Properties

Label 315.3.ca.b.37.14
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 37.14
Character \(\chi\) \(=\) 315.37
Dual form 315.3.ca.b.298.14

$q$-expansion

\(f(q)\) \(=\) \(q+(2.87375 - 0.770020i) q^{2} +(4.20143 - 2.42570i) q^{4} +(-3.78688 - 3.26489i) q^{5} +(-1.65502 - 6.80154i) q^{7} +(1.79111 - 1.79111i) q^{8} +O(q^{10})\) \(q+(2.87375 - 0.770020i) q^{2} +(4.20143 - 2.42570i) q^{4} +(-3.78688 - 3.26489i) q^{5} +(-1.65502 - 6.80154i) q^{7} +(1.79111 - 1.79111i) q^{8} +(-13.3966 - 6.46653i) q^{10} +(-6.96127 - 12.0573i) q^{11} +(7.79302 - 7.79302i) q^{13} +(-9.99344 - 18.2715i) q^{14} +(-5.93477 + 10.2793i) q^{16} +(6.92421 - 25.8415i) q^{17} +(28.5616 + 16.4901i) q^{19} +(-23.8300 - 4.53140i) q^{20} +(-29.2893 - 29.2893i) q^{22} +(5.48688 + 20.4773i) q^{23} +(3.68094 + 24.7275i) q^{25} +(16.3944 - 28.3960i) q^{26} +(-23.4519 - 24.5616i) q^{28} +18.1531i q^{29} +(-11.5772 - 20.0522i) q^{31} +(-11.7622 + 43.8970i) q^{32} -79.5940i q^{34} +(-15.9389 + 31.1601i) q^{35} +(-20.1574 + 5.40117i) q^{37} +(94.7768 + 25.3954i) q^{38} +(-12.6305 + 0.934937i) q^{40} +1.69819 q^{41} +(26.7992 - 26.7992i) q^{43} +(-58.4946 - 33.7719i) q^{44} +(31.5359 + 54.6218i) q^{46} +(10.2827 - 2.75524i) q^{47} +(-43.5218 + 22.5134i) q^{49} +(29.6188 + 68.2264i) q^{50} +(13.8383 - 51.6453i) q^{52} +(43.0869 + 11.5451i) q^{53} +(-13.0042 + 68.3872i) q^{55} +(-15.1466 - 9.21797i) q^{56} +(13.9783 + 52.1677i) q^{58} +(-9.04603 + 5.22273i) q^{59} +(40.5827 - 70.2914i) q^{61} +(-48.7105 - 48.7105i) q^{62} +87.7280i q^{64} +(-54.9546 + 4.06786i) q^{65} +(10.9599 - 40.9029i) q^{67} +(-33.5921 - 125.367i) q^{68} +(-21.8107 + 101.820i) q^{70} +20.1105 q^{71} +(6.28085 + 1.68295i) q^{73} +(-53.7685 + 31.0433i) q^{74} +160.000 q^{76} +(-70.4869 + 67.3023i) q^{77} +(10.5341 + 6.08184i) q^{79} +(56.0352 - 19.5502i) q^{80} +(4.88019 - 1.30764i) q^{82} +(-20.6649 + 20.6649i) q^{83} +(-110.591 + 75.2519i) q^{85} +(56.3783 - 97.6501i) q^{86} +(-34.0643 - 9.12749i) q^{88} +(145.002 + 83.7168i) q^{89} +(-65.9021 - 40.1069i) q^{91} +(72.7245 + 72.7245i) q^{92} +(27.4284 - 15.8358i) q^{94} +(-54.3212 - 155.697i) q^{95} +(-66.3082 - 66.3082i) q^{97} +(-107.735 + 98.2105i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.87375 0.770020i 1.43688 0.385010i 0.545438 0.838151i \(-0.316363\pi\)
0.891439 + 0.453141i \(0.149697\pi\)
\(3\) 0 0
\(4\) 4.20143 2.42570i 1.05036 0.606424i
\(5\) −3.78688 3.26489i −0.757376 0.652979i
\(6\) 0 0
\(7\) −1.65502 6.80154i −0.236431 0.971648i
\(8\) 1.79111 1.79111i 0.223889 0.223889i
\(9\) 0 0
\(10\) −13.3966 6.46653i −1.33966 0.646653i
\(11\) −6.96127 12.0573i −0.632842 1.09612i −0.986968 0.160917i \(-0.948555\pi\)
0.354126 0.935198i \(-0.384779\pi\)
\(12\) 0 0
\(13\) 7.79302 7.79302i 0.599463 0.599463i −0.340707 0.940170i \(-0.610666\pi\)
0.940170 + 0.340707i \(0.110666\pi\)
\(14\) −9.99344 18.2715i −0.713817 1.30511i
\(15\) 0 0
\(16\) −5.93477 + 10.2793i −0.370923 + 0.642458i
\(17\) 6.92421 25.8415i 0.407307 1.52009i −0.392455 0.919771i \(-0.628374\pi\)
0.799761 0.600318i \(-0.204959\pi\)
\(18\) 0 0
\(19\) 28.5616 + 16.4901i 1.50324 + 0.867898i 0.999993 + 0.00375778i \(0.00119614\pi\)
0.503251 + 0.864140i \(0.332137\pi\)
\(20\) −23.8300 4.53140i −1.19150 0.226570i
\(21\) 0 0
\(22\) −29.2893 29.2893i −1.33133 1.33133i
\(23\) 5.48688 + 20.4773i 0.238560 + 0.890318i 0.976512 + 0.215464i \(0.0691265\pi\)
−0.737952 + 0.674854i \(0.764207\pi\)
\(24\) 0 0
\(25\) 3.68094 + 24.7275i 0.147238 + 0.989101i
\(26\) 16.3944 28.3960i 0.630555 1.09215i
\(27\) 0 0
\(28\) −23.4519 24.5616i −0.837569 0.877201i
\(29\) 18.1531i 0.625971i 0.949758 + 0.312985i \(0.101329\pi\)
−0.949758 + 0.312985i \(0.898671\pi\)
\(30\) 0 0
\(31\) −11.5772 20.0522i −0.373457 0.646846i 0.616638 0.787247i \(-0.288494\pi\)
−0.990095 + 0.140401i \(0.955161\pi\)
\(32\) −11.7622 + 43.8970i −0.367567 + 1.37178i
\(33\) 0 0
\(34\) 79.5940i 2.34100i
\(35\) −15.9389 + 31.1601i −0.455398 + 0.890288i
\(36\) 0 0
\(37\) −20.1574 + 5.40117i −0.544796 + 0.145978i −0.520712 0.853732i \(-0.674333\pi\)
−0.0240837 + 0.999710i \(0.507667\pi\)
\(38\) 94.7768 + 25.3954i 2.49413 + 0.668299i
\(39\) 0 0
\(40\) −12.6305 + 0.934937i −0.315762 + 0.0233734i
\(41\) 1.69819 0.0414193 0.0207097 0.999786i \(-0.493407\pi\)
0.0207097 + 0.999786i \(0.493407\pi\)
\(42\) 0 0
\(43\) 26.7992 26.7992i 0.623236 0.623236i −0.323121 0.946358i \(-0.604732\pi\)
0.946358 + 0.323121i \(0.104732\pi\)
\(44\) −58.4946 33.7719i −1.32942 0.767542i
\(45\) 0 0
\(46\) 31.5359 + 54.6218i 0.685563 + 1.18743i
\(47\) 10.2827 2.75524i 0.218781 0.0586222i −0.147763 0.989023i \(-0.547207\pi\)
0.366544 + 0.930401i \(0.380541\pi\)
\(48\) 0 0
\(49\) −43.5218 + 22.5134i −0.888200 + 0.459456i
\(50\) 29.6188 + 68.2264i 0.592376 + 1.36453i
\(51\) 0 0
\(52\) 13.8383 51.6453i 0.266122 0.993179i
