Properties

Label 504.2.q.d.25.9
Level $504$
Weight $2$
Character 504.25
Analytic conductor $4.024$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(22\)
Relative dimension: \(11\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.9
Character \(\chi\) \(=\) 504.25
Dual form 504.2.q.d.121.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.34477 + 1.09160i) q^{3} +(0.918286 - 1.59052i) q^{5} +(-0.361656 - 2.62092i) q^{7} +(0.616838 + 2.93590i) q^{9} +O(q^{10})\) \(q+(1.34477 + 1.09160i) q^{3} +(0.918286 - 1.59052i) q^{5} +(-0.361656 - 2.62092i) q^{7} +(0.616838 + 2.93590i) q^{9} +(1.54860 + 2.68225i) q^{11} +(2.40225 + 4.16081i) q^{13} +(2.97109 - 1.13649i) q^{15} +(1.87185 - 3.24214i) q^{17} +(-2.71408 - 4.70093i) q^{19} +(2.37464 - 3.91932i) q^{21} +(3.97914 - 6.89208i) q^{23} +(0.813503 + 1.40903i) q^{25} +(-2.37531 + 4.62146i) q^{27} +(-0.325267 + 0.563379i) q^{29} +1.03668 q^{31} +(-0.845416 + 5.29746i) q^{33} +(-4.50072 - 1.83153i) q^{35} +(0.873712 + 1.51331i) q^{37} +(-1.31144 + 8.21764i) q^{39} +(2.52260 + 4.36927i) q^{41} +(-6.09645 + 10.5594i) q^{43} +(5.23603 + 1.71490i) q^{45} -4.61383 q^{47} +(-6.73841 + 1.89574i) q^{49} +(6.05632 - 2.31664i) q^{51} +(4.55082 - 7.88226i) q^{53} +5.68821 q^{55} +(1.48168 - 9.28438i) q^{57} -5.79727 q^{59} -4.81245 q^{61} +(7.47167 - 2.67847i) q^{63} +8.82379 q^{65} -14.4774 q^{67} +(12.8744 - 4.92468i) q^{69} -5.00714 q^{71} +(-1.81364 + 3.14131i) q^{73} +(-0.444111 + 2.78284i) q^{75} +(6.46989 - 5.02879i) q^{77} -14.3581 q^{79} +(-8.23902 + 3.62195i) q^{81} +(3.83139 - 6.63616i) q^{83} +(-3.43778 - 5.95441i) q^{85} +(-1.05239 + 0.402558i) q^{87} +(-5.76798 - 9.99043i) q^{89} +(10.0364 - 7.80087i) q^{91} +(1.39411 + 1.13164i) q^{93} -9.96922 q^{95} +(-1.04480 + 1.80964i) q^{97} +(-6.91957 + 6.20103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + 2q^{3} + 3q^{5} - 5q^{7} + 10q^{9} + O(q^{10}) \) \( 22q + 2q^{3} + 3q^{5} - 5q^{7} + 10q^{9} - 3q^{11} - 3q^{13} - q^{15} + 7q^{17} - q^{19} + 2q^{23} - 10q^{25} - 4q^{27} + 9q^{29} + 8q^{31} + 29q^{33} + 14q^{35} + 2q^{37} - 16q^{39} + 16q^{41} + q^{45} - 10q^{47} + 15q^{49} + 7q^{51} + 11q^{53} + 22q^{55} + 7q^{57} + 38q^{59} + 26q^{61} + 48q^{63} - 26q^{65} - 52q^{67} - 4q^{69} - 48q^{71} - 35q^{73} - 23q^{75} + 17q^{77} - 20q^{79} - 38q^{81} - 28q^{83} - 20q^{85} - 33q^{87} + 6q^{89} - 37q^{91} + 19q^{93} - 24q^{95} - 29q^{97} - 56q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(3\) 1.34477 + 1.09160i 0.776406 + 0.630233i
\(4\) 0 0
\(5\) 0.918286 1.59052i 0.410670 0.711301i −0.584293 0.811543i \(-0.698628\pi\)
0.994963 + 0.100242i \(0.0319616\pi\)
\(6\) 0 0
\(7\) −0.361656 2.62092i −0.136693 0.990613i
\(8\) 0 0
\(9\) 0.616838 + 2.93590i 0.205613 + 0.978633i
\(10\) 0 0
\(11\) 1.54860 + 2.68225i 0.466919 + 0.808728i 0.999286 0.0377862i \(-0.0120306\pi\)
−0.532367 + 0.846514i \(0.678697\pi\)
\(12\) 0 0
\(13\) 2.40225 + 4.16081i 0.666263 + 1.15400i 0.978941 + 0.204143i \(0.0654406\pi\)
−0.312678 + 0.949859i \(0.601226\pi\)
\(14\) 0 0
\(15\) 2.97109 1.13649i 0.767132 0.293441i
\(16\) 0 0
\(17\) 1.87185 3.24214i 0.453990 0.786333i −0.544640 0.838670i \(-0.683334\pi\)
0.998629 + 0.0523367i \(0.0166669\pi\)
\(18\) 0 0
\(19\) −2.71408 4.70093i −0.622654 1.07847i −0.988990 0.147985i \(-0.952721\pi\)
0.366336 0.930483i \(-0.380612\pi\)
\(20\) 0 0
\(21\) 2.37464 3.91932i 0.518188 0.855267i
\(22\) 0 0
\(23\) 3.97914 6.89208i 0.829709 1.43710i −0.0685581 0.997647i \(-0.521840\pi\)
0.898267 0.439450i \(-0.144827\pi\)
\(24\) 0 0
\(25\) 0.813503 + 1.40903i 0.162701 + 0.281806i
\(26\) 0 0
\(27\) −2.37531 + 4.62146i −0.457128 + 0.889401i
\(28\) 0 0
\(29\) −0.325267 + 0.563379i −0.0604006 + 0.104617i −0.894645 0.446779i \(-0.852571\pi\)
0.834244 + 0.551396i \(0.185904\pi\)
\(30\) 0 0
\(31\) 1.03668 0.186194 0.0930970 0.995657i \(-0.470323\pi\)
0.0930970 + 0.995657i \(0.470323\pi\)
\(32\) 0 0
\(33\) −0.845416 + 5.29746i −0.147168 + 0.922169i
\(34\) 0 0
\(35\) −4.50072 1.83153i −0.760760 0.309585i
\(36\) 0 0
\(37\) 0.873712 + 1.51331i 0.143637 + 0.248787i 0.928864 0.370422i \(-0.120787\pi\)
−0.785226 + 0.619209i \(0.787453\pi\)
\(38\) 0 0
\(39\) −1.31144 + 8.21764i −0.209999 + 1.31588i
\(40\) 0 0
\(41\) 2.52260 + 4.36927i 0.393964 + 0.682365i 0.992968 0.118381i \(-0.0377703\pi\)
−0.599005 + 0.800745i \(0.704437\pi\)
\(42\) 0 0
