Properties

Label 384.2.n.a.145.5
Level $384$
Weight $2$
Character 384.145
Analytic conductor $3.066$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 384.n (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.06625543762\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 145.5
Character \(\chi\) \(=\) 384.145
Dual form 384.2.n.a.241.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.382683 - 0.923880i) q^{3} +(-3.09318 + 1.28124i) q^{5} +(1.73503 - 1.73503i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\) \(q+(0.382683 - 0.923880i) q^{3} +(-3.09318 + 1.28124i) q^{5} +(1.73503 - 1.73503i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(-2.39923 - 5.79225i) q^{11} +(0.0173304 + 0.00717850i) q^{13} +3.34804i q^{15} -5.57978i q^{17} +(1.03052 + 0.426856i) q^{19} +(-0.938989 - 2.26692i) q^{21} +(-2.01868 - 2.01868i) q^{23} +(4.39068 - 4.39068i) q^{25} +(-0.923880 + 0.382683i) q^{27} +(-0.706079 + 1.70463i) q^{29} -1.38048 q^{31} -6.26948 q^{33} +(-3.14377 + 7.58973i) q^{35} +(-2.87315 + 1.19010i) q^{37} +(0.0132641 - 0.0132641i) q^{39} +(6.97897 + 6.97897i) q^{41} +(-1.67010 - 4.03197i) q^{43} +(3.09318 + 1.28124i) q^{45} -1.15993i q^{47} +0.979375i q^{49} +(-5.15504 - 2.13529i) q^{51} +(2.56680 + 6.19681i) q^{53} +(14.8425 + 14.8425i) q^{55} +(0.788727 - 0.788727i) q^{57} +(0.735935 - 0.304834i) q^{59} +(4.82262 - 11.6428i) q^{61} -2.45370 q^{63} -0.0628036 q^{65} +(2.05899 - 4.97085i) q^{67} +(-2.63753 + 1.09250i) q^{69} +(1.78298 - 1.78298i) q^{71} +(1.67500 + 1.67500i) q^{73} +(-2.37622 - 5.73670i) q^{75} +(-14.2124 - 5.88697i) q^{77} +2.67236i q^{79} +1.00000i q^{81} +(6.91877 + 2.86585i) q^{83} +(7.14903 + 17.2593i) q^{85} +(1.30466 + 1.30466i) q^{87} +(6.73869 - 6.73869i) q^{89} +(0.0425236 - 0.0176139i) q^{91} +(-0.528286 + 1.27540i) q^{93} -3.73450 q^{95} -1.75001 q^{97} +(-2.39923 + 5.79225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{23} + 48q^{31} + 48q^{35} + 16q^{43} - 16q^{51} - 32q^{53} - 32q^{55} - 64q^{59} - 32q^{61} - 16q^{63} - 16q^{67} - 32q^{69} - 64q^{71} - 32q^{75} - 32q^{77} + 48q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(1\)

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 0
\(3\) 0.382683 0.923880i 0.220942 0.533402i
\(4\) 0 0
\(5\) −3.09318 + 1.28124i −1.38331 + 0.572987i −0.945365 0.326013i \(-0.894295\pi\)
−0.437949 + 0.899000i \(0.644295\pi\)
\(6\) 0 0
\(7\) 1.73503 1.73503i 0.655778 0.655778i −0.298600 0.954378i \(-0.596520\pi\)
0.954378 + 0.298600i \(0.0965198\pi\)
\(8\) 0 0
\(9\) −0.707107 0.707107i −0.235702 0.235702i
\(10\) 0 0
\(11\) −2.39923 5.79225i −0.723394 1.74643i −0.663443 0.748227i \(-0.730905\pi\)
−0.0599515 0.998201i \(-0.519095\pi\)
\(12\) 0 0
\(13\) 0.0173304 + 0.00717850i 0.00480660 + 0.00199096i 0.385085 0.922881i \(-0.374172\pi\)
−0.380279 + 0.924872i \(0.624172\pi\)
\(14\) 0 0
\(15\) 3.34804i 0.864460i
\(16\) 0 0
\(17\) 5.57978i 1.35329i −0.736307 0.676647i \(-0.763432\pi\)
0.736307 0.676647i \(-0.236568\pi\)
\(18\) 0 0
\(19\) 1.03052 + 0.426856i 0.236418 + 0.0979274i 0.497747 0.867322i \(-0.334161\pi\)
−0.261329 + 0.965250i \(0.584161\pi\)
\(20\) 0 0
\(21\) −0.938989 2.26692i −0.204904 0.494682i
\(22\) 0 0
\(23\) −2.01868 2.01868i −0.420923 0.420923i 0.464598 0.885522i \(-0.346199\pi\)
−0.885522 + 0.464598i \(0.846199\pi\)
\(24\) 0 0
\(25\) 4.39068 4.39068i 0.878136 0.878136i
\(26\) 0 0
\(27\) −0.923880 + 0.382683i −0.177801 + 0.0736475i
\(28\) 0 0
\(29\) −0.706079 + 1.70463i −0.131116 + 0.316541i −0.975780 0.218756i \(-0.929800\pi\)
0.844664 + 0.535297i \(0.179800\pi\)
\(30\) 0 0
\(31\) −1.38048 −0.247941 −0.123971 0.992286i \(-0.539563\pi\)
−0.123971 + 0.992286i \(0.539563\pi\)
\(32\) 0 0
\(33\) −6.26948 −1.09138
\(34\) 0 0
\(35\) −3.14377 + 7.58973i −0.531394 + 1.28290i
\(36\) 0 0
\(37\) −2.87315 + 1.19010i −0.472342 + 0.195651i −0.606140 0.795358i \(-0.707283\pi\)
0.133797 + 0.991009i \(0.457283\pi\)
\(38\) 0 0
\(39\) 0.0132641 0.0132641i 0.00212396 0.00212396i
\(40\) 0 0
\(41\) 6.97897 + 6.97897i 1.08993 + 1.08993i 0.995535 + 0.0943974i \(0.0300924\pi\)
0.0943974 + 0.995535i \(0.469908\pi\)
\(42\) 0 0
\(43\) −1.67010 4.03197i −0.254687 0.614869i 0.743884 0.668309i \(-0.232982\pi\)
−0.998571 + 0.0534396i \(0.982982\pi\)
\(44\) 0 0
\(45\) 3.09318 + 1.28124i 0.461105 + 0.190996i
