Properties

Label 1183.2.e.j.170.3
Level $1183$
Weight $2$
Character 1183.170
Analytic conductor $9.446$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 170.3
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.j.508.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.689527 + 1.19430i) q^{2} +(-1.44060 - 2.49520i) q^{3} +(0.0491037 + 0.0850501i) q^{4} +(-0.402974 + 0.697972i) q^{5} +3.97334 q^{6} +(-1.26180 - 2.32548i) q^{7} -2.89354 q^{8} +(-2.65067 + 4.59109i) q^{9} +O(q^{10})\) \(q+(-0.689527 + 1.19430i) q^{2} +(-1.44060 - 2.49520i) q^{3} +(0.0491037 + 0.0850501i) q^{4} +(-0.402974 + 0.697972i) q^{5} +3.97334 q^{6} +(-1.26180 - 2.32548i) q^{7} -2.89354 q^{8} +(-2.65067 + 4.59109i) q^{9} +(-0.555723 - 0.962541i) q^{10} +(-2.63579 - 4.56532i) q^{11} +(0.141478 - 0.245047i) q^{12} +(3.64736 + 0.0965159i) q^{14} +2.32210 q^{15} +(1.89697 - 3.28565i) q^{16} +(0.280051 + 0.485062i) q^{17} +(-3.65541 - 6.33136i) q^{18} +(-2.92234 + 5.06165i) q^{19} -0.0791501 q^{20} +(-3.98477 + 6.49853i) q^{21} +7.26980 q^{22} +(0.802438 - 1.38986i) q^{23} +(4.16844 + 7.21995i) q^{24} +(2.17522 + 3.76760i) q^{25} +6.63060 q^{27} +(0.135823 - 0.221506i) q^{28} +2.28015 q^{29} +(-1.60115 + 2.77328i) q^{30} +(-1.73795 - 3.01022i) q^{31} +(-0.277517 - 0.480674i) q^{32} +(-7.59424 + 13.1536i) q^{33} -0.772411 q^{34} +(2.13159 + 0.0564059i) q^{35} -0.520630 q^{36} +(-0.620979 + 1.07557i) q^{37} +(-4.03007 - 6.98029i) q^{38} +(1.16602 - 2.01961i) q^{40} +0.927702 q^{41} +(-5.01357 - 9.23991i) q^{42} +4.44711 q^{43} +(0.258854 - 0.448348i) q^{44} +(-2.13630 - 3.70018i) q^{45} +(1.10661 + 1.91670i) q^{46} +(1.92209 - 3.32915i) q^{47} -10.9311 q^{48} +(-3.81571 + 5.86859i) q^{49} -5.99951 q^{50} +(0.806883 - 1.39756i) q^{51} +(-2.72727 - 4.72377i) q^{53} +(-4.57198 + 7.91890i) q^{54} +4.24862 q^{55} +(3.65108 + 6.72888i) q^{56} +16.8397 q^{57} +(-1.57223 + 2.72318i) q^{58} +(5.49698 + 9.52106i) q^{59} +(0.114024 + 0.197495i) q^{60} +(-3.65107 + 6.32385i) q^{61} +4.79346 q^{62} +(14.0211 + 0.371024i) q^{63} +8.35330 q^{64} +(-10.4729 - 18.1396i) q^{66} +(3.67278 + 6.36144i) q^{67} +(-0.0275031 + 0.0476367i) q^{68} -4.62397 q^{69} +(-1.53716 + 2.50686i) q^{70} +9.31460 q^{71} +(7.66982 - 13.2845i) q^{72} +(2.50073 + 4.33139i) q^{73} +(-0.856364 - 1.48327i) q^{74} +(6.26726 - 10.8552i) q^{75} -0.573991 q^{76} +(-7.29072 + 11.8900i) q^{77} +(-5.68437 + 9.84562i) q^{79} +(1.52886 + 2.64806i) q^{80} +(-1.60006 - 2.77138i) q^{81} +(-0.639676 + 1.10795i) q^{82} -5.81962 q^{83} +(-0.748368 - 0.0198032i) q^{84} -0.451413 q^{85} +(-3.06641 + 5.31117i) q^{86} +(-3.28479 - 5.68943i) q^{87} +(7.62677 + 13.2100i) q^{88} +(-2.50473 + 4.33832i) q^{89} +5.89215 q^{90} +0.157611 q^{92} +(-5.00739 + 8.67305i) q^{93} +(2.65067 + 4.59109i) q^{94} +(-2.35526 - 4.07942i) q^{95} +(-0.799583 + 1.38492i) q^{96} -10.6483 q^{97} +(-4.37780 - 8.60364i) q^{98} +27.9464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} + O(q^{10}) \) \( 24q - 6q^{3} - 8q^{4} - 2q^{9} - 24q^{10} + 2q^{12} + 8q^{14} - 16q^{16} - 34q^{17} + 60q^{22} - 6q^{23} + 10q^{25} + 24q^{27} + 4q^{29} - 22q^{30} - 24q^{35} - 52q^{36} - 38q^{38} - 2q^{40} + 32q^{42} + 44q^{43} - 76q^{48} + 12q^{49} - 8q^{51} - 16q^{53} + 60q^{55} + 54q^{56} + 10q^{61} + 164q^{62} - 4q^{64} - 68q^{66} - 22q^{68} + 28q^{69} - 66q^{74} - 2q^{75} + 38q^{77} - 70q^{79} + 28q^{81} - 10q^{82} + 20q^{87} + 28q^{88} - 132q^{92} + 2q^{94} - 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.689527 + 1.19430i −0.487570 + 0.844495i −0.999898 0.0142944i \(-0.995450\pi\)
0.512328 + 0.858790i \(0.328783\pi\)
\(3\) −1.44060 2.49520i −0.831732 1.44060i −0.896664 0.442712i \(-0.854016\pi\)
0.0649323 0.997890i \(-0.479317\pi\)
\(4\) 0.0491037 + 0.0850501i 0.0245518 + 0.0425250i
\(5\) −0.402974 + 0.697972i −0.180216 + 0.312142i −0.941954 0.335742i \(-0.891013\pi\)
0.761738 + 0.647885i \(0.224346\pi\)
\(6\) 3.97334 1.62211
\(7\) −1.26180 2.32548i −0.476916 0.878949i
\(8\) −2.89354 −1.02302
\(9\) −2.65067 + 4.59109i −0.883555 + 1.53036i
\(10\) −0.555723 0.962541i −0.175735 0.304382i
\(11\) −2.63579 4.56532i −0.794720 1.37650i −0.923017 0.384760i \(-0.874284\pi\)
0.128296 0.991736i \(-0.459049\pi\)
\(12\) 0.141478 0.245047i 0.0408411 0.0707389i
\(13\) 0 0
\(14\) 3.64736 + 0.0965159i 0.974798 + 0.0257950i
\(15\) 2.32210 0.599564
\(16\) 1.89697 3.28565i 0.474243 0.821412i
\(17\) 0.280051 + 0.485062i 0.0679223 + 0.117645i 0.897987 0.440023i \(-0.145030\pi\)
−0.830064 + 0.557668i \(0.811696\pi\)
\(18\) −3.65541 6.33136i −0.861589 1.49232i
\(19\) −2.92234 + 5.06165i −0.670431 + 1.16122i 0.307351 + 0.951596i \(0.400558\pi\)
−0.977782 + 0.209625i \(0.932776\pi\)
\(20\) −0.0791501 −0.0176985
\(21\) −3.98477 + 6.49853i −0.869548 + 1.41810i
\(22\) 7.26980 1.54993
\(23\) 0.802438 1.38986i 0.167320 0.289807i −0.770157 0.637855i \(-0.779822\pi\)
0.937477 + 0.348048i \(0.113155\pi\)
\(24\) 4.16844 + 7.21995i 0.850880 + 1.47377i
\(25\) 2.17522 + 3.76760i 0.435045 + 0.753520i
\(26\) 0 0
\(27\) 6.63060 1.27606
\(28\) 0.135823 0.221506i 0.0256682 0.0418607i
\(29\) 2.28015 0.423414 0.211707 0.977333i \(-0.432098\pi\)
0.211707 + 0.977333i \(0.432098\pi\)
\(30\) −1.60115 + 2.77328i −0.292329 + 0.506329i
\(31\) −1.73795 3.01022i −0.312145 0.540651i 0.666681 0.745343i \(-0.267714\pi\)
−0.978827 + 0.204692i \(0.934381\pi\)
\(32\) −0.277517 0.480674i −0.0490585 0.0849719i
\(33\) −7.59424 + 13.1536i −1.32199 + 2.28975i
\(34\) −0.772411 −0.132467
\(35\) 2.13159 + 0.0564059i 0.360305 + 0.00953433i
\(36\) −0.520630 −0.0867716
