Properties

Label 105.3.l.a.22.6
Level 105
Weight 3
Character 105.22
Analytic conductor 2.861
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.6
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.408558 + 0.408558i) q^{2} +(-1.22474 + 1.22474i) q^{3} -3.66616i q^{4} +(0.563288 - 4.96817i) q^{5} -1.00076 q^{6} +(-1.87083 - 1.87083i) q^{7} +(3.13207 - 3.13207i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(0.408558 + 0.408558i) q^{2} +(-1.22474 + 1.22474i) q^{3} -3.66616i q^{4} +(0.563288 - 4.96817i) q^{5} -1.00076 q^{6} +(-1.87083 - 1.87083i) q^{7} +(3.13207 - 3.13207i) q^{8} -3.00000i q^{9} +(2.25992 - 1.79965i) q^{10} -6.25808 q^{11} +(4.49011 + 4.49011i) q^{12} +(16.4621 - 16.4621i) q^{13} -1.52868i q^{14} +(5.39486 + 6.77462i) q^{15} -12.1054 q^{16} +(20.4811 + 20.4811i) q^{17} +(1.22567 - 1.22567i) q^{18} -7.15227i q^{19} +(-18.2141 - 2.06511i) q^{20} +4.58258 q^{21} +(-2.55679 - 2.55679i) q^{22} +(-12.0129 + 12.0129i) q^{23} +7.67197i q^{24} +(-24.3654 - 5.59702i) q^{25} +13.4514 q^{26} +(3.67423 + 3.67423i) q^{27} +(-6.85876 + 6.85876i) q^{28} +18.1286i q^{29} +(-0.563715 + 4.97193i) q^{30} -33.3500 q^{31} +(-17.4740 - 17.4740i) q^{32} +(7.66455 - 7.66455i) q^{33} +16.7354i q^{34} +(-10.3484 + 8.24078i) q^{35} -10.9985 q^{36} +(18.8529 + 18.8529i) q^{37} +(2.92211 - 2.92211i) q^{38} +40.3237i q^{39} +(-13.7964 - 17.3249i) q^{40} +50.8319 q^{41} +(1.87225 + 1.87225i) q^{42} +(53.3589 - 53.3589i) q^{43} +22.9431i q^{44} +(-14.9045 - 1.68986i) q^{45} -9.81596 q^{46} +(46.9338 + 46.9338i) q^{47} +(14.8260 - 14.8260i) q^{48} +7.00000i q^{49} +(-7.66797 - 12.2414i) q^{50} -50.1682 q^{51} +(-60.3527 - 60.3527i) q^{52} +(-28.9805 + 28.9805i) q^{53} +3.00227i q^{54} +(-3.52510 + 31.0912i) q^{55} -11.7191 q^{56} +(8.75971 + 8.75971i) q^{57} +(-7.40656 + 7.40656i) q^{58} -10.0079i q^{59} +(24.8369 - 19.7784i) q^{60} +85.6806 q^{61} +(-13.6254 - 13.6254i) q^{62} +(-5.61249 + 5.61249i) q^{63} +34.1432i q^{64} +(-72.5135 - 91.0593i) q^{65} +6.26283 q^{66} +(11.9931 + 11.9931i) q^{67} +(75.0869 - 75.0869i) q^{68} -29.4256i q^{69} +(-7.59476 - 0.861089i) q^{70} -20.8660 q^{71} +(-9.39621 - 9.39621i) q^{72} +(35.2913 - 35.2913i) q^{73} +15.4050i q^{74} +(36.6963 - 22.9865i) q^{75} -26.2214 q^{76} +(11.7078 + 11.7078i) q^{77} +(-16.4746 + 16.4746i) q^{78} +31.9858i q^{79} +(-6.81882 + 60.1416i) q^{80} -9.00000 q^{81} +(20.7677 + 20.7677i) q^{82} +(6.49178 - 6.49178i) q^{83} -16.8005i q^{84} +(113.290 - 90.2167i) q^{85} +43.6003 q^{86} +(-22.2029 - 22.2029i) q^{87} +(-19.6007 + 19.6007i) q^{88} -145.472i q^{89} +(-5.39894 - 6.77976i) q^{90} -61.5955 q^{91} +(44.0414 + 44.0414i) q^{92} +(40.8453 - 40.8453i) q^{93} +38.3503i q^{94} +(-35.5337 - 4.02879i) q^{95} +42.8024 q^{96} +(31.5344 + 31.5344i) q^{97} +(-2.85990 + 2.85990i) q^{98} +18.7742i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} - 40q^{10} - 48q^{12} + 64q^{13} - 184q^{16} + 24q^{17} + 24q^{18} + 72q^{20} + 8q^{22} + 8q^{23} - 136q^{25} - 80q^{26} + 96q^{30} + 96q^{31} + 56q^{32} - 72q^{33} + 168q^{36} + 8q^{37} + 56q^{38} + 232q^{40} + 320q^{41} - 112q^{43} - 72q^{45} + 320q^{46} + 64q^{47} + 192q^{48} - 256q^{50} - 192q^{51} + 96q^{52} - 72q^{53} - 80q^{55} - 336q^{56} + 48q^{57} - 512q^{58} - 192q^{60} - 496q^{61} - 776q^{62} + 312q^{65} - 192q^{66} - 192q^{67} + 568q^{68} + 112q^{70} - 144q^{71} + 144q^{72} + 224q^{73} + 144q^{75} + 416q^{76} + 112q^{77} - 216q^{78} - 528q^{80} - 216q^{81} + 352q^{82} - 32q^{83} + 24q^{85} + 240q^{86} + 384q^{87} + 216q^{88} - 24q^{90} + 1304q^{92} + 376q^{95} + 168q^{96} - 816q^{97} - 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.408558 + 0.408558i 0.204279 + 0.204279i 0.801830 0.597552i \(-0.203860\pi\)
−0.597552 + 0.801830i \(0.703860\pi\)
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 3.66616i 0.916540i
\(5\) 0.563288 4.96817i 0.112658 0.993634i
\(6\) −1.00076 −0.166793
\(7\) −1.87083 1.87083i −0.267261 0.267261i
\(8\) 3.13207 3.13207i 0.391509 0.391509i
\(9\) 3.00000i 0.333333i
\(10\) 2.25992 1.79965i 0.225992 0.179965i
\(11\) −6.25808 −0.568917 −0.284458 0.958688i \(-0.591814\pi\)
−0.284458 + 0.958688i \(0.591814\pi\)
\(12\) 4.49011 + 4.49011i 0.374176 + 0.374176i
\(13\) 16.4621 16.4621i 1.26631 1.26631i 0.318337 0.947978i \(-0.396876\pi\)
0.947978 0.318337i \(-0.103124\pi\)
\(14\) 1.52868i 0.109192i
\(15\) 5.39486 + 6.77462i 0.359657 + 0.451642i
\(16\) −12.1054 −0.756586
\(17\) 20.4811 + 20.4811i 1.20477 + 1.20477i 0.972699 + 0.232071i \(0.0745500\pi\)
0.232071 + 0.972699i \(0.425450\pi\)
\(18\) 1.22567 1.22567i 0.0680929 0.0680929i
\(19\) 7.15227i 0.376435i −0.982127 0.188218i \(-0.939729\pi\)
0.982127 0.188218i \(-0.0602710\pi\)
\(20\) −18.2141 2.06511i −0.910705 0.103255i
\(21\) 4.58258 0.218218
\(22\) −2.55679 2.55679i −0.116218 0.116218i
\(23\) −12.0129 + 12.0129i −0.522302 + 0.522302i −0.918266 0.395964i \(-0.870410\pi\)
0.395964 + 0.918266i \(0.370410\pi\)
\(24\) 7.67197i 0.319665i
\(25\) −24.3654 5.59702i −0.974617 0.223881i
\(26\) 13.4514 0.517362
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −6.85876 + 6.85876i −0.244956 + 0.244956i
\(29\) 18.1286i 0.625123i 0.949898 + 0.312561i \(0.101187\pi\)
−0.949898 + 0.312561i \(0.898813\pi\)
\(30\) −0.563715 + 4.97193i −0.0187905 + 0.165731i
\(31\) −33.3500 −1.07581 −0.537904 0.843006i \(-0.680784\pi\)
−0.537904 + 0.843006i \(0.680784\pi\)
\(32\) −17.4740 17.4740i −0.546063 0.546063i
\(33\) 7.66455 7.66455i 0.232259 0.232259i
\(34\) 16.7354i 0.492218i
