Properties

Label 288.2.w.a.179.3
Level $288$
Weight $2$
Character 288.179
Analytic conductor $2.300$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.29969157821\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 179.3
Character \(\chi\) \(=\) 288.179
Dual form 288.2.w.a.251.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.850468 + 1.12991i) q^{2} +(-0.553410 - 1.92191i) q^{4} +(0.352978 + 0.852163i) q^{5} +(-3.43393 - 3.43393i) q^{7} +(2.64225 + 1.00922i) q^{8} +O(q^{10})\) \(q+(-0.850468 + 1.12991i) q^{2} +(-0.553410 - 1.92191i) q^{4} +(0.352978 + 0.852163i) q^{5} +(-3.43393 - 3.43393i) q^{7} +(2.64225 + 1.00922i) q^{8} +(-1.26307 - 0.325903i) q^{10} +(-1.44650 - 3.49216i) q^{11} +(-0.258636 - 0.107131i) q^{13} +(6.80049 - 0.959599i) q^{14} +(-3.38747 + 2.12721i) q^{16} -5.30575 q^{17} +(2.72546 - 6.57983i) q^{19} +(1.44244 - 1.14999i) q^{20} +(5.17604 + 1.33555i) q^{22} +(2.23882 + 2.23882i) q^{23} +(2.93394 - 2.93394i) q^{25} +(0.341010 - 0.201126i) q^{26} +(-4.69934 + 8.50008i) q^{28} +(-3.16953 - 1.31286i) q^{29} +3.46749i q^{31} +(0.477376 - 5.63668i) q^{32} +(4.51237 - 5.99504i) q^{34} +(1.71417 - 4.13837i) q^{35} +(1.27512 - 0.528171i) q^{37} +(5.11673 + 8.67547i) q^{38} +(0.0726377 + 2.60786i) q^{40} +(5.28251 - 5.28251i) q^{41} +(2.46955 - 1.02292i) q^{43} +(-5.91111 + 4.71264i) q^{44} +(-4.43371 + 0.625628i) q^{46} +0.423698i q^{47} +16.5838i q^{49} +(0.819880 + 5.81033i) q^{50} +(-0.0627636 + 0.556363i) q^{52} +(-12.5563 + 5.20097i) q^{53} +(2.46531 - 2.46531i) q^{55} +(-5.60772 - 12.5389i) q^{56} +(4.17901 - 2.46475i) q^{58} +(-5.24194 + 2.17128i) q^{59} +(0.0138304 - 0.0333895i) q^{61} +(-3.91796 - 2.94899i) q^{62} +(5.96296 + 5.33320i) q^{64} -0.258215i q^{65} +(-9.82224 - 4.06850i) q^{67} +(2.93626 + 10.1972i) q^{68} +(3.21816 + 5.45642i) q^{70} +(4.64969 - 4.64969i) q^{71} +(3.96752 + 3.96752i) q^{73} +(-0.487659 + 1.88997i) q^{74} +(-14.1541 - 1.59674i) q^{76} +(-7.02466 + 16.9590i) q^{77} -12.7319 q^{79} +(-3.00843 - 2.13583i) q^{80} +(1.47618 + 10.4614i) q^{82} +(-0.867335 - 0.359262i) q^{83} +(-1.87281 - 4.52137i) q^{85} +(-0.944460 + 3.66034i) q^{86} +(-0.297669 - 10.6870i) q^{88} +(4.82033 + 4.82033i) q^{89} +(0.520260 + 1.25602i) q^{91} +(3.06382 - 5.54178i) q^{92} +(-0.478742 - 0.360341i) q^{94} +6.56912 q^{95} +8.78058 q^{97} +(-18.7382 - 14.1040i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{2} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{2} - 4 q^{8} + 8 q^{10} - 8 q^{11} + 12 q^{14} + 8 q^{16} + 32 q^{20} + 16 q^{22} - 36 q^{26} - 16 q^{29} - 24 q^{32} + 24 q^{35} + 32 q^{38} - 32 q^{40} + 8 q^{44} - 32 q^{46} + 8 q^{50} - 56 q^{52} - 16 q^{53} - 32 q^{55} + 40 q^{56} - 32 q^{58} + 32 q^{59} + 32 q^{61} - 68 q^{62} - 48 q^{64} - 16 q^{67} - 72 q^{68} - 48 q^{70} + 16 q^{71} + 60 q^{74} - 8 q^{76} - 16 q^{77} - 32 q^{79} + 96 q^{80} + 40 q^{82} - 40 q^{83} - 40 q^{86} + 40 q^{88} - 48 q^{91} - 16 q^{92} + 72 q^{94} - 80 q^{95} - 44 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.850468 + 1.12991i −0.601371 + 0.798970i
\(3\) 0 0
\(4\) −0.553410 1.92191i −0.276705 0.960955i
\(5\) 0.352978 + 0.852163i 0.157856 + 0.381099i 0.982944 0.183906i \(-0.0588742\pi\)
−0.825087 + 0.565005i \(0.808874\pi\)
\(6\) 0 0
\(7\) −3.43393 3.43393i −1.29790 1.29790i −0.929774 0.368130i \(-0.879998\pi\)
−0.368130 0.929774i \(-0.620002\pi\)
\(8\) 2.64225 + 1.00922i 0.934176 + 0.356812i
\(9\) 0 0
\(10\) −1.26307 0.325903i −0.399417 0.103060i
\(11\) −1.44650 3.49216i −0.436136 1.05293i −0.977272 0.211991i \(-0.932005\pi\)
0.541135 0.840936i \(-0.317995\pi\)
\(12\) 0 0
\(13\) −0.258636 0.107131i −0.0717328 0.0297127i 0.346529 0.938039i \(-0.387360\pi\)
−0.418261 + 0.908327i \(0.637360\pi\)
\(14\) 6.80049 0.959599i 1.81751 0.256464i
\(15\) 0 0
\(16\) −3.38747 + 2.12721i −0.846869 + 0.531802i
\(17\) −5.30575 −1.28683 −0.643417 0.765516i \(-0.722484\pi\)
−0.643417 + 0.765516i \(0.722484\pi\)
\(18\) 0 0
\(19\) 2.72546 6.57983i 0.625263 1.50952i −0.220185 0.975458i \(-0.570666\pi\)
0.845447 0.534059i \(-0.179334\pi\)
\(20\) 1.44244 1.14999i 0.322539 0.257145i
\(21\) 0 0
\(22\) 5.17604 + 1.33555i 1.10354 + 0.284740i
\(23\) 2.23882 + 2.23882i 0.466825 + 0.466825i 0.900884 0.434059i \(-0.142919\pi\)
−0.434059 + 0.900884i \(0.642919\pi\)
\(24\) 0 0
\(25\) 2.93394 2.93394i 0.586789 0.586789i
\(26\) 0.341010 0.201126i 0.0668776 0.0394440i
\(27\) 0 0
\(28\) −4.69934 + 8.50008i −0.888091 + 1.60636i
\(29\) −3.16953 1.31286i −0.588568 0.243793i 0.0684666 0.997653i \(-0.478189\pi\)
−0.657034 + 0.753861i \(0.728189\pi\)
\(30\) 0 0
\(31\) 3.46749i 0.622779i 0.950282 + 0.311390i \(0.100794\pi\)
−0.950282 + 0.311390i \(0.899206\pi\)
\(32\) 0.477376 5.63668i 0.0843889 0.996433i
\(33\) 0 0
\(34\) 4.51237 5.99504i 0.773865 1.02814i
\(35\) 1.71417 4.13837i 0.289748 0.699513i
\(36\) 0 0
\(37\) 1.27512 0.528171i 0.209628 0.0868308i −0.275399 0.961330i \(-0.588810\pi\)
0.485027 + 0.874499i \(0.338810\pi\)
\(38\) 5.11673 + 8.67547i 0.830044 + 1.40735i