\(37\) −0.620979 + 1.07557i −0.102088 + 0.176822i −0.912545 0.408977i \(-0.865886\pi\)
0.810457 + 0.585799i \(0.199219\pi\)
\(38\) −4.03007 6.98029i −0.653764 1.13235i
\(39\) 0 0
\(40\) 1.16602 2.01961i 0.184364 0.319329i
\(41\) 0.927702 0.144883 0.0724413 0.997373i \(-0.476921\pi\)
0.0724413 + 0.997373i \(0.476921\pi\)
\(42\) −5.01357 9.23991i −0.773610 1.42575i
\(43\) 4.44711 0.678179 0.339089 0.940754i \(-0.389881\pi\)
0.339089 + 0.940754i \(0.389881\pi\)
\(44\) 0.258854 0.448348i 0.0390237 0.0675910i
\(45\) −2.13630 3.70018i −0.318461 0.551590i
\(46\) 1.10661 + 1.91670i 0.163160 + 0.282602i
\(47\) 1.92209 3.32915i 0.280365 0.485607i −0.691109 0.722750i \(-0.742878\pi\)
0.971475 + 0.237143i \(0.0762110\pi\)
\(48\) −10.9311 −1.57777
\(49\) −3.81571 + 5.86859i −0.545101 + 0.838370i
\(50\) −5.99951 −0.848458
\(51\) 0.806883 1.39756i 0.112986 0.195698i
\(52\) 0 0
\(53\) −2.72727 4.72377i −0.374620 0.648860i 0.615650 0.788019i \(-0.288893\pi\)
−0.990270 + 0.139159i \(0.955560\pi\)
\(54\) −4.57198 + 7.91890i −0.622168 + 1.07763i
\(55\) 4.24862 0.572884
\(56\) 3.65108 + 6.72888i 0.487896 + 0.899184i
\(57\) 16.8397 2.23048
\(58\) −1.57223 + 2.72318i −0.206444 + 0.357571i
\(59\) 5.49698 + 9.52106i 0.715646 + 1.23954i 0.962710 + 0.270537i \(0.0872011\pi\)
−0.247063 + 0.968999i \(0.579466\pi\)
\(60\) 0.114024 + 0.197495i 0.0147204 + 0.0254965i
\(61\) −3.65107 + 6.32385i −0.467472 + 0.809686i −0.999309 0.0371610i \(-0.988169\pi\)
0.531837 + 0.846847i \(0.321502\pi\)
\(62\) 4.79346 0.608770
\(63\) 14.0211 + 0.371024i 1.76649 + 0.0467446i
\(64\) 8.35330 1.04416
\(65\) 0 0
\(66\) −10.4729 18.1396i −1.28912 2.23283i
\(67\) 3.67278 + 6.36144i 0.448701 + 0.777174i 0.998302 0.0582541i \(-0.0185534\pi\)
−0.549600 + 0.835428i \(0.685220\pi\)
\(68\) −0.0275031 + 0.0476367i −0.00333524 + 0.00577680i
\(69\) −4.62397 −0.556661
\(70\) −1.53716 + 2.50686i −0.183725 + 0.299627i
\(71\) 9.31460 1.10544 0.552720 0.833367i \(-0.313590\pi\)
0.552720 + 0.833367i \(0.313590\pi\)
\(72\) 7.66982 13.2845i 0.903896 1.56559i
\(73\) 2.50073 + 4.33139i 0.292688 + 0.506951i 0.974444 0.224629i \(-0.0721169\pi\)
−0.681756 + 0.731579i \(0.738784\pi\)
\(74\) −0.856364 1.48327i −0.0995503 0.172426i
\(75\) 6.26726 10.8552i 0.723681 1.25345i
\(76\) −0.573991 −0.0658413
\(77\) −7.29072 + 11.8900i −0.830854 + 1.35499i
\(78\) 0 0
\(79\) −5.68437 + 9.84562i −0.639542 + 1.10772i 0.345992 + 0.938238i \(0.387543\pi\)
−0.985533 + 0.169481i \(0.945791\pi\)
\(80\) 1.52886 + 2.64806i 0.170932 + 0.296062i
\(81\) −1.60006 2.77138i −0.177784 0.307931i
\(82\) −0.639676 + 1.10795i −0.0706404 + 0.122353i
\(83\) −5.81962 −0.638786 −0.319393 0.947622i \(-0.603479\pi\)
−0.319393 + 0.947622i \(0.603479\pi\)
\(84\) −0.748368 0.0198032i −0.0816536 0.00216071i
\(85\) −0.451413 −0.0489626
\(86\) −3.06641 + 5.31117i −0.330659 + 0.572719i
\(87\) −3.28479 5.68943i −0.352167 0.609971i
\(88\) 7.62677 + 13.2100i 0.813016 + 1.40819i
\(89\) −2.50473 + 4.33832i −0.265501 + 0.459861i −0.967695 0.252125i \(-0.918871\pi\)
0.702194 + 0.711986i \(0.252204\pi\)
\(90\) 5.89215 0.621087
\(91\) 0 0
\(92\) 0.157611 0.0164320
\(93\) −5.00739 + 8.67305i −0.519242 + 0.899354i
\(94\) 2.65067 + 4.59109i 0.273395 + 0.473534i
\(95\) −2.35526 4.07942i −0.241644 0.418540i
\(96\) −0.799583 + 1.38492i −0.0816071 + 0.141348i
\(97\) −10.6483 −1.08117 −0.540586 0.841289i \(-0.681798\pi\)
−0.540586 + 0.841289i \(0.681798\pi\)
\(98\) −4.37780 8.60364i −0.442225 0.869099i
\(99\) 27.9464 2.80872
\(100\) −0.213623 + 0.370006i −0.0213623 + 0.0370006i
\(101\) −1.95777 3.39096i −0.194805 0.337413i 0.752031 0.659127i \(-0.229074\pi\)
−0.946837 + 0.321715i \(0.895741\pi\)
\(102\) 1.11274 + 1.92732i 0.110177 + 0.190833i
\(103\) −4.22690 + 7.32120i −0.416488 + 0.721379i −0.995583 0.0938810i \(-0.970073\pi\)
0.579095 + 0.815260i \(0.303406\pi\)
\(104\) 0 0
\(105\) −2.93003 5.40000i −0.285942 0.526986i
\(106\) 7.52212 0.730613
\(107\) 4.83761 8.37899i 0.467670 0.810028i −0.531648 0.846965i \(-0.678427\pi\)
0.999318 + 0.0369379i \(0.0117604\pi\)
\(108\) 0.325587 + 0.563933i 0.0313296 + 0.0542645i
\(109\) 7.28189 + 12.6126i 0.697478 + 1.20807i 0.969338 + 0.245731i \(0.0790279\pi\)
−0.271860 + 0.962337i \(0.587639\pi\)
\(110\) −2.92954 + 5.07411i −0.279321 + 0.483798i
\(111\) 3.57833 0.339640
\(112\) −10.0343 0.265526i −0.948153 0.0250899i
\(113\) 19.5114 1.83548 0.917741 0.397180i \(-0.130011\pi\)
0.917741 + 0.397180i \(0.130011\pi\)
\(114\) −11.6115 + 20.1116i −1.08751 + 1.88363i
\(115\) 0.646723 + 1.12016i 0.0603073 + 0.104455i
\(116\) 0.111964 + 0.193927i 0.0103956 + 0.0180057i
\(117\) 0 0
\(118\) −15.1613 −1.39571
\(119\) 0.774634 1.26331i 0.0710106 0.115807i
\(120\) −6.71910 −0.613367
\(121\) −8.39477 + 14.5402i −0.763161 + 1.32183i
\(122\) −5.03503 8.72093i −0.455850 0.789556i
\(123\) −1.33645 2.31480i −0.120503 0.208718i
\(124\) 0.170680 0.295626i 0.0153275 0.0265480i
\(125\) −7.53598 −0.674038
\(126\) −10.1110 + 16.4895i −0.900763 + 1.46900i
\(127\) −1.91731 −0.170134 −0.0850670 0.996375i \(-0.527110\pi\)
−0.0850670 + 0.996375i \(0.527110\pi\)
\(128\) −5.20480 + 9.01498i −0.460044 + 0.796819i
\(129\) −6.40652 11.0964i −0.564063 0.976985i
\(130\) 0 0
\(131\) −7.79078 + 13.4940i −0.680684 + 1.17898i 0.294089 + 0.955778i \(0.404984\pi\)
−0.974772 + 0.223201i \(0.928349\pi\)
\(132\) −1.49162 −0.129829
\(133\) 15.4582 + 0.409052i 1.34039 + 0.0354693i
\(134\) −10.1299 −0.875093
\(135\) −2.67196 + 4.62797i −0.229966 + 0.398312i
\(136\) −0.810339 1.40355i −0.0694860 0.120353i
\(137\) 3.92553 + 6.79921i 0.335380 + 0.580896i 0.983558 0.180594i \(-0.0578019\pi\)
