Properties

Label 3150.2.bf.f.1151.2
Level 3150
Weight 2
Character 3150.1151
Analytic conductor 25.153
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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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: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.2
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.f.1601.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.54232 + 0.732536i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.54232 + 0.732536i) q^{7} +1.00000i q^{8} +(2.07577 + 1.19845i) q^{11} -5.67714i q^{13} +(-2.56798 + 0.636766i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.03596 + 1.79434i) q^{17} +(5.12164 - 2.95698i) q^{19} -2.39690 q^{22} +(1.61233 - 0.930877i) q^{23} +(2.83857 + 4.91654i) q^{26} +(1.90555 - 1.83545i) q^{28} -4.88913i q^{29} +(-3.92008 - 2.26326i) q^{31} +(0.866025 + 0.500000i) q^{32} -2.07192i q^{34} +(-1.48455 - 2.57132i) q^{37} +(-2.95698 + 5.12164i) q^{38} +7.04428 q^{41} -8.55956 q^{43} +(2.07577 - 1.19845i) q^{44} +(-0.930877 + 1.61233i) q^{46} +(-2.78941 - 4.83140i) q^{47} +(5.92678 + 3.72468i) q^{49} +(-4.91654 - 2.83857i) q^{52} +(-3.62931 - 2.09538i) q^{53} +(-0.732536 + 2.54232i) q^{56} +(2.44457 + 4.23411i) q^{58} +(-1.00312 + 1.73746i) q^{59} +(10.7862 - 6.22739i) q^{61} +4.52651 q^{62} -1.00000 q^{64} +(3.81111 - 6.60103i) q^{67} +(1.03596 + 1.79434i) q^{68} +9.14126i q^{71} +(0.937339 + 0.541173i) q^{73} +(2.57132 + 1.48455i) q^{74} -5.91397i q^{76} +(4.39937 + 4.56742i) q^{77} +(-8.38392 - 14.5214i) q^{79} +(-6.10053 + 3.52214i) q^{82} -13.6122 q^{83} +(7.41279 - 4.27978i) q^{86} +(-1.19845 + 2.07577i) q^{88} +(6.63129 + 11.4857i) q^{89} +(4.15870 - 14.4331i) q^{91} -1.86175i q^{92} +(4.83140 + 2.78941i) q^{94} +12.8260i q^{97} +(-6.99508 - 0.262276i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 16q^{4} + O(q^{10}) \) \( 32q + 16q^{4} - 16q^{16} - 48q^{19} + 24q^{31} - 16q^{46} + 56q^{49} + 48q^{61} - 32q^{64} - 8q^{79} - 56q^{91} + 120q^{94} + O(q^{100}) \)

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
\(7\) 2.54232 + 0.732536i 0.960907 + 0.276872i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) 2.07577 + 1.19845i 0.625869 + 0.361346i 0.779150 0.626837i \(-0.215651\pi\)
−0.153282 + 0.988183i \(0.548984\pi\)
\(12\) 0 0
\(13\) 5.67714i 1.57455i −0.616599 0.787277i \(-0.711490\pi\)
0.616599 0.787277i \(-0.288510\pi\)
\(14\) −2.56798 + 0.636766i −0.686322 + 0.170183i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.03596 + 1.79434i −0.251258 + 0.435191i −0.963872 0.266365i \(-0.914177\pi\)
0.712615 + 0.701556i \(0.247511\pi\)
\(18\) 0 0
\(19\) 5.12164 2.95698i 1.17499 0.678378i 0.220136 0.975469i \(-0.429350\pi\)
0.954849 + 0.297091i \(0.0960164\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.39690 −0.511020
\(23\) 1.61233 0.930877i 0.336193 0.194101i −0.322394 0.946606i \(-0.604488\pi\)
0.658587 + 0.752504i \(0.271154\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 2.83857 + 4.91654i 0.556689 + 0.964214i
\(27\) 0 0
\(28\) 1.90555 1.83545i 0.360116 0.346867i
\(29\) 4.88913i 0.907889i −0.891030 0.453944i \(-0.850016\pi\)
0.891030 0.453944i \(-0.149984\pi\)
\(30\) 0 0
\(31\) −3.92008 2.26326i −0.704067 0.406493i 0.104794 0.994494i \(-0.466582\pi\)
−0.808860 + 0.588001i \(0.799915\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 2.07192i 0.355332i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.48455 2.57132i −0.244059 0.422723i 0.717807 0.696242i \(-0.245146\pi\)
−0.961867 + 0.273519i \(0.911812\pi\)
\(38\) −2.95698 + 5.12164i −0.479686 + 0.830840i
\(39\) 0 0
\(40\) 0 0
\(41\) 7.04428 1.10013 0.550066 0.835121i \(-0.314603\pi\)
0.550066 + 0.835121i \(0.314603\pi\)
\(42\) 0 0
\(43\) −8.55956 −1.30532 −0.652660 0.757651i \(-0.726347\pi\)
−0.652660 + 0.757651i \(0.726347\pi\)
\(44\) 2.07577 1.19845i 0.312934 0.180673i
\(45\) 0 0
\(46\) −0.930877 + 1.61233i −0.137250 + 0.237725i
\(47\) −2.78941 4.83140i −0.406877 0.704732i 0.587661 0.809107i \(-0.300049\pi\)
−0.994538 + 0.104375i \(0.966716\pi\)
\(48\) 0 0
\(49\) 5.92678 + 3.72468i 0.846683 + 0.532097i
\(50\) 0 0
\(51\) 0 0
\(52\) −4.91654 2.83857i −0.681802 0.393639i
\(53\) −3.62931 2.09538i −0.498524 0.287823i 0.229580 0.973290i \(-0.426265\pi\)
