Properties

Label 819.2.et.c.145.7
Level $819$
Weight $2$
Character 819.145
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 145.7
Character \(\chi\) \(=\) 819.145
Dual form 819.2.et.c.514.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.926196 - 0.926196i) q^{2} +0.284323i q^{4} +(-0.409991 + 0.109857i) q^{5} +(-2.25606 + 1.38209i) q^{7} +(2.11573 + 2.11573i) q^{8} +O(q^{10})\) \(q+(0.926196 - 0.926196i) q^{2} +0.284323i q^{4} +(-0.409991 + 0.109857i) q^{5} +(-2.25606 + 1.38209i) q^{7} +(2.11573 + 2.11573i) q^{8} +(-0.277983 + 0.481481i) q^{10} +(-1.35455 + 0.362951i) q^{11} +(-3.54669 + 0.648849i) q^{13} +(-0.809468 + 3.36964i) q^{14} +3.35051 q^{16} +6.94638 q^{17} +(-0.143382 + 0.535108i) q^{19} +(-0.0312348 - 0.116570i) q^{20} +(-0.918416 + 1.59074i) q^{22} +7.84271i q^{23} +(-4.17410 + 2.40992i) q^{25} +(-2.68397 + 3.88589i) q^{26} +(-0.392961 - 0.641450i) q^{28} +(3.01567 + 5.22330i) q^{29} +(-2.17020 + 8.09928i) q^{31} +(-1.12823 + 1.12823i) q^{32} +(6.43371 - 6.43371i) q^{34} +(0.773134 - 0.814490i) q^{35} +(-4.24059 - 4.24059i) q^{37} +(0.362815 + 0.628415i) q^{38} +(-1.09986 - 0.635004i) q^{40} +(0.434817 - 1.62276i) q^{41} +(6.49491 + 3.74984i) q^{43} +(-0.103195 - 0.385130i) q^{44} +(7.26389 + 7.26389i) q^{46} +(-2.62582 - 9.79969i) q^{47} +(3.17964 - 6.23618i) q^{49} +(-1.63398 + 6.09809i) q^{50} +(-0.184483 - 1.00840i) q^{52} +(-3.77860 - 6.54472i) q^{53} +(0.515482 - 0.297614i) q^{55} +(-7.69736 - 1.84909i) q^{56} +(7.63090 + 2.04469i) q^{58} +(4.83450 - 4.83450i) q^{59} +(2.38809 - 1.37876i) q^{61} +(5.49149 + 9.51155i) q^{62} +8.79095i q^{64} +(1.38283 - 0.655650i) q^{65} +(3.70163 + 13.8147i) q^{67} +1.97502i q^{68} +(-0.0383037 - 1.47045i) q^{70} +(-1.00255 - 3.74157i) q^{71} +(-11.0713 - 2.96655i) q^{73} -7.85524 q^{74} +(-0.152144 - 0.0407667i) q^{76} +(2.55432 - 2.69096i) q^{77} +(4.32696 - 7.49452i) q^{79} +(-1.37368 + 0.368077i) q^{80} +(-1.10027 - 1.90572i) q^{82} +(2.26360 + 2.26360i) q^{83} +(-2.84796 + 0.763108i) q^{85} +(9.48864 - 2.54247i) q^{86} +(-3.63377 - 2.09796i) q^{88} +(8.19285 - 8.19285i) q^{89} +(7.10478 - 6.36569i) q^{91} -2.22986 q^{92} +(-11.5085 - 6.64441i) q^{94} -0.235141i q^{95} +(15.5709 - 4.17221i) q^{97} +(-2.83095 - 8.72089i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.926196 0.926196i 0.654919 0.654919i −0.299254 0.954173i \(-0.596738\pi\)
0.954173 + 0.299254i \(0.0967378\pi\)
\(3\) 0 0
\(4\) 0.284323i 0.142161i
\(5\) −0.409991 + 0.109857i −0.183354 + 0.0491295i −0.349328 0.937001i \(-0.613590\pi\)
0.165974 + 0.986130i \(0.446923\pi\)
\(6\) 0 0
\(7\) −2.25606 + 1.38209i −0.852712 + 0.522382i
\(8\) 2.11573 + 2.11573i 0.748024 + 0.748024i
\(9\) 0 0
\(10\) −0.277983 + 0.481481i −0.0879060 + 0.152258i
\(11\) −1.35455 + 0.362951i −0.408413 + 0.109434i −0.457175 0.889377i \(-0.651139\pi\)
0.0487628 + 0.998810i \(0.484472\pi\)
\(12\) 0 0
\(13\) −3.54669 + 0.648849i −0.983674 + 0.179958i
\(14\) −0.809468 + 3.36964i −0.216339 + 0.900575i
\(15\) 0 0
\(16\) 3.35051 0.837629
\(17\) 6.94638 1.68475 0.842373 0.538895i \(-0.181158\pi\)
0.842373 + 0.538895i \(0.181158\pi\)
\(18\) 0 0
\(19\) −0.143382 + 0.535108i −0.0328941 + 0.122762i −0.980421 0.196915i \(-0.936908\pi\)
0.947527 + 0.319677i \(0.103574\pi\)
\(20\) −0.0312348 0.116570i −0.00698432 0.0260658i
\(21\) 0 0
\(22\) −0.918416 + 1.59074i −0.195807 + 0.339148i
\(23\) 7.84271i 1.63532i 0.575702 + 0.817659i \(0.304729\pi\)
−0.575702 + 0.817659i \(0.695271\pi\)
\(24\) 0 0
\(25\) −4.17410 + 2.40992i −0.834821 + 0.481984i
\(26\) −2.68397 + 3.88589i −0.526369 + 0.762085i
\(27\) 0 0
\(28\) −0.392961 0.641450i −0.0742626 0.121223i
\(29\) 3.01567 + 5.22330i 0.559997 + 0.969943i 0.997496 + 0.0707238i \(0.0225309\pi\)
−0.437499 + 0.899219i \(0.644136\pi\)
\(30\) 0 0
\(31\) −2.17020 + 8.09928i −0.389779 + 1.45467i 0.440715 + 0.897647i \(0.354725\pi\)
−0.830494 + 0.557027i \(0.811942\pi\)
\(32\) −1.12823 + 1.12823i −0.199444 + 0.199444i
\(33\) 0 0
\(34\) 6.43371 6.43371i 1.10337 1.10337i
\(35\) 0.773134 0.814490i 0.130684 0.137674i
\(36\) 0 0
\(37\) −4.24059 4.24059i −0.697149 0.697149i 0.266646 0.963795i \(-0.414085\pi\)
−0.963795 + 0.266646i \(0.914085\pi\)
\(38\) 0.362815 + 0.628415i 0.0588564 + 0.101942i
\(39\) 0 0
\(40\) −1.09986 0.635004i −0.173903 0.100403i
\(41\) 0.434817 1.62276i 0.0679070 0.253433i −0.923625 0.383299i \(-0.874788\pi\)
0.991532 + 0.129866i \(0.0414547\pi\)
\(42\) 0 0
\(43\) 6.49491 + 3.74984i 0.990464 + 0.571845i 0.905413 0.424532i \(-0.139561\pi\)
0.0850513 + 0.996377i \(0.472895\pi\)
\(44\) −0.103195 0.385130i −0.0155573 0.0580605i
\(45\) 0 0
\(46\) 7.26389 + 7.26389i 1.07100 + 1.07100i
\(47\) −2.62582 9.79969i −0.383015 1.42943i −0.841272 0.540612i \(-0.818193\pi\)
0.458257 0.888820i \(-0.348474\pi\)
\(48\) 0 0
\(49\) 3.17964 6.23618i 0.454234 0.890882i
\(50\) −1.63398 + 6.09809i −0.231080 + 0.862401i
\(51\) 0 0
\(52\) −0.184483 1.00840i −0.0255831 0.139841i
