Properties

Label 3150.2.bf.e.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.e.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 \(-0.986443\pi\)
−0.536419 0.843952i \(-0.680223\pi\)
\(12\) 0 0
\(13\) 4.05674i 1.12514i −0.826751 0.562569i \(-0.809813\pi\)
0.826751 0.562569i \(-0.190187\pi\)
\(14\) 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 \(-0.998761\pi\)
0.999992 0.00389092i \(-0.00123852\pi\)
\(30\) 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 0.818589 0.574379i \(-0.194757\pi\)
−0.906722 + 0.421729i \(0.861423\pi\)
\(38\) −3.06435 + 5.30761i −0.497103 + 0.861008i
\(39\) 0 0
\(40\) 0 0
\(41\) 8.61559 1.34553 0.672765 0.739856i \(-0.265107\pi\)
0.672765 + 0.739856i \(0.265107\pi\)
\(42\) 0 0
\(43\) −11.0724 −1.68852 −0.844259 0.535935i \(-0.819959\pi\)
−0.844259 + 0.535935i \(0.819959\pi\)
\(44\) −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 \(0.510330\pi\)
−0.849345 + 0.527838i \(0.823003\pi\)
\(60\) 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 \(-0.552319\pi\)
0.936166 0.351558i \(-0.114348\pi\)
\(68\) −0.214504 0.371532i −0.0260125 0.0450549i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.54990i 0.302617i 0.988487 + 0.151308i \(0.0483487\pi\)
−0.988487 + 0.151308i \(0.951651\pi\)
\(72\) 0 0
\(73\) −8.08328 4.66689i −0.946077 0.546218i −0.0542168 0.998529i \(-0.517266\pi\)
−0.891860 + 0.452311i \(0.850600\pi\)
\(74\) 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 0.983403 0.181434i \(-0.0580739\pi\)
−0.648828 + 0.760935i \(0.724741\pi\)
\(90\) 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 \(0.0419764\pi\)
−0.991317 + 0.131491i \(0.958024\pi\)
\(98\) 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 \(0.340454\pi\)
−0.999750 + 0.0223696i \(0.992879\pi\)
\(102\) 0 0
\(103\) 4.28191 2.47216i 0.421909 0.243589i −0.273985 0.961734i \(-0.588342\pi\)
0.695894 + 0.718145i \(0.255008\pi\)
\(104\) 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 \(-0.662719\pi\)
−0.489221 + 0.872160i \(0.662719\pi\)
\(128\) 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 \(-0.857928\pi\)
0.0771893 0.997016i \(-0.475405\pi\)
\(132\) 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 −0.811446 0.584428i \(-0.801319\pi\)
0.100407 + 0.994946i \(0.467986\pi\)
\(150\) 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 0.826189 0.563394i \(-0.190505\pi\)
−0.0748190 + 0.997197i \(0.523838\pi\)
\(158\) 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 0.579525 0.814955i \(-0.303238\pi\)
−0.995534 + 0.0944058i \(0.969905\pi\)
\(164\) 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 0.586324 0.810077i \(-0.300575\pi\)
−0.408385 + 0.912810i \(0.633908\pi\)
\(180\) 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 \(-0.315326\pi\)
0.998400 0.0565412i \(-0.0180072\pi\)
\(192\) 0 0
\(193\) 0.343610 0.595151i 0.0247336 0.0428399i −0.853394 0.521267i \(-0.825460\pi\)
0.878127 + 0.478427i \(0.158793\pi\)
\(194\) −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 \(0.336117\pi\)
−0.492409 + 0.870364i \(0.663883\pi\)
\(224\) 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 \(-0.730198\pi\)
0.661779 0.749699i \(-0.269802\pi\)
\(240\) 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 \(-0.754578\pi\)
−0.717203 + 0.696865i \(0.754578\pi\)
\(252\) 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 −0.846772 0.531956i \(-0.821457\pi\)
0.884074 + 0.467348i \(0.154790\pi\)
\(270\) 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 −0.993201 0.116416i \(-0.962860\pi\)
0.597419 + 0.801929i \(0.296193\pi\)
\(278\) 8.38250 + 14.5189i 0.502749 + 0.870786i
\(279\) 0 0
\(280\) 0 0
\(281\) 5.72433i 0.341485i 0.985316 + 0.170742i \(0.0546166\pi\)
−0.985316 + 0.170742i \(0.945383\pi\)
\(282\) 0 0
\(283\) −13.9838 8.07354i −0.831249 0.479922i 0.0230311 0.999735i \(-0.492668\pi\)
−0.854280 + 0.519813i \(0.826002\pi\)
\(284\) 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 \(0.184417\pi\)
−0.836812 + 0.547490i \(0.815583\pi\)
\(308\) 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 \(-0.455738\pi\)
0.788363 0.615210i \(-0.210929\pi\)
\(312\) 0 0
\(313\) 16.9151 9.76593i 0.956097 0.552003i 0.0611276 0.998130i \(-0.480530\pi\)
0.894970 + 0.446127i \(0.147197\pi\)
\(314\) −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 \(-0.591088\pi\)
−0.282271 + 0.959335i \(0.591088\pi\)
\(338\) 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 0.0974241 0.995243i \(-0.468940\pi\)
0.910618 + 0.413250i \(0.135606\pi\)
\(360\) 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 0.424139 0.905597i \(-0.360577\pi\)
−0.572200 + 0.820114i \(0.693910\pi\)
