Properties

Label 1134.2.d.a.1133.11
Level $1134$
Weight $2$
Character 1134.1133
Analytic conductor $9.055$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} + 9 x^{12} + 54 x^{10} - 288 x^{8} + 486 x^{6} + 729 x^{4} - 4374 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{6} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1133.11
Root \(1.69547 + 0.354107i\) of defining polynomial
Character \(\chi\) \(=\) 1134.1133
Dual form 1134.2.d.a.1133.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} -1.79035 q^{5} +(2.28052 + 1.34136i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} -1.79035 q^{5} +(2.28052 + 1.34136i) q^{7} -1.00000i q^{8} -1.79035i q^{10} -2.40150i q^{11} -4.89133i q^{13} +(-1.34136 + 2.28052i) q^{14} +1.00000 q^{16} -3.66466 q^{17} +3.01701i q^{19} +1.79035 q^{20} +2.40150 q^{22} -3.76638i q^{23} -1.79465 q^{25} +4.89133 q^{26} +(-2.28052 - 1.34136i) q^{28} -6.56103i q^{29} -4.64661i q^{31} +1.00000i q^{32} -3.66466i q^{34} +(-4.08292 - 2.40150i) q^{35} +9.36404 q^{37} -3.01701 q^{38} +1.79035i q^{40} -8.08188 q^{41} +6.96254 q^{43} +2.40150i q^{44} +3.76638 q^{46} +5.13604 q^{47} +(3.40150 + 6.11799i) q^{49} -1.79465i q^{50} +4.89133i q^{52} +4.29953i q^{55} +(1.34136 - 2.28052i) q^{56} +6.56103 q^{58} +14.5900 q^{59} -11.3283i q^{61} +4.64661 q^{62} -1.00000 q^{64} +8.75718i q^{65} +0.570231 q^{67} +3.66466 q^{68} +(2.40150 - 4.08292i) q^{70} -5.96254i q^{71} -12.3814i q^{73} +9.36404i q^{74} -3.01701i q^{76} +(3.22128 - 5.47667i) q^{77} +3.03663 q^{79} -1.79035 q^{80} -8.08188i q^{82} -14.0054 q^{83} +6.56103 q^{85} +6.96254i q^{86} -2.40150 q^{88} +3.74863 q^{89} +(6.56103 - 11.1547i) q^{91} +3.76638i q^{92} +5.13604i q^{94} -5.40150i q^{95} -5.51087i q^{97} +(-6.11799 + 3.40150i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 4 q^{7} + O(q^{10}) \) \( 16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −1.79035 −0.800669 −0.400334 0.916369i \(-0.631106\pi\)
−0.400334 + 0.916369i \(0.631106\pi\)
\(6\) 0 0
\(7\) 2.28052 + 1.34136i 0.861954 + 0.506987i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.79035i 0.566158i
\(11\) 2.40150i 0.724081i −0.932162 0.362040i \(-0.882080\pi\)
0.932162 0.362040i \(-0.117920\pi\)
\(12\) 0 0
\(13\) 4.89133i 1.35661i −0.734781 0.678305i \(-0.762715\pi\)
0.734781 0.678305i \(-0.237285\pi\)
\(14\) −1.34136 + 2.28052i −0.358494 + 0.609493i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.66466 −0.888812 −0.444406 0.895826i \(-0.646585\pi\)
−0.444406 + 0.895826i \(0.646585\pi\)
\(18\) 0 0
\(19\) 3.01701i 0.692150i 0.938207 + 0.346075i \(0.112486\pi\)
−0.938207 + 0.346075i \(0.887514\pi\)
\(20\) 1.79035 0.400334
\(21\) 0 0
\(22\) 2.40150 0.512002
\(23\) 3.76638i 0.785345i −0.919678 0.392673i \(-0.871551\pi\)
0.919678 0.392673i \(-0.128449\pi\)
\(24\) 0 0
\(25\) −1.79465 −0.358930