\(43\) −6.09645 + 10.5594i −0.929699 + 1.61029i −0.145876 + 0.989303i \(0.546600\pi\)
−0.783824 + 0.620984i \(0.786733\pi\)
\(44\) 0 0
\(45\) 5.23603 + 1.71490i 0.780542 + 0.255643i
\(46\) 0 0
\(47\) −4.61383 −0.672996 −0.336498 0.941684i \(-0.609243\pi\)
−0.336498 + 0.941684i \(0.609243\pi\)
\(48\) 0 0
\(49\) −6.73841 + 1.89574i −0.962630 + 0.270820i
\(50\) 0 0
\(51\) 6.05632 2.31664i 0.848054 0.324395i
\(52\) 0 0
\(53\) 4.55082 7.88226i 0.625104 1.08271i −0.363417 0.931626i \(-0.618390\pi\)
0.988521 0.151085i \(-0.0482766\pi\)
\(54\) 0 0
\(55\) 5.68821 0.766998
\(56\) 0 0
\(57\) 1.48168 9.28438i 0.196254 1.22975i
\(58\) 0 0
\(59\) −5.79727 −0.754740 −0.377370 0.926063i \(-0.623172\pi\)
−0.377370 + 0.926063i \(0.623172\pi\)
\(60\) 0 0
\(61\) −4.81245 −0.616172 −0.308086 0.951359i \(-0.599688\pi\)
−0.308086 + 0.951359i \(0.599688\pi\)
\(62\) 0 0
\(63\) 7.47167 2.67847i 0.941342 0.337455i
\(64\) 0 0
\(65\) 8.82379 1.09446
\(66\) 0 0
\(67\) −14.4774 −1.76870 −0.884348 0.466828i \(-0.845397\pi\)
−0.884348 + 0.466828i \(0.845397\pi\)
\(68\) 0 0
\(69\) 12.8744 4.92468i 1.54990 0.592861i
\(70\) 0 0
\(71\) −5.00714 −0.594238 −0.297119 0.954840i \(-0.596026\pi\)
−0.297119 + 0.954840i \(0.596026\pi\)
\(72\) 0 0
\(73\) −1.81364 + 3.14131i −0.212270 + 0.367662i −0.952425 0.304774i \(-0.901419\pi\)
0.740155 + 0.672437i \(0.234752\pi\)
\(74\) 0 0
\(75\) −0.444111 + 2.78284i −0.0512816 + 0.321335i
\(76\) 0 0
\(77\) 6.46989 5.02879i 0.737312 0.573084i
\(78\) 0 0
\(79\) −14.3581 −1.61541 −0.807705 0.589587i \(-0.799290\pi\)
−0.807705 + 0.589587i \(0.799290\pi\)
\(80\) 0 0
\(81\) −8.23902 + 3.62195i −0.915447 + 0.402439i
\(82\) 0 0
\(83\) 3.83139 6.63616i 0.420550 0.728414i −0.575443 0.817842i \(-0.695171\pi\)
0.995993 + 0.0894279i \(0.0285038\pi\)
\(84\) 0 0
\(85\) −3.43778 5.95441i −0.372880 0.645847i
\(86\) 0 0
\(87\) −1.05239 + 0.402558i −0.112828 + 0.0431587i
\(88\) 0 0
\(89\) −5.76798 9.99043i −0.611405 1.05898i −0.991004 0.133833i \(-0.957271\pi\)
0.379599 0.925151i \(-0.376062\pi\)
\(90\) 0 0
\(91\) 10.0364 7.80087i 1.05210 0.817753i
\(92\) 0 0
\(93\) 1.39411 + 1.13164i 0.144562 + 0.117346i
\(94\) 0 0
\(95\) −9.96922 −1.02282
\(96\) 0 0
\(97\) −1.04480 + 1.80964i −0.106083 + 0.183741i −0.914180 0.405308i \(-0.867164\pi\)
0.808097 + 0.589049i \(0.200498\pi\)
\(98\) 0 0
\(99\) −6.91957 + 6.20103i −0.695443 + 0.623227i
\(100\) 0 0
\(101\) 8.22661 + 14.2489i 0.818578 + 1.41782i 0.906730 + 0.421712i \(0.138571\pi\)
−0.0881520 + 0.996107i \(0.528096\pi\)
\(102\) 0 0
\(103\) 3.87346 6.70903i 0.381663 0.661060i −0.609637 0.792681i \(-0.708685\pi\)
0.991300 + 0.131621i \(0.0420181\pi\)
\(104\) 0 0
\(105\) −4.05316 7.37596i −0.395548 0.719820i
\(106\) 0 0
\(107\) 3.74746 + 6.49080i 0.362281 + 0.627489i 0.988336 0.152290i \(-0.0486647\pi\)
−0.626055 + 0.779779i \(0.715331\pi\)
\(108\) 0 0
\(109\) −4.30644 + 7.45897i −0.412482 + 0.714440i −0.995160 0.0982628i \(-0.968671\pi\)
0.582678 + 0.812703i \(0.302005\pi\)
\(110\) 0 0
\(111\) −0.476981 + 2.98881i −0.0452730 + 0.283685i
\(112\) 0 0
\(113\) −1.55747 2.69762i −0.146514 0.253771i 0.783422 0.621490i \(-0.213472\pi\)
−0.929937 + 0.367719i \(0.880139\pi\)
\(114\) 0 0
\(115\) −7.30798 12.6578i −0.681473 1.18035i
\(116\) 0 0
\(117\) −10.7339 + 9.61930i −0.992353 + 0.889305i
\(118\) 0 0
\(119\) −9.17433 3.73342i −0.841010 0.342242i
\(120\) 0 0
\(121\) 0.703704 1.21885i 0.0639731 0.110805i
\(122\) 0 0
\(123\) −1.37715 + 8.62934i −0.124173 + 0.778081i
\(124\) 0 0
\(125\) 12.1710 1.08860
\(126\) 0 0
\(127\) 10.8866 0.966033 0.483017 0.875611i \(-0.339541\pi\)
0.483017 + 0.875611i \(0.339541\pi\)
\(128\) 0 0
\(129\) −19.7249 + 7.54510i −1.73668 + 0.664309i
\(130\) 0 0
\(131\) 8.02790 13.9047i 0.701401 1.21486i −0.266574 0.963815i \(-0.585892\pi\)
0.967975 0.251048i \(-0.0807751\pi\)
\(132\) 0 0
\(133\) −11.3392 + 8.81351i −0.983232 + 0.764228i
\(134\) 0 0
\(135\) 5.16930 + 8.02179i 0.444903 + 0.690406i
\(136\) 0 0
\(137\) −6.72031 11.6399i −0.574155 0.994465i −0.996133 0.0878590i \(-0.971998\pi\)
0.421978 0.906606i \(-0.361336\pi\)
\(138\) 0 0
\(139\) −4.06953 7.04863i −0.345173 0.597857i 0.640212 0.768198i \(-0.278846\pi\)
−0.985385 + 0.170341i \(0.945513\pi\)
\(140\) 0 0
\(141\) −6.20456 5.03644i −0.522518 0.424144i
\(142\) 0 0
\(143\) −7.44022 + 12.8868i −0.622182 + 1.07765i
\(144\) 0 0
