Properties

Label 315.3.ca.b.163.3
Level 315
Weight 3
Character 315.163
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 163.3
Character \(\chi\) \(=\) 315.163
Dual form 315.3.ca.b.172.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.770020 - 2.87375i) q^{2} +(-4.20143 + 2.42570i) q^{4} +(4.72092 + 1.64709i) q^{5} +(-6.80154 + 1.65502i) q^{7} +(1.79111 + 1.79111i) q^{8} +O(q^{10})\) \(q+(-0.770020 - 2.87375i) q^{2} +(-4.20143 + 2.42570i) q^{4} +(4.72092 + 1.64709i) q^{5} +(-6.80154 + 1.65502i) q^{7} +(1.79111 + 1.79111i) q^{8} +(1.09812 - 14.8351i) q^{10} +(-6.96127 - 12.0573i) q^{11} +(7.79302 + 7.79302i) q^{13} +(9.99344 + 18.2715i) q^{14} +(-5.93477 + 10.2793i) q^{16} +(-25.8415 - 6.92421i) q^{17} +(-28.5616 - 16.4901i) q^{19} +(-23.8300 + 4.53140i) q^{20} +(-29.2893 + 29.2893i) q^{22} +(-20.4773 + 5.48688i) q^{23} +(19.5742 + 15.5516i) q^{25} +(16.3944 - 28.3960i) q^{26} +(24.5616 - 23.4519i) q^{28} -18.1531i q^{29} +(-11.5772 - 20.0522i) q^{31} +(43.8970 + 11.7622i) q^{32} +79.5940i q^{34} +(-34.8355 - 3.38952i) q^{35} +(5.40117 + 20.1574i) q^{37} +(-25.3954 + 94.7768i) q^{38} +(5.50557 + 11.4058i) q^{40} +1.69819 q^{41} +(26.7992 + 26.7992i) q^{43} +(58.4946 + 33.7719i) q^{44} +(31.5359 + 54.6218i) q^{46} +(-2.75524 - 10.2827i) q^{47} +(43.5218 - 22.5134i) q^{49} +(29.6188 - 68.2264i) q^{50} +(-51.6453 - 13.8383i) q^{52} +(-11.5451 + 43.0869i) q^{53} +(-13.0042 - 68.3872i) q^{55} +(-15.1466 - 9.21797i) q^{56} +(-52.1677 + 13.9783i) q^{58} +(9.04603 - 5.22273i) q^{59} +(40.5827 - 70.2914i) q^{61} +(-48.7105 + 48.7105i) q^{62} -87.7280i q^{64} +(23.9544 + 49.6260i) q^{65} +(-40.9029 - 10.9599i) q^{67} +(125.367 - 33.5921i) q^{68} +(17.0834 + 102.719i) q^{70} +20.1105 q^{71} +(-1.68295 + 6.28085i) q^{73} +(53.7685 - 31.0433i) q^{74} +160.000 q^{76} +(67.3023 + 70.4869i) q^{77} +(-10.5341 - 6.08184i) q^{79} +(-44.9486 + 38.7528i) q^{80} +(-1.30764 - 4.88019i) q^{82} +(-20.6649 - 20.6649i) q^{83} +(-110.591 - 75.2519i) q^{85} +(56.3783 - 97.6501i) q^{86} +(9.12749 - 34.0643i) q^{88} +(-145.002 - 83.7168i) q^{89} +(-65.9021 - 40.1069i) q^{91} +(72.7245 - 72.7245i) q^{92} +(-27.4284 + 15.8358i) q^{94} +(-107.677 - 124.892i) q^{95} +(-66.3082 + 66.3082i) q^{97} +(-98.2105 - 107.735i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.770020 2.87375i −0.385010 1.43688i −0.838151 0.545438i \(-0.816363\pi\)
0.453141 0.891439i \(-0.350303\pi\)
\(3\) 0 0
\(4\) −4.20143 + 2.42570i −1.05036 + 0.606424i
\(5\) 4.72092 + 1.64709i 0.944184 + 0.329418i
\(6\) 0 0
\(7\) −6.80154 + 1.65502i −0.971648 + 0.236431i
\(8\) 1.79111 + 1.79111i 0.223889 + 0.223889i
\(9\) 0 0
\(10\) 1.09812 14.8351i 0.109812 1.48351i
\(11\) −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 0.940170 0.340707i \(-0.110666\pi\)
−0.340707 + 0.940170i \(0.610666\pi\)
\(14\) 9.99344 + 18.2715i 0.713817 + 1.30511i
\(15\) 0 0
\(16\) −5.93477 + 10.2793i −0.370923 + 0.642458i
\(17\) −25.8415 6.92421i −1.52009 0.407307i −0.600318 0.799761i \(-0.704959\pi\)
−0.919771 + 0.392455i \(0.871626\pi\)
\(18\) 0 0
\(19\) −28.5616 16.4901i −1.50324 0.867898i −0.999993 0.00375778i \(-0.998804\pi\)
−0.503251 0.864140i \(-0.667863\pi\)
\(20\) −23.8300 + 4.53140i −1.19150 + 0.226570i
\(21\) 0 0
\(22\) −29.2893 + 29.2893i −1.33133 + 1.33133i
\(23\) −20.4773 + 5.48688i −0.890318 + 0.238560i −0.674854 0.737952i \(-0.735793\pi\)
−0.215464 + 0.976512i \(0.569127\pi\)
\(24\) 0 0
\(25\) 19.5742 + 15.5516i 0.782968 + 0.622062i
\(26\) 16.3944 28.3960i 0.630555 1.09215i
\(27\) 0 0
\(28\) 24.5616 23.4519i 0.877201 0.837569i
\(29\) 18.1531i 0.625971i −0.949758 0.312985i \(-0.898671\pi\)
0.949758 0.312985i \(-0.101329\pi\)
\(30\) 0 0
\(31\) −11.5772 20.0522i −0.373457 0.646846i 0.616638 0.787247i \(-0.288494\pi\)
−0.990095 + 0.140401i \(0.955161\pi\)
\(32\) 43.8970 + 11.7622i 1.37178 + 0.367567i
\(33\) 0 0
\(34\) 79.5940i 2.34100i
\(35\) −34.8355 3.38952i −0.995300 0.0968434i
\(36\) 0 0
\(37\) 5.40117 + 20.1574i 0.145978 + 0.544796i 0.999710 + 0.0240837i \(0.00766681\pi\)
−0.853732 + 0.520712i \(0.825667\pi\)
\(38\) −25.3954 + 94.7768i −0.668299 + 2.49413i
\(39\) 0 0
\(40\) 5.50557 + 11.4058i 0.137639 + 0.285145i
