Properties

Label 403.2.c.b.311.11
Level 403
Weight 2
Character 403.311
Analytic conductor 3.218
Analytic rank 0
Dimension 32
CM No

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Newspace parameters

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

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(32\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 311.11
Character \(\chi\) = 403.311
Dual form 403.2.c.b.311.22

$q$-expansion

\(f(q)\) \(=\) \(q-1.40506i q^{2} +1.52886 q^{3} +0.0258025 q^{4} -1.01618i q^{5} -2.14814i q^{6} -2.90958i q^{7} -2.84638i q^{8} -0.662589 q^{9} +O(q^{10})\) \(q-1.40506i q^{2} +1.52886 q^{3} +0.0258025 q^{4} -1.01618i q^{5} -2.14814i q^{6} -2.90958i q^{7} -2.84638i q^{8} -0.662589 q^{9} -1.42779 q^{10} +2.94134i q^{11} +0.0394484 q^{12} +(3.36248 + 1.30143i) q^{13} -4.08813 q^{14} -1.55359i q^{15} -3.94773 q^{16} -5.52858 q^{17} +0.930978i q^{18} +3.13639i q^{19} -0.0262199i q^{20} -4.44833i q^{21} +4.13277 q^{22} +3.87847 q^{23} -4.35171i q^{24} +3.96739 q^{25} +(1.82859 - 4.72449i) q^{26} -5.59958 q^{27} -0.0750744i q^{28} +5.59296 q^{29} -2.18289 q^{30} -1.00000i q^{31} -0.145952i q^{32} +4.49690i q^{33} +7.76799i q^{34} -2.95664 q^{35} -0.0170965 q^{36} -3.92962i q^{37} +4.40682 q^{38} +(5.14076 + 1.98970i) q^{39} -2.89242 q^{40} +12.1899i q^{41} -6.25018 q^{42} +3.52296 q^{43} +0.0758940i q^{44} +0.673307i q^{45} -5.44949i q^{46} -9.64114i q^{47} -6.03552 q^{48} -1.46564 q^{49} -5.57442i q^{50} -8.45242 q^{51} +(0.0867605 + 0.0335801i) q^{52} -11.3388 q^{53} +7.86776i q^{54} +2.98892 q^{55} -8.28175 q^{56} +4.79510i q^{57} -7.85846i q^{58} +12.4904i q^{59} -0.0400865i q^{60} +5.57570 q^{61} -1.40506 q^{62} +1.92785i q^{63} -8.10053 q^{64} +(1.32248 - 3.41687i) q^{65} +6.31842 q^{66} +4.26478i q^{67} -0.142651 q^{68} +5.92963 q^{69} +4.15426i q^{70} +9.44757i q^{71} +1.88598i q^{72} +0.784520i q^{73} -5.52136 q^{74} +6.06558 q^{75} +0.0809267i q^{76} +8.55806 q^{77} +(2.79565 - 7.22309i) q^{78} +6.11817 q^{79} +4.01159i q^{80} -6.57321 q^{81} +17.1275 q^{82} -8.81342i q^{83} -0.114778i q^{84} +5.61801i q^{85} -4.94997i q^{86} +8.55086 q^{87} +8.37217 q^{88} -6.58407i q^{89} +0.946037 q^{90} +(3.78660 - 9.78340i) q^{91} +0.100074 q^{92} -1.52886i q^{93} -13.5464 q^{94} +3.18712 q^{95} -0.223140i q^{96} +6.44332i q^{97} +2.05931i q^{98} -1.94890i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + O(q^{10}) \) \( 32q - 4q^{3} - 36q^{4} + 20q^{9} + 4q^{10} - 16q^{12} + 10q^{13} - 16q^{14} + 28q^{16} - 8q^{17} - 16q^{22} - 8q^{23} + 4q^{25} + 18q^{26} + 20q^{27} - 16q^{29} + 40q^{30} - 4q^{35} - 44q^{36} + 12q^{38} + 4q^{39} + 28q^{40} + 28q^{42} - 32q^{43} - 64q^{49} - 64q^{52} - 12q^{53} + 44q^{55} + 8q^{56} + 16q^{61} + 8q^{62} - 76q^{64} - 66q^{65} - 68q^{66} + 64q^{68} + 20q^{69} + 16q^{74} - 32q^{77} - 20q^{78} + 64q^{79} - 16q^{81} + 12q^{82} - 72q^{87} + 80q^{88} + 68q^{90} + 22q^{91} + 28q^{92} + 88q^{94} + 4q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.40506i 0.993528i −0.867886 0.496764i \(-0.834521\pi\)
0.867886 0.496764i \(-0.165479\pi\)
\(3\) 1.52886 0.882687 0.441344 0.897338i \(-0.354502\pi\)
0.441344 + 0.897338i \(0.354502\pi\)
\(4\) 0.0258025 0.0129013
\(5\) 1.01618i 0.454448i −0.973843 0.227224i \(-0.927035\pi\)
0.973843 0.227224i \(-0.0729649\pi\)
\(6\) 2.14814i 0.876975i
\(7\) 2.90958i 1.09972i −0.835258 0.549858i \(-0.814682\pi\)
0.835258 0.549858i \(-0.185318\pi\)
\(8\) 2.84638i 1.00635i
\(9\) −0.662589 −0.220863
\(10\) −1.42779 −0.451507
\(11\) 2.94134i 0.886848i 0.896312 + 0.443424i \(0.146236\pi\)
−0.896312 + 0.443424i \(0.853764\pi\)
\(12\) 0.0394484 0.0113878
\(13\) 3.36248 + 1.30143i 0.932585 + 0.360951i
\(14\) −4.08813 −1.09260
\(15\) 1.55359i 0.401135i
\(16\) −3.94773 −0.986932
\(17\) −5.52858 −1.34088 −0.670438 0.741965i \(-0.733894\pi\)
−0.670438 + 0.741965i \(0.733894\pi\)
\(18\) 0.930978i 0.219434i
\(19\) 3.13639i 0.719537i 0.933042 + 0.359768i \(0.117144\pi\)
−0.933042 + 0.359768i \(0.882856\pi\)
\(20\) 0.0262199i 0.00586295i
\(21\) 4.44833i 0.970706i
\(22\) 4.13277 0.881109
\(23\) 3.87847 0.808717 0.404358 0.914601i \(-0.367495\pi\)
0.404358 + 0.914601i \(0.367495\pi\)
\(24\) 4.35171i 0.888289i
\(25\) 3.96739 0.793477
\(26\) 1.82859 4.72449i 0.358615 0.926549i
\(27\) −5.59958 −1.07764
\(28\) 0.0750744i 0.0141877i
\(29\) 5.59296 1.03859 0.519294 0.854596i \(-0.326195\pi\)
0.519294 + 0.854596i \(0.326195\pi\)