\(46\) 0 0
\(47\) 1.15993i 0.169193i −0.996415 0.0845966i \(-0.973040\pi\)
0.996415 0.0845966i \(-0.0269601\pi\)
\(48\) 0 0
\(49\) 0.979375i 0.139911i
\(50\) 0 0
\(51\) −5.15504 2.13529i −0.721850 0.299000i
\(52\) 0 0
\(53\) 2.56680 + 6.19681i 0.352577 + 0.851197i 0.996300 + 0.0859383i \(0.0273888\pi\)
−0.643723 + 0.765258i \(0.722611\pi\)
\(54\) 0 0
\(55\) 14.8425 + 14.8425i 2.00136 + 2.00136i
\(56\) 0 0
\(57\) 0.788727 0.788727i 0.104469 0.104469i
\(58\) 0 0
\(59\) 0.735935 0.304834i 0.0958106 0.0396860i −0.334263 0.942480i \(-0.608487\pi\)
0.430074 + 0.902794i \(0.358487\pi\)
\(60\) 0 0
\(61\) 4.82262 11.6428i 0.617473 1.49071i −0.237156 0.971472i \(-0.576215\pi\)
0.854629 0.519240i \(-0.173785\pi\)
\(62\) 0 0
\(63\) −2.45370 −0.309137
\(64\) 0 0
\(65\) −0.0628036 −0.00778983
\(66\) 0 0
\(67\) 2.05899 4.97085i 0.251546 0.607286i −0.746783 0.665068i \(-0.768403\pi\)
0.998329 + 0.0577816i \(0.0184027\pi\)
\(68\) 0 0
\(69\) −2.63753 + 1.09250i −0.317521 + 0.131522i
\(70\) 0 0
\(71\) 1.78298 1.78298i 0.211600 0.211600i −0.593347 0.804947i \(-0.702194\pi\)
0.804947 + 0.593347i \(0.202194\pi\)
\(72\) 0 0
\(73\) 1.67500 + 1.67500i 0.196044 + 0.196044i 0.798302 0.602258i \(-0.205732\pi\)
−0.602258 + 0.798302i \(0.705732\pi\)
\(74\) 0 0
\(75\) −2.37622 5.73670i −0.274382 0.662417i
\(76\) 0 0
\(77\) −14.2124 5.88697i −1.61965 0.670883i
\(78\) 0 0
\(79\) 2.67236i 0.300664i 0.988636 + 0.150332i \(0.0480343\pi\)
−0.988636 + 0.150332i \(0.951966\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) 6.91877 + 2.86585i 0.759433 + 0.314568i 0.728584 0.684956i \(-0.240179\pi\)
0.0308494 + 0.999524i \(0.490179\pi\)
\(84\) 0 0
\(85\) 7.14903 + 17.2593i 0.775421 + 1.87203i
\(86\) 0 0
\(87\) 1.30466 + 1.30466i 0.139875 + 0.139875i
\(88\) 0 0
\(89\) 6.73869 6.73869i 0.714300 0.714300i −0.253132 0.967432i \(-0.581461\pi\)
0.967432 + 0.253132i \(0.0814607\pi\)
\(90\) 0 0
\(91\) 0.0425236 0.0176139i 0.00445769 0.00184643i
\(92\) 0 0
\(93\) −0.528286 + 1.27540i −0.0547807 + 0.132252i
\(94\) 0 0
\(95\) −3.73450 −0.383151
\(96\) 0 0
\(97\) −1.75001 −0.177686 −0.0888431 0.996046i \(-0.528317\pi\)
−0.0888431 + 0.996046i \(0.528317\pi\)
\(98\) 0 0
\(99\) −2.39923 + 5.79225i −0.241131 + 0.582143i
\(100\) 0 0
\(101\) −7.71200 + 3.19442i −0.767373 + 0.317856i −0.731808 0.681511i \(-0.761323\pi\)
−0.0355651 + 0.999367i \(0.511323\pi\)
\(102\) 0 0
\(103\) 3.90293 3.90293i 0.384567 0.384567i −0.488177 0.872744i \(-0.662338\pi\)
0.872744 + 0.488177i \(0.162338\pi\)
\(104\) 0 0
\(105\) 5.80893 + 5.80893i 0.566894 + 0.566894i
\(106\) 0 0
\(107\) 5.55747 + 13.4169i 0.537261 + 1.29706i 0.926628 + 0.375981i \(0.122694\pi\)
−0.389366 + 0.921083i \(0.627306\pi\)
\(108\) 0 0
\(109\) 14.8488 + 6.15056i 1.42225 + 0.589117i 0.955426 0.295231i \(-0.0953967\pi\)
0.466828 + 0.884348i \(0.345397\pi\)
\(110\) 0 0
\(111\) 3.10987i 0.295176i
\(112\) 0 0
\(113\) 2.72924i 0.256745i 0.991726 + 0.128373i \(0.0409753\pi\)
−0.991726 + 0.128373i \(0.959025\pi\)
\(114\) 0 0
\(115\) 8.83055 + 3.65773i 0.823453 + 0.341085i
\(116\) 0 0
\(117\) −0.00717850 0.0173304i −0.000663652 0.00160220i
\(118\) 0 0
\(119\) −9.68106 9.68106i −0.887461 0.887461i
\(120\) 0 0
\(121\) −20.0157 + 20.0157i −1.81961 + 1.81961i
\(122\) 0 0
\(123\) 9.11846 3.77699i 0.822184 0.340560i
\(124\) 0 0
\(125\) −1.54948 + 3.74078i −0.138590 + 0.334585i
\(126\) 0 0
\(127\) −15.3336 −1.36064 −0.680319 0.732916i \(-0.738159\pi\)
−0.680319 + 0.732916i \(0.738159\pi\)
\(128\) 0 0
\(129\) −4.36417 −0.384244
\(130\) 0 0
\(131\) −5.70595 + 13.7754i −0.498531 + 1.20356i 0.451744 + 0.892148i \(0.350802\pi\)
−0.950275 + 0.311412i \(0.899198\pi\)
\(132\) 0 0
\(133\) 2.52859 1.04737i 0.219256 0.0908189i
\(134\) 0 0
\(135\) 2.36742 2.36742i 0.203755 0.203755i
\(136\) 0 0
\(137\) −3.06155 3.06155i −0.261566 0.261566i 0.564124 0.825690i \(-0.309214\pi\)
−0.825690 + 0.564124i \(0.809214\pi\)
\(138\) 0 0
\(139\) −0.621401 1.50020i −0.0527066 0.127245i 0.895333 0.445397i \(-0.146938\pi\)
−0.948040 + 0.318152i \(0.896938\pi\)
\(140\) 0 0
\(141\) −1.07164 0.443886i −0.0902480 0.0373819i
\(142\) 0 0
\(143\) 0.117605i 0.00983462i
\(144\) 0 0
\(145\) 6.17738i 0.513003i
\(146\) 0 0
\(147\) 0.904825 + 0.374791i 0.0746287 + 0.0309122i
\(148\) 0 0
\(149\) −8.53959 20.6164i −0.699591 1.68896i −0.724503 0.689272i \(-0.757930\pi\)