\(26\) 4.89133 0.959268
\(27\) 0 0
\(28\) −2.28052 1.34136i −0.430977 0.253493i
\(29\) 6.56103i 1.21835i −0.793035 0.609176i \(-0.791500\pi\)
0.793035 0.609176i \(-0.208500\pi\)
\(30\) 0 0
\(31\) 4.64661i 0.834556i −0.908779 0.417278i \(-0.862984\pi\)
0.908779 0.417278i \(-0.137016\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 3.66466i 0.628485i
\(35\) −4.08292 2.40150i −0.690140 0.405928i
\(36\) 0 0
\(37\) 9.36404 1.53944 0.769719 0.638382i \(-0.220396\pi\)
0.769719 + 0.638382i \(0.220396\pi\)
\(38\) −3.01701 −0.489424
\(39\) 0 0
\(40\) 1.79035i 0.283079i
\(41\) −8.08188 −1.26218 −0.631088 0.775711i \(-0.717392\pi\)
−0.631088 + 0.775711i \(0.717392\pi\)
\(42\) 0 0
\(43\) 6.96254 1.06178 0.530888 0.847442i \(-0.321858\pi\)
0.530888 + 0.847442i \(0.321858\pi\)
\(44\) 2.40150i 0.362040i
\(45\) 0 0
\(46\) 3.76638 0.555323
\(47\) 5.13604 0.749169 0.374584 0.927193i \(-0.377785\pi\)
0.374584 + 0.927193i \(0.377785\pi\)
\(48\) 0 0
\(49\) 3.40150 + 6.11799i 0.485929 + 0.873998i
\(50\) 1.79465i 0.253802i
\(51\) 0 0
\(52\) 4.89133i 0.678305i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 4.29953i 0.579749i
\(56\) 1.34136 2.28052i 0.179247 0.304747i
\(57\) 0 0
\(58\) 6.56103 0.861506
\(59\) 14.5900 1.89946 0.949729 0.313073i \(-0.101359\pi\)
0.949729 + 0.313073i \(0.101359\pi\)
\(60\) 0 0
\(61\) 11.3283i 1.45044i −0.688518 0.725219i \(-0.741738\pi\)
0.688518 0.725219i \(-0.258262\pi\)
\(62\) 4.64661 0.590120
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 8.75718i 1.08619i
\(66\) 0 0
\(67\) 0.570231 0.0696648 0.0348324 0.999393i \(-0.488910\pi\)
0.0348324 + 0.999393i \(0.488910\pi\)
\(68\) 3.66466 0.444406
\(69\) 0 0
\(70\) 2.40150 4.08292i 0.287035 0.488002i
\(71\) 5.96254i 0.707623i −0.935317 0.353811i \(-0.884885\pi\)
0.935317 0.353811i \(-0.115115\pi\)
\(72\) 0 0
\(73\) 12.3814i 1.44913i −0.689204 0.724567i \(-0.742040\pi\)
0.689204 0.724567i \(-0.257960\pi\)
\(74\) 9.36404i 1.08855i
\(75\) 0 0
\(76\) 3.01701i 0.346075i
\(77\) 3.22128 5.47667i 0.367099 0.624124i
\(78\) 0 0
\(79\) 3.03663 0.341647 0.170824 0.985302i \(-0.445357\pi\)
0.170824 + 0.985302i \(0.445357\pi\)
\(80\) −1.79035 −0.200167
\(81\) 0 0
\(82\) 8.08188i 0.892494i
\(83\) −14.0054 −1.53729 −0.768646 0.639674i \(-0.779069\pi\)
−0.768646 + 0.639674i \(0.779069\pi\)
\(84\) 0 0
\(85\) 6.56103 0.711644
\(86\) 6.96254i 0.750790i
\(87\) 0 0
\(88\) −2.40150 −0.256001
\(89\) 3.74863 0.397354 0.198677 0.980065i \(-0.436336\pi\)
0.198677 + 0.980065i \(0.436336\pi\)
\(90\) 0 0
\(91\) 6.56103 11.1547i 0.687783 1.16934i
\(92\) 3.76638i 0.392673i
\(93\) 0 0
\(94\) 5.13604i 0.529742i
\(95\) 5.40150i 0.554183i
\(96\) 0 0
\(97\) 5.51087i 0.559545i −0.960066 0.279772i \(-0.909741\pi\)
0.960066 0.279772i \(-0.0902590\pi\)
\(98\) −6.11799 + 3.40150i −0.618010 + 0.343604i
\(99\) 0 0