\(39\) 0 0
\(40\) 0.0726377 + 2.60786i 0.0114850 + 0.412339i
\(41\) 5.28251 5.28251i 0.824989 0.824989i −0.161830 0.986819i \(-0.551740\pi\)
0.986819 + 0.161830i \(0.0517396\pi\)
\(42\) 0 0
\(43\) 2.46955 1.02292i 0.376603 0.155994i −0.186349 0.982484i \(-0.559666\pi\)
0.562952 + 0.826489i \(0.309666\pi\)
\(44\) −5.91111 + 4.71264i −0.891134 + 0.710457i
\(45\) 0 0
\(46\) −4.43371 + 0.625628i −0.653715 + 0.0922439i
\(47\) 0.423698i 0.0618027i 0.999522 + 0.0309013i \(0.00983776\pi\)
−0.999522 + 0.0309013i \(0.990162\pi\)
\(48\) 0 0
\(49\) 16.5838i 2.36911i
\(50\) 0.819880 + 5.81033i 0.115948 + 0.821705i
\(51\) 0 0
\(52\) −0.0627636 + 0.556363i −0.00870374 + 0.0771536i
\(53\) −12.5563 + 5.20097i −1.72474 + 0.714409i −0.725066 + 0.688679i \(0.758191\pi\)
−0.999669 + 0.0257295i \(0.991809\pi\)
\(54\) 0 0
\(55\) 2.46531 2.46531i 0.332422 0.332422i
\(56\) −5.60772 12.5389i −0.749364 1.67558i
\(57\) 0 0
\(58\) 4.17901 2.46475i 0.548731 0.323638i
\(59\) −5.24194 + 2.17128i −0.682442 + 0.282677i −0.696847 0.717220i \(-0.745414\pi\)
0.0144054 + 0.999896i \(0.495414\pi\)
\(60\) 0 0
\(61\) 0.0138304 0.0333895i 0.00177080 0.00427509i −0.922992 0.384820i \(-0.874264\pi\)
0.924762 + 0.380545i \(0.124264\pi\)
\(62\) −3.91796 2.94899i −0.497582 0.374522i
\(63\) 0 0
\(64\) 5.96296 + 5.33320i 0.745371 + 0.666650i
\(65\) 0.258215i 0.0320276i
\(66\) 0 0
\(67\) −9.82224 4.06850i −1.19998 0.497047i −0.308986 0.951067i \(-0.599990\pi\)
−0.890992 + 0.454020i \(0.849990\pi\)
\(68\) 2.93626 + 10.1972i 0.356073 + 1.23659i
\(69\) 0 0
\(70\) 3.21816 + 5.45642i 0.384643 + 0.652166i
\(71\) 4.64969 4.64969i 0.551817 0.551817i −0.375148 0.926965i \(-0.622408\pi\)
0.926965 + 0.375148i \(0.122408\pi\)
\(72\) 0 0
\(73\) 3.96752 + 3.96752i 0.464363 + 0.464363i 0.900082 0.435720i \(-0.143506\pi\)
−0.435720 + 0.900082i \(0.643506\pi\)
\(74\) −0.487659 + 1.88997i −0.0566892 + 0.219704i
\(75\) 0 0
\(76\) −14.1541 1.59674i −1.62359 0.183158i
\(77\) −7.02466 + 16.9590i −0.800534 + 1.93266i
\(78\) 0 0
\(79\) −12.7319 −1.43245 −0.716224 0.697870i \(-0.754131\pi\)
−0.716224 + 0.697870i \(0.754131\pi\)
\(80\) −3.00843 2.13583i −0.336353 0.238793i
\(81\) 0 0
\(82\) 1.47618 + 10.4614i 0.163016 + 1.15527i
\(83\) −0.867335 0.359262i −0.0952024 0.0394341i 0.334574 0.942369i \(-0.391408\pi\)
−0.429776 + 0.902935i \(0.641408\pi\)
\(84\) 0 0
\(85\) −1.87281 4.52137i −0.203135 0.490411i
\(86\) −0.944460 + 3.66034i −0.101844 + 0.394705i
\(87\) 0 0
\(88\) −0.297669 10.6870i −0.0317316 1.13924i
\(89\) 4.82033 + 4.82033i 0.510954 + 0.510954i 0.914819 0.403865i \(-0.132333\pi\)
−0.403865 + 0.914819i \(0.632333\pi\)
\(90\) 0 0
\(91\) 0.520260 + 1.25602i 0.0545381 + 0.131667i
\(92\) 3.06382 5.54178i 0.319425 0.577771i
\(93\) 0 0
\(94\) −0.478742 0.360341i −0.0493784 0.0371663i
\(95\) 6.56912 0.673977
\(96\) 0 0
\(97\) 8.78058 0.891532 0.445766 0.895149i \(-0.352931\pi\)
0.445766 + 0.895149i \(0.352931\pi\)
\(98\) −18.7382 14.1040i −1.89285 1.42472i
\(99\) 0 0
\(100\) −7.26245 4.01510i −0.726245 0.401510i
\(101\) −4.37141 10.5535i −0.434972 1.05011i −0.977662 0.210182i \(-0.932594\pi\)
0.542691 0.839933i \(-0.317406\pi\)
\(102\) 0 0
\(103\) 2.54327 + 2.54327i 0.250596 + 0.250596i 0.821215 0.570619i \(-0.193297\pi\)
−0.570619 + 0.821215i \(0.693297\pi\)
\(104\) −0.575264 0.544086i −0.0564092 0.0533520i
\(105\) 0 0
\(106\) 4.80204 18.6108i 0.466415 1.80764i
\(107\) −1.34953 3.25806i −0.130464 0.314968i 0.845126 0.534567i \(-0.179525\pi\)
−0.975590 + 0.219599i \(0.929525\pi\)
\(108\) 0 0
\(109\) 11.5904 + 4.80089i 1.11016 + 0.459842i 0.860992 0.508619i \(-0.169844\pi\)
0.249165 + 0.968461i \(0.419844\pi\)
\(110\) 0.688921 + 4.88225i 0.0656861 + 0.465505i
\(111\) 0 0
\(112\) 18.9370 + 4.32767i 1.78938 + 0.408926i
\(113\) 16.5004 1.55223 0.776115 0.630591i \(-0.217188\pi\)
0.776115 + 0.630591i \(0.217188\pi\)
\(114\) 0 0
\(115\) −1.11758 + 2.69809i −0.104215 + 0.251598i
\(116\) −0.769155 + 6.81811i −0.0714142 + 0.633046i
\(117\) 0 0
\(118\) 2.00474 7.76954i 0.184551 0.715244i
\(119\) 18.2196 + 18.2196i 1.67019 + 1.67019i
\(120\) 0 0
\(121\) −2.32465 + 2.32465i −0.211332 + 0.211332i
\(122\) 0.0259650 + 0.0440238i 0.00235076 + 0.00398573i
\(123\) 0 0
\(124\) 6.66420 1.91894i 0.598463 0.172326i
\(125\) 7.79663 + 3.22947i 0.697352 + 0.288853i
\(126\) 0 0
\(127\) 9.43014i 0.836790i 0.908265 + 0.418395i \(0.137407\pi\)
−0.908265 + 0.418395i \(0.862593\pi\)
\(128\) −11.0974 + 2.20192i −0.980878 + 0.194624i
\(129\) 0 0
\(130\) 0.291761 + 0.219604i 0.0255891 + 0.0192605i
\(131\) 6.19791 14.9631i 0.541514 1.30733i −0.382140 0.924104i \(-0.624813\pi\)
0.923654 0.383227i \(-0.125187\pi\)
\(132\) 0 0
\(133\) −31.9537 + 13.2357i −2.77074 + 1.14768i
\(134\) 12.9506 7.63815i 1.11876 0.659836i
\(135\) 0 0
\(136\) −14.0191 5.35465i −1.20213 0.459158i
\(137\) 5.01737 5.01737i 0.428663 0.428663i −0.459510 0.888173i \(-0.651975\pi\)
0.888173 + 0.459510i \(0.151975\pi\)
\(138\) 0 0
\(139\) 19.0610 7.89534i 1.61674 0.669674i 0.623083 0.782156i \(-0.285880\pi\)