\(35\) −10.3484 + 8.24078i −0.295669 + 0.235451i
\(36\) −10.9985 −0.305513
\(37\) 18.8529 + 18.8529i 0.509538 + 0.509538i 0.914384 0.404847i \(-0.132675\pi\)
−0.404847 + 0.914384i \(0.632675\pi\)
\(38\) 2.92211 2.92211i 0.0768978 0.0768978i
\(39\) 40.3237i 1.03394i
\(40\) −13.7964 17.3249i −0.344910 0.433123i
\(41\) 50.8319 1.23980 0.619901 0.784680i \(-0.287173\pi\)
0.619901 + 0.784680i \(0.287173\pi\)
\(42\) 1.87225 + 1.87225i 0.0445773 + 0.0445773i
\(43\) 53.3589 53.3589i 1.24090 1.24090i 0.281277 0.959627i \(-0.409242\pi\)
0.959627 0.281277i \(-0.0907581\pi\)
\(44\) 22.9431i 0.521435i
\(45\) −14.9045 1.68986i −0.331211 0.0375525i
\(46\) −9.81596 −0.213390
\(47\) 46.9338 + 46.9338i 0.998592 + 0.998592i 0.999999 0.00140698i \(-0.000447856\pi\)
−0.00140698 + 0.999999i \(0.500448\pi\)
\(48\) 14.8260 14.8260i 0.308875 0.308875i
\(49\) 7.00000i 0.142857i
\(50\) −7.66797 12.2414i −0.153359 0.244828i
\(51\) −50.1682 −0.983690
\(52\) −60.3527 60.3527i −1.16063 1.16063i
\(53\) −28.9805 + 28.9805i −0.546801 + 0.546801i −0.925514 0.378713i \(-0.876367\pi\)
0.378713 + 0.925514i \(0.376367\pi\)
\(54\) 3.00227i 0.0555977i
\(55\) −3.52510 + 31.0912i −0.0640928 + 0.565295i
\(56\) −11.7191 −0.209270
\(57\) 8.75971 + 8.75971i 0.153679 + 0.153679i
\(58\) −7.40656 + 7.40656i −0.127699 + 0.127699i
\(59\) 10.0079i 0.169626i −0.996397 0.0848128i \(-0.972971\pi\)
0.996397 0.0848128i \(-0.0270292\pi\)
\(60\) 24.8369 19.7784i 0.413948 0.329640i
\(61\) 85.6806 1.40460 0.702300 0.711881i \(-0.252157\pi\)
0.702300 + 0.711881i \(0.252157\pi\)
\(62\) −13.6254 13.6254i −0.219765 0.219765i
\(63\) −5.61249 + 5.61249i −0.0890871 + 0.0890871i
\(64\) 34.1432i 0.533488i
\(65\) −72.5135 91.0593i −1.11559 1.40091i
\(66\) 6.26283 0.0948913
\(67\) 11.9931 + 11.9931i 0.179001 + 0.179001i 0.790920 0.611919i \(-0.209602\pi\)
−0.611919 + 0.790920i \(0.709602\pi\)
\(68\) 75.0869 75.0869i 1.10422 1.10422i
\(69\) 29.4256i 0.426458i
\(70\) −7.59476 0.861089i −0.108497 0.0123013i
\(71\) −20.8660 −0.293887 −0.146943 0.989145i \(-0.546944\pi\)
−0.146943 + 0.989145i \(0.546944\pi\)
\(72\) −9.39621 9.39621i −0.130503 0.130503i
\(73\) 35.2913 35.2913i 0.483443 0.483443i −0.422787 0.906229i \(-0.638948\pi\)
0.906229 + 0.422787i \(0.138948\pi\)
\(74\) 15.4050i 0.208176i
\(75\) 36.6963 22.9865i 0.489285 0.306487i
\(76\) −26.2214 −0.345018
\(77\) 11.7078 + 11.7078i 0.152049 + 0.152049i
\(78\) −16.4746 + 16.4746i −0.211212 + 0.211212i
\(79\) 31.9858i 0.404884i 0.979294 + 0.202442i \(0.0648877\pi\)
−0.979294 + 0.202442i \(0.935112\pi\)
\(80\) −6.81882 + 60.1416i −0.0852352 + 0.751770i
\(81\) −9.00000 −0.111111
\(82\) 20.7677 + 20.7677i 0.253265 + 0.253265i
\(83\) 6.49178 6.49178i 0.0782142 0.0782142i −0.666917 0.745132i \(-0.732387\pi\)
0.745132 + 0.666917i \(0.232387\pi\)
\(84\) 16.8005i 0.200005i
\(85\) 113.290 90.2167i 1.33283 1.06137i
\(86\) 43.6003 0.506981
\(87\) −22.2029 22.2029i −0.255205 0.255205i
\(88\) −19.6007 + 19.6007i −0.222736 + 0.222736i
\(89\) 145.472i 1.63452i −0.576273 0.817258i \(-0.695493\pi\)
0.576273 0.817258i \(-0.304507\pi\)
\(90\) −5.39894 6.77976i −0.0599883 0.0753306i
\(91\) −61.5955 −0.676873
\(92\) 44.0414 + 44.0414i 0.478711 + 0.478711i
\(93\) 40.8453 40.8453i 0.439197 0.439197i
\(94\) 38.3503i 0.407982i
\(95\) −35.5337 4.02879i −0.374039 0.0424083i
\(96\) 42.8024 0.445859
\(97\) 31.5344 + 31.5344i 0.325097 + 0.325097i 0.850719 0.525621i \(-0.176167\pi\)
−0.525621 + 0.850719i \(0.676167\pi\)
\(98\) −2.85990 + 2.85990i −0.0291827 + 0.0291827i
\(99\) 18.7742i 0.189639i
\(100\) −20.5196 + 89.3275i −0.205196 + 0.893275i
\(101\) −128.207 −1.26938 −0.634688 0.772768i \(-0.718871\pi\)
−0.634688 + 0.772768i \(0.718871\pi\)
\(102\) −20.4966 20.4966i −0.200947 0.200947i
\(103\) −89.6356 + 89.6356i −0.870248 + 0.870248i −0.992499 0.122251i \(-0.960989\pi\)
0.122251 + 0.992499i \(0.460989\pi\)
\(104\) 103.121i 0.991546i
\(105\) 2.58131 22.7670i 0.0245839 0.216829i
\(106\) −23.6804 −0.223400
\(107\) 32.4213 + 32.4213i 0.303003 + 0.303003i 0.842188 0.539185i \(-0.181268\pi\)
−0.539185 + 0.842188i \(0.681268\pi\)
\(108\) 13.4703 13.4703i 0.124725 0.124725i
\(109\) 87.2642i 0.800589i 0.916387 + 0.400294i \(0.131092\pi\)
−0.916387 + 0.400294i \(0.868908\pi\)
\(110\) −14.1428 + 11.2623i −0.128571 + 0.102385i
\(111\) −46.1800 −0.416036
\(112\) 22.6471 + 22.6471i 0.202206 + 0.202206i
\(113\) −14.4360 + 14.4360i −0.127752 + 0.127752i −0.768092 0.640340i \(-0.778794\pi\)
0.640340 + 0.768092i \(0.278794\pi\)
\(114\) 7.15769i 0.0627868i
\(115\) 52.9156 + 66.4491i 0.460136 + 0.577818i
\(116\) 66.4622 0.572950
\(117\) −49.3863 49.3863i −0.422105 0.422105i
\(118\) 4.08881 4.08881i 0.0346509 0.0346509i
\(119\) 76.6332i 0.643976i
\(120\) 38.1157 + 4.32153i 0.317630 + 0.0360128i
\(121\) −81.8364 −0.676334
\(122\) 35.0055 + 35.0055i 0.286930 + 0.286930i
\(123\) −62.2561 + 62.2561i −0.506147 + 0.506147i
\(124\) 122.267i 0.986021i
\(125\) −41.5317 + 117.899i −0.332254 + 0.943190i
\(126\) −4.58605 −0.0363972
\(127\) −54.2946 54.2946i −0.427517 0.427517i 0.460265 0.887782i \(-0.347754\pi\)
−0.887782 + 0.460265i \(0.847754\pi\)
\(128\) −83.8456 + 83.8456i −0.655044 + 0.655044i
\(129\) 130.702i 1.01319i
\(130\) 7.57703 66.8289i 0.0582848 0.514069i
\(131\) 36.7377 0.280440 0.140220 0.990120i \(-0.455219\pi\)
0.140220 + 0.990120i \(0.455219\pi\)
\(132\) −28.0995 28.0995i −0.212875 0.212875i
\(133\) −13.3807 + 13.3807i −0.100607 + 0.100607i
\(134\) 9.79973i 0.0731323i
\(135\) 20.3239 16.1846i 0.150547 0.119886i
