Properties

Label 525.2.m.c.307.3
Level $525$
Weight $2$
Character 525.307
Analytic conductor $4.192$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [525,2,Mod(118,525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(525, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("525.118");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.m (of order \(4\), 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: \(4.19214610612\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.3
Character \(\chi\) \(=\) 525.307
Dual form 525.2.m.c.118.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.11266 - 1.11266i) q^{2} +(-0.707107 - 0.707107i) q^{3} +0.476024i q^{4} +1.57354i q^{6} +(-1.62049 + 2.09141i) q^{7} +(-1.69567 + 1.69567i) q^{8} +1.00000i q^{9} +O(q^{10})\) \(q+(-1.11266 - 1.11266i) q^{2} +(-0.707107 - 0.707107i) q^{3} +0.476024i q^{4} +1.57354i q^{6} +(-1.62049 + 2.09141i) q^{7} +(-1.69567 + 1.69567i) q^{8} +1.00000i q^{9} +5.20147 q^{11} +(0.336600 - 0.336600i) q^{12} +(2.22988 + 2.22988i) q^{13} +(4.13009 - 0.523976i) q^{14} +4.72545 q^{16} +(3.11335 - 3.11335i) q^{17} +(1.11266 - 1.11266i) q^{18} -4.13009 q^{19} +(2.62471 - 0.332992i) q^{21} +(-5.78747 - 5.78747i) q^{22} +(2.97914 - 2.97914i) q^{23} +2.39804 q^{24} -4.96218i q^{26} +(0.707107 - 0.707107i) q^{27} +(-0.995562 - 0.771392i) q^{28} +0.249425i q^{29} +10.4242i q^{31} +(-1.86648 - 1.86648i) q^{32} +(-3.67800 - 3.67800i) q^{33} -6.92820 q^{34} -0.476024 q^{36} +(1.69567 + 1.69567i) q^{37} +(4.59538 + 4.59538i) q^{38} -3.15352i q^{39} -6.92820i q^{41} +(-3.29092 - 2.54990i) q^{42} +(4.39191 - 4.39191i) q^{43} +2.47602i q^{44} -6.62954 q^{46} +(-3.11335 + 3.11335i) q^{47} +(-3.34140 - 3.34140i) q^{48} +(-1.74802 - 6.77823i) q^{49} -4.40294 q^{51} +(-1.06147 + 1.06147i) q^{52} +(4.89898 - 4.89898i) q^{53} -1.57354 q^{54} +(-0.798528 - 6.29415i) q^{56} +(2.92041 + 2.92041i) q^{57} +(0.277525 - 0.277525i) q^{58} +11.8904 q^{59} -2.16407i q^{61} +(11.5986 - 11.5986i) q^{62} +(-2.09141 - 1.62049i) q^{63} -5.29738i q^{64} +8.18472i q^{66} +(2.50822 + 2.50822i) q^{67} +(1.48203 + 1.48203i) q^{68} -4.21314 q^{69} -0.798528 q^{71} +(-1.69567 - 1.69567i) q^{72} +(5.94178 + 5.94178i) q^{73} -3.77340i q^{74} -1.96602i q^{76} +(-8.42894 + 10.8784i) q^{77} +(-3.50879 + 3.50879i) q^{78} +5.29738i q^{79} -1.00000 q^{81} +(-7.70873 + 7.70873i) q^{82} +(4.59538 + 4.59538i) q^{83} +(0.158512 + 1.24943i) q^{84} -9.77340 q^{86} +(0.176370 - 0.176370i) q^{87} +(-8.81997 + 8.81997i) q^{88} +6.29415 q^{89} +(-8.27708 + 1.05010i) q^{91} +(1.41814 + 1.41814i) q^{92} +(7.37105 - 7.37105i) q^{93} +6.92820 q^{94} +2.63960i q^{96} +(12.1972 - 12.1972i) q^{97} +(-5.59692 + 9.48682i) q^{98} +5.20147i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 48 q^{11} + 24 q^{16} + 12 q^{21} - 24 q^{36} - 120 q^{46} + 48 q^{51} - 96 q^{56} - 96 q^{71} - 24 q^{81} - 120 q^{86} + 108 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(176\) \(451\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11266 1.11266i −0.786769 0.786769i 0.194194 0.980963i \(-0.437791\pi\)
−0.980963 + 0.194194i \(0.937791\pi\)
\(3\) −0.707107 0.707107i −0.408248 0.408248i
\(4\) 0.476024i 0.238012i
\(5\) 0 0
\(6\) 1.57354i 0.642394i
\(7\) −1.62049 + 2.09141i −0.612488 + 0.790480i
\(8\) −1.69567 + 1.69567i −0.599509 + 0.599509i
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 5.20147 1.56830 0.784151 0.620569i \(-0.213099\pi\)
0.784151 + 0.620569i \(0.213099\pi\)
\(12\) 0.336600 0.336600i 0.0971679 0.0971679i
\(13\) 2.22988 + 2.22988i 0.618456 + 0.618456i 0.945135 0.326679i \(-0.105930\pi\)
−0.326679 + 0.945135i \(0.605930\pi\)
\(14\) 4.13009 0.523976i 1.10381 0.140039i
\(15\) 0 0
\(16\) 4.72545 1.18136
\(17\) 3.11335 3.11335i 0.755099 0.755099i −0.220327 0.975426i \(-0.570713\pi\)
0.975426 + 0.220327i \(0.0707125\pi\)
\(18\) 1.11266 1.11266i 0.262256 0.262256i
\(19\) −4.13009 −0.947507 −0.473753 0.880658i \(-0.657101\pi\)
−0.473753 + 0.880658i \(0.657101\pi\)
\(20\) 0 0
\(21\) 2.62471 0.332992i 0.572759 0.0726649i
\(22\) −5.78747 5.78747i −1.23389 1.23389i
\(23\) 2.97914 2.97914i 0.621194 0.621194i −0.324643 0.945837i \(-0.605244\pi\)
0.945837 + 0.324643i \(0.105244\pi\)
\(24\) 2.39804 0.489497
\(25\) 0 0
\(26\) 4.96218i 0.973164i
\(27\) 0.707107 0.707107i 0.136083 0.136083i
\(28\) −0.995562 0.771392i −0.188144 0.145779i
\(29\) 0.249425i 0.0463171i 0.999732 + 0.0231585i \(0.00737225\pi\)
−0.999732 + 0.0231585i \(0.992628\pi\)
\(30\) 0 0
\(31\) 10.4242i 1.87225i 0.351669 + 0.936124i \(0.385614\pi\)
−0.351669 + 0.936124i \(0.614386\pi\)
\(32\) −1.86648 1.86648i −0.329951 0.329951i
\(33\) −3.67800 3.67800i −0.640257 0.640257i
\(34\) −6.92820 −1.18818
\(35\) 0 0
\(36\) −0.476024 −0.0793373
\(37\) 1.69567 + 1.69567i 0.278766 + 0.278766i 0.832616 0.553850i \(-0.186842\pi\)
−0.553850 + 0.832616i \(0.686842\pi\)
\(38\) 4.59538 + 4.59538i 0.745469 + 0.745469i
\(39\) 3.15352i 0.504967i
\(40\) 0 0
\(41\) 6.92820i 1.08200i −0.841021 0.541002i \(-0.818045\pi\)
0.841021 0.541002i \(-0.181955\pi\)
\(42\) −3.29092 2.54990i −0.507800 0.393459i
\(43\) 4.39191 4.39191i 0.669760 0.669760i −0.287900 0.957660i \(-0.592957\pi\)
0.957660 + 0.287900i \(0.0929572\pi\)
\(44\) 2.47602i 0.373275i
\(45\) 0 0
\(46\) −6.62954 −0.977473
\(47\) −3.11335 + 3.11335i −0.454129 + 0.454129i −0.896722 0.442593i \(-0.854059\pi\)
0.442593 + 0.896722i \(0.354059\pi\)
\(48\) −3.34140 3.34140i −0.482289 0.482289i
\(49\) −1.74802 6.77823i −0.249717 0.968319i
\(50\) 0 0
\(51\) −4.40294 −0.616536
\(52\) −1.06147 + 1.06147i −0.147200 + 0.147200i
\(53\) 4.89898 4.89898i 0.672927 0.672927i −0.285463 0.958390i \(-0.592147\pi\)
0.958390 + 0.285463i \(0.0921474\pi\)
\(54\) −1.57354 −0.214131
\(55\) 0 0
\(56\) −0.798528 6.29415i −0.106708 0.841092i
\(57\) 2.92041 + 2.92041i 0.386818 + 0.386818i
\(58\) 0.277525 0.277525i 0.0364409 0.0364409i
\(59\) 11.8904 1.54800 0.773998 0.633188i \(-0.218254\pi\)
0.773998 + 0.633188i \(0.218254\pi\)
\(60\) 0 0
\(61\) 2.16407i 0.277080i −0.990357 0.138540i \(-0.955759\pi\)
0.990357 0.138540i \(-0.0442410\pi\)
\(62\) 11.5986 11.5986i 1.47303 1.47303i
\(63\) −2.09141 1.62049i −0.263493 0.204163i