0.0249118 0.999690i \(-0.492070\pi\)
\(150\) 0 0
\(151\) −9.42348 9.42348i −0.766872 0.766872i 0.210683 0.977555i \(-0.432431\pi\)
−0.977555 + 0.210683i \(0.932431\pi\)
\(152\) 0 0
\(153\) −3.94550 + 3.94550i −0.318975 + 0.318975i
\(154\) 0 0
\(155\) 4.27007 1.76872i 0.342981 0.142067i
\(156\) 0 0
\(157\) 7.53965 18.2023i 0.601729 1.45270i −0.270070 0.962841i \(-0.587047\pi\)
0.871800 0.489863i \(-0.162953\pi\)
\(158\) 0 0
\(159\) 6.70737 0.531929
\(160\) 0 0
\(161\) −7.00491 −0.552064
\(162\) 0 0
\(163\) 6.01448 14.5202i 0.471090 1.13731i −0.492592 0.870260i \(-0.663950\pi\)
0.963682 0.267052i \(-0.0860495\pi\)
\(164\) 0 0
\(165\) 19.3927 8.03271i 1.50972 0.625345i
\(166\) 0 0
\(167\) 11.8392 11.8392i 0.916142 0.916142i −0.0806038 0.996746i \(-0.525685\pi\)
0.996746 + 0.0806038i \(0.0256848\pi\)
\(168\) 0 0
\(169\) −9.19214 9.19214i −0.707088 0.707088i
\(170\) 0 0
\(171\) −0.426856 1.03052i −0.0326425 0.0788059i
\(172\) 0 0
\(173\) 21.0615 + 8.72397i 1.60128 + 0.663271i 0.991596 0.129374i \(-0.0412968\pi\)
0.609683 + 0.792645i \(0.291297\pi\)
\(174\) 0 0
\(175\) 15.2359i 1.15172i
\(176\) 0 0
\(177\) 0.796570i 0.0598739i
\(178\) 0 0
\(179\) 4.75826 + 1.97094i 0.355649 + 0.147315i 0.553353 0.832947i \(-0.313348\pi\)
−0.197703 + 0.980262i \(0.563348\pi\)
\(180\) 0 0
\(181\) −3.71100 8.95914i −0.275836 0.665928i 0.723876 0.689931i \(-0.242359\pi\)
−0.999712 + 0.0240027i \(0.992359\pi\)
\(182\) 0 0
\(183\) −8.91104 8.91104i −0.658723 0.658723i
\(184\) 0 0
\(185\) 7.36237 7.36237i 0.541293 0.541293i
\(186\) 0 0
\(187\) −32.3195 + 13.3872i −2.36343 + 0.978966i
\(188\) 0 0
\(189\) −0.938989 + 2.26692i −0.0683014 + 0.164894i
\(190\) 0 0
\(191\) −11.4844 −0.830980 −0.415490 0.909598i \(-0.636390\pi\)
−0.415490 + 0.909598i \(0.636390\pi\)
\(192\) 0 0
\(193\) 19.2681 1.38695 0.693474 0.720482i \(-0.256079\pi\)
0.693474 + 0.720482i \(0.256079\pi\)
\(194\) 0 0
\(195\) −0.0240339 + 0.0580229i −0.00172110 + 0.00415511i
\(196\) 0 0
\(197\) 6.48659 2.68683i 0.462151 0.191429i −0.139445 0.990230i \(-0.544532\pi\)
0.601596 + 0.798801i \(0.294532\pi\)
\(198\) 0 0
\(199\) −14.6525 + 14.6525i −1.03868 + 1.03868i −0.0394638 + 0.999221i \(0.512565\pi\)
−0.999221 + 0.0394638i \(0.987435\pi\)
\(200\) 0 0
\(201\) −3.80452 3.80452i −0.268350 0.268350i
\(202\) 0 0
\(203\) 1.73250 + 4.18263i 0.121598 + 0.293563i
\(204\) 0 0
\(205\) −30.5290 12.6455i −2.13224 0.883201i
\(206\) 0 0
\(207\) 2.85484i 0.198425i
\(208\) 0 0
\(209\) 6.99316i 0.483727i
\(210\) 0 0
\(211\) 2.80379 + 1.16137i 0.193021 + 0.0799519i 0.477100 0.878849i \(-0.341688\pi\)
−0.284079 + 0.958801i \(0.591688\pi\)
\(212\) 0 0
\(213\) −0.964940 2.32957i −0.0661166 0.159620i
\(214\) 0 0
\(215\) 10.3318 + 10.3318i 0.704625 + 0.704625i
\(216\) 0 0
\(217\) −2.39517 + 2.39517i −0.162594 + 0.162594i
\(218\) 0 0
\(219\) 2.18850 0.906505i 0.147885 0.0612559i
\(220\) 0 0
\(221\) 0.0400544 0.0966999i 0.00269435 0.00650474i
\(222\) 0 0
\(223\) 6.12103 0.409894 0.204947 0.978773i \(-0.434298\pi\)
0.204947 + 0.978773i \(0.434298\pi\)
\(224\) 0 0
\(225\) −6.20936 −0.413957
\(226\) 0 0
\(227\) 6.52469 15.7520i 0.433059 1.04550i −0.545237 0.838282i \(-0.683560\pi\)
0.978296 0.207214i \(-0.0664397\pi\)
\(228\) 0 0
\(229\) −8.60895 + 3.56595i −0.568896 + 0.235644i −0.648542 0.761179i \(-0.724621\pi\)
0.0796463 + 0.996823i \(0.474621\pi\)
\(230\) 0 0
\(231\) −10.8777 + 10.8777i −0.715701 + 0.715701i
\(232\) 0 0
\(233\) 7.99720 + 7.99720i 0.523914 + 0.523914i 0.918751 0.394837i \(-0.129199\pi\)
−0.394837 + 0.918751i \(0.629199\pi\)
\(234\) 0 0
\(235\) 1.48615 + 3.58788i 0.0969456 + 0.234047i
\(236\) 0 0
\(237\) 2.46894 + 1.02267i 0.160375 + 0.0664295i
\(238\) 0 0
\(239\) 6.26707i 0.405383i −0.979243 0.202692i \(-0.935031\pi\)
0.979243 0.202692i \(-0.0649689\pi\)
\(240\) 0 0
\(241\) 15.7602i 1.01520i 0.861592 + 0.507601i \(0.169468\pi\)
−0.861592 + 0.507601i \(0.830532\pi\)
\(242\) 0 0
\(243\) 0.923880 + 0.382683i 0.0592669 + 0.0245492i
\(244\) 0 0
\(245\) −1.25481 3.02939i −0.0801671 0.193541i
\(246\) 0 0
\(247\) 0.0147952 + 0.0147952i 0.000941395 + 0.000941395i
\(248\) 0 0
\(249\) 5.29540 5.29540i 0.335582 0.335582i
\(250\) 0 0
\(251\) 19.0196 7.87816i 1.20050 0.497265i 0.309342 0.950951i \(-0.399891\pi\)
0.891162 + 0.453686i \(0.149891\pi\)
