Properties

Label 1183.2.e.j.170.10
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 170.10
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.j.508.10

$q$-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 −0.512328 0.858790i \(-0.671217\pi\)
0.999898 + 0.0142944i \(0.00455022\pi\)
\(3\) −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 −0.761738 0.647885i \(-0.775654\pi\)
0.941954 + 0.335742i \(0.108987\pi\)
\(6\) −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 \(0.125716\pi\)
−0.128296 + 0.991736i \(0.540951\pi\)
\(12\) 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 \(-0.599442\pi\)
0.977782 0.209625i \(-0.0672243\pi\)
\(20\) 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 0.978827 0.204692i \(-0.0656191\pi\)
−0.666681 + 0.745343i \(0.732286\pi\)
\(32\) 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 −0.810457 0.585799i \(-0.800781\pi\)
0.912545 + 0.408977i \(0.134114\pi\)
\(38\) −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 \(-0.523079\pi\)
−0.0724413 + 0.997373i \(0.523079\pi\)
\(42\) −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 −0.971475 0.237143i \(-0.923789\pi\)
0.691109 + 0.722750i \(0.257122\pi\)
\(48\) −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 \(-0.912799\pi\)
0.247063 0.968999i \(-0.420534\pi\)
\(60\) −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 0.549600 0.835428i \(-0.314780\pi\)
−0.998302 + 0.0582541i \(0.981447\pi\)
\(68\) −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 \(-0.686410\pi\)
−0.552720 + 0.833367i \(0.686410\pi\)
\(72\) −7.66982 + 13.2845i −0.903896 + 1.56559i
\(73\) −2.50073 4.33139i −0.292688 0.506951i 0.681756 0.731579i \(-0.261216\pi\)
−0.974444 + 0.224629i \(0.927883\pi\)
\(74\) −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 \(-0.396521\pi\)
0.319393 + 0.947622i \(0.396521\pi\)
\(84\) 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 −0.702194 0.711986i \(-0.747796\pi\)
0.967695 + 0.252125i \(0.0811294\pi\)
\(90\) 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 \(-0.318202\pi\)
0.540586 + 0.841289i \(0.318202\pi\)
\(98\) 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 \(-0.920972\pi\)
0.271860 0.962337i \(-0.412361\pi\)
\(110\) 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 0.648178 0.761489i \(-0.275531\pi\)
−0.983558 + 0.180594i \(0.942198\pi\)
\(138\) −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 −0.657003 0.753888i \(-0.728176\pi\)
0.981388 + 0.192037i \(0.0615093\pi\)
\(150\) −8.64290 14.9699i −0.705690 1.22229i
\(151\) −0.750582 1.30005i −0.0610815 0.105796i 0.833868 0.551965i \(-0.186122\pi\)
−0.894949 + 0.446168i \(0.852788\pi\)
\(152\) 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 \(0.356794\pi\)
−0.997285 + 0.0736372i \(0.976539\pi\)
\(164\) −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 \(-0.555972\pi\)
−0.174937 + 0.984580i \(0.555972\pi\)
\(168\) 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 0.578283 0.815836i \(-0.303723\pi\)
−0.995676 + 0.0928898i \(0.970390\pi\)
\(194\) 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 \(-0.328260\pi\)
0.513738 + 0.857947i \(0.328260\pi\)
\(198\) −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 \(-0.779801\pi\)
−0.770115 + 0.637905i \(0.779801\pi\)
\(224\) −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 0.858405 0.512973i \(-0.171456\pi\)
−0.873450 + 0.486914i \(0.838123\pi\)
\(228\) −0.826893 1.43222i −0.0547623 0.0948511i
\(229\) 8.66674 15.0112i 0.572714 0.991970i −0.423571 0.905863i \(-0.639224\pi\)
0.996286 0.0861077i \(-0.0274429\pi\)
\(230\) −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 \(-0.355815\pi\)
0.437638 + 0.899151i \(0.355815\pi\)
\(240\) −4.40496 + 7.62961i −0.284339 + 0.492489i
\(241\) 11.2796 + 19.5369i 0.726583 + 1.25848i 0.958319 + 0.285701i \(0.0922263\pi\)
−0.231736 + 0.972779i \(0.574440\pi\)
\(242\) 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 −0.934303 0.356481i \(-0.883977\pi\)
0.775873 + 0.630890i \(0.217310\pi\)
\(272\) 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 \(-0.520359\pi\)
−0.0639153 + 0.997955i \(0.520359\pi\)
\(282\) 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 \(-0.263633\pi\)
0.676182 + 0.736735i \(0.263633\pi\)
\(294\) 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 \(-0.461429\pi\)
0.120878 + 0.992667i \(0.461429\pi\)
\(308\) −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 \(0.402940\pi\)
−0.976186 + 0.216937i \(0.930393\pi\)
\(318\) 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 −0.857384 0.514677i \(-0.827912\pi\)
0.874416 + 0.485178i \(0.161245\pi\)
\(332\) 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 \(-0.703763\pi\)
−0.597307 + 0.802012i \(0.703763\pi\)
