Properties

Label 315.3.ca.b.37.6
Level 315
Weight 3
Character 315.37
Analytic conductor 8.583
Analytic rank 0
Dimension 64
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 315.ca (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.58312832735\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 37.6
Character \(\chi\) \(=\) 315.37
Dual form 315.3.ca.b.298.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.984292 + 0.263740i) q^{2} +(-2.56483 + 1.48081i) q^{4} +(4.04958 + 2.93273i) q^{5} +(-5.81621 + 3.89508i) q^{7} +(5.01620 - 5.01620i) q^{8} +O(q^{10})\) \(q+(-0.984292 + 0.263740i) q^{2} +(-2.56483 + 1.48081i) q^{4} +(4.04958 + 2.93273i) q^{5} +(-5.81621 + 3.89508i) q^{7} +(5.01620 - 5.01620i) q^{8} +(-4.75945 - 1.81862i) q^{10} +(2.58885 + 4.48403i) q^{11} +(-3.12416 + 3.12416i) q^{13} +(4.69756 - 5.36787i) q^{14} +(2.30879 - 3.99894i) q^{16} +(-4.02869 + 15.0353i) q^{17} +(-17.1897 - 9.92450i) q^{19} +(-14.7293 - 1.52531i) q^{20} +(-3.73081 - 3.73081i) q^{22} +(-9.71406 - 36.2534i) q^{23} +(7.79821 + 23.7526i) q^{25} +(2.25112 - 3.89905i) q^{26} +(9.14974 - 18.6029i) q^{28} +11.8306i q^{29} +(-9.02952 - 15.6396i) q^{31} +(-8.56207 + 31.9541i) q^{32} -15.8616i q^{34} +(-34.9764 - 1.28394i) q^{35} +(-70.9224 + 19.0036i) q^{37} +(19.5372 + 5.23498i) q^{38} +(35.0247 - 5.60235i) q^{40} -60.6872 q^{41} +(-33.1804 + 33.1804i) q^{43} +(-13.2799 - 7.66718i) q^{44} +(19.1229 + 33.1219i) q^{46} +(19.9094 - 5.33470i) q^{47} +(18.6567 - 45.3092i) q^{49} +(-13.9402 - 21.3228i) q^{50} +(3.38666 - 12.6392i) q^{52} +(6.28105 + 1.68300i) q^{53} +(-2.66666 + 25.7508i) q^{55} +(-9.63679 + 48.7138i) q^{56} +(-3.12020 - 11.6447i) q^{58} +(32.2232 - 18.6041i) q^{59} +(-6.88336 + 11.9223i) q^{61} +(13.0125 + 13.0125i) q^{62} -15.2400i q^{64} +(-21.8138 + 3.48922i) q^{65} +(-0.969242 + 3.61726i) q^{67} +(-11.9314 - 44.5287i) q^{68} +(34.7657 - 7.96093i) q^{70} +77.9344 q^{71} +(-123.630 - 33.1265i) q^{73} +(64.7964 - 37.4102i) q^{74} +58.7850 q^{76} +(-32.5230 - 15.9963i) q^{77} +(73.5670 + 42.4739i) q^{79} +(21.0774 - 9.42297i) q^{80} +(59.7339 - 16.0057i) q^{82} +(10.0091 - 10.0091i) q^{83} +(-60.4089 + 49.0715i) q^{85} +(23.9082 - 41.4102i) q^{86} +(35.4790 + 9.50657i) q^{88} +(95.4344 + 55.0991i) q^{89} +(6.00193 - 30.3396i) q^{91} +(78.5990 + 78.5990i) q^{92} +(-18.1897 + 10.5018i) q^{94} +(-40.5054 - 90.6029i) q^{95} +(30.0049 + 30.0049i) q^{97} +(-6.41377 + 49.5181i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.984292 + 0.263740i −0.492146 + 0.131870i −0.496353 0.868121i \(-0.665328\pi\)
0.00420656 + 0.999991i \(0.498661\pi\)
\(3\) 0 0
\(4\) −2.56483 + 1.48081i −0.641207 + 0.370201i
\(5\) 4.04958 + 2.93273i 0.809916 + 0.586546i
\(6\) 0 0
\(7\) −5.81621 + 3.89508i −0.830888 + 0.556440i
\(8\) 5.01620 5.01620i 0.627025 0.627025i
\(9\) 0 0
\(10\) −4.75945 1.81862i −0.475945 0.181862i
\(11\) 2.58885 + 4.48403i 0.235350 + 0.407639i 0.959374 0.282136i \(-0.0910429\pi\)
−0.724024 + 0.689775i \(0.757710\pi\)
\(12\) 0 0
\(13\) −3.12416 + 3.12416i −0.240320 + 0.240320i −0.816982 0.576663i \(-0.804355\pi\)
0.576663 + 0.816982i \(0.304355\pi\)
\(14\) 4.69756 5.36787i 0.335540 0.383419i
\(15\) 0 0
\(16\) 2.30879 3.99894i 0.144299 0.249934i
\(17\) −4.02869 + 15.0353i −0.236982 + 0.884429i 0.740263 + 0.672317i \(0.234701\pi\)
−0.977245 + 0.212112i \(0.931966\pi\)
\(18\) 0 0
\(19\) −17.1897 9.92450i −0.904723 0.522342i −0.0259936 0.999662i \(-0.508275\pi\)
−0.878730 + 0.477320i \(0.841608\pi\)
\(20\) −14.7293 1.52531i −0.736464 0.0762655i
\(21\) 0 0
\(22\) −3.73081 3.73081i −0.169582 0.169582i
\(23\) −9.71406 36.2534i −0.422350 1.57623i −0.769642 0.638476i \(-0.779565\pi\)
0.347292 0.937757i \(-0.387101\pi\)
\(24\) 0 0
\(25\) 7.79821 + 23.7526i 0.311928 + 0.950106i
\(26\) 2.25112 3.89905i 0.0865814 0.149963i
\(27\) 0 0
\(28\) 9.14974 18.6029i 0.326777 0.664389i
\(29\) 11.8306i 0.407951i 0.978976 + 0.203975i \(0.0653863\pi\)
−0.978976 + 0.203975i \(0.934614\pi\)
\(30\) 0 0
\(31\) −9.02952 15.6396i −0.291275 0.504503i 0.682837 0.730571i \(-0.260746\pi\)
−0.974111 + 0.226068i \(0.927413\pi\)
\(32\) −8.56207 + 31.9541i −0.267565 + 0.998565i
\(33\) 0 0
\(34\) 15.8616i 0.466519i
\(35\) −34.9764 1.28394i −0.999327 0.0366839i
\(36\) 0 0
\(37\) −70.9224 + 19.0036i −1.91682 + 0.513611i −0.926189 + 0.377059i \(0.876935\pi\)
−0.990633 + 0.136552i \(0.956398\pi\)
\(38\) 19.5372 + 5.23498i 0.514137 + 0.137763i
\(39\) 0 0
\(40\) 35.0247 5.60235i 0.875617 0.140059i
\(41\) −60.6872 −1.48018 −0.740088 0.672510i \(-0.765216\pi\)
−0.740088 + 0.672510i \(0.765216\pi\)
\(42\) 0 0
\(43\) −33.1804 + 33.1804i −0.771637 + 0.771637i −0.978393 0.206756i \(-0.933709\pi\)
0.206756 + 0.978393i \(0.433709\pi\)
\(44\) −13.2799 7.66718i −0.301817 0.174254i
\(45\) 0 0
\(46\) 19.1229 + 33.1219i 0.415716 + 0.720041i
\(47\) 19.9094 5.33470i 0.423604 0.113504i −0.0407183 0.999171i \(-0.512965\pi\)
