0.632700 | + | 1.35541i | ||||
\(193\) | 23.1161 | − | 40.0383i | 0.119773 | − | 0.207452i | −0.799905 | − | 0.600127i | \(-0.795117\pi\) |
0.919678 | + | 0.392674i | \(0.128450\pi\) | |||||||
\(194\) | 115.982 | + | 29.2845i | 0.597846 | + | 0.150951i | ||||
\(195\) | −8.67159 | − | 5.00655i | −0.0444697 | − | 0.0256746i | ||||
\(196\) | 12.0981 | − | 7.46001i | 0.0617252 | − | 0.0380613i | ||||
\(197\) | 76.2113 | 0.386859 | 0.193430 | − | 0.981114i | \(-0.438039\pi\) | ||||
0.193430 | + | 0.981114i | \(0.438039\pi\) | |||||||
\(198\) | 187.600 | + | 182.245i | 0.947474 | + | 0.920429i | ||||
\(199\) | −89.6573 | + | 51.7637i | −0.450539 | + | 0.260119i | −0.708058 | − | 0.706154i | \(-0.750428\pi\) |
0.257519 | + | 0.966273i | \(0.417095\pi\) | |||||||
\(200\) | 43.2030 | − | 194.691i | 0.216015 | − | 0.973457i | ||||
\(201\) | −61.5898 | −0.306417 | ||||||||
\(202\) | −81.5731 | + | 83.9699i | −0.403827 | + | 0.415693i | ||||
\(203\) | −323.841 | + | 186.969i | −1.59527 | + | 0.921032i | ||||
\(204\) | 121.319 | − | 224.929i | 0.594703 | − | 1.10259i | ||||
\(205\) | −10.3241 | − | 17.8819i | −0.0503614 | − | 0.0872285i | ||||
\(206\) | 197.553 | − | 56.0118i | 0.958997 | − | 0.271902i | ||||
\(207\) | 239.335 | + | 138.180i | 1.15621 | + | 0.667537i | ||||
\(208\) | 133.218 | − | 7.72333i | 0.640472 | − | 0.0371314i | ||||
\(209\) | 173.347 | + | 140.448i | 0.829411 | + | 0.671999i | ||||
\(210\) | −12.1292 | + | 12.4856i | −0.0577580 | + | 0.0594551i | ||||
\(211\) | 107.264 | + | 61.9287i | 0.508359 | + | 0.293501i | 0.732159 | − | 0.681134i | \(-0.238513\pi\) |
−0.223800 | + | 0.974635i | \(0.571846\pi\) | |||||||
\(212\) | 61.6754 | + | 33.2657i | 0.290922 | + | 0.156914i | ||||
\(213\) | −103.041 | − | 178.473i | −0.483761 | − | 0.837899i | ||||
\(214\) | 34.3466 | − | 9.73822i | 0.160498 | − | 0.0455057i | ||||
\(215\) | −8.03171 | + | 4.63711i | −0.0373568 | + | 0.0215680i | ||||
\(216\) | 51.8413 | − | 56.5521i | 0.240006 | − | 0.261815i | ||||
\(217\) | −190.928 | −0.879852 | ||||||||
\(218\) | −373.861 | − | 94.3965i | −1.71496 | − | 0.433012i | ||||
\(219\) | 155.945 | − | 90.0348i | 0.712077 | − | 0.411118i | ||||
\(220\) | −12.5611 | + | 0.363809i | −0.0570958 | + | 0.00165368i | ||||
\(221\) | −118.743 | −0.537300 | ||||||||
\(222\) | 44.2155 | − | 175.117i | 0.199169 | − | 0.788817i | ||||
\(223\) | −189.587 | − | 109.458i | −0.850167 | − | 0.490844i | 0.0105403 | − | 0.999944i | \(-0.496645\pi\) |
−0.860707 | + | 0.509100i | \(0.829978\pi\) | |||||||
\(224\) | 43.6774 | − | 227.831i | 0.194988 | − | 1.01710i | ||||
\(225\) | −138.814 | + | 240.433i | −0.616952 | + | 1.06859i | ||||
\(226\) | 104.499 | + | 368.568i | 0.462387 | + | 1.63083i | ||||
\(227\) | 116.805i | 0.514558i | 0.966337 | + | 0.257279i | \(0.0828260\pi\) | ||||
−0.966337 | + | 0.257279i | \(0.917174\pi\) | |||||||
\(228\) | 206.933 | − | 271.091i | 0.907602 | − | 1.18899i | ||||
\(229\) | 162.657 | 0.710291 | 0.355145 | − | 0.934811i | \(-0.384431\pi\) | ||||
0.355145 | + | 0.934811i | \(0.384431\pi\) | |||||||
\(230\) | −12.7745 | + | 3.62193i | −0.0555414 | + | 0.0157475i | ||||
\(231\) | −330.810 | − | 190.993i | −1.43208 | − | 0.826812i | ||||
\(232\) | −89.3964 | + | 402.859i | −0.385329 | + | 1.73646i | ||||
\(233\) | 144.534 | − | 250.340i | 0.620316 | − | 1.07442i | −0.369111 | − | 0.929385i | \(-0.620338\pi\) |
0.989427 | − | 0.145034i | \(-0.0463290\pi\) | |||||||
\(234\) | −180.116 | − | 45.4776i | −0.769725 | − | 0.194349i | ||||
\(235\) | − | 9.88493i | − | 0.0420635i | ||||||
\(236\) | 382.619 | − | 11.0819i | 1.62127 | − | 0.0469571i | ||||
\(237\) | 274.765 | + | 475.906i | 1.15934 | + | 2.00804i | ||||
\(238\) | −50.5351 | + | 200.146i | −0.212332 | + | 0.840949i | ||||
\(239\) | − | 283.451i | − | 1.18599i | −0.805208 | − | 0.592993i | \(-0.797946\pi\) | ||
0.805208 | − | 0.592993i | \(-0.202054\pi\) | |||||||
\(240\) | 1.11180 | + | 19.1773i | 0.00463252 | + | 0.0799054i | ||||
\(241\) | 224.651 | + | 389.108i | 0.932164 | + | 1.61456i | 0.779615 | + | 0.626259i | \(0.215415\pi\) |
0.152549 | + | 0.988296i | \(0.451252\pi\) | |||||||
\(242\) | −9.20896 | − | 32.4799i | −0.0380535 | − | 0.134215i | ||||
\(243\) | 297.037 | − | 171.494i | 1.22237 | − | 0.705737i | ||||
\(244\) | −184.529 | − | 99.5291i | −0.756267 | − | 0.407906i | ||||
\(245\) | 0.475337 | − | 0.823308i | 0.00194015 | − | 0.00336044i | ||||
\(246\) | −496.814 | − | 482.633i | −2.01957 | − | 1.96192i | ||||
\(247\) | −156.505 | − | 24.8295i | −0.633623 | − | 0.100524i | ||||
\(248\) | −142.376 | + | 155.314i | −0.574098 | + | 0.626266i | ||||
\(249\) | −243.299 | + | 421.405i | −0.977103 | + | 1.69239i | ||||
\(250\) | −7.28755 | − | 25.7031i | −0.0291502 | − | 0.102813i | ||||
\(251\) | −59.8145 | + | 34.5339i | −0.238305 | + | 0.137585i | −0.614397 | − | 0.788997i | \(-0.710601\pi\) |
0.376093 | + | 0.926582i | \(0.377267\pi\) | |||||||
\(252\) | −153.308 | + | 284.237i | −0.608365 | + | 1.12792i | ||||
\(253\) | −145.689 | − | 252.341i | −0.575847 | − | 0.997396i | ||||
\(254\) | 85.0813 | + | 82.6527i | 0.334966 | + | 0.325405i | ||||
\(255\) | − | 17.0936i | − | 0.0670336i | ||||||
\(256\) | −152.763 | − | 205.425i | −0.596730 | − | 0.802442i | ||||
\(257\) | 55.5635 | + | 96.2387i | 0.216200 | + | 0.374470i | 0.953643 | − | 0.300940i | \(-0.0973003\pi\) |
−0.737443 | + | 0.675409i | \(0.763967\pi\) | |||||||
\(258\) | −216.777 | + | 223.146i | −0.840220 | + | 0.864907i | ||||
\(259\) | 145.889i | 0.563277i | ||||||||
\(260\) | 7.59723 | − | 4.68464i | 0.0292201 | − | 0.0180179i | ||||
\(261\) | 287.237 | − | 497.509i | 1.10052 | − | 1.90616i | ||||
\(262\) | −14.3071 | + | 56.6637i | −0.0546072 | + | 0.216274i | ||||
\(263\) | −168.328 | − | 97.1841i | −0.640030 | − | 0.369521i | 0.144596 | − | 0.989491i | \(-0.453812\pi\) |
−0.784626 | + | 0.619969i | \(0.787145\pi\) | |||||||
\(264\) | −402.055 | + | 126.679i | −1.52294 | + | 0.479844i | ||||
\(265\) | 4.68705 | 0.0176870 | ||||||||
\(266\) | −108.457 | + | 253.227i | −0.407732 | + | 0.951983i | ||||
\(267\) | − | 235.453i | − | 0.881845i | ||||||
\(268\) | 26.0620 | − | 48.3194i | 0.0972461 | − | 0.180296i | ||||
\(269\) | −122.994 | + | 213.032i | −0.457226 | + | 0.791939i | −0.998813 | − | 0.0487054i | \(-0.984490\pi\) |
0.541587 | + | 0.840645i | \(0.317824\pi\) | |||||||
\(270\) | 1.25621 | − | 4.97526i | 0.00465263 | − | 0.0184269i | ||||
\(271\) | 361.577 | + | 208.757i | 1.33423 | + | 0.770320i | 0.985945 | − | 0.167068i | \(-0.0534300\pi\) |
0.348287 | + | 0.937388i | \(0.386763\pi\) | |||||||
\(272\) | 125.128 | + | 190.359i | 0.460030 | + | 0.699849i | ||||
\(273\) | 271.313 | 0.993819 | ||||||||
\(274\) | −7.90126 | + | 8.13342i | −0.0288367 | + | 0.0296840i | ||||
\(275\) | 253.499 | − | 146.358i | 0.921814 | − | 0.532210i | ||||
\(276\) | −379.131 | + | 233.781i | −1.37366 | + | 0.847034i | ||||
\(277\) | −408.968 | −1.47642 | −0.738209 | − | 0.674572i | \(-0.764328\pi\) | ||||
−0.738209 | + | 0.674572i | \(0.764328\pi\) | |||||||
\(278\) | 72.0602 | + | 70.0033i | 0.259209 | + | 0.251810i | ||||
\(279\) | 254.021 | − | 146.659i | 0.910469 | − | 0.525660i | ||||
\(280\) | −4.66287 | − | 14.7991i | −0.0166531 | − | 0.0528539i | ||||
\(281\) | 39.1063 | + | 67.7340i | 0.139168 | + | 0.241046i | 0.927182 | − | 0.374611i | \(-0.122224\pi\) |
−0.788014 | + | 0.615658i | \(0.788890\pi\) | |||||||
\(282\) | −90.4500 | − | 319.017i | −0.320745 | − | 1.13126i | ||||
\(283\) | −101.132 | − | 58.3887i | −0.357357 | − | 0.206320i | 0.310563 | − | 0.950553i | \(-0.399482\pi\) |
−0.667921 | + | 0.744232i | \(0.732816\pi\) | |||||||
\(284\) | 183.620 | − | 5.31824i | 0.646551 | − | 0.0187262i | ||||
\(285\) | 3.57430 | − | 22.5295i | 0.0125414 | − | 0.0790509i | ||||
\(286\) | 140.487 | + | 136.477i | 0.491213 | + | 0.477191i | ||||
\(287\) | 484.523 | + | 279.739i | 1.68823 | + | 0.974702i | ||||
\(288\) | 116.895 | + | 336.669i | 0.405885 | + | 1.16899i | ||||
\(289\) | 43.1454 | + | 74.7300i | 0.149292 | + | 0.258581i | ||||