\(53\) −3.77860 6.54472i −0.519030 0.898986i −0.999755 0.0221152i \(-0.992960\pi\)
0.480725 0.876871i \(-0.340373\pi\)
\(54\) 0 0
\(55\) 0.515482 0.297614i 0.0695076 0.0401302i
\(56\) −7.69736 1.84909i −1.02860 0.247094i
\(57\) 0 0
\(58\) 7.63090 + 2.04469i 1.00199 + 0.268482i
\(59\) 4.83450 4.83450i 0.629398 0.629398i −0.318519 0.947917i \(-0.603185\pi\)
0.947917 + 0.318519i \(0.103185\pi\)
\(60\) 0 0
\(61\) 2.38809 1.37876i 0.305763 0.176533i −0.339266 0.940691i \(-0.610179\pi\)
0.645029 + 0.764158i \(0.276845\pi\)
\(62\) 5.49149 + 9.51155i 0.697421 + 1.20797i
\(63\) 0 0
\(64\) 8.79095i 1.09887i
\(65\) 1.38283 0.655650i 0.171519 0.0813234i
\(66\) 0 0
\(67\) 3.70163 + 13.8147i 0.452226 + 1.68773i 0.696118 + 0.717927i \(0.254909\pi\)
−0.243893 + 0.969802i \(0.578424\pi\)
\(68\) 1.97502i 0.239506i
\(69\) 0 0
\(70\) −0.0383037 1.47045i −0.00457817 0.175752i
\(71\) −1.00255 3.74157i −0.118981 0.444042i 0.880573 0.473910i \(-0.157158\pi\)
−0.999554 + 0.0298681i \(0.990491\pi\)
\(72\) 0 0
\(73\) −11.0713 2.96655i −1.29580 0.347209i −0.455940 0.890011i \(-0.650697\pi\)
−0.839861 + 0.542802i \(0.817363\pi\)
\(74\) −7.85524 −0.913153
\(75\) 0 0
\(76\) −0.152144 0.0407667i −0.0174521 0.00467627i
\(77\) 2.55432 2.69096i 0.291092 0.306663i
\(78\) 0 0
\(79\) 4.32696 7.49452i 0.486821 0.843199i −0.513064 0.858350i \(-0.671490\pi\)
0.999885 + 0.0151513i \(0.00482300\pi\)
\(80\) −1.37368 + 0.368077i −0.153582 + 0.0411523i
\(81\) 0 0
\(82\) −1.10027 1.90572i −0.121504 0.210452i
\(83\) 2.26360 + 2.26360i 0.248462 + 0.248462i 0.820339 0.571877i \(-0.193785\pi\)
−0.571877 + 0.820339i \(0.693785\pi\)
\(84\) 0 0
\(85\) −2.84796 + 0.763108i −0.308904 + 0.0827707i
\(86\) 9.48864 2.54247i 1.02319 0.274162i
\(87\) 0 0
\(88\) −3.63377 2.09796i −0.387361 0.223643i
\(89\) 8.19285 8.19285i 0.868441 0.868441i −0.123859 0.992300i \(-0.539527\pi\)
0.992300 + 0.123859i \(0.0395271\pi\)
\(90\) 0 0
\(91\) 7.10478 6.36569i 0.744784 0.667306i
\(92\) −2.22986 −0.232479
\(93\) 0 0
\(94\) −11.5085 6.64441i −1.18701 0.685318i
\(95\) 0.235141i 0.0241250i
\(96\) 0 0
\(97\) 15.5709 4.17221i 1.58099 0.423624i 0.641755 0.766910i \(-0.278207\pi\)
0.939231 + 0.343286i \(0.111540\pi\)
\(98\) −2.83095 8.72089i −0.285969 0.880943i
\(99\) 0 0
\(100\) −0.685195 1.18679i −0.0685195 0.118679i
\(101\) −3.55466 + 6.15686i −0.353702 + 0.612630i −0.986895 0.161364i \(-0.948411\pi\)
0.633193 + 0.773994i \(0.281744\pi\)
\(102\) 0 0
\(103\) 5.13973 8.90227i 0.506432 0.877167i −0.493540 0.869723i \(-0.664297\pi\)
0.999972 0.00744360i \(-0.00236939\pi\)
\(104\) −8.87662 6.13105i −0.870425 0.601198i
\(105\) 0 0
\(106\) −9.56141 2.56197i −0.928686 0.248841i
\(107\) −4.49430 −0.434480 −0.217240 0.976118i \(-0.569705\pi\)
−0.217240 + 0.976118i \(0.569705\pi\)
\(108\) 0 0
\(109\) −4.38513 1.17499i −0.420019 0.112544i 0.0426183 0.999091i \(-0.486430\pi\)
−0.462637 + 0.886548i \(0.653097\pi\)
\(110\) 0.201789 0.753085i 0.0192398 0.0718039i
\(111\) 0 0
\(112\) −7.55897 + 4.63072i −0.714256 + 0.437562i
\(113\) 3.41572 5.91619i 0.321324 0.556549i −0.659438 0.751759i \(-0.729206\pi\)
0.980761 + 0.195210i \(0.0625390\pi\)
\(114\) 0 0
\(115\) −0.861576 3.21544i −0.0803424 0.299842i
\(116\) −1.48510 + 0.857425i −0.137888 + 0.0796099i
\(117\) 0 0
\(118\) 8.95538i 0.824410i
\(119\) −15.6715 + 9.60054i −1.43660 + 0.880080i
\(120\) 0 0
\(121\) −7.82320 + 4.51673i −0.711200 + 0.410612i
\(122\) 0.934832 3.48884i 0.0846357 0.315865i
\(123\) 0 0
\(124\) −2.30281 0.617036i −0.206799 0.0554115i
\(125\) 2.94727 2.94727i 0.263612 0.263612i
\(126\) 0 0
\(127\) 0.727835 0.420216i 0.0645850 0.0372881i −0.467360 0.884067i \(-0.654795\pi\)
0.531945 + 0.846779i \(0.321461\pi\)
\(128\) 5.88568 + 5.88568i 0.520226 + 0.520226i
\(129\) 0 0
\(130\) 0.673512 1.88803i 0.0590709 0.165591i
\(131\) 15.6642 + 9.04371i 1.36858 + 0.790152i 0.990747 0.135720i \(-0.0433347\pi\)
0.377837 + 0.925872i \(0.376668\pi\)
\(132\) 0 0
\(133\) −0.416091 1.40541i −0.0360796 0.121864i
\(134\) 16.2235 + 9.36665i 1.40150 + 0.809155i
\(135\) 0 0
\(136\) 14.6967 + 14.6967i 1.26023 + 1.26023i
\(137\) 10.2762 + 10.2762i 0.877957 + 0.877957i 0.993323 0.115366i \(-0.0368040\pi\)
−0.115366 + 0.993323i \(0.536804\pi\)
\(138\) 0 0
\(139\) −10.1485 5.85922i −0.860782 0.496973i 0.00349232 0.999994i \(-0.498888\pi\)
−0.864274 + 0.503021i \(0.832222\pi\)
\(140\) 0.231578 + 0.219820i 0.0195719 + 0.0185782i
\(141\) 0 0
\(142\) −4.39398 2.53687i −0.368735 0.212889i
\(143\) 4.56867 2.16617i 0.382051 0.181144i
\(144\) 0 0
\(145\) −1.81022 1.81022i −0.150330 0.150330i
\(146\) −13.0018 + 7.50661i −1.07604 + 0.621251i
\(147\) 0 0
\(148\) 1.20570 1.20570i 0.0991077 0.0991077i
\(149\) −6.09666 1.63360i −0.499458 0.133829i 0.000290536 1.00000i \(-0.499908\pi\)
−0.499748 + 0.866171i \(0.666574\pi\)
\(150\) 0 0
\(151\) 1.46708 5.47520i 0.119389 0.445565i −0.880189 0.474624i \(-0.842584\pi\)
0.999578 + 0.0290583i \(0.00925084\pi\)