\(100\) 1.79465 0.179465
\(101\) −0.250324 −0.0249082 −0.0124541 0.999922i \(-0.503964\pi\)
−0.0124541 + 0.999922i \(0.503964\pi\)
\(102\) 0 0
\(103\) 0.167931i 0.0165468i 0.999966 + 0.00827339i \(0.00263353\pi\)
−0.999966 + 0.00827339i \(0.997366\pi\)
\(104\) −4.89133 −0.479634
\(105\) 0 0
\(106\) 0 0
\(107\) 7.99080i 0.772500i 0.922394 + 0.386250i \(0.126230\pi\)
−0.922394 + 0.386250i \(0.873770\pi\)
\(108\) 0 0
\(109\) −18.9533 −1.81540 −0.907700 0.419619i \(-0.862164\pi\)
−0.907700 + 0.419619i \(0.862164\pi\)
\(110\) −4.29953 −0.409944
\(111\) 0 0
\(112\) 2.28052 + 1.34136i 0.215488 + 0.126747i
\(113\) 1.15953i 0.109079i 0.998512 + 0.0545396i \(0.0173691\pi\)
−0.998512 + 0.0545396i \(0.982631\pi\)
\(114\) 0 0
\(115\) 6.74314i 0.628801i
\(116\) 6.56103i 0.609176i
\(117\) 0 0
\(118\) 14.5900i 1.34312i
\(119\) −8.35733 4.91564i −0.766115 0.450616i
\(120\) 0 0
\(121\) 5.23278 0.475707
\(122\) 11.3283 1.02561
\(123\) 0 0
\(124\) 4.64661i 0.417278i
\(125\) 12.1648 1.08805
\(126\) 0 0
\(127\) 1.40150 0.124363 0.0621817 0.998065i \(-0.480194\pi\)
0.0621817 + 0.998065i \(0.480194\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) −8.75718 −0.768056
\(131\) −10.4918 −0.916671 −0.458335 0.888779i \(-0.651554\pi\)
−0.458335 + 0.888779i \(0.651554\pi\)
\(132\) 0 0
\(133\) −4.04690 + 6.88034i −0.350911 + 0.596601i
\(134\) 0.570231i 0.0492604i
\(135\) 0 0
\(136\) 3.66466i 0.314242i
\(137\) 4.72056i 0.403305i −0.979457 0.201652i \(-0.935369\pi\)
0.979457 0.201652i \(-0.0646311\pi\)
\(138\) 0 0
\(139\) 2.36375i 0.200491i −0.994963 0.100245i \(-0.968037\pi\)
0.994963 0.100245i \(-0.0319628\pi\)
\(140\) 4.08292 + 2.40150i 0.345070 + 0.202964i
\(141\) 0 0
\(142\) 5.96254 0.500365
\(143\) −11.7465 −0.982295
\(144\) 0 0
\(145\) 11.7465i 0.975497i
\(146\) 12.3814 1.02469
\(147\) 0 0
\(148\) −9.36404 −0.769719
\(149\) 17.3640i 1.42252i 0.702930 + 0.711259i \(0.251875\pi\)
−0.702930 + 0.711259i \(0.748125\pi\)
\(150\) 0 0
\(151\) −11.2328 −0.914110 −0.457055 0.889438i \(-0.651096\pi\)
−0.457055 + 0.889438i \(0.651096\pi\)
\(152\) 3.01701 0.244712
\(153\) 0 0
\(154\) 5.47667 + 3.22128i 0.441322 + 0.259578i
\(155\) 8.31905i 0.668203i
\(156\) 0 0
\(157\) 13.8431i 1.10480i 0.833580 + 0.552399i \(0.186287\pi\)
−0.833580 + 0.552399i \(0.813713\pi\)
\(158\) 3.03663i 0.241581i
\(159\) 0 0
\(160\) 1.79035i 0.141540i
\(161\) 5.05208 8.58930i 0.398159 0.676931i
\(162\) 0 0
\(163\) −4.33577 −0.339604 −0.169802 0.985478i \(-0.554313\pi\)
−0.169802 + 0.985478i \(0.554313\pi\)
\(164\) 8.08188 0.631088
\(165\) 0 0
\(166\) 14.0054i 1.08703i
\(167\) −12.4151 −0.960711 −0.480355 0.877074i \(-0.659492\pi\)
−0.480355 + 0.877074i \(0.659492\pi\)
\(168\) 0 0
\(169\) −10.9251 −0.840390
\(170\) 6.56103i 0.503208i
\(171\) 0 0
\(172\) −6.96254 −0.530888
\(173\) 17.4182 1.32428 0.662139 0.749381i \(-0.269649\pi\)