\(290\) | 7.52895 | + | 26.5546i | 0.0259619 | + | 0.0915674i | ||||
\(291\) | 232.439 | − | 134.199i | 0.798761 | − | 0.461165i | ||||
\(292\) | 4.64694 | + | 160.443i | 0.0159142 | + | 0.549462i | ||||
\(293\) | 121.092 | 0.413284 | 0.206642 | − | 0.978417i | \(-0.433746\pi\) | ||||
0.206642 | + | 0.978417i | \(0.433746\pi\) | |||||||
\(294\) | 7.80705 | − | 30.9201i | 0.0265546 | − | 0.105170i | ||||
\(295\) | 22.1726 | − | 12.8014i | 0.0751614 | − | 0.0433945i | ||||
\(296\) | 118.676 | + | 108.790i | 0.400932 | + | 0.367534i | ||||
\(297\) | 112.605 | 0.379142 | ||||||||
\(298\) | 314.160 | + | 79.3227i | 1.05423 | + | 0.266183i | ||||
\(299\) | 179.230 | + | 103.478i | 0.599430 | + | 0.346081i | ||||
\(300\) | −234.854 | − | 380.870i | −0.782847 | − | 1.26957i | ||||
\(301\) | 125.646 | − | 217.626i | 0.417429 | − | 0.723009i | ||||
\(302\) | −237.740 | + | 67.4060i | −0.787220 | + | 0.223199i | ||||
\(303\) | 262.669i | 0.866895i | ||||||||
\(304\) | 125.116 | + | 277.060i | 0.411565 | + | 0.911380i | ||||
\(305\) | −14.0234 | −0.0459783 | ||||||||
\(306\) | −86.5051 | − | 305.103i | −0.282696 | − | 0.997068i | ||||
\(307\) | −459.430 | − | 265.252i | −1.49652 | − | 0.864013i | −0.496523 | − | 0.868023i | \(-0.665390\pi\) |
−0.999992 | + | 0.00401001i | \(0.998724\pi\) | |||||||
\(308\) | 289.825 | − | 178.713i | 0.940990 | − | 0.580238i | ||||
\(309\) | 230.363 | − | 399.000i | 0.745510 | − | 1.29126i | ||||
\(310\) | −3.45004 | + | 13.6640i | −0.0111291 | + | 0.0440774i | ||||
\(311\) | − | 54.0586i | − | 0.173822i | −0.996216 | − | 0.0869109i | \(-0.972300\pi\) | ||
0.996216 | − | 0.0869109i | \(-0.0276995\pi\) | |||||||
\(312\) | 202.320 | − | 220.704i | 0.648461 | − | 0.707386i | ||||
\(313\) | 157.796 | + | 273.310i | 0.504139 | + | 0.873195i | 0.999989 | + | 0.00478603i | \(0.00152345\pi\) |
−0.495849 | + | 0.868409i | \(0.665143\pi\) | |||||||
\(314\) | −449.826 | − | 113.577i | −1.43257 | − | 0.361711i | ||||
\(315\) | 21.6007i | 0.0685736i | ||||||||
\(316\) | −489.633 | + | 14.1814i | −1.54947 | + | 0.0448777i | ||||
\(317\) | −140.142 | − | 242.732i | −0.442087 | − | 0.765717i | 0.555757 | − | 0.831345i | \(-0.312428\pi\) |
−0.997844 | + | 0.0656277i | \(0.979095\pi\) | |||||||
\(318\) | 151.265 | − | 42.8879i | 0.475677 | − | 0.134868i | ||||
\(319\) | −524.544 | + | 302.846i | −1.64434 | + | 0.949360i | ||||
\(320\) | −15.5157 | − | 7.24269i | −0.0484867 | − | 0.0226334i | ||||
\(321\) | 40.0508 | − | 69.3701i | 0.124769 | − | 0.216106i | ||||
\(322\) | 250.693 | − | 258.059i | 0.778550 | − | 0.801425i | ||||
\(323\) | −96.8783 | − | 252.572i | −0.299933 | − | 0.781957i | ||||
\(324\) | 6.62399 | + | 228.704i | 0.0204444 | + | 0.705875i | ||||
\(325\) | −103.953 | + | 180.052i | −0.319855 | + | 0.554006i | ||||
\(326\) | −139.008 | + | 39.4125i | −0.426404 | + | 0.120897i | ||||
\(327\) | −749.253 | + | 432.581i | −2.29129 | + | 1.32288i | ||||
\(328\) | 588.872 | − | 185.541i | 1.79534 | − | 0.565673i | ||||
\(329\) | 133.920 | + | 231.956i | 0.407052 | + | 0.705034i | ||||
\(330\) | −19.6464 | + | 20.2236i | −0.0595344 | + | 0.0612837i | ||||
\(331\) | − | 443.490i | − | 1.33985i | −0.742429 | − | 0.669924i | \(-0.766327\pi\) | ||
0.742429 | − | 0.669924i | \(-0.233673\pi\) | |||||||
\(332\) | −227.655 | − | 369.196i | −0.685708 | − | 1.11204i | ||||
\(333\) | −112.063 | − | 194.098i | −0.336524 | − | 0.582877i | ||||
\(334\) | −167.343 | − | 162.566i | −0.501027 | − | 0.486725i | ||||
\(335\) | − | 3.67206i | − | 0.0109614i | ||||||
\(336\) | −285.901 | − | 434.945i | −0.850896 | − | 1.29448i | ||||
\(337\) | 94.1888 | − | 163.140i | 0.279492 | − | 0.484094i | −0.691767 | − | 0.722121i | \(-0.743167\pi\) |
0.971259 | + | 0.238027i | \(0.0765007\pi\) | |||||||
\(338\) | 192.833 | + | 48.6886i | 0.570512 | + | 0.144049i | ||||
\(339\) | 744.400 | + | 429.779i | 2.19587 | + | 1.26779i | ||||
\(340\) | 13.4105 | + | 7.23320i | 0.0394427 | + | 0.0212741i | ||||
\(341\) | −309.258 | −0.906914 | ||||||||
\(342\) | −50.2170 | − | 420.217i | −0.146833 | − | 1.22871i | ||||
\(343\) | − | 329.460i | − | 0.960524i | ||||||
\(344\) | −83.3364 | − | 264.494i | −0.242257 | − | 0.768879i | ||||
\(345\) | −14.8961 | + | 25.8008i | −0.0431771 | + | 0.0747849i | ||||
\(346\) | 257.925 | + | 65.1237i | 0.745447 | + | 0.188219i | ||||
\(347\) | −468.604 | − | 270.549i | −1.35044 | − | 0.779679i | −0.362132 | − | 0.932127i | \(-0.617951\pi\) |
−0.988312 | + | 0.152447i | \(0.951285\pi\) | |||||||
\(348\) | 485.964 | + | 788.104i | 1.39645 | + | 2.26467i | ||||
\(349\) | 39.0675 | 0.111941 | 0.0559706 | − | 0.998432i | \(-0.482175\pi\) | ||||
0.0559706 | + | 0.998432i | \(0.482175\pi\) | |||||||
\(350\) | 259.243 | + | 251.843i | 0.740694 | + | 0.719552i | ||||
\(351\) | −69.2645 | + | 39.9899i | −0.197335 | + | 0.113931i | ||||
\(352\) | 70.7469 | − | 369.031i | 0.200985 | − | 1.04838i | ||||
\(353\) | −389.987 | −1.10478 | −0.552389 | − | 0.833586i | \(-0.686284\pi\) | ||||
−0.552389 | + | 0.833586i | \(0.686284\pi\) | |||||||
\(354\) | 598.441 | − | 616.025i | 1.69051 | − | 1.74018i | ||||
\(355\) | 10.6407 | − | 6.14344i | 0.0299739 | − | 0.0173055i | ||||
\(356\) | 184.721 | + | 99.6326i | 0.518879 | + | 0.279867i | ||||
\(357\) | 231.582 | + | 401.112i | 0.648689 | + | 1.12356i | ||||
\(358\) | 191.189 | − | 54.2074i | 0.534047 | − | 0.151417i | ||||
\(359\) | 475.099 | + | 274.299i | 1.32340 | + | 0.764063i | 0.984269 | − | 0.176677i | \(-0.0565349\pi\) |
0.339127 | + | 0.940740i | \(0.389868\pi\) | |||||||
\(360\) | 17.5715 | + | 16.1078i | 0.0488097 | + | 0.0447439i | ||||
\(361\) | −74.8733 | − | 353.150i | −0.207405 | − | 0.978255i | ||||
\(362\) | 61.1600 | − | 62.9570i | 0.168950 | − | 0.173914i | ||||
\(363\) | −65.5999 | − | 37.8741i | −0.180716 | − | 0.104336i | ||||
\(364\) | −114.807 | + | 212.855i | −0.315404 | + | 0.584766i | ||||
\(365\) | 5.36798 | + | 9.29762i | 0.0147068 | + | 0.0254729i | ||||
\(366\) | −452.577 | + | 128.318i | −1.23655 | + | 0.350596i | ||||
\(367\) | −193.800 | + | 111.891i | −0.528066 | + | 0.304879i | −0.740228 | − | 0.672355i | \(-0.765283\pi\) |
0.212163 | + | 0.977234i | \(0.431949\pi\) | |||||||
\(368\) | −22.9794 | − | 396.367i | −0.0624441 | − | 1.07709i | ||||
\(369\) | −859.514 | −2.32931 | ||||||||
\(370\) | 10.4407 | + | 2.63618i | 0.0282181 | + | 0.00712482i | ||||
\(371\) | −109.985 | + | 63.4996i | −0.296454 | + | 0.171158i | ||||
\(372\) | 13.6865 | + | 472.547i | 0.0367916 | + | 1.27029i | ||||
\(373\) | −655.054 | −1.75618 | −0.878089 | − | 0.478498i | \(-0.841182\pi\) | ||||
−0.878089 | + | 0.478498i | \(0.841182\pi\) | |||||||
\(374\) | −81.8547 | + | 324.188i | −0.218863 | + | 0.866814i | ||||
\(375\) | −51.9128 | − | 29.9719i | −0.138434 | − | 0.0799250i | ||||
\(376\) | 288.554 | + | 64.0317i | 0.767432 | + | 0.170297i | ||||
\(377\) | 215.101 | − | 372.566i | 0.570561 | − | 0.988240i | ||||
\(378\) | 37.9266 | + | 133.767i | 0.100335 | + | 0.353880i | ||||
\(379\) | − | 205.788i | − | 0.542977i | −0.962442 | − | 0.271488i | \(-0.912484\pi\) | ||
0.962442 | − | 0.271488i | \(-0.0875159\pi\) | |||||||
\(380\) | 16.1627 | + | 12.3376i | 0.0425335 | + | 0.0324674i | ||||
\(381\) | 266.146 | 0.698545 | ||||||||
\(382\) | 121.676 | − | 34.4987i | 0.318525 | − | 0.0903106i | ||||
\(383\) | −107.827 | − | 62.2538i | −0.281532 | − | 0.162542i | 0.352585 | − | 0.935780i | \(-0.385303\pi\) |
−0.634117 | + | 0.773237i | \(0.718636\pi\) | |||||||
\(384\) | −567.013 | − | 91.7698i | −1.47660 | − | 0.238984i | ||||
\(385\) | 11.3873 | − | 19.7233i | 0.0295773 | − | 0.0512294i | ||||
\(386\) | 89.6510 | + | 22.6361i | 0.232256 | + | 0.0586427i | ||||
\(387\) | 386.054i | 0.997557i | ||||||||
\(388\) | 6.92637 | + | 239.144i | 0.0178515 | + | 0.616350i | ||||
\(389\) | 210.874 | + | 365.244i | 0.542092 | + | 0.938932i | 0.998784 | + | 0.0493064i | \(0.0157011\pi\) |
−0.456691 | + | 0.889625i | \(0.650966\pi\) | |||||||
\(390\) | 4.90257 | − | 19.4168i | 0.0125707 | − | 0.0497867i | ||||
\(391\) | 353.300i | 0.903580i | ||||||||