\(152\) −1.43550 + 0.828788i −0.116435 + 0.0672235i
\(153\) 0 0
\(154\) −0.126550 4.85815i −0.0101977 0.391481i
\(155\) 3.55905i 0.285870i
\(156\) 0 0
\(157\) −4.05121 + 2.33897i −0.323322 + 0.186670i −0.652872 0.757468i \(-0.726436\pi\)
0.329550 + 0.944138i \(0.393103\pi\)
\(158\) −2.93378 10.9490i −0.233399 0.871056i
\(159\) 0 0
\(160\) 0.338620 0.586507i 0.0267703 0.0463675i
\(161\) −10.8394 17.6937i −0.854261 1.39446i
\(162\) 0 0
\(163\) −3.11598 + 11.6290i −0.244063 + 0.910855i 0.729789 + 0.683672i \(0.239618\pi\)
−0.973852 + 0.227183i \(0.927049\pi\)
\(164\) 0.461388 + 0.123629i 0.0360283 + 0.00965376i
\(165\) 0 0
\(166\) 4.19307 0.325445
\(167\) −2.16916 0.581223i −0.167854 0.0449764i 0.173913 0.984761i \(-0.444359\pi\)
−0.341767 + 0.939785i \(0.611025\pi\)
\(168\) 0 0
\(169\) 12.1580 4.60253i 0.935230 0.354041i
\(170\) −1.93098 + 3.34455i −0.148099 + 0.256516i
\(171\) 0 0
\(172\) −1.06616 + 1.84665i −0.0812943 + 0.140806i
\(173\) −5.82086 10.0820i −0.442552 0.766523i 0.555326 0.831633i \(-0.312593\pi\)
−0.997878 + 0.0651101i \(0.979260\pi\)
\(174\) 0 0
\(175\) 6.08631 11.2059i 0.460082 0.847088i
\(176\) −4.53844 + 1.21607i −0.342098 + 0.0916649i
\(177\) 0 0
\(178\) 15.1764i 1.13752i
\(179\) 16.3721 + 9.45241i 1.22370 + 0.706506i 0.965706 0.259639i \(-0.0836035\pi\)
0.257999 + 0.966145i \(0.416937\pi\)
\(180\) 0 0
\(181\) 0.400647 0.0297799 0.0148899 0.999889i \(-0.495260\pi\)
0.0148899 + 0.999889i \(0.495260\pi\)
\(182\) 0.684540 12.4763i 0.0507415 0.924805i
\(183\) 0 0
\(184\) −16.5931 + 16.5931i −1.22326 + 1.22326i
\(185\) 2.20446 + 1.27275i 0.162075 + 0.0935743i
\(186\) 0 0
\(187\) −9.40923 + 2.52120i −0.688071 + 0.184368i
\(188\) 2.78628 0.746580i 0.203210 0.0544500i
\(189\) 0 0
\(190\) −0.217787 0.217787i −0.0157999 0.0157999i
\(191\) −5.12611 8.87869i −0.370912 0.642439i 0.618794 0.785554i \(-0.287622\pi\)
−0.989706 + 0.143114i \(0.954288\pi\)
\(192\) 0 0
\(193\) −8.65734 + 2.31973i −0.623169 + 0.166978i −0.556568 0.830802i \(-0.687882\pi\)
−0.0666009 + 0.997780i \(0.521215\pi\)
\(194\) 10.5574 18.2860i 0.757979 1.31286i
\(195\) 0 0
\(196\) 1.77309 + 0.904045i 0.126649 + 0.0645746i
\(197\) 4.04286 + 1.08328i 0.288042 + 0.0771806i 0.399947 0.916538i \(-0.369029\pi\)
−0.111905 + 0.993719i \(0.535695\pi\)
\(198\) 0 0
\(199\) 0.0731516 0.00518558 0.00259279 0.999997i \(-0.499175\pi\)
0.00259279 + 0.999997i \(0.499175\pi\)
\(200\) −13.9300 3.73254i −0.985001 0.263930i
\(201\) 0 0
\(202\) 2.41014 + 8.99477i 0.169577 + 0.632870i
\(203\) −14.0226 7.61615i −0.984196 0.534549i
\(204\) 0 0
\(205\) 0.713085i 0.0498040i
\(206\) −3.48485 13.0056i −0.242801 0.906146i
\(207\) 0 0
\(208\) −11.8832 + 2.17398i −0.823954 + 0.150738i
\(209\) 0.776872i 0.0537374i
\(210\) 0 0
\(211\) 10.3736 + 17.9676i 0.714148 + 1.23694i 0.963287 + 0.268472i \(0.0865188\pi\)
−0.249140 + 0.968468i \(0.580148\pi\)
\(212\) 1.86081 1.07434i 0.127801 0.0737861i
\(213\) 0 0
\(214\) −4.16260 + 4.16260i −0.284549 + 0.284549i
\(215\) −3.07480 0.823891i −0.209700 0.0561889i
\(216\) 0 0
\(217\) −6.29786 21.2719i −0.427526 1.44403i
\(218\) −5.14976 + 2.97321i −0.348785 + 0.201371i
\(219\) 0 0
\(220\) 0.0846184 + 0.146563i 0.00570497 + 0.00988129i
\(221\) −24.6367 + 4.50715i −1.65724 + 0.303184i
\(222\) 0 0
\(223\) −0.0283672 + 0.105868i −0.00189961 + 0.00708942i −0.966869 0.255273i \(-0.917835\pi\)
0.964970 + 0.262362i \(0.0845015\pi\)
\(224\) 0.986038 4.10467i 0.0658824 0.274255i
\(225\) 0 0
\(226\) −2.31593 8.64317i −0.154053 0.574935i
\(227\) −2.22859 2.22859i −0.147917 0.147917i 0.629270 0.777187i \(-0.283354\pi\)
−0.777187 + 0.629270i \(0.783354\pi\)
\(228\) 0 0
\(229\) 4.14901 + 15.4843i 0.274174 + 1.02323i 0.956393 + 0.292084i \(0.0943486\pi\)
−0.682218 + 0.731148i \(0.738985\pi\)
\(230\) −3.77612 2.18014i −0.248990 0.143754i
\(231\) 0 0
\(232\) −4.67074 + 17.4314i −0.306649 + 1.14443i
\(233\) 21.8559 + 12.6185i 1.43183 + 0.826668i 0.997260 0.0739699i \(-0.0235669\pi\)
0.434570 + 0.900638i \(0.356900\pi\)
\(234\) 0 0
\(235\) 2.15313 + 3.72932i 0.140454 + 0.243274i
\(236\) 1.37456 + 1.37456i 0.0894761 + 0.0894761i
\(237\) 0 0
\(238\) −5.62287 + 23.4068i −0.364477 + 1.51724i
\(239\) −3.59516 + 3.59516i −0.232552 + 0.232552i −0.813757 0.581205i \(-0.802581\pi\)
0.581205 + 0.813757i \(0.302581\pi\)
\(240\) 0 0
\(241\) 2.15492 2.15492i 0.138811 0.138811i −0.634287 0.773098i \(-0.718706\pi\)
0.773098 + 0.634287i \(0.218706\pi\)
\(242\) −3.06244 + 11.4292i −0.196861 + 0.734696i
\(243\) 0 0
\(244\) 0.392014 + 0.678988i 0.0250961 + 0.0434678i
\(245\) −0.618539 + 2.90608i −0.0395170 + 0.185663i
\(246\) 0 0
\(247\) 0.161326 1.99090i 0.0102649 0.126678i
\(248\) −21.7274 + 12.5443i −1.37969 + 0.796567i
\(249\) 0 0
\(250\) 5.45950i 0.345289i
\(251\) −3.62476 + 6.27826i −0.228793 + 0.396280i −0.957451 0.288597i \(-0.906811\pi\)
0.728658 + 0.684878i \(0.240144\pi\)
\(252\) 0 0
\(253\) −2.84652 10.6234i −0.178959 0.667885i