0.662139 + 0.749381i \(0.269649\pi\)
\(174\) 0 0
\(175\) −4.09272 2.40727i −0.309381 0.181973i
\(176\) 2.40150i 0.181020i
\(177\) 0 0
\(178\) 3.74863i 0.280972i
\(179\) 13.1221i 0.980789i −0.871501 0.490395i \(-0.836853\pi\)
0.871501 0.490395i \(-0.163147\pi\)
\(180\) 0 0
\(181\) 13.3577i 0.992873i 0.868073 + 0.496437i \(0.165359\pi\)
−0.868073 + 0.496437i \(0.834641\pi\)
\(182\) 11.1547 + 6.56103i 0.826845 + 0.486336i
\(183\) 0 0
\(184\) −3.76638 −0.277661
\(185\) −16.7649 −1.23258
\(186\) 0 0
\(187\) 8.80071i 0.643572i
\(188\) −5.13604 −0.374584
\(189\) 0 0
\(190\) 5.40150 0.391866
\(191\) 9.25333i 0.669547i −0.942299 0.334774i \(-0.891340\pi\)
0.942299 0.334774i \(-0.108660\pi\)
\(192\) 0 0
\(193\) −24.5602 −1.76788 −0.883941 0.467599i \(-0.845119\pi\)
−0.883941 + 0.467599i \(0.845119\pi\)
\(194\) 5.51087 0.395658
\(195\) 0 0
\(196\) −3.40150 6.11799i −0.242965 0.436999i
\(197\) 12.4861i 0.889598i 0.895630 + 0.444799i \(0.146725\pi\)
−0.895630 + 0.444799i \(0.853275\pi\)
\(198\) 0 0
\(199\) 0.179145i 0.0126993i 0.999980 + 0.00634964i \(0.00202117\pi\)
−0.999980 + 0.00634964i \(0.997979\pi\)
\(200\) 1.79465i 0.126901i
\(201\) 0 0
\(202\) 0.250324i 0.0176127i
\(203\) 8.80071 14.9625i 0.617689 1.05016i
\(204\) 0 0
\(205\) 14.4694 1.01059
\(206\) −0.167931 −0.0117003
\(207\) 0 0
\(208\) 4.89133i 0.339152i
\(209\) 7.24536 0.501172
\(210\) 0 0
\(211\) −15.1221 −1.04105 −0.520523 0.853848i \(-0.674263\pi\)
−0.520523 + 0.853848i \(0.674263\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −7.99080 −0.546240
\(215\) −12.4654 −0.850131
\(216\) 0 0
\(217\) 6.23278 10.5967i 0.423109 0.719348i
\(218\) 18.9533i 1.28368i
\(219\) 0 0
\(220\) 4.29953i 0.289874i
\(221\) 17.9251i 1.20577i
\(222\) 0 0
\(223\) 8.39524i 0.562187i 0.959680 + 0.281093i \(0.0906971\pi\)
−0.959680 + 0.281093i \(0.909303\pi\)
\(224\) −1.34136 + 2.28052i −0.0896234 + 0.152373i
\(225\) 0 0
\(226\) −1.15953 −0.0771306
\(227\) 2.42522 0.160967 0.0804836 0.996756i \(-0.474354\pi\)
0.0804836 + 0.996756i \(0.474354\pi\)
\(228\) 0 0
\(229\) 2.01975i 0.133469i 0.997771 + 0.0667344i \(0.0212580\pi\)
−0.997771 + 0.0667344i \(0.978742\pi\)
\(230\) −6.74314 −0.444630
\(231\) 0 0
\(232\) −6.56103 −0.430753
\(233\) 12.7289i 0.833899i −0.908930 0.416950i \(-0.863099\pi\)
0.908930 0.416950i \(-0.136901\pi\)
\(234\) 0 0
\(235\) −9.19531 −0.599836
\(236\) −14.5900 −0.949729
\(237\) 0 0
\(238\) 4.91564 8.35733i 0.318633 0.541725i
\(239\) 17.4495i 1.12871i −0.825531 0.564356i \(-0.809124\pi\)
0.825531 0.564356i \(-0.190876\pi\)
\(240\) 0 0
\(241\) 11.4332i 0.736476i −0.929732 0.368238i \(-0.879961\pi\)
0.929732 0.368238i \(-0.120039\pi\)
\(242\) 5.23278i 0.336376i
\(243\) 0 0
\(244\) 11.3283i 0.725219i
\(245\) −6.08988 10.9533i −0.389068 0.699783i
\(246\) 0 0
\(247\) 14.7572 0.938977