\(41\) 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 0.946358 0.323121i \(-0.104732\pi\)
−0.323121 + 0.946358i \(0.604732\pi\)
\(44\) 58.4946 + 33.7719i 1.32942 + 0.767542i
\(45\) 0 0
\(46\) 31.5359 + 54.6218i 0.685563 + 1.18743i
\(47\) −2.75524 10.2827i −0.0586222 0.218781i 0.930401 0.366544i \(-0.119459\pi\)
−0.989023 + 0.147763i \(0.952793\pi\)
\(48\) 0 0
\(49\) 43.5218 22.5134i 0.888200 0.459456i
\(50\) 29.6188 68.2264i 0.592376 1.36453i
\(51\) 0 0
\(52\) −51.6453 13.8383i −0.993179 0.266122i
\(53\) −11.5451 + 43.0869i −0.217832 + 0.812961i 0.767318 + 0.641267i \(0.221591\pi\)
−0.985150 + 0.171694i \(0.945076\pi\)
\(54\) 0 0
\(55\) −13.0042 68.3872i −0.236440 1.24340i
\(56\) −15.1466 9.21797i −0.270475 0.164607i
\(57\) 0 0
\(58\) −52.1677 + 13.9783i −0.899443 + 0.241005i
\(59\) 9.04603 5.22273i 0.153323 0.0885208i −0.421376 0.906886i \(-0.638453\pi\)
0.574698 + 0.818365i \(0.305119\pi\)
\(60\) 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
\(65\) 23.9544 + 49.6260i 0.368530 + 0.763477i
\(66\) 0 0
\(67\) −40.9029 10.9599i −0.610491 0.163581i −0.0596898 0.998217i \(-0.519011\pi\)
−0.550801 + 0.834636i \(0.685678\pi\)
\(68\) 125.367 33.5921i 1.84364 0.494001i
\(69\) 0 0
\(70\) 17.0834 + 102.719i 0.244048 + 1.46741i
\(71\) 20.1105 0.283247 0.141623 0.989921i \(-0.454768\pi\)
0.141623 + 0.989921i \(0.454768\pi\)
\(72\) 0 0
\(73\) −1.68295 + 6.28085i −0.0230541 + 0.0860390i −0.976494 0.215543i \(-0.930848\pi\)
0.953440 + 0.301582i \(0.0975146\pi\)
\(74\) 53.7685 31.0433i 0.726602 0.419504i
\(75\) 0 0
\(76\) 160.000 2.10526
\(77\) 67.3023 + 70.4869i 0.874056 + 0.915415i
\(78\) 0 0
\(79\) −10.5341 6.08184i −0.133342 0.0769853i 0.431845 0.901948i \(-0.357863\pi\)
−0.565187 + 0.824963i \(0.691196\pi\)
\(80\) −44.9486 + 38.7528i −0.561857 + 0.484410i
\(81\) 0 0
\(82\) −1.30764 4.88019i −0.0159469 0.0595145i
\(83\) −20.6649 20.6649i −0.248975 0.248975i 0.571575 0.820550i \(-0.306333\pi\)
−0.820550 + 0.571575i \(0.806333\pi\)
\(84\) 0 0
\(85\) −110.591 75.2519i −1.30107 0.885317i
\(86\) 56.3783 97.6501i 0.655562 1.13547i
\(87\) 0 0
\(88\) 9.12749 34.0643i 0.103721 0.387094i
\(89\) −145.002 83.7168i −1.62923 0.940638i −0.984322 0.176381i \(-0.943561\pi\)
−0.644911 0.764257i \(-0.723106\pi\)
\(90\) 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
\(95\) −107.677 124.892i −1.13344 1.31465i
\(96\) 0 0
\(97\) −66.3082 + 66.3082i −0.683589 + 0.683589i −0.960807 0.277218i \(-0.910588\pi\)
0.277218 + 0.960807i \(0.410588\pi\)
\(98\) −98.2105 107.735i −1.00215 1.09934i
\(99\) 0 0
\(100\) −119.963 17.8577i −1.19963 0.178577i
\(101\) 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
\(103\) −21.1782 + 5.67468i −0.205614 + 0.0550940i −0.360156 0.932892i \(-0.617276\pi\)
0.154542 + 0.987986i \(0.450610\pi\)
\(104\) 27.9163i 0.268426i
\(105\) 0 0
\(106\) 132.711 1.25199
\(107\) −26.1382 97.5490i −0.244282 0.911673i −0.973743 0.227650i \(-0.926896\pi\)
0.729461 0.684022i \(-0.239771\pi\)
\(108\) 0 0
\(109\) 109.890 63.4449i 1.00816 0.582064i 0.0975104 0.995235i \(-0.468912\pi\)
0.910654 + 0.413171i \(0.135579\pi\)
\(110\) −186.515 + 90.0304i −1.69559 + 0.818458i
\(111\) 0 0
\(112\) 23.3531 79.7374i 0.208510 0.711941i
\(113\) 10.2422 + 10.2422i 0.0906391 + 0.0906391i 0.750973 0.660333i \(-0.229585\pi\)
−0.660333 + 0.750973i \(0.729585\pi\)
\(114\) 0 0
\(115\) −105.709 7.82482i −0.919210 0.0680419i
\(116\) 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
\(122\) −233.250 62.4991i −1.91188 0.512287i
\(123\) 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 0.0926732 0.995697i \(-0.470459\pi\)
0.995697 0.0926732i \(-0.0295412\pi\)
\(128\) −76.5208 + 20.5037i −0.597819 + 0.160185i
\(129\) 0 0
\(130\) 124.168 107.052i 0.955135 0.823478i
\(131\) −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
\(133\) 221.554 + 64.8877i 1.66582 + 0.487878i
\(134\) 125.984i 0.940181i
\(135\) 0 0
\(136\) −33.8829 58.6870i −0.249139 0.431522i
\(137\) −207.089 55.4894i −1.51160 0.405032i −0.594634 0.803997i \(-0.702703\pi\)
−0.916966 + 0.398965i \(0.869370\pi\)
\(138\) 0 0
\(139\) 203.695i 1.46543i 0.680534 + 0.732716i \(0.261748\pi\)
−0.680534 + 0.732716i \(0.738252\pi\)
\(140\) 154.581 70.2595i 1.10415 0.501854i
\(141\) 0 0
\(142\) −15.4855 57.7926i −0.109053 0.406990i