\(64\) 5.29738i 0.662172i
\(65\) 0 0
\(66\) 8.18472i 1.00747i
\(67\) 2.50822 + 2.50822i 0.306428 + 0.306428i 0.843522 0.537094i \(-0.180478\pi\)
−0.537094 + 0.843522i \(0.680478\pi\)
\(68\) 1.48203 + 1.48203i 0.179722 + 0.179722i
\(69\) −4.21314 −0.507203
\(70\) 0 0
\(71\) −0.798528 −0.0947678 −0.0473839 0.998877i \(-0.515088\pi\)
−0.0473839 + 0.998877i \(0.515088\pi\)
\(72\) −1.69567 1.69567i −0.199836 0.199836i
\(73\) 5.94178 + 5.94178i 0.695433 + 0.695433i 0.963422 0.267989i \(-0.0863592\pi\)
−0.267989 + 0.963422i \(0.586359\pi\)
\(74\) 3.77340i 0.438649i
\(75\) 0 0
\(76\) 1.96602i 0.225518i
\(77\) −8.42894 + 10.8784i −0.960567 + 1.23971i
\(78\) −3.50879 + 3.50879i −0.397293 + 0.397293i
\(79\) 5.29738i 0.596002i 0.954566 + 0.298001i \(0.0963198\pi\)
−0.954566 + 0.298001i \(0.903680\pi\)
\(80\) 0 0
\(81\) −1.00000 −0.111111
\(82\) −7.70873 + 7.70873i −0.851287 + 0.851287i
\(83\) 4.59538 + 4.59538i 0.504409 + 0.504409i 0.912805 0.408396i \(-0.133912\pi\)
−0.408396 + 0.912805i \(0.633912\pi\)
\(84\) 0.158512 + 1.24943i 0.0172951 + 0.136323i
\(85\) 0 0
\(86\) −9.77340 −1.05389
\(87\) 0.176370 0.176370i 0.0189089 0.0189089i
\(88\) −8.81997 + 8.81997i −0.940212 + 0.940212i
\(89\) 6.29415 0.667179 0.333590 0.942718i \(-0.391740\pi\)
0.333590 + 0.942718i \(0.391740\pi\)
\(90\) 0 0
\(91\) −8.27708 + 1.05010i −0.867674 + 0.110080i
\(92\) 1.41814 + 1.41814i 0.147852 + 0.147852i
\(93\) 7.37105 7.37105i 0.764342 0.764342i
\(94\) 6.92820 0.714590
\(95\) 0 0
\(96\) 2.63960i 0.269404i
\(97\) 12.1972 12.1972i 1.23844 1.23844i 0.277797 0.960640i \(-0.410396\pi\)
0.960640 0.277797i \(-0.0896041\pi\)
\(98\) −5.59692 + 9.48682i −0.565374 + 0.958313i
\(99\) 5.20147i 0.522768i
\(100\) 0 0
\(101\) 6.29415i 0.626292i 0.949705 + 0.313146i \(0.101383\pi\)
−0.949705 + 0.313146i \(0.898617\pi\)
\(102\) 4.89898 + 4.89898i 0.485071 + 0.485071i
\(103\) −10.5372 10.5372i −1.03826 1.03826i −0.999238 0.0390188i \(-0.987577\pi\)
−0.0390188 0.999238i \(-0.512423\pi\)
\(104\) −7.56225 −0.741540
\(105\) 0 0
\(106\) −10.9018 −1.05888
\(107\) 10.8573 + 10.8573i 1.04961 + 1.04961i 0.998703 + 0.0509079i \(0.0162115\pi\)
0.0509079 + 0.998703i \(0.483788\pi\)
\(108\) 0.336600 + 0.336600i 0.0323893 + 0.0323893i
\(109\) 15.9018i 1.52312i 0.648097 + 0.761558i \(0.275565\pi\)
−0.648097 + 0.761558i \(0.724435\pi\)
\(110\) 0 0
\(111\) 2.39804i 0.227611i
\(112\) −7.65755 + 9.88287i −0.723570 + 0.933843i
\(113\) −8.47834 + 8.47834i −0.797575 + 0.797575i −0.982713 0.185138i \(-0.940727\pi\)
0.185138 + 0.982713i \(0.440727\pi\)
\(114\) 6.49885i 0.608673i
\(115\) 0 0
\(116\) −0.118732 −0.0110240
\(117\) −2.22988 + 2.22988i −0.206152 + 0.206152i
\(118\) −13.2300 13.2300i −1.21792 1.21792i
\(119\) 1.46615 + 11.5565i 0.134401 + 1.05938i
\(120\) 0 0
\(121\) 16.0553 1.45957
\(122\) −2.40787 + 2.40787i −0.217998 + 0.217998i
\(123\) −4.89898 + 4.89898i −0.441726 + 0.441726i
\(124\) −4.96218 −0.445617
\(125\) 0 0
\(126\) 0.523976 + 4.13009i 0.0466795 + 0.367937i
\(127\) 12.3288 + 12.3288i 1.09400 + 1.09400i 0.995097 + 0.0989036i \(0.0315335\pi\)
0.0989036 + 0.995097i \(0.468466\pi\)
\(128\) −9.62714 + 9.62714i −0.850927 + 0.850927i
\(129\) −6.21110 −0.546857
\(130\) 0 0
\(131\) 15.8863i 1.38799i −0.719979 0.693996i \(-0.755848\pi\)
0.719979 0.693996i \(-0.244152\pi\)
\(132\) 1.75081 1.75081i 0.152389 0.152389i
\(133\) 6.69277 8.63772i 0.580337 0.748985i
\(134\) 5.58159i 0.482176i
\(135\) 0 0
\(136\) 10.5584i 0.905377i
\(137\) −3.95713 3.95713i −0.338081 0.338081i 0.517564 0.855645i \(-0.326839\pi\)
−0.855645 + 0.517564i \(0.826839\pi\)
\(138\) 4.68779 + 4.68779i 0.399052 + 0.399052i
\(139\) −11.8904 −1.00853 −0.504265 0.863549i \(-0.668236\pi\)
−0.504265 + 0.863549i \(0.668236\pi\)
\(140\) 0 0
\(141\) 4.40294 0.370795
\(142\) 0.888490 + 0.888490i 0.0745604 + 0.0745604i
\(143\) 11.5986 + 11.5986i 0.969926 + 0.969926i
\(144\) 4.72545i 0.393787i
\(145\) 0 0
\(146\) 13.2224i 1.09429i
\(147\) −3.55690 + 6.02897i −0.293368 + 0.497261i
\(148\) −0.807178 + 0.807178i −0.0663496 + 0.0663496i
\(149\) 0.249425i 0.0204337i −0.999948 0.0102169i \(-0.996748\pi\)
0.999948 0.0102169i \(-0.00325218\pi\)
\(150\) 0 0
\(151\) 2.35499 0.191647 0.0958233 0.995398i \(-0.469452\pi\)
0.0958233 + 0.995398i \(0.469452\pi\)
\(152\) 7.00325 7.00325i 0.568039 0.568039i
\(153\) 3.11335 + 3.11335i 0.251700 + 0.251700i
\(154\) 21.4825 2.72545i 1.73111 0.219623i
\(155\) 0 0
\(156\) 1.50115 0.120188
\(157\) 5.34323 5.34323i 0.426436 0.426436i −0.460976 0.887412i \(-0.652501\pi\)
0.887412 + 0.460976i \(0.152501\pi\)
\(158\) 5.89418 5.89418i 0.468916 0.468916i
\(159\) −6.92820 −0.549442
\(160\) 0 0
\(161\) 1.40294 + 11.0583i 0.110568 + 0.871515i
\(162\) 1.11266 + 1.11266i 0.0874188 + 0.0874188i
\(163\) −15.2130 + 15.2130i −1.19158 + 1.19158i −0.214951 + 0.976625i \(0.568959\pi\)
−0.976625 + 0.214951i \(0.931041\pi\)
\(164\) 3.29799 0.257530
\(165\) 0 0
\(166\) 10.2262i 0.793706i
\(167\) −4.74468 + 4.74468i −0.367154 + 0.367154i −0.866438 0.499284i \(-0.833596\pi\)
0.499284 + 0.866438i \(0.333596\pi\)
\(168\) −3.88599 + 5.01528i −0.299811 + 0.386938i
\(169\) 3.05531i 0.235024i
\(170\) 0 0
\(171\) 4.13009i 0.315836i
\(172\) 2.09065 + 2.09065i 0.159411 + 0.159411i
\(173\) −6.07741 6.07741i −0.462057 0.462057i 0.437272 0.899329i \(-0.355945\pi\)
−0.899329 + 0.437272i \(0.855945\pi\)
\(174\) −0.392480 −0.0297538
\(175\) 0 0
\(176\) 24.5793 1.85273
\(177\) −8.40777 8.40777i −0.631967 0.631967i
\(178\) −7.00325 7.00325i −0.524916 0.524916i
\(179\) 2.30704i 0.172436i 0.996276 + 0.0862181i \(0.0274782\pi\)
−0.996276 + 0.0862181i \(0.972522\pi\)
\(180\) 0 0
\(181\) 0.134178i 0.00997334i −0.999988 0.00498667i \(-0.998413\pi\)
0.999988 0.00498667i \(-0.00158731\pi\)
\(182\) 10.3780 + 8.04117i 0.769267 + 0.596052i
\(183\) −1.53023 + 1.53023i −0.113118 + 0.113118i
\(184\) 10.1033i 0.744823i
\(185\) 0 0
\(186\) −16.4029 −1.20272
\(187\) 16.1940 16.1940i 1.18422 1.18422i
\(188\) −1.48203 1.48203i −0.108088 0.108088i
\(189\) 0.332992 + 2.62471i 0.0242216 + 0.190920i
\(190\) 0 0
\(191\) −27.3047 −1.97570 −0.987851 0.155405i \(-0.950332\pi\)
−0.987851 + 0.155405i \(0.950332\pi\)
\(192\) −3.74581 + 3.74581i −0.270331 + 0.270331i