−0.648178 + 0.761489i \(0.724469\pi\)
\(138\) 3.18836 5.52240i 0.271411 0.470098i
\(139\) 9.92481 0.841812 0.420906 0.907104i \(-0.361712\pi\)
0.420906 + 0.907104i \(0.361712\pi\)
\(140\) 0.0998717 + 0.184062i 0.00844070 + 0.0155561i
\(141\) −11.0759 −0.932755
\(142\) −6.42267 + 11.1244i −0.538979 + 0.933538i
\(143\) 0 0
\(144\) 10.0565 + 17.4183i 0.838039 + 1.45153i
\(145\) −0.918843 + 1.59148i −0.0763058 + 0.132165i
\(146\) −6.89728 −0.570823
\(147\) 20.1402 + 1.06664i 1.66114 + 0.0879750i
\(148\) −0.121969 −0.0100258
\(149\) −3.95962 + 6.85827i −0.324385 + 0.561851i −0.981388 0.192037i \(-0.938491\pi\)
0.657003 + 0.753888i \(0.271824\pi\)
\(150\) 8.64290 + 14.9699i 0.705690 + 1.22229i
\(151\) 0.750582 + 1.30005i 0.0610815 + 0.105796i 0.894949 0.446168i \(-0.147212\pi\)
−0.833868 + 0.551965i \(0.813878\pi\)
\(152\) 8.45592 14.6461i 0.685866 1.18795i
\(153\) −2.96928 −0.240052
\(154\) −9.17305 16.9058i −0.739185 1.36231i
\(155\) 2.80140 0.225014
\(156\) 0 0
\(157\) −1.92846 3.34019i −0.153908 0.266576i 0.778753 0.627331i \(-0.215853\pi\)
−0.932661 + 0.360754i \(0.882519\pi\)
\(158\) −7.83906 13.5777i −0.623642 1.08018i
\(159\) −7.85782 + 13.6102i −0.623166 + 1.07936i
\(160\) 0.447329 0.0353644
\(161\) −4.24462 0.112320i −0.334523 0.00885209i
\(162\) 4.41314 0.346729
\(163\) 7.18042 12.4369i 0.562414 0.974130i −0.434871 0.900493i \(-0.643206\pi\)
0.997285 0.0736372i \(-0.0234607\pi\)
\(164\) 0.0455536 + 0.0789011i 0.00355714 + 0.00616114i
\(165\) −6.12057 10.6011i −0.476486 0.825297i
\(166\) 4.01279 6.95035i 0.311453 0.539452i
\(167\) 4.52138 0.349875 0.174937 0.984580i \(-0.444028\pi\)
0.174937 + 0.984580i \(0.444028\pi\)
\(168\) 11.5301 18.8038i 0.889567 1.45074i
\(169\) 0 0
\(170\) 0.311262 0.539121i 0.0238727 0.0413487i
\(171\) −15.4923 26.8335i −1.18473 2.05201i
\(172\) 0.218370 + 0.378227i 0.0166505 + 0.0288396i
\(173\) 9.75896 16.9030i 0.741960 1.28511i −0.209642 0.977778i \(-0.567230\pi\)
0.951602 0.307334i \(-0.0994369\pi\)
\(174\) 9.05982 0.686823
\(175\) 6.01677 9.81240i 0.454825 0.741748i
\(176\) −20.0001 −1.50756
\(177\) 15.8379 27.4321i 1.19045 2.06192i
\(178\) −3.45416 5.98278i −0.258900 0.448428i
\(179\) −10.4098 18.0303i −0.778065 1.34765i −0.933055 0.359733i \(-0.882868\pi\)
0.154990 0.987916i \(-0.450465\pi\)
\(180\) 0.209800 0.363385i 0.0156376 0.0270851i
\(181\) −16.5522 −1.23031 −0.615157 0.788405i \(-0.710907\pi\)
−0.615157 + 0.788405i \(0.710907\pi\)
\(182\) 0 0
\(183\) 21.0390 1.55525
\(184\) −2.32189 + 4.02163i −0.171172 + 0.296478i
\(185\) −0.500477 0.866851i −0.0367958 0.0637322i
\(186\) −6.90546 11.9606i −0.506333 0.876995i
\(187\) 1.47631 2.55704i 0.107958 0.186990i
\(188\) 0.377527 0.0275340
\(189\) −8.36651 15.4193i −0.608574 1.12159i
\(190\) 6.49606 0.471274
\(191\) 2.12504 3.68068i 0.153762 0.266324i −0.778845 0.627216i \(-0.784194\pi\)
0.932608 + 0.360892i \(0.117528\pi\)
\(192\) −12.0338 20.8431i −0.868463 1.50422i
\(193\) 5.79861 + 10.0435i 0.417393 + 0.722946i 0.995676 0.0928898i \(-0.0296104\pi\)
−0.578283 + 0.815836i \(0.696277\pi\)
\(194\) 7.34231 12.7172i 0.527147 0.913045i
\(195\) 0 0
\(196\) −0.686490 0.0363570i −0.0490350 0.00259693i
\(197\) −14.4213 −1.02748 −0.513738 0.857947i \(-0.671740\pi\)
−0.513738 + 0.857947i \(0.671740\pi\)
\(198\) −19.2698 + 33.3763i −1.36944 + 2.37195i
\(199\) −3.52962 6.11348i −0.250208 0.433373i 0.713375 0.700783i \(-0.247166\pi\)
−0.963583 + 0.267409i \(0.913832\pi\)
\(200\) −6.29410 10.9017i −0.445060 0.770867i
\(201\) 10.5820 18.3286i 0.746398 1.29280i
\(202\) 5.39974 0.379925
\(203\) −2.87710 5.30245i −0.201933 0.372159i
\(204\) 0.158484 0.0110961
\(205\) −0.373840 + 0.647509i −0.0261101 + 0.0452240i
\(206\) −5.82912 10.0963i −0.406134 0.703445i
\(207\) 4.25399 + 7.36812i 0.295673 + 0.512120i
\(208\) 0 0
\(209\) 30.8107 2.13122
\(210\) 8.46954 + 0.224120i 0.584454 + 0.0154657i
\(211\) −26.4226 −1.81901 −0.909505 0.415693i \(-0.863539\pi\)
−0.909505 + 0.415693i \(0.863539\pi\)
\(212\) 0.267838 0.463909i 0.0183952 0.0318614i
\(213\) −13.4186 23.2417i −0.919429 1.59250i
\(214\) 6.67133 + 11.5551i 0.456043 + 0.789890i
\(215\) −1.79207 + 3.10396i −0.122218 + 0.211688i
\(216\) −19.1859 −1.30544
\(217\) −4.80725 + 7.83987i −0.326338 + 0.532205i
\(218\) −20.0842 −1.36028
\(219\) 7.20511 12.4796i 0.486876 0.843294i
\(220\) 0.208623 + 0.361345i 0.0140654 + 0.0243619i
\(221\) 0 0
\(222\) −2.46736 + 4.27359i −0.165598 + 0.286825i
\(223\) 23.0005 1.54023 0.770115 0.637905i \(-0.220199\pi\)
0.770115 + 0.637905i \(0.220199\pi\)
\(224\) −0.767625 + 1.25188i −0.0512891 + 0.0836444i
\(225\) −23.0632 −1.53754
\(226\) −13.4537 + 23.3024i −0.894925 + 1.55006i
\(227\) 0.226684 + 0.392628i 0.0150455 + 0.0260596i 0.873450 0.486914i \(-0.161877\pi\)
−0.858405 + 0.512973i \(0.828544\pi\)
\(228\) 0.826893 + 1.43222i 0.0547623 + 0.0948511i
\(229\) −8.66674 + 15.0112i −0.572714 + 0.991970i 0.423571 + 0.905863i \(0.360776\pi\)
−0.996286 + 0.0861077i \(0.972557\pi\)
\(230\) −1.78373 −0.117616
\(231\) 40.1709 + 1.06300i 2.64305 + 0.0699400i
\(232\) −6.59772 −0.433162
\(233\) −3.90756 + 6.76809i −0.255992 + 0.443392i −0.965165 0.261643i \(-0.915736\pi\)
0.709172 + 0.705035i \(0.249069\pi\)
\(234\) 0 0
\(235\) 1.54910 + 2.68313i 0.101052 + 0.175028i
\(236\) −0.539844 + 0.935038i −0.0351409 + 0.0608658i
\(237\) 32.7557 2.12771
\(238\) 0.974630 + 1.79623i 0.0631759 + 0.116432i
\(239\) −13.5314 −0.875276 −0.437638 0.899151i \(-0.644185\pi\)
−0.437638 + 0.899151i \(0.644185\pi\)
\(240\) 4.40496 7.62961i 0.284339 0.492489i