\(143\) 39.7132 148.212i 0.277715 1.03645i
\(144\) 0 0
\(145\) 29.8998 85.6996i 0.206206 0.591032i
\(146\) 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 0.813157 0.582044i \(-0.197747\pi\)
−0.0974859 + 0.995237i \(0.531080\pi\)
\(150\) 0 0
\(151\) −50.6434 87.7170i −0.335387 0.580907i 0.648172 0.761494i \(-0.275534\pi\)
−0.983559 + 0.180587i \(0.942200\pi\)
\(152\) −21.6215 80.6925i −0.142247 0.530872i
\(153\) 0 0
\(154\) 150.738 247.687i 0.978818 1.60836i
\(155\) −21.6271 113.734i −0.139529 0.733765i
\(156\) 0 0
\(157\) 70.0141 + 18.7602i 0.445950 + 0.119492i 0.474804 0.880092i \(-0.342519\pi\)
−0.0288540 + 0.999584i \(0.509186\pi\)
\(158\) −9.36628 + 34.9554i −0.0592802 + 0.221237i
\(159\) 0 0
\(160\) 187.861 + 127.830i 1.17413 + 0.798940i
\(161\) 130.196 71.2096i 0.808673 0.442295i
\(162\) 0 0
\(163\) −175.917 + 47.1369i −1.07925 + 0.289183i −0.754287 0.656545i \(-0.772017\pi\)
−0.324960 + 0.945728i \(0.605351\pi\)
\(164\) −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 0.141505 0.989938i \(-0.454806\pi\)
0.989938 0.141505i \(-0.0451940\pi\)
\(168\) 0 0
\(169\) 47.5377i 0.281288i
\(170\) −131.098 + 375.757i −0.771167 + 2.21033i
\(171\) 0 0
\(172\) −177.601 47.5882i −1.03257 0.276675i
\(173\) −8.81487 + 2.36194i −0.0509530 + 0.0136528i −0.284206 0.958763i \(-0.591730\pi\)
0.233253 + 0.972416i \(0.425063\pi\)
\(174\) 0 0
\(175\) −158.873 73.3788i −0.907844 0.419307i
\(176\) 165.254 0.938944
\(177\) 0 0
\(178\) −128.927 + 481.163i −0.724310 + 2.70316i
\(179\) 232.008 133.950i 1.29613 0.748322i 0.316398 0.948626i \(-0.397526\pi\)
0.979734 + 0.200304i \(0.0641931\pi\)
\(180\) 0 0
\(181\) −226.975 −1.25401 −0.627004 0.779016i \(-0.715719\pi\)
−0.627004 + 0.779016i \(0.715719\pi\)
\(182\) −64.5115 + 220.270i −0.354459 + 1.21027i
\(183\) 0 0
\(184\) −46.5047 26.8495i −0.252743 0.145921i
\(185\) −7.70259 + 104.058i −0.0416356 + 0.562475i
\(186\) 0 0
\(187\) 96.4026 + 359.779i 0.515522 + 1.92395i
\(188\) 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
\(193\) 54.4390 203.169i 0.282067 1.05269i −0.668889 0.743363i \(-0.733230\pi\)
0.950956 0.309327i \(-0.100104\pi\)
\(194\) 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 −0.411018 0.911627i \(-0.634827\pi\)
0.911627 + 0.411018i \(0.134827\pi\)
\(198\) 0 0
\(199\) 35.8210 20.6813i 0.180005 0.103926i −0.407290 0.913299i \(-0.633526\pi\)
0.587295 + 0.809373i \(0.300193\pi\)
\(200\) 7.20499 + 62.9140i 0.0360250 + 0.314570i
\(201\) 0 0
\(202\) 96.4140 96.4140i 0.477297 0.477297i
\(203\) 30.0438 + 123.469i 0.147999 + 0.608223i
\(204\) 0 0
\(205\) 8.01703 + 2.79707i 0.0391075 + 0.0136443i
\(206\) 32.6153 + 56.4913i 0.158327 + 0.274230i
\(207\) 0 0
\(208\) −126.357 + 33.8572i −0.607485 + 0.162775i
\(209\) 459.167i 2.19697i
\(210\) 0 0
\(211\) 326.483 1.54731 0.773655 0.633607i \(-0.218426\pi\)
0.773655 + 0.633607i \(0.218426\pi\)
\(212\) −56.0099 209.032i −0.264198 0.985999i
\(213\) 0 0
\(214\) −260.205 + 150.229i −1.21591 + 0.702006i
\(215\) 82.3761 + 170.657i 0.383145 + 0.793755i
\(216\) 0 0
\(217\) 111.929 + 117.226i 0.515803 + 0.540210i
\(218\) −266.943 266.943i −1.22451 1.22451i
\(219\) 0 0
\(220\) 220.523 + 255.780i 1.00238 + 1.16264i
\(221\) −147.423 255.344i −0.667072 1.15540i
\(222\) 0 0
\(223\) −39.2007 39.2007i −0.175788 0.175788i 0.613729 0.789517i \(-0.289669\pi\)
−0.789517 + 0.613729i \(0.789669\pi\)
\(224\) −318.033 7.35042i −1.41979 0.0328144i
\(225\) 0 0
\(226\) 21.5469 37.3203i 0.0953403 0.165134i
\(227\) 3.48231 + 0.933082i 0.0153406 + 0.00411049i 0.266481 0.963840i \(-0.414139\pi\)
−0.251141 + 0.967951i \(0.580806\pi\)
\(228\) 0 0
\(229\) 46.0053 + 26.5612i 0.200896 + 0.115988i 0.597074 0.802186i \(-0.296330\pi\)
−0.396177 + 0.918174i \(0.629663\pi\)
\(230\) 58.9116 + 309.807i 0.256137 + 1.34699i
\(231\) 0 0
\(232\) 32.5143 32.5143i 0.140148 0.140148i
\(233\) −124.839 + 33.4506i −0.535791 + 0.143565i −0.516561 0.856250i \(-0.672788\pi\)
−0.0192298 + 0.999815i \(0.506121\pi\)
\(234\) 0 0
\(235\) 3.92924 53.0820i 0.0167202 0.225881i
\(236\) −25.3375 + 43.8859i −0.107362 + 0.185957i
\(237\) 0 0
\(238\) −131.730 541.361i −0.553485 2.27463i
\(239\) 365.148i 1.52782i 0.645325 + 0.763908i \(0.276722\pi\)
