Properties

Label 1512.2.c.e.757.5
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 20
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.5
Root \(-0.885915 - 1.10234i\)
Character \(\chi\) = 1512.757
Dual form 1512.2.c.e.757.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.885915 - 1.10234i) q^{2} +(-0.430309 + 1.95316i) q^{4} +3.50133i q^{5} -1.00000 q^{7} +(2.53426 - 1.25599i) q^{8} +O(q^{10})\) \(q+(-0.885915 - 1.10234i) q^{2} +(-0.430309 + 1.95316i) q^{4} +3.50133i q^{5} -1.00000 q^{7} +(2.53426 - 1.25599i) q^{8} +(3.85966 - 3.10188i) q^{10} -3.01331i q^{11} -3.90632i q^{13} +(0.885915 + 1.10234i) q^{14} +(-3.62967 - 1.68092i) q^{16} -1.38839 q^{17} -4.79460i q^{19} +(-6.83867 - 1.50665i) q^{20} +(-3.32169 + 2.66954i) q^{22} +5.06853 q^{23} -7.25934 q^{25} +(-4.30609 + 3.46067i) q^{26} +(0.430309 - 1.95316i) q^{28} +4.91070i q^{29} +1.13938 q^{31} +(1.36263 + 5.49029i) q^{32} +(1.22999 + 1.53047i) q^{34} -3.50133i q^{35} -9.45610i q^{37} +(-5.28528 + 4.24761i) q^{38} +(4.39763 + 8.87330i) q^{40} -4.11364 q^{41} +1.51868i q^{43} +(5.88547 + 1.29665i) q^{44} +(-4.49029 - 5.58724i) q^{46} +10.7641 q^{47} +1.00000 q^{49} +(6.43116 + 8.00226i) q^{50} +(7.62967 + 1.68092i) q^{52} +0.431457i q^{53} +10.5506 q^{55} +(-2.53426 + 1.25599i) q^{56} +(5.41326 - 4.35046i) q^{58} +7.40936i q^{59} -12.9520i q^{61} +(-1.00940 - 1.25599i) q^{62} +(4.84499 - 6.36601i) q^{64} +13.6773 q^{65} -3.36185i q^{67} +(0.597435 - 2.71174i) q^{68} +(-3.85966 + 3.10188i) q^{70} +6.26892 q^{71} +10.0859 q^{73} +(-10.4238 + 8.37730i) q^{74} +(9.36462 + 2.06316i) q^{76} +3.01331i q^{77} +12.9346 q^{79} +(5.88547 - 12.7087i) q^{80} +(3.64434 + 4.53464i) q^{82} -17.4139i q^{83} -4.86120i q^{85} +(1.67411 - 1.34543i) q^{86} +(-3.78468 - 7.63652i) q^{88} +0.818403 q^{89} +3.90632i q^{91} +(-2.18103 + 9.89965i) q^{92} +(-9.53606 - 11.8657i) q^{94} +16.7875 q^{95} -11.4727 q^{97} +(-0.885915 - 1.10234i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 2q^{4} - 20q^{7} + O(q^{10}) \) \( 20q - 2q^{4} - 20q^{7} - 12q^{10} - 14q^{16} + 8q^{22} - 28q^{25} + 2q^{28} + 36q^{31} - 6q^{34} - 16q^{40} - 18q^{46} + 20q^{49} + 94q^{52} + 48q^{55} + 66q^{58} + 22q^{64} + 12q^{70} + 12q^{76} + 64q^{79} - 92q^{88} - 24q^{94} + 56q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.885915 1.10234i −0.626437 0.779472i
\(3\) 0 0
\(4\) −0.430309 + 1.95316i −0.215154 + 0.976580i
\(5\) 3.50133i 1.56584i 0.622120 + 0.782922i \(0.286272\pi\)
−0.622120 + 0.782922i \(0.713728\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 2.53426 1.25599i 0.895998 0.444059i
\(9\) 0 0
\(10\) 3.85966 3.10188i 1.22053 0.980902i
\(11\) 3.01331i 0.908547i −0.890862 0.454273i \(-0.849899\pi\)
0.890862 0.454273i \(-0.150101\pi\)
\(12\) 0 0
\(13\) 3.90632i 1.08342i −0.840566 0.541709i \(-0.817777\pi\)
0.840566 0.541709i \(-0.182223\pi\)
\(14\) 0.885915 + 1.10234i 0.236771 + 0.294613i
\(15\) 0 0
\(16\) −3.62967 1.68092i −0.907417 0.420231i
\(17\) −1.38839 −0.336733 −0.168367 0.985724i \(-0.553849\pi\)
−0.168367 + 0.985724i \(0.553849\pi\)
\(18\) 0 0
\(19\) 4.79460i 1.09996i −0.835179 0.549978i \(-0.814636\pi\)
0.835179 0.549978i \(-0.185364\pi\)
\(20\) −6.83867 1.50665i −1.52917 0.336898i
\(21\) 0 0
\(22\) −3.32169 + 2.66954i −0.708187 + 0.569147i
\(23\) 5.06853 1.05686 0.528431 0.848976i \(-0.322781\pi\)
0.528431 + 0.848976i \(0.322781\pi\)
\(24\) 0 0
\(25\) −7.25934 −1.45187
\(26\) −4.30609 + 3.46067i −0.844495 + 0.678693i
\(27\) 0 0
\(28\) 0.430309 1.95316i 0.0813207 0.369113i
\(29\) 4.91070i 0.911893i 0.890007 + 0.455947i \(0.150699\pi\)
−0.890007 + 0.455947i \(0.849301\pi\)
\(30\) 0 0
\(31\) 1.13938 0.204639 0.102320 0.994752i \(-0.467374\pi\)
0.102320 + 0.994752i \(0.467374\pi\)
\(32\) 1.36263 + 5.49029i 0.240881 + 0.970555i
\(33\) 0 0
\(34\) 1.22999 + 1.53047i 0.210942 + 0.262474i
\(35\) 3.50133i 0.591833i
\(36\) 0 0
\(37\) 9.45610i 1.55457i −0.629146 0.777287i \(-0.716595\pi\)
0.629146 0.777287i \(-0.283405\pi\)
\(38\) −5.28528 + 4.24761i −0.857386 + 0.689053i
\(39\) 0 0
\(40\) 4.39763 + 8.87330i 0.695327 + 1.40299i
\(41\) −4.11364 −0.642443 −0.321222 0.947004i \(-0.604093\pi\)
−0.321222 + 0.947004i \(0.604093\pi\)
\(42\) 0 0
\(43\) 1.51868i 0.231597i 0.993273 + 0.115799i \(0.0369427\pi\)
−0.993273 + 0.115799i \(0.963057\pi\)
\(44\) 5.88547 + 1.29665i 0.887269 + 0.195478i
\(45\) 0 0