\(252\) 0 0
\(253\) −6.84941 + 16.5359i −0.430619 + 1.03961i
\(254\) 0 0
\(255\) 18.6813 1.16987
\(256\) 0 0
\(257\) −5.22771 −0.326096 −0.163048 0.986618i \(-0.552132\pi\)
−0.163048 + 0.986618i \(0.552132\pi\)
\(258\) 0 0
\(259\) −2.92013 + 7.04983i −0.181448 + 0.438055i
\(260\) 0 0
\(261\) 1.70463 0.706079i 0.105514 0.0437052i
\(262\) 0 0
\(263\) −5.59065 + 5.59065i −0.344734 + 0.344734i −0.858144 0.513410i \(-0.828382\pi\)
0.513410 + 0.858144i \(0.328382\pi\)
\(264\) 0 0
\(265\) −15.8792 15.8792i −0.975450 0.975450i
\(266\) 0 0
\(267\) −3.64695 8.80452i −0.223190 0.538828i
\(268\) 0 0
\(269\) 9.92617 + 4.11155i 0.605209 + 0.250686i 0.664179 0.747574i \(-0.268781\pi\)
−0.0589693 + 0.998260i \(0.518781\pi\)
\(270\) 0 0
\(271\) 15.4368i 0.937717i −0.883273 0.468858i \(-0.844665\pi\)
0.883273 0.468858i \(-0.155335\pi\)
\(272\) 0 0
\(273\) 0.0460272i 0.00278569i
\(274\) 0 0
\(275\) −35.9662 14.8977i −2.16884 0.898363i
\(276\) 0 0
\(277\) 1.79136 + 4.32473i 0.107633 + 0.259848i 0.968515 0.248956i \(-0.0800876\pi\)
−0.860882 + 0.508804i \(0.830088\pi\)
\(278\) 0 0
\(279\) 0.976146 + 0.976146i 0.0584403 + 0.0584403i
\(280\) 0 0
\(281\) −3.70347 + 3.70347i −0.220931 + 0.220931i −0.808890 0.587960i \(-0.799931\pi\)
0.587960 + 0.808890i \(0.299931\pi\)
\(282\) 0 0
\(283\) 16.1605 6.69389i 0.960641 0.397910i 0.153421 0.988161i \(-0.450971\pi\)
0.807220 + 0.590250i \(0.200971\pi\)
\(284\) 0 0
\(285\) −1.42913 + 3.45022i −0.0846543 + 0.204374i
\(286\) 0 0
\(287\) 24.2174 1.42951
\(288\) 0 0
\(289\) −14.1339 −0.831407
\(290\) 0 0
\(291\) −0.669698 + 1.61679i −0.0392584 + 0.0947782i
\(292\) 0 0
\(293\) 13.5656 5.61904i 0.792509 0.328268i 0.0505573 0.998721i \(-0.483900\pi\)
0.741952 + 0.670453i \(0.233900\pi\)
\(294\) 0 0
\(295\) −1.88582 + 1.88582i −0.109796 + 0.109796i
\(296\) 0 0
\(297\) 4.43319 + 4.43319i 0.257240 + 0.257240i
\(298\) 0 0
\(299\) −0.0204935 0.0494756i −0.00118517 0.00286125i
\(300\) 0 0
\(301\) −9.89322 4.09791i −0.570236 0.236199i
\(302\) 0 0
\(303\) 8.34741i 0.479546i
\(304\) 0 0
\(305\) 42.1923i 2.41593i
\(306\) 0 0
\(307\) −15.6321 6.47504i −0.892173 0.369550i −0.110968 0.993824i \(-0.535395\pi\)
−0.781206 + 0.624274i \(0.785395\pi\)
\(308\) 0 0
\(309\) −2.11225 5.09942i −0.120162 0.290096i
\(310\) 0 0
\(311\) −22.8167 22.8167i −1.29381 1.29381i −0.932408 0.361407i \(-0.882297\pi\)
−0.361407 0.932408i \(-0.617703\pi\)
\(312\) 0 0
\(313\) 7.52178 7.52178i 0.425156 0.425156i −0.461819 0.886974i \(-0.652803\pi\)
0.886974 + 0.461819i \(0.152803\pi\)
\(314\) 0 0
\(315\) 7.58973 3.14377i 0.427633 0.177131i
\(316\) 0 0
\(317\) −9.98241 + 24.0997i −0.560668 + 1.35357i 0.348565 + 0.937285i \(0.386669\pi\)
−0.909233 + 0.416288i \(0.863331\pi\)
\(318\) 0 0
\(319\) 11.5677 0.647665
\(320\) 0 0
\(321\) 14.5224 0.810560
\(322\) 0 0
\(323\) 2.38176 5.75008i 0.132525 0.319943i
\(324\) 0 0
\(325\) 0.107611 0.0445739i 0.00596918 0.00247251i
\(326\) 0 0
\(327\) 11.3648 11.3648i 0.628472 0.628472i
\(328\) 0 0
\(329\) −2.01251 2.01251i −0.110953 0.110953i
\(330\) 0 0
\(331\) 12.9034 + 31.1516i 0.709235 + 1.71225i 0.701903 + 0.712272i \(0.252334\pi\)
0.00733222 + 0.999973i \(0.497666\pi\)
\(332\) 0 0
\(333\) 2.87315 + 1.19010i 0.157447 + 0.0652169i
\(334\) 0 0
\(335\) 18.0138i 0.984200i
\(336\) 0 0
\(337\) 0.925243i 0.0504012i −0.999682 0.0252006i \(-0.991978\pi\)
0.999682 0.0252006i \(-0.00802245\pi\)
\(338\) 0 0
\(339\) 2.52149 + 1.04443i 0.136948 + 0.0567259i
\(340\) 0 0
\(341\) 3.31208 + 7.99607i 0.179359 + 0.433012i
\(342\) 0 0
\(343\) 13.8444 + 13.8444i 0.747528 + 0.747528i
\(344\) 0 0
\(345\) 6.75861 6.75861i 0.363871 0.363871i
\(346\) 0 0
\(347\) −8.68292 + 3.59658i −0.466123 + 0.193075i −0.603369 0.797462i \(-0.706175\pi\)
0.137245 + 0.990537i \(0.456175\pi\)
\(348\) 0 0
\(349\) 0.586633 1.41626i 0.0314017 0.0758105i −0.907401 0.420266i \(-0.861937\pi\)
0.938802 + 0.344456i \(0.111937\pi\)
\(350\) 0 0
\(351\) −0.0187583 −0.00100125
\(352\) 0 0
\(353\) 10.8550 0.577751 0.288876 0.957367i \(-0.406719\pi\)
0.288876 + 0.957367i \(0.406719\pi\)
\(354\) 0 0
\(355\) −3.23066 + 7.79949i −0.171465 + 0.413954i
\(356\) 0 0
\(357\) −12.6489 + 5.23935i −0.669451 + 0.277296i
\(358\) 0 0
\(359\) −21.6767 + 21.6767i −1.14406 + 1.14406i −0.156354 + 0.987701i \(0.549974\pi\)