0.993654 + 0.112482i \(0.0358800\pi\)
\(140\) −8.90222 1.00426i −0.752375 0.0848758i
\(141\) 0 0
\(142\) 1.29934 + 9.20816i 0.109038 + 0.772731i
\(143\) 1.05816i 0.0884881i
\(144\) 0 0
\(145\) 3.16437i 0.262787i
\(146\) −7.85720 + 1.10871i −0.650266 + 0.0917573i
\(147\) 0 0
\(148\) −1.72076 2.15837i −0.141446 0.177417i
\(149\) 20.8124 8.62076i 1.70502 0.706240i 0.705019 0.709188i \(-0.250938\pi\)
0.999996 + 0.00294754i \(0.000938232\pi\)
\(150\) 0 0
\(151\) 4.68070 4.68070i 0.380910 0.380910i −0.490520 0.871430i \(-0.663193\pi\)
0.871430 + 0.490520i \(0.163193\pi\)
\(152\) 13.8418 14.6350i 1.12272 1.18705i
\(153\) 0 0
\(154\) −13.1880 22.3604i −1.06272 1.80185i
\(155\) −2.95487 + 1.22395i −0.237341 + 0.0983097i
\(156\) 0 0
\(157\) 6.17384 14.9050i 0.492726 1.18955i −0.460601 0.887607i \(-0.652366\pi\)
0.953327 0.301939i \(-0.0976340\pi\)
\(158\) 10.8280 14.3859i 0.861433 1.14448i
\(159\) 0 0
\(160\) 4.97187 1.58282i 0.393061 0.125133i
\(161\) 15.3759i 1.21179i
\(162\) 0 0
\(163\) −2.13457 0.884169i −0.167193 0.0692534i 0.297517 0.954716i \(-0.403841\pi\)
−0.464710 + 0.885463i \(0.653841\pi\)
\(164\) −13.0759 7.22911i −1.02106 0.564498i
\(165\) 0 0
\(166\) 1.14358 0.674473i 0.0887587 0.0523493i
\(167\) −14.2052 + 14.2052i −1.09923 + 1.09923i −0.104733 + 0.994500i \(0.533399\pi\)
−0.994500 + 0.104733i \(0.966601\pi\)
\(168\) 0 0
\(169\) −9.13697 9.13697i −0.702844 0.702844i
\(170\) 6.70152 + 1.72916i 0.513983 + 0.132621i
\(171\) 0 0
\(172\) −3.33264 4.18016i −0.254111 0.318734i
\(173\) −4.53353 + 10.9449i −0.344678 + 0.832127i 0.652552 + 0.757744i \(0.273699\pi\)
−0.997230 + 0.0743825i \(0.976301\pi\)
\(174\) 0 0
\(175\) −20.1499 −1.52319
\(176\) 12.3285 + 8.75260i 0.929299 + 0.659752i
\(177\) 0 0
\(178\) −9.54609 + 1.34702i −0.715510 + 0.100964i
\(179\) −9.00945 3.73184i −0.673398 0.278931i 0.0196661 0.999807i \(-0.493740\pi\)
−0.693064 + 0.720876i \(0.743740\pi\)
\(180\) 0 0
\(181\) −5.75935 13.9043i −0.428089 1.03350i −0.979893 0.199524i \(-0.936060\pi\)
0.551804 0.833974i \(-0.313940\pi\)
\(182\) −1.86166 0.480354i −0.137995 0.0356062i
\(183\) 0 0
\(184\) 3.65606 + 8.17496i 0.269528 + 0.602666i
\(185\) 0.900176 + 0.900176i 0.0661823 + 0.0661823i
\(186\) 0 0
\(187\) 7.67477 + 18.5285i 0.561235 + 1.35494i
\(188\) 0.814309 0.234478i 0.0593896 0.0171011i
\(189\) 0 0
\(190\) −5.58682 + 7.42254i −0.405311 + 0.538487i
\(191\) −6.18207 −0.447319 −0.223660 0.974667i \(-0.571800\pi\)
−0.223660 + 0.974667i \(0.571800\pi\)
\(192\) 0 0
\(193\) −11.2515 −0.809899 −0.404949 0.914339i \(-0.632711\pi\)
−0.404949 + 0.914339i \(0.632711\pi\)
\(194\) −7.46759 + 9.92129i −0.536142 + 0.712307i
\(195\) 0 0
\(196\) 31.8725 9.17763i 2.27661 0.655545i
\(197\) 2.59303 + 6.26014i 0.184746 + 0.446016i 0.988934 0.148359i \(-0.0473992\pi\)
−0.804187 + 0.594376i \(0.797399\pi\)
\(198\) 0 0
\(199\) 8.67622 + 8.67622i 0.615041 + 0.615041i 0.944255 0.329214i \(-0.106784\pi\)
−0.329214 + 0.944255i \(0.606784\pi\)
\(200\) 10.7132 4.79123i 0.757538 0.338791i
\(201\) 0 0
\(202\) 15.6423 + 4.03611i 1.10059 + 0.283980i
\(203\) 6.37568 + 15.3922i 0.447485 + 1.08032i
\(204\) 0 0
\(205\) 6.36616 + 2.63695i 0.444632 + 0.184173i
\(206\) −5.03665 + 0.710708i −0.350920 + 0.0495174i
\(207\) 0 0
\(208\) 1.10401 0.187271i 0.0765495 0.0129849i
\(209\) −26.9202 −1.86211
\(210\) 0 0
\(211\) 3.18497 7.68919i 0.219262 0.529345i −0.775525 0.631317i \(-0.782515\pi\)
0.994787 + 0.101971i \(0.0325149\pi\)
\(212\) 16.9446 + 21.2537i 1.16376 + 1.45971i
\(213\) 0 0
\(214\) 4.82906 + 1.24602i 0.330108 + 0.0851760i
\(215\) 1.74339 + 1.74339i 0.118898 + 0.118898i
\(216\) 0 0
\(217\) 11.9071 11.9071i 0.808308 0.808308i
\(218\) −15.2818 + 9.01313i −1.03502 + 0.610446i
\(219\) 0 0
\(220\) −6.10243 3.37378i −0.411426 0.227460i
\(221\) 1.37226 + 0.568409i 0.0923082 + 0.0382353i
\(222\) 0 0
\(223\) 12.9728i 0.868722i 0.900739 + 0.434361i \(0.143026\pi\)
−0.900739 + 0.434361i \(0.856974\pi\)
\(224\) −20.9952 + 17.7167i −1.40280 + 1.18375i
\(225\) 0 0
\(226\) −14.0331 + 18.6441i −0.933467 + 1.24018i
\(227\) 3.79613 9.16468i 0.251958 0.608281i −0.746404 0.665493i \(-0.768221\pi\)
0.998362 + 0.0572122i \(0.0182212\pi\)
\(228\) 0 0
\(229\) 4.91823 2.03720i 0.325006 0.134622i −0.214214 0.976787i \(-0.568719\pi\)
0.539220 + 0.842165i \(0.318719\pi\)
\(230\) −2.09814 3.55741i −0.138347 0.234569i
\(231\) 0 0
\(232\) −7.04974 6.66766i −0.462838 0.437753i
\(233\) 10.8493 10.8493i 0.710759 0.710759i −0.255935 0.966694i \(-0.582383\pi\)
0.966694 + 0.255935i \(0.0823834\pi\)
\(234\) 0 0
\(235\) −0.361060 + 0.149556i −0.0235529 + 0.00975594i
\(236\) 7.07394 + 8.87292i 0.460475 + 0.577578i
\(237\) 0 0
\(238\) −36.0817 + 5.09140i −2.33883 + 0.330026i
\(239\) 7.69444i 0.497712i −0.968540 0.248856i \(-0.919945\pi\)
0.968540 0.248856i \(-0.0800546\pi\)
\(240\) 0 0
\(241\) 14.5669i 0.938338i 0.883108 + 0.469169i \(0.155447\pi\)
−0.883108 + 0.469169i \(0.844553\pi\)
\(242\) −0.649615 4.60370i −0.0417588 0.295937i