\(193\) 3.67423 3.67423i 0.264477 0.264477i −0.562393 0.826870i \(-0.690119\pi\)
0.826870 + 0.562393i \(0.190119\pi\)
\(194\) −27.1426 −1.94873
\(195\) 0 0
\(196\) 3.22660 0.832098i 0.230471 0.0594356i
\(197\) −11.9871 11.9871i −0.854048 0.854048i 0.136581 0.990629i \(-0.456389\pi\)
−0.990629 + 0.136581i \(0.956389\pi\)
\(198\) 5.78747 5.78747i 0.411298 0.411298i
\(199\) 24.2806 1.72121 0.860605 0.509274i \(-0.170086\pi\)
0.860605 + 0.509274i \(0.170086\pi\)
\(200\) 0 0
\(201\) 3.54716i 0.250197i
\(202\) 7.00325 7.00325i 0.492747 0.492747i
\(203\) −0.521651 0.404191i −0.0366127 0.0283687i
\(204\) 2.09591i 0.146743i
\(205\) 0 0
\(206\) 23.4485i 1.63374i
\(207\) 2.97914 + 2.97914i 0.207065 + 0.207065i
\(208\) 10.5372 + 10.5372i 0.730621 + 0.730621i
\(209\) −21.4825 −1.48598
\(210\) 0 0
\(211\) −26.0553 −1.79372 −0.896861 0.442313i \(-0.854158\pi\)
−0.896861 + 0.442313i \(0.854158\pi\)
\(212\) 2.33203 + 2.33203i 0.160164 + 0.160164i
\(213\) 0.564644 + 0.564644i 0.0386888 + 0.0386888i
\(214\) 24.1609i 1.65160i
\(215\) 0 0
\(216\) 2.39804i 0.163166i
\(217\) −21.8014 16.8924i −1.47998 1.14673i
\(218\) 17.6933 17.6933i 1.19834 1.19834i
\(219\) 8.40294i 0.567818i
\(220\) 0 0
\(221\) 13.8848 0.933991
\(222\) −2.66820 + 2.66820i −0.179078 + 0.179078i
\(223\) 3.99683 + 3.99683i 0.267647 + 0.267647i 0.828152 0.560504i \(-0.189393\pi\)
−0.560504 + 0.828152i \(0.689393\pi\)
\(224\) 6.92820 0.878968i 0.462910 0.0587285i
\(225\) 0 0
\(226\) 18.8670 1.25501
\(227\) −16.1940 + 16.1940i −1.07483 + 1.07483i −0.0778711 + 0.996963i \(0.524812\pi\)
−0.996963 + 0.0778711i \(0.975188\pi\)
\(228\) −1.39019 + 1.39019i −0.0920673 + 0.0920673i
\(229\) 11.7562 0.776872 0.388436 0.921476i \(-0.373015\pi\)
0.388436 + 0.921476i \(0.373015\pi\)
\(230\) 0 0
\(231\) 13.6524 1.73205i 0.898260 0.113961i
\(232\) −0.422942 0.422942i −0.0277675 0.0277675i
\(233\) 12.4806 12.4806i 0.817634 0.817634i −0.168131 0.985765i \(-0.553773\pi\)
0.985765 + 0.168131i \(0.0537732\pi\)
\(234\) 4.96218 0.324388
\(235\) 0 0
\(236\) 5.66011i 0.368441i
\(237\) 3.74581 3.74581i 0.243317 0.243317i
\(238\) 11.2271 14.4897i 0.727744 0.939230i
\(239\) 8.80589i 0.569606i 0.958586 + 0.284803i \(0.0919281\pi\)
−0.958586 + 0.284803i \(0.908072\pi\)
\(240\) 0 0
\(241\) 22.3146i 1.43741i −0.695314 0.718706i \(-0.744735\pi\)
0.695314 0.718706i \(-0.255265\pi\)
\(242\) −17.8641 17.8641i −1.14835 1.14835i
\(243\) 0.707107 + 0.707107i 0.0453609 + 0.0453609i
\(244\) 1.03015 0.0659484
\(245\) 0 0
\(246\) 10.9018 0.695073
\(247\) −9.20958 9.20958i −0.585991 0.585991i
\(248\) −17.6760 17.6760i −1.12243 1.12243i
\(249\) 6.49885i 0.411848i
\(250\) 0 0
\(251\) 15.8863i 1.00273i 0.865235 + 0.501367i \(0.167169\pi\)
−0.865235 + 0.501367i \(0.832831\pi\)
\(252\) 0.771392 0.995562i 0.0485931 0.0627145i
\(253\) 15.4959 15.4959i 0.974220 0.974220i
\(254\) 27.4354i 1.72145i
\(255\) 0 0
\(256\) 10.8287 0.676795
\(257\) −2.25858 + 2.25858i −0.140886 + 0.140886i −0.774032 0.633146i \(-0.781763\pi\)
0.633146 + 0.774032i \(0.281763\pi\)
\(258\) 6.91084 + 6.91084i 0.430250 + 0.430250i
\(259\) −6.29415 + 0.798528i −0.391100 + 0.0496181i
\(260\) 0 0
\(261\) −0.249425 −0.0154390
\(262\) −17.6760 + 17.6760i −1.09203 + 1.09203i
\(263\) 2.03730 2.03730i 0.125625 0.125625i −0.641499 0.767124i \(-0.721687\pi\)
0.767124 + 0.641499i \(0.221687\pi\)
\(264\) 12.4733 0.767680
\(265\) 0 0
\(266\) −17.0576 + 2.16407i −1.04587 + 0.132688i
\(267\) −4.45064 4.45064i −0.272375 0.272375i
\(268\) −1.19397 + 1.19397i −0.0729334 + 0.0729334i
\(269\) 15.1884 0.926052 0.463026 0.886345i \(-0.346764\pi\)
0.463026 + 0.886345i \(0.346764\pi\)
\(270\) 0 0
\(271\) 14.5543i 0.884112i 0.896987 + 0.442056i \(0.145751\pi\)
−0.896987 + 0.442056i \(0.854249\pi\)
\(272\) 14.7120 14.7120i 0.892045 0.892045i
\(273\) 6.59531 + 5.11025i 0.399166 + 0.309286i
\(274\) 8.80589i 0.531983i
\(275\) 0 0
\(276\) 2.00556i 0.120720i
\(277\) 0.353463 + 0.353463i 0.0212375 + 0.0212375i 0.717646 0.696408i \(-0.245220\pi\)
−0.696408 + 0.717646i \(0.745220\pi\)
\(278\) 13.2300 + 13.2300i 0.793480 + 0.793480i
\(279\) −10.4242 −0.624083
\(280\) 0 0
\(281\) 6.03829 0.360214 0.180107 0.983647i \(-0.442356\pi\)
0.180107 + 0.983647i \(0.442356\pi\)
\(282\) −4.89898 4.89898i −0.291730 0.291730i
\(283\) 1.37510 + 1.37510i 0.0817412 + 0.0817412i 0.746795 0.665054i \(-0.231591\pi\)
−0.665054 + 0.746795i \(0.731591\pi\)
\(284\) 0.380118i 0.0225559i
\(285\) 0 0
\(286\) 25.8107i 1.52622i
\(287\) 14.4897 + 11.2271i 0.855302 + 0.662714i
\(288\) 1.86648 1.86648i 0.109984 0.109984i
\(289\) 2.38592i 0.140348i
\(290\) 0 0
\(291\) −17.2494 −1.01118
\(292\) −2.82843 + 2.82843i −0.165521 + 0.165521i
\(293\) −11.5986 11.5986i −0.677599 0.677599i 0.281857 0.959456i \(-0.409050\pi\)
−0.959456 + 0.281857i \(0.909050\pi\)
\(294\) 10.6658 2.75057i 0.622043 0.160417i
\(295\) 0 0
\(296\) −5.75057 −0.334245
\(297\) 3.67800 3.67800i 0.213419 0.213419i
\(298\) −0.277525 + 0.277525i −0.0160766 + 0.0160766i
\(299\) 13.2862 0.768362
\(300\) 0 0
\(301\) 2.06825 + 16.3023i 0.119212 + 0.939652i
\(302\) −2.62030 2.62030i −0.150782 0.150782i
\(303\) 4.45064 4.45064i 0.255683 0.255683i
\(304\) −19.5165 −1.11935
\(305\) 0 0
\(306\) 6.92820i 0.396059i
\(307\) −6.82526 + 6.82526i −0.389538 + 0.389538i −0.874523 0.484985i \(-0.838825\pi\)
0.484985 + 0.874523i \(0.338825\pi\)
\(308\) −5.17839 4.01237i −0.295066 0.228626i
\(309\) 14.9018i 0.847733i
\(310\) 0 0
\(311\) 24.1465i 1.36922i −0.728909 0.684610i \(-0.759972\pi\)
0.728909 0.684610i \(-0.240028\pi\)
\(312\) 5.34732 + 5.34732i 0.302732 + 0.302732i
\(313\) −0.598552 0.598552i −0.0338322 0.0338322i 0.689988 0.723820i \(-0.257616\pi\)
−0.723820 + 0.689988i \(0.757616\pi\)
\(314\) −11.8904 −0.671013
\(315\) 0 0
\(316\) −2.52168 −0.141855
\(317\) −13.5399 13.5399i −0.760479 0.760479i 0.215930 0.976409i \(-0.430722\pi\)
−0.976409 + 0.215930i \(0.930722\pi\)
\(318\) 7.70873 + 7.70873i 0.432284 + 0.432284i
\(319\) 1.29738i 0.0726392i
\(320\) 0 0
\(321\) 15.3545i 0.857004i
\(322\) 10.7431 13.8651i 0.598690 0.772673i
\(323\) −12.8584 + 12.8584i −0.715461 + 0.715461i
\(324\) 0.476024i 0.0264458i
\(325\) 0 0
\(326\) 33.8538 1.87499
