Properties

Label 804.2.y.b.49.3
Level 804
Weight 2
Character 804.49
Analytic conductor 6.420
Analytic rank 0
Dimension 120
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.y (of order \(33\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(6\) over \(\Q(\zeta_{33})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label 49.3
Character \(\chi\) = 804.49
Dual form 804.2.y.b.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.841254 - 0.540641i) q^{3} +(-0.166640 - 1.15901i) q^{5} +(-3.32963 - 0.317941i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\) \(q+(-0.841254 - 0.540641i) q^{3} +(-0.166640 - 1.15901i) q^{5} +(-3.32963 - 0.317941i) q^{7} +(0.415415 + 0.909632i) q^{9} +(0.135033 + 0.0540592i) q^{11} +(0.954845 + 0.910443i) q^{13} +(-0.486420 + 1.06511i) q^{15} +(0.000287460 - 0.000830562i) q^{17} +(-4.79439 + 0.457809i) q^{19} +(2.62917 + 2.06760i) q^{21} +(-0.346097 + 7.26546i) q^{23} +(3.48194 - 1.02239i) q^{25} +(0.142315 - 0.989821i) q^{27} +(-3.06768 + 5.31337i) q^{29} +(-2.23622 + 2.13224i) q^{31} +(-0.0843707 - 0.118482i) q^{33} +(0.186354 + 3.91204i) q^{35} +(1.40568 + 2.43471i) q^{37} +(-0.311044 - 1.28214i) q^{39} +(-2.34812 + 0.452564i) q^{41} +(5.01284 + 5.78512i) q^{43} +(0.985044 - 0.633050i) q^{45} +(-0.146019 + 0.0752781i) q^{47} +(4.11186 + 0.792495i) q^{49} +(-0.000690862 + 0.000543300i) q^{51} +(-6.16018 + 7.10923i) q^{53} +(0.0401530 - 0.165513i) q^{55} +(4.28081 + 2.20691i) q^{57} +(-6.09362 - 1.78925i) q^{59} +(3.83552 - 1.53551i) q^{61} +(-1.09397 - 3.16082i) q^{63} +(0.896094 - 1.25839i) q^{65} +(-7.35865 - 3.58472i) q^{67} +(4.21916 - 5.92498i) q^{69} +(1.52879 + 4.41715i) q^{71} +(5.95457 - 2.38385i) q^{73} +(-3.48194 - 1.02239i) q^{75} +(-0.432424 - 0.222930i) q^{77} +(1.07456 - 4.42940i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(-11.0604 + 8.69800i) q^{83} +(-0.00101053 - 0.000194763i) q^{85} +(5.45332 - 2.81138i) q^{87} +(-8.69824 + 5.59002i) q^{89} +(-2.88981 - 3.33502i) q^{91} +(3.03401 - 0.584757i) q^{93} +(1.32954 + 5.48044i) q^{95} +(1.06715 + 1.84837i) q^{97} +(0.00692091 + 0.145288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + O(q^{10}) \) \( 120q + 12q^{3} - 2q^{5} + q^{7} - 12q^{9} + 11q^{11} + 2q^{13} - 9q^{15} + 48q^{17} - 4q^{19} - q^{21} + 22q^{23} - 42q^{25} + 12q^{27} - q^{29} + 27q^{31} + 17q^{35} - 8q^{37} - 2q^{39} - 58q^{41} - 17q^{43} - 2q^{45} - 84q^{47} + 101q^{49} - 26q^{51} + 28q^{53} - 9q^{55} + 26q^{57} + 34q^{59} + 16q^{61} + 12q^{63} + 144q^{65} + 23q^{67} + 11q^{69} + 173q^{71} - 2q^{73} + 42q^{75} + 128q^{77} + 31q^{79} - 12q^{81} + 47q^{83} - 75q^{85} - 10q^{87} - 67q^{89} + 16q^{91} + 6q^{93} - 79q^{95} + 10q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{33}\right)\) \(1\)

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 0
\(3\) −0.841254 0.540641i −0.485698 0.312139i
\(4\) 0 0
\(5\) −0.166640 1.15901i −0.0745236 0.518323i −0.992553 0.121811i \(-0.961130\pi\)
0.918030 0.396512i \(-0.129779\pi\)
\(6\) 0 0
\(7\) −3.32963 0.317941i −1.25848 0.120170i −0.555584 0.831461i \(-0.687505\pi\)
−0.702899 + 0.711290i \(0.748111\pi\)
\(8\) 0 0
\(9\) 0.415415 + 0.909632i 0.138472 + 0.303211i
\(10\) 0 0
\(11\) 0.135033 + 0.0540592i 0.0407141 + 0.0162995i 0.391930 0.919995i \(-0.371807\pi\)
−0.351216 + 0.936294i \(0.614232\pi\)
\(12\) 0 0
\(13\) 0.954845 + 0.910443i 0.264826 + 0.252511i 0.810844 0.585262i \(-0.199008\pi\)
−0.546018 + 0.837774i \(0.683857\pi\)
\(14\) 0 0
\(15\) −0.486420 + 1.06511i −0.125593 + 0.275010i
\(16\) 0 0
\(17\) 0.000287460 0 0.000830562i 6.97193e−5 0 0.000201441i −0.944966 0.327169i \(-0.893905\pi\)
0.945036 + 0.326967i \(0.106027\pi\)
\(18\) 0 0
\(19\) −4.79439 + 0.457809i −1.09991 + 0.105029i −0.629188 0.777253i \(-0.716612\pi\)
−0.470722 + 0.882282i \(0.656006\pi\)
\(20\) 0 0
\(21\) 2.62917 + 2.06760i 0.573732 + 0.451188i
\(22\) 0 0
\(23\) −0.346097 + 7.26546i −0.0721661 + 1.51495i 0.615043 + 0.788494i \(0.289139\pi\)
−0.687209 + 0.726460i \(0.741164\pi\)
\(24\) 0 0
\(25\) 3.48194 1.02239i 0.696388 0.204478i
\(26\) 0 0
\(27\) 0.142315 0.989821i 0.0273885 0.190491i
\(28\) 0 0
\(29\) −3.06768 + 5.31337i −0.569653 + 0.986669i 0.426947 + 0.904277i \(0.359589\pi\)
−0.996600 + 0.0823918i \(0.973744\pi\)
\(30\) 0 0
\(31\) −2.23622 + 2.13224i −0.401638 + 0.382961i −0.863800 0.503834i \(-0.831922\pi\)
0.462162 + 0.886795i \(0.347074\pi\)
\(32\) 0 0
\(33\) −0.0843707 0.118482i −0.0146871 0.0206251i
\(34\) 0 0
\(35\) 0.186354 + 3.91204i 0.0314995 + 0.661256i
\(36\) 0 0
