Properties

Label 3150.2.bf.f.1151.14
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 1151.14
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.f.1601.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.07665 + 1.63937i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.07665 + 1.63937i) q^{7} -1.00000i q^{8} +(-5.48223 - 3.16517i) q^{11} -1.05290i q^{13} +(2.61811 + 0.381412i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.31842 + 4.01562i) q^{17} +(-5.35129 + 3.08957i) q^{19} -6.33033 q^{22} +(-6.10091 + 3.52236i) q^{23} +(-0.526449 - 0.911836i) q^{26} +(2.45806 - 0.978745i) q^{28} -2.98101i q^{29} +(5.46948 + 3.15781i) q^{31} +(-0.866025 - 0.500000i) q^{32} +4.63684i q^{34} +(1.73991 + 3.01361i) q^{37} +(-3.08957 + 5.35129i) q^{38} -6.97007 q^{41} -2.58650 q^{43} +(-5.48223 + 3.16517i) q^{44} +(-3.52236 + 6.10091i) q^{46} +(4.07711 + 7.06176i) q^{47} +(1.62493 + 6.80879i) q^{49} +(-0.911836 - 0.526449i) q^{52} +(-7.68480 - 4.43682i) q^{53} +(1.63937 - 2.07665i) q^{56} +(-1.49051 - 2.58163i) q^{58} +(-0.452296 + 0.783400i) q^{59} +(-8.81047 + 5.08673i) q^{61} +6.31561 q^{62} -1.00000 q^{64} +(4.91612 - 8.51497i) q^{67} +(2.31842 + 4.01562i) q^{68} +14.4282i q^{71} +(-7.24574 - 4.18333i) q^{73} +(3.01361 + 1.73991i) q^{74} +6.17914i q^{76} +(-6.19578 - 15.5603i) q^{77} +(-2.73283 - 4.73340i) q^{79} +(-6.03626 + 3.48504i) q^{82} +14.6297 q^{83} +(-2.23997 + 1.29325i) q^{86} +(-3.16517 + 5.48223i) q^{88} +(-1.91982 - 3.32522i) q^{89} +(1.72609 - 2.18650i) q^{91} +7.04472i q^{92} +(7.06176 + 4.07711i) q^{94} -5.87891i q^{97} +(4.81163 + 5.08412i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 16q^{4} + O(q^{10}) \) \( 32q + 16q^{4} - 16q^{16} - 48q^{19} + 24q^{31} - 16q^{46} + 56q^{49} + 48q^{61} - 32q^{64} - 8q^{79} - 56q^{91} + 120q^{94} + O(q^{100}) \)

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
\(7\) 2.07665 + 1.63937i 0.784899 + 0.619624i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) −5.48223 3.16517i −1.65295 0.954334i −0.975849 0.218448i \(-0.929901\pi\)
−0.677106 0.735886i \(-0.736766\pi\)
\(12\) 0 0
\(13\) 1.05290i 0.292021i −0.989283 0.146011i \(-0.953357\pi\)
0.989283 0.146011i \(-0.0466434\pi\)
\(14\) 2.61811 + 0.381412i 0.699721 + 0.101937i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.31842 + 4.01562i −0.562299 + 0.973931i 0.434996 + 0.900432i \(0.356750\pi\)
−0.997295 + 0.0734985i \(0.976584\pi\)
\(18\) 0 0
\(19\) −5.35129 + 3.08957i −1.22767 + 0.708795i −0.966542 0.256509i \(-0.917428\pi\)
−0.261128 + 0.965304i \(0.584094\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −6.33033 −1.34963
\(23\) −6.10091 + 3.52236i −1.27213 + 0.734463i −0.975388 0.220496i \(-0.929232\pi\)
−0.296739 + 0.954959i \(0.595899\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −0.526449 0.911836i −0.103245 0.178826i
\(27\) 0 0
\(28\) 2.45806 0.978745i 0.464530 0.184965i
\(29\) 2.98101i 0.553560i −0.960933 0.276780i \(-0.910733\pi\)
0.960933 0.276780i \(-0.0892674\pi\)
\(30\) 0 0
\(31\) 5.46948 + 3.15781i 0.982348 + 0.567159i 0.902978 0.429686i \(-0.141376\pi\)
0.0793697 + 0.996845i \(0.474709\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 4.63684i 0.795211i
\(35\) 0 0
\(36\) 0 0
\(37\) 1.73991 + 3.01361i 0.286039 + 0.495434i 0.972861 0.231392i \(-0.0743279\pi\)
−0.686821 + 0.726826i \(0.740995\pi\)
\(38\) −3.08957 + 5.35129i −0.501194 + 0.868094i
\(39\) 0 0
\(40\) 0 0
\(41\) −6.97007 −1.08854 −0.544271 0.838909i \(-0.683194\pi\)
−0.544271 + 0.838909i \(0.683194\pi\)
\(42\) 0 0
\(43\) −2.58650 −0.394437 −0.197218 0.980360i \(-0.563191\pi\)
−0.197218 + 0.980360i \(0.563191\pi\)
\(44\) −5.48223 + 3.16517i −0.826477 + 0.477167i
\(45\) 0 0
\(46\) −3.52236 + 6.10091i −0.519344 + 0.899529i
\(47\) 4.07711 + 7.06176i 0.594707 + 1.03006i 0.993588 + 0.113060i \(0.0360654\pi\)
−0.398881 + 0.917003i \(0.630601\pi\)
\(48\) 0 0
\(49\) 1.62493 + 6.80879i 0.232133 + 0.972684i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.911836 0.526449i −0.126449 0.0730053i
\(53\) −7.68480 4.43682i −1.05559 0.609445i −0.131380 0.991332i \(-0.541941\pi\)
−0.924209 + 0.381887i \(0.875274\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.63937 2.07665i 0.219070 0.277504i
