Properties

Label 483.2.h.a.160.7
Level $483$
Weight $2$
Character 483.160
Analytic conductor $3.857$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.342102016.5
Defining polynomial: \(x^{8} + x^{6} + 4 x^{4} + 4 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{23}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 160.7
Root \(1.17915 - 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 483.160
Dual form 483.2.h.a.160.3

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.69614 q^{5} -1.00000i q^{6} +(-2.17238 - 1.51022i) q^{7} +3.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000i q^{3} -1.00000 q^{4} +1.69614 q^{5} -1.00000i q^{6} +(-2.17238 - 1.51022i) q^{7} +3.00000 q^{8} -1.00000 q^{9} -1.69614 q^{10} +1.32431i q^{11} -1.00000i q^{12} +5.12311i q^{13} +(2.17238 + 1.51022i) q^{14} +1.69614i q^{15} -1.00000 q^{16} -1.69614 q^{17} +1.00000 q^{18} +7.73704 q^{19} -1.69614 q^{20} +(1.51022 - 2.17238i) q^{21} -1.32431i q^{22} +(-2.56155 + 4.05444i) q^{23} +3.00000i q^{24} -2.12311 q^{25} -5.12311i q^{26} -1.00000i q^{27} +(2.17238 + 1.51022i) q^{28} -8.24621 q^{29} -1.69614i q^{30} +6.24621i q^{31} -5.00000 q^{32} -1.32431 q^{33} +1.69614 q^{34} +(-3.68466 - 2.56155i) q^{35} +1.00000 q^{36} +6.04090i q^{37} -7.73704 q^{38} -5.12311 q^{39} +5.08842 q^{40} +2.87689i q^{41} +(-1.51022 + 2.17238i) q^{42} +3.02045i q^{43} -1.32431i q^{44} -1.69614 q^{45} +(2.56155 - 4.05444i) q^{46} -1.12311i q^{47} -1.00000i q^{48} +(2.43845 + 6.56155i) q^{49} +2.12311 q^{50} -1.69614i q^{51} -5.12311i q^{52} +5.08842i q^{53} +1.00000i q^{54} +2.24621i q^{55} +(-6.51713 - 4.53067i) q^{56} +7.73704i q^{57} +8.24621 q^{58} +1.12311i q^{59} -1.69614i q^{60} +6.04090 q^{61} -6.24621i q^{62} +(2.17238 + 1.51022i) q^{63} +7.00000 q^{64} +8.68951i q^{65} +1.32431 q^{66} -15.1022i q^{67} +1.69614 q^{68} +(-4.05444 - 2.56155i) q^{69} +(3.68466 + 2.56155i) q^{70} -2.87689 q^{71} -3.00000 q^{72} +10.2462i q^{73} -6.04090i q^{74} -2.12311i q^{75} -7.73704 q^{76} +(2.00000 - 2.87689i) q^{77} +5.12311 q^{78} -2.27678i q^{79} -1.69614 q^{80} +1.00000 q^{81} -2.87689i q^{82} +5.29723 q^{83} +(-1.51022 + 2.17238i) q^{84} -2.87689 q^{85} -3.02045i q^{86} -8.24621i q^{87} +3.97292i q^{88} +5.08842 q^{89} +1.69614 q^{90} +(7.73704 - 11.1293i) q^{91} +(2.56155 - 4.05444i) q^{92} -6.24621 q^{93} +1.12311i q^{94} +13.1231 q^{95} -5.00000i q^{96} -6.04090 q^{97} +(-2.43845 - 6.56155i) q^{98} -1.32431i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{2} - 8q^{4} + 24q^{8} - 8q^{9} + O(q^{10}) \) \( 8q - 8q^{2} - 8q^{4} + 24q^{8} - 8q^{9} - 8q^{16} + 8q^{18} - 4q^{23} + 16q^{25} - 40q^{32} + 20q^{35} + 8q^{36} - 8q^{39} + 4q^{46} + 36q^{49} - 16q^{50} + 56q^{64} - 20q^{70} - 56q^{71} - 24q^{72} + 16q^{77} + 8q^{78} + 8q^{81} - 56q^{85} + 4q^{92} + 16q^{93} + 72q^{95} - 36q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 1.69614 0.758537 0.379269 0.925287i \(-0.376176\pi\)
0.379269 + 0.925287i \(0.376176\pi\)
\(6\) 1.00000i 0.408248i
\(7\) −2.17238 1.51022i −0.821081 0.570811i
\(8\) 3.00000 1.06066
\(9\) −1.00000 −0.333333
\(10\) −1.69614 −0.536367
\(11\) 1.32431i 0.399294i 0.979868 + 0.199647i \(0.0639795\pi\)
−0.979868 + 0.199647i \(0.936021\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 5.12311i 1.42089i 0.703751 + 0.710447i \(0.251507\pi\)
−0.703751 + 0.710447i \(0.748493\pi\)
\(14\) 2.17238 + 1.51022i 0.580592 + 0.403624i
\(15\) 1.69614i 0.437942i
\(16\) −1.00000 −0.250000
\(17\) −1.69614 −0.411375 −0.205687 0.978618i \(-0.565943\pi\)
−0.205687 + 0.978618i \(0.565943\pi\)
\(18\) 1.00000 0.235702
\(19\) 7.73704 1.77500 0.887499 0.460810i \(-0.152441\pi\)
0.887499 + 0.460810i \(0.152441\pi\)
\(20\) −1.69614 −0.379269
\(21\) 1.51022 2.17238i 0.329558 0.474052i
\(22\) 1.32431i 0.282343i
\(23\) −2.56155 + 4.05444i −0.534121 + 0.845408i
\(24\) 3.00000i 0.612372i
\(25\) −2.12311 −0.424621
\(26\) 5.12311i 1.00472i
\(27\) 1.00000i 0.192450i
\(28\) 2.17238 + 1.51022i 0.410541 + 0.285406i
\(29\) −8.24621 −1.53128 −0.765641 0.643268i \(-0.777578\pi\)
−0.765641 + 0.643268i \(0.777578\pi\)
\(30\) 1.69614i 0.309672i
\(31\) 6.24621i 1.12185i 0.827866 + 0.560926i \(0.189555\pi\)
−0.827866 + 0.560926i \(0.810445\pi\)
\(32\) −5.00000 −0.883883
\(33\) −1.32431 −0.230532
\(34\) 1.69614 0.290886
\(35\) −3.68466 2.56155i −0.622821 0.432981i
\(36\) 1.00000 0.166667
\(37\) 6.04090i 0.993117i 0.868003 + 0.496559i \(0.165403\pi\)
−0.868003 + 0.496559i \(0.834597\pi\)
\(38\) −7.73704 −1.25511
\(39\) −5.12311 −0.820353
\(40\) 5.08842 0.804550
\(41\) 2.87689i 0.449295i 0.974440 + 0.224648i \(0.0721231\pi\)