\(136\) 128.296 0.943355
\(137\) −90.1192 90.1192i −0.657804 0.657804i 0.297056 0.954860i \(-0.403995\pi\)
−0.954860 + 0.297056i \(0.903995\pi\)
\(138\) 12.0220 12.0220i 0.0871163 0.0871163i
\(139\) 88.5028i 0.636711i 0.947971 + 0.318355i \(0.103131\pi\)
−0.947971 + 0.318355i \(0.896869\pi\)
\(140\) 30.2120 + 37.9389i 0.215800 + 0.270992i
\(141\) −114.964 −0.815347
\(142\) −8.52495 8.52495i −0.0600349 0.0600349i
\(143\) −103.021 + 103.021i −0.720427 + 0.720427i
\(144\) 36.3161i 0.252195i
\(145\) 90.0657 + 10.2116i 0.621143 + 0.0704248i
\(146\) 28.8371 0.197514
\(147\) −8.57321 8.57321i −0.0583212 0.0583212i
\(148\) 69.1177 69.1177i 0.467012 0.467012i
\(149\) 205.375i 1.37835i −0.724594 0.689176i \(-0.757973\pi\)
0.724594 0.689176i \(-0.242027\pi\)
\(150\) 24.3839 + 5.60126i 0.162559 + 0.0373418i
\(151\) 175.527 1.16243 0.581214 0.813751i \(-0.302578\pi\)
0.581214 + 0.813751i \(0.302578\pi\)
\(152\) −22.4014 22.4014i −0.147378 0.147378i
\(153\) 61.4432 61.4432i 0.401590 0.401590i
\(154\) 9.56662i 0.0621209i
\(155\) −18.7857 + 165.689i −0.121198 + 1.06896i
\(156\) 147.833 0.947649
\(157\) 22.5653 + 22.5653i 0.143728 + 0.143728i 0.775310 0.631581i \(-0.217594\pi\)
−0.631581 + 0.775310i \(0.717594\pi\)
\(158\) −13.0681 + 13.0681i −0.0827092 + 0.0827092i
\(159\) 70.9874i 0.446461i
\(160\) −96.6568 + 76.9710i −0.604105 + 0.481069i
\(161\) 44.9483 0.279182
\(162\) −3.67702 3.67702i −0.0226976 0.0226976i
\(163\) −6.70761 + 6.70761i −0.0411510 + 0.0411510i −0.727383 0.686232i \(-0.759264\pi\)
0.686232 + 0.727383i \(0.259264\pi\)
\(164\) 186.358i 1.13633i
\(165\) −33.7615 42.3962i −0.204615 0.256946i
\(166\) 5.30453 0.0319550
\(167\) 105.816 + 105.816i 0.633630 + 0.633630i 0.948977 0.315347i \(-0.102121\pi\)
−0.315347 + 0.948977i \(0.602121\pi\)
\(168\) 14.3529 14.3529i 0.0854342 0.0854342i
\(169\) 373.001i 2.20710i
\(170\) 83.1443 + 9.42686i 0.489084 + 0.0554521i
\(171\) −21.4568 −0.125478
\(172\) −195.622 195.622i −1.13734 1.13734i
\(173\) −174.772 + 174.772i −1.01024 + 1.01024i −0.0102943 + 0.999947i \(0.503277\pi\)
−0.999947 + 0.0102943i \(0.996723\pi\)
\(174\) 18.1423i 0.104266i
\(175\) 35.1124 + 56.0546i 0.200643 + 0.320312i
\(176\) 75.7565 0.430435
\(177\) 12.2571 + 12.2571i 0.0692494 + 0.0692494i
\(178\) 59.4336 59.4336i 0.333897 0.333897i
\(179\) 18.1770i 0.101547i −0.998710 0.0507736i \(-0.983831\pi\)
0.998710 0.0507736i \(-0.0161687\pi\)
\(180\) −6.19532 + 54.6423i −0.0344184 + 0.303568i
\(181\) −120.550 −0.666021 −0.333010 0.942923i \(-0.608064\pi\)
−0.333010 + 0.942923i \(0.608064\pi\)
\(182\) −25.1653 25.1653i −0.138271 0.138271i
\(183\) −104.937 + 104.937i −0.573425 + 0.573425i
\(184\) 75.2507i 0.408971i
\(185\) 104.284 83.0447i 0.563697 0.448891i
\(186\) 33.3753 0.179437
\(187\) −128.172 128.172i −0.685413 0.685413i
\(188\) 172.067 172.067i 0.915250 0.915250i
\(189\) 13.7477i 0.0727393i
\(190\) −12.8716 16.1636i −0.0677451 0.0850713i
\(191\) 58.8671 0.308205 0.154102 0.988055i \(-0.450751\pi\)
0.154102 + 0.988055i \(0.450751\pi\)
\(192\) −41.8168 41.8168i −0.217796 0.217796i
\(193\) 3.25902 3.25902i 0.0168861 0.0168861i −0.698613 0.715499i \(-0.746199\pi\)
0.715499 + 0.698613i \(0.246199\pi\)
\(194\) 25.7673i 0.132821i
\(195\) 200.335 + 22.7139i 1.02736 + 0.116481i
\(196\) 25.6631 0.130934
\(197\) −12.5485 12.5485i −0.0636980 0.0636980i 0.674540 0.738238i \(-0.264342\pi\)
−0.738238 + 0.674540i \(0.764342\pi\)
\(198\) −7.67036 + 7.67036i −0.0387392 + 0.0387392i
\(199\) 391.240i 1.96603i −0.183526 0.983015i \(-0.558751\pi\)
0.183526 0.983015i \(-0.441249\pi\)
\(200\) −93.8444 + 58.7839i −0.469222 + 0.293919i
\(201\) −29.3769 −0.146154
\(202\) −52.3800 52.3800i −0.259307 0.259307i
\(203\) 33.9154 33.9154i 0.167071 0.167071i
\(204\) 183.925i 0.901592i
\(205\) 28.6330 252.541i 0.139673 1.23191i
\(206\) −73.2426 −0.355547
\(207\) 36.0388 + 36.0388i 0.174101 + 0.174101i
\(208\) −199.280 + 199.280i −0.958076 + 0.958076i
\(209\) 44.7595i 0.214160i
\(210\) 10.3563 8.24702i 0.0493155 0.0392715i
\(211\) −80.9281 −0.383546 −0.191773 0.981439i \(-0.561424\pi\)
−0.191773 + 0.981439i \(0.561424\pi\)
\(212\) 106.247 + 106.247i 0.501166 + 0.501166i
\(213\) 25.5555 25.5555i 0.119979 0.119979i
\(214\) 26.4919i 0.123794i
\(215\) −235.039 295.152i −1.09321 1.37280i
\(216\) 23.0159 0.106555
\(217\) 62.3922 + 62.3922i 0.287522 + 0.287522i
\(218\) −35.6525 + 35.6525i −0.163543 + 0.163543i
\(219\) 86.4457i 0.394729i
\(220\) 113.985 + 12.9236i 0.518115 + 0.0587436i
\(221\) 674.323 3.05123
\(222\) −18.8672 18.8672i −0.0849873 0.0849873i
\(223\) −227.428 + 227.428i −1.01986 + 1.01986i −0.0200565 + 0.999799i \(0.506385\pi\)
−0.999799 + 0.0200565i \(0.993615\pi\)
\(224\) 65.3818i 0.291883i
\(225\) −16.7911 + 73.0962i −0.0746270 + 0.324872i
\(226\) −11.7959 −0.0521941
\(227\) 186.163 + 186.163i 0.820101 + 0.820101i 0.986122 0.166022i \(-0.0530921\pi\)
−0.166022 + 0.986122i \(0.553092\pi\)
\(228\) 32.1145 32.1145i 0.140853 0.140853i
\(229\) 299.882i 1.30953i 0.755832 + 0.654765i \(0.227232\pi\)
−0.755832 + 0.654765i \(0.772768\pi\)
\(230\) −5.52921 + 48.7674i −0.0240401 + 0.212032i
\(231\) −28.6781 −0.124148
\(232\) 56.7799 + 56.7799i 0.244741 + 0.244741i
\(233\) 46.9263 46.9263i 0.201400 0.201400i −0.599199 0.800600i \(-0.704514\pi\)
0.800600 + 0.599199i \(0.204514\pi\)
\(234\) 40.3543i 0.172454i
\(235\) 259.612 206.738i 1.10473 0.879736i
\(236\) −36.6906 −0.155469
\(237\) −39.1745 39.1745i −0.165293 0.165293i
\(238\) 31.3091 31.3091i 0.131551 0.131551i