\(37\) 1.40568 + 2.43471i 0.231093 + 0.400264i 0.958130 0.286334i \(-0.0924366\pi\)
−0.727037 + 0.686598i \(0.759103\pi\)
\(38\) 0 0
\(39\) −0.311044 1.28214i −0.0498069 0.205307i
\(40\) 0 0
\(41\) −2.34812 + 0.452564i −0.366715 + 0.0706786i −0.369280 0.929318i \(-0.620396\pi\)
0.00256473 + 0.999997i \(0.499184\pi\)
\(42\) 0 0
\(43\) 5.01284 + 5.78512i 0.764450 + 0.882223i 0.995885 0.0906279i \(-0.0288874\pi\)
−0.231435 + 0.972850i \(0.574342\pi\)
\(44\) 0 0
\(45\) 0.985044 0.633050i 0.146842 0.0943695i
\(46\) 0 0
\(47\) −0.146019 + 0.0752781i −0.0212991 + 0.0109804i −0.468843 0.883281i \(-0.655329\pi\)
0.447544 + 0.894262i \(0.352299\pi\)
\(48\) 0 0
\(49\) 4.11186 + 0.792495i 0.587408 + 0.113214i
\(50\) 0 0
\(51\) −0.000690862 0 0.000543300i −9.67401e−5 0 7.60772e-5i
\(52\) 0 0
\(53\) −6.16018 + 7.10923i −0.846166 + 0.976528i −0.999933 0.0115791i \(-0.996314\pi\)
0.153767 + 0.988107i \(0.450860\pi\)
\(54\) 0 0
\(55\) 0.0401530 0.165513i 0.00541423 0.0223178i
\(56\) 0 0
\(57\) 4.28081 + 2.20691i 0.567007 + 0.292313i
\(58\) 0 0
\(59\) −6.09362 1.78925i −0.793322 0.232940i −0.140131 0.990133i \(-0.544752\pi\)
−0.653192 + 0.757193i \(0.726570\pi\)
\(60\) 0 0
\(61\) 3.83552 1.53551i 0.491088 0.196602i −0.112883 0.993608i \(-0.536009\pi\)
0.603971 + 0.797006i \(0.293584\pi\)
\(62\) 0 0
\(63\) −1.09397 3.16082i −0.137827 0.398225i
\(64\) 0 0
\(65\) 0.896094 1.25839i 0.111147 0.156084i
\(66\) 0 0
\(67\) −7.35865 3.58472i −0.899002 0.437944i
\(68\) 0 0
\(69\) 4.21916 5.92498i 0.507927 0.713284i
\(70\) 0 0
\(71\) 1.52879 + 4.41715i 0.181434 + 0.524219i 0.998641 0.0521260i \(-0.0165998\pi\)
−0.817207 + 0.576345i \(0.804479\pi\)
\(72\) 0 0
\(73\) 5.95457 2.38385i 0.696930 0.279008i 0.00397740 0.999992i \(-0.498734\pi\)
0.692952 + 0.720984i \(0.256310\pi\)
\(74\) 0 0
\(75\) −3.48194 1.02239i −0.402060 0.118055i
\(76\) 0 0
\(77\) −0.432424 0.222930i −0.0492793 0.0254052i
\(78\) 0 0
\(79\) 1.07456 4.42940i 0.120898 0.498346i −0.878876 0.477051i \(-0.841706\pi\)
0.999773 0.0212956i \(-0.00677910\pi\)
\(80\) 0 0
\(81\) −0.654861 + 0.755750i −0.0727623 + 0.0839722i
\(82\) 0 0
\(83\) −11.0604 + 8.69800i −1.21404 + 0.954730i −0.999757 0.0220421i \(-0.992983\pi\)
−0.214281 + 0.976772i \(0.568741\pi\)
\(84\) 0 0
\(85\) −0.00101053 0.000194763i −0.000109607 2.11251e-5i
\(86\) 0 0
\(87\) 5.45332 2.81138i 0.584657 0.301412i
\(88\) 0 0
\(89\) −8.69824 + 5.59002i −0.922012 + 0.592541i −0.913241 0.407421i \(-0.866428\pi\)
−0.00877101 + 0.999962i \(0.502792\pi\)
\(90\) 0 0
\(91\) −2.88981 3.33502i −0.302935 0.349605i
\(92\) 0 0
\(93\) 3.03401 0.584757i 0.314612 0.0606364i
\(94\) 0 0
\(95\) 1.32954 + 5.48044i 0.136408 + 0.562282i
\(96\) 0 0
\(97\) 1.06715 + 1.84837i 0.108353 + 0.187673i 0.915103 0.403220i \(-0.132109\pi\)
−0.806750 + 0.590893i \(0.798776\pi\)
\(98\) 0 0
\(99\) 0.00692091 + 0.145288i 0.000695577 + 0.0146020i
\(100\) 0 0
\(101\) 1.11527 + 1.56618i 0.110973 + 0.155840i 0.866327 0.499477i \(-0.166474\pi\)
−0.755354 + 0.655317i \(0.772535\pi\)
\(102\) 0 0
\(103\) −4.44633 + 4.23956i −0.438110 + 0.417737i −0.876765 0.480919i \(-0.840303\pi\)
0.438656 + 0.898655i \(0.355455\pi\)
\(104\) 0 0
\(105\) 1.95824 3.39177i 0.191105 0.331003i
\(106\) 0 0
\(107\) 0.140607 0.977941i 0.0135930 0.0945411i −0.981896 0.189423i \(-0.939338\pi\)
0.995489 + 0.0948819i \(0.0302474\pi\)
\(108\) 0 0
\(109\) 2.57299 0.755499i 0.246448 0.0723636i −0.156176 0.987729i \(-0.549917\pi\)
0.402624 + 0.915366i \(0.368098\pi\)
\(110\) 0 0
\(111\) 0.133770 2.80818i 0.0126969 0.266540i
\(112\) 0 0
\(113\) 3.00763 + 2.36523i 0.282934 + 0.222502i 0.749533 0.661967i \(-0.230278\pi\)
−0.466598 + 0.884469i \(0.654521\pi\)
\(114\) 0 0
\(115\) 8.47839 0.809588i 0.790614 0.0754944i
\(116\) 0 0
\(117\) −0.431511 + 1.24677i −0.0398932 + 0.115264i
\(118\) 0 0
\(119\) −0.00122121 + 0.00267407i −0.000111948 + 0.000245131i
\(120\) 0 0
\(121\) −7.94576 7.57627i −0.722342 0.688752i
\(122\) 0 0
\(123\) 2.22004 + 0.888771i 0.200175 + 0.0801378i
\(124\) 0 0
\(125\) −4.19728 9.19077i −0.375416 0.822047i
\(126\) 0 0
\(127\) 11.2684 + 1.07601i 0.999913 + 0.0954801i 0.582155 0.813078i \(-0.302210\pi\)
0.417758 + 0.908558i \(0.362816\pi\)
\(128\) 0 0
\(129\) −1.08939 7.57690i −0.0959157 0.667108i
\(130\) 0 0
\(131\) −13.0073 8.35932i −1.13646 0.730357i −0.169559 0.985520i \(-0.554234\pi\)
−0.966898 + 0.255163i \(0.917871\pi\)
\(132\) 0 0
\(133\) 16.1091 1.39684
\(134\) 0 0
\(135\) −1.17092 −0.100777
\(136\) 0 0
\(137\) −3.57702 2.29881i −0.305605 0.196401i 0.378845 0.925460i \(-0.376321\pi\)
−0.684450 + 0.729059i \(0.739958\pi\)