\(327\) 11.2443 11.2443i 0.621809 0.621809i
\(328\) 11.7479 + 11.7479i 0.648671 + 0.648671i
\(329\) −1.46615 11.5565i −0.0808313 0.637128i
\(330\) 0 0
\(331\) 22.4103 1.23178 0.615891 0.787831i \(-0.288796\pi\)
0.615891 + 0.787831i \(0.288796\pi\)
\(332\) −2.18751 + 2.18751i −0.120055 + 0.120055i
\(333\) −1.69567 + 1.69567i −0.0929220 + 0.0929220i
\(334\) 10.5584 0.577731
\(335\) 0 0
\(336\) 12.4029 1.57354i 0.676636 0.0858436i
\(337\) −0.588382 0.588382i −0.0320512 0.0320512i 0.690900 0.722951i \(-0.257215\pi\)
−0.722951 + 0.690900i \(0.757215\pi\)
\(338\) −3.39953 + 3.39953i −0.184910 + 0.184910i
\(339\) 11.9902 0.651217
\(340\) 0 0
\(341\) 54.2214i 2.93625i
\(342\) −4.59538 + 4.59538i −0.248490 + 0.248490i
\(343\) 17.0087 + 7.32823i 0.918385 + 0.395687i
\(344\) 14.8944i 0.803054i
\(345\) 0 0
\(346\) 13.5242i 0.727064i
\(347\) −21.0674 21.0674i −1.13096 1.13096i −0.990018 0.140940i \(-0.954988\pi\)
−0.140940 0.990018i \(-0.545012\pi\)
\(348\) 0.0839564 + 0.0839564i 0.00450053 + 0.00450053i
\(349\) −23.1467 −1.23902 −0.619508 0.784990i \(-0.712668\pi\)
−0.619508 + 0.784990i \(0.712668\pi\)
\(350\) 0 0
\(351\) 3.15352 0.168322
\(352\) −9.70846 9.70846i −0.517462 0.517462i
\(353\) −10.8221 10.8221i −0.576001 0.576001i 0.357798 0.933799i \(-0.383528\pi\)
−0.933799 + 0.357798i \(0.883528\pi\)
\(354\) 18.7100i 0.994424i
\(355\) 0 0
\(356\) 2.99617i 0.158796i
\(357\) 7.13493 9.20838i 0.377621 0.487359i
\(358\) 2.56695 2.56695i 0.135668 0.135668i
\(359\) 12.7985i 0.675480i 0.941239 + 0.337740i \(0.109663\pi\)
−0.941239 + 0.337740i \(0.890337\pi\)
\(360\) 0 0
\(361\) −1.94239 −0.102231
\(362\) −0.149294 + 0.149294i −0.00784671 + 0.00784671i
\(363\) −11.3528 11.3528i −0.595869 0.595869i
\(364\) −0.499871 3.94009i −0.0262004 0.206517i
\(365\) 0 0
\(366\) 3.40524 0.177995
\(367\) −4.14612 + 4.14612i −0.216426 + 0.216426i −0.806990 0.590565i \(-0.798905\pi\)
0.590565 + 0.806990i \(0.298905\pi\)
\(368\) 14.0778 14.0778i 0.733855 0.733855i
\(369\) 6.92820 0.360668
\(370\) 0 0
\(371\) 2.30704 + 18.1845i 0.119776 + 0.944094i
\(372\) 3.50879 + 3.50879i 0.181923 + 0.181923i
\(373\) −22.8670 + 22.8670i −1.18401 + 1.18401i −0.205310 + 0.978697i \(0.565820\pi\)
−0.978697 + 0.205310i \(0.934180\pi\)
\(374\) −36.0369 −1.86342
\(375\) 0 0
\(376\) 10.5584i 0.544509i
\(377\) −0.556187 + 0.556187i −0.0286451 + 0.0286451i
\(378\) 2.54990 3.29092i 0.131153 0.169267i
\(379\) 21.3527i 1.09681i −0.836212 0.548407i \(-0.815234\pi\)
0.836212 0.548407i \(-0.184766\pi\)
\(380\) 0 0
\(381\) 17.4355i 0.893248i
\(382\) 30.3809 + 30.3809i 1.55442 + 1.55442i
\(383\) −21.7152 21.7152i −1.10960 1.10960i −0.993203 0.116394i \(-0.962867\pi\)
−0.116394 0.993203i \(-0.537133\pi\)
\(384\) 13.6148 0.694779
\(385\) 0 0
\(386\) −8.17635 −0.416165
\(387\) 4.39191 + 4.39191i 0.223253 + 0.223253i
\(388\) 5.80615 + 5.80615i 0.294763 + 0.294763i
\(389\) 28.0530i 1.42234i −0.703018 0.711172i \(-0.748165\pi\)
0.703018 0.711172i \(-0.251835\pi\)
\(390\) 0 0
\(391\) 18.5502i 0.938126i
\(392\) 14.4577 + 8.52957i 0.730223 + 0.430808i
\(393\) −11.2333 + 11.2333i −0.566645 + 0.566645i
\(394\) 26.6752i 1.34388i
\(395\) 0 0
\(396\) −2.47602 −0.124425
\(397\) −1.37510 + 1.37510i −0.0690143 + 0.0690143i −0.740771 0.671757i \(-0.765540\pi\)
0.671757 + 0.740771i \(0.265540\pi\)
\(398\) −27.0161 27.0161i −1.35419 1.35419i
\(399\) −10.8403 + 1.37529i −0.542693 + 0.0688505i
\(400\) 0 0
\(401\) −4.15352 −0.207417 −0.103708 0.994608i \(-0.533071\pi\)
−0.103708 + 0.994608i \(0.533071\pi\)
\(402\) −3.94678 + 3.94678i −0.196848 + 0.196848i
\(403\) −23.2448 + 23.2448i −1.15790 + 1.15790i
\(404\) −2.99617 −0.149065
\(405\) 0 0
\(406\) 0.130693 + 1.03015i 0.00648618 + 0.0511254i
\(407\) 8.81997 + 8.81997i 0.437189 + 0.437189i
\(408\) 7.46593 7.46593i 0.369619 0.369619i
\(409\) −6.79403 −0.335943 −0.167971 0.985792i \(-0.553722\pi\)
−0.167971 + 0.985792i \(0.553722\pi\)
\(410\) 0 0
\(411\) 5.59623i 0.276042i
\(412\) 5.01594 5.01594i 0.247117 0.247117i
\(413\) −19.2683 + 24.8677i −0.948129 + 1.22366i
\(414\) 6.62954i 0.325824i
\(415\) 0 0
\(416\) 8.32404i 0.408120i
\(417\) 8.40777 + 8.40777i 0.411730 + 0.411730i
\(418\) 23.9027 + 23.9027i 1.16912 + 1.16912i
\(419\) 23.4485 1.14554 0.572768 0.819717i \(-0.305869\pi\)
0.572768 + 0.819717i \(0.305869\pi\)
\(420\) 0 0
\(421\) 10.9594 0.534129 0.267064 0.963679i \(-0.413946\pi\)
0.267064 + 0.963679i \(0.413946\pi\)
\(422\) 28.9907 + 28.9907i 1.41125 + 1.41125i
\(423\) −3.11335 3.11335i −0.151376 0.151376i
\(424\) 16.6141i 0.806851i
\(425\) 0 0
\(426\) 1.25651i 0.0608783i
\(427\) 4.52596 + 3.50685i 0.219027 + 0.169708i
\(428\) −5.16831 + 5.16831i −0.249820 + 0.249820i
\(429\) 16.4029i 0.791942i
\(430\) 0 0
\(431\) −3.30474 −0.159184 −0.0795919 0.996828i \(-0.525362\pi\)
−0.0795919 + 0.996828i \(0.525362\pi\)
\(432\) 3.34140 3.34140i 0.160763 0.160763i
\(433\) 12.3328 + 12.3328i 0.592677 + 0.592677i 0.938354 0.345676i \(-0.112351\pi\)
−0.345676 + 0.938354i \(0.612351\pi\)
\(434\) 5.46206 + 43.0530i 0.262187 + 2.06661i
\(435\) 0 0
\(436\) −7.56963 −0.362520
\(437\) −12.3041 + 12.3041i −0.588586 + 0.588586i
\(438\) −9.34962 + 9.34962i −0.446742 + 0.446742i
\(439\) −33.1749 −1.58335 −0.791675 0.610942i \(-0.790791\pi\)
−0.791675 + 0.610942i \(0.790791\pi\)
\(440\) 0 0
\(441\) 6.77823 1.74802i 0.322773 0.0832390i
\(442\) −15.4490 15.4490i −0.734835 0.734835i
\(443\) −14.8596 + 14.8596i −0.705999 + 0.705999i −0.965691 0.259692i \(-0.916379\pi\)
0.259692 + 0.965691i \(0.416379\pi\)
\(444\) 1.14152 0.0541742
\(445\) 0 0
\(446\) 8.89422i 0.421154i
\(447\) −0.176370 + 0.176370i −0.00834202 + 0.00834202i
\(448\) 11.0790 + 8.58435i 0.523434 + 0.405573i
\(449\) 7.84648i 0.370298i −0.982710 0.185149i \(-0.940723\pi\)
0.982710 0.185149i \(-0.0592768\pi\)
\(450\) 0 0
\(451\) 36.0369i 1.69691i
\(452\) −4.03589 4.03589i −0.189832 0.189832i
\(453\) −1.66523 1.66523i −0.0782394 0.0782394i
\(454\) 36.0369 1.69129
\(455\) 0 0
\(456\) −9.90409 −0.463802
\(457\) 6.52235 + 6.52235i 0.305103 + 0.305103i 0.843006 0.537904i \(-0.180784\pi\)
−0.537904 + 0.843006i \(0.680784\pi\)
\(458\) −13.0807 13.0807i −0.611219 0.611219i
\(459\) 4.40294i 0.205512i
\(460\) 0 0