\(239\) 155.118i 0.649030i 0.945881 + 0.324515i \(0.105201\pi\)
−0.945881 + 0.324515i \(0.894799\pi\)
\(240\) −65.3068 82.0094i −0.272112 0.341706i
\(241\) −113.600 −0.471370 −0.235685 0.971829i \(-0.575733\pi\)
−0.235685 + 0.971829i \(0.575733\pi\)
\(242\) −33.4349 33.4349i −0.138161 0.138161i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 314.119i 1.28737i
\(245\) 34.7772 + 3.94302i 0.141948 + 0.0160939i
\(246\) −50.8704 −0.206790
\(247\) −117.741 117.741i −0.476685 0.476685i
\(248\) −104.455 + 104.455i −0.421188 + 0.421188i
\(249\) 15.9015i 0.0638616i
\(250\) −65.1365 + 31.2004i −0.260546 + 0.124801i
\(251\) −295.062 −1.17554 −0.587772 0.809027i \(-0.699995\pi\)
−0.587772 + 0.809027i \(0.699995\pi\)
\(252\) 20.5763 + 20.5763i 0.0816519 + 0.0816519i
\(253\) 75.1780 75.1780i 0.297146 0.297146i
\(254\) 44.3650i 0.174665i
\(255\) −28.2591 + 249.244i −0.110820 + 0.977428i
\(256\) 68.0615 0.265865
\(257\) 18.1666 + 18.1666i 0.0706872 + 0.0706872i 0.741567 0.670879i \(-0.234083\pi\)
−0.670879 + 0.741567i \(0.734083\pi\)
\(258\) −53.3993 + 53.3993i −0.206974 + 0.206974i
\(259\) 70.5411i 0.272359i
\(260\) −333.838 + 265.846i −1.28399 + 1.02249i
\(261\) 54.3857 0.208374
\(262\) 15.0095 + 15.0095i 0.0572880 + 0.0572880i
\(263\) −364.409 + 364.409i −1.38559 + 1.38559i −0.551237 + 0.834349i \(0.685844\pi\)
−0.834349 + 0.551237i \(0.814156\pi\)
\(264\) 48.0118i 0.181863i
\(265\) 127.656 + 160.304i 0.481719 + 0.604922i
\(266\) −10.9336 −0.0411036
\(267\) 178.166 + 178.166i 0.667288 + 0.667288i
\(268\) 43.9686 43.9686i 0.164062 0.164062i
\(269\) 0.809793i 0.00301038i −0.999999 0.00150519i \(-0.999521\pi\)
0.999999 0.00150519i \(-0.000479118\pi\)
\(270\) 14.9158 + 1.69114i 0.0552437 + 0.00626350i
\(271\) −341.910 −1.26166 −0.630831 0.775921i \(-0.717286\pi\)
−0.630831 + 0.775921i \(0.717286\pi\)
\(272\) −247.931 247.931i −0.911512 0.911512i
\(273\) 75.4388 75.4388i 0.276332 0.276332i
\(274\) 73.6378i 0.268751i
\(275\) 152.481 + 35.0266i 0.554476 + 0.127370i
\(276\) −107.879 −0.390866
\(277\) 279.570 + 279.570i 1.00928 + 1.00928i 0.999957 + 0.00932280i \(0.00296758\pi\)
0.00932280 + 0.999957i \(0.497032\pi\)
\(278\) −36.1585 + 36.1585i −0.130067 + 0.130067i
\(279\) 100.050i 0.358602i
\(280\) −6.60125 + 58.2226i −0.0235759 + 0.207938i
\(281\) −383.827 −1.36593 −0.682967 0.730449i \(-0.739311\pi\)
−0.682967 + 0.730449i \(0.739311\pi\)
\(282\) −46.9694 46.9694i −0.166558 0.166558i
\(283\) 335.505 335.505i 1.18553 1.18553i 0.207238 0.978291i \(-0.433553\pi\)
0.978291 0.207238i \(-0.0664474\pi\)
\(284\) 76.4980i 0.269359i
\(285\) 48.4539 38.5855i 0.170014 0.135388i
\(286\) −84.1801 −0.294336
\(287\) −95.0977 95.0977i −0.331351 0.331351i
\(288\) −52.4221 + 52.4221i −0.182021 + 0.182021i
\(289\) 549.949i 1.90294i
\(290\) 32.6250 + 40.9691i 0.112500 + 0.141273i
\(291\) −77.2432 −0.265441
\(292\) −129.384 129.384i −0.443095 0.443095i
\(293\) 222.379 222.379i 0.758972 0.758972i −0.217163 0.976135i \(-0.569680\pi\)
0.976135 + 0.217163i \(0.0696804\pi\)
\(294\) 7.00530i 0.0238276i
\(295\) −49.7210 5.63734i −0.168546 0.0191096i
\(296\) 118.097 0.398977
\(297\) −22.9937 22.9937i −0.0774197 0.0774197i
\(298\) 83.9073 83.9073i 0.281568 0.281568i
\(299\) 395.516i 1.32280i
\(300\) −84.2722 134.535i −0.280907 0.448449i
\(301\) −199.651 −0.663291
\(302\) 71.7128 + 71.7128i 0.237460 + 0.237460i
\(303\) 157.021 157.021i 0.518221 0.518221i
\(304\) 86.5810i 0.284806i
\(305\) 48.2629 425.676i 0.158239 1.39566i
\(306\) 50.2062 0.164073
\(307\) 264.406 + 264.406i 0.861257 + 0.861257i 0.991484 0.130227i \(-0.0415706\pi\)
−0.130227 + 0.991484i \(0.541571\pi\)
\(308\) 42.9227 42.9227i 0.139359 0.139359i
\(309\) 219.561i 0.710555i
\(310\) −75.3684 + 60.0183i −0.243124 + 0.193607i
\(311\) 307.452 0.988592 0.494296 0.869294i \(-0.335426\pi\)
0.494296 + 0.869294i \(0.335426\pi\)
\(312\) 126.297 + 126.297i 0.404797 + 0.404797i
\(313\) −67.0805 + 67.0805i −0.214315 + 0.214315i −0.806098 0.591783i \(-0.798424\pi\)
0.591783 + 0.806098i \(0.298424\pi\)
\(314\) 18.4385i 0.0587213i
\(315\) 24.7223 + 31.0452i 0.0784836 + 0.0985563i
\(316\) 117.265 0.371092
\(317\) −96.9267 96.9267i −0.305762 0.305762i 0.537501 0.843263i \(-0.319369\pi\)
−0.843263 + 0.537501i \(0.819369\pi\)
\(318\) 29.0024 29.0024i 0.0912026 0.0912026i
\(319\) 113.450i 0.355643i
\(320\) 169.629 + 19.2325i 0.530092 + 0.0601015i
\(321\) −79.4157 −0.247401
\(322\) 18.3640 + 18.3640i 0.0570310 + 0.0570310i
\(323\) 146.486 146.486i 0.453518 0.453518i
\(324\) 32.9955i 0.101838i
\(325\) −493.244 + 308.967i −1.51767 + 0.950667i
\(326\) −5.48089 −0.0168126
\(327\) −106.876 106.876i −0.326839 0.326839i
\(328\) 159.209 159.209i 0.485393 0.485393i
\(329\) 175.610i 0.533770i
\(330\) 3.52777 31.1148i 0.0106902 0.0942872i
\(331\) 300.702 0.908464 0.454232 0.890883i \(-0.349914\pi\)
0.454232 + 0.890883i \(0.349914\pi\)
\(332\) −23.7999 23.7999i −0.0716864 0.0716864i
\(333\) 56.5587 56.5587i 0.169846 0.169846i
\(334\) 86.4640i 0.258874i
\(335\) 66.3392 52.8281i 0.198028 0.157696i
\(336\) −55.4738 −0.165101
\(337\) −43.5765 43.5765i −0.129307 0.129307i 0.639491 0.768798i \(-0.279145\pi\)
−0.768798 + 0.639491i \(0.779145\pi\)
\(338\) 152.392 152.392i 0.450865 0.450865i
\(339\) 35.3608i 0.104309i
\(340\) −330.749 415.340i −0.972791 1.22159i
\(341\) 208.707 0.612045
\(342\) −8.76634 8.76634i −0.0256326 0.0256326i
\(343\) 13.0958 13.0958i 0.0381802 0.0381802i
\(344\) 334.247i 0.971649i
\(345\) −146.191 16.5751i −0.423743 0.0480437i