−0.645325 + 0.763908i \(0.723278\pi\)
\(240\) 0 0
\(241\) −196.782 340.837i −0.816525 1.41426i −0.908228 0.418476i \(-0.862564\pi\)
0.0917031 0.995786i \(-0.470769\pi\)
\(242\) 209.315 + 56.0859i 0.864939 + 0.231760i
\(243\) 0 0
\(244\) 393.766i 1.61379i
\(245\) 242.545 34.5995i 0.989978 0.141222i
\(246\) 0 0
\(247\) −94.0739 351.089i −0.380866 1.42141i
\(248\) 15.1798 56.6516i 0.0612087 0.228434i
\(249\) 0 0
\(250\) 252.203 273.307i 1.00881 1.09323i
\(251\) −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
\(257\) 14.5977 + 54.4792i 0.0568002 + 0.211981i 0.988493 0.151266i \(-0.0483348\pi\)
−0.931693 + 0.363247i \(0.881668\pi\)
\(258\) 0 0
\(259\) −70.0972 128.163i −0.270646 0.494836i
\(260\) −221.021 150.394i −0.850079 0.578439i
\(261\) 0 0
\(262\) 63.3739 + 16.9810i 0.241885 + 0.0648129i
\(263\) −73.5553 + 274.512i −0.279678 + 1.04377i 0.672963 + 0.739676i \(0.265021\pi\)
−0.952641 + 0.304097i \(0.901645\pi\)
\(264\) 0 0
\(265\) −125.472 + 184.394i −0.473477 + 0.695827i
\(266\) 15.8701 686.658i 0.0596620 2.58142i
\(267\) 0 0
\(268\) 198.436 53.1708i 0.740433 0.198399i
\(269\) 228.544 131.950i 0.849607 0.490521i −0.0109111 0.999940i \(-0.503473\pi\)
0.860518 + 0.509419i \(0.170140\pi\)
\(270\) 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
\(275\) 51.2480 344.270i 0.186356 1.25189i
\(276\) 0 0
\(277\) 253.335 + 67.8808i 0.914566 + 0.245057i 0.685261 0.728297i \(-0.259688\pi\)
0.229305 + 0.973355i \(0.426355\pi\)
\(278\) 585.370 156.849i 2.10565 0.564206i
\(279\) 0 0
\(280\) −56.3231 68.4651i −0.201154 0.244518i
\(281\) −394.591 −1.40424 −0.702119 0.712060i \(-0.747762\pi\)
−0.702119 + 0.712060i \(0.747762\pi\)
\(282\) 0 0
\(283\) −79.1013 + 295.210i −0.279510 + 1.04315i 0.673249 + 0.739416i \(0.264898\pi\)
−0.952758 + 0.303729i \(0.901768\pi\)
\(284\) −84.4929 + 48.7820i −0.297510 + 0.171768i
\(285\) 0 0
\(286\) −456.504 −1.59617
\(287\) −11.5503 + 2.81054i −0.0402450 + 0.00979282i
\(288\) 0 0
\(289\) 369.558 + 213.364i 1.27875 + 0.738285i
\(290\) −269.303 19.9344i −0.928631 0.0687393i
\(291\) 0 0
\(292\) −8.16464 30.4709i −0.0279611 0.104352i
\(293\) −232.731 232.731i −0.794304 0.794304i 0.187887 0.982191i \(-0.439836\pi\)
−0.982191 + 0.187887i \(0.939836\pi\)
\(294\) 0 0
\(295\) 51.3079 9.75647i 0.173925 0.0330728i
\(296\) −26.4301 + 45.7782i −0.0892908 + 0.154656i
\(297\) 0 0
\(298\) 94.8138 353.850i 0.318167 1.18742i
\(299\) −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
\(305\) 307.364 264.997i 1.00775 0.868842i
\(306\) 0 0
\(307\) 192.175 192.175i 0.625976 0.625976i −0.321077 0.947053i \(-0.604045\pi\)
0.947053 + 0.321077i \(0.104045\pi\)
\(308\) −453.746 132.891i −1.47320 0.431464i
\(309\) 0 0
\(310\) −310.189 + 149.728i −1.00061 + 0.482993i
\(311\) −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
\(313\) −47.2333 + 12.6561i −0.150905 + 0.0404349i −0.333481 0.942757i \(-0.608223\pi\)
0.182576 + 0.983192i \(0.441557\pi\)
\(314\) 215.649i 0.686780i
\(315\) 0 0
\(316\) 59.0108 0.186743
\(317\) 77.1789 + 288.036i 0.243467 + 0.908630i 0.974148 + 0.225911i \(0.0725359\pi\)
−0.730681 + 0.682719i \(0.760797\pi\)
\(318\) 0 0
\(319\) −218.877 + 126.369i −0.686136 + 0.396141i
\(320\) 144.496 414.157i 0.451549 1.29424i
\(321\) 0 0
\(322\) −304.893 319.319i −0.946871 0.991675i
\(323\) 623.895 + 623.895i 1.93156 + 1.93156i
\(324\) 0 0
\(325\) 31.3485 + 273.736i 0.0964571 + 0.842263i
\(326\) 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 \(0.208878\pi\)
\(332\) 136.949 + 36.6954i 0.412498 + 0.110528i
\(333\) 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 −0.406359 0.913713i \(-0.633202\pi\)
0.913713 + 0.406359i \(0.133202\pi\)
\(338\) −136.612 + 36.6050i −0.404177 + 0.108299i
\(339\) 0 0
\(340\) 647.179 + 47.9056i 1.90347 + 0.140899i
\(341\) −161.183 + 279.178i −0.472678 + 0.818703i
\(342\) 0 0
\(343\) −258.755 + 225.155i −0.754389 + 0.656428i
\(344\) 96.0004i 0.279071i
\(345\) 0 0
\(346\) 13.5753 + 23.5130i 0.0392348 + 0.0679567i
\(347\) −64.4278 17.2634i −0.185671 0.0497504i 0.164785 0.986329i \(-0.447307\pi\)
−0.350456 + 0.936579i \(0.613974\pi\)
\(348\) 0 0
\(349\) 445.265i 1.27583i −0.770106 0.637915i \(-0.779797\pi\)
0.770106 0.637915i \(-0.220203\pi\)