\(30\) −2.18289 −0.398539
\(31\) 1.00000i 0.179605i
\(32\) 0.145952i 0.0258009i
\(33\) 4.49690i 0.782810i
\(34\) 7.76799i 1.33220i
\(35\) −2.95664 −0.499764
\(36\) −0.0170965 −0.00284941
\(37\) 3.92962i 0.646025i −0.946395 0.323013i \(-0.895304\pi\)
0.946395 0.323013i \(-0.104696\pi\)
\(38\) 4.40682 0.714880
\(39\) 5.14076 + 1.98970i 0.823181 + 0.318607i
\(40\) −2.89242 −0.457332
\(41\) 12.1899i 1.90374i 0.306509 + 0.951868i \(0.400839\pi\)
−0.306509 + 0.951868i \(0.599161\pi\)
\(42\) −6.25018 −0.964424
\(43\) 3.52296 0.537246 0.268623 0.963245i \(-0.413431\pi\)
0.268623 + 0.963245i \(0.413431\pi\)
\(44\) 0.0758940i 0.0114415i
\(45\) 0.673307i 0.100371i
\(46\) 5.44949i 0.803483i
\(47\) 9.64114i 1.40630i −0.711040 0.703152i \(-0.751775\pi\)
0.711040 0.703152i \(-0.248225\pi\)
\(48\) −6.03552 −0.871153
\(49\) −1.46564 −0.209377
\(50\) 5.57442i 0.788342i
\(51\) −8.45242 −1.18358
\(52\) 0.0867605 + 0.0335801i 0.0120315 + 0.00465672i
\(53\) −11.3388 −1.55751 −0.778753 0.627330i \(-0.784148\pi\)
−0.778753 + 0.627330i \(0.784148\pi\)
\(54\) 7.86776i 1.07067i
\(55\) 2.98892 0.403026
\(56\) −8.28175 −1.10670
\(57\) 4.79510i 0.635126i
\(58\) 7.85846i 1.03187i
\(59\) 12.4904i 1.62611i 0.582190 + 0.813053i \(0.302196\pi\)
−0.582190 + 0.813053i \(0.697804\pi\)
\(60\) 0.0400865i 0.00517515i
\(61\) 5.57570 0.713895 0.356947 0.934125i \(-0.383818\pi\)
0.356947 + 0.934125i \(0.383818\pi\)
\(62\) −1.40506 −0.178443
\(63\) 1.92785i 0.242887i
\(64\) −8.10053 −1.01257
\(65\) 1.32248 3.41687i 0.164033 0.423811i
\(66\) 6.31842 0.777744
\(67\) 4.26478i 0.521026i 0.965470 + 0.260513i \(0.0838916\pi\)
−0.965470 + 0.260513i \(0.916108\pi\)
\(68\) −0.142651 −0.0172990
\(69\) 5.92963 0.713844
\(70\) 4.15426i 0.496530i
\(71\) 9.44757i 1.12122i 0.828080 + 0.560610i \(0.189433\pi\)
−0.828080 + 0.560610i \(0.810567\pi\)
\(72\) 1.88598i 0.222265i
\(73\) 0.784520i 0.0918211i 0.998946 + 0.0459106i \(0.0146189\pi\)
−0.998946 + 0.0459106i \(0.985381\pi\)
\(74\) −5.52136 −0.641845
\(75\) 6.06558 0.700392
\(76\) 0.0809267i 0.00928293i
\(77\) 8.55806 0.975282
\(78\) 2.79565 7.22309i 0.316545 0.817854i
\(79\) 6.11817 0.688348 0.344174 0.938906i \(-0.388159\pi\)
0.344174 + 0.938906i \(0.388159\pi\)
\(80\) 4.01159i 0.448509i
\(81\) −6.57321 −0.730357
\(82\) 17.1275 1.89142
\(83\) 8.81342i 0.967399i −0.875234 0.483699i \(-0.839293\pi\)
0.875234 0.483699i \(-0.160707\pi\)
\(84\) 0.114778i 0.0125233i
\(85\) 5.61801i 0.609358i
\(86\) 4.94997i 0.533769i
\(87\) 8.55086 0.916748
\(88\) 8.37217 0.892476
\(89\) 6.58407i 0.697910i −0.937140 0.348955i \(-0.886537\pi\)
0.937140 0.348955i \(-0.113463\pi\)
\(90\) 0.946037 0.0997211
\(91\) 3.78660 9.78340i 0.396944 1.02558i
\(92\) 0.100074 0.0104335
\(93\) 1.52886i 0.158535i
\(94\) −13.5464 −1.39720
\(95\) 3.18712 0.326992
\(96\) 0.223140i 0.0227741i
\(97\) 6.44332i 0.654220i 0.944986 + 0.327110i \(0.106075\pi\)
−0.944986 + 0.327110i \(0.893925\pi\)
\(98\) 2.05931i 0.208022i
\(99\) 1.94890i 0.195872i
\(100\) 0.102369 0.0102369
\(101\) −18.1325 −1.80425 −0.902123 0.431478i \(-0.857992\pi\)
−0.902123 + 0.431478i \(0.857992\pi\)
\(102\) 11.8762i 1.17592i
\(103\) 17.3257 1.70715 0.853575 0.520970i \(-0.174430\pi\)
0.853575 + 0.520970i \(0.174430\pi\)
\(104\) 3.70435 9.57089i 0.363242 0.938503i
\(105\) −4.52029 −0.441135
\(106\) 15.9317i 1.54743i
\(107\) −7.73734 −0.747997 −0.373998 0.927429i \(-0.622013\pi\)
−0.373998 + 0.927429i \(0.622013\pi\)
\(108\) −0.144483 −0.0139029
\(109\) 11.1918i 1.07198i 0.844224 + 0.535991i \(0.180062\pi\)
−0.844224 + 0.535991i \(0.819938\pi\)
\(110\) 4.19962i 0.400418i
\(111\) 6.00784i 0.570238i
\(112\) 11.4862i 1.08535i
\(113\) 14.3095 1.34612 0.673061 0.739587i \(-0.264979\pi\)
0.673061 + 0.739587i \(0.264979\pi\)
\(114\) 6.73741 0.631016
\(115\) 3.94121i 0.367519i
\(116\) 0.144313 0.0133991
\(117\) −2.22794 0.862311i −0.205973 0.0797207i
\(118\) 17.5497 1.61558
\(119\) 16.0858i 1.47458i
\(120\) −4.42210 −0.403681
\(121\) 2.34851 0.213501
\(122\) 7.83419i 0.709275i
\(123\) 18.6366i 1.68040i
\(124\) 0.0258025i 0.00231713i
\(125\) 9.11244i 0.815042i
\(126\) 2.70875 0.241315
\(127\) −17.9788 −1.59536 −0.797682 0.603079i \(-0.793940\pi\)
−0.797682 + 0.603079i \(0.793940\pi\)
\(128\) 11.0898i 0.980212i
\(129\) 5.38611 0.474220
\(130\) −4.80092 1.85816i −0.421068 0.162972i
\(131\) −8.60202 −0.751562 −0.375781 0.926708i \(-0.622626\pi\)
−0.375781 + 0.926708i \(0.622626\pi\)
