Properties

Label 1512.2.c.e.757.17
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 20
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.17
Root \(1.19566 - 0.755240i\)
Character \(\chi\) = 1512.757
Dual form 1512.2.c.e.757.18

$q$-expansion

\(f(q)\) \(=\) \(q+(1.19566 - 0.755240i) q^{2} +(0.859226 - 1.80603i) q^{4} -3.16969i q^{5} -1.00000 q^{7} +(-0.336637 - 2.80832i) q^{8} +O(q^{10})\) \(q+(1.19566 - 0.755240i) q^{2} +(0.859226 - 1.80603i) q^{4} -3.16969i q^{5} -1.00000 q^{7} +(-0.336637 - 2.80832i) q^{8} +(-2.39387 - 3.78988i) q^{10} -5.44696i q^{11} +3.61205i q^{13} +(-1.19566 + 0.755240i) q^{14} +(-2.52346 - 3.10357i) q^{16} -3.27628 q^{17} +3.20627i q^{19} +(-5.72454 - 2.72348i) q^{20} +(-4.11376 - 6.51273i) q^{22} -0.673274 q^{23} -5.04692 q^{25} +(2.72797 + 4.31880i) q^{26} +(-0.859226 + 1.80603i) q^{28} +2.85127i q^{29} +3.71845 q^{31} +(-5.36115 - 1.80501i) q^{32} +(-3.91734 + 2.47438i) q^{34} +3.16969i q^{35} -11.9988i q^{37} +(2.42150 + 3.83363i) q^{38} +(-8.90151 + 1.06703i) q^{40} +7.44602 q^{41} +12.5741i q^{43} +(-9.83735 - 4.68017i) q^{44} +(-0.805009 + 0.508483i) q^{46} +4.06341 q^{47} +1.00000 q^{49} +(-6.03442 + 3.81164i) q^{50} +(6.52346 + 3.10357i) q^{52} +0.291601i q^{53} -17.2652 q^{55} +(0.336637 + 2.80832i) q^{56} +(2.15339 + 3.40916i) q^{58} +0.0209587i q^{59} -5.34034i q^{61} +(4.44602 - 2.80832i) q^{62} +(-7.77335 + 1.89077i) q^{64} +11.4491 q^{65} -6.20714i q^{67} +(-2.81507 + 5.91705i) q^{68} +(2.39387 + 3.78988i) q^{70} -15.5050 q^{71} +1.35371 q^{73} +(-9.06200 - 14.3466i) q^{74} +(5.79061 + 2.75491i) q^{76} +5.44696i q^{77} -11.0846 q^{79} +(-9.83735 + 7.99858i) q^{80} +(8.90294 - 5.62353i) q^{82} -13.6442i q^{83} +10.3848i q^{85} +(9.49646 + 15.0344i) q^{86} +(-15.2968 + 1.83365i) q^{88} +5.93965 q^{89} -3.61205i q^{91} +(-0.578494 + 1.21595i) q^{92} +(4.85848 - 3.06885i) q^{94} +10.1629 q^{95} +9.60073 q^{97} +(1.19566 - 0.755240i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 2q^{4} - 20q^{7} + O(q^{10}) \) \( 20q - 2q^{4} - 20q^{7} - 12q^{10} - 14q^{16} + 8q^{22} - 28q^{25} + 2q^{28} + 36q^{31} - 6q^{34} - 16q^{40} - 18q^{46} + 20q^{49} + 94q^{52} + 48q^{55} + 66q^{58} + 22q^{64} + 12q^{70} + 12q^{76} + 64q^{79} - 92q^{88} - 24q^{94} + 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19566 0.755240i 0.845462 0.534035i
\(3\) 0 0
\(4\) 0.859226 1.80603i 0.429613 0.903013i
\(5\) 3.16969i 1.41753i −0.705446 0.708764i \(-0.749253\pi\)
0.705446 0.708764i \(-0.250747\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −0.336637 2.80832i −0.119019 0.992892i
\(9\) 0 0
\(10\) −2.39387 3.78988i −0.757009 1.19847i
\(11\) 5.44696i 1.64232i −0.570699 0.821160i \(-0.693327\pi\)
0.570699 0.821160i \(-0.306673\pi\)
\(12\) 0 0
\(13\) 3.61205i 1.00180i 0.865504 + 0.500902i \(0.166998\pi\)
−0.865504 + 0.500902i \(0.833002\pi\)
\(14\) −1.19566 + 0.755240i −0.319555 + 0.201846i
\(15\) 0 0
\(16\) −2.52346 3.10357i −0.630865 0.775892i
\(17\) −3.27628 −0.794616 −0.397308 0.917685i \(-0.630055\pi\)
−0.397308 + 0.917685i \(0.630055\pi\)
\(18\) 0 0
\(19\) 3.20627i 0.735569i 0.929911 + 0.367785i \(0.119884\pi\)
−0.929911 + 0.367785i \(0.880116\pi\)
\(20\) −5.72454 2.72348i −1.28005 0.608988i
\(21\) 0 0
\(22\) −4.11376 6.51273i −0.877056 1.38852i
\(23\) −0.673274 −0.140387 −0.0701936 0.997533i \(-0.522362\pi\)
−0.0701936 + 0.997533i \(0.522362\pi\)
\(24\) 0 0
\(25\) −5.04692 −1.00938
\(26\) 2.72797 + 4.31880i 0.534998 + 0.846987i
\(27\) 0 0
\(28\) −0.859226 + 1.80603i −0.162378 + 0.341307i
\(29\) 2.85127i 0.529468i 0.964322 + 0.264734i \(0.0852841\pi\)
−0.964322 + 0.264734i \(0.914716\pi\)
\(30\) 0 0
\(31\) 3.71845 0.667854 0.333927 0.942599i \(-0.391626\pi\)
0.333927 + 0.942599i \(0.391626\pi\)
\(32\) −5.36115 1.80501i −0.947727 0.319084i
\(33\) 0 0
\(34\) −3.91734 + 2.47438i −0.671817 + 0.424353i
\(35\) 3.16969i 0.535775i
\(36\) 0 0
\(37\) 11.9988i 1.97260i −0.164971 0.986298i \(-0.552753\pi\)
0.164971 0.986298i \(-0.447247\pi\)
\(38\) 2.42150 + 3.83363i 0.392820 + 0.621896i
\(39\) 0 0
\(40\) −8.90151 + 1.06703i −1.40745 + 0.168713i
\(41\) 7.44602 1.16287 0.581436 0.813592i \(-0.302491\pi\)
0.581436 + 0.813592i \(0.302491\pi\)
\(42\) 0 0
\(43\) 12.5741i 1.91753i 0.284195 + 0.958766i \(0.408274\pi\)
−0.284195 + 0.958766i \(0.591726\pi\)
\(44\) −9.83735 4.68017i −1.48304 0.705562i
\(45\) 0 0