\(392\) | 20.9544 | + | 19.2089i | 0.0534550 | + | 0.0490022i | ||||
\(393\) | 65.5636 | + | 113.560i | 0.166829 | + | 0.288956i | ||||
\(394\) | 41.5772 | + | 146.642i | 0.105526 | + | 0.372189i | ||||
\(395\) | −28.3741 | + | 16.3818i | −0.0718331 | + | 0.0414729i | ||||
\(396\) | −248.322 | + | 460.395i | −0.627077 | + | 1.16261i | ||||
\(397\) | 312.624 | − | 541.481i | 0.787467 | − | 1.36393i | −0.140047 | − | 0.990145i | \(-0.544725\pi\) |
0.927514 | − | 0.373788i | \(-0.121941\pi\) | |||||||
\(398\) | −148.514 | − | 144.275i | −0.373151 | − | 0.362500i | ||||
\(399\) | 221.354 | + | 577.094i | 0.554772 | + | 1.44635i | ||||
\(400\) | 398.186 | − | 23.0849i | 0.995465 | − | 0.0577121i | ||||
\(401\) | 61.9807 | − | 107.354i | 0.154565 | − | 0.267715i | −0.778335 | − | 0.627849i | \(-0.783936\pi\) |
0.932901 | + | 0.360134i | \(0.117269\pi\) | |||||||
\(402\) | −33.6004 | − | 118.508i | −0.0835831 | − | 0.294797i | ||||
\(403\) | 190.227 | − | 109.828i | 0.472028 | − | 0.272525i | ||||
\(404\) | −206.073 | − | 111.149i | −0.510083 | − | 0.275122i | ||||
\(405\) | 7.65179 | + | 13.2533i | 0.0188933 | + | 0.0327242i | ||||
\(406\) | −536.430 | − | 521.118i | −1.32126 | − | 1.28354i | ||||
\(407\) | 236.305i | 0.580601i | ||||||||
\(408\) | 498.984 | + | 110.727i | 1.22300 | + | 0.271390i | ||||
\(409\) | −50.9014 | − | 88.1639i | −0.124453 | − | 0.215560i | 0.797066 | − | 0.603893i | \(-0.206384\pi\) |
−0.921519 | + | 0.388333i | \(0.873051\pi\) | |||||||
\(410\) | 28.7751 | − | 29.6206i | 0.0701833 | − | 0.0722454i | ||||
\(411\) | 25.4424i | 0.0619037i | ||||||||
\(412\) | 215.551 | + | 349.566i | 0.523182 | + | 0.848461i | ||||
\(413\) | −346.863 | + | 600.785i | −0.839863 | + | 1.45468i | ||||
\(414\) | −135.311 | + | 535.902i | −0.326837 | + | 1.29445i | ||||
\(415\) | −25.1247 | − | 14.5057i | −0.0605414 | − | 0.0349536i | ||||
\(416\) | 87.5383 | + | 252.119i | 0.210429 | + | 0.606056i | ||||
\(417\) | 225.414 | 0.540561 | ||||||||
\(418\) | −175.674 | + | 410.168i | −0.420272 | + | 0.981263i | ||||
\(419\) | − | 155.139i | − | 0.370261i | −0.982714 | − | 0.185130i | \(-0.940729\pi\) | ||
0.982714 | − | 0.185130i | \(-0.0592708\pi\) | |||||||
\(420\) | −30.6413 | − | 16.5269i | −0.0729554 | − | 0.0393498i | ||||
\(421\) | 114.921 | − | 199.049i | 0.272972 | − | 0.472802i | −0.696649 | − | 0.717412i | \(-0.745327\pi\) |
0.969621 | + | 0.244610i | \(0.0786600\pi\) | |||||||
\(422\) | −60.6426 | + | 240.177i | −0.143703 | + | 0.569140i | ||||
\(423\) | −356.349 | − | 205.738i | −0.842432 | − | 0.486379i | ||||
\(424\) | −30.3613 | + | 136.821i | −0.0716069 | + | 0.322692i | ||||
\(425\) | −354.921 | −0.835108 | ||||||||
\(426\) | 287.195 | − | 295.633i | 0.674166 | − | 0.693975i | ||||
\(427\) | 329.067 | − | 189.987i | 0.770650 | − | 0.444935i | ||||
\(428\) | 37.4757 | + | 60.7755i | 0.0875600 | + | 0.141999i | ||||
\(429\) | 439.461 | 1.02439 | ||||||||
\(430\) | −13.3042 | − | 12.9245i | −0.0309401 | − | 0.0300569i | ||||
\(431\) | −21.9723 | + | 12.6857i | −0.0509799 | + | 0.0294333i | −0.525273 | − | 0.850934i | \(-0.676037\pi\) |
0.474293 | + | 0.880367i | \(0.342704\pi\) | |||||||
\(432\) | 137.097 | + | 68.8987i | 0.317355 | + | 0.159488i | ||||
\(433\) | −325.392 | − | 563.595i | −0.751482 | − | 1.30160i | −0.947104 | − | 0.320926i | \(-0.896006\pi\) |
0.195623 | − | 0.980679i | \(-0.437327\pi\) | |||||||
\(434\) | −104.161 | − | 367.375i | −0.240002 | − | 0.846486i | ||||
\(435\) | 53.6324 | + | 30.9647i | 0.123293 | + | 0.0711832i | ||||
\(436\) | −22.3267 | − | 770.864i | −0.0512080 | − | 1.76804i | ||||
\(437\) | −73.8757 | + | 465.653i | −0.169052 | + | 1.06557i | ||||
\(438\) | 258.317 | + | 250.944i | 0.589765 | + | 0.572931i | ||||
\(439\) | −582.157 | − | 336.108i | −1.32610 | − | 0.765623i | −0.341404 | − | 0.939917i | \(-0.610902\pi\) |
−0.984694 | + | 0.174294i | \(0.944236\pi\) | |||||||
\(440\) | −7.55274 | − | 23.9710i | −0.0171653 | − | 0.0544795i | ||||
\(441\) | −19.7867 | − | 34.2715i | −0.0448677 | − | 0.0777132i | ||||
\(442\) | −64.7806 | − | 228.481i | −0.146562 | − | 0.516924i | ||||
\(443\) | 98.6335 | − | 56.9461i | 0.222649 | − | 0.128546i | −0.384527 | − | 0.923114i | \(-0.625636\pi\) |
0.607176 | + | 0.794567i | \(0.292302\pi\) | |||||||
\(444\) | 361.075 | − | 10.4579i | 0.813231 | − | 0.0235538i | ||||
\(445\) | 14.0380 | 0.0315460 | ||||||||
\(446\) | 107.185 | − | 424.510i | 0.240325 | − | 0.951817i | ||||
\(447\) | 629.607 | − | 363.504i | 1.40852 | − | 0.813208i | ||||
\(448\) | 462.210 | − | 40.2513i | 1.03172 | − | 0.0898467i | ||||
\(449\) | 96.0975 | 0.214026 | 0.107013 | − | 0.994258i | \(-0.465871\pi\) | ||||
0.107013 | + | 0.994258i | \(0.465871\pi\) | |||||||
\(450\) | −538.361 | − | 135.931i | −1.19636 | − | 0.302070i | ||||
\(451\) | 784.811 | + | 453.111i | 1.74016 | + | 1.00468i | ||||
\(452\) | −652.173 | + | 402.146i | −1.44286 | + | 0.889703i | ||||
\(453\) | −277.224 | + | 480.166i | −0.611973 | + | 1.05997i | ||||
\(454\) | −224.750 | + | 63.7230i | −0.495045 | + | 0.140359i | ||||
\(455\) | 16.1760i | 0.0355516i | ||||||||
\(456\) | 634.513 | + | 250.278i | 1.39148 | + | 0.548855i | ||||
\(457\) | 526.215 | 1.15146 | 0.575728 | − | 0.817641i | \(-0.304719\pi\) | ||||
0.575728 | + | 0.817641i | \(0.304719\pi\) | |||||||
\(458\) | 88.7375 | + | 312.977i | 0.193750 | + | 0.683355i | ||||
\(459\) | −118.243 | − | 68.2676i | −0.257610 | − | 0.148731i | ||||
\(460\) | −13.9383 | − | 22.6042i | −0.0303007 | − | 0.0491396i | ||||
\(461\) | −243.622 | + | 421.966i | −0.528464 | + | 0.915327i | 0.470985 | + | 0.882141i | \(0.343899\pi\) |
−0.999449 | + | 0.0331859i | \(0.989435\pi\) | |||||||
\(462\) | 187.027 | − | 740.727i | 0.404820 | − | 1.60331i | ||||
\(463\) | − | 151.027i | − | 0.326193i | −0.986610 | − | 0.163096i | \(-0.947852\pi\) | ||
0.986610 | − | 0.163096i | \(-0.0521481\pi\) | |||||||
\(464\) | −823.933 | + | 47.7676i | −1.77572 | + | 0.102947i | ||||
\(465\) | 15.8101 | + | 27.3839i | 0.0340003 | + | 0.0588902i | ||||
\(466\) | 560.543 | + | 141.532i | 1.20288 | + | 0.303717i | ||||
\(467\) | 211.728i | 0.453379i | 0.973967 | + | 0.226690i | \(0.0727903\pi\) | ||||
−0.973967 | + | 0.226690i | \(0.927210\pi\) | |||||||
\(468\) | −10.7564 | − | 371.381i | −0.0229837 | − | 0.793549i | ||||
\(469\) | 49.7486 | + | 86.1672i | 0.106074 | + | 0.183725i | ||||
\(470\) | 19.0201 | − | 5.39274i | 0.0404684 | − | 0.0114739i | ||||
\(471\) | −901.495 | + | 520.478i | −1.91400 | + | 1.10505i | ||||
\(472\) | 230.061 | + | 730.172i | 0.487418 | + | 1.54697i | ||||
\(473\) | 203.517 | − | 352.501i | 0.430268 | − | 0.745246i | ||||
\(474\) | −765.819 | + | 788.321i | −1.61565 | + | 1.66312i | ||||
\(475\) | −467.789 | − | 74.2147i | −0.984820 | − | 0.156241i | ||||
\(476\) | −412.681 | + | 11.9526i | −0.866977 | + | 0.0251104i | ||||
\(477\) | 97.5530 | − | 168.967i | 0.204514 | − | 0.354228i | ||||
\(478\) | 545.403 | − | 154.637i | 1.14101 | − | 0.323508i | ||||
\(479\) | 88.5573 | − | 51.1286i | 0.184879 | − | 0.106740i | −0.404704 | − | 0.914448i | \(-0.632625\pi\) |
0.589583 | + | 0.807708i | \(0.299292\pi\) | |||||||
\(480\) | −36.2935 | + | 12.6015i | −0.0756115 | + | 0.0262531i | ||||
\(481\) | −83.9197 | − | 145.353i | −0.174469 | − | 0.302190i | ||||
\(482\) | −626.145 | + | 644.543i | −1.29906 | + | 1.33723i | ||||
\(483\) | − | 807.243i | − | 1.67131i | ||||||
\(484\) | 57.4724 | − | 35.4389i | 0.118745 | − | 0.0732209i | ||||
\(485\) | 8.00110 | + | 13.8583i | 0.0164971 | + | 0.0285738i | ||||
\(486\) | 492.030 | + | 477.986i | 1.01241 | + | 0.983509i | ||||
\(487\) | − | 15.7559i | − | 0.0323530i | −0.999869 | − | 0.0161765i | \(-0.994851\pi\) | ||
0.999869 | − | 0.0161765i | \(-0.00514936\pi\) | |||||||
\(488\) | 90.8393 | − | 409.361i | 0.186146 | − | 0.838854i | ||||
\(489\) | −162.094 | + | 280.755i | −0.331480 | + | 0.574140i | ||||
\(490\) | 1.84349 | + | 0.465465i | 0.00376223 | + | 0.000949930i | ||||
\(491\) | −181.944 | − | 105.045i | −0.370558 | − | 0.213942i | 0.303144 | − | 0.952945i | \(-0.401964\pi\) |