0.464322 + 0.885666i \(0.346298\pi\)
\(48\) 0 0
\(49\) 18.6567 45.3092i 0.380749 0.924678i
\(50\) −13.9402 21.3228i −0.278805 0.426457i
\(51\) 0 0
\(52\) 3.38666 12.6392i 0.0651281 0.243062i
\(53\) 6.28105 + 1.68300i 0.118510 + 0.0317547i 0.317587 0.948229i \(-0.397128\pi\)
−0.199076 + 0.979984i \(0.563794\pi\)
\(54\) 0 0
\(55\) −2.66666 + 25.7508i −0.0484847 + 0.468197i
\(56\) −9.63679 + 48.7138i −0.172086 + 0.869889i
\(57\) 0 0
\(58\) −3.12020 11.6447i −0.0537965 0.200771i
\(59\) 32.2232 18.6041i 0.546155 0.315323i −0.201415 0.979506i \(-0.564554\pi\)
0.747570 + 0.664183i \(0.231221\pi\)
\(60\) 0 0
\(61\) −6.88336 + 11.9223i −0.112842 + 0.195448i −0.916915 0.399082i \(-0.869329\pi\)
0.804073 + 0.594530i \(0.202662\pi\)
\(62\) 13.0125 + 13.0125i 0.209879 + 0.209879i
\(63\) 0 0
\(64\) 15.2400i 0.238125i
\(65\) −21.8138 + 3.48922i −0.335597 + 0.0536803i
\(66\) 0 0
\(67\) −0.969242 + 3.61726i −0.0144663 + 0.0539889i −0.972782 0.231723i \(-0.925564\pi\)
0.958315 + 0.285712i \(0.0922302\pi\)
\(68\) −11.9314 44.5287i −0.175462 0.654833i
\(69\) 0 0
\(70\) 34.7657 7.96093i 0.496652 0.113728i
\(71\) 77.9344 1.09767 0.548834 0.835932i \(-0.315072\pi\)
0.548834 + 0.835932i \(0.315072\pi\)
\(72\) 0 0
\(73\) −123.630 33.1265i −1.69356 0.453788i −0.722256 0.691626i \(-0.756895\pi\)
−0.971305 + 0.237838i \(0.923561\pi\)
\(74\) 64.7964 37.4102i 0.875626 0.505543i
\(75\) 0 0
\(76\) 58.7850 0.773487
\(77\) −32.5230 15.9963i −0.422376 0.207744i
\(78\) 0 0
\(79\) 73.5670 + 42.4739i 0.931227 + 0.537644i 0.887200 0.461386i \(-0.152648\pi\)
0.0440278 + 0.999030i \(0.485981\pi\)
\(80\) 21.0774 9.42297i 0.263468 0.117787i
\(81\) 0 0
\(82\) 59.7339 16.0057i 0.728463 0.195191i
\(83\) 10.0091 10.0091i 0.120591 0.120591i −0.644236 0.764827i \(-0.722824\pi\)
0.764827 + 0.644236i \(0.222824\pi\)
\(84\) 0 0
\(85\) −60.4089 + 49.0715i −0.710693 + 0.577312i
\(86\) 23.9082 41.4102i 0.278002 0.481514i
\(87\) 0 0
\(88\) 35.4790 + 9.50657i 0.403170 + 0.108029i
\(89\) 95.4344 + 55.0991i 1.07230 + 0.619091i 0.928808 0.370561i \(-0.120835\pi\)
0.143489 + 0.989652i \(0.454168\pi\)
\(90\) 0 0
\(91\) 6.00193 30.3396i 0.0659552 0.333402i
\(92\) 78.5990 + 78.5990i 0.854337 + 0.854337i
\(93\) 0 0
\(94\) −18.1897 + 10.5018i −0.193507 + 0.111721i
\(95\) −40.5054 90.6029i −0.426372 0.953715i
\(96\) 0 0
\(97\) 30.0049 + 30.0049i 0.309328 + 0.309328i 0.844649 0.535321i \(-0.179809\pi\)
−0.535321 + 0.844649i \(0.679809\pi\)
\(98\) −6.41377 + 49.5181i −0.0654466 + 0.505286i
\(99\) 0 0
\(100\) −55.1741 49.3739i −0.551741 0.493739i
\(101\) 34.2964 + 59.4032i 0.339569 + 0.588150i 0.984352 0.176215i \(-0.0563855\pi\)
−0.644783 + 0.764366i \(0.723052\pi\)
\(102\) 0 0
\(103\) 33.3675 + 124.529i 0.323956 + 1.20902i 0.915357 + 0.402643i \(0.131908\pi\)
−0.591401 + 0.806378i \(0.701425\pi\)
\(104\) 31.3428i 0.301373i
\(105\) 0 0
\(106\) −6.62626 −0.0625119
\(107\) −22.9093 + 6.13854i −0.214106 + 0.0573695i −0.364278 0.931290i \(-0.618684\pi\)
0.150172 + 0.988660i \(0.452017\pi\)
\(108\) 0 0
\(109\) 167.284 96.5816i 1.53472 0.886070i 0.535583 0.844482i \(-0.320092\pi\)
0.999135 0.0415874i \(-0.0132415\pi\)
\(110\) −4.16676 26.0497i −0.0378796 0.236815i
\(111\) 0 0
\(112\) 2.14778 + 32.2516i 0.0191766 + 0.287961i
\(113\) −129.366 + 129.366i −1.14483 + 1.14483i −0.157275 + 0.987555i \(0.550271\pi\)
−0.987555 + 0.157275i \(0.949729\pi\)
\(114\) 0 0
\(115\) 66.9834 175.300i 0.582464 1.52434i
\(116\) −17.5188 30.3434i −0.151024 0.261581i
\(117\) 0 0
\(118\) −26.8104 + 26.8104i −0.227206 + 0.227206i
\(119\) −35.1319 103.141i −0.295226 0.866727i
\(120\) 0 0
\(121\) 47.0957 81.5721i 0.389220 0.674149i
\(122\) 3.63084 13.5505i 0.0297610 0.111069i
\(123\) 0 0
\(124\) 46.3184 + 26.7419i 0.373535 + 0.215661i
\(125\) −38.0806 + 119.058i −0.304645 + 0.952466i
\(126\) 0 0
\(127\) 54.2797 + 54.2797i 0.427400 + 0.427400i 0.887742 0.460342i \(-0.152273\pi\)
−0.460342 + 0.887742i \(0.652273\pi\)
\(128\) −30.2289 112.816i −0.236163 0.881373i
\(129\) 0 0
\(130\) 20.5509 9.18760i 0.158084 0.0706738i
\(131\) 9.27972 16.0730i 0.0708376 0.122694i −0.828431 0.560091i \(-0.810766\pi\)
0.899269 + 0.437397i \(0.144099\pi\)
\(132\) 0 0
\(133\) 138.636 9.23239i 1.04238 0.0694165i
\(134\) 3.81607i 0.0284781i
\(135\) 0 0
\(136\) 55.2113 + 95.6288i 0.405965 + 0.703153i
\(137\) −27.9757 + 104.407i −0.204202 + 0.762094i 0.785489 + 0.618876i \(0.212412\pi\)
−0.989691 + 0.143218i \(0.954255\pi\)
\(138\) 0 0
\(139\) 135.516i 0.974938i 0.873140 + 0.487469i \(0.162080\pi\)
−0.873140 + 0.487469i \(0.837920\pi\)
\(140\) 91.6099 48.5002i 0.654356 0.346430i
\(141\) 0 0
\(142\) −76.7102 + 20.5544i −0.540213 + 0.144750i
\(143\) −22.0968 5.92082i −0.154523 0.0414043i
\(144\) 0 0
\(145\) −34.6959 + 47.9089i −0.239282 + 0.330406i
\(146\) 130.425 0.893320
\(147\) 0 0
\(148\) 153.763 153.763i 1.03894 1.03894i