\(57\) 0 0
\(58\) −1.49051 2.58163i −0.195713 0.338985i
\(59\) −0.452296 + 0.783400i −0.0588839 + 0.101990i −0.893965 0.448137i \(-0.852088\pi\)
0.835081 + 0.550127i \(0.185421\pi\)
\(60\) 0 0
\(61\) −8.81047 + 5.08673i −1.12807 + 0.651289i −0.943448 0.331522i \(-0.892438\pi\)
−0.184618 + 0.982810i \(0.559105\pi\)
\(62\) 6.31561 0.802084
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 4.91612 8.51497i 0.600600 1.04027i −0.392131 0.919909i \(-0.628262\pi\)
0.992730 0.120360i \(-0.0384047\pi\)
\(68\) 2.31842 + 4.01562i 0.281150 + 0.486965i
\(69\) 0 0
\(70\) 0 0
\(71\) 14.4282i 1.71232i 0.516713 + 0.856159i \(0.327156\pi\)
−0.516713 + 0.856159i \(0.672844\pi\)
\(72\) 0 0
\(73\) −7.24574 4.18333i −0.848050 0.489622i 0.0119423 0.999929i \(-0.496199\pi\)
−0.859992 + 0.510307i \(0.829532\pi\)
\(74\) 3.01361 + 1.73991i 0.350325 + 0.202260i
\(75\) 0 0
\(76\) 6.17914i 0.708795i
\(77\) −6.19578 15.5603i −0.706075 1.77327i
\(78\) 0 0
\(79\) −2.73283 4.73340i −0.307467 0.532549i 0.670340 0.742054i \(-0.266148\pi\)
−0.977808 + 0.209505i \(0.932815\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −6.03626 + 3.48504i −0.666593 + 0.384858i
\(83\) 14.6297 1.60581 0.802907 0.596105i \(-0.203286\pi\)
0.802907 + 0.596105i \(0.203286\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.23997 + 1.29325i −0.241542 + 0.139455i
\(87\) 0 0
\(88\) −3.16517 + 5.48223i −0.337408 + 0.584408i
\(89\) −1.91982 3.32522i −0.203500 0.352473i 0.746154 0.665774i \(-0.231898\pi\)
−0.949654 + 0.313301i \(0.898565\pi\)
\(90\) 0 0
\(91\) 1.72609 2.18650i 0.180943 0.229207i
\(92\) 7.04472i 0.734463i
\(93\) 0 0
\(94\) 7.06176 + 4.07711i 0.728365 + 0.420522i
\(95\) 0 0
\(96\) 0 0
\(97\) 5.87891i 0.596913i −0.954423 0.298457i \(-0.903528\pi\)
0.954423 0.298457i \(-0.0964718\pi\)
\(98\) 4.81163 + 5.08412i 0.486048 + 0.513573i
\(99\) 0 0
\(100\) 0 0
\(101\) 3.35408 5.80944i 0.333744 0.578061i −0.649499 0.760362i \(-0.725021\pi\)
0.983243 + 0.182301i \(0.0583547\pi\)
\(102\) 0 0
\(103\) 4.30789 2.48716i 0.424469 0.245067i −0.272519 0.962151i \(-0.587857\pi\)
0.696988 + 0.717083i \(0.254523\pi\)
\(104\) −1.05290 −0.103245
\(105\) 0 0
\(106\) −8.87365 −0.861885
\(107\) 6.35602 3.66965i 0.614460 0.354759i −0.160249 0.987077i \(-0.551230\pi\)
0.774709 + 0.632318i \(0.217896\pi\)
\(108\) 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
\(112\) 0.381412 2.61811i 0.0360400 0.247389i
\(113\) 0.184551i 0.0173611i −0.999962 0.00868054i \(-0.997237\pi\)
0.999962 0.00868054i \(-0.00276314\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.58163 1.49051i −0.239699 0.138390i
\(117\) 0 0
\(118\) 0.904592i 0.0832745i
\(119\) −11.3976 + 4.53828i −1.04482 + 0.416024i
\(120\) 0 0
\(121\) 14.5366 + 25.1781i 1.32151 + 2.28891i
\(122\) −5.08673 + 8.81047i −0.460531 + 0.797663i
\(123\) 0 0
\(124\) 5.46948 3.15781i 0.491174 0.283579i
\(125\) 0 0
\(126\) 0 0
\(127\) −6.70276 −0.594774 −0.297387 0.954757i \(-0.596115\pi\)
−0.297387 + 0.954757i \(0.596115\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −2.24116 3.88180i −0.195811 0.339155i 0.751355 0.659898i \(-0.229401\pi\)
−0.947166 + 0.320743i \(0.896067\pi\)
\(132\) 0 0
\(133\) −16.1777 2.35680i −1.40278 0.204360i
\(134\) 9.83224i 0.849376i
\(135\) 0 0
\(136\) 4.01562 + 2.31842i 0.344337 + 0.198803i
\(137\) −15.2098 8.78137i −1.29946 0.750243i −0.319149 0.947705i \(-0.603397\pi\)
−0.980311 + 0.197461i \(0.936730\pi\)
\(138\) 0 0
\(139\) 6.02268i 0.510837i 0.966831 + 0.255418i \(0.0822132\pi\)
−0.966831 + 0.255418i \(0.917787\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 7.21412 + 12.4952i 0.605396 + 1.04858i
\(143\) −3.33260 + 5.77223i −0.278686 + 0.482698i
\(144\) 0 0
\(145\) 0 0
\(146\) −8.36666 −0.692430
\(147\) 0 0
\(148\) 3.47982 0.286039
\(149\) −6.06548 + 3.50191i −0.496903 + 0.286887i −0.727434 0.686178i \(-0.759287\pi\)
0.230530 + 0.973065i \(0.425954\pi\)
\(150\) 0 0
\(151\) −6.43540 + 11.1464i −0.523706 + 0.907085i 0.475913 + 0.879492i \(0.342118\pi\)
−0.999619 + 0.0275929i \(0.991216\pi\)
\(152\) 3.08957 + 5.35129i 0.250597 + 0.434047i
\(153\) 0 0
\(154\) −13.1459 10.3778i −1.05932 0.836263i
\(155\) 0 0
\(156\) 0 0
\(157\) −9.56427 5.52193i −0.763312 0.440698i 0.0671718 0.997741i \(-0.478602\pi\)