−0.987701 + 0.156354i \(0.950026\pi\)
\(360\) 0 0
\(361\) −12.5553 12.5553i −0.660803 0.660803i
\(362\) 0 0
\(363\) 10.8324 + 26.1517i 0.568553 + 1.37261i
\(364\) 0 0
\(365\) −7.32717 3.03501i −0.383521 0.158860i
\(366\) 0 0
\(367\) 0.154514i 0.00806555i 0.999992 + 0.00403277i \(0.00128367\pi\)
−0.999992 + 0.00403277i \(0.998716\pi\)
\(368\) 0 0
\(369\) 9.86975i 0.513799i
\(370\) 0 0
\(371\) 15.2051 + 6.29815i 0.789408 + 0.326984i
\(372\) 0 0
\(373\) 5.40842 + 13.0571i 0.280037 + 0.676070i 0.999836 0.0181131i \(-0.00576589\pi\)
−0.719799 + 0.694183i \(0.755766\pi\)
\(374\) 0 0
\(375\) 2.86307 + 2.86307i 0.147848 + 0.147848i
\(376\) 0 0
\(377\) −0.0244733 + 0.0244733i −0.00126044 + 0.00126044i
\(378\) 0 0
\(379\) −17.4888 + 7.24410i −0.898340 + 0.372105i −0.783582 0.621289i \(-0.786609\pi\)
−0.114758 + 0.993393i \(0.536609\pi\)
\(380\) 0 0
\(381\) −5.86792 + 14.1664i −0.300623 + 0.725767i
\(382\) 0 0
\(383\) 30.0898 1.53752 0.768759 0.639538i \(-0.220874\pi\)
0.768759 + 0.639538i \(0.220874\pi\)
\(384\) 0 0
\(385\) 51.5042 2.62490
\(386\) 0 0
\(387\) −1.67010 + 4.03197i −0.0848957 + 0.204956i
\(388\) 0 0
\(389\) 11.7666 4.87387i 0.596589 0.247115i −0.0638936 0.997957i \(-0.520352\pi\)
0.660482 + 0.750842i \(0.270352\pi\)
\(390\) 0 0
\(391\) −11.2638 + 11.2638i −0.569633 + 0.569633i
\(392\) 0 0
\(393\) 10.5432 + 10.5432i 0.531835 + 0.531835i
\(394\) 0 0
\(395\) −3.42394 8.26611i −0.172277 0.415913i
\(396\) 0 0
\(397\) 15.2331 + 6.30976i 0.764527 + 0.316678i 0.730653 0.682749i \(-0.239216\pi\)
0.0338739 + 0.999426i \(0.489216\pi\)
\(398\) 0 0
\(399\) 2.73692i 0.137017i
\(400\) 0 0
\(401\) 35.7766i 1.78660i −0.449463 0.893299i \(-0.648385\pi\)
0.449463 0.893299i \(-0.351615\pi\)
\(402\) 0 0
\(403\) −0.0239243 0.00990976i −0.00119175 0.000493641i
\(404\) 0 0
\(405\) −1.28124 3.09318i −0.0636653 0.153702i
\(406\) 0 0
\(407\) 13.7867 + 13.7867i 0.683380 + 0.683380i
\(408\) 0 0
\(409\) −4.31657 + 4.31657i −0.213440 + 0.213440i −0.805727 0.592287i \(-0.798225\pi\)
0.592287 + 0.805727i \(0.298225\pi\)
\(410\) 0 0
\(411\) −4.00011 + 1.65690i −0.197311 + 0.0817289i
\(412\) 0 0
\(413\) 0.747970 1.80576i 0.0368052 0.0888557i
\(414\) 0 0
\(415\) −25.0729 −1.23078
\(416\) 0 0
\(417\) −1.62380 −0.0795178
\(418\) 0 0
\(419\) 7.37576 17.8067i 0.360330 0.869913i −0.634922 0.772576i \(-0.718968\pi\)
0.995252 0.0973364i \(-0.0310323\pi\)
\(420\) 0 0
\(421\) −5.03356 + 2.08497i −0.245321 + 0.101615i −0.501956 0.864893i \(-0.667386\pi\)
0.256635 + 0.966508i \(0.417386\pi\)
\(422\) 0 0
\(423\) −0.820194 + 0.820194i −0.0398792 + 0.0398792i
\(424\) 0 0
\(425\) −24.4990 24.4990i −1.18838 1.18838i
\(426\) 0 0
\(427\) −11.8332 28.5680i −0.572651 1.38250i
\(428\) 0 0
\(429\) −0.108653 0.0450055i −0.00524581 0.00217288i
\(430\) 0 0
\(431\) 18.4128i 0.886914i 0.896296 + 0.443457i \(0.146248\pi\)
−0.896296 + 0.443457i \(0.853752\pi\)
\(432\) 0 0
\(433\) 0.227663i 0.0109408i 0.999985 + 0.00547038i \(0.00174129\pi\)
−0.999985 + 0.00547038i \(0.998259\pi\)
\(434\) 0 0
\(435\) −5.70715 2.36398i −0.273637 0.113344i
\(436\) 0 0
\(437\) −1.21860 2.94197i −0.0582938 0.140734i
\(438\) 0 0
\(439\) 19.0619 + 19.0619i 0.909774 + 0.909774i 0.996254 0.0864799i \(-0.0275618\pi\)
−0.0864799 + 0.996254i \(0.527562\pi\)
\(440\) 0 0
\(441\) 0.692523 0.692523i 0.0329773 0.0329773i
\(442\) 0 0
\(443\) −28.0493 + 11.6184i −1.33266 + 0.552008i −0.931414 0.363961i \(-0.881424\pi\)
−0.401250 + 0.915968i \(0.631424\pi\)
\(444\) 0 0
\(445\) −12.2101 + 29.4779i −0.578816 + 1.39739i
\(446\) 0 0
\(447\) −22.3150 −1.05546
\(448\) 0 0
\(449\) 33.0005 1.55739 0.778696 0.627401i \(-0.215881\pi\)
0.778696 + 0.627401i \(0.215881\pi\)
\(450\) 0 0
\(451\) 23.6798 57.1681i 1.11504 2.69194i
\(452\) 0 0
\(453\) −12.3124 + 5.09995i −0.578486 + 0.239617i
\(454\) 0 0
\(455\) −0.108966 + 0.108966i −0.00510839 + 0.00510839i
\(456\) 0 0
\(457\) 19.3344 + 19.3344i 0.904423 + 0.904423i 0.995815 0.0913920i \(-0.0291316\pi\)
−0.0913920 + 0.995815i \(0.529132\pi\)
\(458\) 0 0
\(459\) 2.13529 + 5.15504i 0.0996667 + 0.240617i
\(460\) 0 0
\(461\) −19.0532 7.89211i −0.887398 0.367572i −0.108037 0.994147i \(-0.534456\pi\)
−0.779361 + 0.626575i \(0.784456\pi\)
\(462\) 0 0
\(463\) 18.6664i 0.867499i 0.901034 + 0.433749i \(0.142810\pi\)
−0.901034 + 0.433749i \(0.857190\pi\)
