Properties

Label 403.2.c.b.311.6
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.6
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.27

$q$-expansion

\(f(q)\) \(=\) \(q-1.99449i q^{2} -1.58843 q^{3} -1.97798 q^{4} -2.66789i q^{5} +3.16810i q^{6} +1.73927i q^{7} -0.0439183i q^{8} -0.476895 q^{9} +O(q^{10})\) \(q-1.99449i q^{2} -1.58843 q^{3} -1.97798 q^{4} -2.66789i q^{5} +3.16810i q^{6} +1.73927i q^{7} -0.0439183i q^{8} -0.476895 q^{9} -5.32107 q^{10} -2.93947i q^{11} +3.14188 q^{12} +(-3.42506 + 1.12648i) q^{13} +3.46896 q^{14} +4.23775i q^{15} -4.04355 q^{16} -1.90448 q^{17} +0.951161i q^{18} +4.24721i q^{19} +5.27703i q^{20} -2.76271i q^{21} -5.86273 q^{22} +3.75923 q^{23} +0.0697611i q^{24} -2.11762 q^{25} +(2.24675 + 6.83124i) q^{26} +5.52280 q^{27} -3.44025i q^{28} -4.27051 q^{29} +8.45213 q^{30} -1.00000i q^{31} +7.97698i q^{32} +4.66914i q^{33} +3.79847i q^{34} +4.64018 q^{35} +0.943288 q^{36} -3.05862i q^{37} +8.47100 q^{38} +(5.44046 - 1.78933i) q^{39} -0.117169 q^{40} +5.80663i q^{41} -5.51019 q^{42} -11.6866 q^{43} +5.81421i q^{44} +1.27230i q^{45} -7.49773i q^{46} -10.5119i q^{47} +6.42290 q^{48} +3.97493 q^{49} +4.22356i q^{50} +3.02514 q^{51} +(6.77470 - 2.22816i) q^{52} -13.8094 q^{53} -11.0152i q^{54} -7.84217 q^{55} +0.0763859 q^{56} -6.74639i q^{57} +8.51748i q^{58} -13.7930i q^{59} -8.38218i q^{60} +5.05405 q^{61} -1.99449 q^{62} -0.829450i q^{63} +7.82288 q^{64} +(3.00532 + 9.13767i) q^{65} +9.31253 q^{66} -12.7046i q^{67} +3.76703 q^{68} -5.97127 q^{69} -9.25478i q^{70} -5.83066i q^{71} +0.0209444i q^{72} +4.92019i q^{73} -6.10039 q^{74} +3.36368 q^{75} -8.40089i q^{76} +5.11254 q^{77} +(-3.56881 - 10.8509i) q^{78} +0.743732 q^{79} +10.7877i q^{80} -7.34189 q^{81} +11.5812 q^{82} +0.165627i q^{83} +5.46459i q^{84} +5.08094i q^{85} +23.3087i q^{86} +6.78340 q^{87} -0.129096 q^{88} -1.85214i q^{89} +2.53759 q^{90} +(-1.95926 - 5.95712i) q^{91} -7.43568 q^{92} +1.58843i q^{93} -20.9659 q^{94} +11.3311 q^{95} -12.6709i q^{96} -6.35644i q^{97} -7.92795i q^{98} +1.40182i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.99449i 1.41032i −0.709050 0.705158i \(-0.750876\pi\)
0.709050 0.705158i \(-0.249124\pi\)
\(3\) −1.58843 −0.917080 −0.458540 0.888674i \(-0.651627\pi\)
−0.458540 + 0.888674i \(0.651627\pi\)
\(4\) −1.97798 −0.988990
\(5\) 2.66789i 1.19311i −0.802570 0.596557i \(-0.796535\pi\)
0.802570 0.596557i \(-0.203465\pi\)
\(6\) 3.16810i 1.29337i
\(7\) 1.73927i 0.657383i 0.944437 + 0.328692i \(0.106608\pi\)
−0.944437 + 0.328692i \(0.893392\pi\)
\(8\) 0.0439183i 0.0155275i
\(9\) −0.476895 −0.158965
\(10\) −5.32107 −1.68267
\(11\) 2.93947i 0.886283i −0.896452 0.443142i \(-0.853864\pi\)
0.896452 0.443142i \(-0.146136\pi\)
\(12\) 3.14188 0.906983
\(13\) −3.42506 + 1.12648i −0.949941 + 0.312430i
\(14\) 3.46896 0.927118
\(15\) 4.23775i 1.09418i
\(16\) −4.04355 −1.01089
\(17\) −1.90448 −0.461905 −0.230952 0.972965i \(-0.574184\pi\)
−0.230952 + 0.972965i \(0.574184\pi\)
\(18\) 0.951161i 0.224191i
\(19\) 4.24721i 0.974376i 0.873297 + 0.487188i \(0.161977\pi\)
−0.873297 + 0.487188i \(0.838023\pi\)
\(20\) 5.27703i 1.17998i
\(21\) 2.76271i 0.602873i
\(22\) −5.86273 −1.24994
\(23\) 3.75923 0.783853 0.391927 0.919996i \(-0.371809\pi\)
0.391927 + 0.919996i \(0.371809\pi\)
\(24\) 0.0697611i 0.0142399i
\(25\) −2.11762 −0.423523
\(26\) 2.24675 + 6.83124i 0.440624 + 1.33972i
\(27\) 5.52280 1.06286
\(28\) 3.44025i 0.650146i
\(29\) −4.27051 −0.793014 −0.396507 0.918032i \(-0.629778\pi\)
−0.396507 + 0.918032i \(0.629778\pi\)
\(30\) 8.45213 1.54314
\(31\) 1.00000i 0.179605i
\(32\) 7.97698i 1.41014i
\(33\) 4.66914i 0.812792i
\(34\) 3.79847i 0.651432i
\(35\) 4.64018 0.784334
\(36\) 0.943288 0.157215
\(37\) 3.05862i 0.502835i −0.967879 0.251417i \(-0.919103\pi\)
0.967879 0.251417i \(-0.0808967\pi\)
\(38\) 8.47100 1.37418
\(39\) 5.44046 1.78933i 0.871171 0.286523i
\(40\) −0.117169 −0.0185260
\(41\) 5.80663i 0.906843i 0.891296 + 0.453421i \(0.149797\pi\)
−0.891296 + 0.453421i \(0.850203\pi\)
\(42\) −5.51019 −0.850241
\(43\) −11.6866 −1.78218 −0.891092 0.453822i \(-0.850060\pi\)
−0.891092 + 0.453822i \(0.850060\pi\)
\(44\) 5.81421i 0.876525i
\(45\) 1.27230i 0.189663i
\(46\) 7.49773i 1.10548i
\(47\) 10.5119i 1.53332i −0.642054 0.766659i \(-0.721917\pi\)