\(346\) −142.809 −0.412742
\(347\) −190.647 190.647i −0.549416 0.549416i 0.376856 0.926272i \(-0.377005\pi\)
−0.926272 + 0.376856i \(0.877005\pi\)
\(348\) −81.3992 + 81.3992i −0.233906 + 0.233906i
\(349\) 186.770i 0.535158i 0.963536 + 0.267579i \(0.0862237\pi\)
−0.963536 + 0.267579i \(0.913776\pi\)
\(350\) −8.55607 + 37.2470i −0.0244459 + 0.106420i
\(351\) 120.971 0.344647
\(352\) 109.354 + 109.354i 0.310664 + 0.310664i
\(353\) 105.217 105.217i 0.298066 0.298066i −0.542190 0.840256i \(-0.682405\pi\)
0.840256 + 0.542190i \(0.182405\pi\)
\(354\) 10.0155i 0.0282924i
\(355\) −11.7536 + 103.666i −0.0331086 + 0.292016i
\(356\) −533.323 −1.49810
\(357\) 93.8561 + 93.8561i 0.262902 + 0.262902i
\(358\) 7.42633 7.42633i 0.0207440 0.0207440i
\(359\) 44.2544i 0.123271i 0.998099 + 0.0616356i \(0.0196317\pi\)
−0.998099 + 0.0616356i \(0.980368\pi\)
\(360\) −51.9747 + 41.3892i −0.144374 + 0.114970i
\(361\) 309.845 0.858297
\(362\) −49.2515 49.2515i −0.136054 0.136054i
\(363\) 100.229 100.229i 0.276112 0.276112i
\(364\) 225.819i 0.620382i
\(365\) −155.454 195.212i −0.425901 0.534828i
\(366\) −85.7455 −0.234277
\(367\) 133.204 + 133.204i 0.362953 + 0.362953i 0.864899 0.501946i \(-0.167382\pi\)
−0.501946 + 0.864899i \(0.667382\pi\)
\(368\) 145.421 145.421i 0.395167 0.395167i
\(369\) 152.496i 0.413267i
\(370\) 76.5346 + 8.67745i 0.206850 + 0.0234526i
\(371\) 108.435 0.292278
\(372\) −149.745 149.745i −0.402541 0.402541i
\(373\) 54.6349 54.6349i 0.146474 0.146474i −0.630067 0.776541i \(-0.716972\pi\)
0.776541 + 0.630067i \(0.216972\pi\)
\(374\) 104.732i 0.280031i
\(375\) −93.5302 195.262i −0.249414 0.520698i
\(376\) 294.000 0.781915
\(377\) 298.434 + 298.434i 0.791602 + 0.791602i
\(378\) 5.61674 5.61674i 0.0148591 0.0148591i
\(379\) 189.045i 0.498799i −0.968401 0.249400i \(-0.919767\pi\)
0.968401 0.249400i \(-0.0802333\pi\)
\(380\) −14.7702 + 130.272i −0.0388689 + 0.342822i
\(381\) 132.994 0.349066
\(382\) 24.0506 + 24.0506i 0.0629597 + 0.0629597i
\(383\) 477.999 477.999i 1.24804 1.24804i 0.291455 0.956585i \(-0.405861\pi\)
0.956585 0.291455i \(-0.0941394\pi\)
\(384\) 205.379i 0.534841i
\(385\) 64.7612 51.5715i 0.168211 0.133952i
\(386\) 2.66300 0.00689896
\(387\) −160.077 160.077i −0.413635 0.413635i
\(388\) 115.610 115.610i 0.297965 0.297965i
\(389\) 667.365i 1.71559i 0.513990 + 0.857796i \(0.328167\pi\)
−0.513990 + 0.857796i \(0.671833\pi\)
\(390\) 72.5685 + 91.1283i 0.186073 + 0.233662i
\(391\) −492.076 −1.25851
\(392\) 21.9245 + 21.9245i 0.0559298 + 0.0559298i
\(393\) −44.9943 + 44.9943i −0.114489 + 0.114489i
\(394\) 10.2536i 0.0260243i
\(395\) 158.911 + 18.0172i 0.402306 + 0.0456132i
\(396\) 68.8294 0.173812
\(397\) 98.8649 + 98.8649i 0.249030 + 0.249030i 0.820572 0.571543i \(-0.193655\pi\)
−0.571543 + 0.820572i \(0.693655\pi\)
\(398\) 159.844 159.844i 0.401618 0.401618i
\(399\) 32.7758i 0.0821449i
\(400\) 294.953 + 67.7541i 0.737382 + 0.169385i
\(401\) −505.616 −1.26089 −0.630444 0.776235i \(-0.717127\pi\)
−0.630444 + 0.776235i \(0.717127\pi\)
\(402\) −12.0022 12.0022i −0.0298561 0.0298561i
\(403\) −549.011 + 549.011i −1.36231 + 1.36231i
\(404\) 470.028i 1.16343i
\(405\) −5.06959 + 44.7135i −0.0125175 + 0.110404i
\(406\) 27.7128 0.0682581
\(407\) −117.983 117.983i −0.289884 0.289884i
\(408\) −157.130 + 157.130i −0.385123 + 0.385123i
\(409\) 173.212i 0.423502i 0.977324 + 0.211751i \(0.0679166\pi\)
−0.977324 + 0.211751i \(0.932083\pi\)
\(410\) 114.876 91.4795i 0.280185 0.223121i
\(411\) 220.746 0.537095
\(412\) 328.619 + 328.619i 0.797618 + 0.797618i
\(413\) −18.7231 + 18.7231i −0.0453344 + 0.0453344i
\(414\) 29.4479i 0.0711301i
\(415\) −28.5955 35.9090i −0.0689048 0.0865277i
\(416\) −575.318 −1.38298
\(417\) −108.393 108.393i −0.259936 0.259936i
\(418\) −18.2868 + 18.2868i −0.0437484 + 0.0437484i
\(419\) 69.3107i 0.165419i −0.996574 0.0827096i \(-0.973643\pi\)
0.996574 0.0827096i \(-0.0263574\pi\)
\(420\) −83.4675 9.46350i −0.198732 0.0225321i
\(421\) 153.026 0.363483 0.181742 0.983346i \(-0.441827\pi\)
0.181742 + 0.983346i \(0.441827\pi\)
\(422\) −33.0638 33.0638i −0.0783502 0.0783502i
\(423\) 140.801 140.801i 0.332864 0.332864i
\(424\) 181.538i 0.428155i
\(425\) −384.397 613.663i −0.904463 1.44391i
\(426\) 20.8818 0.0490183
\(427\) −160.294 160.294i −0.375395 0.375395i
\(428\) 118.862 118.862i 0.277714 0.277714i
\(429\) 252.349i 0.588226i
\(430\) 24.5596 216.614i 0.0571153 0.503753i
\(431\) −138.173 −0.320588 −0.160294 0.987069i \(-0.551244\pi\)
−0.160294 + 0.987069i \(0.551244\pi\)
\(432\) −44.4780 44.4780i −0.102958 0.102958i
\(433\) 79.3560 79.3560i 0.183270 0.183270i −0.609509 0.792779i \(-0.708633\pi\)
0.792779 + 0.609509i \(0.208633\pi\)
\(434\) 50.9816i 0.117469i
\(435\) −122.814 + 97.8009i −0.282331 + 0.224830i
\(436\) 319.925 0.733772
\(437\) 85.9198 + 85.9198i 0.196613 + 0.196613i
\(438\) −35.3180 + 35.3180i −0.0806348 + 0.0806348i
\(439\) 541.986i 1.23459i −0.786731 0.617296i \(-0.788228\pi\)
0.786731 0.617296i \(-0.211772\pi\)
\(440\) 86.3390 + 108.421i 0.196225 + 0.246411i
\(441\) 21.0000 0.0476190
\(442\) 275.500 + 275.500i 0.623302 + 0.623302i
\(443\) −395.555 + 395.555i −0.892901 + 0.892901i −0.994795 0.101894i \(-0.967510\pi\)
0.101894 + 0.994795i \(0.467510\pi\)
\(444\) 169.303i 0.381314i
\(445\) −722.729 81.9426i −1.62411 0.184141i
\(446\) −185.835 −0.416670
\(447\) 251.531 + 251.531i 0.562710 + 0.562710i
\(448\) 63.8762 63.8762i 0.142581 0.142581i
\(449\) 478.107i 1.06483i 0.846485 + 0.532413i \(0.178715\pi\)
−0.846485 + 0.532413i \(0.821285\pi\)