\(138\) 0 0
\(139\) −3.02873 21.0653i −0.256894 1.78673i −0.554641 0.832090i \(-0.687144\pi\)
0.297747 0.954645i \(-0.403765\pi\)
\(140\) 0 0
\(141\) 0.163537 + 0.0156159i 0.0137723 + 0.00131510i
\(142\) 0 0
\(143\) 0.0797181 + 0.174558i 0.00666636 + 0.0145973i
\(144\) 0 0
\(145\) 6.66943 + 2.67004i 0.553866 + 0.221734i
\(146\) 0 0
\(147\) −3.03066 2.88973i −0.249965 0.238341i
\(148\) 0 0
\(149\) 1.22998 2.69328i 0.100764 0.220642i −0.852535 0.522670i \(-0.824936\pi\)
0.953299 + 0.302027i \(0.0976634\pi\)
\(150\) 0 0
\(151\) 0.605102 1.74833i 0.0492425 0.142277i −0.917698 0.397278i \(-0.869955\pi\)
0.966941 + 0.255001i \(0.0820759\pi\)
\(152\) 0 0
\(153\) 0.000874921 0 8.35448e-5i 7.07332e−5 0 6.75420e-6i
\(154\) 0 0
\(155\) 2.84392 + 2.23648i 0.228429 + 0.179639i
\(156\) 0 0
\(157\) 0.206296 4.33068i 0.0164642 0.345626i −0.975573 0.219678i \(-0.929499\pi\)
0.992037 0.125949i \(-0.0401975\pi\)
\(158\) 0 0
\(159\) 9.02582 2.65022i 0.715794 0.210176i
\(160\) 0 0
\(161\) 3.46236 24.0813i 0.272872 1.89787i
\(162\) 0 0
\(163\) −8.32642 + 14.4218i −0.652176 + 1.12960i 0.330418 + 0.943835i \(0.392810\pi\)
−0.982594 + 0.185767i \(0.940523\pi\)
\(164\) 0 0
\(165\) −0.123262 + 0.117530i −0.00959593 + 0.00914970i
\(166\) 0 0
\(167\) 4.78393 + 6.71809i 0.370192 + 0.519861i 0.957087 0.289802i \(-0.0935893\pi\)
−0.586895 + 0.809663i \(0.699650\pi\)
\(168\) 0 0
\(169\) −0.535742 11.2466i −0.0412109 0.865124i
\(170\) 0 0
\(171\) −2.40810 4.17095i −0.184152 0.318961i
\(172\) 0 0
\(173\) −0.0556620 0.229442i −0.00423190 0.0174441i 0.969656 0.244472i \(-0.0786145\pi\)
−0.973888 + 0.227027i \(0.927099\pi\)
\(174\) 0 0
\(175\) −11.9186 + 2.29713i −0.900964 + 0.173647i
\(176\) 0 0
\(177\) 4.15894 + 4.79967i 0.312605 + 0.360766i
\(178\) 0 0
\(179\) 16.5006 10.6043i 1.23331 0.792603i 0.248910 0.968527i \(-0.419928\pi\)
0.984404 + 0.175924i \(0.0562912\pi\)
\(180\) 0 0
\(181\) 15.7742 8.13217i 1.17249 0.604459i 0.241818 0.970322i \(-0.422256\pi\)
0.930669 + 0.365862i \(0.119226\pi\)
\(182\) 0 0
\(183\) −4.05680 0.781884i −0.299887 0.0577985i
\(184\) 0 0
\(185\) 2.58760 2.03491i 0.190244 0.149610i
\(186\) 0 0
\(187\) 8.37162e−5 0 9.66137e-5i 6.12194e−6 0 7.06509e-6i
\(188\) 0 0
\(189\) −0.788561 + 3.25049i −0.0573594 + 0.236439i
\(190\) 0 0
\(191\) −3.95415 2.03851i −0.286112 0.147501i 0.309196 0.950998i \(-0.399940\pi\)
−0.595309 + 0.803497i \(0.702970\pi\)
\(192\) 0 0
\(193\) −11.8283 3.47309i −0.851416 0.249998i −0.173224 0.984883i \(-0.555418\pi\)
−0.678193 + 0.734884i \(0.737237\pi\)
\(194\) 0 0
\(195\) −1.43418 + 0.574158i −0.102704 + 0.0411163i
\(196\) 0 0
\(197\) 0.833637 + 2.40864i 0.0593942 + 0.171608i 0.970794 0.239913i \(-0.0771189\pi\)
−0.911400 + 0.411521i \(0.864998\pi\)
\(198\) 0 0
\(199\) 7.88437 11.0721i 0.558908 0.784877i −0.434357 0.900741i \(-0.643024\pi\)
0.993265 + 0.115864i \(0.0369636\pi\)
\(200\) 0 0
\(201\) 4.25244 + 6.99405i 0.299944 + 0.493322i
\(202\) 0 0
\(203\) 11.9036 16.7162i 0.835467 1.17325i
\(204\) 0 0
\(205\) 0.915816 + 2.64608i 0.0639633 + 0.184810i
\(206\) 0 0
\(207\) −6.75267 + 2.70336i −0.469343 + 0.187897i
\(208\) 0 0
\(209\) −0.672152 0.197362i −0.0464937 0.0136518i
\(210\) 0 0
\(211\) −16.5467 8.53041i −1.13912 0.587257i −0.217774 0.975999i \(-0.569879\pi\)
−0.921347 + 0.388742i \(0.872910\pi\)
\(212\) 0 0
\(213\) 1.10199 4.54247i 0.0755071 0.311245i
\(214\) 0 0
\(215\) 5.86965 6.77394i 0.400307 0.461979i
\(216\) 0 0
\(217\) 8.12373 6.38857i 0.551475 0.433684i
\(218\) 0 0
\(219\) −6.29811 1.21386i −0.425587 0.0820251i
\(220\) 0 0
\(221\) 0.00103066 0.000531342i 6.93296e−5 3.57419e-5i
\(222\) 0 0
\(223\) −5.65846 + 3.63647i −0.378919 + 0.243516i −0.716211 0.697884i \(-0.754125\pi\)
0.337292 + 0.941400i \(0.390489\pi\)
\(224\) 0 0
\(225\) 2.37645 + 2.74257i 0.158430 + 0.182838i
\(226\) 0 0
\(227\) −19.5805 + 3.77383i −1.29960 + 0.250478i −0.791687 0.610927i \(-0.790797\pi\)
−0.507918 + 0.861406i \(0.669585\pi\)
\(228\) 0 0
\(229\) 0.107523 + 0.443217i 0.00710533 + 0.0292886i 0.975254 0.221088i \(-0.0709608\pi\)
−0.968149 + 0.250376i \(0.919446\pi\)
\(230\) 0 0
\(231\) 0.243253 + 0.421326i 0.0160049 + 0.0277212i
\(232\) 0 0
\(233\) 0.342513 + 7.19024i 0.0224388 + 0.471048i 0.981922 + 0.189284i \(0.0606167\pi\)
−0.959484 + 0.281764i \(0.909080\pi\)
\(234\) 0 0
\(235\) 0.111580 + 0.156693i 0.00727870 + 0.0102215i
\(236\) 0 0
\(237\) −3.29869 + 3.14530i −0.214273 + 0.204309i
\(238\) 0 0
\(239\) −12.0771 + 20.9181i −0.781199 + 1.35308i 0.150044 + 0.988679i \(0.452058\pi\)
−0.931243 + 0.364398i \(0.881275\pi\)