\(254\) 0.284916 1.06332i 0.0178772 0.0667187i
\(255\) 0 0
\(256\) −6.67931 −0.417457
\(257\) 11.4669 0.715289 0.357644 0.933858i \(-0.383580\pi\)
0.357644 + 0.933858i \(0.383580\pi\)
\(258\) 0 0
\(259\) 15.4279 + 3.70615i 0.958645 + 0.230289i
\(260\) 0.186416 + 0.393171i 0.0115611 + 0.0243834i
\(261\) 0 0
\(262\) 22.8843 6.13184i 1.41380 0.378826i
\(263\) −8.29386 + 14.3654i −0.511421 + 0.885808i 0.488491 + 0.872569i \(0.337547\pi\)
−0.999912 + 0.0132387i \(0.995786\pi\)
\(264\) 0 0
\(265\) 2.26817 + 2.26817i 0.139333 + 0.139333i
\(266\) −1.68706 0.916299i −0.103440 0.0561819i
\(267\) 0 0
\(268\) −3.92782 + 1.05246i −0.239930 + 0.0642891i
\(269\) 9.39879i 0.573055i −0.958072 0.286527i \(-0.907499\pi\)
0.958072 0.286527i \(-0.0925009\pi\)
\(270\) 0 0
\(271\) 16.6976 16.6976i 1.01431 1.01431i 0.0144118 0.999896i \(-0.495412\pi\)
0.999896 0.0144118i \(-0.00458758\pi\)
\(272\) 23.2740 1.41119
\(273\) 0 0
\(274\) 19.0356 1.14998
\(275\) 4.77935 4.77935i 0.288206 0.288206i
\(276\) 0 0
\(277\) 7.83005i 0.470462i 0.971940 + 0.235231i \(0.0755846\pi\)
−0.971940 + 0.235231i \(0.924415\pi\)
\(278\) −14.8263 + 3.97268i −0.889219 + 0.238266i
\(279\) 0 0
\(280\) 3.35898 0.0874981i 0.200738 0.00522901i
\(281\) −7.60467 7.60467i −0.453656 0.453656i 0.442910 0.896566i \(-0.353946\pi\)
−0.896566 + 0.442910i \(0.853946\pi\)
\(282\) 0 0
\(283\) −6.54596 + 11.3379i −0.389117 + 0.673971i −0.992331 0.123609i \(-0.960553\pi\)
0.603214 + 0.797580i \(0.293887\pi\)
\(284\) 1.06381 0.285048i 0.0631257 0.0169145i
\(285\) 0 0
\(286\) 2.22518 6.23778i 0.131578 0.368848i
\(287\) 1.26183 + 4.26201i 0.0744834 + 0.251578i
\(288\) 0 0
\(289\) 31.2522 1.83837
\(290\) −3.35323 −0.196908
\(291\) 0 0
\(292\) 0.843459 3.14783i 0.0493597 0.184213i
\(293\) −1.63802 6.11317i −0.0956941 0.357135i 0.901430 0.432926i \(-0.142519\pi\)
−0.997124 + 0.0757902i \(0.975852\pi\)
\(294\) 0 0
\(295\) −1.45100 + 2.51321i −0.0844805 + 0.146324i
\(296\) 17.9439i 1.04297i
\(297\) 0 0
\(298\) −7.15973 + 4.13367i −0.414752 + 0.239457i
\(299\) −5.08873 27.8157i −0.294289 1.60862i
\(300\) 0 0
\(301\) −19.8355 + 0.516695i −1.14330 + 0.0297818i
\(302\) −3.71231 6.42991i −0.213619 0.369999i
\(303\) 0 0
\(304\) −0.480403 + 1.79289i −0.0275530 + 0.102829i
\(305\) −0.827629 + 0.827629i −0.0473899 + 0.0473899i
\(306\) 0 0
\(307\) −0.930901 + 0.930901i −0.0531293 + 0.0531293i −0.733172 0.680043i \(-0.761961\pi\)
0.680043 + 0.733172i \(0.261961\pi\)
\(308\) 0.765100 + 0.726252i 0.0435956 + 0.0413821i
\(309\) 0 0
\(310\) −3.29637 3.29637i −0.187221 0.187221i
\(311\) 15.2632 + 26.4366i 0.865495 + 1.49908i 0.866555 + 0.499081i \(0.166329\pi\)
−0.00106060 + 0.999999i \(0.500338\pi\)
\(312\) 0 0
\(313\) −15.9124 9.18705i −0.899425 0.519283i −0.0224111 0.999749i \(-0.507134\pi\)
−0.877013 + 0.480466i \(0.840468\pi\)
\(314\) −1.58587 + 5.91856i −0.0894960 + 0.334004i
\(315\) 0 0
\(316\) 2.13086 + 1.23025i 0.119870 + 0.0692072i
\(317\) 4.00188 + 14.9352i 0.224768 + 0.838845i 0.982497 + 0.186276i \(0.0596420\pi\)
−0.757730 + 0.652569i \(0.773691\pi\)
\(318\) 0 0
\(319\) −5.98069 5.98069i −0.334854 0.334854i
\(320\) −0.965746 3.60421i −0.0539868 0.201482i
\(321\) 0 0
\(322\) −26.4272 6.34842i −1.47273 0.353784i
\(323\) −0.995985 + 3.71707i −0.0554181 + 0.206823i
\(324\) 0 0
\(325\) 13.2406 11.2556i 0.734454 0.624348i
\(326\) 7.88473 + 13.6568i 0.436695 + 0.756378i
\(327\) 0 0
\(328\) 4.35328 2.51337i 0.240370 0.138777i
\(329\) 19.4681 + 18.4796i 1.07331 + 1.01881i
\(330\) 0 0
\(331\) 25.7839 + 6.90877i 1.41721 + 0.379740i 0.884493 0.466553i \(-0.154504\pi\)
0.532717 + 0.846293i \(0.321171\pi\)
\(332\) −0.643592 + 0.643592i −0.0353217 + 0.0353217i
\(333\) 0 0
\(334\) −2.54739 + 1.47074i −0.139387 + 0.0804751i
\(335\) −3.03527 5.25724i −0.165835 0.287234i
\(336\) 0 0
\(337\) 25.3802i 1.38255i −0.722592 0.691275i \(-0.757049\pi\)
0.722592 0.691275i \(-0.242951\pi\)
\(338\) 6.99784 15.5235i 0.380632 0.844368i
\(339\) 0 0
\(340\) −0.216969 0.809740i −0.0117668 0.0439143i
\(341\) 11.7586i 0.636762i
\(342\) 0 0
\(343\) 1.44550 + 18.4638i 0.0780498 + 0.996949i
\(344\) 5.80783 + 21.6751i 0.313137 + 1.16864i
\(345\) 0 0
\(346\) −14.7292 3.94668i −0.791846 0.212175i
\(347\) 2.33363 0.125276 0.0626380 0.998036i \(-0.480049\pi\)
0.0626380 + 0.998036i \(0.480049\pi\)
\(348\) 0 0
\(349\) −28.6493 7.67654i −1.53356 0.410916i −0.609381 0.792878i \(-0.708582\pi\)
−0.924178 + 0.381962i \(0.875249\pi\)
\(350\) −4.74177 16.0160i −0.253458 0.856091i
\(351\) 0 0
\(352\) 1.11875 1.93773i 0.0596296 0.103282i
\(353\) −4.21930 + 1.13056i −0.224571 + 0.0601736i −0.369350 0.929290i \(-0.620420\pi\)
0.144779 + 0.989464i \(0.453753\pi\)
\(354\) 0 0
\(355\) 0.822073 + 1.42387i 0.0436311 + 0.0755713i
\(356\) 2.32942 + 2.32942i 0.123459 + 0.123459i
\(357\) 0 0
\(358\) 23.9185 6.40895i 1.26413 0.338723i
\(359\) 20.7047 5.54780i 1.09275 0.292802i 0.332941 0.942948i \(-0.391959\pi\)