\(46\) −4.49029 5.58724i −0.662057 0.823794i
\(47\) 10.7641 1.57010 0.785051 0.619431i \(-0.212637\pi\)
0.785051 + 0.619431i \(0.212637\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 6.43116 + 8.00226i 0.909503 + 1.13169i
\(51\) 0 0
\(52\) 7.62967 + 1.68092i 1.05804 + 0.233102i
\(53\) 0.431457i 0.0592651i 0.999561 + 0.0296326i \(0.00943372\pi\)
−0.999561 + 0.0296326i \(0.990566\pi\)
\(54\) 0 0
\(55\) 10.5506 1.42264
\(56\) −2.53426 + 1.25599i −0.338655 + 0.167838i
\(57\) 0 0
\(58\) 5.41326 4.35046i 0.710796 0.571243i
\(59\) 7.40936i 0.964617i 0.876002 + 0.482308i \(0.160202\pi\)
−0.876002 + 0.482308i \(0.839798\pi\)
\(60\) 0 0
\(61\) 12.9520i 1.65834i −0.559000 0.829168i \(-0.688815\pi\)
0.559000 0.829168i \(-0.311185\pi\)
\(62\) −1.00940 1.25599i −0.128193 0.159511i
\(63\) 0 0
\(64\) 4.84499 6.36601i 0.605624 0.795751i
\(65\) 13.6773 1.69646
\(66\) 0 0
\(67\) 3.36185i 0.410715i −0.978687 0.205357i \(-0.934164\pi\)
0.978687 0.205357i \(-0.0658357\pi\)
\(68\) 0.597435 2.71174i 0.0724496 0.328847i
\(69\) 0 0
\(70\) −3.85966 + 3.10188i −0.461318 + 0.370746i
\(71\) 6.26892 0.743984 0.371992 0.928236i \(-0.378675\pi\)
0.371992 + 0.928236i \(0.378675\pi\)
\(72\) 0 0
\(73\) 10.0859 1.18046 0.590230 0.807235i \(-0.299037\pi\)
0.590230 + 0.807235i \(0.299037\pi\)
\(74\) −10.4238 + 8.37730i −1.21175 + 0.973842i
\(75\) 0 0
\(76\) 9.36462 + 2.06316i 1.07420 + 0.236660i
\(77\) 3.01331i 0.343398i
\(78\) 0 0
\(79\) 12.9346 1.45526 0.727631 0.685969i \(-0.240622\pi\)
0.727631 + 0.685969i \(0.240622\pi\)
\(80\) 5.88547 12.7087i 0.658016 1.42087i
\(81\) 0 0
\(82\) 3.64434 + 4.53464i 0.402450 + 0.500767i
\(83\) 17.4139i 1.91142i −0.294307 0.955711i \(-0.595089\pi\)
0.294307 0.955711i \(-0.404911\pi\)
\(84\) 0 0
\(85\) 4.86120i 0.527272i
\(86\) 1.67411 1.34543i 0.180524 0.145081i
\(87\) 0 0
\(88\) −3.78468 7.63652i −0.403448 0.814056i
\(89\) 0.818403 0.0867506 0.0433753 0.999059i \(-0.486189\pi\)
0.0433753 + 0.999059i \(0.486189\pi\)
\(90\) 0 0
\(91\) 3.90632i 0.409494i
\(92\) −2.18103 + 9.89965i −0.227388 + 1.03211i
\(93\) 0 0
\(94\) −9.53606 11.8657i −0.983569 1.22385i
\(95\) 16.7875 1.72236
\(96\) 0 0
\(97\) −11.4727 −1.16488 −0.582441 0.812873i \(-0.697902\pi\)
−0.582441 + 0.812873i \(0.697902\pi\)
\(98\) −0.885915 1.10234i −0.0894909 0.111353i
\(99\) 0 0
\(100\) 3.12376 14.1786i 0.312376 1.41786i
\(101\) 5.38541i 0.535868i 0.963437 + 0.267934i \(0.0863410\pi\)
−0.963437 + 0.267934i \(0.913659\pi\)
\(102\) 0 0
\(103\) −4.82652 −0.475571 −0.237785 0.971318i \(-0.576421\pi\)
−0.237785 + 0.971318i \(0.576421\pi\)
\(104\) −4.90629 9.89965i −0.481101 0.970740i
\(105\) 0 0
\(106\) 0.475612 0.382234i 0.0461955 0.0371258i
\(107\) 4.92215i 0.475842i 0.971284 + 0.237921i \(0.0764660\pi\)
−0.971284 + 0.237921i \(0.923534\pi\)
\(108\) 0 0
\(109\) 20.1342i 1.92851i 0.264974 + 0.964255i \(0.414637\pi\)
−0.264974 + 0.964255i \(0.585363\pi\)
\(110\) −9.34694 11.6304i −0.891195 1.10891i
\(111\) 0 0
\(112\) 3.62967 + 1.68092i 0.342971 + 0.158832i
\(113\) 13.2438 1.24587 0.622937 0.782272i \(-0.285939\pi\)
0.622937 + 0.782272i \(0.285939\pi\)
\(114\) 0 0
\(115\) 17.7466i 1.65488i
\(116\) −9.59137 2.11311i −0.890537 0.196198i
\(117\) 0 0
\(118\) 8.16764 6.56407i 0.751892 0.604271i
\(119\) 1.38839 0.127273
\(120\) 0 0
\(121\) 1.91997 0.174543
\(122\) −14.2775 + 11.4744i −1.29263 + 1.03884i
\(123\) 0 0
\(124\) −0.490286 + 2.22540i −0.0440290 + 0.199847i
\(125\) 7.91070i 0.707554i
\(126\) 0 0
\(127\) 10.2252 0.907343 0.453671 0.891169i \(-0.350114\pi\)
0.453671 + 0.891169i \(0.350114\pi\)
\(128\) −11.3098 + 0.298914i −0.999651 + 0.0264205i
\(129\) 0 0
\(130\) −12.1170 15.0771i −1.06273 1.32235i
\(131\) 1.54726i 0.135185i −0.997713 0.0675924i \(-0.978468\pi\)
0.997713 0.0675924i \(-0.0215317\pi\)
\(132\) 0 0
\(133\) 4.79460i 0.415744i
\(134\) −3.70590 + 2.97831i −0.320141 + 0.257287i
\(135\) 0 0
\(136\) −3.51854 + 1.74380i −0.301712 + 0.149529i
\(137\) −7.46379 −0.637674 −0.318837 0.947809i \(-0.603292\pi\)
−0.318837 + 0.947809i \(0.603292\pi\)
\(138\) 0 0
\(139\) 16.6383i 1.41125i −0.708588 0.705623i \(-0.750667\pi\)
0.708588 0.705623i \(-0.249333\pi\)
\(140\) 6.83867 + 1.50665i 0.577973 + 0.127336i
\(141\) 0 0
\(142\) −5.55373 6.91048i −0.466059 0.579915i
\(143\) −11.7709 −0.984336
\(144\) 0 0
\(145\) −17.1940 −1.42788
\(146\) −8.93521 11.1180i −0.739483 0.920136i