\(149\) −34.6086 19.9813i −0.232273 0.134103i 0.379347 0.925254i \(-0.376149\pi\)
−0.611620 + 0.791152i \(0.709482\pi\)
\(150\) 0 0
\(151\) −20.0625 34.7493i −0.132864 0.230128i 0.791915 0.610631i \(-0.209084\pi\)
−0.924780 + 0.380503i \(0.875751\pi\)
\(152\) −136.010 + 36.4439i −0.894806 + 0.239762i
\(153\) 0 0
\(154\) 36.2310 + 7.16738i 0.235266 + 0.0465414i
\(155\) 9.30090 89.8149i 0.0600058 0.579451i
\(156\) 0 0
\(157\) −39.9568 + 149.121i −0.254502 + 0.949813i 0.713865 + 0.700283i \(0.246943\pi\)
−0.968367 + 0.249530i \(0.919724\pi\)
\(158\) −83.6134 22.4042i −0.529199 0.141798i
\(159\) 0 0
\(160\) −128.385 + 104.290i −0.802409 + 0.651815i
\(161\) 197.709 + 173.020i 1.22800 + 1.07466i
\(162\) 0 0
\(163\) −56.0733 209.268i −0.344008 1.28386i −0.893767 0.448532i \(-0.851947\pi\)
0.549759 0.835324i \(-0.314720\pi\)
\(164\) 155.652 89.8659i 0.949100 0.547963i
\(165\) 0 0
\(166\) −7.21206 + 12.4917i −0.0434461 + 0.0752509i
\(167\) −66.5271 66.5271i −0.398366 0.398366i 0.479290 0.877656i \(-0.340894\pi\)
−0.877656 + 0.479290i \(0.840894\pi\)
\(168\) 0 0
\(169\) 149.479i 0.884493i
\(170\) 46.5179 64.2330i 0.273635 0.377841i
\(171\) 0 0
\(172\) 35.9684 134.236i 0.209118 0.780440i
\(173\) 55.0739 + 205.539i 0.318346 + 1.18808i 0.920833 + 0.389956i \(0.127510\pi\)
−0.602487 + 0.798129i \(0.705824\pi\)
\(174\) 0 0
\(175\) −137.874 107.776i −0.787854 0.615862i
\(176\) 23.9085 0.135844
\(177\) 0 0
\(178\) −108.467 29.0637i −0.609366 0.163279i
\(179\) 254.711 147.057i 1.42296 0.821549i 0.426413 0.904529i \(-0.359777\pi\)
0.996551 + 0.0829801i \(0.0264438\pi\)
\(180\) 0 0
\(181\) −160.740 −0.888065 −0.444032 0.896011i \(-0.646452\pi\)
−0.444032 + 0.896011i \(0.646452\pi\)
\(182\) 2.09413 + 31.4460i 0.0115062 + 0.172780i
\(183\) 0 0
\(184\) −230.582 133.126i −1.25316 0.723513i
\(185\) −342.938 131.040i −1.85372 0.708322i
\(186\) 0 0
\(187\) −77.8483 + 20.8594i −0.416301 + 0.111548i
\(188\) −43.1645 + 43.1645i −0.229599 + 0.229599i
\(189\) 0 0
\(190\) 63.7647 + 78.4968i 0.335604 + 0.413141i
\(191\) −73.6284 + 127.528i −0.385489 + 0.667686i −0.991837 0.127513i \(-0.959300\pi\)
0.606348 + 0.795199i \(0.292634\pi\)
\(192\) 0 0
\(193\) −96.7332 25.9196i −0.501208 0.134298i −0.000647439 1.00000i \(-0.500206\pi\)
−0.500561 + 0.865702i \(0.666873\pi\)
\(194\) −37.4470 21.6200i −0.193026 0.111444i
\(195\) 0 0
\(196\) 19.2429 + 143.837i 0.0981781 + 0.733864i
\(197\) −130.900 130.900i −0.664467 0.664467i 0.291963 0.956430i \(-0.405692\pi\)
−0.956430 + 0.291963i \(0.905692\pi\)
\(198\) 0 0
\(199\) −113.445 + 65.4975i −0.570076 + 0.329133i −0.757180 0.653207i \(-0.773423\pi\)
0.187104 + 0.982340i \(0.440090\pi\)
\(200\) 158.265 + 80.0306i 0.791327 + 0.400153i
\(201\) 0 0
\(202\) −49.4247 49.4247i −0.244677 0.244677i
\(203\) −46.0811 68.8092i −0.227000 0.338961i
\(204\) 0 0
\(205\) −245.758 177.979i −1.19882 0.868191i
\(206\) −65.6867 113.773i −0.318867 0.552295i
\(207\) 0 0
\(208\) 5.28030 + 19.7063i 0.0253860 + 0.0947420i
\(209\) 102.772i 0.491734i
\(210\) 0 0
\(211\) −284.859 −1.35004 −0.675021 0.737798i \(-0.735866\pi\)
−0.675021 + 0.737798i \(0.735866\pi\)
\(212\) −18.6020 + 4.98439i −0.0877453 + 0.0235113i
\(213\) 0 0
\(214\) 20.9305 12.0842i 0.0978061 0.0564684i
\(215\) −231.676 + 37.0576i −1.07756 + 0.172361i
\(216\) 0 0
\(217\) 113.435 + 55.7925i 0.522742 + 0.257108i
\(218\) −139.184 + 139.184i −0.638459 + 0.638459i
\(219\) 0 0
\(220\) −31.2924 69.9953i −0.142238 0.318161i
\(221\) −34.3863 59.5589i −0.155594 0.269497i
\(222\) 0 0
\(223\) −163.068 + 163.068i −0.731248 + 0.731248i −0.970867 0.239619i \(-0.922977\pi\)
0.239619 + 0.970867i \(0.422977\pi\)
\(224\) −74.6649 219.202i −0.333325 0.978579i
\(225\) 0 0
\(226\) 93.2148 161.453i 0.412455 0.714393i
\(227\) −87.4422 + 326.339i −0.385208 + 1.43762i 0.452631 + 0.891698i \(0.350486\pi\)
−0.837839 + 0.545918i \(0.816181\pi\)
\(228\) 0 0
\(229\) −196.388 113.385i −0.857590 0.495130i 0.00561424 0.999984i \(-0.498213\pi\)
−0.863205 + 0.504854i \(0.831546\pi\)
\(230\) −19.6977 + 190.212i −0.0856420 + 0.827009i
\(231\) 0 0
\(232\) 59.3446 + 59.3446i 0.255795 + 0.255795i
\(233\) −41.7928 155.973i −0.179368 0.669411i −0.995766 0.0919215i \(-0.970699\pi\)
0.816398 0.577489i \(-0.195968\pi\)
\(234\) 0 0
\(235\) 96.2699 + 36.7855i 0.409659 + 0.156534i
\(236\) −55.0979 + 95.4324i −0.233466 + 0.404375i
\(237\) 0 0
\(238\) 61.7824 + 92.2547i 0.259590 + 0.387625i
\(239\) 62.1386i 0.259994i 0.991514 + 0.129997i \(0.0414968\pi\)
−0.991514 + 0.129997i \(0.958503\pi\)
\(240\) 0 0
\(241\) 204.217 + 353.714i 0.847373 + 1.46769i 0.883545 + 0.468347i \(0.155150\pi\)
−0.0361717 + 0.999346i \(0.511516\pi\)
\(242\) −24.8420 + 92.7118i −0.102653 + 0.383107i
\(243\) 0 0
\(244\) 40.7717i 0.167097i
\(245\) 208.432 128.768i 0.850741 0.525585i
\(246\) 0 0
\(247\) 84.7092 22.6978i 0.342952 0.0918937i
\(248\) −123.745 33.1574i −0.498973 0.133699i