−0.673702 | + | 0.739003i | \(0.735297\pi\) | |||||||
\(492\) | 657.623 | − | 1219.25i | 1.33663 | − | 2.47815i | ||||
\(493\) | 734.408 | 1.48967 | ||||||||
\(494\) | −37.6057 | − | 314.686i | −0.0761249 | − | 0.637015i | ||||
\(495\) | 34.9879i | 0.0706827i | ||||||||
\(496\) | −376.522 | − | 189.222i | −0.759117 | − | 0.381497i | ||||
\(497\) | −166.461 | + | 288.319i | −0.334932 | + | 0.580119i | ||||
\(498\) | −943.581 | − | 238.246i | −1.89474 | − | 0.478405i | ||||
\(499\) | 208.860 | + | 120.586i | 0.418558 | + | 0.241655i | 0.694460 | − | 0.719531i | \(-0.255643\pi\) |
−0.275902 | + | 0.961186i | \(0.588977\pi\) | |||||||
\(500\) | 45.4811 | − | 28.0448i | 0.0909622 | − | 0.0560895i | ||||
\(501\) | −523.471 | −1.04485 | ||||||||
\(502\) | −99.0805 | − | 96.2524i | −0.197372 | − | 0.191738i | ||||
\(503\) | −8.31936 | + | 4.80318i | −0.0165395 | + | 0.00954908i | −0.508247 | − | 0.861211i | \(-0.669706\pi\) |
0.491707 | + | 0.870760i | \(0.336373\pi\) | |||||||
\(504\) | −630.553 | − | 139.923i | −1.25110 | − | 0.277625i | ||||
\(505\) | −15.6606 | −0.0310112 | ||||||||
\(506\) | 406.063 | − | 417.994i | 0.802495 | − | 0.826074i | ||||
\(507\) | 386.456 | − | 223.120i | 0.762240 | − | 0.440080i | ||||
\(508\) | −112.621 | + | 208.801i | −0.221694 | + | 0.411025i | ||||
\(509\) | 66.9546 | + | 115.969i | 0.131541 | + | 0.227836i | 0.924271 | − | 0.381737i | \(-0.124674\pi\) |
−0.792730 | + | 0.609574i | \(0.791341\pi\) | |||||||
\(510\) | 32.8907 | − | 9.32542i | 0.0644915 | − | 0.0182851i | ||||
\(511\) | −251.926 | − | 145.450i | −0.493007 | − | 0.284637i | ||||
\(512\) | 311.930 | − | 406.009i | 0.609239 | − | 0.792987i | ||||
\(513\) | −141.571 | − | 114.702i | −0.275966 | − | 0.223591i | ||||
\(514\) | −154.866 | + | 159.416i | −0.301295 | + | 0.310148i | ||||
\(515\) | 23.7888 | + | 13.7345i | 0.0461919 | + | 0.0266689i | ||||
\(516\) | −547.631 | − | 295.374i | −1.06130 | − | 0.572431i | ||||
\(517\) | 216.918 | + | 375.714i | 0.419571 | + | 0.726719i | ||||
\(518\) | −280.712 | + | 79.5897i | −0.541916 | + | 0.153648i | ||||
\(519\) | 516.906 | − | 298.436i | 0.995964 | − | 0.575020i | ||||
\(520\) | 13.1587 | + | 12.0625i | 0.0253051 | + | 0.0231972i | ||||
\(521\) | 869.670 | 1.66923 | 0.834616 | − | 0.550832i | \(-0.185689\pi\) | ||||
0.834616 | + | 0.550832i | \(0.185689\pi\) | |||||||
\(522\) | 1113.99 | + | 281.272i | 2.13407 | + | 0.538834i | ||||
\(523\) | −775.040 | + | 447.469i | −1.48191 | + | 0.855582i | −0.999789 | − | 0.0205217i | \(-0.993467\pi\) |
−0.482122 | + | 0.876104i | \(0.660134\pi\) | |||||||
\(524\) | −116.835 | + | 3.38392i | −0.222968 | + | 0.00645786i | ||||
\(525\) | 810.947 | 1.54466 | ||||||||
\(526\) | 95.1659 | − | 376.908i | 0.180924 | − | 0.716555i | ||||
\(527\) | 324.741 | + | 187.489i | 0.616207 | + | 0.355767i | ||||
\(528\) | −463.091 | − | 704.506i | −0.877067 | − | 1.33429i | ||||
\(529\) | 43.3812 | − | 75.1384i | 0.0820060 | − | 0.142039i | ||||
\(530\) | 2.55703 | + | 9.01861i | 0.00482458 | + | 0.0170162i | ||||
\(531\) | − | 1065.76i | − | 2.00707i | ||||||
\(532\) | −546.418 | − | 70.5389i | −1.02710 | − | 0.132592i | ||||
\(533\) | −643.659 | −1.20762 | ||||||||
\(534\) | 453.047 | − | 128.451i | 0.848403 | − | 0.240546i | ||||
\(535\) | 4.13592 | + | 2.38788i | 0.00773070 | + | 0.00446332i | ||||
\(536\) | 107.192 | + | 23.7865i | 0.199986 | + | 0.0443778i | ||||
\(537\) | 222.941 | − | 386.146i | 0.415161 | − | 0.719079i | ||||
\(538\) | −477.006 | − | 120.440i | −0.886628 | − | 0.223866i | ||||
\(539\) | 41.7238i | 0.0774097i | ||||||||
\(540\) | 10.2585 | − | 0.297119i | 0.0189972 | − | 0.000550221i | ||||
\(541\) | −473.984 | − | 820.965i | −0.876127 | − | 1.51750i | −0.855558 | − | 0.517707i | \(-0.826786\pi\) |
−0.0205687 | − | 0.999788i | \(-0.506548\pi\) | |||||||
\(542\) | −204.421 | + | 809.618i | −0.377161 | + | 1.49376i | ||||
\(543\) | − | 196.938i | − | 0.362685i | ||||||
\(544\) | −298.016 | + | 344.617i | −0.547824 | + | 0.633486i | ||||
\(545\) | −25.7910 | − | 44.6713i | −0.0473229 | − | 0.0819657i | ||||
\(546\) | 148.015 | + | 522.048i | 0.271090 | + | 0.956131i | ||||
\(547\) | 476.141 | − | 274.900i | 0.870459 | − | 0.502560i | 0.00295823 | − | 0.999996i | \(-0.499058\pi\) |
0.867501 | + | 0.497436i | \(0.165725\pi\) | |||||||
\(548\) | −19.9605 | − | 10.7661i | −0.0364243 | − | 0.0196461i | ||||
\(549\) | −291.873 | + | 505.538i | −0.531644 | + | 0.920835i | ||||
\(550\) | 419.912 | + | 407.926i | 0.763476 | + | 0.741683i | ||||
\(551\) | 967.958 | + | 153.566i | 1.75673 | + | 0.278705i | ||||
\(552\) | −656.667 | − | 601.967i | −1.18961 | − | 1.09052i | ||||
\(553\) | 443.877 | − | 768.818i | 0.802672 | − | 1.39027i | ||||
\(554\) | −223.113 | − | 786.917i | −0.402731 | − | 1.42043i | ||||
\(555\) | 20.9242 | − | 12.0806i | 0.0377012 | − | 0.0217668i | ||||
\(556\) | −95.3847 | + | 176.845i | −0.171555 | + | 0.318067i | ||||
\(557\) | −293.392 | − | 508.170i | −0.526736 | − | 0.912334i | −0.999515 | − | 0.0311523i | \(-0.990082\pi\) |
0.472779 | − | 0.881181i | \(-0.343251\pi\) | |||||||
\(558\) | 420.776 | + | 408.766i | 0.754079 | + | 0.732555i | ||||
\(559\) | 289.102i | 0.517178i | ||||||||
\(560\) | 25.9319 | − | 17.0458i | 0.0463070 | − | 0.0304389i | ||||
\(561\) | 375.107 | + | 649.705i | 0.668640 | + | 1.15812i | ||||
\(562\) | −108.996 | + | 112.199i | −0.193944 | + | 0.199642i | ||||
\(563\) | − | 545.417i | − | 0.968770i | −0.874855 | − | 0.484385i | \(-0.839043\pi\) | ||
0.874855 | − | 0.484385i | \(-0.160957\pi\) | |||||||
\(564\) | 564.492 | − | 348.080i | 1.00087 | − | 0.617163i | ||||
\(565\) | −25.6240 | + | 44.3820i | −0.0453521 | + | 0.0785522i | ||||
\(566\) | 57.1761 | − | 226.448i | 0.101018 | − | 0.400085i | ||||
\(567\) | −359.109 | − | 207.331i | −0.633348 | − | 0.365664i | ||||
\(568\) | 110.407 | + | 350.413i | 0.194379 | + | 0.616924i | ||||
\(569\) | −548.968 | −0.964795 | −0.482397 | − | 0.875953i | \(-0.660234\pi\) | ||||
−0.482397 | + | 0.875953i | \(0.660234\pi\) | |||||||
\(570\) | 45.3002 | − | 5.41349i | 0.0794741 | − | 0.00949735i | ||||
\(571\) | 1004.32i | 1.75888i | 0.476012 | + | 0.879439i | \(0.342082\pi\) | ||||
−0.476012 | + | 0.879439i | \(0.657918\pi\) | |||||||
\(572\) | −185.960 | + | 344.774i | −0.325104 | + | 0.602751i | ||||
\(573\) | 141.884 | − | 245.751i | 0.247617 | − | 0.428884i | ||||
\(574\) | −273.930 | + | 1084.91i | −0.477230 | + | 1.89009i | ||||
\(575\) | 535.713 | + | 309.294i | 0.931674 | + | 0.537902i | ||||
\(576\) | −584.031 | + | 408.594i | −1.01394 | + | 0.709364i | ||||
\(577\) | 377.294 | 0.653890 | 0.326945 | − | 0.945043i | \(-0.393981\pi\) | ||||
0.326945 | + | 0.945043i | \(0.393981\pi\) | |||||||
\(578\) | −120.254 | + | 123.787i | −0.208052 | + | 0.214165i | ||||
\(579\) | 179.669 | − | 103.732i | 0.310309 | − | 0.179157i | ||||
\(580\) | −46.9877 | + | 28.9737i | −0.0810132 | + | 0.0499547i | ||||
\(581\) | 786.089 | 1.35299 | ||||||||
\(582\) | 385.027 | + | 374.037i | 0.661559 | + | 0.642675i | ||||
\(583\) | −178.149 | + | 102.854i | −0.305572 | + | 0.176422i | ||||
\(584\) | −306.182 | + | 96.4713i | −0.524284 | + | 0.165191i | ||||
\(585\) | −12.4254 | − | 21.5214i | −0.0212400 | − | 0.0367887i | ||||
\(586\) | 66.0621 | + | 233.000i | 0.112734 | + | 0.397612i | ||||
\(587\) | 262.988 | + | 151.836i | 0.448020 | + | 0.258665i | 0.706994 | − | 0.707220i | \(-0.250051\pi\) |
−0.258973 | + | 0.965884i | \(0.583384\pi\) | |||||||
\(588\) | 63.7542 | − | 1.84653i | 0.108426 | − | 0.00314035i | ||||
\(589\) | 388.808 | + | 315.017i | 0.660115 | + | 0.534833i | ||||
\(590\) | 36.7281 | + | 35.6798i | 0.0622511 | + | 0.0604742i | ||||
\(591\) | 296.174 | + | 170.996i | 0.501141 | + | 0.289334i | ||||
\(592\) | −144.585 | + | 287.701i | −0.244232 | + | 0.485982i | ||||
\(593\) | 51.2041 | + | 88.6881i | 0.0863475 | + | 0.149558i | 0.905965 | − | 0.423353i | \(-0.139147\pi\) |
−0.819617 | + | 0.572912i | \(0.805814\pi\) | |||||||
\(594\) | 61.4319 | + | 216.670i | 0.103421 | + | 0.364764i | ||||