\(147\) 0 0
\(148\) 18.4693 + 4.06904i 1.51817 + 0.334473i
\(149\) 21.3846i 1.75190i −0.482405 0.875948i \(-0.660237\pi\)
0.482405 0.875948i \(-0.339763\pi\)
\(150\) 0 0
\(151\) 1.21341 0.0987459 0.0493730 0.998780i \(-0.484278\pi\)
0.0493730 + 0.998780i \(0.484278\pi\)
\(152\) −6.02196 12.1508i −0.488445 0.985558i
\(153\) 0 0
\(154\) 3.32169 2.66954i 0.267670 0.215117i
\(155\) 3.98936i 0.320433i
\(156\) 0 0
\(157\) 8.15645i 0.650955i 0.945550 + 0.325478i \(0.105525\pi\)
−0.945550 + 0.325478i \(0.894475\pi\)
\(158\) −11.4590 14.2584i −0.911629 1.13434i
\(159\) 0 0
\(160\) −19.2233 + 4.77102i −1.51974 + 0.377182i
\(161\) −5.06853 −0.399456
\(162\) 0 0
\(163\) 22.8278i 1.78801i 0.448055 + 0.894006i \(0.352117\pi\)
−0.448055 + 0.894006i \(0.647883\pi\)
\(164\) 1.77014 8.03461i 0.138224 0.627397i
\(165\) 0 0
\(166\) −19.1960 + 15.4272i −1.48990 + 1.19738i
\(167\) −17.3575 −1.34316 −0.671581 0.740931i \(-0.734384\pi\)
−0.671581 + 0.740931i \(0.734384\pi\)
\(168\) 0 0
\(169\) −2.25934 −0.173795
\(170\) −5.35870 + 4.30661i −0.410994 + 0.330302i
\(171\) 0 0
\(172\) −2.96623 0.653503i −0.226173 0.0498291i
\(173\) 23.5784i 1.79263i −0.443415 0.896316i \(-0.646233\pi\)
0.443415 0.896316i \(-0.353767\pi\)
\(174\) 0 0
\(175\) 7.25934 0.548754
\(176\) −5.06514 + 10.9373i −0.381799 + 0.824431i
\(177\) 0 0
\(178\) −0.725036 0.902159i −0.0543437 0.0676197i
\(179\) 12.0965i 0.904134i −0.891984 0.452067i \(-0.850687\pi\)
0.891984 0.452067i \(-0.149313\pi\)
\(180\) 0 0
\(181\) 3.70662i 0.275511i −0.990466 0.137755i \(-0.956011\pi\)
0.990466 0.137755i \(-0.0439888\pi\)
\(182\) 4.30609 3.46067i 0.319189 0.256522i
\(183\) 0 0
\(184\) 12.8450 6.36601i 0.946945 0.469308i
\(185\) 33.1090 2.43422
\(186\) 0 0
\(187\) 4.18364i 0.305938i
\(188\) −4.63188 + 21.0240i −0.337814 + 1.53333i
\(189\) 0 0
\(190\) −14.8723 18.5055i −1.07895 1.34253i
\(191\) −11.2770 −0.815977 −0.407988 0.912987i \(-0.633770\pi\)
−0.407988 + 0.912987i \(0.633770\pi\)
\(192\) 0 0
\(193\) −3.15188 −0.226877 −0.113439 0.993545i \(-0.536187\pi\)
−0.113439 + 0.993545i \(0.536187\pi\)
\(194\) 10.1639 + 12.6469i 0.729724 + 0.907993i
\(195\) 0 0
\(196\) −0.430309 + 1.95316i −0.0307363 + 0.139511i
\(197\) 11.4819i 0.818052i 0.912523 + 0.409026i \(0.134131\pi\)
−0.912523 + 0.409026i \(0.865869\pi\)
\(198\) 0 0
\(199\) −3.38405 −0.239889 −0.119944 0.992781i \(-0.538272\pi\)
−0.119944 + 0.992781i \(0.538272\pi\)
\(200\) −18.3971 + 9.11764i −1.30087 + 0.644714i
\(201\) 0 0
\(202\) 5.93656 4.77102i 0.417695 0.335688i
\(203\) 4.91070i 0.344663i
\(204\) 0 0
\(205\) 14.4032i 1.00597i
\(206\) 4.27588 + 5.32046i 0.297915 + 0.370694i
\(207\) 0 0
\(208\) −6.56623 + 14.1786i −0.455286 + 0.983112i
\(209\) −14.4476 −0.999362
\(210\) 0 0
\(211\) 17.0774i 1.17565i −0.808987 0.587827i \(-0.799984\pi\)
0.808987 0.587827i \(-0.200016\pi\)
\(212\) −0.842704 0.185659i −0.0578771 0.0127511i
\(213\) 0 0
\(214\) 5.42588 4.36061i 0.370906 0.298085i
\(215\) −5.31742 −0.362645
\(216\) 0 0
\(217\) −1.13938 −0.0773463
\(218\) 22.1948 17.8372i 1.50322 1.20809i
\(219\) 0 0
\(220\) −4.54001 + 20.6070i −0.306088 + 1.38932i
\(221\) 5.42348i 0.364823i
\(222\) 0 0
\(223\) 24.1161 1.61494 0.807468 0.589912i \(-0.200837\pi\)
0.807468 + 0.589912i \(0.200837\pi\)
\(224\) −1.36263 5.49029i −0.0910445 0.366835i
\(225\) 0 0
\(226\) −11.7329 14.5992i −0.780461 0.971125i
\(227\) 7.60050i 0.504463i 0.967667 + 0.252231i \(0.0811644\pi\)
−0.967667 + 0.252231i \(0.918836\pi\)
\(228\) 0 0
\(229\) 24.0017i 1.58608i −0.609171 0.793039i \(-0.708498\pi\)
0.609171 0.793039i \(-0.291502\pi\)
\(230\) 19.5628 15.7220i 1.28993 1.03668i
\(231\) 0 0
\(232\) 6.16777 + 12.4450i 0.404934 + 0.817054i
\(233\) 10.6276 0.696237 0.348118 0.937451i \(-0.386821\pi\)
0.348118 + 0.937451i \(0.386821\pi\)
\(234\) 0 0
\(235\) 37.6886i 2.45853i
\(236\) −14.4717 3.18831i −0.942025 0.207541i
\(237\) 0 0
\(238\) −1.22999 1.53047i −0.0797286 0.0992059i
\(239\) 28.0645 1.81534 0.907671 0.419682i \(-0.137858\pi\)
0.907671 + 0.419682i \(0.137858\pi\)
\(240\) 0 0
\(241\) −20.7612 −1.33734 −0.668672 0.743558i \(-0.733137\pi\)
−0.668672 + 0.743558i \(0.733137\pi\)
\(242\) −1.70093 2.11646i −0.109340 0.136051i
\(243\) 0 0
\(244\) 25.2974 + 5.57336i 1.61950 + 0.356798i
\(245\) 3.50133i 0.223692i
\(246\) 0 0
\(247\) −18.7292 −1.19171
\(248\) 2.88750 1.43105i 0.183356 0.0908718i