\(53\) 43.0869 + 11.5451i 0.812961 + 0.217832i 0.641267 0.767318i \(-0.278409\pi\)
0.171694 + 0.985150i \(0.445076\pi\)
\(54\) 0 0
\(55\) −13.0042 + 68.3872i −0.236440 + 1.24340i
\(56\) −15.1466 9.21797i −0.270475 0.164607i
\(57\) 0 0
\(58\) 13.9783 + 52.1677i 0.241005 + 0.899443i
\(59\) −9.04603 + 5.22273i −0.153323 + 0.0885208i −0.574698 0.818365i \(-0.694881\pi\)
0.421376 + 0.906886i \(0.361547\pi\)
\(60\) 0 0
\(61\) 40.5827 70.2914i 0.665291 1.15232i −0.313915 0.949451i \(-0.601641\pi\)
0.979206 0.202867i \(-0.0650258\pi\)
\(62\) −48.7105 48.7105i −0.785654 0.785654i
\(63\) 0 0
\(64\) 87.7280i 1.37075i
\(65\) −54.9546 + 4.06786i −0.845455 + 0.0625825i
\(66\) 0 0
\(67\) 10.9599 40.9029i 0.163581 0.610491i −0.834636 0.550801i \(-0.814322\pi\)
0.998217 0.0596898i \(-0.0190112\pi\)
\(68\) −33.5921 125.367i −0.494001 1.84364i
\(69\) 0 0
\(70\) −21.8107 + 101.820i −0.311581 + 1.45457i
\(71\) 20.1105 0.283247 0.141623 0.989921i \(-0.454768\pi\)
0.141623 + 0.989921i \(0.454768\pi\)
\(72\) 0 0
\(73\) 6.28085 + 1.68295i 0.0860390 + 0.0230541i 0.301582 0.953440i \(-0.402485\pi\)
−0.215543 + 0.976494i \(0.569152\pi\)
\(74\) −53.7685 + 31.0433i −0.726602 + 0.419504i
\(75\) 0 0
\(76\) 160.000 2.10526
\(77\) −70.4869 + 67.3023i −0.915415 + 0.874056i
\(78\) 0 0
\(79\) 10.5341 + 6.08184i 0.133342 + 0.0769853i 0.565187 0.824963i \(-0.308804\pi\)
−0.431845 + 0.901948i \(0.642137\pi\)
\(80\) 56.0352 19.5502i 0.700440 0.244377i
\(81\) 0 0
\(82\) 4.88019 1.30764i 0.0595145 0.0159469i
\(83\) −20.6649 + 20.6649i −0.248975 + 0.248975i −0.820550 0.571575i \(-0.806333\pi\)
0.571575 + 0.820550i \(0.306333\pi\)
\(84\) 0 0
\(85\) −110.591 + 75.2519i −1.30107 + 0.885317i
\(86\) 56.3783 97.6501i 0.655562 1.13547i
\(87\) 0 0
\(88\) −34.0643 9.12749i −0.387094 0.103721i
\(89\) 145.002 + 83.7168i 1.62923 + 0.940638i 0.984322 + 0.176381i \(0.0564390\pi\)
0.644911 + 0.764257i \(0.276894\pi\)
\(90\) 0 0
\(91\) −65.9021 40.1069i −0.724199 0.440735i
\(92\) 72.7245 + 72.7245i 0.790484 + 0.790484i
\(93\) 0 0
\(94\) 27.4284 15.8358i 0.291791 0.168466i
\(95\) −54.3212 155.697i −0.571802 1.63891i
\(96\) 0 0
\(97\) −66.3082 66.3082i −0.683589 0.683589i 0.277218 0.960807i \(-0.410588\pi\)
−0.960807 + 0.277218i \(0.910588\pi\)
\(98\) −107.735 + 98.2105i −1.09934 + 1.00215i
\(99\) 0 0
\(100\) 75.4467 + 94.9622i 0.754467 + 0.949622i
\(101\) 22.9150 + 39.6899i 0.226881 + 0.392969i 0.956882 0.290477i \(-0.0938138\pi\)
−0.730001 + 0.683446i \(0.760481\pi\)
\(102\) 0 0
\(103\) 5.67468 + 21.1782i 0.0550940 + 0.205614i 0.987986 0.154542i \(-0.0493902\pi\)
−0.932892 + 0.360156i \(0.882724\pi\)
\(104\) 27.9163i 0.268426i
\(105\) 0 0
\(106\) 132.711 1.25199
\(107\) 97.5490 26.1382i 0.911673 0.244282i 0.227650 0.973743i \(-0.426896\pi\)
0.684022 + 0.729461i \(0.260229\pi\)
\(108\) 0 0
\(109\) −109.890 + 63.4449i −1.00816 + 0.582064i −0.910654 0.413171i \(-0.864421\pi\)
−0.0975104 + 0.995235i \(0.531088\pi\)
\(110\) 15.2887 + 206.542i 0.138988 + 1.87765i
\(111\) 0 0
\(112\) 79.7374 + 23.3531i 0.711941 + 0.208510i
\(113\) 10.2422 10.2422i 0.0906391 0.0906391i −0.660333 0.750973i \(-0.729585\pi\)
0.750973 + 0.660333i \(0.229585\pi\)
\(114\) 0 0
\(115\) 46.0781 95.4592i 0.400679 0.830080i
\(116\) 44.0340 + 76.2692i 0.379604 + 0.657493i
\(117\) 0 0
\(118\) −21.9745 + 21.9745i −0.186224 + 0.186224i
\(119\) −187.222 4.32709i −1.57329 0.0363621i
\(120\) 0 0
\(121\) −36.4184 + 63.0786i −0.300979 + 0.521311i
\(122\) 62.4991 233.250i 0.512287 1.91188i
\(123\) 0 0
\(124\) −97.2812 56.1654i −0.784526 0.452946i
\(125\) 66.7935 105.658i 0.534348 0.845265i
\(126\) 0 0
\(127\) 138.223 + 138.223i 1.08837 + 1.08837i 0.995697 + 0.0926732i \(0.0295412\pi\)
0.0926732 + 0.995697i \(0.470459\pi\)
\(128\) 20.5037 + 76.5208i 0.160185 + 0.597819i
\(129\) 0 0
\(130\) −154.794 + 54.0062i −1.19072 + 0.415432i
\(131\) −11.0263 + 19.0981i −0.0841704 + 0.145787i −0.905037 0.425332i \(-0.860157\pi\)
0.820867 + 0.571119i \(0.193491\pi\)
\(132\) 0 0
\(133\) 64.8877 221.554i 0.487878 1.66582i
\(134\) 125.984i 0.940181i
\(135\) 0 0
\(136\) −33.8829 58.6870i −0.249139 0.431522i
\(137\) 55.4894 207.089i 0.405032 1.51160i −0.398965 0.916966i \(-0.630630\pi\)
0.803997 0.594634i \(-0.202703\pi\)
\(138\) 0 0
\(139\) 203.695i 1.46543i −0.680534 0.732716i \(-0.738252\pi\)
0.680534 0.732716i \(-0.261748\pi\)
\(140\) 8.61859 + 169.580i 0.0615613 + 1.21129i
\(141\) 0 0
\(142\) 57.7926 15.4855i 0.406990 0.109053i
\(143\) −148.212 39.7132i −1.03645 0.277715i
\(144\) 0 0
\(145\) 59.2681 68.7438i 0.408745 0.474095i
\(146\) 19.3455 0.132504
\(147\) 0 0
\(148\) −71.5885 + 71.5885i −0.483706 + 0.483706i
\(149\) −106.635 61.5658i −0.715672 0.413193i 0.0974859 0.995237i \(-0.468920\pi\)
−0.813157 + 0.582044i \(0.802253\pi\)
\(150\) 0 0
\(151\) −50.6434 87.7170i −0.335387 0.580907i 0.648172 0.761494i \(-0.275534\pi\)
