Properties

Label 690.3.g.a.461.13
Level $690$
Weight $3$
Character 690.461
Analytic conductor $18.801$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 461.13
Character \(\chi\) \(=\) 690.461
Dual form 690.3.g.a.461.14

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-1.34299 - 2.68261i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-3.79378 + 1.89928i) q^{6} -8.50482 q^{7} +2.82843i q^{8} +(-5.39274 + 7.20544i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(-1.34299 - 2.68261i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-3.79378 + 1.89928i) q^{6} -8.50482 q^{7} +2.82843i q^{8} +(-5.39274 + 7.20544i) q^{9} -3.16228 q^{10} -13.2166i q^{11} +(2.68599 + 5.36521i) q^{12} +3.60104 q^{13} +12.0276i q^{14} +(-5.99849 + 3.00302i) q^{15} +4.00000 q^{16} +0.776501i q^{17} +(10.1900 + 7.62649i) q^{18} -36.7798 q^{19} +4.47214i q^{20} +(11.4219 + 22.8151i) q^{21} -18.6911 q^{22} +4.79583i q^{23} +(7.58755 - 3.79856i) q^{24} -5.00000 q^{25} -5.09264i q^{26} +(26.5718 + 4.78975i) q^{27} +17.0096 q^{28} +25.4478i q^{29} +(4.24692 + 8.48314i) q^{30} +34.1895 q^{31} -5.65685i q^{32} +(-35.4549 + 17.7498i) q^{33} +1.09814 q^{34} +19.0174i q^{35} +(10.7855 - 14.4109i) q^{36} +33.7342 q^{37} +52.0144i q^{38} +(-4.83617 - 9.66016i) q^{39} +6.32456 q^{40} +41.1741i q^{41} +(32.2654 - 16.1530i) q^{42} +30.1714 q^{43} +26.4332i q^{44} +(16.1118 + 12.0585i) q^{45} +6.78233 q^{46} +6.22979i q^{47} +(-5.37197 - 10.7304i) q^{48} +23.3320 q^{49} +7.07107i q^{50} +(2.08305 - 1.04284i) q^{51} -7.20208 q^{52} -15.6386i q^{53} +(6.77372 - 37.5781i) q^{54} -29.5532 q^{55} -24.0553i q^{56} +(49.3949 + 98.6656i) q^{57} +35.9886 q^{58} -70.7460i q^{59} +(11.9970 - 6.00605i) q^{60} -71.2693 q^{61} -48.3513i q^{62} +(45.8643 - 61.2810i) q^{63} -8.00000 q^{64} -8.05217i q^{65} +(25.1020 + 50.1408i) q^{66} -107.782 q^{67} -1.55300i q^{68} +(12.8653 - 6.44077i) q^{69} +26.8946 q^{70} -110.094i q^{71} +(-20.3801 - 15.2530i) q^{72} +86.0156 q^{73} -47.7074i q^{74} +(6.71496 + 13.4130i) q^{75} +73.5595 q^{76} +112.405i q^{77} +(-13.6615 + 6.83937i) q^{78} +72.6189 q^{79} -8.94427i q^{80} +(-22.8367 - 77.7141i) q^{81} +58.2290 q^{82} +150.313i q^{83} +(-22.8438 - 45.6302i) q^{84} +1.73631 q^{85} -42.6687i q^{86} +(68.2664 - 34.1762i) q^{87} +37.3822 q^{88} +135.965i q^{89} +(17.0533 - 22.7856i) q^{90} -30.6262 q^{91} -9.59166i q^{92} +(-45.9163 - 91.7170i) q^{93} +8.81025 q^{94} +82.2420i q^{95} +(-15.1751 + 7.59711i) q^{96} +187.823 q^{97} -32.9965i q^{98} +(95.2313 + 71.2736i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + O(q^{10}) \) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + 16q^{12} + 80q^{13} - 40q^{15} + 224q^{16} - 32q^{18} - 64q^{19} + 56q^{21} - 96q^{22} - 32q^{24} - 280q^{25} + 40q^{27} + 32q^{28} - 80q^{31} + 32q^{33} + 192q^{34} + 240q^{37} - 56q^{39} - 144q^{43} - 32q^{48} + 72q^{49} - 24q^{51} - 160q^{52} + 16q^{54} - 16q^{57} + 80q^{60} + 112q^{61} - 64q^{63} - 448q^{64} + 160q^{66} + 832q^{67} + 64q^{72} - 608q^{73} + 40q^{75} + 128q^{76} - 320q^{78} + 48q^{79} - 32q^{81} - 448q^{82} - 112q^{84} + 240q^{85} + 200q^{87} + 192q^{88} + 80q^{91} - 232q^{93} + 160q^{94} + 64q^{96} - 448q^{97} + 464q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) −1.34299 2.68261i −0.447664 0.894202i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) −3.79378 + 1.89928i −0.632296 + 0.316546i
\(7\) −8.50482 −1.21497 −0.607487 0.794329i \(-0.707822\pi\)
−0.607487 + 0.794329i \(0.707822\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −5.39274 + 7.20544i −0.599194 + 0.800604i
\(10\) −3.16228 −0.316228
\(11\) 13.2166i 1.20151i −0.799434 0.600754i \(-0.794867\pi\)
0.799434 0.600754i \(-0.205133\pi\)
\(12\) 2.68599 + 5.36521i 0.223832 + 0.447101i
\(13\) 3.60104 0.277003 0.138501 0.990362i \(-0.455771\pi\)
0.138501 + 0.990362i \(0.455771\pi\)
\(14\) 12.0276i 0.859117i
\(15\) −5.99849 + 3.00302i −0.399899 + 0.200202i
\(16\) 4.00000 0.250000
\(17\) 0.776501i 0.0456765i 0.999739 + 0.0228383i \(0.00727028\pi\)
−0.999739 + 0.0228383i \(0.992730\pi\)
\(18\) 10.1900 + 7.62649i 0.566113 + 0.423694i
\(19\) −36.7798 −1.93578 −0.967888 0.251380i \(-0.919116\pi\)
−0.967888 + 0.251380i \(0.919116\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 11.4219 + 22.8151i 0.543901 + 1.08643i
\(22\) −18.6911 −0.849594
\(23\) 4.79583i 0.208514i
\(24\) 7.58755 3.79856i 0.316148 0.158273i
\(25\) −5.00000 −0.200000
\(26\) 5.09264i 0.195871i
\(27\) 26.5718 + 4.78975i 0.984139 + 0.177398i
\(28\) 17.0096 0.607487
\(29\) 25.4478i 0.877511i 0.898607 + 0.438755i \(0.144581\pi\)
−0.898607 + 0.438755i \(0.855419\pi\)
\(30\) 4.24692 + 8.48314i 0.141564 + 0.282771i
\(31\) 34.1895 1.10289 0.551444 0.834212i \(-0.314077\pi\)
0.551444 + 0.834212i \(0.314077\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −35.4549 + 17.7498i −1.07439 + 0.537872i
\(34\) 1.09814 0.0322982
\(35\) 19.0174i 0.543353i
\(36\) 10.7855 14.4109i 0.299597 0.400302i