\(249\) 0 0
\(250\) −8.72028 + 7.00820i −0.551519 + 0.443238i
\(251\) 21.4352i 1.35298i 0.736454 + 0.676488i \(0.236499\pi\)
−0.736454 + 0.676488i \(0.763501\pi\)
\(252\) 0 0
\(253\) 15.2730i 0.960208i
\(254\) −9.05869 11.2717i −0.568393 0.707249i
\(255\) 0 0
\(256\) 10.3490 + 12.2024i 0.646812 + 0.762649i
\(257\) 13.6807 0.853380 0.426690 0.904398i \(-0.359680\pi\)
0.426690 + 0.904398i \(0.359680\pi\)
\(258\) 0 0
\(259\) 9.45610i 0.587574i
\(260\) −5.88547 + 26.7140i −0.365002 + 1.65673i
\(261\) 0 0
\(262\) −1.70561 + 1.37074i −0.105373 + 0.0846847i
\(263\) 18.8063 1.15965 0.579823 0.814743i \(-0.303122\pi\)
0.579823 + 0.814743i \(0.303122\pi\)
\(264\) 0 0
\(265\) −1.51067 −0.0927999
\(266\) 5.28528 4.24761i 0.324061 0.260438i
\(267\) 0 0
\(268\) 6.56623 + 1.44663i 0.401096 + 0.0883671i
\(269\) 27.1654i 1.65630i −0.560504 0.828152i \(-0.689393\pi\)
0.560504 0.828152i \(-0.310607\pi\)
\(270\) 0 0
\(271\) 0.618132 0.0375488 0.0187744 0.999824i \(-0.494024\pi\)
0.0187744 + 0.999824i \(0.494024\pi\)
\(272\) 5.03938 + 2.33377i 0.305558 + 0.141506i
\(273\) 0 0
\(274\) 6.61228 + 8.22763i 0.399463 + 0.497050i
\(275\) 21.8746i 1.31909i
\(276\) 0 0
\(277\) 16.4479i 0.988260i −0.869388 0.494130i \(-0.835487\pi\)
0.869388 0.494130i \(-0.164513\pi\)
\(278\) −18.3411 + 14.7402i −1.10003 + 0.884056i
\(279\) 0 0
\(280\) −4.39763 8.87330i −0.262809 0.530281i
\(281\) −26.6482 −1.58970 −0.794849 0.606807i \(-0.792450\pi\)
−0.794849 + 0.606807i \(0.792450\pi\)
\(282\) 0 0
\(283\) 5.96019i 0.354297i 0.984184 + 0.177148i \(0.0566872\pi\)
−0.984184 + 0.177148i \(0.943313\pi\)
\(284\) −2.69757 + 12.2442i −0.160071 + 0.726560i
\(285\) 0 0
\(286\) 10.4281 + 12.9756i 0.616624 + 0.767263i
\(287\) 4.11364 0.242821
\(288\) 0 0
\(289\) −15.0724 −0.886611
\(290\) 15.2324 + 18.9536i 0.894478 + 1.11300i
\(291\) 0 0
\(292\) −4.34003 + 19.6993i −0.253981 + 1.15281i
\(293\) 1.52262i 0.0889522i 0.999010 + 0.0444761i \(0.0141619\pi\)
−0.999010 + 0.0444761i \(0.985838\pi\)
\(294\) 0 0
\(295\) −25.9426 −1.51044
\(296\) −11.8767 23.9643i −0.690322 1.39289i
\(297\) 0 0
\(298\) −23.5731 + 18.9450i −1.36556 + 1.09745i
\(299\) 19.7993i 1.14502i
\(300\) 0 0
\(301\) 1.51868i 0.0875355i
\(302\) −1.07498 1.33759i −0.0618581 0.0769697i
\(303\) 0 0
\(304\) −8.05935 + 17.4028i −0.462236 + 0.998119i
\(305\) 45.3493 2.59669
\(306\) 0 0
\(307\) 5.29191i 0.302025i 0.988532 + 0.151013i \(0.0482534\pi\)
−0.988532 + 0.151013i \(0.951747\pi\)
\(308\) −5.88547 1.29665i −0.335356 0.0738837i
\(309\) 0 0
\(310\) 4.39763 3.53423i 0.249769 0.200731i
\(311\) −6.95423 −0.394338 −0.197169 0.980370i \(-0.563175\pi\)
−0.197169 + 0.980370i \(0.563175\pi\)
\(312\) 0 0
\(313\) −11.7834 −0.666039 −0.333020 0.942920i \(-0.608068\pi\)
−0.333020 + 0.942920i \(0.608068\pi\)
\(314\) 8.99118 7.22592i 0.507402 0.407782i
\(315\) 0 0
\(316\) −5.56589 + 25.2634i −0.313106 + 1.42118i
\(317\) 1.74196i 0.0978384i −0.998803 0.0489192i \(-0.984422\pi\)
0.998803 0.0489192i \(-0.0155777\pi\)
\(318\) 0 0
\(319\) 14.7974 0.828498
\(320\) 22.2895 + 16.9639i 1.24602 + 0.948313i
\(321\) 0 0
\(322\) 4.49029 + 5.58724i 0.250234 + 0.311365i
\(323\) 6.65676i 0.370392i
\(324\) 0 0
\(325\) 28.3573i 1.57298i
\(326\) 25.1640 20.2235i 1.39371 1.12008i
\(327\) 0 0
\(328\) −10.4251 + 5.16669i −0.575628 + 0.285282i
\(329\) −10.7641 −0.593443
\(330\) 0 0
\(331\) 22.6068i 1.24258i −0.783579 0.621292i \(-0.786608\pi\)
0.783579 0.621292i \(-0.213392\pi\)
\(332\) 34.0121 + 7.49335i 1.86666 + 0.411251i
\(333\) 0 0
\(334\) 15.3772 + 19.1338i 0.841406 + 1.04696i
\(335\) 11.7709 0.643116
\(336\) 0 0
\(337\) 24.7468 1.34804 0.674021 0.738712i \(-0.264566\pi\)
0.674021 + 0.738712i \(0.264566\pi\)
\(338\) 2.00158 + 2.49056i 0.108872 + 0.135469i
\(339\) 0 0
\(340\) 9.49471 + 2.09182i 0.514923 + 0.113445i
\(341\) 3.43331i 0.185924i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 1.90745 + 3.84875i 0.102843 + 0.207511i
\(345\) 0 0
\(346\) −25.9914 + 20.8885i −1.39731 + 1.12297i
\(347\) 3.17968i 0.170694i −0.996351 0.0853471i \(-0.972800\pi\)
0.996351 0.0853471i \(-0.0271999\pi\)
\(348\) 0 0
\(349\) 12.0444i 0.644722i −0.946617 0.322361i \(-0.895523\pi\)
0.946617 0.322361i \(-0.104477\pi\)
\(350\) −6.43116 8.00226i −0.343760 0.427739i
\(351\) 0 0
\(352\) 16.5439 4.10602i 0.881794 0.218852i
\(353\) −28.3700 −1.50998 −0.754991 0.655736i \(-0.772359\pi\)