0.759809 + 0.650146i \(0.225292\pi\)
\(360\) 0 0
\(361\) 16.1887 + 9.34655i 0.852037 + 0.491924i
\(362\) 0.371078 0.371078i 0.0195034 0.0195034i
\(363\) 0 0
\(364\) 1.80991 + 2.02005i 0.0948652 + 0.105880i
\(365\) 4.86505 0.254648
\(366\) 0 0
\(367\) 10.9156 + 6.30214i 0.569791 + 0.328969i 0.757066 0.653338i \(-0.226632\pi\)
−0.187275 + 0.982308i \(0.559965\pi\)
\(368\) 26.2771i 1.36979i
\(369\) 0 0
\(370\) 3.22058 0.862952i 0.167430 0.0448627i
\(371\) 17.5702 + 9.54293i 0.912197 + 0.495444i
\(372\) 0 0
\(373\) 7.97476 + 13.8127i 0.412917 + 0.715194i 0.995207 0.0977873i \(-0.0311765\pi\)
−0.582290 + 0.812981i \(0.697843\pi\)
\(374\) −6.37967 + 11.0499i −0.329885 + 0.571377i
\(375\) 0 0
\(376\) 15.1780 26.2890i 0.782744 1.35575i
\(377\) −14.0848 16.5687i −0.725403 0.853331i
\(378\) 0 0
\(379\) −33.0651 8.85976i −1.69844 0.455095i −0.725893 0.687808i \(-0.758573\pi\)
−0.972545 + 0.232713i \(0.925240\pi\)
\(380\) 0.0668561 0.00342964
\(381\) 0 0
\(382\) −12.9712 3.47562i −0.663664 0.177828i
\(383\) 3.37726 12.6041i 0.172570 0.644039i −0.824383 0.566032i \(-0.808478\pi\)
0.996953 0.0780068i \(-0.0248556\pi\)
\(384\) 0 0
\(385\) −0.751630 + 1.38388i −0.0383066 + 0.0705290i
\(386\) −5.86987 + 10.1669i −0.298768 + 0.517482i
\(387\) 0 0
\(388\) 1.18626 + 4.42717i 0.0602230 + 0.224755i
\(389\) 14.8252 8.55933i 0.751667 0.433975i −0.0746290 0.997211i \(-0.523777\pi\)
0.826296 + 0.563236i \(0.190444\pi\)
\(390\) 0 0
\(391\) 54.4785i 2.75510i
\(392\) 19.9213 6.46680i 1.00618 0.326623i
\(393\) 0 0
\(394\) 4.74781 2.74115i 0.239191 0.138097i
\(395\) −0.950693 + 3.54803i −0.0478345 + 0.178521i
\(396\) 0 0
\(397\) −9.36386 2.50904i −0.469959 0.125925i 0.0160646 0.999871i \(-0.494886\pi\)
−0.486023 + 0.873946i \(0.661553\pi\)
\(398\) 0.0677527 0.0677527i 0.00339613 0.00339613i
\(399\) 0 0
\(400\) −13.9854 + 8.07447i −0.699270 + 0.403723i
\(401\) 5.44277 + 5.44277i 0.271799 + 0.271799i 0.829824 0.558025i \(-0.188441\pi\)
−0.558025 + 0.829824i \(0.688441\pi\)
\(402\) 0 0
\(403\) 2.44180 30.1338i 0.121635 1.50107i
\(404\) −1.75054 1.01067i −0.0870924 0.0502828i
\(405\) 0 0
\(406\) −20.0418 + 5.93365i −0.994656 + 0.294482i
\(407\) 7.28323 + 4.20497i 0.361016 + 0.208433i
\(408\) 0 0
\(409\) −2.18322 2.18322i −0.107954 0.107954i 0.651067 0.759020i \(-0.274322\pi\)
−0.759020 + 0.651067i \(0.774322\pi\)
\(410\) 0.660457 + 0.660457i 0.0326176 + 0.0326176i
\(411\) 0 0
\(412\) 2.53112 + 1.46134i 0.124699 + 0.0719952i
\(413\) −4.22521 + 17.5887i −0.207909 + 0.865481i
\(414\) 0 0
\(415\) −1.17673 0.679384i −0.0577633 0.0333496i
\(416\) 3.26942 4.73352i 0.160297 0.232080i
\(417\) 0 0
\(418\) −0.719536 0.719536i −0.0351937 0.0351937i
\(419\) 2.29397 1.32442i 0.112068 0.0647023i −0.442918 0.896562i \(-0.646057\pi\)
0.554986 + 0.831860i \(0.312724\pi\)
\(420\) 0 0
\(421\) 8.96466 8.96466i 0.436911 0.436911i −0.454060 0.890971i \(-0.650025\pi\)
0.890971 + 0.454060i \(0.150025\pi\)
\(422\) 26.2495 + 7.03353i 1.27780 + 0.342387i
\(423\) 0 0
\(424\) 5.85237 21.8414i 0.284216 1.06071i
\(425\) −28.9949 + 16.7402i −1.40646 + 0.812020i
\(426\) 0 0
\(427\) −3.48210 + 6.41114i −0.168511 + 0.310257i
\(428\) 1.27783i 0.0617663i
\(429\) 0 0
\(430\) −3.61095 + 2.08478i −0.174136 + 0.100537i
\(431\) 3.00230 + 11.2048i 0.144616 + 0.539714i 0.999772 + 0.0213436i \(0.00679441\pi\)
−0.855156 + 0.518370i \(0.826539\pi\)
\(432\) 0 0
\(433\) −1.08503 + 1.87932i −0.0521430 + 0.0903143i −0.890919 0.454163i \(-0.849938\pi\)
0.838776 + 0.544477i \(0.183272\pi\)
\(434\) −25.5350 13.8689i −1.22572 0.665728i
\(435\) 0 0
\(436\) 0.334077 1.24679i 0.0159994 0.0597105i
\(437\) −4.19670 1.12450i −0.200755 0.0537923i
\(438\) 0 0
\(439\) 20.7361 0.989680 0.494840 0.868984i \(-0.335227\pi\)
0.494840 + 0.868984i \(0.335227\pi\)
\(440\) 1.72029 + 0.460950i 0.0820116 + 0.0219749i
\(441\) 0 0
\(442\) −18.6439 + 26.9929i −0.886798 + 1.28392i
\(443\) 9.36776 16.2254i 0.445075 0.770893i −0.552982 0.833193i \(-0.686510\pi\)
0.998057 + 0.0622999i \(0.0198435\pi\)
\(444\) 0 0
\(445\) −2.45896 + 4.25904i −0.116566 + 0.201898i
\(446\) 0.0717806 + 0.124328i 0.00339891 + 0.00588709i
\(447\) 0 0
\(448\) −12.1499 19.8329i −0.574029 0.937018i
\(449\) −14.2069 + 3.80673i −0.670465 + 0.179651i −0.577964 0.816062i \(-0.696153\pi\)
−0.0925007 + 0.995713i \(0.529486\pi\)
\(450\) 0 0
\(451\) 2.35593i 0.110936i
\(452\) 1.68211 + 0.971166i 0.0791198 + 0.0456798i
\(453\) 0 0
\(454\) −4.12822 −0.193747
\(455\) −2.21358 + 3.39039i −0.103774 + 0.158944i
\(456\) 0 0
\(457\) 17.1891 17.1891i 0.804074 0.804074i −0.179655 0.983730i \(-0.557498\pi\)
0.983730 + 0.179655i \(0.0574982\pi\)
\(458\) 18.1843 + 10.4987i 0.849697 + 0.490573i
\(459\) 0 0
\(460\) 0.914225 0.244966i 0.0426259 0.0114216i
\(461\) 3.71656 0.995848i 0.173097 0.0463813i −0.171229 0.985231i \(-0.554774\pi\)
0.344327 + 0.938850i \(0.388107\pi\)
\(462\) 0 0
\(463\) −4.99628 4.99628i −0.232197 0.232197i 0.581412 0.813609i \(-0.302500\pi\)
