Properties

Label 3150.2.bf.d.1151.6
Level 3150
Weight 2
Character 3150.1151
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.bf (of order \(6\), degree \(2\), 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 1151.6
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.d.1601.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.717905 + 2.54649i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.717905 + 2.54649i) q^{7} +1.00000i q^{8} +(5.09272 + 2.94028i) q^{11} +4.05674i q^{13} +(-1.89497 - 1.84637i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.214504 - 0.371532i) q^{17} +(5.30761 - 3.06435i) q^{19} -5.88057 q^{22} +(1.51729 - 0.876005i) q^{23} +(-2.02837 - 3.51324i) q^{26} +(2.56428 + 0.651521i) q^{28} +0.0419065i q^{29} +(7.92389 + 4.57486i) q^{31} +(0.866025 + 0.500000i) q^{32} +0.429009i q^{34} +(0.536089 + 0.928534i) q^{37} +(-3.06435 + 5.30761i) q^{38} -8.61559 q^{41} +11.0724 q^{43} +(5.09272 - 2.94028i) q^{44} +(-0.876005 + 1.51729i) q^{46} +(0.481567 + 0.834099i) q^{47} +(-5.96922 + 3.65628i) q^{49} +(3.51324 + 2.02837i) q^{52} +(-11.3848 - 6.57304i) q^{53} +(-2.54649 + 0.717905i) q^{56} +(-0.0209532 - 0.0362921i) q^{58} +(6.77318 - 11.7315i) q^{59} +(1.05635 - 0.609885i) q^{61} -9.14972 q^{62} -1.00000 q^{64} +(-6.32352 + 10.9527i) q^{67} +(-0.214504 - 0.371532i) q^{68} -2.54990i q^{71} +(8.08328 + 4.66689i) q^{73} +(-0.928534 - 0.536089i) q^{74} -6.12870i q^{76} +(-3.83131 + 15.0794i) q^{77} +(-5.35961 - 9.28312i) q^{79} +(7.46132 - 4.30780i) q^{82} -10.1027 q^{83} +(-9.58894 + 5.53618i) q^{86} +(-2.94028 + 5.09272i) q^{88} +(-3.15638 - 5.46700i) q^{89} +(-10.3304 + 2.91235i) q^{91} -1.75201i q^{92} +(-0.834099 - 0.481567i) q^{94} -2.59007i q^{97} +(3.34136 - 6.15104i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 12q^{4} - 4q^{7} + O(q^{10}) \) \( 24q + 12q^{4} - 4q^{7} - 12q^{16} + 12q^{19} + 4q^{28} + 28q^{37} + 96q^{43} - 8q^{46} - 52q^{49} - 12q^{52} + 8q^{58} - 12q^{61} - 24q^{64} - 4q^{67} - 12q^{73} + 4q^{79} + 68q^{91} - 24q^{94} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.717905 + 2.54649i 0.271343 + 0.962483i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) 5.09272 + 2.94028i 1.53551 + 0.886529i 0.999093 + 0.0425771i \(0.0135568\pi\)
0.536419 + 0.843952i \(0.319777\pi\)
\(12\) 0 0
\(13\) 4.05674i 1.12514i 0.826751 + 0.562569i \(0.190187\pi\)
−0.826751 + 0.562569i \(0.809813\pi\)
\(14\) −1.89497 1.84637i −0.506452 0.493464i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0.214504 0.371532i 0.0520249 0.0901098i −0.838840 0.544378i \(-0.816766\pi\)
0.890865 + 0.454268i \(0.150099\pi\)
\(18\) 0 0
\(19\) 5.30761 3.06435i 1.21765 0.703010i 0.253234 0.967405i \(-0.418506\pi\)
0.964414 + 0.264395i \(0.0851723\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −5.88057 −1.25374
\(23\) 1.51729 0.876005i 0.316376 0.182660i −0.333400 0.942785i \(-0.608196\pi\)
0.649776 + 0.760126i \(0.274863\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −2.02837 3.51324i −0.397796 0.689003i
\(27\) 0 0
\(28\) 2.56428 + 0.651521i 0.484603 + 0.123126i
\(29\) 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 0.996569 0.0827694i \(-0.0263765\pi\)
0.426604 + 0.904439i \(0.359710\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 0.429009i 0.0735744i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.536089 + 0.928534i 0.0881326 + 0.152650i 0.906722 0.421729i \(-0.138577\pi\)
−0.818589 + 0.574379i \(0.805243\pi\)
\(38\) −3.06435 + 5.30761i −0.497103 + 0.861008i
\(39\) 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
\(43\) 11.0724 1.68852 0.844259 0.535935i \(-0.180041\pi\)
0.844259 + 0.535935i \(0.180041\pi\)
\(44\) 5.09272 2.94028i 0.767756 0.443264i
\(45\) 0 0
\(46\) −0.876005 + 1.51729i −0.129160 + 0.223712i
\(47\) 0.481567 + 0.834099i 0.0702438 + 0.121666i 0.899008 0.437932i \(-0.144289\pi\)
−0.828764 + 0.559598i \(0.810956\pi\)
\(48\) 0 0
\(49\) −5.96922 + 3.65628i −0.852746 + 0.522325i
\(50\) 0 0
\(51\) 0 0
\(52\) 3.51324 + 2.02837i 0.487199 + 0.281284i
\(53\) −11.3848 6.57304i −1.56383 0.902877i −0.996864 0.0791353i \(-0.974784\pi\)