−0.830484 + 0.557043i \(0.811936\pi\)
\(158\) −4.73340 2.73283i −0.376569 0.217412i
\(159\) 0 0
\(160\) 0 0
\(161\) −18.4439 2.68694i −1.45358 0.211760i
\(162\) 0 0
\(163\) 3.62287 + 6.27500i 0.283765 + 0.491496i 0.972309 0.233699i \(-0.0750830\pi\)
−0.688544 + 0.725195i \(0.741750\pi\)
\(164\) −3.48504 + 6.03626i −0.272136 + 0.471353i
\(165\) 0 0
\(166\) 12.6697 7.31483i 0.983356 0.567741i
\(167\) −13.8606 −1.07257 −0.536283 0.844038i \(-0.680172\pi\)
−0.536283 + 0.844038i \(0.680172\pi\)
\(168\) 0 0
\(169\) 11.8914 0.914724
\(170\) 0 0
\(171\) 0 0
\(172\) −1.29325 + 2.23997i −0.0986092 + 0.170796i
\(173\) 0.479402 + 0.830348i 0.0364482 + 0.0631302i 0.883674 0.468103i \(-0.155062\pi\)
−0.847226 + 0.531233i \(0.821729\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.33033i 0.477167i
\(177\) 0 0
\(178\) −3.32522 1.91982i −0.249236 0.143896i
\(179\) −20.2531 11.6931i −1.51379 0.873984i −0.999870 0.0161436i \(-0.994861\pi\)
−0.513916 0.857841i \(-0.671806\pi\)
\(180\) 0 0
\(181\) 19.2865i 1.43355i 0.697303 + 0.716776i \(0.254383\pi\)
−0.697303 + 0.716776i \(0.745617\pi\)
\(182\) 0.401588 2.75661i 0.0297677 0.204333i
\(183\) 0 0
\(184\) 3.52236 + 6.10091i 0.259672 + 0.449765i
\(185\) 0 0
\(186\) 0 0
\(187\) 25.4202 14.6764i 1.85891 1.07324i
\(188\) 8.15421 0.594707
\(189\) 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
\(193\) 4.10862 7.11634i 0.295745 0.512246i −0.679413 0.733756i \(-0.737765\pi\)
0.975158 + 0.221511i \(0.0710987\pi\)
\(194\) −2.93946 5.09129i −0.211041 0.365533i
\(195\) 0 0
\(196\) 6.70905 + 1.99716i 0.479218 + 0.142654i
\(197\) 3.51321i 0.250306i 0.992137 + 0.125153i \(0.0399422\pi\)
−0.992137 + 0.125153i \(0.960058\pi\)
\(198\) 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
\(202\) 6.70816i 0.471985i
\(203\) 4.88698 6.19052i 0.342999 0.434489i
\(204\) 0 0
\(205\) 0 0
\(206\) 2.48716 4.30789i 0.173289 0.300145i
\(207\) 0 0
\(208\) −0.911836 + 0.526449i −0.0632245 + 0.0365027i
\(209\) 39.1160 2.70571
\(210\) 0 0
\(211\) −9.96592 −0.686082 −0.343041 0.939320i \(-0.611457\pi\)
−0.343041 + 0.939320i \(0.611457\pi\)
\(212\) −7.68480 + 4.43682i −0.527795 + 0.304722i
\(213\) 0 0
\(214\) 3.66965 6.35602i 0.250852 0.434489i
\(215\) 0 0
\(216\) 0 0
\(217\) 6.18138 + 15.5242i 0.419619 + 1.05385i
\(218\) 2.00000i 0.135457i
\(219\) 0 0
\(220\) 0 0
\(221\) 4.22804 + 2.44106i 0.284408 + 0.164203i
\(222\) 0 0
\(223\) 11.1087i 0.743894i 0.928254 + 0.371947i \(0.121310\pi\)
−0.928254 + 0.371947i \(0.878690\pi\)
\(224\) −0.978745 2.45806i −0.0653952 0.164236i
\(225\) 0 0
\(226\) −0.0922754 0.159826i −0.00613807 0.0106314i
\(227\) 11.7619 20.3722i 0.780665 1.35215i −0.150889 0.988551i \(-0.548214\pi\)
0.931555 0.363602i \(-0.118453\pi\)
\(228\) 0 0
\(229\) 8.21579 4.74339i 0.542915 0.313452i −0.203345 0.979107i \(-0.565181\pi\)
0.746259 + 0.665655i \(0.231848\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −2.98101 −0.195713
\(233\) −8.98361 + 5.18669i −0.588536 + 0.339791i −0.764518 0.644602i \(-0.777023\pi\)
0.175982 + 0.984393i \(0.443690\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.452296 + 0.783400i 0.0294420 + 0.0509950i
\(237\) 0 0
\(238\) −7.60149 + 9.62908i −0.492732 + 0.624161i
\(239\) 12.3746i 0.800444i 0.916418 + 0.400222i \(0.131067\pi\)
−0.916418 + 0.400222i \(0.868933\pi\)
\(240\) 0 0
\(241\) −10.8208 6.24737i −0.697027 0.402429i 0.109212 0.994018i \(-0.465167\pi\)
−0.806239 + 0.591590i \(0.798501\pi\)
\(242\) 25.1781 + 14.5366i 1.61851 + 0.934445i
\(243\) 0 0
\(244\) 10.1735i 0.651289i
\(245\) 0 0
\(246\) 0 0
\(247\) 3.25300 + 5.63436i 0.206983 + 0.358506i
\(248\) 3.15781 5.46948i 0.200521 0.347312i
\(249\) 0 0
\(250\) 0 0
\(251\) 13.5304 0.854034 0.427017 0.904244i \(-0.359564\pi\)
0.427017 + 0.904244i \(0.359564\pi\)
\(252\) 0 0
\(253\) 44.5954 2.80369
\(254\) −5.80476 + 3.35138i −0.364223 + 0.210284i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −2.20899 3.82609i −0.137793 0.238665i 0.788868 0.614563i \(-0.210668\pi\)
−0.926661 + 0.375898i \(0.877334\pi\)
\(258\) 0 0
\(259\) −1.32724 + 9.11056i −0.0824709 + 0.566103i
\(260\) 0 0
\(261\) 0 0
\(262\) −3.88180 2.24116i −0.239819 0.138459i
