Properties

Label 3150.2.bf.d.1601.7
Level 3150
Weight 2
Character 3150.1601
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 1601.7
Character \(\chi\) = 3150.1601
Dual form 3150.2.bf.d.1151.7

$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 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 −0.536419 + 0.843952i \(0.680223\pi\)
−0.999093 + 0.0425771i \(0.986443\pi\)
\(12\) 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 \(-0.183234\pi\)
−0.890865 + 0.454268i \(0.849901\pi\)
\(18\) 0 0
\(19\) 5.30761 + 3.06435i 1.21765 + 0.703010i 0.964414 0.264395i \(-0.0851723\pi\)
0.253234 + 0.967405i \(0.418506\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −5.88057 −1.25374
\(23\) −1.51729 0.876005i −0.316376 0.182660i 0.333400 0.942785i \(-0.391804\pi\)
−0.649776 + 0.760126i \(0.725137\pi\)
\(24\) 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 0.426604 0.904439i \(-0.359710\pi\)
0.996569 + 0.0827694i \(0.0263765\pi\)
\(32\) −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 \(-0.805243\pi\)
0.906722 + 0.421729i \(0.138577\pi\)
\(38\) 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 \(-0.180041\pi\)
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 \(-0.855711\pi\)
0.828764 + 0.559598i \(0.189044\pi\)
\(48\) 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 0.566965 0.823742i \(-0.308117\pi\)
0.996864 0.0791353i \(-0.0252159\pi\)
\(54\) 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 −0.849345 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 \(0.641785\pi\)
\(62\) 9.14972 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 −0.936166 0.351558i \(-0.885652\pi\)
0.163625 0.986523i \(-0.447681\pi\)
\(68\) 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 0.0542168 0.998529i \(-0.482734\pi\)
0.891860 + 0.452311i \(0.149400\pi\)
\(74\) 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 0.389360 + 0.921086i \(0.372696\pi\)
−0.992364 + 0.123347i \(0.960637\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 7.46132 + 4.30780i 0.823965 + 0.475717i
\(83\) 10.1027 1.10891 0.554457 0.832212i \(-0.312926\pi\)
0.554457 + 0.832212i \(0.312926\pi\)
\(84\) 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 \(-0.724741\pi\)
0.983403 + 0.181434i \(0.0580739\pi\)
\(90\) 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 −0.999750 0.0223696i \(-0.992879\pi\)
0.480502 0.876993i \(-0.340454\pi\)
\(102\) 0 0
\(103\) −4.28191 2.47216i −0.421909 0.243589i 0.273985 0.961734i \(-0.411658\pi\)
−0.695894 + 0.718145i \(0.744992\pi\)
\(104\) 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 \(-0.344041\pi\)
−0.528844 + 0.848719i \(0.677374\pi\)
\(108\) 0 0
\(109\) −2.98417 5.16874i −0.285832 0.495076i 0.686979 0.726678i \(-0.258937\pi\)
−0.972811 + 0.231602i \(0.925603\pi\)
\(110\) 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 0.0771893 + 0.997016i \(0.475405\pi\)
−0.902036 + 0.431660i \(0.857928\pi\)
\(132\) 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 \(-0.877070\pi\)
−0.136970 + 0.990575i \(0.543736\pi\)
\(138\) 0 0
\(139\) 16.7650i 1.42199i 0.703198 + 0.710994i \(0.251755\pi\)
−0.703198 + 0.710994i \(0.748245\pi\)
\(140\) 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 \(-0.467986\pi\)
−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 \(-0.366128\pi\)
\(152\) −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 \(-0.809495\pi\)
0.0748190 + 0.997197i \(0.476162\pi\)
\(158\) −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 \(-0.696762\pi\)
0.995534 + 0.0944058i \(0.0300951\pi\)
\(164\) 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 \(-0.457341\pi\)
0.133617 + 0.991033i \(0.457341\pi\)
\(168\) 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 \(-0.931125\pi\)
0.674271 + 0.738484i \(0.264458\pi\)
\(174\) 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 \(-0.633908\pi\)
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 \(-0.0804943\pi\)
\(182\) −7.49025 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 0.998400 + 0.0565412i \(0.0180072\pi\)
0.548166 + 0.836369i \(0.315326\pi\)
\(192\) 0 0
\(193\) −0.343610 0.595151i −0.0247336 0.0428399i 0.853394 0.521267i \(-0.174540\pi\)
−0.878127 + 0.478427i \(0.841207\pi\)
\(194\) −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 −0.512699 0.858569i \(-0.671354\pi\)