−0.566965 0.823742i \(-0.691883\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.54649 + 0.717905i −0.340289 + 0.0959341i
\(57\) 0 0
\(58\) −0.0209532 0.0362921i −0.00275129 0.00476538i
\(59\) 6.77318 11.7315i 0.881793 1.52731i 0.0324481 0.999473i \(-0.489670\pi\)
0.849345 0.527838i \(-0.176997\pi\)
\(60\) 0 0
\(61\) 1.05635 0.609885i 0.135252 0.0780878i −0.430847 0.902425i \(-0.641785\pi\)
0.566099 + 0.824337i \(0.308452\pi\)
\(62\) −9.14972 −1.16202
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −6.32352 + 10.9527i −0.772541 + 1.33808i 0.163625 + 0.986523i \(0.447681\pi\)
−0.936166 + 0.351558i \(0.885652\pi\)
\(68\) −0.214504 0.371532i −0.0260125 0.0450549i
\(69\) 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
\(73\) 8.08328 + 4.66689i 0.946077 + 0.546218i 0.891860 0.452311i \(-0.149400\pi\)
0.0542168 + 0.998529i \(0.482734\pi\)
\(74\) −0.928534 0.536089i −0.107940 0.0623191i
\(75\) 0 0
\(76\) 6.12870i 0.703010i
\(77\) −3.83131 + 15.0794i −0.436619 + 1.71846i
\(78\) 0 0
\(79\) −5.35961 9.28312i −0.603003 1.04443i −0.992364 0.123347i \(-0.960637\pi\)
0.389360 0.921086i \(-0.372696\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 7.46132 4.30780i 0.823965 0.475717i
\(83\) −10.1027 −1.10891 −0.554457 0.832212i \(-0.687074\pi\)
−0.554457 + 0.832212i \(0.687074\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −9.58894 + 5.53618i −1.03400 + 0.596981i
\(87\) 0 0
\(88\) −2.94028 + 5.09272i −0.313435 + 0.542886i
\(89\) −3.15638 5.46700i −0.334575 0.579501i 0.648828 0.760935i \(-0.275259\pi\)
−0.983403 + 0.181434i \(0.941926\pi\)
\(90\) 0 0
\(91\) −10.3304 + 2.91235i −1.08293 + 0.305298i
\(92\) 1.75201i 0.182660i
\(93\) 0 0
\(94\) −0.834099 0.481567i −0.0860307 0.0496698i
\(95\) 0 0
\(96\) 0 0
\(97\) 2.59007i 0.262982i −0.991317 0.131491i \(-0.958024\pi\)
0.991317 0.131491i \(-0.0419764\pi\)
\(98\) 3.34136 6.15104i 0.337529 0.621349i
\(99\) 0 0
\(100\) 0 0
\(101\) 5.21837 9.03849i 0.519248 0.899363i −0.480502 0.876993i \(-0.659546\pi\)
0.999750 0.0223696i \(-0.00712105\pi\)
\(102\) 0 0
\(103\) −4.28191 + 2.47216i −0.421909 + 0.243589i −0.695894 0.718145i \(-0.744992\pi\)
0.273985 + 0.961734i \(0.411658\pi\)
\(104\) −4.05674 −0.397796
\(105\) 0 0
\(106\) 13.1461 1.27686
\(107\) 0.602588 0.347904i 0.0582544 0.0336332i −0.470590 0.882352i \(-0.655959\pi\)
0.528844 + 0.848719i \(0.322626\pi\)
\(108\) 0 0
\(109\) −2.98417 + 5.16874i −0.285832 + 0.495076i −0.972811 0.231602i \(-0.925603\pi\)
0.686979 + 0.726678i \(0.258937\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.84637 1.89497i 0.174466 0.179058i
\(113\) 0.809894i 0.0761884i −0.999274 0.0380942i \(-0.987871\pi\)
0.999274 0.0380942i \(-0.0121287\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.0362921 + 0.0209532i 0.00336963 + 0.00194546i
\(117\) 0 0
\(118\) 13.5464i 1.24704i
\(119\) 1.10010 + 0.279508i 0.100846 + 0.0256225i
\(120\) 0 0
\(121\) 11.7905 + 20.4218i 1.07187 + 1.85653i
\(122\) −0.609885 + 1.05635i −0.0552164 + 0.0956376i
\(123\) 0 0
\(124\) 7.92389 4.57486i 0.711586 0.410835i
\(125\) 0 0
\(126\) 0 0
\(127\) 11.0265 0.978442 0.489221 0.872160i \(-0.337281\pi\)
0.489221 + 0.872160i \(0.337281\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) 9.44080 + 16.3520i 0.824847 + 1.42868i 0.902036 + 0.431660i \(0.142072\pi\)
−0.0771893 + 0.997016i \(0.524595\pi\)
\(132\) 0 0
\(133\) 11.6137 + 11.3159i 1.00704 + 0.981210i
\(134\) 12.6470i 1.09254i
\(135\) 0 0
\(136\) 0.371532 + 0.214504i 0.0318586 + 0.0183936i
\(137\) 12.4458 + 7.18560i 1.06332 + 0.613907i 0.926348 0.376668i \(-0.122930\pi\)
0.136970 + 0.990575i \(0.456264\pi\)
\(138\) 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
\(142\) 1.27495 + 2.20827i 0.106991 + 0.185314i
\(143\) −11.9280 + 20.6598i −0.997466 + 1.72766i
\(144\) 0 0
\(145\) 0 0
\(146\) −9.33377 −0.772469
\(147\) 0 0
\(148\) 1.07218 0.0881326
\(149\) 8.67934 5.01102i 0.711039 0.410519i −0.100407 0.994946i \(-0.532014\pi\)
0.811446 + 0.584428i \(0.198681\pi\)
\(150\) 0 0
\(151\) −7.20599 + 12.4811i −0.586415 + 1.01570i 0.408283 + 0.912856i \(0.366128\pi\)
−0.994697 + 0.102845i \(0.967206\pi\)
\(152\) 3.06435 + 5.30761i 0.248552 + 0.430504i
\(153\) 0 0
