Properties

Label 315.3.ca.b.37.8
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 37.8
Character \(\chi\) \(=\) 315.37
Dual form 315.3.ca.b.298.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.232416 + 0.0622758i) q^{2} +(-3.41396 + 1.97105i) q^{4} +(2.65242 - 4.23847i) q^{5} +(-4.06422 + 5.69931i) q^{7} +(1.35127 - 1.35127i) q^{8} +O(q^{10})\) \(q+(-0.232416 + 0.0622758i) q^{2} +(-3.41396 + 1.97105i) q^{4} +(2.65242 - 4.23847i) q^{5} +(-4.06422 + 5.69931i) q^{7} +(1.35127 - 1.35127i) q^{8} +(-0.352512 + 1.15027i) q^{10} +(-2.22825 - 3.85944i) q^{11} +(10.0930 - 10.0930i) q^{13} +(0.589662 - 1.57771i) q^{14} +(7.65430 - 13.2576i) q^{16} +(2.55748 - 9.54465i) q^{17} +(11.1120 + 6.41554i) q^{19} +(-0.701025 + 19.6981i) q^{20} +(0.758230 + 0.758230i) q^{22} +(-3.20215 - 11.9506i) q^{23} +(-10.9293 - 22.4844i) q^{25} +(-1.71723 + 2.97433i) q^{26} +(2.64146 - 27.4680i) q^{28} -36.7743i q^{29} +(-8.59913 - 14.8941i) q^{31} +(-2.93176 + 10.9415i) q^{32} +2.37760i q^{34} +(13.3763 + 32.3431i) q^{35} +(54.2699 - 14.5416i) q^{37} +(-2.98215 - 0.799066i) q^{38} +(-2.14319 - 9.31149i) q^{40} +46.8347 q^{41} +(25.0932 - 25.0932i) q^{43} +(15.2143 + 8.78398i) q^{44} +(1.48846 + 2.57809i) q^{46} +(-44.9155 + 12.0351i) q^{47} +(-15.9642 - 46.3265i) q^{49} +(3.94038 + 4.54512i) q^{50} +(-14.5633 + 54.3510i) q^{52} +(-58.8689 - 15.7739i) q^{53} +(-22.2684 - 0.792499i) q^{55} +(2.20945 + 13.1932i) q^{56} +(2.29015 + 8.54695i) q^{58} +(99.7443 - 57.5874i) q^{59} +(-22.1961 + 38.4447i) q^{61} +(2.92612 + 2.92612i) q^{62} +58.5089i q^{64} +(-16.0080 - 69.5498i) q^{65} +(-18.2625 + 68.1567i) q^{67} +(10.0819 + 37.6260i) q^{68} +(-5.12307 - 6.68403i) q^{70} -85.0378 q^{71} +(-11.2757 - 3.02132i) q^{73} +(-11.7076 + 6.75940i) q^{74} -50.5815 q^{76} +(31.0522 + 2.98613i) q^{77} +(57.2212 + 33.0366i) q^{79} +(-35.8897 - 67.6074i) q^{80} +(-10.8851 + 2.91666i) q^{82} +(-65.5612 + 65.5612i) q^{83} +(-33.6712 - 36.1563i) q^{85} +(-4.26937 + 7.39477i) q^{86} +(-8.22613 - 2.20418i) q^{88} +(10.9662 + 6.33133i) q^{89} +(16.5030 + 98.5433i) q^{91} +(34.4872 + 34.4872i) q^{92} +(9.68960 - 5.59429i) q^{94} +(56.6660 - 30.0814i) q^{95} +(-125.573 - 125.573i) q^{97} +(6.59537 + 9.77284i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} + O(q^{10}) \) \( 64q - 4q^{5} - 4q^{7} - 24q^{8} - 16q^{10} - 16q^{11} + 80q^{16} - 56q^{17} - 96q^{22} - 72q^{23} - 4q^{25} + 288q^{26} - 380q^{28} - 136q^{31} + 48q^{32} - 76q^{35} - 28q^{37} + 68q^{38} + 164q^{40} - 128q^{41} + 344q^{43} + 240q^{46} - 412q^{47} + 72q^{50} + 388q^{52} + 40q^{53} - 8q^{55} + 864q^{56} + 56q^{58} - 216q^{61} + 912q^{62} - 20q^{65} - 368q^{67} + 492q^{68} + 416q^{70} - 784q^{71} - 316q^{73} - 32q^{76} - 844q^{77} - 908q^{80} + 556q^{82} - 1408q^{83} - 536q^{85} - 1024q^{86} + 372q^{88} - 1064q^{91} + 1704q^{92} - 260q^{95} + 352q^{97} - 272q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.232416 + 0.0622758i −0.116208 + 0.0311379i −0.316454 0.948608i \(-0.602492\pi\)
0.200246 + 0.979746i \(0.435826\pi\)
\(3\) 0 0
\(4\) −3.41396 + 1.97105i −0.853491 + 0.492763i
\(5\) 2.65242 4.23847i 0.530485 0.847694i
\(6\) 0 0
\(7\) −4.06422 + 5.69931i −0.580603 + 0.814187i
\(8\) 1.35127 1.35127i 0.168909 0.168909i
\(9\) 0 0
\(10\) −0.352512 + 1.15027i −0.0352512 + 0.115027i
\(11\) −2.22825 3.85944i −0.202568 0.350858i 0.746787 0.665063i \(-0.231595\pi\)
−0.949355 + 0.314205i \(0.898262\pi\)
\(12\) 0 0
\(13\) 10.0930 10.0930i 0.776385 0.776385i −0.202829 0.979214i \(-0.565014\pi\)
0.979214 + 0.202829i \(0.0650137\pi\)
\(14\) 0.589662 1.57771i 0.0421187 0.112694i
\(15\) 0 0
\(16\) 7.65430 13.2576i 0.478394 0.828603i
\(17\) 2.55748 9.54465i 0.150440 0.561450i −0.849013 0.528372i \(-0.822802\pi\)
0.999453 0.0330776i \(-0.0105309\pi\)
\(18\) 0 0
\(19\) 11.1120 + 6.41554i 0.584845 + 0.337660i 0.763056 0.646332i \(-0.223698\pi\)
−0.178212 + 0.983992i \(0.557031\pi\)
\(20\) −0.701025 + 19.6981i −0.0350513 + 0.984903i
\(21\) 0 0
\(22\) 0.758230 + 0.758230i 0.0344650 + 0.0344650i
\(23\) −3.20215 11.9506i −0.139224 0.519590i −0.999945 0.0105132i \(-0.996653\pi\)
0.860721 0.509077i \(-0.170013\pi\)
\(24\) 0 0
\(25\) −10.9293 22.4844i −0.437172 0.899378i
\(26\) −1.71723 + 2.97433i −0.0660472 + 0.114397i
\(27\) 0 0
\(28\) 2.64146 27.4680i 0.0943378 0.981001i
\(29\) 36.7743i 1.26808i −0.773301 0.634040i \(-0.781396\pi\)
0.773301 0.634040i \(-0.218604\pi\)
\(30\) 0 0
\(31\) −8.59913 14.8941i −0.277391 0.480456i 0.693344 0.720606i \(-0.256136\pi\)
−0.970736 + 0.240151i \(0.922803\pi\)
\(32\) −2.93176 + 10.9415i −0.0916174 + 0.341921i
\(33\) 0 0
\(34\) 2.37760i 0.0699295i
\(35\) 13.3763 + 32.3431i 0.382181 + 0.924088i
\(36\) 0 0
\(37\) 54.2699 14.5416i 1.46675 0.393016i 0.564937 0.825134i \(-0.308900\pi\)
0.901817 + 0.432118i \(0.142234\pi\)
\(38\) −2.98215 0.799066i −0.0784777 0.0210280i
\(39\) 0 0
\(40\) −2.14319 9.31149i −0.0535796 0.232787i
\(41\) 46.8347 1.14231 0.571155 0.820843i \(-0.306496\pi\)