\(595\) | −23.9147 | + | 13.8072i | −0.0401928 | + | 0.0232053i | ||||
\(596\) | 18.7614 | + | 647.768i | 0.0314789 | + | 1.08686i | ||||
\(597\) | −464.572 | −0.778177 | ||||||||
\(598\) | −101.329 | + | 401.318i | −0.169447 | + | 0.671101i | ||||
\(599\) | −669.678 | + | 386.639i | −1.11799 | + | 0.645474i | −0.940888 | − | 0.338718i | \(-0.890007\pi\) |
−0.177105 | + | 0.984192i | \(0.556673\pi\) | |||||||
\(600\) | 604.729 | − | 659.680i | 1.00788 | − | 1.09947i | ||||
\(601\) | 399.651 | 0.664977 | 0.332489 | − | 0.943107i | \(-0.392112\pi\) | ||||
0.332489 | + | 0.943107i | \(0.392112\pi\) | |||||||
\(602\) | 487.292 | + | 123.037i | 0.809455 | + | 0.204380i | ||||
\(603\) | −132.377 | − | 76.4277i | −0.219530 | − | 0.126746i | ||||
\(604\) | −259.399 | − | 420.676i | −0.429469 | − | 0.696484i | ||||
\(605\) | 2.25810 | − | 3.91114i | 0.00373239 | − | 0.00646470i | ||||
\(606\) | −505.416 | + | 143.299i | −0.834020 | + | 0.236468i | ||||
\(607\) | − | 244.707i | − | 0.403142i | −0.979474 | − | 0.201571i | \(-0.935395\pi\) | ||
0.979474 | − | 0.201571i | \(-0.0646046\pi\) | |||||||
\(608\) | −464.849 | + | 391.892i | −0.764554 | + | 0.644560i | ||||
\(609\) | −1678.02 | −2.75538 | ||||||||
\(610\) | −7.65047 | − | 26.9831i | −0.0125418 | − | 0.0442347i | ||||
\(611\) | −266.857 | − | 154.070i | −0.436754 | − | 0.252160i | ||||
\(612\) | 539.872 | − | 332.899i | 0.882144 | − | 0.543952i | ||||
\(613\) | −396.466 | + | 686.700i | −0.646764 | + | 1.12023i | 0.337127 | + | 0.941459i | \(0.390545\pi\) |
−0.983891 | + | 0.178769i | \(0.942789\pi\) | |||||||
\(614\) | 259.744 | − | 1028.72i | 0.423035 | − | 1.67545i | ||||
\(615\) | − | 92.6573i | − | 0.150662i | ||||||
\(616\) | 501.986 | + | 460.171i | 0.814913 | + | 0.747031i | ||||
\(617\) | −142.607 | − | 247.003i | −0.231130 | − | 0.400328i | 0.727011 | − | 0.686626i | \(-0.240909\pi\) |
−0.958141 | + | 0.286297i | \(0.907576\pi\) | |||||||
\(618\) | 893.412 | + | 225.579i | 1.44565 | + | 0.365014i | ||||
\(619\) | 249.474i | 0.403028i | 0.979486 | + | 0.201514i | \(0.0645861\pi\) | ||||
−0.979486 | + | 0.201514i | \(0.935414\pi\) | |||||||
\(620\) | −28.1738 | + | 0.816004i | −0.0454416 | + | 0.00131614i | ||||
\(621\) | 118.983 | + | 206.084i | 0.191599 | + | 0.331859i | ||||
\(622\) | 104.017 | − | 29.4917i | 0.167230 | − | 0.0474144i | ||||
\(623\) | −329.410 | + | 190.185i | −0.528747 | + | 0.305272i | ||||
\(624\) | 535.045 | + | 268.889i | 0.857445 | + | 0.430912i | ||||
\(625\) | −309.818 | + | 536.621i | −0.495709 | + | 0.858594i | ||||
\(626\) | −439.805 | + | 452.728i | −0.702564 | + | 0.723207i | ||||
\(627\) | 358.541 | + | 934.753i | 0.571835 | + | 1.49083i | ||||
\(628\) | −26.8633 | − | 927.498i | −0.0427760 | − | 1.47691i | ||||
\(629\) | 143.261 | − | 248.135i | 0.227760 | − | 0.394492i | ||||
\(630\) | −41.5631 | + | 11.7843i | −0.0659731 | + | 0.0187052i | ||||
\(631\) | −672.867 | + | 388.480i | −1.06635 | + | 0.615658i | −0.927182 | − | 0.374611i | \(-0.877776\pi\) |
−0.139169 | + | 0.990269i | \(0.544443\pi\) | |||||||
\(632\) | −294.407 | − | 934.394i | −0.465834 | − | 1.47847i | ||||
\(633\) | 277.901 | + | 481.338i | 0.439022 | + | 0.760408i | ||||
\(634\) | 390.600 | − | 402.077i | 0.616089 | − | 0.634191i | ||||
\(635\) | 15.8679i | 0.0249888i | ||||||||
\(636\) | 165.046 | + | 267.660i | 0.259506 | + | 0.420849i | ||||
\(637\) | −14.8175 | − | 25.6647i | −0.0232614 | − | 0.0402900i | ||||
\(638\) | −868.888 | − | 844.087i | −1.36189 | − | 1.32302i | ||||
\(639\) | − | 511.461i | − | 0.800408i | ||||||
\(640\) | 5.47142 | − | 33.8060i | 0.00854910 | − | 0.0528218i | ||||
\(641\) | −237.718 | + | 411.740i | −0.370855 | + | 0.642340i | −0.989697 | − | 0.143175i | \(-0.954269\pi\) |
0.618842 | + | 0.785515i | \(0.287602\pi\) | |||||||
\(642\) | 155.329 | + | 39.2191i | 0.241945 | + | 0.0610889i | ||||
\(643\) | 153.600 | + | 88.6809i | 0.238880 | + | 0.137917i | 0.614662 | − | 0.788791i | \(-0.289292\pi\) |
−0.375782 | + | 0.926708i | \(0.622626\pi\) | |||||||
\(644\) | 633.311 | + | 341.588i | 0.983403 | + | 0.530416i | ||||
\(645\) | −41.6174 | −0.0645231 | ||||||||
\(646\) | 433.136 | − | 324.200i | 0.670489 | − | 0.501858i | ||||
\(647\) | − | 779.535i | − | 1.20484i | −0.798177 | − | 0.602422i | \(-0.794202\pi\) | ||
0.798177 | − | 0.602422i | \(-0.205798\pi\) | |||||||
\(648\) | −436.447 | + | 137.515i | −0.673530 | + | 0.212215i | ||||
\(649\) | −561.835 | + | 973.127i | −0.865694 | + | 1.49943i | ||||
\(650\) | −403.160 | − | 101.794i | −0.620245 | − | 0.156606i | ||||
\(651\) | −741.990 | − | 428.388i | −1.13977 | − | 0.658046i | ||||
\(652\) | −151.672 | − | 245.971i | −0.232625 | − | 0.377256i | ||||
\(653\) | −235.113 | −0.360050 | −0.180025 | − | 0.983662i | \(-0.557618\pi\) | ||||
−0.180025 | + | 0.983662i | \(0.557618\pi\) | |||||||
\(654\) | −1241.11 | − | 1205.68i | −1.89772 | − | 1.84355i | ||||
\(655\) | −6.77055 | + | 3.90898i | −0.0103367 | + | 0.00596791i | ||||
\(656\) | 678.269 | + | 1031.86i | 1.03395 | + | 1.57295i | ||||
\(657\) | 446.902 | 0.680216 | ||||||||
\(658\) | −373.260 | + | 384.227i | −0.567264 | + | 0.583932i | ||||
\(659\) | −713.472 | + | 411.923i | −1.08266 | + | 0.625073i | −0.931612 | − | 0.363454i | \(-0.881597\pi\) |
−0.151046 | + | 0.988527i | \(0.548264\pi\) | |||||||
\(660\) | −49.6315 | − | 26.7696i | −0.0751992 | − | 0.0405600i | ||||
\(661\) | −448.256 | − | 776.402i | −0.678148 | − | 1.17459i | −0.975538 | − | 0.219830i | \(-0.929450\pi\) |
0.297390 | − | 0.954756i | \(-0.403884\pi\) | |||||||
\(662\) | 853.343 | − | 241.946i | 1.28904 | − | 0.365478i | ||||
\(663\) | −461.464 | − | 266.426i | −0.696024 | − | 0.401849i | ||||
\(664\) | 586.192 | − | 639.459i | 0.882820 | − | 0.963041i | ||||
\(665\) | −34.4070 | + | 13.1974i | −0.0517398 | + | 0.0198457i | ||||
\(666\) | 312.339 | − | 321.516i | 0.468978 | − | 0.482757i | ||||
\(667\) | −1108.51 | − | 639.996i | −1.66193 | − | 0.959514i | ||||
\(668\) | 221.509 | − | 410.682i | 0.331600 | − | 0.614793i | ||||
\(669\) | −491.186 | − | 850.759i | −0.734209 | − | 1.27169i | ||||
\(670\) | 7.06561 | − | 2.00330i | 0.0105457 | − | 0.00298999i | ||||
\(671\) | 533.010 | − | 307.734i | 0.794352 | − | 0.458619i | ||||
\(672\) | 680.928 | − | 787.403i | 1.01329 | − | 1.17173i | ||||
\(673\) | 769.535 | 1.14344 | 0.571720 | − | 0.820449i | \(-0.306276\pi\) | ||||
0.571720 | + | 0.820449i | \(0.306276\pi\) | |||||||
\(674\) | 365.291 | + | 92.2327i | 0.541975 | + | 0.136844i | ||||
\(675\) | −207.030 | + | 119.529i | −0.306711 | + | 0.177080i | ||||
\(676\) | 11.5159 | + | 397.603i | 0.0170353 | + | 0.588170i | ||||
\(677\) | 371.960 | 0.549424 | 0.274712 | − | 0.961527i | \(-0.411417\pi\) | ||||
0.274712 | + | 0.961527i | \(0.411417\pi\) | |||||||
\(678\) | −420.854 | + | 1666.81i | −0.620729 | + | 2.45842i | ||||
\(679\) | −375.502 | − | 216.796i | −0.553022 | − | 0.319287i | ||||
\(680\) | −6.60168 | + | 29.7500i | −0.00970835 | + | 0.0437500i | ||||
\(681\) | −262.076 | + | 453.930i | −0.384841 | + | 0.666564i | ||||
\(682\) | −168.716 | − | 595.060i | −0.247384 | − | 0.872521i | ||||
\(683\) | 1047.47i | 1.53363i | 0.641866 | + | 0.766817i | \(0.278160\pi\) | ||||
−0.641866 | + | 0.766817i | \(0.721840\pi\) | |||||||
\(684\) | 781.167 | − | 325.875i | 1.14206 | − | 0.476426i | ||||
\(685\) | −1.51691 | −0.00221446 | ||||||||
\(686\) | 633.932 | − | 179.737i | 0.924099 | − | 0.262008i | ||||
\(687\) | 632.121 | + | 364.955i | 0.920117 | + | 0.531230i | ||||
\(688\) | 463.464 | − | 304.647i | 0.673639 | − | 0.442801i | ||||
\(689\) | 73.0539 | − | 126.533i | 0.106029 | − | 0.183647i | ||||
\(690\) | −57.7713 | − | 14.5867i | −0.0837266 | − | 0.0211402i | ||||
\(691\) | 75.1204i | 0.108713i | 0.998522 | + | 0.0543563i | \(0.0173107\pi\) | ||||
−0.998522 | + | 0.0543563i | \(0.982689\pi\) | |||||||
\(692\) | 15.4031 | + | 531.815i | 0.0222588 | + | 0.768519i | ||||
\(693\) | −474.013 | − | 821.014i | −0.684001 | − | 1.18472i | ||||
\(694\) | 264.930 | − | 1049.27i | 0.381744 | − | 1.51191i | ||||
\(695\) | 13.4394i | 0.0193373i | ||||||||