−0.983559 + 0.180587i \(0.942200\pi\)
\(152\) 80.6925 21.6215i 0.530872 0.142247i
\(153\) 0 0
\(154\) −150.738 + 247.687i −0.978818 + 1.60836i
\(155\) −21.6271 + 113.734i −0.139529 + 0.733765i
\(156\) 0 0
\(157\) −18.7602 + 70.0141i −0.119492 + 0.445950i −0.999584 0.0288540i \(-0.990814\pi\)
0.880092 + 0.474804i \(0.157481\pi\)
\(158\) 34.9554 + 9.36628i 0.221237 + 0.0592802i
\(159\) 0 0
\(160\) 187.861 127.830i 1.17413 0.798940i
\(161\) 130.196 71.2096i 0.808673 0.442295i
\(162\) 0 0
\(163\) 47.1369 + 175.917i 0.289183 + 1.07925i 0.945728 + 0.324960i \(0.105351\pi\)
−0.656545 + 0.754287i \(0.727983\pi\)
\(164\) 7.13484 4.11930i 0.0435051 0.0251177i
\(165\) 0 0
\(166\) −43.4735 + 75.2984i −0.261889 + 0.453605i
\(167\) 188.951 + 188.951i 1.13144 + 1.13144i 0.989938 + 0.141505i \(0.0451940\pi\)
0.141505 + 0.989938i \(0.454806\pi\)
\(168\) 0 0
\(169\) 47.5377i 0.281288i
\(170\) −259.866 + 301.413i −1.52862 + 1.77302i
\(171\) 0 0
\(172\) 47.5882 177.601i 0.276675 1.03257i
\(173\) 2.36194 + 8.81487i 0.0136528 + 0.0509530i 0.972416 0.233253i \(-0.0749369\pi\)
−0.958763 + 0.284206i \(0.908270\pi\)
\(174\) 0 0
\(175\) 162.093 65.9606i 0.926247 0.376918i
\(176\) 165.254 0.938944
\(177\) 0 0
\(178\) 481.163 + 128.927i 2.70316 + 0.724310i
\(179\) −232.008 + 133.950i −1.29613 + 0.748322i −0.979734 0.200304i \(-0.935807\pi\)
−0.316398 + 0.948626i \(0.602474\pi\)
\(180\) 0 0
\(181\) −226.975 −1.25401 −0.627004 0.779016i \(-0.715719\pi\)
−0.627004 + 0.779016i \(0.715719\pi\)
\(182\) −220.270 64.5115i −1.21027 0.354459i
\(183\) 0 0
\(184\) 46.5047 + 26.8495i 0.252743 + 0.145921i
\(185\) 93.9681 + 45.3583i 0.507936 + 0.245180i
\(186\) 0 0
\(187\) −359.779 + 96.4026i −1.92395 + 0.515522i
\(188\) 36.5187 36.5187i 0.194248 0.194248i
\(189\) 0 0
\(190\) −275.995 405.605i −1.45261 2.13477i
\(191\) −77.8090 + 134.769i −0.407377 + 0.705597i −0.994595 0.103831i \(-0.966890\pi\)
0.587218 + 0.809429i \(0.300223\pi\)
\(192\) 0 0
\(193\) −203.169 54.4390i −1.05269 0.282067i −0.309327 0.950956i \(-0.600104\pi\)
−0.743363 + 0.668889i \(0.766770\pi\)
\(194\) −241.612 139.495i −1.24542 0.719045i
\(195\) 0 0
\(196\) −128.243 + 200.159i −0.654303 + 1.02122i
\(197\) 98.6199 + 98.6199i 0.500609 + 0.500609i 0.911627 0.411018i \(-0.134827\pi\)
−0.411018 + 0.911627i \(0.634827\pi\)
\(198\) 0 0
\(199\) −35.8210 + 20.6813i −0.180005 + 0.103926i −0.587295 0.809373i \(-0.699807\pi\)
0.407290 + 0.913299i \(0.366474\pi\)
\(200\) 50.8826 + 37.6967i 0.254413 + 0.188484i
\(201\) 0 0
\(202\) 96.4140 + 96.4140i 0.477297 + 0.477297i
\(203\) 123.469 30.0438i 0.608223 0.147999i
\(204\) 0 0
\(205\) −6.43085 5.54442i −0.0313700 0.0270459i
\(206\) 32.6153 + 56.4913i 0.158327 + 0.274230i
\(207\) 0 0
\(208\) 33.8572 + 126.357i 0.162775 + 0.607485i
\(209\) 459.167i 2.19697i
\(210\) 0 0
\(211\) 326.483 1.54731 0.773655 0.633607i \(-0.218426\pi\)
0.773655 + 0.633607i \(0.218426\pi\)
\(212\) 209.032 56.0099i 0.985999 0.264198i
\(213\) 0 0
\(214\) 260.205 150.229i 1.21591 0.702006i
\(215\) −188.982 + 13.9888i −0.878984 + 0.0650644i
\(216\) 0 0
\(217\) −117.226 + 111.929i −0.540210 + 0.515803i
\(218\) −266.943 + 266.943i −1.22451 + 1.22451i
\(219\) 0 0
\(220\) 111.250 + 318.868i 0.505684 + 1.44940i
\(221\) −147.423 255.344i −0.667072 1.15540i
\(222\) 0 0
\(223\) −39.2007 + 39.2007i −0.175788 + 0.175788i −0.789517 0.613729i \(-0.789669\pi\)
0.613729 + 0.789517i \(0.289669\pi\)
\(224\) 318.033 + 7.35042i 1.41979 + 0.0328144i
\(225\) 0 0
\(226\) 21.5469 37.3203i 0.0953403 0.165134i
\(227\) −0.933082 + 3.48231i −0.00411049 + 0.0153406i −0.967951 0.251141i \(-0.919194\pi\)
0.963840 + 0.266481i \(0.0858610\pi\)
\(228\) 0 0
\(229\) −46.0053 26.5612i −0.200896 0.115988i 0.396177 0.918174i \(-0.370337\pi\)
−0.597074 + 0.802186i \(0.703670\pi\)
\(230\) 58.9116 309.807i 0.256137 1.34699i
\(231\) 0 0
\(232\) 32.5143 + 32.5143i 0.140148 + 0.140148i
\(233\) 33.4506 + 124.839i 0.143565 + 0.535791i 0.999815 + 0.0192298i \(0.00612140\pi\)
−0.856250 + 0.516561i \(0.827212\pi\)
\(234\) 0 0
\(235\) −47.9350 23.1382i −0.203979 0.0984603i
\(236\) −25.3375 + 43.8859i −0.107362 + 0.185957i
\(237\) 0 0
\(238\) −541.361 + 131.730i −2.27463 + 0.553485i
\(239\) 365.148i 1.52782i −0.645325 0.763908i \(-0.723278\pi\)
0.645325 0.763908i \(-0.276722\pi\)
\(240\) 0 0
\(241\) −196.782 340.837i −0.816525 1.41426i −0.908228 0.418476i \(-0.862564\pi\)
0.0917031 0.995786i \(-0.470769\pi\)
\(242\) −56.0859 + 209.315i −0.231760 + 0.864939i
\(243\) 0 0
\(244\) 393.766i 1.61379i
\(245\) 238.316 + 56.8387i 0.972717 + 0.231995i
\(246\) 0 0
\(247\) 351.089 94.0739i 1.42141 0.380866i
\(248\) −56.6516 15.1798i −0.228434 0.0612087i
\(249\) 0 0
\(250\) 110.589 355.068i 0.442357 1.42027i
\(251\) −353.349 −1.40777 −0.703883 0.710316i \(-0.748552\pi\)
−0.703883 + 0.710316i \(0.748552\pi\)