\(46\) −0.805009 + 0.508483i −0.118692 + 0.0749717i
\(47\) 4.06341 0.592710 0.296355 0.955078i \(-0.404229\pi\)
0.296355 + 0.955078i \(0.404229\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −6.03442 + 3.81164i −0.853397 + 0.539047i
\(51\) 0 0
\(52\) 6.52346 + 3.10357i 0.904641 + 0.430388i
\(53\) 0.291601i 0.0400545i 0.999799 + 0.0200272i \(0.00637529\pi\)
−0.999799 + 0.0200272i \(0.993625\pi\)
\(54\) 0 0
\(55\) −17.2652 −2.32803
\(56\) 0.336637 + 2.80832i 0.0449850 + 0.375278i
\(57\) 0 0
\(58\) 2.15339 + 3.40916i 0.282754 + 0.447645i
\(59\) 0.0209587i 0.00272859i 0.999999 + 0.00136430i \(0.000434269\pi\)
−0.999999 + 0.00136430i \(0.999566\pi\)
\(60\) 0 0
\(61\) 5.34034i 0.683760i −0.939744 0.341880i \(-0.888936\pi\)
0.939744 0.341880i \(-0.111064\pi\)
\(62\) 4.44602 2.80832i 0.564645 0.356657i
\(63\) 0 0
\(64\) −7.77335 + 1.89077i −0.971669 + 0.236346i
\(65\) 11.4491 1.42008
\(66\) 0 0
\(67\) 6.20714i 0.758323i −0.925331 0.379161i \(-0.876213\pi\)
0.925331 0.379161i \(-0.123787\pi\)
\(68\) −2.81507 + 5.91705i −0.341377 + 0.717548i
\(69\) 0 0
\(70\) 2.39387 + 3.78988i 0.286123 + 0.452978i
\(71\) −15.5050 −1.84010 −0.920050 0.391801i \(-0.871852\pi\)
−0.920050 + 0.391801i \(0.871852\pi\)
\(72\) 0 0
\(73\) 1.35371 0.158440 0.0792198 0.996857i \(-0.474757\pi\)
0.0792198 + 0.996857i \(0.474757\pi\)
\(74\) −9.06200 14.3466i −1.05344 1.66776i
\(75\) 0 0
\(76\) 5.79061 + 2.75491i 0.664229 + 0.316010i
\(77\) 5.44696i 0.620738i
\(78\) 0 0
\(79\) −11.0846 −1.24711 −0.623555 0.781779i \(-0.714312\pi\)
−0.623555 + 0.781779i \(0.714312\pi\)
\(80\) −9.83735 + 7.99858i −1.09985 + 0.894269i
\(81\) 0 0
\(82\) 8.90294 5.62353i 0.983165 0.621015i
\(83\) 13.6442i 1.49765i −0.662768 0.748824i \(-0.730619\pi\)
0.662768 0.748824i \(-0.269381\pi\)
\(84\) 0 0
\(85\) 10.3848i 1.12639i
\(86\) 9.49646 + 15.0344i 1.02403 + 1.62120i
\(87\) 0 0
\(88\) −15.2968 + 1.83365i −1.63065 + 0.195467i
\(89\) 5.93965 0.629601 0.314801 0.949158i \(-0.398062\pi\)
0.314801 + 0.949158i \(0.398062\pi\)
\(90\) 0 0
\(91\) 3.61205i 0.378646i
\(92\) −0.578494 + 1.21595i −0.0603122 + 0.126772i
\(93\) 0 0
\(94\) 4.85848 3.06885i 0.501114 0.316528i
\(95\) 10.1629 1.04269
\(96\) 0 0
\(97\) 9.60073 0.974807 0.487403 0.873177i \(-0.337944\pi\)
0.487403 + 0.873177i \(0.337944\pi\)
\(98\) 1.19566 0.755240i 0.120780 0.0762907i
\(99\) 0 0
\(100\) −4.33645 + 9.11487i −0.433645 + 0.911487i
\(101\) 14.2123i 1.41418i −0.707124 0.707090i \(-0.750008\pi\)
0.707124 0.707090i \(-0.249992\pi\)
\(102\) 0 0
\(103\) 1.69321 0.166837 0.0834187 0.996515i \(-0.473416\pi\)
0.0834187 + 0.996515i \(0.473416\pi\)
\(104\) 10.1438 1.21595i 0.994682 0.119234i
\(105\) 0 0
\(106\) 0.220228 + 0.348657i 0.0213905 + 0.0338645i
\(107\) 11.6644i 1.12764i −0.825897 0.563821i \(-0.809331\pi\)
0.825897 0.563821i \(-0.190669\pi\)
\(108\) 0 0
\(109\) 14.0521i 1.34595i −0.739667 0.672973i \(-0.765017\pi\)
0.739667 0.672973i \(-0.234983\pi\)
\(110\) −20.6433 + 13.0393i −1.96826 + 1.24325i
\(111\) 0 0
\(112\) 2.52346 + 3.10357i 0.238445 + 0.293260i
\(113\) 14.9455 1.40596 0.702979 0.711211i \(-0.251853\pi\)
0.702979 + 0.711211i \(0.251853\pi\)
\(114\) 0 0
\(115\) 2.13407i 0.199003i
\(116\) 5.14947 + 2.44989i 0.478116 + 0.227466i
\(117\) 0 0
\(118\) 0.0158289 + 0.0250596i 0.00145716 + 0.00230692i
\(119\) 3.27628 0.300336
\(120\) 0 0
\(121\) −18.6693 −1.69721
\(122\) −4.03324 6.38525i −0.365152 0.578094i
\(123\) 0 0
\(124\) 3.19499 6.71562i 0.286919 0.603081i
\(125\) 0.148729i 0.0133028i
\(126\) 0 0
\(127\) 4.07216 0.361346 0.180673 0.983543i \(-0.442172\pi\)
0.180673 + 0.983543i \(0.442172\pi\)
\(128\) −7.86633 + 8.13147i −0.695292 + 0.718727i
\(129\) 0 0
\(130\) 13.6893 8.64680i 1.20063 0.758374i
\(131\) 17.8643i 1.56081i 0.625275 + 0.780404i \(0.284987\pi\)
−0.625275 + 0.780404i \(0.715013\pi\)
\(132\) 0 0
\(133\) 3.20627i 0.278019i
\(134\) −4.68788 7.42165i −0.404971 0.641133i
\(135\) 0 0
\(136\) 1.10292 + 9.20086i 0.0945744 + 0.788967i
\(137\) 21.1351 1.80569 0.902847 0.429963i \(-0.141473\pi\)
0.902847 + 0.429963i \(0.141473\pi\)
\(138\) 0 0
\(139\) 7.39359i 0.627116i 0.949569 + 0.313558i \(0.101521\pi\)
−0.949569 + 0.313558i \(0.898479\pi\)
\(140\) 5.72454 + 2.72348i 0.483812 + 0.230176i
\(141\) 0 0
\(142\) −18.5387 + 11.7100i −1.55574 + 0.982678i
\(143\) 19.6747 1.64528
\(144\) 0 0
\(145\) 9.03764 0.750535
\(146\) 1.61858 1.02237i 0.133955 0.0846123i