\(145\) 0.597376 + 1.03469i 0.0496094 + 0.0859260i
\(146\) 0 0
\(147\) −11.1310 4.80628i −0.918071 0.396415i
\(148\) 0 0
\(149\) −3.76479 + 6.52081i −0.308424 + 0.534205i −0.978018 0.208522i \(-0.933135\pi\)
0.669594 + 0.742727i \(0.266468\pi\)
\(150\) 0 0
\(151\) 2.83616 + 4.91237i 0.230803 + 0.399763i 0.958045 0.286619i \(-0.0925313\pi\)
−0.727241 + 0.686382i \(0.759198\pi\)
\(152\) 0 0
\(153\) 10.6732 + 3.49569i 0.862878 + 0.282610i
\(154\) 0 0
\(155\) 0.951973 1.64886i 0.0764643 0.132440i
\(156\) 0 0
\(157\) 0.436763 0.0348575 0.0174287 0.999848i \(-0.494452\pi\)
0.0174287 + 0.999848i \(0.494452\pi\)
\(158\) 0 0
\(159\) 14.7241 5.63220i 1.16769 0.446663i
\(160\) 0 0
\(161\) −19.5026 7.93644i −1.53702 0.625479i
\(162\) 0 0
\(163\) 9.12649 + 15.8076i 0.714842 + 1.23814i 0.963020 + 0.269429i \(0.0868348\pi\)
−0.248178 + 0.968714i \(0.579832\pi\)
\(164\) 0 0
\(165\) 7.64936 + 6.20923i 0.595502 + 0.483388i
\(166\) 0 0
\(167\) 0.765108 + 1.32521i 0.0592058 + 0.102548i 0.894109 0.447849i \(-0.147810\pi\)
−0.834903 + 0.550397i \(0.814477\pi\)
\(168\) 0 0
\(169\) −5.04157 + 8.73226i −0.387813 + 0.671713i
\(170\) 0 0
\(171\) 12.1273 10.8680i 0.927399 0.831096i
\(172\) 0 0
\(173\) 2.16949 0.164943 0.0824716 0.996593i \(-0.473719\pi\)
0.0824716 + 0.996593i \(0.473719\pi\)
\(174\) 0 0
\(175\) 3.39874 2.64171i 0.256921 0.199694i
\(176\) 0 0
\(177\) −7.79602 6.32827i −0.585985 0.475662i
\(178\) 0 0
\(179\) −1.08263 + 1.87517i −0.0809195 + 0.140157i −0.903645 0.428282i \(-0.859119\pi\)
0.822726 + 0.568439i \(0.192452\pi\)
\(180\) 0 0
\(181\) 0.557838 0.0414638 0.0207319 0.999785i \(-0.493400\pi\)
0.0207319 + 0.999785i \(0.493400\pi\)
\(182\) 0 0
\(183\) −6.47167 5.25325i −0.478399 0.388332i
\(184\) 0 0
\(185\) 3.20927 0.235950
\(186\) 0 0
\(187\) 11.5949 0.847906
\(188\) 0 0
\(189\) 12.9715 + 4.55411i 0.943539 + 0.331262i
\(190\) 0 0
\(191\) −23.9997 −1.73655 −0.868277 0.496079i \(-0.834773\pi\)
−0.868277 + 0.496079i \(0.834773\pi\)
\(192\) 0 0
\(193\) −21.2794 −1.53172 −0.765862 0.643005i \(-0.777687\pi\)
−0.765862 + 0.643005i \(0.777687\pi\)
\(194\) 0 0
\(195\) 11.8660 + 9.63201i 0.849743 + 0.689763i
\(196\) 0 0
\(197\) −14.8768 −1.05993 −0.529964 0.848020i \(-0.677795\pi\)
−0.529964 + 0.848020i \(0.677795\pi\)
\(198\) 0 0
\(199\) 6.17884 10.7021i 0.438006 0.758649i −0.559530 0.828810i \(-0.689018\pi\)
0.997536 + 0.0701616i \(0.0223515\pi\)
\(200\) 0 0
\(201\) −19.4688 15.8035i −1.37323 1.11469i
\(202\) 0 0
\(203\) 1.59420 + 0.648749i 0.111891 + 0.0455332i
\(204\) 0 0
\(205\) 9.26586 0.647156
\(206\) 0 0
\(207\) 22.6889 + 7.43107i 1.57699 + 0.516495i
\(208\) 0 0
\(209\) 8.40604 14.5597i 0.581458 1.00711i
\(210\) 0 0
\(211\) 8.65802 + 14.9961i 0.596043 + 1.03238i 0.993399 + 0.114712i \(0.0365944\pi\)
−0.397356 + 0.917664i \(0.630072\pi\)
\(212\) 0 0
\(213\) −6.73347 5.46577i −0.461370 0.374508i
\(214\) 0 0
\(215\) 11.1966 + 19.3930i 0.763599 + 1.32259i
\(216\) 0 0
\(217\) −0.374923 2.71706i −0.0254514 0.184446i
\(218\) 0 0
\(219\) −5.86797 + 2.24460i −0.396521 + 0.151676i
\(220\) 0 0
\(221\) 17.9866 1.20991
\(222\) 0 0
\(223\) 1.14489 1.98301i 0.0766677 0.132792i −0.825143 0.564925i \(-0.808905\pi\)
0.901810 + 0.432132i \(0.142239\pi\)
\(224\) 0 0
\(225\) −3.63497 + 3.25751i −0.242331 + 0.217167i
\(226\) 0 0
\(227\) 1.78013 + 3.08328i 0.118152 + 0.204644i 0.919035 0.394176i \(-0.128970\pi\)
−0.800884 + 0.598820i \(0.795636\pi\)
\(228\) 0 0
\(229\) 13.4799 23.3478i 0.890775 1.54287i 0.0518260 0.998656i \(-0.483496\pi\)
0.838949 0.544211i \(-0.183171\pi\)
\(230\) 0 0
\(231\) 14.1899 + 0.299909i 0.933630 + 0.0197325i
\(232\) 0 0
\(233\) 10.7321 + 18.5885i 0.703081 + 1.21777i 0.967380 + 0.253332i \(0.0815264\pi\)
−0.264298 + 0.964441i \(0.585140\pi\)
\(234\) 0 0
\(235\) −4.23681 + 7.33837i −0.276379 + 0.478703i
\(236\) 0 0
\(237\) −19.3084 15.6732i −1.25421 1.01808i
\(238\) 0 0
\(239\) 4.65970 + 8.07083i 0.301411 + 0.522059i 0.976456 0.215718i \(-0.0692091\pi\)
−0.675045 + 0.737777i \(0.735876\pi\)
\(240\) 0 0
\(241\) 10.1003 + 17.4943i 0.650620 + 1.12691i 0.982973 + 0.183752i \(0.0588242\pi\)
−0.332353 + 0.943155i \(0.607842\pi\)
\(242\) 0 0
\(243\) −15.0333 4.12297i −0.964389 0.264489i
\(244\) 0 0
\(245\) −3.17258 + 12.4584i −0.202689 + 0.795937i
\(246\) 0 0
\(247\) 13.0398 22.5856i 0.829702 1.43709i
\(248\) 0 0
\(249\) 12.3964 4.74182i 0.785588 0.300500i
\(250\) 0 0