\(249\) 0 0
\(250\) 6.08196 127.231i 0.0243278 0.508926i
\(251\) 106.431 0.424030 0.212015 0.977266i \(-0.431997\pi\)
0.212015 + 0.977266i \(0.431997\pi\)
\(252\) 0 0
\(253\) 137.413 137.413i 0.543133 0.543133i
\(254\) −67.7429 39.1114i −0.266704 0.153982i
\(255\) 0 0
\(256\) 89.9881 + 155.864i 0.351516 + 0.608843i
\(257\) 377.542 101.162i 1.46904 0.393627i 0.566435 0.824107i \(-0.308322\pi\)
0.902600 + 0.430480i \(0.141656\pi\)
\(258\) 0 0
\(259\) 338.479 386.778i 1.30687 1.49335i
\(260\) 50.7819 41.2513i 0.195315 0.158659i
\(261\) 0 0
\(262\) −4.89487 + 18.2679i −0.0186827 + 0.0697249i
\(263\) 302.308 + 81.0033i 1.14946 + 0.307997i 0.782749 0.622337i \(-0.213817\pi\)
0.366712 + 0.930335i \(0.380483\pi\)
\(264\) 0 0
\(265\) 20.4998 + 25.2361i 0.0773578 + 0.0952304i
\(266\) −134.023 + 45.6512i −0.503847 + 0.171621i
\(267\) 0 0
\(268\) −2.87052 10.7129i −0.0107109 0.0399736i
\(269\) −218.161 + 125.955i −0.811007 + 0.468235i −0.847305 0.531106i \(-0.821777\pi\)
0.0362986 + 0.999341i \(0.488443\pi\)
\(270\) 0 0
\(271\) −146.480 + 253.711i −0.540517 + 0.936203i 0.458357 + 0.888768i \(0.348438\pi\)
−0.998874 + 0.0474352i \(0.984895\pi\)
\(272\) 50.8238 + 50.8238i 0.186852 + 0.186852i
\(273\) 0 0
\(274\) 110.145i 0.401990i
\(275\) −86.3191 + 96.4595i −0.313888 + 0.350762i
\(276\) 0 0
\(277\) −35.8623 + 133.840i −0.129467 + 0.483177i −0.999959 0.00900462i \(-0.997134\pi\)
0.870493 + 0.492182i \(0.163800\pi\)
\(278\) −35.7411 133.388i −0.128565 0.479812i
\(279\) 0 0
\(280\) −181.889 + 169.008i −0.649605 + 0.603601i
\(281\) 127.812 0.454848 0.227424 0.973796i \(-0.426970\pi\)
0.227424 + 0.973796i \(0.426970\pi\)
\(282\) 0 0
\(283\) 242.594 + 65.0029i 0.857223 + 0.229692i 0.660555 0.750778i \(-0.270321\pi\)
0.196668 + 0.980470i \(0.436988\pi\)
\(284\) −199.888 + 115.406i −0.703832 + 0.406358i
\(285\) 0 0
\(286\) 23.3113 0.0815079
\(287\) 352.970 236.382i 1.22986 0.823629i
\(288\) 0 0
\(289\) 40.4518 + 23.3549i 0.139972 + 0.0808127i
\(290\) 21.5154 56.3070i 0.0741909 0.194162i
\(291\) 0 0
\(292\) 366.144 98.1079i 1.25392 0.335986i
\(293\) 21.9976 21.9976i 0.0750770 0.0750770i −0.668571 0.743648i \(-0.733094\pi\)
0.743648 + 0.668571i \(0.233094\pi\)
\(294\) 0 0
\(295\) 185.051 + 19.1632i 0.627291 + 0.0649599i
\(296\) −260.435 + 451.087i −0.879849 + 1.52394i
\(297\) 0 0
\(298\) 39.3349 + 10.5397i 0.131996 + 0.0353683i
\(299\) 143.609 + 82.9129i 0.480299 + 0.277301i
\(300\) 0 0
\(301\) 63.7440 322.225i 0.211774 1.07051i
\(302\) 28.9121 + 28.9121i 0.0957356 + 0.0957356i
\(303\) 0 0
\(304\) −79.3749 + 45.8271i −0.261102 + 0.150747i
\(305\) −62.8397 + 28.0934i −0.206032 + 0.0921095i
\(306\) 0 0
\(307\) −121.636 121.636i −0.396210 0.396210i 0.480684 0.876894i \(-0.340388\pi\)
−0.876894 + 0.480684i \(0.840388\pi\)
\(308\) 107.103 7.13249i 0.347738 0.0231574i
\(309\) 0 0
\(310\) 14.5330 + 90.8571i 0.0468807 + 0.293087i
\(311\) −301.676 522.518i −0.970020 1.68012i −0.695477 0.718548i \(-0.744807\pi\)
−0.274542 0.961575i \(-0.588526\pi\)
\(312\) 0 0
\(313\) −56.5067 210.886i −0.180533 0.673757i −0.995543 0.0943104i \(-0.969935\pi\)
0.815010 0.579447i \(-0.196731\pi\)
\(314\) 157.316i 0.501008i
\(315\) 0 0
\(316\) −251.582 −0.796146
\(317\) 9.46959 2.53737i 0.0298725 0.00800432i −0.243852 0.969812i \(-0.578411\pi\)
0.273724 + 0.961808i \(0.411744\pi\)
\(318\) 0 0
\(319\) −53.0486 + 30.6276i −0.166297 + 0.0960114i
\(320\) 44.6948 61.7156i 0.139671 0.192861i
\(321\) 0 0
\(322\) −240.236 118.159i −0.746073 0.366952i
\(323\) 218.470 218.470i 0.676377 0.676377i
\(324\) 0 0
\(325\) −98.5698 49.8442i −0.303292 0.153367i
\(326\) 110.385 + 191.193i 0.338604 + 0.586480i
\(327\) 0 0
\(328\) −304.419 + 304.419i −0.928107 + 0.928107i
\(329\) −95.0181 + 108.576i −0.288809 + 0.330020i
\(330\) 0 0
\(331\) 229.481 397.473i 0.693296 1.20082i −0.277455 0.960738i \(-0.589491\pi\)
0.970752 0.240086i \(-0.0771756\pi\)
\(332\) −10.8501 + 40.4931i −0.0326810 + 0.121967i
\(333\) 0 0
\(334\) 83.0280 + 47.9362i 0.248587 + 0.143522i
\(335\) −14.5335 + 11.8059i −0.0433835 + 0.0352414i
\(336\) 0 0
\(337\) 75.1343 + 75.1343i 0.222951 + 0.222951i 0.809740 0.586789i \(-0.199608\pi\)
−0.586789 + 0.809740i \(0.699608\pi\)
\(338\) −39.4237 147.131i −0.116638 0.435300i
\(339\) 0 0
\(340\) 82.2732 215.314i 0.241980 0.633277i
\(341\) 46.7522 80.9772i 0.137103 0.237470i
\(342\) 0 0
\(343\) 67.9718 + 336.198i 0.198168 + 0.980168i
\(344\) 332.879i 0.967671i
\(345\) 0 0
\(346\) −108.418 187.785i −0.313346 0.542731i
\(347\) −2.16426 + 8.07713i −0.00623706 + 0.0232770i −0.968974 0.247162i \(-0.920502\pi\)
0.962737 + 0.270439i \(0.0871688\pi\)
\(348\) 0 0
\(349\) 571.222i 1.63674i 0.574693 + 0.818369i \(0.305122\pi\)
−0.574693 + 0.818369i \(0.694878\pi\)
\(350\) 164.134 + 69.7198i 0.468953 + 0.199199i
\(351\) 0 0
\(352\) −165.449 + 44.3319i −0.470025 + 0.125943i