\(154\) −4.22169 14.9748i −0.340193 1.20670i
\(155\) 0 0
\(156\) 0 0
\(157\) −9.41463 5.43554i −0.751370 0.433803i 0.0748190 0.997197i \(-0.476162\pi\)
−0.826189 + 0.563394i \(0.809495\pi\)
\(158\) 9.28312 + 5.35961i 0.738525 + 0.426388i
\(159\) 0 0
\(160\) 0 0
\(161\) 3.32001 + 3.23486i 0.261653 + 0.254943i
\(162\) 0 0
\(163\) 5.31125 + 9.19935i 0.416009 + 0.720549i 0.995534 0.0944058i \(-0.0300951\pi\)
−0.579525 + 0.814955i \(0.696762\pi\)
\(164\) −4.30780 + 7.46132i −0.336382 + 0.582631i
\(165\) 0 0
\(166\) 8.74919 5.05134i 0.679068 0.392060i
\(167\) −3.45341 −0.267233 −0.133617 0.991033i \(-0.542659\pi\)
−0.133617 + 0.991033i \(0.542659\pi\)
\(168\) 0 0
\(169\) −3.45714 −0.265934
\(170\) 0 0
\(171\) 0 0
\(172\) 5.53618 9.58894i 0.422130 0.731150i
\(173\) 3.97759 + 6.88939i 0.302411 + 0.523790i 0.976681 0.214694i \(-0.0688753\pi\)
−0.674271 + 0.738484i \(0.735542\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.88057i 0.443264i
\(177\) 0 0
\(178\) 5.46700 + 3.15638i 0.409769 + 0.236580i
\(179\) −2.38066 1.37447i −0.177939 0.102733i 0.408385 0.912810i \(-0.366092\pi\)
−0.586324 + 0.810077i \(0.699425\pi\)
\(180\) 0 0
\(181\) 6.73202i 0.500387i 0.968196 + 0.250194i \(0.0804943\pi\)
−0.968196 + 0.250194i \(0.919506\pi\)
\(182\) 7.49025 7.68740i 0.555215 0.569828i
\(183\) 0 0
\(184\) 0.876005 + 1.51729i 0.0645800 + 0.111856i
\(185\) 0 0
\(186\) 0 0
\(187\) 2.18482 1.26141i 0.159770 0.0922432i
\(188\) 0.963134 0.0702438
\(189\) 0 0
\(190\) 0 0
\(191\) −21.3740 + 12.3403i −1.54657 + 0.892911i −0.548166 + 0.836369i \(0.684674\pi\)
−0.998400 + 0.0565412i \(0.981993\pi\)
\(192\) 0 0
\(193\) −0.343610 + 0.595151i −0.0247336 + 0.0428399i −0.878127 0.478427i \(-0.841207\pi\)
0.853394 + 0.521267i \(0.174540\pi\)
\(194\) 1.29503 + 2.24306i 0.0929780 + 0.161043i
\(195\) 0 0
\(196\) 0.181816 + 6.99764i 0.0129868 + 0.499831i
\(197\) 0.169154i 0.0120517i 0.999982 + 0.00602586i \(0.00191810\pi\)
−0.999982 + 0.00602586i \(0.998082\pi\)
\(198\) 0 0
\(199\) −0.359798 0.207730i −0.0255054 0.0147256i 0.487193 0.873294i \(-0.338021\pi\)
−0.512699 + 0.858569i \(0.671354\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 10.4367i 0.734327i
\(203\) −0.106714 + 0.0300849i −0.00748988 + 0.00211154i
\(204\) 0 0
\(205\) 0 0
\(206\) 2.47216 4.28191i 0.172244 0.298335i
\(207\) 0 0
\(208\) 3.51324 2.02837i 0.243599 0.140642i
\(209\) 36.0402 2.49295
\(210\) 0 0
\(211\) −2.10135 −0.144663 −0.0723313 0.997381i \(-0.523044\pi\)
−0.0723313 + 0.997381i \(0.523044\pi\)
\(212\) −11.3848 + 6.57304i −0.781915 + 0.451439i
\(213\) 0 0
\(214\) −0.347904 + 0.602588i −0.0237823 + 0.0411921i
\(215\) 0 0
\(216\) 0 0
\(217\) −5.96124 + 23.4624i −0.404675 + 1.59273i
\(218\) 5.96835i 0.404227i
\(219\) 0 0
\(220\) 0 0
\(221\) 1.50721 + 0.870188i 0.101386 + 0.0585352i
\(222\) 0 0
\(223\) 25.9946i 1.74073i −0.492409 0.870364i \(-0.663883\pi\)
0.492409 0.870364i \(-0.336117\pi\)
\(224\) −0.651521 + 2.56428i −0.0435316 + 0.171333i
\(225\) 0 0
\(226\) 0.404947 + 0.701389i 0.0269367 + 0.0466557i
\(227\) 7.15363 12.3905i 0.474803 0.822383i −0.524781 0.851238i \(-0.675853\pi\)
0.999584 + 0.0288545i \(0.00918594\pi\)
\(228\) 0 0
\(229\) −1.36736 + 0.789445i −0.0903576 + 0.0521680i −0.544498 0.838762i \(-0.683280\pi\)
0.454140 + 0.890930i \(0.349946\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.0419065 −0.00275129
\(233\) −15.8144 + 9.13044i −1.03604 + 0.598155i −0.918708 0.394938i \(-0.870766\pi\)
−0.117327 + 0.993093i \(0.537433\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −6.77318 11.7315i −0.440897 0.763656i
\(237\) 0 0
\(238\) −1.09247 + 0.307987i −0.0708141 + 0.0199639i
\(239\) 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 0.0934660 0.995622i \(-0.470205\pi\)
−0.815501 + 0.578755i \(0.803539\pi\)
\(242\) −20.4218 11.7905i −1.31276 0.757924i
\(243\) 0 0
\(244\) 1.21977i 0.0780878i
\(245\) 0 0
\(246\) 0 0
\(247\) 12.4313 + 21.5316i 0.790983 + 1.37002i
\(248\) −4.57486 + 7.92389i −0.290504 + 0.503168i
\(249\) 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
\(253\) 10.3028 0.647732