\(251\) 27.1837 1.71582 0.857910 0.513800i \(-0.171762\pi\)
0.857910 + 0.513800i \(0.171762\pi\)
\(252\) 0 0
\(253\) 24.6483 1.54963
\(254\) 0 0
\(255\) 1.87677 11.7600i 0.117528 0.736441i
\(256\) 0 0
\(257\) −14.2411 + 24.6662i −0.888333 + 1.53864i −0.0464876 + 0.998919i \(0.514803\pi\)
−0.841845 + 0.539719i \(0.818531\pi\)
\(258\) 0 0
\(259\) 3.65028 2.83722i 0.226818 0.176297i
\(260\) 0 0
\(261\) −1.85466 0.607438i −0.114801 0.0375995i
\(262\) 0 0
\(263\) −1.79907 3.11608i −0.110935 0.192146i 0.805212 0.592987i \(-0.202051\pi\)
−0.916148 + 0.400841i \(0.868718\pi\)
\(264\) 0 0
\(265\) −8.35791 14.4763i −0.513422 0.889274i
\(266\) 0 0
\(267\) 3.14888 19.7312i 0.192708 1.20753i
\(268\) 0 0
\(269\) 11.2261 19.4443i 0.684470 1.18554i −0.289133 0.957289i \(-0.593367\pi\)
0.973603 0.228248i \(-0.0732997\pi\)
\(270\) 0 0
\(271\) −14.7935 25.6231i −0.898642 1.55649i −0.829231 0.558906i \(-0.811221\pi\)
−0.0694115 0.997588i \(-0.522112\pi\)
\(272\) 0 0
\(273\) 22.0120 + 0.465231i 1.33223 + 0.0281570i
\(274\) 0 0
\(275\) −2.51958 + 4.36403i −0.151936 + 0.263161i
\(276\) 0 0
\(277\) 10.1933 + 17.6554i 0.612459 + 1.06081i 0.990825 + 0.135153i \(0.0431527\pi\)
−0.378366 + 0.925656i \(0.623514\pi\)
\(278\) 0 0
\(279\) 0.639467 + 3.04360i 0.0382839 + 0.182216i
\(280\) 0 0
\(281\) −2.23968 + 3.87924i −0.133608 + 0.231416i −0.925065 0.379809i \(-0.875990\pi\)
0.791457 + 0.611225i \(0.209323\pi\)
\(282\) 0 0
\(283\) 2.07680 0.123453 0.0617264 0.998093i \(-0.480339\pi\)
0.0617264 + 0.998093i \(0.480339\pi\)
\(284\) 0 0
\(285\) −13.4064 10.8824i −0.794124 0.644615i
\(286\) 0 0
\(287\) 10.5392 8.19169i 0.622108 0.483540i
\(288\) 0 0
\(289\) 1.49237 + 2.58486i 0.0877865 + 0.152051i
\(290\) 0 0
\(291\) −3.38041 + 1.29306i −0.198163 + 0.0758007i
\(292\) 0 0
\(293\) −0.887340 1.53692i −0.0518389 0.0897877i 0.838942 0.544222i \(-0.183175\pi\)
−0.890780 + 0.454434i \(0.849842\pi\)
\(294\) 0 0
\(295\) −5.32355 + 9.22066i −0.309949 + 0.536847i
\(296\) 0 0
\(297\) −16.0743 + 0.785616i −0.932725 + 0.0455860i
\(298\) 0 0
\(299\) 38.2355 2.21122
\(300\) 0 0
\(301\) 29.8800 + 12.1594i 1.72225 + 0.700858i
\(302\) 0 0
\(303\) −4.49111 + 28.1417i −0.258007 + 1.61670i
\(304\) 0 0
\(305\) −4.41921 + 7.65429i −0.253043 + 0.438283i
\(306\) 0 0
\(307\) 19.6315 1.12043 0.560215 0.828347i \(-0.310718\pi\)
0.560215 + 0.828347i \(0.310718\pi\)
\(308\) 0 0
\(309\) 12.5325 4.79388i 0.712948 0.272714i
\(310\) 0 0
\(311\) −13.3159 −0.755076 −0.377538 0.925994i \(-0.623229\pi\)
−0.377538 + 0.925994i \(0.623229\pi\)
\(312\) 0 0
\(313\) 4.65281 0.262992 0.131496 0.991317i \(-0.458022\pi\)
0.131496 + 0.991317i \(0.458022\pi\)
\(314\) 0 0
\(315\) 2.60098 14.3434i 0.146548 0.808160i
\(316\) 0 0
\(317\) −4.12552 −0.231713 −0.115856 0.993266i \(-0.536961\pi\)
−0.115856 + 0.993266i \(0.536961\pi\)
\(318\) 0 0
\(319\) −2.01483 −0.112809
\(320\) 0 0
\(321\) −2.04583 + 12.8194i −0.114187 + 0.715508i
\(322\) 0 0
\(323\) −20.3214 −1.13071
\(324\) 0 0
\(325\) −3.90847 + 6.76967i −0.216803 + 0.375514i
\(326\) 0 0
\(327\) −13.9334 + 5.32975i −0.770517 + 0.294736i
\(328\) 0 0
\(329\) 1.66862 + 12.0925i 0.0919939 + 0.666679i
\(330\) 0 0
\(331\) 0.0440594 0.00242172 0.00121086 0.999999i \(-0.499615\pi\)
0.00121086 + 0.999999i \(0.499615\pi\)
\(332\) 0 0
\(333\) −3.90400 + 3.49860i −0.213938 + 0.191722i
\(334\) 0 0
\(335\) −13.2944 + 23.0266i −0.726350 + 1.25808i
\(336\) 0 0
\(337\) −13.3351 23.0970i −0.726407 1.25817i −0.958392 0.285454i \(-0.907856\pi\)
0.231986 0.972719i \(-0.425478\pi\)
\(338\) 0 0
\(339\) 0.850261 5.32782i 0.0461798 0.289367i
\(340\) 0 0
\(341\) 1.60541 + 2.78064i 0.0869376 + 0.150580i
\(342\) 0 0
\(343\) 7.40556 + 16.9752i 0.399863 + 0.916575i
\(344\) 0 0
\(345\) 3.98960 24.9992i 0.214793 1.34591i
\(346\) 0 0
\(347\) 10.8252 0.581126 0.290563 0.956856i \(-0.406157\pi\)
0.290563 + 0.956856i \(0.406157\pi\)
\(348\) 0 0
\(349\) −2.69555 + 4.66884i −0.144290 + 0.249917i −0.929108 0.369809i \(-0.879423\pi\)
0.784818 + 0.619726i \(0.212756\pi\)
\(350\) 0 0
\(351\) −24.9351 + 1.21868i −1.33094 + 0.0650483i
\(352\) 0 0
\(353\) 4.47307 + 7.74759i 0.238078 + 0.412362i 0.960163 0.279442i \(-0.0901494\pi\)
−0.722085 + 0.691804i \(0.756816\pi\)
\(354\) 0 0
\(355\) −4.59798 + 7.96394i −0.244036 + 0.422682i
\(356\) 0 0
\(357\) −8.26203 15.0353i −0.437273 0.795751i
\(358\) 0 0
