Properties

Label 3150.2.bp.h.1349.3
Level 3150
Weight 2
Character 3150.1349
Analytic conductor 25.153
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bp (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1349.3
Character \(\chi\) = 3150.1349
Dual form 3150.2.bp.h.899.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.54649 - 0.717905i) q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.54649 - 0.717905i) q^{7} -1.00000 q^{8} +(-5.09272 + 2.94028i) q^{11} +4.05674 q^{13} +(-1.89497 + 1.84637i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.371532 + 0.214504i) q^{17} +(-5.30761 - 3.06435i) q^{19} +5.88057i q^{22} +(0.876005 - 1.51729i) q^{23} +(2.02837 - 3.51324i) q^{26} +(0.651521 + 2.56428i) q^{28} -0.0419065i q^{29} +(7.92389 - 4.57486i) q^{31} +(0.500000 + 0.866025i) q^{32} +0.429009i q^{34} +(-0.928534 - 0.536089i) q^{37} +(-5.30761 + 3.06435i) q^{38} +8.61559 q^{41} +11.0724i q^{43} +(5.09272 + 2.94028i) q^{44} +(-0.876005 - 1.51729i) q^{46} +(0.834099 + 0.481567i) q^{47} +(5.96922 + 3.65628i) q^{49} +(-2.02837 - 3.51324i) q^{52} +(6.57304 + 11.3848i) q^{53} +(2.54649 + 0.717905i) q^{56} +(-0.0362921 - 0.0209532i) q^{58} +(6.77318 + 11.7315i) q^{59} +(1.05635 + 0.609885i) q^{61} -9.14972i q^{62} +1.00000 q^{64} +(-10.9527 + 6.32352i) q^{67} +(0.371532 + 0.214504i) q^{68} -2.54990i q^{71} +(4.66689 + 8.08328i) q^{73} +(-0.928534 + 0.536089i) q^{74} +6.12870i q^{76} +(15.0794 - 3.83131i) q^{77} +(5.35961 - 9.28312i) q^{79} +(4.30780 - 7.46132i) q^{82} +10.1027i q^{83} +(9.58894 + 5.53618i) q^{86} +(5.09272 - 2.94028i) q^{88} +(-3.15638 + 5.46700i) q^{89} +(-10.3304 - 2.91235i) q^{91} -1.75201 q^{92} +(0.834099 - 0.481567i) q^{94} +2.59007 q^{97} +(6.15104 - 3.34136i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 12q^{2} - 12q^{4} - 24q^{8} + O(q^{10}) \) \( 24q + 12q^{2} - 12q^{4} - 24q^{8} - 12q^{16} - 24q^{17} - 12q^{19} + 8q^{23} + 12q^{32} - 12q^{38} - 8q^{46} + 24q^{47} + 52q^{49} + 32q^{53} - 12q^{61} + 24q^{64} + 24q^{68} + 16q^{77} - 4q^{79} + 68q^{91} - 16q^{92} + 24q^{94} + 20q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −2.54649 0.717905i −0.962483 0.271343i
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −5.09272 + 2.94028i −1.53551 + 0.886529i −0.536419 + 0.843952i \(0.680223\pi\)
−0.999093 + 0.0425771i \(0.986443\pi\)
\(12\) 0 0
\(13\) 4.05674 1.12514 0.562569 0.826751i \(-0.309813\pi\)
0.562569 + 0.826751i \(0.309813\pi\)
\(14\) −1.89497 + 1.84637i −0.506452 + 0.493464i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −0.371532 + 0.214504i −0.0901098 + 0.0520249i −0.544378 0.838840i \(-0.683234\pi\)
0.454268 + 0.890865i \(0.349901\pi\)
\(18\) 0 0
\(19\) −5.30761 3.06435i −1.21765 0.703010i −0.253234 0.967405i \(-0.581494\pi\)
−0.964414 + 0.264395i \(0.914828\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 5.88057i 1.25374i
\(23\) 0.876005 1.51729i 0.182660 0.316376i −0.760126 0.649776i \(-0.774863\pi\)
0.942785 + 0.333400i \(0.108196\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.02837 3.51324i 0.397796 0.689003i
\(27\) 0 0
\(28\) 0.651521 + 2.56428i 0.123126 + 0.484603i
\(29\) 0.0419065i 0.00778184i −0.999992 0.00389092i \(-0.998761\pi\)
0.999992 0.00389092i \(-0.00123852\pi\)
\(30\) 0 0
\(31\) 7.92389 4.57486i 1.42317 0.821669i 0.426604 0.904439i \(-0.359710\pi\)
0.996569 + 0.0827694i \(0.0263765\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 0.429009i 0.0735744i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.928534 0.536089i −0.152650 0.0881326i 0.421729 0.906722i \(-0.361423\pi\)
−0.574379 + 0.818589i \(0.694757\pi\)
\(38\) −5.30761 + 3.06435i −0.861008 + 0.497103i
\(39\) 0 0
\(40\) 0 0
\(41\) 8.61559 1.34553 0.672765 0.739856i \(-0.265107\pi\)
0.672765 + 0.739856i \(0.265107\pi\)
\(42\) 0 0
\(43\) 11.0724i 1.68852i 0.535935 + 0.844259i \(0.319959\pi\)
−0.535935 + 0.844259i \(0.680041\pi\)
\(44\) 5.09272 + 2.94028i 0.767756 + 0.443264i
\(45\) 0 0
\(46\) −0.876005 1.51729i −0.129160 0.223712i
\(47\) 0.834099 + 0.481567i 0.121666 + 0.0702438i 0.559598 0.828764i \(-0.310956\pi\)
−0.437932 + 0.899008i \(0.644289\pi\)
\(48\) 0 0
\(49\) 5.96922 + 3.65628i 0.852746 + 0.522325i
\(50\) 0 0
\(51\) 0 0
\(52\) −2.02837 3.51324i −0.281284 0.487199i
\(53\) 6.57304 + 11.3848i 0.902877 + 1.56383i 0.823742 + 0.566965i \(0.191883\pi\)
