Properties

Label 124.5.l.a.35.7
Level $124$
Weight $5$
Character 124.35
Analytic conductor $12.818$
Analytic rank $0$
Dimension $248$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [124,5,Mod(35,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.35");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 124.l (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: \(12.8178754224\)
Analytic rank: \(0\)
Dimension: \(248\)
Relative dimension: \(62\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 35.7
Character \(\chi\) \(=\) 124.35
Dual form 124.5.l.a.39.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.83059 - 1.15178i) q^{2} +(14.8017 + 4.80936i) q^{3} +(13.3468 + 8.82396i) q^{4} -27.7531 q^{5} +(-51.1599 - 35.4709i) q^{6} +(-6.94187 - 9.55467i) q^{7} +(-40.9630 - 49.1735i) q^{8} +(130.430 + 94.7627i) q^{9} +O(q^{10})\) \(q+(-3.83059 - 1.15178i) q^{2} +(14.8017 + 4.80936i) q^{3} +(13.3468 + 8.82396i) q^{4} -27.7531 q^{5} +(-51.1599 - 35.4709i) q^{6} +(-6.94187 - 9.55467i) q^{7} +(-40.9630 - 49.1735i) q^{8} +(130.430 + 94.7627i) q^{9} +(106.311 + 31.9653i) q^{10} +(106.777 + 146.966i) q^{11} +(155.118 + 194.799i) q^{12} +(6.70197 - 20.6265i) q^{13} +(15.5866 + 44.5955i) q^{14} +(-410.792 - 133.475i) q^{15} +(100.275 + 235.544i) q^{16} +(259.665 + 188.658i) q^{17} +(-390.477 - 513.223i) q^{18} +(-222.161 + 72.1845i) q^{19} +(-370.415 - 244.892i) q^{20} +(-56.7996 - 174.811i) q^{21} +(-239.747 - 685.949i) q^{22} +(-377.641 + 519.778i) q^{23} +(-369.828 - 924.857i) q^{24} +145.234 q^{25} +(-49.4297 + 71.2926i) q^{26} +(733.847 + 1010.05i) q^{27} +(-8.34189 - 188.779i) q^{28} +(383.845 + 1181.35i) q^{29} +(1419.84 + 984.427i) q^{30} +(913.603 - 298.079i) q^{31} +(-112.820 - 1017.77i) q^{32} +(873.667 + 2688.87i) q^{33} +(-777.379 - 1021.75i) q^{34} +(192.658 + 265.171i) q^{35} +(904.639 + 2415.69i) q^{36} -2245.75 q^{37} +(934.148 - 20.6293i) q^{38} +(198.401 - 273.075i) q^{39} +(1136.85 + 1364.72i) q^{40} +(507.784 + 1562.80i) q^{41} +(16.2325 + 735.050i) q^{42} +(1968.46 - 639.591i) q^{43} +(128.312 + 2903.72i) q^{44} +(-3619.82 - 2629.96i) q^{45} +(2045.26 - 1556.10i) q^{46} +(-1617.60 - 525.591i) q^{47} +(351.429 + 3968.70i) q^{48} +(698.848 - 2150.83i) q^{49} +(-556.330 - 167.277i) q^{50} +(2936.16 + 4041.28i) q^{51} +(271.458 - 216.161i) q^{52} +(509.911 + 370.472i) q^{53} +(-1647.71 - 4714.33i) q^{54} +(-2963.39 - 4078.76i) q^{55} +(-185.477 + 732.744i) q^{56} -3635.52 q^{57} +(-109.697 - 4967.39i) q^{58} +(2318.05 + 753.181i) q^{59} +(-4305.00 - 5406.28i) q^{60} +2692.22 q^{61} +(-3842.96 + 89.5521i) q^{62} -1904.04i q^{63} +(-740.073 + 4028.59i) q^{64} +(-186.000 + 572.450i) q^{65} +(-249.682 - 11306.2i) q^{66} -2951.88i q^{67} +(1800.99 + 4809.26i) q^{68} +(-8089.53 + 5877.38i) q^{69} +(-432.577 - 1237.66i) q^{70} +(4437.89 - 6108.23i) q^{71} +(-682.968 - 10295.4i) q^{72} +(-1251.66 + 909.383i) q^{73} +(8602.56 + 2586.61i) q^{74} +(2149.70 + 698.480i) q^{75} +(-3602.10 - 996.907i) q^{76} +(662.978 - 2040.44i) q^{77} +(-1074.51 + 817.526i) q^{78} +(-604.434 + 831.932i) q^{79} +(-2782.95 - 6537.06i) q^{80} +(1969.07 + 6060.17i) q^{81} +(-145.117 - 6571.29i) q^{82} +(-9249.60 + 3005.38i) q^{83} +(784.433 - 2834.37i) q^{84} +(-7206.51 - 5235.83i) q^{85} +(-8277.03 + 182.786i) q^{86} +19332.1i q^{87} +(2852.93 - 11270.8i) q^{88} +(7451.21 - 5413.62i) q^{89} +(10836.9 + 14243.5i) q^{90} +(-243.604 + 79.1517i) q^{91} +(-9626.81 + 3605.10i) q^{92} +(14956.4 - 18.2283i) q^{93} +(5591.00 + 3876.44i) q^{94} +(6165.65 - 2003.34i) q^{95} +(3224.88 - 15607.2i) q^{96} +(-6048.22 + 4394.29i) q^{97} +(-5154.28 + 7434.04i) q^{98} +29287.2i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 248 q - 3 q^{2} - 31 q^{4} - 16 q^{5} - 10 q^{6} - 237 q^{8} + 1560 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 248 q - 3 q^{2} - 31 q^{4} - 16 q^{5} - 10 q^{6} - 237 q^{8} + 1560 q^{9} - 250 q^{10} - 210 q^{12} + 346 q^{13} + 226 q^{14} + 73 q^{16} - 6 q^{17} + 818 q^{18} - 975 q^{20} + 102 q^{21} + 1540 q^{22} + 1023 q^{24} + 26248 q^{25} - 360 q^{26} + 160 q^{28} - 6 q^{29} - 4022 q^{30} + 6862 q^{32} + 1110 q^{33} + 3067 q^{34} - 4568 q^{36} - 2096 q^{37} + 5050 q^{38} - 3206 q^{40} - 6 q^{41} - 3884 q^{42} - 5660 q^{44} - 10272 q^{45} + 3185 q^{46} - 16516 q^{48} + 12392 q^{49} - 7878 q^{50} - 5935 q^{52} - 8454 q^{53} + 1362 q^{54} + 39536 q^{56} + 10892 q^{57} - 1105 q^{58} - 1267 q^{60} + 11696 q^{61} - 21020 q^{62} - 24493 q^{64} - 3756 q^{65} - 33182 q^{66} - 31014 q^{68} + 31734 q^{69} + 4205 q^{70} - 59598 q^{72} - 16646 q^{73} - 7683 q^{74} - 16019 q^{76} - 16618 q^{77} - 11625 q^{78} + 63150 q^{80} - 33864 q^{81} - 25974 q^{82} - 43055 q^{84} + 23956 q^{85} - 26357 q^{86} - 34700 q^{88} + 4170 q^{89} + 20102 q^{90} - 22738 q^{92} + 35990 q^{93} - 25646 q^{94} + 50490 q^{96} - 6614 q^{97} - 49748 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.83059 1.15178i −0.957647 0.287944i
\(3\) 14.8017 + 4.80936i 1.64463 + 0.534373i 0.977567 0.210626i \(-0.0675503\pi\)
0.667065 + 0.744999i \(0.267550\pi\)
\(4\) 13.3468 + 8.82396i 0.834176 + 0.551498i
\(5\) −27.7531 −1.11012 −0.555062 0.831809i \(-0.687305\pi\)
−0.555062 + 0.831809i \(0.687305\pi\)
\(6\) −51.1599 35.4709i −1.42111 0.985303i
\(7\) −6.94187 9.55467i −0.141671 0.194993i 0.732285 0.680998i \(-0.238454\pi\)
−0.873956 + 0.486005i \(0.838454\pi\)
\(8\) −40.9630 49.1735i −0.640046 0.768336i
\(9\) 130.430 + 94.7627i 1.61024 + 1.16991i
\(10\) 106.311 + 31.9653i 1.06311 + 0.319653i
\(11\) 106.777 + 146.966i 0.882454 + 1.21459i 0.975735 + 0.218954i \(0.0702645\pi\)
−0.0932811 + 0.995640i \(0.529736\pi\)
\(12\) 155.118 + 194.799i 1.07721 + 1.35277i
\(13\) 6.70197 20.6265i 0.0396566 0.122051i −0.929268 0.369405i \(-0.879561\pi\)
0.968925 + 0.247355i \(0.0795614\pi\)
\(14\) 15.5866 + 44.5955i 0.0795235 + 0.227528i
\(15\) −410.792 133.475i −1.82574 0.593220i
\(16\) 100.275 + 235.544i 0.391700 + 0.920093i
\(17\) 259.665 + 188.658i 0.898495 + 0.652795i 0.938079 0.346421i \(-0.112603\pi\)
−0.0395839 + 0.999216i \(0.512603\pi\)
\(18\) −390.477 513.223i −1.20518 1.58402i
\(19\) −222.161 + 72.1845i −0.615404 + 0.199957i −0.600099 0.799926i \(-0.704872\pi\)
−0.0153056 + 0.999883i \(0.504872\pi\)
\(20\) −370.415 244.892i −0.926039 0.612230i
\(21\) −56.7996 174.811i −0.128797 0.396397i
\(22\) −239.747 685.949i −0.495345 1.41725i
\(23\) −377.641 + 519.778i −0.713877 + 0.982568i 0.285828 + 0.958281i \(0.407731\pi\)
−0.999705 + 0.0242867i \(0.992269\pi\)
\(24\) −369.828 924.857i −0.642062 1.60565i
\(25\) 145.234 0.232374
\(26\) −49.4297 + 71.2926i −0.0731208 + 0.105462i
\(27\) 733.847 + 1010.05i 1.00665 + 1.38553i
\(28\) −8.34189 188.779i −0.0106402 0.240790i
\(29\) 383.845 + 1181.35i 0.456415 + 1.40470i 0.869466 + 0.493994i \(0.164463\pi\)
−0.413050 + 0.910708i \(0.635537\pi\)
\(30\) 1419.84 + 984.427i 1.57760 + 1.09381i
\(31\) 913.603 298.079i 0.950679 0.310176i
\(32\) −112.820 1017.77i −0.110176 0.993912i
\(33\) 873.667 + 2688.87i 0.802266 + 2.46912i
\(34\) −777.379 1021.75i −0.672473 0.883864i
\(35\) 192.658 + 265.171i 0.157272 + 0.216466i
\(36\) 904.639 + 2415.69i 0.698024 + 1.86396i
\(37\) −2245.75 −1.64043 −0.820217 0.572052i \(-0.806147\pi\)
−0.820217 + 0.572052i \(0.806147\pi\)
\(38\) 934.148 20.6293i 0.646917 0.0142862i
\(39\) 198.401 273.075i 0.130441 0.179537i
\(40\) 1136.85 + 1364.72i 0.710530 + 0.852948i
\(41\) 507.784 + 1562.80i 0.302072 + 0.929683i 0.980753 + 0.195250i \(0.0625519\pi\)
−0.678681 + 0.734433i \(0.737448\pi\)
\(42\) 16.2325 + 735.050i 0.00920210 + 0.416695i
\(43\) 1968.46 639.591i 1.06461 0.345912i 0.276222 0.961094i \(-0.410917\pi\)
0.788385 + 0.615182i \(0.210917\pi\)
\(44\) 128.312 + 2903.72i 0.0662766 + 1.49986i
\(45\) −3619.82 2629.96i −1.78757 1.29874i
\(46\) 2045.26 1556.10i 0.966567 0.735396i
\(47\) −1617.60 525.591i −0.732278 0.237931i −0.0809396 0.996719i \(-0.525792\pi\)