\(350\) −88.5374 + 513.064i −0.252964 + 1.46590i
\(351\) 0 0
\(352\) −163.759 611.157i −0.465224 1.73624i
\(353\) −95.8678 + 357.784i −0.271580 + 1.01355i 0.686518 + 0.727112i \(0.259138\pi\)
−0.958099 + 0.286439i \(0.907529\pi\)
\(354\) 0 0
\(355\) 94.9401 + 33.1238i 0.267437 + 0.0933064i
\(356\) 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 −0.417446 0.908702i \(-0.637075\pi\)
−0.995682 + 0.0928320i \(0.970408\pi\)
\(360\) 0 0
\(361\) 363.345 + 629.331i 1.00649 + 1.74330i
\(362\) 174.776 + 652.272i 0.482806 + 1.80186i
\(363\) 0 0
\(364\) 374.170 + 8.64786i 1.02794 + 0.0237579i
\(365\) −18.2902 + 26.8794i −0.0501101 + 0.0736422i
\(366\) 0 0
\(367\) −291.219 78.0318i −0.793511 0.212621i −0.160778 0.986991i \(-0.551400\pi\)
−0.632733 + 0.774370i \(0.718067\pi\)
\(368\) 65.1268 243.056i 0.176975 0.660479i
\(369\) 0 0
\(370\) 304.968 57.9913i 0.824238 0.156733i
\(371\) 7.21478 312.165i 0.0194469 0.841414i
\(372\) 0 0
\(373\) −510.035 + 136.663i −1.36739 + 0.366390i −0.866523 0.499137i \(-0.833650\pi\)
−0.500862 + 0.865527i \(0.666984\pi\)
\(374\) 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 \(-0.924952\pi\)
0.972335 0.233591i \(-0.0750476\pi\)
\(380\) 755.346 + 263.534i 1.98775 + 0.693509i
\(381\) 0 0
\(382\) 447.208 + 119.829i 1.17070 + 0.313688i
\(383\) −260.649 + 69.8407i −0.680545 + 0.182352i −0.582500 0.812830i \(-0.697926\pi\)
−0.0980450 + 0.995182i \(0.531259\pi\)
\(384\) 0 0
\(385\) 201.631 + 443.616i 0.523716 + 1.15225i
\(386\) −625.777 −1.62118
\(387\) 0 0
\(388\) 117.746 439.433i 0.303468 1.13256i
\(389\) 161.408 93.1891i 0.414931 0.239561i −0.277975 0.960588i \(-0.589663\pi\)
0.692906 + 0.721028i \(0.256330\pi\)
\(390\) 0 0
\(391\) 567.157 1.45053
\(392\) 118.276 + 37.6284i 0.301725 + 0.0959909i
\(393\) 0 0
\(394\) −359.349 207.470i −0.912053 0.526574i
\(395\) −39.7131 46.0624i −0.100540 0.116614i
\(396\) 0 0
\(397\) 176.603 + 659.091i 0.444844 + 1.66018i 0.716349 + 0.697742i \(0.245812\pi\)
−0.271506 + 0.962437i \(0.587522\pi\)
\(398\) −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
\(403\) 66.0463 246.488i 0.163887 0.611634i
\(404\) −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 −0.580329 0.814382i \(-0.697076\pi\)
0.415111 + 0.909771i \(0.363743\pi\)
\(410\) 1.86482 25.1928i 0.00454835 0.0614458i
\(411\) 0 0
\(412\) 75.2137 75.2137i 0.182558 0.182558i
\(413\) −52.8832 + 50.4939i −0.128046 + 0.122261i
\(414\) 0 0
\(415\) −63.5206 131.595i −0.153062 0.317095i
\(416\) 250.427 + 433.752i 0.601988 + 1.04267i
\(417\) 0 0
\(418\) 1319.53 353.568i 3.15678 0.845856i
\(419\) 38.0855i 0.0908962i −0.998967 0.0454481i \(-0.985528\pi\)
0.998967 0.0454481i \(-0.0144716\pi\)
\(420\) 0 0
\(421\) −151.613 −0.360126 −0.180063 0.983655i \(-0.557630\pi\)
−0.180063 + 0.983655i \(0.557630\pi\)
\(422\) −251.398 938.231i −0.595730 2.22330i
\(423\) 0 0
\(424\) −97.8519 + 56.4948i −0.230783 + 0.133242i
\(425\) −398.145 537.412i −0.936811 1.26450i
\(426\) 0 0
\(427\) −159.691 + 545.255i −0.373985 + 1.27694i
\(428\) 346.442 + 346.442i 0.809444 + 0.809444i
\(429\) 0 0
\(430\) 426.996 368.138i 0.993014 0.856136i
\(431\) 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 0.999652 0.0263739i \(-0.00839605\pi\)
−0.0263739 + 0.999652i \(0.508396\pi\)
\(434\) 250.690 411.923i 0.577626 0.949132i
\(435\) 0 0
\(436\) −307.796 + 533.119i −0.705955 + 1.22275i
\(437\) 675.344 + 180.958i 1.54541 + 0.414092i
\(438\) 0 0
\(439\) −411.292 237.460i −0.936884 0.540910i −0.0479017 0.998852i \(-0.515253\pi\)
−0.888982 + 0.457942i \(0.848587\pi\)
\(440\) 99.1970 145.781i 0.225448 0.331320i
\(441\) 0 0
\(442\) −620.277 + 620.277i −1.40334 + 1.40334i
\(443\) 90.9998 24.3833i 0.205417 0.0550414i −0.154643 0.987970i \(-0.549423\pi\)
0.360060 + 0.932929i \(0.382756\pi\)
\(444\) 0 0
\(445\) −546.653 634.051i −1.22843 1.42483i
\(446\) −82.4678 + 142.839i −0.184905 + 0.320266i
\(447\) 0 0
\(448\) 145.192 + 596.685i 0.324088 + 1.33189i
\(449\) 521.631i 1.16176i 0.813989 + 0.580881i \(0.197292\pi\)
−0.813989 + 0.580881i \(0.802708\pi\)
\(450\) 0 0
\(451\) −11.8216 20.4756i −0.0262119 0.0454003i
\(452\) −67.8765 18.1875i −0.150169 0.0402377i
\(453\) 0 0
\(454\) 10.7258i 0.0236251i