\(461\) 0.966276i 0.0450039i 0.999747 + 0.0225020i \(0.00716320\pi\)
−0.999747 + 0.0225020i \(0.992837\pi\)
\(462\) −17.1176 13.2633i −0.796384 0.617063i
\(463\) −7.79681 + 7.79681i −0.362348 + 0.362348i −0.864677 0.502328i \(-0.832477\pi\)
0.502328 + 0.864677i \(0.332477\pi\)
\(464\) 1.17865i 0.0547173i
\(465\) 0 0
\(466\) −27.7734 −1.28658
\(467\) 19.3074 19.3074i 0.893438 0.893438i −0.101407 0.994845i \(-0.532334\pi\)
0.994845 + 0.101407i \(0.0323343\pi\)
\(468\) −1.06147 1.06147i −0.0490666 0.0490666i
\(469\) −9.31027 + 1.18118i −0.429908 + 0.0545417i
\(470\) 0 0
\(471\) −7.55646 −0.348183
\(472\) −20.1621 + 20.1621i −0.928038 + 0.928038i
\(473\) 22.8444 22.8444i 1.05039 1.05039i
\(474\) −8.33563 −0.382868
\(475\) 0 0
\(476\) −5.50115 + 0.697921i −0.252145 + 0.0319891i
\(477\) 4.89898 + 4.89898i 0.224309 + 0.224309i
\(478\) 9.79796 9.79796i 0.448148 0.448148i
\(479\) −4.62996 −0.211548 −0.105774 0.994390i \(-0.533732\pi\)
−0.105774 + 0.994390i \(0.533732\pi\)
\(480\) 0 0
\(481\) 7.56225i 0.344809i
\(482\) −24.8286 + 24.8286i −1.13091 + 1.13091i
\(483\) 6.82736 8.81142i 0.310656 0.400934i
\(484\) 7.64271i 0.347396i
\(485\) 0 0
\(486\) 1.57354i 0.0713772i
\(487\) 7.85554 + 7.85554i 0.355968 + 0.355968i 0.862325 0.506356i \(-0.169008\pi\)
−0.506356 + 0.862325i \(0.669008\pi\)
\(488\) 3.66954 + 3.66954i 0.166112 + 0.166112i
\(489\) 21.5145 0.972918
\(490\) 0 0
\(491\) −5.48919 −0.247724 −0.123862 0.992299i \(-0.539528\pi\)
−0.123862 + 0.992299i \(0.539528\pi\)
\(492\) −2.33203 2.33203i −0.105136 0.105136i
\(493\) 0.776548 + 0.776548i 0.0349740 + 0.0349740i
\(494\) 20.4943i 0.922080i
\(495\) 0 0
\(496\) 49.2592i 2.21180i
\(497\) 1.29401 1.67005i 0.0580441 0.0749120i
\(498\) −7.23101 + 7.23101i −0.324029 + 0.324029i
\(499\) 15.5565i 0.696403i −0.937420 0.348201i \(-0.886793\pi\)
0.937420 0.348201i \(-0.113207\pi\)
\(500\) 0 0
\(501\) 6.70998 0.299780
\(502\) 17.6760 17.6760i 0.788920 0.788920i
\(503\) 23.1973 + 23.1973i 1.03432 + 1.03432i 0.999390 + 0.0349251i \(0.0111193\pi\)
0.0349251 + 0.999390i \(0.488881\pi\)
\(504\) 6.29415 0.798528i 0.280364 0.0355692i
\(505\) 0 0
\(506\) −34.4834 −1.53297
\(507\) −2.16043 + 2.16043i −0.0959482 + 0.0959482i
\(508\) −5.86878 + 5.86878i −0.260385 + 0.260385i
\(509\) 11.8904 0.527032 0.263516 0.964655i \(-0.415118\pi\)
0.263516 + 0.964655i \(0.415118\pi\)
\(510\) 0 0
\(511\) −22.0553 + 2.79812i −0.975670 + 0.123781i
\(512\) 7.20561 + 7.20561i 0.318446 + 0.318446i
\(513\) −2.92041 + 2.92041i −0.128939 + 0.128939i
\(514\) 5.02606 0.221690
\(515\) 0 0
\(516\) 2.95663i 0.130158i
\(517\) −16.1940 + 16.1940i −0.712212 + 0.712212i
\(518\) 7.89174 + 6.11476i 0.346743 + 0.268667i
\(519\) 8.59476i 0.377268i
\(520\) 0 0
\(521\) 5.59623i 0.245175i −0.992458 0.122588i \(-0.960881\pi\)
0.992458 0.122588i \(-0.0391193\pi\)
\(522\) 0.277525 + 0.277525i 0.0121470 + 0.0121470i
\(523\) −12.6314 12.6314i −0.552333 0.552333i 0.374781 0.927113i \(-0.377718\pi\)
−0.927113 + 0.374781i \(0.877718\pi\)
\(524\) 7.56225 0.330359
\(525\) 0 0
\(526\) −4.53364 −0.197676
\(527\) 32.4543 + 32.4543i 1.41373 + 1.41373i
\(528\) −17.3802 17.3802i −0.756375 0.756375i
\(529\) 5.24943i 0.228236i
\(530\) 0 0
\(531\) 11.8904i 0.515999i
\(532\) 4.11176 + 3.18592i 0.178267 + 0.138127i
\(533\) 15.4490 15.4490i 0.669172 0.669172i
\(534\) 9.90409i 0.428592i
\(535\) 0 0
\(536\) −8.50621 −0.367412
\(537\) 1.63132 1.63132i 0.0703968 0.0703968i
\(538\) −16.8995 16.8995i −0.728589 0.728589i
\(539\) −9.09227 35.2568i −0.391632 1.51862i
\(540\) 0 0
\(541\) −0.712283 −0.0306234 −0.0153117 0.999883i \(-0.504874\pi\)
−0.0153117 + 0.999883i \(0.504874\pi\)
\(542\) 16.1940 16.1940i 0.695592 0.695592i
\(543\) −0.0948778 + 0.0948778i −0.00407160 + 0.00407160i
\(544\) −11.6220 −0.498291
\(545\) 0 0
\(546\) −1.65237 13.0243i −0.0707149 0.557389i
\(547\) 14.8234 + 14.8234i 0.633803 + 0.633803i 0.949020 0.315216i \(-0.102077\pi\)
−0.315216 + 0.949020i \(0.602077\pi\)
\(548\) 1.88369 1.88369i 0.0804672 0.0804672i
\(549\) 2.16407 0.0923602
\(550\) 0 0
\(551\) 1.03015i 0.0438858i
\(552\) 7.14409 7.14409i 0.304073 0.304073i
\(553\) −11.0790 8.58435i −0.471127 0.365044i
\(554\) 0.786567i 0.0334180i
\(555\) 0 0
\(556\) 5.66011i 0.240042i
\(557\) −17.4971 17.4971i −0.741375 0.741375i 0.231468 0.972843i \(-0.425647\pi\)
−0.972843 + 0.231468i \(0.925647\pi\)
\(558\) 11.5986 + 11.5986i 0.491009 + 0.491009i
\(559\) 19.5868 0.828434
\(560\) 0 0
\(561\) −22.9018 −0.966915
\(562\) −6.71856 6.71856i −0.283406 0.283406i
\(563\) 9.81802 + 9.81802i 0.413780 + 0.413780i 0.883053 0.469273i \(-0.155484\pi\)
−0.469273 + 0.883053i \(0.655484\pi\)
\(564\) 2.09591i 0.0882535i
\(565\) 0 0
\(566\) 3.06004i 0.128623i
\(567\) 1.62049 2.09141i 0.0680542 0.0878311i
\(568\) 1.35404 1.35404i 0.0568141 0.0568141i
\(569\) 23.1512i 0.970550i 0.874362 + 0.485275i \(0.161280\pi\)
−0.874362 + 0.485275i \(0.838720\pi\)
\(570\) 0 0
\(571\) −38.1586 −1.59689 −0.798443 0.602070i \(-0.794343\pi\)
−0.798443 + 0.602070i \(0.794343\pi\)
\(572\) −5.52122 + 5.52122i −0.230854 + 0.230854i
\(573\) 19.3074 + 19.3074i 0.806577 + 0.806577i
\(574\) −3.63021 28.6141i −0.151522 1.19433i
\(575\) 0 0
\(576\) 5.29738 0.220724
\(577\) −0.598552 + 0.598552i −0.0249180 + 0.0249180i −0.719456 0.694538i \(-0.755609\pi\)
0.694538 + 0.719456i \(0.255609\pi\)
\(578\) −2.65472 + 2.65472i −0.110422 + 0.110422i
\(579\) −5.19615 −0.215945
\(580\) 0 0
\(581\) −17.0576 + 2.16407i −0.707669 + 0.0897807i
\(582\) 19.1927 + 19.1927i 0.795565 + 0.795565i
\(583\) 25.4819 25.4819i 1.05535 1.05535i
\(584\) −20.1506 −0.833836
\(585\) 0 0
\(586\) 25.8107i 1.06623i
\(587\) −15.4885 + 15.4885i −0.639280 + 0.639280i −0.950378 0.311098i \(-0.899303\pi\)
0.311098 + 0.950378i \(0.399303\pi\)
\(588\) −2.86993 1.69317i −0.118354 0.0698250i
\(589\) 43.0530i 1.77397i
\(590\) 0 0
\(591\) 16.9524i 0.697327i
\(592\) 8.01279 + 8.01279i 0.329324 + 0.329324i
\(593\) −6.22670 6.22670i −0.255700 0.255700i 0.567603 0.823303i \(-0.307871\pi\)
−0.823303 + 0.567603i \(0.807871\pi\)
\(594\) −8.18472 −0.335823
\(595\) 0 0
\(596\) 0.118732 0.00486346
\(597\) −17.1690 17.1690i −0.702681 0.702681i
\(598\) −14.7831 14.7831i −0.604524 0.604524i