\(263\) −5.30558 3.06318i −0.327156 0.188884i 0.327422 0.944878i \(-0.393820\pi\)
−0.654578 + 0.755995i \(0.727154\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −15.1887 + 6.04780i −0.931278 + 0.370814i
\(267\) 0 0
\(268\) −4.91612 8.51497i −0.300300 0.520135i
\(269\) −2.09370 + 3.62639i −0.127655 + 0.221105i −0.922768 0.385357i \(-0.874078\pi\)
0.795113 + 0.606462i \(0.207412\pi\)
\(270\) 0 0
\(271\) 0.253692 0.146469i 0.0154107 0.00889737i −0.492275 0.870440i \(-0.663835\pi\)
0.507686 + 0.861542i \(0.330501\pi\)
\(272\) 4.63684 0.281150
\(273\) 0 0
\(274\) −17.5627 −1.06100
\(275\) 0 0
\(276\) 0 0
\(277\) −7.31099 + 12.6630i −0.439275 + 0.760847i −0.997634 0.0687531i \(-0.978098\pi\)
0.558359 + 0.829600i \(0.311431\pi\)
\(278\) 3.01134 + 5.21579i 0.180608 + 0.312822i
\(279\) 0 0
\(280\) 0 0
\(281\) 18.1691i 1.08388i 0.840419 + 0.541938i \(0.182309\pi\)
−0.840419 + 0.541938i \(0.817691\pi\)
\(282\) 0 0
\(283\) 18.3712 + 10.6066i 1.09206 + 0.630499i 0.934123 0.356951i \(-0.116184\pi\)
0.157933 + 0.987450i \(0.449517\pi\)
\(284\) 12.4952 + 7.21412i 0.741455 + 0.428079i
\(285\) 0 0
\(286\) 6.66519i 0.394121i
\(287\) −14.4744 11.4265i −0.854396 0.674486i
\(288\) 0 0
\(289\) −2.25013 3.89734i −0.132361 0.229256i
\(290\) 0 0
\(291\) 0 0
\(292\) −7.24574 + 4.18333i −0.424025 + 0.244811i
\(293\) −7.64481 −0.446615 −0.223307 0.974748i \(-0.571685\pi\)
−0.223307 + 0.974748i \(0.571685\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.01361 1.73991i 0.175163 0.101130i
\(297\) 0 0
\(298\) −3.50191 + 6.06548i −0.202860 + 0.351364i
\(299\) 3.70868 + 6.42363i 0.214479 + 0.371488i
\(300\) 0 0
\(301\) −5.37124 4.24022i −0.309593 0.244402i
\(302\) 12.8708i 0.740632i
\(303\) 0 0
\(304\) 5.35129 + 3.08957i 0.306917 + 0.177199i
\(305\) 0 0
\(306\) 0 0
\(307\) 13.1561i 0.750859i −0.926851 0.375429i \(-0.877495\pi\)
0.926851 0.375429i \(-0.122505\pi\)
\(308\) −16.5735 2.41446i −0.944365 0.137577i
\(309\) 0 0
\(310\) 0 0
\(311\) −3.13043 + 5.42207i −0.177511 + 0.307457i −0.941027 0.338331i \(-0.890138\pi\)
0.763517 + 0.645788i \(0.223471\pi\)
\(312\) 0 0
\(313\) 15.1392 8.74065i 0.855721 0.494051i −0.00685609 0.999976i \(-0.502182\pi\)
0.862577 + 0.505926i \(0.168849\pi\)
\(314\) −11.0439 −0.623241
\(315\) 0 0
\(316\) −5.46566 −0.307467
\(317\) −1.32832 + 0.766906i −0.0746058 + 0.0430737i −0.536839 0.843685i \(-0.680382\pi\)
0.462233 + 0.886758i \(0.347048\pi\)
\(318\) 0 0
\(319\) −9.43540 + 16.3426i −0.528281 + 0.915010i
\(320\) 0 0
\(321\) 0 0
\(322\) −17.3163 + 6.89498i −0.965002 + 0.384242i
\(323\) 28.6516i 1.59422i
\(324\) 0 0
\(325\) 0 0
\(326\) 6.27500 + 3.62287i 0.347540 + 0.200652i
\(327\) 0 0
\(328\) 6.97007i 0.384858i
\(329\) −3.11011 + 21.3487i −0.171466 + 1.17699i
\(330\) 0 0
\(331\) 0.756607 + 1.31048i 0.0415869 + 0.0720306i 0.886070 0.463552i \(-0.153425\pi\)
−0.844483 + 0.535583i \(0.820092\pi\)
\(332\) 7.31483 12.6697i 0.401453 0.695337i
\(333\) 0 0
\(334\) −12.0036 + 6.93030i −0.656810 + 0.379209i
\(335\) 0 0
\(336\) 0 0
\(337\) −3.14064 −0.171082 −0.0855408 0.996335i \(-0.527262\pi\)
−0.0855408 + 0.996335i \(0.527262\pi\)
\(338\) 10.2983 5.94570i 0.560152 0.323404i
\(339\) 0 0
\(340\) 0 0
\(341\) −19.9900 34.6236i −1.08252 1.87498i
\(342\) 0 0
\(343\) −7.78771 + 16.8033i −0.420497 + 0.907294i
\(344\) 2.58650i 0.139455i
\(345\) 0 0
\(346\) 0.830348 + 0.479402i 0.0446398 + 0.0257728i
\(347\) 23.7336 + 13.7026i 1.27408 + 0.735593i 0.975754 0.218870i \(-0.0702370\pi\)
0.298330 + 0.954463i \(0.403570\pi\)
\(348\) 0 0
\(349\) 19.5594i 1.04699i 0.852028 + 0.523496i \(0.175373\pi\)
−0.852028 + 0.523496i \(0.824627\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 3.16517 + 5.48223i 0.168704 + 0.292204i
\(353\) 7.40515 12.8261i 0.394136 0.682664i −0.598854 0.800858i \(-0.704377\pi\)
0.992991 + 0.118194i \(0.0377105\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −3.83964 −0.203500
\(357\) 0 0
\(358\) −23.3862 −1.23600
\(359\) 14.3492 8.28450i 0.757321 0.437239i −0.0710122 0.997475i \(-0.522623\pi\)
0.828333 + 0.560236i \(0.189290\pi\)
\(360\) 0 0
\(361\) 9.59086 16.6119i 0.504782 0.874308i
\(362\) 9.64324 + 16.7026i 0.506837 + 0.877868i
\(363\) 0 0
\(364\) −1.03052 2.58809i −0.0540138 0.135653i
\(365\) 0 0
\(366\) 0 0