−0.651338 + 0.758788i \(0.725792\pi\)
\(48\) 351.429 + 3968.70i 0.152530 + 1.72253i
\(49\) 698.848 2150.83i 0.291065 0.895807i
\(50\) −556.330 167.277i −0.222532 0.0669106i
\(51\) 2936.16 + 4041.28i 1.12886 + 1.55374i
\(52\) 271.458 216.161i 0.100391 0.0799412i
\(53\) 509.911 + 370.472i 0.181528 + 0.131888i 0.674838 0.737966i \(-0.264213\pi\)
−0.493311 + 0.869853i \(0.664213\pi\)
\(54\) −1647.71 4714.33i −0.565058 1.61671i
\(55\) −2963.39 4078.76i −0.979633 1.34835i
\(56\) −185.477 + 732.744i −0.0591445 + 0.233656i
\(57\) −3635.52 −1.11897
\(58\) −109.697 4967.39i −0.0326092 1.47663i
\(59\) 2318.05 + 753.181i 0.665916 + 0.216369i 0.622419 0.782684i \(-0.286150\pi\)
0.0434971 + 0.999054i \(0.486150\pi\)
\(60\) −4305.00 5406.28i −1.19583 1.50174i
\(61\) 2692.22 0.723522 0.361761 0.932271i \(-0.382176\pi\)
0.361761 + 0.932271i \(0.382176\pi\)
\(62\) −3842.96 + 89.5521i −0.999729 + 0.0232966i
\(63\) 1904.04i 0.479728i
\(64\) −740.073 + 4028.59i −0.180682 + 0.983542i
\(65\) −186.000 + 572.450i −0.0440238 + 0.135491i
\(66\) −249.682 11306.2i −0.0573190 2.59555i
\(67\) 2951.88i 0.657580i −0.944403 0.328790i \(-0.893359\pi\)
0.944403 0.328790i \(-0.106641\pi\)
\(68\) 1800.99 + 4809.26i 0.389489 + 1.04006i
\(69\) −8089.53 + 5877.38i −1.69912 + 1.23449i
\(70\) −432.577 1237.66i −0.0882809 0.252584i
\(71\) 4437.89 6108.23i 0.880359 1.21171i −0.0959626 0.995385i \(-0.530593\pi\)
0.976321 0.216325i \(-0.0694071\pi\)
\(72\) −682.968 10295.4i −0.131745 1.98600i
\(73\) −1251.66 + 909.383i −0.234877 + 0.170648i −0.698998 0.715124i \(-0.746370\pi\)
0.464121 + 0.885772i \(0.346370\pi\)
\(74\) 8602.56 + 2586.61i 1.57096 + 0.472353i
\(75\) 2149.70 + 698.480i 0.382169 + 0.124174i
\(76\) −3602.10 996.907i −0.623632 0.172595i
\(77\) 662.978 2040.44i 0.111820 0.344145i
\(78\) −1074.51 + 817.526i −0.176613 + 0.134373i
\(79\) −604.434 + 831.932i −0.0968489 + 0.133301i −0.854691 0.519137i \(-0.826254\pi\)
0.757842 + 0.652438i \(0.226254\pi\)
\(80\) −2782.95 6537.06i −0.434836 1.02142i
\(81\) 1969.07 + 6060.17i 0.300117 + 0.923665i
\(82\) −145.117 6571.29i −0.0215820 0.977288i
\(83\) −9249.60 + 3005.38i −1.34266 + 0.436257i −0.890218 0.455536i \(-0.849448\pi\)
−0.452444 + 0.891793i \(0.649448\pi\)
\(84\) 784.433 2834.37i 0.111172 0.401696i
\(85\) −7206.51 5235.83i −0.997440 0.724683i
\(86\) −8277.03 + 182.786i −1.11912 + 0.0247142i
\(87\) 19332.1i 2.55411i
\(88\) 2852.93 11270.8i 0.368405 1.45542i
\(89\) 7451.21 5413.62i 0.940690 0.683451i −0.00789670 0.999969i \(-0.502514\pi\)
0.948587 + 0.316518i \(0.102514\pi\)
\(90\) 10836.9 + 14243.5i 1.33789 + 1.75846i
\(91\) −243.604 + 79.1517i −0.0294172 + 0.00955823i
\(92\) −9626.81 + 3605.10i −1.13738 + 0.425933i
\(93\) 14956.4 18.2283i 1.72927 0.00210756i
\(94\) 5591.00 + 3876.44i 0.632753 + 0.438710i
\(95\) 6165.65 2003.34i 0.683175 0.221977i
\(96\) 3224.88 15607.2i 0.349922 1.69349i
\(97\) −6048.22 + 4394.29i −0.642812 + 0.467030i −0.860815 0.508918i \(-0.830046\pi\)
0.218003 + 0.975948i \(0.430046\pi\)
\(98\) −5154.28 + 7434.04i −0.536680 + 0.774056i
\(99\) 29287.2i 2.98818i
\(100\) 1938.41 + 1281.54i 0.193841 + 0.128154i
\(101\) −5615.83 4080.14i −0.550518 0.399974i 0.277459 0.960738i \(-0.410508\pi\)
−0.827976 + 0.560763i \(0.810508\pi\)
\(102\) −6592.57 18862.3i −0.633657 1.81298i
\(103\) 15780.4 5127.37i 1.48745 0.483303i 0.551124 0.834423i \(-0.314199\pi\)
0.936331 + 0.351120i \(0.114199\pi\)
\(104\) −1288.81 + 515.365i −0.119158 + 0.0476484i
\(105\) 1576.36 + 4851.55i 0.142981 + 0.440050i
\(106\) −1526.56 2006.43i −0.135863 0.178572i
\(107\) 5955.16 8196.58i 0.520147 0.715921i −0.465442 0.885078i \(-0.654105\pi\)
0.985589 + 0.169157i \(0.0541046\pi\)
\(108\) 881.848 + 19956.4i 0.0756042 + 1.71094i
\(109\) 3987.10 12271.0i 0.335586 1.03283i −0.630846 0.775908i \(-0.717292\pi\)
0.966433 0.256920i \(-0.0827078\pi\)
\(110\) 6653.71 + 19037.2i 0.549894 + 1.57332i
\(111\) −33241.0 10800.6i −2.69791 0.876604i
\(112\) 1554.44 2593.21i 0.123919 0.206729i
\(113\) −1145.40 + 832.183i −0.0897017 + 0.0651721i −0.631732 0.775187i \(-0.717656\pi\)
0.542030 + 0.840359i \(0.317656\pi\)
\(114\) 13926.2 + 4187.31i 1.07157 + 0.322200i
\(115\) 10480.7 14425.4i 0.792492 1.09077i
\(116\) −5301.11 + 19154.4i −0.393959 + 1.42348i
\(117\) 2828.76 2055.22i 0.206645 0.150136i
\(118\) −8012.01 5555.01i −0.575410 0.398952i
\(119\) 3790.65i 0.267682i
\(120\) 10263.9 + 25667.6i 0.712768 + 1.78247i
\(121\) −5673.33 + 17460.7i −0.387496 + 1.19259i
\(122\) −10312.8 3100.84i −0.692878 0.208334i
\(123\) 25574.2i 1.69041i
\(124\) 14823.9 + 4083.19i 0.964095 + 0.265556i
\(125\) 13315.0 0.852160
\(126\) −2193.03 + 7293.60i −0.138135 + 0.459410i
\(127\) 7377.80 + 2397.19i 0.457425 + 0.148626i 0.528661 0.848833i \(-0.322694\pi\)
−0.0712361 + 0.997459i \(0.522694\pi\)
\(128\) 7474.94 14579.5i 0.456234 0.889860i
\(129\) 32212.5 1.93573
\(130\) 1371.83 1978.59i 0.0811731 0.117076i
\(131\) −17639.7 24278.9i −1.02789 1.41477i −0.906518 0.422166i \(-0.861270\pi\)
−0.121375 0.992607i \(-0.538730\pi\)
\(132\) −12065.8 + 43597.1i −0.692483 + 2.50213i
\(133\) 2231.91 + 1621.58i 0.126175 + 0.0916716i
\(134\) −3399.90 + 11307.4i −0.189346 + 0.629730i
\(135\) −20366.5 28032.1i −1.11750 1.53811i
\(136\) −1359.68 20496.6i −0.0735123 1.10817i
\(137\) 3565.51 10973.5i 0.189968 0.584662i −0.810030 0.586388i \(-0.800549\pi\)
0.999999 + 0.00172596i \(0.000549391\pi\)
\(138\) 37757.1 13196.5i 1.98262 0.692949i
\(139\) −27046.0 8787.77i −1.39982 0.454830i −0.490689 0.871335i \(-0.663255\pi\)
−0.909133 + 0.416505i \(0.863255\pi\)
\(140\) 231.513 + 5239.21i 0.0118119 + 0.267306i
\(141\) −21415.5 15559.3i −1.07718 0.782619i
\(142\) −24035.0 + 18286.7i −1.19198 + 0.906896i
\(143\) 3747.01 1217.48i 0.183237 0.0595373i
\(144\) −9241.88 + 40224.2i −0.445693 + 1.93983i
\(145\) −10652.9 32786.2i −0.506677 1.55939i
\(146\) 5841.99 2041.84i 0.274066 0.0957892i
\(147\) 20688.3 28474.9i 0.957390 1.31773i
\(148\) −29973.7 19816.5i −1.36841 0.904696i
\(149\) −15455.5 −0.696161 −0.348080 0.937465i \(-0.613166\pi\)
−0.348080 + 0.937465i \(0.613166\pi\)
\(150\) −7430.13 5151.57i −0.330228 0.228958i
\(151\) 1252.63 + 1724.10i 0.0549375 + 0.0756149i 0.835602 0.549336i \(-0.185119\pi\)
−0.780664 + 0.624951i \(0.785119\pi\)
\(152\) 12649.9 + 7967.55i 0.547522 + 0.344856i
\(153\) 15990.3 + 49213.1i 0.683084 + 2.10232i
\(154\) −4889.72 + 7052.47i −0.206178 + 0.297372i
\(155\) −25355.3 + 8272.61i −1.05537 + 0.344333i
\(156\) 5057.63 1894.01i 0.207825 0.0778274i
\(157\) −5873.54 18076.9i −0.238287 0.733373i −0.996668 0.0815613i \(-0.974009\pi\)
0.758381 0.651811i \(-0.225991\pi\)
\(158\) 3273.54 2490.62i 0.131130 0.0997683i
\(159\) 5765.81 + 7935.96i 0.228069 + 0.313910i
\(160\) 3131.10 + 28246.1i 0.122309 + 1.10336i
\(161\) 7587.84 0.292730
\(162\) −562.731 25481.9i −0.0214423 0.970962i
\(163\) 14666.0 20186.1i 0.551998 0.759760i −0.438283 0.898837i \(-0.644413\pi\)
0.990282 + 0.139076i \(0.0444134\pi\)
\(164\) −7012.77 + 25339.0i −0.260737 + 0.942112i
\(165\) −24247.0 74624.5i −0.890614 2.74103i
\(166\) 38892.9 858.893i 1.41141 0.0311690i
\(167\) 5729.92 1861.76i 0.205455 0.0667562i −0.204482 0.978870i \(-0.565551\pi\)
0.409936 + 0.912114i \(0.365551\pi\)
\(168\) −6269.40 + 9953.82i −0.222130 + 0.352672i
\(169\) 22725.8 + 16511.3i 0.795693 + 0.578105i
\(170\) 21574.7 + 28356.6i 0.746528 + 0.981198i
\(171\) −35816.8 11637.6i −1.22488 0.397988i
\(172\) 31916.4 + 8833.11i 1.07884 + 0.298577i
\(173\) −15993.1 + 49221.8i −0.534369 + 1.64462i 0.210640 + 0.977564i \(0.432445\pi\)
−0.745009 + 0.667054i \(0.767555\pi\)
\(174\) 22266.2 74053.3i 0.735442 2.44594i
\(175\) −1008.19 1387.66i −0.0329206 0.0453113i
\(176\) −23909.8 + 39887.7i −0.771881 + 1.28770i
\(177\) 30688.8 + 22296.7i 0.979565 + 0.711695i
\(178\) −34777.8 + 12155.2i −1.09764 + 0.383639i
\(179\) 27024.3 + 37195.7i 0.843428 + 1.16088i 0.985273 + 0.170990i \(0.0546965\pi\)