−0.974440 + 0.224648i \(0.927877\pi\)
\(42\) −1.51022 + 2.17238i −0.233033 + 0.335205i
\(43\) 3.02045i 0.460614i 0.973118 + 0.230307i \(0.0739730\pi\)
−0.973118 + 0.230307i \(0.926027\pi\)
\(44\) 1.32431i 0.199647i
\(45\) −1.69614 −0.252846
\(46\) 2.56155 4.05444i 0.377680 0.597794i
\(47\) 1.12311i 0.163822i −0.996640 0.0819109i \(-0.973898\pi\)
0.996640 0.0819109i \(-0.0261023\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 2.43845 + 6.56155i 0.348350 + 0.937365i
\(50\) 2.12311 0.300252
\(51\) 1.69614i 0.237507i
\(52\) 5.12311i 0.710447i
\(53\) 5.08842i 0.698949i 0.936946 + 0.349474i \(0.113640\pi\)
−0.936946 + 0.349474i \(0.886360\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 2.24621i 0.302879i
\(56\) −6.51713 4.53067i −0.870888 0.605436i
\(57\) 7.73704i 1.02480i
\(58\) 8.24621 1.08278
\(59\) 1.12311i 0.146216i 0.997324 + 0.0731079i \(0.0232918\pi\)
−0.997324 + 0.0731079i \(0.976708\pi\)
\(60\) 1.69614i 0.218971i
\(61\) 6.04090 0.773457 0.386729 0.922194i \(-0.373605\pi\)
0.386729 + 0.922194i \(0.373605\pi\)
\(62\) 6.24621i 0.793270i
\(63\) 2.17238 + 1.51022i 0.273694 + 0.190270i
\(64\) 7.00000 0.875000
\(65\) 8.68951i 1.07780i
\(66\) 1.32431 0.163011
\(67\) 15.1022i 1.84503i −0.385959 0.922516i \(-0.626129\pi\)
0.385959 0.922516i \(-0.373871\pi\)
\(68\) 1.69614 0.205687
\(69\) −4.05444 2.56155i −0.488097 0.308375i
\(70\) 3.68466 + 2.56155i 0.440401 + 0.306164i
\(71\) −2.87689 −0.341425 −0.170712 0.985321i \(-0.554607\pi\)
−0.170712 + 0.985321i \(0.554607\pi\)
\(72\) −3.00000 −0.353553
\(73\) 10.2462i 1.19923i 0.800289 + 0.599614i \(0.204679\pi\)
−0.800289 + 0.599614i \(0.795321\pi\)
\(74\) 6.04090i 0.702240i
\(75\) 2.12311i 0.245155i
\(76\) −7.73704 −0.887499
\(77\) 2.00000 2.87689i 0.227921 0.327853i
\(78\) 5.12311 0.580077
\(79\) 2.27678i 0.256158i −0.991764 0.128079i \(-0.959119\pi\)
0.991764 0.128079i \(-0.0408811\pi\)
\(80\) −1.69614 −0.189634
\(81\) 1.00000 0.111111
\(82\) 2.87689i 0.317700i
\(83\) 5.29723 0.581446 0.290723 0.956807i \(-0.406104\pi\)
0.290723 + 0.956807i \(0.406104\pi\)
\(84\) −1.51022 + 2.17238i −0.164779 + 0.237026i
\(85\) −2.87689 −0.312043
\(86\) 3.02045i 0.325703i
\(87\) 8.24621i 0.884087i
\(88\) 3.97292i 0.423515i
\(89\) 5.08842 0.539372 0.269686 0.962948i \(-0.413080\pi\)
0.269686 + 0.962948i \(0.413080\pi\)
\(90\) 1.69614 0.178789
\(91\) 7.73704 11.1293i 0.811062 1.16667i
\(92\) 2.56155 4.05444i 0.267060 0.422704i
\(93\) −6.24621 −0.647702
\(94\) 1.12311i 0.115840i
\(95\) 13.1231 1.34640
\(96\) 5.00000i 0.510310i
\(97\) −6.04090 −0.613360 −0.306680 0.951813i \(-0.599218\pi\)
−0.306680 + 0.951813i \(0.599218\pi\)
\(98\) −2.43845 6.56155i −0.246320 0.662817i
\(99\) 1.32431i 0.133098i
\(100\) 2.12311 0.212311
\(101\) 5.12311i 0.509768i −0.966972 0.254884i \(-0.917963\pi\)
0.966972 0.254884i \(-0.0820373\pi\)
\(102\) 1.69614i 0.167943i
\(103\) 4.34475 0.428101 0.214051 0.976823i \(-0.431334\pi\)
0.214051 + 0.976823i \(0.431334\pi\)
\(104\) 15.3693i 1.50709i
\(105\) 2.56155 3.68466i 0.249982 0.359586i
\(106\) 5.08842i 0.494231i
\(107\) 8.10887i 0.783914i −0.919984 0.391957i \(-0.871798\pi\)
0.919984 0.391957i \(-0.128202\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 14.7304i 1.41092i 0.708751 + 0.705458i \(0.249259\pi\)
−0.708751 + 0.705458i \(0.750741\pi\)
\(110\) 2.24621i 0.214168i
\(111\) −6.04090 −0.573376
\(112\) 2.17238 + 1.51022i 0.205270 + 0.142703i
\(113\) 16.4265i 1.54528i −0.634845 0.772640i \(-0.718936\pi\)
0.634845 0.772640i \(-0.281064\pi\)
\(114\) 7.73704i 0.724640i
\(115\) −4.34475 + 6.87689i −0.405150 + 0.641274i
\(116\) 8.24621 0.765641
\(117\) 5.12311i 0.473631i
\(118\) 1.12311i 0.103390i
\(119\) 3.68466 + 2.56155i 0.337772 + 0.234817i
\(120\) 5.08842i 0.464507i
\(121\) 9.24621 0.840565
\(122\) −6.04090 −0.546917
\(123\) −2.87689 −0.259401
\(124\) 6.24621i 0.560926i
\(125\) −12.0818 −1.08063
\(126\) −2.17238 1.51022i −0.193531 0.134541i
\(127\) 10.2462 0.909204 0.454602 0.890695i \(-0.349781\pi\)
0.454602 + 0.890695i \(0.349781\pi\)
\(128\) 3.00000 0.265165
\(129\) −3.02045 −0.265936
\(130\) 8.68951i 0.762120i
\(131\) 12.0000i 1.04844i −0.851581 0.524222i \(-0.824356\pi\)
0.851581 0.524222i \(-0.175644\pi\)
\(132\) 1.32431 0.115266
\(133\) −16.8078 11.6847i −1.45742 1.01319i
\(134\) 15.1022i 1.30463i
\(135\) 1.69614i 0.145981i
\(136\) −5.08842 −0.436329
\(137\) 14.5216i 1.24066i 0.784339 + 0.620332i \(0.213002\pi\)
−0.784339 + 0.620332i \(0.786998\pi\)
\(138\) 4.05444 + 2.56155i 0.345136 + 0.218054i
\(139\) 12.0000i 1.01783i −0.860818 0.508913i \(-0.830047\pi\)