\(241\) −11.2796 19.5369i −0.726583 1.25848i −0.958319 0.285701i \(-0.907774\pi\)
0.231736 0.972779i \(-0.425560\pi\)
\(242\) −11.5768 20.0517i −0.744188 1.28897i
\(243\) 5.33581 9.24189i 0.342292 0.592868i
\(244\) −0.717125 −0.0459092
\(245\) −2.55848 5.02815i −0.163455 0.321237i
\(246\) 3.68607 0.235015
\(247\) 0 0
\(248\) 5.02884 + 8.71020i 0.319331 + 0.553098i
\(249\) 8.38375 + 14.5211i 0.531299 + 0.920236i
\(250\) 5.19626 9.00019i 0.328641 0.569222i
\(251\) −6.73236 −0.424943 −0.212471 0.977167i \(-0.568151\pi\)
−0.212471 + 0.977167i \(0.568151\pi\)
\(252\) 0.656932 + 1.21071i 0.0413828 + 0.0762678i
\(253\) −8.46023 −0.531890
\(254\) 1.32204 2.28984i 0.0829521 0.143677i
\(255\) 0.650306 + 1.12636i 0.0407238 + 0.0705356i
\(256\) 1.17560 + 2.03620i 0.0734750 + 0.127262i
\(257\) −8.26907 + 14.3225i −0.515811 + 0.893410i 0.484021 + 0.875056i \(0.339176\pi\)
−0.999832 + 0.0183536i \(0.994158\pi\)
\(258\) 17.6699 1.10008
\(259\) 3.28476 + 0.0869209i 0.204105 + 0.00540100i
\(260\) 0 0
\(261\) −6.04392 + 10.4684i −0.374110 + 0.647977i
\(262\) −10.7439 18.6090i −0.663761 1.14967i
\(263\) 5.01137 + 8.67994i 0.309014 + 0.535228i 0.978147 0.207915i \(-0.0666676\pi\)
−0.669133 + 0.743143i \(0.733334\pi\)
\(264\) 21.9743 38.0606i 1.35242 2.34247i
\(265\) 4.39608 0.270049
\(266\) −11.1474 + 18.1796i −0.683489 + 1.11466i
\(267\) 14.4333 0.883302
\(268\) −0.360694 + 0.624740i −0.0220329 + 0.0381621i
\(269\) 7.86149 + 13.6165i 0.479323 + 0.830212i 0.999719 0.0237130i \(-0.00754880\pi\)
−0.520395 + 0.853925i \(0.674215\pi\)
\(270\) −3.68478 6.38223i −0.224249 0.388410i
\(271\) 2.60809 4.51734i 0.158430 0.274409i −0.775873 0.630890i \(-0.782690\pi\)
0.934303 + 0.356481i \(0.116023\pi\)
\(272\) 2.12499 0.128847
\(273\) 0 0
\(274\) −10.8270 −0.654085
\(275\) 11.4669 19.8612i 0.691478 1.19767i
\(276\) −0.227054 0.393269i −0.0136671 0.0236720i
\(277\) 9.63619 + 16.6904i 0.578983 + 1.00283i 0.995596 + 0.0937439i \(0.0298835\pi\)
−0.416614 + 0.909084i \(0.636783\pi\)
\(278\) −6.84343 + 11.8532i −0.410442 + 0.710906i
\(279\) 18.4269 1.10319
\(280\) −6.16786 0.163213i −0.368600 0.00975383i
\(281\) 2.14283 0.127831 0.0639153 0.997955i \(-0.479641\pi\)
0.0639153 + 0.997955i \(0.479641\pi\)
\(282\) 7.63711 13.2279i 0.454783 0.787707i
\(283\) 7.87512 + 13.6401i 0.468127 + 0.810820i 0.999337 0.0364203i \(-0.0115955\pi\)
−0.531209 + 0.847241i \(0.678262\pi\)
\(284\) 0.457381 + 0.792207i 0.0271406 + 0.0470089i
\(285\) −6.78597 + 11.7537i −0.401966 + 0.696226i
\(286\) 0 0
\(287\) −1.17058 2.15735i −0.0690969 0.127344i
\(288\) 2.94242 0.173384
\(289\) 8.34314 14.4507i 0.490773 0.850044i
\(290\) −1.26714 2.19474i −0.0744087 0.128880i
\(291\) 15.3400 + 26.5696i 0.899246 + 1.55754i
\(292\) −0.245590 + 0.425374i −0.0143721 + 0.0248932i
\(293\) −23.1487 −1.35236 −0.676182 0.736735i \(-0.736367\pi\)
−0.676182 + 0.736735i \(0.736367\pi\)
\(294\) −15.1611 + 23.3179i −0.884214 + 1.35993i
\(295\) −8.86057 −0.515882
\(296\) 1.79683 3.11220i 0.104439 0.180893i
\(297\) −17.4769 30.2708i −1.01411 1.75649i
\(298\) −5.46054 9.45793i −0.316320 0.547883i
\(299\) 0 0
\(300\) 1.23098 0.0710708
\(301\) −5.61138 10.3417i −0.323434 0.596084i
\(302\) −2.07019 −0.119126
\(303\) −5.64073 + 9.77003i −0.324052 + 0.561274i
\(304\) 11.0872 + 19.2036i 0.635894 + 1.10140i
\(305\) −2.94258 5.09669i −0.168491 0.291836i
\(306\) 2.04740 3.54621i 0.117042 0.202723i
\(307\) −4.23590 −0.241756 −0.120878 0.992667i \(-0.538571\pi\)
−0.120878 + 0.992667i \(0.538571\pi\)
\(308\) −1.36925 0.0362328i −0.0780201 0.00206456i
\(309\) 24.3571 1.38563
\(310\) −1.93164 + 3.34570i −0.109710 + 0.190023i
\(311\) −13.6251 23.5993i −0.772606 1.33819i −0.936130 0.351654i \(-0.885619\pi\)
0.163524 0.986539i \(-0.447714\pi\)
\(312\) 0 0
\(313\) −1.34849 + 2.33565i −0.0762209 + 0.132018i −0.901617 0.432536i \(-0.857619\pi\)
0.825396 + 0.564555i \(0.190952\pi\)
\(314\) 5.31891 0.300163
\(315\) −5.90910 + 9.63681i −0.332940 + 0.542973i
\(316\) −1.11649 −0.0628077
\(317\) 12.0352 20.8456i 0.675966 1.17081i −0.300220 0.953870i \(-0.597060\pi\)
0.976186 0.216937i \(-0.0696066\pi\)
\(318\) −10.8364 18.7691i −0.607674 1.05252i
\(319\) −6.01000 10.4096i −0.336496 0.582828i
\(320\) −3.36617 + 5.83037i −0.188174 + 0.325928i
\(321\) −27.8763 −1.55590
\(322\) 3.06092 4.99188i 0.170579 0.278187i
\(323\) −3.27362 −0.182149
\(324\) 0.157138 0.272170i 0.00872986 0.0151206i
\(325\) 0 0
\(326\) 9.90220 + 17.1511i 0.548432 + 0.949912i
\(327\) 20.9806 36.3394i 1.16023 2.00958i
\(328\) −2.68434 −0.148218
\(329\) −10.1672 0.269042i −0.560535 0.0148328i
\(330\) 16.8812 0.929279
\(331\) −0.309862 + 0.536696i −0.0170315 + 0.0294995i −0.874416 0.485178i \(-0.838755\pi\)
0.857384 + 0.514677i \(0.172088\pi\)
\(332\) −0.285765 0.494959i −0.0156834 0.0271644i
\(333\) −3.29201 5.70194i −0.180401 0.312464i
\(334\) −3.11762 + 5.39987i −0.170588 + 0.295468i
\(335\) −5.92014 −0.323452
\(336\) 13.7929 + 25.4201i 0.752465 + 1.38678i
\(337\) 5.72118 0.311652 0.155826 0.987784i \(-0.450196\pi\)
0.155826 + 0.987784i \(0.450196\pi\)
\(338\) 0 0
\(339\) −28.1082 48.6848i −1.52663 2.64420i
\(340\) −0.0221660 0.0383927i −0.00120212 0.00208214i
\(341\) −9.16174 + 15.8686i −0.496136 + 0.859333i
\(342\) 42.7295 2.31055
\(343\) 18.4620 + 1.46836i 0.996852 + 0.0792837i
\(344\) −12.8679 −0.693792
\(345\) 1.86334 3.22740i 0.100319 0.173757i
\(346\) 13.4581 + 23.3102i 0.723514 + 1.25316i
\(347\) 0.932429 + 1.61501i 0.0500554 + 0.0866985i 0.889968 0.456024i \(-0.150727\pi\)
−0.839912 + 0.542722i \(0.817394\pi\)
\(348\) 0.322591 0.558744i 0.0172927 0.0299518i