\(147\) 0 0
\(148\) −21.6702 10.3097i −1.78128 0.847453i
\(149\) 13.0541i 1.06944i 0.845030 + 0.534719i \(0.179582\pi\)
−0.845030 + 0.534719i \(0.820418\pi\)
\(150\) 0 0
\(151\) −17.6477 −1.43615 −0.718073 0.695968i \(-0.754976\pi\)
−0.718073 + 0.695968i \(0.754976\pi\)
\(152\) 9.00425 1.07935i 0.730341 0.0875468i
\(153\) 0 0
\(154\) 4.11376 + 6.51273i 0.331496 + 0.524811i
\(155\) 11.7863i 0.946701i
\(156\) 0 0
\(157\) 3.00087i 0.239495i 0.992804 + 0.119748i \(0.0382085\pi\)
−0.992804 + 0.119748i \(0.961791\pi\)
\(158\) −13.2534 + 8.37150i −1.05438 + 0.666001i
\(159\) 0 0
\(160\) −5.72132 + 16.9932i −0.452310 + 1.34343i
\(161\) 0.673274 0.0530614
\(162\) 0 0
\(163\) 0.871148i 0.0682335i 0.999418 + 0.0341168i \(0.0108618\pi\)
−0.999418 + 0.0341168i \(0.989138\pi\)
\(164\) 6.39781 13.4477i 0.499585 1.05009i
\(165\) 0 0
\(166\) −10.3047 16.3139i −0.799797 1.26621i
\(167\) −7.49952 −0.580330 −0.290165 0.956977i \(-0.593710\pi\)
−0.290165 + 0.956977i \(0.593710\pi\)
\(168\) 0 0
\(169\) −0.0469224 −0.00360941
\(170\) 7.84301 + 12.4167i 0.601531 + 0.952320i
\(171\) 0 0
\(172\) 22.7092 + 10.8040i 1.73156 + 0.823797i
\(173\) 0.652919i 0.0496405i −0.999692 0.0248203i \(-0.992099\pi\)
0.999692 0.0248203i \(-0.00790135\pi\)
\(174\) 0 0
\(175\) 5.04692 0.381511
\(176\) −16.9050 + 13.7452i −1.27426 + 1.03608i
\(177\) 0 0
\(178\) 7.10182 4.48586i 0.532304 0.336229i
\(179\) 4.43263i 0.331310i −0.986184 0.165655i \(-0.947026\pi\)
0.986184 0.165655i \(-0.0529738\pi\)
\(180\) 0 0
\(181\) 21.9779i 1.63360i −0.576920 0.816801i \(-0.695746\pi\)
0.576920 0.816801i \(-0.304254\pi\)
\(182\) −2.72797 4.31880i −0.202210 0.320131i
\(183\) 0 0
\(184\) 0.226649 + 1.89077i 0.0167088 + 0.139389i
\(185\) −38.0326 −2.79621
\(186\) 0 0
\(187\) 17.8458i 1.30501i
\(188\) 3.49139 7.33863i 0.254636 0.535224i
\(189\) 0 0
\(190\) 12.1514 7.67541i 0.881555 0.556833i
\(191\) 6.67327 0.482861 0.241430 0.970418i \(-0.422383\pi\)
0.241430 + 0.970418i \(0.422383\pi\)
\(192\) 0 0
\(193\) 25.0305 1.80174 0.900868 0.434092i \(-0.142931\pi\)
0.900868 + 0.434092i \(0.142931\pi\)
\(194\) 11.4793 7.25086i 0.824162 0.520581i
\(195\) 0 0
\(196\) 0.859226 1.80603i 0.0613733 0.129002i
\(197\) 3.77971i 0.269293i −0.990894 0.134646i \(-0.957010\pi\)
0.990894 0.134646i \(-0.0429899\pi\)
\(198\) 0 0
\(199\) −7.18059 −0.509019 −0.254509 0.967070i \(-0.581914\pi\)
−0.254509 + 0.967070i \(0.581914\pi\)
\(200\) 1.69898 + 14.1734i 0.120136 + 1.00221i
\(201\) 0 0
\(202\) −10.7337 16.9932i −0.755222 1.19564i
\(203\) 2.85127i 0.200120i
\(204\) 0 0
\(205\) 23.6016i 1.64840i
\(206\) 2.02452 1.27878i 0.141055 0.0890970i
\(207\) 0 0
\(208\) 11.2103 9.11487i 0.777291 0.632003i
\(209\) 17.4644 1.20804
\(210\) 0 0
\(211\) 5.30442i 0.365171i −0.983190 0.182586i \(-0.941553\pi\)
0.983190 0.182586i \(-0.0584467\pi\)
\(212\) 0.526639 + 0.250551i 0.0361697 + 0.0172079i
\(213\) 0 0
\(214\) −8.80943 13.9467i −0.602200 0.953379i
\(215\) 39.8560 2.71816
\(216\) 0 0
\(217\) −3.71845 −0.252425
\(218\) −10.6127 16.8016i −0.718782 1.13795i
\(219\) 0 0
\(220\) −14.8347 + 31.1813i −1.00015 + 2.10224i
\(221\) 11.8341i 0.796048i
\(222\) 0 0
\(223\) 4.62678 0.309832 0.154916 0.987928i \(-0.450489\pi\)
0.154916 + 0.987928i \(0.450489\pi\)
\(224\) 5.36115 + 1.80501i 0.358207 + 0.120602i
\(225\) 0 0
\(226\) 17.8698 11.2875i 1.18868 0.750831i
\(227\) 9.92356i 0.658650i 0.944217 + 0.329325i \(0.106821\pi\)
−0.944217 + 0.329325i \(0.893179\pi\)
\(228\) 0 0
\(229\) 2.32546i 0.153671i 0.997044 + 0.0768355i \(0.0244816\pi\)
−0.997044 + 0.0768355i \(0.975518\pi\)
\(230\) 1.61173 + 2.55163i 0.106274 + 0.168249i
\(231\) 0 0
\(232\) 8.00729 0.959843i 0.525704 0.0630167i
\(233\) 3.23031 0.211625 0.105812 0.994386i \(-0.466256\pi\)
0.105812 + 0.994386i \(0.466256\pi\)
\(234\) 0 0
\(235\) 12.8797i 0.840182i
\(236\) 0.0378520 + 0.0180083i 0.00246396 + 0.00117224i
\(237\) 0 0
\(238\) 3.91734 2.47438i 0.253923 0.160390i
\(239\) 3.48961 0.225724 0.112862 0.993611i \(-0.463998\pi\)
0.112862 + 0.993611i \(0.463998\pi\)
\(240\) 0 0
\(241\) 9.77778 0.629842 0.314921 0.949118i \(-0.398022\pi\)
0.314921 + 0.949118i \(0.398022\pi\)
\(242\) −22.3223 + 14.0998i −1.43493 + 0.906371i
\(243\) 0 0
\(244\) −9.64479 4.58856i −0.617445 0.293752i
\(245\) 3.16969i 0.202504i
\(246\) 0 0
\(247\) −11.5812 −0.736896
\(248\) −1.25177 10.4426i −0.0794873 0.663107i