\(240\) 0 0
\(241\) −3.25859 + 22.6640i −0.209904 + 1.45992i 0.563559 + 0.826076i \(0.309432\pi\)
−0.773463 + 0.633841i \(0.781477\pi\)
\(242\) 0 0
\(243\) 0.959493 0.281733i 0.0615515 0.0180732i
\(244\) 0 0
\(245\) 0.233308 4.89773i 0.0149055 0.312904i
\(246\) 0 0
\(247\) −4.99471 3.92789i −0.317806 0.249925i
\(248\) 0 0
\(249\) 14.0071 1.33752i 0.887664 0.0847617i
\(250\) 0 0
\(251\) −0.103287 + 0.298428i −0.00651942 + 0.0188366i −0.948214 0.317633i \(-0.897112\pi\)
0.941694 + 0.336470i \(0.109233\pi\)
\(252\) 0 0
\(253\) −0.439500 + 0.962370i −0.0276311 + 0.0605037i
\(254\) 0 0
\(255\) 0.000744814 0 0.000710178i 4.66420e−5 0 4.44731e-5i
\(256\) 0 0
\(257\) 23.7797 + 9.51997i 1.48334 + 0.593839i 0.965213 0.261465i \(-0.0842057\pi\)
0.518126 + 0.855304i \(0.326630\pi\)
\(258\) 0 0
\(259\) −3.90631 8.55362i −0.242726 0.531496i
\(260\) 0 0
\(261\) −6.10757 0.583203i −0.378049 0.0360993i
\(262\) 0 0
\(263\) 3.05352 + 21.2377i 0.188288 + 1.30957i 0.836438 + 0.548061i \(0.184634\pi\)
−0.648150 + 0.761513i \(0.724457\pi\)
\(264\) 0 0
\(265\) 9.26618 + 5.95501i 0.569217 + 0.365813i
\(266\) 0 0
\(267\) 10.3396 0.632774
\(268\) 0 0
\(269\) −13.4055 −0.817350 −0.408675 0.912680i \(-0.634009\pi\)
−0.408675 + 0.912680i \(0.634009\pi\)
\(270\) 0 0
\(271\) 6.54992 + 4.20938i 0.397880 + 0.255702i 0.724246 0.689542i \(-0.242188\pi\)
−0.326367 + 0.945243i \(0.605824\pi\)
\(272\) 0 0
\(273\) 0.628017 + 4.36795i 0.0380093 + 0.264360i
\(274\) 0 0
\(275\) 0.525447 + 0.0501741i 0.0316857 + 0.00302562i
\(276\) 0 0
\(277\) −2.45278 5.37084i −0.147373 0.322702i 0.821521 0.570179i \(-0.193126\pi\)
−0.968894 + 0.247476i \(0.920399\pi\)
\(278\) 0 0
\(279\) −2.86851 1.14838i −0.171733 0.0687516i
\(280\) 0 0
\(281\) 3.73654 + 3.56279i 0.222903 + 0.212538i 0.793299 0.608832i \(-0.208362\pi\)
−0.570396 + 0.821370i \(0.693210\pi\)
\(282\) 0 0
\(283\) 6.30989 13.8167i 0.375084 0.821320i −0.624116 0.781332i \(-0.714541\pi\)
0.999200 0.0399880i \(-0.0127320\pi\)
\(284\) 0 0
\(285\) 1.84447 5.32925i 0.109257 0.315677i
\(286\) 0 0
\(287\) 7.96228 0.760305i 0.469998 0.0448794i
\(288\) 0 0
\(289\) 13.3629 + 10.5087i 0.786053 + 0.618159i
\(290\) 0 0
\(291\) 0.101554 2.13189i 0.00595323 0.124974i
\(292\) 0 0
\(293\) −28.3209 + 8.31576i −1.65452 + 0.485812i −0.969985 0.243165i \(-0.921815\pi\)
−0.684539 + 0.728977i \(0.739996\pi\)
\(294\) 0 0
\(295\) −1.05831 + 7.36071i −0.0616172 + 0.428557i
\(296\) 0 0
\(297\) 0.0727262 0.125965i 0.00422000 0.00730926i
\(298\) 0 0
\(299\) −6.94525 + 6.62229i −0.401654 + 0.382977i
\(300\) 0 0
\(301\) −14.8516 20.8561i −0.856030 1.20213i
\(302\) 0 0
\(303\) −0.0914852 1.92051i −0.00525569 0.110330i
\(304\) 0 0
\(305\) −2.41881 4.18951i −0.138501 0.239891i
\(306\) 0 0
\(307\) 6.09522 + 25.1248i 0.347873 + 1.43395i 0.829958 + 0.557826i \(0.188364\pi\)
−0.482086 + 0.876124i \(0.660121\pi\)
\(308\) 0 0
\(309\) 6.03257 1.16268i 0.343181 0.0661427i
\(310\) 0 0
\(311\) −2.89473 3.34070i −0.164145 0.189434i 0.667718 0.744414i \(-0.267271\pi\)
−0.831863 + 0.554981i \(0.812726\pi\)
\(312\) 0 0
\(313\) 7.14223 4.59003i 0.403703 0.259444i −0.322996 0.946400i \(-0.604690\pi\)
0.726699 + 0.686956i \(0.241054\pi\)
\(314\) 0 0
\(315\) −3.48111 + 1.79464i −0.196138 + 0.101116i
\(316\) 0 0
\(317\) 6.58581 + 1.26931i 0.369896 + 0.0712916i 0.370812 0.928708i \(-0.379079\pi\)
−0.000916009 1.00000i \(0.500292\pi\)
\(318\) 0 0
\(319\) −0.701476 + 0.551646i −0.0392751 + 0.0308863i
\(320\) 0 0
\(321\) −0.647000 + 0.746678i −0.0361120 + 0.0416755i
\(322\) 0 0
\(323\) −0.000997959 0.00411364i −5.55279e−5 0.000228889i
\(324\) 0 0
\(325\) 4.25554 + 2.19388i 0.236055 + 0.121695i
\(326\) 0 0
\(327\) −2.57299 0.755499i −0.142287 0.0417792i
\(328\) 0 0
\(329\) 0.510124 0.204223i 0.0281240 0.0112592i
\(330\) 0 0
\(331\) −8.97060 25.9188i −0.493069 1.42463i −0.867530 0.497386i \(-0.834293\pi\)
0.374461 0.927243i \(-0.377828\pi\)
\(332\) 0 0
\(333\) −1.63075 + 2.29007i −0.0893646 + 0.125495i
\(334\) 0 0
\(335\) −2.92847 + 9.12608i −0.159999 + 0.498611i
\(336\) 0 0
\(337\) −11.7908 + 16.5579i −0.642287 + 0.901966i −0.999486 0.0320622i \(-0.989793\pi\)
0.357199 + 0.934028i \(0.383732\pi\)
\(338\) 0 0
\(339\) −1.25144 3.61581i −0.0679690 0.196384i
\(340\) 0 0
\(341\) −0.417232 + 0.167034i −0.0225944 + 0.00904542i
\(342\) 0 0
\(343\) 9.02603 + 2.65028i 0.487360 + 0.143102i
\(344\) 0 0
\(345\) −7.57017 3.90269i −0.407564 0.210114i
\(346\) 0 0
\(347\) 8.36165 34.4672i 0.448877 1.85030i −0.0730821 0.997326i \(-0.523284\pi\)
0.521959 0.852970i \(-0.325201\pi\)