\(248\) −4.64661 −0.295060
\(249\) 0 0
\(250\) 12.1648i 0.769369i
\(251\) 27.3560 1.72669 0.863347 0.504611i \(-0.168364\pi\)
0.863347 + 0.504611i \(0.168364\pi\)
\(252\) 0 0
\(253\) −9.04499 −0.568653
\(254\) 1.40150i 0.0879382i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 3.49673 0.218120 0.109060 0.994035i \(-0.465216\pi\)
0.109060 + 0.994035i \(0.465216\pi\)
\(258\) 0 0
\(259\) 21.3548 + 12.5606i 1.32693 + 0.780475i
\(260\) 8.75718i 0.543097i
\(261\) 0 0
\(262\) 10.4918i 0.648184i
\(263\) 9.64348i 0.594643i −0.954777 0.297321i \(-0.903907\pi\)
0.954777 0.297321i \(-0.0960932\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −6.88034 4.04690i −0.421861 0.248131i
\(267\) 0 0
\(268\) −0.570231 −0.0348324
\(269\) 6.91107 0.421376 0.210688 0.977553i \(-0.432430\pi\)
0.210688 + 0.977553i \(0.432430\pi\)
\(270\) 0 0
\(271\) 20.6312i 1.25326i 0.779318 + 0.626629i \(0.215566\pi\)
−0.779318 + 0.626629i \(0.784434\pi\)
\(272\) −3.66466 −0.222203
\(273\) 0 0
\(274\) 4.72056 0.285179
\(275\) 4.30986i 0.259894i
\(276\) 0 0
\(277\) −15.5144 −0.932168 −0.466084 0.884740i \(-0.654336\pi\)
−0.466084 + 0.884740i \(0.654336\pi\)
\(278\) 2.36375 0.141768
\(279\) 0 0
\(280\) −2.40150 + 4.08292i −0.143517 + 0.244001i
\(281\) 13.5977i 0.811168i 0.914058 + 0.405584i \(0.132932\pi\)
−0.914058 + 0.405584i \(0.867068\pi\)
\(282\) 0 0
\(283\) 5.44783i 0.323840i −0.986804 0.161920i \(-0.948231\pi\)
0.986804 0.161920i \(-0.0517687\pi\)
\(284\) 5.96254i 0.353811i
\(285\) 0 0
\(286\) 11.7465i 0.694587i
\(287\) −18.4308 10.8407i −1.08794 0.639907i
\(288\) 0 0
\(289\) −3.57023 −0.210014
\(290\) −11.7465 −0.689781
\(291\) 0 0
\(292\) 12.3814i 0.724567i
\(293\) 24.4622 1.42910 0.714550 0.699585i \(-0.246632\pi\)
0.714550 + 0.699585i \(0.246632\pi\)
\(294\) 0 0
\(295\) −26.1212 −1.52084
\(296\) 9.36404i 0.544274i
\(297\) 0 0
\(298\) −17.3640 −1.00587
\(299\) −18.4226 −1.06541
\(300\) 0 0
\(301\) 15.8782 + 9.33927i 0.915203 + 0.538307i
\(302\) 11.2328i 0.646374i
\(303\) 0 0
\(304\) 3.01701i 0.173037i
\(305\) 20.2816i 1.16132i
\(306\) 0 0
\(307\) 31.2223i 1.78195i −0.454053 0.890975i \(-0.650022\pi\)
0.454053 0.890975i \(-0.349978\pi\)
\(308\) −3.22128 + 5.47667i −0.183550 + 0.312062i
\(309\) 0 0
\(310\) −8.31905 −0.472491
\(311\) −10.9100 −0.618651 −0.309325 0.950956i \(-0.600103\pi\)
−0.309325 + 0.950956i \(0.600103\pi\)
\(312\) 0 0
\(313\) 3.42405i 0.193539i −0.995307 0.0967694i \(-0.969149\pi\)
0.995307 0.0967694i \(-0.0308509\pi\)
\(314\) −13.8431 −0.781210
\(315\) 0 0
\(316\) −3.03663 −0.170824
\(317\) 19.0471i 1.06979i 0.844917 + 0.534897i \(0.179650\pi\)
−0.844917 + 0.534897i \(0.820350\pi\)
\(318\) 0 0
\(319\) −15.7563 −0.882186
\(320\) 1.79035 0.100084
\(321\) 0 0
\(322\) 8.58930 + 5.05208i 0.478663 + 0.281541i
\(323\) 11.0563i 0.615191i
\(324\) 0 0