\(599\) 19.0097i 0.776714i −0.921509 0.388357i \(-0.873043\pi\)
0.921509 0.388357i \(-0.126957\pi\)
\(600\) 0 0
\(601\) 10.3604i 0.422608i −0.977420 0.211304i \(-0.932229\pi\)
0.977420 0.211304i \(-0.0677710\pi\)
\(602\) 15.8377 20.4402i 0.645497 0.833081i
\(603\) −2.50822 + 2.50822i −0.102143 + 0.102143i
\(604\) 1.12103i 0.0456141i
\(605\) 0 0
\(606\) −9.90409 −0.402326
\(607\) −10.4015 + 10.4015i −0.422185 + 0.422185i −0.885955 0.463770i \(-0.846496\pi\)
0.463770 + 0.885955i \(0.346496\pi\)
\(608\) 7.70873 + 7.70873i 0.312630 + 0.312630i
\(609\) 0.0830567 + 0.654669i 0.00336563 + 0.0265285i
\(610\) 0 0
\(611\) −13.8848 −0.561718
\(612\) −1.48203 + 1.48203i −0.0599075 + 0.0599075i
\(613\) −5.08700 + 5.08700i −0.205462 + 0.205462i −0.802335 0.596873i \(-0.796409\pi\)
0.596873 + 0.802335i \(0.296409\pi\)
\(614\) 15.1884 0.612953
\(615\) 0 0
\(616\) −4.15352 32.7389i −0.167350 1.31909i
\(617\) −8.33721 8.33721i −0.335643 0.335643i 0.519081 0.854725i \(-0.326274\pi\)
−0.854725 + 0.519081i \(0.826274\pi\)
\(618\) 16.5806 16.5806i 0.666971 0.666971i
\(619\) −30.9070 −1.24226 −0.621129 0.783708i \(-0.713326\pi\)
−0.621129 + 0.783708i \(0.713326\pi\)
\(620\) 0 0
\(621\) 4.21314i 0.169068i
\(622\) −26.8668 + 26.8668i −1.07726 + 1.07726i
\(623\) −10.1996 + 13.1637i −0.408639 + 0.527392i
\(624\) 14.9018i 0.596549i
\(625\) 0 0
\(626\) 1.33197i 0.0532362i
\(627\) 15.1904 + 15.1904i 0.606648 + 0.606648i
\(628\) 2.54350 + 2.54350i 0.101497 + 0.101497i
\(629\) 10.5584 0.420992
\(630\) 0 0
\(631\) 10.4509 0.416044 0.208022 0.978124i \(-0.433297\pi\)
0.208022 + 0.978124i \(0.433297\pi\)
\(632\) −8.98259 8.98259i −0.357308 0.357308i
\(633\) 18.4239 + 18.4239i 0.732284 + 0.732284i
\(634\) 30.1307i 1.19664i
\(635\) 0 0
\(636\) 3.29799i 0.130774i
\(637\) 11.2167 19.0125i 0.444424 0.753302i
\(638\) 1.44354 1.44354i 0.0571503 0.0571503i
\(639\) 0.798528i 0.0315893i
\(640\) 0 0
\(641\) 46.2641 1.82732 0.913662 0.406475i \(-0.133242\pi\)
0.913662 + 0.406475i \(0.133242\pi\)
\(642\) −17.0843 + 17.0843i −0.674264 + 0.674264i
\(643\) −11.8836 11.8836i −0.468642 0.468642i 0.432833 0.901474i \(-0.357514\pi\)
−0.901474 + 0.432833i \(0.857514\pi\)
\(644\) −5.26401 + 0.667835i −0.207431 + 0.0263164i
\(645\) 0 0
\(646\) 28.6141 1.12581
\(647\) 26.1613 26.1613i 1.02851 1.02851i 0.0289263 0.999582i \(-0.490791\pi\)
0.999582 0.0289263i \(-0.00920880\pi\)
\(648\) 1.69567 1.69567i 0.0666121 0.0666121i
\(649\) 61.8475 2.42773
\(650\) 0 0
\(651\) 3.47119 + 27.3606i 0.136047 + 1.07235i
\(652\) −7.24176 7.24176i −0.283609 0.283609i
\(653\) −0.0451641 + 0.0451641i −0.00176741 + 0.00176741i −0.707990 0.706223i \(-0.750398\pi\)
0.706223 + 0.707990i \(0.250398\pi\)
\(654\) −25.0221 −0.978441
\(655\) 0 0
\(656\) 32.7389i 1.27824i
\(657\) −5.94178 + 5.94178i −0.231811 + 0.231811i
\(658\) −11.2271 + 14.4897i −0.437678 + 0.564869i
\(659\) 16.1918i 0.630743i −0.948968 0.315372i \(-0.897871\pi\)
0.948968 0.315372i \(-0.102129\pi\)
\(660\) 0 0
\(661\) 17.1544i 0.667229i −0.942710 0.333614i \(-0.891732\pi\)
0.942710 0.333614i \(-0.108268\pi\)
\(662\) −24.9350 24.9350i −0.969128 0.969128i
\(663\) −9.81802 9.81802i −0.381300 0.381300i
\(664\) −15.5845 −0.604795
\(665\) 0 0
\(666\) 3.77340 0.146216
\(667\) 0.743073 + 0.743073i 0.0287719 + 0.0287719i
\(668\) −2.25858 2.25858i −0.0873870 0.0873870i
\(669\) 5.65237i 0.218533i
\(670\) 0 0
\(671\) 11.2563i 0.434546i
\(672\) −5.52050 4.27746i −0.212958 0.165006i
\(673\) 7.91427 7.91427i 0.305073 0.305073i −0.537922 0.842995i \(-0.680790\pi\)
0.842995 + 0.537922i \(0.180790\pi\)
\(674\) 1.30934i 0.0504338i
\(675\) 0 0
\(676\) 1.45440 0.0559385
\(677\) −16.0447 + 16.0447i −0.616649 + 0.616649i −0.944670 0.328022i \(-0.893618\pi\)
0.328022 + 0.944670i \(0.393618\pi\)
\(678\) −13.3410 13.3410i −0.512358 0.512358i
\(679\) 5.74393 + 45.2748i 0.220432 + 1.73749i
\(680\) 0 0
\(681\) 22.9018 0.877599
\(682\) 60.3300 60.3300i 2.31015 2.31015i
\(683\) −10.2553 + 10.2553i −0.392409 + 0.392409i −0.875545 0.483136i \(-0.839498\pi\)
0.483136 + 0.875545i \(0.339498\pi\)
\(684\) 1.96602 0.0751726
\(685\) 0 0
\(686\) −10.7711 27.0788i −0.411243 1.03387i
\(687\) −8.31290 8.31290i −0.317157 0.317157i
\(688\) 20.7537 20.7537i 0.791229 0.791229i
\(689\) 21.8482 0.832351
\(690\) 0 0
\(691\) 5.26401i 0.200252i −0.994975 0.100126i \(-0.968075\pi\)
0.994975 0.100126i \(-0.0319246\pi\)
\(692\) 2.89299 2.89299i 0.109975 0.109975i
\(693\) −10.8784 8.42894i −0.413237 0.320189i
\(694\) 46.8817i 1.77961i
\(695\) 0 0
\(696\) 0.598130i 0.0226721i
\(697\) −21.5699 21.5699i −0.817020 0.817020i
\(698\) 25.7544 + 25.7544i 0.974820 + 0.974820i
\(699\) −17.6503 −0.667595
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) −3.50879 3.50879i −0.132431 0.132431i
\(703\) −7.00325 7.00325i −0.264133 0.264133i
\(704\) 27.5542i 1.03849i
\(705\) 0 0
\(706\) 24.0826i 0.906361i
\(707\) −13.1637 10.1996i −0.495071 0.383596i
\(708\) 4.00230 4.00230i 0.150416 0.150416i
\(709\) 24.6694i 0.926478i −0.886233 0.463239i \(-0.846687\pi\)
0.886233 0.463239i \(-0.153313\pi\)
\(710\) 0 0
\(711\) −5.29738 −0.198667
\(712\) −10.6728 + 10.6728i −0.399980 + 0.399980i
\(713\) 31.0553 + 31.0553i 1.16303 + 1.16303i
\(714\) −18.1845 + 2.30704i −0.680539 + 0.0863388i
\(715\) 0 0
\(716\) −1.09821 −0.0410418
\(717\) 6.22670 6.22670i 0.232541 0.232541i
\(718\) 14.2404 14.2404i 0.531447 0.531447i
\(719\) −17.8523 −0.665779 −0.332890 0.942966i \(-0.608024\pi\)
−0.332890 + 0.942966i \(0.608024\pi\)
\(720\) 0 0
\(721\) 39.1129 4.96218i 1.45664 0.184801i
\(722\) 2.16121 + 2.16121i 0.0804321 + 0.0804321i
\(723\) −15.7788 + 15.7788i −0.586821 + 0.586821i
\(724\) 0.0638717 0.00237377
\(725\) 0 0
\(726\) 25.2637i 0.937622i
\(727\) 1.73825 1.73825i 0.0644682 0.0644682i −0.674138 0.738606i \(-0.735485\pi\)
0.738606 + 0.674138i \(0.235485\pi\)
\(728\) 12.2546 15.8158i 0.454184 0.586172i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 27.3471i 1.01147i
\(732\) −0.728424 0.728424i −0.0269233 0.0269233i
\(733\) −12.5108 12.5108i −0.462097 0.462097i 0.437245 0.899342i \(-0.355954\pi\)
−0.899342 + 0.437245i \(0.855954\pi\)
\(734\) 9.22645 0.340554
\(735\) 0 0
\(736\) −11.1210 −0.409927