\(132\) 0.116031i 0.0100992i
\(133\) 9.12556 0.791287
\(134\) 5.99228 0.517654
\(135\) 5.69016i 0.489731i
\(136\) 15.7364i 1.34939i
\(137\) 13.4868i 1.15226i −0.817360 0.576128i \(-0.804563\pi\)
0.817360 0.576128i \(-0.195437\pi\)
\(138\) 8.33150i 0.709224i
\(139\) −8.93572 −0.757918 −0.378959 0.925414i \(-0.623718\pi\)
−0.378959 + 0.925414i \(0.623718\pi\)
\(140\) −0.0762888 −0.00644758
\(141\) 14.7399i 1.24133i
\(142\) 13.2744 1.11396
\(143\) −3.82794 + 9.89021i −0.320109 + 0.827061i
\(144\) 2.61572 0.217977
\(145\) 5.68344i 0.471984i
\(146\) 1.10230 0.0912269
\(147\) −2.24076 −0.184814
\(148\) 0.101394i 0.00833454i
\(149\) 2.58006i 0.211367i −0.994400 0.105683i \(-0.966297\pi\)
0.994400 0.105683i \(-0.0337030\pi\)
\(150\) 8.52251i 0.695860i
\(151\) 1.75601i 0.142902i 0.997444 + 0.0714510i \(0.0227629\pi\)
−0.997444 + 0.0714510i \(0.977237\pi\)
\(152\) 8.92734 0.724103
\(153\) 3.66317 0.296150
\(154\) 12.0246i 0.968970i
\(155\) −1.01618 −0.0816212
\(156\) 0.132645 + 0.0513393i 0.0106201 + 0.00411043i
\(157\) −19.0327 −1.51898 −0.759489 0.650520i \(-0.774551\pi\)
−0.759489 + 0.650520i \(0.774551\pi\)
\(158\) 8.59640i 0.683893i
\(159\) −17.3355 −1.37479
\(160\) −0.148313 −0.0117252
\(161\) 11.2847i 0.889359i
\(162\) 9.23576i 0.725630i
\(163\) 7.89713i 0.618551i 0.950973 + 0.309275i \(0.100086\pi\)
−0.950973 + 0.309275i \(0.899914\pi\)
\(164\) 0.314529i 0.0245606i
\(165\) 4.56964 0.355746
\(166\) −12.3834 −0.961138
\(167\) 6.55351i 0.507126i 0.967319 + 0.253563i \(0.0816025\pi\)
−0.967319 + 0.253563i \(0.918398\pi\)
\(168\) −12.6616 −0.976866
\(169\) 9.61257 + 8.75205i 0.739429 + 0.673235i
\(170\) 7.89364 0.605415
\(171\) 2.07814i 0.158919i
\(172\) 0.0909012 0.00693115
\(173\) −21.5664 −1.63966 −0.819832 0.572604i \(-0.805933\pi\)
−0.819832 + 0.572604i \(0.805933\pi\)
\(174\) 12.0145i 0.910815i
\(175\) 11.5434i 0.872600i
\(176\) 11.6116i 0.875259i
\(177\) 19.0960i 1.43534i
\(178\) −9.25102 −0.693393
\(179\) −5.03686 −0.376472 −0.188236 0.982124i \(-0.560277\pi\)
−0.188236 + 0.982124i \(0.560277\pi\)
\(180\) 0.0173730i 0.00129491i
\(181\) 9.32320 0.692988 0.346494 0.938052i \(-0.387372\pi\)
0.346494 + 0.938052i \(0.387372\pi\)
\(182\) −13.7463 5.32041i −1.01894 0.394375i
\(183\) 8.52445 0.630146
\(184\) 11.0396i 0.813849i
\(185\) −3.99318 −0.293585
\(186\) −2.14814 −0.157509
\(187\) 16.2614i 1.18915i
\(188\) 0.248766i 0.0181431i
\(189\) 16.2924i 1.18510i
\(190\) 4.47810i 0.324876i
\(191\) 10.5572 0.763892 0.381946 0.924185i \(-0.375254\pi\)
0.381946 + 0.924185i \(0.375254\pi\)
\(192\) −12.3846 −0.893779
\(193\) 16.1267i 1.16082i −0.814324 0.580411i \(-0.802892\pi\)
0.814324 0.580411i \(-0.197108\pi\)
\(194\) 9.05326 0.649986
\(195\) 2.02189 5.22392i 0.144790 0.374093i
\(196\) −0.0378172 −0.00270123
\(197\) 4.22408i 0.300953i 0.988614 + 0.150477i \(0.0480808\pi\)
−0.988614 + 0.150477i \(0.951919\pi\)
\(198\) −2.73832 −0.194604
\(199\) 2.01987 0.143185 0.0715923 0.997434i \(-0.477192\pi\)
0.0715923 + 0.997434i \(0.477192\pi\)
\(200\) 11.2927i 0.798513i
\(201\) 6.52025i 0.459903i
\(202\) 25.4772i 1.79257i
\(203\) 16.2732i 1.14215i
\(204\) −0.218094 −0.0152696
\(205\) 12.3870 0.865148
\(206\) 24.3436i 1.69610i
\(207\) −2.56983 −0.178615
\(208\) −13.2742 5.13768i −0.920398 0.356234i
\(209\) −9.22519 −0.638120
\(210\) 6.35129i 0.438280i
\(211\) −24.2401 −1.66876 −0.834379 0.551191i \(-0.814174\pi\)
−0.834379 + 0.551191i \(0.814174\pi\)
\(212\) −0.292570 −0.0200938
\(213\) 14.4440i 0.989687i
\(214\) 10.8714i 0.743156i
\(215\) 3.57995i 0.244150i
\(216\) 15.9385i 1.08448i
\(217\) −2.90958 −0.197515
\(218\) 15.7252 1.06504
\(219\) 1.19942i 0.0810494i
\(220\) 0.0771217 0.00519954
\(221\) −18.5897 7.19504i −1.25048 0.483991i
\(222\) −8.44138 −0.566548
\(223\) 5.61510i 0.376015i 0.982168 + 0.188008i \(0.0602029\pi\)
−0.982168 + 0.188008i \(0.939797\pi\)
\(224\) −0.424658 −0.0283737
\(225\) −2.62875 −0.175250
\(226\) 20.1057i 1.33741i
\(227\) 8.69104i 0.576845i −0.957503 0.288422i \(-0.906869\pi\)
0.957503 0.288422i \(-0.0931307\pi\)
\(228\) 0.123726i 0.00819393i
\(229\) 27.5444i 1.82018i −0.414407 0.910092i \(-0.636011\pi\)
0.414407 0.910092i \(-0.363989\pi\)
\(230\) −5.53764 −0.365141
\(231\) 13.0841 0.860869
\(232\) 15.9197i 1.04518i
\(233\) −13.7931 −0.903615 −0.451808 0.892115i \(-0.649221\pi\)
−0.451808 + 0.892115i \(0.649221\pi\)
\(234\) −1.21160 + 3.13040i −0.0792048 + 0.204640i
\(235\) −9.79709 −0.639092