−0.141845 + 0.989889i \(0.545303\pi\)
\(180\) −25106.5 67042.7i −0.774892 2.06922i
\(181\) −11381.8 −0.347419 −0.173710 0.984797i \(-0.555575\pi\)
−0.173710 + 0.984797i \(0.555575\pi\)
\(182\) 1024.31 22.6204i 0.0309236 0.000682901i
\(183\) 39849.5 + 12947.9i 1.18993 + 0.386631i
\(184\) 41028.6 2721.71i 1.21186 0.0803908i
\(185\) 62326.6 1.82108
\(186\) −57312.9 17156.6i −1.65663 0.495914i
\(187\) 58306.2i 1.66737i
\(188\) −16952.0 21288.6i −0.479630 0.602326i
\(189\) 4556.45 14023.3i 0.127557 0.392579i
\(190\) −25925.5 + 572.526i −0.718157 + 0.0158595i
\(191\) 11799.7i 0.323447i −0.986836 0.161724i \(-0.948295\pi\)
0.986836 0.161724i \(-0.0517053\pi\)
\(192\) −30329.2 + 56070.6i −0.822733 + 1.52101i
\(193\) −57426.9 + 41723.1i −1.54170 + 1.12011i −0.592448 + 0.805609i \(0.701838\pi\)
−0.949256 + 0.314504i \(0.898162\pi\)
\(194\) 28229.5 9866.51i 0.750066 0.262156i
\(195\) −5506.24 + 7578.69i −0.144806 + 0.199308i
\(196\) 28306.3 22540.2i 0.736835 0.586739i
\(197\) −14561.4 + 10579.5i −0.375208 + 0.272605i −0.759367 0.650662i \(-0.774491\pi\)
0.384159 + 0.923267i \(0.374491\pi\)
\(198\) 33732.3 112187.i 0.860429 2.86162i
\(199\) 58191.8 + 18907.7i 1.46945 + 0.477454i 0.930943 0.365165i \(-0.118987\pi\)
0.538510 + 0.842619i \(0.318987\pi\)
\(200\) −5949.19 7141.64i −0.148730 0.178541i
\(201\) 14196.6 43692.7i 0.351393 1.08148i
\(202\) 16812.5 + 22097.5i 0.412031 + 0.541553i
\(203\) 8622.84 11868.3i 0.209247 0.288003i
\(204\) 3528.32 + 79846.7i 0.0847827 + 1.91866i
\(205\) −14092.6 43372.4i −0.335338 1.03206i
\(206\) −66353.8 + 1465.33i −1.56362 + 0.0345303i
\(207\) −98511.2 + 32008.2i −2.29903 + 0.747000i
\(208\) 5530.50 489.726i 0.127831 0.0113195i
\(209\) −34330.3 24942.4i −0.785933 0.571014i
\(210\) −450.502 20399.9i −0.0102155 0.462583i
\(211\) 12269.6i 0.275592i 0.990461 + 0.137796i \(0.0440018\pi\)
−0.990461 + 0.137796i \(0.955998\pi\)
\(212\) 3536.66 + 9444.06i 0.0786904 + 0.210130i
\(213\) 95064.9 69068.7i 2.09537 1.52238i
\(214\) −32252.4 + 24538.7i −0.704263 + 0.535826i
\(215\) −54630.8 + 17750.6i −1.18185 + 0.384005i
\(216\) 19607.4 77460.6i 0.420254 1.66025i
\(217\) −9190.16 6659.94i −0.195166 0.141433i
\(218\) −29406.4 + 42413.0i −0.618770 + 0.892455i
\(219\) −22900.2 + 7440.73i −0.477476 + 0.155141i
\(220\) −3561.04 80587.3i −0.0735752 1.66503i
\(221\) 5631.63 4091.62i 0.115305 0.0837742i
\(222\) 114893. + 79659.0i 2.33123 + 1.61633i
\(223\) 58403.3i 1.17443i −0.809431 0.587215i \(-0.800224\pi\)
0.809431 0.587215i \(-0.199776\pi\)
\(224\) −8941.23 + 8143.16i −0.178197 + 0.162292i
\(225\) 18942.8 + 13762.7i 0.374178 + 0.271856i
\(226\) 5346.05 1868.50i 0.104669 0.0365828i
\(227\) 65555.6 21300.3i 1.27221 0.413365i 0.406378 0.913705i \(-0.366792\pi\)
0.865829 + 0.500340i \(0.166792\pi\)
\(228\) −48522.6 32079.7i −0.933415 0.617107i
\(229\) 6129.04 + 18863.2i 0.116875 + 0.359704i 0.992333 0.123589i \(-0.0394405\pi\)
−0.875459 + 0.483293i \(0.839441\pi\)
\(230\) −56762.2 + 43186.5i −1.07301 + 0.816381i
\(231\) 19626.4 27013.4i 0.367804 0.506239i
\(232\) 42367.9 67266.8i 0.787157 1.24975i
\(233\) −14058.4 + 43267.4i −0.258956 + 0.796983i 0.734069 + 0.679075i \(0.237619\pi\)
−0.993024 + 0.117908i \(0.962381\pi\)
\(234\) −13203.0 + 4614.59i −0.241124 + 0.0842754i
\(235\) 44893.4 + 14586.8i 0.812919 + 0.264133i
\(236\) 24292.6 + 30507.0i 0.436164 + 0.547741i
\(237\) −12947.7 + 9407.05i −0.230513 + 0.167478i
\(238\) −4365.98 + 14520.4i −0.0770776 + 0.256345i
\(239\) −27787.6 + 38246.4i −0.486470 + 0.669568i −0.979732 0.200312i \(-0.935804\pi\)
0.493262 + 0.869881i \(0.335804\pi\)
\(240\) −9753.25 110144.i −0.169327 1.91222i
\(241\) 73488.0 53392.1i 1.26527 0.919270i 0.266263 0.963900i \(-0.414211\pi\)
0.999004 + 0.0446302i \(0.0142110\pi\)
\(242\) 41843.0 60350.4i 0.714484 1.03050i
\(243\) 1957.45i 0.0331495i
\(244\) 35932.6 + 23756.1i 0.603545 + 0.399021i
\(245\) −19395.2 + 59692.2i −0.323118 + 0.994456i
\(246\) 29455.7 97964.1i 0.486742 1.61881i
\(247\) 5066.19i 0.0830401i
\(248\) −52081.5 32714.9i −0.846798 0.531915i
\(249\) −151364. −2.44131
\(250\) −51004.3 15335.9i −0.816069 0.245374i
\(251\) −2877.15 934.842i −0.0456683 0.0148385i 0.286094 0.958202i \(-0.407643\pi\)
−0.331762 + 0.943363i \(0.607643\pi\)
\(252\) 16801.2 25412.9i 0.264569 0.400178i
\(253\) −116713. −1.82338
\(254\) −25500.3 17680.2i −0.395255 0.274044i
\(255\) −81487.5 112158.i −1.25317 1.72484i
\(256\) −45425.7 + 47238.5i −0.693141 + 0.720802i
\(257\) −32027.3 23269.2i −0.484902 0.352302i 0.318319 0.947984i \(-0.396882\pi\)
−0.803220 + 0.595682i \(0.796882\pi\)
\(258\) −123393. 37101.7i −1.85375 0.557383i
\(259\) 15589.7 + 21457.4i 0.232402 + 0.319874i
\(260\) −7533.79 + 5999.13i −0.111447 + 0.0887445i
\(261\) −61883.5 + 190458.i −0.908435 + 2.79587i
\(262\) 39606.4 + 113320.i 0.576983 + 1.65083i
\(263\) 20167.0 + 6552.64i 0.291561 + 0.0947338i 0.451145 0.892450i \(-0.351016\pi\)
−0.159585 + 0.987184i \(0.551016\pi\)
\(264\) 96433.3 153105.i 1.38363 2.19676i
\(265\) −14151.6 10281.7i −0.201518 0.146411i
\(266\) −6681.84 8782.27i −0.0944350 0.124120i
\(267\) 136326. 44295.1i 1.91231 0.621346i
\(268\) 26047.2 39398.2i 0.362654 0.548538i
\(269\) 13733.7 + 42267.9i 0.189794 + 0.584125i 0.999998 0.00202259i \(-0.000643811\pi\)
−0.810204 + 0.586148i \(0.800644\pi\)
\(270\) 45729.0 + 130837.i 0.627284 + 1.79475i
\(271\) 52069.5 71667.5i 0.708997 0.975851i −0.290821 0.956778i \(-0.593928\pi\)
0.999818 0.0190734i \(-0.00607162\pi\)
\(272\) −18399.1 + 80080.2i −0.248691 + 1.08240i
\(273\) −3986.42 −0.0534882
\(274\) −26297.1 + 37928.4i −0.350273 + 0.505200i
\(275\) 15507.6 + 21344.4i 0.205059 + 0.282240i
\(276\) −159831. + 7062.72i −2.09818 + 0.0927159i
\(277\) −2276.00 7004.80i −0.0296628 0.0912927i 0.935129 0.354307i \(-0.115283\pi\)
−0.964792 + 0.263015i \(0.915283\pi\)
\(278\) 93480.4 + 64813.2i 1.20957 + 0.838637i
\(279\) 147408. + 47697.1i 1.89370 + 0.612750i
\(280\) 5147.56 20335.9i 0.0656577 0.259386i
\(281\) 12810.1 + 39425.5i 0.162234 + 0.499303i 0.998822 0.0485287i \(-0.0154533\pi\)
−0.836588 + 0.547832i \(0.815453\pi\)
\(282\) 64113.1 + 84267.0i 0.806211 + 1.05964i
\(283\) 70355.3 + 96835.7i 0.878464 + 1.20910i 0.976844 + 0.213953i \(0.0686339\pi\)
−0.0983802 + 0.995149i \(0.531366\pi\)
\(284\) 113131. 42365.7i 1.40263 0.525264i
\(285\) 100897. 1.24219
\(286\) −15755.5 + 347.938i −0.192620 + 0.00425373i
\(287\) 11407.0 15700.4i 0.138487 0.190611i
\(288\) 81731.2 143438.i 0.985378 1.72933i
\(289\) 6024.82 + 18542.5i 0.0721353 + 0.222010i
\(290\) 3044.44 + 137860.i 0.0362003 + 1.63924i
\(291\) −110658. + 35954.8i −1.30676 + 0.424591i
\(292\) −24730.0 + 1092.79i −0.290041 + 0.0128165i
\(293\) 7567.74 + 5498.29i 0.0881518 + 0.0640460i 0.630988 0.775792i \(-0.282650\pi\)
−0.542836 + 0.839838i \(0.682650\pi\)
\(294\) −112045. + 85247.5i −1.29628 + 0.986250i
\(295\) −64333.1 20903.1i −0.739249 0.240196i
\(296\) 91992.8 + 110432.i 1.04995 + 1.26041i
\(297\) −70085.5 + 215701.i −0.794539 + 2.44534i
\(298\) 59203.5 + 17801.2i 0.666677 + 0.200455i
\(299\) 8190.29 + 11273.0i 0.0916130 + 0.126094i
\(300\) 22528.3 + 28291.4i 0.250315 + 0.314349i
\(301\) −19775.9 14368.0i −0.218274 0.158586i
\(302\) −2812.53 8047.05i −0.0308378 0.0882313i
\(303\) −63500.9 87401.5i −0.691663 0.951993i
\(304\) −39279.9 45090.3i −0.425033 0.487906i
\(305\) −74717.5 −0.803198
\(306\) −4569.80 206932.i −0.0488039 2.20997i
\(307\) 8212.73 + 2668.48i 0.0871386 + 0.0283131i 0.352262 0.935901i \(-0.385413\pi\)
−0.265123 + 0.964215i \(0.585413\pi\)
\(308\) 26853.4 21383.2i 0.283072 0.225409i
\(309\) 258236. 2.70458
\(310\) 106654. 2485.35i 1.10982 0.0258621i
\(311\) 18315.3i 0.189363i 0.995508 + 0.0946813i \(0.0301832\pi\)
−0.995508 + 0.0946813i \(0.969817\pi\)
\(312\) −21555.2 + 1429.90i −0.221433 + 0.0146892i
\(313\) 48333.4 148755.i 0.493354 1.51839i −0.326153 0.945317i \(-0.605753\pi\)
0.819507 0.573069i \(-0.194247\pi\)