\(252\) 0 0
\(253\) 208.705 208.705i 0.824920 0.824920i
\(254\) 503.653 + 290.784i 1.98289 + 1.14482i
\(255\) 0 0
\(256\) −57.6108 99.7848i −0.225042 0.389784i
\(257\) −54.4792 + 14.5977i −0.211981 + 0.0568002i −0.363247 0.931693i \(-0.618332\pi\)
0.151266 + 0.988493i \(0.451665\pi\)
\(258\) 0 0
\(259\) 70.0972 + 128.163i 0.270646 + 0.494836i
\(260\) −221.021 + 150.394i −0.850079 + 0.578439i
\(261\) 0 0
\(262\) −16.9810 + 63.3739i −0.0648129 + 0.241885i
\(263\) 274.512 + 73.5553i 1.04377 + 0.279678i 0.739676 0.672963i \(-0.234979\pi\)
0.304097 + 0.952641i \(0.401645\pi\)
\(264\) 0 0
\(265\) −125.472 184.394i −0.473477 0.695827i
\(266\) 15.8701 686.658i 0.0596620 2.58142i
\(267\) 0 0
\(268\) −53.1708 198.436i −0.198399 0.740433i
\(269\) −228.544 + 131.950i −0.849607 + 0.490521i −0.860518 0.509419i \(-0.829860\pi\)
0.0109111 + 0.999940i \(0.496527\pi\)
\(270\) 0 0
\(271\) 50.4495 87.3810i 0.186160 0.322439i −0.757807 0.652479i \(-0.773729\pi\)
0.943967 + 0.330040i \(0.107062\pi\)
\(272\) 224.540 + 224.540i 0.825514 + 0.825514i
\(273\) 0 0
\(274\) 637.851i 2.32792i
\(275\) 272.522 216.517i 0.990991 0.787334i
\(276\) 0 0
\(277\) −67.8808 + 253.335i −0.245057 + 0.914566i 0.728297 + 0.685261i \(0.240312\pi\)
−0.973355 + 0.229305i \(0.926355\pi\)
\(278\) −156.849 585.370i −0.564206 2.10565i
\(279\) 0 0
\(280\) 27.2627 + 84.3594i 0.0973669 + 0.301284i
\(281\) −394.591 −1.40424 −0.702119 0.712060i \(-0.747762\pi\)
−0.702119 + 0.712060i \(0.747762\pi\)
\(282\) 0 0
\(283\) 295.210 + 79.1013i 1.04315 + 0.279510i 0.739416 0.673249i \(-0.235102\pi\)
0.303729 + 0.952758i \(0.401768\pi\)
\(284\) 84.4929 48.7820i 0.297510 0.171768i
\(285\) 0 0
\(286\) −456.504 −1.59617
\(287\) −2.81054 11.5503i −0.00979282 0.0402450i
\(288\) 0 0
\(289\) −369.558 213.364i −1.27875 0.738285i
\(290\) 117.388 243.190i 0.404786 0.838588i
\(291\) 0 0
\(292\) 30.4709 8.16464i 0.104352 0.0279611i
\(293\) −232.731 + 232.731i −0.794304 + 0.794304i −0.982191 0.187887i \(-0.939836\pi\)
0.187887 + 0.982191i \(0.439836\pi\)
\(294\) 0 0
\(295\) 51.3079 + 9.75647i 0.173925 + 0.0330728i
\(296\) −26.4301 + 45.7782i −0.0892908 + 0.154656i
\(297\) 0 0
\(298\) −353.850 94.8138i −1.18742 0.318167i
\(299\) 202.339 + 116.821i 0.676720 + 0.390705i
\(300\) 0 0
\(301\) −226.629 137.922i −0.752919 0.458214i
\(302\) −213.081 213.081i −0.705565 0.705565i
\(303\) 0 0
\(304\) −339.014 + 195.730i −1.11518 + 0.643847i
\(305\) −383.176 + 133.687i −1.25631 + 0.438317i
\(306\) 0 0
\(307\) 192.175 + 192.175i 0.625976 + 0.625976i 0.947053 0.321077i \(-0.104045\pi\)
−0.321077 + 0.947053i \(0.604045\pi\)
\(308\) −132.891 + 453.746i −0.431464 + 1.47320i
\(309\) 0 0
\(310\) 25.4263 + 343.496i 0.0820203 + 1.10805i
\(311\) −69.8332 120.955i −0.224544 0.388922i 0.731638 0.681693i \(-0.238756\pi\)
−0.956183 + 0.292771i \(0.905423\pi\)
\(312\) 0 0
\(313\) 12.6561 + 47.2333i 0.0404349 + 0.150905i 0.983192 0.182576i \(-0.0584434\pi\)
−0.942757 + 0.333481i \(0.891777\pi\)
\(314\) 215.649i 0.686780i
\(315\) 0 0
\(316\) 59.0108 0.186743
\(317\) −288.036 + 77.1789i −0.908630 + 0.243467i −0.682719 0.730681i \(-0.739203\pi\)
−0.225911 + 0.974148i \(0.572536\pi\)
\(318\) 0 0
\(319\) 218.877 126.369i 0.686136 0.396141i
\(320\) 286.423 332.215i 0.895070 1.03817i
\(321\) 0 0
\(322\) 319.319 304.893i 0.991675 0.946871i
\(323\) 623.895 623.895i 1.93156 1.93156i
\(324\) 0 0
\(325\) 221.388 + 164.016i 0.681193 + 0.504666i
\(326\) 270.920 + 469.247i 0.831042 + 1.43941i
\(327\) 0 0
\(328\) 3.04165 3.04165i 0.00927331 0.00927331i
\(329\) −35.7580 65.3782i −0.108687 0.198718i
\(330\) 0 0
\(331\) −43.7659 + 75.8048i −0.132223 + 0.229018i −0.924533 0.381101i \(-0.875545\pi\)
0.792310 + 0.610119i \(0.208878\pi\)
\(332\) −36.6954 + 136.949i −0.110528 + 0.412498i
\(333\) 0 0
\(334\) 688.494 + 397.502i 2.06136 + 1.19013i
\(335\) −175.047 + 119.112i −0.522530 + 0.355557i
\(336\) 0 0
\(337\) 170.978 + 170.978i 0.507354 + 0.507354i 0.913713 0.406359i \(-0.133202\pi\)
−0.406359 + 0.913713i \(0.633202\pi\)
\(338\) 36.6050 + 136.612i 0.108299 + 0.404177i
\(339\) 0 0
\(340\) −282.102 + 584.426i −0.829712 + 1.71890i
\(341\) −161.183 + 279.178i −0.472678 + 0.818703i
\(342\) 0 0
\(343\) 225.155 + 258.755i 0.656428 + 0.754389i
\(344\) 96.0004i 0.279071i
\(345\) 0 0
\(346\) 13.5753 + 23.5130i 0.0392348 + 0.0679567i
\(347\) 17.2634 64.4278i 0.0497504 0.185671i −0.936579 0.350456i \(-0.886026\pi\)
0.986329 + 0.164785i \(0.0526932\pi\)
\(348\) 0 0
\(349\) 445.265i 1.27583i 0.770106 + 0.637915i \(0.220203\pi\)
−0.770106 + 0.637915i \(0.779797\pi\)
\(350\) 415.025 314.370i 1.18579 0.898199i
\(351\) 0 0
\(352\) 611.157 163.759i 1.73624 0.465224i
\(353\) 357.784 + 95.8678i 1.01355 + 0.271580i 0.727112 0.686518i \(-0.240862\pi\)
0.286439 + 0.958099i \(0.407529\pi\)
\(354\) 0 0