0.642054 0.766659i \(-0.278083\pi\)
\(48\) 6.42290 0.927065
\(49\) 3.97493 0.567847
\(50\) 4.22356i 0.597301i
\(51\) 3.02514 0.423604
\(52\) 6.77470 2.22816i 0.939482 0.308990i
\(53\) −13.8094 −1.89687 −0.948433 0.316979i \(-0.897332\pi\)
−0.948433 + 0.316979i \(0.897332\pi\)
\(54\) 11.0152i 1.49897i
\(55\) −7.84217 −1.05744
\(56\) 0.0763859 0.0102075
\(57\) 6.74639i 0.893581i
\(58\) 8.51748i 1.11840i
\(59\) 13.7930i 1.79569i −0.440308 0.897847i \(-0.645131\pi\)
0.440308 0.897847i \(-0.354869\pi\)
\(60\) 8.38218i 1.08213i
\(61\) 5.05405 0.647104 0.323552 0.946210i \(-0.395123\pi\)
0.323552 + 0.946210i \(0.395123\pi\)
\(62\) −1.99449 −0.253300
\(63\) 0.829450i 0.104501i
\(64\) 7.82288 0.977860
\(65\) 3.00532 + 9.13767i 0.372764 + 1.13339i
\(66\) 9.31253 1.14629
\(67\) 12.7046i 1.55211i −0.630664 0.776056i \(-0.717218\pi\)
0.630664 0.776056i \(-0.282782\pi\)
\(68\) 3.76703 0.456819
\(69\) −5.97127 −0.718856
\(70\) 9.25478i 1.10616i
\(71\) 5.83066i 0.691971i −0.938240 0.345986i \(-0.887545\pi\)
0.938240 0.345986i \(-0.112455\pi\)
\(72\) 0.0209444i 0.00246832i
\(73\) 4.92019i 0.575865i 0.957651 + 0.287932i \(0.0929678\pi\)
−0.957651 + 0.287932i \(0.907032\pi\)
\(74\) −6.10039 −0.709156
\(75\) 3.36368 0.388405
\(76\) 8.40089i 0.963648i
\(77\) 5.11254 0.582628
\(78\) −3.56881 10.8509i −0.404088 1.22863i
\(79\) 0.743732 0.0836764 0.0418382 0.999124i \(-0.486679\pi\)
0.0418382 + 0.999124i \(0.486679\pi\)
\(80\) 10.7877i 1.20611i
\(81\) −7.34189 −0.815765
\(82\) 11.5812 1.27893
\(83\) 0.165627i 0.0181799i 0.999959 + 0.00908994i \(0.00289346\pi\)
−0.999959 + 0.00908994i \(0.997107\pi\)
\(84\) 5.46459i 0.596235i
\(85\) 5.08094i 0.551106i
\(86\) 23.3087i 2.51344i
\(87\) 6.78340 0.727257
\(88\) −0.129096 −0.0137617
\(89\) 1.85214i 0.196326i −0.995170 0.0981631i \(-0.968703\pi\)
0.995170 0.0981631i \(-0.0312967\pi\)
\(90\) 2.53759 0.267485
\(91\) −1.95926 5.95712i −0.205386 0.624475i
\(92\) −7.43568 −0.775223
\(93\) 1.58843i 0.164712i
\(94\) −20.9659 −2.16246
\(95\) 11.3311 1.16254
\(96\) 12.6709i 1.29321i
\(97\) 6.35644i 0.645399i −0.946501 0.322699i \(-0.895410\pi\)
0.946501 0.322699i \(-0.104590\pi\)
\(98\) 7.92795i 0.800844i
\(99\) 1.40182i 0.140888i
\(100\) 4.18860 0.418860
\(101\) 3.11790 0.310243 0.155122 0.987895i \(-0.450423\pi\)
0.155122 + 0.987895i \(0.450423\pi\)
\(102\) 6.03359i 0.597415i
\(103\) 2.88258 0.284029 0.142015 0.989865i \(-0.454642\pi\)
0.142015 + 0.989865i \(0.454642\pi\)
\(104\) 0.0494731 + 0.150423i 0.00485124 + 0.0147502i
\(105\) −7.37060 −0.719297
\(106\) 27.5427i 2.67518i
\(107\) −7.35117 −0.710664 −0.355332 0.934740i \(-0.615632\pi\)
−0.355332 + 0.934740i \(0.615632\pi\)
\(108\) −10.9240 −1.05116
\(109\) 12.9872i 1.24395i −0.783038 0.621974i \(-0.786331\pi\)
0.783038 0.621974i \(-0.213669\pi\)
\(110\) 15.6411i 1.49132i
\(111\) 4.85841i 0.461140i
\(112\) 7.03285i 0.664541i
\(113\) −7.63258 −0.718013 −0.359006 0.933335i \(-0.616884\pi\)
−0.359006 + 0.933335i \(0.616884\pi\)
\(114\) −13.4556 −1.26023
\(115\) 10.0292i 0.935227i
\(116\) 8.44698 0.784282
\(117\) 1.63339 0.537213i 0.151007 0.0496653i
\(118\) −27.5099 −2.53249
\(119\) 3.31242i 0.303649i
\(120\) 0.186115 0.0169899
\(121\) 2.35952 0.214502
\(122\) 10.0802i 0.912621i
\(123\) 9.22341i 0.831647i
\(124\) 1.97798i 0.177628i
\(125\) 7.68987i 0.687803i
\(126\) −1.65433 −0.147379
\(127\) −0.0992933 −0.00881085 −0.00440543 0.999990i \(-0.501402\pi\)
−0.00440543 + 0.999990i \(0.501402\pi\)
\(128\) 0.351325i 0.0310530i
\(129\) 18.5633 1.63440
\(130\) 18.2250 5.99408i 1.59844 0.525715i
\(131\) 1.56404 0.136651 0.0683256 0.997663i \(-0.478234\pi\)
0.0683256 + 0.997663i \(0.478234\pi\)
\(132\) 9.23546i 0.803843i
\(133\) −7.38705 −0.640539
\(134\) −25.3391 −2.18897
\(135\) 14.7342i 1.26812i
\(136\) 0.0836416i 0.00717221i
\(137\) 7.31021i 0.624553i −0.949991 0.312277i \(-0.898908\pi\)
0.949991 0.312277i \(-0.101092\pi\)
\(138\) 11.9096i 1.01381i
\(139\) 8.35831 0.708943 0.354471 0.935067i \(-0.384661\pi\)
0.354471 + 0.935067i \(0.384661\pi\)
\(140\) −9.17819 −0.775698
\(141\) 16.6974i 1.40618i
\(142\) −11.6292 −0.975898
\(143\) 3.31126 + 10.0679i 0.276901 + 0.841917i
\(144\) 1.92835 0.160696
\(145\) 11.3932i 0.946156i
\(146\) 9.81326 0.812151
\(147\) −6.31389 −0.520761
\(148\) 6.04990i 0.497299i