\(455\) −245.059 297.888i −0.538591 0.654699i
\(456\) 0 0
\(457\) −107.539 401.339i −0.235314 0.878204i −0.978007 0.208572i \(-0.933118\pi\)
0.742693 0.669632i \(-0.233548\pi\)
\(458\) 40.9053 152.661i 0.0893128 0.333320i
\(459\) 0 0
\(460\) 463.110 223.543i 1.00676 0.485963i
\(461\) −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 0.260444 0.965489i \(-0.416131\pi\)
−0.965489 + 0.260444i \(0.916131\pi\)
\(464\) 186.602 + 107.735i 0.402160 + 0.232187i
\(465\) 0 0
\(466\) 192.257 + 333.000i 0.412570 + 0.714592i
\(467\) −109.999 410.520i −0.235543 0.879058i −0.977903 0.209057i \(-0.932960\pi\)
0.742360 0.670001i \(-0.233706\pi\)
\(468\) 0 0
\(469\) 296.342 + 6.84907i 0.631858 + 0.0146036i
\(470\) −155.570 + 29.5825i −0.331000 + 0.0629415i
\(471\) 0 0
\(472\) 25.5569 + 6.84795i 0.0541459 + 0.0145084i
\(473\) 136.569 509.681i 0.288728 1.07755i
\(474\) 0 0
\(475\) −302.625 766.958i −0.637105 1.61465i
\(476\) −797.096 + 435.963i −1.67457 + 0.915889i
\(477\) 0 0
\(478\) 1049.35 281.171i 2.19529 0.588225i
\(479\) −183.280 + 105.817i −0.382630 + 0.220912i −0.678962 0.734173i \(-0.737570\pi\)
0.296332 + 0.955085i \(0.404237\pi\)
\(480\) 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
\(485\) −422.251 + 203.820i −0.870621 + 0.420248i
\(486\) 0 0
\(487\) −46.3134 12.4096i −0.0950993 0.0254818i 0.210956 0.977496i \(-0.432342\pi\)
−0.306055 + 0.952014i \(0.599009\pi\)
\(488\) 198.588 53.2114i 0.406942 0.109040i
\(489\) 0 0
\(490\) −286.195 670.371i −0.584071 1.36810i
\(491\) 784.457 1.59767 0.798836 0.601549i \(-0.205449\pi\)
0.798836 + 0.601549i \(0.205449\pi\)
\(492\) 0 0
\(493\) −125.696 + 469.105i −0.254962 + 0.951531i
\(494\) −936.504 + 540.691i −1.89576 + 1.09452i
\(495\) 0 0
\(496\) 274.831 0.554095
\(497\) −136.782 + 33.2833i −0.275216 + 0.0669684i
\(498\) 0 0
\(499\) 50.6730 + 29.2561i 0.101549 + 0.0586294i 0.549914 0.835221i \(-0.314660\pi\)
−0.448365 + 0.893850i \(0.647994\pi\)
\(500\) −536.923 281.894i −1.07385 0.563789i
\(501\) 0 0
\(502\) 272.086 + 1015.44i 0.542004 + 2.02279i
\(503\) −144.269 144.269i −0.286816 0.286816i 0.549004 0.835820i \(-0.315007\pi\)
−0.835820 + 0.549004i \(0.815007\pi\)
\(504\) 0 0
\(505\) 42.8070 + 225.116i 0.0847664 + 0.445774i
\(506\) 439.059 760.473i 0.867706 1.50291i
\(507\) 0 0
\(508\) −245.447 + 916.021i −0.483164 + 1.80319i
\(509\) −38.7059 22.3469i −0.0760431 0.0439035i 0.461496 0.887142i \(-0.347313\pi\)
−0.537539 + 0.843239i \(0.680646\pi\)
\(510\) 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
\(515\) −109.327 8.09265i −0.212286 0.0157139i
\(516\) 0 0
\(517\) −104.801 + 104.801i −0.202711 + 0.202711i
\(518\) −314.331 + 300.130i −0.606817 + 0.579401i
\(519\) 0 0
\(520\) −45.9806 + 131.791i −0.0884242 + 0.253443i
\(521\) −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
\(523\) −238.051 + 63.7856i −0.455165 + 0.121961i −0.479115 0.877752i \(-0.659042\pi\)
0.0239502 + 0.999713i \(0.492376\pi\)
\(524\) 106.986i 0.204172i
\(525\) 0 0
\(526\) 845.520 1.60745
\(527\) 160.325 + 598.343i 0.304223 + 1.13537i
\(528\) 0 0
\(529\) −68.9129 + 39.7869i −0.130270 + 0.0752115i
\(530\) 626.519 + 218.587i 1.18211 + 0.412429i
\(531\) 0 0
\(532\) −1088.24 + 264.802i −2.04557 + 0.497749i
\(533\) 13.2340 + 13.2340i 0.0248293 + 0.0248293i
\(534\) 0 0
\(535\) 37.2756 503.573i 0.0696740 0.941258i
\(536\) −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 \(0.908996\pi\)
\(542\) −289.959 77.6942i −0.534979 0.143347i
\(543\) 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 −0.735947 0.677039i \(-0.763263\pi\)
0.677039 + 0.735947i \(0.263263\pi\)
\(548\) 1004.67 269.201i 1.83334 0.491243i
\(549\) 0 0
\(550\) −1028.81 + 117.820i −1.87056 + 0.214219i
\(551\) −299.347 + 518.484i −0.543279 + 0.940986i
\(552\) 0 0
\(553\) 81.7133 + 23.9318i 0.147764 + 0.0432763i
\(554\) 780.291i 1.40847i
\(555\) 0 0
\(556\) −494.103 855.811i −0.888674 1.53923i
\(557\) −805.560 215.849i −1.44625 0.387521i −0.551531 0.834155i \(-0.685956\pi\)
−0.894717 + 0.446634i \(0.852623\pi\)
\(558\) 0 0
\(559\) 417.693i 0.747214i
\(560\) 241.583 337.969i 0.431398 0.603517i
\(561\) 0 0
\(562\) 303.843 + 1133.96i 0.540646 + 2.01772i
\(563\) −217.180 + 810.525i −0.385754 + 1.43965i 0.451221 + 0.892412i \(0.350989\pi\)