0.0791353 + 0.996864i \(0.474784\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.54649 + 0.717905i 0.340289 + 0.0959341i
\(57\) 0 0
\(58\) −0.0362921 0.0209532i −0.00476538 0.00275129i
\(59\) 6.77318 + 11.7315i 0.881793 + 1.52731i 0.849345 + 0.527838i \(0.176997\pi\)
0.0324481 + 0.999473i \(0.489670\pi\)
\(60\) 0 0
\(61\) 1.05635 + 0.609885i 0.135252 + 0.0780878i 0.566099 0.824337i \(-0.308452\pi\)
−0.430847 + 0.902425i \(0.641785\pi\)
\(62\) 9.14972i 1.16202i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −10.9527 + 6.32352i −1.33808 + 0.772541i −0.986523 0.163625i \(-0.947681\pi\)
−0.351558 + 0.936166i \(0.614348\pi\)
\(68\) 0.371532 + 0.214504i 0.0450549 + 0.0260125i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.54990i 0.302617i −0.988487 0.151308i \(-0.951651\pi\)
0.988487 0.151308i \(-0.0483487\pi\)
\(72\) 0 0
\(73\) 4.66689 + 8.08328i 0.546218 + 0.946077i 0.998529 + 0.0542168i \(0.0172662\pi\)
−0.452311 + 0.891860i \(0.649400\pi\)
\(74\) −0.928534 + 0.536089i −0.107940 + 0.0623191i
\(75\) 0 0
\(76\) 6.12870i 0.703010i
\(77\) 15.0794 3.83131i 1.71846 0.436619i
\(78\) 0 0
\(79\) 5.35961 9.28312i 0.603003 1.04443i −0.389360 0.921086i \(-0.627304\pi\)
0.992364 0.123347i \(-0.0393628\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 4.30780 7.46132i 0.475717 0.823965i
\(83\) 10.1027i 1.10891i 0.832212 + 0.554457i \(0.187074\pi\)
−0.832212 + 0.554457i \(0.812926\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 9.58894 + 5.53618i 1.03400 + 0.596981i
\(87\) 0 0
\(88\) 5.09272 2.94028i 0.542886 0.313435i
\(89\) −3.15638 + 5.46700i −0.334575 + 0.579501i −0.983403 0.181434i \(-0.941926\pi\)
0.648828 + 0.760935i \(0.275259\pi\)
\(90\) 0 0
\(91\) −10.3304 2.91235i −1.08293 0.305298i
\(92\) −1.75201 −0.182660
\(93\) 0 0
\(94\) 0.834099 0.481567i 0.0860307 0.0496698i
\(95\) 0 0
\(96\) 0 0
\(97\) 2.59007 0.262982 0.131491 0.991317i \(-0.458024\pi\)
0.131491 + 0.991317i \(0.458024\pi\)
\(98\) 6.15104 3.34136i 0.621349 0.337529i
\(99\) 0 0
\(100\) 0 0
\(101\) −5.21837 9.03849i −0.519248 0.899363i −0.999750 0.0223696i \(-0.992879\pi\)
0.480502 0.876993i \(-0.340454\pi\)
\(102\) 0 0
\(103\) 2.47216 4.28191i 0.243589 0.421909i −0.718145 0.695894i \(-0.755008\pi\)
0.961734 + 0.273985i \(0.0883418\pi\)
\(104\) −4.05674 −0.397796
\(105\) 0 0
\(106\) 13.1461 1.27686
\(107\) −0.347904 + 0.602588i −0.0336332 + 0.0582544i −0.882352 0.470590i \(-0.844041\pi\)
0.848719 + 0.528844i \(0.177374\pi\)
\(108\) 0 0
\(109\) 2.98417 + 5.16874i 0.285832 + 0.495076i 0.972811 0.231602i \(-0.0743967\pi\)
−0.686979 + 0.726678i \(0.741063\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.89497 1.84637i 0.179058 0.174466i
\(113\) 0.809894 0.0761884 0.0380942 0.999274i \(-0.487871\pi\)
0.0380942 + 0.999274i \(0.487871\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.0362921 + 0.0209532i −0.00336963 + 0.00194546i
\(117\) 0 0
\(118\) 13.5464 1.24704
\(119\) 1.10010 0.279508i 0.100846 0.0256225i
\(120\) 0 0
\(121\) 11.7905 20.4218i 1.07187 1.85653i
\(122\) 1.05635 0.609885i 0.0956376 0.0552164i
\(123\) 0 0
\(124\) −7.92389 4.57486i −0.711586 0.410835i
\(125\) 0 0
\(126\) 0 0
\(127\) 11.0265i 0.978442i −0.872160 0.489221i \(-0.837281\pi\)
0.872160 0.489221i \(-0.162719\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) −9.44080 + 16.3520i −0.824847 + 1.42868i 0.0771893 + 0.997016i \(0.475405\pi\)
−0.902036 + 0.431660i \(0.857928\pi\)
\(132\) 0 0
\(133\) 11.3159 + 11.6137i 0.981210 + 1.00704i
\(134\) 12.6470i 1.09254i
\(135\) 0 0
\(136\) 0.371532 0.214504i 0.0318586 0.0183936i
\(137\) 7.18560 + 12.4458i 0.613907 + 1.06332i 0.990575 + 0.136970i \(0.0437364\pi\)
−0.376668 + 0.926348i \(0.622930\pi\)
\(138\) 0 0
\(139\) 16.7650i 1.42199i −0.703198 0.710994i \(-0.748245\pi\)
0.703198 0.710994i \(-0.251755\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2.20827 1.27495i −0.185314 0.106991i
\(143\) −20.6598 + 11.9280i −1.72766 + 0.997466i
\(144\) 0 0
\(145\) 0 0
\(146\) 9.33377 0.772469
\(147\) 0 0
\(148\) 1.07218i 0.0881326i
\(149\) 8.67934 + 5.01102i 0.711039 + 0.410519i 0.811446 0.584428i \(-0.198681\pi\)
−0.100407 + 0.994946i \(0.532014\pi\)
\(150\) 0 0
\(151\) −7.20599 12.4811i −0.586415 1.01570i −0.994697 0.102845i \(-0.967206\pi\)
0.408283 0.912856i \(-0.366128\pi\)