−0.754991 + 0.655736i \(0.772359\pi\)
\(354\) 0 0
\(355\) 21.9496i 1.16496i
\(356\) −0.352166 + 1.59847i −0.0186648 + 0.0847189i
\(357\) 0 0
\(358\) −13.3345 + 10.7165i −0.704748 + 0.566383i
\(359\) −26.2701 −1.38648 −0.693241 0.720706i \(-0.743818\pi\)
−0.693241 + 0.720706i \(0.743818\pi\)
\(360\) 0 0
\(361\) −3.98817 −0.209904
\(362\) −4.08596 + 3.28375i −0.214753 + 0.172590i
\(363\) 0 0
\(364\) −7.62967 1.68092i −0.399903 0.0881043i
\(365\) 35.3139i 1.84842i
\(366\) 0 0
\(367\) 15.6261 0.815678 0.407839 0.913054i \(-0.366283\pi\)
0.407839 + 0.913054i \(0.366283\pi\)
\(368\) −18.3971 8.51981i −0.959014 0.444126i
\(369\) 0 0
\(370\) −29.3317 36.4974i −1.52488 1.89741i
\(371\) 0.431457i 0.0224001i
\(372\) 0 0
\(373\) 3.63905i 0.188423i 0.995552 + 0.0942113i \(0.0300329\pi\)
−0.995552 + 0.0942113i \(0.969967\pi\)
\(374\) 4.61179 3.70635i 0.238470 0.191651i
\(375\) 0 0
\(376\) 27.2790 13.5195i 1.40681 0.697217i
\(377\) 19.1827 0.987962
\(378\) 0 0
\(379\) 4.66150i 0.239445i −0.992807 0.119723i \(-0.961799\pi\)
0.992807 0.119723i \(-0.0382005\pi\)
\(380\) −7.22380 + 32.7887i −0.370573 + 1.68202i
\(381\) 0 0
\(382\) 9.99049 + 12.4311i 0.511158 + 0.636031i
\(383\) −11.9040 −0.608268 −0.304134 0.952629i \(-0.598367\pi\)
−0.304134 + 0.952629i \(0.598367\pi\)
\(384\) 0 0
\(385\) −10.5506 −0.537708
\(386\) 2.79230 + 3.47444i 0.142124 + 0.176845i
\(387\) 0 0
\(388\) 4.93682 22.4081i 0.250629 1.13760i
\(389\) 35.6321i 1.80662i 0.428987 + 0.903311i \(0.358871\pi\)
−0.428987 + 0.903311i \(0.641129\pi\)
\(390\) 0 0
\(391\) −7.03708 −0.355880
\(392\) 2.53426 1.25599i 0.128000 0.0634369i
\(393\) 0 0
\(394\) 12.6570 10.1720i 0.637649 0.512458i
\(395\) 45.2885i 2.27871i
\(396\) 0 0
\(397\) 10.9738i 0.550760i 0.961335 + 0.275380i \(0.0888037\pi\)
−0.961335 + 0.275380i \(0.911196\pi\)
\(398\) 2.99798 + 3.73037i 0.150275 + 0.186987i
\(399\) 0 0
\(400\) 26.3490 + 12.2024i 1.31745 + 0.610120i
\(401\) 6.65382 0.332276 0.166138 0.986103i \(-0.446870\pi\)
0.166138 + 0.986103i \(0.446870\pi\)
\(402\) 0 0
\(403\) 4.45079i 0.221710i
\(404\) −10.5186 2.31739i −0.523318 0.115294i
\(405\) 0 0
\(406\) −5.41326 + 4.35046i −0.268655 + 0.215910i
\(407\) −28.4942 −1.41240
\(408\) 0 0
\(409\) −33.8304 −1.67281 −0.836404 0.548114i \(-0.815346\pi\)
−0.836404 + 0.548114i \(0.815346\pi\)
\(410\) −15.8773 + 12.7600i −0.784123 + 0.630174i
\(411\) 0 0
\(412\) 2.07689 9.42696i 0.102321 0.464433i
\(413\) 7.40936i 0.364591i
\(414\) 0 0
\(415\) 60.9718 2.99299
\(416\) 21.4468 5.32286i 1.05152 0.260975i
\(417\) 0 0
\(418\) 12.7994 + 15.9262i 0.626037 + 0.778975i
\(419\) 10.6763i 0.521571i −0.965397 0.260786i \(-0.916018\pi\)
0.965397 0.260786i \(-0.0839816\pi\)
\(420\) 0 0
\(421\) 15.4063i 0.750855i 0.926852 + 0.375427i \(0.122504\pi\)
−0.926852 + 0.375427i \(0.877496\pi\)
\(422\) −18.8251 + 15.1291i −0.916390 + 0.736473i
\(423\) 0 0
\(424\) 0.541904 + 1.09342i 0.0263172 + 0.0531014i
\(425\) 10.0788 0.488892
\(426\) 0 0
\(427\) 12.9520i 0.626792i
\(428\) −9.61375 2.11804i −0.464698 0.102379i
\(429\) 0 0
\(430\) 4.71078 + 5.86161i 0.227174 + 0.282672i
\(431\) 25.7179 1.23879 0.619393 0.785081i \(-0.287379\pi\)
0.619393 + 0.785081i \(0.287379\pi\)
\(432\) 0 0
\(433\) −7.26219 −0.348998 −0.174499 0.984657i \(-0.555831\pi\)
−0.174499 + 0.984657i \(0.555831\pi\)
\(434\) 1.00940 + 1.25599i 0.0484526 + 0.0602893i
\(435\) 0 0
\(436\) −39.3254 8.66394i −1.88335 0.414928i
\(437\) 24.3016i 1.16250i
\(438\) 0 0
\(439\) 28.7252 1.37098 0.685488 0.728084i \(-0.259589\pi\)
0.685488 + 0.728084i \(0.259589\pi\)
\(440\) 26.7380 13.2514i 1.27468 0.631737i
\(441\) 0 0
\(442\) 5.97852 4.80475i 0.284369 0.228538i
\(443\) 5.70732i 0.271163i −0.990766 0.135582i \(-0.956710\pi\)
0.990766 0.135582i \(-0.0432903\pi\)
\(444\) 0 0
\(445\) 2.86550i 0.135838i
\(446\) −21.3648 26.5842i −1.01165 1.25880i
\(447\) 0 0
\(448\) −4.84499 + 6.36601i −0.228904 + 0.300766i
\(449\) −33.9514 −1.60227 −0.801134 0.598485i \(-0.795770\pi\)
−0.801134 + 0.598485i \(0.795770\pi\)
\(450\) 0 0
\(451\) 12.3957i 0.583690i
\(452\) −5.69893 + 25.8673i −0.268055 + 1.21670i
\(453\) 0 0
\(454\) 8.37833 6.73339i 0.393215 0.316014i
\(455\) −13.6773 −0.641203
\(456\) 0 0
\(457\) 35.4661 1.65903 0.829517 0.558482i \(-0.188616\pi\)
0.829517 + 0.558482i \(0.188616\pi\)
\(458\) −26.4581 + 21.2635i −1.23630 + 0.993578i
\(459\) 0 0