0.571155 + 0.820843i \(0.306496\pi\)
\(42\) 0 0
\(43\) 25.0932 25.0932i 0.583563 0.583563i −0.352317 0.935881i \(-0.614606\pi\)
0.935881 + 0.352317i \(0.114606\pi\)
\(44\) 15.2143 + 8.78398i 0.345780 + 0.199636i
\(45\) 0 0
\(46\) 1.48846 + 2.57809i 0.0323579 + 0.0560455i
\(47\) −44.9155 + 12.0351i −0.955649 + 0.256065i −0.702758 0.711429i \(-0.748048\pi\)
−0.252891 + 0.967495i \(0.581382\pi\)
\(48\) 0 0
\(49\) −15.9642 46.3265i −0.325801 0.945438i
\(50\) 3.94038 + 4.54512i 0.0788076 + 0.0909024i
\(51\) 0 0
\(52\) −14.5633 + 54.3510i −0.280063 + 1.04521i
\(53\) −58.8689 15.7739i −1.11073 0.297620i −0.343606 0.939114i \(-0.611648\pi\)
−0.767128 + 0.641494i \(0.778315\pi\)
\(54\) 0 0
\(55\) −22.2684 0.792499i −0.404879 0.0144091i
\(56\) 2.20945 + 13.1932i 0.0394545 + 0.235593i
\(57\) 0 0
\(58\) 2.29015 + 8.54695i 0.0394853 + 0.147361i
\(59\) 99.7443 57.5874i 1.69058 0.976058i 0.736535 0.676399i \(-0.236460\pi\)
0.954046 0.299659i \(-0.0968729\pi\)
\(60\) 0 0
\(61\) −22.1961 + 38.4447i −0.363870 + 0.630241i −0.988594 0.150604i \(-0.951878\pi\)
0.624724 + 0.780845i \(0.285211\pi\)
\(62\) 2.92612 + 2.92612i 0.0471955 + 0.0471955i
\(63\) 0 0
\(64\) 58.5089i 0.914201i
\(65\) −16.0080 69.5498i −0.246277 1.07000i
\(66\) 0 0
\(67\) −18.2625 + 68.1567i −0.272575 + 1.01726i 0.684874 + 0.728662i \(0.259857\pi\)
−0.957449 + 0.288602i \(0.906809\pi\)
\(68\) 10.0819 + 37.6260i 0.148263 + 0.553324i
\(69\) 0 0
\(70\) −5.12307 6.68403i −0.0731867 0.0954862i
\(71\) −85.0378 −1.19772 −0.598858 0.800855i \(-0.704379\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(72\) 0 0
\(73\) −11.2757 3.02132i −0.154462 0.0413879i 0.180760 0.983527i \(-0.442144\pi\)
−0.335221 + 0.942139i \(0.608811\pi\)
\(74\) −11.7076 + 6.75940i −0.158211 + 0.0913432i
\(75\) 0 0
\(76\) −50.5815 −0.665546
\(77\) 31.0522 + 2.98613i 0.403275 + 0.0387809i
\(78\) 0 0
\(79\) 57.2212 + 33.0366i 0.724318 + 0.418185i 0.816340 0.577572i \(-0.196000\pi\)
−0.0920217 + 0.995757i \(0.529333\pi\)
\(80\) −35.8897 67.6074i −0.448621 0.845093i
\(81\) 0 0
\(82\) −10.8851 + 2.91666i −0.132746 + 0.0355691i
\(83\) −65.5612 + 65.5612i −0.789894 + 0.789894i −0.981476 0.191583i \(-0.938638\pi\)
0.191583 + 0.981476i \(0.438638\pi\)
\(84\) 0 0
\(85\) −33.6712 36.1563i −0.396132 0.425368i
\(86\) −4.26937 + 7.39477i −0.0496439 + 0.0859857i
\(87\) 0 0
\(88\) −8.22613 2.20418i −0.0934787 0.0250475i
\(89\) 10.9662 + 6.33133i 0.123216 + 0.0711385i 0.560341 0.828262i \(-0.310670\pi\)
−0.437125 + 0.899401i \(0.644003\pi\)
\(90\) 0 0
\(91\) 16.5030 + 98.5433i 0.181351 + 1.08289i
\(92\) 34.4872 + 34.4872i 0.374861 + 0.374861i
\(93\) 0 0
\(94\) 9.68960 5.59429i 0.103081 0.0595138i
\(95\) 56.6660 30.0814i 0.596484 0.316646i
\(96\) 0 0
\(97\) −125.573 125.573i −1.29456 1.29456i −0.931932 0.362632i \(-0.881878\pi\)
−0.362632 0.931932i \(-0.618122\pi\)
\(98\) 6.59537 + 9.77284i 0.0672997 + 0.0997229i
\(99\) 0 0
\(100\) 81.6302 + 55.2189i 0.816302 + 0.552189i
\(101\) 57.5790 + 99.7297i 0.570089 + 0.987422i 0.996556 + 0.0829196i \(0.0264245\pi\)
−0.426468 + 0.904503i \(0.640242\pi\)
\(102\) 0 0
\(103\) 25.0098 + 93.3379i 0.242814 + 0.906193i 0.974470 + 0.224519i \(0.0720810\pi\)
−0.731656 + 0.681674i \(0.761252\pi\)
\(104\) 27.2768i 0.262277i
\(105\) 0 0
\(106\) 14.6644 0.138344
\(107\) −119.300 + 31.9665i −1.11496 + 0.298752i −0.768841 0.639440i \(-0.779166\pi\)
−0.346116 + 0.938192i \(0.612500\pi\)
\(108\) 0 0
\(109\) 43.0410 24.8497i 0.394871 0.227979i −0.289397 0.957209i \(-0.593455\pi\)
0.684269 + 0.729230i \(0.260122\pi\)
\(110\) 5.22488 1.20259i 0.0474990 0.0109326i
\(111\) 0 0
\(112\) 44.4506 + 97.5062i 0.396881 + 0.870591i
\(113\) 42.4036 42.4036i 0.375253 0.375253i −0.494133 0.869386i \(-0.664514\pi\)
0.869386 + 0.494133i \(0.164514\pi\)
\(114\) 0 0
\(115\) −59.1456 18.1258i −0.514310 0.157615i
\(116\) 72.4841 + 125.546i 0.624863 + 1.08229i
\(117\) 0 0
\(118\) −19.5959 + 19.5959i −0.166067 + 0.166067i
\(119\) 44.0038 + 53.3674i 0.369779 + 0.448466i
\(120\) 0 0
\(121\) 50.5698 87.5895i 0.417933 0.723880i
\(122\) 2.76455 10.3174i 0.0226603 0.0845693i
\(123\) 0 0
\(124\) 58.7142 + 33.8987i 0.473502 + 0.273376i
\(125\) −124.289 13.3148i −0.994311 0.106518i
\(126\) 0 0
\(127\) −62.2747 62.2747i −0.490352 0.490352i 0.418065 0.908417i \(-0.362708\pi\)
−0.908417 + 0.418065i \(0.862708\pi\)
\(128\) −15.3707 57.3643i −0.120084 0.448158i
\(129\) 0 0
\(130\) 8.05178 + 15.1676i 0.0619368 + 0.116674i
\(131\) −7.67305 + 13.2901i −0.0585729 + 0.101451i −0.893825 0.448416i \(-0.851988\pi\)
0.835252 + 0.549867i \(0.185322\pi\)
\(132\) 0 0
\(133\) −81.7260 + 37.2568i −0.614481 + 0.280126i
\(134\) 16.9780i 0.126702i
\(135\) 0 0
\(136\) −9.44158 16.3533i −0.0694234 0.120245i
\(137\) −58.8789 + 219.739i −0.429773 + 1.60394i 0.323500 + 0.946228i \(0.395140\pi\)
−0.753273 + 0.657708i \(0.771526\pi\)
\(138\) 0 0
\(139\) 102.047i 0.734151i −0.930191 0.367076i \(-0.880359\pi\)