\(37\) 33.7342 0.911736 0.455868 0.890047i \(-0.349329\pi\)
0.455868 + 0.890047i \(0.349329\pi\)
\(38\) 52.0144i 1.36880i
\(39\) −4.83617 9.66016i −0.124004 0.247697i
\(40\) 6.32456 0.158114
\(41\) 41.1741i 1.00425i 0.864796 + 0.502124i \(0.167448\pi\)
−0.864796 + 0.502124i \(0.832552\pi\)
\(42\) 32.2654 16.1530i 0.768224 0.384596i
\(43\) 30.1714 0.701659 0.350830 0.936439i \(-0.385900\pi\)
0.350830 + 0.936439i \(0.385900\pi\)
\(44\) 26.4332i 0.600754i
\(45\) 16.1118 + 12.0585i 0.358041 + 0.267967i
\(46\) 6.78233 0.147442
\(47\) 6.22979i 0.132549i 0.997801 + 0.0662743i \(0.0211112\pi\)
−0.997801 + 0.0662743i \(0.978889\pi\)
\(48\) −5.37197 10.7304i −0.111916 0.223550i
\(49\) 23.3320 0.476164
\(50\) 7.07107i 0.141421i
\(51\) 2.08305 1.04284i 0.0408440 0.0204478i
\(52\) −7.20208 −0.138501
\(53\) 15.6386i 0.295068i −0.989057 0.147534i \(-0.952866\pi\)
0.989057 0.147534i \(-0.0471336\pi\)
\(54\) 6.77372 37.5781i 0.125439 0.695891i
\(55\) −29.5532 −0.537331
\(56\) 24.0553i 0.429558i
\(57\) 49.3949 + 98.6656i 0.866578 + 1.73097i
\(58\) 35.9886 0.620494
\(59\) 70.7460i 1.19908i −0.800343 0.599542i \(-0.795349\pi\)
0.800343 0.599542i \(-0.204651\pi\)
\(60\) 11.9970 6.00605i 0.199950 0.100101i
\(61\) −71.2693 −1.16835 −0.584174 0.811628i \(-0.698582\pi\)
−0.584174 + 0.811628i \(0.698582\pi\)
\(62\) 48.3513i 0.779860i
\(63\) 45.8643 61.2810i 0.728005 0.972714i
\(64\) −8.00000 −0.125000
\(65\) 8.05217i 0.123879i
\(66\) 25.1020 + 50.1408i 0.380333 + 0.759709i
\(67\) −107.782 −1.60869 −0.804346 0.594162i \(-0.797484\pi\)
−0.804346 + 0.594162i \(0.797484\pi\)
\(68\) 1.55300i 0.0228383i
\(69\) 12.8653 6.44077i 0.186454 0.0933444i
\(70\) 26.8946 0.384209
\(71\) 110.094i 1.55062i −0.631581 0.775310i \(-0.717594\pi\)
0.631581 0.775310i \(-0.282406\pi\)
\(72\) −20.3801 15.2530i −0.283056 0.211847i
\(73\) 86.0156 1.17830 0.589148 0.808025i \(-0.299464\pi\)
0.589148 + 0.808025i \(0.299464\pi\)
\(74\) 47.7074i 0.644695i
\(75\) 6.71496 + 13.4130i 0.0895328 + 0.178840i
\(76\) 73.5595 0.967888
\(77\) 112.405i 1.45980i
\(78\) −13.6615 + 6.83937i −0.175148 + 0.0876843i
\(79\) 72.6189 0.919227 0.459614 0.888119i \(-0.347988\pi\)
0.459614 + 0.888119i \(0.347988\pi\)
\(80\) 8.94427i 0.111803i
\(81\) −22.8367 77.7141i −0.281934 0.959434i
\(82\) 58.2290 0.710110
\(83\) 150.313i 1.81100i 0.424350 + 0.905498i \(0.360503\pi\)
−0.424350 + 0.905498i \(0.639497\pi\)
\(84\) −22.8438 45.6302i −0.271950 0.543216i
\(85\) 1.73631 0.0204272
\(86\) 42.6687i 0.496148i
\(87\) 68.2664 34.1762i 0.784672 0.392830i
\(88\) 37.3822 0.424797
\(89\) 135.965i 1.52770i 0.645396 + 0.763849i \(0.276693\pi\)
−0.645396 + 0.763849i \(0.723307\pi\)
\(90\) 17.0533 22.7856i 0.189482 0.253173i
\(91\) −30.6262 −0.336552
\(92\) 9.59166i 0.104257i
\(93\) −45.9163 91.7170i −0.493723 0.986204i
\(94\) 8.81025 0.0937260
\(95\) 82.2420i 0.865706i
\(96\) −15.1751 + 7.59711i −0.158074 + 0.0791366i
\(97\) 187.823 1.93632 0.968160 0.250331i \(-0.0805396\pi\)
0.968160 + 0.250331i \(0.0805396\pi\)
\(98\) 32.9965i 0.336699i
\(99\) 95.2313 + 71.2736i 0.961932 + 0.719936i
\(100\) 10.0000 0.100000
\(101\) 44.1749i 0.437375i −0.975795 0.218687i \(-0.929822\pi\)
0.975795 0.218687i \(-0.0701775\pi\)
\(102\) −1.47479 2.94587i −0.0144587 0.0288811i
\(103\) −50.1604 −0.486994 −0.243497 0.969902i \(-0.578295\pi\)
−0.243497 + 0.969902i \(0.578295\pi\)
\(104\) 10.1853i 0.0979353i
\(105\) 51.0161 25.5402i 0.485867 0.243240i
\(106\) −22.1163 −0.208645
\(107\) 156.326i 1.46099i 0.682917 + 0.730496i \(0.260711\pi\)
−0.682917 + 0.730496i \(0.739289\pi\)
\(108\) −53.1435 9.57949i −0.492070 0.0886990i
\(109\) −199.822 −1.83322 −0.916612 0.399777i \(-0.869088\pi\)
−0.916612 + 0.399777i \(0.869088\pi\)
\(110\) 41.7945i 0.379950i
\(111\) −45.3048 90.4957i −0.408152 0.815276i
\(112\) −34.0193 −0.303744
\(113\) 9.47173i 0.0838207i 0.999121 + 0.0419103i \(0.0133444\pi\)
−0.999121 + 0.0419103i \(0.986656\pi\)
\(114\) 139.534 69.8550i 1.22398 0.612763i
\(115\) 10.7238 0.0932505
\(116\) 50.8956i 0.438755i
\(117\) −19.4195 + 25.9471i −0.165978 + 0.221770i
\(118\) −100.050 −0.847880
\(119\) 6.60401i 0.0554959i
\(120\) −8.49383 16.9663i −0.0707819 0.141386i
\(121\) −53.6782 −0.443621
\(122\) 100.790i 0.826147i
\(123\) 110.454 55.2966i 0.897999 0.449565i
\(124\) −68.3791 −0.551444
\(125\) 11.1803i 0.0894427i
\(126\) −86.6644 64.8619i −0.687813 0.514777i
\(127\) 87.0946 0.685784 0.342892 0.939375i \(-0.388594\pi\)
0.342892 + 0.939375i \(0.388594\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −40.5199 80.9378i −0.314108 0.627425i
\(130\) −11.3875 −0.0875960
\(131\) 55.2935i 0.422088i 0.977477 + 0.211044i \(0.0676863\pi\)
−0.977477 + 0.211044i \(0.932314\pi\)
\(132\) 70.9098 35.4996i 0.537195 0.268936i
\(133\) 312.805 2.35192
\(134\) 152.427i 1.13752i
\(135\) 10.7102 59.4163i 0.0793348 0.440120i
\(136\) −2.19628 −0.0161491
\(137\) 128.257i 0.936181i 0.883681 + 0.468090i \(0.155058\pi\)
−0.883681 + 0.468090i \(0.844942\pi\)
\(138\) −9.10862 18.1943i −0.0660045 0.131843i