\(254\) −9.54921 + 5.51324i −0.599171 + 0.345931i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.50065 + 6.06331i 0.218365 + 0.378219i 0.954308 0.298824i \(-0.0965944\pi\)
−0.735943 + 0.677043i \(0.763261\pi\)
\(258\) 0 0
\(259\) −1.97964 + 2.03175i −0.123009 + 0.126247i
\(260\) 0 0
\(261\) 0 0
\(262\) −16.3520 9.44080i −1.01023 0.583255i
\(263\) −10.4091 6.00972i −0.641855 0.370575i 0.143473 0.989654i \(-0.454173\pi\)
−0.785329 + 0.619079i \(0.787506\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −15.7157 3.99298i −0.963590 0.244825i
\(267\) 0 0
\(268\) 6.32352 + 10.9527i 0.386271 + 0.669040i
\(269\) −0.611792 + 1.05966i −0.0373016 + 0.0646083i −0.884074 0.467348i \(-0.845210\pi\)
0.846772 + 0.531956i \(0.178543\pi\)
\(270\) 0 0
\(271\) 14.1888 8.19190i 0.861908 0.497623i −0.00274289 0.999996i \(-0.500873\pi\)
0.864651 + 0.502374i \(0.167540\pi\)
\(272\) −0.429009 −0.0260125
\(273\) 0 0
\(274\) −14.3712 −0.868196
\(275\) 0 0
\(276\) 0 0
\(277\) 6.58712 11.4092i 0.395781 0.685514i −0.597419 0.801929i \(-0.703807\pi\)
0.993201 + 0.116416i \(0.0371404\pi\)
\(278\) 8.38250 + 14.5189i 0.502749 + 0.870786i
\(279\) 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
\(283\) 13.9838 + 8.07354i 0.831249 + 0.479922i 0.854280 0.519813i \(-0.173998\pi\)
−0.0230311 + 0.999735i \(0.507332\pi\)
\(284\) −2.20827 1.27495i −0.131037 0.0756542i
\(285\) 0 0
\(286\) 23.8559i 1.41063i
\(287\) −6.18518 21.9395i −0.365100 1.29505i
\(288\) 0 0
\(289\) 8.40798 + 14.5630i 0.494587 + 0.856649i
\(290\) 0 0
\(291\) 0 0
\(292\) 8.08328 4.66689i 0.473038 0.273109i
\(293\) −24.2757 −1.41820 −0.709100 0.705108i \(-0.750898\pi\)
−0.709100 + 0.705108i \(0.750898\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.928534 + 0.536089i −0.0539699 + 0.0311596i
\(297\) 0 0
\(298\) −5.01102 + 8.67934i −0.290280 + 0.502780i
\(299\) 3.55372 + 6.15523i 0.205517 + 0.355966i
\(300\) 0 0
\(301\) 7.94890 + 28.1956i 0.458167 + 1.62517i
\(302\) 14.4120i 0.829316i
\(303\) 0 0
\(304\) −5.30761 3.06435i −0.304412 0.175752i
\(305\) 0 0
\(306\) 0 0
\(307\) 19.1856i 1.09498i −0.836812 0.547490i \(-0.815583\pi\)
0.836812 0.547490i \(-0.184417\pi\)
\(308\) 11.1435 + 10.8577i 0.634959 + 0.618676i
\(309\) 0 0
\(310\) 0 0
\(311\) −16.3473 + 28.3143i −0.926969 + 1.60556i −0.138606 + 0.990348i \(0.544262\pi\)
−0.788363 + 0.615210i \(0.789071\pi\)
\(312\) 0 0
\(313\) −16.9151 + 9.76593i −0.956097 + 0.552003i −0.894970 0.446127i \(-0.852803\pi\)
−0.0611276 + 0.998130i \(0.519470\pi\)
\(314\) 10.8711 0.613491
\(315\) 0 0
\(316\) −10.7192 −0.603003
\(317\) −12.6110 + 7.28095i −0.708303 + 0.408939i −0.810432 0.585832i \(-0.800768\pi\)
0.102129 + 0.994771i \(0.467434\pi\)
\(318\) 0 0
\(319\) −0.123217 + 0.213418i −0.00689882 + 0.0119491i
\(320\) 0 0
\(321\) 0 0
\(322\) −4.49264 1.14147i −0.250365 0.0636117i
\(323\) 2.62926i 0.146296i
\(324\) 0 0
\(325\) 0 0
\(326\) −9.19935 5.31125i −0.509505 0.294163i
\(327\) 0 0
\(328\) 8.61559i 0.475717i
\(329\) −1.77830 + 1.82511i −0.0980411 + 0.100622i
\(330\) 0 0
\(331\) 4.44833 + 7.70473i 0.244502 + 0.423490i 0.961992 0.273079i \(-0.0880422\pi\)
−0.717489 + 0.696569i \(0.754709\pi\)
\(332\) −5.05134 + 8.74919i −0.277229 + 0.480174i
\(333\) 0 0
\(334\) 2.99074 1.72671i 0.163646 0.0944812i
\(335\) 0 0
\(336\) 0 0
\(337\) 10.3636 0.564543 0.282271 0.959335i \(-0.408912\pi\)
0.282271 + 0.959335i \(0.408912\pi\)
\(338\) 2.99397 1.72857i 0.162850 0.0940217i
\(339\) 0 0
\(340\) 0 0
\(341\) 26.9028 + 46.5970i 1.45687 + 2.52337i
\(342\) 0 0
\(343\) −13.5960 12.5757i −0.734115 0.679025i
\(344\) 11.0724i 0.596981i
\(345\) 0 0
\(346\) −6.88939 3.97759i −0.370376 0.213837i
\(347\) 25.5373 + 14.7440i 1.37091 + 0.791497i 0.991043 0.133542i \(-0.0426353\pi\)
0.379870 + 0.925040i \(0.375969\pi\)
\(348\) 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
\(352\) 2.94028 + 5.09272i 0.156718 + 0.271443i
\(353\) 8.56472 14.8345i 0.455854 0.789562i −0.542883 0.839808i \(-0.682667\pi\)
0.998737 + 0.0502461i \(0.0160006\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.31275 −0.334575
\(357\) 0 0
\(358\) 2.74895 0.145286
\(359\) −19.0997 + 11.0272i −1.00804 + 0.581993i −0.910618 0.413250i \(-0.864394\pi\)
−0.0974241 + 0.995243i \(0.531060\pi\)