\(152\) 5.30761 + 3.06435i 0.430504 + 0.248552i
\(153\) 0 0
\(154\) 4.22169 14.9748i 0.340193 1.20670i
\(155\) 0 0
\(156\) 0 0
\(157\) 5.43554 + 9.41463i 0.433803 + 0.751370i 0.997197 0.0748190i \(-0.0238379\pi\)
−0.563394 + 0.826189i \(0.690505\pi\)
\(158\) −5.35961 9.28312i −0.426388 0.738525i
\(159\) 0 0
\(160\) 0 0
\(161\) −3.32001 + 3.23486i −0.261653 + 0.254943i
\(162\) 0 0
\(163\) 9.19935 + 5.31125i 0.720549 + 0.416009i 0.814955 0.579525i \(-0.196762\pi\)
−0.0944058 + 0.995534i \(0.530095\pi\)
\(164\) −4.30780 7.46132i −0.336382 0.582631i
\(165\) 0 0
\(166\) 8.74919 + 5.05134i 0.679068 + 0.392060i
\(167\) 3.45341i 0.267233i −0.991033 0.133617i \(-0.957341\pi\)
0.991033 0.133617i \(-0.0426591\pi\)
\(168\) 0 0
\(169\) 3.45714 0.265934
\(170\) 0 0
\(171\) 0 0
\(172\) 9.58894 5.53618i 0.731150 0.422130i
\(173\) −6.88939 3.97759i −0.523790 0.302411i 0.214694 0.976681i \(-0.431125\pi\)
−0.738484 + 0.674271i \(0.764458\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.88057i 0.443264i
\(177\) 0 0
\(178\) 3.15638 + 5.46700i 0.236580 + 0.409769i
\(179\) −2.38066 + 1.37447i −0.177939 + 0.102733i −0.586324 0.810077i \(-0.699425\pi\)
0.408385 + 0.912810i \(0.366092\pi\)
\(180\) 0 0
\(181\) 6.73202i 0.500387i −0.968196 0.250194i \(-0.919506\pi\)
0.968196 0.250194i \(-0.0804943\pi\)
\(182\) −7.68740 + 7.49025i −0.569828 + 0.555215i
\(183\) 0 0
\(184\) −0.876005 + 1.51729i −0.0645800 + 0.111856i
\(185\) 0 0
\(186\) 0 0
\(187\) 1.26141 2.18482i 0.0922432 0.159770i
\(188\) 0.963134i 0.0702438i
\(189\) 0 0
\(190\) 0 0
\(191\) 21.3740 + 12.3403i 1.54657 + 0.892911i 0.998400 + 0.0565412i \(0.0180072\pi\)
0.548166 + 0.836369i \(0.315326\pi\)
\(192\) 0 0
\(193\) 0.595151 0.343610i 0.0428399 0.0247336i −0.478427 0.878127i \(-0.658793\pi\)
0.521267 + 0.853394i \(0.325460\pi\)
\(194\) 1.29503 2.24306i 0.0929780 0.161043i
\(195\) 0 0
\(196\) 0.181816 6.99764i 0.0129868 0.499831i
\(197\) 0.169154 0.0120517 0.00602586 0.999982i \(-0.498082\pi\)
0.00602586 + 0.999982i \(0.498082\pi\)
\(198\) 0 0
\(199\) 0.359798 0.207730i 0.0255054 0.0147256i −0.487193 0.873294i \(-0.661979\pi\)
0.512699 + 0.858569i \(0.328646\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −10.4367 −0.734327
\(203\) −0.0300849 + 0.106714i −0.00211154 + 0.00748988i
\(204\) 0 0
\(205\) 0 0
\(206\) −2.47216 4.28191i −0.172244 0.298335i
\(207\) 0 0
\(208\) −2.02837 + 3.51324i −0.140642 + 0.243599i
\(209\) 36.0402 2.49295
\(210\) 0 0
\(211\) −2.10135 −0.144663 −0.0723313 0.997381i \(-0.523044\pi\)
−0.0723313 + 0.997381i \(0.523044\pi\)
\(212\) 6.57304 11.3848i 0.451439 0.781915i
\(213\) 0 0
\(214\) 0.347904 + 0.602588i 0.0237823 + 0.0411921i
\(215\) 0 0
\(216\) 0 0
\(217\) −23.4624 + 5.96124i −1.59273 + 0.404675i
\(218\) 5.96835 0.404227
\(219\) 0 0
\(220\) 0 0
\(221\) −1.50721 + 0.870188i −0.101386 + 0.0585352i
\(222\) 0 0
\(223\) −25.9946 −1.74073 −0.870364 0.492409i \(-0.836117\pi\)
−0.870364 + 0.492409i \(0.836117\pi\)
\(224\) −0.651521 2.56428i −0.0435316 0.171333i
\(225\) 0 0
\(226\) 0.404947 0.701389i 0.0269367 0.0466557i
\(227\) −12.3905 + 7.15363i −0.822383 + 0.474803i −0.851238 0.524781i \(-0.824147\pi\)
0.0288545 + 0.999584i \(0.490814\pi\)
\(228\) 0 0
\(229\) 1.36736 + 0.789445i 0.0903576 + 0.0521680i 0.544498 0.838762i \(-0.316720\pi\)
−0.454140 + 0.890930i \(0.650054\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.0419065i 0.00275129i
\(233\) −9.13044 + 15.8144i −0.598155 + 1.03604i 0.394938 + 0.918708i \(0.370766\pi\)
−0.993093 + 0.117327i \(0.962567\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6.77318 11.7315i 0.440897 0.763656i
\(237\) 0 0
\(238\) 0.307987 1.09247i 0.0199639 0.0708141i
\(239\) 23.1801i 1.49940i −0.661779 0.749699i \(-0.730198\pi\)
0.661779 0.749699i \(-0.269802\pi\)
\(240\) 0 0
\(241\) −11.2090 + 6.47152i −0.722035 + 0.416867i −0.815501 0.578755i \(-0.803539\pi\)
0.0934660 + 0.995622i \(0.470205\pi\)
\(242\) −11.7905 20.4218i −0.757924 1.31276i
\(243\) 0 0
\(244\) 1.21977i 0.0780878i
\(245\) 0 0
\(246\) 0 0
\(247\) −21.5316 12.4313i −1.37002 0.790983i
\(248\) −7.92389 + 4.57486i −0.503168 + 0.290504i
\(249\) 0 0
\(250\) 0 0
\(251\) −22.7253 −1.43441 −0.717203 0.696865i \(-0.754578\pi\)
−0.717203 + 0.696865i \(0.754578\pi\)
\(252\) 0 0
\(253\) 10.3028i 0.647732i