\(325\) 8.77821i 0.486927i
\(326\) 4.33577i 0.240136i
\(327\) 0 0
\(328\) 8.08188i 0.446247i
\(329\) 11.7128 + 6.88929i 0.645749 + 0.379819i
\(330\) 0 0
\(331\) 0.0732502 0.00402620 0.00201310 0.999998i \(-0.499359\pi\)
0.00201310 + 0.999998i \(0.499359\pi\)
\(332\) 14.0054 0.768646
\(333\) 0 0
\(334\) 12.4151i 0.679325i
\(335\) −1.02091 −0.0557784
\(336\) 0 0
\(337\) −2.23278 −0.121627 −0.0608136 0.998149i \(-0.519370\pi\)
−0.0608136 + 0.998149i \(0.519370\pi\)
\(338\) 10.9251i 0.594246i
\(339\) 0 0
\(340\) −6.56103 −0.355822
\(341\) −11.1589 −0.604286
\(342\) 0 0
\(343\) −0.449242 + 18.5148i −0.0242568 + 0.999706i
\(344\) 6.96254i 0.375395i
\(345\) 0 0
\(346\) 17.4182i 0.936406i
\(347\) 31.8409i 1.70931i −0.519195 0.854656i \(-0.673768\pi\)
0.519195 0.854656i \(-0.326232\pi\)
\(348\) 0 0
\(349\) 14.7354i 0.788770i 0.918945 + 0.394385i \(0.129042\pi\)
−0.918945 + 0.394385i \(0.870958\pi\)
\(350\) 2.40727 4.09272i 0.128674 0.218765i
\(351\) 0 0
\(352\) 2.40150 0.128001
\(353\) −2.15957 −0.114943 −0.0574713 0.998347i \(-0.518304\pi\)
−0.0574713 + 0.998347i \(0.518304\pi\)
\(354\) 0 0
\(355\) 10.6750i 0.566571i
\(356\) −3.74863 −0.198677
\(357\) 0 0
\(358\) 13.1221 0.693523
\(359\) 32.6448i 1.72293i 0.507820 + 0.861463i \(0.330451\pi\)
−0.507820 + 0.861463i \(0.669549\pi\)
\(360\) 0 0
\(361\) 9.89765 0.520929
\(362\) −13.3577 −0.702067
\(363\) 0 0
\(364\) −6.56103 + 11.1547i −0.343891 + 0.584668i
\(365\) 22.1670i 1.16028i
\(366\) 0 0
\(367\) 29.7003i 1.55034i −0.631751 0.775171i \(-0.717664\pi\)
0.631751 0.775171i \(-0.282336\pi\)
\(368\) 3.76638i 0.196336i
\(369\) 0 0
\(370\) 16.7649i 0.871566i
\(371\) 0 0
\(372\) 0 0
\(373\) −2.01672 −0.104422 −0.0522109 0.998636i \(-0.516627\pi\)
−0.0522109 + 0.998636i \(0.516627\pi\)
\(374\) −8.80071 −0.455074
\(375\) 0 0
\(376\) 5.13604i 0.264871i
\(377\) −32.0921 −1.65283
\(378\) 0 0
\(379\) −18.8709 −0.969332 −0.484666 0.874699i \(-0.661059\pi\)
−0.484666 + 0.874699i \(0.661059\pi\)
\(380\) 5.40150i 0.277091i
\(381\) 0 0
\(382\) 9.25333 0.473441
\(383\) −0.836511 −0.0427437 −0.0213719 0.999772i \(-0.506803\pi\)
−0.0213719 + 0.999772i \(0.506803\pi\)
\(384\) 0 0
\(385\) −5.76722 + 9.80515i −0.293925 + 0.499717i
\(386\) 24.5602i 1.25008i
\(387\) 0 0
\(388\) 5.51087i 0.279772i
\(389\) 24.8219i 1.25852i 0.777195 + 0.629260i \(0.216642\pi\)
−0.777195 + 0.629260i \(0.783358\pi\)
\(390\) 0 0
\(391\) 13.8025i 0.698024i
\(392\) 6.11799 3.40150i 0.309005 0.171802i
\(393\) 0 0
\(394\) −12.4861 −0.629041
\(395\) −5.43662 −0.273546
\(396\) 0 0
\(397\) 3.03390i 0.152267i −0.997098 0.0761336i \(-0.975742\pi\)
0.997098 0.0761336i \(-0.0242575\pi\)
\(398\) −0.179145 −0.00897975
\(399\) 0 0
\(400\) −1.79465 −0.0897324
\(401\) 13.0771i 0.653038i −0.945191 0.326519i \(-0.894124\pi\)
0.945191 0.326519i \(-0.105876\pi\)
\(402\) 0 0