\(243\) 0 0
\(244\) −0.0718255 0.00810267i −0.00459815 0.000518720i
\(245\) −14.1321 + 5.85370i −0.902866 + 0.373979i
\(246\) 0 0
\(247\) −1.40980 + 1.40980i −0.0897037 + 0.0897037i
\(248\) −3.49945 + 9.16197i −0.222215 + 0.581786i
\(249\) 0 0
\(250\) −10.2798 + 6.06296i −0.650152 + 0.383455i
\(251\) −14.1528 + 5.86227i −0.893315 + 0.370023i −0.781646 0.623722i \(-0.785620\pi\)
−0.111669 + 0.993745i \(0.535620\pi\)
\(252\) 0 0
\(253\) 4.57986 11.0568i 0.287933 0.695132i
\(254\) −10.6552 8.02003i −0.668570 0.503221i
\(255\) 0 0
\(256\) 6.94997 14.4117i 0.434373 0.900733i
\(257\) 19.4990i 1.21632i 0.793816 + 0.608159i \(0.208092\pi\)
−0.793816 + 0.608159i \(0.791908\pi\)
\(258\) 0 0
\(259\) −6.19237 2.56496i −0.384775 0.159379i
\(260\) −0.496266 + 0.142899i −0.0307771 + 0.00886221i
\(261\) 0 0
\(262\) 11.6359 + 19.7287i 0.718867 + 1.21884i
\(263\) 9.65433 9.65433i 0.595312 0.595312i −0.343750 0.939061i \(-0.611697\pi\)
0.939061 + 0.343750i \(0.111697\pi\)
\(264\) 0 0
\(265\) −8.86416 8.86416i −0.544521 0.544521i
\(266\) 12.2204 47.3615i 0.749284 2.90392i
\(267\) 0 0
\(268\) −2.38357 + 21.1290i −0.145600 + 1.29066i
\(269\) 7.95451 19.2039i 0.484995 1.17088i −0.472214 0.881484i \(-0.656545\pi\)
0.957209 0.289397i \(-0.0934549\pi\)
\(270\) 0 0
\(271\) 19.1213 1.16154 0.580770 0.814068i \(-0.302752\pi\)
0.580770 + 0.814068i \(0.302752\pi\)
\(272\) 17.9731 11.2864i 1.08978 0.684341i
\(273\) 0 0
\(274\) 1.40208 + 9.93630i 0.0847030 + 0.600274i
\(275\) −14.4898 6.00186i −0.873765 0.361926i
\(276\) 0 0
\(277\) −0.609964 1.47258i −0.0366492 0.0884789i 0.904495 0.426484i \(-0.140248\pi\)
−0.941144 + 0.338005i \(0.890248\pi\)
\(278\) −7.28974 + 28.2521i −0.437210 + 1.69445i
\(279\) 0 0
\(280\) 8.70578 9.20464i 0.520270 0.550083i
\(281\) 8.76628 + 8.76628i 0.522953 + 0.522953i 0.918462 0.395509i \(-0.129432\pi\)
−0.395509 + 0.918462i \(0.629432\pi\)
\(282\) 0 0
\(283\) 7.64026 + 18.4452i 0.454166 + 1.09645i 0.970723 + 0.240201i \(0.0772134\pi\)
−0.516557 + 0.856253i \(0.672787\pi\)
\(284\) −11.5095 6.36310i −0.682961 0.377580i
\(285\) 0 0
\(286\) −1.19563 0.899934i −0.0706993 0.0532142i
\(287\) −36.2795 −2.14151
\(288\) 0 0
\(289\) 11.1510 0.655942
\(290\) 3.57547 + 2.69120i 0.209959 + 0.158032i
\(291\) 0 0
\(292\) 5.42955 9.82087i 0.317740 0.574723i
\(293\) −8.73727 21.0936i −0.510437 1.23230i −0.943630 0.331002i \(-0.892613\pi\)
0.433194 0.901301i \(-0.357387\pi\)
\(294\) 0 0
\(295\) −3.70057 3.70057i −0.215456 0.215456i
\(296\) 3.90222 0.108690i 0.226812 0.00631748i
\(297\) 0 0
\(298\) −7.95952 + 30.8479i −0.461083 + 1.78697i
\(299\) −0.339193 0.818885i −0.0196160 0.0473573i
\(300\) 0 0
\(301\) −11.9929 4.96763i −0.691260 0.286329i
\(302\) 1.30800 + 9.26957i 0.0752671 + 0.533404i
\(303\) 0 0
\(304\) 4.76426 + 28.0866i 0.273249 + 1.61088i
\(305\) 0.0333351 0.00190876
\(306\) 0 0
\(307\) 2.29860 5.54931i 0.131188 0.316716i −0.844613 0.535378i \(-0.820169\pi\)
0.975801 + 0.218662i \(0.0701693\pi\)
\(308\) 36.4812 + 4.11547i 2.07871 + 0.234501i
\(309\) 0 0
\(310\) 1.13007 4.37967i 0.0641834 0.248749i
\(311\) −12.3351 12.3351i −0.699460 0.699460i 0.264834 0.964294i \(-0.414683\pi\)
−0.964294 + 0.264834i \(0.914683\pi\)
\(312\) 0 0
\(313\) 9.07712 9.07712i 0.513069 0.513069i −0.402397 0.915465i \(-0.631823\pi\)
0.915465 + 0.402397i \(0.131823\pi\)
\(314\) 11.5907 + 19.6521i 0.654100 + 1.10903i
\(315\) 0 0
\(316\) 7.04595 + 24.4695i 0.396366 + 1.37652i
\(317\) −14.7317 6.10208i −0.827416 0.342727i −0.0715366 0.997438i \(-0.522790\pi\)
−0.755879 + 0.654711i \(0.772790\pi\)
\(318\) 0 0
\(319\) 12.9676i 0.726045i
\(320\) −2.43997 + 6.96392i −0.136398 + 0.389295i
\(321\) 0 0
\(322\) 17.3734 + 13.0767i 0.968183 + 0.728735i
\(323\) −14.4606 + 34.9110i −0.804609 + 1.94250i
\(324\) 0 0
\(325\) −1.07314 + 0.444509i −0.0595271 + 0.0246569i
\(326\) 2.81442 1.65993i 0.155876 0.0919348i
\(327\) 0 0
\(328\) 19.2889 8.62651i 1.06505 0.476319i
\(329\) 1.45495 1.45495i 0.0802139 0.0802139i
\(330\) 0 0
\(331\) −20.7207 + 8.58281i −1.13892 + 0.471754i −0.870802 0.491633i \(-0.836400\pi\)
−0.268113 + 0.963387i \(0.586400\pi\)
\(332\) −0.210477 + 1.86576i −0.0115514 + 0.102397i
\(333\) 0 0
\(334\) −3.96960 28.1318i −0.217207 1.53930i
\(335\) 9.80624i 0.535772i
\(336\) 0 0
\(337\) 12.9981i 0.708052i 0.935236 + 0.354026i \(0.115188\pi\)
−0.935236 + 0.354026i \(0.884812\pi\)
\(338\) 18.0947 2.55329i 0.984221 0.138881i
\(339\) 0 0
\(340\) −7.65323 + 6.10155i −0.415055 + 0.330903i
\(341\) 12.1090 5.01573i 0.655741 0.271617i
\(342\) 0 0
\(343\) 32.9100 32.9100i 1.77697 1.77697i
\(344\) 7.55752 0.210502i 0.407474 0.0113495i
\(345\) 0 0
\(346\) −8.51119 14.4308i −0.457564 0.775805i
\(347\) −24.4093 + 10.1107i −1.31036 + 0.542769i −0.924990 0.379992i \(-0.875927\pi\)
−0.385372 + 0.922762i \(0.625927\pi\)
\(348\) 0 0
\(349\) −3.82444 + 9.23301i −0.204717 + 0.494231i −0.992576 0.121624i \(-0.961190\pi\)
0.787859 + 0.615856i \(0.211190\pi\)
\(350\) 17.1369 22.7677i 0.916004 1.21698i
\(351\) 0 0