\(450\) −36.7241 + 23.0039i −0.0816092 + 0.0511198i
\(451\) −318.110 −0.705344
\(452\) 52.9246 + 52.9246i 0.117090 + 0.117090i
\(453\) −214.975 + 214.975i −0.474560 + 0.474560i
\(454\) 152.117i 0.335058i
\(455\) −34.6960 + 306.017i −0.0762550 + 0.672564i
\(456\) 54.8720 0.120333
\(457\) −6.40164 6.40164i −0.0140080 0.0140080i 0.700068 0.714076i \(-0.253153\pi\)
−0.714076 + 0.700068i \(0.753153\pi\)
\(458\) −122.519 + 122.519i −0.267509 + 0.267509i
\(459\) 150.505i 0.327897i
\(460\) 243.613 193.997i 0.529594 0.421733i
\(461\) 227.575 0.493655 0.246828 0.969059i \(-0.420612\pi\)
0.246828 + 0.969059i \(0.420612\pi\)
\(462\) −11.7167 11.7167i −0.0253608 0.0253608i
\(463\) −5.28403 + 5.28403i −0.0114126 + 0.0114126i −0.712790 0.701377i \(-0.752569\pi\)
0.701377 + 0.712790i \(0.252569\pi\)
\(464\) 219.453i 0.472959i
\(465\) −179.919 225.934i −0.386922 0.485879i
\(466\) 38.3442 0.0822836
\(467\) 176.806 + 176.806i 0.378599 + 0.378599i 0.870597 0.491997i \(-0.163733\pi\)
−0.491997 + 0.870597i \(0.663733\pi\)
\(468\) −181.058 + 181.058i −0.386876 + 0.386876i
\(469\) 44.8740i 0.0956802i
\(470\) 190.531 + 21.6023i 0.405385 + 0.0459623i
\(471\) −55.2735 −0.117354
\(472\) −31.3455 31.3455i −0.0664099 0.0664099i
\(473\) −333.924 + 333.924i −0.705971 + 0.705971i
\(474\) 32.0101i 0.0675318i
\(475\) −40.0314 + 174.268i −0.0842766 + 0.366880i
\(476\) −280.950 −0.590230
\(477\) 86.9414 + 86.9414i 0.182267 + 0.182267i
\(478\) −63.3747 + 63.3747i −0.132583 + 0.132583i
\(479\) 355.453i 0.742074i −0.928618 0.371037i \(-0.879002\pi\)
0.928618 0.371037i \(-0.120998\pi\)
\(480\) 24.1101 212.650i 0.0502294 0.443020i
\(481\) 620.716 1.29047
\(482\) −46.4123 46.4123i −0.0962910 0.0962910i
\(483\) −55.0502 + 55.0502i −0.113976 + 0.113976i
\(484\) 300.025i 0.619887i
\(485\) 174.431 138.905i 0.359652 0.286403i
\(486\) 9.00682 0.0185326
\(487\) −261.155 261.155i −0.536253 0.536253i 0.386173 0.922426i \(-0.373797\pi\)
−0.922426 + 0.386173i \(0.873797\pi\)
\(488\) 268.358 268.358i 0.549913 0.549913i
\(489\) 16.4302i 0.0335997i
\(490\) 12.5975 + 15.8194i 0.0257093 + 0.0322846i
\(491\) 648.152 1.32006 0.660032 0.751237i \(-0.270543\pi\)
0.660032 + 0.751237i \(0.270543\pi\)
\(492\) 228.241 + 228.241i 0.463904 + 0.463904i
\(493\) −371.292 + 371.292i −0.753129 + 0.753129i
\(494\) 96.2082i 0.194753i
\(495\) 93.2736 + 10.5753i 0.188432 + 0.0213643i
\(496\) 403.715 0.813941
\(497\) 39.0367 + 39.0367i 0.0785446 + 0.0785446i
\(498\) −6.49670 + 6.49670i −0.0130456 + 0.0130456i
\(499\) 177.417i 0.355545i −0.984072 0.177772i \(-0.943111\pi\)
0.984072 0.177772i \(-0.0568891\pi\)
\(500\) 432.236 + 152.262i 0.864472 + 0.304524i
\(501\) −259.196 −0.517357
\(502\) −120.550 120.550i −0.240139 0.240139i
\(503\) −336.836 + 336.836i −0.669654 + 0.669654i −0.957636 0.287982i \(-0.907016\pi\)
0.287982 + 0.957636i \(0.407016\pi\)
\(504\) 35.1574i 0.0697567i
\(505\) −72.2175 + 636.954i −0.143005 + 1.26130i
\(506\) 61.4291 0.121401
\(507\) 456.831 + 456.831i 0.901046 + 0.901046i
\(508\) −199.053 + 199.053i −0.391836 + 0.391836i
\(509\) 315.435i 0.619715i 0.950783 + 0.309857i \(0.100281\pi\)
−0.950783 + 0.309857i \(0.899719\pi\)
\(510\) −113.376 + 90.2851i −0.222306 + 0.177030i
\(511\) −132.048 −0.258411
\(512\) 363.189 + 363.189i 0.709354 + 0.709354i
\(513\) 26.2791 26.2791i 0.0512263 0.0512263i
\(514\) 14.8442i 0.0288798i
\(515\) 394.834 + 495.815i 0.766668 + 0.962748i
\(516\) 479.175 0.928633
\(517\) −293.716 293.716i −0.568116 0.568116i
\(518\) 28.8201 28.8201i 0.0556372 0.0556372i
\(519\) 428.102i 0.824859i
\(520\) −512.321 58.0867i −0.985234 0.111705i
\(521\) −999.113 −1.91768 −0.958842 0.283940i \(-0.908358\pi\)
−0.958842 + 0.283940i \(0.908358\pi\)
\(522\) 22.2197 + 22.2197i 0.0425664 + 0.0425664i
\(523\) 284.638 284.638i 0.544241 0.544241i −0.380529 0.924769i \(-0.624258\pi\)
0.924769 + 0.380529i \(0.124258\pi\)
\(524\) 134.686i 0.257035i
\(525\) −111.656 25.6488i −0.212679 0.0488548i
\(526\) −297.764 −0.566092
\(527\) −683.045 683.045i −1.29610 1.29610i
\(528\) −92.7824 + 92.7824i −0.175724 + 0.175724i
\(529\) 240.378i 0.454402i
\(530\) −13.3389 + 117.648i −0.0251677 + 0.221978i
\(531\) −30.0237 −0.0565419
\(532\) 49.0557 + 49.0557i 0.0922100 + 0.0922100i
\(533\) 836.799 836.799i 1.56998 1.56998i
\(534\) 145.582i 0.272626i
\(535\) 179.337 142.812i 0.335210 0.266938i
\(536\) 75.1263 0.140161
\(537\) 22.2621 + 22.2621i 0.0414565 + 0.0414565i
\(538\) 0.330847 0.330847i 0.000614958 0.000614958i
\(539\) 43.8066i 0.0812738i
\(540\) −59.3352 74.5106i −0.109880 0.137983i
\(541\) −662.246 −1.22411 −0.612057 0.790814i \(-0.709658\pi\)
−0.612057 + 0.790814i \(0.709658\pi\)
\(542\) −139.690 139.690i −0.257731 0.257731i
\(543\) 147.643 147.643i 0.271902 0.271902i
\(544\) 715.774i 1.31576i
\(545\) 433.543 + 49.1549i 0.795492 + 0.0901925i
\(546\) 61.6422 0.112898
\(547\) −596.362 596.362i −1.09024 1.09024i −0.995502 0.0947395i \(-0.969798\pi\)
−0.0947395 0.995502i \(-0.530202\pi\)
\(548\) −330.391 + 330.391i −0.602904 + 0.602904i
\(549\) 257.042i 0.468200i
\(550\) 47.9868 + 76.6076i 0.0872487 + 0.139287i
\(551\) 129.660 0.235318
\(552\) −92.1629 92.1629i −0.166962 0.166962i
\(553\) 59.8400 59.8400i 0.108210 0.108210i
\(554\) 228.441i 0.412349i
\(555\) −26.0126 + 229.430i −0.0468696 + 0.413387i
\(556\) 324.465 0.583571
\(557\) −703.702 703.702i −1.26338 1.26338i −0.949444 0.313935i \(-0.898353\pi\)
−0.313935 0.949444i \(-0.601647\pi\)
\(558\) −40.8762 + 40.8762i −0.0732549 + 0.0732549i
\(559\) 1756.80i 3.14275i