\(314\) 1678.57 + 76010.2i 0.0170248 + 0.770926i
\(315\) 52843.0i 0.532558i
\(316\) −15408.2 + 5770.14i −0.154304 + 0.0577846i
\(317\) −85920.4 + 62424.8i −0.855022 + 0.621210i −0.926526 0.376230i \(-0.877220\pi\)
0.0715038 + 0.997440i \(0.477220\pi\)
\(318\) −12946.0 37040.3i −0.128021 0.366286i
\(319\) −132633. + 182554.i −1.30338 + 1.79394i
\(320\) 20539.3 111806.i 0.200579 1.09185i
\(321\) 127567. 92682.7i 1.23802 0.899474i
\(322\) −29065.9 8739.50i −0.280332 0.0842898i
\(323\) −71305.6 23168.6i −0.683469 0.222073i
\(324\) −27193.9 + 98259.0i −0.259049 + 0.936014i
\(325\) 973.351 2995.67i 0.00921516 0.0283613i
\(326\) −79429.4 + 60432.6i −0.747388 + 0.568638i
\(327\) 118032. 162457.i 1.10383 1.51929i
\(328\) 56048.0 88986.3i 0.520969 0.827133i
\(329\) 6207.34 + 19104.2i 0.0573474 + 0.176497i
\(330\) 6929.43 + 313783.i 0.0636311 + 2.88138i
\(331\) −60708.5 + 19725.4i −0.554107 + 0.180040i −0.572668 0.819788i \(-0.694092\pi\)
0.0185610 + 0.999828i \(0.494092\pi\)
\(332\) −149972. 41505.9i −1.36061 0.376559i
\(333\) −292913. 212814.i −2.64150 1.91916i
\(334\) −24093.3 + 532.066i −0.215975 + 0.00476949i
\(335\) 81923.7i 0.729995i
\(336\) 35480.1 30908.0i 0.314272 0.273774i
\(337\) −90951.1 + 66079.9i −0.800845 + 0.581848i −0.911162 0.412049i \(-0.864813\pi\)
0.110317 + 0.993896i \(0.464813\pi\)
\(338\) −68035.9 89422.9i −0.595532 0.782736i
\(339\) −20956.1 + 6809.06i −0.182353 + 0.0592499i
\(340\) −49983.2 133472.i −0.432380 1.15460i
\(341\) 141359. + 102440.i 1.21567 + 0.880973i
\(342\) 123795. + 85831.7i 1.05841 + 0.733830i
\(343\) −52370.3 + 17016.1i −0.445140 + 0.144635i
\(344\) −112085. 70596.6i −0.947175 0.596577i
\(345\) 224509. 163116.i 1.88624 1.37043i
\(346\) 117956. 170128.i 0.985295 1.42110i
\(347\) 176281.i 1.46402i −0.681293 0.732011i \(-0.738582\pi\)
0.681293 0.732011i \(-0.261418\pi\)
\(348\) −170586. + 258022.i −1.40859 + 2.13058i
\(349\) 103464. + 75170.8i 0.849449 + 0.617161i 0.924994 0.379981i \(-0.124070\pi\)
−0.0755448 + 0.997142i \(0.524070\pi\)
\(350\) 2263.70 + 6476.76i 0.0184792 + 0.0528715i
\(351\) 25752.1 8367.38i 0.209025 0.0679165i
\(352\) 137530. 125255.i 1.10997 1.01090i
\(353\) −6944.79 21373.9i −0.0557327 0.171527i 0.919315 0.393522i \(-0.128743\pi\)
−0.975048 + 0.221994i \(0.928743\pi\)
\(354\) −91875.3 120756.i −0.733149 0.963613i
\(355\) −123165. + 169522.i −0.977307 + 1.34515i
\(356\) 147219. 6505.43i 1.16162 0.0513305i
\(357\) 18230.6 56108.0i 0.143042 0.440239i
\(358\) −60677.7 173607.i −0.473438 1.35457i
\(359\) 53882.8 + 17507.6i 0.418082 + 0.135843i 0.510501 0.859877i \(-0.329460\pi\)
−0.0924190 + 0.995720i \(0.529460\pi\)
\(360\) 18954.5 + 285730.i 0.146254 + 2.20471i
\(361\) −61287.0 + 44527.6i −0.470277 + 0.341676i
\(362\) 43599.0 + 13109.3i 0.332705 + 0.100037i
\(363\) −167950. + 231163.i −1.27458 + 1.75430i
\(364\) −3949.77 1093.13i −0.0298105 0.00825028i
\(365\) 34737.4 25238.2i 0.260742 0.189440i
\(366\) −137734. 95495.6i −1.02820 0.712888i
\(367\) 158238.i 1.17484i −0.809283 0.587419i \(-0.800144\pi\)
0.809283 0.587419i \(-0.199856\pi\)
\(368\) −160299. 36830.0i −1.18368 0.271961i
\(369\) −81864.8 + 251954.i −0.601235 + 1.85041i
\(370\) −238748. 71786.3i −1.74396 0.524371i
\(371\) 7443.80i 0.0540813i
\(372\) 199782. + 131732.i 1.44368 + 0.951929i
\(373\) 241670. 1.73702 0.868512 0.495669i \(-0.165077\pi\)
0.868512 + 0.495669i \(0.165077\pi\)
\(374\) 67155.7 223347.i 0.480109 1.59675i
\(375\) 197084. + 64036.6i 1.40149 + 0.455371i
\(376\) 40416.6 + 101073.i 0.285880 + 0.714923i
\(377\) 26939.8 0.189545
\(378\) −33605.6 + 48469.6i −0.235195 + 0.339223i
\(379\) 150095. + 206588.i 1.04493 + 1.43823i 0.893121 + 0.449816i \(0.148510\pi\)
0.151810 + 0.988410i \(0.451490\pi\)
\(380\) 99969.3 + 27667.2i 0.692308 + 0.191601i
\(381\) 97674.9 + 70965.0i 0.672873 + 0.488871i
\(382\) −13590.6 + 45199.7i −0.0931347 + 0.309748i
\(383\) −54272.0 74699.0i −0.369980 0.509234i 0.582916 0.812533i \(-0.301912\pi\)
−0.952895 + 0.303299i \(0.901912\pi\)
\(384\) 180760. 179851.i 1.22585 1.21969i
\(385\) −18399.7 + 56628.4i −0.124133 + 0.382043i
\(386\) 268035. 93681.1i 1.79894 0.628749i
\(387\) 317355. + 103115.i 2.11896 + 0.688492i
\(388\) −119500. + 5280.52i −0.793785 + 0.0350763i
\(389\) 212586. + 154453.i 1.40487 + 1.02070i 0.994044 + 0.108982i \(0.0347589\pi\)
0.410824 + 0.911715i \(0.365241\pi\)
\(390\) 29821.1 22688.9i 0.196062 0.149171i
\(391\) −196120. + 63723.4i −1.28283 + 0.416817i
\(392\) −134391. + 53739.6i −0.874576 + 0.349722i
\(393\) −144331. 444205.i −0.934488 2.87606i
\(394\) 67964.1 23754.2i 0.437812 0.153020i
\(395\) 16774.9 23088.7i 0.107514 0.147981i
\(396\) −258429. + 390891.i −1.64798 + 2.49267i
\(397\) −282588. −1.79297 −0.896485 0.443074i \(-0.853888\pi\)
−0.896485 + 0.443074i \(0.853888\pi\)
\(398\) −201132. 139451.i −1.26974 0.880353i
\(399\) 25237.3 + 34736.2i 0.158525 + 0.218191i
\(400\) 14563.3 + 34208.8i 0.0910209 + 0.213805i
\(401\) −81255.1 250078.i −0.505315 1.55520i −0.800241 0.599679i \(-0.795295\pi\)
0.294926 0.955520i \(-0.404705\pi\)
\(402\) −104706. + 151018.i −0.647916 + 0.934492i
\(403\) −25.4016 20842.2i −0.000156405 0.128331i
\(404\) −38950.5 104011.i −0.238644 0.637258i
\(405\) −54647.7 168188.i −0.333167 1.02538i
\(406\) −46700.2 + 35531.1i −0.283313 + 0.215554i
\(407\) −239795. 330049.i −1.44761 1.99246i
\(408\) 78450.1 309924.i 0.471273 1.86181i
\(409\) −85518.7 −0.511228 −0.255614 0.966779i \(-0.582278\pi\)
−0.255614 + 0.966779i \(0.582278\pi\)
\(410\) 4027.45 + 182373.i 0.0239587 + 1.08491i
\(411\) 105551. 145279.i 0.624856 0.860040i
\(412\) 255862. + 70811.7i 1.50734 + 0.417168i
\(413\) −8895.23 27376.7i −0.0521503 0.160502i
\(414\) 414222. 9147.49i 2.41675 0.0533705i
\(415\) 256705. 83408.4i 1.49052 0.484299i
\(416\) −21749.1 4493.96i −0.125677 0.0259682i
\(417\) −358062. 260148.i −2.05914 1.49606i
\(418\) 102777. + 135085.i 0.588226 + 0.773134i
\(419\) −179295. 58256.6i −1.02127 0.331831i −0.249937 0.968262i \(-0.580410\pi\)
−0.771334 + 0.636431i \(0.780410\pi\)
\(420\) −21770.4 + 78662.5i −0.123415 + 0.445933i
\(421\) −69854.2 + 214989.i −0.394120 + 1.21298i 0.535525 + 0.844519i \(0.320114\pi\)
−0.929645 + 0.368456i \(0.879886\pi\)
\(422\) 14131.9 46999.9i 0.0793550 0.263920i
\(423\) −161177. 221841.i −0.900786 1.23983i
\(424\) −2670.04 40249.8i −0.0148521 0.223888i
\(425\) 37712.1 + 27399.4i 0.208787 + 0.151692i
\(426\) −443706. + 155080.i −2.44499 + 0.854550i
\(427\) −18689.1 25723.3i −0.102502 0.141082i
\(428\) 151809. 56850.1i 0.828723 0.310344i
\(429\) 61317.4 0.333173
\(430\) 229713. 5072.87i 1.24236 0.0274358i
\(431\) 18329.0 + 5955.44i 0.0986696 + 0.0320597i 0.357936 0.933746i \(-0.383481\pi\)
−0.259266 + 0.965806i \(0.583481\pi\)
\(432\) −164325. + 274137.i −0.880514 + 1.46892i
\(433\) −16712.0 −0.0891359 −0.0445679 0.999006i \(-0.514191\pi\)
−0.0445679 + 0.999006i \(0.514191\pi\)
\(434\) 27533.0 + 36096.5i 0.146175 + 0.191640i
\(435\) 536525.i 2.83538i
\(436\) 161494. 128597.i 0.849541 0.676486i
\(437\) 46377.2 142734.i 0.242852 0.747421i
\(438\) 96291.3 2126.45i 0.501925 0.0110843i
\(439\) 71036.1i 0.368595i −0.982870 0.184298i \(-0.940999\pi\)
0.982870 0.184298i \(-0.0590011\pi\)
\(440\) −79177.6 + 312798.i −0.408975 + 1.61569i
\(441\) 294969. 214308.i 1.51670 1.10195i
\(442\) −26285.1 + 9186.92i −0.134544 + 0.0470246i
\(443\) 68270.8 93966.6i 0.347878 0.478813i −0.598843 0.800866i \(-0.704373\pi\)
0.946722 + 0.322053i \(0.104373\pi\)
\(444\) −348357. 437471.i −1.76709 2.21913i
\(445\) −206794. + 150245.i −1.04428 + 0.758715i
\(446\) −67267.5 + 223719.i −0.338170 + 1.12469i
\(447\) −228767. 74330.9i −1.14493 0.372010i
\(448\) 43629.3 20894.8i 0.217381 0.104107i
\(449\) 102823. 316456.i 0.510032 1.56972i −0.282112 0.959381i \(-0.591035\pi\)
0.792144 0.610335i \(-0.208965\pi\)
\(450\) −56710.3 74537.1i −0.280051 0.368085i
\(451\) −175458. + 241498.i −0.862622 + 1.18730i