\(352\) −20.3747 + 6.48638i −1.08598 + 0.345725i
\(353\) 24.4035i 1.29887i −0.760418 0.649434i \(-0.775006\pi\)
0.760418 0.649434i \(-0.224994\pi\)
\(354\) 0 0
\(355\) 5.60353 + 2.32106i 0.297405 + 0.123189i
\(356\) 6.59662 11.9319i 0.349620 0.632387i
\(357\) 0 0
\(358\) 11.8789 7.00609i 0.627819 0.370284i
\(359\) 6.52733 6.52733i 0.344500 0.344500i −0.513556 0.858056i \(-0.671672\pi\)
0.858056 + 0.513556i \(0.171672\pi\)
\(360\) 0 0
\(361\) −22.4311 22.4311i −1.18058 1.18058i
\(362\) 20.6088 + 5.31758i 1.08317 + 0.279486i
\(363\) 0 0
\(364\) 2.12604 1.69499i 0.111435 0.0888414i
\(365\) −1.98053 + 4.78142i −0.103666 + 0.250271i
\(366\) 0 0
\(367\) 19.4291 1.01419 0.507096 0.861889i \(-0.330719\pi\)
0.507096 + 0.861889i \(0.330719\pi\)
\(368\) −12.3464 2.82150i −0.643598 0.147081i
\(369\) 0 0
\(370\) −1.78269 + 0.251551i −0.0926778 + 0.0130775i
\(371\) 60.9771 + 25.2576i 3.16577 + 1.31131i
\(372\) 0 0
\(373\) −4.15808 10.0385i −0.215297 0.519773i 0.778925 0.627117i \(-0.215765\pi\)
−0.994222 + 0.107344i \(0.965765\pi\)
\(374\) −27.4628 7.08609i −1.42007 0.366413i
\(375\) 0 0
\(376\) −0.427603 + 1.11951i −0.0220519 + 0.0577346i
\(377\) 0.679109 + 0.679109i 0.0349759 + 0.0349759i
\(378\) 0 0
\(379\) 1.96668 + 4.74798i 0.101021 + 0.243887i 0.966307 0.257392i \(-0.0828631\pi\)
−0.865286 + 0.501279i \(0.832863\pi\)
\(380\) −3.63542 12.6253i −0.186493 0.647662i
\(381\) 0 0
\(382\) 5.25765 6.98521i 0.269005 0.357394i
\(383\) −6.30106 −0.321969 −0.160985 0.986957i \(-0.551467\pi\)
−0.160985 + 0.986957i \(0.551467\pi\)
\(384\) 0 0
\(385\) −16.9314 −0.862905
\(386\) 9.56901 12.7132i 0.487050 0.647085i
\(387\) 0 0
\(388\) −4.85926 16.8755i −0.246691 0.856722i
\(389\) −0.331782 0.800993i −0.0168220 0.0406119i 0.915245 0.402897i \(-0.131997\pi\)
−0.932067 + 0.362285i \(0.881997\pi\)
\(390\) 0 0
\(391\) −11.8786 11.8786i −0.600727 0.600727i
\(392\) −16.7366 + 43.8185i −0.845327 + 2.21317i
\(393\) 0 0
\(394\) −9.27871 2.39414i −0.467455 0.120615i
\(395\) −4.49407 10.8496i −0.226121 0.545905i
\(396\) 0 0
\(397\) 11.2798 + 4.67225i 0.566118 + 0.234494i 0.647339 0.762202i \(-0.275882\pi\)
−0.0812209 + 0.996696i \(0.525882\pi\)
\(398\) −17.1822 + 2.42454i −0.861267 + 0.121531i
\(399\) 0 0
\(400\) −3.69755 + 16.1798i −0.184878 + 0.808989i
\(401\) −10.7890 −0.538777 −0.269388 0.963032i \(-0.586822\pi\)
−0.269388 + 0.963032i \(0.586822\pi\)
\(402\) 0 0
\(403\) 0.371474 0.896819i 0.0185045 0.0446737i
\(404\) −17.8637 + 14.2419i −0.888754 + 0.708560i
\(405\) 0 0
\(406\) −22.8142 5.88664i −1.13225 0.292149i
\(407\) −3.68892 3.68892i −0.182853 0.182853i
\(408\) 0 0
\(409\) −0.0980818 + 0.0980818i −0.00484983 + 0.00484983i −0.709528 0.704678i \(-0.751092\pi\)
0.704678 + 0.709528i \(0.251092\pi\)
\(410\) −8.39374 + 4.95057i −0.414537 + 0.244491i
\(411\) 0 0
\(412\) 3.48047 6.29541i 0.171470 0.310153i
\(413\) 25.4565 + 10.5444i 1.25263 + 0.518857i
\(414\) 0 0
\(415\) 0.865923i 0.0425065i
\(416\) −0.727328 + 1.40671i −0.0356602 + 0.0689695i
\(417\) 0 0
\(418\) 22.8948 30.4175i 1.11982 1.48777i
\(419\) 11.5665 27.9241i 0.565063 1.36418i −0.340610 0.940205i \(-0.610634\pi\)
0.905673 0.423977i \(-0.139366\pi\)
\(420\) 0 0
\(421\) 18.0670 7.48361i 0.880533 0.364729i 0.103829 0.994595i \(-0.466890\pi\)
0.776703 + 0.629867i \(0.216890\pi\)
\(422\) 5.97941 + 10.1381i 0.291073 + 0.493517i
\(423\) 0 0
\(424\) −38.4257 + 1.07028i −1.86612 + 0.0519776i
\(425\) −15.5668 + 15.5668i −0.755100 + 0.755100i
\(426\) 0 0
\(427\) −0.162150 + 0.0671647i −0.00784698 + 0.00325033i
\(428\) −5.51485 + 4.39672i −0.266570 + 0.212523i
\(429\) 0 0
\(430\) −3.45258 + 0.487185i −0.166498 + 0.0234941i
\(431\) 10.6345i 0.512245i 0.966644 + 0.256123i \(0.0824451\pi\)
−0.966644 + 0.256123i \(0.917555\pi\)
\(432\) 0 0
\(433\) 11.8688i 0.570377i −0.958471 0.285189i \(-0.907944\pi\)
0.958471 0.285189i \(-0.0920562\pi\)
\(434\) 3.32740 + 23.5806i 0.159720 + 1.13191i
\(435\) 0 0
\(436\) 2.81265 24.9325i 0.134702 1.19405i
\(437\) 20.8328 8.62924i 0.996569 0.412793i
\(438\) 0 0
\(439\) −11.2613 + 11.2613i −0.537471 + 0.537471i −0.922785 0.385314i \(-0.874093\pi\)
0.385314 + 0.922785i \(0.374093\pi\)
\(440\) 9.00199 4.02593i 0.429153 0.191929i
\(441\) 0 0
\(442\) −1.80932 + 1.06712i −0.0860604 + 0.0507578i
\(443\) 17.1370 7.09839i 0.814204 0.337255i 0.0635743 0.997977i \(-0.479750\pi\)
0.750630 + 0.660723i \(0.229750\pi\)
\(444\) 0 0
\(445\) −2.40624 + 5.80918i −0.114067 + 0.275381i
\(446\) −14.6581 11.0329i −0.694083 0.522425i
\(447\) 0 0
\(448\) −2.16256 38.7903i −0.102171 1.83267i
\(449\) 38.4537i 1.81474i 0.420331 + 0.907371i \(0.361914\pi\)
−0.420331 + 0.907371i \(0.638086\pi\)
\(450\) 0 0
\(451\) −26.0885 10.8062i −1.22846 0.508845i
\(452\) −9.13150 31.7123i −0.429510 1.49162i
\(453\) 0 0
\(454\) 7.12681 + 12.0836i 0.334478 + 0.567110i
\(455\) −0.886693 + 0.886693i −0.0415688 + 0.0415688i
\(456\) 0 0
\(457\) −11.6258 11.6258i −0.543833 0.543833i 0.380817 0.924650i \(-0.375643\pi\)
−0.924650 + 0.380817i \(0.875643\pi\)