\(353\) 645.496 + 172.960i 1.82860 + 0.489972i 0.997782 0.0665723i \(-0.0212063\pi\)
0.830818 + 0.556544i \(0.187873\pi\)
\(354\) 0 0
\(355\) 315.602 + 228.560i 0.889018 + 0.643832i
\(356\) −326.364 −0.916753
\(357\) 0 0
\(358\) −211.925 + 211.925i −0.591968 + 0.591968i
\(359\) 395.711 + 228.464i 1.10226 + 0.636390i 0.936814 0.349829i \(-0.113760\pi\)
0.165446 + 0.986219i \(0.447094\pi\)
\(360\) 0 0
\(361\) 16.4914 + 28.5640i 0.0456826 + 0.0791246i
\(362\) 158.215 42.3935i 0.437057 0.117109i
\(363\) 0 0
\(364\) 29.5331 + 86.7036i 0.0811350 + 0.238197i
\(365\) −403.498 496.722i −1.10547 1.36088i
\(366\) 0 0
\(367\) 24.7429 92.3418i 0.0674194 0.251613i −0.923988 0.382421i \(-0.875091\pi\)
0.991408 + 0.130808i \(0.0417572\pi\)
\(368\) −167.403 44.8554i −0.454898 0.121890i
\(369\) 0 0
\(370\) 372.112 + 38.5345i 1.00571 + 0.104147i
\(371\) −43.0873 + 14.6765i −0.116138 + 0.0395593i
\(372\) 0 0
\(373\) 34.6037 + 129.143i 0.0927713 + 0.346227i 0.996672 0.0815149i \(-0.0259758\pi\)
−0.903901 + 0.427742i \(0.859309\pi\)
\(374\) 71.1240 41.0635i 0.190171 0.109795i
\(375\) 0 0
\(376\) 73.1095 126.629i 0.194440 0.336780i
\(377\) −36.9606 36.9606i −0.0980387 0.0980387i
\(378\) 0 0
\(379\) 407.491i 1.07517i −0.843208 0.537587i \(-0.819336\pi\)
0.843208 0.537587i \(-0.180664\pi\)
\(380\) 238.055 + 172.400i 0.626460 + 0.453685i
\(381\) 0 0
\(382\) 38.8375 144.944i 0.101669 0.379434i
\(383\) 52.0748 + 194.346i 0.135966 + 0.507430i 0.999992 + 0.00398411i \(0.00126818\pi\)
−0.864026 + 0.503446i \(0.832065\pi\)
\(384\) 0 0
\(385\) −84.7917 160.159i −0.220238 0.415998i
\(386\) 102.050 0.264377
\(387\) 0 0
\(388\) −121.389 32.5260i −0.312857 0.0838299i
\(389\) −184.186 + 106.340i −0.473487 + 0.273368i −0.717698 0.696354i \(-0.754804\pi\)
0.244211 + 0.969722i \(0.421471\pi\)
\(390\) 0 0
\(391\) 584.215 1.49415
\(392\) −133.695 320.866i −0.341057 0.818536i
\(393\) 0 0
\(394\) 163.367 + 94.3202i 0.414638 + 0.239391i
\(395\) 173.351 + 387.753i 0.438863 + 0.981654i
\(396\) 0 0
\(397\) 211.533 56.6800i 0.532828 0.142771i 0.0176340 0.999845i \(-0.494387\pi\)
0.515194 + 0.857074i \(0.327720\pi\)
\(398\) 94.3887 94.3887i 0.237158 0.237158i
\(399\) 0 0
\(400\) 112.990 + 23.6553i 0.282474 + 0.0591382i
\(401\) 248.520 430.449i 0.619750 1.07344i −0.369782 0.929119i \(-0.620567\pi\)
0.989531 0.144319i \(-0.0460992\pi\)
\(402\) 0 0
\(403\) 77.0702 + 20.6509i 0.191241 + 0.0512429i
\(404\) −175.929 101.573i −0.435468 0.251418i
\(405\) 0 0
\(406\) 63.5050 + 55.5749i 0.156416 + 0.136884i
\(407\) −268.820 268.820i −0.660493 0.660493i
\(408\) 0 0
\(409\) −113.088 + 65.2914i −0.276499 + 0.159637i −0.631837 0.775101i \(-0.717699\pi\)
0.355339 + 0.934738i \(0.384366\pi\)
\(410\) 288.838 + 110.367i 0.704482 + 0.269188i
\(411\) 0 0
\(412\) −269.985 269.985i −0.655304 0.655304i
\(413\) −114.953 + 233.717i −0.278335 + 0.565901i
\(414\) 0 0
\(415\) 69.8865 11.1787i 0.168401 0.0269365i
\(416\) −73.0803 126.579i −0.175674 0.304276i
\(417\) 0 0
\(418\) 27.1052 + 101.158i 0.0648450 + 0.242005i
\(419\) 467.512i 1.11578i 0.829915 + 0.557890i \(0.188389\pi\)
−0.829915 + 0.557890i \(0.811611\pi\)
\(420\) 0 0
\(421\) −403.062 −0.957391 −0.478696 0.877981i \(-0.658890\pi\)
−0.478696 + 0.877981i \(0.658890\pi\)
\(422\) 280.384 75.1288i 0.664418 0.178030i
\(423\) 0 0
\(424\) 39.9493 23.0647i 0.0942200 0.0543979i
\(425\) −388.544 + 21.5562i −0.914222 + 0.0507204i
\(426\) 0 0
\(427\) −6.40333 96.1541i −0.0149961 0.225185i
\(428\) 49.6686 49.6686i 0.116048 0.116048i
\(429\) 0 0
\(430\) 218.263 97.5777i 0.507588 0.226925i
\(431\) −185.222 320.815i −0.429750 0.744350i 0.567100 0.823649i \(-0.308065\pi\)
−0.996851 + 0.0792991i \(0.974732\pi\)
\(432\) 0 0
\(433\) 116.395 116.395i 0.268810 0.268810i −0.559811 0.828621i \(-0.689126\pi\)
0.828621 + 0.559811i \(0.189126\pi\)
\(434\) −126.368 24.9987i −0.291170 0.0576007i
\(435\) 0 0
\(436\) −286.037 + 495.431i −0.656048 + 1.13631i
\(437\) −192.814 + 719.593i −0.441223 + 1.64667i
\(438\) 0 0
\(439\) −238.473 137.683i −0.543219 0.313628i 0.203163 0.979145i \(-0.434878\pi\)
−0.746383 + 0.665517i \(0.768211\pi\)
\(440\) 115.795 + 142.548i 0.263170 + 0.323972i
\(441\) 0 0
\(442\) 49.5543 + 49.5543i 0.112114 + 0.112114i
\(443\) −201.380 751.559i −0.454581 1.69652i −0.689315 0.724461i \(-0.742089\pi\)
0.234734 0.972060i \(-0.424578\pi\)
\(444\) 0 0
\(445\) 224.879 + 503.011i 0.505345 + 1.13036i
\(446\) 117.499 203.515i 0.263451 0.456311i
\(447\) 0 0
\(448\) 59.3610 + 88.6391i 0.132502 + 0.197855i
\(449\) 437.111i 0.973521i 0.873536 + 0.486760i \(0.161822\pi\)
−0.873536 + 0.486760i \(0.838178\pi\)
\(450\) 0 0
\(451\) −157.110 272.123i −0.348360 0.603377i
\(452\) 140.236 523.367i 0.310256 1.15789i
\(453\) 0 0
\(454\) 344.275i 0.758315i
\(455\) 113.283 105.261i 0.248974 0.231342i
\(456\) 0 0
\(457\) 161.133 43.1755i 0.352589 0.0944760i −0.0781772 0.996939i \(-0.524910\pi\)
0.430766 + 0.902463i \(0.358243\pi\)
