Properties

Label 1512.2.c.g.757.18
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.18
Character \(\chi\) = 1512.757
Dual form 1512.2.c.g.757.17

$q$-expansion

\(f(q)\) \(=\) \(q+(1.10240 + 0.885841i) q^{2} +(0.430570 + 1.95310i) q^{4} +2.99001i q^{5} +1.00000 q^{7} +(-1.25548 + 2.53452i) q^{8} +O(q^{10})\) \(q+(1.10240 + 0.885841i) q^{2} +(0.430570 + 1.95310i) q^{4} +2.99001i q^{5} +1.00000 q^{7} +(-1.25548 + 2.53452i) q^{8} +(-2.64867 + 3.29619i) q^{10} +2.13956i q^{11} +0.665739i q^{13} +(1.10240 + 0.885841i) q^{14} +(-3.62922 + 1.68190i) q^{16} +7.04931 q^{17} -1.39525i q^{19} +(-5.83980 + 1.28741i) q^{20} +(-1.89531 + 2.35865i) q^{22} +0.184371 q^{23} -3.94016 q^{25} +(-0.589739 + 0.733911i) q^{26} +(0.430570 + 1.95310i) q^{28} +1.27564i q^{29} -7.62308 q^{31} +(-5.49074 - 1.36079i) q^{32} +(7.77116 + 6.24457i) q^{34} +2.99001i q^{35} -6.69127i q^{37} +(1.23597 - 1.53812i) q^{38} +(-7.57823 - 3.75389i) q^{40} -0.274106 q^{41} +2.63971i q^{43} +(-4.17877 + 0.921229i) q^{44} +(0.203250 + 0.163323i) q^{46} -5.77739 q^{47} +1.00000 q^{49} +(-4.34363 - 3.49036i) q^{50} +(-1.30026 + 0.286647i) q^{52} -7.48353i q^{53} -6.39730 q^{55} +(-1.25548 + 2.53452i) q^{56} +(-1.13001 + 1.40626i) q^{58} +9.03787i q^{59} +9.80298i q^{61} +(-8.40369 - 6.75284i) q^{62} +(-4.84755 - 6.36406i) q^{64} -1.99057 q^{65} -10.8191i q^{67} +(3.03522 + 13.7680i) q^{68} +(-2.64867 + 3.29619i) q^{70} +7.93573 q^{71} -2.80408 q^{73} +(5.92740 - 7.37645i) q^{74} +(2.72506 - 0.600752i) q^{76} +2.13956i q^{77} +7.98350 q^{79} +(-5.02888 - 10.8514i) q^{80} +(-0.302174 - 0.242814i) q^{82} -6.76125i q^{83} +21.0775i q^{85} +(-2.33837 + 2.91002i) q^{86} +(-5.42274 - 2.68617i) q^{88} +16.7549 q^{89} +0.665739i q^{91} +(0.0793844 + 0.360095i) q^{92} +(-6.36899 - 5.11785i) q^{94} +4.17180 q^{95} -0.107694 q^{97} +(1.10240 + 0.885841i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 6q^{4} + 24q^{7} + O(q^{10}) \) \( 24q + 6q^{4} + 24q^{7} - 16q^{10} + 2q^{16} + 16q^{22} - 24q^{25} + 6q^{28} + 8q^{31} + 22q^{34} + 26q^{46} + 24q^{49} - 6q^{52} + 16q^{55} - 58q^{58} + 6q^{64} - 16q^{70} + 60q^{76} + 8q^{79} - 28q^{82} + 12q^{88} + 36q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.10240 + 0.885841i 0.779514 + 0.626384i
\(3\) 0 0
\(4\) 0.430570 + 1.95310i 0.215285 + 0.976551i
\(5\) 2.99001i 1.33717i 0.743634 + 0.668587i \(0.233100\pi\)
−0.743634 + 0.668587i \(0.766900\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −1.25548 + 2.53452i −0.443879 + 0.896087i
\(9\) 0 0
\(10\) −2.64867 + 3.29619i −0.837585 + 1.04235i
\(11\) 2.13956i 0.645101i 0.946552 + 0.322550i \(0.104540\pi\)
−0.946552 + 0.322550i \(0.895460\pi\)
\(12\) 0 0
\(13\) 0.665739i 0.184643i 0.995729 + 0.0923214i \(0.0294287\pi\)
−0.995729 + 0.0923214i \(0.970571\pi\)
\(14\) 1.10240 + 0.885841i 0.294629 + 0.236751i
\(15\) 0 0
\(16\) −3.62922 + 1.68190i −0.907305 + 0.420474i
\(17\) 7.04931 1.70971 0.854855 0.518867i \(-0.173646\pi\)
0.854855 + 0.518867i \(0.173646\pi\)
\(18\) 0 0
\(19\) 1.39525i 0.320092i −0.987110 0.160046i \(-0.948836\pi\)
0.987110 0.160046i \(-0.0511642\pi\)
\(20\) −5.83980 + 1.28741i −1.30582 + 0.287873i
\(21\) 0 0
\(22\) −1.89531 + 2.35865i −0.404081 + 0.502865i
\(23\) 0.184371 0.0384439 0.0192220 0.999815i \(-0.493881\pi\)
0.0192220 + 0.999815i \(0.493881\pi\)
\(24\) 0 0
\(25\) −3.94016 −0.788032
\(26\) −0.589739 + 0.733911i −0.115657 + 0.143932i
\(27\) 0 0
\(28\) 0.430570 + 1.95310i 0.0813701 + 0.369102i
\(29\) 1.27564i 0.236880i 0.992961 + 0.118440i \(0.0377893\pi\)
−0.992961 + 0.118440i \(0.962211\pi\)
\(30\) 0 0
\(31\) −7.62308 −1.36915 −0.684573 0.728944i \(-0.740011\pi\)
−0.684573 + 0.728944i \(0.740011\pi\)
\(32\) −5.49074 1.36079i −0.970635 0.240556i
\(33\) 0 0
\(34\) 7.77116 + 6.24457i 1.33274 + 1.07094i
\(35\) 2.99001i 0.505404i
\(36\) 0 0
\(37\) 6.69127i 1.10004i −0.835152 0.550019i \(-0.814621\pi\)
0.835152 0.550019i \(-0.185379\pi\)
\(38\) 1.23597 1.53812i 0.200500 0.249516i
\(39\) 0 0
\(40\) −7.57823 3.75389i −1.19822 0.593543i
\(41\) −0.274106 −0.0428081 −0.0214041 0.999771i \(-0.506814\pi\)
−0.0214041 + 0.999771i \(0.506814\pi\)
\(42\) 0 0
\(43\) 2.63971i 0.402553i 0.979535 + 0.201276i \(0.0645089\pi\)
−0.979535 + 0.201276i \(0.935491\pi\)
\(44\) −4.17877 + 0.921229i −0.629974 + 0.138881i
\(45\) 0 0
\(46\) 0.203250 + 0.163323i 0.0299676 + 0.0240807i