0.860818 0.508913i \(-0.169953\pi\)
\(140\) 3.68466 + 2.56155i 0.311410 + 0.216491i
\(141\) 1.12311 0.0945826
\(142\) 2.87689 0.241424
\(143\) −6.78456 −0.567354
\(144\) 1.00000 0.0833333
\(145\) −13.9867 −1.16154
\(146\) 10.2462i 0.847982i
\(147\) −6.56155 + 2.43845i −0.541188 + 0.201120i
\(148\) 6.04090i 0.496559i
\(149\) 13.7779i 1.12873i −0.825525 0.564366i \(-0.809121\pi\)
0.825525 0.564366i \(-0.190879\pi\)
\(150\) 2.12311i 0.173351i
\(151\) 12.4924 1.01662 0.508309 0.861174i \(-0.330271\pi\)
0.508309 + 0.861174i \(0.330271\pi\)
\(152\) 23.2111 1.88267
\(153\) 1.69614 0.137125
\(154\) −2.00000 + 2.87689i −0.161165 + 0.231827i
\(155\) 10.5945i 0.850967i
\(156\) 5.12311 0.410177
\(157\) −0.743668 −0.0593512 −0.0296756 0.999560i \(-0.509447\pi\)
−0.0296756 + 0.999560i \(0.509447\pi\)
\(158\) 2.27678i 0.181131i
\(159\) −5.08842 −0.403538
\(160\) −8.48071 −0.670459
\(161\) 11.6878 4.93925i 0.921125 0.389267i
\(162\) −1.00000 −0.0785674
\(163\) 12.0000 0.939913 0.469956 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) 2.87689i 0.224648i
\(165\) −2.24621 −0.174867
\(166\) −5.29723 −0.411145
\(167\) 22.2462i 1.72146i 0.509059 + 0.860732i \(0.329994\pi\)
−0.509059 + 0.860732i \(0.670006\pi\)
\(168\) 4.53067 6.51713i 0.349549 0.502808i
\(169\) −13.2462 −1.01894
\(170\) 2.87689 0.220648
\(171\) −7.73704 −0.591666
\(172\) 3.02045i 0.230307i
\(173\) 5.12311i 0.389503i 0.980853 + 0.194751i \(0.0623900\pi\)
−0.980853 + 0.194751i \(0.937610\pi\)
\(174\) 8.24621i 0.625144i
\(175\) 4.61219 + 3.20636i 0.348649 + 0.242378i
\(176\) 1.32431i 0.0998234i
\(177\) −1.12311 −0.0844178
\(178\) −5.08842 −0.381393
\(179\) −4.00000 −0.298974 −0.149487 0.988764i \(-0.547762\pi\)
−0.149487 + 0.988764i \(0.547762\pi\)
\(180\) 1.69614 0.126423
\(181\) 14.7304 1.09490 0.547451 0.836838i \(-0.315598\pi\)
0.547451 + 0.836838i \(0.315598\pi\)
\(182\) −7.73704 + 11.1293i −0.573507 + 0.824960i
\(183\) 6.04090i 0.446556i
\(184\) −7.68466 + 12.1633i −0.566521 + 0.896691i
\(185\) 10.2462i 0.753316i
\(186\) 6.24621 0.457994
\(187\) 2.24621i 0.164259i
\(188\) 1.12311i 0.0819109i
\(189\) −1.51022 + 2.17238i −0.109853 + 0.158017i
\(190\) −13.1231 −0.952050
\(191\) 26.2316i 1.89805i −0.315202 0.949024i \(-0.602072\pi\)
0.315202 0.949024i \(-0.397928\pi\)
\(192\) 7.00000i 0.505181i
\(193\) −15.6155 −1.12403 −0.562015 0.827127i \(-0.689974\pi\)
−0.562015 + 0.827127i \(0.689974\pi\)
\(194\) 6.04090 0.433711
\(195\) −8.68951 −0.622269
\(196\) −2.43845 6.56155i −0.174175 0.468682i
\(197\) −14.4924 −1.03254 −0.516271 0.856425i \(-0.672680\pi\)
−0.516271 + 0.856425i \(0.672680\pi\)
\(198\) 1.32431i 0.0941144i
\(199\) 4.34475 0.307992 0.153996 0.988072i \(-0.450786\pi\)
0.153996 + 0.988072i \(0.450786\pi\)
\(200\) −6.36932 −0.450379
\(201\) 15.1022 1.06523
\(202\) 5.12311i 0.360460i
\(203\) 17.9139 + 12.4536i 1.25731 + 0.874073i
\(204\) 1.69614i 0.118754i
\(205\) 4.87962i 0.340807i
\(206\) −4.34475 −0.302713
\(207\) 2.56155 4.05444i 0.178040 0.281803i
\(208\) 5.12311i 0.355223i
\(209\) 10.2462i 0.708745i
\(210\) −2.56155 + 3.68466i −0.176764 + 0.254266i
\(211\) 6.24621 0.430007 0.215003 0.976613i \(-0.431024\pi\)
0.215003 + 0.976613i \(0.431024\pi\)
\(212\) 5.08842i 0.349474i
\(213\) 2.87689i 0.197122i
\(214\) 8.10887i 0.554311i
\(215\) 5.12311i 0.349393i
\(216\) 3.00000i 0.204124i
\(217\) 9.43318 13.5691i 0.640366 0.921132i
\(218\) 14.7304i 0.997669i
\(219\) −10.2462 −0.692375
\(220\) 2.24621i 0.151440i
\(221\) 8.68951i 0.584520i
\(222\) 6.04090 0.405438
\(223\) 4.00000i 0.267860i −0.990991 0.133930i \(-0.957240\pi\)
0.990991 0.133930i \(-0.0427597\pi\)
\(224\) 10.8619 + 7.55112i 0.725740 + 0.504530i
\(225\) 2.12311 0.141540
\(226\) 16.4265i 1.09268i
\(227\) −3.39228 −0.225154 −0.112577 0.993643i \(-0.535910\pi\)
−0.112577 + 0.993643i \(0.535910\pi\)
\(228\) 7.73704i 0.512398i
\(229\) 14.7304 0.973413 0.486706 0.873566i \(-0.338198\pi\)
0.486706 + 0.873566i \(0.338198\pi\)
\(230\) 4.34475 6.87689i 0.286485 0.453449i
\(231\) 2.87689 + 2.00000i 0.189286 + 0.131590i
\(232\) −24.7386 −1.62417
\(233\) −20.2462 −1.32637 −0.663187 0.748454i \(-0.730796\pi\)
−0.663187 + 0.748454i \(0.730796\pi\)
\(234\) 5.12311i 0.334908i
\(235\) 1.90495i 0.124265i
\(236\) 1.12311i 0.0731079i
\(237\) 2.27678 0.147893
\(238\) −3.68466 2.56155i −0.238841 0.166041i
\(239\) 23.3693 1.51164 0.755818 0.654782i \(-0.227240\pi\)
0.755818 + 0.654782i \(0.227240\pi\)
\(240\) 1.69614i 0.109485i
\(241\) −12.8255 −0.826161 −0.413080 0.910695i \(-0.635547\pi\)
−0.413080 + 0.910695i \(0.635547\pi\)
\(242\) −9.24621 −0.594369