\(403\) −22.7281 −1.13217
\(404\) 0.250324 0.0124541
\(405\) 0 0
\(406\) 14.9625 + 8.80071i 0.742578 + 0.436772i
\(407\) 22.4878i 1.11468i
\(408\) 0 0
\(409\) 5.56709i 0.275275i 0.990483 + 0.137637i \(0.0439508\pi\)
−0.990483 + 0.137637i \(0.956049\pi\)
\(410\) 14.4694i 0.714592i
\(411\) 0 0
\(412\) 0.167931i 0.00827339i
\(413\) 33.2728 + 19.5705i 1.63725 + 0.963000i
\(414\) 0 0
\(415\) 25.0746 1.23086
\(416\) 4.89133 0.239817
\(417\) 0 0
\(418\) 7.24536i 0.354382i
\(419\) 16.3988 0.801132 0.400566 0.916268i \(-0.368814\pi\)
0.400566 + 0.916268i \(0.368814\pi\)
\(420\) 0 0
\(421\) 15.4578 0.753369 0.376684 0.926342i \(-0.377064\pi\)
0.376684 + 0.926342i \(0.377064\pi\)
\(422\) 15.1221i 0.736131i
\(423\) 0 0
\(424\) 0 0
\(425\) 6.57678 0.319021
\(426\) 0 0
\(427\) 15.1953 25.8343i 0.735353 1.25021i
\(428\) 7.99080i 0.386250i
\(429\) 0 0
\(430\) 12.4654i 0.601134i
\(431\) 25.0266i 1.20549i −0.797935 0.602744i \(-0.794074\pi\)
0.797935 0.602744i \(-0.205926\pi\)
\(432\) 0 0
\(433\) 2.25168i 0.108209i −0.998535 0.0541044i \(-0.982770\pi\)
0.998535 0.0541044i \(-0.0172304\pi\)
\(434\) 10.5967 + 6.23278i 0.508656 + 0.299183i
\(435\) 0 0
\(436\) 18.9533 0.907700
\(437\) 11.3632 0.543576
\(438\) 0 0
\(439\) 18.7400i 0.894412i −0.894431 0.447206i \(-0.852419\pi\)
0.894431 0.447206i \(-0.147581\pi\)
\(440\) 4.29953 0.204972
\(441\) 0 0
\(442\) −17.9251 −0.852609
\(443\) 1.20451i 0.0572281i −0.999591 0.0286141i \(-0.990891\pi\)
0.999591 0.0286141i \(-0.00910938\pi\)
\(444\) 0 0
\(445\) −6.71136 −0.318149
\(446\) −8.39524 −0.397526
\(447\) 0 0
\(448\) −2.28052 1.34136i −0.107744 0.0633733i
\(449\) 26.8022i 1.26487i 0.774612 + 0.632436i \(0.217945\pi\)
−0.774612 + 0.632436i \(0.782055\pi\)
\(450\) 0 0
\(451\) 19.4087i 0.913918i
\(452\) 1.15953i 0.0545396i
\(453\) 0 0
\(454\) 2.42522i 0.113821i
\(455\) −11.7465 + 19.9709i −0.550686 + 0.936250i
\(456\) 0 0
\(457\) 13.8488 0.647821 0.323911 0.946088i \(-0.395002\pi\)
0.323911 + 0.946088i \(0.395002\pi\)
\(458\) −2.01975 −0.0943766
\(459\) 0 0
\(460\) 6.74314i 0.314401i
\(461\) 4.80483 0.223783 0.111892 0.993720i \(-0.464309\pi\)
0.111892 + 0.993720i \(0.464309\pi\)
\(462\) 0 0
\(463\) −21.0388 −0.977755 −0.488877 0.872353i \(-0.662593\pi\)
−0.488877 + 0.872353i \(0.662593\pi\)
\(464\) 6.56103i 0.304588i
\(465\) 0 0
\(466\) 12.7289 0.589656
\(467\) −5.82302 −0.269457 −0.134729 0.990883i \(-0.543016\pi\)
−0.134729 + 0.990883i \(0.543016\pi\)
\(468\) 0 0
\(469\) 1.30042 + 0.764885i 0.0600478 + 0.0353191i
\(470\) 9.19531i 0.424148i
\(471\) 0 0
\(472\) 14.5900i 0.671560i
\(473\) 16.7206i 0.768812i
\(474\) 0 0
\(475\) 5.41447i 0.248433i
\(476\) 8.35733 + 4.91564i 0.383057 + 0.225308i
\(477\) 0 0
\(478\) 17.4495 0.798121
\(479\) 26.9561 1.23166 0.615828 0.787881i \(-0.288822\pi\)
0.615828 + 0.787881i \(0.288822\pi\)