\(359\) 1.84157 + 3.18969i 0.0971942 + 0.168345i 0.910522 0.413460i \(-0.135680\pi\)
−0.813328 + 0.581805i \(0.802347\pi\)
\(360\) 0 0
\(361\) −5.23251 + 9.06297i −0.275395 + 0.476998i
\(362\) 0 0
\(363\) 2.27682 0.870920i 0.119502 0.0457114i
\(364\) 0 0
\(365\) 3.33087 + 5.76924i 0.174346 + 0.301976i
\(366\) 0 0
\(367\) 3.74988 + 6.49498i 0.195742 + 0.339035i 0.947144 0.320810i \(-0.103955\pi\)
−0.751401 + 0.659845i \(0.770622\pi\)
\(368\) 0 0
\(369\) −11.2717 + 10.1012i −0.586781 + 0.525849i
\(370\) 0 0
\(371\) −22.3046 9.07666i −1.15800 0.471237i
\(372\) 0 0
\(373\) −4.11917 + 7.13461i −0.213282 + 0.369416i −0.952740 0.303787i \(-0.901749\pi\)
0.739458 + 0.673203i \(0.235082\pi\)
\(374\) 0 0
\(375\) 16.3672 + 13.2858i 0.845199 + 0.686075i
\(376\) 0 0
\(377\) −3.12549 −0.160971
\(378\) 0 0
\(379\) −3.92853 −0.201795 −0.100897 0.994897i \(-0.532171\pi\)
−0.100897 + 0.994897i \(0.532171\pi\)
\(380\) 0 0
\(381\) 14.6401 + 11.8838i 0.750034 + 0.608826i
\(382\) 0 0
\(383\) −11.9632 + 20.7210i −0.611293 + 1.05879i 0.379729 + 0.925098i \(0.376017\pi\)
−0.991023 + 0.133694i \(0.957316\pi\)
\(384\) 0 0
\(385\) −2.05718 14.9083i −0.104843 0.759799i
\(386\) 0 0
\(387\) −34.7617 11.3851i −1.76704 0.578740i
\(388\) 0 0
\(389\) −6.32875 10.9617i −0.320881 0.555781i 0.659789 0.751451i \(-0.270645\pi\)
−0.980670 + 0.195669i \(0.937312\pi\)
\(390\) 0 0
\(391\) −14.8967 25.8018i −0.753359 1.30486i
\(392\) 0 0
\(393\) 25.9741 9.93551i 1.31022 0.501180i
\(394\) 0 0
\(395\) −13.1848 + 22.8368i −0.663400 + 1.14904i
\(396\) 0 0
\(397\) −17.7703 30.7791i −0.891866 1.54476i −0.837636 0.546229i \(-0.816063\pi\)
−0.0542297 0.998528i \(-0.517270\pi\)
\(398\) 0 0
\(399\) −24.8694 0.525623i −1.24503 0.0263141i
\(400\) 0 0
\(401\) 1.66166 2.87808i 0.0829794 0.143724i −0.821549 0.570138i \(-0.806890\pi\)
0.904528 + 0.426413i \(0.140223\pi\)
\(402\) 0 0
\(403\) 2.49037 + 4.31345i 0.124054 + 0.214868i
\(404\) 0 0
\(405\) −1.80500 + 16.4303i −0.0896912 + 0.816428i
\(406\) 0 0
\(407\) −2.70605 + 4.68702i −0.134134 + 0.232327i
\(408\) 0 0
\(409\) 22.5129 1.11319 0.556595 0.830784i \(-0.312107\pi\)
0.556595 + 0.830784i \(0.312107\pi\)
\(410\) 0 0
\(411\) 3.66878 22.9889i 0.180968 1.13396i
\(412\) 0 0
\(413\) 2.09662 + 15.1942i 0.103168 + 0.747656i
\(414\) 0 0
\(415\) −7.03662 12.1878i −0.345414 0.598275i
\(416\) 0 0
\(417\) 2.22165 13.9211i 0.108795 0.681719i
\(418\) 0 0
\(419\) −3.59772 6.23144i −0.175760 0.304426i 0.764664 0.644429i \(-0.222905\pi\)
−0.940424 + 0.340004i \(0.889572\pi\)
\(420\) 0 0
\(421\) 16.8121 29.1193i 0.819370 1.41919i −0.0867773 0.996228i \(-0.527657\pi\)
0.906147 0.422962i \(-0.139010\pi\)
\(422\) 0 0
\(423\) −2.84599 13.5457i −0.138377 0.658616i
\(424\) 0 0
\(425\) 6.09102 0.295458
\(426\) 0 0
\(427\) 1.74045 + 12.6130i 0.0842264 + 0.610388i
\(428\) 0 0
\(429\) −24.0726 + 9.20818i −1.16224 + 0.444575i
\(430\) 0 0
\(431\) 16.4871 28.5565i 0.794156 1.37552i −0.129217 0.991616i \(-0.541246\pi\)
0.923373 0.383903i \(-0.125420\pi\)
\(432\) 0 0
\(433\) 19.8977 0.956221 0.478110 0.878300i \(-0.341322\pi\)
0.478110 + 0.878300i \(0.341322\pi\)
\(434\) 0 0
\(435\) −0.326122 + 2.04351i −0.0156364 + 0.0979789i
\(436\) 0 0
\(437\) −43.1989 −2.06648
\(438\) 0 0
\(439\) 29.1268 1.39015 0.695074 0.718938i \(-0.255372\pi\)
0.695074 + 0.718938i \(0.255372\pi\)
\(440\) 0 0
\(441\) −9.72221 18.6139i −0.462962 0.886378i
\(442\) 0 0
\(443\) 13.7663 0.654058 0.327029 0.945014i \(-0.393952\pi\)
0.327029 + 0.945014i \(0.393952\pi\)
\(444\) 0 0
\(445\) −21.1866 −1.00434
\(446\) 0 0
\(447\) −12.1809 + 4.65939i −0.576136 + 0.220382i
\(448\) 0 0
\(449\) −12.0958 −0.570838 −0.285419 0.958403i \(-0.592133\pi\)
−0.285419 + 0.958403i \(0.592133\pi\)
\(450\) 0 0
\(451\) −7.81297 + 13.5325i −0.367898 + 0.637218i
\(452\) 0 0
\(453\) −1.54833 + 9.70197i −0.0727468 + 0.455838i
\(454\) 0 0
\(455\) −3.19118 23.1264i −0.149605 1.08418i
\(456\) 0 0
\(457\) −8.35476 −0.390819 −0.195410 0.980722i \(-0.562604\pi\)
−0.195410 + 0.980722i \(0.562604\pi\)
\(458\) 0 0
\(459\) 10.5372 + 16.3517i 0.491834 + 0.763234i
\(460\) 0 0
\(461\) 11.1673 19.3423i 0.520112 0.900860i −0.479615 0.877479i \(-0.659224\pi\)
0.999727 0.0233807i \(-0.00744299\pi\)
\(462\) 0 0
\(463\) −0.0370790 0.0642228i −0.00172321 0.00298469i 0.865163 0.501492i \(-0.167215\pi\)
−0.866886 + 0.498507i \(0.833882\pi\)
\(464\) 0 0