\(149\) 14.9219i 1.22245i 0.791456 + 0.611226i \(0.209323\pi\)
−0.791456 + 0.611226i \(0.790677\pi\)
\(150\) 6.70882i 0.547773i
\(151\) 13.0134i 1.05902i 0.848304 + 0.529509i \(0.177624\pi\)
−0.848304 + 0.529509i \(0.822376\pi\)
\(152\) 0.186530 0.0151296
\(153\) 0.908238 0.0734267
\(154\) 10.1969i 0.821689i
\(155\) −2.66789 −0.214290
\(156\) −10.7611 + 3.53927i −0.861580 + 0.283368i
\(157\) −18.1118 −1.44548 −0.722738 0.691122i \(-0.757117\pi\)
−0.722738 + 0.691122i \(0.757117\pi\)
\(158\) 1.48336i 0.118010i
\(159\) 21.9352 1.73958
\(160\) 21.2817 1.68246
\(161\) 6.53832i 0.515292i
\(162\) 14.6433i 1.15049i
\(163\) 3.67145i 0.287570i 0.989609 + 0.143785i \(0.0459274\pi\)
−0.989609 + 0.143785i \(0.954073\pi\)
\(164\) 11.4854i 0.896858i
\(165\) 12.4567 0.969755
\(166\) 0.330340 0.0256394
\(167\) 3.59433i 0.278138i 0.990283 + 0.139069i \(0.0444110\pi\)
−0.990283 + 0.139069i \(0.955589\pi\)
\(168\) −0.121334 −0.00936108
\(169\) 10.4621 7.71653i 0.804776 0.593579i
\(170\) 10.1339 0.777233
\(171\) 2.02547i 0.154892i
\(172\) 23.1158 1.76256
\(173\) 13.7740 1.04721 0.523607 0.851960i \(-0.324586\pi\)
0.523607 + 0.851960i \(0.324586\pi\)
\(174\) 13.5294i 1.02566i
\(175\) 3.68311i 0.278417i
\(176\) 11.8859i 0.895934i
\(177\) 21.9092i 1.64679i
\(178\) −3.69407 −0.276882
\(179\) 13.7364 1.02671 0.513353 0.858178i \(-0.328403\pi\)
0.513353 + 0.858178i \(0.328403\pi\)
\(180\) 2.51659i 0.187575i
\(181\) −8.36084 −0.621457 −0.310728 0.950499i \(-0.600573\pi\)
−0.310728 + 0.950499i \(0.600573\pi\)
\(182\) −11.8814 + 3.90771i −0.880707 + 0.289659i
\(183\) −8.02799 −0.593446
\(184\) 0.165099i 0.0121712i
\(185\) −8.16006 −0.599940
\(186\) 3.16810 0.232296
\(187\) 5.59817i 0.409379i
\(188\) 20.7923i 1.51644i
\(189\) 9.60565i 0.698709i
\(190\) 22.5997i 1.63955i
\(191\) 25.1884 1.82257 0.911286 0.411774i \(-0.135091\pi\)
0.911286 + 0.411774i \(0.135091\pi\)
\(192\) −12.4261 −0.896776
\(193\) 8.03820i 0.578603i −0.957238 0.289301i \(-0.906577\pi\)
0.957238 0.289301i \(-0.0934229\pi\)
\(194\) −12.6778 −0.910216
\(195\) −4.77374 14.5145i −0.341855 1.03941i
\(196\) −7.86233 −0.561595
\(197\) 2.79581i 0.199193i −0.995028 0.0995964i \(-0.968245\pi\)
0.995028 0.0995964i \(-0.0317552\pi\)
\(198\) 2.79591 0.198696
\(199\) 16.3408 1.15837 0.579183 0.815197i \(-0.303372\pi\)
0.579183 + 0.815197i \(0.303372\pi\)
\(200\) 0.0930021i 0.00657624i
\(201\) 20.1803i 1.42341i
\(202\) 6.21862i 0.437541i
\(203\) 7.42758i 0.521314i
\(204\) −5.98366 −0.418940
\(205\) 15.4914 1.08197
\(206\) 5.74927i 0.400571i
\(207\) −1.79276 −0.124605
\(208\) 13.8494 4.55499i 0.960285 0.315832i
\(209\) 12.4845 0.863573
\(210\) 14.7006i 1.01444i
\(211\) 16.1104 1.10909 0.554544 0.832155i \(-0.312893\pi\)
0.554544 + 0.832155i \(0.312893\pi\)
\(212\) 27.3147 1.87598
\(213\) 9.26158i 0.634593i
\(214\) 14.6618i 1.00226i
\(215\) 31.1784i 2.12635i
\(216\) 0.242552i 0.0165036i
\(217\) 1.73927 0.118070
\(218\) −25.9028 −1.75436
\(219\) 7.81537i 0.528114i
\(220\) 15.5117 1.04580
\(221\) 6.52297 2.14536i 0.438782 0.144313i
\(222\) 9.69003 0.650352
\(223\) 10.5250i 0.704805i −0.935849 0.352403i \(-0.885365\pi\)
0.935849 0.352403i \(-0.114635\pi\)
\(224\) −13.8741 −0.927006
\(225\) 1.00988 0.0673253
\(226\) 15.2231i 1.01262i
\(227\) 1.53439i 0.101841i −0.998703 0.0509204i \(-0.983785\pi\)
0.998703 0.0509204i \(-0.0162155\pi\)
\(228\) 13.3442i 0.883742i
\(229\) 1.33677i 0.0883364i −0.999024 0.0441682i \(-0.985936\pi\)
0.999024 0.0441682i \(-0.0140637\pi\)
\(230\) −20.0031 −1.31897
\(231\) −8.12090 −0.534316
\(232\) 0.187553i 0.0123135i
\(233\) −23.1697 −1.51790 −0.758948 0.651151i \(-0.774287\pi\)
−0.758948 + 0.651151i \(0.774287\pi\)
\(234\) −1.07146 3.25778i −0.0700438 0.212968i
\(235\) −28.0446 −1.82943
\(236\) 27.2822i 1.77592i
\(237\) −1.18137 −0.0767379
\(238\) −6.60657 −0.428240
\(239\) 5.95278i 0.385053i 0.981292 + 0.192527i \(0.0616682\pi\)
−0.981292 + 0.192527i \(0.938332\pi\)
\(240\) 17.1356i 1.10610i
\(241\) 27.2642i 1.75624i 0.478439 + 0.878121i \(0.341203\pi\)
−0.478439 + 0.878121i \(0.658797\pi\)
\(242\) 4.70604i 0.302516i
\(243\) −4.90633 −0.314741
\(244\) −9.99680 −0.639980
\(245\) 10.6047i 0.677507i
\(246\) −18.3960 −1.17288
\(247\) −4.78440 14.5469i −0.304424 0.925600i
\(248\) −0.0439183 −0.00278881
\(249\) 0.263086i 0.0166724i
\(250\) −15.3374 −0.970019