\(47\) −5.77739 −0.842719 −0.421359 0.906894i \(-0.638447\pi\)
−0.421359 + 0.906894i \(0.638447\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −4.34363 3.49036i −0.614283 0.493611i
\(51\) 0 0
\(52\) −1.30026 + 0.286647i −0.180313 + 0.0397508i
\(53\) 7.48353i 1.02794i −0.857808 0.513971i \(-0.828174\pi\)
0.857808 0.513971i \(-0.171826\pi\)
\(54\) 0 0
\(55\) −6.39730 −0.862611
\(56\) −1.25548 + 2.53452i −0.167770 + 0.338689i
\(57\) 0 0
\(58\) −1.13001 + 1.40626i −0.148378 + 0.184651i
\(59\) 9.03787i 1.17663i 0.808632 + 0.588315i \(0.200208\pi\)
−0.808632 + 0.588315i \(0.799792\pi\)
\(60\) 0 0
\(61\) 9.80298i 1.25514i 0.778559 + 0.627571i \(0.215951\pi\)
−0.778559 + 0.627571i \(0.784049\pi\)
\(62\) −8.40369 6.75284i −1.06727 0.857612i
\(63\) 0 0
\(64\) −4.84755 6.36406i −0.605943 0.795508i
\(65\) −1.99057 −0.246900
\(66\) 0 0
\(67\) 10.8191i 1.32177i −0.750488 0.660884i \(-0.770181\pi\)
0.750488 0.660884i \(-0.229819\pi\)
\(68\) 3.03522 + 13.7680i 0.368075 + 1.66962i
\(69\) 0 0
\(70\) −2.64867 + 3.29619i −0.316577 + 0.393970i
\(71\) 7.93573 0.941798 0.470899 0.882187i \(-0.343930\pi\)
0.470899 + 0.882187i \(0.343930\pi\)
\(72\) 0 0
\(73\) −2.80408 −0.328193 −0.164097 0.986444i \(-0.552471\pi\)
−0.164097 + 0.986444i \(0.552471\pi\)
\(74\) 5.92740 7.37645i 0.689047 0.857495i
\(75\) 0 0
\(76\) 2.72506 0.600752i 0.312586 0.0689110i
\(77\) 2.13956i 0.243825i
\(78\) 0 0
\(79\) 7.98350 0.898214 0.449107 0.893478i \(-0.351742\pi\)
0.449107 + 0.893478i \(0.351742\pi\)
\(80\) −5.02888 10.8514i −0.562246 1.21322i
\(81\) 0 0
\(82\) −0.302174 0.242814i −0.0333695 0.0268143i
\(83\) 6.76125i 0.742143i −0.928604 0.371072i \(-0.878990\pi\)
0.928604 0.371072i \(-0.121010\pi\)
\(84\) 0 0
\(85\) 21.0775i 2.28618i
\(86\) −2.33837 + 2.91002i −0.252153 + 0.313795i
\(87\) 0 0
\(88\) −5.42274 2.68617i −0.578066 0.286346i
\(89\) 16.7549 1.77602 0.888010 0.459825i \(-0.152088\pi\)
0.888010 + 0.459825i \(0.152088\pi\)
\(90\) 0 0
\(91\) 0.665739i 0.0697884i
\(92\) 0.0793844 + 0.360095i 0.00827640 + 0.0375425i
\(93\) 0 0
\(94\) −6.36899 5.11785i −0.656911 0.527866i
\(95\) 4.17180 0.428018
\(96\) 0 0
\(97\) −0.107694 −0.0109346 −0.00546732 0.999985i \(-0.501740\pi\)
−0.00546732 + 0.999985i \(0.501740\pi\)
\(98\) 1.10240 + 0.885841i 0.111359 + 0.0894835i
\(99\) 0 0
\(100\) −1.69652 7.69554i −0.169652 0.769554i
\(101\) 14.8524i 1.47787i −0.673775 0.738937i \(-0.735328\pi\)
0.673775 0.738937i \(-0.264672\pi\)
\(102\) 0 0
\(103\) −16.1461 −1.59092 −0.795459 0.606007i \(-0.792770\pi\)
−0.795459 + 0.606007i \(0.792770\pi\)
\(104\) −1.68733 0.835821i −0.165456 0.0819590i
\(105\) 0 0
\(106\) 6.62922 8.24984i 0.643887 0.801295i
\(107\) 15.6131i 1.50937i 0.656084 + 0.754687i \(0.272211\pi\)
−0.656084 + 0.754687i \(0.727789\pi\)
\(108\) 0 0
\(109\) 4.15829i 0.398292i −0.979970 0.199146i \(-0.936183\pi\)
0.979970 0.199146i \(-0.0638167\pi\)
\(110\) −7.05238 5.66699i −0.672418 0.540326i
\(111\) 0 0
\(112\) −3.62922 + 1.68190i −0.342929 + 0.158924i
\(113\) 18.4682 1.73734 0.868672 0.495388i \(-0.164974\pi\)
0.868672 + 0.495388i \(0.164974\pi\)
\(114\) 0 0
\(115\) 0.551270i 0.0514062i
\(116\) −2.49145 + 0.549250i −0.231325 + 0.0509966i
\(117\) 0 0
\(118\) −8.00612 + 9.96334i −0.737023 + 0.917200i
\(119\) 7.04931 0.646209
\(120\) 0 0
\(121\) 6.42230 0.583845
\(122\) −8.68388 + 10.8068i −0.786202 + 0.978402i
\(123\) 0 0
\(124\) −3.28227 14.8887i −0.294757 1.33704i
\(125\) 3.16893i 0.283437i
\(126\) 0 0
\(127\) −4.37444 −0.388169 −0.194084 0.980985i \(-0.562174\pi\)
−0.194084 + 0.980985i \(0.562174\pi\)
\(128\) 0.293616 11.3099i 0.0259523 0.999663i
\(129\) 0 0
\(130\) −2.19440 1.76333i −0.192462 0.154654i
\(131\) 5.76264i 0.503484i 0.967794 + 0.251742i \(0.0810035\pi\)
−0.967794 + 0.251742i \(0.918997\pi\)
\(132\) 0 0
\(133\) 1.39525i 0.120983i
\(134\) 9.58404 11.9270i 0.827935 1.03034i
\(135\) 0 0
\(136\) −8.85026 + 17.8666i −0.758904 + 1.53205i
\(137\) −10.5191 −0.898704 −0.449352 0.893355i \(-0.648345\pi\)
−0.449352 + 0.893355i \(0.648345\pi\)
\(138\) 0 0
\(139\) 7.27000i 0.616633i 0.951284 + 0.308316i \(0.0997656\pi\)
−0.951284 + 0.308316i \(0.900234\pi\)
\(140\) −5.83980 + 1.28741i −0.493553 + 0.108806i
\(141\) 0 0
\(142\) 8.74835 + 7.02980i 0.734145 + 0.589928i
\(143\) −1.42439 −0.119113
\(144\) 0 0
\(145\) −3.81416 −0.316749
\(146\) −3.09122 2.48397i −0.255831 0.205575i
\(147\) 0 0