0.930191 0.367076i \(-0.119641\pi\)
\(140\) −109.416 84.0526i −0.781544 0.600375i
\(141\) 0 0
\(142\) 19.7642 5.29579i 0.139184 0.0372943i
\(143\) −61.4430 16.4636i −0.429671 0.115130i
\(144\) 0 0
\(145\) −155.867 97.5410i −1.07494 0.672697i
\(146\) 2.80881 0.0192384
\(147\) 0 0
\(148\) −156.613 + 156.613i −1.05820 + 1.05820i
\(149\) 253.568 + 146.397i 1.70180 + 0.982532i 0.943944 + 0.330104i \(0.107084\pi\)
0.757851 + 0.652428i \(0.226249\pi\)
\(150\) 0 0
\(151\) 103.721 + 179.651i 0.686897 + 1.18974i 0.972837 + 0.231492i \(0.0743608\pi\)
−0.285940 + 0.958247i \(0.592306\pi\)
\(152\) 23.6846 6.34626i 0.155820 0.0417517i
\(153\) 0 0
\(154\) −7.40300 + 1.23977i −0.0480714 + 0.00805048i
\(155\) −85.9369 3.05837i −0.554431 0.0197314i
\(156\) 0 0
\(157\) 19.6048 73.1661i 0.124871 0.466026i −0.874964 0.484188i \(-0.839115\pi\)
0.999835 + 0.0181625i \(0.00578162\pi\)
\(158\) −15.3565 4.11476i −0.0971931 0.0260428i
\(159\) 0 0
\(160\) 38.5988 + 41.4476i 0.241243 + 0.259047i
\(161\) 81.1243 + 30.3197i 0.503877 + 0.188321i
\(162\) 0 0
\(163\) −50.8403 189.738i −0.311903 1.16404i −0.926838 0.375461i \(-0.877484\pi\)
0.614935 0.788578i \(-0.289182\pi\)
\(164\) −159.892 + 92.3136i −0.974950 + 0.562888i
\(165\) 0 0
\(166\) 11.1546 19.3204i 0.0671965 0.116388i
\(167\) −189.235 189.235i −1.13314 1.13314i −0.989652 0.143492i \(-0.954167\pi\)
−0.143492 0.989652i \(-0.545833\pi\)
\(168\) 0 0
\(169\) 34.7373i 0.205546i
\(170\) 10.0774 + 6.30641i 0.0592788 + 0.0370965i
\(171\) 0 0
\(172\) −36.2073 + 135.127i −0.210507 + 0.785624i
\(173\) −49.4475 184.540i −0.285823 1.06671i −0.948236 0.317568i \(-0.897134\pi\)
0.662412 0.749140i \(-0.269533\pi\)
\(174\) 0 0
\(175\) 172.565 + 29.0923i 0.986085 + 0.166242i
\(176\) −68.2227 −0.387629
\(177\) 0 0
\(178\) −2.94301 0.788577i −0.0165338 0.00443021i
\(179\) 158.096 91.2766i 0.883216 0.509925i 0.0114988 0.999934i \(-0.496340\pi\)
0.871718 + 0.490009i \(0.163006\pi\)
\(180\) 0 0
\(181\) −103.223 −0.570290 −0.285145 0.958484i \(-0.592042\pi\)
−0.285145 + 0.958484i \(0.592042\pi\)
\(182\) −9.97241 21.8753i −0.0547935 0.120194i
\(183\) 0 0
\(184\) −20.4755 11.8215i −0.111280 0.0642474i
\(185\) 82.3127 268.592i 0.444934 1.45185i
\(186\) 0 0
\(187\) −42.5357 + 11.3974i −0.227463 + 0.0609487i
\(188\) 129.618 129.618i 0.689458 0.689458i
\(189\) 0 0
\(190\) −11.2968 + 10.5203i −0.0594566 + 0.0553701i
\(191\) 129.306 223.965i 0.676996 1.17259i −0.298885 0.954289i \(-0.596615\pi\)
0.975881 0.218302i \(-0.0700519\pi\)
\(192\) 0 0
\(193\) 88.4965 + 23.7126i 0.458531 + 0.122863i 0.480688 0.876891i \(-0.340387\pi\)
−0.0221573 + 0.999754i \(0.507053\pi\)
\(194\) 37.0053 + 21.3650i 0.190749 + 0.110129i
\(195\) 0 0
\(196\) 145.813 + 126.691i 0.743945 + 0.646380i
\(197\) 186.124 + 186.124i 0.944793 + 0.944793i 0.998554 0.0537607i \(-0.0171208\pi\)
−0.0537607 + 0.998554i \(0.517121\pi\)
\(198\) 0 0
\(199\) 234.511 135.395i 1.17844 0.680375i 0.222791 0.974866i \(-0.428483\pi\)
0.955654 + 0.294491i \(0.0951500\pi\)
\(200\) −45.1511 15.6142i −0.225756 0.0780709i
\(201\) 0 0
\(202\) −19.5930 19.5930i −0.0969952 0.0969952i
\(203\) 209.588 + 149.459i 1.03245 + 0.736250i
\(204\) 0 0
\(205\) 124.225 198.507i 0.605978 0.968329i
\(206\) −11.6254 20.1357i −0.0564338 0.0977463i
\(207\) 0 0
\(208\) −56.5545 211.064i −0.271897 1.01473i
\(209\) 57.1817i 0.273596i
\(210\) 0 0
\(211\) 294.597 1.39619 0.698096 0.716004i \(-0.254031\pi\)
0.698096 + 0.716004i \(0.254031\pi\)
\(212\) 232.067 62.1823i 1.09466 0.293313i
\(213\) 0 0
\(214\) 25.7366 14.8590i 0.120265 0.0694348i
\(215\) −39.7991 172.915i −0.185112 0.804255i
\(216\) 0 0
\(217\) 119.835 + 11.5239i 0.552235 + 0.0531056i
\(218\) −8.45589 + 8.45589i −0.0387885 + 0.0387885i
\(219\) 0 0
\(220\) 77.5854 41.1866i 0.352661 0.187212i
\(221\) −70.5215 122.147i −0.319102 0.552701i
\(222\) 0 0
\(223\) 8.97417 8.97417i 0.0402429 0.0402429i −0.686699 0.726942i \(-0.740941\pi\)
0.726942 + 0.686699i \(0.240941\pi\)
\(224\) −50.4435 61.1775i −0.225194 0.273114i
\(225\) 0 0
\(226\) −7.21458 + 12.4960i −0.0319229 + 0.0552921i
\(227\) −93.1104 + 347.493i −0.410178 + 1.53080i 0.384124 + 0.923281i \(0.374503\pi\)
−0.794302 + 0.607523i \(0.792163\pi\)
\(228\) 0 0
\(229\) −201.351 116.250i −0.879261 0.507642i −0.00884639 0.999961i \(-0.502816\pi\)
−0.870415 + 0.492319i \(0.836149\pi\)
\(230\) 14.8752 + 0.529387i 0.0646748 + 0.00230168i
\(231\) 0 0
\(232\) −49.6921 49.6921i −0.214190 0.214190i
\(233\) −8.52601 31.8195i −0.0365923 0.136564i 0.945213 0.326454i \(-0.105854\pi\)
−0.981805 + 0.189889i \(0.939187\pi\)
\(234\) 0 0
\(235\) −68.1246 + 222.295i −0.289892 + 0.945937i
\(236\) −227.016 + 393.203i −0.961931 + 1.66611i
\(237\) 0 0
\(238\) −13.5507 9.66309i −0.0569357 0.0406012i
\(239\) 133.557i 0.558817i −0.960172 0.279408i \(-0.909862\pi\)
0.960172 0.279408i \(-0.0901383\pi\)
\(240\) 0 0
\(241\) −230.800 399.758i −0.957678 1.65875i −0.728117 0.685453i \(-0.759604\pi\)