\(249\) 0 0
\(250\) 0.112326 + 0.177830i 0.00710414 + 0.0112470i
\(251\) 25.2169i 1.59168i 0.605509 + 0.795838i \(0.292969\pi\)
−0.605509 + 0.795838i \(0.707031\pi\)
\(252\) 0 0
\(253\) 3.66729i 0.230561i
\(254\) 4.86894 3.07546i 0.305504 0.192971i
\(255\) 0 0
\(256\) −3.26429 + 15.6635i −0.204018 + 0.978967i
\(257\) −6.12920 −0.382329 −0.191165 0.981558i \(-0.561226\pi\)
−0.191165 + 0.981558i \(0.561226\pi\)
\(258\) 0 0
\(259\) 11.9988i 0.745572i
\(260\) 9.83735 20.6773i 0.610086 1.28235i
\(261\) 0 0
\(262\) 13.4918 + 21.3597i 0.833526 + 1.31960i
\(263\) 1.27084 0.0783635 0.0391818 0.999232i \(-0.487525\pi\)
0.0391818 + 0.999232i \(0.487525\pi\)
\(264\) 0 0
\(265\) 0.924284 0.0567783
\(266\) −2.42150 3.83363i −0.148472 0.235055i
\(267\) 0 0
\(268\) −11.2103 5.33334i −0.684775 0.325785i
\(269\) 19.8081i 1.20772i −0.797091 0.603859i \(-0.793629\pi\)
0.797091 0.603859i \(-0.206371\pi\)
\(270\) 0 0
\(271\) 24.1532 1.46720 0.733600 0.679581i \(-0.237838\pi\)
0.733600 + 0.679581i \(0.237838\pi\)
\(272\) 8.26757 + 10.1682i 0.501295 + 0.616536i
\(273\) 0 0
\(274\) 25.2705 15.9621i 1.52665 0.964304i
\(275\) 27.4904i 1.65773i
\(276\) 0 0
\(277\) 1.31816i 0.0792005i 0.999216 + 0.0396003i \(0.0126084\pi\)
−0.999216 + 0.0396003i \(0.987392\pi\)
\(278\) 5.58393 + 8.84025i 0.334902 + 0.530203i
\(279\) 0 0
\(280\) 8.90151 1.06703i 0.531967 0.0637675i
\(281\) −24.7284 −1.47517 −0.737587 0.675252i \(-0.764035\pi\)
−0.737587 + 0.675252i \(0.764035\pi\)
\(282\) 0 0
\(283\) 18.6573i 1.10906i 0.832163 + 0.554532i \(0.187103\pi\)
−0.832163 + 0.554532i \(0.812897\pi\)
\(284\) −13.3223 + 28.0024i −0.790531 + 1.66163i
\(285\) 0 0
\(286\) 23.5243 14.8591i 1.39102 0.878638i
\(287\) −7.44602 −0.439525
\(288\) 0 0
\(289\) −6.26596 −0.368586
\(290\) 10.8060 6.82558i 0.634549 0.400812i
\(291\) 0 0
\(292\) 1.16314 2.44483i 0.0680677 0.143073i
\(293\) 14.4030i 0.841431i 0.907193 + 0.420715i \(0.138221\pi\)
−0.907193 + 0.420715i \(0.861779\pi\)
\(294\) 0 0
\(295\) 0.0664326 0.00386786
\(296\) −33.6966 + 4.03925i −1.95858 + 0.234777i
\(297\) 0 0
\(298\) 9.85901 + 15.6084i 0.571117 + 0.904169i
\(299\) 2.43190i 0.140640i
\(300\) 0 0
\(301\) 12.5741i 0.724759i
\(302\) −21.1007 + 13.3282i −1.21421 + 0.766952i
\(303\) 0 0
\(304\) 9.95089 8.09090i 0.570723 0.464045i
\(305\) −16.9272 −0.969249
\(306\) 0 0
\(307\) 27.3734i 1.56228i 0.624353 + 0.781142i \(0.285363\pi\)
−0.624353 + 0.781142i \(0.714637\pi\)
\(308\) 9.83735 + 4.68017i 0.560535 + 0.266677i
\(309\) 0 0
\(310\) −8.90151 14.0925i −0.505572 0.800400i
\(311\) 27.9767 1.58641 0.793206 0.608953i \(-0.208410\pi\)
0.793206 + 0.608953i \(0.208410\pi\)
\(312\) 0 0
\(313\) 27.5228 1.55568 0.777841 0.628461i \(-0.216315\pi\)
0.777841 + 0.628461i \(0.216315\pi\)
\(314\) 2.26637 + 3.58803i 0.127899 + 0.202484i
\(315\) 0 0
\(316\) −9.52414 + 20.0190i −0.535775 + 1.12616i
\(317\) 1.73928i 0.0976879i −0.998806 0.0488440i \(-0.984446\pi\)
0.998806 0.0488440i \(-0.0155537\pi\)
\(318\) 0 0
\(319\) 15.5307 0.869555
\(320\) 5.99315 + 24.6391i 0.335027 + 1.37737i
\(321\) 0 0
\(322\) 0.805009 0.508483i 0.0448614 0.0283366i
\(323\) 10.5047i 0.584495i
\(324\) 0 0
\(325\) 18.2297i 1.01120i
\(326\) 0.657925 + 1.04160i 0.0364391 + 0.0576889i
\(327\) 0 0
\(328\) −2.50660 20.9108i −0.138404 1.15461i
\(329\) −4.06341 −0.224023
\(330\) 0 0
\(331\) 13.7965i 0.758323i 0.925331 + 0.379161i \(0.123788\pi\)
−0.925331 + 0.379161i \(0.876212\pi\)
\(332\) −24.6418 11.7235i −1.35240 0.643409i
\(333\) 0 0
\(334\) −8.96691 + 5.66394i −0.490648 + 0.309917i
\(335\) −19.6747 −1.07494
\(336\) 0 0
\(337\) −1.96903 −0.107260 −0.0536300 0.998561i \(-0.517079\pi\)
−0.0536300 + 0.998561i \(0.517079\pi\)
\(338\) −0.0561034 + 0.0354376i −0.00305162 + 0.00192755i
\(339\) 0 0
\(340\) 18.7552 + 8.92289i 1.01714 + 0.483912i
\(341\) 20.2542i 1.09683i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 35.3121 4.23291i 1.90390 0.228223i
\(345\) 0 0
\(346\) −0.493110 0.780672i −0.0265098 0.0419692i
\(347\) 21.4183i 1.14979i −0.818226 0.574897i \(-0.805042\pi\)
0.818226 0.574897i \(-0.194958\pi\)
\(348\) 0 0
\(349\) 24.2315i 1.29708i 0.761180 + 0.648541i \(0.224620\pi\)
−0.761180 + 0.648541i \(0.775380\pi\)
\(350\) 6.03442 3.81164i 0.322554 0.203741i
\(351\) 0 0
\(352\) −9.83181 + 29.2020i −0.524037 + 1.55647i
\(353\) −20.1659 −1.07332 −0.536662 0.843797i \(-0.680315\pi\)
