Properties

Label 3150.2.bp.g.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.g.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 \(-0.319777\pi\)
0.999093 0.0425771i \(-0.0135568\pi\)
\(12\) 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 −0.454268 0.890865i \(-0.650099\pi\)
0.544378 + 0.838840i \(0.316766\pi\)
\(18\) 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 −0.942785 0.333400i \(-0.891804\pi\)
0.760126 + 0.649776i \(0.225137\pi\)
\(24\) 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 \(0.00123852\pi\)
−0.999992 + 0.00389092i \(0.998761\pi\)
\(30\) 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 \(-0.734893\pi\)
−0.672765 + 0.739856i \(0.734893\pi\)
\(42\) 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 0.437932 0.899008i \(-0.355711\pi\)
−0.559598 + 0.828764i \(0.689044\pi\)
\(48\) 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 \(-0.808117\pi\)
−0.0791353 0.996864i \(-0.525216\pi\)
\(54\) 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 \(-0.823003\pi\)
−0.0324481 0.999473i \(-0.510330\pi\)
\(60\) 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 \(0.0483487\pi\)
−0.988487 + 0.151308i \(0.951651\pi\)
\(72\) 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 \(-0.812926\pi\)
0.832212 0.554457i \(-0.187074\pi\)
\(84\) 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 −0.648828 0.760935i \(-0.724741\pi\)
0.983403 + 0.181434i \(0.0580739\pi\)
\(90\) 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 \(0.00712105\pi\)
−0.480502 + 0.876993i \(0.659546\pi\)
\(102\) 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 −0.848719 0.528844i \(-0.822626\pi\)
0.882352 + 0.470590i \(0.155959\pi\)
\(108\) 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 \(-0.512129\pi\)
−0.0380942 + 0.999274i \(0.512129\pi\)
\(114\) 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 \(-0.524595\pi\)
0.902036 0.431660i \(-0.142072\pi\)
\(132\) 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 \(-0.956264\pi\)
0.376668 0.926348i \(-0.377070\pi\)
\(138\) 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 0.100407 0.994946i \(-0.467986\pi\)
−0.811446 + 0.584428i \(0.801319\pi\)
\(150\) 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 \(0.0426591\pi\)
−0.991033 + 0.133617i \(0.957341\pi\)
\(168\) 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 0.738484 0.674271i \(-0.235542\pi\)
−0.214694 + 0.976681i \(0.568875\pi\)
\(174\) 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 −0.408385 0.912810i \(-0.633908\pi\)
0.586324 + 0.810077i \(0.300575\pi\)
\(180\) 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 \(-0.981993\pi\)
−0.548166 0.836369i \(-0.684674\pi\)
\(192\) 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 \(-0.501918\pi\)
−0.00602586 + 0.999982i \(0.501918\pi\)
\(198\) 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 −0.0288545 0.999584i \(-0.509186\pi\)
0.851238 + 0.524781i \(0.175853\pi\)
\(228\) 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 \(-0.629234\pi\)
0.993093 0.117327i \(-0.0374327\pi\)
\(234\) 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 \(0.269802\pi\)
−0.661779 + 0.749699i \(0.730198\pi\)
\(240\) 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 \(-0.245422\pi\)
0.717203 + 0.696865i \(0.245422\pi\)
\(252\) 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 0.298824 0.954308i \(-0.403406\pi\)
−0.677043 + 0.735943i \(0.736739\pi\)
\(258\) 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 0.619079 0.785329i \(-0.287506\pi\)
−0.989654 + 0.143473i \(0.954173\pi\)
\(264\) 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 0.884074 0.467348i \(-0.154790\pi\)
−0.846772 + 0.531956i \(0.821457\pi\)
\(270\) 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 \(0.0546166\pi\)
−0.985316 + 0.170742i \(0.945383\pi\)
\(282\) 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 \(-0.749102\pi\)
0.705108 0.709100i \(-0.250898\pi\)
\(294\) 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 \(-0.789071\pi\)
−0.138606 0.990348i \(-0.544262\pi\)
\(312\) 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 −0.994771 0.102129i \(-0.967434\pi\)
0.585832 + 0.810432i \(0.300768\pi\)
\(318\) 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 \(-0.875969\pi\)
0.133542 0.991043i \(-0.457365\pi\)
\(348\) 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 −0.839808 0.542883i \(-0.817333\pi\)