\(251\) −26.2008 −1.65378 −0.826888 0.562366i \(-0.809891\pi\)
−0.826888 + 0.562366i \(0.809891\pi\)
\(252\) 1.64064i 0.103350i
\(253\) 11.0501i 0.694716i
\(254\) 0.198039i 0.0124261i
\(255\) 8.07072i 0.505408i
\(256\) 16.3465 1.02165
\(257\) 19.4518 1.21337 0.606684 0.794943i \(-0.292499\pi\)
0.606684 + 0.794943i \(0.292499\pi\)
\(258\) 37.0242i 2.30503i
\(259\) 5.31978 0.330555
\(260\) −5.94447 18.0741i −0.368660 1.12091i
\(261\) 2.03658 0.126061
\(262\) 3.11947i 0.192721i
\(263\) −29.8002 −1.83756 −0.918781 0.394768i \(-0.870825\pi\)
−0.918781 + 0.394768i \(0.870825\pi\)
\(264\) 0.205060 0.0126206
\(265\) 36.8419i 2.26318i
\(266\) 14.7334i 0.903362i
\(267\) 2.94199i 0.180047i
\(268\) 25.1294i 1.53502i
\(269\) 7.60454 0.463657 0.231829 0.972757i \(-0.425529\pi\)
0.231829 + 0.972757i \(0.425529\pi\)
\(270\) −29.3872 −1.78845
\(271\) 22.1272i 1.34413i −0.740493 0.672065i \(-0.765408\pi\)
0.740493 0.672065i \(-0.234592\pi\)
\(272\) 7.70088 0.466935
\(273\) 3.11214 + 9.46245i 0.188355 + 0.572694i
\(274\) −14.5801 −0.880817
\(275\) 6.22467i 0.375362i
\(276\) 11.8110 0.710941
\(277\) −9.45363 −0.568013 −0.284007 0.958822i \(-0.591664\pi\)
−0.284007 + 0.958822i \(0.591664\pi\)
\(278\) 16.6705i 0.999833i
\(279\) 0.476895i 0.0285509i
\(280\) 0.203789i 0.0121787i
\(281\) 12.6507i 0.754676i 0.926076 + 0.377338i \(0.123160\pi\)
−0.926076 + 0.377338i \(0.876840\pi\)
\(282\) 33.3028 1.98315
\(283\) 17.2687 1.02652 0.513258 0.858234i \(-0.328438\pi\)
0.513258 + 0.858234i \(0.328438\pi\)
\(284\) 11.5329i 0.684353i
\(285\) −17.9986 −1.06614
\(286\) 20.0802 6.60426i 1.18737 0.390518i
\(287\) −10.0993 −0.596143
\(288\) 3.80418i 0.224164i
\(289\) −13.3729 −0.786644
\(290\) 22.7237 1.33438
\(291\) 10.0968i 0.591882i
\(292\) 9.73204i 0.569525i
\(293\) 6.27750i 0.366736i −0.983044 0.183368i \(-0.941300\pi\)
0.983044 0.183368i \(-0.0586999\pi\)
\(294\) 12.5930i 0.734437i
\(295\) −36.7981 −2.14247
\(296\) −0.134330 −0.00780775
\(297\) 16.2341i 0.941998i
\(298\) 29.7616 1.72404
\(299\) −12.8756 + 4.23470i −0.744614 + 0.244899i
\(300\) −6.65330 −0.384128
\(301\) 20.3261i 1.17158i
\(302\) 25.9551 1.49355
\(303\) −4.95257 −0.284518
\(304\) 17.1738i 0.984986i
\(305\) 13.4836i 0.772070i
\(306\) 1.81147i 0.103555i
\(307\) 17.0517i 0.973191i −0.873627 0.486595i \(-0.838239\pi\)
0.873627 0.486595i \(-0.161761\pi\)
\(308\) −10.1125 −0.576213
\(309\) −4.57877 −0.260477
\(310\) 5.32107i 0.302216i
\(311\) 4.01012 0.227393 0.113697 0.993516i \(-0.463731\pi\)
0.113697 + 0.993516i \(0.463731\pi\)
\(312\) −0.0785845 0.238936i −0.00444897 0.0135271i
\(313\) −6.03967 −0.341382 −0.170691 0.985325i \(-0.554600\pi\)
−0.170691 + 0.985325i \(0.554600\pi\)
\(314\) 36.1237i 2.03858i
\(315\) −2.21288 −0.124682
\(316\) −1.47109 −0.0827551
\(317\) 14.0309i 0.788056i 0.919098 + 0.394028i \(0.128919\pi\)
−0.919098 + 0.394028i \(0.871081\pi\)
\(318\) 43.7495i 2.45335i
\(319\) 12.5530i 0.702834i
\(320\) 20.8706i 1.16670i
\(321\) 11.6768 0.651736
\(322\) 13.0406 0.726724
\(323\) 8.08873i 0.450069i
\(324\) 14.5221 0.806784
\(325\) 7.25296 2.38545i 0.402322 0.132321i
\(326\) 7.32265 0.405564
\(327\) 20.6292i 1.14080i
\(328\) 0.255017 0.0140810
\(329\) 18.2831 1.00798
\(330\) 24.8448i 1.36766i
\(331\) 11.1671i 0.613802i −0.951741 0.306901i \(-0.900708\pi\)
0.951741 0.306901i \(-0.0992920\pi\)
\(332\) 0.327606i 0.0179797i
\(333\) 1.45864i 0.0799331i
\(334\) 7.16885 0.392262
\(335\) −33.8944 −1.85185
\(336\) 11.1712i 0.609437i
\(337\) −5.01505 −0.273187 −0.136594 0.990627i \(-0.543615\pi\)
−0.136594 + 0.990627i \(0.543615\pi\)
\(338\) −15.3905 20.8665i −0.837134 1.13499i
\(339\) 12.1238 0.658475
\(340\) 10.0500i 0.545038i
\(341\) −2.93947 −0.159181
\(342\) −4.03978 −0.218446
\(343\) 19.0884i 1.03068i
\(344\) 0.513254i 0.0276728i
\(345\) 15.9307i 0.857678i
\(346\) 27.4720i 1.47690i
\(347\) −0.923189 −0.0495594 −0.0247797 0.999693i \(-0.507888\pi\)
−0.0247797 + 0.999693i \(0.507888\pi\)
\(348\) −13.4174 −0.719250
\(349\) 13.5903i 0.727473i −0.931502 0.363736i \(-0.881501\pi\)
0.931502 0.363736i \(-0.118499\pi\)
\(350\) −7.34592 −0.392656
\(351\) −18.9159 + 6.22133i −1.00966 + 0.332070i
\(352\) 23.4481 1.24979
\(353\) 23.8408i 1.26892i 0.772957 + 0.634459i \(0.218777\pi\)
−0.772957 + 0.634459i \(0.781223\pi\)