\(254\) −9.54921 5.51324i −0.599171 0.345931i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 6.06331 + 3.50065i 0.378219 + 0.218365i 0.677043 0.735943i \(-0.263261\pi\)
−0.298824 + 0.954308i \(0.596594\pi\)
\(258\) 0 0
\(259\) 1.97964 + 2.03175i 0.123009 + 0.126247i
\(260\) 0 0
\(261\) 0 0
\(262\) 9.44080 + 16.3520i 0.583255 + 1.01023i
\(263\) 6.00972 + 10.4091i 0.370575 + 0.641855i 0.989654 0.143473i \(-0.0458272\pi\)
−0.619079 + 0.785329i \(0.712494\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 15.7157 3.99298i 0.963590 0.244825i
\(267\) 0 0
\(268\) 10.9527 + 6.32352i 0.669040 + 0.386271i
\(269\) −0.611792 1.05966i −0.0373016 0.0646083i 0.846772 0.531956i \(-0.178543\pi\)
−0.884074 + 0.467348i \(0.845210\pi\)
\(270\) 0 0
\(271\) 14.1888 + 8.19190i 0.861908 + 0.497623i 0.864651 0.502374i \(-0.167540\pi\)
−0.00274289 + 0.999996i \(0.500873\pi\)
\(272\) 0.429009i 0.0260125i
\(273\) 0 0
\(274\) 14.3712 0.868196
\(275\) 0 0
\(276\) 0 0
\(277\) 11.4092 6.58712i 0.685514 0.395781i −0.116416 0.993201i \(-0.537140\pi\)
0.801929 + 0.597419i \(0.203807\pi\)
\(278\) −14.5189 8.38250i −0.870786 0.502749i
\(279\) 0 0
\(280\) 0 0
\(281\) 5.72433i 0.341485i −0.985316 0.170742i \(-0.945383\pi\)
0.985316 0.170742i \(-0.0546166\pi\)
\(282\) 0 0
\(283\) 8.07354 + 13.9838i 0.479922 + 0.831249i 0.999735 0.0230311i \(-0.00733167\pi\)
−0.519813 + 0.854280i \(0.673998\pi\)
\(284\) −2.20827 + 1.27495i −0.131037 + 0.0756542i
\(285\) 0 0
\(286\) 23.8559i 1.41063i
\(287\) −21.9395 6.18518i −1.29505 0.365100i
\(288\) 0 0
\(289\) −8.40798 + 14.5630i −0.494587 + 0.856649i
\(290\) 0 0
\(291\) 0 0
\(292\) 4.66689 8.08328i 0.273109 0.473038i
\(293\) 24.2757i 1.41820i 0.705108 + 0.709100i \(0.250898\pi\)
−0.705108 + 0.709100i \(0.749102\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.928534 + 0.536089i 0.0539699 + 0.0311596i
\(297\) 0 0
\(298\) 8.67934 5.01102i 0.502780 0.290280i
\(299\) 3.55372 6.15523i 0.205517 0.355966i
\(300\) 0 0
\(301\) 7.94890 28.1956i 0.458167 1.62517i
\(302\) −14.4120 −0.829316
\(303\) 0 0
\(304\) 5.30761 3.06435i 0.304412 0.175752i
\(305\) 0 0
\(306\) 0 0
\(307\) 19.1856 1.09498 0.547490 0.836812i \(-0.315583\pi\)
0.547490 + 0.836812i \(0.315583\pi\)
\(308\) −10.8577 11.1435i −0.618676 0.634959i
\(309\) 0 0
\(310\) 0 0
\(311\) 16.3473 + 28.3143i 0.926969 + 1.60556i 0.788363 + 0.615210i \(0.210929\pi\)
0.138606 + 0.990348i \(0.455738\pi\)
\(312\) 0 0
\(313\) 9.76593 16.9151i 0.552003 0.956097i −0.446127 0.894970i \(-0.647197\pi\)
0.998130 0.0611276i \(-0.0194696\pi\)
\(314\) 10.8711 0.613491
\(315\) 0 0
\(316\) −10.7192 −0.603003
\(317\) 7.28095 12.6110i 0.408939 0.708303i −0.585832 0.810432i \(-0.699232\pi\)
0.994771 + 0.102129i \(0.0325655\pi\)
\(318\) 0 0
\(319\) 0.123217 + 0.213418i 0.00689882 + 0.0119491i
\(320\) 0 0
\(321\) 0 0
\(322\) 1.14147 + 4.49264i 0.0636117 + 0.250365i
\(323\) 2.62926 0.146296
\(324\) 0 0
\(325\) 0 0
\(326\) 9.19935 5.31125i 0.509505 0.294163i
\(327\) 0 0
\(328\) −8.61559 −0.475717
\(329\) −1.77830 1.82511i −0.0980411 0.100622i
\(330\) 0 0
\(331\) 4.44833 7.70473i 0.244502 0.423490i −0.717489 0.696569i \(-0.754709\pi\)
0.961992 + 0.273079i \(0.0880422\pi\)
\(332\) 8.74919 5.05134i 0.480174 0.277229i
\(333\) 0 0
\(334\) −2.99074 1.72671i −0.163646 0.0944812i
\(335\) 0 0
\(336\) 0 0
\(337\) 10.3636i 0.564543i −0.959335 0.282271i \(-0.908912\pi\)
0.959335 0.282271i \(-0.0910879\pi\)
\(338\) 1.72857 2.99397i 0.0940217 0.162850i
\(339\) 0 0
\(340\) 0 0
\(341\) −26.9028 + 46.5970i −1.45687 + 2.52337i
\(342\) 0 0
\(343\) −12.5757 13.5960i −0.679025 0.734115i
\(344\) 11.0724i 0.596981i
\(345\) 0 0
\(346\) −6.88939 + 3.97759i −0.370376 + 0.213837i
\(347\) 14.7440 + 25.5373i 0.791497 + 1.37091i 0.925040 + 0.379870i \(0.124031\pi\)
−0.133542 + 0.991043i \(0.542635\pi\)
\(348\) 0 0
\(349\) 8.85764i 0.474138i −0.971493 0.237069i \(-0.923813\pi\)
0.971493 0.237069i \(-0.0761868\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5.09272 2.94028i −0.271443 0.156718i
\(353\) 14.8345 8.56472i 0.789562 0.455854i −0.0502461 0.998737i \(-0.516001\pi\)
0.839808 + 0.542883i \(0.182667\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.31275 0.334575
\(357\) 0 0
\(358\) 2.74895i 0.145286i
\(359\) −19.0997 11.0272i −1.00804 0.581993i −0.0974241 0.995243i \(-0.531060\pi\)
−0.910618 + 0.413250i \(0.864394\pi\)