\(367\) 12.1357 + 7.00655i 0.633479 + 0.365739i 0.782098 0.623155i \(-0.214150\pi\)
−0.148619 + 0.988894i \(0.547483\pi\)
\(368\) 6.10091 + 3.52236i 0.318032 + 0.183616i
\(369\) 0 0
\(370\) 0 0
\(371\) −8.68504 21.8120i −0.450905 1.13242i
\(372\) 0 0
\(373\) −7.31099 12.6630i −0.378549 0.655666i 0.612303 0.790624i \(-0.290243\pi\)
−0.990851 + 0.134958i \(0.956910\pi\)
\(374\) 14.6764 25.4202i 0.758897 1.31445i
\(375\) 0 0
\(376\) 7.06176 4.07711i 0.364182 0.210261i
\(377\) −3.13870 −0.161651
\(378\) 0 0
\(379\) 4.68145 0.240470 0.120235 0.992745i \(-0.461635\pi\)
0.120235 + 0.992745i \(0.461635\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −1.41421 + 2.44949i −0.0723575 + 0.125327i
\(383\) −5.83621 10.1086i −0.298216 0.516526i 0.677511 0.735512i \(-0.263058\pi\)
−0.975728 + 0.218986i \(0.929725\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 8.21725i 0.418247i
\(387\) 0 0
\(388\) −5.09129 2.93946i −0.258471 0.149228i
\(389\) −11.3452 6.55018i −0.575226 0.332107i 0.184008 0.982925i \(-0.441093\pi\)
−0.759234 + 0.650818i \(0.774426\pi\)
\(390\) 0 0
\(391\) 32.6652i 1.65195i
\(392\) 6.80879 1.62493i 0.343896 0.0820715i
\(393\) 0 0
\(394\) 1.75661 + 3.04253i 0.0884966 + 0.153281i
\(395\) 0 0
\(396\) 0 0
\(397\) 26.5700 15.3402i 1.33351 0.769903i 0.347675 0.937615i \(-0.386971\pi\)
0.985836 + 0.167712i \(0.0536378\pi\)
\(398\) 3.46410 0.173640
\(399\) 0 0
\(400\) 0 0
\(401\) 6.88085 3.97266i 0.343613 0.198385i −0.318255 0.948005i \(-0.603097\pi\)
0.661869 + 0.749620i \(0.269764\pi\)
\(402\) 0 0
\(403\) 3.32485 5.75880i 0.165622 0.286866i
\(404\) −3.35408 5.80944i −0.166872 0.289030i
\(405\) 0 0
\(406\) 1.13699 7.80464i 0.0564281 0.387338i
\(407\) 22.0284i 1.09191i
\(408\) 0 0
\(409\) −34.4957 19.9161i −1.70570 0.984789i −0.939729 0.341919i \(-0.888923\pi\)
−0.765975 0.642870i \(-0.777744\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 4.97432i 0.245067i
\(413\) −2.22354 + 0.885365i −0.109413 + 0.0435660i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.526449 + 0.911836i −0.0258113 + 0.0447064i
\(417\) 0 0
\(418\) 33.8754 19.5580i 1.65690 0.956613i
\(419\) −11.0357 −0.539131 −0.269566 0.962982i \(-0.586880\pi\)
−0.269566 + 0.962982i \(0.586880\pi\)
\(420\) 0 0
\(421\) −7.78421 −0.379379 −0.189690 0.981844i \(-0.560748\pi\)
−0.189690 + 0.981844i \(0.560748\pi\)
\(422\) −8.63074 + 4.98296i −0.420138 + 0.242567i
\(423\) 0 0
\(424\) −4.43682 + 7.68480i −0.215471 + 0.373207i
\(425\) 0 0
\(426\) 0 0
\(427\) −26.6353 3.88028i −1.28897 0.187780i
\(428\) 7.33930i 0.354759i
\(429\) 0 0
\(430\) 0 0
\(431\) −8.86273 5.11690i −0.426903 0.246472i 0.271124 0.962545i \(-0.412605\pi\)
−0.698026 + 0.716072i \(0.745938\pi\)
\(432\) 0 0
\(433\) 40.3902i 1.94103i −0.241047 0.970513i \(-0.577491\pi\)
0.241047 0.970513i \(-0.422509\pi\)
\(434\) 13.1153 + 10.3536i 0.629555 + 0.496990i
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) 21.7651 37.6983i 1.04117 1.80336i
\(438\) 0 0
\(439\) 11.2331 6.48543i 0.536126 0.309533i −0.207381 0.978260i \(-0.566494\pi\)
0.743508 + 0.668728i \(0.233161\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.88212 0.232219
\(443\) 7.49547 4.32751i 0.356120 0.205606i −0.311257 0.950326i \(-0.600750\pi\)
0.667378 + 0.744720i \(0.267417\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 5.55435 + 9.62042i 0.263006 + 0.455540i
\(447\) 0 0
\(448\) −2.07665 1.63937i −0.0981124 0.0774529i
\(449\) 25.4407i 1.20062i −0.799768 0.600310i \(-0.795044\pi\)
0.799768 0.600310i \(-0.204956\pi\)
\(450\) 0 0
\(451\) 38.2115 + 22.0614i 1.79931 + 1.03883i
\(452\) −0.159826 0.0922754i −0.00751757 0.00434027i
\(453\) 0 0
\(454\) 23.5238i 1.10403i
\(455\) 0 0
\(456\) 0 0
\(457\) 15.2697 + 26.4480i 0.714289 + 1.23718i 0.963233 + 0.268666i \(0.0865829\pi\)
−0.248945 + 0.968518i \(0.580084\pi\)
\(458\) 4.74339 8.21579i 0.221644 0.383899i
\(459\) 0 0
\(460\) 0 0
\(461\) 15.6680 0.729734 0.364867 0.931060i \(-0.381114\pi\)
0.364867 + 0.931060i \(0.381114\pi\)
\(462\) 0 0
\(463\) −32.0462 −1.48931 −0.744656 0.667448i \(-0.767387\pi\)
−0.744656 + 0.667448i \(0.767387\pi\)
\(464\) −2.58163 + 1.49051i −0.119849 + 0.0691950i
\(465\) 0 0
\(466\) −5.18669 + 8.98361i −0.240269 + 0.416158i