\(464\) 0 0
\(465\) 4.62190i 0.214335i
\(466\) 0 0
\(467\) 1.38748 + 0.574712i 0.0642048 + 0.0265945i 0.414555 0.910024i \(-0.363937\pi\)
−0.350350 + 0.936619i \(0.613937\pi\)
\(468\) 0 0
\(469\) −5.05214 12.1970i −0.233286 0.563203i
\(470\) 0 0
\(471\) −13.9315 13.9315i −0.641927 0.641927i
\(472\) 0 0
\(473\) −19.3472 + 19.3472i −0.889586 + 0.889586i
\(474\) 0 0
\(475\) 6.39888 2.65050i 0.293601 0.121613i
\(476\) 0 0
\(477\) 2.56680 6.19681i 0.117526 0.283732i
\(478\) 0 0
\(479\) 20.1621 0.921229 0.460615 0.887600i \(-0.347629\pi\)
0.460615 + 0.887600i \(0.347629\pi\)
\(480\) 0 0
\(481\) −0.0583360 −0.00265989
\(482\) 0 0
\(483\) −2.68066 + 6.47169i −0.121974 + 0.294472i
\(484\) 0 0
\(485\) 5.41309 2.24218i 0.245796 0.101812i
\(486\) 0 0
\(487\) 14.3589 14.3589i 0.650665 0.650665i −0.302488 0.953153i \(-0.597817\pi\)
0.953153 + 0.302488i \(0.0978173\pi\)
\(488\) 0 0
\(489\) −11.1133 11.1133i −0.502561 0.502561i
\(490\) 0 0
\(491\) −7.84066 18.9290i −0.353844 0.854255i −0.996138 0.0877968i \(-0.972017\pi\)
0.642294 0.766458i \(-0.277983\pi\)
\(492\) 0 0
\(493\) 9.51144 + 3.93977i 0.428374 + 0.177438i
\(494\) 0 0
\(495\) 20.9905i 0.943452i
\(496\) 0 0
\(497\) 6.18702i 0.277526i
\(498\) 0 0
\(499\) −11.1249 4.60809i −0.498020 0.206286i 0.119512 0.992833i \(-0.461867\pi\)
−0.617531 + 0.786546i \(0.711867\pi\)
\(500\) 0 0
\(501\) −6.40731 15.4686i −0.286258 0.691087i
\(502\) 0 0
\(503\) 10.7388 + 10.7388i 0.478820 + 0.478820i 0.904754 0.425934i \(-0.140054\pi\)
−0.425934 + 0.904754i \(0.640054\pi\)
\(504\) 0 0
\(505\) 19.7618 19.7618i 0.879390 0.879390i
\(506\) 0 0
\(507\) −12.0101 + 4.97475i −0.533388 + 0.220936i
\(508\) 0 0
\(509\) −7.73386 + 18.6712i −0.342797 + 0.827586i 0.654633 + 0.755947i \(0.272823\pi\)
−0.997431 + 0.0716392i \(0.977177\pi\)
\(510\) 0 0
\(511\) 5.81234 0.257123
\(512\) 0 0
\(513\) −1.11543 −0.0492473
\(514\) 0 0
\(515\) −7.07189 + 17.0731i −0.311625 + 0.752329i
\(516\) 0 0
\(517\) −6.71860 + 2.78294i −0.295484 + 0.122393i
\(518\) 0 0
\(519\) 16.1198 16.1198i 0.707581 0.707581i
\(520\) 0 0
\(521\) 13.6485 + 13.6485i 0.597953 + 0.597953i 0.939767 0.341815i \(-0.111042\pi\)
−0.341815 + 0.939767i \(0.611042\pi\)
\(522\) 0 0
\(523\) 6.91544 + 16.6954i 0.302391 + 0.730037i 0.999909 + 0.0134697i \(0.00428766\pi\)
−0.697518 + 0.716567i \(0.745712\pi\)
\(524\) 0 0
\(525\) −14.0761 5.83052i −0.614332 0.254465i
\(526\) 0 0
\(527\) 7.70276i 0.335538i
\(528\) 0 0
\(529\) 14.8499i 0.645647i
\(530\) 0 0
\(531\) −0.735935 0.304834i −0.0319369 0.0132287i
\(532\) 0 0
\(533\) 0.0708500 + 0.171047i 0.00306885 + 0.00740887i
\(534\) 0 0
\(535\) −34.3806 34.3806i −1.48640 1.48640i
\(536\) 0 0
\(537\) 3.64182 3.64182i 0.157156 0.157156i
\(538\) 0 0
\(539\) 5.67279 2.34974i 0.244344 0.101211i
\(540\) 0 0
\(541\) 9.51555 22.9726i 0.409106 0.987668i −0.576268 0.817261i \(-0.695492\pi\)
0.985374 0.170407i \(-0.0545084\pi\)
\(542\) 0 0
\(543\) −9.69731 −0.416151
\(544\) 0 0
\(545\) −53.8103 −2.30498
\(546\) 0 0
\(547\) −11.3958 + 27.5119i −0.487250 + 1.17633i 0.468848 + 0.883279i \(0.344669\pi\)
−0.956098 + 0.293046i \(0.905331\pi\)
\(548\) 0 0
\(549\) −11.6428 + 4.82262i −0.496904 + 0.205824i
\(550\) 0 0
\(551\) −1.45526 + 1.45526i −0.0619961 + 0.0619961i
\(552\) 0 0
\(553\) 4.63662 + 4.63662i 0.197169 + 0.197169i
\(554\) 0 0
\(555\) −3.98449 9.61941i −0.169132 0.408321i
\(556\) 0 0
\(557\) 1.70939 + 0.708053i 0.0724292 + 0.0300012i 0.418604 0.908169i \(-0.362520\pi\)
−0.346175 + 0.938170i \(0.612520\pi\)
\(558\) 0 0
\(559\) 0.0818645i 0.00346250i
\(560\) 0 0
\(561\) 34.9823i 1.47695i
\(562\) 0 0
\(563\) −19.1605 7.93652i −0.807517 0.334485i −0.0595542 0.998225i \(-0.518968\pi\)
−0.747963 + 0.663741i \(0.768968\pi\)
\(564\) 0 0
\(565\) −3.49681 8.44204i −0.147112 0.355159i
\(566\) 0 0
\(567\) 1.73503 + 1.73503i 0.0728642 + 0.0728642i
\(568\) 0 0
\(569\) −15.1289 + 15.1289i −0.634235 + 0.634235i −0.949127 0.314892i \(-0.898032\pi\)
0.314892 + 0.949127i \(0.398032\pi\)
\(570\) 0 0
\(571\) 12.1094 5.01587i 0.506761 0.209907i −0.114629 0.993408i \(-0.536568\pi\)
0.621391 + 0.783501i \(0.286568\pi\)
\(572\) 0 0
\(573\) −4.39488 + 10.6102i −0.183599 + 0.443246i
\(574\) 0 0
\(575\) −17.7267 −0.739256
\(576\) 0 0
\(577\) −35.7790 −1.48950 −0.744749 0.667344i \(-0.767431\pi\)
−0.744749 + 0.667344i \(0.767431\pi\)