\(452\) −22630.6 + 1000.02i −0.110769 + 0.00489474i
\(453\) 10249.2 + 31543.9i 0.0499453 + 0.153716i
\(454\) −275650. + 6087.32i −1.33735 + 0.0295334i
\(455\) 6760.76 2196.70i 0.0326567 0.0106108i
\(456\) 148922. + 178771.i 0.716190 + 0.859742i
\(457\) 54891.7 + 39881.2i 0.262830 + 0.190957i 0.711394 0.702794i \(-0.248064\pi\)
−0.448564 + 0.893751i \(0.648064\pi\)
\(458\) −1751.59 79316.6i −0.00835029 0.378123i
\(459\) 400722.i 1.90203i
\(460\) 267174. 100053.i 1.26264 0.472838i
\(461\) 251912. 183024.i 1.18535 0.861206i 0.192584 0.981281i \(-0.438313\pi\)
0.992765 + 0.120074i \(0.0383132\pi\)
\(462\) −106294. + 80872.0i −0.497995 + 0.378891i
\(463\) 65773.1 21371.0i 0.306822 0.0996925i −0.151559 0.988448i \(-0.548429\pi\)
0.458381 + 0.888756i \(0.348429\pi\)
\(464\) −239770. + 208873.i −1.11368 + 0.970167i
\(465\) −415087. + 505.891i −1.91970 + 0.00233965i
\(466\) 103687. 149548.i 0.477475 0.688664i
\(467\) −199136. + 64703.1i −0.913094 + 0.296682i −0.727631 0.685969i \(-0.759379\pi\)
−0.185463 + 0.982651i \(0.559379\pi\)
\(468\) 55890.1 2469.71i 0.255178 0.0112760i
\(469\) −28204.2 + 20491.5i −0.128224 + 0.0931599i
\(470\) −155168. 107583.i −0.702434 0.487022i
\(471\) 295817.i 1.33346i
\(472\) −57917.7 144839.i −0.259973 0.650134i
\(473\) 304184. + 221003.i 1.35961 + 0.987815i
\(474\) 60432.1 21121.7i 0.268975 0.0940096i
\(475\) −32265.2 + 10483.6i −0.143004 + 0.0464647i
\(476\) 33448.6 50593.1i 0.147626 0.223294i
\(477\) 31400.6 + 96641.1i 0.138007 + 0.424742i
\(478\) 150494. 114501.i 0.658665 0.501134i
\(479\) −4277.99 + 5888.14i −0.0186453 + 0.0256630i −0.818238 0.574880i \(-0.805049\pi\)
0.799593 + 0.600543i \(0.205049\pi\)
\(480\) −89500.3 + 433149.i −0.388456 + 1.87999i
\(481\) −15051.0 + 46322.2i −0.0650541 + 0.200216i
\(482\) −342998. + 119882.i −1.47638 + 0.516010i
\(483\) 112313. + 36492.7i 0.481432 + 0.156427i
\(484\) −229794. + 182984.i −0.980951 + 0.781127i
\(485\) 167857. 121955.i 0.713601 0.518461i
\(486\) −2254.54 + 7498.17i −0.00954521 + 0.0317456i
\(487\) 11409.8 15704.2i 0.0481081 0.0662152i −0.784285 0.620400i \(-0.786970\pi\)
0.832393 + 0.554185i \(0.186970\pi\)
\(488\) −110281. 132386.i −0.463087 0.555908i
\(489\) 314164. 228254.i 1.31383 0.954553i
\(490\) 143047. 206317.i 0.595781 0.859298i
\(491\) 411544.i 1.70708i 0.521031 + 0.853538i \(0.325548\pi\)
−0.521031 + 0.853538i \(0.674452\pi\)
\(492\) −225665. + 341334.i −0.932255 + 1.41010i
\(493\) −123200. + 379172.i −0.506895 + 1.56006i
\(494\) 5835.12 19406.5i 0.0239109 0.0795231i
\(495\) 812809.i 3.31725i
\(496\) 161822. + 185303.i 0.657772 + 0.753217i
\(497\) −89169.3 −0.360996
\(498\) 579812. + 174337.i 2.33791 + 0.702960i
\(499\) 343414. + 111582.i 1.37917 + 0.448119i 0.902396 0.430908i \(-0.141806\pi\)
0.476773 + 0.879027i \(0.341806\pi\)
\(500\) 177713. + 117491.i 0.710852 + 0.469964i
\(501\) 93766.4 0.373570
\(502\) 9944.44 + 6894.83i 0.0394614 + 0.0273600i
\(503\) −49085.8 67560.8i −0.194008 0.267029i 0.700920 0.713240i \(-0.252773\pi\)
−0.894928 + 0.446211i \(0.852773\pi\)
\(504\) −93628.4 + 77995.2i −0.368593 + 0.307048i
\(505\) 155857. + 113236.i 0.611142 + 0.444021i
\(506\) 447080. + 134427.i 1.74616 + 0.525033i
\(507\) 256972. + 353691.i 0.999699 + 1.37597i
\(508\) 77317.5 + 97096.4i 0.299606 + 0.376249i
\(509\) −99949.6 + 307613.i −0.385785 + 1.18732i 0.550124 + 0.835083i \(0.314581\pi\)
−0.935909 + 0.352242i \(0.885419\pi\)
\(510\) 182964. + 523486.i 0.703438 + 2.01263i
\(511\) 17377.7 + 5646.36i 0.0665504 + 0.0216235i
\(512\) 228415. 128631.i 0.871336 0.490688i
\(513\) −235942. 171422.i −0.896543 0.651377i
\(514\) 95882.4 + 126023.i 0.362922 + 0.477005i
\(515\) −437955. + 142300.i −1.65126 + 0.536526i
\(516\) 429935. + 284242.i 1.61474 + 1.06755i
\(517\) −95478.7 293853.i −0.357211 1.09938i
\(518\) −35003.7 100151.i −0.130453 0.373245i
\(519\) −473450. + 651648.i −1.75768 + 2.41924i
\(520\) 35768.5 14303.0i 0.132280 0.0528956i
\(521\) 234443. 0.863698 0.431849 0.901946i \(-0.357861\pi\)
0.431849 + 0.901946i \(0.357861\pi\)
\(522\) 456415. 658289.i 1.67502 2.41588i
\(523\) 111042. + 152836.i 0.405961 + 0.558757i 0.962227 0.272247i \(-0.0877668\pi\)
−0.556267 + 0.831004i \(0.687767\pi\)
\(524\) −21197.2 479698.i −0.0771998 1.74705i
\(525\) −8249.20 25388.4i −0.0299291 0.0921122i
\(526\) −69704.1 48328.3i −0.251934 0.174675i
\(527\) 293466. + 94957.5i 1.05666 + 0.341907i
\(528\) −545740. + 475414.i −1.95757 + 1.70531i
\(529\) −41081.1 126435.i −0.146802 0.451809i
\(530\) 42366.7 + 55684.6i 0.150825 + 0.198236i
\(531\) 230969. + 317902.i 0.819153 + 1.12747i
\(532\) 15480.2 + 41337.2i 0.0546956 + 0.146056i
\(533\) 35638.3 0.125448
\(534\) −573229. + 12658.9i −2.01023 + 0.0443929i
\(535\) −165274. + 227480.i −0.577427 + 0.794760i
\(536\) −145154. + 120918.i −0.505243 + 0.420881i
\(537\) 221117. + 680529.i 0.766786 + 2.35992i
\(538\) −3924.88 177729.i −0.0135601 0.614036i
\(539\) 390720. 126953.i 1.34489 0.436982i
\(540\) −24474.0 553853.i −0.0839300 1.89936i
\(541\) −401507. 291712.i −1.37183 0.996690i −0.997592 0.0693553i \(-0.977906\pi\)
−0.374234 0.927334i \(-0.622094\pi\)
\(542\) −282002. + 214556.i −0.959960 + 0.730369i
\(543\) −168470. 54739.2i −0.571377 0.185652i
\(544\) 162714. 285563.i 0.549829 0.964947i
\(545\) −110654. + 340559.i −0.372542 + 1.14657i
\(546\) 15270.3 + 4591.46i 0.0512228 + 0.0154016i
\(547\) −137767. 189620.i −0.460437 0.633737i 0.514162 0.857693i \(-0.328103\pi\)
−0.974599 + 0.223956i \(0.928103\pi\)
\(548\) 144418. 115000.i 0.480907 0.382944i
\(549\) 351146. + 255122.i 1.16504 + 0.846455i
\(550\) −34819.3 99622.8i −0.115105 0.329331i
\(551\) −170551. 234743.i −0.561760 0.773196i
\(552\) 620383. + 157036.i 2.03602 + 0.515371i
\(553\) 12144.7 0.0397134
\(554\) 650.447 + 29453.9i 0.00211930 + 0.0959674i
\(555\) 922539. + 299751.i 2.99501 + 0.973139i
\(556\) −283435. 355941.i −0.916861 1.15141i
\(557\) 203756. 0.656750 0.328375 0.944548i \(-0.393499\pi\)
0.328375 + 0.944548i \(0.393499\pi\)
\(558\) −509722. 352489.i −1.63706 1.13208i
\(559\) 44889.0i 0.143654i
\(560\) −43140.6 + 71969.6i −0.137566 + 0.229495i
\(561\) −280415. + 863030.i −0.890997 + 2.74221i
\(562\) −3660.95 165777.i −0.0115910 0.524871i
\(563\) 171014.i 0.539528i 0.962926 + 0.269764i \(0.0869457\pi\)
−0.962926 + 0.269764i \(0.913054\pi\)
\(564\) −148534. 396636.i −0.466948 1.24691i
\(565\) 31788.4 23095.6i 0.0995800 0.0723491i
\(566\) −157969. 451971.i −0.493105 1.41084i
\(567\) 44233.9 60882.7i 0.137591 0.189377i
\(568\) −482152. + 31984.5i −1.49447 + 0.0991386i
\(569\) −259571. + 188589.i −0.801736 + 0.582495i −0.911423 0.411471i \(-0.865015\pi\)
0.109687 + 0.993966i \(0.465015\pi\)
\(570\) −386494. 116211.i −1.18958 0.357681i
\(571\) 52453.0 + 17043.0i 0.160879 + 0.0522726i 0.388349 0.921512i \(-0.373046\pi\)
−0.227470 + 0.973785i \(0.573046\pi\)
\(572\) 60753.7 + 16814.0i 0.185687 + 0.0513902i
\(573\) 56748.9 174655.i 0.172841 0.531951i
\(574\) −61779.1 + 47003.6i −0.187507 + 0.142662i
\(575\) −54846.1 + 75489.2i −0.165886 + 0.228323i
\(576\) −478287. + 455316.i −1.44160 + 1.37236i
\(577\) 339.529 + 1044.96i 0.00101982 + 0.00313869i 0.951565 0.307447i \(-0.0994748\pi\)
−0.950545 + 0.310586i \(0.899475\pi\)
\(578\) −1721.81 77967.9i −0.00515381 0.233378i
\(579\) −1.05068e6 + 341386.i −3.13409 + 1.01833i
\(580\) 147122. 531593.i 0.437343 1.58024i
\(581\) 92924.9 + 67513.9i 0.275283 + 0.200005i
\(582\) 465295. 10275.4i 1.37367 0.0303355i
\(583\) 114497.i 0.336867i
\(584\) 95989.2 + 24297.4i 0.281447 + 0.0712418i
\(585\) −78506.9 + 57038.6i −0.229401 + 0.166670i
\(586\) −22656.1 29778.0i −0.0659767 0.0867163i
\(587\) 597595. 194170.i 1.73433 0.563517i 0.740262 0.672318i \(-0.234701\pi\)
0.994063 + 0.108802i \(0.0347013\pi\)
\(588\) 527384. 197498.i 1.52536 0.571225i
\(589\) −181450. + 132169.i −0.523030 + 0.380979i
\(590\) 222358. + 154169.i 0.638776 + 0.442886i