\(236\) 0.322283i 0.0209788i
\(237\) 9.35382 0.607596
\(238\) 22.6016 1.46504
\(239\) 1.37922i 0.0892146i −0.999005 0.0446073i \(-0.985796\pi\)
0.999005 0.0446073i \(-0.0142037\pi\)
\(240\) 6.13315i 0.395893i
\(241\) 27.8626i 1.79479i −0.441231 0.897394i \(-0.645458\pi\)
0.441231 0.897394i \(-0.354542\pi\)
\(242\) 3.29980i 0.212119i
\(243\) 6.74924 0.432964
\(244\) 0.143867 0.00921014
\(245\) 1.48935i 0.0951509i
\(246\) 26.1855 1.66953
\(247\) −4.08178 + 10.5461i −0.259718 + 0.671029i
\(248\) −2.84638 −0.180745
\(249\) 13.4745i 0.853911i
\(250\) −12.8035 −0.809767
\(251\) 5.04891 0.318685 0.159342 0.987223i \(-0.449063\pi\)
0.159342 + 0.987223i \(0.449063\pi\)
\(252\) 0.0497435i 0.00313354i
\(253\) 11.4079i 0.717209i
\(254\) 25.2614i 1.58504i
\(255\) 8.58914i 0.537873i
\(256\) −0.619157 −0.0386973
\(257\) −21.7141 −1.35449 −0.677243 0.735759i \(-0.736825\pi\)
−0.677243 + 0.735759i \(0.736825\pi\)
\(258\) 7.56781i 0.471151i
\(259\) −11.4335 −0.710445
\(260\) 0.0341233 0.0881640i 0.00211624 0.00546770i
\(261\) −3.70584 −0.229385
\(262\) 12.0864i 0.746698i
\(263\) 21.0672 1.29906 0.649529 0.760337i \(-0.274966\pi\)
0.649529 + 0.760337i \(0.274966\pi\)
\(264\) 12.7999 0.787777
\(265\) 11.5222i 0.707805i
\(266\) 12.8220i 0.786166i
\(267\) 10.0661i 0.616036i
\(268\) 0.110042i 0.00672189i
\(269\) 11.1314 0.678696 0.339348 0.940661i \(-0.389794\pi\)
0.339348 + 0.940661i \(0.389794\pi\)
\(270\) 7.99503 0.486562
\(271\) 17.2105i 1.04546i 0.852498 + 0.522731i \(0.175087\pi\)
−0.852498 + 0.522731i \(0.824913\pi\)
\(272\) 21.8253 1.32335
\(273\) 5.78918 14.9574i 0.350377 0.905266i
\(274\) −18.9498 −1.14480
\(275\) 11.6694i 0.703694i
\(276\) 0.152999 0.00920949
\(277\) 1.64549 0.0988681 0.0494340 0.998777i \(-0.484258\pi\)
0.0494340 + 0.998777i \(0.484258\pi\)
\(278\) 12.5552i 0.753013i
\(279\) 0.662589i 0.0396681i
\(280\) 8.41572i 0.502935i
\(281\) 21.4692i 1.28075i −0.768064 0.640374i \(-0.778780\pi\)
0.768064 0.640374i \(-0.221220\pi\)
\(282\) −20.7105 −1.23329
\(283\) −2.52897 −0.150332 −0.0751660 0.997171i \(-0.523949\pi\)
−0.0751660 + 0.997171i \(0.523949\pi\)
\(284\) 0.243771i 0.0144652i
\(285\) 4.87266 0.288632
\(286\) 13.8964 + 5.37849i 0.821709 + 0.318037i
\(287\) 35.4673 2.09357
\(288\) 0.0967061i 0.00569846i
\(289\) 13.5652 0.797950
\(290\) −7.98558 −0.468929
\(291\) 9.85093i 0.577472i
\(292\) 0.0202426i 0.00118461i
\(293\) 8.49502i 0.496284i 0.968724 + 0.248142i \(0.0798200\pi\)
−0.968724 + 0.248142i \(0.920180\pi\)
\(294\) 3.14840i 0.183618i
\(295\) 12.6924 0.738980
\(296\) −11.1852 −0.650125
\(297\) 16.4703i 0.955703i
\(298\) −3.62514 −0.209999
\(299\) 13.0413 + 5.04754i 0.754197 + 0.291907i
\(300\) 0.156507 0.00903594
\(301\) 10.2503i 0.590819i
\(302\) 2.46730 0.141977
\(303\) −27.7220 −1.59259
\(304\) 12.3816i 0.710134i
\(305\) 5.66589i 0.324428i
\(306\) 5.14698i 0.294233i
\(307\) 24.6040i 1.40423i 0.712065 + 0.702113i \(0.247760\pi\)
−0.712065 + 0.702113i \(0.752240\pi\)
\(308\) 0.220820 0.0125824
\(309\) 26.4885 1.50688
\(310\) 1.42779i 0.0810930i
\(311\) −8.07331 −0.457795 −0.228898 0.973451i \(-0.573512\pi\)
−0.228898 + 0.973451i \(0.573512\pi\)
\(312\) 5.66343 14.6325i 0.320629 0.828405i
\(313\) −14.6297 −0.826922 −0.413461 0.910522i \(-0.635680\pi\)
−0.413461 + 0.910522i \(0.635680\pi\)
\(314\) 26.7422i 1.50915i
\(315\) 1.95904 0.110379
\(316\) 0.157864 0.00888055
\(317\) 6.32778i 0.355403i −0.984084 0.177702i \(-0.943134\pi\)
0.984084 0.177702i \(-0.0568662\pi\)
\(318\) 24.3574i 1.36589i
\(319\) 16.4508i 0.921069i
\(320\) 8.23156i 0.460158i
\(321\) −11.8293 −0.660247
\(322\) −15.8557 −0.883604
\(323\) 17.3398i 0.964810i
\(324\) −0.169605 −0.00942252
\(325\) 13.3403 + 5.16326i 0.739985 + 0.286406i
\(326\) 11.0959 0.614548
\(327\) 17.1107i 0.946224i
\(328\) 34.6969 1.91582
\(329\) −28.0516 −1.54654
\(330\) 6.42063i 0.353444i
\(331\) 8.95949i 0.492458i 0.969212 + 0.246229i \(0.0791915\pi\)
−0.969212 + 0.246229i \(0.920808\pi\)
\(332\) 0.227408i 0.0124807i
\(333\) 2.60372i 0.142683i
\(334\) 9.20808 0.503844
\(335\) 4.33377 0.236779
\(336\) 17.5608i 0.958021i
\(337\) −19.7375 −1.07517 −0.537586 0.843209i \(-0.680664\pi\)
−0.537586 + 0.843209i \(0.680664\pi\)
\(338\) 12.2972 13.5063i 0.668878 0.734644i
\(339\) 21.8772 1.18820
\(340\) 0.144959i 0.00786149i
\(341\) 2.94134 0.159283
\(342\) −2.91991 −0.157891
\(343\) 16.1027i 0.869461i
\(344\) 10.0277i 0.540656i
\(345\) 6.02555i 0.324405i
\(346\) 30.3021i 1.62905i