−0.728104 + 0.685467i \(0.759598\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −0.732536 + 2.54232i −0.0978892 + 0.339732i
\(57\) 0 0
\(58\) 2.44457 + 4.23411i 0.320987 + 0.555966i
\(59\) −1.00312 + 1.73746i −0.130595 + 0.226198i −0.923906 0.382619i \(-0.875022\pi\)
0.793311 + 0.608817i \(0.208356\pi\)
\(60\) 0 0
\(61\) 10.7862 6.22739i 1.38103 0.797335i 0.388744 0.921346i \(-0.372909\pi\)
0.992281 + 0.124011i \(0.0395757\pi\)
\(62\) 4.52651 0.574868
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 3.81111 6.60103i 0.465601 0.806445i −0.533627 0.845720i \(-0.679171\pi\)
0.999228 + 0.0392750i \(0.0125048\pi\)
\(68\) 1.03596 + 1.79434i 0.125629 + 0.217596i
\(69\) 0 0
\(70\) 0 0
\(71\) 9.14126i 1.08487i 0.840099 + 0.542434i \(0.182497\pi\)
−0.840099 + 0.542434i \(0.817503\pi\)
\(72\) 0 0
\(73\) 0.937339 + 0.541173i 0.109707 + 0.0633395i 0.553850 0.832617i \(-0.313158\pi\)
−0.444142 + 0.895956i \(0.646492\pi\)
\(74\) 2.57132 + 1.48455i 0.298910 + 0.172576i
\(75\) 0 0
\(76\) 5.91397i 0.678378i
\(77\) 4.39937 + 4.56742i 0.501355 + 0.520505i
\(78\) 0 0
\(79\) −8.38392 14.5214i −0.943265 1.63378i −0.759189 0.650870i \(-0.774404\pi\)
−0.184076 0.982912i \(-0.558929\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −6.10053 + 3.52214i −0.673690 + 0.388955i
\(83\) −13.6122 −1.49414 −0.747068 0.664747i \(-0.768539\pi\)
−0.747068 + 0.664747i \(0.768539\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 7.41279 4.27978i 0.799342 0.461500i
\(87\) 0 0
\(88\) −1.19845 + 2.07577i −0.127755 + 0.221278i
\(89\) 6.63129 + 11.4857i 0.702916 + 1.21749i 0.967438 + 0.253106i \(0.0814523\pi\)
−0.264523 + 0.964379i \(0.585214\pi\)
\(90\) 0 0
\(91\) 4.15870 14.4331i 0.435951 1.51300i
\(92\) 1.86175i 0.194101i
\(93\) 0 0
\(94\) 4.83140 + 2.78941i 0.498321 + 0.287706i
\(95\) 0 0
\(96\) 0 0
\(97\) 12.8260i 1.30229i 0.758955 + 0.651143i \(0.225710\pi\)
−0.758955 + 0.651143i \(0.774290\pi\)
\(98\) −6.99508 0.262276i −0.706610 0.0264939i
\(99\) 0 0
\(100\) 0 0
\(101\) 4.45573 7.71756i 0.443362 0.767926i −0.554574 0.832134i \(-0.687119\pi\)
0.997937 + 0.0642084i \(0.0204523\pi\)
\(102\) 0 0
\(103\) −9.37021 + 5.40989i −0.923274 + 0.533053i −0.884678 0.466202i \(-0.845622\pi\)
−0.0385960 + 0.999255i \(0.512289\pi\)
\(104\) 5.67714 0.556689
\(105\) 0 0
\(106\) 4.19077 0.407043
\(107\) −4.82989 + 2.78854i −0.466923 + 0.269578i −0.714951 0.699175i \(-0.753551\pi\)
0.248028 + 0.968753i \(0.420218\pi\)
\(108\) 0 0
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.636766 2.56798i −0.0601687 0.242651i
\(113\) 14.5030i 1.36432i 0.731202 + 0.682161i \(0.238960\pi\)
−0.731202 + 0.682161i \(0.761040\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −4.23411 2.44457i −0.393127 0.226972i
\(117\) 0 0
\(118\) 2.00624i 0.184690i
\(119\) −3.94816 + 3.80290i −0.361928 + 0.348612i
\(120\) 0 0
\(121\) −2.62745 4.55087i −0.238859 0.413715i
\(122\) −6.22739 + 10.7862i −0.563801 + 0.976532i
\(123\) 0 0
\(124\) −3.92008 + 2.26326i −0.352033 + 0.203247i
\(125\) 0 0
\(126\) 0 0
\(127\) 19.2462 1.70783 0.853913 0.520416i \(-0.174223\pi\)
0.853913 + 0.520416i \(0.174223\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −2.34970 4.06980i −0.205294 0.355580i 0.744932 0.667140i \(-0.232482\pi\)
−0.950226 + 0.311560i \(0.899149\pi\)
\(132\) 0 0
\(133\) 15.1870 3.76581i 1.31688 0.326537i
\(134\) 7.62222i 0.658459i
\(135\) 0 0
\(136\) −1.79434 1.03596i −0.153863 0.0888330i
\(137\) −19.8185 11.4422i −1.69321 0.977577i −0.951896 0.306421i \(-0.900868\pi\)
−0.741317 0.671155i \(-0.765798\pi\)
\(138\) 0 0
\(139\) 9.13862i 0.775127i 0.921843 + 0.387564i \(0.126683\pi\)
−0.921843 + 0.387564i \(0.873317\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −4.57063 7.91656i −0.383559 0.664343i
\(143\) 6.80375 11.7844i 0.568958 0.985465i
\(144\) 0 0
\(145\) 0 0
\(146\) −1.08235 −0.0895756
\(147\) 0 0
\(148\) −2.96911 −0.244059
\(149\) 9.05052 5.22532i 0.741448 0.428075i −0.0811477 0.996702i \(-0.525859\pi\)
0.822596 + 0.568627i \(0.192525\pi\)
\(150\) 0 0
\(151\) 8.85937 15.3449i 0.720965 1.24875i −0.239648 0.970860i \(-0.577032\pi\)
0.960613 0.277888i \(-0.0896346\pi\)
\(152\) 2.95698 + 5.12164i 0.239843 + 0.415420i
\(153\) 0 0
\(154\) −6.09368 1.75581i −0.491042 0.141487i
\(155\) 0 0