\(458\) −1.88094 + 7.28974i −0.0878904 + 0.340627i
\(459\) 0 0
\(460\) 5.80397 + 0.654748i 0.270611 + 0.0305278i
\(461\) 1.95672 4.72395i 0.0911337 0.220016i −0.871740 0.489969i \(-0.837008\pi\)
0.962874 + 0.269953i \(0.0870081\pi\)
\(462\) 0 0
\(463\) −24.2082 −1.12505 −0.562524 0.826781i \(-0.690170\pi\)
−0.562524 + 0.826781i \(0.690170\pi\)
\(464\) 13.5295 2.29496i 0.628089 0.106541i
\(465\) 0 0
\(466\) 3.03178 + 21.4857i 0.140445 + 0.995304i
\(467\) −5.35140 2.21662i −0.247633 0.102573i 0.255415 0.966832i \(-0.417788\pi\)
−0.503048 + 0.864259i \(0.667788\pi\)
\(468\) 0 0
\(469\) 19.7579 + 47.6999i 0.912336 + 2.20257i
\(470\) 0.138084 0.535159i 0.00636936 0.0246850i
\(471\) 0 0
\(472\) −16.0418 + 0.446818i −0.738383 + 0.0205665i
\(473\) −7.14442 7.14442i −0.328501 0.328501i
\(474\) 0 0
\(475\) −11.3085 27.3012i −0.518871 1.25267i
\(476\) 24.9335 45.0993i 1.14283 2.06712i
\(477\) 0 0
\(478\) 8.69406 + 6.54388i 0.397657 + 0.299310i
\(479\) 26.4282 1.20754 0.603768 0.797160i \(-0.293665\pi\)
0.603768 + 0.797160i \(0.293665\pi\)
\(480\) 0 0
\(481\) −0.386375 −0.0176172
\(482\) −16.4594 12.3887i −0.749704 0.564290i
\(483\) 0 0
\(484\) 5.75426 + 3.18129i 0.261557 + 0.144604i
\(485\) 3.09935 + 7.48249i 0.140734 + 0.339762i
\(486\) 0 0
\(487\) −9.32733 9.32733i −0.422662 0.422662i 0.463457 0.886119i \(-0.346609\pi\)
−0.886119 + 0.463457i \(0.846609\pi\)
\(488\) 0.0702406 0.0742655i 0.00317964 0.00336184i
\(489\) 0 0
\(490\) 5.40470 20.9464i 0.244160 0.946263i
\(491\) 2.97593 + 7.18453i 0.134302 + 0.324233i 0.976696 0.214629i \(-0.0688543\pi\)
−0.842394 + 0.538862i \(0.818854\pi\)
\(492\) 0 0
\(493\) 16.8168 + 6.96573i 0.757389 + 0.313721i
\(494\) −0.393964 2.79195i −0.0177253 0.125616i
\(495\) 0 0
\(496\) −7.37607 11.7460i −0.331195 0.527412i
\(497\) −31.9334 −1.43241
\(498\) 0 0
\(499\) −10.3839 + 25.0689i −0.464846 + 1.12224i 0.501538 + 0.865136i \(0.332768\pi\)
−0.966384 + 0.257103i \(0.917232\pi\)
\(500\) 1.89202 16.7716i 0.0846136 0.750051i
\(501\) 0 0
\(502\) 5.41261 20.9771i 0.241577 0.936253i
\(503\) 3.53224 + 3.53224i 0.157495 + 0.157495i 0.781456 0.623961i \(-0.214478\pi\)
−0.623961 + 0.781456i \(0.714478\pi\)
\(504\) 0 0
\(505\) 7.45031 7.45031i 0.331535 0.331535i
\(506\) 8.59816 + 14.5783i 0.382235 + 0.648082i
\(507\) 0 0
\(508\) 18.1239 5.21873i 0.804117 0.231544i
\(509\) 19.0074 + 7.87311i 0.842487 + 0.348969i 0.761834 0.647773i \(-0.224299\pi\)
0.0806532 + 0.996742i \(0.474299\pi\)
\(510\) 0 0
\(511\) 27.2484i 1.20540i
\(512\) 10.3733 + 20.1096i 0.458439 + 0.888726i
\(513\) 0 0
\(514\) −22.0322 16.5833i −0.971800 0.731458i
\(515\) −1.26957 + 3.06500i −0.0559437 + 0.135060i
\(516\) 0 0
\(517\) 1.47962 0.612879i 0.0650736 0.0269544i
\(518\) 8.16460 4.81543i 0.358732 0.211578i
\(519\) 0 0
\(520\) 0.260595 0.682269i 0.0114278 0.0299195i
\(521\) −12.5687 + 12.5687i −0.550643 + 0.550643i −0.926626 0.375984i \(-0.877305\pi\)
0.375984 + 0.926626i \(0.377305\pi\)
\(522\) 0 0
\(523\) 9.66162 4.00197i 0.422473 0.174994i −0.161310 0.986904i \(-0.551572\pi\)
0.583783 + 0.811910i \(0.301572\pi\)
\(524\) −32.1877 3.63111i −1.40613 0.158626i
\(525\) 0 0
\(526\) 2.69787 + 19.1193i 0.117633 + 0.833639i
\(527\) 18.3976i 0.801414i
\(528\) 0 0
\(529\) 12.9754i 0.564148i
\(530\) 17.5544 2.47706i 0.762515 0.107596i
\(531\) 0 0
\(532\) 43.1213 + 54.0874i 1.86954 + 2.34499i
\(533\) −1.93217 + 0.800329i −0.0836914 + 0.0346661i
\(534\) 0 0
\(535\) 2.30004 2.30004i 0.0994395 0.0994395i
\(536\) −21.8468 20.6628i −0.943638 0.892496i
\(537\) 0 0
\(538\) 14.9337 + 25.3202i 0.643837 + 1.09163i
\(539\) 57.9132 23.9884i 2.49450 1.03326i
\(540\) 0 0
\(541\) −14.6046 + 35.2587i −0.627901 + 1.51589i 0.214324 + 0.976763i \(0.431245\pi\)
−0.842225 + 0.539125i \(0.818755\pi\)
\(542\) −16.2621 + 21.6055i −0.698516 + 0.928034i
\(543\) 0 0
\(544\) −2.53284 + 29.9068i −0.108595 + 1.28224i
\(545\) 11.5715i 0.495669i
\(546\) 0 0
\(547\) −9.22367 3.82057i −0.394376 0.163356i 0.176677 0.984269i \(-0.443465\pi\)
−0.571053 + 0.820913i \(0.693465\pi\)
\(548\) −12.4196 6.86627i −0.530538 0.293312i
\(549\) 0 0
\(550\) 19.1046 11.2678i 0.814625 0.480460i
\(551\) −17.2769 + 17.2769i −0.736019 + 0.736019i
\(552\) 0 0
\(553\) 43.7204 + 43.7204i 1.85918 + 1.85918i
\(554\) 2.18265 + 0.563178i 0.0927317 + 0.0239271i
\(555\) 0 0
\(556\) −25.7227 32.2642i −1.09089 1.36831i
\(557\) 8.65349 20.8914i 0.366660 0.885196i −0.627632 0.778510i \(-0.715976\pi\)
0.994293 0.106686i \(-0.0340241\pi\)
\(558\) 0 0
\(559\) −0.748302 −0.0316498
\(560\) 2.99647 + 17.6650i 0.126624 + 0.746484i
\(561\) 0 0
\(562\) −17.3606 + 2.44970i −0.732312 + 0.103335i
\(563\) −3.53958 1.46614i −0.149175 0.0617905i 0.306847 0.951759i \(-0.400726\pi\)
−0.456022 + 0.889969i \(0.650726\pi\)
\(564\) 0 0
\(565\) 5.82428 + 14.0611i 0.245029 + 0.591553i
\(566\) −27.3393 7.05422i −1.14916 0.296511i
\(567\) 0 0
\(568\) 16.9782 7.59310i 0.712389 0.318599i
\(569\) 0.855711 + 0.855711i 0.0358733 + 0.0358733i 0.724816 0.688943i \(-0.241925\pi\)