\(347\) 13.0978 0.703127 0.351563 0.936164i \(-0.385650\pi\)
0.351563 + 0.936164i \(0.385650\pi\)
\(348\) 0.220634 0.0118272
\(349\) 7.30002i 0.390761i −0.980728 0.195381i \(-0.937406\pi\)
0.980728 0.195381i \(-0.0625942\pi\)
\(350\) −16.2192 −0.866953
\(351\) −18.8285 7.28745i −1.00499 0.388975i
\(352\) 0.429295 0.0228815
\(353\) 34.9174i 1.85846i −0.369497 0.929232i \(-0.620470\pi\)
0.369497 0.929232i \(-0.379530\pi\)
\(354\) 26.8310 1.42605
\(355\) 9.60039 0.509536
\(356\) 0.169885i 0.00900391i
\(357\) 24.5930i 1.30160i
\(358\) 7.07709i 0.374036i
\(359\) 11.6905i 0.617002i 0.951224 + 0.308501i \(0.0998273\pi\)
−0.951224 + 0.308501i \(0.900173\pi\)
\(360\) 1.91648 0.101008
\(361\) 9.16307 0.482267
\(362\) 13.0997i 0.688503i
\(363\) 3.59054 0.188454
\(364\) 0.0977039 0.252436i 0.00512108 0.0132313i
\(365\) 0.797211 0.0417279
\(366\) 11.9774i 0.626068i
\(367\) 19.0286 0.993286 0.496643 0.867955i \(-0.334566\pi\)
0.496643 + 0.867955i \(0.334566\pi\)
\(368\) −15.3111 −0.798149
\(369\) 8.07686i 0.420465i
\(370\) 5.61067i 0.291685i
\(371\) 32.9912i 1.71282i
\(372\) 0.0394484i 0.00204531i
\(373\) 8.09393 0.419088 0.209544 0.977799i \(-0.432802\pi\)
0.209544 + 0.977799i \(0.432802\pi\)
\(374\) −22.8483 −1.18146
\(375\) 13.9316i 0.719427i
\(376\) −27.4423 −1.41523
\(377\) 18.8062 + 7.27884i 0.968571 + 0.374879i
\(378\) 22.8918 1.17743
\(379\) 8.82330i 0.453222i 0.973985 + 0.226611i \(0.0727647\pi\)
−0.973985 + 0.226611i \(0.927235\pi\)
\(380\) 0.0822358 0.00421861
\(381\) −27.4871 −1.40821
\(382\) 14.8335i 0.758948i
\(383\) 36.6362i 1.87202i 0.351973 + 0.936010i \(0.385511\pi\)
−0.351973 + 0.936010i \(0.614489\pi\)
\(384\) 16.9548i 0.865221i
\(385\) 8.69650i 0.443215i
\(386\) −22.6589 −1.15331
\(387\) −2.33427 −0.118658
\(388\) 0.166254i 0.00844026i
\(389\) −7.70656 −0.390738 −0.195369 0.980730i \(-0.562590\pi\)
−0.195369 + 0.980730i \(0.562590\pi\)
\(390\) −7.33993 2.84087i −0.371672 0.143853i
\(391\) −21.4424 −1.08439
\(392\) 4.17176i 0.210706i
\(393\) −13.1513 −0.663394
\(394\) 5.93509 0.299006
\(395\) 6.21714i 0.312818i
\(396\) 0.0502865i 0.00252699i
\(397\) 8.55515i 0.429371i −0.976683 0.214685i \(-0.931127\pi\)
0.976683 0.214685i \(-0.0688726\pi\)
\(398\) 2.83804i 0.142258i
\(399\) 13.9517 0.698459
\(400\) −15.6622 −0.783108
\(401\) 2.11758i 0.105747i −0.998601 0.0528734i \(-0.983162\pi\)
0.998601 0.0528734i \(-0.0168380\pi\)
\(402\) 9.16135 0.456926
\(403\) 1.30143 3.36248i 0.0648287 0.167497i
\(404\) −0.467863 −0.0232771
\(405\) 6.67954i 0.331909i
\(406\) −22.8648 −1.13476
\(407\) 11.5584 0.572926
\(408\) 24.0588i 1.19109i
\(409\) 4.47719i 0.221383i 0.993855 + 0.110691i \(0.0353065\pi\)
−0.993855 + 0.110691i \(0.964694\pi\)
\(410\) 17.4046i 0.859550i
\(411\) 20.6194i 1.01708i
\(412\) 0.447046 0.0220244
\(413\) 36.3416 1.78826
\(414\) 3.61077i 0.177460i
\(415\) −8.95599 −0.439632
\(416\) 0.189946 0.490761i 0.00931286 0.0240615i
\(417\) −13.6615 −0.669004
\(418\) 12.9620i 0.633990i
\(419\) 34.4369 1.68235 0.841176 0.540761i \(-0.181864\pi\)
0.841176 + 0.540761i \(0.181864\pi\)
\(420\) −0.116635 −0.00569120
\(421\) 33.7742i 1.64605i −0.568002 0.823027i \(-0.692283\pi\)
0.568002 0.823027i \(-0.307717\pi\)
\(422\) 34.0589i 1.65796i
\(423\) 6.38811i 0.310600i
\(424\) 32.2745i 1.56739i
\(425\) −21.9340 −1.06396
\(426\) 20.2947 0.983282
\(427\) 16.2229i 0.785082i
\(428\) −0.199643 −0.00965010
\(429\) −5.85239 + 15.1207i −0.282556 + 0.730036i
\(430\) −5.03004 −0.242570
\(431\) 17.7153i 0.853318i −0.904413 0.426659i \(-0.859690\pi\)
0.904413 0.426659i \(-0.140310\pi\)
\(432\) 22.1056 1.06356
\(433\) −4.59958 −0.221042 −0.110521 0.993874i \(-0.535252\pi\)
−0.110521 + 0.993874i \(0.535252\pi\)
\(434\) 4.08813i 0.196237i
\(435\) 8.68918i 0.416614i
\(436\) 0.288777i 0.0138299i
\(437\) 12.1644i 0.581901i
\(438\) 1.68526 0.0805249
\(439\) −25.5577 −1.21980 −0.609900 0.792478i \(-0.708791\pi\)
−0.609900 + 0.792478i \(0.708791\pi\)
\(440\) 8.50760i 0.405584i
\(441\) 0.971115 0.0462436
\(442\) −10.1095 + 26.1197i −0.480859 + 1.24239i
\(443\) 24.7736 1.17703 0.588515 0.808486i \(-0.299713\pi\)
0.588515 + 0.808486i \(0.299713\pi\)
\(444\) 0.155017i 0.00735679i
\(445\) −6.69057 −0.317163
\(446\) 7.88956 0.373582
\(447\) 3.94455i 0.186571i
\(448\) 23.5691i 1.11354i
\(449\) 38.0058i 1.79360i −0.442433 0.896801i \(-0.645885\pi\)
0.442433 0.896801i \(-0.354115\pi\)
\(450\) 3.69355i 0.174116i
\(451\) −35.8545 −1.68832