−0.229561 0.973294i \(-0.573729\pi\)
\(242\) −6.29855 + 23.5065i −0.0260271 + 0.0971343i
\(243\) 0 0
\(244\) 174.998i 0.717206i
\(245\) −238.697 55.2135i −0.974275 0.225361i
\(246\) 0 0
\(247\) 176.906 47.4018i 0.716219 0.191910i
\(248\) −31.7458 8.50627i −0.128007 0.0342995i
\(249\) 0 0
\(250\) 29.7159 4.64561i 0.118864 0.0185824i
\(251\) 125.961 0.501837 0.250919 0.968008i \(-0.419267\pi\)
0.250919 + 0.968008i \(0.419267\pi\)
\(252\) 0 0
\(253\) −38.9873 + 38.9873i −0.154100 + 0.154100i
\(254\) 18.3519 + 10.5955i 0.0722515 + 0.0417144i
\(255\) 0 0
\(256\) −109.873 190.305i −0.429191 0.743381i
\(257\) 236.058 63.2516i 0.918515 0.246115i 0.231564 0.972820i \(-0.425616\pi\)
0.686950 + 0.726704i \(0.258949\pi\)
\(258\) 0 0
\(259\) −137.688 + 368.401i −0.531613 + 1.42240i
\(260\) 191.737 + 205.888i 0.737450 + 0.791876i
\(261\) 0 0
\(262\) 0.955690 3.56669i 0.00364767 0.0136133i
\(263\) −116.745 31.2818i −0.443898 0.118942i 0.0299446 0.999552i \(-0.490467\pi\)
−0.473843 + 0.880609i \(0.657134\pi\)
\(264\) 0 0
\(265\) −223.002 + 207.675i −0.841519 + 0.783680i
\(266\) 16.6742 13.7486i 0.0626851 0.0516866i
\(267\) 0 0
\(268\) −71.9928 268.681i −0.268630 1.00254i
\(269\) −221.456 + 127.858i −0.823258 + 0.475308i −0.851539 0.524292i \(-0.824330\pi\)
0.0282806 + 0.999600i \(0.490997\pi\)
\(270\) 0 0
\(271\) −24.1359 + 41.8046i −0.0890625 + 0.154261i −0.907115 0.420883i \(-0.861720\pi\)
0.818053 + 0.575143i \(0.195054\pi\)
\(272\) −106.964 106.964i −0.393249 0.393249i
\(273\) 0 0
\(274\) 54.7377i 0.199773i
\(275\) −62.4241 + 92.2818i −0.226997 + 0.335570i
\(276\) 0 0
\(277\) −26.8253 + 100.113i −0.0968423 + 0.361420i −0.997292 0.0735390i \(-0.976571\pi\)
0.900450 + 0.434960i \(0.143237\pi\)
\(278\) 6.35506 + 23.7174i 0.0228599 + 0.0853143i
\(279\) 0 0
\(280\) 61.7794 + 25.6293i 0.220641 + 0.0915330i
\(281\) −357.942 −1.27382 −0.636908 0.770940i \(-0.719787\pi\)
−0.636908 + 0.770940i \(0.719787\pi\)
\(282\) 0 0
\(283\) 174.344 + 46.7152i 0.616055 + 0.165072i 0.553334 0.832960i \(-0.313355\pi\)
0.0627214 + 0.998031i \(0.480022\pi\)
\(284\) 290.316 167.614i 1.02224 0.590190i
\(285\) 0 0
\(286\) 15.3056 0.0535162
\(287\) −190.346 + 266.925i −0.663228 + 0.930053i
\(288\) 0 0
\(289\) 165.722 + 95.6795i 0.573431 + 0.331071i
\(290\) 42.3004 + 12.9634i 0.145864 + 0.0447014i
\(291\) 0 0
\(292\) 44.4500 11.9103i 0.152226 0.0407889i
\(293\) −116.627 + 116.627i −0.398046 + 0.398046i −0.877543 0.479497i \(-0.840819\pi\)
0.479497 + 0.877543i \(0.340819\pi\)
\(294\) 0 0
\(295\) 20.4816 575.510i 0.0694290 1.95088i
\(296\) 53.6838 92.9832i 0.181364 0.314132i
\(297\) 0 0
\(298\) −68.0502 18.2340i −0.228356 0.0611879i
\(299\) −152.936 88.2979i −0.511493 0.295311i
\(300\) 0 0
\(301\) 41.0297 + 244.998i 0.136311 + 0.813948i
\(302\) −35.2944 35.2944i −0.116869 0.116869i
\(303\) 0 0
\(304\) 170.110 98.2130i 0.559572 0.323069i
\(305\) 104.073 + 196.049i 0.341224 + 0.642784i
\(306\) 0 0
\(307\) 102.316 + 102.316i 0.333276 + 0.333276i 0.853829 0.520553i \(-0.174274\pi\)
−0.520553 + 0.853829i \(0.674274\pi\)
\(308\) −111.897 + 51.0110i −0.363302 + 0.165620i
\(309\) 0 0
\(310\) 20.1636 4.64097i 0.0650438 0.0149709i
\(311\) 5.34944 + 9.26551i 0.0172008 + 0.0297926i 0.874498 0.485030i \(-0.161191\pi\)
−0.857297 + 0.514822i \(0.827858\pi\)
\(312\) 0 0
\(313\) 123.581 + 461.210i 0.394827 + 1.47351i 0.822075 + 0.569380i \(0.192816\pi\)
−0.427248 + 0.904135i \(0.640517\pi\)
\(314\) 18.2259i 0.0580442i
\(315\) 0 0
\(316\) −260.468 −0.824265
\(317\) 71.5544 19.1729i 0.225724 0.0604825i −0.144184 0.989551i \(-0.546056\pi\)
0.369908 + 0.929068i \(0.379389\pi\)
\(318\) 0 0
\(319\) −141.928 + 81.9422i −0.444916 + 0.256872i
\(320\) 247.988 + 155.190i 0.774963 + 0.484970i
\(321\) 0 0
\(322\) −20.7428 1.99473i −0.0644186 0.00619480i
\(323\) 89.6530 89.6530i 0.277563 0.277563i
\(324\) 0 0
\(325\) −337.245 116.626i −1.03768 0.358850i
\(326\) 23.6322 + 40.9322i 0.0724914 + 0.125559i
\(327\) 0 0
\(328\) 63.2865 63.2865i 0.192947 0.192947i
\(329\) 113.955 304.900i 0.346367 0.926749i
\(330\) 0 0
\(331\) −186.461 + 322.960i −0.563327 + 0.975711i 0.433876 + 0.900972i \(0.357145\pi\)
−0.997203 + 0.0747382i \(0.976188\pi\)
\(332\) 94.5989 353.048i 0.284937 1.06340i
\(333\) 0 0
\(334\) 55.7660 + 32.1965i 0.166964 + 0.0963968i
\(335\) 240.440 + 258.186i 0.717732 + 0.770703i
\(336\) 0 0
\(337\) −1.52001 1.52001i −0.00451041 0.00451041i 0.704848 0.709358i \(-0.251015\pi\)
−0.709358 + 0.704848i \(0.751015\pi\)
\(338\) 2.16329 + 8.07351i 0.00640027 + 0.0238861i
\(339\) 0 0
\(340\) 186.218 + 57.0684i 0.547701 + 0.167848i
\(341\) −38.3220 + 66.3756i −0.112381 + 0.194650i
\(342\) 0 0
\(343\) 328.911 + 97.2959i 0.958925 + 0.283661i
\(344\) 67.8156i 0.197138i
\(345\) 0 0
\(346\) 22.9848 + 39.8108i 0.0664300 + 0.115060i
\(347\) 54.2716 202.544i 0.156402 0.583701i −0.842579 0.538573i \(-0.818964\pi\)
0.998981 0.0451282i \(-0.0143696\pi\)
\(348\) 0 0
\(349\) 256.040i 0.733639i 0.930292 + 0.366820i \(0.119553\pi\)