\(360\) 0 0
\(361\) 9.28047 16.0743i 0.488446 0.846013i
\(362\) −3.36601 5.83010i −0.176914 0.306423i
\(363\) 0 0
\(364\) −2.64305 + 10.4026i −0.138534 + 0.545245i
\(365\) 0 0
\(366\) 0 0
\(367\) 2.83644 + 1.63762i 0.148061 + 0.0854831i 0.572200 0.820114i \(-0.306090\pi\)
−0.424139 + 0.905597i \(0.639423\pi\)
\(368\) −1.51729 0.876005i −0.0790940 0.0456649i
\(369\) 0 0
\(370\) 0 0
\(371\) 8.56495 33.7102i 0.444670 1.75015i
\(372\) 0 0
\(373\) −18.7209 32.4255i −0.969331 1.67893i −0.697498 0.716587i \(-0.745703\pi\)
−0.271834 0.962344i \(-0.587630\pi\)
\(374\) −1.26141 + 2.18482i −0.0652258 + 0.112974i
\(375\) 0 0
\(376\) −0.834099 + 0.481567i −0.0430154 + 0.0248349i
\(377\) −0.170004 −0.00875563
\(378\) 0 0
\(379\) −37.2066 −1.91117 −0.955587 0.294708i \(-0.904777\pi\)
−0.955587 + 0.294708i \(0.904777\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 12.3403 21.3740i 0.631383 1.09359i
\(383\) −9.13135 15.8160i −0.466590 0.808158i 0.532682 0.846316i \(-0.321184\pi\)
−0.999272 + 0.0381579i \(0.987851\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.687221i 0.0349786i
\(387\) 0 0
\(388\) −2.24306 1.29503i −0.113874 0.0657454i
\(389\) 2.21119 + 1.27663i 0.112112 + 0.0647278i 0.555007 0.831845i \(-0.312715\pi\)
−0.442896 + 0.896573i \(0.646049\pi\)
\(390\) 0 0
\(391\) 0.751627i 0.0380114i
\(392\) −3.65628 5.96922i −0.184670 0.301491i
\(393\) 0 0
\(394\) −0.0845770 0.146492i −0.00426093 0.00738014i
\(395\) 0 0
\(396\) 0 0
\(397\) −17.2994 + 9.98784i −0.868234 + 0.501275i −0.866761 0.498724i \(-0.833802\pi\)
−0.00147306 + 0.999999i \(0.500469\pi\)
\(398\) 0.415459 0.0208251
\(399\) 0 0
\(400\) 0 0
\(401\) 21.2087 12.2448i 1.05911 0.611477i 0.133924 0.990992i \(-0.457242\pi\)
0.925186 + 0.379514i \(0.123909\pi\)
\(402\) 0 0
\(403\) −18.5590 + 32.1452i −0.924490 + 1.60126i
\(404\) −5.21837 9.03849i −0.259624 0.449682i
\(405\) 0 0
\(406\) 0.0773750 0.0794115i 0.00384006 0.00394113i
\(407\) 6.30502i 0.312528i
\(408\) 0 0
\(409\) 14.0020 + 8.08403i 0.692352 + 0.399730i 0.804493 0.593963i \(-0.202437\pi\)
−0.112140 + 0.993692i \(0.535771\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 4.94432i 0.243589i
\(413\) 34.7366 + 8.82575i 1.70928 + 0.434287i
\(414\) 0 0
\(415\) 0 0
\(416\) −2.02837 + 3.51324i −0.0994490 + 0.172251i
\(417\) 0 0
\(418\) −31.2117 + 18.0201i −1.52662 + 0.881392i
\(419\) −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 \(0.677444\pi\)
\(422\) 1.81982 1.05067i 0.0885874 0.0511460i
\(423\) 0 0
\(424\) 6.57304 11.3848i 0.319215 0.552897i
\(425\) 0 0
\(426\) 0 0
\(427\) 2.31143 + 2.25215i 0.111858 + 0.108989i
\(428\) 0.695809i 0.0336332i
\(429\) 0 0
\(430\) 0 0
\(431\) −3.08126 1.77897i −0.148419 0.0856899i 0.423951 0.905685i \(-0.360643\pi\)
−0.572371 + 0.819995i \(0.693976\pi\)
\(432\) 0 0
\(433\) 9.86329i 0.473999i 0.971510 + 0.237000i \(0.0761641\pi\)
−0.971510 + 0.237000i \(0.923836\pi\)
\(434\) −6.56863 23.2997i −0.315304 1.11842i
\(435\) 0 0
\(436\) 2.98417 + 5.16874i 0.142916 + 0.247538i
\(437\) 5.36877 9.29898i 0.256823 0.444831i
\(438\) 0 0
\(439\) −12.1701 + 7.02641i −0.580847 + 0.335352i −0.761470 0.648200i \(-0.775522\pi\)
0.180623 + 0.983552i \(0.442189\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −1.74038 −0.0827812
\(443\) 13.3752 7.72219i 0.635476 0.366892i −0.147394 0.989078i \(-0.547088\pi\)
0.782870 + 0.622186i \(0.213755\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 12.9973 + 22.5120i 0.615440 + 1.06597i
\(447\) 0 0
\(448\) −0.717905 2.54649i −0.0339178 0.120310i
\(449\) 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
\(452\) −0.701389 0.404947i −0.0329906 0.0190471i
\(453\) 0 0
\(454\) 14.3073i 0.671473i
\(455\) 0 0
\(456\) 0 0
\(457\) 6.58150 + 11.3995i 0.307870 + 0.533246i 0.977896 0.209091i \(-0.0670506\pi\)
−0.670026 + 0.742337i \(0.733717\pi\)
\(458\) 0.789445 1.36736i 0.0368883 0.0638925i
\(459\) 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
\(463\) 17.7932 0.826920 0.413460 0.910522i \(-0.364320\pi\)
0.413460 + 0.910522i \(0.364320\pi\)
\(464\) 0.0362921 0.0209532i 0.00168482 0.000972730i
\(465\) 0 0
\(466\) 9.13044 15.8144i 0.422960 0.732587i