−0.536662 + 0.843797i \(0.680315\pi\)
\(354\) 0 0
\(355\) 49.1459i 2.60839i
\(356\) 5.10350 10.7272i 0.270485 0.568538i
\(357\) 0 0
\(358\) −3.34769 5.29993i −0.176931 0.280110i
\(359\) 19.8643 1.04840 0.524198 0.851597i \(-0.324365\pi\)
0.524198 + 0.851597i \(0.324365\pi\)
\(360\) 0 0
\(361\) 8.71982 0.458938
\(362\) −16.5985 26.2781i −0.872400 1.38115i
\(363\) 0 0
\(364\) −6.52346 3.10357i −0.341922 0.162671i
\(365\) 4.29083i 0.224592i
\(366\) 0 0
\(367\) 37.1713 1.94033 0.970163 0.242454i \(-0.0779523\pi\)
0.970163 + 0.242454i \(0.0779523\pi\)
\(368\) 1.69898 + 2.08955i 0.0885654 + 0.108925i
\(369\) 0 0
\(370\) −45.4742 + 28.7237i −2.36409 + 1.49327i
\(371\) 0.291601i 0.0151392i
\(372\) 0 0
\(373\) 23.6106i 1.22251i 0.791433 + 0.611256i \(0.209335\pi\)
−0.791433 + 0.611256i \(0.790665\pi\)
\(374\) 13.4778 + 21.3376i 0.696922 + 1.10334i
\(375\) 0 0
\(376\) −1.36789 11.4114i −0.0705437 0.588497i
\(377\) −10.2989 −0.530422
\(378\) 0 0
\(379\) 15.2051i 0.781034i −0.920596 0.390517i \(-0.872296\pi\)
0.920596 0.390517i \(-0.127704\pi\)
\(380\) 8.73221 18.3544i 0.447953 0.941563i
\(381\) 0 0
\(382\) 7.97899 5.03992i 0.408241 0.257865i
\(383\) 1.26331 0.0645522 0.0322761 0.999479i \(-0.489724\pi\)
0.0322761 + 0.999479i \(0.489724\pi\)
\(384\) 0 0
\(385\) 17.2652 0.879914
\(386\) 29.9281 18.9040i 1.52330 0.962191i
\(387\) 0 0
\(388\) 8.24920 17.3392i 0.418790 0.880263i
\(389\) 12.3813i 0.627754i −0.949464 0.313877i \(-0.898372\pi\)
0.949464 0.313877i \(-0.101628\pi\)
\(390\) 0 0
\(391\) 2.20584 0.111554
\(392\) −0.336637 2.80832i −0.0170027 0.141842i
\(393\) 0 0
\(394\) −2.85458 4.51926i −0.143812 0.227677i
\(395\) 35.1346i 1.76781i
\(396\) 0 0
\(397\) 19.0272i 0.954948i 0.878646 + 0.477474i \(0.158447\pi\)
−0.878646 + 0.477474i \(0.841553\pi\)
\(398\) −8.58558 + 5.42307i −0.430356 + 0.271834i
\(399\) 0 0
\(400\) 12.7357 + 15.6635i 0.636786 + 0.783174i
\(401\) −6.06885 −0.303064 −0.151532 0.988452i \(-0.548421\pi\)
−0.151532 + 0.988452i \(0.548421\pi\)
\(402\) 0 0
\(403\) 13.4312i 0.669058i
\(404\) −25.6678 12.2116i −1.27702 0.607550i
\(405\) 0 0
\(406\) −2.15339 3.40916i −0.106871 0.169194i
\(407\) −65.3572 −3.23963
\(408\) 0 0
\(409\) 28.9491 1.43144 0.715720 0.698387i \(-0.246099\pi\)
0.715720 + 0.698387i \(0.246099\pi\)
\(410\) −17.8248 28.2195i −0.880306 1.39366i
\(411\) 0 0
\(412\) 1.45485 3.05799i 0.0716755 0.150656i
\(413\) 0.0209587i 0.00103131i
\(414\) 0 0
\(415\) −43.2480 −2.12296
\(416\) 6.51979 19.3648i 0.319659 0.949435i
\(417\) 0 0
\(418\) 20.8816 13.1898i 1.02135 0.645136i
\(419\) 4.30387i 0.210258i −0.994459 0.105129i \(-0.966474\pi\)
0.994459 0.105129i \(-0.0335255\pi\)
\(420\) 0 0
\(421\) 18.0243i 0.878453i −0.898376 0.439226i \(-0.855253\pi\)
0.898376 0.439226i \(-0.144747\pi\)
\(422\) −4.00611 6.34231i −0.195014 0.308739i
\(423\) 0 0
\(424\) 0.818909 0.0981635i 0.0397697 0.00476724i
\(425\) 16.5351 0.802073
\(426\) 0 0
\(427\) 5.34034i 0.258437i
\(428\) −21.0662 10.0224i −1.01828 0.484450i
\(429\) 0 0
\(430\) 47.6544 30.1008i 2.29810 1.45159i
\(431\) 11.0189 0.530760 0.265380 0.964144i \(-0.414503\pi\)
0.265380 + 0.964144i \(0.414503\pi\)
\(432\) 0 0
\(433\) 11.0881 0.532861 0.266430 0.963854i \(-0.414156\pi\)
0.266430 + 0.963854i \(0.414156\pi\)
\(434\) −4.44602 + 2.80832i −0.213416 + 0.134804i
\(435\) 0 0
\(436\) −25.3784 12.0739i −1.21541 0.578236i
\(437\) 2.15870i 0.103265i
\(438\) 0 0
\(439\) −32.6928 −1.56034 −0.780171 0.625567i \(-0.784868\pi\)
−0.780171 + 0.625567i \(0.784868\pi\)
\(440\) 5.81209 + 48.4861i 0.277080 + 2.31149i
\(441\) 0 0
\(442\) −8.93759 14.1496i −0.425118 0.673029i
\(443\) 23.6225i 1.12234i −0.827700 0.561171i \(-0.810351\pi\)
0.827700 0.561171i \(-0.189649\pi\)
\(444\) 0 0
\(445\) 18.8268i 0.892477i
\(446\) 5.53208 3.49433i 0.261951 0.165461i
\(447\) 0 0
\(448\) 7.77335 1.89077i 0.367256 0.0893305i
\(449\) −8.75599 −0.413220 −0.206610 0.978423i \(-0.566243\pi\)
−0.206610 + 0.978423i \(0.566243\pi\)
\(450\) 0 0
\(451\) 40.5581i 1.90981i
\(452\) 12.8416 26.9920i 0.604018 1.26960i
\(453\) 0 0
\(454\) 7.49467 + 11.8652i 0.351742 + 0.556864i
\(455\) −11.4491 −0.536741
\(456\) 0 0
\(457\) 15.8326 0.740618 0.370309 0.928909i \(-0.379252\pi\)
0.370309 + 0.928909i \(0.379252\pi\)
\(458\) 1.75628 + 2.78048i 0.0820657 + 0.129923i
\(459\) 0 0
\(460\) 3.85418 + 1.83365i 0.179702 + 0.0854942i