\(452\) 0.369220 0.0173667
\(453\) 2.68469i 0.126138i
\(454\) −12.2114 −0.573111
\(455\) −9.94166 3.84786i −0.466072 0.180390i
\(456\) 13.6487 0.639157
\(457\) 0.690146i 0.0322837i −0.999870 0.0161418i \(-0.994862\pi\)
0.999870 0.0161418i \(-0.00513833\pi\)
\(458\) −38.7015 −1.80840
\(459\) 30.9577 1.44498
\(460\) 0.101693i 0.00474146i
\(461\) 3.50495i 0.163242i 0.996663 + 0.0816210i \(0.0260097\pi\)
−0.996663 + 0.0816210i \(0.973990\pi\)
\(462\) 18.3839i 0.855298i
\(463\) 11.0533i 0.513691i −0.966453 0.256845i \(-0.917317\pi\)
0.966453 0.256845i \(-0.0826831\pi\)
\(464\) −22.0795 −1.02502
\(465\) −1.55359 −0.0720460
\(466\) 19.3801i 0.897768i
\(467\) −13.4125 −0.620655 −0.310328 0.950630i \(-0.600439\pi\)
−0.310328 + 0.950630i \(0.600439\pi\)
\(468\) −0.0574865 0.0222498i −0.00265732 0.00102850i
\(469\) 12.4087 0.572981
\(470\) 13.7655i 0.634956i
\(471\) −29.0984 −1.34078
\(472\) 35.5523 1.63643
\(473\) 10.3622i 0.476456i
\(474\) 13.1427i 0.603664i
\(475\) 12.4433i 0.570936i
\(476\) 0.415055i 0.0190240i
\(477\) 7.51297 0.343995
\(478\) −1.93790 −0.0886373
\(479\) 9.11526i 0.416487i 0.978077 + 0.208243i \(0.0667746\pi\)
−0.978077 + 0.208243i \(0.933225\pi\)
\(480\) −0.226750 −0.0103497
\(481\) 5.11411 13.2133i 0.233183 0.602473i
\(482\) −39.1487 −1.78317
\(483\) 17.2527i 0.785026i
\(484\) 0.0605974 0.00275443
\(485\) 6.54755 0.297309
\(486\) 9.48309i 0.430162i
\(487\) 7.68894i 0.348419i 0.984709 + 0.174210i \(0.0557370\pi\)
−0.984709 + 0.174210i \(0.944263\pi\)
\(488\) 15.8705i 0.718425i
\(489\) 12.0736i 0.545987i
\(490\) 2.09262 0.0945351
\(491\) 2.30951 0.104227 0.0521134 0.998641i \(-0.483404\pi\)
0.0521134 + 0.998641i \(0.483404\pi\)
\(492\) 0.480871i 0.0216793i
\(493\) −30.9211 −1.39262
\(494\) 14.8179 + 5.73515i 0.666687 + 0.258037i
\(495\) −1.98043 −0.0890135
\(496\) 3.94773i 0.177258i
\(497\) 27.4884 1.23302
\(498\) −18.9325 −0.848384
\(499\) 16.9769i 0.759992i −0.924988 0.379996i \(-0.875925\pi\)
0.924988 0.379996i \(-0.124075\pi\)
\(500\) 0.235124i 0.0105151i
\(501\) 10.0194i 0.447633i
\(502\) 7.09403i 0.316622i
\(503\) 9.24502 0.412215 0.206108 0.978529i \(-0.433920\pi\)
0.206108 + 0.978529i \(0.433920\pi\)
\(504\) 5.48740 0.244428
\(505\) 18.4258i 0.819936i
\(506\) 16.0288 0.712567
\(507\) 14.6963 + 13.3807i 0.652684 + 0.594256i
\(508\) −0.463899 −0.0205822
\(509\) 1.38544i 0.0614086i 0.999529 + 0.0307043i \(0.00977501\pi\)
−0.999529 + 0.0307043i \(0.990225\pi\)
\(510\) 12.0683 0.534392
\(511\) 2.28262 0.100977
\(512\) 23.0496i 1.01866i
\(513\) 17.5625i 0.775402i
\(514\) 30.5096i 1.34572i
\(515\) 17.6059i 0.775810i
\(516\) 0.138975 0.00611804
\(517\) 28.3579 1.24718
\(518\) 16.0648i 0.705847i
\(519\) −32.9720 −1.44731
\(520\) −9.72571 3.76427i −0.426501 0.165074i
\(521\) 5.80992 0.254537 0.127268 0.991868i \(-0.459379\pi\)
0.127268 + 0.991868i \(0.459379\pi\)
\(522\) 5.20693i 0.227901i
\(523\) −2.01451 −0.0880885 −0.0440443 0.999030i \(-0.514024\pi\)
−0.0440443 + 0.999030i \(0.514024\pi\)
\(524\) −0.221954 −0.00969610
\(525\) 17.6483i 0.770233i
\(526\) 29.6007i 1.29065i
\(527\) 5.52858i 0.240829i
\(528\) 17.7525i 0.772580i
\(529\) −7.95748 −0.345977
\(530\) 16.1894 0.703225
\(531\) 8.27597i 0.359146i
\(532\) 0.235463 0.0102086
\(533\) −15.8642 + 40.9882i −0.687155 + 1.77540i
\(534\) −14.1435 −0.612049
\(535\) 7.86250i 0.339926i
\(536\) 12.1392 0.524332
\(537\) −7.70065 −0.332307
\(538\) 15.6404i 0.674304i
\(539\) 4.31094i 0.185685i
\(540\) 0.146821i 0.00631815i
\(541\) 21.4836i 0.923652i −0.886971 0.461826i \(-0.847194\pi\)
0.886971 0.461826i \(-0.152806\pi\)
\(542\) 24.1818 1.03870
\(543\) 14.2539 0.611692
\(544\) 0.806906i 0.0345958i
\(545\) 11.3729 0.487160
\(546\) −21.0161 8.13416i −0.899407 0.348110i
\(547\) 7.77420 0.332401 0.166200 0.986092i \(-0.446850\pi\)
0.166200 + 0.986092i \(0.446850\pi\)
\(548\) 0.347993i 0.0148655i
\(549\) −3.69439 −0.157673
\(550\) 16.3963 0.699140
\(551\) 17.5417i 0.747302i
\(552\) 16.8780i 0.718374i
\(553\) 17.8013i 0.756987i
\(554\) 2.31202i 0.0982282i
\(555\) −6.10502 −0.259144
\(556\) −0.230564 −0.00977809
\(557\) 8.44764i 0.357938i 0.983855 + 0.178969i \(0.0572762\pi\)
−0.983855 + 0.178969i \(0.942724\pi\)
\(558\) 0.930978 0.0394114
\(559\) 11.8459 + 4.58487i 0.501028 + 0.193920i
\(560\) 11.6720 0.493233
\(561\) 24.8614i 1.04965i
\(562\) −30.1656 −1.27246
\(563\) −35.3836 −1.49124 −0.745620 0.666371i \(-0.767847\pi\)
−0.745620 + 0.666371i \(0.767847\pi\)