\(139\) −142.423 −1.02463 −0.512313 0.858799i \(-0.671211\pi\)
−0.512313 + 0.858799i \(0.671211\pi\)
\(140\) 38.0347i 0.271677i
\(141\) 16.7121 8.36656i 0.118525 0.0593373i
\(142\) −155.696 −1.09645
\(143\) 47.5934i 0.332821i
\(144\) −21.5710 + 28.8218i −0.149798 + 0.200151i
\(145\) 56.9030 0.392435
\(146\) 121.644i 0.833181i
\(147\) −31.3347 62.5906i −0.213161 0.425786i
\(148\) −67.4685 −0.455868
\(149\) 143.307i 0.961793i 0.876777 + 0.480897i \(0.159689\pi\)
−0.876777 + 0.480897i \(0.840311\pi\)
\(150\) 18.9689 9.49639i 0.126459 0.0633093i
\(151\) −146.838 −0.972439 −0.486219 0.873837i \(-0.661624\pi\)
−0.486219 + 0.873837i \(0.661624\pi\)
\(152\) 104.029i 0.684400i
\(153\) −5.59503 4.18747i −0.0365688 0.0273691i
\(154\) 158.964 1.03224
\(155\) 76.4501i 0.493226i
\(156\) 9.67234 + 19.3203i 0.0620022 + 0.123848i
\(157\) −200.244 −1.27544 −0.637720 0.770269i \(-0.720122\pi\)
−0.637720 + 0.770269i \(0.720122\pi\)
\(158\) 102.699i 0.649992i
\(159\) −41.9522 + 21.0025i −0.263850 + 0.132091i
\(160\) −12.6491 −0.0790569
\(161\) 40.7877i 0.253340i
\(162\) −109.904 + 32.2959i −0.678422 + 0.199358i
\(163\) −185.503 −1.13805 −0.569027 0.822319i \(-0.692680\pi\)
−0.569027 + 0.822319i \(0.692680\pi\)
\(164\) 82.3483i 0.502124i
\(165\) 39.6897 + 79.2795i 0.240544 + 0.480482i
\(166\) 212.574 1.28057
\(167\) 158.560i 0.949462i 0.880131 + 0.474731i \(0.157455\pi\)
−0.880131 + 0.474731i \(0.842545\pi\)
\(168\) −64.5308 + 32.3061i −0.384112 + 0.192298i
\(169\) −156.033 −0.923269
\(170\) 2.45551i 0.0144442i
\(171\) 198.344 265.014i 1.15990 1.54979i
\(172\) −60.3427 −0.350830
\(173\) 55.2641i 0.319446i −0.987162 0.159723i \(-0.948940\pi\)
0.987162 0.159723i \(-0.0510601\pi\)
\(174\) −48.3325 96.5433i −0.277773 0.554847i
\(175\) 42.5241 0.242995
\(176\) 52.8663i 0.300377i
\(177\) −189.783 + 95.0113i −1.07222 + 0.536787i
\(178\) 192.284 1.08024
\(179\) 103.383i 0.577558i −0.957396 0.288779i \(-0.906751\pi\)
0.957396 0.288779i \(-0.0932493\pi\)
\(180\) −32.2237 24.1171i −0.179021 0.133984i
\(181\) −161.443 −0.891949 −0.445974 0.895046i \(-0.647143\pi\)
−0.445974 + 0.895046i \(0.647143\pi\)
\(182\) 43.3120i 0.237978i
\(183\) 95.7141 + 191.187i 0.523028 + 1.04474i
\(184\) −13.5647 −0.0737210
\(185\) 75.4321i 0.407741i
\(186\) −129.707 + 64.9354i −0.697352 + 0.349115i
\(187\) 10.2627 0.0548807
\(188\) 12.4596i 0.0662743i
\(189\) −225.988 40.7359i −1.19570 0.215534i
\(190\) 116.308 0.612146
\(191\) 57.0826i 0.298862i 0.988772 + 0.149431i \(0.0477442\pi\)
−0.988772 + 0.149431i \(0.952256\pi\)
\(192\) 10.7439 + 21.4608i 0.0559580 + 0.111775i
\(193\) −106.150 −0.549998 −0.274999 0.961445i \(-0.588678\pi\)
−0.274999 + 0.961445i \(0.588678\pi\)
\(194\) 265.622i 1.36919i
\(195\) −21.6008 + 10.8140i −0.110773 + 0.0554564i
\(196\) −46.6640 −0.238082
\(197\) 188.120i 0.954925i 0.878652 + 0.477463i \(0.158443\pi\)
−0.878652 + 0.477463i \(0.841557\pi\)
\(198\) 100.796 134.677i 0.509071 0.680189i
\(199\) −258.348 −1.29823 −0.649115 0.760691i \(-0.724860\pi\)
−0.649115 + 0.760691i \(0.724860\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) 144.751 + 289.137i 0.720154 + 1.43849i
\(202\) −62.4727 −0.309271
\(203\) 216.429i 1.06615i
\(204\) −4.16609 + 2.08567i −0.0204220 + 0.0102239i
\(205\) 92.0682 0.449113
\(206\) 70.9376i 0.344357i
\(207\) −34.5561 25.8627i −0.166938 0.124940i
\(208\) 14.4042 0.0692507
\(209\) 486.103i 2.32585i
\(210\) −36.1193 72.1476i −0.171997 0.343560i
\(211\) −8.22042 −0.0389593 −0.0194797 0.999810i \(-0.506201\pi\)
−0.0194797 + 0.999810i \(0.506201\pi\)
\(212\) 31.2772i 0.147534i
\(213\) −295.339 + 147.855i −1.38657 + 0.694157i
\(214\) 221.078 1.03308
\(215\) 67.4652i 0.313792i
\(216\) −13.5474 + 75.1563i −0.0627197 + 0.347946i
\(217\) −290.776 −1.33998
\(218\) 282.590i 1.29629i
\(219\) −115.518 230.746i −0.527481 1.05363i
\(220\) 59.1064 0.268665
\(221\) 2.79621i 0.0126525i
\(222\) −127.980 + 64.0707i −0.576487 + 0.288607i
\(223\) 134.067 0.601198 0.300599 0.953751i \(-0.402813\pi\)
0.300599 + 0.953751i \(0.402813\pi\)
\(224\) 48.1105i 0.214779i
\(225\) 26.9637 36.0272i 0.119839 0.160121i
\(226\) 13.3951 0.0592702
\(227\) 252.146i 1.11078i 0.831591 + 0.555388i \(0.187430\pi\)
−0.831591 + 0.555388i \(0.812570\pi\)
\(228\) −98.7899 197.331i −0.433289 0.865487i
\(229\) −405.638 −1.77134 −0.885672 0.464312i \(-0.846302\pi\)
−0.885672 + 0.464312i \(0.846302\pi\)
\(230\) 15.1658i 0.0659380i
\(231\) 301.538 150.959i 1.30536 0.653501i
\(232\) −71.9773 −0.310247
\(233\) 176.120i 0.755879i 0.925830 + 0.377940i \(0.123367\pi\)
−0.925830 + 0.377940i \(0.876633\pi\)
\(234\) 36.6947 + 27.4633i 0.156815 + 0.117364i
\(235\) 13.9302 0.0592776
\(236\) 141.492i 0.599542i
\(237\) −97.5267 194.808i −0.411505 0.821974i
\(238\) −9.33948 −0.0392415
\(239\) 52.4894i 0.219621i −0.993953 0.109810i \(-0.964976\pi\)
0.993953 0.109810i \(-0.0350244\pi\)
\(240\) −23.9940 + 12.0121i −0.0999748 + 0.0500504i
\(241\) 240.203 0.996692 0.498346 0.866978i \(-0.333941\pi\)