\(355\) −76.1561 65.6587i −0.214524 0.184954i
\(356\) 812.287 2.28170
\(357\) 0 0
\(358\) −563.589 + 563.589i −1.57427 + 1.57427i
\(359\) 507.313 + 292.897i 1.41313 + 0.815870i 0.995682 0.0928320i \(-0.0295919\pi\)
0.417446 + 0.908702i \(0.362925\pi\)
\(360\) 0 0
\(361\) 363.345 + 629.331i 1.00649 + 1.74330i
\(362\) −652.272 + 174.776i −1.80186 + 0.482806i
\(363\) 0 0
\(364\) −374.170 8.64786i −1.02794 0.0237579i
\(365\) −18.2902 26.8794i −0.0501101 0.0736422i
\(366\) 0 0
\(367\) 78.0318 291.219i 0.212621 0.793511i −0.774370 0.632733i \(-0.781933\pi\)
0.986991 0.160778i \(-0.0514003\pi\)
\(368\) −243.056 65.1268i −0.660479 0.176975i
\(369\) 0 0
\(370\) 304.968 + 57.9913i 0.824238 + 0.156733i
\(371\) 7.21478 312.165i 0.0194469 0.841414i
\(372\) 0 0
\(373\) 136.663 + 510.035i 0.366390 + 1.36739i 0.865527 + 0.500862i \(0.166984\pi\)
−0.499137 + 0.866523i \(0.666350\pi\)
\(374\) −959.686 + 554.075i −2.56600 + 1.48148i
\(375\) 0 0
\(376\) 13.4825 23.3524i 0.0358577 0.0621074i
\(377\) 141.468 + 141.468i 0.375246 + 0.375246i
\(378\) 0 0
\(379\) 177.062i 0.467182i 0.972335 + 0.233591i \(0.0750476\pi\)
−0.972335 + 0.233591i \(0.924952\pi\)
\(380\) −605.900 522.382i −1.59447 1.37469i
\(381\) 0 0
\(382\) −119.829 + 447.208i −0.313688 + 1.17070i
\(383\) 69.8407 + 260.649i 0.182352 + 0.680545i 0.995182 + 0.0980450i \(0.0312589\pi\)
−0.812830 + 0.582500i \(0.802074\pi\)
\(384\) 0 0
\(385\) 486.661 24.7336i 1.26405 0.0642432i
\(386\) −625.777 −1.62118
\(387\) 0 0
\(388\) −439.433 117.746i −1.13256 0.303468i
\(389\) −161.408 + 93.1891i −0.414931 + 0.239561i −0.692906 0.721028i \(-0.743670\pi\)
0.277975 + 0.960588i \(0.410337\pi\)
\(390\) 0 0
\(391\) 567.157 1.45053
\(392\) −37.6284 + 118.276i −0.0959909 + 0.301725i
\(393\) 0 0
\(394\) 359.349 + 207.470i 0.912053 + 0.526574i
\(395\) −20.0347 57.4238i −0.0507206 0.145377i
\(396\) 0 0
\(397\) −659.091 + 176.603i −1.66018 + 0.444844i −0.962437 0.271506i \(-0.912478\pi\)
−0.697742 + 0.716349i \(0.745812\pi\)
\(398\) −87.0158 + 87.0158i −0.218633 + 0.218633i
\(399\) 0 0
\(400\) −276.028 108.915i −0.690070 0.272287i
\(401\) −63.9305 + 110.731i −0.159428 + 0.276137i −0.934662 0.355536i \(-0.884298\pi\)
0.775235 + 0.631673i \(0.217632\pi\)
\(402\) 0 0
\(403\) −246.488 66.0463i −0.611634 0.163887i
\(404\) 192.551 + 111.170i 0.476612 + 0.275172i
\(405\) 0 0
\(406\) 331.686 181.412i 0.816961 0.446829i
\(407\) 205.445 + 205.445i 0.504778 + 0.504778i
\(408\) 0 0
\(409\) 67.5742 39.0140i 0.165218 0.0953887i −0.415111 0.909771i \(-0.636257\pi\)
0.580329 + 0.814382i \(0.302924\pi\)
\(410\) −22.7500 10.9814i −0.0554878 0.0267839i
\(411\) 0 0
\(412\) 75.2137 + 75.2137i 0.182558 + 0.182558i
\(413\) 50.4939 + 52.8832i 0.122261 + 0.128046i
\(414\) 0 0
\(415\) 145.725 10.7868i 0.351143 0.0259924i
\(416\) 250.427 + 433.752i 0.601988 + 1.04267i
\(417\) 0 0
\(418\) −353.568 1319.53i −0.845856 3.15678i
\(419\) 38.0855i 0.0908962i 0.998967 + 0.0454481i \(0.0144716\pi\)
−0.998967 + 0.0454481i \(0.985528\pi\)
\(420\) 0 0
\(421\) −151.613 −0.360126 −0.180063 0.983655i \(-0.557630\pi\)
−0.180063 + 0.983655i \(0.557630\pi\)
\(422\) 938.231 251.398i 2.22330 0.595730i
\(423\) 0 0
\(424\) 97.8519 56.4948i 0.230783 0.133242i
\(425\) 664.484 + 76.0976i 1.56349 + 0.179053i
\(426\) 0 0
\(427\) −545.255 159.691i −1.27694 0.373985i
\(428\) 346.442 346.442i 0.809444 0.809444i
\(429\) 0 0
\(430\) −532.315 + 185.720i −1.23794 + 0.431907i
\(431\) 268.299 + 464.707i 0.622503 + 1.07821i 0.989018 + 0.147795i \(0.0472175\pi\)
−0.366515 + 0.930412i \(0.619449\pi\)
\(432\) 0 0
\(433\) 421.429 421.429i 0.973278 0.973278i −0.0263739 0.999652i \(-0.508396\pi\)
0.999652 + 0.0263739i \(0.00839605\pi\)
\(434\) −250.690 + 411.923i −0.577626 + 0.949132i
\(435\) 0 0
\(436\) −307.796 + 533.119i −0.705955 + 1.22275i
\(437\) −180.958 + 675.344i −0.414092 + 1.54541i
\(438\) 0 0
\(439\) 411.292 + 237.460i 0.936884 + 0.540910i 0.888982 0.457942i \(-0.151413\pi\)
0.0479017 + 0.998852i \(0.484747\pi\)
\(440\) 99.1970 + 145.781i 0.225448 + 0.331320i
\(441\) 0 0
\(442\) −620.277 620.277i −1.40334 1.40334i
\(443\) −24.3833 90.9998i −0.0550414 0.205417i 0.932929 0.360060i \(-0.117244\pi\)
−0.987970 + 0.154643i \(0.950577\pi\)
\(444\) 0 0
\(445\) −275.778 790.441i −0.619726 1.77627i
\(446\) −82.4678 + 142.839i −0.184905 + 0.320266i
\(447\) 0 0
\(448\) 596.685 145.192i 1.33189 0.324088i
\(449\) 521.631i 1.16176i −0.813989 0.580881i \(-0.802708\pi\)
0.813989 0.580881i \(-0.197292\pi\)
\(450\) 0 0
\(451\) −11.8216 20.4756i −0.0262119 0.0454003i
\(452\) 18.1875 67.8765i 0.0402377 0.150169i
\(453\) 0 0
\(454\) 10.7258i 0.0236251i
\(455\) 118.619 + 367.043i 0.260700 + 0.806689i
\(456\) 0 0
\(457\) 401.339 107.539i 0.878204 0.235314i 0.208572 0.978007i \(-0.433118\pi\)
0.669632 + 0.742693i \(0.266452\pi\)
\(458\) −152.661 40.9053i −0.333320 0.0893128i