\(349\) 22.3172 1.19461 0.597307 0.802012i \(-0.296237\pi\)
0.597307 + 0.802012i \(0.296237\pi\)
\(350\) 7.57019 + 13.9517i 0.404644 + 0.745751i
\(351\) 0 0
\(352\) −1.46295 + 2.53391i −0.0779756 + 0.135058i
\(353\) 1.16600 + 2.01956i 0.0620597 + 0.107491i 0.895386 0.445291i \(-0.146900\pi\)
−0.833326 + 0.552781i \(0.813566\pi\)
\(354\) 21.8414 + 37.8304i 1.16086 + 2.01066i
\(355\) −3.75354 + 6.50133i −0.199217 + 0.345055i
\(356\) −0.491966 −0.0260741
\(357\) −4.26813 0.112943i −0.225893 0.00597756i
\(358\) 28.7114 1.51744
\(359\) 1.63553 2.83281i 0.0863197 0.149510i −0.819633 0.572889i \(-0.805823\pi\)
0.905953 + 0.423379i \(0.139156\pi\)
\(360\) 6.18147 + 10.7066i 0.325792 + 0.564289i
\(361\) −7.58017 13.1292i −0.398956 0.691013i
\(362\) 11.4132 19.7682i 0.599863 1.03899i
\(363\) 48.3741 2.53898
\(364\) 0 0
\(365\) −4.03092 −0.210988
\(366\) −14.5070 + 25.1268i −0.758291 + 1.31340i
\(367\) −2.07645 3.59652i −0.108390 0.187737i 0.806728 0.590923i \(-0.201236\pi\)
−0.915118 + 0.403186i \(0.867903\pi\)
\(368\) −3.04440 5.27306i −0.158700 0.274877i
\(369\) −2.45903 + 4.25916i −0.128012 + 0.221723i
\(370\) 1.38037 0.0717620
\(371\) −7.54376 + 12.3027i −0.391653 + 0.638724i
\(372\) −0.983525 −0.0509934
\(373\) 5.55446 9.62061i 0.287599 0.498136i −0.685637 0.727944i \(-0.740476\pi\)
0.973236 + 0.229807i \(0.0738096\pi\)
\(374\) 2.03591 + 3.52630i 0.105275 + 0.182341i
\(375\) 10.8563 + 18.8037i 0.560619 + 0.971021i
\(376\) −5.56165 + 9.63305i −0.286820 + 0.496787i
\(377\) 0 0
\(378\) 24.1842 + 0.639958i 1.24390 + 0.0329159i
\(379\) −4.64030 −0.238356 −0.119178 0.992873i \(-0.538026\pi\)
−0.119178 + 0.992873i \(0.538026\pi\)
\(380\) 0.231304 0.400630i 0.0118656 0.0205519i
\(381\) 2.76208 + 4.78407i 0.141506 + 0.245095i
\(382\) 2.93055 + 5.07586i 0.149940 + 0.259703i
\(383\) 1.83466 3.17773i 0.0937469 0.162374i −0.815338 0.578985i \(-0.803449\pi\)
0.909085 + 0.416611i \(0.136782\pi\)
\(384\) 29.9922 1.53053
\(385\) −5.36092 9.88008i −0.273218 0.503535i
\(386\) −15.9932 −0.814033
\(387\) −11.7878 + 20.4171i −0.599208 + 1.03786i
\(388\) −0.522872 0.905640i −0.0265448 0.0459769i
\(389\) −8.44156 14.6212i −0.428004 0.741324i 0.568692 0.822551i \(-0.307450\pi\)
−0.996696 + 0.0812262i \(0.974116\pi\)
\(390\) 0 0
\(391\) 0.898894 0.0454590
\(392\) 11.0409 16.9810i 0.557651 0.857671i
\(393\) 44.8937 2.26459
\(394\) 9.94390 17.2233i 0.500966 0.867699i
\(395\) −4.58131 7.93506i −0.230511 0.399256i
\(396\) 1.37227 + 2.37684i 0.0689592 + 0.119441i
\(397\) −8.35428 + 14.4700i −0.419289 + 0.726230i −0.995868 0.0908114i \(-0.971054\pi\)
0.576579 + 0.817041i \(0.304387\pi\)
\(398\) 9.73508 0.487976
\(399\) −21.2484 39.1604i −1.06375 1.96047i
\(400\) 16.5053 0.825267
\(401\) −12.6567 + 21.9221i −0.632046 + 1.09474i 0.355087 + 0.934833i \(0.384451\pi\)
−0.987133 + 0.159902i \(0.948882\pi\)
\(402\) 14.5932 + 25.2761i 0.727842 + 1.26066i
\(403\) 0 0
\(404\) 0.192267 0.333017i 0.00956566 0.0165682i
\(405\) 2.57913 0.128158
\(406\) 8.31654 + 0.220071i 0.412743 + 0.0109219i
\(407\) 6.54708 0.324527
\(408\) −2.33475 + 4.04391i −0.115587 + 0.200203i
\(409\) −2.86671 4.96529i −0.141750 0.245518i 0.786406 0.617710i \(-0.211940\pi\)
−0.928156 + 0.372192i \(0.878606\pi\)
\(410\) −0.515546 0.892951i −0.0254610 0.0440997i
\(411\) 11.3102 19.5899i 0.557893 0.966299i
\(412\) −0.830225 −0.0409022
\(413\) 15.2049 24.7968i 0.748185 1.22017i
\(414\) −11.7330 −0.576644
\(415\) 2.34516 4.06193i 0.115119 0.199392i
\(416\) 0 0
\(417\) −14.2977 24.7643i −0.700161 1.21272i
\(418\) −21.2448 + 36.7971i −1.03912 + 1.79981i
\(419\) −34.3458 −1.67790 −0.838950 0.544208i \(-0.816830\pi\)
−0.838950 + 0.544208i \(0.816830\pi\)
\(420\) 0.315395 0.514359i 0.0153897 0.0250982i
\(421\) −2.94167 −0.143368 −0.0716842 0.997427i \(-0.522837\pi\)
−0.0716842 + 0.997427i \(0.522837\pi\)
\(422\) 18.2191 31.5565i 0.886894 1.53614i
\(423\) 10.1896 + 17.6489i 0.495437 + 0.858121i
\(424\) 7.89148 + 13.6684i 0.383244 + 0.663798i
\(425\) −1.21835 + 2.11024i −0.0590985 + 0.102362i
\(426\) 37.0100 1.79314
\(427\) 19.3129 + 0.511055i 0.934617 + 0.0247317i
\(428\) 0.950178 0.0459286
\(429\) 0 0
\(430\) −2.47137 4.28053i −0.119180 0.206426i
\(431\) 19.8478 + 34.3773i 0.956033 + 1.65590i 0.731985 + 0.681321i \(0.238594\pi\)
0.224048 + 0.974578i \(0.428073\pi\)
\(432\) 12.5781 21.7858i 0.605162 1.04817i
\(433\) −9.83653 −0.472714 −0.236357 0.971666i \(-0.575953\pi\)
−0.236357 + 0.971666i \(0.575953\pi\)
\(434\) −6.04840 11.1471i −0.290332 0.535078i
\(435\) 5.29475 0.253864
\(436\) −0.715135 + 1.23865i −0.0342488 + 0.0593206i
\(437\) 4.69000 + 8.12331i 0.224353 + 0.388591i
\(438\) 9.93624 + 17.2101i 0.474772 + 0.822329i
\(439\) −14.2733 + 24.7220i −0.681226 + 1.17992i 0.293381 + 0.955996i \(0.405220\pi\)
−0.974607 + 0.223922i \(0.928114\pi\)
\(440\) −12.2936 −0.586073
\(441\) −16.8290 33.0739i −0.801383 1.57495i
\(442\) 0 0
\(443\) −1.66951 + 2.89167i −0.0793207 + 0.137387i −0.902957 0.429731i \(-0.858608\pi\)
0.823636 + 0.567118i \(0.191942\pi\)
\(444\) 0.175709 + 0.304337i 0.00833880 + 0.0144432i
\(445\) −2.01868 3.49646i −0.0956947 0.165748i
\(446\) −15.8595 + 27.4695i −0.750969 + 1.30072i
\(447\) 22.8170 1.07921
\(448\) −10.5402 19.4254i −0.497978 0.917766i
\(449\) 18.1851 0.858206 0.429103 0.903256i \(-0.358830\pi\)
0.429103 + 0.903256i \(0.358830\pi\)
\(450\) 15.9027 27.5443i 0.749660 1.29845i
\(451\) −2.44523 4.23526i −0.115141 0.199430i
\(452\) 0.958084 + 1.65945i 0.0450645 + 0.0780539i
\(453\) 2.16258 3.74570i 0.101607 0.175988i
\(454\) −0.625219 −0.0293430
\(455\) 0 0