\(148\) 13.0687 2.88106i 1.07424 0.236822i
\(149\) 3.06625i 0.251197i 0.992081 + 0.125599i \(0.0400851\pi\)
−0.992081 + 0.125599i \(0.959915\pi\)
\(150\) 0 0
\(151\) −15.8992 −1.29386 −0.646930 0.762549i \(-0.723947\pi\)
−0.646930 + 0.762549i \(0.723947\pi\)
\(152\) 3.53628 + 1.75170i 0.286830 + 0.142082i
\(153\) 0 0
\(154\) −1.89531 + 2.35865i −0.152728 + 0.190065i
\(155\) 22.7931i 1.83079i
\(156\) 0 0
\(157\) 18.3211i 1.46219i 0.682278 + 0.731093i \(0.260989\pi\)
−0.682278 + 0.731093i \(0.739011\pi\)
\(158\) 8.80101 + 7.07211i 0.700171 + 0.562627i
\(159\) 0 0
\(160\) 4.06878 16.4174i 0.321665 1.29791i
\(161\) 0.184371 0.0145304
\(162\) 0 0
\(163\) 22.0479i 1.72692i −0.504415 0.863462i \(-0.668292\pi\)
0.504415 0.863462i \(-0.331708\pi\)
\(164\) −0.118022 0.535357i −0.00921595 0.0418043i
\(165\) 0 0
\(166\) 5.98939 7.45360i 0.464867 0.578511i
\(167\) 10.2650 0.794332 0.397166 0.917747i \(-0.369994\pi\)
0.397166 + 0.917747i \(0.369994\pi\)
\(168\) 0 0
\(169\) 12.5568 0.965907
\(170\) −18.6713 + 23.2358i −1.43203 + 1.78211i
\(171\) 0 0
\(172\) −5.15563 + 1.13658i −0.393113 + 0.0866636i
\(173\) 15.5234i 1.18022i 0.807322 + 0.590111i \(0.200916\pi\)
−0.807322 + 0.590111i \(0.799084\pi\)
\(174\) 0 0
\(175\) −3.94016 −0.297848
\(176\) −3.59851 7.76492i −0.271248 0.585303i
\(177\) 0 0
\(178\) 18.4706 + 14.8422i 1.38443 + 1.11247i
\(179\) 17.2028i 1.28580i −0.765952 0.642898i \(-0.777732\pi\)
0.765952 0.642898i \(-0.222268\pi\)
\(180\) 0 0
\(181\) 10.5145i 0.781538i 0.920489 + 0.390769i \(0.127791\pi\)
−0.920489 + 0.390769i \(0.872209\pi\)
\(182\) −0.589739 + 0.733911i −0.0437144 + 0.0544011i
\(183\) 0 0
\(184\) −0.231473 + 0.467290i −0.0170644 + 0.0344491i
\(185\) 20.0070 1.47094
\(186\) 0 0
\(187\) 15.0824i 1.10293i
\(188\) −2.48757 11.2838i −0.181425 0.822958i
\(189\) 0 0
\(190\) 4.59900 + 3.69556i 0.333646 + 0.268104i
\(191\) 14.3893 1.04117 0.520587 0.853808i \(-0.325713\pi\)
0.520587 + 0.853808i \(0.325713\pi\)
\(192\) 0 0
\(193\) 11.3579 0.817562 0.408781 0.912632i \(-0.365954\pi\)
0.408781 + 0.912632i \(0.365954\pi\)
\(194\) −0.118721 0.0953995i −0.00852370 0.00684928i
\(195\) 0 0
\(196\) 0.430570 + 1.95310i 0.0307550 + 0.139507i
\(197\) 6.44465i 0.459163i 0.973289 + 0.229581i \(0.0737357\pi\)
−0.973289 + 0.229581i \(0.926264\pi\)
\(198\) 0 0
\(199\) −6.48055 −0.459394 −0.229697 0.973262i \(-0.573774\pi\)
−0.229697 + 0.973262i \(0.573774\pi\)
\(200\) 4.94679 9.98641i 0.349791 0.706146i
\(201\) 0 0
\(202\) 13.1569 16.3733i 0.925717 1.15202i
\(203\) 1.27564i 0.0895321i
\(204\) 0 0
\(205\) 0.819579i 0.0572419i
\(206\) −17.7994 14.3028i −1.24014 0.996527i
\(207\) 0 0
\(208\) −1.11970 2.41611i −0.0776375 0.167527i
\(209\) 2.98521 0.206491
\(210\) 0 0
\(211\) 10.3150i 0.710112i −0.934845 0.355056i \(-0.884462\pi\)
0.934845 0.355056i \(-0.115538\pi\)
\(212\) 14.6161 3.22218i 1.00384 0.221300i
\(213\) 0 0
\(214\) −13.8307 + 17.2119i −0.945449 + 1.17658i
\(215\) −7.89277 −0.538283
\(216\) 0 0
\(217\) −7.62308 −0.517489
\(218\) 3.68358 4.58409i 0.249484 0.310474i
\(219\) 0 0
\(220\) −2.75448 12.4946i −0.185707 0.842384i
\(221\) 4.69300i 0.315686i
\(222\) 0 0
\(223\) 23.8589 1.59771 0.798854 0.601526i \(-0.205440\pi\)
0.798854 + 0.601526i \(0.205440\pi\)
\(224\) −5.49074 1.36079i −0.366866 0.0909217i
\(225\) 0 0
\(226\) 20.3594 + 16.3599i 1.35428 + 1.08825i
\(227\) 1.88092i 0.124841i −0.998050 0.0624206i \(-0.980118\pi\)
0.998050 0.0624206i \(-0.0198820\pi\)
\(228\) 0 0
\(229\) 18.8128i 1.24319i 0.783340 + 0.621594i \(0.213515\pi\)
−0.783340 + 0.621594i \(0.786485\pi\)
\(230\) −0.488338 + 0.607720i −0.0322000 + 0.0400719i
\(231\) 0 0
\(232\) −3.23312 1.60153i −0.212265 0.105146i
\(233\) 9.18759 0.601899 0.300949 0.953640i \(-0.402696\pi\)
0.300949 + 0.953640i \(0.402696\pi\)
\(234\) 0 0
\(235\) 17.2745i 1.12686i
\(236\) −17.6519 + 3.89144i −1.14904 + 0.253311i
\(237\) 0 0
\(238\) 7.77116 + 6.24457i 0.503729 + 0.404776i
\(239\) 29.1200 1.88362 0.941808 0.336152i \(-0.109126\pi\)
0.941808 + 0.336152i \(0.109126\pi\)
\(240\) 0 0
\(241\) 25.4640 1.64028 0.820142 0.572160i \(-0.193894\pi\)
0.820142 + 0.572160i \(0.193894\pi\)
\(242\) 7.07994 + 5.68914i 0.455116 + 0.365712i
\(243\) 0 0
\(244\) −19.1462 + 4.22087i −1.22571 + 0.270213i
\(245\) 2.99001i 0.191025i
\(246\) 0 0
\(247\) 0.928871 0.0591027
\(248\) 9.57062 19.3208i 0.607735 1.22687i
\(249\) 0 0