0.487193 + 0.873294i \(0.338021\pi\)
\(200\) 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 \(-0.324147\pi\)
−0.999584 + 0.0288545i \(0.990814\pi\)
\(228\) 0 0
\(229\) −1.36736 0.789445i −0.0903576 0.0521680i 0.454140 0.890930i \(-0.349946\pi\)
−0.544498 + 0.838762i \(0.683280\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.0419065 −0.00275129
\(233\) 15.8144 + 9.13044i 1.03604 + 0.598155i 0.918708 0.394938i \(-0.129234\pi\)
0.117327 + 0.993093i \(0.462567\pi\)
\(234\) 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 −0.815501 0.578755i \(-0.803539\pi\)
0.0934660 + 0.995622i \(0.470205\pi\)
\(242\) 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 \(-0.903406\pi\)
0.735943 + 0.677043i \(0.236739\pi\)
\(258\) 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 \(-0.545827\pi\)
0.785329 + 0.619079i \(0.212494\pi\)
\(264\) 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 \(-0.154790\pi\)
−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 \(0.500873\pi\)
\(272\) 0.429009 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 \(-0.0371404\pi\)
−0.597419 + 0.801929i \(0.703807\pi\)
\(278\) −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 −0.0230311 0.999735i \(-0.507332\pi\)
0.854280 + 0.519813i \(0.173998\pi\)
\(284\) 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 \(-0.249102\pi\)
0.709100 + 0.705108i \(0.249102\pi\)
\(294\) 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 0.788363 + 0.615210i \(0.210929\pi\)
0.138606 + 0.990348i \(0.455738\pi\)
\(312\) 0 0
\(313\) −16.9151 9.76593i −0.956097 0.552003i −0.0611276 0.998130i \(-0.519470\pi\)
−0.894970 + 0.446127i \(0.852803\pi\)
\(314\) −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 \(-0.199232\pi\)
−0.102129 + 0.994771i \(0.532566\pi\)
\(318\) 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 −0.717489 0.696569i \(-0.754709\pi\)
0.961992 + 0.273079i \(0.0880422\pi\)
\(332\) 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 \(-0.957365\pi\)
−0.379870 + 0.925040i \(0.624031\pi\)
\(348\) 0 0
\(349\) 8.85764i 0.474138i 0.971493 + 0.237069i \(0.0761868\pi\)
−0.971493 + 0.237069i \(0.923813\pi\)
\(350\) 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 \(-0.317333\pi\)
−0.998737 + 0.0502461i \(0.983999\pi\)
\(354\) 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 \(-0.135606\pi\)
0.0974241 + 0.995243i \(0.468940\pi\)
\(360\) 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 \(-0.639423\pi\)
0.572200 + 0.820114i \(0.306090\pi\)
\(368\) 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 −0.271834 + 0.962344i \(0.587630\pi\)
−0.697498 + 0.716587i \(0.745703\pi\)
\(374\) 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 \(-0.678816\pi\)
0.999272 + 0.0381579i \(0.0121490\pi\)
\(384\) 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 \(-0.687285\pi\)
0.442896 + 0.896573i \(0.353951\pi\)
\(390\) 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 \(-0.500469\pi\)
−0.866761 + 0.498724i \(0.833802\pi\)
\(398\) −0.415459 −0.0208251
\(399\) 0 0
\(400\) 0 0
\(401\) −21.2087 12.2448i −1.05911 0.611477i −0.133924 0.990992i \(-0.542758\pi\)
−0.925186 + 0.379514i \(0.876091\pi\)
\(402\) 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 −0.112140 0.993692i \(-0.535771\pi\)
0.804493 + 0.593963i \(0.202437\pi\)
\(410\) 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 −0.423951 0.905685i \(-0.639357\pi\)
0.572371 + 0.819995i \(0.306024\pi\)
\(432\) 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 0.180623 0.983552i \(-0.442189\pi\)
−0.761470 + 0.648200i \(0.775522\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −1.74038 −0.0827812
\(443\) −13.3752 7.72219i −0.635476 0.366892i 0.147394 0.989078i \(-0.452912\pi\)
−0.782870 + 0.622186i \(0.786245\pi\)
\(444\) 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 −0.670026 0.742337i \(-0.733717\pi\)
0.977896 + 0.209091i \(0.0670506\pi\)
\(458\) −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 \(-0.364320\pi\)
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 \(-0.817405\pi\)
0.889951 + 0.456055i \(0.150738\pi\)
\(468\) 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 \(-0.0706561\pi\)
−0.678392 + 0.734700i \(0.737323\pi\)
\(480\) 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 \(-0.212311\pi\)