0.498346 + 0.866978i \(0.333941\pi\)
\(242\) 75.9124i 0.313688i
\(243\) −177.807 + 165.631i −0.731715 + 0.681610i
\(244\) 142.539 0.584174
\(245\) 52.1720i 0.212947i
\(246\) −78.2011 156.205i −0.317891 0.634982i
\(247\) −132.445 −0.536216
\(248\) 96.7026i 0.389930i
\(249\) 403.230 201.869i 1.61940 0.810718i
\(250\) 15.8114 0.0632456
\(251\) 207.455i 0.826514i −0.910614 0.413257i \(-0.864391\pi\)
0.910614 0.413257i \(-0.135609\pi\)
\(252\) −91.7286 + 122.562i −0.364002 + 0.486357i
\(253\) 63.3845 0.250532
\(254\) 123.170i 0.484922i
\(255\) −2.33185 4.65783i −0.00914451 0.0182660i
\(256\) 16.0000 0.0625000
\(257\) 97.7262i 0.380257i −0.981759 0.190129i \(-0.939109\pi\)
0.981759 0.190129i \(-0.0608905\pi\)
\(258\) −114.463 + 57.3038i −0.443657 + 0.222108i
\(259\) −286.904 −1.10774
\(260\) 16.1043i 0.0619397i
\(261\) −183.363 137.233i −0.702539 0.525799i
\(262\) 78.1968 0.298461
\(263\) 93.5480i 0.355696i −0.984058 0.177848i \(-0.943086\pi\)
0.984058 0.177848i \(-0.0569135\pi\)
\(264\) −50.2040 100.282i −0.190167 0.379854i
\(265\) −34.9690 −0.131958
\(266\) 442.374i 1.66306i
\(267\) 364.741 182.600i 1.36607 0.683895i
\(268\) 215.565 0.804346
\(269\) 213.987i 0.795492i 0.917496 + 0.397746i \(0.130207\pi\)
−0.917496 + 0.397746i \(0.869793\pi\)
\(270\) −84.0273 15.1465i −0.311212 0.0560982i
\(271\) 287.786 1.06194 0.530970 0.847391i \(-0.321828\pi\)
0.530970 + 0.847391i \(0.321828\pi\)
\(272\) 3.10601i 0.0114191i
\(273\) 41.1308 + 82.1580i 0.150662 + 0.300945i
\(274\) 181.382 0.661980
\(275\) 66.0829i 0.240302i
\(276\) −25.7306 + 12.8815i −0.0932270 + 0.0466722i
\(277\) 122.451 0.442060 0.221030 0.975267i \(-0.429058\pi\)
0.221030 + 0.975267i \(0.429058\pi\)
\(278\) 201.417i 0.724520i
\(279\) −184.375 + 246.351i −0.660843 + 0.882977i
\(280\) −53.7892 −0.192104
\(281\) 180.885i 0.643718i −0.946788 0.321859i \(-0.895692\pi\)
0.946788 0.321859i \(-0.104308\pi\)
\(282\) −11.8321 23.6344i −0.0419578 0.0838100i
\(283\) 156.462 0.552869 0.276435 0.961033i \(-0.410847\pi\)
0.276435 + 0.961033i \(0.410847\pi\)
\(284\) 220.188i 0.775310i
\(285\) 220.623 110.450i 0.774116 0.387545i
\(286\) −67.3073 −0.235340
\(287\) 350.179i 1.22013i
\(288\) 40.7601 + 30.5060i 0.141528 + 0.105923i
\(289\) 288.397 0.997914
\(290\) 80.4730i 0.277493i
\(291\) −252.245 503.855i −0.866821 1.73146i
\(292\) −172.031 −0.589148
\(293\) 2.88676i 0.00985241i −0.999988 0.00492620i \(-0.998432\pi\)
0.999988 0.00492620i \(-0.00156807\pi\)
\(294\) −88.5165 + 44.3140i −0.301076 + 0.150728i
\(295\) −158.193 −0.536247
\(296\) 95.4149i 0.322347i
\(297\) 63.3041 351.188i 0.213145 1.18245i
\(298\) 202.667 0.680090
\(299\) 17.2700i 0.0577591i
\(300\) −13.4299 26.8261i −0.0447664 0.0894202i
\(301\) −256.602 −0.852498
\(302\) 207.661i 0.687618i
\(303\) −118.504 + 59.3265i −0.391101 + 0.195797i
\(304\) −147.119 −0.483944
\(305\) 159.363i 0.522501i
\(306\) −5.92198 + 7.91257i −0.0193529 + 0.0258581i
\(307\) −271.452 −0.884207 −0.442104 0.896964i \(-0.645768\pi\)
−0.442104 + 0.896964i \(0.645768\pi\)
\(308\) 224.809i 0.729901i
\(309\) 67.3651 + 134.561i 0.218010 + 0.435471i
\(310\) −108.117 −0.348764
\(311\) 198.082i 0.636918i −0.947937 0.318459i \(-0.896835\pi\)
0.947937 0.318459i \(-0.103165\pi\)
\(312\) 27.3231 13.6787i 0.0875740 0.0438421i
\(313\) −67.5994 −0.215973 −0.107986 0.994152i \(-0.534440\pi\)
−0.107986 + 0.994152i \(0.534440\pi\)
\(314\) 283.188i 0.901872i
\(315\) −137.028 102.556i −0.435011 0.325574i
\(316\) −145.238 −0.459614
\(317\) 397.841i 1.25502i 0.778609 + 0.627509i \(0.215926\pi\)
−0.778609 + 0.627509i \(0.784074\pi\)
\(318\) 29.7021 + 59.3294i 0.0934028 + 0.186570i
\(319\) 336.333 1.05434
\(320\) 17.8885i 0.0559017i
\(321\) 419.361 209.945i 1.30642 0.654034i
\(322\) −57.6825 −0.179138
\(323\) 28.5595i 0.0884196i
\(324\) 45.6734 + 155.428i 0.140967 + 0.479717i
\(325\) −18.0052 −0.0554006
\(326\) 262.341i 0.804726i
\(327\) 268.359 + 536.042i 0.820669 + 1.63927i
\(328\) −116.458 −0.355055
\(329\) 52.9832i 0.161043i
\(330\) 112.118 56.1297i 0.339752 0.170090i
\(331\) −426.686 −1.28908 −0.644540 0.764570i \(-0.722951\pi\)
−0.644540 + 0.764570i \(0.722951\pi\)
\(332\) 300.625i 0.905498i
\(333\) −181.920 + 243.070i −0.546307 + 0.729940i
\(334\) 224.238 0.671371
\(335\) 241.009i 0.719429i
\(336\) 45.6877 + 91.2603i 0.135975 + 0.271608i
\(337\) −480.323 −1.42529 −0.712646 0.701524i \(-0.752503\pi\)
−0.712646 + 0.701524i \(0.752503\pi\)
\(338\) 220.663i 0.652850i
\(339\) 25.4089 12.7205i 0.0749526 0.0375235i
\(340\) −3.47262 −0.0102136
\(341\) 451.869i 1.32513i
\(342\) −374.787 280.500i −1.09587 0.820177i
\(343\) 218.302 0.636448
\(344\) 85.3375i 0.248074i
\(345\) −14.4020 28.7677i −0.0417449 0.0833847i
\(346\) −78.1553 −0.225882
\(347\) 397.363i 1.14514i −0.819857 0.572569i \(-0.805947\pi\)
0.819857 0.572569i \(-0.194053\pi\)
\(348\) −136.533 + 68.3524i −0.392336 + 0.196415i
\(349\) 504.033 1.44422 0.722110 0.691778i \(-0.243172\pi\)
0.722110 + 0.691778i \(0.243172\pi\)
