Properties

Label 105.3.l.a.43.6
Level 105
Weight 3
Character 105.43
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 43.6
Character \(\chi\) \(=\) 105.43
Dual form 105.3.l.a.22.6

$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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 −0.597552 0.801830i \(-0.703860\pi\)
0.801830 + 0.597552i \(0.203860\pi\)
\(3\) −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 0.947978 + 0.318337i \(0.103124\pi\)
0.318337 + 0.947978i \(0.396876\pi\)
\(14\) 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 0.232071 0.972699i \(-0.425450\pi\)
0.972699 0.232071i \(-0.0745500\pi\)
\(18\) 1.22567 + 1.22567i 0.0680929 + 0.0680929i
\(19\) 7.15227i 0.376435i 0.982127 + 0.188218i \(0.0602710\pi\)
−0.982127 + 0.188218i \(0.939729\pi\)
\(20\) −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 0.395964 0.918266i \(-0.370410\pi\)
−0.918266 + 0.395964i \(0.870410\pi\)
\(24\) 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 \(-0.898813\pi\)
0.949898 0.312561i \(-0.101187\pi\)
\(30\) −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 −0.404847 0.914384i \(-0.632675\pi\)
0.914384 + 0.404847i \(0.132675\pi\)
\(38\) 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 0.959627 + 0.281277i \(0.0907581\pi\)
0.281277 + 0.959627i \(0.409242\pi\)
\(44\) 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 −0.00140698 0.999999i \(-0.500448\pi\)
0.999999 + 0.00140698i \(0.000447856\pi\)
\(48\) 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 0.378713 0.925514i \(-0.376367\pi\)
−0.925514 + 0.378713i \(0.876367\pi\)
\(54\) 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 \(0.0270292\pi\)
−0.996397 + 0.0848128i \(0.972971\pi\)
\(60\) 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 −0.611919 0.790920i \(-0.709602\pi\)
0.790920 + 0.611919i \(0.209602\pi\)
\(68\) 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 0.906229 0.422787i \(-0.138948\pi\)
−0.422787 + 0.906229i \(0.638948\pi\)
\(74\) 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 \(-0.935112\pi\)
0.979294 0.202442i \(-0.0648877\pi\)
\(80\) −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 0.745132 0.666917i \(-0.232387\pi\)
−0.666917 + 0.745132i \(0.732387\pi\)
\(84\) 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 \(0.304507\pi\)
−0.576273 + 0.817258i \(0.695493\pi\)
\(90\) −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 −0.525621 0.850719i \(-0.676167\pi\)
0.850719 + 0.525621i \(0.176167\pi\)
\(98\) −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 0.122251 0.992499i \(-0.460989\pi\)
−0.992499 + 0.122251i \(0.960989\pi\)
\(104\) 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 −0.539185 0.842188i \(-0.681268\pi\)
0.842188 + 0.539185i \(0.181268\pi\)
\(108\) 13.4703 + 13.4703i 0.124725 + 0.124725i
\(109\) 87.2642i 0.800589i −0.916387 0.400294i \(-0.868908\pi\)
0.916387 0.400294i \(-0.131092\pi\)
\(110\) −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 0.640340 0.768092i \(-0.278794\pi\)
−0.768092 + 0.640340i \(0.778794\pi\)
\(114\) 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 −0.887782 0.460265i \(-0.847754\pi\)
0.460265 + 0.887782i \(0.347754\pi\)
\(128\) −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 −0.954860 0.297056i \(-0.903995\pi\)
0.297056 + 0.954860i \(0.403995\pi\)
\(138\) 12.0220 + 12.0220i 0.0871163 + 0.0871163i
\(139\) 88.5028i 0.636711i −0.947971 0.318355i \(-0.896869\pi\)
0.947971 0.318355i \(-0.103131\pi\)
\(140\) 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 \(0.242027\pi\)
−0.724594 + 0.689176i \(0.757973\pi\)
\(150\) 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 −0.631581 0.775310i \(-0.717594\pi\)
0.775310 + 0.631581i \(0.217594\pi\)
\(158\) −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 0.686232 0.727383i \(-0.259264\pi\)
−0.727383 + 0.686232i \(0.759264\pi\)
\(164\) 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 −0.315347 0.948977i \(-0.602121\pi\)
0.948977 + 0.315347i \(0.102121\pi\)
\(168\) 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 −0.999947 0.0102943i \(-0.996723\pi\)
−0.0102943 0.999947i \(-0.503277\pi\)
\(174\) 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 \(0.0161687\pi\)
−0.998710 + 0.0507736i \(0.983831\pi\)
\(180\) −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 0.715499 0.698613i \(-0.246199\pi\)
−0.698613 + 0.715499i \(0.746199\pi\)
\(194\) 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 −0.738238 0.674540i \(-0.764342\pi\)
0.674540 + 0.738238i \(0.264342\pi\)
\(198\) −7.67036 7.67036i −0.0387392 0.0387392i