\(460\) −34.6620 7.63652i −1.61612 0.356055i
\(461\) 26.3291i 1.22627i 0.789979 + 0.613134i \(0.210092\pi\)
−0.789979 + 0.613134i \(0.789908\pi\)
\(462\) 0 0
\(463\) −5.45714 −0.253615 −0.126807 0.991927i \(-0.540473\pi\)
−0.126807 + 0.991927i \(0.540473\pi\)
\(464\) 8.25450 17.8242i 0.383206 0.827468i
\(465\) 0 0
\(466\) −9.41515 11.7152i −0.436148 0.542697i
\(467\) 5.77349i 0.267165i 0.991038 + 0.133583i \(0.0426482\pi\)
−0.991038 + 0.133583i \(0.957352\pi\)
\(468\) 0 0
\(469\) 3.36185i 0.155236i
\(470\) 41.5457 33.3889i 1.91636 1.54012i
\(471\) 0 0
\(472\) 9.30607 + 18.7773i 0.428346 + 0.864294i
\(473\) 4.57626 0.210417
\(474\) 0 0
\(475\) 34.8056i 1.59699i
\(476\) −0.597435 + 2.71174i −0.0273834 + 0.124292i
\(477\) 0 0
\(478\) −24.8628 30.9366i −1.13720 1.41501i
\(479\) −31.3044 −1.43033 −0.715167 0.698954i \(-0.753649\pi\)
−0.715167 + 0.698954i \(0.753649\pi\)
\(480\) 0 0
\(481\) −36.9386 −1.68425
\(482\) 18.3926 + 22.8859i 0.837761 + 1.04242i
\(483\) 0 0
\(484\) −0.826180 + 3.75001i −0.0375536 + 0.170455i
\(485\) 40.1699i 1.82402i
\(486\) 0 0
\(487\) −25.7136 −1.16519 −0.582597 0.812761i \(-0.697963\pi\)
−0.582597 + 0.812761i \(0.697963\pi\)
\(488\) −16.2676 32.8238i −0.736398 1.48586i
\(489\) 0 0
\(490\) 3.85966 3.10188i 0.174362 0.140129i
\(491\) 12.7216i 0.574116i −0.957913 0.287058i \(-0.907323\pi\)
0.957913 0.287058i \(-0.0926773\pi\)
\(492\) 0 0
\(493\) 6.81794i 0.307065i
\(494\) 16.5925 + 20.6460i 0.746533 + 0.928907i
\(495\) 0 0
\(496\) −4.13558 1.91522i −0.185693 0.0859957i
\(497\) −6.26892 −0.281199
\(498\) 0 0
\(499\) 37.9382i 1.69835i −0.528115 0.849173i \(-0.677101\pi\)
0.528115 0.849173i \(-0.322899\pi\)
\(500\) 15.4509 + 3.40404i 0.690983 + 0.152233i
\(501\) 0 0
\(502\) 23.6288 18.9897i 1.05461 0.847554i
\(503\) 16.9704 0.756674 0.378337 0.925668i \(-0.376496\pi\)
0.378337 + 0.925668i \(0.376496\pi\)
\(504\) 0 0
\(505\) −18.8561 −0.839086
\(506\) −16.8361 + 13.5306i −0.748455 + 0.601509i
\(507\) 0 0
\(508\) −4.40001 + 19.9715i −0.195219 + 0.886093i
\(509\) 11.6789i 0.517656i −0.965923 0.258828i \(-0.916664\pi\)
0.965923 0.258828i \(-0.0833363\pi\)
\(510\) 0 0
\(511\) −10.0859 −0.446172
\(512\) 4.28286 22.2184i 0.189277 0.981924i
\(513\) 0 0
\(514\) −12.1200 15.0808i −0.534588 0.665186i
\(515\) 16.8992i 0.744670i
\(516\) 0 0
\(517\) 32.4355i 1.42651i
\(518\) 10.4238 8.37730i 0.457997 0.368078i
\(519\) 0 0
\(520\) 34.6620 17.1786i 1.52003 0.753330i
\(521\) −4.82516 −0.211394 −0.105697 0.994398i \(-0.533707\pi\)
−0.105697 + 0.994398i \(0.533707\pi\)
\(522\) 0 0
\(523\) 24.7958i 1.08424i 0.840300 + 0.542121i \(0.182379\pi\)
−0.840300 + 0.542121i \(0.817621\pi\)
\(524\) 3.02205 + 0.665800i 0.132019 + 0.0290856i
\(525\) 0 0
\(526\) −16.6608 20.7309i −0.726444 0.903911i
\(527\) −1.58190 −0.0689088
\(528\) 0 0
\(529\) 2.68998 0.116956
\(530\) 1.33833 + 1.66528i 0.0581333 + 0.0723350i
\(531\) 0 0
\(532\) −9.36462 2.06316i −0.406008 0.0894492i
\(533\) 16.0692i 0.696035i
\(534\) 0 0
\(535\) −17.2341 −0.745095
\(536\) −4.22244 8.51981i −0.182382 0.368000i
\(537\) 0 0
\(538\) −29.9455 + 24.0662i −1.29104 + 1.03757i
\(539\) 3.01331i 0.129792i
\(540\) 0 0
\(541\) 14.0510i 0.604100i −0.953292 0.302050i \(-0.902329\pi\)
0.953292 0.302050i \(-0.0976709\pi\)
\(542\) −0.547613 0.681392i −0.0235220 0.0292683i
\(543\) 0 0
\(544\) −1.89186 7.62264i −0.0811126 0.326818i
\(545\) −70.4967 −3.01975
\(546\) 0 0
\(547\) 8.56879i 0.366375i −0.983078 0.183188i \(-0.941358\pi\)
0.983078 0.183188i \(-0.0586416\pi\)
\(548\) 3.21173 14.5780i 0.137198 0.622740i
\(549\) 0 0
\(550\) 24.1133 19.3791i 1.02819 0.826326i
\(551\) 23.5448 1.00304
\(552\) 0 0
\(553\) −12.9346 −0.550037
\(554\) −18.1312 + 14.5715i −0.770321 + 0.619082i
\(555\) 0 0
\(556\) 32.4973 + 7.15962i 1.37819 + 0.303636i
\(557\) 3.47669i 0.147312i 0.997284 + 0.0736560i \(0.0234667\pi\)
−0.997284 + 0.0736560i \(0.976533\pi\)
\(558\) 0 0
\(559\) 5.93247 0.250917
\(560\) −5.88547 + 12.7087i −0.248707 + 0.537040i
\(561\) 0 0
\(562\) 23.6080 + 29.3754i 0.995845 + 1.23913i
\(563\) 6.82325i 0.287566i 0.989609 + 0.143783i \(0.0459267\pi\)
−0.989609 + 0.143783i \(0.954073\pi\)
\(564\) 0 0
\(565\) 46.3711i 1.95085i
\(566\) 6.57016 5.28023i 0.276165 0.221944i
\(567\) 0 0
\(568\) 15.8871 7.87368i 0.666608 0.330372i
\(569\) −25.1322 −1.05360 −0.526799 0.849990i \(-0.676608\pi\)