0.0502461 + 0.998737i \(0.483999\pi\)
\(354\) 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 0.910618 0.413250i \(-0.135606\pi\)
0.0974241 + 0.995243i \(0.468940\pi\)
\(360\) 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 0.0381579 0.999272i \(-0.487851\pi\)
−0.846316 + 0.532682i \(0.821184\pi\)
\(384\) 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 −0.555007 0.831845i \(-0.687285\pi\)
0.442896 + 0.896573i \(0.353951\pi\)
\(390\) 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 0.925186 0.379514i \(-0.123909\pi\)
0.133924 + 0.990992i \(0.457242\pi\)
\(402\) 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 \(-0.387553\pi\)
0.345960 + 0.938249i \(0.387553\pi\)
\(420\) 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 −0.572371 0.819995i \(-0.693976\pi\)
0.423951 + 0.905685i \(0.360643\pi\)
\(432\) 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 −0.989078 0.147394i \(-0.952912\pi\)
0.622186 + 0.782870i \(0.286245\pi\)
\(444\) 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 \(-0.998799\pi\)
0.999993 0.00377192i \(-0.00120064\pi\)
\(450\) 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 \(-0.339415\pi\)
0.483363 + 0.875420i \(0.339415\pi\)
\(462\) 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 0.542693 0.839931i \(-0.317405\pi\)
−0.456055 + 0.889951i \(0.650738\pi\)
\(468\) 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 0.975465 0.220154i \(-0.0706561\pi\)
−0.678392 + 0.734700i \(0.737323\pi\)
\(480\) 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 \(0.107348\pi\)
−0.943670 + 0.330888i \(0.892652\pi\)
\(492\) 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 \(-0.715406\pi\)
0.626237 0.779633i \(-0.284594\pi\)
\(504\) 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 −0.996418 0.0845605i \(-0.973051\pi\)
0.571441 + 0.820643i \(0.306385\pi\)
\(510\) 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 0.997858 0.0654110i \(-0.0208358\pi\)
−0.555577 + 0.831465i \(0.687503\pi\)
\(522\) 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 \(0.0906138\pi\)
−0.236660 + 0.971592i \(0.576053\pi\)
\(558\) 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 0.154512 0.987991i \(-0.450620\pi\)
0.932881 + 0.360185i \(0.117286\pi\)
\(564\) 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 0.165315 0.986241i \(-0.447136\pi\)
−0.771452 + 0.636287i \(0.780469\pi\)
\(570\) 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 \(-0.823503\pi\)
0.850174 0.526502i \(-0.176497\pi\)
\(588\) 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 −0.436871 0.899524i \(-0.643913\pi\)
−0.997446 + 0.0714207i \(0.977247\pi\)
\(594\) 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 −0.848204 0.529669i \(-0.822316\pi\)
0.0346046 + 0.999401i \(0.488983\pi\)
\(600\) 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 \(-0.191801\pi\)
0.823887 + 0.566755i \(0.191801\pi\)
\(618\) 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 −0.463546 0.886073i \(-0.653423\pi\)
0.535589 + 0.844479i \(0.320090\pi\)
\(642\) 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 −0.104179 0.994559i \(-0.533221\pi\)
0.809223 + 0.587501i \(0.199888\pi\)
\(648\) 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 \(0.343863\pi\)
−0.999453 + 0.0330748i \(0.989470\pi\)
\(654\) 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 \(0.0957133\pi\)
−0.955132 + 0.296181i \(0.904287\pi\)
\(660\) 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 \(-0.950270\pi\)
−0.628662 0.777679i \(-0.716397\pi\)
\(678\) 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 0.723852 0.689956i \(-0.242370\pi\)
−0.959445 + 0.281896i \(0.909037\pi\)
\(684\) 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 \(0.0130045\pi\)
−0.999166 + 0.0408435i \(0.986995\pi\)
\(702\) 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 −0.655979 0.754779i \(-0.727744\pi\)
0.981647 + 0.190705i \(0.0610773\pi\)
\(720\) 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 \(-0.589782\pi\)
−0.278333 + 0.960485i \(0.589782\pi\)
\(744\) 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 −0.803559 0.595226i \(-0.797063\pi\)
0.917260 + 0.398289i \(0.130396\pi\)
\(762\) 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 −0.992851 0.119361i \(-0.961915\pi\)
−0.393055 + 0.919515i \(0.628582\pi\)
\(774\) 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