\(156\) 0 0
\(157\) 5.26801 + 3.04149i 0.420433 + 0.242737i 0.695263 0.718756i \(-0.255288\pi\)
−0.274830 + 0.961493i \(0.588621\pi\)
\(158\) 14.5214 + 8.38392i 1.15526 + 0.666989i
\(159\) 0 0
\(160\) 0 0
\(161\) 4.78095 1.18550i 0.376792 0.0934305i
\(162\) 0 0
\(163\) −0.468670 0.811759i −0.0367090 0.0635819i 0.847087 0.531454i \(-0.178354\pi\)
−0.883796 + 0.467872i \(0.845021\pi\)
\(164\) 3.52214 6.10053i 0.275033 0.476371i
\(165\) 0 0
\(166\) 11.7885 6.80611i 0.914968 0.528257i
\(167\) 17.2101 1.33176 0.665879 0.746060i \(-0.268057\pi\)
0.665879 + 0.746060i \(0.268057\pi\)
\(168\) 0 0
\(169\) −19.2299 −1.47922
\(170\) 0 0
\(171\) 0 0
\(172\) −4.27978 + 7.41279i −0.326330 + 0.565220i
\(173\) −0.988114 1.71146i −0.0751249 0.130120i 0.826016 0.563647i \(-0.190602\pi\)
−0.901141 + 0.433527i \(0.857269\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.39690i 0.180673i
\(177\) 0 0
\(178\) −11.4857 6.63129i −0.860893 0.497037i
\(179\) 0.768461 + 0.443671i 0.0574375 + 0.0331615i 0.528444 0.848968i \(-0.322776\pi\)
−0.471006 + 0.882130i \(0.656109\pi\)
\(180\) 0 0
\(181\) 4.89973i 0.364194i −0.983281 0.182097i \(-0.941712\pi\)
0.983281 0.182097i \(-0.0582885\pi\)
\(182\) 3.61500 + 14.5788i 0.267962 + 1.08065i
\(183\) 0 0
\(184\) 0.930877 + 1.61233i 0.0686252 + 0.118862i
\(185\) 0 0
\(186\) 0 0
\(187\) −4.30084 + 2.48309i −0.314509 + 0.181582i
\(188\) −5.57882 −0.406877
\(189\) 0 0
\(190\) 0 0
\(191\) −2.44949 + 1.41421i −0.177239 + 0.102329i −0.585995 0.810315i \(-0.699296\pi\)
0.408756 + 0.912644i \(0.365963\pi\)
\(192\) 0 0
\(193\) 9.74828 16.8845i 0.701697 1.21537i −0.266174 0.963925i \(-0.585760\pi\)
0.967871 0.251449i \(-0.0809071\pi\)
\(194\) −6.41301 11.1077i −0.460428 0.797484i
\(195\) 0 0
\(196\) 6.18906 3.27040i 0.442076 0.233600i
\(197\) 27.1576i 1.93490i −0.253069 0.967448i \(-0.581440\pi\)
0.253069 0.967448i \(-0.418560\pi\)
\(198\) 0 0
\(199\) 3.00000 + 1.73205i 0.212664 + 0.122782i 0.602549 0.798082i \(-0.294152\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 8.91147i 0.627009i
\(203\) 3.58146 12.4297i 0.251369 0.872396i
\(204\) 0 0
\(205\) 0 0
\(206\) 5.40989 9.37021i 0.376925 0.652853i
\(207\) 0 0
\(208\) −4.91654 + 2.83857i −0.340901 + 0.196819i
\(209\) 14.1752 0.980516
\(210\) 0 0
\(211\) −4.06071 −0.279551 −0.139775 0.990183i \(-0.544638\pi\)
−0.139775 + 0.990183i \(0.544638\pi\)
\(212\) −3.62931 + 2.09538i −0.249262 + 0.143912i
\(213\) 0 0
\(214\) 2.78854 4.82989i 0.190620 0.330164i
\(215\) 0 0
\(216\) 0 0
\(217\) −8.30817 8.62552i −0.563996 0.585538i
\(218\) 2.00000i 0.135457i
\(219\) 0 0
\(220\) 0 0
\(221\) 10.1867 + 5.88130i 0.685232 + 0.395619i
\(222\) 0 0
\(223\) 16.1486i 1.08139i 0.841218 + 0.540696i \(0.181839\pi\)
−0.841218 + 0.540696i \(0.818161\pi\)
\(224\) 1.83545 + 1.90555i 0.122636 + 0.127320i
\(225\) 0 0
\(226\) −7.25148 12.5599i −0.482361 0.835474i
\(227\) 0.839901 1.45475i 0.0557462 0.0965552i −0.836806 0.547500i \(-0.815580\pi\)
0.892552 + 0.450945i \(0.148913\pi\)
\(228\) 0 0
\(229\) 10.9143 6.30136i 0.721236 0.416406i −0.0939717 0.995575i \(-0.529956\pi\)
0.815207 + 0.579169i \(0.196623\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.88913 0.320987
\(233\) 12.5715 7.25818i 0.823589 0.475499i −0.0280635 0.999606i \(-0.508934\pi\)
0.851653 + 0.524107i \(0.175601\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 1.00312 + 1.73746i 0.0652977 + 0.113099i
\(237\) 0 0
\(238\) 1.51776 5.26749i 0.0983816 0.341441i
\(239\) 0.207089i 0.0133955i 0.999978 + 0.00669774i \(0.00213197\pi\)
−0.999978 + 0.00669774i \(0.997868\pi\)
\(240\) 0 0
\(241\) 9.04172 + 5.22024i 0.582428 + 0.336265i 0.762098 0.647462i \(-0.224169\pi\)
−0.179669 + 0.983727i \(0.557503\pi\)
\(242\) 4.55087 + 2.62745i 0.292541 + 0.168899i
\(243\) 0 0
\(244\) 12.4548i 0.797335i
\(245\) 0 0
\(246\) 0 0
\(247\) −16.7872 29.0763i −1.06814 1.85008i
\(248\) 2.26326 3.92008i 0.143717 0.248925i
\(249\) 0 0
\(250\) 0 0
\(251\) 28.6464 1.80815 0.904074 0.427377i \(-0.140562\pi\)
0.904074 + 0.427377i \(0.140562\pi\)
\(252\) 0 0
\(253\) 4.46243 0.280551
\(254\) −16.6677 + 9.62311i −1.04583 + 0.603808i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −12.4595 21.5805i −0.777202 1.34615i −0.933548 0.358452i \(-0.883305\pi\)
0.156346 0.987702i \(-0.450029\pi\)