\(360\) 0 0
\(361\) 9.28047 + 16.0743i 0.488446 + 0.846013i
\(362\) −5.83010 3.36601i −0.306423 0.176914i
\(363\) 0 0
\(364\) 2.64305 + 10.4026i 0.138534 + 0.545245i
\(365\) 0 0
\(366\) 0 0
\(367\) −1.63762 2.83644i −0.0854831 0.148061i 0.820114 0.572200i \(-0.193910\pi\)
−0.905597 + 0.424139i \(0.860577\pi\)
\(368\) 0.876005 + 1.51729i 0.0456649 + 0.0790940i
\(369\) 0 0
\(370\) 0 0
\(371\) −8.56495 33.7102i −0.444670 1.75015i
\(372\) 0 0
\(373\) −32.4255 18.7209i −1.67893 0.969331i −0.962344 0.271834i \(-0.912370\pi\)
−0.716587 0.697498i \(-0.754297\pi\)
\(374\) −1.26141 2.18482i −0.0652258 0.112974i
\(375\) 0 0
\(376\) −0.834099 0.481567i −0.0430154 0.0248349i
\(377\) 0.170004i 0.00875563i
\(378\) 0 0
\(379\) 37.2066 1.91117 0.955587 0.294708i \(-0.0952225\pi\)
0.955587 + 0.294708i \(0.0952225\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 21.3740 12.3403i 1.09359 0.631383i
\(383\) 15.8160 + 9.13135i 0.808158 + 0.466590i 0.846316 0.532682i \(-0.178816\pi\)
−0.0381579 + 0.999272i \(0.512149\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.687221i 0.0349786i
\(387\) 0 0
\(388\) −1.29503 2.24306i −0.0657454 0.113874i
\(389\) 2.21119 1.27663i 0.112112 0.0647278i −0.442896 0.896573i \(-0.646049\pi\)
0.555007 + 0.831845i \(0.312715\pi\)
\(390\) 0 0
\(391\) 0.751627i 0.0380114i
\(392\) −5.96922 3.65628i −0.301491 0.184670i
\(393\) 0 0
\(394\) 0.0845770 0.146492i 0.00426093 0.00738014i
\(395\) 0 0
\(396\) 0 0
\(397\) −9.98784 + 17.2994i −0.501275 + 0.868234i 0.498724 + 0.866761i \(0.333802\pi\)
−0.999999 + 0.00147306i \(0.999531\pi\)
\(398\) 0.415459i 0.0208251i
\(399\) 0 0
\(400\) 0 0
\(401\) −21.2087 12.2448i −1.05911 0.611477i −0.133924 0.990992i \(-0.542758\pi\)
−0.925186 + 0.379514i \(0.876091\pi\)
\(402\) 0 0
\(403\) 32.1452 18.5590i 1.60126 0.924490i
\(404\) −5.21837 + 9.03849i −0.259624 + 0.449682i
\(405\) 0 0
\(406\) 0.0773750 + 0.0794115i 0.00384006 + 0.00394113i
\(407\) 6.30502 0.312528
\(408\) 0 0
\(409\) −14.0020 + 8.08403i −0.692352 + 0.399730i −0.804493 0.593963i \(-0.797563\pi\)
0.112140 + 0.993692i \(0.464229\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.94432 −0.243589
\(413\) −8.82575 34.7366i −0.434287 1.70928i
\(414\) 0 0
\(415\) 0 0
\(416\) 2.02837 + 3.51324i 0.0994490 + 0.172251i
\(417\) 0 0
\(418\) 18.0201 31.2117i 0.881392 1.52662i
\(419\) −14.1632 −0.691920 −0.345960 0.938249i \(-0.612447\pi\)
−0.345960 + 0.938249i \(0.612447\pi\)
\(420\) 0 0
\(421\) −21.7096 −1.05806 −0.529031 0.848603i \(-0.677444\pi\)
−0.529031 + 0.848603i \(0.677444\pi\)
\(422\) −1.05067 + 1.81982i −0.0511460 + 0.0885874i
\(423\) 0 0
\(424\) −6.57304 11.3848i −0.319215 0.552897i
\(425\) 0 0
\(426\) 0 0
\(427\) −2.25215 2.31143i −0.108989 0.111858i
\(428\) 0.695809 0.0336332
\(429\) 0 0
\(430\) 0 0
\(431\) 3.08126 1.77897i 0.148419 0.0856899i −0.423951 0.905685i \(-0.639357\pi\)
0.572371 + 0.819995i \(0.306024\pi\)
\(432\) 0 0
\(433\) 9.86329 0.473999 0.237000 0.971510i \(-0.423836\pi\)
0.237000 + 0.971510i \(0.423836\pi\)
\(434\) −6.56863 + 23.2997i −0.315304 + 1.11842i
\(435\) 0 0
\(436\) 2.98417 5.16874i 0.142916 0.247538i
\(437\) −9.29898 + 5.36877i −0.444831 + 0.256823i
\(438\) 0 0
\(439\) 12.1701 + 7.02641i 0.580847 + 0.335352i 0.761470 0.648200i \(-0.224478\pi\)
−0.180623 + 0.983552i \(0.557811\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 1.74038i 0.0827812i
\(443\) 7.72219 13.3752i 0.366892 0.635476i −0.622186 0.782870i \(-0.713755\pi\)
0.989078 + 0.147394i \(0.0470884\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −12.9973 + 22.5120i −0.615440 + 1.06597i
\(447\) 0 0
\(448\) −2.54649 0.717905i −0.120310 0.0339178i
\(449\) 0.159851i 0.00754383i 0.999993 + 0.00377192i \(0.00120064\pi\)
−0.999993 + 0.00377192i \(0.998799\pi\)
\(450\) 0 0
\(451\) −43.8768 + 25.3323i −2.06608 + 1.19285i
\(452\) −0.404947 0.701389i −0.0190471 0.0329906i
\(453\) 0 0
\(454\) 14.3073i 0.671473i
\(455\) 0 0
\(456\) 0 0
\(457\) −11.3995 6.58150i −0.533246 0.307870i 0.209091 0.977896i \(-0.432949\pi\)
−0.742337 + 0.670026i \(0.766283\pi\)
\(458\) 1.36736 0.789445i 0.0638925 0.0368883i
\(459\) 0 0
\(460\) 0 0
\(461\) −20.7565 −0.966725 −0.483363 0.875420i \(-0.660585\pi\)
−0.483363 + 0.875420i \(0.660585\pi\)
\(462\) 0 0
\(463\) 17.7932i 0.826920i 0.910522 + 0.413460i \(0.135680\pi\)