\(465\) 3.08008 1.17818i 0.142835 0.0546369i
\(466\) 0 0
\(467\) 14.5828 + 25.2581i 0.674810 + 1.16880i 0.976524 + 0.215407i \(0.0691077\pi\)
−0.301715 + 0.953398i \(0.597559\pi\)
\(468\) 0 0
\(469\) 5.23584 + 37.9441i 0.241769 + 1.75209i
\(470\) 0 0
\(471\) 0.587348 + 0.476768i 0.0270635 + 0.0219683i
\(472\) 0 0
\(473\) −37.7637 −1.73638
\(474\) 0 0
\(475\) 4.41583 7.64845i 0.202612 0.350935i
\(476\) 0 0
\(477\) 25.9486 + 8.49869i 1.18811 + 0.389128i
\(478\) 0 0
\(479\) −13.9551 24.1710i −0.637626 1.10440i −0.985952 0.167027i \(-0.946583\pi\)
0.348326 0.937373i \(-0.386750\pi\)
\(480\) 0 0
\(481\) −4.19774 + 7.27070i −0.191401 + 0.331515i
\(482\) 0 0
\(483\) −17.5633 31.9617i −0.799157 1.45431i
\(484\) 0 0
\(485\) 1.91884 + 3.32353i 0.0871301 + 0.150914i
\(486\) 0 0
\(487\) −2.14409 + 3.71367i −0.0971580 + 0.168283i −0.910507 0.413493i \(-0.864309\pi\)
0.813349 + 0.581776i \(0.197642\pi\)
\(488\) 0 0
\(489\) −4.98238 + 31.2200i −0.225311 + 1.41182i
\(490\) 0 0
\(491\) −5.22215 9.04503i −0.235672 0.408196i 0.723796 0.690015i \(-0.242396\pi\)
−0.959468 + 0.281818i \(0.909063\pi\)
\(492\) 0 0
\(493\) 1.21770 + 2.10912i 0.0548425 + 0.0949900i
\(494\) 0 0
\(495\) 3.50871 + 16.7000i 0.157705 + 0.750610i
\(496\) 0 0
\(497\) 1.81086 + 13.1233i 0.0812282 + 0.588660i
\(498\) 0 0
\(499\) 3.06312 5.30548i 0.137124 0.237506i −0.789283 0.614030i \(-0.789547\pi\)
0.926407 + 0.376524i \(0.122881\pi\)
\(500\) 0 0
\(501\) −0.417691 + 2.61729i −0.0186611 + 0.116932i
\(502\) 0 0
\(503\) −12.4469 −0.554982 −0.277491 0.960728i \(-0.589503\pi\)
−0.277491 + 0.960728i \(0.589503\pi\)
\(504\) 0 0
\(505\) 30.2175 1.34466
\(506\) 0 0
\(507\) −16.3119 + 6.23957i −0.724436 + 0.277109i
\(508\) 0 0
\(509\) −5.90450 + 10.2269i −0.261712 + 0.453299i −0.966697 0.255923i \(-0.917620\pi\)
0.704985 + 0.709222i \(0.250954\pi\)
\(510\) 0 0
\(511\) 8.88902 + 3.61731i 0.393227 + 0.160021i
\(512\) 0 0
\(513\) 28.1720 1.37688i 1.24382 0.0607906i
\(514\) 0 0
\(515\) −7.11388 12.3216i −0.313475 0.542955i
\(516\) 0 0
\(517\) −7.14495 12.3754i −0.314235 0.544271i
\(518\) 0 0
\(519\) 2.91748 + 2.36821i 0.128063 + 0.103953i
\(520\) 0 0
\(521\) 5.54828 9.60991i 0.243075 0.421018i −0.718514 0.695513i \(-0.755177\pi\)
0.961589 + 0.274495i \(0.0885107\pi\)
\(522\) 0 0
\(523\) 10.6209 + 18.3960i 0.464421 + 0.804401i 0.999175 0.0406065i \(-0.0129290\pi\)
−0.534754 + 0.845008i \(0.679596\pi\)
\(524\) 0 0
\(525\) 7.45422 + 0.157547i 0.325329 + 0.00687592i
\(526\) 0 0
\(527\) 1.94052 3.36107i 0.0845302 0.146411i
\(528\) 0 0
\(529\) −20.1672 34.9305i −0.876833 1.51872i
\(530\) 0 0
\(531\) −3.57598 17.0202i −0.155184 0.738614i
\(532\) 0 0
\(533\) −12.1198 + 20.9921i −0.524967 + 0.909269i
\(534\) 0 0
\(535\) 13.7650 0.595111
\(536\) 0 0
\(537\) −3.50282 + 1.33989i −0.151158 + 0.0578204i
\(538\) 0 0
\(539\) −15.5199 15.1383i −0.668490 0.652054i
\(540\) 0 0
\(541\) −6.33567 10.9737i −0.272392 0.471796i 0.697082 0.716991i \(-0.254481\pi\)
−0.969474 + 0.245195i \(0.921148\pi\)
\(542\) 0 0
\(543\) 0.750167 + 0.608934i 0.0321928 + 0.0261319i
\(544\) 0 0
\(545\) 7.90908 + 13.6989i 0.338788 + 0.586798i
\(546\) 0 0
\(547\) −21.4805 + 37.2053i −0.918438 + 1.59078i −0.116651 + 0.993173i \(0.537216\pi\)
−0.801788 + 0.597609i \(0.796117\pi\)
\(548\) 0 0
\(549\) −2.96850 14.1289i −0.126693 0.603006i
\(550\) 0 0
\(551\) 3.53121 0.150435
\(552\) 0 0
\(553\) 5.19268 + 37.6313i 0.220815 + 1.60025i
\(554\) 0 0
\(555\) 4.31574 + 3.50322i 0.183193 + 0.148704i
\(556\) 0 0
\(557\) 16.5129 28.6012i 0.699673 1.21187i −0.268906 0.963166i \(-0.586662\pi\)
0.968580 0.248703i \(-0.0800044\pi\)
\(558\) 0 0
\(559\) −58.5807 −2.47770
\(560\) 0 0
\(561\) 15.5926 + 12.6570i 0.658319 + 0.534378i
\(562\) 0 0
\(563\) 36.8132 1.55149 0.775746 0.631046i \(-0.217374\pi\)
0.775746 + 0.631046i \(0.217374\pi\)
\(564\) 0 0
\(565\) −5.72081 −0.240676
\(566\) 0 0
\(567\) 12.4725 + 20.2839i 0.523797 + 0.851843i
\(568\) 0 0
\(569\) 44.3571 1.85955 0.929774 0.368132i \(-0.120002\pi\)
0.929774 + 0.368132i \(0.120002\pi\)
\(570\) 0 0
\(571\) −42.5872 −1.78222 −0.891110 0.453787i \(-0.850073\pi\)
−0.891110 + 0.453787i \(0.850073\pi\)
\(572\) 0 0
\(573\) −32.2741 26.1979i −1.34827 1.09443i
\(574\) 0 0
\(575\) 12.9482 0.539977
\(576\) 0 0
\(577\) 16.3209 28.2687i 0.679450 1.17684i −0.295697 0.955282i \(-0.595552\pi\)