\(459\) 0 0
\(460\) −37.9613 512.837i −0.0825246 1.11486i
\(461\) −280.539 −0.608544 −0.304272 0.952585i \(-0.598413\pi\)
−0.304272 + 0.952585i \(0.598413\pi\)
\(462\) 0 0
\(463\) −326.436 + 326.436i −0.705045 + 0.705045i −0.965489 0.260444i \(-0.916131\pi\)
0.260444 + 0.965489i \(0.416131\pi\)
\(464\) −186.602 107.735i −0.402160 0.232187i
\(465\) 0 0
\(466\) 192.257 + 333.000i 0.412570 + 0.714592i
\(467\) 410.520 109.999i 0.879058 0.235543i 0.209057 0.977903i \(-0.432960\pi\)
0.670001 + 0.742360i \(0.266294\pi\)
\(468\) 0 0
\(469\) −296.342 6.84907i −0.631858 0.0146036i
\(470\) −155.570 29.5825i −0.331000 0.0629415i
\(471\) 0 0
\(472\) −6.84795 + 25.5569i −0.0145084 + 0.0541459i
\(473\) −509.681 136.569i −1.07755 0.288728i
\(474\) 0 0
\(475\) −302.625 + 766.958i −0.637105 + 1.61465i
\(476\) −797.096 + 435.963i −1.67457 + 0.915889i
\(477\) 0 0
\(478\) −281.171 1049.35i −0.588225 2.19529i
\(479\) 183.280 105.817i 0.382630 0.220912i −0.296332 0.955085i \(-0.595763\pi\)
0.678962 + 0.734173i \(0.262430\pi\)
\(480\) 0 0
\(481\) −114.996 + 199.179i −0.239077 + 0.414093i
\(482\) −827.956 827.956i −1.71775 1.71775i
\(483\) 0 0
\(484\) 353.361i 0.730084i
\(485\) 34.6121 + 467.590i 0.0713651 + 0.964104i
\(486\) 0 0
\(487\) 12.4096 46.3134i 0.0254818 0.0950993i −0.952014 0.306055i \(-0.900991\pi\)
0.977496 + 0.210956i \(0.0676575\pi\)
\(488\) −53.2114 198.588i −0.109040 0.406942i
\(489\) 0 0
\(490\) 728.628 20.1673i 1.48700 0.0411578i
\(491\) 784.457 1.59767 0.798836 0.601549i \(-0.205449\pi\)
0.798836 + 0.601549i \(0.205449\pi\)
\(492\) 0 0
\(493\) 469.105 + 125.696i 0.951531 + 0.254962i
\(494\) 936.504 540.691i 1.89576 1.09452i
\(495\) 0 0
\(496\) 274.831 0.554095
\(497\) −33.2833 136.782i −0.0669684 0.275216i
\(498\) 0 0
\(499\) −50.6730 29.2561i −0.101549 0.0586294i 0.448365 0.893850i \(-0.352006\pi\)
−0.549914 + 0.835221i \(0.685340\pi\)
\(500\) 24.3336 605.936i 0.0486671 1.21187i
\(501\) 0 0
\(502\) −1015.44 + 272.086i −2.02279 + 0.542004i
\(503\) −144.269 + 144.269i −0.286816 + 0.286816i −0.835820 0.549004i \(-0.815007\pi\)
0.549004 + 0.835820i \(0.315007\pi\)
\(504\) 0 0
\(505\) 42.8070 225.116i 0.0847664 0.445774i
\(506\) 439.059 760.473i 0.867706 1.50291i
\(507\) 0 0
\(508\) 916.021 + 245.447i 1.80319 + 0.483164i
\(509\) 38.7059 + 22.3469i 0.0760431 + 0.0439035i 0.537539 0.843239i \(-0.319354\pi\)
−0.461496 + 0.887142i \(0.652687\pi\)
\(510\) 0 0
\(511\) 1.05171 45.5047i 0.00205814 0.0890503i
\(512\) −466.464 466.464i −0.911063 0.911063i
\(513\) 0 0
\(514\) −145.319 + 83.9001i −0.282722 + 0.163230i
\(515\) 47.6552 98.7266i 0.0925344 0.191702i
\(516\) 0 0
\(517\) −104.801 104.801i −0.202711 0.202711i
\(518\) 300.130 + 314.331i 0.579401 + 0.606817i
\(519\) 0 0
\(520\) −91.1437 + 105.716i −0.175276 + 0.203299i
\(521\) −139.872 242.266i −0.268469 0.465001i 0.699998 0.714145i \(-0.253184\pi\)
−0.968467 + 0.249143i \(0.919851\pi\)
\(522\) 0 0
\(523\) 63.7856 + 238.051i 0.121961 + 0.455165i 0.999713 0.0239502i \(-0.00762432\pi\)
−0.877752 + 0.479115i \(0.840958\pi\)
\(524\) 106.986i 0.204172i
\(525\) 0 0
\(526\) 845.520 1.60745
\(527\) −598.343 + 160.325i −1.13537 + 0.304223i
\(528\) 0 0
\(529\) 68.9129 39.7869i 0.130270 0.0752115i
\(530\) −502.562 433.288i −0.948229 0.817524i
\(531\) 0 0
\(532\) −264.802 1088.24i −0.497749 2.04557i
\(533\) 13.2340 13.2340i 0.0248293 0.0248293i
\(534\) 0 0
\(535\) −454.745 219.505i −0.849990 0.410289i
\(536\) −53.6312 92.8919i −0.100058 0.173306i
\(537\) 0 0
\(538\) −555.176 + 555.176i −1.03193 + 1.03193i
\(539\) 574.416 + 368.033i 1.06571 + 0.682807i
\(540\) 0 0
\(541\) −391.651 + 678.360i −0.723939 + 1.25390i 0.235470 + 0.971882i \(0.424337\pi\)
−0.959409 + 0.282018i \(0.908996\pi\)
\(542\) 77.6942 289.959i 0.143347 0.534979i
\(543\) 0 0
\(544\) 1052.92 + 607.904i 1.93552 + 1.11747i
\(545\) 623.281 + 118.520i 1.14363 + 0.217468i
\(546\) 0 0
\(547\) −32.2224 32.2224i −0.0589074 0.0589074i 0.677039 0.735947i \(-0.263263\pi\)
−0.735947 + 0.677039i \(0.763263\pi\)
\(548\) −269.201 1004.67i −0.491243 1.83334i
\(549\) 0 0
\(550\) 616.440 832.064i 1.12080 1.51284i
\(551\) −299.347 + 518.484i −0.543279 + 0.940986i
\(552\) 0 0
\(553\) 23.9318 81.7133i 0.0432763 0.147764i
\(554\) 780.291i 1.40847i
\(555\) 0 0
\(556\) −494.103 855.811i −0.888674 1.53923i
\(557\) 215.849 805.560i 0.387521 1.44625i −0.446634 0.894717i \(-0.647377\pi\)
0.834155 0.551531i \(-0.185956\pi\)
\(558\) 0 0
\(559\) 417.693i 0.747214i
\(560\) −225.711 348.770i −0.403055 0.622803i
\(561\) 0 0
\(562\) −1133.96 + 303.843i −2.01772 + 0.540646i
\(563\) 810.525 + 217.180i 1.43965 + 0.385754i 0.892412 0.451221i \(-0.149011\pi\)
0.547241 + 0.836975i \(0.315678\pi\)
\(564\) 0 0
\(565\) −72.2258 + 5.34631i −0.127833 + 0.00946250i
\(566\) 909.271 1.60649
\(567\) 0 0
\(568\) 36.0201 36.0201i 0.0634157 0.0634157i