\(467\) 0.349579 + 0.605489i 0.0161766 + 0.0280187i 0.874000 0.485925i \(-0.161517\pi\)
−0.857824 + 0.513944i \(0.828184\pi\)
\(468\) 0 0
\(469\) 24.1682 9.62326i 1.11599 0.444361i
\(470\) 0 0
\(471\) 0 0
\(472\) 0.783400 + 0.452296i 0.0360589 + 0.0208186i
\(473\) 14.1798 + 8.18669i 0.651986 + 0.376424i
\(474\) 0 0
\(475\) 0 0
\(476\) −1.76855 + 12.1398i −0.0810611 + 0.556426i
\(477\) 0 0
\(478\) 6.18728 + 10.7167i 0.283000 + 0.490170i
\(479\) −4.27280 + 7.40071i −0.195229 + 0.338147i −0.946976 0.321305i \(-0.895878\pi\)
0.751746 + 0.659452i \(0.229212\pi\)
\(480\) 0 0
\(481\) 3.17302 1.83195i 0.144677 0.0835295i
\(482\) −12.4947 −0.569120
\(483\) 0 0
\(484\) 29.0731 1.32151
\(485\) 0 0
\(486\) 0 0
\(487\) −11.9089 + 20.6268i −0.539643 + 0.934689i 0.459280 + 0.888292i \(0.348108\pi\)
−0.998923 + 0.0463978i \(0.985226\pi\)
\(488\) 5.08673 + 8.81047i 0.230265 + 0.398831i
\(489\) 0 0
\(490\) 0 0
\(491\) 12.9104i 0.582638i 0.956626 + 0.291319i \(0.0940941\pi\)
−0.956626 + 0.291319i \(0.905906\pi\)
\(492\) 0 0
\(493\) 11.9706 + 6.91124i 0.539129 + 0.311267i
\(494\) 5.63436 + 3.25300i 0.253502 + 0.146359i
\(495\) 0 0
\(496\) 6.31561i 0.283579i
\(497\) −23.6532 + 29.9624i −1.06099 + 1.34400i
\(498\) 0 0
\(499\) −8.16823 14.1478i −0.365660 0.633342i 0.623222 0.782045i \(-0.285823\pi\)
−0.988882 + 0.148703i \(0.952490\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 11.7177 6.76522i 0.522987 0.301947i
\(503\) 28.3413 1.26368 0.631838 0.775100i \(-0.282301\pi\)
0.631838 + 0.775100i \(0.282301\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 38.6208 22.2977i 1.71690 0.991254i
\(507\) 0 0
\(508\) −3.35138 + 5.80476i −0.148693 + 0.257545i
\(509\) −1.18911 2.05959i −0.0527062 0.0912898i 0.838469 0.544950i \(-0.183451\pi\)
−0.891175 + 0.453660i \(0.850118\pi\)
\(510\) 0 0
\(511\) −8.18883 20.5658i −0.362253 0.909776i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −3.82609 2.20899i −0.168762 0.0974346i
\(515\) 0 0
\(516\) 0 0
\(517\) 51.6189i 2.27020i
\(518\) 3.40585 + 8.55360i 0.149645 + 0.375824i
\(519\) 0 0
\(520\) 0 0
\(521\) −4.14185 + 7.17389i −0.181458 + 0.314294i −0.942377 0.334552i \(-0.891415\pi\)
0.760919 + 0.648846i \(0.224748\pi\)
\(522\) 0 0
\(523\) −36.2532 + 20.9308i −1.58524 + 0.915239i −0.591166 + 0.806550i \(0.701332\pi\)
−0.994076 + 0.108689i \(0.965335\pi\)
\(524\) −4.48232 −0.195811
\(525\) 0 0
\(526\) −6.12635 −0.267122
\(527\) −25.3611 + 14.6422i −1.10475 + 0.637826i
\(528\) 0 0
\(529\) 13.3140 23.0606i 0.578871 1.00263i
\(530\) 0 0
\(531\) 0 0
\(532\) −10.1299 + 12.8319i −0.439186 + 0.556333i
\(533\) 7.33877i 0.317877i
\(534\) 0 0
\(535\) 0 0
\(536\) −8.51497 4.91612i −0.367791 0.212344i
\(537\) 0 0
\(538\) 4.18740i 0.180531i
\(539\) 12.6427 42.4705i 0.544559 1.82933i
\(540\) 0 0
\(541\) −22.9652 39.7769i −0.987352 1.71014i −0.630978 0.775801i \(-0.717346\pi\)
−0.356374 0.934343i \(-0.615987\pi\)
\(542\) 0.146469 0.253692i 0.00629139 0.0108970i
\(543\) 0 0
\(544\) 4.01562 2.31842i 0.172168 0.0994014i
\(545\) 0 0
\(546\) 0 0
\(547\) −4.88688 −0.208948 −0.104474 0.994528i \(-0.533316\pi\)
−0.104474 + 0.994528i \(0.533316\pi\)
\(548\) −15.2098 + 8.78137i −0.649730 + 0.375122i
\(549\) 0 0
\(550\) 0 0
\(551\) 9.21004 + 15.9523i 0.392361 + 0.679589i
\(552\) 0 0
\(553\) 2.08467 14.3097i 0.0886490 0.608511i
\(554\) 14.6220i 0.621229i
\(555\) 0 0
\(556\) 5.21579 + 3.01134i 0.221199 + 0.127709i
\(557\) −25.4332 14.6839i −1.07764 0.622175i −0.147380 0.989080i \(-0.547084\pi\)
−0.930258 + 0.366905i \(0.880417\pi\)
\(558\) 0 0
\(559\) 2.72332i 0.115184i
\(560\) 0 0
\(561\) 0 0
\(562\) 9.08453 + 15.7349i 0.383208 + 0.663735i
\(563\) −1.36961 + 2.37223i −0.0577220 + 0.0999775i −0.893442 0.449178i \(-0.851717\pi\)
0.835720 + 0.549155i \(0.185050\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 21.2133 0.891660
\(567\) 0 0
\(568\) 14.4282 0.605396
\(569\) 0.798865 0.461225i 0.0334902 0.0193356i −0.483161 0.875531i \(-0.660512\pi\)
0.516652 + 0.856196i \(0.327178\pi\)
\(570\) 0 0
\(571\) 12.2761 21.2629i 0.513740 0.889824i −0.486133 0.873885i \(-0.661593\pi\)
0.999873 0.0159389i \(-0.00507372\pi\)
\(572\) 3.33260 + 5.77223i 0.139343 + 0.241349i
\(573\) 0 0
\(574\) −18.2484 2.65847i −0.761675 0.110962i