\(461\) 36.1188i 1.68222i 0.540865 + 0.841109i \(0.318097\pi\)
−0.540865 + 0.841109i \(0.681903\pi\)
\(462\) 0 0
\(463\) 8.28903 0.385224 0.192612 0.981275i \(-0.438304\pi\)
0.192612 + 0.981275i \(0.438304\pi\)
\(464\) 8.84912 7.19507i 0.410810 0.334023i
\(465\) 0 0
\(466\) 3.86237 2.43966i 0.178921 0.113015i
\(467\) 22.7640i 1.05339i −0.850053 0.526697i \(-0.823430\pi\)
0.850053 0.526697i \(-0.176570\pi\)
\(468\) 0 0
\(469\) 6.20714i 0.286619i
\(470\) −9.72730 15.3999i −0.448687 0.710342i
\(471\) 0 0
\(472\) 0.0588589 0.00705548i 0.00270920 0.000324755i
\(473\) 68.4906 3.14920
\(474\) 0 0
\(475\) 16.1818i 0.742472i
\(476\) 2.81507 5.91705i 0.129028 0.271208i
\(477\) 0 0
\(478\) 4.17241 2.63549i 0.190841 0.120545i
\(479\) −38.1931 −1.74509 −0.872543 0.488537i \(-0.837531\pi\)
−0.872543 + 0.488537i \(0.837531\pi\)
\(480\) 0 0
\(481\) 43.3404 1.97615
\(482\) 11.6909 7.38456i 0.532508 0.336358i
\(483\) 0 0
\(484\) −16.0412 + 33.7173i −0.729145 + 1.53261i
\(485\) 30.4313i 1.38182i
\(486\) 0 0
\(487\) 8.84028 0.400591 0.200296 0.979735i \(-0.435810\pi\)
0.200296 + 0.979735i \(0.435810\pi\)
\(488\) −14.9974 + 1.79775i −0.678900 + 0.0813805i
\(489\) 0 0
\(490\) −2.39387 3.78988i −0.108144 0.171209i
\(491\) 28.9660i 1.30722i −0.756833 0.653608i \(-0.773254\pi\)
0.756833 0.653608i \(-0.226746\pi\)
\(492\) 0 0
\(493\) 9.34157i 0.420723i
\(494\) −13.8473 + 8.74660i −0.623017 + 0.393528i
\(495\) 0 0
\(496\) −9.38337 11.5405i −0.421326 0.518183i
\(497\) 15.5050 0.695492
\(498\) 0 0
\(499\) 0.417929i 0.0187091i −0.999956 0.00935453i \(-0.997022\pi\)
0.999956 0.00935453i \(-0.00297768\pi\)
\(500\) 0.268609 + 0.127792i 0.0120126 + 0.00571504i
\(501\) 0 0
\(502\) 19.0448 + 30.1509i 0.850011 + 1.34570i
\(503\) −10.3133 −0.459848 −0.229924 0.973209i \(-0.573848\pi\)
−0.229924 + 0.973209i \(0.573848\pi\)
\(504\) 0 0
\(505\) −45.0487 −2.00464
\(506\) 2.76968 + 4.38485i 0.123127 + 0.194930i
\(507\) 0 0
\(508\) 3.49891 7.35443i 0.155239 0.326300i
\(509\) 22.2340i 0.985505i 0.870169 + 0.492753i \(0.164009\pi\)
−0.870169 + 0.492753i \(0.835991\pi\)
\(510\) 0 0
\(511\) −1.35371 −0.0598845
\(512\) 7.92669 + 21.1936i 0.350313 + 0.936633i
\(513\) 0 0
\(514\) −7.32847 + 4.62902i −0.323245 + 0.204177i
\(515\) 5.36696i 0.236497i
\(516\) 0 0
\(517\) 22.1332i 0.973418i
\(518\) 9.06200 + 14.3466i 0.398161 + 0.630353i
\(519\) 0 0
\(520\) −3.85418 32.1527i −0.169017 1.40999i
\(521\) −29.3079 −1.28400 −0.642001 0.766704i \(-0.721896\pi\)
−0.642001 + 0.766704i \(0.721896\pi\)
\(522\) 0 0
\(523\) 1.15302i 0.0504181i 0.999682 + 0.0252090i \(0.00802514\pi\)
−0.999682 + 0.0252090i \(0.991975\pi\)
\(524\) 32.2633 + 15.3494i 1.40943 + 0.670544i
\(525\) 0 0
\(526\) 1.51950 0.959791i 0.0662534 0.0418489i
\(527\) −12.1827 −0.530687
\(528\) 0 0
\(529\) −22.5467 −0.980291
\(530\) 1.10513 0.698056i 0.0480039 0.0303216i
\(531\) 0 0
\(532\) −5.79061 2.75491i −0.251055 0.119441i
\(533\) 26.8954i 1.16497i
\(534\) 0 0
\(535\) −36.9726 −1.59846
\(536\) −17.4316 + 2.08955i −0.752933 + 0.0902549i
\(537\) 0 0
\(538\) −14.9598 23.6838i −0.644964 1.02108i
\(539\) 5.44696i 0.234617i
\(540\) 0 0
\(541\) 34.3825i 1.47822i −0.673586 0.739109i \(-0.735247\pi\)
0.673586 0.739109i \(-0.264753\pi\)
\(542\) 28.8791 18.2414i 1.24046 0.783537i
\(543\) 0 0
\(544\) 17.5647 + 5.91372i 0.753078 + 0.253549i
\(545\) −44.5407 −1.90792
\(546\) 0 0
\(547\) 17.1388i 0.732802i −0.930457 0.366401i \(-0.880590\pi\)
0.930457 0.366401i \(-0.119410\pi\)
\(548\) 18.1598 38.1705i 0.775749 1.63056i
\(549\) 0 0
\(550\) 20.7618 + 32.8693i 0.885287 + 1.40155i
\(551\) −9.14195 −0.389460
\(552\) 0 0
\(553\) 11.0846 0.471363
\(554\) 0.995526 + 1.57608i 0.0422958 + 0.0669610i
\(555\) 0 0
\(556\) 13.3530 + 6.35277i 0.566294 + 0.269417i
\(557\) 29.0976i 1.23290i 0.787393 + 0.616452i \(0.211430\pi\)
−0.787393 + 0.616452i \(0.788570\pi\)
\(558\) 0 0
\(559\) −45.4183 −1.92099
\(560\) 9.83735 7.99858i 0.415704 0.338002i
\(561\) 0 0
\(562\) −29.5669 + 18.6759i −1.24720 + 0.787795i
\(563\) 31.6652i 1.33453i 0.744821 + 0.667264i \(0.232535\pi\)
−0.744821 + 0.667264i \(0.767465\pi\)
\(564\) 0 0
\(565\) 47.3727i 1.99298i
\(566\) 14.0908 + 22.3079i 0.592279 + 0.937671i
\(567\) 0 0
\(568\) 5.21954 + 43.5429i 0.219007 + 1.82702i
\(569\) 6.16080 0.258274 0.129137 0.991627i \(-0.458779\pi\)
0.129137 + 0.991627i \(0.458779\pi\)
\(570\) 0 0