\(591\) −266415. + 86563.4i −0.762752 + 0.247833i
\(592\) −225194. 528974.i −0.642559 1.50935i
\(593\) 66833.1 48557.1i 0.190056 0.138084i −0.488688 0.872459i \(-0.662524\pi\)
0.678744 + 0.734375i \(0.262524\pi\)
\(594\) 516908. 745539.i 1.46501 2.11299i
\(595\) 105202.i 0.297161i
\(596\) −206281. 136378.i −0.580721 0.383931i
\(597\) 770403. + 559731.i 2.16157 + 1.57047i
\(598\) −18389.7 52615.5i −0.0514248 0.147133i
\(599\) −402470. + 130770.i −1.12171 + 0.364465i −0.810419 0.585851i \(-0.800760\pi\)
−0.311288 + 0.950316i \(0.600760\pi\)
\(600\) −53711.4 134320.i −0.149198 0.373112i
\(601\) 48243.0 + 148477.i 0.133563 + 0.411064i 0.995364 0.0961826i \(-0.0306633\pi\)
−0.861801 + 0.507247i \(0.830663\pi\)
\(602\) 59204.5 + 77815.3i 0.163366 + 0.214720i
\(603\) 279728. 385012.i 0.769309 1.05886i
\(604\) 1505.26 + 34064.4i 0.00412607 + 0.0933741i
\(605\) 157452. 484589.i 0.430168 1.32392i
\(606\) 142579. + 407938.i 0.388249 + 1.11083i
\(607\) 186636. + 60641.8i 0.506546 + 0.164587i 0.551131 0.834419i \(-0.314197\pi\)
−0.0445849 + 0.999006i \(0.514197\pi\)
\(608\) 98531.1 + 217964.i 0.266542 + 0.589628i
\(609\) 184712. 134201.i 0.498035 0.361843i
\(610\) 286212. + 86057.9i 0.769180 + 0.231276i
\(611\) −21682.2 + 29843.0i −0.0580793 + 0.0799394i
\(612\) −220835. + 797937.i −0.589610 + 2.13042i
\(613\) 10679.6 7759.18i 0.0284206 0.0206488i −0.573484 0.819217i \(-0.694409\pi\)
0.601905 + 0.798568i \(0.294409\pi\)
\(614\) −28386.1 19681.1i −0.0752955 0.0522050i
\(615\) 709762.i 1.87656i
\(616\) −127493. + 50981.3i −0.335989 + 0.134354i
\(617\) 156174. 480655.i 0.410241 1.26259i −0.506197 0.862418i \(-0.668949\pi\)
0.916439 0.400175i \(-0.131051\pi\)
\(618\) −989196. 297430.i −2.59003 0.778768i
\(619\) 425683.i 1.11098i −0.831524 0.555489i \(-0.812531\pi\)
0.831524 0.555489i \(-0.187469\pi\)
\(620\) −411410. 113321.i −1.07026 0.294800i
\(621\) −802135. −2.08000
\(622\) 21095.2 70158.5i 0.0545258 0.181343i
\(623\) −103451. 33613.1i −0.266537 0.0866030i
\(624\) 84215.9 + 19349.4i 0.216284 + 0.0496933i
\(625\) −460303. −1.17838
\(626\) −356478. + 514149.i −0.909669 + 1.31202i
\(627\) −388190. 534297.i −0.987436 1.35909i
\(628\) 81116.8 293097.i 0.205680 0.743177i
\(629\) −583144. 423679.i −1.47392 1.07087i
\(630\) 60863.3 202420.i 0.153347 0.510002i
\(631\) −37556.1 51691.6i −0.0943240 0.129826i 0.759247 0.650803i \(-0.225568\pi\)
−0.853571 + 0.520977i \(0.825568\pi\)
\(632\) 65668.4 4356.24i 0.164408 0.0109063i
\(633\) −59009.0 + 181611.i −0.147269 + 0.453247i
\(634\) 401025. 140163.i 0.997684 0.348702i
\(635\) −204757. 66529.5i −0.507798 0.164993i
\(636\) 6928.65 + 156797.i 0.0171291 + 0.387636i
\(637\) −39680.6 28829.6i −0.0977911 0.0710494i
\(638\) 718323. 546524.i 1.76473 1.34267i
\(639\) 1.15766e6 376148.i 2.83518 0.921206i
\(640\) −207453. + 404625.i −0.506476 + 0.987854i
\(641\) −232002. 714030.i −0.564646 1.73780i −0.669001 0.743262i \(-0.733278\pi\)
0.104355 0.994540i \(-0.466722\pi\)
\(642\) −595405. + 208101.i −1.44458 + 0.504898i
\(643\) −192621. + 265120.i −0.465887 + 0.641239i −0.975717 0.219037i \(-0.929709\pi\)
0.509829 + 0.860276i \(0.329709\pi\)
\(644\) 101274. + 66954.9i 0.244188 + 0.161440i
\(645\) −893997. −2.14890
\(646\) 246458. + 170878.i 0.590578 + 0.409468i
\(647\) 73882.8 + 101691.i 0.176496 + 0.242926i 0.888095 0.459660i \(-0.152029\pi\)
−0.711599 + 0.702586i \(0.752029\pi\)
\(648\) 217341. 345068.i 0.517597 0.821779i
\(649\) 136823. + 421097.i 0.324839 + 0.999753i
\(650\) −7178.84 + 10354.1i −0.0169913 + 0.0245067i
\(651\) −104000. 142777.i −0.245398 0.336897i
\(652\) 373866. 140007.i 0.879470 0.329348i
\(653\) −32007.2 98508.0i −0.0750622 0.231018i 0.906485 0.422238i \(-0.138755\pi\)
−0.981547 + 0.191221i \(0.938755\pi\)
\(654\) −639244. + 486358.i −1.49455 + 1.13711i
\(655\) 489555. + 673815.i 1.14109 + 1.57057i
\(656\) −317189. + 276315.i −0.737073 + 0.642092i
\(657\) −249429. −0.577851
\(658\) −1773.97 80329.9i −0.00409726 0.185535i
\(659\) 324012. 445965.i 0.746089 1.02690i −0.252156 0.967687i \(-0.581140\pi\)
0.998245 0.0592168i \(-0.0188603\pi\)
\(660\) 334864. 1.20995e6i 0.768741 2.77767i
\(661\) 32657.3 + 100509.i 0.0747443 + 0.230039i 0.981448 0.191729i \(-0.0614095\pi\)
−0.906704 + 0.421768i \(0.861410\pi\)
\(662\) 255269. 5637.23i 0.582480 0.0128632i
\(663\) 103036. 33478.3i 0.234401 0.0761616i
\(664\) 526676. + 331726.i 1.19456 + 0.752391i
\(665\) −61942.4 45003.8i −0.140070 0.101767i
\(666\) 876915. + 1.15257e6i 1.97701 + 2.59848i
\(667\) −758998. 246613.i −1.70604 0.554326i
\(668\) 92904.4 + 25712.0i 0.208201 + 0.0576213i
\(669\) 280882. 864467.i 0.627584 1.93151i
\(670\) 94357.7 313816.i 0.210198 0.699077i
\(671\) 287467. + 395665.i 0.638475 + 0.878785i
\(672\) −171509. + 77530.8i −0.379794 + 0.171686i
\(673\) −368333. 267610.i −0.813225 0.590842i 0.101539 0.994832i \(-0.467623\pi\)
−0.914764 + 0.403989i \(0.867623\pi\)
\(674\) 424506. 148369.i 0.934466 0.326606i
\(675\) 106579. + 146694.i 0.233919 + 0.321961i
\(676\) 157622. + 420904.i 0.344925 + 0.921065i
\(677\) −395475. −0.862863 −0.431432 0.902146i \(-0.641991\pi\)
−0.431432 + 0.902146i \(0.641991\pi\)
\(678\) 88116.9 1945.93i 0.191690 0.00423320i
\(679\) 83971.9 + 27284.1i 0.182135 + 0.0591794i
\(680\) 37735.4 + 568845.i 0.0816077 + 1.23020i
\(681\) 1.07277e6 2.31320
\(682\) −423500. 555221.i −0.910510 1.19371i
\(683\) 234403.i 0.502483i 0.967924 + 0.251241i \(0.0808388\pi\)
−0.967924 + 0.251241i \(0.919161\pi\)
\(684\) −375351. 471371.i −0.802278 1.00751i
\(685\) −98954.0 + 304549.i −0.210888 + 0.649047i
\(686\) 220208. 4862.97i 0.467934 0.0103336i
\(687\) 308685.i 0.654036i
\(688\) 348040. + 399523.i 0.735279 + 0.844044i
\(689\) 11059.0 8034.81i 0.0232957 0.0169253i
\(690\) −1.04788e6 + 366244.i −2.20096 + 0.769259i
\(691\) 155137. 213528.i 0.324907 0.447197i −0.615050 0.788488i \(-0.710864\pi\)
0.939958 + 0.341291i \(0.110864\pi\)
\(692\) −647788. + 515831.i −1.35276 + 1.07720i
\(693\) 279829. 203308.i 0.582675 0.423338i
\(694\) −203037. + 675262.i −0.421556 + 1.40202i
\(695\) 750609. + 243888.i 1.55398 + 0.504917i
\(696\) 950627. 791899.i 1.96242 1.63475i
\(697\) −162980. + 501601.i −0.335482 + 1.03251i
\(698\) −309747. 407116.i −0.635765 0.835616i
\(699\) −416177. + 572819.i −0.851773 + 1.17237i
\(700\) −1211.52 27417.1i −0.00247250 0.0559532i
\(701\) 74431.5 + 229077.i 0.151468 + 0.466170i 0.997786 0.0665077i \(-0.0211857\pi\)
−0.846318 + 0.532678i \(0.821186\pi\)
\(702\) −108283. + 2391.28i −0.219729 + 0.00485239i
\(703\) 498919. 162109.i 1.00953 0.328016i
\(704\) −671087. + 321395.i −1.35405 + 0.648475i
\(705\) 594346. + 431817.i 1.19581 + 0.868804i
\(706\) 1984.72 + 89873.4i 0.00398190 + 0.180311i
\(707\) 81981.2i 0.164012i
\(708\) 212852. + 568387.i 0.424631 + 1.13391i
\(709\) −110288. + 80128.9i −0.219399 + 0.159403i −0.692056 0.721844i \(-0.743295\pi\)
0.472657 + 0.881247i \(0.343295\pi\)
\(710\) 667046. 507511.i 1.32324 1.00677i
\(711\) −157672. + 51230.8i −0.311900 + 0.101343i
\(712\) −571430. 144644.i −1.12721 0.285326i
\(713\) −190079. + 587438.i −0.373899 + 1.15553i
\(714\) −134458. + 193929.i −0.263748 + 0.380406i
\(715\) −103991. + 33788.8i −0.203416 + 0.0660938i
\(716\) 32474.5 + 734906.i 0.0633455 + 1.43353i
\(717\) −595245. + 432471.i −1.15786 + 0.841237i
\(718\) −186238. 129125.i −0.361260 0.250474i
\(719\) 541790.i 1.04803i −0.851710 0.524014i \(-0.824434\pi\)
0.851710 0.524014i \(-0.175566\pi\)
\(720\) 256491. 1.11635e6i 0.494774 2.15345i
\(721\) −158536. 115183.i −0.304970 0.221574i
\(722\) 286051. 99978.0i 0.548743 0.191792i
\(723\) 1.34453e6 436864.i 2.57213 0.835736i
\(724\) −151911. 100433.i −0.289809 0.191601i
\(725\) 55747.2 + 171572.i 0.106059 + 0.326416i
\(726\) 909594. 692050.i 1.72574 1.31300i
\(727\) 171573. 236150.i 0.324623 0.446806i −0.615248 0.788333i \(-0.710944\pi\)
0.939872 + 0.341528i \(0.110944\pi\)
\(728\) 13870.9 + 8736.58i 0.0261723 + 0.0164846i