\(458\) 223.207 + 59.8083i 0.487353 + 0.130586i
\(459\) 0 0
\(460\) 87.7835 + 548.803i 0.190834 + 1.19305i
\(461\) 350.553 0.760418 0.380209 0.924901i \(-0.375852\pi\)
0.380209 + 0.924901i \(0.375852\pi\)
\(462\) 0 0
\(463\) 394.302 394.302i 0.851623 0.851623i −0.138710 0.990333i \(-0.544295\pi\)
0.990333 + 0.138710i \(0.0442955\pi\)
\(464\) 47.3098 + 27.3143i 0.101961 + 0.0588670i
\(465\) 0 0
\(466\) 82.2726 + 142.500i 0.176551 + 0.305795i
\(467\) −148.947 + 39.9101i −0.318944 + 0.0854607i −0.414739 0.909940i \(-0.636127\pi\)
0.0957955 + 0.995401i \(0.469461\pi\)
\(468\) 0 0
\(469\) −8.45220 24.8140i −0.0180217 0.0529084i
\(470\) −104.460 10.8174i −0.222254 0.0230158i
\(471\) 0 0
\(472\) 68.3162 254.959i 0.144738 0.540168i
\(473\) −234.681 62.8826i −0.496154 0.132944i
\(474\) 0 0
\(475\) 101.684 485.695i 0.214072 1.02252i
\(476\) 242.838 + 212.514i 0.510165 + 0.446459i
\(477\) 0 0
\(478\) −16.3885 61.1626i −0.0342855 0.127955i
\(479\) −24.0342 + 13.8762i −0.0501758 + 0.0289690i −0.524878 0.851177i \(-0.675889\pi\)
0.474702 + 0.880146i \(0.342556\pi\)
\(480\) 0 0
\(481\) 162.203 280.943i 0.337219 0.584081i
\(482\) −294.298 294.298i −0.610576 0.610576i
\(483\) 0 0
\(484\) 278.958i 0.576360i
\(485\) 33.5110 + 209.503i 0.0690948 + 0.431965i
\(486\) 0 0
\(487\) 7.42611 27.7146i 0.0152487 0.0569089i −0.957882 0.287161i \(-0.907288\pi\)
0.973131 + 0.230252i \(0.0739551\pi\)
\(488\) 25.2765 + 94.3331i 0.0517961 + 0.193306i
\(489\) 0 0
\(490\) −171.196 + 181.718i −0.349380 + 0.370852i
\(491\) −220.188 −0.448449 −0.224224 0.974538i \(-0.571985\pi\)
−0.224224 + 0.974538i \(0.571985\pi\)
\(492\) 0 0
\(493\) −177.876 47.6618i −0.360804 0.0966770i
\(494\) −77.3922 + 44.6824i −0.156664 + 0.0904503i
\(495\) 0 0
\(496\) −83.3890 −0.168123
\(497\) −453.283 + 303.561i −0.912038 + 0.610786i
\(498\) 0 0
\(499\) 523.463 + 302.222i 1.04902 + 0.605654i 0.922376 0.386293i \(-0.126245\pi\)
0.126648 + 0.991948i \(0.459578\pi\)
\(500\) −78.6319 361.754i −0.157264 0.723508i
\(501\) 0 0
\(502\) −104.760 + 28.0703i −0.208684 + 0.0559168i
\(503\) −597.944 + 597.944i −1.18876 + 1.18876i −0.211343 + 0.977412i \(0.567784\pi\)
−0.977412 + 0.211343i \(0.932216\pi\)
\(504\) 0 0
\(505\) −35.3272 + 341.140i −0.0699549 + 0.675525i
\(506\) −99.0130 + 171.496i −0.195678 + 0.338924i
\(507\) 0 0
\(508\) −219.596 58.8406i −0.432276 0.115828i
\(509\) −578.494 333.993i −1.13653 0.656176i −0.190961 0.981598i \(-0.561160\pi\)
−0.945569 + 0.325422i \(0.894494\pi\)
\(510\) 0 0
\(511\) 848.089 288.877i 1.65966 0.565318i
\(512\) 200.665 + 200.665i 0.391924 + 0.391924i
\(513\) 0 0
\(514\) −344.931 + 199.146i −0.671072 + 0.387444i
\(515\) −230.086 + 602.148i −0.446769 + 1.16922i
\(516\) 0 0
\(517\) 75.4635 + 75.4635i 0.145964 + 0.145964i
\(518\) −231.154 + 469.973i −0.446243 + 0.907283i
\(519\) 0 0
\(520\) −91.9199 + 126.925i −0.176769 + 0.244087i
\(521\) −66.0241 114.357i −0.126726 0.219495i 0.795681 0.605717i \(-0.207113\pi\)
−0.922406 + 0.386221i \(0.873780\pi\)
\(522\) 0 0
\(523\) −9.74425 36.3660i −0.0186314 0.0695335i 0.955984 0.293418i \(-0.0947928\pi\)
−0.974616 + 0.223885i \(0.928126\pi\)
\(524\) 54.9659i 0.104897i
\(525\) 0 0
\(526\) −318.923 −0.606318
\(527\) 271.523 72.7543i 0.515224 0.138054i
\(528\) 0 0
\(529\) −761.815 + 439.834i −1.44010 + 0.831445i
\(530\) −26.8336 19.4330i −0.0506294 0.0366661i
\(531\) 0 0
\(532\) −341.906 + 228.972i −0.642681 + 0.430399i
\(533\) 189.596 189.596i 0.355716 0.355716i
\(534\) 0 0
\(535\) −110.776 42.3284i −0.207058 0.0791185i
\(536\) 13.2830 + 23.0068i 0.0247817 + 0.0429232i
\(537\) 0 0
\(538\) 181.515 181.515i 0.337388 0.337388i
\(539\) 251.467 33.6419i 0.466544 0.0624154i
\(540\) 0 0
\(541\) −272.705 + 472.340i −0.504077 + 0.873086i 0.495912 + 0.868373i \(0.334834\pi\)
−0.999989 + 0.00471373i \(0.998500\pi\)
\(542\) 77.2654 288.359i 0.142556 0.532027i
\(543\) 0 0
\(544\) −445.945 257.466i −0.819751 0.473284i
\(545\) 960.679 + 99.4843i 1.76271 + 0.182540i
\(546\) 0 0
\(547\) −470.178 470.178i −0.859558 0.859558i 0.131728 0.991286i \(-0.457948\pi\)
−0.991286 + 0.131728i \(0.957948\pi\)
\(548\) −82.8532 309.212i −0.151192 0.564256i
\(549\) 0 0
\(550\) 59.5229 117.710i 0.108223 0.214018i
\(551\) 117.413 203.365i 0.213090 0.369083i
\(552\) 0 0
\(553\) −593.320 + 39.5119i −1.07291 + 0.0714501i
\(554\) 141.196i 0.254866i
\(555\) 0 0
\(556\) −200.673 347.576i −0.360923 0.625137i
\(557\) 169.860 633.927i 0.304955 1.13811i −0.628028 0.778190i \(-0.716138\pi\)
0.932984 0.359918i \(-0.117195\pi\)
\(558\) 0 0
\(559\) 207.322i 0.370879i
\(560\) −85.8876 + 136.904i −0.153371 + 0.244472i
\(561\) 0 0
\(562\) −125.805 + 33.7092i −0.223851 + 0.0599808i
\(563\) 1076.55 + 288.461i 1.91217 + 0.512364i 0.992936 + 0.118651i \(0.0378570\pi\)
0.919233 + 0.393713i \(0.128810\pi\)
\(564\) 0 0
\(565\) −903.272 + 144.482i −1.59871 + 0.255721i