\(467\) −1.08094 1.87225i −0.0500201 0.0866373i 0.839931 0.542693i \(-0.182595\pi\)
−0.889951 + 0.456055i \(0.849262\pi\)
\(468\) 0 0
\(469\) −32.4305 8.23982i −1.49750 0.380479i
\(470\) 0 0
\(471\) 0 0
\(472\) 11.7315 + 6.77318i 0.539986 + 0.311761i
\(473\) 56.3884 + 32.5559i 2.59274 + 1.49692i
\(474\) 0 0
\(475\) 0 0
\(476\) 0.792110 0.812958i 0.0363063 0.0372619i
\(477\) 0 0
\(478\) −11.5901 20.0746i −0.530117 0.918190i
\(479\) −6.50176 + 11.2614i −0.297073 + 0.514546i −0.975465 0.220154i \(-0.929344\pi\)
0.678392 + 0.734700i \(0.262677\pi\)
\(480\) 0 0
\(481\) −3.76682 + 2.17478i −0.171752 + 0.0991612i
\(482\) 12.9430 0.589539
\(483\) 0 0
\(484\) 23.5811 1.07187
\(485\) 0 0
\(486\) 0 0
\(487\) −3.15363 + 5.46224i −0.142904 + 0.247518i −0.928589 0.371109i \(-0.878978\pi\)
0.785685 + 0.618627i \(0.212311\pi\)
\(488\) 0.609885 + 1.05635i 0.0276082 + 0.0478188i
\(489\) 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
\(493\) 0.0155696 + 0.00898912i 0.000701220 + 0.000404849i
\(494\) −21.5316 12.4313i −0.968752 0.559309i
\(495\) 0 0
\(496\) 9.14972i 0.410835i
\(497\) 6.49328 1.83058i 0.291264 0.0821129i
\(498\) 0 0
\(499\) 12.1113 + 20.9774i 0.542176 + 0.939076i 0.998779 + 0.0494053i \(0.0157326\pi\)
−0.456603 + 0.889670i \(0.650934\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −19.6806 + 11.3626i −0.878390 + 0.507139i
\(503\) −34.9707 −1.55927 −0.779633 0.626237i \(-0.784594\pi\)
−0.779633 + 0.626237i \(0.784594\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −8.92250 + 5.15141i −0.396653 + 0.229008i
\(507\) 0 0
\(508\) 5.51324 9.54921i 0.244610 0.423678i
\(509\) 9.58793 + 16.6068i 0.424978 + 0.736083i 0.996418 0.0845605i \(-0.0269486\pi\)
−0.571441 + 0.820643i \(0.693615\pi\)
\(510\) 0 0
\(511\) −6.08115 + 23.9344i −0.269014 + 1.05879i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −6.06331 3.50065i −0.267441 0.154407i
\(515\) 0 0
\(516\) 0 0
\(517\) 5.66377i 0.249092i
\(518\) 0.698547 2.74936i 0.0306924 0.120800i
\(519\) 0 0
\(520\) 0 0
\(521\) 10.0953 17.4855i 0.442282 0.766054i −0.555577 0.831465i \(-0.687503\pi\)
0.997858 + 0.0654110i \(0.0208358\pi\)
\(522\) 0 0
\(523\) −8.69476 + 5.01992i −0.380195 + 0.219506i −0.677903 0.735151i \(-0.737111\pi\)
0.297708 + 0.954657i \(0.403778\pi\)
\(524\) 18.8816 0.824847
\(525\) 0 0
\(526\) 12.0194 0.524073
\(527\) 3.39942 1.96265i 0.148081 0.0854946i
\(528\) 0 0
\(529\) −9.96523 + 17.2603i −0.433271 + 0.750447i
\(530\) 0 0
\(531\) 0 0
\(532\) 15.6067 4.39982i 0.676635 0.190757i
\(533\) 34.9512i 1.51391i
\(534\) 0 0
\(535\) 0 0
\(536\) −10.9527 6.32352i −0.473083 0.273135i
\(537\) 0 0
\(538\) 1.22358i 0.0527525i
\(539\) −41.1501 + 1.06918i −1.77246 + 0.0460528i
\(540\) 0 0
\(541\) 8.68907 + 15.0499i 0.373572 + 0.647046i 0.990112 0.140277i \(-0.0447994\pi\)
−0.616540 + 0.787324i \(0.711466\pi\)
\(542\) −8.19190 + 14.1888i −0.351872 + 0.609461i
\(543\) 0 0
\(544\) 0.371532 0.214504i 0.0159293 0.00919679i
\(545\) 0 0
\(546\) 0 0
\(547\) −32.6253 −1.39496 −0.697478 0.716606i \(-0.745695\pi\)
−0.697478 + 0.716606i \(0.745695\pi\)
\(548\) 12.4458 7.18560i 0.531659 0.306954i
\(549\) 0 0
\(550\) 0 0
\(551\) 0.128416 + 0.222423i 0.00547071 + 0.00947555i
\(552\) 0 0
\(553\) 19.7917 20.3126i 0.841628 0.863780i
\(554\) 13.1742i 0.559720i
\(555\) 0 0
\(556\) −14.5189 8.38250i −0.615739 0.355497i
\(557\) −29.5585 17.0656i −1.25243 0.723094i −0.280842 0.959754i \(-0.590614\pi\)
−0.971592 + 0.236660i \(0.923947\pi\)
\(558\) 0 0
\(559\) 44.9177i 1.89981i
\(560\) 0 0
\(561\) 0 0
\(562\) 2.86216 + 4.95741i 0.120733 + 0.209116i
\(563\) −14.8964 + 25.8012i −0.627806 + 1.08739i 0.360185 + 0.932881i \(0.382714\pi\)
−0.987991 + 0.154512i \(0.950620\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −16.1471 −0.678712
\(567\) 0 0
\(568\) 2.54990 0.106991
\(569\) 14.4586 8.34769i 0.606137 0.349953i −0.165315 0.986241i \(-0.552864\pi\)
0.771452 + 0.636287i \(0.219531\pi\)
\(570\) 0 0
\(571\) 0.984264 1.70480i 0.0411902 0.0713435i −0.844695 0.535247i \(-0.820218\pi\)
0.885886 + 0.463904i \(0.153552\pi\)
\(572\) 11.9280 + 20.6598i 0.498733 + 0.863831i
\(573\) 0 0
\(574\) 16.3263 + 15.9076i 0.681446 + 0.663970i