\(564\) 0.380328i 0.0160147i
\(565\) 14.5409i 0.611742i
\(566\) 3.55336i 0.149359i
\(567\) 19.1253i 0.803185i
\(568\) 26.8913 1.12834
\(569\) −20.3682 −0.853881 −0.426940 0.904280i \(-0.640409\pi\)
−0.426940 + 0.904280i \(0.640409\pi\)
\(570\) 6.84639i 0.286764i
\(571\) 18.7808 0.785951 0.392976 0.919549i \(-0.371446\pi\)
0.392976 + 0.919549i \(0.371446\pi\)
\(572\) −0.0987706 + 0.255192i −0.00412980 + 0.0106701i
\(573\) 16.1405 0.674278
\(574\) 49.8338i 2.08002i
\(575\) 15.3874 0.641698
\(576\) 5.36732 0.223638
\(577\) 33.7171i 1.40366i 0.712345 + 0.701830i \(0.247633\pi\)
−0.712345 + 0.701830i \(0.752367\pi\)
\(578\) 19.0599i 0.792786i
\(579\) 24.6554i 1.02464i
\(580\) 0.146647i 0.00608918i
\(581\) −25.6433 −1.06386
\(582\) 13.8412 0.573735
\(583\) 33.3513i 1.38127i
\(584\) 2.23304 0.0924039
\(585\) −0.876260 + 2.26398i −0.0362289 + 0.0936041i
\(586\) 11.9360 0.493072
\(587\) 33.1106i 1.36662i 0.730129 + 0.683310i \(0.239460\pi\)
−0.730129 + 0.683310i \(0.760540\pi\)
\(588\) −0.0578171 −0.00238434
\(589\) 3.13639 0.129233
\(590\) 17.8336i 0.734198i
\(591\) 6.45803i 0.265648i
\(592\) 15.5131i 0.637583i
\(593\) 30.7925i 1.26449i 0.774767 + 0.632247i \(0.217867\pi\)
−0.774767 + 0.632247i \(0.782133\pi\)
\(594\) −23.1418 −0.949518
\(595\) 16.3460 0.670122
\(596\) 0.0665721i 0.00272690i
\(597\) 3.08809 0.126387
\(598\) 7.09211 18.3238i 0.290018 0.749316i
\(599\) 3.80719 0.155558 0.0777788 0.996971i \(-0.475217\pi\)
0.0777788 + 0.996971i \(0.475217\pi\)
\(600\) 17.2649i 0.704837i
\(601\) 7.77021 0.316954 0.158477 0.987363i \(-0.449342\pi\)
0.158477 + 0.987363i \(0.449342\pi\)
\(602\) −14.4023 −0.586995
\(603\) 2.82579i 0.115075i
\(604\) 0.0453094i 0.00184361i
\(605\) 2.38650i 0.0970249i
\(606\) 38.9511i 1.58228i
\(607\) −15.3747 −0.624042 −0.312021 0.950075i \(-0.601006\pi\)
−0.312021 + 0.950075i \(0.601006\pi\)
\(608\) 0.457762 0.0185647
\(609\) 24.8794i 1.00816i
\(610\) −7.96092 −0.322328
\(611\) 12.5472 32.4181i 0.507607 1.31150i
\(612\) 0.0945191 0.00382071
\(613\) 37.2449i 1.50431i −0.658987 0.752154i \(-0.729015\pi\)
0.658987 0.752154i \(-0.270985\pi\)
\(614\) 34.5702 1.39514
\(615\) 18.9380 0.763656
\(616\) 24.3595i 0.981471i
\(617\) 12.2249i 0.492154i −0.969250 0.246077i \(-0.920858\pi\)
0.969250 0.246077i \(-0.0791417\pi\)
\(618\) 37.2180i 1.49713i
\(619\) 35.0566i 1.40904i −0.709683 0.704521i \(-0.751162\pi\)
0.709683 0.704521i \(-0.248838\pi\)
\(620\) −0.0262199 −0.00105302
\(621\) −21.7178 −0.871506
\(622\) 11.3435i 0.454832i
\(623\) −19.1568 −0.767503
\(624\) −20.2943 7.85479i −0.812424 0.314443i
\(625\) 10.5771 0.423083
\(626\) 20.5557i 0.821571i
\(627\) −14.1040 −0.563260
\(628\) −0.491093 −0.0195967
\(629\) 21.7252i 0.866240i
\(630\) 2.75257i 0.109665i
\(631\) 7.46467i 0.297164i −0.988900 0.148582i \(-0.952529\pi\)
0.988900 0.148582i \(-0.0474708\pi\)
\(632\) 17.4146i 0.692716i
\(633\) −37.0597 −1.47299
\(634\) −8.89092 −0.353103
\(635\) 18.2697i 0.725009i
\(636\) −0.447298 −0.0177365
\(637\) −4.92818 1.90742i −0.195262 0.0755748i
\(638\) 23.1144 0.915108
\(639\) 6.25985i 0.247636i
\(640\) 11.2692 0.445455
\(641\) 35.1991 1.39028 0.695141 0.718873i \(-0.255342\pi\)
0.695141 + 0.718873i \(0.255342\pi\)
\(642\) 16.6209i 0.655975i
\(643\) 20.9264i 0.825257i 0.910899 + 0.412628i \(0.135389\pi\)
−0.910899 + 0.412628i \(0.864611\pi\)
\(644\) 0.291174i 0.0114739i
\(645\) 5.47323i 0.215508i
\(646\) −24.3634 −0.958567
\(647\) 48.3523 1.90092 0.950462 0.310841i \(-0.100611\pi\)
0.950462 + 0.310841i \(0.100611\pi\)
\(648\) 18.7098i 0.734992i
\(649\) −36.7384 −1.44211
\(650\) 7.25470 18.7439i 0.284553 0.735196i
\(651\) −4.44833 −0.174344
\(652\) 0.203766i 0.00798008i
\(653\) −13.8535 −0.542127 −0.271064 0.962561i \(-0.587375\pi\)
−0.271064 + 0.962561i \(0.587375\pi\)
\(654\) 24.0416 0.940101
\(655\) 8.74117i 0.341546i
\(656\) 48.1223i 1.87886i
\(657\) 0.519814i 0.0202799i
\(658\) 39.4143i 1.53653i
\(659\) 24.2242 0.943639 0.471820 0.881695i \(-0.343597\pi\)
0.471820 + 0.881695i \(0.343597\pi\)
\(660\) 0.117908 0.00458957
\(661\) 22.2852i 0.866795i 0.901203 + 0.433397i \(0.142685\pi\)
−0.901203 + 0.433397i \(0.857315\pi\)
\(662\) 12.5886 0.489271
\(663\) −28.4211 11.0002i −1.10378 0.427213i
\(664\) −25.0863 −0.973538
\(665\) 9.27318i 0.359599i
\(666\) 3.65839 0.141760
\(667\) 21.6921 0.839923
\(668\) 0.169097i 0.00654256i
\(669\) 8.58470i 0.331904i
\(670\) 6.08921i 0.235247i
\(671\) 16.4000i 0.633116i