\(578\) 0 0
\(579\) 7.37358 17.8014i 0.306435 0.739801i
\(580\) 0 0
\(581\) 16.9766 7.03192i 0.704306 0.291733i
\(582\) 0 0
\(583\) 29.7351 29.7351i 1.23150 1.23150i
\(584\) 0 0
\(585\) 0.0444088 + 0.0444088i 0.00183608 + 0.00183608i
\(586\) 0 0
\(587\) −10.9958 26.5462i −0.453845 1.09568i −0.970848 0.239696i \(-0.922952\pi\)
0.517003 0.855984i \(-0.327048\pi\)
\(588\) 0 0
\(589\) −1.42261 0.589265i −0.0586177 0.0242803i
\(590\) 0 0
\(591\) 7.02104i 0.288807i
\(592\) 0 0
\(593\) 13.4778i 0.553469i −0.960946 0.276734i \(-0.910748\pi\)
0.960946 0.276734i \(-0.0892522\pi\)
\(594\) 0 0
\(595\) 42.3490 + 17.5415i 1.73614 + 0.719133i
\(596\) 0 0
\(597\) 7.92985 + 19.1444i 0.324547 + 0.783526i
\(598\) 0 0
\(599\) 11.7247 + 11.7247i 0.479059 + 0.479059i 0.904831 0.425771i \(-0.139997\pi\)
−0.425771 + 0.904831i \(0.639997\pi\)
\(600\) 0 0
\(601\) −14.2752 + 14.2752i −0.582299 + 0.582299i −0.935535 0.353235i \(-0.885082\pi\)
0.353235 + 0.935535i \(0.385082\pi\)
\(602\) 0 0
\(603\) −4.97085 + 2.05899i −0.202429 + 0.0838487i
\(604\) 0 0
\(605\) 36.2673 87.5570i 1.47447 3.55970i
\(606\) 0 0
\(607\) 30.9234 1.25514 0.627571 0.778559i \(-0.284049\pi\)
0.627571 + 0.778559i \(0.284049\pi\)
\(608\) 0 0
\(609\) 4.52725 0.183453
\(610\) 0 0
\(611\) 0.00832655 0.0201021i 0.000336856 0.000813243i
\(612\) 0 0
\(613\) 34.3535 14.2297i 1.38753 0.574732i 0.441043 0.897486i \(-0.354609\pi\)
0.946483 + 0.322754i \(0.104609\pi\)
\(614\) 0 0
\(615\) −23.3659 + 23.3659i −0.942202 + 0.942202i
\(616\) 0 0
\(617\) −10.2583 10.2583i −0.412985 0.412985i 0.469792 0.882777i \(-0.344329\pi\)
−0.882777 + 0.469792i \(0.844329\pi\)
\(618\) 0 0
\(619\) 8.23548 + 19.8822i 0.331012 + 0.799133i 0.998512 + 0.0545238i \(0.0173641\pi\)
−0.667501 + 0.744609i \(0.732636\pi\)
\(620\) 0 0
\(621\) 2.63753 + 1.09250i 0.105840 + 0.0438405i
\(622\) 0 0
\(623\) 23.3836i 0.936844i
\(624\) 0 0
\(625\) 17.4906i 0.699626i
\(626\) 0 0
\(627\) −6.46083 2.67617i −0.258021 0.106876i
\(628\) 0 0
\(629\) 6.64047 + 16.0315i 0.264773 + 0.639219i
\(630\) 0 0
\(631\) −10.2772 10.2772i −0.409128 0.409128i 0.472307 0.881434i \(-0.343421\pi\)
−0.881434 + 0.472307i \(0.843421\pi\)
\(632\) 0 0
\(633\) 2.14593 2.14593i 0.0852930 0.0852930i
\(634\) 0 0
\(635\) 47.4297 19.6460i 1.88219 0.779629i
\(636\) 0 0
\(637\) −0.00703045 + 0.0169730i −0.000278556 + 0.000672495i
\(638\) 0 0
\(639\) −2.52151 −0.0997494
\(640\) 0 0
\(641\) −14.5702 −0.575489 −0.287745 0.957707i \(-0.592905\pi\)
−0.287745 + 0.957707i \(0.592905\pi\)
\(642\) 0 0
\(643\) −7.72635 + 18.6531i −0.304698 + 0.735605i 0.695162 + 0.718853i \(0.255333\pi\)
−0.999860 + 0.0167519i \(0.994667\pi\)
\(644\) 0 0
\(645\) 13.4992 5.59154i 0.531530 0.220167i
\(646\) 0 0
\(647\) −5.45944 + 5.45944i −0.214633 + 0.214633i −0.806232 0.591599i \(-0.798497\pi\)
0.591599 + 0.806232i \(0.298497\pi\)
\(648\) 0 0
\(649\) −3.53135 3.53135i −0.138618 0.138618i
\(650\) 0 0
\(651\) 1.29625 + 3.12943i 0.0508042 + 0.122652i
\(652\) 0 0
\(653\) −8.05307 3.33569i −0.315141 0.130536i 0.219506 0.975611i \(-0.429555\pi\)
−0.534647 + 0.845075i \(0.679555\pi\)
\(654\) 0 0
\(655\) 49.9204i 1.95055i
\(656\) 0 0
\(657\) 2.36881i 0.0924161i
\(658\) 0 0
\(659\) −11.5755 4.79474i −0.450919 0.186777i 0.145654 0.989336i \(-0.453471\pi\)
−0.596573 + 0.802559i \(0.703471\pi\)
\(660\) 0 0
\(661\) −4.73190 11.4238i −0.184049 0.444335i 0.804745 0.593621i \(-0.202302\pi\)
−0.988794 + 0.149287i \(0.952302\pi\)
\(662\) 0 0
\(663\) −0.0740109 0.0740109i −0.00287435 0.00287435i
\(664\) 0 0
\(665\) −6.47944 + 6.47944i −0.251262 + 0.251262i
\(666\) 0 0
\(667\) 4.86643 2.01574i 0.188429 0.0780499i
\(668\) 0 0
\(669\) 2.34242 5.65509i 0.0905631 0.218639i
\(670\) 0 0
\(671\) −79.0087 −3.05010
\(672\) 0 0
\(673\) 11.7838 0.454233 0.227117 0.973868i \(-0.427070\pi\)
0.227117 + 0.973868i \(0.427070\pi\)
\(674\) 0 0
\(675\) −2.37622 + 5.73670i −0.0914607 + 0.220806i
\(676\) 0 0
\(677\) −31.1449 + 12.9006i −1.19700 + 0.495812i −0.890027 0.455907i \(-0.849315\pi\)
−0.306969 + 0.951719i \(0.599315\pi\)
\(678\) 0 0
\(679\) −3.03630 + 3.03630i −0.116523 + 0.116523i
\(680\) 0 0
\(681\) −12.0560 12.0560i −0.461989 0.461989i
\(682\) 0 0
\(683\) 2.44866 + 5.91159i 0.0936954 + 0.226201i 0.963778 0.266705i \(-0.0859349\pi\)
−0.870083 + 0.492905i \(0.835935\pi\)