\(250\) −2.80717 + 3.49342i −0.177541 + 0.220943i
\(251\) 2.72427i 0.171955i 0.996297 + 0.0859773i \(0.0274012\pi\)
−0.996297 + 0.0859773i \(0.972599\pi\)
\(252\) 0 0
\(253\) 0.394471i 0.0248002i
\(254\) −4.82238 3.87506i −0.302583 0.243143i
\(255\) 0 0
\(256\) 10.3425 12.2079i 0.646404 0.762996i
\(257\) −17.6181 −1.09899 −0.549494 0.835498i \(-0.685179\pi\)
−0.549494 + 0.835498i \(0.685179\pi\)
\(258\) 0 0
\(259\) 6.69127i 0.415775i
\(260\) −0.857079 3.88778i −0.0531538 0.241110i
\(261\) 0 0
\(262\) −5.10479 + 6.35273i −0.315375 + 0.392473i
\(263\) 5.42576 0.334567 0.167283 0.985909i \(-0.446501\pi\)
0.167283 + 0.985909i \(0.446501\pi\)
\(264\) 0 0
\(265\) 22.3758 1.37454
\(266\) 1.23597 1.53812i 0.0757821 0.0943082i
\(267\) 0 0
\(268\) 21.1309 4.65840i 1.29077 0.284557i
\(269\) 17.6635i 1.07696i −0.842637 0.538482i \(-0.818998\pi\)
0.842637 0.538482i \(-0.181002\pi\)
\(270\) 0 0
\(271\) 11.5223 0.699929 0.349965 0.936763i \(-0.386194\pi\)
0.349965 + 0.936763i \(0.386194\pi\)
\(272\) −25.5835 + 11.8562i −1.55123 + 0.718888i
\(273\) 0 0
\(274\) −11.5962 9.31822i −0.700553 0.562935i
\(275\) 8.43020i 0.508360i
\(276\) 0 0
\(277\) 7.84872i 0.471584i −0.971804 0.235792i \(-0.924232\pi\)
0.971804 0.235792i \(-0.0757684\pi\)
\(278\) −6.44006 + 8.01444i −0.386249 + 0.480674i
\(279\) 0 0
\(280\) −7.57823 3.75389i −0.452886 0.224338i
\(281\) −31.1308 −1.85711 −0.928555 0.371195i \(-0.878948\pi\)
−0.928555 + 0.371195i \(0.878948\pi\)
\(282\) 0 0
\(283\) 24.7863i 1.47339i −0.676224 0.736696i \(-0.736385\pi\)
0.676224 0.736696i \(-0.263615\pi\)
\(284\) 3.41689 + 15.4993i 0.202755 + 0.919714i
\(285\) 0 0
\(286\) −1.57024 1.26178i −0.0928505 0.0746107i
\(287\) −0.274106 −0.0161800
\(288\) 0 0
\(289\) 32.6928 1.92311
\(290\) −4.20473 3.37874i −0.246910 0.198407i
\(291\) 0 0
\(292\) −1.20735 5.47666i −0.0706551 0.320497i
\(293\) 28.9898i 1.69360i 0.531909 + 0.846802i \(0.321475\pi\)
−0.531909 + 0.846802i \(0.678525\pi\)
\(294\) 0 0
\(295\) −27.0233 −1.57336
\(296\) 16.9591 + 8.40074i 0.985729 + 0.488283i
\(297\) 0 0
\(298\) −2.71621 + 3.38023i −0.157346 + 0.195812i
\(299\) 0.122743i 0.00709839i
\(300\) 0 0
\(301\) 2.63971i 0.152151i
\(302\) −17.5273 14.0842i −1.00858 0.810454i
\(303\) 0 0
\(304\) 2.34666 + 5.06366i 0.134590 + 0.290421i
\(305\) −29.3110 −1.67834
\(306\) 0 0
\(307\) 18.8831i 1.07772i −0.842397 0.538858i \(-0.818856\pi\)
0.842397 0.538858i \(-0.181144\pi\)
\(308\) −4.17877 + 0.921229i −0.238108 + 0.0524919i
\(309\) 0 0
\(310\) 20.1911 25.1271i 1.14678 1.42712i
\(311\) 0.147540 0.00836624 0.00418312 0.999991i \(-0.498668\pi\)
0.00418312 + 0.999991i \(0.498668\pi\)
\(312\) 0 0
\(313\) −23.3154 −1.31786 −0.658932 0.752202i \(-0.728992\pi\)
−0.658932 + 0.752202i \(0.728992\pi\)
\(314\) −16.2296 + 20.1972i −0.915890 + 1.13979i
\(315\) 0 0
\(316\) 3.43746 + 15.5926i 0.193372 + 0.877152i
\(317\) 1.43318i 0.0804954i −0.999190 0.0402477i \(-0.987185\pi\)
0.999190 0.0402477i \(-0.0128147\pi\)
\(318\) 0 0
\(319\) −2.72929 −0.152811
\(320\) 19.0286 14.4942i 1.06373 0.810251i
\(321\) 0 0
\(322\) 0.203250 + 0.163323i 0.0113267 + 0.00910164i
\(323\) 9.83554i 0.547264i
\(324\) 0 0
\(325\) 2.62312i 0.145505i
\(326\) 19.5309 24.3056i 1.08172 1.34616i
\(327\) 0 0
\(328\) 0.344134 0.694726i 0.0190016 0.0383598i
\(329\) −5.77739 −0.318518
\(330\) 0 0
\(331\) 23.3196i 1.28176i −0.767640 0.640882i \(-0.778569\pi\)
0.767640 0.640882i \(-0.221431\pi\)
\(332\) 13.2054 2.91119i 0.724741 0.159772i
\(333\) 0 0
\(334\) 11.3162 + 9.09319i 0.619193 + 0.497557i
\(335\) 32.3493 1.76743
\(336\) 0 0
\(337\) 0.484629 0.0263994 0.0131997 0.999913i \(-0.495798\pi\)
0.0131997 + 0.999913i \(0.495798\pi\)
\(338\) 13.8426 + 11.1233i 0.752938 + 0.605029i
\(339\) 0 0
\(340\) −41.1666 + 9.07535i −2.23257 + 0.492180i
\(341\) 16.3100i 0.883237i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −6.69040 3.31410i −0.360722 0.178685i
\(345\) 0 0
\(346\) −13.7513 + 17.1130i −0.739272 + 0.919999i
\(347\) 10.0395i 0.538947i 0.963008 + 0.269473i \(0.0868496\pi\)
−0.963008 + 0.269473i \(0.913150\pi\)
\(348\) 0 0
\(349\) 9.55791i 0.511623i −0.966727 0.255812i \(-0.917657\pi\)
0.966727 0.255812i \(-0.0823427\pi\)
\(350\) −4.34363 3.49036i −0.232177 0.186568i
\(351\) 0 0
\(352\) 2.91149 11.7478i 0.155183 0.626157i
\(353\) 28.2931 1.50589 0.752945 0.658083i \(-0.228632\pi\)
0.752945 + 0.658083i \(0.228632\pi\)
\(354\) 0 0