\(729\) 168909. 519847.i 0.317831 0.978184i
\(730\) −162133. + 56667.4i −0.304247 + 0.106338i
\(731\) 631804. + 205286.i 1.18235 + 0.384170i
\(732\) 417612. + 524443.i 0.779383 + 0.978760i
\(733\) −395401. + 287276.i −0.735918 + 0.534676i −0.891430 0.453158i \(-0.850297\pi\)
0.155512 + 0.987834i \(0.450297\pi\)
\(734\) −182254. + 606143.i −0.338287 + 1.12508i
\(735\) −574163. + 790267.i −1.06282 + 1.46285i
\(736\) 571618. + 325709.i 1.05524 + 0.601276i
\(737\) 433825. 315192.i 0.798692 0.580284i
\(738\) 603785. 870842.i 1.10859 1.59892i
\(739\) 529726.i 0.969980i 0.874520 + 0.484990i \(0.161177\pi\)
−0.874520 + 0.484990i \(0.838823\pi\)
\(740\) 831862. + 549968.i 1.51911 + 1.00432i
\(741\) −24365.1 + 74988.2i −0.0443744 + 0.136570i
\(742\) −8573.60 + 28514.1i −0.0155724 + 0.0517908i
\(743\) 146434.i 0.265256i 0.991166 + 0.132628i \(0.0423415\pi\)
−0.991166 + 0.132628i \(0.957658\pi\)
\(744\) −613556. 734714.i −1.10843 1.32731i
\(745\) 428937. 0.772824
\(746\) −925740. 278350.i −1.66346 0.500166i
\(747\) −1.49122e6 484526.i −2.67239 0.868313i
\(748\) −514492. + 778203.i −0.919550 + 1.39088i
\(749\) −119656. −0.213289
\(750\) −681194. 472295.i −1.21101 0.839636i
\(751\) −123399. 169845.i −0.218793 0.301143i 0.685485 0.728087i \(-0.259590\pi\)
−0.904278 + 0.426944i \(0.859590\pi\)
\(752\) −38405.9 433720.i −0.0679145 0.766961i
\(753\) −38090.6 27674.5i −0.0671782 0.0488078i
\(754\) −103195. 31028.6i −0.181517 0.0545782i
\(755\) −34764.3 47849.0i −0.0609874 0.0839419i
\(756\) 184556. 146961.i 0.322911 0.257133i
\(757\) 253596. 780487.i 0.442537 1.36199i −0.442625 0.896707i \(-0.645953\pi\)
0.885162 0.465283i \(-0.154047\pi\)
\(758\) −337009. 964230.i −0.586548 1.67819i
\(759\) −1.72755e6 561315.i −2.99880 0.974368i
\(760\) −351075. 221124.i −0.607816 0.382833i
\(761\) 60016.9 + 43604.8i 0.103634 + 0.0752949i 0.638396 0.769708i \(-0.279598\pi\)
−0.534761 + 0.845003i \(0.679598\pi\)
\(762\) −292417. 384337.i −0.503608 0.661916i
\(763\) −144924. + 47088.5i −0.248937 + 0.0808846i
\(764\) 104120. 157488.i 0.178380 0.269812i
\(765\) −443780. 1.36582e6i −0.758307 2.33383i
\(766\) 121857. + 348650.i 0.207679 + 0.594200i
\(767\) 31071.0 42765.6i 0.0528160 0.0726949i
\(768\) −899564. + 480740.i −1.52514 + 0.815057i
\(769\) 455.371 0.000770040 0.000385020 1.00000i \(-0.499877\pi\)
0.000385020 1.00000i \(0.499877\pi\)
\(770\) 135705. 195728.i 0.228883 0.330119i
\(771\) −362148. 498454.i −0.609224 0.838525i
\(772\) −1.13463e6 + 50137.7i −1.90379 + 0.0841260i
\(773\) −156291. 481015.i −0.261562 0.805006i −0.992465 0.122525i \(-0.960901\pi\)
0.730903 0.682481i \(-0.239099\pi\)
\(774\) −1.09689e6 760512.i −1.83097 1.26948i
\(775\) 132686. 43291.1i 0.220913 0.0720767i
\(776\) 463836. + 117409.i 0.770266 + 0.194975i
\(777\) 127558. + 392583.i 0.211283 + 0.650263i
\(778\) −636435. 836497.i −1.05146 1.38199i
\(779\) −225619. 310539.i −0.371793 0.511730i
\(780\) −140365. + 52564.5i −0.230711 + 0.0863980i
\(781\) 1.37157e6 2.24861
\(782\) 824652. 18211.2i 1.34852 0.0297801i
\(783\) −911548. + 1.25464e6i −1.48681 + 2.04642i
\(784\) 576692. 51066.2i 0.938236 0.0830809i
\(785\) 163009. + 501690.i 0.264528 + 0.814134i
\(786\) 41247.7 + 1.86780e6i 0.0667658 + 3.02333i
\(787\) 362754. 117866.i 0.585684 0.190300i −0.00116145 0.999999i \(-0.500370\pi\)
0.586845 + 0.809699i \(0.300370\pi\)
\(788\) −287702. + 12713.2i −0.463330 + 0.0204739i
\(789\) 266991. + 193980.i 0.428887 + 0.311604i
\(790\) −90850.7 + 69122.3i −0.145571 + 0.110755i
\(791\) 15902.5 + 5167.02i 0.0254162 + 0.00825824i
\(792\) 1.44015e6 1.19969e6i 2.29593 1.91257i
\(793\) 18043.2 55531.3i 0.0286924 0.0883062i
\(794\) 1.08248e6 + 325478.i 1.71703 + 0.516275i
\(795\) −160019. 220247.i −0.253185 0.348479i
\(796\) 609835. + 765840.i 0.962468 + 1.20868i
\(797\) −967168. 702688.i −1.52260 1.10623i −0.960181 0.279377i \(-0.909872\pi\)
−0.562416 0.826855i \(-0.690128\pi\)
\(798\) −56665.4 162128.i −0.0889841 0.254596i
\(799\) −320878. 441651.i −0.502628 0.691808i
\(800\) −16385.2 147814.i −0.0256019 0.230959i
\(801\) 1.48487e6 2.31431
\(802\) 23221.5 + 1.05153e6i 0.0361029 + 1.63483i
\(803\) −267297. 86849.9i −0.414536 0.134691i
\(804\) 575023. 457889.i 0.889556 0.708350i
\(805\) −210586. −0.324966
\(806\) −23908.2 + 79867.1i −0.0368025 + 0.122941i
\(807\) 691686.i 1.06209i
\(808\) 29406.1 + 443285.i 0.0450417 + 0.678985i
\(809\) 126725. 390019.i 0.193627 0.595921i −0.806363 0.591420i \(-0.798567\pi\)
0.999990 0.00450070i \(-0.00143262\pi\)
\(810\) 15617.5 + 707202.i 0.0238036 + 1.07789i
\(811\) 135474.i 0.205975i −0.994683 0.102987i \(-0.967160\pi\)
0.994683 0.102987i \(-0.0328401\pi\)
\(812\) 219813. 82316.7i 0.333382 0.124846i
\(813\) 1.11539e6 810379.i 1.68751 1.22605i
\(814\) 538412. + 1.54047e6i 0.812580 + 2.32491i
\(815\) −407028. + 560226.i −0.612786 + 0.843428i
\(816\) −657473. + 1.09683e6i −0.987410 + 1.64725i
\(817\) −391146. + 284185.i −0.585997 + 0.425752i
\(818\) 327587. + 98498.4i 0.489576 + 0.147205i
\(819\) −39273.8 12760.8i −0.0585511 0.0190244i
\(820\) 194626. 703237.i 0.289450 1.04586i
\(821\) −211278. + 650247.i −0.313450 + 0.964699i 0.662938 + 0.748674i \(0.269309\pi\)
−0.976388 + 0.216025i \(0.930691\pi\)
\(822\) −571652. + 434932.i −0.846035 + 0.643691i
\(823\) 660412. 908978.i 0.975023 1.34200i 0.0355553 0.999368i \(-0.488680\pi\)
0.939468 0.342637i \(-0.111320\pi\)
\(824\) −898543. 565946.i −1.32338 0.833529i
\(825\) 126886. + 390514.i 0.186425 + 0.573758i
\(826\) 2542.13 + 115114.i 0.00372595 + 0.168721i
\(827\) −644597. + 209442.i −0.942492 + 0.306234i −0.739661 0.672980i \(-0.765014\pi\)
−0.202831 + 0.979214i \(0.565014\pi\)
\(828\) −1.59725e6 442051.i −2.32977 0.644780i
\(829\) 917751. + 666785.i 1.33541 + 0.970235i 0.999599 + 0.0283068i \(0.00901155\pi\)
0.335815 + 0.941928i \(0.390988\pi\)
\(830\) −1.07940e6 + 23836.9i −1.56684 + 0.0346014i
\(831\) 114629.i 0.165994i
\(832\) 78135.9 + 42264.6i 0.112877 + 0.0610563i
\(833\) 587238. 426653.i 0.846299 0.614872i
\(834\) 1.07196e6 + 1.40893e6i 1.54115 + 2.02561i
\(835\) −159023. + 51669.7i −0.228080 + 0.0741077i
\(836\) −238110. 635832.i −0.340694 0.909766i
\(837\) 971520. + 704043.i 1.38676 + 1.00496i
\(838\) 619708. + 429665.i 0.882469 + 0.611846i
\(839\) 470515. 152880.i 0.668420 0.217183i 0.0449015 0.998991i \(-0.485703\pi\)
0.623519 + 0.781809i \(0.285703\pi\)
\(840\) 173995. 276249.i 0.246592 0.391509i
\(841\) −676058. + 491185.i −0.955855 + 0.694469i
\(842\) 515202. 743078.i 0.726697 1.04812i
\(843\) 645172.i 0.907864i
\(844\) −108267. + 163760.i −0.151988 + 0.229892i
\(845\) −630711. 458238.i −0.883318 0.641768i
\(846\) 361891. + 1.03542e6i 0.505635 + 1.44669i
\(847\) 206215. 67003.2i 0.287444 0.0933962i
\(848\) −36130.9 + 157256.i −0.0502443 + 0.218683i
\(849\) 575659. + 1.77170e6i 0.798638 + 2.45795i
\(850\) −112901. 148392.i −0.156265 0.205387i
\(851\) 848089. 1.16729e6i 1.17107 1.61184i
\(852\) 1.87827e6 82998.3i 2.58750 0.114338i
\(853\) −108469. + 333833.i −0.149076 + 0.458809i −0.997513 0.0704883i \(-0.977544\pi\)
0.848437 + 0.529297i \(0.177544\pi\)
\(854\) 41962.7 + 120061.i 0.0575370 + 0.164621i
\(855\) 994026. + 322979.i 1.35977 + 0.441816i
\(856\) −646996. + 42919.7i −0.882986 + 0.0585746i
\(857\) 724715. 526536.i 0.986747 0.716913i 0.0275403 0.999621i \(-0.491233\pi\)
0.959206 + 0.282707i \(0.0912325\pi\)
\(858\) −234882. 70624.0i −0.319062 0.0959351i
\(859\) −479943. + 660585.i −0.650434 + 0.895245i −0.999118 0.0419950i \(-0.986629\pi\)
0.348684 + 0.937240i \(0.386629\pi\)
\(860\) −885779. 245146.i −1.19765 0.331457i
\(861\) 244352. 177532.i 0.329618 0.239481i
\(862\) −63351.4 43923.7i −0.0852593 0.0591132i
\(863\) 356357.i 0.478480i −0.970960 0.239240i \(-0.923102\pi\)
0.970960 0.239240i \(-0.0768983\pi\)
\(864\) 945206. 860839.i 1.26619 1.15317i
\(865\) 443858. 1.36606e6i 0.593215 1.82573i