\(569\) −663.998 383.359i −1.16696 0.673742i −0.213995 0.976835i \(-0.568648\pi\)
−0.952961 + 0.303093i \(0.901981\pi\)
\(570\) 0 0
\(571\) −525.520 910.227i −0.920350 1.59409i −0.798874 0.601498i \(-0.794571\pi\)
−0.121476 0.992594i \(-0.538763\pi\)
\(572\) −719.034 + 192.665i −1.25705 + 0.336826i
\(573\) 0 0
\(574\) −16.9708 31.0286i −0.0295658 0.0540568i
\(575\) −486.156 + 211.053i −0.845490 + 0.367048i
\(576\) 0 0
\(577\) 51.2986 191.449i 0.0889058 0.331801i −0.907119 0.420873i \(-0.861724\pi\)
0.996025 + 0.0890726i \(0.0283903\pi\)
\(578\) −1226.31 328.590i −2.12165 0.568494i
\(579\) 0 0
\(580\) 82.2591 432.589i 0.141826 0.745843i
\(581\) 174.754 + 106.352i 0.300782 + 0.183051i
\(582\) 0 0
\(583\) −160.737 599.879i −0.275707 1.02895i
\(584\) 14.2640 8.23534i 0.0244247 0.0141016i
\(585\) 0 0
\(586\) −489.604 + 848.019i −0.835502 + 1.44713i
\(587\) −425.592 425.592i −0.725029 0.725029i 0.244596 0.969625i \(-0.421345\pi\)
−0.969625 + 0.244596i \(0.921345\pi\)
\(588\) 0 0
\(589\) 763.632i 1.29649i
\(590\) 154.959 11.4704i 0.262642 0.0194414i
\(591\) 0 0
\(592\) 64.1094 239.260i 0.108293 0.404155i
\(593\) −139.637 521.131i −0.235475 0.878805i −0.977934 0.208914i \(-0.933007\pi\)
0.742459 0.669892i \(-0.233659\pi\)
\(594\) 0 0
\(595\) 694.859 + 627.645i 1.16783 + 1.05487i
\(596\) −597.360 −1.00228
\(597\) 0 0
\(598\) 671.428 + 179.909i 1.12279 + 0.300851i
\(599\) 329.578 190.282i 0.550213 0.317666i −0.198995 0.980001i \(-0.563768\pi\)
0.749208 + 0.662335i \(0.230434\pi\)
\(600\) 0 0
\(601\) −566.492 −0.942582 −0.471291 0.881978i \(-0.656212\pi\)
−0.471291 + 0.881978i \(0.656212\pi\)
\(602\) −757.478 221.846i −1.25827 0.368516i
\(603\) 0 0
\(604\) −425.550 245.691i −0.704552 0.406773i
\(605\) 343.857 119.969i 0.568359 0.198296i
\(606\) 0 0
\(607\) 1039.09 278.422i 1.71184 0.458685i 0.735963 0.677021i \(-0.236730\pi\)
0.975874 + 0.218336i \(0.0700629\pi\)
\(608\) −1059.81 + 1059.81i −1.74311 + 1.74311i
\(609\) 0 0
\(610\) −998.212 + 679.236i −1.63641 + 1.11350i
\(611\) 58.6616 101.605i 0.0960092 0.166293i
\(612\) 0 0
\(613\) 405.242 + 108.584i 0.661079 + 0.177136i 0.573733 0.819042i \(-0.305495\pi\)
0.0873463 + 0.996178i \(0.472161\pi\)
\(614\) 700.241 + 404.284i 1.14046 + 0.658444i
\(615\) 0 0
\(616\) −5.70396 + 246.795i −0.00925968 + 0.400642i
\(617\) 504.052 + 504.052i 0.816940 + 0.816940i 0.985663 0.168724i \(-0.0539645\pi\)
−0.168724 + 0.985663i \(0.553965\pi\)
\(618\) 0 0
\(619\) −210.689 + 121.641i −0.340369 + 0.196512i −0.660435 0.750883i \(-0.729628\pi\)
0.320066 + 0.947395i \(0.396295\pi\)
\(620\) 185.019 + 530.304i 0.298417 + 0.855330i
\(621\) 0 0
\(622\) −293.821 293.821i −0.472381 0.472381i
\(623\) 329.422 1124.79i 0.528768 1.80544i
\(624\) 0 0
\(625\) −597.901 + 182.041i −0.956642 + 0.291266i
\(626\) 72.7413 + 125.992i 0.116200 + 0.201264i
\(627\) 0 0
\(628\) 91.0132 + 339.666i 0.144926 + 0.540869i
\(629\) 558.298i 0.887596i
\(630\) 0 0
\(631\) 912.593 1.44626 0.723132 0.690710i \(-0.242702\pi\)
0.723132 + 0.690710i \(0.242702\pi\)
\(632\) 29.7609 7.97440i 0.0470900 0.0126177i
\(633\) 0 0
\(634\) −768.315 + 443.587i −1.21185 + 0.699663i
\(635\) −72.1507 974.717i −0.113623 1.53499i
\(636\) 0 0
\(637\) −163.719 + 514.613i −0.257016 + 0.807870i
\(638\) 531.693 531.693i 0.833375 0.833375i
\(639\) 0 0
\(640\) 172.187 356.718i 0.269043 0.557371i
\(641\) −114.103 197.632i −0.178007 0.308318i 0.763191 0.646173i \(-0.223632\pi\)
−0.941198 + 0.337856i \(0.890298\pi\)
\(642\) 0 0
\(643\) 434.914 434.914i 0.676382 0.676382i −0.282797 0.959180i \(-0.591262\pi\)
0.959180 + 0.282797i \(0.0912624\pi\)
\(644\) 374.278 614.999i 0.581177 0.954967i
\(645\) 0 0
\(646\) 1312.51 2273.33i 2.03175 3.51909i
\(647\) −92.6027 + 345.598i −0.143126 + 0.534155i 0.856705 + 0.515806i \(0.172508\pi\)
−0.999832 + 0.0183485i \(0.994159\pi\)
\(648\) 0 0
\(649\) 125.944 + 72.7136i 0.194058 + 0.112039i
\(650\) 762.510 + 300.870i 1.17309 + 0.462877i
\(651\) 0 0
\(652\) 624.764 + 624.764i 0.958228 + 0.958228i
\(653\) −177.811 663.599i −0.272298 1.01623i −0.957630 0.288000i \(-0.907010\pi\)
0.685332 0.728231i \(-0.259657\pi\)
\(654\) 0 0
\(655\) 104.109 36.3226i 0.158945 0.0554544i
\(656\) −10.0784 + 17.4563i −0.0153634 + 0.0266102i
\(657\) 0 0
\(658\) −153.102 160.347i −0.232678 0.243688i
\(659\) 619.112i 0.939471i 0.882807 + 0.469736i \(0.155651\pi\)
−0.882807 + 0.469736i \(0.844349\pi\)
\(660\) 0 0
\(661\) −249.541 432.217i −0.377520 0.653884i 0.613181 0.789943i \(-0.289890\pi\)
−0.990701 + 0.136059i \(0.956556\pi\)
\(662\) −67.4013 + 251.545i −0.101815 + 0.379978i
\(663\) 0 0
\(664\) 74.0263i 0.111485i
\(665\) −969.074 + 627.149i −1.45725 + 0.943081i
\(666\) 0 0
\(667\) −371.728 + 99.6041i −0.557313 + 0.149332i
\(668\) 1252.20 + 335.526i 1.87455 + 0.502285i
\(669\) 0 0