\(456\) −48.7265 −2.28183
\(457\) 4.36466 7.55982i 0.204170 0.353633i −0.745698 0.666284i \(-0.767884\pi\)
0.949868 + 0.312651i \(0.101217\pi\)
\(458\) −11.9519 20.7013i −0.558476 0.967309i
\(459\) 1.85691 + 3.21625i 0.0866729 + 0.150122i
\(460\) −0.0635130 + 0.110008i −0.00296131 + 0.00512914i
\(461\) 2.27124 0.105782 0.0528910 0.998600i \(-0.483156\pi\)
0.0528910 + 0.998600i \(0.483156\pi\)
\(462\) −28.9685 + 47.2430i −1.34774 + 2.19794i
\(463\) 5.48326 0.254829 0.127414 0.991850i \(-0.459332\pi\)
0.127414 + 0.991850i \(0.459332\pi\)
\(464\) 4.32538 7.49178i 0.200801 0.347797i
\(465\) −4.03570 6.99003i −0.187151 0.324155i
\(466\) −5.38873 9.33356i −0.249628 0.432369i
\(467\) −9.44095 + 16.3522i −0.436875 + 0.756690i −0.997447 0.0714164i \(-0.977248\pi\)
0.560572 + 0.828106i \(0.310581\pi\)
\(468\) 0 0
\(469\) 10.1591 16.5679i 0.469103 0.765032i
\(470\) −4.27260 −0.197080
\(471\) −5.55629 + 9.62377i −0.256020 + 0.443440i
\(472\) −15.9058 27.5496i −0.732122 1.26807i
\(473\) −11.7217 20.3025i −0.538962 0.933510i
\(474\) −22.5859 + 39.1200i −1.03741 + 1.79684i
\(475\) −25.4270 −1.16667
\(476\) 0.145482 + 0.00384971i 0.00666814 + 0.000176451i
\(477\) 28.9163 1.32399
\(478\) 9.33030 16.1606i 0.426758 0.739166i
\(479\) 16.5677 + 28.6961i 0.756997 + 1.31116i 0.944375 + 0.328869i \(0.106668\pi\)
−0.187378 + 0.982288i \(0.559999\pi\)
\(480\) −0.644422 1.11617i −0.0294137 0.0509461i
\(481\) 0 0
\(482\) 31.1104 1.41704
\(483\) 5.83454 + 10.7530i 0.265481 + 0.489276i
\(484\) −1.64886 −0.0749480
\(485\) 4.29100 7.43222i 0.194844 0.337480i
\(486\) 7.35838 + 12.7451i 0.333783 + 0.578129i
\(487\) 7.97814 + 13.8185i 0.361524 + 0.626178i 0.988212 0.153093i \(-0.0489233\pi\)
−0.626688 + 0.779270i \(0.715590\pi\)
\(488\) 10.5645 18.2983i 0.478234 0.828326i
\(489\) −41.3765 −1.87111
\(490\) 7.76924 + 0.411465i 0.350979 + 0.0185881i
\(491\) −31.6928 −1.43028 −0.715138 0.698983i \(-0.753636\pi\)
−0.715138 + 0.698983i \(0.753636\pi\)
\(492\) 0.131249 0.227330i 0.00591717 0.0102488i
\(493\) 0.638559 + 1.10602i 0.0287593 + 0.0498125i
\(494\) 0 0
\(495\) −11.2617 + 19.5058i −0.506174 + 0.876720i
\(496\) −13.1874 −0.592130
\(497\) −11.7532 21.6609i −0.527202 0.971624i
\(498\) −23.1233 −1.03618
\(499\) 12.1092 20.9738i 0.542083 0.938916i −0.456701 0.889620i \(-0.650969\pi\)
0.998784 0.0492955i \(-0.0156976\pi\)
\(500\) −0.370044 0.640935i −0.0165489 0.0286635i
\(501\) −6.51351 11.2817i −0.291002 0.504030i
\(502\) 4.64215 8.04043i 0.207189 0.358862i
\(503\) 0.854498 0.0381002 0.0190501 0.999819i \(-0.493936\pi\)
0.0190501 + 0.999819i \(0.493936\pi\)
\(504\) −40.5706 1.07357i −1.80716 0.0478208i
\(505\) 3.15572 0.140428
\(506\) 5.83356 10.1040i 0.259333 0.449179i
\(507\) 0 0
\(508\) −0.0941471 0.163068i −0.00417710 0.00723495i
\(509\) −0.650000 + 1.12583i −0.0288108 + 0.0499017i −0.880071 0.474842i \(-0.842505\pi\)
0.851261 + 0.524743i \(0.175839\pi\)
\(510\) −1.79362 −0.0794227
\(511\) 6.91713 11.2807i 0.305996 0.499031i
\(512\) −24.0616 −1.06338
\(513\) −19.3769 + 33.5618i −0.855511 + 1.48179i
\(514\) −11.4035 19.7514i −0.502987 0.871199i
\(515\) −3.40666 5.90051i −0.150115 0.260007i
\(516\) 0.629167 1.08975i 0.0276976 0.0479736i
\(517\) −20.2649 −0.891248
\(518\) −2.36874 + 3.86305i −0.104077 + 0.169732i
\(519\) −56.2351 −2.46845
\(520\) 0 0
\(521\) 12.5228 + 21.6901i 0.548632 + 0.950259i 0.998369 + 0.0570974i \(0.0181846\pi\)
−0.449736 + 0.893161i \(0.648482\pi\)
\(522\) −8.33490 14.4365i −0.364809 0.631867i
\(523\) −6.41197 + 11.1059i −0.280376 + 0.485625i −0.971477 0.237133i \(-0.923792\pi\)
0.691101 + 0.722758i \(0.257126\pi\)
\(524\) −1.53022 −0.0668482
\(525\) −33.1516 0.877253i −1.44686 0.0382865i
\(526\) −13.8219 −0.602664
\(527\) 0.973429 1.68603i 0.0424032 0.0734446i
\(528\) 28.8121 + 49.9040i 1.25389 + 2.17179i
\(529\) 10.2122 + 17.6880i 0.444008 + 0.769045i
\(530\) −3.03122 + 5.25022i −0.131668 + 0.228055i
\(531\) −58.2827 −2.52925
\(532\) 0.724263 + 1.33480i 0.0314008 + 0.0578711i
\(533\) 0 0
\(534\) −9.95213 + 17.2376i −0.430671 + 0.745944i
\(535\) 3.89886 + 6.75303i 0.168563 + 0.291959i
\(536\) −10.6273 18.4071i −0.459031 0.795066i
\(537\) −29.9928 + 51.9490i −1.29428 + 2.24176i
\(538\) −21.6828 −0.934814
\(539\) 36.8494 + 1.95157i 1.58722 + 0.0840602i
\(540\) −0.524813 −0.0225843
\(541\) 14.3725 24.8938i 0.617920 1.07027i −0.371944 0.928255i \(-0.621309\pi\)
0.989865 0.142014i \(-0.0453578\pi\)
\(542\) 3.59670 + 6.22966i 0.154491 + 0.267587i
\(543\) 23.8451 + 41.3009i 1.02329 + 1.77239i
\(544\) 0.155438 0.269226i 0.00666434 0.0115430i
\(545\) −11.7376 −0.502785
\(546\) 0 0
\(547\) −8.88085 −0.379718 −0.189859 0.981811i \(-0.560803\pi\)
−0.189859 + 0.981811i \(0.560803\pi\)
\(548\) −0.385516 + 0.667733i −0.0164684 + 0.0285241i
\(549\) −19.3556 33.5248i −0.826075 1.43080i
\(550\) 15.8134 + 27.3897i 0.674287 + 1.16790i
\(551\) −6.66339 + 11.5413i −0.283870 + 0.491677i
\(552\) 13.3797 0.569476
\(553\) 30.0683 + 0.795664i 1.27864 + 0.0338351i
\(554\) −26.5777 −1.12918
\(555\) −1.44198 + 2.49757i −0.0612084 + 0.106016i
\(556\) 0.487345 + 0.844106i 0.0206680 + 0.0357981i
\(557\) −19.3637 33.5389i −0.820465 1.42109i −0.905336 0.424695i \(-0.860381\pi\)
0.0848711 0.996392i \(-0.472952\pi\)
\(558\) −12.7059 + 22.0072i −0.537882 + 0.931639i
\(559\) 0 0
\(560\) 4.22890 6.89666i 0.178704 0.291437i
\(561\) −8.50710 −0.359170
\(562\) −1.47754 + 2.55918i −0.0623263 + 0.107952i
\(563\) −3.45441 5.98321i −0.145586 0.252162i 0.784005 0.620754i \(-0.213173\pi\)
−0.929591 + 0.368592i \(0.879840\pi\)
\(564\) −0.543865 0.942002i −0.0229009 0.0396655i