−0.910522 + 0.413460i \(0.864320\pi\)
\(464\) 0.0362921 + 0.0209532i 0.00168482 + 0.000972730i
\(465\) 0 0
\(466\) 9.13044 + 15.8144i 0.422960 + 0.732587i
\(467\) −1.87225 1.08094i −0.0866373 0.0500201i 0.456055 0.889951i \(-0.349262\pi\)
−0.542693 + 0.839931i \(0.682595\pi\)
\(468\) 0 0
\(469\) 32.4305 8.23982i 1.49750 0.380479i
\(470\) 0 0
\(471\) 0 0
\(472\) −6.77318 11.7315i −0.311761 0.539986i
\(473\) −32.5559 56.3884i −1.49692 2.59274i
\(474\) 0 0
\(475\) 0 0
\(476\) −0.792110 0.812958i −0.0363063 0.0372619i
\(477\) 0 0
\(478\) −20.0746 11.5901i −0.918190 0.530117i
\(479\) −6.50176 11.2614i −0.297073 0.514546i 0.678392 0.734700i \(-0.262677\pi\)
−0.975465 + 0.220154i \(0.929344\pi\)
\(480\) 0 0
\(481\) −3.76682 2.17478i −0.171752 0.0991612i
\(482\) 12.9430i 0.589539i
\(483\) 0 0
\(484\) −23.5811 −1.07187
\(485\) 0 0
\(486\) 0 0
\(487\) −5.46224 + 3.15363i −0.247518 + 0.142904i −0.618627 0.785685i \(-0.712311\pi\)
0.371109 + 0.928589i \(0.378978\pi\)
\(488\) −1.05635 0.609885i −0.0478188 0.0276082i
\(489\) 0 0
\(490\) 0 0
\(491\) 14.6640i 0.661776i −0.943670 0.330888i \(-0.892652\pi\)
0.943670 0.330888i \(-0.107348\pi\)
\(492\) 0 0
\(493\) 0.00898912 + 0.0155696i 0.000404849 + 0.000701220i
\(494\) −21.5316 + 12.4313i −0.968752 + 0.559309i
\(495\) 0 0
\(496\) 9.14972i 0.410835i
\(497\) −1.83058 + 6.49328i −0.0821129 + 0.291264i
\(498\) 0 0
\(499\) −12.1113 + 20.9774i −0.542176 + 0.939076i 0.456603 + 0.889670i \(0.349066\pi\)
−0.998779 + 0.0494053i \(0.984267\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −11.3626 + 19.6806i −0.507139 + 0.878390i
\(503\) 34.9707i 1.55927i 0.626237 + 0.779633i \(0.284594\pi\)
−0.626237 + 0.779633i \(0.715406\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 8.92250 + 5.15141i 0.396653 + 0.229008i
\(507\) 0 0
\(508\) −9.54921 + 5.51324i −0.423678 + 0.244610i
\(509\) 9.58793 16.6068i 0.424978 0.736083i −0.571441 0.820643i \(-0.693615\pi\)
0.996418 + 0.0845605i \(0.0269486\pi\)
\(510\) 0 0
\(511\) −6.08115 23.9344i −0.269014 1.05879i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 6.06331 3.50065i 0.267441 0.154407i
\(515\) 0 0
\(516\) 0 0
\(517\) −5.66377 −0.249092
\(518\) 2.74936 0.698547i 0.120800 0.0306924i
\(519\) 0 0
\(520\) 0 0
\(521\) −10.0953 17.4855i −0.442282 0.766054i 0.555577 0.831465i \(-0.312497\pi\)
−0.997858 + 0.0654110i \(0.979164\pi\)
\(522\) 0 0
\(523\) 5.01992 8.69476i 0.219506 0.380195i −0.735151 0.677903i \(-0.762889\pi\)
0.954657 + 0.297708i \(0.0962222\pi\)
\(524\) 18.8816 0.824847
\(525\) 0 0
\(526\) 12.0194 0.524073
\(527\) −1.96265 + 3.39942i −0.0854946 + 0.148081i
\(528\) 0 0
\(529\) 9.96523 + 17.2603i 0.433271 + 0.750447i
\(530\) 0 0
\(531\) 0 0
\(532\) 4.39982 15.6067i 0.190757 0.676635i
\(533\) 34.9512 1.51391
\(534\) 0 0
\(535\) 0 0
\(536\) 10.9527 6.32352i 0.473083 0.273135i
\(537\) 0 0
\(538\) −1.22358 −0.0527525
\(539\) −41.1501 1.06918i −1.77246 0.0460528i
\(540\) 0 0
\(541\) 8.68907 15.0499i 0.373572 0.647046i −0.616540 0.787324i \(-0.711466\pi\)
0.990112 + 0.140277i \(0.0447994\pi\)
\(542\) 14.1888 8.19190i 0.609461 0.351872i
\(543\) 0 0
\(544\) −0.371532 0.214504i −0.0159293 0.00919679i
\(545\) 0 0
\(546\) 0 0
\(547\) 32.6253i 1.39496i 0.716606 + 0.697478i \(0.245695\pi\)
−0.716606 + 0.697478i \(0.754305\pi\)
\(548\) 7.18560 12.4458i 0.306954 0.531659i
\(549\) 0 0
\(550\) 0 0
\(551\) −0.128416 + 0.222423i −0.00547071 + 0.00947555i
\(552\) 0 0
\(553\) −20.3126 + 19.7917i −0.863780 + 0.841628i
\(554\) 13.1742i 0.559720i
\(555\) 0 0
\(556\) −14.5189 + 8.38250i −0.615739 + 0.355497i
\(557\) −17.0656 29.5585i −0.723094 1.25243i −0.959754 0.280842i \(-0.909386\pi\)
0.236660 0.971592i \(-0.423947\pi\)
\(558\) 0 0
\(559\) 44.9177i 1.89981i
\(560\) 0 0
\(561\) 0 0
\(562\) −4.95741 2.86216i −0.209116 0.120733i
\(563\) −25.8012 + 14.8964i −1.08739 + 0.627806i −0.932881 0.360185i \(-0.882714\pi\)
−0.154512 + 0.987991i \(0.549380\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 16.1471 0.678712
\(567\) 0 0
\(568\) 2.54990i 0.106991i
\(569\) 14.4586 + 8.34769i 0.606137 + 0.349953i 0.771452 0.636287i \(-0.219531\pi\)
−0.165315 + 0.986241i \(0.552864\pi\)
\(570\) 0 0
\(571\) 0.984264 + 1.70480i 0.0411902 + 0.0713435i 0.885886 0.463904i \(-0.153552\pi\)
−0.844695 + 0.535247i \(0.820218\pi\)
\(572\) 20.6598 + 11.9280i 0.863831 + 0.498733i