\(354\) 43.6976 2.32250
\(355\) −15.5555 −0.825602
\(356\) 3.66349i 0.194165i
\(357\) 5.26154i 0.278470i
\(358\) 27.3970i 1.44798i
\(359\) 5.95185i 0.314127i −0.987589 0.157063i \(-0.949797\pi\)
0.987589 0.157063i \(-0.0502027\pi\)
\(360\) 0.0558773 0.00294499
\(361\) 0.961228 0.0505910
\(362\) 16.6756i 0.876450i
\(363\) −3.74794 −0.196716
\(364\) 3.87537 + 11.7831i 0.203125 + 0.617600i
\(365\) 13.1265 0.687073
\(366\) 16.0117i 0.836947i
\(367\) 28.6410 1.49505 0.747523 0.664236i \(-0.231243\pi\)
0.747523 + 0.664236i \(0.231243\pi\)
\(368\) −15.2006 −0.792388
\(369\) 2.76915i 0.144156i
\(370\) 16.2751i 0.846104i
\(371\) 24.0183i 1.24697i
\(372\) 3.14188i 0.162899i
\(373\) −32.6896 −1.69260 −0.846302 0.532704i \(-0.821176\pi\)
−0.846302 + 0.532704i \(0.821176\pi\)
\(374\) 11.1655 0.577353
\(375\) 12.2148i 0.630770i
\(376\) −0.461665 −0.0238085
\(377\) 14.6268 4.81065i 0.753316 0.247761i
\(378\) 19.1584 0.985400
\(379\) 13.9594i 0.717044i 0.933521 + 0.358522i \(0.116719\pi\)
−0.933521 + 0.358522i \(0.883281\pi\)
\(380\) −22.4126 −1.14974
\(381\) 0.157720 0.00808025
\(382\) 50.2380i 2.57040i
\(383\) 4.62452i 0.236302i 0.992996 + 0.118151i \(0.0376967\pi\)
−0.992996 + 0.118151i \(0.962303\pi\)
\(384\) 0.558055i 0.0284781i
\(385\) 13.6397i 0.695142i
\(386\) −16.0321 −0.816012
\(387\) 5.57326 0.283305
\(388\) 12.5729i 0.638293i
\(389\) −28.4539 −1.44267 −0.721336 0.692585i \(-0.756472\pi\)
−0.721336 + 0.692585i \(0.756472\pi\)
\(390\) −28.9491 + 9.52117i −1.46589 + 0.482123i
\(391\) −7.15939 −0.362066
\(392\) 0.174572i 0.00881722i
\(393\) −2.48437 −0.125320
\(394\) −5.57620 −0.280925
\(395\) 1.98419i 0.0998356i
\(396\) 2.77277i 0.139337i
\(397\) 4.82894i 0.242358i 0.992631 + 0.121179i \(0.0386674\pi\)
−0.992631 + 0.121179i \(0.961333\pi\)
\(398\) 32.5915i 1.63366i
\(399\) 11.7338 0.587425
\(400\) 8.56270 0.428135
\(401\) 33.7317i 1.68448i −0.539101 0.842241i \(-0.681236\pi\)
0.539101 0.842241i \(-0.318764\pi\)
\(402\) 40.2494 2.00746
\(403\) 1.12648 + 3.42506i 0.0561140 + 0.170614i
\(404\) −6.16715 −0.306827
\(405\) 19.5873i 0.973302i
\(406\) −14.8142 −0.735217
\(407\) −8.99073 −0.445654
\(408\) 0.132859i 0.00657749i
\(409\) 34.0260i 1.68248i 0.540664 + 0.841239i \(0.318173\pi\)
−0.540664 + 0.841239i \(0.681827\pi\)
\(410\) 30.8974i 1.52592i
\(411\) 11.6117i 0.572765i
\(412\) −5.70169 −0.280902
\(413\) 23.9898 1.18046
\(414\) 3.57563i 0.175733i
\(415\) 0.441873 0.0216907
\(416\) −8.98592 27.3216i −0.440571 1.33955i
\(417\) −13.2766 −0.650157
\(418\) 24.9002i 1.21791i
\(419\) 19.7565 0.965166 0.482583 0.875850i \(-0.339699\pi\)
0.482583 + 0.875850i \(0.339699\pi\)
\(420\) 14.5789 0.711377
\(421\) 24.0860i 1.17388i 0.809631 + 0.586940i \(0.199667\pi\)
−0.809631 + 0.586940i \(0.800333\pi\)
\(422\) 32.1320i 1.56416i
\(423\) 5.01307i 0.243744i
\(424\) 0.606485i 0.0294535i
\(425\) 4.03296 0.195628
\(426\) 18.4721 0.894976
\(427\) 8.79037i 0.425396i
\(428\) 14.5405 0.702840
\(429\) −5.25969 15.9921i −0.253940 0.772105i
\(430\) 62.1850 2.99883
\(431\) 34.5870i 1.66600i −0.553276 0.832998i \(-0.686623\pi\)
0.553276 0.832998i \(-0.313377\pi\)
\(432\) −22.3317 −1.07444
\(433\) 19.9707 0.959731 0.479865 0.877342i \(-0.340686\pi\)
0.479865 + 0.877342i \(0.340686\pi\)
\(434\) 3.46896i 0.166515i
\(435\) 18.0973i 0.867701i
\(436\) 25.6884i 1.23025i
\(437\) 15.9662i 0.763768i
\(438\) −15.5877 −0.744807
\(439\) −16.2325 −0.774733 −0.387366 0.921926i \(-0.626615\pi\)
−0.387366 + 0.921926i \(0.626615\pi\)
\(440\) 0.344415i 0.0164193i
\(441\) −1.89562 −0.0902678
\(442\) −4.27890 13.0100i −0.203527 0.618822i
\(443\) 38.9490 1.85052 0.925261 0.379330i \(-0.123846\pi\)
0.925261 + 0.379330i \(0.123846\pi\)
\(444\) 9.60983i 0.456062i
\(445\) −4.94129 −0.234240
\(446\) −20.9919 −0.993997
\(447\) 23.7024i 1.12109i
\(448\) 13.6061i 0.642829i
\(449\) 20.3615i 0.960919i −0.877017 0.480459i \(-0.840470\pi\)
0.877017 0.480459i \(-0.159530\pi\)
\(450\) 2.01419i 0.0949500i
\(451\) 17.0684 0.803719
\(452\) 15.0971 0.710108
\(453\) 20.6709i 0.971204i
\(454\) −3.06032 −0.143628
\(455\) −15.8929 + 5.22708i −0.745071 + 0.245049i
\(456\) −0.296290 −0.0138750
\(457\) 14.9242i 0.698123i −0.937100 0.349061i \(-0.886500\pi\)
0.937100 0.349061i \(-0.113500\pi\)
\(458\) −2.66617 −0.124582
\(459\) −10.5181 −0.490942
\(460\) 19.8375i 0.924930i