\(575\) 0 0
\(576\) 0 0
\(577\) −34.6146 19.9848i −1.44103 0.831977i −0.443108 0.896468i \(-0.646124\pi\)
−0.997918 + 0.0644912i \(0.979458\pi\)
\(578\) −14.5630 8.40798i −0.605743 0.349726i
\(579\) 0 0
\(580\) 0 0
\(581\) −7.25277 25.7264i −0.300896 1.06731i
\(582\) 0 0
\(583\) −38.6532 66.9493i −1.60085 2.77276i
\(584\) −4.66689 + 8.08328i −0.193117 + 0.334489i
\(585\) 0 0
\(586\) 21.0233 12.1378i 0.868466 0.501409i
\(587\) 25.5123 1.05300 0.526502 0.850174i \(-0.323503\pi\)
0.526502 + 0.850174i \(0.323503\pi\)
\(588\) 0 0
\(589\) 56.0759 2.31057
\(590\) 0 0
\(591\) 0 0
\(592\) 0.536089 0.928534i 0.0220331 0.0381625i
\(593\) −20.1656 34.9279i −0.828103 1.43432i −0.899524 0.436871i \(-0.856087\pi\)
0.0714207 0.997446i \(-0.477247\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10.0220i 0.410519i
\(597\) 0 0
\(598\) −6.15523 3.55372i −0.251706 0.145323i
\(599\) 19.9124 + 11.4964i 0.813600 + 0.469732i 0.848204 0.529669i \(-0.177684\pi\)
−0.0346046 + 0.999401i \(0.511017\pi\)
\(600\) 0 0
\(601\) 25.9443i 1.05829i −0.848532 0.529145i \(-0.822513\pi\)
0.848532 0.529145i \(-0.177487\pi\)
\(602\) −20.9818 20.4437i −0.855153 0.833223i
\(603\) 0 0
\(604\) 7.20599 + 12.4811i 0.293207 + 0.507850i
\(605\) 0 0
\(606\) 0 0
\(607\) 32.8311 18.9551i 1.33257 0.769362i 0.346881 0.937909i \(-0.387241\pi\)
0.985694 + 0.168547i \(0.0539076\pi\)
\(608\) 6.12870 0.248552
\(609\) 0 0
\(610\) 0 0
\(611\) −3.38372 + 1.95359i −0.136891 + 0.0790339i
\(612\) 0 0
\(613\) 10.4012 18.0154i 0.420101 0.727637i −0.575848 0.817557i \(-0.695328\pi\)
0.995949 + 0.0899202i \(0.0286612\pi\)
\(614\) 9.59280 + 16.6152i 0.387134 + 0.670536i
\(615\) 0 0
\(616\) −15.0794 3.83131i −0.607566 0.154368i
\(617\) 40.9298i 1.64777i −0.566755 0.823887i \(-0.691801\pi\)
0.566755 0.823887i \(-0.308199\pi\)
\(618\) 0 0
\(619\) −23.2122 13.4016i −0.932976 0.538654i −0.0452247 0.998977i \(-0.514400\pi\)
−0.887752 + 0.460323i \(0.847734\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 32.6946i 1.31093i
\(623\) 11.6557 11.9625i 0.466975 0.479266i
\(624\) 0 0
\(625\) 0 0
\(626\) 9.76593 16.9151i 0.390325 0.676063i
\(627\) 0 0
\(628\) −9.41463 + 5.43554i −0.375685 + 0.216902i
\(629\) 0.459974 0.0183404
\(630\) 0 0
\(631\) −2.28749 −0.0910636 −0.0455318 0.998963i \(-0.514498\pi\)
−0.0455318 + 0.998963i \(0.514498\pi\)
\(632\) 9.28312 5.35961i 0.369263 0.213194i
\(633\) 0 0
\(634\) 7.28095 12.6110i 0.289164 0.500846i
\(635\) 0 0
\(636\) 0 0
\(637\) −14.8326 24.2156i −0.587687 0.959457i
\(638\) 0.246434i 0.00975641i
\(639\) 0 0
\(640\) 0 0
\(641\) 1.82398 + 1.05307i 0.0720428 + 0.0415939i 0.535589 0.844479i \(-0.320090\pi\)
−0.463546 + 0.886073i \(0.653423\pi\)
\(642\) 0 0
\(643\) 44.2035i 1.74322i −0.490203 0.871608i \(-0.663077\pi\)
0.490203 0.871608i \(-0.336923\pi\)
\(644\) 4.46148 1.25778i 0.175807 0.0495634i
\(645\) 0 0
\(646\) 1.31463 + 2.27701i 0.0517235 + 0.0895877i
\(647\) 10.3540 17.9336i 0.407058 0.705044i −0.587501 0.809223i \(-0.699888\pi\)
0.994559 + 0.104179i \(0.0332215\pi\)
\(648\) 0 0
\(649\) 68.9878 39.8302i 2.70801 1.56347i
\(650\) 0 0
\(651\) 0 0
\(652\) 10.6225 0.416009
\(653\) 23.3860 13.5019i 0.915164 0.528370i 0.0330748 0.999453i \(-0.489470\pi\)
0.882089 + 0.471083i \(0.156137\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.30780 + 7.46132i 0.168191 + 0.291316i
\(657\) 0 0
\(658\) 0.627502 2.46974i 0.0244626 0.0962806i
\(659\) 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 −0.401176 0.916001i \(-0.631398\pi\)
−0.993868 + 0.110572i \(0.964732\pi\)
\(662\) −7.70473 4.44833i −0.299453 0.172889i
\(663\) 0 0
\(664\) 10.1027i 0.392060i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.0367103 + 0.0635841i 0.00142143 + 0.00246199i
\(668\) −1.72671 + 2.99074i −0.0668083 + 0.115715i
\(669\) 0 0
\(670\) 0 0
\(671\) 7.17294 0.276908
\(672\) 0 0
\(673\) 15.2809 0.589037 0.294518 0.955646i \(-0.404841\pi\)
0.294518 + 0.955646i \(0.404841\pi\)
\(674\) −8.97517 + 5.18182i −0.345711 + 0.199596i
\(675\) 0 0
\(676\) −1.72857 + 2.99397i −0.0664834 + 0.115153i
\(677\) 24.2831 + 42.0596i 0.933277 + 1.61648i 0.777679 + 0.628662i \(0.216397\pi\)