\(573\) 0 0
\(574\) −16.3263 + 15.9076i −0.681446 + 0.663970i
\(575\) 0 0
\(576\) 0 0
\(577\) 19.9848 + 34.6146i 0.831977 + 1.44103i 0.896468 + 0.443108i \(0.146124\pi\)
−0.0644912 + 0.997918i \(0.520542\pi\)
\(578\) 8.40798 + 14.5630i 0.349726 + 0.605743i
\(579\) 0 0
\(580\) 0 0
\(581\) 7.25277 25.7264i 0.300896 1.06731i
\(582\) 0 0
\(583\) −66.9493 38.6532i −2.77276 1.60085i
\(584\) −4.66689 8.08328i −0.193117 0.334489i
\(585\) 0 0
\(586\) 21.0233 + 12.1378i 0.868466 + 0.501409i
\(587\) 25.5123i 1.05300i 0.850174 + 0.526502i \(0.176497\pi\)
−0.850174 + 0.526502i \(0.823503\pi\)
\(588\) 0 0
\(589\) −56.0759 −2.31057
\(590\) 0 0
\(591\) 0 0
\(592\) 0.928534 0.536089i 0.0381625 0.0220331i
\(593\) 34.9279 + 20.1656i 1.43432 + 0.828103i 0.997446 0.0714207i \(-0.0227533\pi\)
0.436871 + 0.899524i \(0.356087\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10.0220i 0.410519i
\(597\) 0 0
\(598\) −3.55372 6.15523i −0.145323 0.251706i
\(599\) 19.9124 11.4964i 0.813600 0.469732i −0.0346046 0.999401i \(-0.511017\pi\)
0.848204 + 0.529669i \(0.177684\pi\)
\(600\) 0 0
\(601\) 25.9443i 1.05829i 0.848532 + 0.529145i \(0.177487\pi\)
−0.848532 + 0.529145i \(0.822513\pi\)
\(602\) −20.4437 20.9818i −0.833223 0.855153i
\(603\) 0 0
\(604\) −7.20599 + 12.4811i −0.293207 + 0.507850i
\(605\) 0 0
\(606\) 0 0
\(607\) 18.9551 32.8311i 0.769362 1.33257i −0.168547 0.985694i \(-0.553908\pi\)
0.937909 0.346881i \(-0.112759\pi\)
\(608\) 6.12870i 0.248552i
\(609\) 0 0
\(610\) 0 0
\(611\) 3.38372 + 1.95359i 0.136891 + 0.0790339i
\(612\) 0 0
\(613\) −18.0154 + 10.4012i −0.727637 + 0.420101i −0.817557 0.575848i \(-0.804672\pi\)
0.0899202 + 0.995949i \(0.471339\pi\)
\(614\) 9.59280 16.6152i 0.387134 0.670536i
\(615\) 0 0
\(616\) −15.0794 + 3.83131i −0.607566 + 0.154368i
\(617\) −40.9298 −1.64777 −0.823887 0.566755i \(-0.808199\pi\)
−0.823887 + 0.566755i \(0.808199\pi\)
\(618\) 0 0
\(619\) 23.2122 13.4016i 0.932976 0.538654i 0.0452247 0.998977i \(-0.485600\pi\)
0.887752 + 0.460323i \(0.152266\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 32.6946 1.31093
\(623\) 11.9625 11.6557i 0.479266 0.466975i
\(624\) 0 0
\(625\) 0 0
\(626\) −9.76593 16.9151i −0.390325 0.676063i
\(627\) 0 0
\(628\) 5.43554 9.41463i 0.216902 0.375685i
\(629\) 0.459974 0.0183404
\(630\) 0 0
\(631\) −2.28749 −0.0910636 −0.0455318 0.998963i \(-0.514498\pi\)
−0.0455318 + 0.998963i \(0.514498\pi\)
\(632\) −5.35961 + 9.28312i −0.213194 + 0.369263i
\(633\) 0 0
\(634\) −7.28095 12.6110i −0.289164 0.500846i
\(635\) 0 0
\(636\) 0 0
\(637\) 24.2156 + 14.8326i 0.959457 + 0.587687i
\(638\) 0.246434 0.00975641
\(639\) 0 0
\(640\) 0 0
\(641\) −1.82398 + 1.05307i −0.0720428 + 0.0415939i −0.535589 0.844479i \(-0.679910\pi\)
0.463546 + 0.886073i \(0.346577\pi\)
\(642\) 0 0
\(643\) −44.2035 −1.74322 −0.871608 0.490203i \(-0.836923\pi\)
−0.871608 + 0.490203i \(0.836923\pi\)
\(644\) 4.46148 + 1.25778i 0.175807 + 0.0495634i
\(645\) 0 0
\(646\) 1.31463 2.27701i 0.0517235 0.0895877i
\(647\) −17.9336 + 10.3540i −0.705044 + 0.407058i −0.809223 0.587501i \(-0.800112\pi\)
0.104179 + 0.994559i \(0.466779\pi\)
\(648\) 0 0
\(649\) −68.9878 39.8302i −2.70801 1.56347i
\(650\) 0 0
\(651\) 0 0
\(652\) 10.6225i 0.416009i
\(653\) 13.5019 23.3860i 0.528370 0.915164i −0.471083 0.882089i \(-0.656137\pi\)
0.999453 0.0330748i \(-0.0105299\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −4.30780 + 7.46132i −0.168191 + 0.291316i
\(657\) 0 0
\(658\) −2.46974 + 0.627502i −0.0962806 + 0.0244626i
\(659\) 15.2065i 0.592363i −0.955132 0.296181i \(-0.904287\pi\)
0.955132 0.296181i \(-0.0957133\pi\)
\(660\) 0 0
\(661\) −35.8665 + 20.7075i −1.39504 + 0.805429i −0.993868 0.110572i \(-0.964732\pi\)
−0.401176 + 0.916001i \(0.631398\pi\)
\(662\) −4.44833 7.70473i −0.172889 0.299453i
\(663\) 0 0
\(664\) 10.1027i 0.392060i
\(665\) 0 0
\(666\) 0 0
\(667\) −0.0635841 0.0367103i −0.00246199 0.00142143i
\(668\) −2.99074 + 1.72671i −0.115715 + 0.0668083i
\(669\) 0 0
\(670\) 0 0
\(671\) −7.17294 −0.276908
\(672\) 0 0
\(673\) 15.2809i 0.589037i 0.955646 + 0.294518i \(0.0951592\pi\)
−0.955646 + 0.294518i \(0.904841\pi\)
\(674\) −8.97517 5.18182i −0.345711 0.199596i
\(675\) 0 0
\(676\) −1.72857 2.99397i −0.0664834 0.115153i
\(677\) 42.0596 + 24.2831i 1.61648 + 0.933277i 0.987820 + 0.155598i \(0.0497304\pi\)