\(672\) −0.649243 −0.0250451
\(673\) 20.4711 0.789103 0.394552 0.918874i \(-0.370900\pi\)
0.394552 + 0.918874i \(0.370900\pi\)
\(674\) 27.7325i 1.06821i
\(675\) −22.2157 −0.855083
\(676\) 0.248029 + 0.225825i 0.00953956 + 0.00868558i
\(677\) −2.15024 −0.0826404 −0.0413202 0.999146i \(-0.513156\pi\)
−0.0413202 + 0.999146i \(0.513156\pi\)
\(678\) 30.7388i 1.18052i
\(679\) 18.7473 0.719457
\(680\) 15.9910 0.613226
\(681\) 13.2874i 0.509173i
\(682\) 4.13277i 0.158252i
\(683\) 38.4682i 1.47194i 0.677013 + 0.735971i \(0.263274\pi\)
−0.677013 + 0.735971i \(0.736726\pi\)
\(684\) 0.0536211i 0.00205026i
\(685\) −13.7050 −0.523640
\(686\) −22.6252 −0.863835
\(687\) 42.1115i 1.60665i
\(688\) −13.9077 −0.530226
\(689\) −38.1266 14.7566i −1.45251 0.562183i
\(690\) −8.46627 −0.322305
\(691\) 17.9832i 0.684112i 0.939679 + 0.342056i \(0.111123\pi\)
−0.939679 + 0.342056i \(0.888877\pi\)
\(692\) −0.556468 −0.0211537
\(693\) −5.67047 −0.215404
\(694\) 18.4032i 0.698576i
\(695\) 9.08026i 0.344434i
\(696\) 24.3390i 0.922566i
\(697\) 67.3926i 2.55267i
\(698\) −10.2570 −0.388232
\(699\) −21.0877 −0.797610
\(700\) 0.297849i 0.0112576i
\(701\) 23.3608 0.882327 0.441164 0.897427i \(-0.354566\pi\)
0.441164 + 0.897427i \(0.354566\pi\)
\(702\) −10.2393 + 26.4552i −0.386458 + 0.998487i
\(703\) 12.3248 0.464839
\(704\) 23.8264i 0.897992i
\(705\) −14.9784 −0.564118
\(706\) −49.0610 −1.84644
\(707\) 52.7578i 1.98416i
\(708\) 0.492725i 0.0185177i
\(709\) 33.1442i 1.24476i 0.782717 + 0.622378i \(0.213833\pi\)
−0.782717 + 0.622378i \(0.786167\pi\)
\(710\) 13.4891i 0.506239i
\(711\) −4.05383 −0.152030
\(712\) −18.7407 −0.702339
\(713\) 3.87847i 0.145250i
\(714\) 34.5546 1.29317
\(715\) 10.0502 + 3.88986i 0.375856 + 0.145473i
\(716\) −0.129964 −0.00485697
\(717\) 2.10864i 0.0787486i
\(718\) 16.4259 0.613009
\(719\) −16.8313 −0.627700 −0.313850 0.949473i \(-0.601619\pi\)
−0.313850 + 0.949473i \(0.601619\pi\)
\(720\) 2.65803i 0.0990590i
\(721\) 50.4104i 1.87738i
\(722\) 12.8747i 0.479146i
\(723\) 42.5980i 1.58424i
\(724\) 0.240562 0.00894042
\(725\) 22.1895 0.824096
\(726\) 5.04493i 0.187235i
\(727\) 14.8322 0.550095 0.275047 0.961431i \(-0.411306\pi\)
0.275047 + 0.961431i \(0.411306\pi\)
\(728\) −27.8472 10.7781i −1.03209 0.399463i
\(729\) 30.0383 1.11253
\(730\) 1.12013i 0.0414579i
\(731\) −19.4769 −0.720381
\(732\) 0.219952 0.00812967
\(733\) 31.6000i 1.16717i 0.812050 + 0.583587i \(0.198351\pi\)
−0.812050 + 0.583587i \(0.801649\pi\)
\(734\) 26.7364i 0.986858i
\(735\) 2.27700i 0.0839885i
\(736\) 0.566070i 0.0208656i
\(737\) −12.5442 −0.462070
\(738\) −11.3485 −0.417744
\(739\) 18.2260i 0.670453i 0.942138 + 0.335226i \(0.108813\pi\)
−0.942138 + 0.335226i \(0.891187\pi\)
\(740\) −0.103034 −0.00378761
\(741\) −6.24047 + 16.1234i −0.229249 + 0.592309i
\(742\) 46.3546 1.70173
\(743\) 36.3278i 1.33274i 0.745622 + 0.666369i \(0.232152\pi\)
−0.745622 + 0.666369i \(0.767848\pi\)
\(744\) −4.35171 −0.159541
\(745\) −2.62180 −0.0960552
\(746\) 11.3725i 0.416375i
\(747\) 5.83967i 0.213662i
\(748\) 0.419586i 0.0153416i
\(749\) 22.5124i 0.822585i
\(750\) −19.5748 −0.714771
\(751\) 14.5974 0.532667 0.266333 0.963881i \(-0.414188\pi\)
0.266333 + 0.963881i \(0.414188\pi\)
\(752\) 38.0606i 1.38793i
\(753\) 7.71908 0.281299
\(754\) 10.2272 26.4239i 0.372453 0.962303i
\(755\) 1.78441 0.0649415
\(756\) 0.420385i 0.0152893i
\(757\) 21.1706 0.769457 0.384728 0.923030i \(-0.374295\pi\)
0.384728 + 0.923030i \(0.374295\pi\)
\(758\) 12.3973 0.450289
\(759\) 17.4411i 0.633071i
\(760\) 9.07175i 0.329067i
\(761\) 11.2052i 0.406188i 0.979159 + 0.203094i \(0.0650997\pi\)
−0.979159 + 0.203094i \(0.934900\pi\)
\(762\) 38.6211i 1.39909i
\(763\) 32.5634 1.17888
\(764\) 0.272402 0.00985516
\(765\) 3.72243i 0.134585i
\(766\) 51.4760 1.85991
\(767\) −16.2553 + 41.9986i −0.586944 + 1.51648i
\(768\) −0.946604 −0.0341576
\(769\) 31.9705i 1.15289i 0.817137 + 0.576444i \(0.195560\pi\)
−0.817137 + 0.576444i \(0.804440\pi\)
\(770\) −12.2191 −0.440346
\(771\) −33.1978 −1.19559
\(772\) 0.416108i 0.0149761i
\(773\) 11.6707i 0.419767i 0.977726 + 0.209884i \(0.0673085\pi\)
−0.977726 + 0.209884i \(0.932691\pi\)
\(774\) 3.27980i 0.117890i
\(775\) 3.96739i 0.142513i
\(776\) 18.3401 0.658372
\(777\) −17.4803 −0.627101
\(778\) 10.8282i 0.388210i
\(779\) −38.2321 −1.36981
\(780\) 0.0521697 0.134790i 0.00186798 0.00482627i
\(781\) −27.7885 −0.994352
\(782\) 30.1279i 1.07737i
\(783\) −31.3183