−0.836975 + 0.547241i \(0.815678\pi\)
\(564\) 0 0
\(565\) 31.4829 + 65.2226i 0.0557219 + 0.115438i
\(566\) 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 0.952961 0.303093i \(-0.0980191\pi\)
0.213995 + 0.976835i \(0.431352\pi\)
\(570\) 0 0
\(571\) −525.520 910.227i −0.920350 1.59409i −0.798874 0.601498i \(-0.794571\pi\)
−0.121476 0.992594i \(-0.538763\pi\)
\(572\) 192.665 + 719.034i 0.336826 + 1.25705i
\(573\) 0 0
\(574\) 16.9708 + 31.0286i 0.0295658 + 0.0540568i
\(575\) −486.156 211.053i −0.845490 0.367048i
\(576\) 0 0
\(577\) −191.449 51.2986i −0.331801 0.0889058i 0.0890726 0.996025i \(-0.471610\pi\)
−0.420873 + 0.907119i \(0.638276\pi\)
\(578\) 328.590 1226.31i 0.568494 2.12165i
\(579\) 0 0
\(580\) 82.2591 + 432.589i 0.141826 + 0.745843i
\(581\) 174.754 + 106.352i 0.300782 + 0.183051i
\(582\) 0 0
\(583\) 599.879 160.737i 1.02895 0.275707i
\(584\) −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 −0.969625 0.244596i \(-0.921345\pi\)
0.244596 + 0.969625i \(0.421345\pi\)
\(588\) 0 0
\(589\) 763.632i 1.29649i
\(590\) −67.5458 139.934i −0.114484 0.237176i
\(591\) 0 0
\(592\) −239.260 64.1094i −0.404155 0.108293i
\(593\) 521.131 139.637i 0.878805 0.235475i 0.208914 0.977934i \(-0.433007\pi\)
0.669892 + 0.742459i \(0.266341\pi\)
\(594\) 0 0
\(595\) 876.732 + 328.799i 1.47350 + 0.552603i
\(596\) −597.360 −1.00228
\(597\) 0 0
\(598\) −179.909 + 671.428i −0.300851 + 1.12279i
\(599\) −329.578 + 190.282i −0.550213 + 0.317666i −0.749208 0.662335i \(-0.769566\pi\)
0.198995 + 0.980001i \(0.436232\pi\)
\(600\) 0 0
\(601\) −566.492 −0.942582 −0.471291 0.881978i \(-0.656212\pi\)
−0.471291 + 0.881978i \(0.656212\pi\)
\(602\) −221.846 + 757.478i −0.368516 + 1.25827i
\(603\) 0 0
\(604\) 425.550 + 245.691i 0.704552 + 0.406773i
\(605\) −275.825 + 237.805i −0.455909 + 0.393066i
\(606\) 0 0
\(607\) −278.422 1039.09i −0.458685 1.71184i −0.677021 0.735963i \(-0.736730\pi\)
0.218336 0.975874i \(-0.429937\pi\)
\(608\) −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
\(613\) −108.584 + 405.242i −0.177136 + 0.661079i 0.819042 + 0.573733i \(0.194505\pi\)
−0.996178 + 0.0873463i \(0.972161\pi\)
\(614\) −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 −0.168724 0.985663i \(-0.553965\pi\)
0.985663 + 0.168724i \(0.0539645\pi\)
\(618\) 0 0
\(619\) 210.689 121.641i 0.340369 0.196512i −0.320066 0.947395i \(-0.603705\pi\)
0.660435 + 0.750883i \(0.270372\pi\)
\(620\) 366.748 + 425.383i 0.591529 + 0.686102i
\(621\) 0 0
\(622\) −293.821 + 293.821i −0.472381 + 0.472381i
\(623\) 1124.79 + 329.422i 1.80544 + 0.528768i
\(624\) 0 0
\(625\) 141.298 + 608.818i 0.226077 + 0.974109i
\(626\) 72.7413 + 125.992i 0.116200 + 0.201264i
\(627\) 0 0
\(628\) −339.666 + 91.0132i −0.540869 + 0.144926i
\(629\) 558.298i 0.887596i
\(630\) 0 0
\(631\) 912.593 1.44626 0.723132 0.690710i \(-0.242702\pi\)
0.723132 + 0.690710i \(0.242702\pi\)
\(632\) −7.97440 29.7609i −0.0126177 0.0470900i
\(633\) 0 0
\(634\) 768.315 443.587i 1.21185 0.699663i
\(635\) 880.205 424.874i 1.38615 0.669093i
\(636\) 0 0
\(637\) 514.613 + 163.719i 0.807870 + 0.257016i
\(638\) 531.693 + 531.693i 0.833375 + 0.833375i
\(639\) 0 0
\(640\) −395.020 29.2403i −0.617219 0.0456879i
\(641\) −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 0.959180 0.282797i \(-0.0912624\pi\)
−0.282797 + 0.959180i \(0.591262\pi\)
\(644\) −374.278 + 614.999i −0.581177 + 0.954967i
\(645\) 0 0
\(646\) 1312.51 2273.33i 2.03175 3.51909i
\(647\) 345.598 + 92.6027i 0.534155 + 0.143126i 0.515806 0.856705i \(-0.327492\pi\)
0.0183485 + 0.999832i \(0.494159\pi\)
\(648\) 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
\(653\) 663.599 177.811i 1.01623 0.272298i 0.288000 0.957630i \(-0.407010\pi\)
0.728231 + 0.685332i \(0.240343\pi\)
\(654\) 0 0
\(655\) −83.5107 + 71.9995i −0.127497 + 0.109923i
\(656\) −10.0784 + 17.4563i −0.0153634 + 0.0266102i
\(657\) 0 0
\(658\) 160.347 153.102i 0.243688 0.232678i
\(659\) 619.112i 0.939471i −0.882807 0.469736i \(-0.844349\pi\)
0.882807 0.469736i \(-0.155651\pi\)
\(660\) 0 0
\(661\) −249.541 432.217i −0.377520 0.653884i 0.613181 0.789943i \(-0.289890\pi\)
−0.990701 + 0.136059i \(0.956556\pi\)
\(662\) 251.545 + 67.4013i 0.379978 + 0.101815i
\(663\) 0 0