\(348\) 0 0
\(349\) −11.7696 + 13.5828i −0.630010 + 0.727071i −0.977576 0.210585i \(-0.932463\pi\)
0.347565 + 0.937656i \(0.387009\pi\)
\(350\) 0 0
\(351\) 1.03706 0.815556i 0.0553544 0.0435312i
\(352\) 0 0
\(353\) 3.58337 + 0.690638i 0.190724 + 0.0367590i 0.283718 0.958908i \(-0.408432\pi\)
−0.0929948 + 0.995667i \(0.529644\pi\)
\(354\) 0 0
\(355\) 4.86474 2.50795i 0.258194 0.133108i
\(356\) 0 0
\(357\) 0.00247305 0.00158934i 0.000130888 8.41166e-5i
\(358\) 0 0
\(359\) 10.3305 + 11.9220i 0.545221 + 0.629219i 0.959763 0.280811i \(-0.0906036\pi\)
−0.414542 + 0.910030i \(0.636058\pi\)
\(360\) 0 0
\(361\) 4.11998 0.794062i 0.216841 0.0417927i
\(362\) 0 0
\(363\) 2.58836 + 10.6694i 0.135854 + 0.559997i
\(364\) 0 0
\(365\) −3.75517 6.50414i −0.196554 0.340442i
\(366\) 0 0
\(367\) 0.225953 + 4.74334i 0.0117947 + 0.247600i 0.997063 + 0.0765851i \(0.0244017\pi\)
−0.985268 + 0.171015i \(0.945295\pi\)
\(368\) 0 0
\(369\) −1.38711 1.94793i −0.0722102 0.101405i
\(370\) 0 0
\(371\) 22.7715 21.7125i 1.18224 1.12726i
\(372\) 0 0
\(373\) −17.5031 + 30.3162i −0.906274 + 1.56971i −0.0870771 + 0.996202i \(0.527753\pi\)
−0.819197 + 0.573512i \(0.805581\pi\)
\(374\) 0 0
\(375\) −1.43793 + 10.0010i −0.0742541 + 0.516449i
\(376\) 0 0
\(377\) −7.76668 + 2.28050i −0.400004 + 0.117452i
\(378\) 0 0
\(379\) −0.650668 + 13.6592i −0.0334226 + 0.701626i 0.918525 + 0.395364i \(0.129381\pi\)
−0.951947 + 0.306262i \(0.900922\pi\)
\(380\) 0 0
\(381\) −8.89789 6.99737i −0.455853 0.358486i
\(382\) 0 0
\(383\) 14.4979 1.38438i 0.740810 0.0707388i 0.282174 0.959363i \(-0.408944\pi\)
0.458636 + 0.888624i \(0.348338\pi\)
\(384\) 0 0
\(385\) −0.186318 + 0.538331i −0.00949565 + 0.0274359i
\(386\) 0 0
\(387\) −3.17992 + 6.96306i −0.161645 + 0.353952i
\(388\) 0 0
\(389\) 6.19917 + 5.91090i 0.314310 + 0.299694i 0.830768 0.556618i \(-0.187901\pi\)
−0.516458 + 0.856312i \(0.672750\pi\)
\(390\) 0 0
\(391\) 0.00593492 + 0.00237598i 0.000300142 + 0.000120159i
\(392\) 0 0
\(393\) 6.42309 + 14.0646i 0.324002 + 0.709466i
\(394\) 0 0
\(395\) −5.31277 0.507308i −0.267314 0.0255254i
\(396\) 0 0
\(397\) −3.51897 24.4750i −0.176612 1.22836i −0.864532 0.502578i \(-0.832385\pi\)
0.687920 0.725787i \(-0.258524\pi\)
\(398\) 0 0
\(399\) −13.5519 8.70925i −0.678441 0.436008i
\(400\) 0 0
\(401\) −0.247632 −0.0123662 −0.00618308 0.999981i \(-0.501968\pi\)
−0.00618308 + 0.999981i \(0.501968\pi\)
\(402\) 0 0
\(403\) −4.07653 −0.203066
\(404\) 0 0
\(405\) 0.985044 + 0.633050i 0.0489472 + 0.0314565i
\(406\) 0 0
\(407\) 0.0581953 + 0.404757i 0.00288463 + 0.0200631i
\(408\) 0 0
\(409\) −2.54179 0.242712i −0.125684 0.0120013i 0.0320247 0.999487i \(-0.489804\pi\)
−0.157708 + 0.987486i \(0.550411\pi\)
\(410\) 0 0
\(411\) 1.76635 + 3.86777i 0.0871276 + 0.190783i
\(412\) 0 0
\(413\) 19.7206 + 7.89495i 0.970389 + 0.388485i
\(414\) 0 0
\(415\) 11.9241 + 11.3696i 0.585333 + 0.558114i
\(416\) 0 0
\(417\) −8.84082 + 19.3587i −0.432937 + 0.948000i
\(418\) 0 0
\(419\) −8.84835 + 25.5656i −0.432270 + 1.24896i 0.493125 + 0.869958i \(0.335855\pi\)
−0.925395 + 0.379004i \(0.876267\pi\)
\(420\) 0 0
\(421\) −8.94091 + 0.853753i −0.435753 + 0.0416094i −0.310628 0.950532i \(-0.600539\pi\)
−0.125125 + 0.992141i \(0.539933\pi\)
\(422\) 0 0
\(423\) −0.129134 0.101552i −0.00627870 0.00493763i
\(424\) 0 0
\(425\) 0.000151761 0.00318586i 7.36150e−6 0.000154537i
\(426\) 0 0
\(427\) −13.2591 + 3.89321i −0.641651 + 0.188406i
\(428\) 0 0
\(429\) 0.0273102 0.189947i 0.00131855 0.00917071i
\(430\) 0 0
\(431\) −8.59009 + 14.8785i −0.413770 + 0.716671i −0.995298 0.0968555i \(-0.969122\pi\)
0.581529 + 0.813526i \(0.302455\pi\)
\(432\) 0 0
\(433\) −22.0091 + 20.9856i −1.05769 + 1.00850i −0.0577396 + 0.998332i \(0.518389\pi\)
−0.999948 + 0.0101717i \(0.996762\pi\)
\(434\) 0 0
\(435\) −4.16715 5.85194i −0.199800 0.280579i
\(436\) 0 0
\(437\) −1.66687 34.9919i −0.0797372 1.67389i
\(438\) 0 0
\(439\) −7.68776 13.3156i −0.366917 0.635518i 0.622165 0.782886i \(-0.286253\pi\)
−0.989082 + 0.147368i \(0.952920\pi\)
\(440\) 0 0
\(441\) 0.987248 + 4.06949i 0.0470118 + 0.193785i
\(442\) 0 0
\(443\) 19.7499 3.80648i 0.938345 0.180851i 0.302922 0.953015i \(-0.402038\pi\)
0.635423 + 0.772164i \(0.280826\pi\)
\(444\) 0 0
\(445\) 7.92834 + 9.14979i 0.375839 + 0.433742i
\(446\) 0 0
\(447\) −2.49082 + 1.60075i −0.117812 + 0.0757131i
\(448\) 0 0
\(449\) −16.5943 + 8.55494i −0.783132 + 0.403732i −0.802931 0.596072i \(-0.796727\pi\)
0.0197997 + 0.999804i \(0.493697\pi\)
\(450\) 0 0
\(451\) −0.341540 0.0658265i −0.0160825 0.00309965i
\(452\) 0 0