0.975147 0.221559i \(-0.0711147\pi\)
\(578\) 0 0
\(579\) −28.6160 23.2285i −1.18924 0.965343i
\(580\) 0 0
\(581\) −18.7785 7.64175i −0.779063 0.317033i
\(582\) 0 0
\(583\) 28.1895 1.16749
\(584\) 0 0
\(585\) 5.44285 + 25.9058i 0.225034 + 1.07107i
\(586\) 0 0
\(587\) −13.1270 + 22.7366i −0.541809 + 0.938441i 0.456991 + 0.889471i \(0.348927\pi\)
−0.998800 + 0.0489701i \(0.984406\pi\)
\(588\) 0 0
\(589\) −2.81365 4.87338i −0.115934 0.200804i
\(590\) 0 0
\(591\) −20.0059 16.2394i −0.822934 0.668002i
\(592\) 0 0
\(593\) −2.59998 4.50330i −0.106768 0.184928i 0.807691 0.589606i \(-0.200717\pi\)
−0.914459 + 0.404678i \(0.867384\pi\)
\(594\) 0 0
\(595\) −14.3627 + 11.1636i −0.588814 + 0.457663i
\(596\) 0 0
\(597\) 19.9915 7.64707i 0.818196 0.312974i
\(598\) 0 0
\(599\) 26.3675 1.07735 0.538673 0.842515i \(-0.318926\pi\)
0.538673 + 0.842515i \(0.318926\pi\)
\(600\) 0 0
\(601\) −15.4505 + 26.7611i −0.630239 + 1.09161i 0.357263 + 0.934004i \(0.383710\pi\)
−0.987503 + 0.157603i \(0.949623\pi\)
\(602\) 0 0
\(603\) −8.93021 42.5042i −0.363666 1.73091i
\(604\) 0 0
\(605\) −1.29240 2.23851i −0.0525436 0.0910082i
\(606\) 0 0
\(607\) −3.83661 + 6.64519i −0.155723 + 0.269720i −0.933322 0.359040i \(-0.883104\pi\)
0.777599 + 0.628760i \(0.216437\pi\)
\(608\) 0 0
\(609\) 1.43568 + 2.61265i 0.0581765 + 0.105870i
\(610\) 0 0
\(611\) −11.0836 19.1973i −0.448393 0.776639i
\(612\) 0 0
\(613\) 7.97498 13.8131i 0.322106 0.557905i −0.658816 0.752304i \(-0.728942\pi\)
0.980922 + 0.194399i \(0.0622758\pi\)
\(614\) 0 0
\(615\) 12.4605 + 10.1146i 0.502456 + 0.407859i
\(616\) 0 0
\(617\) −3.67011 6.35682i −0.147753 0.255916i 0.782644 0.622470i \(-0.213871\pi\)
−0.930397 + 0.366554i \(0.880537\pi\)
\(618\) 0 0
\(619\) −10.2842 17.8127i −0.413357 0.715955i 0.581898 0.813262i \(-0.302310\pi\)
−0.995254 + 0.0973072i \(0.968977\pi\)
\(620\) 0 0
\(621\) 22.3998 + 34.7603i 0.898873 + 1.39488i
\(622\) 0 0
\(623\) −24.0981 + 18.7305i −0.965469 + 0.750421i
\(624\) 0 0
\(625\) 7.10891 12.3130i 0.284356 0.492520i
\(626\) 0 0
\(627\) 27.1975 10.4035i 1.08616 0.415476i
\(628\) 0 0
\(629\) 6.54182 0.260840
\(630\) 0 0
\(631\) −5.09394 −0.202787 −0.101393 0.994846i \(-0.532330\pi\)
−0.101393 + 0.994846i \(0.532330\pi\)
\(632\) 0 0
\(633\) −4.72662 + 29.6175i −0.187866 + 1.17719i
\(634\) 0 0
\(635\) 9.99705 17.3154i 0.396721 0.687141i
\(636\) 0 0
\(637\) −24.0751 23.4832i −0.953892 0.930439i
\(638\) 0 0
\(639\) −3.08859 14.7005i −0.122183 0.581541i
\(640\) 0 0
\(641\) −6.31861 10.9442i −0.249570 0.432268i 0.713836 0.700312i \(-0.246956\pi\)
−0.963407 + 0.268044i \(0.913623\pi\)
\(642\) 0 0
\(643\) 12.4329 + 21.5344i 0.490306 + 0.849235i 0.999938 0.0111579i \(-0.00355174\pi\)
−0.509632 + 0.860393i \(0.670218\pi\)
\(644\) 0 0
\(645\) −6.11247 + 38.3013i −0.240678 + 1.50811i
\(646\) 0 0
\(647\) 1.12339 1.94577i 0.0441650 0.0764960i −0.843098 0.537760i \(-0.819271\pi\)
0.887263 + 0.461264i \(0.152604\pi\)
\(648\) 0 0
\(649\) −8.97762 15.5497i −0.352403 0.610379i
\(650\) 0 0
\(651\) 2.46175 4.06310i 0.0964835 0.159246i
\(652\) 0 0
\(653\) −1.02881 + 1.78195i −0.0402604 + 0.0697330i −0.885453 0.464728i \(-0.846152\pi\)
0.845193 + 0.534461i \(0.179485\pi\)
\(654\) 0 0
\(655\) −14.7438 25.5370i −0.576088 0.997815i
\(656\) 0 0
\(657\) −10.3413 3.38697i −0.403452 0.132138i
\(658\) 0 0
\(659\) −4.16599 + 7.21571i −0.162284 + 0.281084i −0.935687 0.352830i \(-0.885219\pi\)
0.773403 + 0.633914i \(0.218553\pi\)
\(660\) 0 0
\(661\) 34.0926 1.32605 0.663024 0.748598i \(-0.269273\pi\)
0.663024 + 0.748598i \(0.269273\pi\)
\(662\) 0 0
\(663\) 24.1879 + 19.6341i 0.939379 + 0.762523i
\(664\) 0 0
\(665\) 3.60543 + 26.1285i 0.139812 + 1.01322i
\(666\) 0 0
\(667\) 2.58857 + 4.48353i 0.100230 + 0.173603i
\(668\) 0 0
\(669\) 3.70427 1.41694i 0.143215 0.0547823i
\(670\) 0 0
\(671\) −7.45255 12.9082i −0.287702 0.498315i
\(672\) 0 0
\(673\) 0.571008 0.989016i 0.0220108 0.0381237i −0.854810 0.518941i \(-0.826327\pi\)
0.876821 + 0.480817i \(0.159660\pi\)
\(674\) 0 0
\(675\) −8.44410 + 0.412697i −0.325013 + 0.0158847i
\(676\) 0 0
\(677\) 36.3812 1.39824 0.699121 0.715004i \(-0.253575\pi\)
0.699121 + 0.715004i \(0.253575\pi\)
\(678\) 0 0
\(679\) 5.12077 + 2.08386i 0.196517 + 0.0799711i
\(680\) 0 0
\(681\) −0.971817 + 6.08950i −0.0372401 + 0.233350i
\(682\) 0 0
\(683\) 3.11274 5.39142i 0.119106 0.206297i −0.800308 0.599589i \(-0.795331\pi\)