−0.930292 + 0.366820i \(0.880447\pi\)
\(350\) −41.9186 + 3.98508i −0.119768 + 0.0113860i
\(351\) 0 0
\(352\) 48.7606 13.0654i 0.138524 0.0371175i
\(353\) 3.09864 + 0.830277i 0.00877800 + 0.00235206i 0.263205 0.964740i \(-0.415220\pi\)
−0.254427 + 0.967092i \(0.581887\pi\)
\(354\) 0 0
\(355\) −225.556 + 360.430i −0.635370 + 1.01530i
\(356\) −49.9175 −0.140218
\(357\) 0 0
\(358\) −31.0597 + 31.0597i −0.0867589 + 0.0867589i
\(359\) 268.238 + 154.867i 0.747181 + 0.431385i 0.824674 0.565608i \(-0.191358\pi\)
−0.0774934 + 0.996993i \(0.524692\pi\)
\(360\) 0 0
\(361\) −98.1816 170.055i −0.271971 0.471068i
\(362\) 23.9906 6.42826i 0.0662724 0.0177576i
\(363\) 0 0
\(364\) −250.574 303.895i −0.688391 0.834876i
\(365\) −42.7137 + 39.7780i −0.117024 + 0.108981i
\(366\) 0 0
\(367\) −90.8527 + 339.067i −0.247555 + 0.923888i 0.724527 + 0.689247i \(0.242058\pi\)
−0.972082 + 0.234642i \(0.924608\pi\)
\(368\) −182.947 49.0204i −0.497138 0.133208i
\(369\) 0 0
\(370\) −2.40405 + 67.5512i −0.00649743 + 0.182571i
\(371\) 329.156 271.404i 0.887214 0.731546i
\(372\) 0 0
\(373\) −25.6741 95.8169i −0.0688313 0.256882i 0.922933 0.384962i \(-0.125785\pi\)
−0.991764 + 0.128080i \(0.959119\pi\)
\(374\) 9.17620 5.29788i 0.0245353 0.0141655i
\(375\) 0 0
\(376\) −44.4305 + 76.9558i −0.118166 + 0.204670i
\(377\) −371.163 371.163i −0.984517 0.984517i
\(378\) 0 0
\(379\) 466.795i 1.23165i 0.787884 + 0.615824i \(0.211177\pi\)
−0.787884 + 0.615824i \(0.788823\pi\)
\(380\) −134.164 + 214.388i −0.353062 + 0.564180i
\(381\) 0 0
\(382\) −16.1053 + 60.1057i −0.0421604 + 0.157345i
\(383\) 59.3027 + 221.321i 0.154837 + 0.577861i 0.999119 + 0.0419615i \(0.0133607\pi\)
−0.844282 + 0.535899i \(0.819973\pi\)
\(384\) 0 0
\(385\) 95.0202 123.693i 0.246806 0.321282i
\(386\) −22.0448 −0.0571108
\(387\) 0 0
\(388\) 676.211 + 181.190i 1.74281 + 0.466985i
\(389\) −465.749 + 268.900i −1.19730 + 0.691260i −0.959952 0.280165i \(-0.909611\pi\)
−0.237346 + 0.971425i \(0.576277\pi\)
\(390\) 0 0
\(391\) −122.254 −0.312669
\(392\) −84.1718 41.0277i −0.214724 0.104663i
\(393\) 0 0
\(394\) −54.8493 31.6673i −0.139211 0.0803738i
\(395\) 291.800 154.903i 0.738733 0.392160i
\(396\) 0 0
\(397\) −79.7937 + 21.3807i −0.200992 + 0.0538555i −0.357910 0.933756i \(-0.616511\pi\)
0.156919 + 0.987612i \(0.449844\pi\)
\(398\) −46.0723 + 46.0723i −0.115759 + 0.115759i
\(399\) 0 0
\(400\) −381.747 27.2061i −0.954367 0.0680152i
\(401\) 72.9306 126.319i 0.181872 0.315011i −0.760646 0.649167i \(-0.775118\pi\)
0.942518 + 0.334156i \(0.108451\pi\)
\(402\) 0 0
\(403\) −237.117 63.5354i −0.588381 0.157656i
\(404\) −393.145 226.982i −0.973131 0.561837i
\(405\) 0 0
\(406\) −58.0193 21.6844i −0.142905 0.0534099i
\(407\) −177.049 177.049i −0.435010 0.435010i
\(408\) 0 0
\(409\) −350.103 + 202.132i −0.855998 + 0.494211i −0.862670 0.505767i \(-0.831209\pi\)
0.00667227 + 0.999978i \(0.497876\pi\)
\(410\) −16.5098 + 53.8726i −0.0402678 + 0.131397i
\(411\) 0 0
\(412\) −269.356 269.356i −0.653777 0.653777i
\(413\) −77.1744 + 802.522i −0.186863 + 1.94315i
\(414\) 0 0
\(415\) 103.983 + 451.775i 0.250562 + 1.08862i
\(416\) 80.8420 + 140.022i 0.194332 + 0.336592i
\(417\) 0 0
\(418\) 3.56103 + 13.2899i 0.00851921 + 0.0317941i
\(419\) 404.689i 0.965844i 0.875663 + 0.482922i \(0.160425\pi\)
−0.875663 + 0.482922i \(0.839575\pi\)
\(420\) 0 0
\(421\) 430.807 1.02329 0.511647 0.859196i \(-0.329035\pi\)
0.511647 + 0.859196i \(0.329035\pi\)
\(422\) −68.4691 + 18.3462i −0.162249 + 0.0434745i
\(423\) 0 0
\(424\) −100.863 + 58.2332i −0.237884 + 0.137342i
\(425\) −242.558 + 46.8128i −0.570724 + 0.110148i
\(426\) 0 0
\(427\) −128.899 282.750i −0.301870 0.662178i
\(428\) 344.280 344.280i 0.804392 0.804392i
\(429\) 0 0
\(430\) 20.0184 + 37.7097i 0.0465543 + 0.0876970i
\(431\) −32.0539 55.5190i −0.0743710 0.128814i 0.826442 0.563023i \(-0.190362\pi\)
−0.900813 + 0.434208i \(0.857028\pi\)
\(432\) 0 0
\(433\) −58.9362 + 58.9362i −0.136111 + 0.136111i −0.771880 0.635769i \(-0.780683\pi\)
0.635769 + 0.771880i \(0.280683\pi\)
\(434\) −28.5693 + 4.78447i −0.0658278 + 0.0110241i
\(435\) 0 0
\(436\) −97.9601 + 169.672i −0.224679 + 0.389156i
\(437\) 41.0870 153.339i 0.0940207 0.350890i
\(438\) 0 0
\(439\) 262.656 + 151.644i 0.598304 + 0.345431i 0.768374 0.640001i \(-0.221066\pi\)
−0.170070 + 0.985432i \(0.554399\pi\)
\(440\) −31.1615 + 29.0198i −0.0708217 + 0.0659540i
\(441\) 0 0
\(442\) 23.9971 + 23.9971i 0.0542922 + 0.0542922i
\(443\) 55.0133 + 205.312i 0.124184 + 0.463459i 0.999809 0.0195310i \(-0.00621730\pi\)
−0.875626 + 0.482990i \(0.839551\pi\)
\(444\) 0 0
\(445\) 55.9221 29.6865i 0.125668 0.0667112i
\(446\) −1.52687 + 2.64461i −0.00342347 + 0.00592963i
\(447\) 0 0
\(448\) −333.460 237.793i −0.744331 0.530788i
\(449\) 266.145i 0.592751i 0.955072 + 0.296375i \(0.0957779\pi\)
−0.955072 + 0.296375i \(0.904222\pi\)
\(450\) 0 0
\(451\) −104.359 180.755i −0.231395 0.400788i