\(575\) 0 0
\(576\) 0 0
\(577\) −23.4982 13.5667i −0.978241 0.564788i −0.0765024 0.997069i \(-0.524375\pi\)
−0.901739 + 0.432282i \(0.857709\pi\)
\(578\) −3.89734 2.25013i −0.162108 0.0935932i
\(579\) 0 0
\(580\) 0 0
\(581\) 30.3806 + 23.9834i 1.26040 + 0.995000i
\(582\) 0 0
\(583\) 28.0866 + 48.6474i 1.16323 + 2.01477i
\(584\) −4.18333 + 7.24574i −0.173108 + 0.299831i
\(585\) 0 0
\(586\) −6.62060 + 3.82240i −0.273494 + 0.157902i
\(587\) 8.71353 0.359646 0.179823 0.983699i \(-0.442448\pi\)
0.179823 + 0.983699i \(0.442448\pi\)
\(588\) 0 0
\(589\) −39.0250 −1.60800
\(590\) 0 0
\(591\) 0 0
\(592\) 1.73991 3.01361i 0.0715098 0.123859i
\(593\) −9.13432 15.8211i −0.375102 0.649695i 0.615241 0.788339i \(-0.289059\pi\)
−0.990342 + 0.138644i \(0.955726\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 7.00381i 0.286887i
\(597\) 0 0
\(598\) 6.42363 + 3.70868i 0.262682 + 0.151659i
\(599\) 9.94576 + 5.74219i 0.406373 + 0.234619i 0.689230 0.724543i \(-0.257949\pi\)
−0.282857 + 0.959162i \(0.591282\pi\)
\(600\) 0 0
\(601\) 34.4022i 1.40329i 0.712525 + 0.701647i \(0.247552\pi\)
−0.712525 + 0.701647i \(0.752448\pi\)
\(602\) −6.77174 0.986520i −0.275996 0.0402076i
\(603\) 0 0
\(604\) 6.43540 + 11.1464i 0.261853 + 0.453543i
\(605\) 0 0
\(606\) 0 0
\(607\) 39.4152 22.7564i 1.59981 0.923653i 0.608293 0.793713i \(-0.291855\pi\)
0.991522 0.129941i \(-0.0414787\pi\)
\(608\) 6.17914 0.250597
\(609\) 0 0
\(610\) 0 0
\(611\) 7.43531 4.29278i 0.300800 0.173667i
\(612\) 0 0
\(613\) −5.85205 + 10.1361i −0.236362 + 0.409391i −0.959668 0.281137i \(-0.909289\pi\)
0.723306 + 0.690528i \(0.242622\pi\)
\(614\) −6.57805 11.3935i −0.265469 0.459805i
\(615\) 0 0
\(616\) −15.5603 + 6.19578i −0.626944 + 0.249635i
\(617\) 24.0582i 0.968547i −0.874917 0.484273i \(-0.839084\pi\)
0.874917 0.484273i \(-0.160916\pi\)
\(618\) 0 0
\(619\) −3.32794 1.92139i −0.133761 0.0772271i 0.431626 0.902053i \(-0.357940\pi\)
−0.565387 + 0.824825i \(0.691273\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 6.26087i 0.251038i
\(623\) 1.46448 10.0526i 0.0586733 0.402749i
\(624\) 0 0
\(625\) 0 0
\(626\) 8.74065 15.1392i 0.349347 0.605086i
\(627\) 0 0
\(628\) −9.56427 + 5.52193i −0.381656 + 0.220349i
\(629\) −16.1353 −0.643358
\(630\) 0 0
\(631\) −25.4387 −1.01270 −0.506349 0.862328i \(-0.669005\pi\)
−0.506349 + 0.862328i \(0.669005\pi\)
\(632\) −4.73340 + 2.73283i −0.188284 + 0.108706i
\(633\) 0 0
\(634\) −0.766906 + 1.32832i −0.0304577 + 0.0527543i
\(635\) 0 0
\(636\) 0 0
\(637\) 7.16896 1.71089i 0.284044 0.0677879i
\(638\) 18.8708i 0.747102i
\(639\) 0 0
\(640\) 0 0
\(641\) 34.2380 + 19.7673i 1.35232 + 0.780762i 0.988574 0.150737i \(-0.0481647\pi\)
0.363745 + 0.931499i \(0.381498\pi\)
\(642\) 0 0
\(643\) 12.2816i 0.484341i −0.970234 0.242170i \(-0.922141\pi\)
0.970234 0.242170i \(-0.0778593\pi\)
\(644\) −11.5489 + 14.6294i −0.455090 + 0.576479i
\(645\) 0 0
\(646\) −14.3258 24.8131i −0.563642 0.976257i
\(647\) 6.69470 11.5956i 0.263196 0.455869i −0.703893 0.710306i \(-0.748557\pi\)
0.967089 + 0.254437i \(0.0818901\pi\)
\(648\) 0 0
\(649\) 4.95918 2.86319i 0.194665 0.112390i
\(650\) 0 0
\(651\) 0 0
\(652\) 7.24574 0.283765
\(653\) −42.9355 + 24.7888i −1.68020 + 0.970062i −0.718670 + 0.695352i \(0.755249\pi\)
−0.961527 + 0.274710i \(0.911418\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.48504 + 6.03626i 0.136068 + 0.235676i
\(657\) 0 0
\(658\) 7.98090 + 20.0435i 0.311128 + 0.781379i
\(659\) 40.7622i 1.58787i 0.608002 + 0.793936i \(0.291971\pi\)
−0.608002 + 0.793936i \(0.708029\pi\)
\(660\) 0 0
\(661\) −30.9652 17.8778i −1.20441 0.695365i −0.242875 0.970057i \(-0.578091\pi\)
−0.961532 + 0.274692i \(0.911424\pi\)
\(662\) 1.31048 + 0.756607i 0.0509333 + 0.0294064i
\(663\) 0 0
\(664\) 14.6297i 0.567741i
\(665\) 0 0
\(666\) 0 0
\(667\) 10.5002 + 18.1869i 0.406569 + 0.704199i
\(668\) −6.93030 + 12.0036i −0.268141 + 0.464435i
\(669\) 0 0
\(670\) 0 0
\(671\) 64.4014 2.48619
\(672\) 0 0
\(673\) −35.1987 −1.35681 −0.678406 0.734687i \(-0.737329\pi\)
−0.678406 + 0.734687i \(0.737329\pi\)
\(674\) −2.71987 + 1.57032i −0.104766 + 0.0604865i
\(675\) 0 0
\(676\) 5.94570 10.2983i 0.228681 0.396087i
\(677\) 19.2211 + 33.2919i 0.738727 + 1.27951i 0.953069 + 0.302754i \(0.0979061\pi\)