\(243\) 1.00000i 0.0641500i
\(244\) −6.04090 −0.386729
\(245\) 4.13595 + 11.1293i 0.264236 + 0.711026i
\(246\) 2.87689 0.183424
\(247\) 39.6377i 2.52208i
\(248\) 18.7386i 1.18990i
\(249\) 5.29723i 0.335698i
\(250\) 12.0818 0.764120
\(251\) −27.5559 −1.73931 −0.869655 0.493659i \(-0.835659\pi\)
−0.869655 + 0.493659i \(0.835659\pi\)
\(252\) −2.17238 1.51022i −0.136847 0.0951352i
\(253\) −5.36932 3.39228i −0.337566 0.213271i
\(254\) −10.2462 −0.642904
\(255\) 2.87689i 0.180158i
\(256\) −17.0000 −1.06250
\(257\) 7.36932i 0.459685i 0.973228 + 0.229843i \(0.0738212\pi\)
−0.973228 + 0.229843i \(0.926179\pi\)
\(258\) 3.02045 0.188045
\(259\) 9.12311 13.1231i 0.566882 0.815430i
\(260\) 8.68951i 0.538901i
\(261\) 8.24621 0.510428
\(262\) 12.0000i 0.741362i
\(263\) 20.9343i 1.29087i 0.763817 + 0.645433i \(0.223323\pi\)
−0.763817 + 0.645433i \(0.776677\pi\)
\(264\) −3.97292 −0.244516
\(265\) 8.63068i 0.530179i
\(266\) 16.8078 + 11.6847i 1.03055 + 0.716432i
\(267\) 5.08842i 0.311406i
\(268\) 15.1022i 0.922516i
\(269\) 31.3693i 1.91262i 0.292353 + 0.956311i \(0.405562\pi\)
−0.292353 + 0.956311i \(0.594438\pi\)
\(270\) 1.69614i 0.103224i
\(271\) 16.4924i 1.00184i 0.865493 + 0.500922i \(0.167006\pi\)
−0.865493 + 0.500922i \(0.832994\pi\)
\(272\) 1.69614 0.102844
\(273\) 11.1293 + 7.73704i 0.673577 + 0.468267i
\(274\) 14.5216i 0.877282i
\(275\) 2.81164i 0.169548i
\(276\) 4.05444 + 2.56155i 0.244048 + 0.154187i
\(277\) −0.246211 −0.0147934 −0.00739670 0.999973i \(-0.502354\pi\)
−0.00739670 + 0.999973i \(0.502354\pi\)
\(278\) 12.0000i 0.719712i
\(279\) 6.24621i 0.373951i
\(280\) −11.0540 7.68466i −0.660601 0.459246i
\(281\) 9.64198i 0.575192i −0.957752 0.287596i \(-0.907144\pi\)
0.957752 0.287596i \(-0.0928561\pi\)
\(282\) −1.12311 −0.0668800
\(283\) −25.1161 −1.49299 −0.746497 0.665388i \(-0.768266\pi\)
−0.746497 + 0.665388i \(0.768266\pi\)
\(284\) 2.87689 0.170712
\(285\) 13.1231i 0.777346i
\(286\) 6.78456 0.401180
\(287\) 4.34475 6.24970i 0.256463 0.368908i
\(288\) 5.00000 0.294628
\(289\) −14.1231 −0.830771
\(290\) 13.9867 0.821329
\(291\) 6.04090i 0.354124i
\(292\) 10.2462i 0.599614i
\(293\) 32.6443 1.90710 0.953550 0.301235i \(-0.0973990\pi\)
0.953550 + 0.301235i \(0.0973990\pi\)
\(294\) 6.56155 2.43845i 0.382678 0.142213i
\(295\) 1.90495i 0.110910i
\(296\) 18.1227i 1.05336i
\(297\) 1.32431 0.0768441
\(298\) 13.7779i 0.798134i
\(299\) −20.7713 13.1231i −1.20124 0.758929i
\(300\) 2.12311i 0.122578i
\(301\) 4.56155 6.56155i 0.262924 0.378202i
\(302\) −12.4924 −0.718858
\(303\) 5.12311 0.294315
\(304\) −7.73704 −0.443749
\(305\) 10.2462 0.586696
\(306\) −1.69614 −0.0969619
\(307\) 14.2462i 0.813074i 0.913634 + 0.406537i \(0.133264\pi\)
−0.913634 + 0.406537i \(0.866736\pi\)
\(308\) −2.00000 + 2.87689i −0.113961 + 0.163926i
\(309\) 4.34475i 0.247164i
\(310\) 10.5945i 0.601725i
\(311\) 27.3693i 1.55197i −0.630750 0.775986i \(-0.717253\pi\)
0.630750 0.775986i \(-0.282747\pi\)
\(312\) −15.3693 −0.870116
\(313\) −28.2995 −1.59958 −0.799792 0.600277i \(-0.795057\pi\)
−0.799792 + 0.600277i \(0.795057\pi\)
\(314\) 0.743668 0.0419676
\(315\) 3.68466 + 2.56155i 0.207607 + 0.144327i
\(316\) 2.27678i 0.128079i
\(317\) −14.0000 −0.786318 −0.393159 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) 5.08842 0.285345
\(319\) 10.9205i 0.611431i
\(320\) 11.8730 0.663720
\(321\) 8.10887 0.452593
\(322\) −11.6878 + 4.93925i −0.651334 + 0.275253i
\(323\) −13.1231 −0.730189
\(324\) −1.00000 −0.0555556
\(325\) 10.8769i 0.603342i
\(326\) −12.0000 −0.664619
\(327\) −14.7304 −0.814593
\(328\) 8.63068i 0.476550i
\(329\) −1.69614 + 2.43981i −0.0935113 + 0.134511i
\(330\) 2.24621 0.123650
\(331\) 16.4924 0.906506 0.453253 0.891382i \(-0.350263\pi\)
0.453253 + 0.891382i \(0.350263\pi\)
\(332\) −5.29723 −0.290723
\(333\) 6.04090i 0.331039i
\(334\) 22.2462i 1.21726i
\(335\) 25.6155i 1.39953i
\(336\) −1.51022 + 2.17238i −0.0823895 + 0.118513i
\(337\) 3.39228i 0.184789i −0.995722 0.0923947i \(-0.970548\pi\)
0.995722 0.0923947i \(-0.0294521\pi\)
\(338\) 13.2462 0.720499
\(339\) 16.4265 0.892168
\(340\) 2.87689 0.156022
\(341\) −8.27190 −0.447949
\(342\) 7.73704 0.418371
\(343\) 4.61219 17.9368i 0.249035 0.968495i
\(344\) 9.06134i 0.488555i
\(345\) −6.87689 4.34475i −0.370240 0.233914i
\(346\) 5.12311i 0.275420i
\(347\) 16.4924 0.885360 0.442680 0.896680i \(-0.354028\pi\)
0.442680 + 0.896680i \(0.354028\pi\)
\(348\) 8.24621i 0.442043i
\(349\) 15.3693i 0.822701i −0.911477 0.411350i \(-0.865057\pi\)
0.911477 0.411350i \(-0.134943\pi\)
\(350\) −4.61219 3.20636i −0.246532 0.171387i
\(351\) 5.12311 0.273451