\(461\) 17.9790i 0.837367i −0.908132 0.418683i \(-0.862492\pi\)
0.908132 0.418683i \(-0.137508\pi\)
\(462\) 16.1970i 0.753554i
\(463\) 40.4466i 1.87971i 0.341571 + 0.939856i \(0.389041\pi\)
−0.341571 + 0.939856i \(0.610959\pi\)
\(464\) 17.2680 0.801648
\(465\) 4.23775 0.196521
\(466\) 46.2117i 2.14071i
\(467\) 37.4781 1.73428 0.867139 0.498066i \(-0.165956\pi\)
0.867139 + 0.498066i \(0.165956\pi\)
\(468\) −3.23082 + 1.06260i −0.149345 + 0.0491185i
\(469\) 22.0967 1.02033
\(470\) 55.9345i 2.58007i
\(471\) 28.7692 1.32562
\(472\) −0.605764 −0.0278826
\(473\) 34.3523i 1.57952i
\(474\) 2.35622i 0.108225i
\(475\) 8.99396i 0.412671i
\(476\) 6.55189i 0.300306i
\(477\) 6.58562 0.301535
\(478\) 11.8727 0.543047
\(479\) 4.59305i 0.209862i −0.994480 0.104931i \(-0.966538\pi\)
0.994480 0.104931i \(-0.0334622\pi\)
\(480\) −33.8044 −1.54295
\(481\) 3.44548 + 10.4760i 0.157100 + 0.477663i
\(482\) 54.3781 2.47685
\(483\) 10.3857i 0.472564i
\(484\) −4.66709 −0.212141
\(485\) −16.9583 −0.770035
\(486\) 9.78562i 0.443885i
\(487\) 29.6112i 1.34181i −0.741542 0.670906i \(-0.765905\pi\)
0.741542 0.670906i \(-0.234095\pi\)
\(488\) 0.221965i 0.0100479i
\(489\) 5.83183i 0.263725i
\(490\) −21.1509 −0.955499
\(491\) 35.0863 1.58342 0.791712 0.610894i \(-0.209190\pi\)
0.791712 + 0.610894i \(0.209190\pi\)
\(492\) 18.2437i 0.822491i
\(493\) 8.13311 0.366297
\(494\) −29.0137 + 9.54242i −1.30539 + 0.429334i
\(495\) 3.73989 0.168095
\(496\) 4.04355i 0.181561i
\(497\) 10.1411 0.454891
\(498\) −0.524722 −0.0235133
\(499\) 3.07949i 0.137857i 0.997622 + 0.0689284i \(0.0219580\pi\)
−0.997622 + 0.0689284i \(0.978042\pi\)
\(500\) 15.2104i 0.680230i
\(501\) 5.70934i 0.255075i
\(502\) 52.2571i 2.33235i
\(503\) 10.3434 0.461189 0.230594 0.973050i \(-0.425933\pi\)
0.230594 + 0.973050i \(0.425933\pi\)
\(504\) −0.0364280 −0.00162263
\(505\) 8.31821i 0.370156i
\(506\) −22.0394 −0.979769
\(507\) −16.6183 + 12.2572i −0.738043 + 0.544359i
\(508\) 0.196400 0.00871385
\(509\) 4.96830i 0.220216i −0.993920 0.110108i \(-0.964880\pi\)
0.993920 0.110108i \(-0.0351197\pi\)
\(510\) −16.0969 −0.712785
\(511\) −8.55755 −0.378564
\(512\) 31.9002i 1.40980i
\(513\) 23.4565i 1.03563i
\(514\) 38.7963i 1.71123i
\(515\) 7.69039i 0.338879i
\(516\) −36.7178 −1.61641
\(517\) −30.8994 −1.35895
\(518\) 10.6102i 0.466187i
\(519\) −21.8789 −0.960379
\(520\) 0.401311 0.131989i 0.0175986 0.00578808i
\(521\) −6.67995 −0.292654 −0.146327 0.989236i \(-0.546745\pi\)
−0.146327 + 0.989236i \(0.546745\pi\)
\(522\) 4.06194i 0.177786i
\(523\) 11.6369 0.508846 0.254423 0.967093i \(-0.418114\pi\)
0.254423 + 0.967093i \(0.418114\pi\)
\(524\) −3.09365 −0.135147
\(525\) 5.85036i 0.255331i
\(526\) 59.4362i 2.59154i
\(527\) 1.90448i 0.0829606i
\(528\) 18.8799i 0.821642i
\(529\) −8.86820 −0.385574
\(530\) 73.4807 3.19180
\(531\) 6.57780i 0.285452i
\(532\) 14.6114 0.633486
\(533\) −6.54105 19.8880i −0.283324 0.861447i
\(534\) 5.86776 0.253923
\(535\) 19.6121i 0.847904i
\(536\) −0.557963 −0.0241003
\(537\) −21.8193 −0.941571
\(538\) 15.1672i 0.653903i
\(539\) 11.6842i 0.503273i
\(540\) 29.1440i 1.25416i
\(541\) 8.27417i 0.355734i −0.984054 0.177867i \(-0.943080\pi\)
0.984054 0.177867i \(-0.0569198\pi\)
\(542\) −44.1323 −1.89565
\(543\) 13.2806 0.569925
\(544\) 15.1920i 0.651353i
\(545\) −34.6483 −1.48417
\(546\) 18.8727 6.20713i 0.807679 0.265640i
\(547\) −9.31963 −0.398479 −0.199239 0.979951i \(-0.563847\pi\)
−0.199239 + 0.979951i \(0.563847\pi\)
\(548\) 14.4595i 0.617677i
\(549\) −2.41025 −0.102867
\(550\) 12.4150 0.529378
\(551\) 18.1377i 0.772694i
\(552\) 0.262248i 0.0111620i
\(553\) 1.29355i 0.0550075i
\(554\) 18.8551i 0.801078i
\(555\) 12.9617 0.550192
\(556\) −16.5326 −0.701137
\(557\) 22.3462i 0.946839i −0.880837 0.473419i \(-0.843020\pi\)
0.880837 0.473419i \(-0.156980\pi\)
\(558\) 0.951161 0.0402658
\(559\) 40.0272 13.1647i 1.69297 0.556807i
\(560\) −18.7628 −0.792874
\(561\) 8.89229i 0.375433i
\(562\) 25.2316 1.06433
\(563\) −19.9509 −0.840832 −0.420416 0.907332i \(-0.638116\pi\)
−0.420416 + 0.907332i \(0.638116\pi\)
\(564\) 33.0271i 1.39069i
\(565\) 20.3629i 0.856672i
\(566\) 34.4422i 1.44771i
\(567\) 12.7695i 0.536270i
\(568\) −0.256072 −0.0107446
\(569\) −30.1940 −1.26580 −0.632898 0.774235i \(-0.718135\pi\)
−0.632898 + 0.774235i \(0.718135\pi\)