−0.526799 + 0.849990i \(0.676608\pi\)
\(570\) 0 0
\(571\) 14.1758i 0.593238i 0.954996 + 0.296619i \(0.0958591\pi\)
−0.954996 + 0.296619i \(0.904141\pi\)
\(572\) 5.06514 22.9905i 0.211784 0.961283i
\(573\) 0 0
\(574\) −3.64434 4.53464i −0.152112 0.189272i
\(575\) −36.7942 −1.53442
\(576\) 0 0
\(577\) 18.3021 0.761927 0.380963 0.924590i \(-0.375592\pi\)
0.380963 + 0.924590i \(0.375592\pi\)
\(578\) 13.3529 + 16.6149i 0.555405 + 0.691089i
\(579\) 0 0
\(580\) 7.39872 33.5826i 0.307215 1.39444i
\(581\) 17.4139i 0.722450i
\(582\) 0 0
\(583\) 1.30011 0.0538451
\(584\) 25.5602 12.6677i 1.05769 0.524193i
\(585\) 0 0
\(586\) 1.67844 1.34891i 0.0693358 0.0557229i
\(587\) 6.70640i 0.276803i −0.990376 0.138401i \(-0.955804\pi\)
0.990376 0.138401i \(-0.0441964\pi\)
\(588\) 0 0
\(589\) 5.46288i 0.225094i
\(590\) 22.9830 + 28.5976i 0.946194 + 1.17735i
\(591\) 0 0
\(592\) −15.8950 + 34.3225i −0.653280 + 1.41065i
\(593\) 17.9084 0.735411 0.367706 0.929942i \(-0.380143\pi\)
0.367706 + 0.929942i \(0.380143\pi\)
\(594\) 0 0
\(595\) 4.86120i 0.199290i
\(596\) 41.7676 + 9.20199i 1.71087 + 0.376928i
\(597\) 0 0
\(598\) −21.8256 + 17.5405i −0.892514 + 0.717284i
\(599\) 23.9838 0.979953 0.489976 0.871736i \(-0.337005\pi\)
0.489976 + 0.871736i \(0.337005\pi\)
\(600\) 0 0
\(601\) −17.2548 −0.703840 −0.351920 0.936030i \(-0.614471\pi\)
−0.351920 + 0.936030i \(0.614471\pi\)
\(602\) −1.67411 + 1.34543i −0.0682315 + 0.0548354i
\(603\) 0 0
\(604\) −0.522141 + 2.36998i −0.0212456 + 0.0964333i
\(605\) 6.72246i 0.273307i
\(606\) 0 0
\(607\) 38.0189 1.54314 0.771569 0.636146i \(-0.219472\pi\)
0.771569 + 0.636146i \(0.219472\pi\)
\(608\) 26.3237 6.53326i 1.06757 0.264959i
\(609\) 0 0
\(610\) −40.1756 49.9904i −1.62666 2.02405i
\(611\) 42.0479i 1.70108i
\(612\) 0 0
\(613\) 33.1990i 1.34089i 0.741957 + 0.670447i \(0.233898\pi\)
−0.741957 + 0.670447i \(0.766102\pi\)
\(614\) 5.83349 4.68818i 0.235420 0.189200i
\(615\) 0 0
\(616\) 3.78468 + 7.63652i 0.152489 + 0.307684i
\(617\) −0.827310 −0.0333062 −0.0166531 0.999861i \(-0.505301\pi\)
−0.0166531 + 0.999861i \(0.505301\pi\)
\(618\) 0 0
\(619\) 42.3695i 1.70297i −0.524377 0.851486i \(-0.675702\pi\)
0.524377 0.851486i \(-0.324298\pi\)
\(620\) −7.79186 1.71666i −0.312928 0.0689426i
\(621\) 0 0
\(622\) 6.16085 + 7.66593i 0.247028 + 0.307376i
\(623\) −0.818403 −0.0327886
\(624\) 0 0
\(625\) −8.59870 −0.343948
\(626\) 10.4391 + 12.9894i 0.417231 + 0.519159i
\(627\) 0 0
\(628\) −15.9308 3.50979i −0.635710 0.140056i
\(629\) 13.1287i 0.523477i
\(630\) 0 0
\(631\) −18.5333 −0.737801 −0.368901 0.929469i \(-0.620266\pi\)
−0.368901 + 0.929469i \(0.620266\pi\)
\(632\) 32.7798 16.2458i 1.30391 0.646221i
\(633\) 0 0
\(634\) −1.92024 + 1.54323i −0.0762624 + 0.0612896i
\(635\) 35.8020i 1.42076i
\(636\) 0 0
\(637\) 3.90632i 0.154774i
\(638\) −13.1093 16.3118i −0.519001 0.645791i
\(639\) 0 0
\(640\) −1.04660 39.5992i −0.0413704 1.56530i
\(641\) −13.3013 −0.525371 −0.262686 0.964881i \(-0.584608\pi\)
−0.262686 + 0.964881i \(0.584608\pi\)
\(642\) 0 0
\(643\) 12.1885i 0.480668i 0.970690 + 0.240334i \(0.0772570\pi\)
−0.970690 + 0.240334i \(0.922743\pi\)
\(644\) 2.18103 9.89965i 0.0859447 0.390101i
\(645\) 0 0
\(646\) 7.33801 5.89732i 0.288710 0.232027i
\(647\) −18.4813 −0.726576 −0.363288 0.931677i \(-0.618346\pi\)
−0.363288 + 0.931677i \(0.618346\pi\)
\(648\) 0 0
\(649\) 22.3267 0.876399
\(650\) 31.2594 25.1222i 1.22609 0.985372i
\(651\) 0 0
\(652\) −44.5864 9.82300i −1.74614 0.384699i
\(653\) 25.0787i 0.981405i 0.871327 + 0.490703i \(0.163260\pi\)
−0.871327 + 0.490703i \(0.836740\pi\)
\(654\) 0 0
\(655\) 5.41748 0.211678
\(656\) 14.9312 + 6.91472i 0.582964 + 0.269975i
\(657\) 0 0
\(658\) 9.53606 + 11.8657i 0.371754 + 0.462572i
\(659\) 40.3331i 1.57115i −0.618764 0.785577i \(-0.712366\pi\)
0.618764 0.785577i \(-0.287634\pi\)
\(660\) 0 0
\(661\) 21.1566i 0.822896i −0.911433 0.411448i \(-0.865023\pi\)
0.911433 0.411448i \(-0.134977\pi\)
\(662\) −24.9204 + 20.0277i −0.968560 + 0.778401i
\(663\) 0 0
\(664\) −21.8716 44.1314i −0.848783 1.71263i
\(665\) −16.7875 −0.650991
\(666\) 0 0
\(667\) 24.8900i 0.963745i
\(668\) 7.46907 33.9019i 0.288987 1.31170i
\(669\) 0 0
\(670\) −10.4281 12.9756i −0.402871 0.501291i
\(671\) −39.0284 −1.50667
\(672\) 0 0
\(673\) 45.8540 1.76754 0.883772 0.467918i \(-0.154996\pi\)
0.883772 + 0.467918i \(0.154996\pi\)