\(664\) 74.0263i 0.111485i
\(665\) 939.065 + 671.250i 1.41213 + 1.00940i
\(666\) 0 0
\(667\) 99.6041 + 371.728i 0.149332 + 0.557313i
\(668\) −335.526 + 1252.20i −0.502285 + 1.87455i
\(669\) 0 0
\(670\) −207.507 + 594.762i −0.309712 + 0.887704i
\(671\) −1130.03 −1.68410
\(672\) 0 0
\(673\) 588.355 + 588.355i 0.874227 + 0.874227i 0.992930 0.118703i \(-0.0378735\pi\)
−0.118703 + 0.992930i \(0.537874\pi\)
\(674\) −623.006 359.693i −0.924341 0.533669i
\(675\) 0 0
\(676\) 115.312 + 199.727i 0.170580 + 0.295454i
\(677\) 221.070 + 825.046i 0.326544 + 1.21868i 0.912750 + 0.408518i \(0.133954\pi\)
−0.586206 + 0.810162i \(0.699379\pi\)
\(678\) 0 0
\(679\) 341.256 560.739i 0.502586 0.825830i
\(680\) −63.2961 332.865i −0.0930824 0.489507i
\(681\) 0 0
\(682\) 926.403 + 248.229i 1.35836 + 0.363972i
\(683\) 77.6050 289.626i 0.113624 0.424050i −0.885557 0.464532i \(-0.846223\pi\)
0.999180 + 0.0404821i \(0.0128894\pi\)
\(684\) 0 0
\(685\) −886.256 603.055i −1.29380 0.880373i
\(686\) 846.287 + 570.225i 1.23365 + 0.831232i
\(687\) 0 0
\(688\) −434.524 + 116.430i −0.631576 + 0.169230i
\(689\) −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
\(695\) −335.504 + 961.629i −0.482740 + 1.38364i
\(696\) 0 0
\(697\) −43.8839 11.7586i −0.0629611 0.0168704i
\(698\) −1279.58 + 342.863i −1.83321 + 0.491208i
\(699\) 0 0
\(700\) 845.488 77.0813i 1.20784 0.110116i
\(701\) 177.525 0.253245 0.126623 0.991951i \(-0.459586\pi\)
0.126623 + 0.991951i \(0.459586\pi\)
\(702\) 0 0
\(703\) 178.131 664.795i 0.253387 0.945654i
\(704\) −1057.76 + 610.698i −1.50250 + 0.867469i
\(705\) 0 0
\(706\) 1102.00 1.56091
\(707\) −221.545 232.028i −0.313359 0.328186i
\(708\) 0 0
\(709\) 488.278 + 281.907i 0.688685 + 0.397613i 0.803119 0.595818i \(-0.203172\pi\)
−0.114434 + 0.993431i \(0.536505\pi\)
\(710\) 22.0838 298.341i 0.0311040 0.420198i
\(711\) 0 0
\(712\) −109.768 409.660i −0.154169 0.575365i
\(713\) 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
\(718\) −451.074 + 1683.43i −0.628236 + 2.34461i
\(719\) −340.465 196.567i −0.473525 0.273390i 0.244189 0.969728i \(-0.421478\pi\)
−0.717714 + 0.696338i \(0.754812\pi\)
\(720\) 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
\(725\) 282.310 355.333i 0.389393 0.490115i
\(726\) 0 0
\(727\) −110.762 + 110.762i −0.152356 + 0.152356i −0.779169 0.626814i \(-0.784359\pi\)
0.626814 + 0.779169i \(0.284359\pi\)
\(728\) −46.2020 189.874i −0.0634643 0.260815i
\(729\) 0 0
\(730\) 91.3287 + 31.8638i 0.125108 + 0.0436490i
\(731\) −506.968 878.094i −0.693527 1.20122i
\(732\) 0 0
\(733\) 673.766 180.535i 0.919190 0.246296i 0.231951 0.972727i \(-0.425489\pi\)
0.687239 + 0.726431i \(0.258822\pi\)
\(734\) 896.977i 1.22204i
\(735\) 0 0
\(736\) −963.429 −1.30901
\(737\) 152.590 + 569.472i 0.207042 + 0.772689i
\(738\) 0 0
\(739\) −701.070 + 404.763i −0.948675 + 0.547717i −0.892669 0.450713i \(-0.851170\pi\)
−0.0560056 + 0.998430i \(0.517836\pi\)
\(740\) −220.051 455.876i −0.297366 0.616049i
\(741\) 0 0
\(742\) −902.640 + 219.640i −1.21650 + 0.296010i
\(743\) −615.379 615.379i −0.828235 0.828235i 0.159037 0.987273i \(-0.449161\pi\)
−0.987273 + 0.159037i \(0.949161\pi\)
\(744\) 0 0
\(745\) 402.011 + 466.285i 0.539613 + 0.625885i
\(746\) 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 \(0.818959\pi\)
\(752\) 122.051 + 32.7035i 0.162302 + 0.0434887i
\(753\) 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 0.208047 0.978119i \(-0.433289\pi\)
0.978119 0.208047i \(-0.0667106\pi\)
\(758\) −508.832 + 136.341i −0.671283 + 0.179870i
\(759\) 0 0
\(760\) 30.8343 416.555i 0.0405715 0.548099i
\(761\) 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
\(763\) −642.417 + 613.393i −0.841963 + 0.803923i
\(764\) 754.964i 0.988173i
\(765\) 0 0
\(766\) 401.410 + 695.262i 0.524034 + 0.907653i
\(767\) 111.197 + 29.7951i 0.144976 + 0.0388462i
\(768\) 0 0
\(769\) 246.046i 0.319956i −0.987121 0.159978i \(-0.948858\pi\)
0.987121 0.159978i \(-0.0511424\pi\)
\(770\) 1119.58 921.031i 1.45401 1.19614i
\(771\) 0 0
\(772\) 264.105 + 985.653i 0.342105 + 1.27675i
\(773\) 203.881 760.894i 0.263753 0.984339i −0.699257 0.714871i \(-0.746485\pi\)
0.963009 0.269468i \(-0.0868479\pi\)
\(774\) 0 0
\(775\) 85.2297 572.549i 0.109974