\(570\) 35.8980i 1.50360i
\(571\) −35.6144 −1.49042 −0.745208 0.666832i \(-0.767650\pi\)
−0.745208 + 0.666832i \(0.767650\pi\)
\(572\) −6.54960 19.9140i −0.273852 0.832647i
\(573\) −40.0100 −1.67144
\(574\) 20.1429i 0.840750i
\(575\) −7.96060 −0.331980
\(576\) −3.73069 −0.155445
\(577\) 30.0336i 1.25032i −0.780498 0.625158i \(-0.785035\pi\)
0.780498 0.625158i \(-0.214965\pi\)
\(578\) 26.6722i 1.10942i
\(579\) 12.7681i 0.530625i
\(580\) 22.5356i 0.935739i
\(581\) −0.288070 −0.0119511
\(582\) 20.1378 0.834741
\(583\) 40.5923i 1.68116i
\(584\) 0.216086 0.00894172
\(585\) −1.43322 4.35771i −0.0592565 0.180169i
\(586\) −12.5204 −0.517213
\(587\) 16.0884i 0.664039i 0.943272 + 0.332020i \(0.107730\pi\)
−0.943272 + 0.332020i \(0.892270\pi\)
\(588\) 12.4888 0.515027
\(589\) 4.24721 0.175003
\(590\) 73.3934i 3.02156i
\(591\) 4.44094i 0.182676i
\(592\) 12.3677i 0.508310i
\(593\) 7.42015i 0.304709i 0.988326 + 0.152355i \(0.0486856\pi\)
−0.988326 + 0.152355i \(0.951314\pi\)
\(594\) −32.3787 −1.32851
\(595\) −8.83715 −0.362288
\(596\) 29.5153i 1.20899i
\(597\) −25.9561 −1.06231
\(598\) 8.44605 + 25.6802i 0.345385 + 1.05014i
\(599\) 30.1928 1.23364 0.616822 0.787102i \(-0.288420\pi\)
0.616822 + 0.787102i \(0.288420\pi\)
\(600\) 0.147727i 0.00603094i
\(601\) 30.9392 1.26204 0.631019 0.775767i \(-0.282637\pi\)
0.631019 + 0.775767i \(0.282637\pi\)
\(602\) −40.5402 −1.65230
\(603\) 6.05875i 0.246731i
\(604\) 25.7403i 1.04736i
\(605\) 6.29494i 0.255926i
\(606\) 9.87783i 0.401260i
\(607\) −0.0358681 −0.00145584 −0.000727920 1.00000i \(-0.500232\pi\)
−0.000727920 1.00000i \(0.500232\pi\)
\(608\) −33.8799 −1.37401
\(609\) 11.7982i 0.478086i
\(610\) −26.8929 −1.08886
\(611\) 11.8415 + 36.0039i 0.479054 + 1.45656i
\(612\) −1.79648 −0.0726183
\(613\) 38.0409i 1.53646i −0.640176 0.768228i \(-0.721139\pi\)
0.640176 0.768228i \(-0.278861\pi\)
\(614\) −34.0094 −1.37251
\(615\) −24.6070 −0.992250
\(616\) 0.224534i 0.00904673i
\(617\) 29.8852i 1.20313i 0.798822 + 0.601567i \(0.205457\pi\)
−0.798822 + 0.601567i \(0.794543\pi\)
\(618\) 9.13230i 0.367355i
\(619\) 10.9872i 0.441612i 0.975318 + 0.220806i \(0.0708687\pi\)
−0.975318 + 0.220806i \(0.929131\pi\)
\(620\) 5.27703 0.211930
\(621\) 20.7615 0.833129
\(622\) 7.99814i 0.320696i
\(623\) 3.22137 0.129062
\(624\) −21.9988 + 7.23527i −0.880657 + 0.289643i
\(625\) −31.1038 −1.24415
\(626\) 12.0460i 0.481457i
\(627\) −19.8308 −0.791965
\(628\) 35.8247 1.42956
\(629\) 5.82510i 0.232262i
\(630\) 4.41356i 0.175840i
\(631\) 7.51654i 0.299229i 0.988744 + 0.149614i \(0.0478032\pi\)
−0.988744 + 0.149614i \(0.952197\pi\)
\(632\) 0.0326634i 0.00129928i
\(633\) −25.5903 −1.01712
\(634\) 27.9845 1.11141
\(635\) 0.264903i 0.0105124i
\(636\) −43.3874 −1.72042
\(637\) −13.6144 + 4.47768i −0.539421 + 0.177412i
\(638\) 25.0369 0.991218
\(639\) 2.78061i 0.109999i
\(640\) 0.937295 0.0370498
\(641\) −19.8746 −0.785001 −0.392501 0.919752i \(-0.628390\pi\)
−0.392501 + 0.919752i \(0.628390\pi\)
\(642\) 23.2892i 0.919153i
\(643\) 33.0105i 1.30181i 0.759160 + 0.650904i \(0.225610\pi\)
−0.759160 + 0.650904i \(0.774390\pi\)
\(644\) 12.9327i 0.509619i
\(645\) 49.5247i 1.95003i
\(646\) −16.1329 −0.634740
\(647\) −11.6044 −0.456215 −0.228107 0.973636i \(-0.573254\pi\)
−0.228107 + 0.973636i \(0.573254\pi\)
\(648\) 0.322443i 0.0126668i
\(649\) −40.5440 −1.59149
\(650\) −4.75776 14.4659i −0.186615 0.567401i
\(651\) −2.76271 −0.108279
\(652\) 7.26205i 0.284404i
\(653\) 43.0663 1.68531 0.842656 0.538452i \(-0.180991\pi\)
0.842656 + 0.538452i \(0.180991\pi\)
\(654\) 41.1447 1.60889
\(655\) 4.17269i 0.163041i
\(656\) 23.4794i 0.916717i
\(657\) 2.34641i 0.0915423i
\(658\) 36.4654i 1.42157i
\(659\) 22.3540 0.870787 0.435393 0.900240i \(-0.356609\pi\)
0.435393 + 0.900240i \(0.356609\pi\)
\(660\) −24.6391 −0.959078
\(661\) 39.9481i 1.55380i 0.629624 + 0.776900i \(0.283209\pi\)
−0.629624 + 0.776900i \(0.716791\pi\)
\(662\) −22.2727 −0.865654
\(663\) −10.3613 + 3.40776i −0.402398 + 0.132346i
\(664\) 0.00727403 0.000282287
\(665\) 19.7078i 0.764236i
\(666\) 2.90924 0.112731
\(667\) −16.0538 −0.621606
\(668\) 7.10952i 0.275076i
\(669\) 16.7182i 0.646362i
\(670\) 67.6019i 2.61169i
\(671\) 14.8562i 0.573518i
\(672\) 22.0381 0.850138
\(673\) −4.24478 −0.163624 −0.0818121 0.996648i \(-0.526071\pi\)