\(352\) 6.62153i 0.352929i
\(353\) 7.36932i 0.392229i −0.980581 0.196115i \(-0.937168\pi\)
0.980581 0.196115i \(-0.0628325\pi\)
\(354\) 1.12311 0.0596924
\(355\) −4.87962 −0.258983
\(356\) −5.08842 −0.269686
\(357\) −2.56155 + 3.68466i −0.135572 + 0.195013i
\(358\) 4.00000 0.211407
\(359\) 30.3675i 1.60274i −0.598172 0.801368i \(-0.704106\pi\)
0.598172 0.801368i \(-0.295894\pi\)
\(360\) −5.08842 −0.268183
\(361\) 40.8617 2.15062
\(362\) −14.7304 −0.774213
\(363\) 9.24621i 0.485300i
\(364\) −7.73704 + 11.1293i −0.405531 + 0.583335i
\(365\) 17.3790i 0.909659i
\(366\) 6.04090i 0.315763i
\(367\) 28.5083 1.48812 0.744062 0.668111i \(-0.232897\pi\)
0.744062 + 0.668111i \(0.232897\pi\)
\(368\) 2.56155 4.05444i 0.133530 0.211352i
\(369\) 2.87689i 0.149765i
\(370\) 10.2462i 0.532675i
\(371\) 7.68466 11.0540i 0.398968 0.573894i
\(372\) 6.24621 0.323851
\(373\) 0.743668i 0.0385057i −0.999815 0.0192528i \(-0.993871\pi\)
0.999815 0.0192528i \(-0.00612875\pi\)
\(374\) 2.24621i 0.116149i
\(375\) 12.0818i 0.623901i
\(376\) 3.36932i 0.173759i
\(377\) 42.2462i 2.17579i
\(378\) 1.51022 2.17238i 0.0776775 0.111735i
\(379\) 20.3995i 1.04785i −0.851764 0.523925i \(-0.824467\pi\)
0.851764 0.523925i \(-0.175533\pi\)
\(380\) −13.1231 −0.673201
\(381\) 10.2462i 0.524929i
\(382\) 26.2316i 1.34212i
\(383\) −22.2586 −1.13736 −0.568682 0.822558i \(-0.692546\pi\)
−0.568682 + 0.822558i \(0.692546\pi\)
\(384\) 3.00000i 0.153093i
\(385\) 3.39228 4.87962i 0.172887 0.248688i
\(386\) 15.6155 0.794809
\(387\) 3.02045i 0.153538i
\(388\) 6.04090 0.306680
\(389\) 34.5492i 1.75172i −0.482569 0.875858i \(-0.660296\pi\)
0.482569 0.875858i \(-0.339704\pi\)
\(390\) 8.68951 0.440010
\(391\) 4.34475 6.87689i 0.219724 0.347779i
\(392\) 7.31534 + 19.6847i 0.369481 + 0.994225i
\(393\) 12.0000 0.605320
\(394\) 14.4924 0.730118
\(395\) 3.86174i 0.194305i
\(396\) 1.32431i 0.0665489i
\(397\) 12.4924i 0.626977i 0.949592 + 0.313488i \(0.101498\pi\)
−0.949592 + 0.313488i \(0.898502\pi\)
\(398\) −4.34475 −0.217783
\(399\) 11.6847 16.8078i 0.584965 0.841441i
\(400\) 2.12311 0.106155
\(401\) 0.952473i 0.0475642i 0.999717 + 0.0237821i \(0.00757079\pi\)
−0.999717 + 0.0237821i \(0.992429\pi\)
\(402\) −15.1022 −0.753231
\(403\) −32.0000 −1.59403
\(404\) 5.12311i 0.254884i
\(405\) 1.69614 0.0842819
\(406\) −17.9139 12.4536i −0.889051 0.618063i
\(407\) −8.00000 −0.396545
\(408\) 5.08842i 0.251914i
\(409\) 23.3693i 1.15554i −0.816200 0.577769i \(-0.803923\pi\)
0.816200 0.577769i \(-0.196077\pi\)
\(410\) 4.87962i 0.240987i
\(411\) −14.5216 −0.716298
\(412\) −4.34475 −0.214051
\(413\) 1.69614 2.43981i 0.0834616 0.120055i
\(414\) −2.56155 + 4.05444i −0.125893 + 0.199265i
\(415\) 8.98485 0.441049
\(416\) 25.6155i 1.25590i
\(417\) 12.0000 0.587643
\(418\) 10.2462i 0.501159i
\(419\) 18.8664 0.921682 0.460841 0.887483i \(-0.347548\pi\)
0.460841 + 0.887483i \(0.347548\pi\)
\(420\) −2.56155 + 3.68466i −0.124991 + 0.179793i
\(421\) 7.94584i 0.387257i −0.981075 0.193628i \(-0.937974\pi\)
0.981075 0.193628i \(-0.0620256\pi\)
\(422\) −6.24621 −0.304061
\(423\) 1.12311i 0.0546073i
\(424\) 15.2653i 0.741347i
\(425\) 3.60109 0.174678
\(426\) 2.87689i 0.139386i
\(427\) −13.1231 9.12311i −0.635072 0.441498i
\(428\) 8.10887i 0.391957i
\(429\) 6.78456i 0.327562i
\(430\) 5.12311i 0.247058i
\(431\) 30.7851i 1.48287i 0.671026 + 0.741433i \(0.265854\pi\)
−0.671026 + 0.741433i \(0.734146\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 16.2177 0.779375 0.389687 0.920947i \(-0.372583\pi\)
0.389687 + 0.920947i \(0.372583\pi\)
\(434\) −9.43318 + 13.5691i −0.452807 + 0.651339i
\(435\) 13.9867i 0.670613i
\(436\) 14.7304i 0.705458i
\(437\) −19.8188 + 31.3693i −0.948063 + 1.50060i
\(438\) 10.2462 0.489583
\(439\) 38.2462i 1.82539i 0.408639 + 0.912696i \(0.366003\pi\)
−0.408639 + 0.912696i \(0.633997\pi\)
\(440\) 6.73863i 0.321252i
\(441\) −2.43845 6.56155i −0.116117 0.312455i
\(442\) 8.68951i 0.413318i
\(443\) 4.63068 0.220010 0.110005 0.993931i \(-0.464913\pi\)
0.110005 + 0.993931i \(0.464913\pi\)
\(444\) 6.04090 0.286688
\(445\) 8.63068 0.409134
\(446\) 4.00000i 0.189405i
\(447\) 13.7779 0.651674
\(448\) −15.2066 10.5716i −0.718446 0.499460i
\(449\) 34.4924 1.62780 0.813899 0.581006i \(-0.197341\pi\)
0.813899 + 0.581006i \(0.197341\pi\)
\(450\) −2.12311 −0.100084
\(451\) −3.80989 −0.179401
\(452\) 16.4265i 0.772640i
\(453\) 12.4924i 0.586945i
\(454\) 3.39228 0.159208
\(455\) 13.1231 18.8769i 0.615221 0.884962i
\(456\) 23.2111i 1.08696i
\(457\) 29.0432i 1.35858i 0.733868 + 0.679292i \(0.237713\pi\)
−0.733868 + 0.679292i \(0.762287\pi\)
\(458\) −14.7304 −0.688307