\(452\) −61.1846 + 228.344i −0.135364 + 0.505186i
\(453\) 0 0
\(454\) 86.5615i 0.190664i
\(455\) 461.446 + 191.431i 1.01417 + 0.420728i
\(456\) 0 0
\(457\) 304.655 81.6321i 0.666641 0.178626i 0.0904000 0.995906i \(-0.471185\pi\)
0.576241 + 0.817280i \(0.304519\pi\)
\(458\) 54.0368 + 14.4791i 0.117984 + 0.0316138i
\(459\) 0 0
\(460\) 237.648 54.6984i 0.516626 0.118910i
\(461\) 613.866 1.33160 0.665799 0.746132i \(-0.268091\pi\)
0.665799 + 0.746132i \(0.268091\pi\)
\(462\) 0 0
\(463\) 140.640 140.640i 0.303758 0.303758i −0.538724 0.842482i \(-0.681093\pi\)
0.842482 + 0.538724i \(0.181093\pi\)
\(464\) −487.540 281.482i −1.05073 0.606641i
\(465\) 0 0
\(466\) 3.96317 + 6.86440i 0.00850465 + 0.0147305i
\(467\) 309.664 82.9741i 0.663091 0.177675i 0.0884506 0.996081i \(-0.471808\pi\)
0.574641 + 0.818406i \(0.305142\pi\)
\(468\) 0 0
\(469\) −314.223 381.088i −0.669985 0.812553i
\(470\) 1.98967 55.9075i 0.00423334 0.118952i
\(471\) 0 0
\(472\) 56.9655 212.598i 0.120690 0.450420i
\(473\) −152.760 40.9318i −0.322959 0.0865366i
\(474\) 0 0
\(475\) 22.8031 319.966i 0.0480066 0.673612i
\(476\) −255.417 95.4607i −0.536591 0.200548i
\(477\) 0 0
\(478\) 8.31737 + 31.0409i 0.0174004 + 0.0649390i
\(479\) −459.429 + 265.251i −0.959141 + 0.553761i −0.895909 0.444238i \(-0.853474\pi\)
−0.0632327 + 0.997999i \(0.520141\pi\)
\(480\) 0 0
\(481\) 400.978 694.514i 0.833634 1.44390i
\(482\) 78.5370 + 78.5370i 0.162940 + 0.162940i
\(483\) 0 0
\(484\) 398.703i 0.823767i
\(485\) −865.309 + 199.165i −1.78414 + 0.410648i
\(486\) 0 0
\(487\) 36.7674 137.218i 0.0754977 0.281761i −0.917848 0.396932i \(-0.870075\pi\)
0.993346 + 0.115171i \(0.0367415\pi\)
\(488\) 21.9564 + 81.9423i 0.0449925 + 0.167914i
\(489\) 0 0
\(490\) 58.9156 2.03255i 0.120236 0.00414807i
\(491\) 98.2025 0.200005 0.100003 0.994987i \(-0.468115\pi\)
0.100003 + 0.994987i \(0.468115\pi\)
\(492\) 0 0
\(493\) −350.998 94.0496i −0.711963 0.190770i
\(494\) −38.1638 + 22.0339i −0.0772548 + 0.0446031i
\(495\) 0 0
\(496\) −263.281 −0.530809
\(497\) 345.612 484.657i 0.695397 0.975164i
\(498\) 0 0
\(499\) 75.4381 + 43.5542i 0.151179 + 0.0872830i 0.573681 0.819079i \(-0.305515\pi\)
−0.422502 + 0.906362i \(0.638848\pi\)
\(500\) 450.562 199.524i 0.901123 0.399047i
\(501\) 0 0
\(502\) −29.2754 + 7.84433i −0.0583176 + 0.0156261i
\(503\) −360.582 + 360.582i −0.716863 + 0.716863i −0.967962 0.251098i \(-0.919208\pi\)
0.251098 + 0.967962i \(0.419208\pi\)
\(504\) 0 0
\(505\) 575.425 + 20.4786i 1.13946 + 0.0405516i
\(506\) 6.63332 11.4893i 0.0131093 0.0227060i
\(507\) 0 0
\(508\) 335.350 + 89.8569i 0.660139 + 0.176884i
\(509\) 203.239 + 117.340i 0.399291 + 0.230531i 0.686178 0.727434i \(-0.259287\pi\)
−0.286887 + 0.957964i \(0.592620\pi\)
\(510\) 0 0
\(511\) 63.0464 51.9845i 0.123378 0.101731i
\(512\) 205.362 + 205.362i 0.401098 + 0.401098i
\(513\) 0 0
\(514\) −50.9247 + 29.4014i −0.0990754 + 0.0572012i
\(515\) 461.947 + 141.568i 0.896984 + 0.274890i
\(516\) 0 0
\(517\) 146.531 + 146.531i 0.283426 + 0.283426i
\(518\) 9.05844 94.1970i 0.0174873 0.181848i
\(519\) 0 0
\(520\) −115.612 72.3497i −0.222331 0.139134i
\(521\) −264.414 457.979i −0.507513 0.879038i −0.999962 0.00869711i \(-0.997232\pi\)
0.492449 0.870341i \(-0.336102\pi\)
\(522\) 0 0
\(523\) −96.7747 361.168i −0.185038 0.690570i −0.994622 0.103567i \(-0.966974\pi\)
0.809585 0.587003i \(-0.199692\pi\)
\(524\) 60.4960i 0.115450i
\(525\) 0 0
\(526\) 29.0816 0.0552882
\(527\) −164.151 + 43.9842i −0.311483 + 0.0834615i
\(528\) 0 0
\(529\) 325.565 187.965i 0.615435 0.355321i
\(530\) 38.8963 62.1548i 0.0733892 0.117273i
\(531\) 0 0
\(532\) 205.574 288.280i 0.386418 0.541879i
\(533\) 472.702 472.702i 0.886871 0.886871i
\(534\) 0 0
\(535\) −180.946 + 590.440i −0.338217 + 1.10363i
\(536\) 67.4207 + 116.776i 0.125785 + 0.217866i
\(537\) 0 0
\(538\) 43.5076 43.5076i 0.0808692 0.0808692i
\(539\) −143.222 + 164.840i −0.265718 + 0.305825i
\(540\) 0 0
\(541\) 90.3132 156.427i 0.166937 0.289144i −0.770404 0.637556i \(-0.779946\pi\)
0.937342 + 0.348412i \(0.113279\pi\)
\(542\) 3.00617 11.2192i 0.00554643 0.0206996i
\(543\) 0 0
\(544\) 96.9346 + 55.9652i 0.178189 + 0.102877i
\(545\) 8.83806 248.340i 0.0162166 0.455669i
\(546\) 0 0
\(547\) −17.8276 17.8276i −0.0325916 0.0325916i 0.690623 0.723215i \(-0.257336\pi\)
−0.723215 + 0.690623i \(0.757336\pi\)
\(548\) −232.107 866.235i −0.423553 1.58072i
\(549\) 0 0
\(550\) 8.76146 25.3353i 0.0159299 0.0460642i
\(551\) 235.927 408.638i 0.428180 0.741629i
\(552\) 0 0
\(553\) −420.845 + 191.853i −0.761022 + 0.346931i
\(554\) 24.9386i 0.0450155i
\(555\) 0 0
\(556\) 201.140 + 348.385i 0.361763 + 0.626591i
\(557\) 189.707 707.997i 0.340587 1.27109i −0.557096 0.830448i \(-0.688085\pi\)
0.897683 0.440641i \(-0.145249\pi\)
\(558\) 0 0
\(559\) 506.532i 0.906139i
\(560\) 531.179 + 70.2250i 0.948534 + 0.125402i
\(561\) 0 0
\(562\) 83.1916 22.2911i 0.148028 0.0396639i
\(563\) 805.856 + 215.928i 1.43136 + 0.383532i 0.889499 0.456936i \(-0.151053\pi\)