\(737\) 13.0464 + 13.0464i 0.480572 + 0.480572i
\(738\) −7.70873 7.70873i −0.283762 0.283762i
\(739\) 10.5874i 0.389464i −0.980857 0.194732i \(-0.937616\pi\)
0.980857 0.194732i \(-0.0623836\pi\)
\(740\) 0 0
\(741\) 13.0243i 0.478460i
\(742\) 17.6663 22.8002i 0.648549 0.837020i
\(743\) −12.5060 + 12.5060i −0.458802 + 0.458802i −0.898262 0.439460i \(-0.855170\pi\)
0.439460 + 0.898262i \(0.355170\pi\)
\(744\) 24.9977i 0.916460i
\(745\) 0 0
\(746\) 50.8863 1.86308
\(747\) −4.59538 + 4.59538i −0.168136 + 0.168136i
\(748\) 7.70873 + 7.70873i 0.281859 + 0.281859i
\(749\) −40.3011 + 5.11293i −1.47257 + 0.186822i
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) −14.7120 + 14.7120i −0.536491 + 0.536491i
\(753\) 11.2333 11.2333i 0.409365 0.409365i
\(754\) 1.23769 0.0450741
\(755\) 0 0
\(756\) −1.24943 + 0.158512i −0.0454412 + 0.00576503i
\(757\) −13.7308 13.7308i −0.499054 0.499054i 0.412090 0.911143i \(-0.364799\pi\)
−0.911143 + 0.412090i \(0.864799\pi\)
\(758\) −23.7583 + 23.7583i −0.862940 + 0.862940i
\(759\) −21.9145 −0.795448
\(760\) 0 0
\(761\) 13.8564i 0.502294i 0.967949 + 0.251147i \(0.0808078\pi\)
−0.967949 + 0.251147i \(0.919192\pi\)
\(762\) −19.3998 + 19.3998i −0.702780 + 0.702780i
\(763\) −33.2572 25.7687i −1.20399 0.932890i
\(764\) 12.9977i 0.470240i
\(765\) 0 0
\(766\) 48.3233i 1.74599i
\(767\) 26.5141 + 26.5141i 0.957368 + 0.957368i
\(768\) −7.65706 7.65706i −0.276300 0.276300i
\(769\) 25.9448 0.935595 0.467797 0.883836i \(-0.345048\pi\)
0.467797 + 0.883836i \(0.345048\pi\)
\(770\) 0 0
\(771\) 3.19411 0.115033
\(772\) 1.74902 + 1.74902i 0.0629487 + 0.0629487i
\(773\) 11.7479 + 11.7479i 0.422544 + 0.422544i 0.886079 0.463535i \(-0.153419\pi\)
−0.463535 + 0.886079i \(0.653419\pi\)
\(774\) 9.77340i 0.351298i
\(775\) 0 0
\(776\) 41.3647i 1.48491i
\(777\) 5.01528 + 3.88599i 0.179922 + 0.139409i
\(778\) −31.2135 + 31.2135i −1.11906 + 1.11906i
\(779\) 28.6141i 1.02521i
\(780\) 0 0
\(781\) −4.15352 −0.148625
\(782\) −20.6401 + 20.6401i −0.738089 + 0.738089i
\(783\) 0.176370 + 0.176370i 0.00630296 + 0.00630296i
\(784\) −8.26017 32.0302i −0.295006 1.14394i
\(785\) 0 0
\(786\) 24.9977 0.891638
\(787\) 20.3401 20.3401i 0.725048 0.725048i −0.244581 0.969629i \(-0.578650\pi\)
0.969629 + 0.244581i \(0.0786505\pi\)
\(788\) 5.70616 5.70616i 0.203273 0.203273i
\(789\) −2.88117 −0.102572
\(790\) 0 0
\(791\) −3.99264 31.4708i −0.141962 1.11897i
\(792\) −8.81997 8.81997i −0.313404 0.313404i
\(793\) 4.82560 4.82560i 0.171362 0.171362i
\(794\) 3.06004 0.108597
\(795\) 0 0
\(796\) 11.5582i 0.409668i
\(797\) 16.4926 16.4926i 0.584198 0.584198i −0.351856 0.936054i \(-0.614449\pi\)
0.936054 + 0.351856i \(0.114449\pi\)
\(798\) 13.5918 + 10.5313i 0.481144 + 0.372805i
\(799\) 19.3859i 0.685825i
\(800\) 0 0
\(801\) 6.29415i 0.222393i
\(802\) 4.62145 + 4.62145i 0.163189 + 0.163189i
\(803\) 30.9060 + 30.9060i 1.09065 + 1.09065i
\(804\) 1.68853 0.0595499
\(805\) 0 0
\(806\) 51.7270 1.82201
\(807\) −10.7398 10.7398i −0.378059 0.378059i
\(808\) −10.6728 10.6728i −0.375467 0.375467i
\(809\) 49.9571i 1.75640i 0.478295 + 0.878199i \(0.341255\pi\)
−0.478295 + 0.878199i \(0.658745\pi\)
\(810\) 0 0
\(811\) 28.5449i 1.00235i 0.865347 + 0.501174i \(0.167098\pi\)
−0.865347 + 0.501174i \(0.832902\pi\)
\(812\) 0.192405 0.248318i 0.00675208 0.00871426i
\(813\) 10.2915 10.2915i 0.360937 0.360937i
\(814\) 19.6272i 0.687935i
\(815\) 0 0
\(816\) −20.8059 −0.728352
\(817\) −18.1390 + 18.1390i −0.634602 + 0.634602i
\(818\) 7.55944 + 7.55944i 0.264310 + 0.264310i
\(819\) −1.05010 8.27708i −0.0366934 0.289225i
\(820\) 0 0
\(821\) 6.00000 0.209401 0.104701 0.994504i \(-0.466612\pi\)
0.104701 + 0.994504i \(0.466612\pi\)
\(822\) 6.22670 6.22670i 0.217181 0.217181i
\(823\) 16.8020 16.8020i 0.585680 0.585680i −0.350778 0.936459i \(-0.614083\pi\)
0.936459 + 0.350778i \(0.114083\pi\)
\(824\) 35.7350 1.24489
\(825\) 0 0
\(826\) 49.1083 6.23028i 1.70870 0.216779i
\(827\) −39.8118 39.8118i −1.38439 1.38439i −0.836641 0.547751i \(-0.815484\pi\)
−0.547751 0.836641i \(-0.684516\pi\)
\(828\) −1.41814 + 1.41814i −0.0492838 + 0.0492838i
\(829\) 27.0788 0.940484 0.470242 0.882537i \(-0.344167\pi\)
0.470242 + 0.882537i \(0.344167\pi\)
\(830\) 0 0
\(831\) 0.499871i 0.0173403i
\(832\) 11.8125 11.8125i 0.409524 0.409524i
\(833\) −26.5452 15.6608i −0.919737 0.542615i
\(834\) 18.7100i 0.647874i
\(835\) 0 0
\(836\) 10.2262i 0.353680i
\(837\) 7.37105 + 7.37105i 0.254781 + 0.254781i
\(838\) −26.0903 26.0903i −0.901273 0.901273i
\(839\) 54.8554 1.89382 0.946910 0.321498i \(-0.104186\pi\)
0.946910 + 0.321498i \(0.104186\pi\)
\(840\) 0 0
\(841\) 28.9378 0.997855
\(842\) −12.1941 12.1941i −0.420236 0.420236i
\(843\) −4.26972 4.26972i −0.147057 0.147057i
\(844\) 12.4029i 0.426927i
\(845\) 0 0
\(846\) 6.92820i 0.238197i
\(847\) −26.0175 + 33.5783i −0.893972 + 1.15376i
\(848\) 23.1499 23.1499i 0.794970 0.794970i
\(849\) 1.94469i 0.0667414i
\(850\) 0 0
\(851\) 10.1033 0.346336
\(852\) −0.268784 + 0.268784i −0.00920839 + 0.00920839i
\(853\) −9.36876 9.36876i −0.320780 0.320780i 0.528286 0.849066i \(-0.322835\pi\)
−0.849066 + 0.528286i \(0.822835\pi\)
\(854\) −1.13392 8.93779i −0.0388020 0.305845i
\(855\) 0 0
\(856\) −36.8206 −1.25850
\(857\) 20.6401 20.6401i 0.705052 0.705052i −0.260438 0.965491i \(-0.583867\pi\)
0.965491 + 0.260438i \(0.0838670\pi\)
\(858\) −18.2509 + 18.2509i −0.623075 + 0.623075i
\(859\) −15.5206 −0.529556 −0.264778 0.964309i \(-0.585299\pi\)
−0.264778 + 0.964309i \(0.585299\pi\)
\(860\) 0 0
\(861\) −2.30704 18.1845i −0.0786237 0.619728i
\(862\) 3.67705 + 3.67705i 0.125241 + 0.125241i
\(863\) 22.6925 22.6925i 0.772462 0.772462i −0.206074 0.978536i \(-0.566069\pi\)
0.978536 + 0.206074i \(0.0660688\pi\)
\(864\) −2.63960 −0.0898012
\(865\) 0 0
\(866\) 27.4445i 0.932601i
\(867\) −1.68710 + 1.68710i −0.0572970 + 0.0572970i
\(868\) 8.04117 10.3780i 0.272935 0.352252i
\(869\) 27.5542i 0.934711i
\(870\) 0 0
\(871\) 11.1860i 0.379024i
\(872\) −26.9642 26.9642i −0.913121 0.913121i
\(873\) 12.1972 + 12.1972i 0.412812 + 0.412812i
\(874\) 27.3806 0.926162
\(875\) 0 0
\(876\) 4.00000 0.135147
\(877\) −10.1514 10.1514i −0.342789 0.342789i 0.514626 0.857415i \(-0.327931\pi\)