\(459\) 1.69614i 0.0791691i
\(460\) 4.34475 6.87689i 0.202575 0.320637i
\(461\) 15.3693i 0.715820i −0.933756 0.357910i \(-0.883489\pi\)
0.933756 0.357910i \(-0.116511\pi\)
\(462\) −2.87689 2.00000i −0.133845 0.0930484i
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) 8.24621 0.382821
\(465\) −10.5945 −0.491306
\(466\) 20.2462 0.937888
\(467\) −3.39228 −0.156976 −0.0784880 0.996915i \(-0.525009\pi\)
−0.0784880 + 0.996915i \(0.525009\pi\)
\(468\) 5.12311i 0.236816i
\(469\) −22.8078 + 32.8078i −1.05316 + 1.51492i
\(470\) 1.90495i 0.0878686i
\(471\) 0.743668i 0.0342664i
\(472\) 3.36932i 0.155085i
\(473\) −4.00000 −0.183920
\(474\) −2.27678 −0.104576
\(475\) −16.4265 −0.753702
\(476\) −3.68466 2.56155i −0.168886 0.117409i
\(477\) 5.08842i 0.232983i
\(478\) −23.3693 −1.06889
\(479\) 30.9481 1.41406 0.707028 0.707185i \(-0.250035\pi\)
0.707028 + 0.707185i \(0.250035\pi\)
\(480\) 8.48071i 0.387089i
\(481\) −30.9481 −1.41111
\(482\) 12.8255 0.584184
\(483\) 4.93925 + 11.6878i 0.224743 + 0.531812i
\(484\) −9.24621 −0.420282
\(485\) −10.2462 −0.465256
\(486\) 1.00000i 0.0453609i
\(487\) 2.24621 0.101786 0.0508928 0.998704i \(-0.483793\pi\)
0.0508928 + 0.998704i \(0.483793\pi\)
\(488\) 18.1227 0.820376
\(489\) 12.0000i 0.542659i
\(490\) −4.13595 11.1293i −0.186843 0.502771i
\(491\) 0.492423 0.0222227 0.0111114 0.999938i \(-0.496463\pi\)
0.0111114 + 0.999938i \(0.496463\pi\)
\(492\) 2.87689 0.129700
\(493\) 13.9867 0.629931
\(494\) 39.6377i 1.78338i
\(495\) 2.24621i 0.100960i
\(496\) 6.24621i 0.280463i
\(497\) 6.24970 + 4.34475i 0.280337 + 0.194889i
\(498\) 5.29723i 0.237374i
\(499\) 22.2462 0.995877 0.497939 0.867212i \(-0.334090\pi\)
0.497939 + 0.867212i \(0.334090\pi\)
\(500\) 12.0818 0.540314
\(501\) −22.2462 −0.993887
\(502\) 27.5559 1.22988
\(503\) −10.5945 −0.472383 −0.236192 0.971706i \(-0.575899\pi\)
−0.236192 + 0.971706i \(0.575899\pi\)
\(504\) 6.51713 + 4.53067i 0.290296 + 0.201812i
\(505\) 8.68951i 0.386678i
\(506\) 5.36932 + 3.39228i 0.238695 + 0.150805i
\(507\) 13.2462i 0.588285i
\(508\) −10.2462 −0.454602
\(509\) 25.6155i 1.13539i 0.823240 + 0.567694i \(0.192164\pi\)
−0.823240 + 0.567694i \(0.807836\pi\)
\(510\) 2.87689i 0.127391i
\(511\) 15.4741 22.2586i 0.684533 0.984664i
\(512\) 11.0000 0.486136
\(513\) 7.73704i 0.341599i
\(514\) 7.36932i 0.325047i
\(515\) 7.36932 0.324731
\(516\) 3.02045 0.132968
\(517\) 1.48734 0.0654130
\(518\) −9.12311 + 13.1231i −0.400846 + 0.576596i
\(519\) −5.12311 −0.224879
\(520\) 26.0685i 1.14318i
\(521\) −1.69614 −0.0743093 −0.0371546 0.999310i \(-0.511829\pi\)
−0.0371546 + 0.999310i \(0.511829\pi\)
\(522\) −8.24621 −0.360927
\(523\) 0.952473 0.0416487 0.0208244 0.999783i \(-0.493371\pi\)
0.0208244 + 0.999783i \(0.493371\pi\)
\(524\) 12.0000i 0.524222i
\(525\) −3.20636 + 4.61219i −0.139937 + 0.201292i
\(526\) 20.9343i 0.912780i
\(527\) 10.5945i 0.461502i
\(528\) 1.32431 0.0576331
\(529\) −9.87689 20.7713i −0.429430 0.903100i
\(530\) 8.63068i 0.374893i
\(531\) 1.12311i 0.0487386i
\(532\) 16.8078 + 11.6847i 0.728709 + 0.506594i
\(533\) −14.7386 −0.638401
\(534\) 5.08842i 0.220198i
\(535\) 13.7538i 0.594628i
\(536\) 45.3067i 1.95695i
\(537\) 4.00000i 0.172613i
\(538\) 31.3693i 1.35243i
\(539\) −8.68951 + 3.22925i −0.374284 + 0.139094i
\(540\) 1.69614i 0.0729903i
\(541\) 31.1231 1.33809 0.669043 0.743223i \(-0.266704\pi\)
0.669043 + 0.743223i \(0.266704\pi\)
\(542\) 16.4924i 0.708410i
\(543\) 14.7304i 0.632142i
\(544\) 8.48071 0.363607
\(545\) 24.9848i 1.07023i
\(546\) −11.1293 7.73704i −0.476291 0.331115i
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 14.5216i 0.620332i
\(549\) −6.04090 −0.257819
\(550\) 2.81164i 0.119889i
\(551\) −63.8012 −2.71802
\(552\) −12.1633 7.68466i −0.517705 0.327081i
\(553\) −3.43845 + 4.94602i −0.146218 + 0.210326i
\(554\) 0.246211 0.0104605
\(555\) −10.2462 −0.434927
\(556\) 12.0000i 0.508913i
\(557\) 36.0366i 1.52692i 0.645856 + 0.763459i \(0.276501\pi\)
−0.645856 + 0.763459i \(0.723499\pi\)
\(558\) 6.24621i 0.264423i
\(559\) −15.4741 −0.654484
\(560\) 3.68466 + 2.56155i 0.155705 + 0.108245i
\(561\) 2.24621 0.0948351
\(562\) 9.64198i 0.406722i
\(563\) 27.5559 1.16134 0.580671 0.814139i \(-0.302790\pi\)
0.580671 + 0.814139i \(0.302790\pi\)
\(564\) −1.12311 −0.0472913
\(565\) 27.8617i 1.17215i
\(566\) 25.1161 1.05571
\(567\) −2.17238 1.51022i −0.0912313 0.0634234i
\(568\) −8.63068 −0.362135
\(569\) 35.2929i 1.47956i 0.672851 + 0.739778i \(0.265069\pi\)
−0.672851 + 0.739778i \(0.734931\pi\)
\(570\) 13.1231i 0.549666i
\(571\) 4.92539i 0.206121i 0.994675 + 0.103061i \(0.0328636\pi\)