−0.813609 + 0.581412i \(0.802500\pi\)
\(464\) 10.1041 + 17.5007i 0.469069 + 0.812452i
\(465\) 0 0
\(466\) 31.9301 8.55565i 1.47913 0.396333i
\(467\) −4.32120 + 7.48453i −0.199961 + 0.346343i −0.948516 0.316731i \(-0.897415\pi\)
0.748554 + 0.663073i \(0.230748\pi\)
\(468\) 0 0
\(469\) −27.4442 26.0507i −1.26726 1.20291i
\(470\) 5.44830 + 1.45987i 0.251311 + 0.0673387i
\(471\) 0 0
\(472\) 20.4570 0.941609
\(473\) −10.1587 2.72201i −0.467097 0.125158i
\(474\) 0 0
\(475\) −0.691077 2.57914i −0.0317088 0.118339i
\(476\) −2.72965 4.45576i −0.125114 0.204229i
\(477\) 0 0
\(478\) 6.65964i 0.304605i
\(479\) 6.58134 + 24.5619i 0.300709 + 1.12226i 0.936576 + 0.350464i \(0.113976\pi\)
−0.635867 + 0.771799i \(0.719357\pi\)
\(480\) 0 0
\(481\) 17.7916 + 12.2886i 0.811225 + 0.560310i
\(482\) 3.99176i 0.181820i
\(483\) 0 0
\(484\) −1.28421 2.22432i −0.0583732 0.101105i
\(485\) −5.92559 + 3.42114i −0.269067 + 0.155346i
\(486\) 0 0
\(487\) −13.1080 + 13.1080i −0.593981 + 0.593981i −0.938704 0.344723i \(-0.887973\pi\)
0.344723 + 0.938704i \(0.387973\pi\)
\(488\) 7.96964 + 2.13546i 0.360769 + 0.0966677i
\(489\) 0 0
\(490\) 2.11871 + 3.26449i 0.0957138 + 0.147475i
\(491\) 25.0489 14.4620i 1.13044 0.652661i 0.186396 0.982475i \(-0.440319\pi\)
0.944046 + 0.329814i \(0.106986\pi\)
\(492\) 0 0
\(493\) 20.9480 + 36.2830i 0.943452 + 1.63411i
\(494\) −1.69454 1.99338i −0.0762409 0.0896863i
\(495\) 0 0
\(496\) −7.27127 + 27.1368i −0.326490 + 1.21848i
\(497\) 7.43301 + 7.05559i 0.333416 + 0.316487i
\(498\) 0 0
\(499\) −7.48822 27.9464i −0.335219 1.25105i −0.903632 0.428310i \(-0.859109\pi\)
0.568413 0.822743i \(-0.307557\pi\)
\(500\) 0.837977 + 0.837977i 0.0374755 + 0.0374755i
\(501\) 0 0
\(502\) 2.45767 + 9.17213i 0.109691 + 0.409372i
\(503\) −4.27955 2.47080i −0.190816 0.110168i 0.401549 0.915838i \(-0.368472\pi\)
−0.592364 + 0.805670i \(0.701805\pi\)
\(504\) 0 0
\(505\) 0.781009 2.91476i 0.0347544 0.129705i
\(506\) −12.4757 7.20287i −0.554614 0.320207i
\(507\) 0 0
\(508\) 0.119477 + 0.206940i 0.00530094 + 0.00918149i
\(509\) 0.555629 + 0.555629i 0.0246278 + 0.0246278i 0.719313 0.694686i \(-0.244457\pi\)
−0.694686 + 0.719313i \(0.744457\pi\)
\(510\) 0 0
\(511\) 29.0777 8.60887i 1.28632 0.380834i
\(512\) −17.9577 + 17.9577i −0.793626 + 0.793626i
\(513\) 0 0
\(514\) 10.6206 10.6206i 0.468456 0.468456i
\(515\) −1.12927 + 4.21449i −0.0497615 + 0.185713i
\(516\) 0 0
\(517\) 7.11361 + 12.3211i 0.312856 + 0.541883i
\(518\) 17.7219 10.8567i 0.778656 0.477014i
\(519\) 0 0
\(520\) 4.31288 + 1.53852i 0.189132 + 0.0674685i
\(521\) 19.1469 11.0545i 0.838840 0.484304i −0.0180299 0.999837i \(-0.505739\pi\)
0.856870 + 0.515533i \(0.172406\pi\)
\(522\) 0 0
\(523\) 28.2350i 1.23463i 0.786716 + 0.617316i \(0.211780\pi\)
−0.786716 + 0.617316i \(0.788220\pi\)
\(524\) −2.57133 + 4.45368i −0.112329 + 0.194560i
\(525\) 0 0
\(526\) 5.62342 + 20.9869i 0.245193 + 0.915072i
\(527\) −15.0750 + 56.2607i −0.656678 + 2.45076i
\(528\) 0 0
\(529\) −38.5081 −1.67427
\(530\) 4.20155 0.182504
\(531\) 0 0
\(532\) 0.399589 0.118304i 0.0173244 0.00512913i
\(533\) −0.489235 + 6.03755i −0.0211911 + 0.261516i
\(534\) 0 0
\(535\) 1.84262 0.493729i 0.0796636 0.0213458i
\(536\) −21.3964 + 37.0597i −0.924186 + 1.60074i
\(537\) 0 0
\(538\) −8.70512 8.70512i −0.375305 0.375305i
\(539\) −2.04356 + 9.60127i −0.0880224 + 0.413556i
\(540\) 0 0
\(541\) 1.19554 0.320344i 0.0514003 0.0137727i −0.233027 0.972470i \(-0.574863\pi\)
0.284428 + 0.958698i \(0.408196\pi\)
\(542\) 30.9305i 1.32858i
\(543\) 0 0
\(544\) −7.83710 + 7.83710i −0.336013 + 0.336013i
\(545\) 1.92694 0.0825412
\(546\) 0 0
\(547\) 1.83004 0.0782468 0.0391234 0.999234i \(-0.487543\pi\)
0.0391234 + 0.999234i \(0.487543\pi\)
\(548\) −2.92177 + 2.92177i −0.124812 + 0.124812i
\(549\) 0 0
\(550\) 8.85324i 0.377503i
\(551\) −3.22742 + 0.864786i −0.137493 + 0.0368411i
\(552\) 0 0
\(553\) 0.596218 + 22.8884i 0.0253538 + 0.973312i
\(554\) 7.25216 + 7.25216i 0.308115 + 0.308115i
\(555\) 0 0
\(556\) 1.66591 2.88544i 0.0706503 0.122370i
\(557\) 12.7054 3.40440i 0.538345 0.144249i 0.0206059 0.999788i \(-0.493440\pi\)
0.517739 + 0.855539i \(0.326774\pi\)
\(558\) 0 0
\(559\) −25.4685 9.08529i −1.07720 0.384267i
\(560\) 2.59040 2.72896i 0.109464 0.115320i
\(561\) 0 0
\(562\) −14.0868 −0.594217
\(563\) −10.6635 −0.449413 −0.224706 0.974427i \(-0.572142\pi\)
−0.224706 + 0.974427i \(0.572142\pi\)
\(564\) 0 0
\(565\) −0.750480 + 2.80083i −0.0315729 + 0.117832i
\(566\) 4.43831 + 16.5640i 0.186556 + 0.696237i
\(567\) 0 0
\(568\) 5.79502 10.0373i 0.243154 0.421154i
\(569\) 33.3642i 1.39870i −0.714780 0.699349i \(-0.753473\pi\)
0.714780 0.699349i \(-0.246527\pi\)
\(570\) 0 0
\(571\) 15.3066 8.83728i 0.640562 0.369829i −0.144269 0.989539i \(-0.546083\pi\)
0.784831 + 0.619710i \(0.212750\pi\)
\(572\) 0.615893 + 1.29898i 0.0257518 + 0.0543130i
\(573\) 0 0
\(574\) 5.11615 + 2.77875i 0.213544 + 0.115983i