\(368\) −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 \(0.254297\pi\)
0.271834 + 0.962344i \(0.412370\pi\)
\(374\) 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 0.442896 0.896573i \(-0.353951\pi\)
−0.555007 + 0.831845i \(0.687285\pi\)
\(390\) 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 0.00147306 0.999999i \(-0.499531\pi\)
0.866761 + 0.498724i \(0.166198\pi\)
\(398\) 0.415459 0.0208251
\(399\) 0 0
\(400\) 0 0
\(401\) −21.2087 + 12.2448i −1.05911 + 0.611477i −0.925186 0.379514i \(-0.876091\pi\)
−0.133924 + 0.990992i \(0.542758\pi\)
\(402\) 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 \(-0.387553\pi\)
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 \(0.677444\pi\)
\(422\) 1.81982 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 0.572371 0.819995i \(-0.306024\pi\)
−0.423951 + 0.905685i \(0.639357\pi\)
\(432\) 0 0
\(433\) 9.86329i 0.473999i −0.971510 0.237000i \(-0.923836\pi\)
0.971510 0.237000i \(-0.0761641\pi\)
\(434\) 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 \(0.00120064\pi\)
−0.999993 + 0.00377192i \(0.998799\pi\)
\(450\) 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 0.670026 0.742337i \(-0.266283\pi\)
−0.977896 + 0.209091i \(0.932949\pi\)
\(458\) 0.789445 1.36736i 0.0368883 0.0638925i
\(459\) 0 0
\(460\) 0 0
\(461\) −20.7565 −0.966725 −0.483363 0.875420i \(-0.660585\pi\)
−0.483363 + 0.875420i \(0.660585\pi\)
\(462\) 0 0
\(463\) −17.7932 −0.826920 −0.413460 0.910522i \(-0.635680\pi\)
−0.413460 + 0.910522i \(0.635680\pi\)
\(464\) −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 −0.678392 0.734700i \(-0.737323\pi\)
0.975465 + 0.220154i \(0.0706561\pi\)
\(480\) 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 −0.785685 0.618627i \(-0.787689\pi\)
0.928589 + 0.371109i \(0.121022\pi\)
\(488\) 0.609885 + 1.05635i 0.0276082 + 0.0478188i
\(489\) 0 0
\(490\) 0 0
\(491\) 14.6640i 0.661776i 0.943670 + 0.330888i \(0.107348\pi\)
−0.943670 + 0.330888i \(0.892652\pi\)
\(492\) 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 0.571441 0.820643i \(-0.306385\pi\)
−0.996418 + 0.0845605i \(0.973051\pi\)
\(510\) 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 −0.997858 0.0654110i \(-0.979164\pi\)
0.555577 + 0.831465i \(0.312497\pi\)
\(522\) 0 0
\(523\) 8.69476 5.01992i 0.380195 0.219506i −0.297708 0.954657i \(-0.596222\pi\)
0.677903 + 0.735151i \(0.262889\pi\)
\(524\) −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 \(-0.254305\pi\)
0.697478 + 0.716606i \(0.254305\pi\)
\(548\) 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 −0.771452 0.636287i \(-0.780469\pi\)
0.165315 + 0.986241i \(0.447136\pi\)
\(570\) 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 0.997918 0.0644912i \(-0.0205424\pi\)
0.443108 + 0.896468i \(0.353876\pi\)
\(578\) −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 0.0346046 0.999401i \(-0.488983\pi\)
−0.848204 + 0.529669i \(0.822316\pi\)
\(600\) 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 −0.985694 0.168547i \(-0.946092\pi\)
−0.346881 + 0.937909i \(0.612759\pi\)
\(608\) 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 −0.995949 0.0899202i \(-0.971339\pi\)
0.575848 + 0.817557i \(0.304672\pi\)
\(614\) −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 0.463546 0.886073i \(-0.346577\pi\)
−0.535589 + 0.844479i \(0.679910\pi\)
\(642\) 0 0
\(643\) 44.2035i 1.74322i 0.490203 + 0.871608i \(0.336923\pi\)
−0.490203 + 0.871608i \(0.663077\pi\)
\(644\) −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 \(-0.904287\pi\)
0.955132 0.296181i \(-0.0957133\pi\)
\(660\) 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 \(-0.595159\pi\)
−0.294518 + 0.955646i \(0.595159\pi\)
\(674\) 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 \(0.0130045\pi\)
−0.999166 + 0.0408435i \(0.986995\pi\)
\(702\) 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 0.981647 0.190705i \(-0.0610773\pi\)
−0.655979 + 0.754779i \(0.727744\pi\)
\(720\) 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 \(0.0741397\pi\)
−0.972997 + 0.230816i \(0.925860\pi\)
\(728\) −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 −0.0977339 0.995213i \(-0.531159\pi\)
0.813012 + 0.582246i \(0.197826\pi\)
\(734\) 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 \(-0.399770\pi\)
0.309704 + 0.950833i \(0.399770\pi\)
\(758\) 32.2219 18.6033i 1.17035 0.675702i
\(759\) 0 0
\(760\) 0 0
\(761\) −3.13659 5.43274i −0.113701 0.196937i 0.803559 0.595226i \(-0.202937\pi\)
−0.917260 + 0.398289i \(0.869604\pi\)
\(762\) 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 0.243626 0.969869i \(-0.421663\pi\)