−0.0818121 + 0.996648i \(0.526071\pi\)
\(674\) 10.0025i 0.385280i
\(675\) −11.6952 −0.450147
\(676\) −20.6938 + 15.2631i −0.795915 + 0.587044i
\(677\) 49.0530 1.88526 0.942629 0.333842i \(-0.108345\pi\)
0.942629 + 0.333842i \(0.108345\pi\)
\(678\) 24.1808i 0.928658i
\(679\) 11.0556 0.424274
\(680\) 0.223146 0.00855727
\(681\) 2.43726i 0.0933962i
\(682\) 5.86273i 0.224496i
\(683\) 45.4851i 1.74044i −0.492666 0.870219i \(-0.663977\pi\)
0.492666 0.870219i \(-0.336023\pi\)
\(684\) 4.00634i 0.153186i
\(685\) −19.5028 −0.745164
\(686\) 38.0716 1.45358
\(687\) 2.12337i 0.0810115i
\(688\) 47.2553 1.80159
\(689\) 47.2980 15.5560i 1.80191 0.592637i
\(690\) 31.7735 1.20960
\(691\) 1.63712i 0.0622791i 0.999515 + 0.0311395i \(0.00991363\pi\)
−0.999515 + 0.0311395i \(0.990086\pi\)
\(692\) −27.2446 −1.03568
\(693\) −2.43814 −0.0926174
\(694\) 1.84129i 0.0698944i
\(695\) 22.2990i 0.845850i
\(696\) 0.297915i 0.0112924i
\(697\) 11.0586i 0.418875i
\(698\) −27.1057 −1.02597
\(699\) 36.8034 1.39203
\(700\) 7.28512i 0.275352i
\(701\) −1.61823 −0.0611197 −0.0305599 0.999533i \(-0.509729\pi\)
−0.0305599 + 0.999533i \(0.509729\pi\)
\(702\) 12.4084 + 37.7276i 0.468323 + 1.42394i
\(703\) 12.9906 0.489950
\(704\) 22.9951i 0.866661i
\(705\) 44.5468 1.67773
\(706\) 47.5502 1.78957
\(707\) 5.42289i 0.203949i
\(708\) 43.3359i 1.62866i
\(709\) 21.6641i 0.813614i −0.913514 0.406807i \(-0.866642\pi\)
0.913514 0.406807i \(-0.133358\pi\)
\(710\) 31.0253i 1.16436i
\(711\) −0.354682 −0.0133016
\(712\) −0.0813427 −0.00304845
\(713\) 3.75923i 0.140784i
\(714\) 10.4941 0.392731
\(715\) 26.8599 8.83405i 1.00450 0.330375i
\(716\) −27.1703 −1.01540
\(717\) 9.45556i 0.353125i
\(718\) −11.8709 −0.443018
\(719\) −11.6958 −0.436178 −0.218089 0.975929i \(-0.569982\pi\)
−0.218089 + 0.975929i \(0.569982\pi\)
\(720\) 5.14462i 0.191729i
\(721\) 5.01359i 0.186716i
\(722\) 1.91716i 0.0713492i
\(723\) 43.3072i 1.61061i
\(724\) 16.5376 0.614614
\(725\) 9.04330 0.335860
\(726\) 7.47521i 0.277431i
\(727\) −10.7050 −0.397026 −0.198513 0.980098i \(-0.563611\pi\)
−0.198513 + 0.980098i \(0.563611\pi\)
\(728\) −0.261626 + 0.0860472i −0.00969652 + 0.00318912i
\(729\) 29.8190 1.10441
\(730\) 26.1807i 0.968990i
\(731\) 22.2569 0.823200
\(732\) 15.8792 0.586912
\(733\) 37.8613i 1.39844i −0.714907 0.699220i \(-0.753531\pi\)
0.714907 0.699220i \(-0.246469\pi\)
\(734\) 57.1240i 2.10849i
\(735\) 16.8447i 0.621328i
\(736\) 29.9873i 1.10535i
\(737\) −37.3447 −1.37561
\(738\) −5.52303 −0.203306
\(739\) 8.15442i 0.299965i 0.988689 + 0.149983i \(0.0479218\pi\)
−0.988689 + 0.149983i \(0.952078\pi\)
\(740\) 16.1404 0.593334
\(741\) 7.59967 + 23.1068i 0.279181 + 0.848849i
\(742\) −47.9042 −1.75862
\(743\) 32.4382i 1.19004i −0.803711 0.595020i \(-0.797144\pi\)
0.803711 0.595020i \(-0.202856\pi\)
\(744\) 0.0697611 0.00255756
\(745\) 39.8100 1.45853
\(746\) 65.1990i 2.38711i
\(747\) 0.0789864i 0.00288996i
\(748\) 11.0731i 0.404871i
\(749\) 12.7857i 0.467179i
\(750\) 24.3623 0.889585
\(751\) −18.4928 −0.674811 −0.337405 0.941359i \(-0.609549\pi\)
−0.337405 + 0.941359i \(0.609549\pi\)
\(752\) 42.5055i 1.55001i
\(753\) 41.6180 1.51665
\(754\) −9.59477 29.1729i −0.349421 1.06241i
\(755\) 34.7184 1.26353
\(756\) 18.9998i 0.691016i
\(757\) 36.0911 1.31175 0.655877 0.754868i \(-0.272299\pi\)
0.655877 + 0.754868i \(0.272299\pi\)
\(758\) 27.8417 1.01126
\(759\) 17.5523i 0.637110i
\(760\) 0.497641i 0.0180513i
\(761\) 6.79105i 0.246175i 0.992396 + 0.123088i \(0.0392797\pi\)
−0.992396 + 0.123088i \(0.960720\pi\)
\(762\) 0.314571i 0.0113957i
\(763\) 22.5883 0.817750
\(764\) −49.8222 −1.80251
\(765\) 2.42308i 0.0876065i
\(766\) 9.22356 0.333261
\(767\) 15.5375 + 47.2418i 0.561028 + 1.70580i
\(768\) −25.9652 −0.936939
\(769\) 8.83997i 0.318777i 0.987216 + 0.159389i \(0.0509523\pi\)
−0.987216 + 0.159389i \(0.949048\pi\)
\(770\) −27.2041 −0.980369
\(771\) −30.8978 −1.11276
\(772\) 15.8994i 0.572232i
\(773\) 40.7935i 1.46724i −0.679559 0.733620i \(-0.737829\pi\)
0.679559 0.733620i \(-0.262171\pi\)
\(774\) 11.1158i 0.399549i
\(775\) 2.11762i 0.0760670i
\(776\) −0.279164 −0.0100214
\(777\) −8.45009 −0.303145
\(778\) 56.7510i 2.03462i
\(779\) −24.6619 −0.883606
\(780\) 9.44236 + 28.7095i 0.338091 + 1.02796i
\(781\) −17.1390 −0.613283
\(782\) 14.2793i 0.510627i