\(355\) 23.7279i 1.25935i
\(356\) 7.21417 + 32.7241i 0.382350 + 1.73437i
\(357\) 0 0
\(358\) 15.2389 18.9643i 0.805402 1.00230i
\(359\) −25.8316 −1.36334 −0.681671 0.731659i \(-0.738746\pi\)
−0.681671 + 0.731659i \(0.738746\pi\)
\(360\) 0 0
\(361\) 17.0533 0.897541
\(362\) −9.31419 + 11.5912i −0.489543 + 0.609220i
\(363\) 0 0
\(364\) −1.30026 + 0.286647i −0.0681520 + 0.0150244i
\(365\) 8.38424i 0.438851i
\(366\) 0 0
\(367\) −1.78123 −0.0929793 −0.0464896 0.998919i \(-0.514803\pi\)
−0.0464896 + 0.998919i \(0.514803\pi\)
\(368\) −0.669121 + 0.310092i −0.0348803 + 0.0161647i
\(369\) 0 0
\(370\) 22.0557 + 17.7230i 1.14662 + 0.921375i
\(371\) 7.48353i 0.388525i
\(372\) 0 0
\(373\) 22.1074i 1.14468i −0.820017 0.572340i \(-0.806036\pi\)
0.820017 0.572340i \(-0.193964\pi\)
\(374\) −13.3606 + 16.6268i −0.690861 + 0.859753i
\(375\) 0 0
\(376\) 7.25339 14.6429i 0.374065 0.755149i
\(377\) −0.849241 −0.0437381
\(378\) 0 0
\(379\) 35.4109i 1.81893i −0.415776 0.909467i \(-0.636490\pi\)
0.415776 0.909467i \(-0.363510\pi\)
\(380\) 1.79625 + 8.14796i 0.0921459 + 0.417982i
\(381\) 0 0
\(382\) 15.8628 + 12.7467i 0.811611 + 0.652176i
\(383\) −24.1927 −1.23619 −0.618095 0.786104i \(-0.712095\pi\)
−0.618095 + 0.786104i \(0.712095\pi\)
\(384\) 0 0
\(385\) −6.39730 −0.326036
\(386\) 12.5210 + 10.0613i 0.637302 + 0.512108i
\(387\) 0 0
\(388\) −0.0463697 0.210337i −0.00235406 0.0106782i
\(389\) 13.0465i 0.661483i 0.943721 + 0.330741i \(0.107299\pi\)
−0.943721 + 0.330741i \(0.892701\pi\)
\(390\) 0 0
\(391\) 1.29969 0.0657279
\(392\) −1.25548 + 2.53452i −0.0634113 + 0.128012i
\(393\) 0 0
\(394\) −5.70894 + 7.10458i −0.287612 + 0.357924i
\(395\) 23.8707i 1.20107i
\(396\) 0 0
\(397\) 36.0707i 1.81034i −0.425053 0.905168i \(-0.639745\pi\)
0.425053 0.905168i \(-0.360255\pi\)
\(398\) −7.14416 5.74074i −0.358104 0.287757i
\(399\) 0 0
\(400\) 14.2997 6.62694i 0.714986 0.331347i
\(401\) −15.5149 −0.774778 −0.387389 0.921916i \(-0.626623\pi\)
−0.387389 + 0.921916i \(0.626623\pi\)
\(402\) 0 0
\(403\) 5.07499i 0.252803i
\(404\) 29.0083 6.39502i 1.44322 0.318164i
\(405\) 0 0
\(406\) −1.13001 + 1.40626i −0.0560815 + 0.0697915i
\(407\) 14.3163 0.709635
\(408\) 0 0
\(409\) −28.6937 −1.41881 −0.709406 0.704800i \(-0.751037\pi\)
−0.709406 + 0.704800i \(0.751037\pi\)
\(410\) 0.726017 0.903504i 0.0358554 0.0446209i
\(411\) 0 0
\(412\) −6.95201 31.5349i −0.342501 1.55361i
\(413\) 9.03787i 0.444724i
\(414\) 0 0
\(415\) 20.2162 0.992374
\(416\) 0.905932 3.65540i 0.0444170 0.179221i
\(417\) 0 0
\(418\) 3.29090 + 2.64442i 0.160963 + 0.129343i
\(419\) 22.9355i 1.12047i 0.828333 + 0.560236i \(0.189290\pi\)
−0.828333 + 0.560236i \(0.810710\pi\)
\(420\) 0 0
\(421\) 13.1562i 0.641193i 0.947216 + 0.320596i \(0.103883\pi\)
−0.947216 + 0.320596i \(0.896117\pi\)
\(422\) 9.13743 11.3712i 0.444803 0.553543i
\(423\) 0 0
\(424\) 18.9671 + 9.39541i 0.921125 + 0.456281i
\(425\) −27.7754 −1.34731
\(426\) 0 0
\(427\) 9.80298i 0.474399i
\(428\) −30.4940 + 6.72253i −1.47398 + 0.324946i
\(429\) 0 0
\(430\) −8.70099 6.99174i −0.419599 0.337172i
\(431\) −39.6373 −1.90926 −0.954631 0.297792i \(-0.903750\pi\)
−0.954631 + 0.297792i \(0.903750\pi\)
\(432\) 0 0
\(433\) 11.5906 0.557010 0.278505 0.960435i \(-0.410161\pi\)
0.278505 + 0.960435i \(0.410161\pi\)
\(434\) −8.40369 6.75284i −0.403390 0.324147i
\(435\) 0 0
\(436\) 8.12156 1.79043i 0.388952 0.0857462i
\(437\) 0.257243i 0.0123056i
\(438\) 0 0
\(439\) −9.88971 −0.472010 −0.236005 0.971752i \(-0.575838\pi\)
−0.236005 + 0.971752i \(0.575838\pi\)
\(440\) 8.03167 16.2141i 0.382895 0.772975i
\(441\) 0 0
\(442\) −4.15726 + 5.17357i −0.197741 + 0.246081i
\(443\) 2.14448i 0.101888i −0.998702 0.0509438i \(-0.983777\pi\)
0.998702 0.0509438i \(-0.0162229\pi\)
\(444\) 0 0
\(445\) 50.0974i 2.37485i
\(446\) 26.3020 + 21.1352i 1.24544 + 1.00078i
\(447\) 0 0
\(448\) −4.84755 6.36406i −0.229025 0.300674i
\(449\) 4.65352 0.219613 0.109807 0.993953i \(-0.464977\pi\)
0.109807 + 0.993953i \(0.464977\pi\)
\(450\) 0 0
\(451\) 0.586465i 0.0276156i
\(452\) 7.95186 + 36.0703i 0.374024 + 1.69661i
\(453\) 0 0
\(454\) 1.66620 2.07353i 0.0781986 0.0973155i
\(455\) −1.99057 −0.0933192
\(456\) 0 0
\(457\) 19.0517 0.891203 0.445601 0.895232i \(-0.352990\pi\)
0.445601 + 0.895232i \(0.352990\pi\)
\(458\) −16.6652 + 20.7393i −0.778713 + 0.969083i
\(459\) 0 0
\(460\) −1.07669 + 0.237360i −0.0502008 + 0.0110670i