\(566\) −255.927 −0.452168
\(567\) 0 0
\(568\) 390.934 390.934i 0.688265 0.688265i
\(569\) −401.795 231.976i −0.706142 0.407691i 0.103489 0.994631i \(-0.466999\pi\)
−0.809631 + 0.586939i \(0.800333\pi\)
\(570\) 0 0
\(571\) −457.777 792.892i −0.801710 1.38860i −0.918490 0.395445i \(-0.870590\pi\)
0.116779 0.993158i \(-0.462743\pi\)
\(572\) 65.4421 17.5352i 0.114409 0.0306559i
\(573\) 0 0
\(574\) −285.082 + 325.761i −0.496659 + 0.567528i
\(575\) 785.361 513.446i 1.36584 0.892949i
\(576\) 0 0
\(577\) −127.163 + 474.579i −0.220387 + 0.822495i 0.763814 + 0.645437i \(0.223325\pi\)
−0.984200 + 0.177058i \(0.943342\pi\)
\(578\) −45.9760 12.3192i −0.0795433 0.0213136i
\(579\) 0 0
\(580\) 18.0453 174.256i 0.0311126 0.300441i
\(581\) −19.2288 + 97.2011i −0.0330960 + 0.167300i
\(582\) 0 0
\(583\) 8.71409 + 32.5214i 0.0149470 + 0.0557829i
\(584\) −786.322 + 453.983i −1.34644 + 0.777368i
\(585\) 0 0
\(586\) −15.8504 + 27.4537i −0.0270484 + 0.0468492i
\(587\) −379.329 379.329i −0.646217 0.646217i 0.305860 0.952077i \(-0.401056\pi\)
−0.952077 + 0.305860i \(0.901056\pi\)
\(588\) 0 0
\(589\) 358.454i 0.608580i
\(590\) −187.198 + 29.9432i −0.317285 + 0.0507512i
\(591\) 0 0
\(592\) −87.7506 + 327.490i −0.148227 + 0.553192i
\(593\) 125.542 + 468.530i 0.211707 + 0.790101i 0.987300 + 0.158868i \(0.0507843\pi\)
−0.775593 + 0.631233i \(0.782549\pi\)
\(594\) 0 0
\(595\) 160.214 520.708i 0.269267 0.875140i
\(596\) 118.354 0.198580
\(597\) 0 0
\(598\) −163.221 43.7350i −0.272945 0.0731354i
\(599\) 63.6790 36.7651i 0.106309 0.0613774i −0.445903 0.895081i \(-0.647117\pi\)
0.552212 + 0.833704i \(0.313784\pi\)
\(600\) 0 0
\(601\) 491.594 0.817960 0.408980 0.912543i \(-0.365885\pi\)
0.408980 + 0.912543i \(0.365885\pi\)
\(602\) 22.2409 + 333.975i 0.0369450 + 0.554776i
\(603\) 0 0
\(604\) 102.914 + 59.4173i 0.170387 + 0.0983730i
\(605\) 429.946 192.214i 0.710655 0.317709i
\(606\) 0 0
\(607\) −664.790 + 178.130i −1.09521 + 0.293459i −0.760811 0.648974i \(-0.775199\pi\)
−0.334395 + 0.942433i \(0.608532\pi\)
\(608\) 464.308 464.308i 0.763664 0.763664i
\(609\) 0 0
\(610\) 54.4432 44.2255i 0.0892512 0.0725008i
\(611\) −45.5336 + 78.8665i −0.0745231 + 0.129078i
\(612\) 0 0
\(613\) 349.460 + 93.6376i 0.570082 + 0.152753i 0.532334 0.846534i \(-0.321315\pi\)
0.0377478 + 0.999287i \(0.487982\pi\)
\(614\) 151.806 + 87.6453i 0.247241 + 0.142745i
\(615\) 0 0
\(616\) −243.382 + 82.9013i −0.395101 + 0.134580i
\(617\) −201.236 201.236i −0.326153 0.326153i 0.524969 0.851121i \(-0.324077\pi\)
−0.851121 + 0.524969i \(0.824077\pi\)
\(618\) 0 0
\(619\) 339.835 196.204i 0.549006 0.316969i −0.199715 0.979854i \(-0.564002\pi\)
0.748721 + 0.662885i \(0.230668\pi\)
\(620\) 109.143 + 244.133i 0.176037 + 0.393762i
\(621\) 0 0
\(622\) 434.746 + 434.746i 0.698949 + 0.698949i
\(623\) −769.682 + 51.2566i −1.23545 + 0.0822739i
\(624\) 0 0
\(625\) −503.376 + 370.456i −0.805402 + 0.592730i
\(626\) 111.238 + 192.670i 0.177697 + 0.307780i
\(627\) 0 0
\(628\) −118.336 441.637i −0.188434 0.703244i
\(629\) 1142.90i 1.81701i
\(630\) 0 0
\(631\) −478.217 −0.757872 −0.378936 0.925423i \(-0.623710\pi\)
−0.378936 + 0.925423i \(0.623710\pi\)
\(632\) 582.084 155.969i 0.921019 0.246786i
\(633\) 0 0
\(634\) −8.65163 + 4.99502i −0.0136461 + 0.00787858i
\(635\) 60.6224 + 378.998i 0.0954684 + 0.596847i
\(636\) 0 0
\(637\) 83.2668 + 199.840i 0.130717 + 0.313720i
\(638\) 44.1376 44.1376i 0.0691812 0.0691812i
\(639\) 0 0
\(640\) 208.444 545.509i 0.325693 0.852358i
\(641\) −321.732 557.257i −0.501922 0.869355i −0.999998 0.00222115i \(-0.999293\pi\)
0.498075 0.867134i \(-0.334040\pi\)
\(642\) 0 0
\(643\) 687.066 687.066i 1.06853 1.06853i 0.0710604 0.997472i \(-0.477362\pi\)
0.997472 0.0710604i \(-0.0226383\pi\)
\(644\) −763.299 150.999i −1.18525 0.234471i
\(645\) 0 0
\(646\) −157.419 + 272.658i −0.243682 + 0.422070i
\(647\) 55.6541 207.704i 0.0860187 0.321026i −0.909486 0.415734i \(-0.863525\pi\)
0.995505 + 0.0947073i \(0.0301915\pi\)
\(648\) 0 0
\(649\) 166.842 + 96.3264i 0.257076 + 0.148423i
\(650\) 110.167 + 23.0644i 0.169488 + 0.0354837i
\(651\) 0 0
\(652\) 453.704 + 453.704i 0.695866 + 0.695866i
\(653\) 165.462 + 617.511i 0.253387 + 0.945652i 0.968981 + 0.247136i \(0.0794894\pi\)
−0.715594 + 0.698516i \(0.753844\pi\)
\(654\) 0 0
\(655\) 84.7166 37.8738i 0.129338 0.0578226i
\(656\) −140.114 + 242.684i −0.213588 + 0.369946i
\(657\) 0 0
\(658\) 64.8896 131.931i 0.0986165 0.200503i
\(659\) 929.680i 1.41074i 0.708837 + 0.705372i \(0.249220\pi\)
−0.708837 + 0.705372i \(0.750780\pi\)
\(660\) 0 0
\(661\) 573.316 + 993.012i 0.867346 + 1.50229i 0.864699 + 0.502291i \(0.167509\pi\)
0.00264699 + 0.999996i \(0.499157\pi\)
\(662\) −121.047 + 451.753i −0.182850 + 0.682406i
\(663\) 0 0
\(664\) 100.415i 0.151228i
\(665\) 588.494 + 369.194i 0.884953 + 0.555179i
\(666\) 0 0
\(667\) 428.898 114.923i 0.643026 0.172298i