\(258\) 0 0
\(259\) −1.89063 7.62462i −0.117478 0.473771i
\(260\) 0 0
\(261\) 0 0
\(262\) 4.06980 + 2.34970i 0.251433 + 0.145165i
\(263\) 16.6197 + 9.59538i 1.02481 + 0.591677i 0.915495 0.402330i \(-0.131800\pi\)
0.109319 + 0.994007i \(0.465133\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −11.2694 + 10.8548i −0.690970 + 0.665548i
\(267\) 0 0
\(268\) −3.81111 6.60103i −0.232801 0.403222i
\(269\) −2.42744 + 4.20446i −0.148004 + 0.256350i −0.930490 0.366318i \(-0.880618\pi\)
0.782486 + 0.622668i \(0.213951\pi\)
\(270\) 0 0
\(271\) −11.8344 + 6.83257i −0.718886 + 0.415049i −0.814342 0.580385i \(-0.802902\pi\)
0.0954567 + 0.995434i \(0.469569\pi\)
\(272\) 2.07192 0.125629
\(273\) 0 0
\(274\) 22.8845 1.38250
\(275\) 0 0
\(276\) 0 0
\(277\) 6.06491 10.5047i 0.364405 0.631168i −0.624276 0.781204i \(-0.714606\pi\)
0.988680 + 0.150036i \(0.0479391\pi\)
\(278\) −4.56931 7.91427i −0.274049 0.474667i
\(279\) 0 0
\(280\) 0 0
\(281\) 32.6206i 1.94598i 0.230839 + 0.972992i \(0.425853\pi\)
−0.230839 + 0.972992i \(0.574147\pi\)
\(282\) 0 0
\(283\) 10.9647 + 6.33045i 0.651781 + 0.376306i 0.789138 0.614216i \(-0.210527\pi\)
−0.137357 + 0.990522i \(0.543861\pi\)
\(284\) 7.91656 + 4.57063i 0.469761 + 0.271217i
\(285\) 0 0
\(286\) 13.6075i 0.804628i
\(287\) 17.9088 + 5.16019i 1.05712 + 0.304596i
\(288\) 0 0
\(289\) 6.35357 + 11.0047i 0.373739 + 0.647335i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.937339 0.541173i 0.0548536 0.0316698i
\(293\) −25.1151 −1.46724 −0.733621 0.679559i \(-0.762171\pi\)
−0.733621 + 0.679559i \(0.762171\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 2.57132 1.48455i 0.149455 0.0862880i
\(297\) 0 0
\(298\) −5.22532 + 9.05052i −0.302695 + 0.524283i
\(299\) −5.28472 9.15340i −0.305623 0.529355i
\(300\) 0 0
\(301\) −21.7611 6.27018i −1.25429 0.361407i
\(302\) 17.7187i 1.01960i
\(303\) 0 0
\(304\) −5.12164 2.95698i −0.293746 0.169595i
\(305\) 0 0
\(306\) 0 0
\(307\) 18.5674i 1.05970i 0.848092 + 0.529849i \(0.177751\pi\)
−0.848092 + 0.529849i \(0.822249\pi\)
\(308\) 6.15518 1.52626i 0.350724 0.0869668i
\(309\) 0 0
\(310\) 0 0
\(311\) −6.21831 + 10.7704i −0.352608 + 0.610735i −0.986706 0.162518i \(-0.948038\pi\)
0.634098 + 0.773253i \(0.281372\pi\)
\(312\) 0 0
\(313\) 10.7504 6.20675i 0.607649 0.350826i −0.164396 0.986394i \(-0.552567\pi\)
0.772045 + 0.635568i \(0.219234\pi\)
\(314\) −6.08297 −0.343282
\(315\) 0 0
\(316\) −16.7678 −0.943265
\(317\) 21.3444 12.3232i 1.19882 0.692141i 0.238530 0.971135i \(-0.423335\pi\)
0.960293 + 0.278995i \(0.0900012\pi\)
\(318\) 0 0
\(319\) 5.85937 10.1487i 0.328062 0.568219i
\(320\) 0 0
\(321\) 0 0
\(322\) −3.54767 + 3.41715i −0.197704 + 0.190430i
\(323\) 12.2533i 0.681791i
\(324\) 0 0
\(325\) 0 0
\(326\) 0.811759 + 0.468670i 0.0449592 + 0.0259572i
\(327\) 0 0
\(328\) 7.04428i 0.388955i
\(329\) −3.55240 14.3263i −0.195850 0.789835i
\(330\) 0 0
\(331\) 12.5788 + 21.7871i 0.691392 + 1.19753i 0.971382 + 0.237524i \(0.0763357\pi\)
−0.279989 + 0.960003i \(0.590331\pi\)
\(332\) −6.80611 + 11.7885i −0.373534 + 0.646980i
\(333\) 0 0
\(334\) −14.9044 + 8.60505i −0.815531 + 0.470847i
\(335\) 0 0
\(336\) 0 0
\(337\) 14.4214 0.785584 0.392792 0.919627i \(-0.371509\pi\)
0.392792 + 0.919627i \(0.371509\pi\)
\(338\) 16.6536 9.61494i 0.905834 0.522984i
\(339\) 0 0
\(340\) 0 0
\(341\) −5.42479 9.39601i −0.293769 0.508823i
\(342\) 0 0
\(343\) 12.3393 + 13.8109i 0.666261 + 0.745719i
\(344\) 8.55956i 0.461500i
\(345\) 0 0
\(346\) 1.71146 + 0.988114i 0.0920088 + 0.0531213i
\(347\) 12.5457 + 7.24329i 0.673491 + 0.388840i 0.797398 0.603454i \(-0.206209\pi\)
−0.123907 + 0.992294i \(0.539543\pi\)
\(348\) 0 0
\(349\) 2.12483i 0.113739i −0.998382 0.0568697i \(-0.981888\pi\)
0.998382 0.0568697i \(-0.0181119\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.19845 + 2.07577i 0.0638775 + 0.110639i
\(353\) 7.26335 12.5805i 0.386589 0.669592i −0.605399 0.795922i \(-0.706987\pi\)
0.991988 + 0.126330i \(0.0403199\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 13.2626 0.702916
\(357\) 0 0
\(358\) −0.887342 −0.0468975
\(359\) −3.42054 + 1.97485i −0.180529 + 0.104228i −0.587541 0.809194i \(-0.699904\pi\)
0.407012 + 0.913423i \(0.366571\pi\)
\(360\) 0 0
\(361\) 7.98749 13.8347i 0.420394 0.728144i