−0.994675 + 0.103061i \(0.967136\pi\)
\(572\) 6.78456 0.283677
\(573\) 26.2316 1.09584
\(574\) −4.34475 + 6.24970i −0.181347 + 0.260857i
\(575\) 5.43845 8.60799i 0.226799 0.358978i
\(576\) −7.00000 −0.291667
\(577\) 18.8769i 0.785855i −0.919569 0.392928i \(-0.871462\pi\)
0.919569 0.392928i \(-0.128538\pi\)
\(578\) 14.1231 0.587444
\(579\) 15.6155i 0.648959i
\(580\) 13.9867 0.580768
\(581\) −11.5076 8.00000i −0.477415 0.331896i
\(582\) 6.04090i 0.250403i
\(583\) −6.73863 −0.279086
\(584\) 30.7386i 1.27197i
\(585\) 8.68951i 0.359267i
\(586\) −32.6443 −1.34852
\(587\) 0.492423i 0.0203245i −0.999948 0.0101622i \(-0.996765\pi\)
0.999948 0.0101622i \(-0.00323479\pi\)
\(588\) 6.56155 2.43845i 0.270594 0.100560i
\(589\) 48.3272i 1.99129i
\(590\) 1.90495i 0.0784254i
\(591\) 14.4924i 0.596139i
\(592\) 6.04090i 0.248279i
\(593\) 7.36932i 0.302622i −0.988486 0.151311i \(-0.951651\pi\)
0.988486 0.151311i \(-0.0483494\pi\)
\(594\) −1.32431 −0.0543370
\(595\) 6.24970 + 4.34475i 0.256213 + 0.178118i
\(596\) 13.7779i 0.564366i
\(597\) 4.34475i 0.177819i
\(598\) 20.7713 + 13.1231i 0.849402 + 0.536644i
\(599\) −39.3693 −1.60859 −0.804293 0.594232i \(-0.797456\pi\)
−0.804293 + 0.594232i \(0.797456\pi\)
\(600\) 6.36932i 0.260026i
\(601\) 8.63068i 0.352053i −0.984385 0.176026i \(-0.943676\pi\)
0.984385 0.176026i \(-0.0563244\pi\)
\(602\) −4.56155 + 6.56155i −0.185915 + 0.267429i
\(603\) 15.1022i 0.615011i
\(604\) −12.4924 −0.508309
\(605\) 15.6829 0.637600
\(606\) −5.12311 −0.208112
\(607\) 26.7386i 1.08529i 0.839963 + 0.542644i \(0.182577\pi\)
−0.839963 + 0.542644i \(0.817423\pi\)
\(608\) −38.6852 −1.56889
\(609\) −12.4536 + 17.9139i −0.504646 + 0.725907i
\(610\) −10.2462 −0.414857
\(611\) 5.75379 0.232773
\(612\) −1.69614 −0.0685624
\(613\) 14.3128i 0.578088i 0.957316 + 0.289044i \(0.0933375\pi\)
−0.957316 + 0.289044i \(0.906663\pi\)
\(614\) 14.2462i 0.574930i
\(615\) −4.87962 −0.196765
\(616\) 6.00000 8.63068i 0.241747 0.347740i
\(617\) 26.6034i 1.07101i −0.844531 0.535506i \(-0.820121\pi\)
0.844531 0.535506i \(-0.179879\pi\)
\(618\) 4.34475i 0.174772i
\(619\) −33.8056 −1.35876 −0.679380 0.733786i \(-0.737751\pi\)
−0.679380 + 0.733786i \(0.737751\pi\)
\(620\) 10.5945i 0.425484i
\(621\) 4.05444 + 2.56155i 0.162699 + 0.102792i
\(622\) 27.3693i 1.09741i
\(623\) −11.0540 7.68466i −0.442868 0.307879i
\(624\) 5.12311 0.205088
\(625\) −9.87689 −0.395076
\(626\) 28.2995 1.13108
\(627\) −10.2462 −0.409194
\(628\) 0.743668 0.0296756
\(629\) 10.2462i 0.408543i
\(630\) −3.68466 2.56155i −0.146800 0.102055i
\(631\) 5.66906i 0.225682i −0.993613 0.112841i \(-0.964005\pi\)
0.993613 0.112841i \(-0.0359950\pi\)
\(632\) 6.83034i 0.271696i
\(633\) 6.24621i 0.248265i
\(634\) 14.0000 0.556011
\(635\) 17.3790 0.689665
\(636\) 5.08842 0.201769
\(637\) −33.6155 + 12.4924i −1.33190 + 0.494968i
\(638\) 10.9205i 0.432347i
\(639\) 2.87689 0.113808
\(640\) 5.08842 0.201138
\(641\) 11.5469i 0.456076i 0.973652 + 0.228038i \(0.0732311\pi\)
−0.973652 + 0.228038i \(0.926769\pi\)
\(642\) −8.10887 −0.320032
\(643\) 2.85742 0.112686 0.0563428 0.998411i \(-0.482056\pi\)
0.0563428 + 0.998411i \(0.482056\pi\)
\(644\) −11.6878 + 4.93925i −0.460562 + 0.194634i
\(645\) −5.12311 −0.201722
\(646\) 13.1231 0.516322
\(647\) 5.61553i 0.220769i −0.993889 0.110385i \(-0.964792\pi\)
0.993889 0.110385i \(-0.0352083\pi\)
\(648\) 3.00000 0.117851
\(649\) −1.48734 −0.0583831
\(650\) 10.8769i 0.426627i
\(651\) 13.5691 + 9.43318i 0.531816 + 0.369715i
\(652\) −12.0000 −0.469956
\(653\) 14.0000 0.547862 0.273931 0.961749i \(-0.411676\pi\)
0.273931 + 0.961749i \(0.411676\pi\)
\(654\) 14.7304 0.576004
\(655\) 20.3537i 0.795285i
\(656\) 2.87689i 0.112324i
\(657\) 10.2462i 0.399743i
\(658\) 1.69614 2.43981i 0.0661225 0.0951137i
\(659\) 8.85254i 0.344846i 0.985023 + 0.172423i \(0.0551596\pi\)
−0.985023 + 0.172423i \(0.944840\pi\)
\(660\) 2.24621 0.0874337
\(661\) 26.3946 1.02663 0.513315 0.858200i \(-0.328417\pi\)
0.513315 + 0.858200i \(0.328417\pi\)
\(662\) −16.4924 −0.640996
\(663\) 8.68951 0.337473
\(664\) 15.8917 0.616717
\(665\) −28.5083 19.8188i −1.10551 0.768541i
\(666\) 6.04090i 0.234080i
\(667\) 21.1231 33.4337i 0.817890 1.29456i
\(668\) 22.2462i 0.860732i
\(669\) 4.00000 0.154649
\(670\) 25.6155i 0.989614i
\(671\) 8.00000i 0.308837i
\(672\) −7.55112 + 10.8619i −0.291291 + 0.419006i
\(673\) −4.87689 −0.187990 −0.0939952 0.995573i \(-0.529964\pi\)
−0.0939952 + 0.995573i \(0.529964\pi\)
\(674\) 3.39228i 0.130666i
\(675\) 2.12311i 0.0817184i
\(676\) 13.2462 0.509470
\(677\) 32.6443 1.25462 0.627311 0.778769i \(-0.284156\pi\)