\(696\) | −1251.32 | + | 1365.02i | −1.79787 | + | 1.96124i | ||||
\(697\) | −549.402 | − | 951.593i | −0.788239 | − | 1.36527i | ||||
\(698\) | 21.3133 | + | 75.1719i | 0.0305348 | + | 0.107696i | ||||
\(699\) | 1123.38 | − | 648.585i | 1.60713 | − | 0.927875i | ||||
\(700\) | −343.155 | + | 636.217i | −0.490222 | + | 0.908882i | ||||
\(701\) | −210.478 | + | 364.558i | −0.300253 | + | 0.520054i | −0.976193 | − | 0.216903i | \(-0.930405\pi\) |
0.675940 | + | 0.736957i | \(0.263738\pi\) | |||||||
\(702\) | −114.734 | − | 111.459i | −0.163439 | − | 0.158774i | ||||
\(703\) | 240.705 | − | 297.089i | 0.342397 | − | 0.422602i | ||||
\(704\) | 748.670 | − | 65.1975i | 1.06345 | − | 0.0926101i | ||||
\(705\) | 22.1790 | − | 38.4151i | 0.0314595 | − | 0.0544895i | ||||
\(706\) | −212.758 | − | 750.395i | −0.301357 | − | 1.06288i | ||||
\(707\) | 367.487 | − | 212.169i | 0.519784 | − | 0.300097i | ||||
\(708\) | 1511.81 | + | 815.421i | 2.13532 | + | 1.15172i | ||||
\(709\) | 562.723 | + | 974.665i | 0.793686 | + | 1.37470i | 0.923670 | + | 0.383188i | \(0.125174\pi\) |
−0.129984 | + | 0.991516i | \(0.541493\pi\) | |||||||
\(710\) | 17.6260 | + | 17.1229i | 0.0248253 | + | 0.0241167i | ||||
\(711\) | 1363.84i | 1.91819i | ||||||||
\(712\) | −90.9337 | + | 409.787i | −0.127716 | + | 0.575543i | ||||
\(713\) | −326.773 | − | 565.987i | −0.458307 | − | 0.793811i | ||||
\(714\) | −645.461 | + | 664.426i | −0.904007 | + | 0.930569i | ||||
\(715\) | 26.2012i | 0.0366450i | ||||||||
\(716\) | 208.607 | + | 338.304i | 0.291350 | + | 0.472492i | ||||
\(717\) | 635.983 | − | 1101.55i | 0.887005 | − | 1.53634i | ||||
\(718\) | −268.602 | + | 1063.81i | −0.374098 | + | 1.48163i | ||||
\(719\) | −185.767 | − | 107.253i | −0.258369 | − | 0.149169i | 0.365221 | − | 0.930921i | \(-0.380993\pi\) |
−0.623590 | + | 0.781751i | \(0.714327\pi\) | |||||||
\(720\) | −21.4077 | + | 42.5979i | −0.0297330 | + | 0.0591637i | ||||
\(721\) | −744.293 | −1.03231 | ||||||||
\(722\) | 638.668 | − | 336.729i | 0.884582 | − | 0.466384i | ||||
\(723\) | 2016.22i | 2.78868i | ||||||||
\(724\) | 154.505 | + | 83.3350i | 0.213405 | + | 0.115104i | ||||
\(725\) | 642.933 | − | 1113.59i | 0.886804 | − | 1.53599i | ||||
\(726\) | 37.0876 | − | 146.887i | 0.0510848 | − | 0.202323i | ||||
\(727\) | 611.381 | + | 352.981i | 0.840964 | + | 0.485531i | 0.857592 | − | 0.514331i | \(-0.171960\pi\) |
−0.0166275 | + | 0.999862i | \(0.505293\pi\) | |||||||
\(728\) | −472.198 | − | 104.783i | −0.648624 | − | 0.143933i | ||||
\(729\) | 1024.34 | 1.40513 | ||||||||
\(730\) | −14.9616 | + | 15.4012i | −0.0204953 | + | 0.0210975i | ||||
\(731\) | −427.412 | + | 246.766i | −0.584695 | + | 0.337574i | ||||
\(732\) | −493.807 | − | 800.823i | −0.674600 | − | 1.09402i | ||||
\(733\) | −333.184 | −0.454549 | −0.227274 | − | 0.973831i | \(-0.572981\pi\) | ||||
−0.227274 | + | 0.973831i | \(0.572981\pi\) | |||||||
\(734\) | −321.023 | − | 311.859i | −0.437361 | − | 0.424877i | ||||
\(735\) | 3.69454 | − | 2.13304i | 0.00502658 | − | 0.00290210i | ||||
\(736\) | 750.136 | − | 260.455i | 1.01921 | − | 0.353879i | ||||
\(737\) | 80.5809 | + | 139.570i | 0.109336 | + | 0.189376i | ||||
\(738\) | −468.909 | − | 1653.84i | −0.635378 | − | 2.24097i | ||||
\(739\) | 103.982 | + | 60.0342i | 0.140707 | + | 0.0812370i | 0.568701 | − | 0.822545i | \(-0.307446\pi\) |
−0.427994 | + | 0.903782i | \(0.640780\pi\) | |||||||
\(740\) | 0.623511 | + | 21.5277i | 0.000842583 | + | 0.0290915i | ||||
\(741\) | −552.504 | − | 447.646i | −0.745619 | − | 0.604110i | ||||
\(742\) | −182.185 | − | 176.985i | −0.245533 | − | 0.238524i | ||||
\(743\) | 207.224 | + | 119.641i | 0.278901 | + | 0.161024i | 0.632926 | − | 0.774212i | \(-0.281854\pi\) |
−0.354025 | + | 0.935236i | \(0.615187\pi\) | |||||||
\(744\) | −901.787 | + | 284.134i | −1.21208 | + | 0.381900i | ||||
\(745\) | 21.6725 | + | 37.5379i | 0.0290906 | + | 0.0503865i | ||||
\(746\) | −357.366 | − | 1260.43i | −0.479043 | − | 1.68958i | ||||
\(747\) | −1045.86 | + | 603.825i | −1.40007 | + | 0.808333i | ||||
\(748\) | −668.445 | + | 19.3603i | −0.893643 | + | 0.0258828i | ||||
\(749\) | −129.403 | −0.172767 | ||||||||
\(750\) | 29.3494 | − | 116.239i | 0.0391326 | − | 0.154986i | ||||
\(751\) | 788.836 | − | 455.435i | 1.05038 | − | 0.606438i | 0.127625 | − | 0.991822i | \(-0.459264\pi\) |
0.922756 | + | 0.385384i | \(0.125931\pi\) | |||||||
\(752\) | 34.2143 | + | 590.156i | 0.0454978 | + | 0.784782i | ||||
\(753\) | −309.937 | −0.411603 | ||||||||
\(754\) | 834.224 | + | 210.634i | 1.10640 | + | 0.279356i | ||||
\(755\) | −28.6280 | − | 16.5284i | −0.0379179 | − | 0.0218919i | ||||
\(756\) | −236.697 | + | 145.953i | −0.313091 | + | 0.193060i | ||||
\(757\) | 387.365 | − | 670.935i | 0.511710 | − | 0.886308i | −0.488198 | − | 0.872733i | \(-0.662345\pi\) |
0.999908 | − | 0.0135751i | \(-0.00432124\pi\) | |||||||
\(758\) | 395.969 | − | 112.268i | 0.522386 | − | 0.148111i | ||||
\(759\) | − | 1307.54i | − | 1.72271i | ||||||
\(760\) | −14.9219 | + | 37.8304i | −0.0196340 | + | 0.0497769i | ||||
\(761\) | 1111.15 | 1.46011 | 0.730057 | − | 0.683386i | \(-0.239494\pi\) | ||||
0.730057 | + | 0.683386i | \(0.239494\pi\) | |||||||
\(762\) | 145.196 | + | 512.106i | 0.190546 | + | 0.672055i | ||||
\(763\) | 1210.41 | + | 698.828i | 1.58638 | + | 0.915895i | ||||
\(764\) | 132.762 | + | 215.304i | 0.173772 | + | 0.281811i | ||||
\(765\) | 21.2116 | − | 36.7396i | 0.0277276 | − | 0.0480257i | ||||
\(766\) | 60.9609 | − | 241.438i | 0.0795835 | − | 0.315193i | ||||
\(767\) | − | 798.106i | − | 1.04056i | ||||||
\(768\) | −132.755 | − | 1141.09i | −0.172858 | − | 1.48579i | ||||
\(769\) | 299.646 | + | 519.002i | 0.389657 | + | 0.674905i | 0.992403 | − | 0.123028i | \(-0.0392603\pi\) |
−0.602747 | + | 0.797933i | \(0.705927\pi\) | |||||||
\(770\) | 44.1630 | + | 11.1508i | 0.0573546 | + | 0.0144815i | ||||
\(771\) | 498.674i | 0.646789i | ||||||||
\(772\) | 5.35389 | + | 184.852i | 0.00693510 | + | 0.239445i | ||||
\(773\) | 104.830 | + | 181.572i | 0.135615 | + | 0.234892i | 0.925832 | − | 0.377935i | \(-0.123366\pi\) |
−0.790217 | + | 0.612827i | \(0.790032\pi\) | |||||||
\(774\) | −742.829 | + | 210.613i | −0.959727 | + | 0.272109i | ||||
\(775\) | 568.584 | − | 328.272i | 0.733657 | − | 0.423577i | ||||
\(776\) | −456.371 | + | 143.793i | −0.588107 | + | 0.185300i | ||||
\(777\) | −327.333 | + | 566.957i | −0.421277 | + | 0.729674i | ||||
\(778\) | −587.744 | + | 605.014i | −0.755456 | + | 0.777653i | ||||
\(779\) | −525.138 | − | 1369.09i | −0.674118 | − | 1.75750i | ||||
\(780\) | 40.0356 | − | 1.15956i | 0.0513277 | − | 0.00148661i | ||||
\(781\) | −269.627 | + | 467.008i | −0.345233 | + | 0.597962i | ||||
\(782\) | −679.804 | + | 192.743i | −0.869314 | + | 0.246475i | ||||
\(783\) | 428.390 | − | 247.331i | 0.547113 | − | 0.315876i | ||||
\(784\) | −25.5292 | + | 50.7989i | −0.0325627 | + | 0.0647945i | ||||
\(785\) | −31.0315 | − | 53.7482i | −0.0395306 | − | 0.0684690i | ||||
\(786\) | −182.738 | + | 188.107i | −0.232491 | + | 0.239322i | ||||
\(787\) | − | 1080.87i | − | 1.37340i | −0.726940 | − | 0.686701i | \(-0.759058\pi\) | ||
0.726940 | − | 0.686701i | \(-0.240942\pi\) | |||||||
\(788\) | −259.480 | + | 160.002i | −0.329289 | + | 0.203048i | ||||
\(789\) | −436.107 | − | 755.359i | −0.552734 | − | 0.957363i | ||||
\(790\) | −47.0006 | − | 45.6590i | −0.0594945 | − | 0.0577963i | ||||
\(791\) | − | 1388.60i | − | 1.75550i | ||||||
\(792\) | −1021.34 | − | 226.642i | −1.28958 | − | 0.286164i | ||||
\(793\) | −218.573 | + | 378.580i | −0.275628 | + | 0.477402i | ||||
\(794\) | 1212.45 | + | 306.132i | 1.52701 | + | 0.385557i | ||||
\(795\) | 18.2149 | + | 10.5164i | 0.0229119 | + | 0.0132282i | ||||
\(796\) | 196.585 | − | 364.473i | 0.246966 | − | 0.457881i | ||||
\(797\) | 180.403 | 0.226353 | 0.113176 | − | 0.993575i | \(-0.463897\pi\) | ||||
0.113176 | + | 0.993575i | \(0.463897\pi\) | |||||||
\(798\) | −989.658 | + | 740.754i | −1.24017 | + | 0.928263i | ||||
\(799\) | − | 526.032i | − | 0.658363i | ||||||