\(350\) 60.1382i 0.171823i
\(351\) 95.6859 + 17.2481i 0.272609 + 0.0491398i
\(352\) −74.7643 −0.212399
\(353\) 567.131i 1.60660i −0.595572 0.803302i \(-0.703075\pi\)
0.595572 0.803302i \(-0.296925\pi\)
\(354\) 134.366 + 268.394i 0.379566 + 0.758176i
\(355\) −246.178 −0.693458
\(356\) 271.930i 0.763849i
\(357\) −17.7159 + 8.86913i −0.0496245 + 0.0248435i
\(358\) −146.206 −0.408395
\(359\) 296.132i 0.824881i 0.910984 + 0.412441i \(0.135324\pi\)
−0.910984 + 0.412441i \(0.864676\pi\)
\(360\) −34.1067 + 45.5712i −0.0947408 + 0.126587i
\(361\) 991.751 2.74723
\(362\) 228.315i 0.630703i
\(363\) 72.0894 + 143.997i 0.198593 + 0.396687i
\(364\) 61.2524 0.168276
\(365\) 192.337i 0.526950i
\(366\) 270.380 135.360i 0.738742 0.369837i
\(367\) −28.7924 −0.0784535 −0.0392268 0.999230i \(-0.512489\pi\)
−0.0392268 + 0.999230i \(0.512489\pi\)
\(368\) 19.1833i 0.0521286i
\(369\) −296.678 222.041i −0.804004 0.601738i
\(370\) −106.677 −0.288316
\(371\) 133.004i 0.358500i
\(372\) 91.8326 + 183.434i 0.246862 + 0.493102i
\(373\) −215.231 −0.577026 −0.288513 0.957476i \(-0.593161\pi\)
−0.288513 + 0.957476i \(0.593161\pi\)
\(374\) 14.5136i 0.0388065i
\(375\) 29.9924 15.0151i 0.0799798 0.0400403i
\(376\) −17.6205 −0.0468630
\(377\) 91.6385i 0.243073i
\(378\) −57.6093 + 319.595i −0.152406 + 0.845491i
\(379\) −557.330 −1.47053 −0.735264 0.677781i \(-0.762942\pi\)
−0.735264 + 0.677781i \(0.762942\pi\)
\(380\) 164.484i 0.432853i
\(381\) −116.967 233.640i −0.307001 0.613229i
\(382\) 80.7270 0.211327
\(383\) 27.7534i 0.0724631i −0.999343 0.0362316i \(-0.988465\pi\)
0.999343 0.0362316i \(-0.0115354\pi\)
\(384\) 30.3502 15.1942i 0.0790370 0.0395683i
\(385\) 251.345 0.652843
\(386\) 150.118i 0.388907i
\(387\) −162.706 + 217.398i −0.420430 + 0.561751i
\(388\) −375.646 −0.968160
\(389\) 352.556i 0.906312i 0.891431 + 0.453156i \(0.149702\pi\)
−0.891431 + 0.453156i \(0.850298\pi\)
\(390\) 15.2933 + 30.5481i 0.0392136 + 0.0783285i
\(391\) −3.72397 −0.00952422
\(392\) 65.9929i 0.168349i
\(393\) 148.331 74.2587i 0.377431 0.188953i
\(394\) 266.042 0.675234
\(395\) 162.381i 0.411091i
\(396\) −190.463 142.547i −0.480966 0.359968i
\(397\) 0.224835 0.000566334 0.000283167 1.00000i \(-0.499910\pi\)
0.000283167 1.00000i \(0.499910\pi\)
\(398\) 365.359i 0.917987i
\(399\) −420.095 839.133i −1.05287 2.10309i
\(400\) −20.0000 −0.0500000
\(401\) 442.929i 1.10456i −0.833658 0.552280i \(-0.813758\pi\)
0.833658 0.552280i \(-0.186242\pi\)
\(402\) 408.902 204.709i 1.01717 0.509225i
\(403\) 123.118 0.305503
\(404\) 88.3497i 0.218687i
\(405\) −173.774 + 51.0644i −0.429072 + 0.126085i
\(406\) −306.077 −0.753884
\(407\) 445.852i 1.09546i
\(408\) 2.94958 + 5.89175i 0.00722937 + 0.0144406i
\(409\) 69.2653 0.169353 0.0846764 0.996409i \(-0.473014\pi\)
0.0846764 + 0.996409i \(0.473014\pi\)
\(410\) 130.204i 0.317571i
\(411\) 344.062 172.248i 0.837134 0.419095i
\(412\) 100.321 0.243497
\(413\) 601.682i 1.45686i
\(414\) −36.5754 + 48.8697i −0.0883463 + 0.118043i
\(415\) 336.109 0.809902
\(416\) 20.3706i 0.0489677i
\(417\) 191.273 + 382.065i 0.458688 + 0.916222i
\(418\) 687.453 1.64463
\(419\) 776.330i 1.85282i −0.376522 0.926408i \(-0.622880\pi\)
0.376522 0.926408i \(-0.377120\pi\)
\(420\) −102.032 + 51.0804i −0.242934 + 0.121620i
\(421\) −700.311 −1.66345 −0.831723 0.555190i \(-0.812645\pi\)
−0.831723 + 0.555190i \(0.812645\pi\)
\(422\) 11.6254i 0.0275484i
\(423\) −44.8883 33.5956i −0.106119 0.0794223i
\(424\) 44.2327 0.104322
\(425\) 3.88251i 0.00913531i
\(426\) 209.099 + 417.672i 0.490843 + 0.980451i
\(427\) 606.133 1.41951
\(428\) 312.652i 0.730496i
\(429\) −127.674 + 63.9176i −0.297609 + 0.148992i
\(430\) −95.4102 −0.221884
\(431\) 554.331i 1.28615i 0.765803 + 0.643075i \(0.222342\pi\)
−0.765803 + 0.643075i \(0.777658\pi\)
\(432\) 106.287 + 19.1590i 0.246035 + 0.0443495i
\(433\) 423.019 0.976950 0.488475 0.872578i \(-0.337553\pi\)
0.488475 + 0.872578i \(0.337553\pi\)
\(434\) 411.219i 0.947510i
\(435\) −76.4203 152.648i −0.175679 0.350916i
\(436\) 399.643 0.916612
\(437\) 176.390i 0.403637i
\(438\) −326.324 + 163.368i −0.745032 + 0.372985i
\(439\) 436.088 0.993366 0.496683 0.867932i \(-0.334551\pi\)
0.496683 + 0.867932i \(0.334551\pi\)
\(440\) 83.5890i 0.189975i
\(441\) −125.824 + 168.117i −0.285314 + 0.381219i
\(442\) 3.95444 0.00894670
\(443\) 425.568i 0.960649i −0.877091 0.480325i \(-0.840519\pi\)
0.877091 0.480325i \(-0.159481\pi\)
\(444\) 90.6097 + 180.991i 0.204076 + 0.407638i
\(445\) 304.027 0.683207
\(446\) 189.600i 0.425111i
\(447\) 384.437 192.460i 0.860037 0.430560i
\(448\) 68.0386 0.151872
\(449\) 355.131i 0.790938i 0.918479 + 0.395469i \(0.129418\pi\)
−0.918479 + 0.395469i \(0.870582\pi\)
\(450\) −50.9501 38.1324i −0.113223 0.0847388i
\(451\) 544.181 1.20661
\(452\) 18.9435i 0.0419103i
\(453\) 197.203 + 393.909i 0.435326 + 0.869556i
\(454\) 356.589 0.785438
\(455\) 68.4823i 0.150510i
\(456\) −279.068 + 139.710i −0.611992 + 0.306382i
\(457\) −398.620 −0.872255 −0.436127 0.899885i \(-0.643650\pi\)