\(674\) −21.9235 27.2794i −0.844463 1.05076i
\(675\) 0 0
\(676\) 0.972213 4.41285i 0.0373928 0.169725i
\(677\) 41.0495i 1.57766i 0.614612 + 0.788830i \(0.289313\pi\)
−0.614612 + 0.788830i \(0.710687\pi\)
\(678\) 0 0
\(679\) 11.4727 0.440284
\(680\) −6.10561 12.3196i −0.234140 0.472434i
\(681\) 0 0
\(682\) −3.78468 + 3.04162i −0.144923 + 0.116470i
\(683\) 7.87089i 0.301171i 0.988597 + 0.150586i \(0.0481159\pi\)
−0.988597 + 0.150586i \(0.951884\pi\)
\(684\) 0 0
\(685\) 26.1332i 0.998499i
\(686\) 0.885915 + 1.10234i 0.0338244 + 0.0420876i
\(687\) 0 0
\(688\) 2.55279 5.51232i 0.0973243 0.210155i
\(689\) 1.68541 0.0642089
\(690\) 0 0
\(691\) 33.4478i 1.27241i 0.771519 + 0.636207i \(0.219497\pi\)
−0.771519 + 0.636207i \(0.780503\pi\)
\(692\) 46.0524 + 10.1460i 1.75065 + 0.385693i
\(693\) 0 0
\(694\) −3.50509 + 2.81693i −0.133051 + 0.106929i
\(695\) 58.2564 2.20979
\(696\) 0 0
\(697\) 5.71133 0.216332
\(698\) −13.2770 + 10.6703i −0.502543 + 0.403878i
\(699\) 0 0
\(700\) −3.12376 + 14.1786i −0.118067 + 0.535903i
\(701\) 19.9716i 0.754317i −0.926149 0.377158i \(-0.876901\pi\)
0.926149 0.377158i \(-0.123099\pi\)
\(702\) 0 0
\(703\) −45.3382 −1.70996
\(704\) −19.1827 14.5995i −0.722977 0.550238i
\(705\) 0 0
\(706\) 25.1334 + 31.2734i 0.945907 + 1.17699i
\(707\) 5.38541i 0.202539i
\(708\) 0 0
\(709\) 38.1379i 1.43230i −0.697947 0.716149i \(-0.745903\pi\)
0.697947 0.716149i \(-0.254097\pi\)
\(710\) 24.1959 19.4455i 0.908056 0.729775i
\(711\) 0 0
\(712\) 2.07405 1.02790i 0.0777283 0.0385223i
\(713\) 5.77499 0.216275
\(714\) 0 0
\(715\) 41.2140i 1.54132i
\(716\) 23.6264 + 5.20523i 0.882960 + 0.194528i
\(717\) 0 0
\(718\) 23.2731 + 28.9586i 0.868543 + 1.08072i
\(719\) −33.8150 −1.26109 −0.630543 0.776155i \(-0.717168\pi\)
−0.630543 + 0.776155i \(0.717168\pi\)
\(720\) 0 0
\(721\) 4.82652 0.179749
\(722\) 3.53318 + 4.39633i 0.131492 + 0.163614i
\(723\) 0 0
\(724\) 7.23962 + 1.59499i 0.269058 + 0.0592774i
\(725\) 35.6484i 1.32395i
\(726\) 0 0
\(727\) −38.9720 −1.44539 −0.722696 0.691166i \(-0.757097\pi\)
−0.722696 + 0.691166i \(0.757097\pi\)
\(728\) 4.90629 + 9.89965i 0.181839 + 0.366905i
\(729\) 0 0
\(730\) 38.9280 31.2852i 1.44079 1.15792i
\(731\) 2.10852i 0.0779865i
\(732\) 0 0
\(733\) 13.2978i 0.491164i −0.969376 0.245582i \(-0.921021\pi\)
0.969376 0.245582i \(-0.0789790\pi\)
\(734\) −13.8434 17.2253i −0.510970 0.635798i
\(735\) 0 0
\(736\) 6.90652 + 27.8277i 0.254578 + 1.02574i
\(737\) −10.1303 −0.373154
\(738\) 0 0
\(739\) 37.4030i 1.37589i −0.725762 0.687946i \(-0.758513\pi\)
0.725762 0.687946i \(-0.241487\pi\)
\(740\) −14.2471 + 64.6671i −0.523733 + 2.37721i
\(741\) 0 0
\(742\) −0.475612 + 0.382234i −0.0174603 + 0.0140322i
\(743\) 31.1138 1.14145 0.570727 0.821140i \(-0.306662\pi\)
0.570727 + 0.821140i \(0.306662\pi\)
\(744\) 0 0
\(745\) 74.8747 2.74320
\(746\) 4.01147 3.22389i 0.146870 0.118035i
\(747\) 0 0
\(748\) −8.17131 1.80026i −0.298773 0.0658239i
\(749\) 4.92215i 0.179851i
\(750\) 0 0
\(751\) 18.6412 0.680227 0.340114 0.940384i \(-0.389534\pi\)
0.340114 + 0.940384i \(0.389534\pi\)
\(752\) −39.0700 18.0936i −1.42474 0.659805i
\(753\) 0 0
\(754\) −16.9943 21.1459i −0.618895 0.770089i
\(755\) 4.24855i 0.154621i
\(756\) 0 0
\(757\) 29.8972i 1.08663i 0.839528 + 0.543317i \(0.182832\pi\)
−0.839528 + 0.543317i \(0.817168\pi\)
\(758\) −5.13856 + 4.12970i −0.186641 + 0.149997i
\(759\) 0 0
\(760\) 42.5439 21.0849i 1.54323 0.764829i
\(761\) −42.6967 −1.54776 −0.773878 0.633335i \(-0.781685\pi\)
−0.773878 + 0.633335i \(0.781685\pi\)
\(762\) 0 0
\(763\) 20.1342i 0.728909i
\(764\) 4.85260 22.0258i 0.175561 0.796867i
\(765\) 0 0
\(766\) 10.5460 + 13.1223i 0.381041 + 0.474128i
\(767\) 28.9433 1.04508
\(768\) 0 0
\(769\) 40.5127 1.46092 0.730462 0.682953i \(-0.239305\pi\)
0.730462 + 0.682953i \(0.239305\pi\)
\(770\) 9.34694 + 11.6304i 0.336840 + 0.419129i
\(771\) 0 0
\(772\) 1.35628 6.15612i 0.0488136 0.221564i
\(773\) 14.6650i 0.527465i 0.964596 + 0.263732i \(0.0849536\pi\)
−0.964596 + 0.263732i \(0.915046\pi\)
\(774\) 0 0
\(775\) −8.27116 −0.297109
\(776\) −29.0750 + 14.4096i −1.04373 + 0.517276i
\(777\) 0 0
\(778\) 39.2787 31.5671i 1.40821 1.13173i
\(779\) 19.7233i 0.706660i
\(780\) 0 0
\(781\) 18.8902i 0.675944i
\(782\) 6.23425 + 7.75725i 0.222936 + 0.277399i
\(783\) 0 0
\(784\) −3.62967 1.68092i −0.129631 0.0600330i
\(785\) −28.5584 −1.01929
\(786\) 0 0
\(787\)