\(800\) | 261.650 | + | 753.578i | 0.327062 | + | 0.941972i | ||||
\(801\) | 292.176 | − | 506.064i | 0.364764 | − | 0.631790i | ||||
\(802\) | 240.379 | + | 60.6935i | 0.299724 | + | 0.0756777i | ||||
\(803\) | −408.060 | − | 235.594i | −0.508170 | − | 0.293392i | ||||
\(804\) | 209.698 | − | 129.305i | 0.260818 | − | 0.160827i | ||||
\(805\) | 48.1288 | 0.0597873 | ||||||||
\(806\) | 315.104 | + | 306.110i | 0.390948 | + | 0.379789i | ||||
\(807\) | −955.965 | + | 551.927i | −1.18459 | + | 0.683924i | ||||
\(808\) | 101.445 | − | 457.155i | 0.125551 | − | 0.565786i | ||||
\(809\) | −514.263 | −0.635677 | −0.317838 | − | 0.948145i | \(-0.602957\pi\) | ||||
−0.317838 | + | 0.948145i | \(0.602957\pi\) | |||||||
\(810\) | −21.3270 | + | 21.9536i | −0.0263296 | + | 0.0271032i | ||||
\(811\) | 666.715 | − | 384.928i | 0.822091 | − | 0.474634i | −0.0290463 | − | 0.999578i | \(-0.509247\pi\) |
0.851137 | + | 0.524944i | \(0.175914\pi\) | |||||||
\(812\) | 710.062 | − | 1316.47i | 0.874461 | − | 1.62127i | ||||
\(813\) | 936.781 | + | 1622.55i | 1.15225 | + | 1.99576i | ||||
\(814\) | −454.687 | + | 128.916i | −0.558583 | + | 0.158374i | ||||
\(815\) | −16.7389 | − | 9.66422i | −0.0205385 | − | 0.0118579i | ||||
\(816\) | 59.1653 | + | 1020.53i | 0.0725065 | + | 1.25065i | ||||
\(817\) | −614.933 | + | 235.868i | −0.752672 | + | 0.288700i | ||||
\(818\) | 141.872 | − | 146.040i | 0.173437 | − | 0.178533i | ||||
\(819\) | 583.139 | + | 336.676i | 0.712014 | + | 0.411081i | ||||
\(820\) | 72.6930 | + | 39.2083i | 0.0886500 | + | 0.0478150i | ||||
\(821\) | 319.298 | + | 553.041i | 0.388914 | + | 0.673619i | 0.992304 | − | 0.123828i | \(-0.0395170\pi\) |
−0.603390 | + | 0.797446i | \(0.706184\pi\) | |||||||
\(822\) | −48.9552 | + | 13.8801i | −0.0595562 | + | 0.0168858i | ||||
\(823\) | −231.049 | + | 133.396i | −0.280740 | + | 0.162085i | −0.633758 | − | 0.773531i | \(-0.718489\pi\) |
0.353019 | + | 0.935616i | \(0.385155\pi\) | |||||||
\(824\) | −555.025 | + | 605.460i | −0.673574 | + | 0.734781i | ||||
\(825\) | 1313.54 | 1.59217 | ||||||||
\(826\) | −1345.24 | − | 339.660i | −1.62861 | − | 0.411211i | ||||
\(827\) | −977.455 | + | 564.334i | −1.18193 | + | 0.682387i | −0.956460 | − | 0.291864i | \(-0.905725\pi\) |
−0.225469 | + | 0.974250i | \(0.572391\pi\) | |||||||
\(828\) | −1104.98 | + | 32.0037i | −1.33451 | + | 0.0386518i | ||||
\(829\) | −554.040 | −0.668323 | −0.334161 | − | 0.942516i | \(-0.608453\pi\) | ||||
−0.334161 | + | 0.942516i | \(0.608453\pi\) | |||||||
\(830\) | 14.2045 | − | 56.2574i | 0.0171139 | − | 0.0677800i | ||||
\(831\) | −1589.34 | − | 917.607i | −1.91257 | − | 1.10422i | ||||
\(832\) | −437.360 | + | 305.981i | −0.525673 | + | 0.367766i | ||||
\(833\) | 25.2953 | − | 43.8128i | 0.0303665 | − | 0.0525964i | ||||
\(834\) | 122.975 | + | 433.731i | 0.147452 | + | 0.520061i | ||||
\(835\) | − | 31.2100i | − | 0.0373772i | ||||||
\(836\) | −885.066 | − | 114.256i | −1.05869 | − | 0.136670i | ||||
\(837\) | 252.567 | 0.301753 | ||||||||
\(838\) | 298.512 | − | 84.6364i | 0.356220 | − | 0.100998i | ||||
\(839\) | 1358.10 | + | 784.099i | 1.61871 | + | 0.934564i | 0.987254 | + | 0.159154i | \(0.0508768\pi\) |
0.631459 | + | 0.775410i | \(0.282457\pi\) | |||||||
\(840\) | 15.0840 | − | 67.9748i | 0.0179571 | − | 0.0809224i | ||||
\(841\) | −909.867 | + | 1575.94i | −1.08189 | + | 1.87388i | ||||
\(842\) | 445.698 | + | 112.535i | 0.529332 | + | 0.133652i | ||||
\(843\) | 350.973i | 0.416338i | ||||||||
\(844\) | −495.222 | + | 14.3432i | −0.586756 | + | 0.0169943i | ||||
\(845\) | 13.3027 | + | 23.0409i | 0.0157428 | + | 0.0272674i | ||||
\(846\) | 201.465 | − | 797.911i | 0.238139 | − | 0.943158i | ||||
\(847\) | 122.370i | 0.144475i | ||||||||
\(848\) | −279.829 | + | 16.2231i | −0.329987 | + | 0.0191310i | ||||
\(849\) | −262.015 | − | 453.824i | −0.308616 | − | 0.534539i | ||||
\(850\) | −193.628 | − | 682.923i | −0.227797 | − | 0.803439i | ||||
\(851\) | −432.473 | + | 249.688i | −0.508193 | + | 0.293406i | ||||
\(852\) | 725.524 | + | 391.324i | 0.851553 | + | 0.459301i | ||||
\(853\) | −377.177 | + | 653.290i | −0.442177 | + | 0.765873i | −0.997851 | − | 0.0655272i | \(-0.979127\pi\) |
0.555674 | + | 0.831401i | \(0.312460\pi\) | |||||||
\(854\) | 545.088 | + | 529.529i | 0.638276 | + | 0.620057i | ||||
\(855\) | 35.6395 | − | 43.9878i | 0.0416836 | − | 0.0514478i | ||||
\(856\) | −96.4966 | + | 105.265i | −0.112730 | + | 0.122973i | ||||
\(857\) | −606.638 | + | 1050.73i | −0.707862 | + | 1.22605i | 0.257786 | + | 0.966202i | \(0.417007\pi\) |
−0.965649 | + | 0.259852i | \(0.916326\pi\) | |||||||
\(858\) | 239.749 | + | 845.592i | 0.279428 | + | 0.985539i | ||||
\(859\) | 85.8983 | − | 49.5934i | 0.0999980 | − | 0.0577339i | −0.449167 | − | 0.893448i | \(-0.648279\pi\) |
0.549165 | + | 0.835714i | \(0.314946\pi\) | |||||||
\(860\) | 17.6106 | − | 32.6504i | 0.0204774 | − | 0.0379656i | ||||
\(861\) | 1255.31 | + | 2174.26i | 1.45797 | + | 2.52528i | ||||
\(862\) | −36.3964 | − | 35.3575i | −0.0422232 | − | 0.0410180i | ||||
\(863\) | 923.487i | 1.07009i | 0.844824 | + | 0.535045i | \(0.179705\pi\) | ||||
−0.844824 | + | 0.535045i | \(0.820295\pi\) | |||||||
\(864\) | −57.7783 | + | 301.384i | −0.0668730 | + | 0.348824i | ||||
\(865\) | 17.7931 | + | 30.8185i | 0.0205700 | + | 0.0356283i | ||||
\(866\) | 906.926 | − | 933.574i | 1.04726 | − | 1.07803i | ||||
\(867\) | 387.224i | 0.446625i | ||||||||
\(868\) | 650.061 | − | 400.844i | 0.748919 | − | 0.461802i | ||||
\(869\) | 718.975 | − | 1245.30i | 0.827359 | − | 1.43303i | ||||
\(870\) | −30.3216 | + | 120.090i | −0.0348524 | + | 0.138034i | ||||
\(871\) | −99.1321 | − | 57.2339i | −0.113814 | − | 0.0657106i | ||||
\(872\) | 1471.08 | − | 463.506i | 1.68702 | − | 0.531544i | ||||
\(873\) | 666.117 | 0.763021 | ||||||||
\(874\) | −936.291 | + | 111.889i | −1.07127 | + | 0.128020i | ||||
\(875\) | 96.8381i | 0.110672i | ||||||||
\(876\) | −341.929 | + | 633.945i | −0.390330 | + | 0.723681i | ||||
\(877\) | −164.229 | + | 284.452i | −0.187262 | + | 0.324347i | −0.944336 | − | 0.328981i | \(-0.893295\pi\) |
0.757074 | + | 0.653329i | \(0.226628\pi\) | |||||||
\(878\) | 329.128 | − | 1303.52i | 0.374861 | − | 1.48465i | ||||
\(879\) | 470.592 | + | 271.697i | 0.535372 | + | 0.309097i | ||||
\(880\) | 42.0035 | − | 27.6100i | 0.0477312 | − | 0.0313751i | ||||
\(881\) | 555.837 | 0.630916 | 0.315458 | − | 0.948940i | \(-0.397842\pi\) | ||||
0.315458 | + | 0.948940i | \(0.397842\pi\) | |||||||
\(882\) | 55.1491 | − | 56.7695i | 0.0625273 | − | 0.0643645i | ||||
\(883\) | 1129.71 | − | 652.239i | 1.27940 | − | 0.738662i | 0.302663 | − | 0.953098i | \(-0.402124\pi\) |
0.976738 | + | 0.214435i | \(0.0687911\pi\) | |||||||
\(884\) | 404.291 | − | 249.296i | 0.457343 | − | 0.282009i | ||||
\(885\) | 114.891 | 0.129820 | ||||||||
\(886\) | 163.383 | + | 158.719i | 0.184405 | + | 0.179141i | ||||
\(887\) | 655.637 | − | 378.532i | 0.739162 | − | 0.426756i | −0.0826023 | − | 0.996583i | \(-0.526323\pi\) |
0.821765 | + | 0.569827i | \(0.192990\pi\) | |||||||
\(888\) | 217.107 | + | 689.058i | 0.244490 | + | 0.775967i | ||||
\(889\) | −214.977 | − | 372.351i | −0.241819 | − | 0.418842i | ||||
\(890\) | 7.65843 | + | 27.0112i | 0.00860497 | + | 0.0303497i | ||||
\(891\) | −581.670 | − | 335.827i | −0.652828 | − | 0.376910i | ||||
\(892\) | 875.299 | − | 25.3515i | 0.981277 | − | 0.0284209i | ||||
\(893\) | 109.994 | − | 693.316i | 0.123174 | − | 0.776390i | ||||
\(894\) | 1042.92 | + | 1013.15i | 1.16658 | + | 1.13328i | ||||
\(895\) | 23.0224 | + | 13.2920i | 0.0257234 | + | 0.0148514i | ||||
\(896\) | 329.609 | + | 867.405i | 0.367867 | + | 0.968086i | ||||
\(897\) | 464.351 | + | 804.280i | 0.517671 | + | 0.896633i | ||||
\(898\) | 52.4261 | + | 184.907i | 0.0583810 | + | 0.205909i | ||||
\(899\) | −1176.52 | + | 679.266i | −1.30870 | + | 0.755580i | ||||
\(900\) | −32.1506 | − | 1110.05i | −0.0357228 | − | 1.23339i | ||||
\(901\) | 249.424 | 0.276830 | ||||||||
\(902\) | −443.701 | + | 1757.29i | −0.491908 | + | 1.94822i | ||||