\(565\) −7.86260 + 13.6184i −0.330782 + 0.572932i
\(566\) −21.7205 −0.912979
\(567\) −4.42583 + 7.21784i −0.185868 + 0.303121i
\(568\) −26.9522 −1.13089
\(569\) 1.41872 2.45730i 0.0594759 0.103015i −0.834754 0.550623i \(-0.814390\pi\)
0.894230 + 0.447607i \(0.147724\pi\)
\(570\) −9.35823 16.2089i −0.391973 0.678917i
\(571\) 23.3362 + 40.4195i 0.976589 + 1.69150i 0.674588 + 0.738195i \(0.264321\pi\)
0.302001 + 0.953307i \(0.402345\pi\)
\(572\) 0 0
\(573\) −12.2453 −0.511557
\(574\) 3.38366 + 0.0895379i 0.141231 + 0.00373724i
\(575\) 6.98193 0.291167
\(576\) −22.1418 + 38.3507i −0.922576 + 1.59795i
\(577\) 5.70441 + 9.88033i 0.237478 + 0.411323i 0.959990 0.280035i \(-0.0903460\pi\)
−0.722512 + 0.691358i \(0.757013\pi\)
\(578\) 11.5057 + 19.9284i 0.478572 + 0.828911i
\(579\) 16.7070 28.9373i 0.694318 1.20259i
\(580\) −0.180474 −0.00749379
\(581\) 7.34321 + 13.5334i 0.304648 + 0.561460i
\(582\) −42.3094 −1.75378
\(583\) −14.3770 + 24.9017i −0.595436 + 1.03132i
\(584\) −7.23597 12.5331i −0.299426 0.518622i
\(585\) 0 0
\(586\) 15.9617 27.6465i 0.659371 1.14206i
\(587\) −46.4410 −1.91683 −0.958413 0.285384i \(-0.907879\pi\)
−0.958413 + 0.285384i \(0.907879\pi\)
\(588\) 0.898240 + 1.76530i 0.0370428 + 0.0727998i
\(589\) 20.3156 0.837088
\(590\) 6.10961 10.5821i 0.251529 0.435660i
\(591\) 20.7754 + 35.9840i 0.854585 + 1.48018i
\(592\) 2.35596 + 4.08064i 0.0968292 + 0.167713i
\(593\) −10.1303 + 17.5462i −0.416001 + 0.720535i −0.995533 0.0944146i \(-0.969902\pi\)
0.579532 + 0.814950i \(0.303235\pi\)
\(594\) 48.2031 1.97780
\(595\) 0.569594 + 1.04975i 0.0233511 + 0.0430356i
\(596\) −0.777728 −0.0318570
\(597\) −10.1696 + 17.6142i −0.416212 + 0.720901i
\(598\) 0 0
\(599\) 19.4938 + 33.7642i 0.796494 + 1.37957i 0.921886 + 0.387462i \(0.126648\pi\)
−0.125391 + 0.992107i \(0.540019\pi\)
\(600\) −18.1346 + 31.4100i −0.740342 + 1.28231i
\(601\) 19.1390 0.780697 0.390348 0.920667i \(-0.372355\pi\)
0.390348 + 0.920667i \(0.372355\pi\)
\(602\) 16.2202 + 0.429217i 0.661087 + 0.0174936i
\(603\) −38.9412 −1.58581
\(604\) −0.0737127 + 0.127674i −0.00299933 + 0.00519499i
\(605\) −6.76575 11.7186i −0.275067 0.476430i
\(606\) −7.77888 13.4734i −0.315995 0.547320i
\(607\) −21.6668 + 37.5280i −0.879428 + 1.52321i −0.0274572 + 0.999623i \(0.508741\pi\)
−0.851970 + 0.523590i \(0.824592\pi\)
\(608\) 3.24400 0.131562
\(609\) −9.08589 + 14.8177i −0.368179 + 0.600442i
\(610\) 8.11595 0.328605
\(611\) 0 0
\(612\) −0.145803 0.252538i −0.00589373 0.0102082i
\(613\) 5.15478 + 8.92834i 0.208200 + 0.360612i 0.951147 0.308737i \(-0.0999063\pi\)
−0.742948 + 0.669349i \(0.766573\pi\)
\(614\) 2.92077 5.05892i 0.117873 0.204161i
\(615\) 2.15422 0.0868664
\(616\) 21.0960 34.4042i 0.849982 1.38619i
\(617\) 11.0699 0.445659 0.222829 0.974857i \(-0.428471\pi\)
0.222829 + 0.974857i \(0.428471\pi\)
\(618\) −16.7949 + 29.0896i −0.675589 + 1.17015i
\(619\) 16.8808 + 29.2384i 0.678498 + 1.17519i 0.975433 + 0.220295i \(0.0707019\pi\)
−0.296936 + 0.954897i \(0.595965\pi\)
\(620\) 0.137559 + 0.238259i 0.00552450 + 0.00956871i
\(621\) 5.32065 9.21563i 0.213510 0.369810i
\(622\) 37.5794 1.50680
\(623\) 13.2491 + 0.350597i 0.530816 + 0.0140464i
\(624\) 0 0
\(625\) −7.83931 + 13.5781i −0.313573 + 0.543124i
\(626\) −1.85964 3.22098i −0.0743260 0.128736i
\(627\) −44.3860 76.8787i −1.77260 3.07024i
\(628\) 0.189389 0.328031i 0.00755745 0.0130899i
\(629\) −0.695623 −0.0277363
\(630\) −7.43473 13.7021i −0.296207 0.545904i
\(631\) 38.5975 1.53654 0.768271 0.640125i \(-0.221117\pi\)
0.768271 + 0.640125i \(0.221117\pi\)
\(632\) 16.4480 28.4887i 0.654265 1.13322i
\(633\) 38.0645 + 65.9296i 1.51293 + 2.62047i
\(634\) 16.5972 + 28.7473i 0.659161 + 1.14170i
\(635\) 0.772627 1.33823i 0.0306608 0.0531060i
\(636\) −1.54339 −0.0611995
\(637\) 0 0
\(638\) 16.5763 0.656260
\(639\) −24.6899 + 42.7641i −0.976717 + 1.69172i
\(640\) −4.19480 7.26560i −0.165814 0.287198i
\(641\) −9.76141 16.9073i −0.385553 0.667797i 0.606293 0.795241i \(-0.292656\pi\)
−0.991846 + 0.127445i \(0.959322\pi\)
\(642\) 19.2215 33.2926i 0.758611 1.31395i
\(643\) −12.4718 −0.491839 −0.245920 0.969290i \(-0.579090\pi\)
−0.245920 + 0.969290i \(0.579090\pi\)
\(644\) −0.198873 0.366520i −0.00783671 0.0144429i
\(645\) 10.3266 0.406611
\(646\) 2.25725 3.90967i 0.0888103 0.153824i
\(647\) −17.9695 31.1241i −0.706455 1.22362i −0.966164 0.257929i \(-0.916960\pi\)
0.259709 0.965687i \(-0.416373\pi\)
\(648\) 4.62984 + 8.01911i 0.181877 + 0.315021i
\(649\) 28.9778 50.1910i 1.13748 1.97017i
\(650\) 0 0
\(651\) 26.4873 + 0.700904i 1.03812 + 0.0274706i
\(652\) 1.41034 0.0552332
\(653\) −2.42944 + 4.20791i −0.0950713 + 0.164668i −0.909638 0.415401i \(-0.863641\pi\)
0.814567 + 0.580069i \(0.196975\pi\)
\(654\) 28.9334 + 50.1141i 1.13138 + 1.95962i
\(655\) −6.27897 10.8755i −0.245340 0.424941i
\(656\) 1.75982 3.04810i 0.0687095 0.119008i
\(657\) −26.5144 −1.03442
\(658\) 7.33186 11.9571i 0.285826 0.466137i
\(659\) −23.6206 −0.920127 −0.460063 0.887886i \(-0.652173\pi\)
−0.460063 + 0.887886i \(0.652173\pi\)
\(660\) 0.601085 1.04111i 0.0233972 0.0405251i
\(661\) −8.19662 14.1970i −0.318812 0.552198i 0.661429 0.750008i \(-0.269950\pi\)
−0.980240 + 0.197810i \(0.936617\pi\)
\(662\) −0.427316 0.740134i −0.0166081 0.0287661i
\(663\) 0 0
\(664\) 16.8393 0.653492
\(665\) −6.51475 + 10.6245i −0.252631 + 0.412002i
\(666\) 9.07974 0.351833
\(667\) 1.82968 3.16910i 0.0708456 0.122708i
\(668\) 0.222016 + 0.384544i 0.00859007 + 0.0148784i
\(669\) −33.1346 57.3908i −1.28106 2.21886i
\(670\) 4.08210 7.07040i 0.157705 0.273154i