\(571\) 41.0313i 1.71711i 0.512724 + 0.858553i \(0.328636\pi\)
−0.512724 + 0.858553i \(0.671364\pi\)
\(572\) 16.9050 35.5330i 0.706834 1.48571i
\(573\) 0 0
\(574\) −8.90294 + 5.62353i −0.371601 + 0.234722i
\(575\) 3.39796 0.141705
\(576\) 0 0
\(577\) −25.4290 −1.05862 −0.529311 0.848428i \(-0.677550\pi\)
−0.529311 + 0.848428i \(0.677550\pi\)
\(578\) −7.49199 + 4.73231i −0.311626 + 0.196838i
\(579\) 0 0
\(580\) 7.76537 16.3222i 0.322440 0.677743i
\(581\) 13.6442i 0.566058i
\(582\) 0 0
\(583\) 1.58834 0.0657822
\(584\) −0.455708 3.80165i −0.0188573 0.157313i
\(585\) 0 0
\(586\) 10.8777 + 17.2211i 0.449354 + 0.711398i
\(587\) 3.55639i 0.146788i −0.997303 0.0733939i \(-0.976617\pi\)
0.997303 0.0733939i \(-0.0233830\pi\)
\(588\) 0 0
\(589\) 11.9224i 0.491253i
\(590\) 0.0794311 0.0501725i 0.00327013 0.00206557i
\(591\) 0 0
\(592\) −37.2392 + 30.2786i −1.53052 + 1.24444i
\(593\) 2.57142 0.105596 0.0527978 0.998605i \(-0.483186\pi\)
0.0527978 + 0.998605i \(0.483186\pi\)
\(594\) 0 0
\(595\) 10.3848i 0.425735i
\(596\) 23.5761 + 11.2165i 0.965716 + 0.459444i
\(597\) 0 0
\(598\) −1.83667 2.90774i −0.0751069 0.118906i
\(599\) −21.8400 −0.892357 −0.446178 0.894944i \(-0.647215\pi\)
−0.446178 + 0.894944i \(0.647215\pi\)
\(600\) 0 0
\(601\) −43.8140 −1.78721 −0.893606 0.448853i \(-0.851833\pi\)
−0.893606 + 0.448853i \(0.851833\pi\)
\(602\) −9.49646 15.0344i −0.387047 0.612757i
\(603\) 0 0
\(604\) −15.1633 + 31.8721i −0.616987 + 1.29686i
\(605\) 59.1760i 2.40585i
\(606\) 0 0
\(607\) 17.9012 0.726588 0.363294 0.931675i \(-0.381652\pi\)
0.363294 + 0.931675i \(0.381652\pi\)
\(608\) 5.78735 17.1893i 0.234708 0.697119i
\(609\) 0 0
\(610\) −20.2393 + 12.7841i −0.819464 + 0.517613i
\(611\) 14.6773i 0.593778i
\(612\) 0 0
\(613\) 15.8902i 0.641798i 0.947113 + 0.320899i \(0.103985\pi\)
−0.947113 + 0.320899i \(0.896015\pi\)
\(614\) 20.6735 + 32.7294i 0.834315 + 1.32085i
\(615\) 0 0
\(616\) 15.2968 1.83365i 0.616326 0.0738797i
\(617\) 20.8402 0.838994 0.419497 0.907757i \(-0.362206\pi\)
0.419497 + 0.907757i \(0.362206\pi\)
\(618\) 0 0
\(619\) 31.4914i 1.26575i −0.774255 0.632873i \(-0.781875\pi\)
0.774255 0.632873i \(-0.218125\pi\)
\(620\) −21.2864 10.1271i −0.854883 0.406715i
\(621\) 0 0
\(622\) 33.4507 21.1291i 1.34125 0.847200i
\(623\) −5.93965 −0.237967
\(624\) 0 0
\(625\) −24.7632 −0.990527
\(626\) 32.9081 20.7863i 1.31527 0.830789i
\(627\) 0 0
\(628\) 5.41964 + 2.57842i 0.216267 + 0.102890i
\(629\) 39.3116i 1.56746i
\(630\) 0 0
\(631\) −10.6786 −0.425109 −0.212555 0.977149i \(-0.568178\pi\)
−0.212555 + 0.977149i \(0.568178\pi\)
\(632\) 3.73147 + 31.1290i 0.148430 + 1.23825i
\(633\) 0 0
\(634\) −1.31358 2.07960i −0.0521688 0.0825915i
\(635\) 12.9075i 0.512218i
\(636\) 0 0
\(637\) 3.61205i 0.143115i
\(638\) 18.5696 11.7294i 0.735176 0.464373i
\(639\) 0 0
\(640\) 25.7742 + 24.9338i 1.01882 + 0.985596i
\(641\) 24.7669 0.978232 0.489116 0.872219i \(-0.337319\pi\)
0.489116 + 0.872219i \(0.337319\pi\)
\(642\) 0 0
\(643\) 11.5834i 0.456805i 0.973567 + 0.228402i \(0.0733502\pi\)
−0.973567 + 0.228402i \(0.926650\pi\)
\(644\) 0.578494 1.21595i 0.0227959 0.0479151i
\(645\) 0 0
\(646\) −7.93353 12.5600i −0.312141 0.494168i
\(647\) −30.1155 −1.18396 −0.591981 0.805952i \(-0.701654\pi\)
−0.591981 + 0.805952i \(0.701654\pi\)
\(648\) 0 0
\(649\) 0.114161 0.00448122
\(650\) −13.7678 21.7967i −0.540019 0.854935i
\(651\) 0 0
\(652\) 1.57332 + 0.748513i 0.0616158 + 0.0293140i
\(653\) 45.7814i 1.79157i −0.444491 0.895783i \(-0.646616\pi\)
0.444491 0.895783i \(-0.353384\pi\)
\(654\) 0 0
\(655\) 56.6242 2.21249
\(656\) −18.7897 23.1092i −0.733616 0.902264i
\(657\) 0 0
\(658\) −4.85848 + 3.06885i −0.189403 + 0.119636i
\(659\) 34.3446i 1.33788i 0.743318 + 0.668938i \(0.233251\pi\)
−0.743318 + 0.668938i \(0.766749\pi\)
\(660\) 0 0
\(661\) 26.5119i 1.03120i 0.856831 + 0.515598i \(0.172430\pi\)
−0.856831 + 0.515598i \(0.827570\pi\)
\(662\) 10.4196 + 16.4960i 0.404971 + 0.641133i
\(663\) 0 0
\(664\) −38.3174 + 4.59315i −1.48700 + 0.178249i
\(665\) −10.1629 −0.394100
\(666\) 0 0
\(667\) 1.91969i 0.0743305i
\(668\) −6.44378 + 13.5443i −0.249318 + 0.524046i
\(669\) 0 0
\(670\) −23.5243 + 14.8591i −0.908824 + 0.574057i
\(671\) −29.0886 −1.12295
\(672\) 0 0
\(673\) −26.2427 −1.01158 −0.505790 0.862657i \(-0.668799\pi\)
−0.505790 + 0.862657i \(0.668799\pi\)
\(674\) −2.35430 + 1.48709i −0.0906843 + 0.0572806i