0.919414 + 0.393292i \(0.128664\pi\)
\(684\) 0 0
\(685\) −24.6846 −0.943152
\(686\) 0 0
\(687\) 43.6138 16.6830i 1.66397 0.636496i
\(688\) 0 0
\(689\) 43.7288 1.66593
\(690\) 0 0
\(691\) −39.8259 −1.51505 −0.757525 0.652806i \(-0.773592\pi\)
−0.757525 + 0.652806i \(0.773592\pi\)
\(692\) 0 0
\(693\) 18.7549 + 15.8930i 0.712440 + 0.603725i
\(694\) 0 0
\(695\) −14.9480 −0.567008
\(696\) 0 0
\(697\) 18.8877 0.715422
\(698\) 0 0
\(699\) −5.85890 + 36.7124i −0.221604 + 1.38859i
\(700\) 0 0
\(701\) −48.3337 −1.82554 −0.912769 0.408477i \(-0.866060\pi\)
−0.912769 + 0.408477i \(0.866060\pi\)
\(702\) 0 0
\(703\) 4.74265 8.21452i 0.178873 0.309816i
\(704\) 0 0
\(705\) −13.7081 + 5.24357i −0.516277 + 0.197484i
\(706\) 0 0
\(707\) 34.3700 26.7145i 1.29262 1.00470i
\(708\) 0 0
\(709\) −16.0840 −0.604046 −0.302023 0.953301i \(-0.597662\pi\)
−0.302023 + 0.953301i \(0.597662\pi\)
\(710\) 0 0
\(711\) −8.85660 42.1539i −0.332149 1.58089i
\(712\) 0 0
\(713\) 4.12512 7.14491i 0.154487 0.267579i
\(714\) 0 0
\(715\) 13.6645 + 23.6676i 0.511023 + 0.885117i
\(716\) 0 0
\(717\) −2.54384 + 15.9400i −0.0950015 + 0.595288i
\(718\) 0 0
\(719\) 21.0734 + 36.5002i 0.785906 + 1.36123i 0.928456 + 0.371442i \(0.121136\pi\)
−0.142550 + 0.989788i \(0.545530\pi\)
\(720\) 0 0
\(721\) −18.9847 7.72566i −0.707026 0.287718i
\(722\) 0 0
\(723\) −5.51402 + 34.5514i −0.205069 + 1.28498i
\(724\) 0 0
\(725\) −1.05842 −0.0393089
\(726\) 0 0
\(727\) −12.9548 + 22.4384i −0.480467 + 0.832192i −0.999749 0.0224103i \(-0.992866\pi\)
0.519282 + 0.854603i \(0.326199\pi\)
\(728\) 0 0
\(729\) −15.7158 21.9548i −0.582068 0.813140i
\(730\) 0 0
\(731\) 22.8232 + 39.5310i 0.844148 + 1.46211i
\(732\) 0 0
\(733\) −10.2027 + 17.6716i −0.376846 + 0.652716i −0.990601 0.136780i \(-0.956325\pi\)
0.613756 + 0.789496i \(0.289658\pi\)
\(734\) 0 0
\(735\) −17.8659 + 13.2906i −0.658994 + 0.490229i
\(736\) 0 0
\(737\) −22.4196 38.8320i −0.825838 1.43039i
\(738\) 0 0
\(739\) −11.8953 + 20.6033i −0.437576 + 0.757903i −0.997502 0.0706392i \(-0.977496\pi\)
0.559926 + 0.828542i \(0.310829\pi\)
\(740\) 0 0
\(741\) 42.1899 16.1383i 1.54989 0.592857i
\(742\) 0 0
\(743\) 21.6320 + 37.4678i 0.793603 + 1.37456i 0.923723 + 0.383062i \(0.125130\pi\)
−0.130120 + 0.991498i \(0.541536\pi\)
\(744\) 0 0
\(745\) 6.91430 + 11.9759i 0.253321 + 0.438764i
\(746\) 0 0
\(747\) 21.8465 + 7.15515i 0.799320 + 0.261793i
\(748\) 0 0
\(749\) 15.6565 12.1692i 0.572078 0.444654i
\(750\) 0 0
\(751\) 7.18465 12.4442i 0.262172 0.454095i −0.704647 0.709558i \(-0.748895\pi\)
0.966819 + 0.255463i \(0.0822280\pi\)
\(752\) 0 0
\(753\) 36.5560 + 29.6736i 1.33217 + 1.08137i
\(754\) 0 0
\(755\) 10.4176 0.379136
\(756\) 0 0
\(757\) 39.7854 1.44603 0.723013 0.690835i \(-0.242757\pi\)
0.723013 + 0.690835i \(0.242757\pi\)
\(758\) 0 0
\(759\) 33.1465 + 26.9060i 1.20314 + 0.976626i
\(760\) 0 0
\(761\) 11.1966 19.3932i 0.405878 0.703002i −0.588545 0.808464i \(-0.700299\pi\)
0.994423 + 0.105463i \(0.0336324\pi\)
\(762\) 0 0
\(763\) 21.1068 + 8.58924i 0.764117 + 0.310951i
\(764\) 0 0
\(765\) 15.3610 13.7659i 0.555378 0.497707i
\(766\) 0 0
\(767\) −13.9265 24.1213i −0.502856 0.870971i
\(768\) 0 0
\(769\) −1.45546 2.52093i −0.0524853 0.0909071i 0.838589 0.544764i \(-0.183381\pi\)
−0.891074 + 0.453857i \(0.850048\pi\)
\(770\) 0 0
\(771\) −46.0766 + 17.6251i −1.65941 + 0.634751i
\(772\) 0 0
\(773\) −6.68612 + 11.5807i −0.240483 + 0.416529i −0.960852 0.277062i \(-0.910639\pi\)
0.720369 + 0.693591i \(0.243972\pi\)
\(774\) 0 0
\(775\) 0.843347 + 1.46072i 0.0302939 + 0.0524706i
\(776\) 0 0
\(777\) 8.00591 + 0.169207i 0.287211 + 0.00607028i
\(778\) 0 0
\(779\) 13.6931 23.7171i 0.490606 0.849754i
\(780\) 0 0
\(781\) −7.75403 13.4304i −0.277461 0.480577i
\(782\) 0 0
\(783\) −1.83103 2.84141i −0.0654355 0.101544i
\(784\) 0 0
\(785\) 0.401073 0.694679i 0.0143149 0.0247941i
\(786\) 0 0
\(787\) −23.8528 −0.850260 −0.425130 0.905132i \(-0.639772\pi\)
−0.425130 + 0.905132i \(0.639772\pi\)
\(788\) 0 0
\(789\) 0.982156 6.15428i 0.0349657 0.219098i
\(790\) 0 0
\(791\) −6.50696 + 5.05761i −0.231361 + 0.179828i
\(792\) 0 0
\(793\) −11.5607 20.0237i −0.410533 0.711063i
\(794\) 0 0
\(795\) 4.56279 28.5909i 0.161825 1.01401i
\(796\) 0 0
\(797\) −6.10559 10.5752i −0.216271 0.374593i 0.737394 0.675463i \(-0.236056\pi\)
−0.953665 + 0.300870i \(0.902723\pi\)
\(798\) <