\(684\) 0 0
\(685\) 13.3925 + 5.54737i 0.511702 + 0.211954i
\(686\) 0 0
\(687\) 9.31826i 0.355514i
\(688\) 0 0
\(689\) 0.125819i 0.00479333i
\(690\) 0 0
\(691\) −6.81893 2.82449i −0.259404 0.107449i 0.249191 0.968454i \(-0.419835\pi\)
−0.508596 + 0.861005i \(0.669835\pi\)
\(692\) 0 0
\(693\) 5.88697 + 14.2124i 0.223628 + 0.539885i
\(694\) 0 0
\(695\) 3.84422 + 3.84422i 0.145819 + 0.145819i
\(696\) 0 0
\(697\) 38.9411 38.9411i 1.47500 1.47500i
\(698\) 0 0
\(699\) 10.4488 4.32805i 0.395212 0.163702i
\(700\) 0 0
\(701\) 2.75369 6.64799i 0.104005 0.251091i −0.863307 0.504679i \(-0.831611\pi\)
0.967312 + 0.253588i \(0.0816108\pi\)
\(702\) 0 0
\(703\) −3.46884 −0.130830
\(704\) 0 0
\(705\) 3.88349 0.146261
\(706\) 0 0
\(707\) −7.83813 + 18.9229i −0.294783 + 0.711669i
\(708\) 0 0
\(709\) −46.0951 + 19.0932i −1.73114 + 0.717061i −0.731770 + 0.681552i \(0.761305\pi\)
−0.999369 + 0.0355098i \(0.988695\pi\)
\(710\) 0 0
\(711\) 1.88965 1.88965i 0.0708673 0.0708673i
\(712\) 0 0
\(713\) 2.78674 + 2.78674i 0.104364 + 0.104364i
\(714\) 0 0
\(715\) 0.150680 + 0.363774i 0.00563512 + 0.0136044i
\(716\) 0 0
\(717\) −5.79002 2.39830i −0.216232 0.0895663i
\(718\) 0 0
\(719\) 22.0801i 0.823447i −0.911309 0.411724i \(-0.864927\pi\)
0.911309 0.411724i \(-0.135073\pi\)
\(720\) 0 0
\(721\) 13.5434i 0.504381i
\(722\) 0 0
\(723\) 14.5605 + 6.03116i 0.541511 + 0.224301i
\(724\) 0 0
\(725\) 4.38430 + 10.5846i 0.162829 + 0.393104i
\(726\) 0 0
\(727\) −12.2216 12.2216i −0.453274 0.453274i 0.443166 0.896440i \(-0.353855\pi\)
−0.896440 + 0.443166i \(0.853855\pi\)
\(728\) 0 0
\(729\) 0.707107 0.707107i 0.0261891 0.0261891i
\(730\) 0 0
\(731\) −22.4975 + 9.31876i −0.832100 + 0.344667i
\(732\) 0 0
\(733\) 10.2112 24.6520i 0.377159 0.910541i −0.615337 0.788264i \(-0.710980\pi\)
0.992496 0.122278i \(-0.0390198\pi\)
\(734\) 0 0
\(735\) −3.27899 −0.120947
\(736\) 0 0
\(737\) −33.7324 −1.24255
\(738\) 0 0
\(739\) −12.9929 + 31.3677i −0.477953 + 1.15388i 0.482614 + 0.875833i \(0.339687\pi\)
−0.960567 + 0.278048i \(0.910313\pi\)
\(740\) 0 0
\(741\) 0.0193308 0.00800710i 0.000710136 0.000294148i
\(742\) 0 0
\(743\) 14.2568 14.2568i 0.523030 0.523030i −0.395455 0.918485i \(-0.629413\pi\)
0.918485 + 0.395455i \(0.129413\pi\)
\(744\) 0 0
\(745\) 52.8291 + 52.8291i 1.93551 + 1.93551i
\(746\) 0 0
\(747\) −2.86585 6.91877i −0.104856 0.253144i
\(748\) 0 0
\(749\) 32.9211 + 13.6364i 1.20291 + 0.498262i
\(750\) 0 0
\(751\) 37.4275i 1.36575i 0.730536 + 0.682874i \(0.239270\pi\)
−0.730536 + 0.682874i \(0.760730\pi\)
\(752\) 0 0
\(753\) 20.5866i 0.750218i
\(754\) 0 0
\(755\) 41.2223 + 17.0748i 1.50023 + 0.621417i
\(756\) 0 0
\(757\) 14.2534 + 34.4107i 0.518048 + 1.25068i 0.939100 + 0.343643i \(0.111661\pi\)
−0.421052 + 0.907036i \(0.638339\pi\)
\(758\) 0 0
\(759\) 12.6561 + 12.6561i 0.459386 + 0.459386i
\(760\) 0 0
\(761\) 4.71958 4.71958i 0.171085 0.171085i −0.616371 0.787456i \(-0.711398\pi\)
0.787456 + 0.616371i \(0.211398\pi\)
\(762\) 0 0
\(763\) 36.4344 15.0916i 1.31901 0.546353i
\(764\) 0 0
\(765\) 7.14903 17.2593i 0.258474 0.624011i
\(766\) 0 0
\(767\) 0.0149423 0.000539536
\(768\) 0 0
\(769\) −0.848264 −0.0305892 −0.0152946 0.999883i \(-0.504869\pi\)
−0.0152946 + 0.999883i \(0.504869\pi\)
\(770\) 0 0
\(771\) −2.00056 + 4.82977i −0.0720483 + 0.173940i
\(772\) 0 0
\(773\) −7.34212 + 3.04121i −0.264078 + 0.109385i −0.510794 0.859703i \(-0.670648\pi\)
0.246716 + 0.969088i \(0.420648\pi\)
\(774\) 0 0
\(775\) −6.06124 + 6.06124i −0.217726 + 0.217726i
\(776\) 0 0
\(777\) 5.39571 + 5.39571i 0.193570 + 0.193570i
\(778\) 0 0
\(779\) 4.21296 + 10.1710i 0.150945 + 0.364413i
\(780\) 0 0
\(781\) −14.6052 6.04967i −0.522615 0.216474i
\(782\) 0 0
\(783\) 1.84507i 0.0659376i
\(784\) 0 0
\(785\) 65.9632i 2.35433i
\(786\) 0 0
\(787\) 19.1514 + 7.93278i 0.682674 + 0.282773i 0.696944 0.717125i \(-0.254542\pi\)
−0.0142701 + 0.999898i \(0.504542\pi\)
\(788\) 0 0
\(789\) 3.02564 + 7.30453i 0.107716 + 0.260048i
\(790\) 0 0
\(791\) 4.73530 + 4.73530i 0.168368 + 0.168368i
\(792\) 0 0
\(793\) 0.167156 0.167156i 0.00593589 0.00593589i
\(794\) 0 0
\(795\) −20.7471 + 8.59375i −0.735825 + 0.304789i
\(796\) 0 0
\(797\) −8.34929 + 20.1570i −0.295747 + 0.713997i 0.704245 + 0.709957i \(0.251286\pi\)
−0.999992 + 0.00403944i \(0.998714\pi\)
\(798\)