\(575\) −18.9003 32.7363i −0.788197 1.36520i
\(576\) 0 0
\(577\) 0.423680 1.58119i 0.0176380 0.0658260i −0.956546 0.291582i \(-0.905818\pi\)
0.974184 + 0.225756i \(0.0724851\pi\)
\(578\) 28.9457 28.9457i 1.20398 1.20398i
\(579\) 0 0
\(580\) 0.514686 0.514686i 0.0213712 0.0213712i
\(581\) −8.23532 1.97832i −0.341659 0.0820744i
\(582\) 0 0
\(583\) 7.49372 + 7.49372i 0.310358 + 0.310358i
\(584\) −17.1475 29.7004i −0.709569 1.22901i
\(585\) 0 0
\(586\) −7.17912 4.14487i −0.296567 0.171223i
\(587\) −0.520017 + 1.94073i −0.0214634 + 0.0801025i −0.975827 0.218545i \(-0.929869\pi\)
0.954363 + 0.298648i \(0.0965355\pi\)
\(588\) 0 0
\(589\) −4.02283 2.32258i −0.165758 0.0957003i
\(590\) 0.983810 + 3.67163i 0.0405028 + 0.151159i
\(591\) 0 0
\(592\) −14.2082 14.2082i −0.583952 0.583952i
\(593\) −11.7799 43.9632i −0.483743 1.80535i −0.585655 0.810561i \(-0.699163\pi\)
0.101912 0.994793i \(-0.467504\pi\)
\(594\) 0 0
\(595\) 5.37049 5.65776i 0.220168 0.231946i
\(596\) 0.464468 1.73342i 0.0190254 0.0710037i
\(597\) 0 0
\(598\) −30.4759 21.0496i −1.24625 0.860781i
\(599\) −19.7690 34.2408i −0.807738 1.39904i −0.914427 0.404751i \(-0.867358\pi\)
0.106689 0.994292i \(-0.465975\pi\)
\(600\) 0 0
\(601\) −0.950504 + 0.548773i −0.0387718 + 0.0223849i −0.519261 0.854616i \(-0.673793\pi\)
0.480489 + 0.877001i \(0.340459\pi\)
\(602\) −17.8930 + 18.8502i −0.729266 + 0.768275i
\(603\) 0 0
\(604\) 1.55672 + 0.417123i 0.0633422 + 0.0169725i
\(605\) 2.71125 2.71125i 0.110228 0.110228i
\(606\) 0 0
\(607\) 13.5220 7.80692i 0.548840 0.316873i −0.199814 0.979834i \(-0.564034\pi\)
0.748654 + 0.662961i \(0.230700\pi\)
\(608\) −0.441957 0.765492i −0.0179237 0.0310448i
\(609\) 0 0
\(610\) 1.53309i 0.0620731i
\(611\) 15.6715 + 33.0527i 0.634000 + 1.33717i
\(612\) 0 0
\(613\) 6.90744 + 25.7789i 0.278989 + 1.04120i 0.953121 + 0.302590i \(0.0978513\pi\)
−0.674132 + 0.738611i \(0.735482\pi\)
\(614\) 1.72439i 0.0695908i
\(615\) 0 0
\(616\) 11.0976 0.289081i 0.447135 0.0116474i
\(617\) 2.13161 + 7.95529i 0.0858155 + 0.320268i 0.995467 0.0951036i \(-0.0303182\pi\)
−0.909652 + 0.415372i \(0.863652\pi\)
\(618\) 0 0
\(619\) 21.9027 + 5.86882i 0.880346 + 0.235888i 0.670556 0.741859i \(-0.266055\pi\)
0.209789 + 0.977747i \(0.432722\pi\)
\(620\) 1.01192 0.0406396
\(621\) 0 0
\(622\) 38.6221 + 10.3488i 1.54861 + 0.414948i
\(623\) −7.16031 + 29.8069i −0.286872 + 1.19419i
\(624\) 0 0
\(625\) 11.1650 19.3384i 0.446601 0.773535i
\(626\) −23.2471 + 6.22903i −0.929139 + 0.248962i
\(627\) 0 0
\(628\) −0.665023 1.15185i −0.0265373 0.0459639i
\(629\) −29.4568 29.4568i −1.17452 1.17452i
\(630\) 0 0
\(631\) 17.2097 4.61132i 0.685106 0.183574i 0.100556 0.994931i \(-0.467938\pi\)
0.584550 + 0.811358i \(0.301271\pi\)
\(632\) 25.0111 6.70169i 0.994886 0.266579i
\(633\) 0 0
\(634\) 17.5395 + 10.1264i 0.696581 + 0.402171i
\(635\) −0.252243 + 0.252243i −0.0100099 + 0.0100099i
\(636\) 0 0
\(637\) −7.23086 + 24.1809i −0.286497 + 0.958081i
\(638\) −11.0786 −0.438605
\(639\) 0 0
\(640\) −3.05966 1.76650i −0.120944 0.0698269i
\(641\) 23.0810i 0.911645i 0.890071 + 0.455822i \(0.150655\pi\)
−0.890071 + 0.455822i \(0.849345\pi\)
\(642\) 0 0
\(643\) −39.1565 + 10.4920i −1.54418 + 0.413763i −0.927615 0.373538i \(-0.878144\pi\)
−0.616569 + 0.787301i \(0.711478\pi\)
\(644\) 5.03071 3.08188i 0.198238 0.121443i
\(645\) 0 0
\(646\) 2.52025 + 4.36521i 0.0991581 + 0.171747i
\(647\) −16.1610 + 27.9916i −0.635353 + 1.10046i 0.351087 + 0.936343i \(0.385812\pi\)
−0.986440 + 0.164121i \(0.947521\pi\)
\(648\) 0 0
\(649\) −4.79389 + 8.30326i −0.188177 + 0.325932i
\(650\) 1.83847 22.6882i 0.0721109 0.889906i
\(651\) 0 0
\(652\) −3.30639 0.885946i −0.129488 0.0346963i
\(653\) −36.5732 −1.43122 −0.715610 0.698500i \(-0.753851\pi\)
−0.715610 + 0.698500i \(0.753851\pi\)
\(654\) 0 0
\(655\) −7.41569 1.98703i −0.289755 0.0776396i
\(656\) 1.45686 5.43708i 0.0568809 0.212282i
\(657\) 0 0
\(658\) 35.1470 0.915542i 1.37017 0.0356916i
\(659\) 21.1206 36.5820i 0.822742 1.42503i −0.0808906 0.996723i \(-0.525776\pi\)
0.903633 0.428308i \(-0.140890\pi\)
\(660\) 0 0
\(661\) −1.49909 5.59468i −0.0583078 0.217608i 0.930624 0.365976i \(-0.119265\pi\)
−0.988932 + 0.148368i \(0.952598\pi\)
\(662\) 30.2798 17.4821i 1.17686 0.679459i
\(663\) 0 0
\(664\) 9.57832i 0.371711i
\(665\) 0.324987 + 0.530494i 0.0126025 + 0.0205717i
\(666\) 0 0
\(667\) −40.9648 + 23.6511i −1.58617 + 0.915773i
\(668\) 0.165255 0.616740i 0.00639391 0.0238624i
\(669\) 0 0
\(670\) −7.68049 2.05798i −0.296723 0.0795067i
\(671\) −2.73436 + 2.73436i −0.105559 + 0.105559i
\(672\) 0 0
\(673\) −36.4698 + 21.0558i −1.40581 + 0.811642i −0.994980 0.100071i \(-0.968093\pi\)
−0.410826 + 0.911714i \(0.634760\pi\)
\(674\) −23.5071 23.5071i −0.905459 0.905459i
\(675\) 0 0
\(676\) 1.30860 + 3.45680i 0.0503309 + 0.132954i
\(677\) −0.771810 0.445605i −0.0296631 0.0171260i 0.485095 0.874461i \(-0.338785\pi\)
−0.514758 + 0.857335i \(0.672118\pi\)
\(678\) 0 0