\(453\) −1.45426 + 1.14364i −0.0683272 + 0.0537331i
\(454\) 0 0
\(455\) −3.38375 + 3.90506i −0.158633 + 0.183072i
\(456\) 0 0
\(457\) −7.01628 + 28.9215i −0.328208 + 1.35289i 0.533634 + 0.845715i \(0.320826\pi\)
−0.861842 + 0.507176i \(0.830689\pi\)
\(458\) 0 0
\(459\) −0.000781198 0 0.000402736i −3.64632e−5 0 1.87981e-5i
\(460\) 0 0
\(461\) −26.6394 7.82203i −1.24072 0.364308i −0.405435 0.914124i \(-0.632880\pi\)
−0.835286 + 0.549816i \(0.814698\pi\)
\(462\) 0 0
\(463\) −1.01921 + 0.408029i −0.0473666 + 0.0189627i −0.395225 0.918584i \(-0.629333\pi\)
0.347858 + 0.937547i \(0.386909\pi\)
\(464\) 0 0
\(465\) −1.18332 3.41899i −0.0548753 0.158552i
\(466\) 0 0
\(467\) 14.5999 20.5027i 0.675604 0.948753i −0.324392 0.945923i \(-0.605160\pi\)
0.999996 0.00283004i \(-0.000900832\pi\)
\(468\) 0 0
\(469\) 23.3619 + 14.2754i 1.07875 + 0.659178i
\(470\) 0 0
\(471\) −2.51489 + 3.53167i −0.115880 + 0.162731i
\(472\) 0 0
\(473\) 0.364161 + 1.05217i 0.0167441 + 0.0483790i
\(474\) 0 0
\(475\) −16.2257 + 6.49580i −0.744487 + 0.298048i
\(476\) 0 0
\(477\) −9.02582 2.65022i −0.413264 0.121345i
\(478\) 0 0
\(479\) 9.53759 + 4.91697i 0.435784 + 0.224662i 0.662136 0.749383i \(-0.269650\pi\)
−0.226353 + 0.974045i \(0.572680\pi\)
\(480\) 0 0
\(481\) −0.874458 + 3.60456i −0.0398718 + 0.164354i
\(482\) 0 0
\(483\) −15.9320 + 18.3866i −0.724933 + 0.836617i
\(484\) 0 0
\(485\) 1.96444 1.54485i 0.0892004 0.0701480i
\(486\) 0 0
\(487\) 23.3678 + 4.50377i 1.05889 + 0.204085i 0.688831 0.724922i \(-0.258124\pi\)
0.370063 + 0.929007i \(0.379336\pi\)
\(488\) 0 0
\(489\) 14.8016 7.63078i 0.669353 0.345076i
\(490\) 0 0
\(491\) 11.5965 7.45263i 0.523343 0.336332i −0.252150 0.967688i \(-0.581138\pi\)
0.775493 + 0.631356i \(0.217501\pi\)
\(492\) 0 0
\(493\) 0.00353125 + 0.00407528i 0.000159039 + 0.000183541i
\(494\) 0 0
\(495\) 0.167236 0.0322321i 0.00751670 0.00144873i
\(496\) 0 0
\(497\) −3.68591 15.1935i −0.165336 0.681523i
\(498\) 0 0
\(499\) 14.2289 + 24.6452i 0.636973 + 1.10327i 0.986093 + 0.166192i \(0.0531472\pi\)
−0.349120 + 0.937078i \(0.613519\pi\)
\(500\) 0 0
\(501\) −0.392425 8.23801i −0.0175322 0.368047i
\(502\) 0 0
\(503\) 12.6654 + 17.7861i 0.564723 + 0.793043i 0.993913 0.110172i \(-0.0351401\pi\)
−0.429189 + 0.903215i \(0.641201\pi\)
\(504\) 0 0
\(505\) 1.62936 1.55359i 0.0725055 0.0691339i
\(506\) 0 0
\(507\) −5.62968 + 9.75090i −0.250023 + 0.433053i
\(508\) 0 0
\(509\) −2.41846 + 16.8207i −0.107196 + 0.745566i 0.863342 + 0.504619i \(0.168367\pi\)
−0.970538 + 0.240947i \(0.922542\pi\)
\(510\) 0 0
\(511\) −20.5844 + 6.04414i −0.910602 + 0.267377i
\(512\) 0 0
\(513\) −0.229164 + 4.81075i −0.0101178 + 0.212400i
\(514\) 0 0
\(515\) 5.65462 + 4.44684i 0.249172 + 0.195951i
\(516\) 0 0
\(517\) −0.0237869 + 0.00227138i −0.00104615 + 9.98950e-5i
\(518\) 0 0
\(519\) −0.0772198 + 0.223112i −0.00338957 + 0.00979353i
\(520\) 0 0
\(521\) 15.3325 33.5734i 0.671727 1.47088i −0.199450 0.979908i \(-0.563916\pi\)
0.871177 0.490969i \(-0.163357\pi\)
\(522\) 0 0
\(523\) 0.666250 + 0.635268i 0.0291331 + 0.0277783i 0.704506 0.709698i \(-0.251169\pi\)
−0.675373 + 0.737477i \(0.736017\pi\)
\(524\) 0 0
\(525\) 11.2685 + 4.51123i 0.491798 + 0.196886i
\(526\) 0 0
\(527\) 0.00112813 + 0.00247026i 4.91420e−5 + 0.000107606i
\(528\) 0 0
\(529\) −29.7713 2.84281i −1.29440 0.123601i
\(530\) 0 0
\(531\) −0.903824 6.28624i −0.0392226 0.272799i
\(532\) 0 0
\(533\) −2.65413 1.70570i −0.114963 0.0738823i
\(534\) 0 0
\(535\) −1.15687 −0.0500158
\(536\) 0 0
\(537\) −19.6143 −0.846421
\(538\) 0 0
\(539\) 0.512396 + 0.329297i 0.0220705 + 0.0141838i
\(540\) 0 0
\(541\) −0.0920435 0.640177i −0.00395726 0.0275233i 0.987747 0.156063i \(-0.0498802\pi\)
−0.991704 + 0.128539i \(0.958971\pi\)
\(542\) 0 0
\(543\) −17.6667 1.68696i −0.758150 0.0723945i
\(544\) 0 0
\(545\) −1.30439 2.85622i −0.0558740 0.122347i
\(546\) 0 0
\(547\) −11.0223 4.41266i −0.471280 0.188672i 0.123851 0.992301i \(-0.460475\pi\)
−0.595131 + 0.803629i \(0.702900\pi\)
\(548\) 0 0
\(549\) 2.99008 + 2.85103i 0.127613 + 0.121679i
\(550\) 0 0
\(551\) 12.2751 26.8788i 0.522939 1.14508i
\(552\) 0 0
\(553\) −4.98618 + 14.4066i −0.212034 + 0.612632i
\(554\) 0 0
\(555\) −3.27699 + 0.312914i −0.139100 + 0.0132825i
\(556\) 0 0
\(557\) −8.78243 6.90658i −0.372124 0.292641i 0.414530 0.910036i \(-0.363946\pi\)
−0.786654 + 0.617394i \(0.788188\pi\)
\(558\) 0 0
\(559\) −0.480541 + 10.0878i −0.0203247 + 0.426668i
\(560\) 0 0
\(561\) −0.000122660 0 3.60162e-5i −5.17870e−6 0 1.52060e-6i
\(562\) 0 0
\(563\) 0.467395 3.25080i 0.0196983 0.137005i −0.977599 0.210476i \(-0.932499\pi\)