−0.436127 + 0.899885i \(0.643650\pi\)
\(458\) 573.658i 1.25253i
\(459\) −3.71924 + 20.6330i −0.00810293 + 0.0449521i
\(460\) −21.4476 −0.0466252
\(461\) 573.580i 1.24421i 0.782935 + 0.622104i \(0.213722\pi\)
−0.782935 + 0.622104i \(0.786278\pi\)
\(462\) −213.488 426.438i −0.462095 0.923027i
\(463\) −268.662 −0.580263 −0.290131 0.956987i \(-0.593699\pi\)
−0.290131 + 0.956987i \(0.593699\pi\)
\(464\) 101.791i 0.219378i
\(465\) −205.085 + 102.672i −0.441044 + 0.220800i
\(466\) 249.071 0.534487
\(467\) 562.394i 1.20427i 0.798394 + 0.602135i \(0.205683\pi\)
−0.798394 + 0.602135i \(0.794317\pi\)
\(468\) 38.8389 51.8941i 0.0829892 0.110885i
\(469\) 916.670 1.95452
\(470\) 19.7003i 0.0419156i
\(471\) 268.926 + 537.175i 0.570968 + 1.14050i
\(472\) 200.100 0.423940
\(473\) 398.762i 0.843049i
\(474\) −275.500 + 137.924i −0.581224 + 0.290978i
\(475\) 183.899 0.387155
\(476\) 13.2080i 0.0277479i
\(477\) 112.683 + 84.3350i 0.236233 + 0.176803i
\(478\) −74.2312 −0.155295
\(479\) 502.529i 1.04912i −0.851373 0.524561i \(-0.824230\pi\)
0.851373 0.524561i \(-0.175770\pi\)
\(480\) 16.9877 + 33.9326i 0.0353910 + 0.0706929i
\(481\) 121.478 0.252554
\(482\) 339.698i 0.704768i
\(483\) −109.417 + 54.7776i −0.226537 + 0.113411i
\(484\) 107.356 0.221811
\(485\) 419.985i 0.865949i
\(486\) 234.238 + 251.457i 0.481971 + 0.517401i
\(487\) 266.197 0.546606 0.273303 0.961928i \(-0.411884\pi\)
0.273303 + 0.961928i \(0.411884\pi\)
\(488\) 201.580i 0.413074i
\(489\) 249.129 + 497.631i 0.509466 + 1.01765i
\(490\) −73.7823 −0.150576
\(491\) 13.7295i 0.0279624i 0.999902 + 0.0139812i \(0.00445049\pi\)
−0.999902 + 0.0139812i \(0.995550\pi\)
\(492\) −220.908 + 110.593i −0.449000 + 0.224783i
\(493\) −19.7603 −0.0400817
\(494\) 187.306i 0.379162i
\(495\) 159.373 212.944i 0.321965 0.430189i
\(496\) 136.758 0.275722
\(497\) 936.330i 1.88396i
\(498\) −285.486 570.253i −0.573265 1.14509i
\(499\) 305.888 0.613002 0.306501 0.951870i \(-0.400842\pi\)
0.306501 + 0.951870i \(0.400842\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 425.354 212.945i 0.849010 0.425040i
\(502\) −293.386 −0.584434
\(503\) 787.569i 1.56574i −0.622183 0.782872i \(-0.713754\pi\)
0.622183 0.782872i \(-0.286246\pi\)
\(504\) 173.329 + 129.724i 0.343906 + 0.257389i
\(505\) −98.7780 −0.195600
\(506\) 89.6393i 0.177153i
\(507\) 209.551 + 418.574i 0.413315 + 0.825589i
\(508\) −174.189 −0.342892
\(509\) 785.384i 1.54299i 0.636233 + 0.771497i \(0.280492\pi\)
−0.636233 + 0.771497i \(0.719508\pi\)
\(510\) −6.58717 + 3.29774i −0.0129160 + 0.00646615i
\(511\) −731.547 −1.43160
\(512\) 22.6274i 0.0441942i
\(513\) −977.303 176.166i −1.90507 0.343403i
\(514\) −138.206 −0.268883
\(515\) 112.162i 0.217791i
\(516\) 81.0398 + 161.876i 0.157054 + 0.313713i
\(517\) 82.3365 0.159258
\(518\) 405.743i 0.783288i
\(519\) −148.252 + 74.2193i −0.285649 + 0.143004i
\(520\) 22.7750 0.0437980
\(521\) 858.879i 1.64852i 0.566211 + 0.824260i \(0.308409\pi\)
−0.566211 + 0.824260i \(0.691591\pi\)
\(522\) −194.077 + 259.314i −0.371796 + 0.496770i
\(523\) −7.44546 −0.0142361 −0.00711803 0.999975i \(-0.502266\pi\)
−0.00711803 + 0.999975i \(0.502266\pi\)
\(524\) 110.587i 0.211044i
\(525\) −57.1096 114.075i −0.108780 0.217287i
\(526\) −132.297 −0.251515
\(527\) 26.5482i 0.0503761i
\(528\) −141.820 + 70.9991i −0.268598 + 0.134468i
\(529\) −23.0000 −0.0434783
\(530\) 49.4536i 0.0933087i
\(531\) 509.756 + 381.515i 0.959992 + 0.718483i
\(532\) −625.611 −1.17596
\(533\) 148.270i 0.278179i
\(534\) −258.235 515.821i −0.483587 0.965957i
\(535\) 349.556 0.653375
\(536\) 304.854i 0.568758i
\(537\) −277.336 + 138.842i −0.516454 + 0.258552i
\(538\) 302.624 0.562497
\(539\) 308.370i 0.572114i
\(540\) −21.4204 + 118.833i −0.0396674 + 0.220060i
\(541\) −90.9543 −0.168123 −0.0840613 0.996461i \(-0.526789\pi\)
−0.0840613 + 0.996461i \(0.526789\pi\)
\(542\) 406.990i 0.750905i
\(543\) 216.816 + 433.087i 0.399294 + 0.797582i
\(544\) 4.39255 0.00807455
\(545\) 446.814i 0.819843i
\(546\) 116.189 58.1677i 0.212800 0.106534i
\(547\) 487.663 0.891522 0.445761 0.895152i \(-0.352933\pi\)
0.445761 + 0.895152i \(0.352933\pi\)
\(548\) 256.514i 0.468090i
\(549\) 384.337 513.526i 0.700067 0.935385i
\(550\) 93.4554 0.169919
\(551\) 935.964i 1.69866i
\(552\) 18.2172 + 36.3886i 0.0330022 + 0.0659214i
\(553\) −617.611 −1.11684
\(554\) 173.171i 0.312584i
\(555\) −202.354 + 101.305i −0.364603 + 0.182531i
\(556\) 284.846 0.512313
\(557\) 571.368i 1.02579i −0.858450 0.512897i \(-0.828572\pi\)
0.858450 0.512897i \(-0.171428\pi\)
\(558\) 348.392 + 260.746i 0.624359 + 0.467287i
\(559\) 108.648 0.194362
\(560\) 76.0695i 0.135838i
\(561\) −13.7827 27.5308i −0.0245681 0.0490744i
\(562\) −255.810 −0.455177
\(563\) 239.855i 0.426031i −0.977049 0.213015i \(-0.931672\pi\)
0.977049 0.213015i \(-0.0683285\pi\)
\(564\) −33.4241 + 16.7331i −0.0592626 + 0.0296686i
\(565\) 21.1794 0.0374857
\(566\) 221.271i 0.390938i
\(567\) 194.222 + 660.945i 0.342543 + 1.16569i
\(568\) 311.393 0.548227