\(461\) 26.0354i 1.21259i 0.795240 + 0.606294i \(0.207345\pi\)
−0.795240 + 0.606294i \(0.792655\pi\)
\(462\) 0 0
\(463\) 29.6096 1.37607 0.688036 0.725676i \(-0.258473\pi\)
0.688036 + 0.725676i \(0.258473\pi\)
\(464\) −2.14548 4.62956i −0.0996016 0.214922i
\(465\) 0 0
\(466\) 10.1284 + 8.13875i 0.469189 + 0.377020i
\(467\) 25.8983i 1.19843i 0.800588 + 0.599216i \(0.204521\pi\)
−0.800588 + 0.599216i \(0.795479\pi\)
\(468\) 0 0
\(469\) 10.8191i 0.499581i
\(470\) 15.3024 19.0434i 0.705848 0.878404i
\(471\) 0 0
\(472\) −22.9066 11.3468i −1.05436 0.522281i
\(473\) −5.64782 −0.259687
\(474\) 0 0
\(475\) 5.49750i 0.252243i
\(476\) 3.03522 + 13.7680i 0.139119 + 0.631057i
\(477\) 0 0
\(478\) 32.1019 + 25.7957i 1.46830 + 1.17987i
\(479\) −19.2498 −0.879544 −0.439772 0.898109i \(-0.644941\pi\)
−0.439772 + 0.898109i \(0.644941\pi\)
\(480\) 0 0
\(481\) 4.45464 0.203114
\(482\) 28.0716 + 22.5571i 1.27862 + 1.02745i
\(483\) 0 0
\(484\) 2.76525 + 12.5434i 0.125693 + 0.570155i
\(485\) 0.322005i 0.0146215i
\(486\) 0 0
\(487\) 2.32047 0.105150 0.0525752 0.998617i \(-0.483257\pi\)
0.0525752 + 0.998617i \(0.483257\pi\)
\(488\) −24.8458 12.3074i −1.12472 0.557131i
\(489\) 0 0
\(490\) −2.64867 + 3.29619i −0.119655 + 0.148907i
\(491\) 0.578109i 0.0260897i −0.999915 0.0130449i \(-0.995848\pi\)
0.999915 0.0130449i \(-0.00415242\pi\)
\(492\) 0 0
\(493\) 8.99235i 0.404995i
\(494\) 1.02399 + 0.822833i 0.0460714 + 0.0370210i
\(495\) 0 0
\(496\) 27.6658 12.8212i 1.24223 0.575690i
\(497\) 7.93573 0.355966
\(498\) 0 0
\(499\) 26.3969i 1.18169i 0.806785 + 0.590845i \(0.201205\pi\)
−0.806785 + 0.590845i \(0.798795\pi\)
\(500\) −6.18924 + 1.36444i −0.276791 + 0.0610198i
\(501\) 0 0
\(502\) −2.41327 + 3.00324i −0.107710 + 0.134041i
\(503\) 8.40780 0.374885 0.187443 0.982276i \(-0.439980\pi\)
0.187443 + 0.982276i \(0.439980\pi\)
\(504\) 0 0
\(505\) 44.4090 1.97617
\(506\) −0.349439 + 0.434865i −0.0155345 + 0.0193321i
\(507\) 0 0
\(508\) −1.88350 8.54373i −0.0835669 0.379067i
\(509\) 32.9679i 1.46128i −0.682764 0.730639i \(-0.739222\pi\)
0.682764 0.730639i \(-0.260778\pi\)
\(510\) 0 0
\(511\) −2.80408 −0.124045
\(512\) 22.2158 4.29624i 0.981809 0.189869i
\(513\) 0 0
\(514\) −19.4222 15.6069i −0.856676 0.688389i
\(515\) 48.2769i 2.12733i
\(516\) 0 0
\(517\) 12.3611i 0.543638i
\(518\) 5.92740 7.37645i 0.260435 0.324103i
\(519\) 0 0
\(520\) 2.49911 5.04513i 0.109593 0.221243i
\(521\) 30.9299 1.35506 0.677531 0.735494i \(-0.263050\pi\)
0.677531 + 0.735494i \(0.263050\pi\)
\(522\) 0 0
\(523\) 2.73852i 0.119747i 0.998206 + 0.0598735i \(0.0190697\pi\)
−0.998206 + 0.0598735i \(0.980930\pi\)
\(524\) −11.2550 + 2.48122i −0.491678 + 0.108393i
\(525\) 0 0
\(526\) 5.98136 + 4.80636i 0.260799 + 0.209567i
\(527\) −53.7375 −2.34084
\(528\) 0 0
\(529\) −22.9660 −0.998522
\(530\) 24.6671 + 19.8214i 1.07147 + 0.860988i
\(531\) 0 0
\(532\) 2.72506 0.600752i 0.118146 0.0260459i
\(533\) 0.182483i 0.00790421i
\(534\) 0 0
\(535\) −46.6833 −2.01830
\(536\) 27.4213 + 13.5832i 1.18442 + 0.586705i
\(537\) 0 0
\(538\) 15.6471 19.4723i 0.674594 0.839509i
\(539\) 2.13956i 0.0921572i
\(540\) 0 0
\(541\) 32.3372i 1.39029i 0.718872 + 0.695143i \(0.244659\pi\)
−0.718872 + 0.695143i \(0.755341\pi\)
\(542\) 12.7022 + 10.2069i 0.545605 + 0.438425i
\(543\) 0 0
\(544\) −38.7060 9.59265i −1.65950 0.411281i
\(545\) 12.4333 0.532585
\(546\) 0 0
\(547\) 20.4045i 0.872434i −0.899842 0.436217i \(-0.856318\pi\)
0.899842 0.436217i \(-0.143682\pi\)
\(548\) −4.52920 20.5448i −0.193478 0.877631i
\(549\) 0 0
\(550\) 7.46782 9.29345i 0.318429 0.396274i
\(551\) 1.77983 0.0758232
\(552\) 0 0
\(553\) 7.98350 0.339493
\(554\) 6.95272 8.65243i 0.295393 0.367606i
\(555\) 0 0
\(556\) −14.1990 + 3.13024i −0.602174 + 0.132752i
\(557\) 4.16560i 0.176502i 0.996098 + 0.0882510i \(0.0281278\pi\)
−0.996098 + 0.0882510i \(0.971872\pi\)
\(558\) 0 0
\(559\) −1.75736 −0.0743285
\(560\) −5.02888 10.8514i −0.212509 0.458555i
\(561\) 0 0
\(562\) −34.3186 27.5770i −1.44764 1.16326i
\(563\) 4.37435i 0.184357i −0.995743 0.0921784i \(-0.970617\pi\)
0.995743 0.0921784i \(-0.0293830\pi\)
\(564\) 0 0
\(565\) 55.2202i 2.32313i
\(566\) 21.9567 27.3244i 0.922910 1.14853i
\(567\) 0 0
\(568\) −9.96315 + 20.1132i −0.418044 + 0.843933i
\(569\) 4.59520 0.192641 0.0963204 0.995350i \(-0.469293\pi\)
0.0963204 + 0.995350i \(0.469293\pi\)
\(570\) 0 0