−0.688943 + 0.724816i \(0.741925\pi\)
\(570\) 0 0
\(571\) 4.33854 + 10.4742i 0.181562 + 0.438330i 0.988289 0.152595i \(-0.0487629\pi\)
−0.806726 + 0.590925i \(0.798763\pi\)
\(572\) 2.03370 0.585599i 0.0850331 0.0244851i
\(573\) 0 0
\(574\) 30.8546 40.9927i 1.28784 1.71100i
\(575\) 13.1371 0.547856
\(576\) 0 0
\(577\) −2.91000 −0.121145 −0.0605724 0.998164i \(-0.519293\pi\)
−0.0605724 + 0.998164i \(0.519293\pi\)
\(578\) −9.48357 + 12.5997i −0.394465 + 0.524078i
\(579\) 0 0
\(580\) −6.08164 + 1.75120i −0.252526 + 0.0727144i
\(581\) 1.74469 + 4.21205i 0.0723819 + 0.174745i
\(582\) 0 0
\(583\) 36.3253 + 36.3253i 1.50444 + 1.50444i
\(584\) 6.47909 + 14.4873i 0.268107 + 0.599487i
\(585\) 0 0
\(586\) 31.2647 + 8.06709i 1.29153 + 0.333248i
\(587\) 18.1052 + 43.7099i 0.747283 + 1.80410i 0.573287 + 0.819355i \(0.305668\pi\)
0.173996 + 0.984746i \(0.444332\pi\)
\(588\) 0 0
\(589\) 22.8155 + 9.45049i 0.940096 + 0.389401i
\(590\) 7.32854 1.03411i 0.301711 0.0425737i
\(591\) 0 0
\(592\) −3.19590 + 4.50161i −0.131351 + 0.185015i
\(593\) 30.7464 1.26260 0.631301 0.775538i \(-0.282521\pi\)
0.631301 + 0.775538i \(0.282521\pi\)
\(594\) 0 0
\(595\) −9.09496 + 21.9572i −0.372857 + 0.900157i
\(596\) −28.0861 35.2287i −1.15045 1.44302i
\(597\) 0 0
\(598\) 1.21374 + 0.313176i 0.0496336 + 0.0128067i
\(599\) −19.3435 19.3435i −0.790354 0.790354i 0.191198 0.981552i \(-0.438763\pi\)
−0.981552 + 0.191198i \(0.938763\pi\)
\(600\) 0 0
\(601\) −28.4893 + 28.4893i −1.16210 + 1.16210i −0.178087 + 0.984015i \(0.556991\pi\)
−0.984015 + 0.178087i \(0.943009\pi\)
\(602\) 15.8126 9.32615i 0.644473 0.380106i
\(603\) 0 0
\(604\) −11.5862 6.40553i −0.471437 0.260638i
\(605\) −2.80153 1.16043i −0.113899 0.0471783i
\(606\) 0 0
\(607\) 31.5078i 1.27886i −0.768848 0.639432i \(-0.779170\pi\)
0.768848 0.639432i \(-0.220830\pi\)
\(608\) −35.7873 18.5036i −1.45137 0.750419i
\(609\) 0 0
\(610\) −0.0283504 + 0.0376658i −0.00114788 + 0.00152504i
\(611\) 0.0453910 0.109584i 0.00183632 0.00443328i
\(612\) 0 0
\(613\) −40.5414 + 16.7928i −1.63745 + 0.678254i −0.996037 0.0889418i \(-0.971651\pi\)
−0.641413 + 0.767196i \(0.721651\pi\)
\(614\) 4.31535 + 7.31672i 0.174154 + 0.295279i
\(615\) 0 0
\(616\) −35.6762 + 37.7206i −1.43744 + 1.51981i
\(617\) −14.1405 + 14.1405i −0.569276 + 0.569276i −0.931926 0.362650i \(-0.881872\pi\)
0.362650 + 0.931926i \(0.381872\pi\)
\(618\) 0 0
\(619\) −17.7763 + 7.36320i −0.714491 + 0.295952i −0.710162 0.704039i \(-0.751378\pi\)
−0.00432943 + 0.999991i \(0.501378\pi\)
\(620\) 3.98757 + 5.00164i 0.160145 + 0.200871i
\(621\) 0 0
\(622\) 24.4282 3.44700i 0.979483 0.138212i
\(623\) 33.1054i 1.32634i
\(624\) 0 0
\(625\) 12.9622i 0.518487i
\(626\) 2.53657 + 17.9761i 0.101382 + 0.718471i
\(627\) 0 0
\(628\) −32.0627 3.61701i −1.27944 0.144334i
\(629\) −6.76546 + 2.80235i −0.269757 + 0.111737i
\(630\) 0 0
\(631\) −14.1654 + 14.1654i −0.563915 + 0.563915i −0.930417 0.366502i \(-0.880555\pi\)
0.366502 + 0.930417i \(0.380555\pi\)
\(632\) −33.6408 12.8492i −1.33816 0.511115i
\(633\) 0 0
\(634\) 19.4237 11.4560i 0.771413 0.454974i
\(635\) −8.03602 + 3.32863i −0.318900 + 0.132093i
\(636\) 0 0
\(637\) 1.77663 4.28917i 0.0703927 0.169943i
\(638\) −14.6522 11.0285i −0.580088 0.436623i
\(639\) 0 0
\(640\) −5.79352 8.67954i −0.229009 0.343089i
\(641\) 3.51722i 0.138922i −0.997585 0.0694610i \(-0.977872\pi\)
0.997585 0.0694610i \(-0.0221279\pi\)
\(642\) 0 0
\(643\) 28.4159 + 11.7702i 1.12061 + 0.464173i 0.864580 0.502496i \(-0.167585\pi\)
0.256032 + 0.966668i \(0.417585\pi\)
\(644\) −29.5511 + 8.50916i −1.16447 + 0.335308i
\(645\) 0 0
\(646\) −27.1481 46.0299i −1.06813 1.81102i
\(647\) 22.2793 22.2793i 0.875889 0.875889i −0.117217 0.993106i \(-0.537397\pi\)
0.993106 + 0.117217i \(0.0373973\pi\)
\(648\) 0 0
\(649\) 15.1649 + 15.1649i 0.595275 + 0.595275i
\(650\) 0.410414 1.59060i 0.0160978 0.0623883i
\(651\) 0 0
\(652\) −0.517999 + 4.59176i −0.0202864 + 0.179827i
\(653\) −1.57865 + 3.81119i −0.0617772 + 0.149143i −0.951754 0.306863i \(-0.900721\pi\)
0.889976 + 0.456007i \(0.150721\pi\)
\(654\) 0 0
\(655\) 14.9387 0.583704
\(656\) −6.65737 + 29.1313i −0.259926 + 1.13739i
\(657\) 0 0
\(658\) 0.406580 + 2.88135i 0.0158501 + 0.112327i
\(659\) −13.2385 5.48357i −0.515699 0.213610i 0.109627 0.993973i \(-0.465034\pi\)
−0.625327 + 0.780363i \(0.715034\pi\)
\(660\) 0 0
\(661\) −9.61142 23.2040i −0.373841 0.902532i −0.993092 0.117339i \(-0.962564\pi\)
0.619251 0.785193i \(-0.287436\pi\)
\(662\) 7.92448 30.7121i 0.307994 1.19366i
\(663\) 0 0
\(664\) −1.92914 1.82459i −0.0748653 0.0708078i
\(665\) −22.5579 22.5579i −0.874758 0.874758i
\(666\) 0 0
\(667\) −4.15674 10.0353i −0.160950 0.388567i
\(668\) 35.1625 + 19.4399i 1.36048 + 0.752151i
\(669\) 0 0
\(670\) 11.0802 + 8.33989i 0.428066 + 0.322198i
\(671\) −0.136607 −0.00527366
\(672\) 0 0
\(673\) −12.4509 −0.479947 −0.239974 0.970779i \(-0.577139\pi\)
−0.239974 + 0.970779i \(0.577139\pi\)
\(674\) −14.6867 11.0545i −0.565712 0.425802i
\(675\) 0 0
\(676\) −12.5039 + 22.6169i −0.480921 + 0.869882i