0.541861 + 0.840468i \(0.317720\pi\)
\(564\) 0 0
\(565\) −67.2542 292.199i −0.119034 0.517166i
\(566\) −43.4295 −0.0767306
\(567\) 0 0
\(568\) −114.909 + 114.909i −0.202305 + 0.202305i
\(569\) 394.493 + 227.761i 0.693309 + 0.400282i 0.804851 0.593478i \(-0.202245\pi\)
−0.111541 + 0.993760i \(0.535579\pi\)
\(570\) 0 0
\(571\) −79.5469 137.779i −0.139312 0.241295i 0.787925 0.615772i \(-0.211156\pi\)
−0.927236 + 0.374477i \(0.877822\pi\)
\(572\) 242.215 64.9012i 0.423452 0.113464i
\(573\) 0 0
\(574\) 27.6166 73.8917i 0.0481126 0.128731i
\(575\) −233.705 + 202.610i −0.406443 + 0.352365i
\(576\) 0 0
\(577\) −193.065 + 720.527i −0.334601 + 1.24875i 0.569700 + 0.821852i \(0.307059\pi\)
−0.904301 + 0.426895i \(0.859607\pi\)
\(578\) −44.4749 11.9170i −0.0769462 0.0206177i
\(579\) 0 0
\(580\) 724.382 + 25.7797i 1.24893 + 0.0444478i
\(581\) −107.198 640.109i −0.184507 1.10174i
\(582\) 0 0
\(583\) 70.2962 + 262.349i 0.120577 + 0.449998i
\(584\) −19.3192 + 11.1539i −0.0330808 + 0.0190992i
\(585\) 0 0
\(586\) 19.8431 34.3692i 0.0338619 0.0586505i
\(587\) 198.400 + 198.400i 0.337990 + 0.337990i 0.855611 0.517620i \(-0.173182\pi\)
−0.517620 + 0.855611i \(0.673182\pi\)
\(588\) 0 0
\(589\) 220.672i 0.374656i
\(590\) 31.0801 + 135.033i 0.0526781 + 0.228870i
\(591\) 0 0
\(592\) 222.611 830.797i 0.376033 1.40337i
\(593\) −126.975 473.876i −0.214123 0.799116i −0.986474 0.163920i \(-0.947586\pi\)
0.772351 0.635196i \(-0.219081\pi\)
\(594\) 0 0
\(595\) 342.913 44.9556i 0.576324 0.0755557i
\(596\) −1154.23 −1.93662
\(597\) 0 0
\(598\) 41.0437 + 10.9976i 0.0686350 + 0.0183907i
\(599\) −821.554 + 474.325i −1.37154 + 0.791861i −0.991122 0.132953i \(-0.957554\pi\)
−0.380421 + 0.924814i \(0.624221\pi\)
\(600\) 0 0
\(601\) 1121.80 1.86655 0.933275 0.359161i \(-0.116937\pi\)
0.933275 + 0.359161i \(0.116937\pi\)
\(602\) −24.7934 54.3865i −0.0411851 0.0903430i
\(603\) 0 0
\(604\) −708.202 408.881i −1.17252 0.676955i
\(605\) −237.113 446.663i −0.391923 0.738287i
\(606\) 0 0
\(607\) 293.221 78.5682i 0.483065 0.129437i −0.00906430 0.999959i \(-0.502885\pi\)
0.492130 + 0.870522i \(0.336219\pi\)
\(608\) −102.773 + 102.773i −0.169035 + 0.169035i
\(609\) 0 0
\(610\) −36.3975 39.0837i −0.0596680 0.0640717i
\(611\) −331.862 + 574.802i −0.543146 + 0.940756i
\(612\) 0 0
\(613\) −306.525 82.1330i −0.500040 0.133985i −2.15317e−5 1.00000i \(-0.500007\pi\)
−0.500019 + 0.866015i \(0.666674\pi\)
\(614\) −30.1516 17.4080i −0.0491069 0.0283519i
\(615\) 0 0
\(616\) 45.9951 37.9249i 0.0746674 0.0615665i
\(617\) 405.225 + 405.225i 0.656767 + 0.656767i 0.954614 0.297847i \(-0.0962685\pi\)
−0.297847 + 0.954614i \(0.596269\pi\)
\(618\) 0 0
\(619\) −906.466 + 523.349i −1.46440 + 0.845474i −0.999210 0.0397346i \(-0.987349\pi\)
−0.465194 + 0.885209i \(0.654015\pi\)
\(620\) 299.413 158.945i 0.482925 0.256363i
\(621\) 0 0
\(622\) −1.82031 1.82031i −0.00292655 0.00292655i
\(623\) −80.6532 + 36.7678i −0.129459 + 0.0590173i
\(624\) 0 0
\(625\) −386.101 + 491.478i −0.617762 + 0.786365i
\(626\) −57.4444 99.4966i −0.0917642 0.158940i
\(627\) 0 0
\(628\) 77.2841 + 288.428i 0.123064 + 0.459281i
\(629\) 555.177i 0.882635i
\(630\) 0 0
\(631\) −340.356 −0.539392 −0.269696 0.962946i \(-0.586923\pi\)
−0.269696 + 0.962946i \(0.586923\pi\)
\(632\) 121.963 32.6799i 0.192979 0.0517087i
\(633\) 0 0
\(634\) −15.4364 + 8.91221i −0.0243476 + 0.0140571i
\(635\) −429.129 + 98.7708i −0.675793 + 0.155545i
\(636\) 0 0
\(637\) −628.700 306.446i −0.986971 0.481077i
\(638\) 27.8834 27.8834i 0.0437044 0.0437044i
\(639\) 0 0
\(640\) −283.907 87.0060i −0.443604 0.135947i
\(641\) −29.6837 51.4137i −0.0463085 0.0802086i 0.841942 0.539568i \(-0.181412\pi\)
−0.888251 + 0.459359i \(0.848079\pi\)
\(642\) 0 0
\(643\) −147.606 + 147.606i −0.229558 + 0.229558i −0.812508 0.582950i \(-0.801898\pi\)
0.582950 + 0.812508i \(0.301898\pi\)
\(644\) −336.717 + 56.3897i −0.522852 + 0.0875616i
\(645\) 0 0
\(646\) −15.2536 + 26.4200i −0.0236124 + 0.0408979i
\(647\) −188.763 + 704.471i −0.291750 + 1.08883i 0.652014 + 0.758207i \(0.273925\pi\)
−0.943764 + 0.330620i \(0.892742\pi\)
\(648\) 0 0
\(649\) −444.510 256.638i −0.684915 0.395436i
\(650\) 85.6442 + 6.10364i 0.131760 + 0.00939021i
\(651\) 0 0
\(652\) 547.551 + 547.551i 0.839802 + 0.839802i
\(653\) −71.0567 265.187i −0.108816 0.406106i 0.889934 0.456089i \(-0.150750\pi\)
−0.998750 + 0.0499826i \(0.984083\pi\)
\(654\) 0 0
\(655\) 35.9776 + 67.7731i 0.0549277 + 0.103470i
\(656\) 358.487 620.917i 0.546474 0.946520i
\(657\) 0 0
\(658\) −7.49706 + 77.9605i −0.0113937 + 0.118481i
\(659\) 153.073i 0.232281i −0.993233 0.116140i \(-0.962948\pi\)
0.993233 0.116140i \(-0.0370523\pi\)
\(660\) 0 0
\(661\) −427.398 740.276i −0.646594 1.11993i −0.983931 0.178549i \(-0.942860\pi\)
0.337337 0.941384i \(-0.390474\pi\)
\(662\) 23.2240 86.6732i 0.0350816 0.130926i
\(663\) 0 0
\(664\) 177.182i 0.266841i
\(665\) −58.8599 + 445.214i −0.0885112 + 0.669495i
\(666\) 0 0