\(679\) −29.3626 + 30.9332i −1.12683 + 1.18711i
\(680\) −7.64004 4.41098i −0.292982 0.169153i
\(681\) 0 0
\(682\) −10.8907 10.8907i −0.417028 0.417028i
\(683\) −9.01592 9.01592i −0.344985 0.344985i 0.513253 0.858238i \(-0.328440\pi\)
−0.858238 + 0.513253i \(0.828440\pi\)
\(684\) 0 0
\(685\) −5.34208 3.08425i −0.204110 0.117843i
\(686\) 18.4399 + 15.7622i 0.704038 + 0.601805i
\(687\) 0 0
\(688\) 21.7613 + 12.5639i 0.829641 + 0.478994i
\(689\) 17.6480 + 20.7603i 0.672337 + 0.790906i
\(690\) 0 0
\(691\) 18.7650 + 18.7650i 0.713855 + 0.713855i 0.967340 0.253484i \(-0.0815766\pi\)
−0.253484 + 0.967340i \(0.581577\pi\)
\(692\) 2.86655 1.65500i 0.108970 0.0629138i
\(693\) 0 0
\(694\) 2.16140 2.16140i 0.0820457 0.0820457i
\(695\) 4.80446 + 1.28735i 0.182244 + 0.0488320i
\(696\) 0 0
\(697\) 3.02041 11.2723i 0.114406 0.426969i
\(698\) −33.6448 + 19.4248i −1.27347 + 0.735241i
\(699\) 0 0
\(700\) 3.18610 + 1.73048i 0.120423 + 0.0654059i
\(701\) 0.589627i 0.0222699i 0.999938 + 0.0111350i \(0.00354444\pi\)
−0.999938 + 0.0111350i \(0.996456\pi\)
\(702\) 0 0
\(703\) 2.87720 1.66115i 0.108516 0.0626515i
\(704\) −3.19068 11.9078i −0.120253 0.448792i
\(705\) 0 0
\(706\) −2.86078 + 4.95502i −0.107667 + 0.186485i
\(707\) −0.489802 18.8031i −0.0184209 0.707165i
\(708\) 0 0
\(709\) 0.917349 3.42359i 0.0344518 0.128576i −0.946558 0.322533i \(-0.895466\pi\)
0.981010 + 0.193957i \(0.0621323\pi\)
\(710\) 2.08019 + 0.557384i 0.0780680 + 0.0209183i
\(711\) 0 0
\(712\) 34.6677 1.29923
\(713\) −63.5203 17.0202i −2.37886 0.637412i
\(714\) 0 0
\(715\) −1.63515 + 1.39001i −0.0611510 + 0.0519835i
\(716\) −2.68754 + 4.65495i −0.100438 + 0.173964i
\(717\) 0 0
\(718\) 14.0382 24.3149i 0.523902 0.907425i
\(719\) −3.90389 6.76173i −0.145590 0.252170i 0.784003 0.620757i \(-0.213175\pi\)
−0.929593 + 0.368587i \(0.879842\pi\)
\(720\) 0 0
\(721\) 0.708210 + 27.1877i 0.0263751 + 1.01252i
\(722\) 23.6506 6.33717i 0.880186 0.235845i
\(723\) 0 0
\(724\) 0.113913i 0.00423355i
\(725\) −25.1755 14.5351i −0.934993 0.539819i
\(726\) 0 0
\(727\) −7.63181 −0.283048 −0.141524 0.989935i \(-0.545200\pi\)
−0.141524 + 0.989935i \(0.545200\pi\)
\(728\) 28.4999 + 1.56371i 1.05628 + 0.0579550i
\(729\) 0 0
\(730\) 4.50598 4.50598i 0.166774 0.166774i
\(731\) 45.1161 + 26.0478i 1.66868 + 0.963413i
\(732\) 0 0
\(733\) −12.0644 + 3.23266i −0.445610 + 0.119401i −0.474645 0.880178i \(-0.657423\pi\)
0.0290344 + 0.999578i \(0.490757\pi\)
\(734\) 15.9470 4.27299i 0.588615 0.157719i
\(735\) 0 0
\(736\) −8.84837 8.84837i −0.326155 0.326155i
\(737\) −10.0281 17.3692i −0.369389 0.639801i
\(738\) 0 0
\(739\) −18.0770 + 4.84371i −0.664972 + 0.178179i −0.575489 0.817810i \(-0.695188\pi\)
−0.0894831 + 0.995988i \(0.528522\pi\)
\(740\) −0.361871 + 0.626780i −0.0133027 + 0.0230409i
\(741\) 0 0
\(742\) 25.1120 7.43478i 0.921892 0.272939i
\(743\) −15.7645 4.22409i −0.578343 0.154967i −0.0422231 0.999108i \(-0.513444\pi\)
−0.536120 + 0.844142i \(0.680111\pi\)
\(744\) 0 0
\(745\) 2.67904 0.0981524
\(746\) 20.1794 + 5.40706i 0.738822 + 0.197967i
\(747\) 0 0
\(748\) −0.716834 2.67526i −0.0262100 0.0978172i
\(749\) 10.1394 6.21154i 0.370486 0.226965i
\(750\) 0 0
\(751\) 1.91061i 0.0697190i 0.999392 + 0.0348595i \(0.0110984\pi\)
−0.999392 + 0.0348595i \(0.988902\pi\)
\(752\) −8.79784 32.8340i −0.320824 1.19733i
\(753\) 0 0
\(754\) −28.3911 2.30059i −1.03394 0.0837826i
\(755\) 2.40595i 0.0875616i
\(756\) 0 0
\(757\) −25.6580 44.4410i −0.932556 1.61523i −0.778935 0.627105i \(-0.784240\pi\)
−0.153622 0.988130i \(-0.549094\pi\)
\(758\) −38.8306 + 22.4189i −1.41039 + 0.814289i
\(759\) 0 0
\(760\) 0.497496 0.497496i 0.0180461 0.0180461i
\(761\) 24.1952 + 6.48309i 0.877076 + 0.235012i 0.669145 0.743132i \(-0.266660\pi\)
0.207931 + 0.978143i \(0.433327\pi\)
\(762\) 0 0
\(763\) 11.5171 3.40980i 0.416946 0.123443i
\(764\) 2.52441 1.45747i 0.0913301 0.0527295i
\(765\) 0 0
\(766\) −8.54586 14.8019i −0.308774 0.534813i
\(767\) −14.0096 + 20.2833i −0.505857 + 0.732388i
\(768\) 0 0
\(769\) 10.9969 41.0409i 0.396558 1.47997i −0.422553 0.906338i \(-0.638866\pi\)
0.819111 0.573635i \(-0.194467\pi\)
\(770\) 0.585586 + 1.97790i 0.0211031 + 0.0712785i
\(771\) 0 0
\(772\) −0.659552 2.46148i −0.0237378 0.0885906i
\(773\) −18.6449 18.6449i −0.670609 0.670609i 0.287248 0.957856i \(-0.407260\pi\)
−0.957856 + 0.287248i \(0.907260\pi\)
\(774\) 0 0
\(775\) −10.4600 39.0372i −0.375734 1.40226i
\(776\) 41.7711 + 24.1166i 1.49950 + 0.865734i
\(777\) 0 0
\(778\) 5.80341 21.6586i 0.208062 0.776500i
\(779\) 0.806008 + 0.465349i 0.0288782 + 0.0166728i
\(780\) 0 0
\(781\) 2.71601 + 4.70427i 0.0971865 + 0.168332i
\(782\) 50.4577 + 50.4577i 1.80437 + 1.80437i
\(783\) 0 0
\(784\) 10.6534 20.8944i 0.380480 0.746228i
\(785\) 1.40401 1.40401i 0.0501113 0.0501113i
\(786\) 0 0
\(787\) −37.4963 + 37.4963i −1.33660 + 1.33660i −0.437270 + 0.899330i \(0.644055\pi\)
−0.899330 + 0.437270i \(0.855945\pi\)
\(788\) −0.308002 + 1.14948i