\(866\) 64016.8 + 19248.5i 0.0853607 + 0.0256661i
\(867\) 303435.i 0.403672i
\(868\) −63892.3 169983.i −0.0848026 0.225614i
\(869\) −186805. −0.247371
\(870\) −617957. + 2.05521e6i −0.816431 + 2.71529i
\(871\) −60887.0 19783.4i −0.0802580 0.0260774i
\(872\) −766733. + 306598.i −1.00835 + 0.403215i
\(873\) −1.20528e6 −1.58147
\(874\) −342050. + 493340.i −0.447782 + 0.645838i
\(875\) −92431.0 127220.i −0.120726 0.166165i
\(876\) −371302. 102761.i −0.483859 0.133912i
\(877\) −834353. 606193.i −1.08480 0.788155i −0.106288 0.994335i \(-0.533897\pi\)
−0.978514 + 0.206181i \(0.933897\pi\)
\(878\) −81817.7 + 272110.i −0.106135 + 0.352984i
\(879\) 85572.1 + 117780.i 0.110753 + 0.152438i
\(880\) 663571. 1.10701e6i 0.856883 1.42950i
\(881\) −207537. + 638734.i −0.267389 + 0.822940i 0.723744 + 0.690069i \(0.242420\pi\)
−0.991133 + 0.132871i \(0.957580\pi\)
\(882\) −1.37674e6 + 481186.i −1.76976 + 0.618551i
\(883\) 117811. + 38279.1i 0.151100 + 0.0490953i 0.383590 0.923503i \(-0.374687\pi\)
−0.232491 + 0.972599i \(0.574687\pi\)
\(884\) 111269. 4916.80i 0.142386 0.00629185i
\(885\) −851708. 618802.i −1.08744 0.790069i
\(886\) −369746. + 281315.i −0.471016 + 0.358365i
\(887\) 117221. 38087.6i 0.148991 0.0484101i −0.233572 0.972339i \(-0.575041\pi\)
0.382563 + 0.923929i \(0.375041\pi\)
\(888\) 830542. + 2.07700e6i 1.05326 + 2.63397i
\(889\) −28311.4 87133.4i −0.0358226 0.110251i
\(890\) 965191. 337345.i 1.21852 0.425887i
\(891\) −680387. + 936472.i −0.857039 + 1.17961i
\(892\) 515348. 779498.i 0.647696 0.979682i
\(893\) 397308. 0.498223
\(894\) 790700. + 548220.i 0.989319 + 0.685929i
\(895\) −750007. 1.03230e6i −0.936309 1.28872i
\(896\) −191192. + 29788.1i −0.238152 + 0.0371046i
\(897\) 67014.4 + 206249.i 0.0832881 + 0.256334i
\(898\) −758359. + 1.09379e6i −0.940421 + 1.35637i
\(899\) 702819. + 964872.i 0.869609 + 1.19385i
\(900\) 131384. + 350839.i 0.162202 + 0.433134i
\(901\) 62513.7 + 192397.i 0.0770062 + 0.237001i
\(902\) 950260. 722989.i 1.16796 0.888626i
\(903\) −223615. 307780.i −0.274237 0.377455i
\(904\) 87840.4 + 22234.8i 0.107487 + 0.0272079i
\(905\) 315880. 0.385678
\(906\) −2929.08 132636.i −0.00356841 0.161587i
\(907\) 418426. 575914.i 0.508632 0.700072i −0.475056 0.879956i \(-0.657572\pi\)
0.983688 + 0.179884i \(0.0575721\pi\)
\(908\) 1.06291e6 + 294169.i 1.28921 + 0.356800i
\(909\) −345826. 1.06434e6i −0.418533 1.28811i
\(910\) −28427.8 + 627.786i −0.0343290 + 0.000758105i
\(911\) −453836. + 147460.i −0.546843 + 0.177680i −0.569393 0.822066i \(-0.692822\pi\)
0.0225499 + 0.999746i \(0.492822\pi\)
\(912\) −364553. 856324.i −0.438299 1.02955i
\(913\) −1.42933e6 1.03847e6i −1.71471 1.24581i
\(914\) −164333. 215991.i −0.196713 0.258550i
\(915\) −1.10595e6 359343.i −1.32097 0.429208i
\(916\) −84645.4 + 305847.i −0.100882 + 0.364513i
\(917\) −109525. + 337082.i −0.130249 + 0.400864i
\(918\) 461542. 1.53500e6i 0.547678 1.82147i
\(919\) −27311.6 37591.2i −0.0323382 0.0445097i 0.792542 0.609818i \(-0.208757\pi\)
−0.824880 + 0.565308i \(0.808757\pi\)
\(920\) −1.13867e6 + 75535.9i −1.34531 + 0.0892437i
\(921\) 108729. + 78995.9i 0.128181 + 0.0931291i
\(922\) −1.17577e6 + 410946.i −1.38313 + 0.483418i
\(923\) −96249.1 132475.i −0.112978 0.155501i
\(924\) 500315. 187361.i 0.586003 0.219449i
\(925\) −326159. −0.381194
\(926\) −276564. + 6107.52i −0.322533 + 0.00712267i
\(927\) 2.54412e6 + 826633.i 2.96058 + 0.961952i
\(928\) 1.15904e6 523945.i 1.34586 0.608401i
\(929\) −419398. −0.485954 −0.242977 0.970032i \(-0.578124\pi\)
−0.242977 + 0.970032i \(0.578124\pi\)
\(930\) 1.59061e6 + 476150.i 1.83907 + 0.550526i
\(931\) 528277.i 0.609484i
\(932\) −569426. + 453432.i −0.655549 + 0.522011i
\(933\) −88085.0 + 271098.i −0.101190 + 0.311432i
\(934\) 837331. 18491.2i 0.959850 0.0211969i
\(935\) 1.61818e6i 1.85098i
\(936\) −216937. 54912.5i −0.247617 0.0626786i
\(937\) 306963. 223022.i 0.349628 0.254020i −0.399085 0.916914i \(-0.630672\pi\)
0.748713 + 0.662894i \(0.230672\pi\)
\(938\) 131640. 46009.8i 0.149618 0.0522931i
\(939\) 1.43083e6 1.96937e6i 1.62277 2.23355i
\(940\) 470472. + 590825.i 0.532449 + 0.668657i
\(941\) 579179. 420798.i 0.654084 0.475220i −0.210576 0.977578i \(-0.567534\pi\)
0.864660 + 0.502358i \(0.167534\pi\)
\(942\) −340715. + 1.13315e6i −0.383963 + 1.27699i
\(943\) −1.00407e6 326242.i −1.12912 0.366873i
\(944\) 55036.4 + 621528.i 0.0617599 + 0.697456i
\(945\) −126456. + 389190.i −0.141604 + 0.435811i
\(946\) −910659. 1.19692e6i −1.01759 1.33747i
\(947\) 145096. 199707.i 0.161791 0.222686i −0.720423 0.693535i \(-0.756052\pi\)
0.882214 + 0.470849i \(0.156052\pi\)
\(948\) −255818. + 11304.2i −0.284652 + 0.0125784i
\(949\) 10368.9 + 31912.0i 0.0115133 + 0.0354342i
\(950\) 135670. 2996.06i 0.150326 0.00331974i
\(951\) −1.57199e6 + 510770.i −1.73816 + 0.564761i
\(952\) −186400. + 155276.i −0.205670 + 0.171329i
\(953\) −769211. 558864.i −0.846954 0.615348i 0.0773507 0.997004i \(-0.475354\pi\)
−0.924304 + 0.381656i \(0.875354\pi\)
\(954\) −8973.84 406359.i −0.00986010 0.446491i
\(955\) 327477.i 0.359066i
\(956\) −708362. + 265271.i −0.775067 + 0.290251i
\(957\) −2.84116e6 + 2.06422e6i −3.10221 + 2.25389i
\(958\) 23169.0 17627.8i 0.0252451 0.0192073i
\(959\) −129600. + 42109.5i −0.140918 + 0.0457871i
\(960\) 841730. 1.55613e6i 0.913335 1.68851i
\(961\) 745819. 544652.i 0.807582 0.589755i
\(962\) 111007. 160106.i 0.119950 0.173004i
\(963\) 1.55346e6 504750.i 1.67513 0.544281i
\(964\) 1.45196e6 64160.2i 1.56243 0.0690417i
\(965\) 1.59377e6 1.15794e6i 1.71148 1.24346i
\(966\) −388193. 269148.i −0.416000 0.288427i
\(967\) 936125.i 1.00111i 0.865705 + 0.500554i \(0.166870\pi\)
−0.865705 + 0.500554i \(0.833130\pi\)
\(968\) 1.09100e6 436265.i 1.16433 0.465585i
\(969\) −944017. 685869.i −1.00539 0.730455i
\(970\) −783455. + 273826.i −0.832665 + 0.291026i
\(971\) 360244. 117050.i 0.382084 0.124147i −0.111676 0.993745i \(-0.535622\pi\)
0.493760 + 0.869598i \(0.335622\pi\)
\(972\) 17272.4 26125.7i 0.0182819 0.0276526i
\(973\) 103785. + 319419.i 0.109625 + 0.337392i
\(974\) −61793.8 + 47014.8i −0.0651369 + 0.0495583i
\(975\) 28814.5 39659.7i 0.0303111 0.0417196i
\(976\) 269964. + 634137.i 0.283404 + 0.665707i
\(977\) −417846. + 1.28600e6i −0.437751 + 1.34726i 0.452490 + 0.891769i \(0.350536\pi\)
−0.890241 + 0.455489i \(0.849464\pi\)
\(978\) −1.46633e6 + 512499.i −1.53304 + 0.535816i
\(979\) 1.59123e6 + 517023.i 1.66023 + 0.539442i
\(980\) −785586. + 625559.i −0.817978 + 0.651353i
\(981\) 1.68287e6 1.22268e6i 1.74869 1.27050i
\(982\) 474006. 1.57645e6i 0.491542 1.63478i
\(983\) 249586. 343526.i 0.258293 0.355510i −0.660101 0.751177i \(-0.729486\pi\)
0.918394 + 0.395667i \(0.129486\pi\)
\(984\) 1.25757e6 1.04759e6i 1.29880 1.08194i
\(985\) 404125. 293614.i 0.416527 0.302625i
\(986\) 908651. 1.31055e6i 0.934638 1.34803i
\(987\) 312628.i 0.320918i
\(988\) −44703.9 + 67617.6i −0.0457964 + 0.0692701i
\(989\) −410925. + 1.26470e6i −0.420117 + 1.29299i
\(990\) −936174. + 3.11354e6i −0.955183 + 3.17676i
\(991\) 308365.i 0.313992i 0.987599 + 0.156996i \(0.0501809\pi\)
−0.987599 + 0.156996i \(0.949819\pi\)
\(992\) −406447. 896205.i −0.413029 0.910718i
\(993\) −993455. −1.00751
\(994\) 341571. + 102703.i 0.345707 + 0.103947i
\(995\) −1.61500e6 524746.i −1.63127 0.530033i
\(996\) −2.02022e6 1.33563e6i −2.03648 1.34638i
\(997\) 1.45110e6 1.45985 0.729923 0.683529i \(-0.239556\pi\)
0.729923 + 0.683529i \(0.239556\pi\)
\(998\) −1.18696e6 822962.i −1.19172 0.826264i
\(999\) −1.64804e6 2.26833e6i −1.65134 2.27288i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 124.5.l.a.35.7 248
4.3 odd 2 inner 124.5.l.a.35.44 yes 248
31.8 even 5 inner 124.5.l.a.39.44 yes 248
124.39 odd 10 inner 124.5.l.a.39.7 yes 248
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
124.5.l.a.35.7 248 1.1 even 1 trivial
124.5.l.a.35.44 yes 248 4.3 odd 2 inner
124.5.l.a.39.7 yes 248 124.39 odd 10 inner
124.5.l.a.39.44 yes 248 31.8 even 5 inner