\(675\) 0 0
\(676\) −0.0403169 + 0.0847431i −0.00155065 + 0.00325935i
\(677\) 3.23458i 0.124315i −0.998066 0.0621576i \(-0.980202\pi\)
0.998066 0.0621576i \(-0.0197981\pi\)
\(678\) 0 0
\(679\) −9.60073 −0.368442
\(680\) 29.1639 3.49590i 1.11838 0.134062i
\(681\) 0 0
\(682\) −15.2968 24.2173i −0.585745 0.927328i
\(683\) 0.708911i 0.0271257i 0.999908 + 0.0135629i \(0.00431733\pi\)
−0.999908 + 0.0135629i \(0.995683\pi\)
\(684\) 0 0
\(685\) 66.9917i 2.55962i
\(686\) −1.19566 + 0.755240i −0.0456507 + 0.0288352i
\(687\) 0 0
\(688\) 39.0246 31.7303i 1.48780 1.20970i
\(689\) −1.05328 −0.0401267
\(690\) 0 0
\(691\) 39.0071i 1.48390i −0.670454 0.741951i \(-0.733901\pi\)
0.670454 0.741951i \(-0.266099\pi\)
\(692\) −1.17919 0.561005i −0.0448260 0.0213262i
\(693\) 0 0
\(694\) −16.1759 25.6091i −0.614030 0.972108i
\(695\) 23.4354 0.888955
\(696\) 0 0
\(697\) −24.3953 −0.924037
\(698\) 18.3006 + 28.9727i 0.692687 + 1.09663i
\(699\) 0 0
\(700\) 4.33645 9.11487i 0.163902 0.344510i
\(701\) 16.2448i 0.613559i −0.951781 0.306779i \(-0.900749\pi\)
0.951781 0.306779i \(-0.0992514\pi\)
\(702\) 0 0
\(703\) 38.4715 1.45098
\(704\) 10.2989 + 42.3411i 0.388156 + 1.59579i
\(705\) 0 0
\(706\) −24.1117 + 15.2301i −0.907456 + 0.573193i
\(707\) 14.2123i 0.534510i
\(708\) 0 0
\(709\) 25.1720i 0.945354i 0.881236 + 0.472677i \(0.156712\pi\)
−0.881236 + 0.472677i \(0.843288\pi\)
\(710\) 37.1169 + 58.7620i 1.39297 + 2.20530i
\(711\) 0 0
\(712\) −1.99950 16.6804i −0.0749345 0.625126i
\(713\) −2.50354 −0.0937581
\(714\) 0 0
\(715\) 62.3626i 2.33223i
\(716\) −8.00544 3.80863i −0.299177 0.142335i
\(717\) 0 0
\(718\) 23.7510 15.0023i 0.886379 0.559880i
\(719\) −7.92289 −0.295474 −0.147737 0.989027i \(-0.547199\pi\)
−0.147737 + 0.989027i \(0.547199\pi\)
\(720\) 0 0
\(721\) −1.69321 −0.0630586
\(722\) 10.4260 6.58555i 0.388015 0.245089i
\(723\) 0 0
\(724\) −39.6926 18.8839i −1.47516 0.701816i
\(725\) 14.3901i 0.534436i
\(726\) 0 0
\(727\) −6.10313 −0.226353 −0.113176 0.993575i \(-0.536102\pi\)
−0.113176 + 0.993575i \(0.536102\pi\)
\(728\) −10.1438 + 1.21595i −0.375955 + 0.0450661i
\(729\) 0 0
\(730\) −3.24061 5.13039i −0.119940 0.189884i
\(731\) 41.1963i 1.52370i
\(732\) 0 0
\(733\) 26.6568i 0.984591i −0.870428 0.492296i \(-0.836158\pi\)
0.870428 0.492296i \(-0.163842\pi\)
\(734\) 44.4444 28.0732i 1.64047 1.03620i
\(735\) 0 0
\(736\) 3.60952 + 1.21526i 0.133049 + 0.0447953i
\(737\) −33.8100 −1.24541
\(738\) 0 0
\(739\) 9.27736i 0.341273i 0.985334 + 0.170637i \(0.0545824\pi\)
−0.985334 + 0.170637i \(0.945418\pi\)
\(740\) −32.6786 + 68.6878i −1.20129 + 2.52501i
\(741\) 0 0
\(742\) −0.220228 0.348657i −0.00808484 0.0127996i
\(743\) 12.6494 0.464062 0.232031 0.972708i \(-0.425463\pi\)
0.232031 + 0.972708i \(0.425463\pi\)
\(744\) 0 0
\(745\) 41.3776 1.51596
\(746\) 17.8317 + 28.2304i 0.652865 + 1.03359i
\(747\) 0 0
\(748\) 32.2299 + 15.3336i 1.17844 + 0.560650i
\(749\) 11.6644i 0.426209i
\(750\) 0 0
\(751\) −7.10625 −0.259311 −0.129655 0.991559i \(-0.541387\pi\)
−0.129655 + 0.991559i \(0.541387\pi\)
\(752\) −10.2539 12.6111i −0.373920 0.459879i
\(753\) 0 0
\(754\) −12.3141 + 7.77817i −0.448452 + 0.283264i
\(755\) 55.9376i 2.03578i
\(756\) 0 0
\(757\) 34.6019i 1.25763i 0.777556 + 0.628814i \(0.216459\pi\)
−0.777556 + 0.628814i \(0.783541\pi\)
\(758\) −11.4835 18.1802i −0.417100 0.660335i
\(759\) 0 0
\(760\) −3.42120 28.5407i −0.124100 1.03528i
\(761\) −21.7114 −0.787039 −0.393520 0.919316i \(-0.628743\pi\)
−0.393520 + 0.919316i \(0.628743\pi\)
\(762\) 0 0
\(763\) 14.0521i 0.508720i
\(764\) 5.73385 12.0521i 0.207443 0.436030i
\(765\) 0 0
\(766\) 1.51050 0.954103i 0.0545764 0.0344731i
\(767\) −0.0757040 −0.00273351
\(768\) 0 0
\(769\) −5.94161 −0.214260 −0.107130 0.994245i \(-0.534166\pi\)
−0.107130 + 0.994245i \(0.534166\pi\)
\(770\) 20.6433 13.0393i 0.743934 0.469905i
\(771\) 0 0
\(772\) 21.5069 45.2058i 0.774050 1.62699i
\(773\) 1.14102i 0.0410398i 0.999789 + 0.0205199i \(0.00653215\pi\)
−0.999789 + 0.0205199i \(0.993468\pi\)
\(774\) 0 0
\(775\) −18.7667 −0.674121
\(776\) −3.23196 26.9620i −0.116021 0.967878i
\(777\) 0 0
\(778\) −9.35081 14.8038i −0.335243 0.530743i
\(779\) 23.8740i 0.855374i
\(780\) 0 0
\(781\) 84.4548i 3.02203i
\(782\) 2.63744 1.66593i 0.0943146 0.0595737i
\(783\) 0 0
\(784\) −2.52346 3.10357i −0.0901236 0.110842i
\(785\) 9.51181 0.339491
\(786\) 0 0
\(787\) <