\(362\) 2.44986 + 4.24329i 0.128762 + 0.223022i
\(363\) 0 0
\(364\) −10.4201 10.8181i −0.546160 0.567022i
\(365\) 0 0
\(366\) 0 0
\(367\) 23.9826 + 13.8464i 1.25188 + 0.722775i 0.971483 0.237109i \(-0.0761997\pi\)
0.280400 + 0.959883i \(0.409533\pi\)
\(368\) −1.61233 0.930877i −0.0840483 0.0485253i
\(369\) 0 0
\(370\) 0 0
\(371\) −7.69193 7.98574i −0.399345 0.414599i
\(372\) 0 0
\(373\) 6.06491 + 10.5047i 0.314029 + 0.543914i 0.979231 0.202750i \(-0.0649878\pi\)
−0.665202 + 0.746664i \(0.731654\pi\)
\(374\) 2.48309 4.30084i 0.128398 0.222391i
\(375\) 0 0
\(376\) 4.83140 2.78941i 0.249160 0.143853i
\(377\) −27.7563 −1.42952
\(378\) 0 0
\(379\) 18.6821 0.959636 0.479818 0.877368i \(-0.340703\pi\)
0.479818 + 0.877368i \(0.340703\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.41421 2.44949i 0.0723575 0.125327i
\(383\) −5.51463 9.55162i −0.281784 0.488065i 0.690040 0.723771i \(-0.257593\pi\)
−0.971824 + 0.235706i \(0.924260\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 19.4966i 0.992349i
\(387\) 0 0
\(388\) 11.1077 + 6.41301i 0.563906 + 0.325571i
\(389\) −29.7662 17.1855i −1.50921 0.871341i −0.999942 0.0107299i \(-0.996584\pi\)
−0.509264 0.860611i \(-0.670082\pi\)
\(390\) 0 0
\(391\) 3.85741i 0.195078i
\(392\) −3.72468 + 5.92678i −0.188125 + 0.299348i
\(393\) 0 0
\(394\) 13.5788 + 23.5191i 0.684089 + 1.18488i
\(395\) 0 0
\(396\) 0 0
\(397\) −26.8561 + 15.5054i −1.34787 + 0.778191i −0.987947 0.154792i \(-0.950529\pi\)
−0.359920 + 0.932983i \(0.617196\pi\)
\(398\) −3.46410 −0.173640
\(399\) 0 0
\(400\) 0 0
\(401\) 8.20771 4.73872i 0.409873 0.236641i −0.280862 0.959748i \(-0.590620\pi\)
0.690735 + 0.723108i \(0.257287\pi\)
\(402\) 0 0
\(403\) −12.8488 + 22.2548i −0.640045 + 1.10859i
\(404\) −4.45573 7.71756i −0.221681 0.383963i
\(405\) 0 0
\(406\) 3.11323 + 12.5552i 0.154507 + 0.623104i
\(407\) 7.11665i 0.352759i
\(408\) 0 0
\(409\) −8.20805 4.73892i −0.405862 0.234324i 0.283148 0.959076i \(-0.408621\pi\)
−0.689010 + 0.724752i \(0.741954\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 10.8198i 0.533053i
\(413\) −3.82301 + 3.68235i −0.188118 + 0.181197i
\(414\) 0 0
\(415\) 0 0
\(416\) 2.83857 4.91654i 0.139172 0.241053i
\(417\) 0 0
\(418\) −12.2760 + 7.08758i −0.600441 + 0.346665i
\(419\) 2.54445 0.124305 0.0621523 0.998067i \(-0.480204\pi\)
0.0621523 + 0.998067i \(0.480204\pi\)
\(420\) 0 0
\(421\) −5.08573 −0.247863 −0.123932 0.992291i \(-0.539550\pi\)
−0.123932 + 0.992291i \(0.539550\pi\)
\(422\) 3.51668 2.03035i 0.171189 0.0988361i
\(423\) 0 0
\(424\) 2.09538 3.62931i 0.101761 0.176255i
\(425\) 0 0
\(426\) 0 0
\(427\) 31.9836 7.93077i 1.54780 0.383797i
\(428\) 5.57707i 0.269578i
\(429\) 0 0
\(430\) 0 0
\(431\) −11.5164 6.64902i −0.554727 0.320272i 0.196299 0.980544i \(-0.437108\pi\)
−0.751027 + 0.660272i \(0.770441\pi\)
\(432\) 0 0
\(433\) 12.7895i 0.614626i −0.951608 0.307313i \(-0.900570\pi\)
0.951608 0.307313i \(-0.0994299\pi\)
\(434\) 11.5078 + 3.31583i 0.552394 + 0.159165i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) 5.50517 9.53524i 0.263348 0.456132i
\(438\) 0 0
\(439\) −0.323211 + 0.186606i −0.0154260 + 0.00890623i −0.507693 0.861538i \(-0.669502\pi\)
0.492267 + 0.870444i \(0.336168\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −11.7626 −0.559490
\(443\) 21.3328 12.3165i 1.01355 0.585175i 0.101323 0.994854i \(-0.467693\pi\)
0.912230 + 0.409679i \(0.134359\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −8.07432 13.9851i −0.382330 0.662215i
\(447\) 0 0
\(448\) −2.54232 0.732536i −0.120113 0.0346091i
\(449\) 40.6223i 1.91708i 0.284950 + 0.958542i \(0.408023\pi\)
−0.284950 + 0.958542i \(0.591977\pi\)
\(450\) 0 0
\(451\) 14.6223 + 8.44220i 0.688538 + 0.397528i
\(452\) 12.5599 + 7.25148i 0.590769 + 0.341081i
\(453\) 0 0
\(454\) 1.67980i 0.0788370i
\(455\) 0 0
\(456\) 0 0
\(457\) 0.495276 + 0.857843i 0.0231680 + 0.0401282i 0.877377 0.479802i \(-0.159291\pi\)
−0.854209 + 0.519930i \(0.825958\pi\)
\(458\) −6.30136 + 10.9143i −0.294443 + 0.509991i
\(459\) 0 0
\(460\) 0 0
\(461\) −20.7397 −0.965945 −0.482972 0.875636i \(-0.660443\pi\)
−0.482972 + 0.875636i \(0.660443\pi\)
\(462\) 0 0
\(463\) 1.46421 0.0680476 0.0340238 0.999421i \(-0.489168\pi\)
0.0340238 + 0.999421i \(0.489168\pi\)
\(464\) −4.23411 + 2.44457i −0.196564 + 0.113486i