\(667\) −439.474 + 117.757i −0.658882 + 0.176547i
\(668\) 1019.03 + 273.049i 1.52550 + 0.408756i
\(669\) 0 0
\(670\) −71.9609 45.0330i −0.107404 0.0672134i
\(671\) 197.833 0.294833
\(672\) 0 0
\(673\) −26.8360 + 26.8360i −0.0398752 + 0.0398752i −0.726763 0.686888i \(-0.758976\pi\)
0.686888 + 0.726763i \(0.258976\pi\)
\(674\) 0.447934 + 0.258615i 0.000664591 + 0.000383702i
\(675\) 0 0
\(676\) 68.4690 + 118.592i 0.101286 + 0.175432i
\(677\) −235.342 + 63.0598i −0.347625 + 0.0931459i −0.428407 0.903586i \(-0.640925\pi\)
0.0807817 + 0.996732i \(0.474258\pi\)
\(678\) 0 0
\(679\) 1226.03 205.323i 1.80565 0.302390i
\(680\) −94.3561 3.35800i −0.138759 0.00493823i
\(681\) 0 0
\(682\) 4.77306 17.8133i 0.00699862 0.0261192i
\(683\) 1285.99 + 344.581i 1.88286 + 0.504511i 0.999348 + 0.0361036i \(0.0114946\pi\)
0.883513 + 0.468407i \(0.155172\pi\)
\(684\) 0 0
\(685\) 775.187 + 832.398i 1.13166 + 1.21518i
\(686\) −82.5035 2.12995i −0.120267 0.00310489i
\(687\) 0 0
\(688\) −140.606 524.748i −0.204369 0.762715i
\(689\) −753.370 + 434.958i −1.09342 + 0.631289i
\(690\) 0 0
\(691\) 260.502 451.203i 0.376993 0.652972i −0.613630 0.789594i \(-0.710291\pi\)
0.990623 + 0.136622i \(0.0436246\pi\)
\(692\) 532.551 + 532.551i 0.769582 + 0.769582i
\(693\) 0 0
\(694\) 50.4544i 0.0727008i
\(695\) −432.523 270.672i −0.622336 0.389456i
\(696\) 0 0
\(697\) 119.779 447.021i 0.171849 0.641350i
\(698\) −15.9451 59.5079i −0.0228440 0.0852549i
\(699\) 0 0
\(700\) −646.472 + 240.814i −0.923532 + 0.344020i
\(701\) 387.575 0.552889 0.276444 0.961030i \(-0.410844\pi\)
0.276444 + 0.961030i \(0.410844\pi\)
\(702\) 0 0
\(703\) 696.342 + 186.584i 0.990529 + 0.265411i
\(704\) 225.811 130.372i 0.320755 0.185188i
\(705\) 0 0
\(706\) −0.771879 −0.00109331
\(707\) −802.404 77.1630i −1.13494 0.109141i
\(708\) 0 0
\(709\) −13.1567 7.59601i −0.0185567 0.0107137i 0.490693 0.871333i \(-0.336744\pi\)
−0.509250 + 0.860619i \(0.670077\pi\)
\(710\) 29.9769 97.8166i 0.0422210 0.137770i
\(711\) 0 0
\(712\) 23.3737 6.26296i 0.0328282 0.00879629i
\(713\) −150.458 + 150.458i −0.211021 + 0.211021i
\(714\) 0 0
\(715\) −232.753 + 216.756i −0.325529 + 0.303155i
\(716\) −359.822 + 623.230i −0.502545 + 0.870433i
\(717\) 0 0
\(718\) −71.9873 19.2890i −0.100261 0.0268648i
\(719\) 35.5781 + 20.5410i 0.0494827 + 0.0285689i 0.524537 0.851387i \(-0.324238\pi\)
−0.475055 + 0.879956i \(0.657572\pi\)
\(720\) 0 0
\(721\) −633.607 236.807i −0.878789 0.328442i
\(722\) 33.4093 + 33.4093i 0.0462733 + 0.0462733i
\(723\) 0 0
\(724\) 352.398 203.457i 0.486737 0.281018i
\(725\) −826.850 + 401.917i −1.14048 + 0.554369i
\(726\) 0 0
\(727\) −198.452 198.452i −0.272974 0.272974i 0.557322 0.830296i \(-0.311829\pi\)
−0.830296 + 0.557322i \(0.811829\pi\)
\(728\) 155.459 + 110.859i 0.213543 + 0.152279i
\(729\) 0 0
\(730\) 7.45016 11.9051i 0.0102057 0.0163083i
\(731\) −175.331 303.682i −0.239850 0.415433i
\(732\) 0 0
\(733\) −68.7887 256.723i −0.0938454 0.350236i 0.902996 0.429648i \(-0.141362\pi\)
−0.996842 + 0.0794121i \(0.974696\pi\)
\(734\) 84.4626i 0.115072i
\(735\) 0 0
\(736\) 140.145 0.190414
\(737\) 303.740 81.3868i 0.412130 0.110430i
\(738\) 0 0
\(739\) 990.596 571.921i 1.34045 0.773912i 0.353581 0.935404i \(-0.384964\pi\)
0.986874 + 0.161492i \(0.0516306\pi\)
\(740\) 248.396 + 1079.21i 0.335671 + 1.45839i
\(741\) 0 0
\(742\) −59.5994 + 83.5771i −0.0803227 + 0.112638i
\(743\) 43.0155 43.0155i 0.0578943 0.0578943i −0.677567 0.735461i \(-0.736966\pi\)
0.735461 + 0.677567i \(0.236966\pi\)
\(744\) 0 0
\(745\) 1293.07 686.431i 1.73566 0.921384i
\(746\) 11.9341 + 20.6705i 0.0159975 + 0.0277085i
\(747\) 0 0
\(748\) 122.750 122.750i 0.164105 0.164105i
\(749\) 302.676 809.849i 0.404107 1.08124i
\(750\) 0 0
\(751\) −627.063 + 1086.11i −0.834971 + 1.44621i 0.0590826 + 0.998253i \(0.481182\pi\)
−0.894054 + 0.447960i \(0.852151\pi\)
\(752\) −184.240 + 687.594i −0.245000 + 0.914353i
\(753\) 0 0
\(754\) 109.379 + 63.1499i 0.145065 + 0.0837531i
\(755\) 1036.56 + 36.8896i 1.37292 + 0.0488604i
\(756\) 0 0
\(757\) −686.443 686.443i −0.906795 0.906795i 0.0892176 0.996012i \(-0.471563\pi\)
−0.996012 + 0.0892176i \(0.971563\pi\)
\(758\) −29.0700 108.491i −0.0383509 0.143128i
\(759\) 0 0
\(760\) 35.9231 117.219i 0.0472672 0.154236i
\(761\) −296.933 + 514.302i −0.390187 + 0.675825i −0.992474 0.122455i \(-0.960923\pi\)
0.602287 + 0.798280i \(0.294256\pi\)
\(762\) 0 0
\(763\) −33.3017 + 346.298i −0.0436458 + 0.453864i
\(764\) 1019.48i 1.33439i
\(765\) 0 0
\(766\) −27.5658 47.7454i −0.0359867 0.0623308i
\(767\) 425.490 1587.95i 0.554745 2.07034i
\(768\) 0 0
\(769\) 712.789i 0.926903i 0.886122 + 0.463452i \(0.153389\pi\)
−0.886122 + 0.463452i \(0.846611\pi\)
\(770\) −14.3811 + 34.6658i −0.0186768 + 0.0450205i
\(771\) 0 0
\(772\) −348.863 + 93.4774i −0.451895 + 0.121085i
\(773\) −79.8406 21.3932i −0.103287 0.0276756i 0.206806 0.978382i \(-0.433693\pi\)
−0.310092 + 0.950706i \(0.600360\pi\)
\(774\) 0 0
\(775\) −240.904