\(569\) 71.0260i 0.124826i 0.998050 + 0.0624130i \(0.0198796\pi\)
−0.998050 + 0.0624130i \(0.980120\pi\)
\(570\) −156.201 312.008i −0.274036 0.547382i
\(571\) 751.566 1.31623 0.658114 0.752919i \(-0.271355\pi\)
0.658114 + 0.752919i \(0.271355\pi\)
\(572\) 95.1869i 0.166411i
\(573\) 153.130 76.6616i 0.267243 0.133790i
\(574\) −495.227 −0.862766
\(575\) 23.9792i 0.0417029i
\(576\) 43.1419 57.6435i 0.0748992 0.100076i
\(577\) 99.6649 0.172729 0.0863647 0.996264i \(-0.472475\pi\)
0.0863647 + 0.996264i \(0.472475\pi\)
\(578\) 407.855i 0.705632i
\(579\) 142.558 + 284.757i 0.246214 + 0.491809i
\(580\) −113.806 −0.196217
\(581\) 1278.38i 2.20032i
\(582\) −712.559 + 356.728i −1.22433 + 0.612935i
\(583\) −206.689 −0.354527
\(584\) 243.289i 0.416590i
\(585\) 58.0194 + 43.4233i 0.0991784 + 0.0742278i
\(586\) −4.08249 −0.00696671
\(587\) 150.122i 0.255744i −0.991791 0.127872i \(-0.959185\pi\)
0.991791 0.127872i \(-0.0408147\pi\)
\(588\) 62.6695 + 125.181i 0.106581 + 0.212893i
\(589\) −1257.48 −2.13494
\(590\) 223.718i 0.379184i
\(591\) 504.652 252.644i 0.853896 0.427486i
\(592\) 134.937 0.227934
\(593\) 482.976i 0.814461i −0.913325 0.407231i \(-0.866495\pi\)
0.913325 0.407231i \(-0.133505\pi\)
\(594\) −496.655 89.5255i −0.836119 0.150716i
\(595\) −14.7670 −0.0248185
\(596\) 286.614i 0.480897i
\(597\) 346.959 + 693.045i 0.581171 + 1.16088i
\(598\) 24.4234 0.0408419
\(599\) 531.979i 0.888112i 0.895999 + 0.444056i \(0.146461\pi\)
−0.895999 + 0.444056i \(0.853539\pi\)
\(600\) −37.9378 + 18.9928i −0.0632296 + 0.0316546i
\(601\) 312.027 0.519180 0.259590 0.965719i \(-0.416413\pi\)
0.259590 + 0.965719i \(0.416413\pi\)
\(602\) 362.890i 0.602807i
\(603\) 581.242 776.619i 0.963917 1.28793i
\(604\) 293.676 0.486219
\(605\) 120.028i 0.198393i
\(606\) 83.9004 + 167.590i 0.138449 + 0.276550i
\(607\) 137.992 0.227335 0.113667 0.993519i \(-0.463740\pi\)
0.113667 + 0.993519i \(0.463740\pi\)
\(608\) 208.058i 0.342200i
\(609\) −580.594 + 290.663i −0.953356 + 0.477279i
\(610\) 225.373 0.369464
\(611\) 22.4337i 0.0367164i
\(612\) 11.1901 + 8.37494i 0.0182844 + 0.0136845i
\(613\) −92.8359 −0.151445 −0.0757226 0.997129i \(-0.524126\pi\)
−0.0757226 + 0.997129i \(0.524126\pi\)
\(614\) 383.891i 0.625229i
\(615\) −123.647 246.983i −0.201052 0.401598i
\(616\) −317.929 −0.516118
\(617\) 954.229i 1.54656i −0.634063 0.773281i \(-0.718614\pi\)
0.634063 0.773281i \(-0.281386\pi\)
\(618\) 190.297 95.2686i 0.307925 0.154156i
\(619\) 36.1660 0.0584265 0.0292132 0.999573i \(-0.490700\pi\)
0.0292132 + 0.999573i \(0.490700\pi\)
\(620\) 152.900i 0.246613i
\(621\) −22.9708 + 127.434i −0.0369900 + 0.205207i
\(622\) −280.130 −0.450369
\(623\) 1156.36i 1.85611i
\(624\) −19.3447 38.6407i −0.0310011 0.0619241i
\(625\) 25.0000 0.0400000
\(626\) 95.6000i 0.152716i
\(627\) 1304.02 652.833i 2.07978 1.04120i
\(628\) 400.488 0.637720
\(629\) 26.1947i 0.0416450i
\(630\) −145.036 + 193.787i −0.230215 + 0.307599i
\(631\) −503.591 −0.798084 −0.399042 0.916933i \(-0.630657\pi\)
−0.399042 + 0.916933i \(0.630657\pi\)
\(632\) 205.397i 0.324996i
\(633\) 11.0400 + 22.0521i 0.0174407 + 0.0348375i
\(634\) 562.632 0.887432
\(635\) 194.749i 0.306692i
\(636\) 83.9044 42.0051i 0.131925 0.0660457i
\(637\) 84.0195 0.131899
\(638\) 475.647i 0.745528i
\(639\) 793.275 + 593.708i 1.24143 + 0.929121i
\(640\) 25.2982 0.0395285
\(641\) 589.686i 0.919947i 0.887933 + 0.459974i \(0.152141\pi\)
−0.887933 + 0.459974i \(0.847859\pi\)
\(642\) −296.907 593.066i −0.462472 0.923779i
\(643\) −53.2769 −0.0828567 −0.0414283 0.999141i \(-0.513191\pi\)
−0.0414283 + 0.999141i \(0.513191\pi\)
\(644\) 81.5754i 0.126670i
\(645\) −180.982 + 90.6053i −0.280593 + 0.140473i
\(646\) −40.3893 −0.0625221
\(647\) 110.016i 0.170040i −0.996379 0.0850202i \(-0.972905\pi\)
0.996379 0.0850202i \(-0.0270955\pi\)
\(648\) 219.809 64.5919i 0.339211 0.0996788i
\(649\) −935.020 −1.44071
\(650\) 25.4632i 0.0391741i
\(651\) 390.510 + 780.037i 0.599862 + 1.19821i
\(652\) 371.006 0.569027
\(653\) 442.472i 0.677599i 0.940859 + 0.338800i \(0.110021\pi\)
−0.940859 + 0.338800i \(0.889979\pi\)
\(654\) 758.078 379.517i 1.15914 0.580301i
\(655\) 123.640 0.188763
\(656\) 164.697i 0.251062i
\(657\) −463.860 + 619.780i −0.706027 + 0.943348i
\(658\) −74.9296 −0.113875
\(659\) 561.159i 0.851531i −0.904833 0.425766i \(-0.860005\pi\)
0.904833 0.425766i \(-0.139995\pi\)
\(660\) −79.3794 158.559i −0.120272 0.240241i
\(661\) −801.121 −1.21198 −0.605992 0.795471i \(-0.707224\pi\)
−0.605992 + 0.795471i \(0.707224\pi\)
\(662\) 603.425i 0.911518i
\(663\) 7.50113 3.75529i 0.0113139 0.00566409i
\(664\) −425.149 −0.640284
\(665\) 699.454i 1.05181i
\(666\) 343.753 + 257.274i 0.516146 + 0.386297i
\(667\) −122.043 −0.182974
\(668\) 317.120i 0.474731i
\(669\) −180.051 359.649i −0.269135 0.537592i
\(670\) 340.838 0.508713
\(671\) 941.937i 1.40378i
\(672\) 129.062 64.6121i 0.192056 0.0961490i
\(673\) −96.4810 −0.143360 −0.0716798 0.997428i \(-0.522836\pi\)
−0.0716798 + 0.997428i \(0.522836\pi\)