0.628662 + 0.777679i \(0.283603\pi\)
\(678\) 0 0
\(679\) −6.59558 1.85942i −0.253115 0.0713581i
\(680\) 0 0
\(681\) 0 0
\(682\) 26.9028 + 46.5970i 1.03016 + 1.78429i
\(683\) 6.15706 + 10.6643i 0.235593 + 0.408059i 0.959445 0.281896i \(-0.0909634\pi\)
−0.723852 + 0.689956i \(0.757630\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −18.0623 + 4.09288i −0.689624 + 0.156267i
\(687\) 0 0
\(688\) −9.58894 5.53618i −0.365575 0.211065i
\(689\) 26.6651 + 46.1854i 1.01586 + 1.75952i
\(690\) 0 0
\(691\) 36.8280 + 21.2626i 1.40100 + 0.808869i 0.994496 0.104779i \(-0.0334134\pi\)
0.406507 + 0.913648i \(0.366747\pi\)
\(692\) 7.95518i 0.302411i
\(693\) 0 0
\(694\) 29.4879 1.11935
\(695\) 0 0
\(696\) 0 0
\(697\) −3.20097 + 1.84808i −0.121245 + 0.0700011i
\(698\) −7.67094 4.42882i −0.290349 0.167633i
\(699\) 0 0
\(700\) 0 0
\(701\) 2.16278i 0.0816870i −0.999166 0.0408435i \(-0.986995\pi\)
0.999166 0.0408435i \(-0.0130045\pi\)
\(702\) 0 0
\(703\) 3.28553 + 5.69071i 0.123916 + 0.214629i
\(704\) −5.09272 + 2.94028i −0.191939 + 0.110816i
\(705\) 0 0
\(706\) 17.1294i 0.644675i
\(707\) 6.79976 + 26.7627i 0.255731 + 1.00652i
\(708\) 0 0
\(709\) −10.4912 + 18.1712i −0.394004 + 0.682435i −0.992974 0.118337i \(-0.962244\pi\)
0.598969 + 0.800772i \(0.295577\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 3.15638 5.46700i 0.118290 0.204885i
\(713\) 16.0304i 0.600343i
\(714\) 0 0
\(715\) 0 0
\(716\) 2.38066 + 1.37447i 0.0889694 + 0.0513665i
\(717\) 0 0
\(718\) −19.0997 + 11.0272i −0.712793 + 0.411531i
\(719\) −8.73253 + 15.1252i −0.325668 + 0.564074i −0.981647 0.190705i \(-0.938923\pi\)
0.655979 + 0.754779i \(0.272256\pi\)
\(720\) 0 0
\(721\) −9.36934 + 9.12906i −0.348932 + 0.339984i
\(722\) 18.5609 0.690767
\(723\) 0 0
\(724\) −5.83010 + 3.36601i −0.216674 + 0.125097i
\(725\) 0 0
\(726\) 0 0
\(727\) 12.4470 0.461633 0.230816 0.972997i \(-0.425860\pi\)
0.230816 + 0.972997i \(0.425860\pi\)
\(728\) 10.3304 + 2.91235i 0.382872 + 0.107939i
\(729\) 0 0
\(730\) 0 0
\(731\) −2.37507 4.11374i −0.0878450 0.152152i
\(732\) 0 0
\(733\) 11.1806 19.3654i 0.412966 0.715279i −0.582246 0.813012i \(-0.697826\pi\)
0.995213 + 0.0977339i \(0.0311594\pi\)
\(734\) −3.27524 −0.120891
\(735\) 0 0
\(736\) 1.75201 0.0645800
\(737\) 37.1859 64.4079i 1.36976 2.37249i
\(738\) 0 0
\(739\) −15.9125 27.5613i −0.585351 1.01386i −0.994832 0.101539i \(-0.967623\pi\)
0.409481 0.912319i \(-0.365710\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −33.4764 9.43764i −1.22896 0.346467i
\(743\) 15.1736 0.556667 0.278333 0.960485i \(-0.410218\pi\)
0.278333 + 0.960485i \(0.410218\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −32.4255 + 18.7209i −1.18718 + 0.685421i
\(747\) 0 0
\(748\) −2.52281 −0.0922432
\(749\) 1.31854 1.28472i 0.0481783 0.0469427i
\(750\) 0 0
\(751\) 10.4956 18.1790i 0.382991 0.663360i −0.608497 0.793556i \(-0.708227\pi\)
0.991488 + 0.130196i \(0.0415607\pi\)
\(752\) −0.834099 + 0.481567i −0.0304164 + 0.0175609i
\(753\) 0 0
\(754\) −0.147227 0.0850018i −0.00536171 0.00309558i
\(755\) 0 0
\(756\) 0 0
\(757\) 17.0421i 0.619407i 0.950833 + 0.309704i \(0.100230\pi\)
−0.950833 + 0.309704i \(0.899770\pi\)
\(758\) 18.6033 32.2219i 0.675702 1.17035i
\(759\) 0 0
\(760\) 0 0
\(761\) −3.13659 + 5.43274i −0.113701 + 0.196937i −0.917260 0.398289i \(-0.869604\pi\)
0.803559 + 0.595226i \(0.202937\pi\)
\(762\) 0 0
\(763\) −3.88850 15.3045i −0.140773 0.554060i
\(764\) 24.6805i 0.892911i
\(765\) 0 0
\(766\) 15.8160 9.13135i 0.571454 0.329929i
\(767\) 27.4770 + 47.5916i 0.992139 + 1.71843i
\(768\) 0 0
\(769\) 20.7852i 0.749534i 0.927119 + 0.374767i \(0.122277\pi\)
−0.927119 + 0.374767i \(0.877723\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.595151 0.343610i −0.0214199 0.0123668i
\(773\) 38.5322 22.2466i 1.38591 0.800153i 0.393055 0.919515i \(-0.371418\pi\)
0.992851 + 0.119361i \(0.0380847\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −2.59007 −0.0929780
\(777\) 0 0
\(778\) 2.55326i 0.0915390i
\(779\) −45.7282 26.4012i −1.63838 0.945921i
\(780\) 0 0
\(781\) 7.49741 + 12.9859i 0.268279 + 0.464672i
\(782\) 0.650928 + 0.375814i 0.0232771 + 0.0134391i
\(783\) 0 0
\(784\) −6.15104 + 3.34136i −0.219680 + 0.119334i
\(785\) 0 0
\(786\) 0 0
\(787\) −7.68522 13.3112i −0.273948 0.474493i 0.695921 0.718118i \(-0.254996\pi\)