0.155598 + 0.987820i \(0.450270\pi\)
\(678\) 0 0
\(679\) 6.59558 1.85942i 0.253115 0.0713581i
\(680\) 0 0
\(681\) 0 0
\(682\) −46.5970 26.9028i −1.78429 1.03016i
\(683\) −10.6643 6.15706i −0.408059 0.235593i 0.281896 0.959445i \(-0.409037\pi\)
−0.689956 + 0.723852i \(0.742370\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 18.0623 + 4.09288i 0.689624 + 0.156267i
\(687\) 0 0
\(688\) −5.53618 9.58894i −0.211065 0.365575i
\(689\) 26.6651 46.1854i 1.01586 1.75952i
\(690\) 0 0
\(691\) 36.8280 21.2626i 1.40100 0.808869i 0.406507 0.913648i \(-0.366747\pi\)
0.994496 + 0.104779i \(0.0334134\pi\)
\(692\) 7.95518 0.302411
\(693\) 0 0
\(694\) −29.4879 −1.11935
\(695\) 0 0
\(696\) 0 0
\(697\) −1.84808 + 3.20097i −0.0700011 + 0.121245i
\(698\) 4.42882 + 7.67094i 0.167633 + 0.290349i
\(699\) 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
\(703\) 5.69071 + 3.28553i 0.214629 + 0.123916i
\(704\) −5.09272 2.94028i −0.191939 0.110816i
\(705\) 0 0
\(706\) 17.1294i 0.644675i
\(707\) 26.7627 + 6.79976i 1.00652 + 0.255731i
\(708\) 0 0
\(709\) 10.4912 + 18.1712i 0.394004 + 0.682435i 0.992974 0.118337i \(-0.0377562\pi\)
−0.598969 + 0.800772i \(0.704423\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 5.46700 3.15638i 0.204885 0.118290i
\(713\) 16.0304 0.600343
\(714\) 0 0
\(715\) 0 0
\(716\) −2.38066 + 1.37447i −0.0889694 + 0.0513665i
\(717\) 0 0
\(718\) 11.0272 19.0997i 0.411531 0.712793i
\(719\) −8.73253 15.1252i −0.325668 0.564074i 0.655979 0.754779i \(-0.272256\pi\)
−0.981647 + 0.190705i \(0.938923\pi\)
\(720\) 0 0
\(721\) −9.36934 9.12906i −0.348932 0.339984i
\(722\) 18.5609i 0.690767i
\(723\) 0 0
\(724\) 5.83010 + 3.36601i 0.216674 + 0.125097i
\(725\) 0 0
\(726\) 0 0
\(727\) 12.4470i 0.461633i −0.972997 0.230816i \(-0.925860\pi\)
0.972997 0.230816i \(-0.0741397\pi\)
\(728\) −2.91235 10.3304i −0.107939 0.382872i
\(729\) 0 0
\(730\) 0 0
\(731\) 2.37507 4.11374i 0.0878450 0.152152i
\(732\) 0 0
\(733\) −19.3654 + 11.1806i −0.715279 + 0.412966i −0.813012 0.582246i \(-0.802174\pi\)
0.0977339 + 0.995213i \(0.468841\pi\)
\(734\) −3.27524 −0.120891
\(735\) 0 0
\(736\) 1.75201 0.0645800
\(737\) −64.4079 + 37.1859i −2.37249 + 1.36976i
\(738\) 0 0
\(739\) 15.9125 27.5613i 0.585351 1.01386i −0.409481 0.912319i \(-0.634290\pi\)
0.994832 0.101539i \(-0.0323765\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 9.43764 + 33.4764i 0.346467 + 1.22896i
\(743\) 15.1736i 0.556667i −0.960485 0.278333i \(-0.910218\pi\)
0.960485 0.278333i \(-0.0897820\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 32.4255 + 18.7209i 1.18718 + 0.685421i
\(747\) 0 0
\(748\) 2.52281i 0.0922432i
\(749\) 1.31854 + 1.28472i 0.0481783 + 0.0469427i
\(750\) 0 0
\(751\) 10.4956 + 18.1790i 0.382991 + 0.663360i 0.991488 0.130196i \(-0.0415607\pi\)
−0.608497 + 0.793556i \(0.708227\pi\)
\(752\) 0.481567 0.834099i 0.0175609 0.0304164i
\(753\) 0 0
\(754\) 0.147227 0.0850018i 0.00536171 0.00309558i
\(755\) 0 0
\(756\) 0 0
\(757\) −17.0421 −0.619407 −0.309704 0.950833i \(-0.600230\pi\)
−0.309704 + 0.950833i \(0.600230\pi\)
\(758\) 32.2219 18.6033i 1.17035 0.675702i
\(759\) 0 0
\(760\) 0 0
\(761\) 3.13659 + 5.43274i 0.113701 + 0.196937i 0.917260 0.398289i \(-0.130396\pi\)
−0.803559 + 0.595226i \(0.797063\pi\)
\(762\) 0 0
\(763\) −15.3045 3.88850i −0.554060 0.140773i
\(764\) 24.6805i 0.892911i
\(765\) 0 0
\(766\) 15.8160 + 9.13135i 0.571454 + 0.329929i
\(767\) 47.5916 + 27.4770i 1.71843 + 0.992139i
\(768\) 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
\(772\) 0.343610 + 0.595151i 0.0123668 + 0.0214199i
\(773\) 22.2466 38.5322i 0.800153 1.38591i −0.119361 0.992851i \(-0.538085\pi\)
0.919515 0.393055i \(-0.128582\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 2.59007 0.0929780
\(777\) 0 0
\(778\) −2.55326 −0.0915390
\(779\) −45.7282 + 26.4012i −1.63838 + 0.945921i
\(780\) 0 0
\(781\) 7.49741 12.9859i 0.268279 0.464672i
\(782\) 0.375814 + 0.650928i 0.0134391 + 0.0232771i
\(783\) 0 0
\(784\) 6.15104 + 3.34136i 0.219680 + 0.119334i
\(785\) 0 0
\(786\) 0 0
\(787\) 13.3112 + 7.68522i 0.474493 + 0.273948i 0.718118 0.695921i \(-0.245004\pi\)
−0.243626 + 0.969869i \(0.578337\pi\)