\(560\) 125.271 99.7578i 0.223699 0.178139i
\(561\) 313.957 0.559638
\(562\) −156.816 156.816i −0.279031 0.279031i
\(563\) 30.9148 30.9148i 0.0549109 0.0549109i −0.679118 0.734029i \(-0.737638\pi\)
0.734029 + 0.679118i \(0.237638\pi\)
\(564\) 421.476i 0.747298i
\(565\) 63.5888 + 79.8520i 0.112546 + 0.141331i
\(566\) 274.146 0.484357
\(567\) 16.8375 + 16.8375i 0.0296957 + 0.0296957i
\(568\) −65.3537 + 65.3537i −0.115059 + 0.115059i
\(569\) 661.719i 1.16295i 0.813564 + 0.581475i \(0.197524\pi\)
−0.813564 + 0.581475i \(0.802476\pi\)
\(570\) 35.5606 + 4.03184i 0.0623870 + 0.00707341i
\(571\) 862.831 1.51109 0.755544 0.655098i \(-0.227373\pi\)
0.755544 + 0.655098i \(0.227373\pi\)
\(572\) 377.692 + 377.692i 0.660301 + 0.660301i
\(573\) −72.0972 + 72.0972i −0.125824 + 0.125824i
\(574\) 77.7058i 0.135376i
\(575\) 359.937 225.464i 0.625977 0.392111i
\(576\) 102.430 0.177829
\(577\) 110.827 + 110.827i 0.192074 + 0.192074i 0.796592 0.604518i \(-0.206634\pi\)
−0.604518 + 0.796592i \(0.706634\pi\)
\(578\) −224.686 + 224.686i −0.388730 + 0.388730i
\(579\) 7.98294i 0.0137875i
\(580\) 37.4374 330.195i 0.0645472 0.569303i
\(581\) −24.2900 −0.0418072
\(582\) −31.5583 31.5583i −0.0542239 0.0542239i
\(583\) 181.362 181.362i 0.311084 0.311084i
\(584\) 221.070i 0.378544i
\(585\) −273.178 + 217.541i −0.466971 + 0.371864i
\(586\) 181.709 0.310084
\(587\) −224.917 224.917i −0.383164 0.383164i 0.489077 0.872241i \(-0.337334\pi\)
−0.872241 + 0.489077i \(0.837334\pi\)
\(588\) −31.4308 + 31.4308i −0.0534537 + 0.0534537i
\(589\) 238.528i 0.404972i
\(590\) −18.0107 22.6171i −0.0305267 0.0383340i
\(591\) 30.7374 0.0520092
\(592\) −228.221 228.221i −0.385509 0.385509i
\(593\) 456.305 456.305i 0.769485 0.769485i −0.208531 0.978016i \(-0.566868\pi\)
0.978016 + 0.208531i \(0.0668681\pi\)
\(594\) 18.7885i 0.0316304i
\(595\) −380.727 43.1666i −0.639877 0.0725488i
\(596\) −752.936 −1.26332
\(597\) 479.169 + 479.169i 0.802628 + 0.802628i
\(598\) −161.591 + 161.591i −0.270219 + 0.270219i
\(599\) 507.846i 0.847823i −0.905704 0.423911i \(-0.860657\pi\)
0.905704 0.423911i \(-0.139343\pi\)
\(600\) 42.9402 186.931i 0.0715670 0.311551i
\(601\) 382.086 0.635751 0.317875 0.948132i \(-0.397031\pi\)
0.317875 + 0.948132i \(0.397031\pi\)
\(602\) −81.5688 81.5688i −0.135496 0.135496i
\(603\) 35.9792 35.9792i 0.0596671 0.0596671i
\(604\) 643.509i 1.06541i
\(605\) −46.0975 + 406.577i −0.0761942 + 0.672028i
\(606\) 128.304 0.211723
\(607\) 138.297 + 138.297i 0.227837 + 0.227837i 0.811788 0.583952i \(-0.198494\pi\)
−0.583952 + 0.811788i \(0.698494\pi\)
\(608\) −124.979 + 124.979i −0.205557 + 0.205557i
\(609\) 83.0755i 0.136413i
\(610\) 193.631 154.195i 0.317428 0.252779i
\(611\) 1545.26 2.52906
\(612\) −225.261 225.261i −0.368073 0.368073i
\(613\) 438.734 438.734i 0.715715 0.715715i −0.252009 0.967725i \(-0.581091\pi\)
0.967725 + 0.252009i \(0.0810914\pi\)
\(614\) 216.050i 0.351873i
\(615\) 274.231 + 344.367i 0.445903 + 0.559946i
\(616\) 73.3393 0.119057
\(617\) −442.672 442.672i −0.717458 0.717458i 0.250626 0.968084i \(-0.419364\pi\)
−0.968084 + 0.250626i \(0.919364\pi\)
\(618\) 89.7035 89.7035i 0.145151 0.145151i
\(619\) 186.618i 0.301483i 0.988573 + 0.150741i \(0.0481661\pi\)
−0.988573 + 0.150741i \(0.951834\pi\)
\(620\) 607.441 + 68.8713i 0.979744 + 0.111083i
\(621\) −88.2767 −0.142153
\(622\) 125.612 + 125.612i 0.201948 + 0.201948i
\(623\) −272.153 + 272.153i −0.436843 + 0.436843i
\(624\) 488.134i 0.782266i
\(625\) 562.347 + 272.747i 0.899755 + 0.436396i
\(626\) −54.8125 −0.0875600
\(627\) −54.8190 54.8190i −0.0874306 0.0874306i
\(628\) 82.7281 82.7281i 0.131733 0.131733i
\(629\) 772.255i 1.22775i
\(630\) −2.58327 + 22.7843i −0.00410042 + 0.0361655i
\(631\) −973.263 −1.54241 −0.771207 0.636585i \(-0.780346\pi\)
−0.771207 + 0.636585i \(0.780346\pi\)
\(632\) 100.182 + 100.182i 0.158516 + 0.158516i
\(633\) 99.1163 99.1163i 0.156582 0.156582i
\(634\) 79.2003i 0.124922i
\(635\) −300.328 + 239.161i −0.472958 + 0.376632i
\(636\) −260.251 −0.409200
\(637\) 115.235 + 115.235i 0.180902 + 0.180902i
\(638\) 46.3509 46.3509i 0.0726502 0.0726502i
\(639\) 62.5979i 0.0979623i
\(640\) 369.330 + 463.788i 0.577078 + 0.724669i
\(641\) 11.4492 0.0178614 0.00893072 0.999960i \(-0.497157\pi\)
0.00893072 + 0.999960i \(0.497157\pi\)
\(642\) −32.4459 32.4459i −0.0505388 0.0505388i
\(643\) 132.472 132.472i 0.206021 0.206021i −0.596553 0.802574i \(-0.703463\pi\)
0.802574 + 0.596553i \(0.203463\pi\)
\(644\) 164.788i 0.255882i
\(645\) 649.350 + 73.6229i 1.00674 + 0.114144i
\(646\) 119.696 0.185288
\(647\) −488.968 488.968i −0.755746 0.755746i 0.219799 0.975545i \(-0.429460\pi\)
−0.975545 + 0.219799i \(0.929460\pi\)
\(648\) −28.1886 + 28.1886i −0.0435010 + 0.0435010i
\(649\) 62.6304i 0.0965029i
\(650\) −327.749 75.2879i −0.504230 0.115828i
\(651\) −152.829 −0.234760
\(652\) 24.5912 + 24.5912i 0.0377166 + 0.0377166i
\(653\) −866.784 + 866.784i −1.32739 + 1.32739i −0.419745 + 0.907642i \(0.637880\pi\)
−0.907642 + 0.419745i \(0.862120\pi\)
\(654\) 87.3303i 0.133533i
\(655\) 20.6939 182.519i 0.0315937 0.278655i
\(656\) −615.339 −0.938017
\(657\) −105.874 105.874i −0.161148 0.161148i
\(658\) 71.7469 71.7469i 0.109038 0.109038i
\(659\) 32.6504i 0.0495454i −0.999693 0.0247727i \(-0.992114\pi\)
0.999693 0.0247727i \(-0.00788620\pi\)
\(660\) −155.431 + 123.775i −0.235502 + 0.187538i
\(661\) −417.442 −0.631532 −0.315766 0.948837i \(-0.602261\pi\)
−0.315766 + 0.948837i \(0.602261\pi\)
\(662\) 122.854 + 122.854i 0.185580 + 0.185580i