−0.928589 + 0.371109i \(0.878978\pi\)
\(488\) −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 −0.456603 0.889670i \(-0.650934\pi\)
0.998779 0.0494053i \(-0.0157326\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −19.6806 11.3626i −0.878390 0.507139i
\(503\) 34.9707 1.55927 0.779633 0.626237i \(-0.215406\pi\)
0.779633 + 0.626237i \(0.215406\pi\)
\(504\) 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 \(-0.973051\pi\)
0.571441 + 0.820643i \(0.306385\pi\)
\(510\) 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 \(-0.312497\pi\)
−0.997858 + 0.0654110i \(0.979164\pi\)
\(522\) 0 0
\(523\) −8.69476 5.01992i −0.380195 0.219506i 0.297708 0.954657i \(-0.403778\pi\)
−0.677903 + 0.735151i \(0.737111\pi\)
\(524\) −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 −0.616540 0.787324i \(-0.711466\pi\)
0.990112 + 0.140277i \(0.0447994\pi\)
\(542\) 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 \(-0.409386\pi\)
0.971592 + 0.236660i \(0.0760528\pi\)
\(558\) 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 0.987991 + 0.154512i \(0.0493804\pi\)
−0.360185 + 0.932881i \(0.617286\pi\)
\(564\) 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 \(-0.447136\pi\)
−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 \(0.820218\pi\)
\(572\) −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 \(-0.979458\pi\)
−0.443108 + 0.896468i \(0.646124\pi\)
\(578\) 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 \(-0.676497\pi\)
−0.526502 + 0.850174i \(0.676497\pi\)
\(588\) 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 −0.0714207 0.997446i \(-0.522753\pi\)
0.899524 0.436871i \(-0.143913\pi\)
\(594\) 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 \(-0.822316\pi\)
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 \(0.822513\pi\)
\(602\) 20.9818 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 \(-0.0539076\pi\)
0.346881 + 0.937909i \(0.387241\pi\)
\(608\) −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 \(-0.0286612\pi\)
−0.575848 + 0.817557i \(0.695328\pi\)
\(614\) −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 −0.887752 0.460323i \(-0.847734\pi\)
−0.0452247 + 0.998977i \(0.514400\pi\)
\(620\) 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 \(-0.679910\pi\)
0.463546 + 0.886073i \(0.346577\pi\)
\(642\) 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 \(-0.300112\pi\)
−0.994559 + 0.104179i \(0.966779\pi\)
\(648\) 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 \(-0.510530\pi\)
−0.882089 + 0.471083i \(0.843863\pi\)
\(654\) 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 −0.993868 0.110572i \(-0.964732\pi\)
−0.401176 + 0.916001i \(0.631398\pi\)
\(662\) 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 −0.155598 + 0.987820i \(0.549730\pi\)
−0.777679 + 0.628662i \(0.783603\pi\)
\(678\) 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 \(-0.590963\pi\)
0.689956 + 0.723852i \(0.257630\pi\)
\(684\) 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 0.994496 0.104779i \(-0.0334134\pi\)
0.406507 + 0.913648i \(0.366747\pi\)
\(692\) −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 −0.598969 0.800772i \(-0.704423\pi\)
0.992974 + 0.118337i \(0.0377562\pi\)
\(710\) 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 \(-0.727744\pi\)
0.981647 + 0.190705i \(0.0610773\pi\)
\(720\) 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 \(-0.468841\pi\)
−0.813012 + 0.582246i \(0.802174\pi\)
\(734\) 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 0.994832 + 0.101539i \(0.0323765\pi\)
−0.409481 + 0.912319i \(0.634290\pi\)
\(740\) 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 −0.608497 0.793556i \(-0.708227\pi\)
0.991488 + 0.130196i \(0.0415607\pi\)
\(752\) −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 \(-0.869604\pi\)
0.803559 + 0.595226i \(0.202937\pi\)
\(762\) 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 \(-0.877723\pi\)
0.927119 0.374767i \(-0.122277\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.343610 0.595151i 0.0123668 0.0214199i
\(773\) −22.2466 38.5322i −0.800153 1.38591i −0.919515 0.393055i \(-0.871418\pi\)
0.119361 0.992851i \(-0.461915\pi\)
\(774\) 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 \(-0.578337\pi\)
0.718118 + 0.695921i \(0.245004\pi\)