\(199\) 391.240i 1.96603i 0.183526 + 0.983015i \(0.441249\pi\)
−0.183526 + 0.983015i \(0.558751\pi\)
\(200\) −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 −0.999799 0.0200565i \(-0.993615\pi\)
−0.0200565 0.999799i \(-0.506385\pi\)
\(224\) 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 −0.166022 0.986122i \(-0.553092\pi\)
0.986122 + 0.166022i \(0.0530921\pi\)
\(228\) 32.1145 + 32.1145i 0.140853 + 0.140853i
\(229\) 299.882i 1.30953i −0.755832 0.654765i \(-0.772768\pi\)
0.755832 0.654765i \(-0.227232\pi\)
\(230\) −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 0.800600 0.599199i \(-0.204514\pi\)
−0.599199 + 0.800600i \(0.704514\pi\)
\(234\) 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 \(-0.894799\pi\)
0.945881 0.324515i \(-0.105201\pi\)
\(240\) −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 −0.670879 0.741567i \(-0.734083\pi\)
0.741567 + 0.670879i \(0.234083\pi\)
\(258\) −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 −0.834349 0.551237i \(-0.814156\pi\)
−0.551237 0.834349i \(-0.685844\pi\)
\(264\) 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 \(0.000479118\pi\)
−0.999999 + 0.00150519i \(0.999521\pi\)
\(270\) 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 0.00932280 0.999957i \(-0.497032\pi\)
0.999957 0.00932280i \(-0.00296758\pi\)
\(278\) −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 0.978291 + 0.207238i \(0.0664474\pi\)
0.207238 + 0.978291i \(0.433553\pi\)
\(284\) 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 0.976135 0.217163i \(-0.0696804\pi\)
−0.217163 + 0.976135i \(0.569680\pi\)
\(294\) 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 −0.130227 0.991484i \(-0.541571\pi\)
0.991484 + 0.130227i \(0.0415706\pi\)
\(308\) 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 0.591783 0.806098i \(-0.298424\pi\)
−0.806098 + 0.591783i \(0.798424\pi\)
\(314\) 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 −0.843263 0.537501i \(-0.819369\pi\)
0.537501 + 0.843263i \(0.319369\pi\)
\(318\) 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 −0.768798 0.639491i \(-0.779145\pi\)
0.639491 + 0.768798i \(0.279145\pi\)
\(338\) 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 −0.926272 0.376856i \(-0.877005\pi\)
0.376856 + 0.926272i \(0.377005\pi\)
\(348\) −81.3992 81.3992i −0.233906 0.233906i
\(349\) 186.770i 0.535158i −0.963536 0.267579i \(-0.913776\pi\)
0.963536 0.267579i \(-0.0862237\pi\)
\(350\) −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 0.840256 0.542190i \(-0.182405\pi\)
−0.542190 + 0.840256i \(0.682405\pi\)
\(354\) 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 \(-0.980368\pi\)
0.998099 0.0616356i \(-0.0196317\pi\)
\(360\) −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 −0.501946 0.864899i \(-0.667382\pi\)
0.864899 + 0.501946i \(0.167382\pi\)
\(368\) 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 0.776541 0.630067i \(-0.216972\pi\)
−0.630067 + 0.776541i \(0.716972\pi\)
\(374\) 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 \(0.0802333\pi\)
−0.968401 + 0.249400i \(0.919767\pi\)
\(380\) −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 0.956585 + 0.291455i \(0.0941394\pi\)
0.291455 + 0.956585i \(0.405861\pi\)
\(384\) 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 \(-0.671833\pi\)
0.513990 0.857796i \(-0.328167\pi\)
\(390\) 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 −0.571543 0.820572i \(-0.693655\pi\)
0.820572 + 0.571543i \(0.193655\pi\)
\(398\) 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 \(-0.932083\pi\)
0.977324 0.211751i \(-0.0679166\pi\)
\(410\) 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 \(0.0263574\pi\)
−0.996574 + 0.0827096i \(0.973643\pi\)
\(420\) −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 0.792779 0.609509i \(-0.208633\pi\)
−0.609509 + 0.792779i \(0.708633\pi\)
\(434\) 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 \(0.211772\pi\)
−0.786731 + 0.617296i \(0.788228\pi\)
\(440\) 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 0.101894 0.994795i \(-0.467510\pi\)
−0.994795 + 0.101894i \(0.967510\pi\)
\(444\) 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 \(-0.821285\pi\)
0.846485 0.532413i \(-0.178715\pi\)
\(450\) −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 −0.714076 0.700068i \(-0.753153\pi\)
0.700068 + 0.714076i \(0.253153\pi\)
\(458\) −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 0.701377 0.712790i \(-0.252569\pi\)
−0.712790 + 0.701377i \(0.752569\pi\)
\(464\) 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 −0.491997 0.870597i \(-0.663733\pi\)