\(465\) 0 0
\(466\) −7.25818 + 12.5715i −0.336229 + 0.582365i
\(467\) −18.1340 31.4090i −0.839142 1.45344i −0.890613 0.454762i \(-0.849724\pi\)
0.0514705 0.998675i \(-0.483609\pi\)
\(468\) 0 0
\(469\) 14.5246 13.9902i 0.670682 0.646006i
\(470\) 0 0
\(471\) 0 0
\(472\) −1.73746 1.00312i −0.0799730 0.0461724i
\(473\) −17.7677 10.2582i −0.816959 0.471672i
\(474\) 0 0
\(475\) 0 0
\(476\) 1.31933 + 5.32066i 0.0604714 + 0.243872i
\(477\) 0 0
\(478\) −0.103545 0.179344i −0.00473602 0.00820302i
\(479\) 5.16288 8.94237i 0.235898 0.408587i −0.723635 0.690183i \(-0.757530\pi\)
0.959533 + 0.281595i \(0.0908635\pi\)
\(480\) 0 0
\(481\) −14.5978 + 8.42802i −0.665600 + 0.384285i
\(482\) −10.4405 −0.475551
\(483\) 0 0
\(484\) −5.25489 −0.238859
\(485\) 0 0
\(486\) 0 0
\(487\) −10.1645 + 17.6055i −0.460599 + 0.797781i −0.998991 0.0449135i \(-0.985699\pi\)
0.538392 + 0.842695i \(0.319032\pi\)
\(488\) 6.22739 + 10.7862i 0.281901 + 0.488266i
\(489\) 0 0
\(490\) 0 0
\(491\) 34.6034i 1.56163i −0.624764 0.780814i \(-0.714805\pi\)
0.624764 0.780814i \(-0.285195\pi\)
\(492\) 0 0
\(493\) 8.77276 + 5.06495i 0.395105 + 0.228114i
\(494\) 29.0763 + 16.7872i 1.30820 + 0.755292i
\(495\) 0 0
\(496\) 4.52651i 0.203247i
\(497\) −6.69630 + 23.2400i −0.300370 + 1.04246i
\(498\) 0 0
\(499\) 1.47545 + 2.55555i 0.0660501 + 0.114402i 0.897159 0.441707i \(-0.145627\pi\)
−0.831109 + 0.556109i \(0.812294\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −24.8085 + 14.3232i −1.10726 + 0.639277i
\(503\) 31.8907 1.42193 0.710967 0.703225i \(-0.248258\pi\)
0.710967 + 0.703225i \(0.248258\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −3.86458 + 2.23121i −0.171801 + 0.0991896i
\(507\) 0 0
\(508\) 9.62311 16.6677i 0.426957 0.739510i
\(509\) −0.421199 0.729538i −0.0186693 0.0323362i 0.856540 0.516081i \(-0.172610\pi\)
−0.875209 + 0.483745i \(0.839276\pi\)
\(510\) 0 0
\(511\) 1.98659 + 2.06247i 0.0878815 + 0.0912383i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 21.5805 + 12.4595i 0.951875 + 0.549565i
\(515\) 0 0
\(516\) 0 0
\(517\) 13.3718i 0.588093i
\(518\) 5.44964 + 5.65780i 0.239443 + 0.248589i
\(519\) 0 0
\(520\) 0 0
\(521\) −2.81499 + 4.87571i −0.123327 + 0.213609i −0.921078 0.389379i \(-0.872690\pi\)
0.797751 + 0.602987i \(0.206023\pi\)
\(522\) 0 0
\(523\) −15.4482 + 8.91899i −0.675500 + 0.390000i −0.798158 0.602449i \(-0.794192\pi\)
0.122657 + 0.992449i \(0.460858\pi\)
\(524\) −4.69940 −0.205294
\(525\) 0 0
\(526\) −19.1908 −0.836757
\(527\) 8.12210 4.68930i 0.353804 0.204269i
\(528\) 0 0
\(529\) −9.76694 + 16.9168i −0.424649 + 0.735514i
\(530\) 0 0
\(531\) 0 0
\(532\) 4.33219 15.0352i 0.187824 0.651858i
\(533\) 39.9913i 1.73222i
\(534\) 0 0
\(535\) 0 0
\(536\) 6.60103 + 3.81111i 0.285121 + 0.164615i
\(537\) 0 0
\(538\) 4.85489i 0.209309i
\(539\) 7.83882 + 14.8345i 0.337642 + 0.638968i
\(540\) 0 0
\(541\) 12.7120 + 22.0179i 0.546533 + 0.946623i 0.998509 + 0.0545925i \(0.0173860\pi\)
−0.451976 + 0.892030i \(0.649281\pi\)
\(542\) 6.83257 11.8344i 0.293484 0.508329i
\(543\) 0 0
\(544\) −1.79434 + 1.03596i −0.0769316 + 0.0444165i
\(545\) 0 0
\(546\) 0 0
\(547\) −12.1182 −0.518138 −0.259069 0.965859i \(-0.583416\pi\)
−0.259069 + 0.965859i \(0.583416\pi\)
\(548\) −19.8185 + 11.4422i −0.846606 + 0.488788i
\(549\) 0 0
\(550\) 0 0
\(551\) −14.4571 25.0404i −0.615892 1.06676i
\(552\) 0 0
\(553\) −10.6772 43.0595i −0.454040 1.83108i
\(554\) 12.1298i 0.515346i
\(555\) 0 0
\(556\) 7.91427 + 4.56931i 0.335640 + 0.193782i
\(557\) −1.33331 0.769786i −0.0564941 0.0326169i 0.471487 0.881873i \(-0.343717\pi\)
−0.527981 + 0.849256i \(0.677051\pi\)
\(558\) 0 0
\(559\) 48.5938i 2.05530i
\(560\) 0 0
\(561\) 0 0
\(562\) −16.3103 28.2503i −0.688009 1.19167i
\(563\) −11.2322 + 19.4548i −0.473381 + 0.819920i −0.999536 0.0304689i \(-0.990300\pi\)
0.526155 + 0.850389i \(0.323633\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −12.6609 −0.532177
\(567\) 0 0
\(568\) −9.14126 −0.383559
\(569\) 9.35810 5.40290i 0.392312 0.226501i −0.290849 0.956769i \(-0.593938\pi\)
0.683161 + 0.730267i \(0.260605\pi\)
\(570\) 0 0
\(571\) 3.98169 6.89649i 0.166629 0.288609i −0.770604 0.637314i \(-0.780045\pi\)
0.937232 + 0.348705i \(0.113379\pi\)
\(572\) −6.80375 11.7844i −0.284479 0.492732i
\(573\) 0 0