\(663\) −825.873 + 825.873i −1.24566 + 1.24566i
\(664\) 40.6654i 0.0612430i
\(665\) 58.9403 + 74.0146i 0.0886320 + 0.111300i
\(666\) 46.2150 0.0693918
\(667\) −217.777 217.777i −0.326503 0.326503i
\(668\) 387.939 387.939i 0.580747 0.580747i
\(669\) 557.082i 0.832708i
\(670\) 48.6867 + 5.52007i 0.0726668 + 0.00823891i
\(671\) −536.196 −0.799100
\(672\) −80.0760 80.0760i −0.119161 0.119161i
\(673\) −668.058 + 668.058i −0.992657 + 0.992657i −0.999973 0.00731589i \(-0.997671\pi\)
0.00731589 + 0.999973i \(0.497671\pi\)
\(674\) 35.6070i 0.0528294i
\(675\) −68.9595 110.089i −0.102162 0.163095i
\(676\) −1367.48 −2.02290
\(677\) 287.193 + 287.193i 0.424214 + 0.424214i 0.886652 0.462438i \(-0.153025\pi\)
−0.462438 + 0.886652i \(0.653025\pi\)
\(678\) 14.4469 14.4469i 0.0213081 0.0213081i
\(679\) 117.991i 0.173772i
\(680\) 72.2678 637.398i 0.106276 0.937350i
\(681\) −456.004 −0.669609
\(682\) 85.2689 + 85.2689i 0.125028 + 0.125028i
\(683\) −142.312 + 142.312i −0.208364 + 0.208364i −0.803572 0.595208i \(-0.797070\pi\)
0.595208 + 0.803572i \(0.297070\pi\)
\(684\) 78.6641i 0.115006i
\(685\) −498.490 + 396.964i −0.727723 + 0.579510i
\(686\) 10.7008 0.0155988
\(687\) −367.279 367.279i −0.534613 0.534613i
\(688\) −645.930 + 645.930i −0.938851 + 0.938851i
\(689\) 954.158i 1.38484i
\(690\) −52.9557 66.4994i −0.0767474 0.0963760i
\(691\) 1281.91 1.85515 0.927577 0.373632i \(-0.121888\pi\)
0.927577 + 0.373632i \(0.121888\pi\)
\(692\) 640.741 + 640.741i 0.925927 + 0.925927i
\(693\) 35.1234 35.1234i 0.0506831 0.0506831i
\(694\) 155.781i 0.224468i
\(695\) 439.697 + 49.8526i 0.632657 + 0.0717303i
\(696\) −139.082 −0.199830
\(697\) 1041.09 + 1041.09i 1.49368 + 1.49368i
\(698\) −76.3064 + 76.3064i −0.109322 + 0.109322i
\(699\) 114.945i 0.164443i
\(700\) 205.505 128.728i 0.293579 0.183897i
\(701\) −122.572 −0.174854 −0.0874268 0.996171i \(-0.527864\pi\)
−0.0874268 + 0.996171i \(0.527864\pi\)
\(702\) 49.4237 + 49.4237i 0.0704041 + 0.0704041i
\(703\) 134.841 134.841i 0.191808 0.191808i
\(704\) 213.671i 0.303510i
\(705\) −64.7578 + 571.160i −0.0918551 + 0.810156i
\(706\) 85.9748 0.121777
\(707\) 239.853 + 239.853i 0.339255 + 0.339255i
\(708\) 44.9367 44.9367i 0.0634699 0.0634699i
\(709\) 140.031i 0.197504i −0.995112 0.0987522i \(-0.968515\pi\)
0.995112 0.0987522i \(-0.0314851\pi\)
\(710\) −47.1554 + 37.5514i −0.0664161 + 0.0528893i
\(711\) 95.9575 0.134961
\(712\) −455.628 455.628i −0.639927 0.639927i
\(713\) 400.632 400.632i 0.561896 0.561896i
\(714\) 76.6913i 0.107411i
\(715\) 453.796 + 569.857i 0.634679 + 0.797003i
\(716\) −66.6396 −0.0930721
\(717\) −189.980 189.980i −0.264965 0.264965i
\(718\) −18.0805 + 18.0805i −0.0251817 + 0.0251817i
\(719\) 247.009i 0.343545i −0.985137 0.171773i \(-0.945051\pi\)
0.985137 0.171773i \(-0.0549494\pi\)
\(720\) 180.425 + 20.4565i 0.250590 + 0.0284117i
\(721\) 335.386 0.465167
\(722\) 126.590 + 126.590i 0.175332 + 0.175332i
\(723\) 139.131 139.131i 0.192436 0.192436i
\(724\) 441.955i 0.610435i
\(725\) 101.466 441.710i 0.139953 0.609255i
\(726\) 81.8984 0.112808
\(727\) −663.212 663.212i −0.912259 0.912259i 0.0841908 0.996450i \(-0.473169\pi\)
−0.996450 + 0.0841908i \(0.973169\pi\)
\(728\) −192.921 + 192.921i −0.265002 + 0.265002i
\(729\) 27.0000i 0.0370370i
\(730\) 16.2436 143.267i 0.0222515 0.196257i
\(731\) 2185.69 2.99001
\(732\) 384.715 + 384.715i 0.525568 + 0.525568i
\(733\) −648.037 + 648.037i −0.884089 + 0.884089i −0.993947 0.109858i \(-0.964960\pi\)
0.109858 + 0.993947i \(0.464960\pi\)
\(734\) 108.843i 0.148287i
\(735\) −47.4224 + 37.7640i −0.0645202 + 0.0513796i
\(736\) 419.829 0.570420
\(737\) −75.0537 75.0537i −0.101837 0.101837i
\(738\) 62.3032 62.3032i 0.0844217 0.0844217i
\(739\) 1233.42i 1.66904i 0.550980 + 0.834519i \(0.314254\pi\)
−0.550980 + 0.834519i \(0.685746\pi\)
\(740\) −304.455 382.322i −0.411426 0.516651i
\(741\) 288.406 0.389212
\(742\) 44.3020 + 44.3020i 0.0597061 + 0.0597061i
\(743\) −877.884 + 877.884i −1.18154 + 1.18154i −0.202195 + 0.979345i \(0.564807\pi\)
−0.979345 + 0.202195i \(0.935193\pi\)
\(744\) 255.860i 0.343898i
\(745\) −1020.34 115.685i −1.36958 0.155282i
\(746\) 44.6430 0.0598431
\(747\) −19.4753 19.4753i −0.0260714 0.0260714i
\(748\) −469.900 + 469.900i −0.628209 + 0.628209i
\(749\) 121.309i 0.161962i
\(750\) 41.5632 117.988i 0.0554176 0.157317i
\(751\) −495.029 −0.659160 −0.329580 0.944128i \(-0.606907\pi\)
−0.329580 + 0.944128i \(0.606907\pi\)
\(752\) −568.152 568.152i −0.755521 0.755521i
\(753\) 361.375 361.375i 0.479914 0.479914i
\(754\) 243.855i 0.323415i
\(755\) 98.8721 872.047i 0.130956 1.15503i
\(756\) −50.4014 −0.0666685
\(757\) 700.188 + 700.188i 0.924951 + 0.924951i 0.997374 0.0724227i \(-0.0230731\pi\)
−0.0724227 + 0.997374i \(0.523073\pi\)
\(758\) 77.2358 77.2358i 0.101894 0.101894i
\(759\) 184.148i 0.242619i
\(760\) −123.912 + 98.6755i −0.163043 + 0.129836i
\(761\) −658.430 −0.865216 −0.432608 0.901582i \(-0.642407\pi\)
−0.432608 + 0.901582i \(0.642407\pi\)
\(762\) 54.3358 + 54.3358i 0.0713068 + 0.0713068i
\(763\) 163.256 163.256i 0.213966 0.213966i
\(764\) 215.816i 0.282482i
\(765\) −270.650 339.871i −0.353791 0.444275i
\(766\) 390.580 0.509896
\(767\) −164.751 164.751i −0.214799 0.214799i
\(768\) −83.3579 + 83.3579i −0.108539 + 0.108539i
\(769\) 121.021i 0.157375i −0.996899 0.0786873i \(-0.974927\pi\)
0.996899 0.0786873i \(-0.0250729\pi\)
\(770\) 47.5286 + 5.38877i 0.0617255 + 0.00699840i
\(771\) −44.4990 −0.0577159
\(772\) −11.9481 11.9481i −0.0154768 0.0154768i