0.627311 + 0.778769i \(0.284156\pi\)
\(678\) −16.4265 −0.630858
\(679\) 13.1231 + 9.12311i 0.503619 + 0.350113i
\(680\) −8.63068 −0.330972
\(681\) 3.39228i 0.129993i
\(682\) 8.27190 0.316747
\(683\) −1.12311 −0.0429744 −0.0214872 0.999769i \(-0.506840\pi\)
−0.0214872 + 0.999769i \(0.506840\pi\)
\(684\) 7.73704 0.295833
\(685\) 24.6307i 0.941090i
\(686\) −4.61219 + 17.9368i −0.176094 + 0.684829i
\(687\) 14.7304i 0.562000i
\(688\) 3.02045i 0.115153i
\(689\) −26.0685 −0.993132
\(690\) 6.87689 + 4.34475i 0.261799 + 0.165402i
\(691\) 14.2462i 0.541951i 0.962586 + 0.270976i \(0.0873463\pi\)
−0.962586 + 0.270976i \(0.912654\pi\)
\(692\) 5.12311i 0.194751i
\(693\) −2.00000 + 2.87689i −0.0759737 + 0.109284i
\(694\) −16.4924 −0.626044
\(695\) 20.3537i 0.772060i
\(696\) 24.7386i 0.937715i
\(697\) 4.87962i 0.184829i
\(698\) 15.3693i 0.581737i
\(699\) 20.2462i 0.765782i
\(700\) −4.61219 3.20636i −0.174324 0.121189i
\(701\) 6.99337i 0.264136i 0.991241 + 0.132068i \(0.0421617\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(702\) −5.12311 −0.193359
\(703\) 46.7386i 1.76278i
\(704\) 9.27015i 0.349382i
\(705\) 1.90495 0.0717444
\(706\) 7.36932i 0.277348i
\(707\) −7.73704 + 11.1293i −0.290981 + 0.418561i
\(708\) 1.12311 0.0422089
\(709\) 35.0841i 1.31761i 0.752313 + 0.658805i \(0.228938\pi\)
−0.752313 + 0.658805i \(0.771062\pi\)
\(710\) 4.87962 0.183129
\(711\) 2.27678i 0.0853859i
\(712\) 15.2653 0.572090
\(713\) −25.3249 16.0000i −0.948423 0.599205i
\(714\) 2.56155 3.68466i 0.0958637 0.137895i
\(715\) −11.5076 −0.430359
\(716\) 4.00000 0.149487
\(717\) 23.3693i 0.872743i
\(718\) 30.3675i 1.13331i
\(719\) 27.3693i 1.02070i −0.859966 0.510352i \(-0.829515\pi\)
0.859966 0.510352i \(-0.170485\pi\)
\(720\) 1.69614 0.0632114
\(721\) −9.43845 6.56155i −0.351506 0.244365i
\(722\) −40.8617 −1.52072
\(723\) 12.8255i 0.476984i
\(724\) −14.7304 −0.547451
\(725\) 17.5076 0.650215
\(726\) 9.24621i 0.343159i
\(727\) −8.15465 −0.302439 −0.151220 0.988500i \(-0.548320\pi\)
−0.151220 + 0.988500i \(0.548320\pi\)
\(728\) 23.2111 33.3880i 0.860261 1.23744i
\(729\) −1.00000 −0.0370370
\(730\) 17.3790i 0.643226i
\(731\) 5.12311i 0.189485i
\(732\) 6.04090i 0.223278i
\(733\) −2.64861 −0.0978288 −0.0489144 0.998803i \(-0.515576\pi\)
−0.0489144 + 0.998803i \(0.515576\pi\)
\(734\) −28.5083 −1.05226
\(735\) −11.1293 + 4.13595i −0.410511 + 0.152557i
\(736\) 12.8078 20.2722i 0.472100 0.747242i
\(737\) 20.0000 0.736709
\(738\) 2.87689i 0.105900i
\(739\) −34.7386 −1.27788 −0.638941 0.769256i \(-0.720627\pi\)
−0.638941 + 0.769256i \(0.720627\pi\)
\(740\) 10.2462i 0.376658i
\(741\) −39.6377 −1.45613
\(742\) −7.68466 + 11.0540i −0.282113 + 0.405804i
\(743\) 14.1498i 0.519105i 0.965729 + 0.259552i \(0.0835750\pi\)
−0.965729 + 0.259552i \(0.916425\pi\)
\(744\) −18.7386 −0.686992
\(745\) 23.3693i 0.856186i
\(746\) 0.743668i 0.0272276i
\(747\) −5.29723 −0.193815
\(748\) 2.24621i 0.0821296i
\(749\) −12.2462 + 17.6155i −0.447467 + 0.643657i
\(750\) 12.0818i 0.441165i
\(751\) 40.0095i 1.45997i −0.683465 0.729984i \(-0.739528\pi\)
0.683465 0.729984i \(-0.260472\pi\)
\(752\) 1.12311i 0.0409554i
\(753\) 27.5559i 1.00419i
\(754\) 42.2462i 1.53852i
\(755\) 21.1889 0.771143
\(756\) 1.51022 2.17238i 0.0549263 0.0790086i
\(757\) 14.7304i 0.535386i −0.963504 0.267693i \(-0.913739\pi\)
0.963504 0.267693i \(-0.0862612\pi\)
\(758\) 20.3995i 0.740942i
\(759\) 3.39228 5.36932i 0.123132 0.194894i
\(760\) 39.3693 1.42808
\(761\) 29.1231i 1.05571i 0.849334 + 0.527856i \(0.177004\pi\)
−0.849334 + 0.527856i \(0.822996\pi\)
\(762\) 10.2462i 0.371181i
\(763\) 22.2462 32.0000i 0.805367 1.15848i
\(764\) 26.2316i 0.949024i
\(765\) 2.87689 0.104014
\(766\) 22.2586 0.804237
\(767\) −5.75379 −0.207757
\(768\) 17.0000i 0.613435i
\(769\) 53.9505 1.94550 0.972752 0.231850i \(-0.0744778\pi\)
0.972752 + 0.231850i \(0.0744778\pi\)
\(770\) −3.39228 + 4.87962i −0.122249 + 0.175849i
\(771\) −7.36932 −0.265399
\(772\) 15.6155 0.562015
\(773\) 34.5492 1.24265 0.621325 0.783553i \(-0.286595\pi\)
0.621325 + 0.783553i \(0.286595\pi\)
\(774\) 3.02045i 0.108568i
\(775\) 13.2614i 0.476362i
\(776\) −18.1227 −0.650567
\(777\) 13.1231 + 9.12311i 0.470789 + 0.327290i
\(778\) 34.5492i 1.23865i
\(779\) 22.2586i 0.797498i
\(780\) 8.68951 0.311134
\(781\) 3.80989i 0.136329i
\(782\) −4.34475 + 6.87689i −0.155368 + 0.245917i
\(783\) 8.24621i 0.294696i
\(784\) −2.43845 6.56155i −0.0870874 0.234341i
\(785\) −1.26137 −0.0450201
\(786\) −12.0000 −0.428026
\(787\) 33.8056 1.20504 0.602519 0.798104i \(-0.294164\pi\)
0.602519 + 0.798104i \(0.294164\pi\)
\(788\) 14.4924