\(670\) −411.325 + 477.087i −0.613918 + 0.712071i
\(671\) −1130.03 −1.68410
\(672\) 0 0
\(673\) 588.355 588.355i 0.874227 0.874227i −0.118703 0.992930i \(-0.537874\pi\)
0.992930 + 0.118703i \(0.0378735\pi\)
\(674\) 623.006 + 359.693i 0.924341 + 0.533669i
\(675\) 0 0
\(676\) 115.312 + 199.727i 0.170580 + 0.295454i
\(677\) −825.046 + 221.070i −1.21868 + 0.326544i −0.810162 0.586206i \(-0.800621\pi\)
−0.408518 + 0.912750i \(0.633954\pi\)
\(678\) 0 0
\(679\) −341.256 + 560.739i −0.502586 + 0.825830i
\(680\) −63.2961 + 332.865i −0.0930824 + 0.489507i
\(681\) 0 0
\(682\) −248.229 + 926.403i −0.363972 + 1.35836i
\(683\) −289.626 77.6050i −0.424050 0.113624i 0.0404821 0.999180i \(-0.487111\pi\)
−0.464532 + 0.885557i \(0.653777\pi\)
\(684\) 0 0
\(685\) −886.256 + 603.055i −1.29380 + 0.880373i
\(686\) 846.287 + 570.225i 1.23365 + 0.831232i
\(687\) 0 0
\(688\) 116.430 + 434.524i 0.169230 + 0.631576i
\(689\) 425.748 245.806i 0.617922 0.356758i
\(690\) 0 0
\(691\) −422.621 + 732.000i −0.611607 + 1.05933i 0.379363 + 0.925248i \(0.376143\pi\)
−0.990970 + 0.134086i \(0.957190\pi\)
\(692\) 31.3057 + 31.3057i 0.0452395 + 0.0452395i
\(693\) 0 0
\(694\) 198.443i 0.285941i
\(695\) −665.043 + 771.369i −0.956896 + 1.10988i
\(696\) 0 0
\(697\) 11.7586 43.8839i 0.0168704 0.0629611i
\(698\) 342.863 + 1279.58i 0.491208 + 1.83321i
\(699\) 0 0
\(700\) 521.023 670.318i 0.744318 0.957597i
\(701\) 177.525 0.253245 0.126623 0.991951i \(-0.459586\pi\)
0.126623 + 0.991951i \(0.459586\pi\)
\(702\) 0 0
\(703\) −664.795 178.131i −0.945654 0.253387i
\(704\) 1057.76 610.698i 1.50250 0.867469i
\(705\) 0 0
\(706\) 1102.00 1.56091
\(707\) 232.028 221.545i 0.328186 0.313359i
\(708\) 0 0
\(709\) −488.278 281.907i −0.688685 0.397613i 0.114434 0.993431i \(-0.463495\pi\)
−0.803119 + 0.595818i \(0.796828\pi\)
\(710\) −269.412 130.045i −0.379454 0.183162i
\(711\) 0 0
\(712\) 409.660 109.768i 0.575365 0.154169i
\(713\) 347.093 347.093i 0.486807 0.486807i
\(714\) 0 0
\(715\) 431.601 + 634.285i 0.603638 + 0.887112i
\(716\) −649.843 + 1125.56i −0.907602 + 1.57201i
\(717\) 0 0
\(718\) 1683.43 + 451.074i 2.34461 + 0.628236i
\(719\) 340.465 + 196.567i 0.473525 + 0.273390i 0.717714 0.696338i \(-0.245188\pi\)
−0.244189 + 0.969728i \(0.578522\pi\)
\(720\) 0 0
\(721\) 134.653 73.6469i 0.186758 0.102146i
\(722\) 1528.76 + 1528.76i 2.11740 + 2.11740i
\(723\) 0 0
\(724\) −953.622 + 550.574i −1.31716 + 0.760461i
\(725\) −448.882 + 66.8207i −0.619148 + 0.0921664i
\(726\) 0 0
\(727\) −110.762 110.762i −0.152356 0.152356i 0.626814 0.779169i \(-0.284359\pi\)
−0.779169 + 0.626814i \(0.784359\pi\)
\(728\) −189.874 + 46.2020i −0.260815 + 0.0634643i
\(729\) 0 0
\(730\) −73.2592 63.1610i −0.100355 0.0865220i
\(731\) −506.968 878.094i −0.693527 1.20122i
\(732\) 0 0
\(733\) −180.535 673.766i −0.246296 0.919190i −0.972727 0.231951i \(-0.925489\pi\)
0.726431 0.687239i \(-0.241178\pi\)
\(734\) 896.977i 1.22204i
\(735\) 0 0
\(736\) −963.429 −1.30901
\(737\) −569.472 + 152.590i −0.772689 + 0.207042i
\(738\) 0 0
\(739\) 701.070 404.763i 0.948675 0.547717i 0.0560056 0.998430i \(-0.482164\pi\)
0.892669 + 0.450713i \(0.148830\pi\)
\(740\) 504.826 37.3683i 0.682197 0.0504977i
\(741\) 0 0
\(742\) −219.640 902.640i −0.296010 1.21650i
\(743\) −615.379 + 615.379i −0.828235 + 0.828235i −0.987273 0.159037i \(-0.949161\pi\)
0.159037 + 0.987273i \(0.449161\pi\)
\(744\) 0 0
\(745\) 202.809 + 581.294i 0.272226 + 0.780261i
\(746\) 785.474 + 1360.48i 1.05291 + 1.82370i
\(747\) 0 0
\(748\) −1277.74 + 1277.74i −1.70821 + 1.70821i
\(749\) −339.225 620.224i −0.452904 0.828069i
\(750\) 0 0
\(751\) −666.673 + 1154.71i −0.887713 + 1.53756i −0.0451417 + 0.998981i \(0.514374\pi\)
−0.842572 + 0.538584i \(0.818959\pi\)
\(752\) −32.7035 + 122.051i −0.0434887 + 0.162302i
\(753\) 0 0
\(754\) 515.477 + 297.611i 0.683656 + 0.394709i
\(755\) −94.6059 + 497.519i −0.125306 + 0.658966i
\(756\) 0 0
\(757\) 897.927 + 897.927i 1.18617 + 1.18617i 0.978119 + 0.208047i \(0.0667106\pi\)
0.208047 + 0.978119i \(0.433289\pi\)
\(758\) 136.341 + 508.832i 0.179870 + 0.671283i
\(759\) 0 0
\(760\) −376.165 181.574i −0.494954 0.238914i
\(761\) 19.9063 34.4788i 0.0261581 0.0453072i −0.852650 0.522483i \(-0.825006\pi\)
0.878808 + 0.477175i \(0.158339\pi\)
\(762\) 0 0
\(763\) 613.393 + 642.417i 0.803923 + 0.841963i
\(764\) 754.964i 0.988173i
\(765\) 0 0
\(766\) 401.410 + 695.262i 0.524034 + 0.907653i
\(767\) −29.7951 + 111.197i −0.0388462 + 0.144976i
\(768\) 0 0
\(769\) 246.046i 0.319956i 0.987121 + 0.159978i \(0.0511424\pi\)
−0.987121 + 0.159978i \(0.948858\pi\)
\(770\) 1379.50 445.817i 1.79155 0.578983i
\(771\) 0 0
\(772\) −985.653 + 264.105i −1.27675 + 0.342105i
\(773\) −760.894 203.881i −0.984339 0.263753i −0.269468 0.963009i \(-0.586848\pi\)
−0.714871 + 0.699257i \(0.753515\pi\)
\(774\) 0 0
\(775\) 453.227 360.086i 0.584809 0.464626i