\(574\) −18.0896 + 4.48555i −0.755045 + 0.187223i
\(575\) 0 0
\(576\) 0 0
\(577\) 21.2980 + 12.2964i 0.886648 + 0.511906i 0.872845 0.487998i \(-0.162273\pi\)
0.0138033 + 0.999905i \(0.495606\pi\)
\(578\) −11.0047 6.35357i −0.457735 0.264274i
\(579\) 0 0
\(580\) 0 0
\(581\) −34.6066 9.97144i −1.43573 0.413685i
\(582\) 0 0
\(583\) −5.02242 8.69908i −0.208007 0.360279i
\(584\) −0.541173 + 0.937339i −0.0223939 + 0.0387874i
\(585\) 0 0
\(586\) 21.7503 12.5576i 0.898498 0.518748i
\(587\) −12.8469 −0.530248 −0.265124 0.964214i \(-0.585413\pi\)
−0.265124 + 0.964214i \(0.585413\pi\)
\(588\) 0 0
\(589\) −26.7696 −1.10302
\(590\) 0 0
\(591\) 0 0
\(592\) −1.48455 + 2.57132i −0.0610148 + 0.105681i
\(593\) −8.58155 14.8637i −0.352402 0.610379i 0.634268 0.773114i \(-0.281302\pi\)
−0.986670 + 0.162735i \(0.947968\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10.4506i 0.428075i
\(597\) 0 0
\(598\) 9.15340 + 5.28472i 0.374310 + 0.216108i
\(599\) −16.9813 9.80416i −0.693837 0.400587i 0.111211 0.993797i \(-0.464527\pi\)
−0.805048 + 0.593210i \(0.797860\pi\)
\(600\) 0 0
\(601\) 28.2340i 1.15169i 0.817560 + 0.575844i \(0.195326\pi\)
−0.817560 + 0.575844i \(0.804674\pi\)
\(602\) 21.9808 5.45043i 0.895870 0.222143i
\(603\) 0 0
\(604\) −8.85937 15.3449i −0.360483 0.624374i
\(605\) 0 0
\(606\) 0 0
\(607\) 8.35987 4.82657i 0.339316 0.195904i −0.320653 0.947197i \(-0.603902\pi\)
0.659970 + 0.751292i \(0.270569\pi\)
\(608\) 5.91397 0.239843
\(609\) 0 0
\(610\) 0 0
\(611\) −27.4285 + 15.8359i −1.10964 + 0.640650i
\(612\) 0 0
\(613\) −4.52794 + 7.84262i −0.182882 + 0.316761i −0.942861 0.333187i \(-0.891876\pi\)
0.759979 + 0.649948i \(0.225209\pi\)
\(614\) −9.28370 16.0798i −0.374660 0.648930i
\(615\) 0 0
\(616\) −4.56742 + 4.39937i −0.184026 + 0.177256i
\(617\) 25.3122i 1.01903i 0.860462 + 0.509515i \(0.170175\pi\)
−0.860462 + 0.509515i \(0.829825\pi\)
\(618\) 0 0
\(619\) −33.6634 19.4356i −1.35304 0.781181i −0.364370 0.931254i \(-0.618716\pi\)
−0.988675 + 0.150073i \(0.952049\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 12.4366i 0.498663i
\(623\) 8.44516 + 34.0581i 0.338348 + 1.36451i
\(624\) 0 0
\(625\) 0 0
\(626\) −6.20675 + 10.7504i −0.248072 + 0.429673i
\(627\) 0 0
\(628\) 5.26801 3.04149i 0.210216 0.121369i
\(629\) 6.15177 0.245287
\(630\) 0 0
\(631\) −23.8670 −0.950129 −0.475065 0.879951i \(-0.657575\pi\)
−0.475065 + 0.879951i \(0.657575\pi\)
\(632\) 14.5214 8.38392i 0.577629 0.333494i
\(633\) 0 0
\(634\) −12.3232 + 21.3444i −0.489417 + 0.847696i
\(635\) 0 0
\(636\) 0 0
\(637\) 21.1455 33.6472i 0.837816 1.33315i
\(638\) 11.7187i 0.463949i
\(639\) 0 0
\(640\) 0 0
\(641\) −30.2066 17.4398i −1.19309 0.688830i −0.234083 0.972217i \(-0.575209\pi\)
−0.959006 + 0.283386i \(0.908542\pi\)
\(642\) 0 0
\(643\) 6.25944i 0.246848i −0.992354 0.123424i \(-0.960612\pi\)
0.992354 0.123424i \(-0.0393875\pi\)
\(644\) 1.36380 4.73317i 0.0537413 0.186513i
\(645\) 0 0
\(646\) −6.12664 10.6117i −0.241050 0.417510i
\(647\) −18.7511 + 32.4778i −0.737181 + 1.27683i 0.216579 + 0.976265i \(0.430510\pi\)
−0.953760 + 0.300570i \(0.902823\pi\)
\(648\) 0 0
\(649\) −4.16451 + 2.40438i −0.163471 + 0.0943801i
\(650\) 0 0
\(651\) 0 0
\(652\) −0.937339 −0.0367090
\(653\) −22.9077 + 13.2258i −0.896449 + 0.517565i −0.876046 0.482227i \(-0.839828\pi\)
−0.0204023 + 0.999792i \(0.506495\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −3.52214 6.10053i −0.137516 0.238186i
\(657\) 0 0
\(658\) 10.2396 + 10.6307i 0.399182 + 0.414430i
\(659\) 19.9524i 0.777234i −0.921399 0.388617i \(-0.872953\pi\)
0.921399 0.388617i \(-0.127047\pi\)
\(660\) 0 0
\(661\) 4.71203 + 2.72049i 0.183277 + 0.105815i 0.588831 0.808256i \(-0.299588\pi\)
−0.405555 + 0.914071i \(0.632922\pi\)
\(662\) −21.7871 12.5788i −0.846779 0.488888i
\(663\) 0 0
\(664\) 13.6122i 0.528257i
\(665\) 0 0
\(666\) 0 0
\(667\) −4.55118 7.88287i −0.176222 0.305226i
\(668\) 8.60505 14.9044i 0.332939 0.576668i
\(669\) 0 0
\(670\) 0 0
\(671\) 29.8528 1.15245
\(672\) 0 0
\(673\) 8.50635 0.327896 0.163948 0.986469i \(-0.447577\pi\)
0.163948 + 0.986469i \(0.447577\pi\)
\(674\) −12.4893 + 7.21070i −0.481070 + 0.277746i
\(675\) 0 0
\(676\) −9.61494 + 16.6536i −0.369805 + 0.640522i
\(677\) 2.54320 + 4.40495i 0.0977430 + 0.169296i 0.910750 0.412958i \(-0.135504\pi\)