0.997297 + 0.0734711i \(0.0234077\pi\)
\(564\) 0 0
\(565\) 2.24012 3.88001i 0.0942427 0.163233i
\(566\) 0 0
\(567\) 2.42073 2.30816i 0.101661 0.0969336i
\(568\) 0 0
\(569\) −15.0157 21.0866i −0.629490 0.883994i 0.369486 0.929236i \(-0.379534\pi\)
−0.998976 + 0.0452417i \(0.985594\pi\)
\(570\) 0 0
\(571\) −1.35467 28.4380i −0.0566912 1.19009i −0.830626 0.556830i \(-0.812017\pi\)
0.773935 0.633265i \(-0.218286\pi\)
\(572\) 0 0
\(573\) 2.22434 + 3.85267i 0.0929232 + 0.160948i
\(574\) 0 0
\(575\) 6.22304 + 25.6517i 0.259519 + 1.06975i
\(576\) 0 0
\(577\) −9.35840 + 1.80368i −0.389595 + 0.0750884i −0.380288 0.924868i \(-0.624175\pi\)
−0.00930792 + 0.999957i \(0.502963\pi\)
\(578\) 0 0
\(579\) 8.07287 + 9.31659i 0.335497 + 0.387184i
\(580\) 0 0
\(581\) 39.5925 25.4446i 1.64258 1.05562i
\(582\) 0 0
\(583\) −1.21615 + 0.626969i −0.0503678 + 0.0259664i
\(584\) 0 0
\(585\) 1.51692 + 0.292362i 0.0627169 + 0.0120877i
\(586\) 0 0
\(587\) 28.9952 22.8021i 1.19676 0.941143i 0.197528 0.980297i \(-0.436709\pi\)
0.999233 + 0.0391543i \(0.0124664\pi\)
\(588\) 0 0
\(589\) 9.74519 11.2465i 0.401543 0.463406i
\(590\) 0 0
\(591\) 0.600907 2.47697i 0.0247180 0.101889i
\(592\) 0 0
\(593\) −2.09304 1.07904i −0.0859508 0.0443107i 0.414715 0.909951i \(-0.363881\pi\)
−0.500666 + 0.865641i \(0.666912\pi\)
\(594\) 0 0
\(595\) 0.00330276 0.000969779i 0.000135400 3.97571e-5i
\(596\) 0 0
\(597\) −12.6188 + 5.05179i −0.516452 + 0.206756i
\(598\) 0 0
\(599\) 14.6010 + 42.1867i 0.596579 + 1.72370i 0.685896 + 0.727699i \(0.259410\pi\)
−0.0893171 + 0.996003i \(0.528468\pi\)
\(600\) 0 0
\(601\) 17.9369 25.1888i 0.731660 1.02747i −0.266317 0.963886i \(-0.585807\pi\)
0.997976 0.0635865i \(-0.0202539\pi\)
\(602\) 0 0
\(603\) 0.203884 8.18281i 0.00830278 0.333230i
\(604\) 0 0
\(605\) −7.45686 + 10.4717i −0.303165 + 0.425735i
\(606\) 0 0
\(607\) 5.31093 + 15.3449i 0.215564 + 0.622831i 0.999997 + 0.00261723i \(0.000833091\pi\)
−0.784433 + 0.620214i \(0.787046\pi\)
\(608\) 0 0
\(609\) −19.0514 + 7.62703i −0.772002 + 0.309063i
\(610\) 0 0
\(611\) −0.207962 0.0610631i −0.00841324 0.00247035i
\(612\) 0 0
\(613\) −9.00806 4.64398i −0.363832 0.187568i 0.266611 0.963804i \(-0.414096\pi\)
−0.630443 + 0.776236i \(0.717127\pi\)
\(614\) 0 0
\(615\) 0.660143 2.72115i 0.0266195 0.109727i
\(616\) 0 0
\(617\) 18.8954 21.8065i 0.760701 0.877896i −0.234858 0.972030i \(-0.575463\pi\)
0.995560 + 0.0941335i \(0.0300081\pi\)
\(618\) 0 0
\(619\) 17.3281 13.6270i 0.696477 0.547715i −0.205948 0.978563i \(-0.566028\pi\)
0.902425 + 0.430848i \(0.141785\pi\)
\(620\) 0 0
\(621\) 7.14225 + 1.37656i 0.286609 + 0.0552393i
\(622\) 0 0
\(623\) 30.7392 15.8472i 1.23154 0.634904i
\(624\) 0 0
\(625\) 5.31155 3.41353i 0.212462 0.136541i
\(626\) 0 0
\(627\) 0.458749 + 0.529424i 0.0183207 + 0.0211432i
\(628\) 0 0
\(629\) 0.00242626 0.000467622i 9.67411e−5 1.86453e-5i
\(630\) 0 0
\(631\) 4.42033 + 18.2209i 0.175971 + 0.725361i 0.989584 + 0.143955i \(0.0459820\pi\)
−0.813614 + 0.581406i \(0.802503\pi\)
\(632\) 0 0
\(633\) 9.30807 + 16.1220i 0.369962 + 0.640794i
\(634\) 0 0
\(635\) −0.630675 13.2395i −0.0250276 0.525394i
\(636\) 0 0
\(637\) 3.20466 + 4.50032i 0.126973 + 0.178309i
\(638\) 0 0
\(639\) −3.38290 + 3.22558i −0.133825 + 0.127602i
\(640\) 0 0
\(641\) 5.98473 10.3658i 0.236382 0.409426i −0.723291 0.690543i \(-0.757372\pi\)
0.959674 + 0.281117i \(0.0907048\pi\)
\(642\) 0 0
\(643\) −1.05921 + 7.36696i −0.0417711 + 0.290525i 0.958219 + 0.286036i \(0.0923378\pi\)
−0.999990 + 0.00448834i \(0.998571\pi\)
\(644\) 0 0
\(645\) −8.60013 + 2.52523i −0.338630 + 0.0994307i
\(646\) 0 0
\(647\) 0.239070 5.01870i 0.00939881 0.197305i −0.989284 0.146002i \(-0.953359\pi\)
0.998683 0.0513034i \(-0.0163375\pi\)
\(648\) 0 0
\(649\) −0.726117 0.571025i −0.0285026 0.0224147i
\(650\) 0 0
\(651\) −10.2880 + 0.982389i −0.403220 + 0.0385028i
\(652\) 0 0
\(653\) −11.0551 + 31.9416i −0.432620 + 1.24997i 0.492505 + 0.870309i \(0.336081\pi\)
−0.925125 + 0.379663i \(0.876040\pi\)
\(654\) 0 0
\(655\) −7.52095 + 16.4686i −0.293868 + 0.643481i
\(656\) 0 0
\(657\) 4.64204 + 4.42618i 0.181103 + 0.172682i
\(658\) 0 0
\(659\) 20.2461 + 8.10532i 0.788676 + 0.315738i 0.730806 0.682586i \(-0.239145\pi\)
0.0578708 + 0.998324i \(0.481569\pi\)
\(660\) 0 0
\(661\) −2.73585 5.99066i −0.106412 0.233010i 0.848934 0.528499i \(-0.177245\pi\)
−0.955346 + 0.295489i \(0.904518\pi\)
\(662\) 0 0
\(663\) −0.00115431 0.000110223i −4.48297e−5 4.28072e-6i
\(664\) 0 0
\(665\) −2.68442 18.6706i −0.104097 0.724014i