0.870597 + 0.491997i \(0.163733\pi\)
\(468\) −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 \(0.120998\pi\)
−0.928618 + 0.371037i \(0.879002\pi\)
\(480\) 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 −0.922426 0.386173i \(-0.873797\pi\)
0.386173 + 0.922426i \(0.373797\pi\)
\(488\) 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 \(0.0568891\pi\)
−0.984072 + 0.177772i \(0.943111\pi\)
\(500\) 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 0.287982 0.957636i \(-0.407016\pi\)
−0.957636 + 0.287982i \(0.907016\pi\)
\(504\) 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 \(-0.899719\pi\)
0.950783 0.309857i \(-0.100281\pi\)
\(510\) −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 0.924769 0.380529i \(-0.124258\pi\)
−0.380529 + 0.924769i \(0.624258\pi\)
\(524\) 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 −0.0947395 + 0.995502i \(0.530202\pi\)
−0.995502 + 0.0947395i \(0.969798\pi\)
\(548\) −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 −0.313935 + 0.949444i \(0.601647\pi\)
−0.949444 + 0.313935i \(0.898353\pi\)
\(558\) −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 0.734029 0.679118i \(-0.237638\pi\)
−0.679118 + 0.734029i \(0.737638\pi\)
\(564\) 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 \(-0.802476\pi\)
0.813564 0.581475i \(-0.197524\pi\)
\(570\) 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 −0.604518 0.796592i \(-0.706634\pi\)
0.796592 + 0.604518i \(0.206634\pi\)
\(578\) −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 −0.872241 0.489077i \(-0.837334\pi\)
0.489077 + 0.872241i \(0.337334\pi\)
\(588\) −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 0.978016 0.208531i \(-0.0668681\pi\)
−0.208531 + 0.978016i \(0.566868\pi\)
\(594\) 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 \(0.139343\pi\)
−0.905704 + 0.423911i \(0.860657\pi\)
\(600\) 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 −0.583952 0.811788i \(-0.698494\pi\)
0.811788 + 0.583952i \(0.198494\pi\)
\(608\) −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 0.967725 0.252009i \(-0.0810914\pi\)
−0.252009 + 0.967725i \(0.581091\pi\)
\(614\) 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 −0.968084 0.250626i \(-0.919364\pi\)
0.250626 + 0.968084i \(0.419364\pi\)
\(618\) 89.7035 + 89.7035i 0.145151 + 0.145151i
\(619\) 186.618i 0.301483i −0.988573 0.150741i \(-0.951834\pi\)
0.988573 0.150741i \(-0.0481661\pi\)
\(620\) 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 0.802574 0.596553i \(-0.203463\pi\)
−0.596553 + 0.802574i \(0.703463\pi\)
\(644\) 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 −0.975545 0.219799i \(-0.929460\pi\)
0.219799 + 0.975545i \(0.429460\pi\)
\(648\) −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 −0.907642 0.419745i \(-0.862120\pi\)
−0.419745 0.907642i \(-0.637880\pi\)
\(654\) 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 \(0.00788620\pi\)
−0.999693 + 0.0247727i \(0.992114\pi\)
\(660\) −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 0.00731589 0.999973i \(-0.497671\pi\)
−0.999973 + 0.00731589i \(0.997671\pi\)
\(674\) 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 −0.462438 0.886652i \(-0.653025\pi\)
0.886652 + 0.462438i \(0.153025\pi\)
\(678\) 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 0.595208 0.803572i \(-0.297070\pi\)
−0.803572 + 0.595208i \(0.797070\pi\)
\(684\) 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 \(0.0314851\pi\)
−0.995112 + 0.0987522i \(0.968515\pi\)
\(710\) −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 \(0.0549494\pi\)
−0.985137 + 0.171773i \(0.945051\pi\)
\(720\) 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 −0.996450 0.0841908i \(-0.973169\pi\)
0.0841908 + 0.996450i \(0.473169\pi\)
\(728\) −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 0.109858 0.993947i \(-0.464960\pi\)
−0.993947 + 0.109858i \(0.964960\pi\)
\(734\) 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 \(-0.685746\pi\)
0.550980 0.834519i \(-0.314254\pi\)
\(740\) −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 −0.979345 0.202195i \(-0.935193\pi\)
−0.202195 0.979345i \(-0.564807\pi\)
\(744\) 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 −0.0724227 0.997374i \(-0.523073\pi\)
0.997374 + 0.0724227i \(0.0230731\pi\)
\(758\) 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 \(0.0250729\pi\)
−0.996899 + 0.0786873i \(0.974927\pi\)
\(770\) 47.5286 5.38877i 0.0617255 0.00699840i
\(771\) −44.4990 −0.0577159
\(772\) −11.9481 + 11.9481i −0.0154768 +