−0.857415 + 0.514626i \(0.827931\pi\)
\(878\) 36.9123 + 36.9123i 1.24573 + 1.24573i
\(879\) 16.4029i 0.553258i
\(880\) 0 0
\(881\) 5.66011i 0.190694i 0.995444 + 0.0953469i \(0.0303960\pi\)
−0.995444 + 0.0953469i \(0.969604\pi\)
\(882\) −9.48682 5.59692i −0.319438 0.188458i
\(883\) −18.2373 + 18.2373i −0.613735 + 0.613735i −0.943917 0.330182i \(-0.892890\pi\)
0.330182 + 0.943917i \(0.392890\pi\)
\(884\) 6.60948i 0.222301i
\(885\) 0 0
\(886\) 33.0673 1.11092
\(887\) 9.11254 9.11254i 0.305969 0.305969i −0.537375 0.843344i \(-0.680584\pi\)
0.843344 + 0.537375i \(0.180584\pi\)
\(888\) 4.06627 + 4.06627i 0.136455 + 0.136455i
\(889\) −45.7632 + 5.80589i −1.53485 + 0.194723i
\(890\) 0 0
\(891\) −5.20147 −0.174256
\(892\) −1.90258 + 1.90258i −0.0637033 + 0.0637033i
\(893\) 12.8584 12.8584i 0.430290 0.430290i
\(894\) 0.392480 0.0131265
\(895\) 0 0
\(896\) −4.53364 35.7350i −0.151458 1.19382i
\(897\) −9.39478 9.39478i −0.313683 0.313683i
\(898\) −8.73046 + 8.73046i −0.291339 + 0.291339i
\(899\) −2.60007 −0.0867171
\(900\) 0 0
\(901\) 30.5045i 1.01625i
\(902\) −40.0968 + 40.0968i −1.33508 + 1.33508i
\(903\) 10.0650 12.9900i 0.334943 0.432279i
\(904\) 28.7529i 0.956306i
\(905\) 0 0
\(906\) 3.70567i 0.123113i
\(907\) −21.5971 21.5971i −0.717119 0.717119i 0.250895 0.968014i \(-0.419275\pi\)
−0.968014 + 0.250895i \(0.919275\pi\)
\(908\) −7.70873 7.70873i −0.255823 0.255823i
\(909\) −6.29415 −0.208764
\(910\) 0 0
\(911\) −29.7003 −0.984016 −0.492008 0.870591i \(-0.663737\pi\)
−0.492008 + 0.870591i \(0.663737\pi\)
\(912\) 13.8003 + 13.8003i 0.456972 + 0.456972i
\(913\) 23.9027 + 23.9027i 0.791065 + 0.791065i
\(914\) 14.5143i 0.480091i
\(915\) 0 0
\(916\) 5.59623i 0.184905i
\(917\) 33.2248 + 25.7436i 1.09718 + 0.850129i
\(918\) −4.89898 + 4.89898i −0.161690 + 0.161690i
\(919\) 14.2591i 0.470364i 0.971951 + 0.235182i \(0.0755686\pi\)
−0.971951 + 0.235182i \(0.924431\pi\)
\(920\) 0 0
\(921\) 9.65237 0.318056
\(922\) 1.07514 1.07514i 0.0354077 0.0354077i
\(923\) −1.78062 1.78062i −0.0586097 0.0586097i
\(924\) 0.824497 + 6.49885i 0.0271240 + 0.213796i
\(925\) 0 0
\(926\) 17.3504 0.570169
\(927\) 10.5372 10.5372i 0.346086 0.346086i
\(928\) 0.465548 0.465548i 0.0152823 0.0152823i
\(929\) −54.9832 −1.80394 −0.901970 0.431799i \(-0.857879\pi\)
−0.901970 + 0.431799i \(0.857879\pi\)
\(930\) 0 0
\(931\) 7.21947 + 27.9947i 0.236609 + 0.917489i
\(932\) 5.94108 + 5.94108i 0.194606 + 0.194606i
\(933\) −17.0741 + 17.0741i −0.558982 + 0.558982i
\(934\) −42.9651 −1.40586
\(935\) 0 0
\(936\) 7.56225i 0.247180i
\(937\) −14.8900 + 14.8900i −0.486434 + 0.486434i −0.907179 0.420745i \(-0.861769\pi\)
0.420745 + 0.907179i \(0.361769\pi\)
\(938\) 11.6734 + 9.04492i 0.381150 + 0.295327i
\(939\) 0.846480i 0.0276238i
\(940\) 0 0
\(941\) 29.1725i 0.950997i 0.879716 + 0.475499i \(0.157732\pi\)
−0.879716 + 0.475499i \(0.842268\pi\)
\(942\) 8.40777 + 8.40777i 0.273940 + 0.273940i
\(943\) −20.6401 20.6401i −0.672134 0.672134i
\(944\) 56.1874 1.82874
\(945\) 0 0
\(946\) −50.8361 −1.65282
\(947\) −6.00345 6.00345i −0.195086 0.195086i 0.602804 0.797890i \(-0.294050\pi\)
−0.797890 + 0.602804i \(0.794050\pi\)
\(948\) 1.78309 + 1.78309i 0.0579122 + 0.0579122i
\(949\) 26.4989i 0.860189i
\(950\) 0 0
\(951\) 19.1484i 0.620928i
\(952\) −22.0820 17.1098i −0.715682 0.554532i
\(953\) 11.4936 11.4936i 0.372315 0.372315i −0.496005 0.868320i \(-0.665200\pi\)
0.868320 + 0.496005i \(0.165200\pi\)
\(954\) 10.9018i 0.352959i
\(955\) 0 0
\(956\) −4.19181 −0.135573
\(957\) 0.917385 0.917385i 0.0296548 0.0296548i
\(958\) 5.15157 + 5.15157i 0.166440 + 0.166440i
\(959\) 14.6885 1.86350i 0.474317 0.0601757i
\(960\) 0 0
\(961\) −77.6648 −2.50532
\(962\) 8.41421 8.41421i 0.271285 0.271285i
\(963\) −10.8573 + 10.8573i −0.349870 + 0.349870i
\(964\) 10.6223 0.342121
\(965\) 0 0
\(966\) −17.4006 + 2.20759i −0.559857 + 0.0710280i
\(967\) 31.4854 + 31.4854i 1.01250 + 1.01250i 0.999921 + 0.0125799i \(0.00400440\pi\)
0.0125799 + 0.999921i \(0.495996\pi\)
\(968\) −27.2245 + 27.2245i −0.875028 + 0.875028i
\(969\) 18.1845 0.584172
\(970\) 0 0
\(971\) 47.9272i 1.53806i −0.639214 0.769029i \(-0.720740\pi\)
0.639214 0.769029i \(-0.279260\pi\)
\(972\) −0.336600 + 0.336600i −0.0107964 + 0.0107964i
\(973\) 19.2683 24.8677i 0.617712 0.797222i
\(974\) 17.4811i 0.560130i
\(975\) 0 0
\(976\) 10.2262i 0.327332i
\(977\) 20.9607 + 20.9607i 0.670592 + 0.670592i 0.957853 0.287260i \(-0.0927444\pi\)
−0.287260 + 0.957853i \(0.592744\pi\)
\(978\) −23.9383 23.9383i −0.765462 0.765462i
\(979\) 32.7389 1.04634
\(980\) 0 0
\(981\) −15.9018 −0.507705
\(982\) 6.10760 + 6.10760i 0.194901 + 0.194901i
\(983\) 34.9452 + 34.9452i 1.11458 + 1.11458i 0.992523 + 0.122055i \(0.0389485\pi\)
0.122055 + 0.992523i \(0.461051\pi\)
\(984\) 16.6141i 0.529637i
\(985\) 0 0
\(986\) 1.72807i 0.0550329i
\(987\) −7.13493 + 9.20838i −0.227107 + 0.293106i
\(988\) 4.38398 4.38398i 0.139473 0.139473i
\(989\) 26.1682i 0.832102i
\(990\) 0 0
\(991\) −28.6620 −0.910479 −0.455240 0.890369i \(-0.650446\pi\)
−0.455240 + 0.890369i \(0.650446\pi\)
\(992\) 19.4567 19.4567i 0.617750 0.617750i
\(993\) −15.8465 15.8465i −0.502873 0.502873i
\(994\) −3.29799 + 0.418410i −0.104606 + 0.0132711i
\(995\) 0 0
\(996\) 3.09361 0.0980247
\(997\) 14.6983 14.6983i 0.465501 0.465501i −0.434953 0.900453i \(-0.643235\pi\)
0.900453 + 0.434953i \(0.143235\pi\)
\(998\) −17.3091 + 17.3091i −0.547908 + 0.547908i
\(999\) 2.39804 0.0758705
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 525.2.m.c.307.3 yes 24
5.2 odd 4 inner 525.2.m.c.118.9 yes 24
5.3 odd 4 inner 525.2.m.c.118.4 yes 24
5.4 even 2 inner 525.2.m.c.307.10 yes 24
7.6 odd 2 inner 525.2.m.c.307.4 yes 24
35.13 even 4 inner 525.2.m.c.118.3 24
35.27 even 4 inner 525.2.m.c.118.10 yes 24
35.34 odd 2 inner 525.2.m.c.307.9 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
525.2.m.c.118.3 24 35.13 even 4 inner
525.2.m.c.118.4 yes 24 5.3 odd 4 inner
525.2.m.c.118.9 yes 24 5.2 odd 4 inner
525.2.m.c.118.10 yes 24 35.27 even 4 inner
525.2.m.c.307.3 yes 24 1.1 even 1 trivial
525.2.m.c.307.4 yes 24 7.6 odd 2 inner
525.2.m.c.307.9 yes 24 35.34 odd 2 inner
525.2.m.c.307.10 yes 24 5.4 even 2 inner