−0.813007 + 0.582254i \(0.802171\pi\)
\(678\) 0 0
\(679\) −9.39552 + 32.6079i −0.360567 + 1.25138i
\(680\) 0 0
\(681\) 0 0
\(682\) 9.39601 + 5.42479i 0.359792 + 0.207726i
\(683\) 18.1991 + 10.5073i 0.696370 + 0.402050i 0.805994 0.591924i \(-0.201631\pi\)
−0.109624 + 0.993973i \(0.534965\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −17.5916 5.79094i −0.671651 0.221099i
\(687\) 0 0
\(688\) 4.27978 + 7.41279i 0.163165 + 0.282610i
\(689\) −11.8958 + 20.6041i −0.453193 + 0.784953i
\(690\) 0 0
\(691\) −21.5723 + 12.4548i −0.820649 + 0.473802i −0.850640 0.525748i \(-0.823785\pi\)
0.0299912 + 0.999550i \(0.490452\pi\)
\(692\) −1.97623 −0.0751249
\(693\) 0 0
\(694\) −14.4866 −0.549903
\(695\) 0 0
\(696\) 0 0
\(697\) −7.29761 + 12.6398i −0.276417 + 0.478767i
\(698\) 1.06241 + 1.84015i 0.0402129 + 0.0696508i
\(699\) 0 0
\(700\) 0 0
\(701\) 22.5321i 0.851025i 0.904953 + 0.425512i \(0.139906\pi\)
−0.904953 + 0.425512i \(0.860094\pi\)
\(702\) 0 0
\(703\) −15.2067 8.77961i −0.573532 0.331129i
\(704\) −2.07577 1.19845i −0.0782336 0.0451682i
\(705\) 0 0
\(706\) 14.5267i 0.546719i
\(707\) 16.9813 16.3565i 0.638647 0.615150i
\(708\) 0 0
\(709\) 12.4504 + 21.5648i 0.467586 + 0.809882i 0.999314 0.0370327i \(-0.0117906\pi\)
−0.531728 + 0.846915i \(0.678457\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −11.4857 + 6.63129i −0.430446 + 0.248518i
\(713\) −8.42726 −0.315603
\(714\) 0 0
\(715\) 0 0
\(716\) 0.768461 0.443671i 0.0287187 0.0165808i
\(717\) 0 0
\(718\) 1.97485 3.42054i 0.0737007 0.127653i
\(719\) 19.9241 + 34.5096i 0.743045 + 1.28699i 0.951103 + 0.308875i \(0.0999526\pi\)
−0.208057 + 0.978117i \(0.566714\pi\)
\(720\) 0 0
\(721\) −27.7850 + 6.88967i −1.03477 + 0.256585i
\(722\) 15.9750i 0.594527i
\(723\) 0 0
\(724\) −4.24329 2.44986i −0.157701 0.0910485i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.124004i 0.00459906i −0.999997 0.00229953i \(-0.999268\pi\)
0.999997 0.00229953i \(-0.000731964\pi\)
\(728\) 14.4331 + 4.15870i 0.534926 + 0.154132i
\(729\) 0 0
\(730\) 0 0
\(731\) 8.86738 15.3587i 0.327972 0.568064i
\(732\) 0 0
\(733\) −24.7231 + 14.2739i −0.913168 + 0.527218i −0.881449 0.472279i \(-0.843431\pi\)
−0.0317189 + 0.999497i \(0.510098\pi\)
\(734\) −27.6927 −1.02216
\(735\) 0 0
\(736\) 1.86175 0.0686252
\(737\) 15.8220 9.13483i 0.582811 0.336486i
\(738\) 0 0
\(739\) −9.51807 + 16.4858i −0.350128 + 0.606439i −0.986272 0.165131i \(-0.947195\pi\)
0.636144 + 0.771571i \(0.280529\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 10.6543 + 3.06989i 0.391131 + 0.112699i
\(743\) 17.0800i 0.626605i −0.949653 0.313303i \(-0.898565\pi\)
0.949653 0.313303i \(-0.101435\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −10.5047 6.06491i −0.384605 0.222052i
\(747\) 0 0
\(748\) 4.96618i 0.181582i
\(749\) −14.3218 + 3.55129i −0.523308 + 0.129761i
\(750\) 0 0
\(751\) 8.44463 + 14.6265i 0.308149 + 0.533730i 0.977957 0.208804i \(-0.0669572\pi\)
−0.669809 + 0.742534i \(0.733624\pi\)
\(752\) −2.78941 + 4.83140i −0.101719 + 0.176183i
\(753\) 0 0
\(754\) 24.0376 13.8781i 0.875399 0.505412i
\(755\) 0 0
\(756\) 0 0
\(757\) 33.4057 1.21415 0.607076 0.794644i \(-0.292342\pi\)
0.607076 + 0.794644i \(0.292342\pi\)
\(758\) −16.1792 + 9.34106i −0.587655 + 0.339282i
\(759\) 0 0
\(760\) 0 0
\(761\) −16.3074 28.2453i −0.591143 1.02389i −0.994079 0.108662i \(-0.965343\pi\)
0.402935 0.915228i \(-0.367990\pi\)
\(762\) 0 0
\(763\) 3.81111 3.67089i 0.137971 0.132895i
\(764\) 2.82843i 0.102329i
\(765\) 0 0
\(766\) 9.55162 + 5.51463i 0.345114 + 0.199252i
\(767\) 9.86379 + 5.69486i 0.356161 + 0.205630i
\(768\) 0 0
\(769\) 22.4396i 0.809192i −0.914495 0.404596i \(-0.867412\pi\)
0.914495 0.404596i \(-0.132588\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −9.74828 16.8845i −0.350848 0.607687i
\(773\) −19.9165 + 34.4965i −0.716348 + 1.24075i 0.246089 + 0.969247i \(0.420855\pi\)
−0.962437 + 0.271505i \(0.912479\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −12.8260 −0.460428
\(777\) 0 0
\(778\) 34.3710 1.23226
\(779\) 36.0783 20.8298i 1.29264 0.746306i
\(780\) 0 0
\(781\) −10.9553 + 18.9752i −0.392012 + 0.678985i
\(782\) −1.92871 3.34062i −0.0689704 0.119460i
\(783\) 0 0
\(784\) 0.262276 6.99508i 0.00936701 0.249824i
\(785\) 0 0
\(786\) 0 0