\(666\) 0 0
\(667\) −37.5424 24.1270i −1.45365 0.934202i
\(668\) 0 0
\(669\) 6.72623 0.260051
\(670\) 0 0
\(671\) 0.600931 0.0231987
\(672\) 0 0
\(673\) 11.9949 + 7.70866i 0.462370 + 0.297147i 0.751010 0.660291i \(-0.229567\pi\)
−0.288641 + 0.957438i \(0.593203\pi\)
\(674\) 0 0
\(675\) −0.516451 3.59200i −0.0198782 0.138256i
\(676\) 0 0
\(677\) 5.92509 + 0.565778i 0.227720 + 0.0217446i 0.208292 0.978067i \(-0.433210\pi\)
0.0194276 + 0.999811i \(0.493816\pi\)
\(678\) 0 0
\(679\) −2.96556 6.49367i −0.113808 0.249204i
\(680\) 0 0
\(681\) 18.5125 + 7.41127i 0.709399 + 0.284001i
\(682\) 0 0
\(683\) −8.06649 7.69138i −0.308656 0.294303i 0.519879 0.854240i \(-0.325977\pi\)
−0.828535 + 0.559937i \(0.810825\pi\)
\(684\) 0 0
\(685\) −2.06826 + 4.52886i −0.0790242 + 0.173039i
\(686\) 0 0
\(687\) 0.149167 0.430989i 0.00569107 0.0164433i
\(688\) 0 0
\(689\) −12.3546 + 1.17972i −0.470672 + 0.0449437i
\(690\) 0 0
\(691\) −3.98785 3.13608i −0.151705 0.119302i 0.539422 0.842036i \(-0.318643\pi\)
−0.691127 + 0.722734i \(0.742885\pi\)
\(692\) 0 0
\(693\) 0.0231489 0.485955i 0.000879353 0.0184599i
\(694\) 0 0
\(695\) −23.9101 + 7.02064i −0.906961 + 0.266308i
\(696\) 0 0
\(697\) −0.000299110 0.00208036i −1.13296e−5 7.87991e-5i
\(698\) 0 0
\(699\) 3.59920 6.23399i 0.136134 0.235791i
\(700\) 0 0
\(701\) −31.9255 + 30.4409i −1.20581 + 1.14974i −0.221151 + 0.975240i \(0.570981\pi\)
−0.984658 + 0.174497i \(0.944170\pi\)
\(702\) 0 0
\(703\) −7.85402 11.0294i −0.296220 0.415983i
\(704\) 0 0
\(705\) −0.00915291 0.192143i −0.000344718 0.00723653i
\(706\) 0 0
\(707\) −3.21548 5.56938i −0.120931 0.209458i
\(708\) 0 0
\(709\) −1.23585 5.09423i −0.0464132 0.191318i 0.943886 0.330273i \(-0.107141\pi\)
−0.990299 + 0.138955i \(0.955626\pi\)
\(710\) 0 0
\(711\) 4.47551 0.862584i 0.167845 0.0323494i
\(712\) 0 0
\(713\) −14.7177 16.9852i −0.551183 0.636099i
\(714\) 0 0
\(715\) 0.189030 0.121482i 0.00706932 0.00454318i
\(716\) 0 0
\(717\) 21.4690 11.0680i 0.801775 0.413344i
\(718\) 0 0
\(719\) 20.5074 + 3.95248i 0.764797 + 0.147403i 0.556709 0.830708i \(-0.312064\pi\)
0.208088 + 0.978110i \(0.433276\pi\)
\(720\) 0 0
\(721\) 16.1526 12.7025i 0.601553 0.473066i
\(722\) 0 0
\(723\) 14.9944 17.3044i 0.557647 0.643559i
\(724\) 0 0
\(725\) −5.24913 + 21.6372i −0.194948 + 0.803585i
\(726\) 0 0
\(727\) −3.37723 1.74108i −0.125254 0.0645732i 0.394460 0.918913i \(-0.370932\pi\)
−0.519715 + 0.854340i \(0.673962\pi\)
\(728\) 0 0
\(729\) −0.959493 0.281733i −0.0355368 0.0104345i
\(730\) 0 0
\(731\) 0.00624589 0.00250048i 0.000231013 9.24835e-5i
\(732\) 0 0
\(733\) −6.26301 18.0958i −0.231330 0.668383i −0.999601 0.0282584i \(-0.991004\pi\)
0.768271 0.640125i \(-0.221117\pi\)
\(734\) 0 0
\(735\) −2.84418 + 3.99410i −0.104909 + 0.147324i
\(736\) 0 0
\(737\) −0.799876 0.881860i −0.0294638 0.0324837i
\(738\) 0 0
\(739\) 8.62960 12.1186i 0.317445 0.445789i −0.624765 0.780813i \(-0.714805\pi\)
0.942210 + 0.335024i \(0.108744\pi\)
\(740\) 0 0
\(741\) 2.07824 + 6.00469i 0.0763462 + 0.220588i
\(742\) 0 0
\(743\) 24.1592 9.67189i 0.886316 0.354827i 0.116573 0.993182i \(-0.462809\pi\)
0.769742 + 0.638355i \(0.220385\pi\)
\(744\) 0 0
\(745\) −3.32649 0.976746i −0.121873 0.0357852i
\(746\) 0 0
\(747\) −12.5066 6.44762i −0.457594 0.235906i
\(748\) 0 0
\(749\) −0.779096 + 3.21148i −0.0284675 + 0.117345i
\(750\) 0 0
\(751\) 12.8350 14.8124i 0.468356 0.540511i −0.471598 0.881814i \(-0.656323\pi\)
0.939954 + 0.341302i \(0.110868\pi\)
\(752\) 0 0
\(753\) 0.248233 0.195213i 0.00904611 0.00711394i
\(754\) 0 0
\(755\) −2.12716 0.409976i −0.0774152 0.0149206i
\(756\) 0 0
\(757\) 33.0051 17.0153i 1.19959 0.618432i 0.261628 0.965169i \(-0.415741\pi\)
0.937962 + 0.346737i \(0.112710\pi\)
\(758\) 0 0
\(759\) 0.890027 0.571986i 0.0323059 0.0207618i
\(760\) 0 0
\(761\) −27.8808 32.1762i −1.01068 1.16639i −0.986009 0.166690i \(-0.946692\pi\)
−0.0246698 0.999696i \(-0.507853\pi\)
\(762\) 0 0
\(763\) −8.80732 + 1.69747i −0.318846 + 0.0614526i
\(764\) 0 0
\(765\) −0.000242626 0.00100012i −8.77215e−6 3.61593e-5i
\(766\) 0 0
\(767\) −4.18946 7.25635i −0.151273 0.262012i
\(768\) 0 0
\(769\) −0.523088 10.9810i −0.0188630 0.395984i −0.988480 0.151354i \(-0.951637\pi\)
0.969617 0.244630i \(-0.0786664\pi\)
\(770\) 0 0
\(771\) −14.8579 20.8650i −0.535094 0.751434i
\(772\) 0 0
\(773\) 28.1887 26.8779i 1.01388 0.966731i 0.0144285 0.999896i \(-0.495407\pi\)
0.999450 + 0.0331648i \(0.0105586\pi\)
\(774\) 0 0
\(775\) −5.60642 + 9.71061i −0.201389 + 0.348815i
\(776\) 0 0
\(777\) −1.33824 + 9.30767i −0.0480091 + 0.333911i