\(674\) 679.279i 1.00783i
\(675\) −132.859 23.9487i −0.196828 0.0354796i
\(676\) 312.065 0.461635
\(677\) 314.499i 0.464549i −0.972650 0.232274i \(-0.925383\pi\)
0.972650 0.232274i \(-0.0746167\pi\)
\(678\) −17.9895 35.9336i −0.0265331 0.0529995i
\(679\) −1597.40 −2.35258
\(680\) 4.91103i 0.00722210i
\(681\) 676.409 338.631i 0.993258 0.497255i
\(682\) −639.039 −0.937007
\(683\) 189.054i 0.276800i 0.990376 + 0.138400i \(0.0441959\pi\)
−0.990376 + 0.138400i \(0.955804\pi\)
\(684\) −396.687 + 530.029i −0.579952 + 0.774896i
\(685\) 286.791 0.418673
\(686\) 308.725i 0.450037i
\(687\) 544.768 + 1088.17i 0.792967 + 1.58394i
\(688\) 120.685 0.175415
\(689\) 56.3152i 0.0817347i
\(690\) −40.6837 + 20.3675i −0.0589619 + 0.0295181i
\(691\) −491.731 −0.711622 −0.355811 0.934558i \(-0.615795\pi\)
−0.355811 + 0.934558i \(0.615795\pi\)
\(692\) 110.528i 0.159723i
\(693\) −809.925 606.170i −1.16872 0.874704i
\(694\) −561.955 −0.809734
\(695\) 318.468i 0.458227i
\(696\) 96.6649 + 193.087i 0.138886 + 0.277423i
\(697\) −31.9718 −0.0458705
\(698\) 712.810i 1.02122i
\(699\) 472.460 236.528i 0.675909 0.338380i
\(700\) −85.0482 −0.121497
\(701\) 873.449i 1.24600i −0.782220 0.623002i \(-0.785913\pi\)
0.782220 0.623002i \(-0.214087\pi\)
\(702\) 24.3924 135.320i 0.0347471 0.192764i
\(703\) −1240.74 −1.76492
\(704\) 105.733i 0.150188i
\(705\) −18.7082 37.3693i −0.0265364 0.0530061i
\(706\) −802.045 −1.13604
\(707\) 375.699i 0.531400i
\(708\) 379.567 190.023i 0.536111 0.268393i
\(709\) −1127.06 −1.58965 −0.794825 0.606839i \(-0.792437\pi\)
−0.794825 + 0.606839i \(0.792437\pi\)
\(710\) 348.148i 0.490349i
\(711\) −391.615 + 523.251i −0.550795 + 0.735937i
\(712\) −384.567 −0.540122
\(713\) 163.967i 0.229968i
\(714\) 12.5428 + 25.0541i 0.0175670 + 0.0350898i
\(715\) −106.422 −0.148842
\(716\) 206.766i 0.288779i
\(717\) −140.808 + 70.4929i −0.196385 + 0.0983164i
\(718\) 418.795 0.583279
\(719\) 826.971i 1.15017i 0.818094 + 0.575084i \(0.195031\pi\)
−0.818094 + 0.575084i \(0.804969\pi\)
\(720\) 64.4474 + 48.2341i 0.0895103 + 0.0669919i
\(721\) 426.606 0.591686
\(722\) 1402.55i 1.94259i
\(723\) −322.591 644.369i −0.446184 0.891244i
\(724\) 322.885 0.445974
\(725\) 127.239i 0.175502i
\(726\) 203.643 101.950i 0.280500 0.140427i
\(727\) 587.838 0.808580 0.404290 0.914631i \(-0.367519\pi\)
0.404290 + 0.914631i \(0.367519\pi\)
\(728\) 86.6240i 0.118989i
\(729\) 683.117 + 254.544i 0.937060 + 0.349169i
\(730\) −272.005 −0.372610
\(731\) 23.4281i 0.0320494i
\(732\) −191.428 382.375i −0.261514 0.522370i
\(733\) 240.718 0.328401 0.164200 0.986427i \(-0.447496\pi\)
0.164200 + 0.986427i \(0.447496\pi\)
\(734\) 40.7187i 0.0554750i
\(735\) −139.957 + 70.0666i −0.190417 + 0.0953287i
\(736\) 27.1293 0.0368605
\(737\) 1424.51i 1.93286i
\(738\) −314.014 + 419.566i −0.425493 + 0.568517i
\(739\) 430.770 0.582909 0.291455 0.956585i \(-0.405861\pi\)
0.291455 + 0.956585i \(0.405861\pi\)
\(740\) 150.864i 0.203870i
\(741\) 177.873 + 355.299i 0.240045 + 0.479485i
\(742\) 188.096 0.253498
\(743\) 1255.07i 1.68919i 0.535408 + 0.844594i \(0.320158\pi\)
−0.535408 + 0.844594i \(0.679842\pi\)
\(744\) 259.415 129.871i 0.348676 0.174558i
\(745\) 320.445 0.430127
\(746\) 304.382i 0.408019i
\(747\) −1083.07 810.598i −1.44989 1.08514i
\(748\) −20.5254 −0.0274404
\(749\) 1329.53i 1.77507i
\(750\) −21.2346 42.4157i −0.0283128 0.0565543i
\(751\) −447.953 −0.596476 −0.298238 0.954492i \(-0.596399\pi\)
−0.298238 + 0.954492i \(0.596399\pi\)
\(752\) 24.9191i 0.0331372i
\(753\) −556.520 + 278.611i −0.739070 + 0.370001i
\(754\) 129.596 0.171879
\(755\) 328.340i 0.434888i
\(756\) 451.976 + 81.4719i 0.597852 + 0.107767i
\(757\) 439.559 0.580660 0.290330 0.956927i \(-0.406235\pi\)
0.290330 + 0.956927i \(0.406235\pi\)
\(758\) 788.184i 1.03982i
\(759\) −85.1250 170.036i −0.112154 0.224026i
\(760\) −232.616 −0.306073
\(761\) 74.4722i 0.0978609i 0.998802 + 0.0489305i \(0.0155813\pi\)
−0.998802 + 0.0489305i \(0.984419\pi\)
\(762\) −330.417 + 165.417i −0.433618 + 0.217082i
\(763\) 1699.45 2.22732
\(764\) 114.165i 0.149431i
\(765\) −9.36347 + 12.5109i −0.0122398 + 0.0163541i
\(766\) −39.2492 −0.0512392
\(767\) 254.759i 0.332150i
\(768\) −21.4879 42.9217i −0.0279790 0.0558876i
\(769\) −496.554 −0.645714 −0.322857 0.946448i \(-0.604643\pi\)
−0.322857 + 0.946448i \(0.604643\pi\)
\(770\) 355.455i 0.461630i
\(771\) −262.161 + 131.246i −0.340027 + 0.170228i
\(772\) 212.299 0.274999
\(773\) 1431.40i 1.85175i 0.377829 + 0.925876i \(0.376671\pi\)
−0.377829 + 0.925876i \(0.623329\pi\)
\(774\) 307.447 + 230.101i 0.397218 + 0.297289i
\(775\) −170.948 −0.220578
\(776\) 531.244i 0.684593i
\(777\) 385.310 + 769.650i 0.495894 + 0.990540i
\(778\) 498.589 0.640860
\(779\) 1514.37i 1.94400i
\(780\) 43.2016 21.6280i 0.0553866 0.0277282i
\(781\) −1455.07 −1.86308
\(782\) 5.26649i 0.00673464i
\(783\) −121.889 + 676.193i −0.155669 + 0.863593i
\(784\) 93.3281 0.119041
\(785\) 447.759i 0.570394i
\(786\) −105.018 209.771i −0.133610