\(350\) 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 0.833326 0.552781i \(-0.186434\pi\)
−0.895386 + 0.445291i \(0.853100\pi\)
\(354\) 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 −0.905953 0.423379i \(-0.860844\pi\)
0.819633 + 0.572889i \(0.194177\pi\)
\(360\) 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 \(-0.461974\pi\)
0.119178 + 0.992873i \(0.461974\pi\)
\(380\) 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 −0.909085 0.416611i \(-0.863218\pi\)
0.815338 + 0.578985i \(0.196551\pi\)
\(384\) −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 −0.576579 0.817041i \(-0.695613\pi\)
0.995868 + 0.0908114i \(0.0289461\pi\)
\(398\) −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 \(-0.615549\pi\)
0.987133 0.159902i \(-0.0511179\pi\)
\(402\) 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 0.928156 0.372192i \(-0.121394\pi\)
−0.786406 + 0.617710i \(0.788060\pi\)
\(410\) 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 \(-0.477163\pi\)
0.0716842 + 0.997427i \(0.477163\pi\)
\(422\) −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 \(-0.761406\pi\)
−0.224048 0.974578i \(-0.571927\pi\)
\(432\) 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 \(-0.641170\pi\)
−0.429103 + 0.903256i \(0.641170\pi\)
\(450\) −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 −0.949868 0.312651i \(-0.898783\pi\)
0.745698 + 0.666284i \(0.232116\pi\)
\(458\) −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 \(-0.516844\pi\)
−0.0528910 + 0.998600i \(0.516844\pi\)
\(462\) 28.9685 47.2430i 1.34774 2.19794i
\(463\) −5.48326 −0.254829 −0.127414 0.991850i \(-0.540668\pi\)
−0.127414 + 0.991850i \(0.540668\pi\)
\(464\) 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 \(-0.893332\pi\)
0.187378 0.982288i \(-0.440001\pi\)
\(480\) −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 0.626688 0.779270i \(-0.284410\pi\)
−0.988212 + 0.153093i \(0.951077\pi\)
\(488\) −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 \(0.349031\pi\)
−0.998784 + 0.0492955i \(0.984302\pi\)
\(500\) 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 −0.851261 0.524743i \(-0.824161\pi\)
0.880071 + 0.474842i \(0.157495\pi\)
\(510\) −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 \(0.378691\pi\)
−0.989865 + 0.142014i \(0.954642\pi\)
\(542\) 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 \(0.139619\pi\)
−0.0848711 + 0.996392i \(0.527048\pi\)
\(558\) −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 0.722512 0.691358i \(-0.242987\pi\)
−0.959990 + 0.280035i \(0.909654\pi\)
\(578\) −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 \(-0.0921211\pi\)
0.958413 + 0.285384i \(0.0921211\pi\)
\(588\) 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 −0.579532 0.814950i \(-0.696765\pi\)
0.995533 + 0.0944146i \(0.0300979\pi\)
\(594\) 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 0.742948 0.669349i \(-0.233427\pi\)
−0.951147 + 0.308737i \(0.900094\pi\)
\(614\) 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 \(-0.571529\pi\)
−0.222829 + 0.974857i \(0.571529\pi\)
\(618\) 16.7949 29.0896i 0.675589 1.17015i
\(619\) −16.8808 29.2384i −0.678498 1.17519i −0.975433 0.220295i \(-0.929298\pi\)
0.296936 0.954897i \(-0.404035\pi\)
\(620\) 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 \(-0.778883\pi\)
−0.768271 + 0.640125i \(0.778883\pi\)
\(632\) −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 \(-0.420910\pi\)
0.245920 + 0.969290i \(0.420910\pi\)
\(644\) 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 0.980240 0.197810i \(-0.0633829\pi\)
−0.661429 + 0.750008i \(0.730050\pi\)
\(662\) −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 0.843987 0.536364i \(-0.180203\pi\)
−0.886498 + 0.462732i \(0.846869\pi\)
\(684\) −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 −0.890042 0.455879i \(-0.849325\pi\)
0.839824 + 0.542859i \(0.182658\pi\)
\(692\) 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 \(-0.557414\pi\)
0.941674 0.336527i \(-0.109252\pi\)
\(710\) 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 −0.717157 0.696912i \(-0.754557\pi\)
0.962122 + 0.272620i \(0.0878901\pi\)
\(734\) −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 0.791564 0.611087i \(-0.209267\pi\)
−0.924999 + 0.379971i \(0.875934\pi\)
\(740\) 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 \(-0.177368\pi\)
0.848730 + 0.528827i \(0.177368\pi\)
\(744\) 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 −0.928097 0.372340i \(-0.878556\pi\)
0.786504 + 0.617585i \(0.211889\pi\)
\(762\) 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 \(-0.650724\pi\)
−0.456017 + 0.889971i \(0.650724\pi\)
\(770\) 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 \(-0.850362\pi\)
0.0534716 0.998569i \(-0.482971\pi\)
\(774\) 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