\(671\) 38.4939 1.48604
\(672\) 4.22951 + 0.111921i 0.163157 + 0.00431744i
\(673\) −14.2536 −0.549434 −0.274717 0.961525i \(-0.588584\pi\)
−0.274717 + 0.961525i \(0.588584\pi\)
\(674\) −3.94491 + 6.83278i −0.151952 + 0.263189i
\(675\) 14.4230 + 24.9814i 0.555143 + 0.961536i
\(676\) 0 0
\(677\) 5.13574 8.89537i 0.197383 0.341877i −0.750296 0.661102i \(-0.770089\pi\)
0.947679 + 0.319225i \(0.103423\pi\)
\(678\) 77.5255 2.97735
\(679\) 13.4361 + 24.7624i 0.515629 + 0.950295i
\(680\) 1.30618 0.0500898
\(681\) 0.653122 1.13124i 0.0250277 0.0433492i
\(682\) −12.6345 21.8837i −0.483802 0.837969i
\(683\) 1.11101 + 1.92432i 0.0425115 + 0.0736321i 0.886498 0.462732i \(-0.153131\pi\)
−0.843987 + 0.536364i \(0.819797\pi\)
\(684\) 1.52146 2.63524i 0.0581744 0.100761i
\(685\) −6.32754 −0.241763
\(686\) −14.4837 + 21.0366i −0.552989 + 0.803181i
\(687\) 49.9413 1.90538
\(688\) 8.43604 14.6117i 0.321621 0.557064i
\(689\) 0 0
\(690\) 2.56965 + 4.45076i 0.0978249 + 0.169438i
\(691\) 1.32007 2.28643i 0.0502179 0.0869800i −0.839824 0.542859i \(-0.817342\pi\)
0.890042 + 0.455879i \(0.150675\pi\)
\(692\) 1.91680 0.0728659
\(693\) −35.2628 64.9887i −1.33952 2.46872i
\(694\) −2.57174 −0.0976220
\(695\) −3.99944 + 6.92724i −0.151708 + 0.262765i
\(696\) 9.50469 + 16.4626i 0.360274 + 0.624014i
\(697\) 0.259804 + 0.449993i 0.00984077 + 0.0170447i
\(698\) −15.3884 + 26.6534i −0.582458 + 1.00885i
\(699\) 22.5169 0.851668
\(700\) 1.12999 + 0.0299017i 0.0427097 + 0.00113018i
\(701\) 8.89991 0.336145 0.168072 0.985775i \(-0.446246\pi\)
0.168072 + 0.985775i \(0.446246\pi\)
\(702\) 0 0
\(703\) −3.62943 6.28635i −0.136886 0.237094i
\(704\) −22.0175 38.1355i −0.829818 1.43729i
\(705\) 4.46328 7.73063i 0.168097 0.291152i
\(706\) −3.21594 −0.121034
\(707\) −5.41528 + 8.83147i −0.203663 + 0.332142i
\(708\) 3.11080 0.116911
\(709\) −20.2972 + 35.1558i −0.762278 + 1.32030i 0.179396 + 0.983777i \(0.442586\pi\)
−0.941674 + 0.336527i \(0.890748\pi\)
\(710\) −5.17634 8.96569i −0.194265 0.336476i
\(711\) −30.1347 52.1949i −1.13014 1.95746i
\(712\) 7.24754 12.5531i 0.271613 0.470448i
\(713\) −5.57839 −0.208912
\(714\) 3.07788 5.01954i 0.115187 0.187851i
\(715\) 0 0
\(716\) 1.02232 1.77071i 0.0382059 0.0661745i
\(717\) 19.4934 + 33.7636i 0.727995 + 1.26092i
\(718\) 2.25548 + 3.90661i 0.0841738 + 0.145793i
\(719\) −7.25674 + 12.5690i −0.270631 + 0.468746i −0.969024 0.246968i \(-0.920566\pi\)
0.698393 + 0.715715i \(0.253899\pi\)
\(720\) −16.2100 −0.604110
\(721\) 22.3588 + 0.591655i 0.832685 + 0.0220344i
\(722\) 20.9069 0.778076
\(723\) −32.4988 + 56.2896i −1.20864 + 2.09343i
\(724\) −0.812773 1.40776i −0.0302065 0.0523191i
\(725\) 4.95984 + 8.59070i 0.184204 + 0.319051i
\(726\) −33.3552 + 57.7730i −1.23793 + 2.14416i
\(727\) −30.6942 −1.13839 −0.569193 0.822204i \(-0.692744\pi\)
−0.569193 + 0.822204i \(0.692744\pi\)
\(728\) 0 0
\(729\) −40.3475 −1.49435
\(730\) 2.77943 4.81411i 0.102871 0.178178i
\(731\) 1.24542 + 2.15713i 0.0460635 + 0.0797842i
\(732\) 1.03309 + 1.78937i 0.0381842 + 0.0661369i
\(733\) −6.63218 + 11.4873i −0.244965 + 0.424292i −0.962122 0.272620i \(-0.912110\pi\)
0.717157 + 0.696912i \(0.245443\pi\)
\(734\) 5.72708 0.211390
\(735\) −8.86046 + 13.6275i −0.326823 + 0.502656i
\(736\) −0.890761 −0.0328339
\(737\) 19.3613 33.5348i 0.713184 1.23527i
\(738\) −3.39113 5.87361i −0.124829 0.216211i
\(739\) 3.62737 + 6.28279i 0.133435 + 0.231116i 0.924999 0.379971i \(-0.124066\pi\)
−0.791564 + 0.611087i \(0.790733\pi\)
\(740\) 0.0491505 0.0851312i 0.00180681 0.00312948i
\(741\) 0 0
\(742\) −9.49142 17.4925i −0.348441 0.642171i
\(743\) −46.2694 −1.69746 −0.848730 0.528827i \(-0.822632\pi\)
−0.848730 + 0.528827i \(0.822632\pi\)
\(744\) 14.4891 25.0959i 0.531196 0.920059i
\(745\) −3.19125 5.52741i −0.116918 0.202509i
\(746\) 7.65991 + 13.2673i 0.280449 + 0.485752i
\(747\) 15.4259 26.7184i 0.564403 0.977574i
\(748\) 0.289969 0.0106023
\(749\) −25.5893 0.677140i −0.935012 0.0247421i
\(750\) −29.9430 −1.09336
\(751\) 18.0130 31.1995i 0.657305 1.13848i −0.324006 0.946055i \(-0.605030\pi\)
0.981311 0.192430i \(-0.0616368\pi\)
\(752\) −7.29229 12.6306i −0.265922 0.460591i
\(753\) 9.69865 + 16.7985i 0.353438 + 0.612173i
\(754\) 0 0
\(755\) −1.20986 −0.0440313
\(756\) 0.900589 1.46872i 0.0327541 0.0534168i
\(757\) −10.5626 −0.383906 −0.191953 0.981404i \(-0.561482\pi\)
−0.191953 + 0.981404i \(0.561482\pi\)
\(758\) 3.19961 5.54189i 0.116215 0.201291i
\(759\) 12.1878 + 21.1099i 0.442390 + 0.766242i
\(760\) 6.81504 + 11.8040i 0.247207 + 0.428176i
\(761\) 3.90601 6.76541i 0.141593 0.245246i −0.786504 0.617585i \(-0.788111\pi\)
0.928097 + 0.372340i \(0.121444\pi\)
\(762\) −7.61813 −0.275976
\(763\) 20.1420 32.8485i 0.729191 1.18919i
\(764\) 0.417389 0.0151006
\(765\) 1.19654 2.07248i 0.0432612 0.0749305i
\(766\) 2.53010 + 4.38226i 0.0914163 + 0.158338i
\(767\) 0 0
\(768\) 3.38714 5.86671i 0.122223 0.211696i
\(769\) 25.2915 0.912033 0.456017 0.889971i \(-0.349276\pi\)
0.456017 + 0.889971i \(0.349276\pi\)
\(770\) 15.4962 + 0.410059i 0.558446 + 0.0147775i
\(771\) 47.6497 1.71606
\(772\) −0.569467 + 0.986345i −0.0204956 + 0.0354993i
\(773\) 23.3002 + 40.3572i 0.838051 + 1.45155i 0.891522 + 0.452977i \(0.149638\pi\)
−0.0534716 + 0.998569i \(0.517029\pi\)
\(774\) −16.2560 28.1563i −0.584311 1.01206i
\(775\) 7.56086 13.0958i 0.271594 0.470415i
\(776\) 30.8114 1.10606
\(777\) −4.51515 8.32134i −0.161980 0.298526i
\(778\) 23.2827 0.834727
\(779\) −2.71106 + 4.69570i −0.0971339 + 0.168241i
\(780\) 0 0
\(781\) −24.5513 42.5241i −0.878515 1.52163i
\(782\) −0.619812 + 1.07355i