\(677\) −6.84859 16.5340i −0.263213 0.635451i 0.735921 0.677067i \(-0.236749\pi\)
−0.999134 + 0.0416159i \(0.986749\pi\)
\(678\) 0 0
\(679\) −30.1519 30.1519i −1.15712 1.15712i
\(680\) −0.385397 13.8367i −0.0147793 0.530612i
\(681\) 0 0
\(682\) −4.63100 + 17.9479i −0.177330 + 0.687260i
\(683\) 9.54777 + 23.0504i 0.365335 + 0.881997i 0.994501 + 0.104726i \(0.0333966\pi\)
−0.629166 + 0.777271i \(0.716603\pi\)
\(684\) 0 0
\(685\) 6.04663 + 2.50460i 0.231030 + 0.0956958i
\(686\) 9.19658 + 65.1744i 0.351127 + 2.48837i
\(687\) 0 0
\(688\) −6.18958 + 8.71837i −0.235975 + 0.332385i
\(689\) 3.80469 0.144947
\(690\) 0 0
\(691\) −0.714680 + 1.72539i −0.0271877 + 0.0656369i −0.936890 0.349623i \(-0.886310\pi\)
0.909703 + 0.415260i \(0.136310\pi\)
\(692\) 23.5440 + 2.65602i 0.895010 + 0.100967i
\(693\) 0 0
\(694\) 9.33515 36.1792i 0.354357 1.37334i
\(695\) 13.4562 + 13.4562i 0.510424 + 0.510424i
\(696\) 0 0
\(697\) −28.0277 + 28.0277i −1.06162 + 1.06162i
\(698\) −7.17994 12.1737i −0.271765 0.460780i
\(699\) 0 0
\(700\) 11.1512 + 38.7264i 0.421475 + 1.46372i
\(701\) −23.2566 9.63319i −0.878388 0.363840i −0.102517 0.994731i \(-0.532690\pi\)
−0.775872 + 0.630891i \(0.782690\pi\)
\(702\) 0 0
\(703\) 9.82957i 0.370729i
\(704\) 9.99897 28.5381i 0.376851 1.07557i
\(705\) 0 0
\(706\) 27.5738 + 20.7544i 1.03776 + 0.781102i
\(707\) −21.2289 + 51.2512i −0.798396 + 1.92750i
\(708\) 0 0
\(709\) 37.2006 15.4090i 1.39710 0.578698i 0.448102 0.893982i \(-0.352100\pi\)
0.948997 + 0.315285i \(0.102100\pi\)
\(710\) −7.38822 + 4.35752i −0.277275 + 0.163535i
\(711\) 0 0
\(712\) 7.87176 + 17.6013i 0.295007 + 0.659636i
\(713\) −7.76307 + 7.76307i −0.290729 + 0.290729i
\(714\) 0 0
\(715\) −0.901729 + 0.373508i −0.0337227 + 0.0139684i
\(716\) −2.18633 + 19.3806i −0.0817071 + 0.724286i
\(717\) 0 0
\(718\) 1.82404 + 12.9266i 0.0680725 + 0.482417i
\(719\) 10.2965i 0.383996i 0.981395 + 0.191998i \(0.0614968\pi\)
−0.981395 + 0.191998i \(0.938503\pi\)
\(720\) 0 0
\(721\) 17.4669i 0.650500i
\(722\) 44.4221 6.26828i 1.65322 0.233281i
\(723\) 0 0
\(724\) −23.5355 + 18.7637i −0.874691 + 0.697348i
\(725\) −13.1511 + 5.44737i −0.488420 + 0.202310i
\(726\) 0 0
\(727\) 13.6565 13.6565i 0.506493 0.506493i −0.406955 0.913448i \(-0.633409\pi\)
0.913448 + 0.406955i \(0.133409\pi\)
\(728\) 0.107062 + 3.84377i 0.00396798 + 0.142460i
\(729\) 0 0
\(730\) −3.71821 6.30427i −0.137617 0.233331i
\(731\) −13.1028 + 5.42737i −0.484626 + 0.200739i
\(732\) 0 0
\(733\) 12.2351 29.5382i 0.451915 1.09102i −0.519678 0.854362i \(-0.673948\pi\)
0.971593 0.236657i \(-0.0760517\pi\)
\(734\) −16.5238 + 21.9532i −0.609906 + 0.810309i
\(735\) 0 0
\(736\) 13.6882 11.5507i 0.504555 0.425765i
\(737\) 40.1859i 1.48027i
\(738\) 0 0
\(739\) −5.26176 2.17949i −0.193557 0.0801739i 0.283800 0.958884i \(-0.408405\pi\)
−0.477356 + 0.878710i \(0.658405\pi\)
\(740\) 1.23189 2.22822i 0.0452852 0.0819112i
\(741\) 0 0
\(742\) −80.3979 + 47.4182i −2.95150 + 1.74078i
\(743\) −17.0314 + 17.0314i −0.624823 + 0.624823i −0.946761 0.321938i \(-0.895666\pi\)
0.321938 + 0.946761i \(0.395666\pi\)
\(744\) 0 0
\(745\) 14.6926 + 14.6926i 0.538295 + 0.538295i
\(746\) 14.8789 + 3.83914i 0.544757 + 0.140561i
\(747\) 0 0
\(748\) 31.3629 25.0041i 1.14674 0.914241i
\(749\) −6.55375 + 15.8221i −0.239469 + 0.578129i
\(750\) 0 0
\(751\) 5.21219 0.190196 0.0950978 0.995468i \(-0.469684\pi\)
0.0950978 + 0.995468i \(0.469684\pi\)
\(752\) −0.901293 1.43527i −0.0328668 0.0523387i
\(753\) 0 0
\(754\) −1.34489 + 0.189774i −0.0489781 + 0.00691117i
\(755\) 5.64090 + 2.33654i 0.205293 + 0.0850353i
\(756\) 0 0
\(757\) 5.99669 + 14.4773i 0.217953 + 0.526186i 0.994604 0.103746i \(-0.0330828\pi\)
−0.776650 + 0.629932i \(0.783083\pi\)
\(758\) −7.03740 1.81583i −0.255610 0.0659537i
\(759\) 0 0
\(760\) 17.3572 + 6.62966i 0.629614 + 0.240483i
\(761\) 16.7870 + 16.7870i 0.608528 + 0.608528i 0.942561 0.334033i \(-0.108410\pi\)
−0.334033 + 0.942561i \(0.608410\pi\)
\(762\) 0 0
\(763\) −23.3146 56.2865i −0.844046 2.03771i
\(764\) 3.42122 + 11.8814i 0.123775 + 0.429854i
\(765\) 0 0
\(766\) 5.35885 7.11965i 0.193623 0.257244i
\(767\) 1.58837 0.0573526
\(768\) 0 0
\(769\) 33.1933 1.19698 0.598491 0.801129i \(-0.295767\pi\)
0.598491 + 0.801129i \(0.295767\pi\)
\(770\) 14.3996 19.1310i 0.518926 0.689435i
\(771\) 0 0
\(772\) 6.22668 + 21.6243i 0.224103 + 0.778276i
\(773\) 5.41657 + 13.0767i 0.194820 + 0.470338i 0.990858 0.134909i \(-0.0430743\pi\)
−0.796038 + 0.605247i \(0.793074\pi\)
\(774\) 0 0
\(775\) 10.1734 + 10.1734i 0.365440 + 0.365440i
\(776\) 23.2005 + 8.86150i 0.832848 + 0.318109i
\(777\) 0 0
\(778\) 1.18722 + 0.306333i 0.0425640 + 0.0109826i
\(779\) −20.3608 49.1552i −0.729500 1.76117i
\(780\) 0 0
\(781\) −22.9632 9.51169i −0.821689 0.340355i
\(782\) 23.5242 3.31943i 0.841222 0.118703i
\(783\) 0 0
\(784\) −35.2771 56.1771i −1.25990 2.00633i
\(785\) 14.8807 0.531115
\(786\) 0 0
\(787\) 18.2278 44.0057i 0.649750 1.56864i −0.163387 0.986562i \(-0.552242\pi\)
0.813136