\(668\) 269.144 + 72.1170i 0.402911 + 0.107960i
\(669\) 0 0
\(670\) 11.1915 15.4535i 0.0167037 0.0230649i
\(671\) −71.2801 −0.106230
\(672\) 0 0
\(673\) −171.530 + 171.530i −0.254874 + 0.254874i −0.822966 0.568091i \(-0.807682\pi\)
0.568091 + 0.822966i \(0.307682\pi\)
\(674\) −93.7701 54.1382i −0.139125 0.0803237i
\(675\) 0 0
\(676\) −221.350 383.389i −0.327440 0.567143i
\(677\) −244.926 + 65.6278i −0.361782 + 0.0969391i −0.435131 0.900367i \(-0.643298\pi\)
0.0733492 + 0.997306i \(0.476631\pi\)
\(678\) 0 0
\(679\) −291.386 57.6433i −0.429140 0.0848945i
\(680\) −56.8706 + 549.176i −0.0836333 + 0.807612i
\(681\) 0 0
\(682\) −24.6609 + 92.0357i −0.0361597 + 0.134950i
\(683\) −900.620 241.320i −1.31862 0.353324i −0.470162 0.882580i \(-0.655804\pi\)
−0.848462 + 0.529256i \(0.822471\pi\)
\(684\) 0 0
\(685\) −419.487 + 340.759i −0.612390 + 0.497458i
\(686\) −155.573 312.990i −0.226783 0.456253i
\(687\) 0 0
\(688\) 56.0798 + 209.293i 0.0815114 + 0.304205i
\(689\) −24.8809 + 14.3650i −0.0361117 + 0.0208491i
\(690\) 0 0
\(691\) −112.934 + 195.607i −0.163435 + 0.283078i −0.936098 0.351738i \(-0.885591\pi\)
0.772663 + 0.634816i \(0.218924\pi\)
\(692\) −445.618 445.618i −0.643956 0.643956i
\(693\) 0 0
\(694\) 8.52106i 0.0122782i
\(695\) −397.433 + 548.784i −0.571846 + 0.789618i
\(696\) 0 0
\(697\) 244.490 912.450i 0.350775 1.30911i
\(698\) −150.654 562.249i −0.215837 0.805514i
\(699\) 0 0
\(700\) 513.220 + 72.2614i 0.733171 + 0.103231i
\(701\) −36.9618 −0.0527273 −0.0263636 0.999652i \(-0.508393\pi\)
−0.0263636 + 0.999652i \(0.508393\pi\)
\(702\) 0 0
\(703\) 1407.74 + 377.203i 2.00247 + 0.536561i
\(704\) 68.3366 39.4541i 0.0970690 0.0560428i
\(705\) 0 0
\(706\) −680.973 −0.964551
\(707\) −430.856 211.914i −0.609414 0.299737i
\(708\) 0 0
\(709\) 903.894 + 521.863i 1.27489 + 0.736055i 0.975903 0.218204i \(-0.0700197\pi\)
0.298982 + 0.954259i \(0.403353\pi\)
\(710\) −370.925 141.733i −0.522429 0.199624i
\(711\) 0 0
\(712\) 755.106 202.330i 1.06054 0.284172i
\(713\) −479.274 + 479.274i −0.672194 + 0.672194i
\(714\) 0 0
\(715\) −72.1186 88.7807i −0.100865 0.124169i
\(716\) −435.526 + 754.353i −0.608277 + 1.05357i
\(717\) 0 0
\(718\) −449.751 120.510i −0.626393 0.167842i
\(719\) 122.057 + 70.4696i 0.169759 + 0.0980106i 0.582472 0.812851i \(-0.302085\pi\)
−0.412713 + 0.910861i \(0.635419\pi\)
\(720\) 0 0
\(721\) −679.123 594.319i −0.941919 0.824298i
\(722\) −23.7659 23.7659i −0.0329167 0.0329167i
\(723\) 0 0
\(724\) 412.270 238.024i 0.569434 0.328763i
\(725\) −281.007 + 92.2573i −0.387597 + 0.127251i
\(726\) 0 0
\(727\) −596.540 596.540i −0.820551 0.820551i 0.165636 0.986187i \(-0.447032\pi\)
−0.986187 + 0.165636i \(0.947032\pi\)
\(728\) −122.083 182.296i −0.167696 0.250407i
\(729\) 0 0
\(730\) 528.165 + 382.500i 0.723514 + 0.523973i
\(731\) −365.203 632.550i −0.499594 0.865322i
\(732\) 0 0
\(733\) −88.6776 330.949i −0.120979 0.451500i 0.878685 0.477401i \(-0.158421\pi\)
−0.999665 + 0.0259012i \(0.991754\pi\)
\(734\) 97.4170i 0.132721i
\(735\) 0 0
\(736\) 1241.61 1.68698
\(737\) −18.7291 + 5.01845i −0.0254126 + 0.00680930i
\(738\) 0 0
\(739\) −781.571 + 451.241i −1.05761 + 0.610610i −0.924769 0.380528i \(-0.875742\pi\)
−0.132838 + 0.991138i \(0.542409\pi\)
\(740\) 1073.62 171.731i 1.45084 0.232069i
\(741\) 0 0
\(742\) 38.5397 25.8098i 0.0519404 0.0347841i
\(743\) 554.070 554.070i 0.745721 0.745721i −0.227952 0.973672i \(-0.573203\pi\)
0.973672 + 0.227952i \(0.0732029\pi\)
\(744\) 0 0
\(745\) −81.5507 182.414i −0.109464 0.244850i
\(746\) −68.1203 117.988i −0.0913140 0.158161i
\(747\) 0 0
\(748\) 168.779 168.779i 0.225640 0.225640i
\(749\) 109.336 124.937i 0.145975 0.166805i
\(750\) 0 0
\(751\) 1.48979 2.58040i 0.00198375 0.00343595i −0.865032 0.501717i \(-0.832702\pi\)
0.867016 + 0.498281i \(0.166035\pi\)
\(752\) 24.6334 91.9331i 0.0327572 0.122251i
\(753\) 0 0
\(754\) 46.1280 + 26.6320i 0.0611777 + 0.0353210i
\(755\) 20.6655 199.558i 0.0273715 0.264315i
\(756\) 0 0
\(757\) −334.049 334.049i −0.441280 0.441280i 0.451162 0.892442i \(-0.351010\pi\)
−0.892442 + 0.451162i \(0.851010\pi\)
\(758\) 107.472 + 401.090i 0.141783 + 0.529143i
\(759\) 0 0
\(760\) −657.665 251.299i −0.865349 0.330657i
\(761\) 381.045 659.989i 0.500716 0.867266i −0.499283 0.866439i \(-0.666403\pi\)
1.00000 0.000827175i \(-0.000263298\pi\)
\(762\) 0 0
\(763\) −596.768 + 1213.33i −0.782134 + 1.59020i
\(764\) 436.117i 0.570834i
\(765\) 0 0
\(766\) −102.514 177.559i −0.133830 0.231800i
\(767\) −42.5482 + 158.792i −0.0554736 + 0.207030i
\(768\) 0 0
\(769\) 903.265i 1.17460i −0.809370 0.587299i \(-0.800191\pi\)
0.809370 0.587299i \(-0.199809\pi\)
\(770\) 125.700 + 135.280i 0.163247 + 0.175689i
\(771\) 0 0
\(772\) 286.486 76.7637i 0.371096 0.0994348i
\(773\) 264.358 + 70.8344i 0.341989 + 0.0916358i 0.425726 0.904852i \(-0.360019\pi\)
−0.0837366 + 0.996488i \(0.526685\pi\)
\(774\) 0 0
\(775\) 301.067 336.436i