\(571\) 30.6111i 1.28103i 0.767944 + 0.640517i \(0.221280\pi\)
−0.767944 + 0.640517i \(0.778720\pi\)
\(572\) −0.613298 2.78197i −0.0256433 0.116320i
\(573\) 0 0
\(574\) −0.302174 0.242814i −0.0126125 0.0101349i
\(575\) −0.726450 −0.0302951
\(576\) 0 0
\(577\) −8.32558 −0.346598 −0.173299 0.984869i \(-0.555443\pi\)
−0.173299 + 0.984869i \(0.555443\pi\)
\(578\) 36.0405 + 28.9606i 1.49909 + 1.20460i
\(579\) 0 0
\(580\) −1.64226 7.44945i −0.0681913 0.309322i
\(581\) 6.76125i 0.280504i
\(582\) 0 0
\(583\) 16.0114 0.663126
\(584\) 3.52047 7.10700i 0.145678 0.294090i
\(585\) 0 0
\(586\) −25.6804 + 31.9584i −1.06085 + 1.32019i
\(587\) 24.4147i 1.00770i 0.863791 + 0.503851i \(0.168084\pi\)
−0.863791 + 0.503851i \(0.831916\pi\)
\(588\) 0 0
\(589\) 10.6361i 0.438252i
\(590\) −29.7905 23.9384i −1.22646 0.985527i
\(591\) 0 0
\(592\) 11.2540 + 24.2841i 0.462537 + 0.998069i
\(593\) −5.57185 −0.228809 −0.114404 0.993434i \(-0.536496\pi\)
−0.114404 + 0.993434i \(0.536496\pi\)
\(594\) 0 0
\(595\) 21.0775i 0.864094i
\(596\) −5.98870 + 1.32024i −0.245307 + 0.0540790i
\(597\) 0 0
\(598\) −0.108731 + 0.135312i −0.00444632 + 0.00553330i
\(599\) −28.6835 −1.17198 −0.585988 0.810319i \(-0.699294\pi\)
−0.585988 + 0.810319i \(0.699294\pi\)
\(600\) 0 0
\(601\) −28.9086 −1.17921 −0.589603 0.807693i \(-0.700716\pi\)
−0.589603 + 0.807693i \(0.700716\pi\)
\(602\) −2.33837 + 2.91002i −0.0953048 + 0.118604i
\(603\) 0 0
\(604\) −6.84573 31.0528i −0.278549 1.26352i
\(605\) 19.2027i 0.780702i
\(606\) 0 0
\(607\) −10.3353 −0.419498 −0.209749 0.977755i \(-0.567265\pi\)
−0.209749 + 0.977755i \(0.567265\pi\)
\(608\) −1.89864 + 7.66094i −0.0770001 + 0.310692i
\(609\) 0 0
\(610\) −32.3124 25.9649i −1.30829 1.05129i
\(611\) 3.84624i 0.155602i
\(612\) 0 0
\(613\) 2.77963i 0.112268i 0.998423 + 0.0561341i \(0.0178774\pi\)
−0.998423 + 0.0561341i \(0.982123\pi\)
\(614\) 16.7274 20.8167i 0.675064 0.840094i
\(615\) 0 0
\(616\) −5.42274 2.68617i −0.218488 0.108229i
\(617\) 22.1145 0.890296 0.445148 0.895457i \(-0.353151\pi\)
0.445148 + 0.895457i \(0.353151\pi\)
\(618\) 0 0
\(619\) 8.20284i 0.329700i −0.986319 0.164850i \(-0.947286\pi\)
0.986319 0.164850i \(-0.0527140\pi\)
\(620\) 44.5173 9.81403i 1.78786 0.394141i
\(621\) 0 0
\(622\) 0.162648 + 0.130697i 0.00652160 + 0.00524048i
\(623\) 16.7549 0.671272
\(624\) 0 0
\(625\) −29.1759 −1.16704
\(626\) −25.7029 20.6537i −1.02729 0.825490i
\(627\) 0 0
\(628\) −35.7830 + 7.88853i −1.42790 + 0.314787i
\(629\) 47.1688i 1.88074i
\(630\) 0 0
\(631\) −28.2572 −1.12490 −0.562450 0.826831i \(-0.690141\pi\)
−0.562450 + 0.826831i \(0.690141\pi\)
\(632\) −10.0231 + 20.2343i −0.398698 + 0.804878i
\(633\) 0 0
\(634\) 1.26957 1.57994i 0.0504211 0.0627473i
\(635\) 13.0796i 0.519049i
\(636\) 0 0
\(637\) 0.665739i 0.0263776i
\(638\) −3.00877 2.41772i −0.119118 0.0957185i
\(639\) 0 0
\(640\) 33.8167 + 0.877916i 1.33672 + 0.0347027i
\(641\) −48.7144 −1.92410 −0.962051 0.272870i \(-0.912027\pi\)
−0.962051 + 0.272870i \(0.912027\pi\)
\(642\) 0 0
\(643\) 23.8806i 0.941757i 0.882198 + 0.470879i \(0.156063\pi\)
−0.882198 + 0.470879i \(0.843937\pi\)
\(644\) 0.0793844 + 0.360095i 0.00312819 + 0.0141897i
\(645\) 0 0
\(646\) 8.71273 10.8427i 0.342798 0.426600i
\(647\) −33.9383 −1.33425 −0.667127 0.744944i \(-0.732476\pi\)
−0.667127 + 0.744944i \(0.732476\pi\)
\(648\) 0 0
\(649\) −19.3370 −0.759045
\(650\) 2.32367 2.89173i 0.0911418 0.113423i
\(651\) 0 0
\(652\) 43.0618 9.49316i 1.68643 0.371781i
\(653\) 35.4564i 1.38752i −0.720208 0.693759i \(-0.755953\pi\)
0.720208 0.693759i \(-0.244047\pi\)
\(654\) 0 0
\(655\) −17.2304 −0.673246
\(656\) 0.994790 0.461017i 0.0388400 0.0179997i
\(657\) 0 0
\(658\) −6.36899 5.11785i −0.248289 0.199515i
\(659\) 4.40093i 0.171436i −0.996319 0.0857179i \(-0.972682\pi\)
0.996319 0.0857179i \(-0.0273184\pi\)
\(660\) 0 0
\(661\) 13.8183i 0.537470i 0.963214 + 0.268735i \(0.0866056\pi\)
−0.963214 + 0.268735i \(0.913394\pi\)
\(662\) 20.6575 25.7076i 0.802876 0.999153i
\(663\) 0 0
\(664\) 17.1365 + 8.48860i 0.665025 + 0.329422i
\(665\) 4.17180 0.161776
\(666\) 0 0
\(667\) 0.235190i 0.00910658i
\(668\) 4.41982 + 20.0487i 0.171008 + 0.775706i
\(669\) 0 0
\(670\) 35.6619 + 28.6564i 1.37774 + 1.10709i
\(671\) −20.9740 −0.809693
\(672\) 0 0
\(673\) 28.7125 1.10679 0.553393 0.832921i \(-0.313333\pi\)
0.553393 + 0.832921i \(0.313333\pi\)
\(674\) 0.534255 + 0.429304i 0.0205787 + 0.0165362i