\(903\) | 976.580 | − | 563.829i | 1.08148 | − | 0.624395i | ||||
\(904\) | −1129.59 | − | 1035.49i | −1.24954 | − | 1.14545i | ||||
\(905\) | 11.7417 | 0.0129742 | ||||||||
\(906\) | −1075.15 | − | 271.467i | −1.18670 | − | 0.299632i | ||||
\(907\) | −139.121 | − | 80.3215i | −0.153386 | − | 0.0885574i | 0.421343 | − | 0.906902i | \(-0.361559\pi\) |
−0.574728 | + | 0.818344i | \(0.694892\pi\) | |||||||
\(908\) | −245.226 | − | 397.691i | −0.270072 | − | 0.437985i | ||||
\(909\) | −325.950 | + | 564.561i | −0.358581 | + | 0.621080i | ||||
\(910\) | −31.1251 | + | 8.82483i | −0.0342034 | + | 0.00969761i | ||||
\(911\) | − | 172.554i | − | 0.189412i | −0.995505 | − | 0.0947060i | \(-0.969809\pi\) | ||
0.995505 | − | 0.0947060i | \(-0.0301911\pi\) | |||||||
\(912\) | −135.415 | + | 1357.44i | −0.148481 | + | 1.48842i | ||||
\(913\) | 1273.28 | 1.39461 | ||||||||
\(914\) | 287.078 | + | 1012.52i | 0.314089 | + | 1.10779i | ||||
\(915\) | −54.4980 | − | 31.4644i | −0.0595607 | − | 0.0343874i | ||||
\(916\) | −553.805 | + | 341.490i | −0.604590 | + | 0.372805i | ||||
\(917\) | 105.917 | − | 183.453i | 0.115504 | − | 0.200058i | ||||
\(918\) | 66.8499 | − | 264.761i | 0.0728212 | − | 0.288411i | ||||
\(919\) | − | 961.277i | − | 1.04600i | −0.852332 | − | 0.523002i | \(-0.824812\pi\) | ||
0.852332 | − | 0.523002i | \(-0.175188\pi\) | |||||||
\(920\) | 35.8900 | − | 39.1513i | 0.0390108 | − | 0.0425557i | ||||
\(921\) | −1190.30 | − | 2061.66i | −1.29240 | − | 2.23850i | ||||
\(922\) | −944.836 | − | 238.563i | −1.02477 | − | 0.258745i | ||||
\(923\) | − | 383.015i | − | 0.414967i | ||||||
\(924\) | 1527.31 | − | 44.2357i | 1.65293 | − | 0.0478742i | ||||
\(925\) | −250.834 | − | 434.457i | −0.271172 | − | 0.469683i | ||||
\(926\) | 290.600 | − | 82.3931i | 0.313823 | − | 0.0889774i | ||||
\(927\) | 990.248 | − | 571.720i | 1.06823 | − | 0.616742i | ||||
\(928\) | −541.410 | − | 1559.32i | −0.583416 | − | 1.68030i | ||||
\(929\) | 203.873 | − | 353.118i | 0.219454 | − | 0.380106i | −0.735187 | − | 0.677864i | \(-0.762906\pi\) |
0.954641 | + | 0.297759i | \(0.0962390\pi\) | |||||||
\(930\) | −44.0657 | + | 45.3605i | −0.0473825 | + | 0.0487747i | ||||
\(931\) | 42.5008 | − | 52.4564i | 0.0456507 | − | 0.0563442i | ||||
\(932\) | 33.4752 | + | 1155.78i | 0.0359176 | + | 1.24011i | ||||
\(933\) | 121.292 | − | 210.084i | 0.130002 | − | 0.225170i | ||||
\(934\) | −407.398 | + | 115.509i | −0.436186 | + | 0.123671i | ||||
\(935\) | −38.7361 | + | 22.3643i | −0.0414290 | + | 0.0239191i | ||||
\(936\) | 708.726 | − | 223.304i | 0.757186 | − | 0.238573i | ||||
\(937\) | −807.332 | − | 1398.34i | −0.861614 | − | 1.49236i | −0.870371 | − | 0.492397i | \(-0.836121\pi\) |
0.00875668 | − | 0.999962i | \(-0.497213\pi\) | |||||||
\(938\) | −138.659 | + | 142.733i | −0.147824 | + | 0.152167i | ||||
\(939\) | 1416.19i | 1.50819i | ||||||||
\(940\) | 20.7529 | + | 33.6557i | 0.0220776 | + | 0.0358039i | ||||
\(941\) | −163.709 | − | 283.552i | −0.173973 | − | 0.301331i | 0.765832 | − | 0.643041i | \(-0.222327\pi\) |
−0.939806 | + | 0.341710i | \(0.888994\pi\) | |||||||
\(942\) | −1493.29 | − | 1450.67i | −1.58524 | − | 1.53999i | ||||
\(943\) | 1915.09i | 2.03085i | ||||||||
\(944\) | −1279.45 | + | 841.020i | −1.35535 | + | 0.890911i | ||||
\(945\) | −9.29985 | + | 16.1078i | −0.00984111 | + | 0.0170453i | ||||
\(946\) | 789.296 | + | 199.290i | 0.834351 | + | 0.210666i | ||||
\(947\) | −1113.67 | − | 642.976i | −1.17599 | − | 0.678961i | −0.220910 | − | 0.975294i | \(-0.570903\pi\) |
−0.955084 | + | 0.296334i | \(0.904236\pi\) | |||||||
\(948\) | −1934.65 | − | 1043.49i | −2.04077 | − | 1.10072i | ||||
\(949\) | 334.669 | 0.352654 | ||||||||
\(950\) | −112.403 | − | 940.588i | −0.118319 | − | 0.990092i | ||||
\(951\) | − | 1257.75i | − | 1.32256i | ||||||
\(952\) | −248.137 | − | 787.542i | −0.260649 | − | 0.827250i | ||||
\(953\) | −95.5405 | + | 165.481i | −0.100252 | + | 0.173642i | −0.911789 | − | 0.410660i | \(-0.865298\pi\) |
0.811536 | + | 0.584302i | \(0.198632\pi\) | |||||||
\(954\) | 378.338 | + | 95.5271i | 0.396581 | + | 0.100133i | ||||
\(955\) | 14.6519 | + | 8.45931i | 0.0153424 | + | 0.00885791i | ||||
\(956\) | 595.091 | + | 965.078i | 0.622480 | + | 1.00950i | ||||
\(957\) | −2718.00 | −2.84012 | ||||||||
\(958\) | 146.692 | + | 142.505i | 0.153123 | + | 0.148752i | ||||
\(959\) | 35.5952 | − | 20.5509i | 0.0371170 | − | 0.0214295i | ||||
\(960\) | −44.0472 | − | 62.9596i | −0.0458825 | − | 0.0655830i | ||||
\(961\) | 267.352 | 0.278202 | ||||||||
\(962\) | 233.900 | − | 240.772i | 0.243139 | − | 0.250283i | ||||
\(963\) | 172.165 | − | 99.3992i | 0.178779 | − | 0.103218i | ||||
\(964\) | −1581.79 | − | 853.169i | −1.64087 | − | 0.885030i | ||||
\(965\) | 6.18463 | + | 10.7121i | 0.00640894 | + | 0.0111006i | ||||
\(966\) | 1553.26 | − | 440.393i | 1.60793 | − | 0.455893i | ||||
\(967\) | −546.396 | − | 315.462i | −0.565042 | − | 0.326227i | 0.190125 | − | 0.981760i | \(-0.439111\pi\) |
−0.755167 | + | 0.655533i | \(0.772444\pi\) | |||||||
\(968\) | 99.5442 | + | 91.2522i | 0.102835 | + | 0.0942688i | ||||
\(969\) | 190.208 | − | 1198.92i | 0.196293 | − | 1.23728i | ||||
\(970\) | −22.3005 | + | 22.9558i | −0.0229902 | + | 0.0236657i | ||||
\(971\) | 187.744 | + | 108.394i | 0.193352 | + | 0.111632i | 0.593551 | − | 0.804797i | \(-0.297726\pi\) |
−0.400199 | + | 0.916428i | \(0.631059\pi\) | |||||||
\(972\) | −651.291 | + | 1207.51i | −0.670052 | + | 1.24229i | ||||
\(973\) | −182.076 | − | 315.365i | −0.187129 | − | 0.324116i | ||||
\(974\) | 30.3168 | − | 8.59566i | 0.0311261 | − | 0.00882511i | ||||
\(975\) | −807.970 | + | 466.482i | −0.828688 | + | 0.478443i | ||||
\(976\) | 837.231 | − | 48.5385i | 0.857819 | − | 0.0497321i | ||||
\(977\) | 794.091 | 0.812785 | 0.406393 | − | 0.913699i | \(-0.366787\pi\) | ||||
0.406393 | + | 0.913699i | \(0.366787\pi\) | |||||||
\(978\) | −628.646 | − | 158.727i | −0.642787 | − | 0.162298i | ||||
\(979\) | −533.565 | + | 308.054i | −0.545010 | + | 0.314662i | ||||
\(980\) | 0.110092 | + | 3.80110i | 0.000112339 | + | 0.00387868i | ||||
\(981\) | −2147.18 | −2.18877 | ||||||||
\(982\) | 102.864 | − | 407.396i | 0.104749 | − | 0.414864i | ||||
\(983\) | 1400.99 | + | 808.863i | 1.42522 | + | 0.822852i | 0.996739 | − | 0.0806982i | \(-0.0257150\pi\) |
0.428483 | + | 0.903550i | \(0.359048\pi\) | |||||||
\(984\) | 2704.79 | + | 600.207i | 2.74877 | + | 0.609966i | ||||
\(985\) | −10.1950 | + | 17.6583i | −0.0103503 | + | 0.0179272i | ||||
\(986\) | 400.657 | + | 1413.12i | 0.406346 | + | 1.43318i | ||||
\(987\) | 1201.91i | 1.21774i | ||||||||
\(988\) | 584.988 | − | 244.036i | 0.592093 | − | 0.247000i | ||||
\(989\) | 860.173 | 0.869740 | ||||||||
\(990\) | −67.3222 | + | 19.0877i | −0.0680022 | + | 0.0192805i | ||||
\(991\) | −33.5516 | − | 19.3710i | −0.0338563 | − | 0.0195469i | 0.482976 | − | 0.875633i | \(-0.339556\pi\) |
−0.516833 | + | 0.856086i | \(0.672889\pi\) | |||||||
\(992\) | 158.681 | − | 827.717i | 0.159961 | − | 0.834392i | ||||
\(993\) | 995.065 | − | 1723.50i | 1.00208 | − | 1.73565i | ||||
\(994\) | −645.584 | − | 163.004i | −0.649481 | − | 0.163988i | ||||
\(995\) | − | 27.6983i | − | 0.0278375i | ||||||
\(996\) | −56.3500 | − | 1945.57i | −0.0565763 | − | 1.95339i | ||||
\(997\) | 368.133 | + | 637.625i | 0.369240 | + | 0.639543i | 0.989447 | − | 0.144895i | \(-0.0462846\pi\) |
−0.620207 | + | 0.784439i | \(0.712951\pi\) | |||||||
\(998\) | −118.081 | + | 467.666i | −0.118318 | + | 0.468603i | ||||
\(999\) | − | 192.988i | − | 0.193181i |
(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 | 76.3.g.c.11.9 | yes | 28 | |
4.3 | odd | 2 | inner | 76.3.g.c.11.2 | yes | 28 | |
19.7 | even | 3 | inner | 76.3.g.c.7.2 | ✓ | 28 | |
76.7 | odd | 6 | inner | 76.3.g.c.7.9 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.g.c.7.2 | ✓ | 28 | 19.7 | even | 3 | inner | |
76.3.g.c.7.9 | yes | 28 | 76.7 | odd | 6 | inner | |
76.3.g.c.11.2 | yes | 28 | 4.3 | odd | 2 | inner | |
76.3.g.c.11.9 | yes | 28 | 1.1 | even | 1 | trivial |