−0.214341 + 0.976759i \(0.568761\pi\)
\(678\) 0 0
\(679\) 9.63771 12.2084i 0.369862 0.468517i
\(680\) 0 0
\(681\) 0 0
\(682\) −34.6236 19.9900i −1.32581 0.765455i
\(683\) 33.2574 + 19.2012i 1.27256 + 0.734712i 0.975469 0.220138i \(-0.0706507\pi\)
0.297089 + 0.954850i \(0.403984\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.65731 + 18.4460i 0.0632764 + 0.704270i
\(687\) 0 0
\(688\) 1.29325 + 2.23997i 0.0493046 + 0.0853981i
\(689\) −4.67152 + 8.09131i −0.177971 + 0.308254i
\(690\) 0 0
\(691\) 17.6209 10.1735i 0.670332 0.387016i −0.125870 0.992047i \(-0.540172\pi\)
0.796203 + 0.605030i \(0.206839\pi\)
\(692\) 0.958803 0.0364482
\(693\) 0 0
\(694\) 27.4052 1.04029
\(695\) 0 0
\(696\) 0 0
\(697\) 16.1595 27.9892i 0.612086 1.06016i
\(698\) 9.77972 + 16.9390i 0.370168 + 0.641149i
\(699\) 0 0
\(700\) 0 0
\(701\) 6.98574i 0.263848i 0.991260 + 0.131924i \(0.0421154\pi\)
−0.991260 + 0.131924i \(0.957885\pi\)
\(702\) 0 0
\(703\) −18.6215 10.7511i −0.702323 0.405487i
\(704\) 5.48223 + 3.16517i 0.206619 + 0.119292i
\(705\) 0 0
\(706\) 14.8103i 0.557393i
\(707\) 16.4891 6.56558i 0.620135 0.246924i
\(708\) 0 0
\(709\) 6.01348 + 10.4157i 0.225841 + 0.391168i 0.956571 0.291498i \(-0.0941537\pi\)
−0.730730 + 0.682666i \(0.760820\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −3.32522 + 1.91982i −0.124618 + 0.0719482i
\(713\) −44.4917 −1.66623
\(714\) 0 0
\(715\) 0 0
\(716\) −20.2531 + 11.6931i −0.756893 + 0.436992i
\(717\) 0 0
\(718\) 8.28450 14.3492i 0.309175 0.535507i
\(719\) 0.835694 + 1.44746i 0.0311661 + 0.0539813i 0.881188 0.472766i \(-0.156745\pi\)
−0.850022 + 0.526748i \(0.823411\pi\)
\(720\) 0 0
\(721\) 13.0233 + 1.89727i 0.485015 + 0.0706579i
\(722\) 19.1817i 0.713869i
\(723\) 0 0
\(724\) 16.7026 + 9.64324i 0.620746 + 0.358388i
\(725\) 0 0
\(726\) 0 0
\(727\) 42.5043i 1.57640i 0.615422 + 0.788198i \(0.288986\pi\)
−0.615422 + 0.788198i \(0.711014\pi\)
\(728\) −2.18650 1.72609i −0.0810370 0.0639731i
\(729\) 0 0
\(730\) 0 0
\(731\) 5.99658 10.3864i 0.221792 0.384154i
\(732\) 0 0
\(733\) 27.6053 15.9379i 1.01963 0.588681i 0.105630 0.994405i \(-0.466314\pi\)
0.913996 + 0.405724i \(0.132981\pi\)
\(734\) 14.0131 0.517233
\(735\) 0 0
\(736\) 7.04472 0.259672
\(737\) −53.9026 + 31.1207i −1.98553 + 1.14634i
\(738\) 0 0
\(739\) 8.20932 14.2190i 0.301985 0.523053i −0.674601 0.738183i \(-0.735684\pi\)
0.976585 + 0.215130i \(0.0690176\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −18.4274 14.5472i −0.676493 0.534044i
\(743\) 4.52385i 0.165964i 0.996551 + 0.0829821i \(0.0264444\pi\)
−0.996551 + 0.0829821i \(0.973556\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −12.6630 7.31099i −0.463626 0.267674i
\(747\) 0 0
\(748\) 29.3527i 1.07324i
\(749\) 19.2151 + 2.79930i 0.702106 + 0.102284i
\(750\) 0 0
\(751\) 8.69875 + 15.0667i 0.317422 + 0.549791i 0.979949 0.199247i \(-0.0638495\pi\)
−0.662527 + 0.749038i \(0.730516\pi\)
\(752\) 4.07711 7.06176i 0.148677 0.257516i
\(753\) 0 0
\(754\) −2.71820 + 1.56935i −0.0989908 + 0.0571524i
\(755\) 0 0
\(756\) 0 0
\(757\) −5.25454 −0.190980 −0.0954898 0.995430i \(-0.530442\pi\)
−0.0954898 + 0.995430i \(0.530442\pi\)
\(758\) 4.05425 2.34072i 0.147257 0.0850189i
\(759\) 0 0
\(760\) 0 0
\(761\) −7.31402 12.6683i −0.265133 0.459224i 0.702465 0.711718i \(-0.252083\pi\)
−0.967598 + 0.252494i \(0.918749\pi\)
\(762\) 0 0
\(763\) 4.91612 1.95749i 0.177975 0.0708659i
\(764\) 2.82843i 0.102329i
\(765\) 0 0
\(766\) −10.1086 5.83621i −0.365239 0.210871i
\(767\) 0.824840 + 0.476222i 0.0297832 + 0.0171954i
\(768\) 0 0
\(769\) 12.4548i 0.449131i −0.974459 0.224566i \(-0.927904\pi\)
0.974459 0.224566i \(-0.0720963\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −4.10862 7.11634i −0.147873 0.256123i
\(773\) −4.15288 + 7.19300i −0.149369 + 0.258714i −0.930994 0.365034i \(-0.881057\pi\)
0.781626 + 0.623748i \(0.214391\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −5.87891 −0.211041
\(777\) 0 0
\(778\) −13.1004 −0.469670
\(779\) 37.2989 21.5345i 1.33637 0.771554i
\(780\) 0 0
\(781\) 45.6678 79.0990i 1.63412 2.83038i
\(782\) −16.3326 28.2889i −0.584053 1.01161i
\(783\) 0 0
\(784\) 5.08412 4.81163i 0.181576 0.171844i
\(785\) 0 0
\(786\) 0 0