\(675\) 0 0
\(676\) 5.40658 + 24.5247i 0.207945 + 0.943258i
\(677\) 30.5789i 1.17524i −0.809136 0.587621i \(-0.800064\pi\)
0.809136 0.587621i \(-0.199936\pi\)
\(678\) 0 0
\(679\) −0.107694 −0.00413290
\(680\) −53.4213 26.4624i −2.04861 1.01479i
\(681\) 0 0
\(682\) 14.4481 17.9802i 0.553246 0.688496i
\(683\) 10.0994i 0.386443i 0.981155 + 0.193221i \(0.0618936\pi\)
−0.981155 + 0.193221i \(0.938106\pi\)
\(684\) 0 0
\(685\) 31.4521i 1.20172i
\(686\) 1.10240 + 0.885841i 0.0420898 + 0.0338216i
\(687\) 0 0
\(688\) −4.43972 9.58010i −0.169263 0.365238i
\(689\) 4.98208 0.189802
\(690\) 0 0
\(691\) 1.93187i 0.0734916i 0.999325 + 0.0367458i \(0.0116992\pi\)
−0.999325 + 0.0367458i \(0.988301\pi\)
\(692\) −30.3188 + 6.68391i −1.15255 + 0.254084i
\(693\) 0 0
\(694\) −8.89338 + 11.0675i −0.337588 + 0.420117i
\(695\) −21.7374 −0.824545
\(696\) 0 0
\(697\) −1.93226 −0.0731895
\(698\) 8.46679 10.5366i 0.320473 0.398818i
\(699\) 0 0
\(700\) −1.69652 7.69554i −0.0641223 0.290864i
\(701\) 23.6511i 0.893288i −0.894712 0.446644i \(-0.852619\pi\)
0.894712 0.446644i \(-0.147381\pi\)
\(702\) 0 0
\(703\) −9.33598 −0.352113
\(704\) 13.6163 10.3716i 0.513183 0.390894i
\(705\) 0 0
\(706\) 31.1903 + 25.0632i 1.17386 + 0.943267i
\(707\) 14.8524i 0.558584i
\(708\) 0 0
\(709\) 20.8417i 0.782728i −0.920236 0.391364i \(-0.872003\pi\)
0.920236 0.391364i \(-0.127997\pi\)
\(710\) −21.0192 + 26.1577i −0.788836 + 0.981680i
\(711\) 0 0
\(712\) −21.0355 + 42.4656i −0.788337 + 1.59147i
\(713\) −1.40547 −0.0526354
\(714\) 0 0
\(715\) 4.25893i 0.159275i
\(716\) 33.5988 7.40700i 1.25565 0.276813i
\(717\) 0 0
\(718\) −28.4768 22.8827i −1.06274 0.853976i
\(719\) 2.81902 0.105132 0.0525658 0.998617i \(-0.483260\pi\)
0.0525658 + 0.998617i \(0.483260\pi\)
\(720\) 0 0
\(721\) −16.1461 −0.601311
\(722\) 18.7995 + 15.1065i 0.699646 + 0.562206i
\(723\) 0 0
\(724\) −20.5359 + 4.52724i −0.763212 + 0.168253i
\(725\) 5.02621i 0.186669i
\(726\) 0 0
\(727\) −14.6918 −0.544887 −0.272444 0.962172i \(-0.587832\pi\)
−0.272444 + 0.962172i \(0.587832\pi\)
\(728\) −1.68733 0.835821i −0.0625365 0.0309776i
\(729\) 0 0
\(730\) 7.42711 9.24278i 0.274890 0.342091i
\(731\) 18.6082i 0.688248i
\(732\) 0 0
\(733\) 45.7679i 1.69048i −0.534389 0.845239i \(-0.679458\pi\)
0.534389 0.845239i \(-0.320542\pi\)
\(734\) −1.96362 1.57788i −0.0724787 0.0582408i
\(735\) 0 0
\(736\) −1.01233 0.250890i −0.0373150 0.00924792i
\(737\) 23.1482 0.852673
\(738\) 0 0
\(739\) 37.7771i 1.38965i 0.719178 + 0.694826i \(0.244519\pi\)
−0.719178 + 0.694826i \(0.755481\pi\)
\(740\) 8.61440 + 39.0756i 0.316672 + 1.43645i
\(741\) 0 0
\(742\) 6.62922 8.24984i 0.243366 0.302861i
\(743\) −6.38675 −0.234307 −0.117154 0.993114i \(-0.537377\pi\)
−0.117154 + 0.993114i \(0.537377\pi\)
\(744\) 0 0
\(745\) −9.16812 −0.335894
\(746\) 19.5837 24.3712i 0.717009 0.892294i
\(747\) 0 0
\(748\) −29.4575 + 6.49403i −1.07707 + 0.237445i
\(749\) 15.6131i 0.570490i
\(750\) 0 0
\(751\) 52.5372 1.91711 0.958554 0.284910i \(-0.0919639\pi\)
0.958554 + 0.284910i \(0.0919639\pi\)
\(752\) 20.9674 9.71696i 0.764603 0.354341i
\(753\) 0 0
\(754\) −0.936203 0.752292i −0.0340945 0.0273969i
\(755\) 47.5388i 1.73012i
\(756\) 0 0
\(757\) 3.80676i 0.138359i 0.997604 + 0.0691794i \(0.0220381\pi\)
−0.997604 + 0.0691794i \(0.977962\pi\)
\(758\) 31.3684 39.0369i 1.13935 1.41788i
\(759\) 0 0
\(760\) −5.23761 + 10.5735i −0.189988 + 0.383541i
\(761\) −25.9307 −0.939986 −0.469993 0.882670i \(-0.655744\pi\)
−0.469993 + 0.882670i \(0.655744\pi\)
\(762\) 0 0
\(763\) 4.15829i 0.150540i
\(764\) 6.19561 + 28.1038i 0.224149 + 1.01676i
\(765\) 0 0
\(766\) −26.6700 21.4309i −0.963627 0.774330i
\(767\) −6.01686 −0.217256
\(768\) 0 0
\(769\) −42.2680 −1.52422 −0.762112 0.647445i \(-0.775838\pi\)
−0.762112 + 0.647445i \(0.775838\pi\)
\(770\) −7.05238 5.66699i −0.254150 0.204224i
\(771\) 0 0
\(772\) 4.89039 + 22.1832i 0.176009 + 0.798392i
\(773\) 13.4481i 0.483696i −0.970314 0.241848i \(-0.922246\pi\)
0.970314 0.241848i \(-0.0777536\pi\)
\(774\) 0 0
\(775\) 30.0362 1.07893
\(776\) 0.135207 0.272951i 0.00485365 0.00979838i
\(777\) 0 0
\(778\) −11.5571 + 14.3824i −0.414343 + 0.515635i
\(779\) 0.382445i 0.0137025i
\(780\) 0 0
\(781\) 16.9790i 0.607555i
\(782\) 1.43277 + 1.15132i 0.0512359 + 0.0411710i
\(783\) 0 0
\(784\) −3.62922 + 1.68190i −0.129615 + 0.0600677i
\(785\) −54.7804 −1.95520
\(786\) 0