\(480\) 0 0
\(481\) 45.8026i 2.08842i
\(482\) 11.4332 0.520767
\(483\) 0 0
\(484\) −5.23278 −0.237854
\(485\) 9.86639i 0.448010i
\(486\) 0 0
\(487\) −13.6268 −0.617487 −0.308744 0.951145i \(-0.599909\pi\)
−0.308744 + 0.951145i \(0.599909\pi\)
\(488\) −11.3283 −0.512807
\(489\) 0 0
\(490\) 10.9533 6.08988i 0.494821 0.275113i
\(491\) 38.9630i 1.75838i 0.476475 + 0.879188i \(0.341914\pi\)
−0.476475 + 0.879188i \(0.658086\pi\)
\(492\) 0 0
\(493\) 24.0440i 1.08289i
\(494\) 14.7572i 0.663957i
\(495\) 0 0
\(496\) 4.64661i 0.208639i
\(497\) 7.99791 13.5977i 0.358755 0.609938i
\(498\) 0 0
\(499\) 26.0097 1.16435 0.582176 0.813063i \(-0.302201\pi\)
0.582176 + 0.813063i \(0.302201\pi\)
\(500\) −12.1648 −0.544026
\(501\) 0 0
\(502\) 27.3560i 1.22096i
\(503\) −10.5271 −0.469378 −0.234689 0.972070i \(-0.575407\pi\)
−0.234689 + 0.972070i \(0.575407\pi\)
\(504\) 0 0
\(505\) 0.448168 0.0199432
\(506\) 9.04499i 0.402099i
\(507\) 0 0
\(508\) −1.40150 −0.0621817
\(509\) 0.938871 0.0416147 0.0208074 0.999784i \(-0.493376\pi\)
0.0208074 + 0.999784i \(0.493376\pi\)
\(510\) 0 0
\(511\) 16.6079 28.2360i 0.734692 1.24909i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 3.49673i 0.154234i
\(515\) 0.300656i 0.0132485i
\(516\) 0 0
\(517\) 12.3342i 0.542459i
\(518\) −12.5606 + 21.3548i −0.551879 + 0.938278i
\(519\) 0 0
\(520\) 8.75718 0.384028
\(521\) 39.5054 1.73076 0.865382 0.501112i \(-0.167076\pi\)
0.865382 + 0.501112i \(0.167076\pi\)
\(522\) 0 0
\(523\) 24.3292i 1.06384i −0.846794 0.531922i \(-0.821470\pi\)
0.846794 0.531922i \(-0.178530\pi\)
\(524\) 10.4918 0.458335
\(525\) 0 0
\(526\) 9.64348 0.420476
\(527\) 17.0283i 0.741763i
\(528\) 0 0
\(529\) 8.81436 0.383233
\(530\) 0 0
\(531\) 0 0
\(532\) 4.04690 6.88034i 0.175455 0.298301i
\(533\) 39.5311i 1.71228i
\(534\) 0 0
\(535\) 14.3063i 0.618516i
\(536\) 0.570231i 0.0246302i
\(537\) 0 0
\(538\) 6.91107i 0.297958i
\(539\) 14.6924 8.16873i 0.632845 0.351852i
\(540\) 0 0
\(541\) 42.7281 1.83702 0.918512 0.395394i \(-0.129392\pi\)
0.918512 + 0.395394i \(0.129392\pi\)
\(542\) −20.6312 −0.886187
\(543\) 0 0
\(544\) 3.66466i 0.157121i
\(545\) 33.9331 1.45353
\(546\) 0 0
\(547\) 24.4953 1.04734 0.523672 0.851920i \(-0.324562\pi\)
0.523672 + 0.851920i \(0.324562\pi\)
\(548\) 4.72056i 0.201652i
\(549\) 0 0
\(550\) −4.30986 −0.183773
\(551\) 19.7947 0.843283
\(552\) 0 0
\(553\) 6.92507 + 4.07321i 0.294484 + 0.173210i
\(554\) 15.5144i 0.659142i
\(555\) 0 0
\(556\) 2.36375i 0.100245i
\(557\) 2.54431i 0.107806i −0.998546 0.0539030i \(-0.982834\pi\)
0.998546 0.0539030i \(-0.0171662\pi\)
\(558\) 0 0
\(559\) 34.0560i 1.44042i
\(560\) −4.08292 2.40150i −0.172535 0.101482i
\(561\) 0 0
\(562\) −13.5977 −0.573583
\(563\) −15.8141 −0.666487 −0.333243 0.942841i \(-0.608143\pi\)
−0.333243 + 0.942841i \(0.608143\pi\)
\(564\) 0 0
\(565\) 2.07596i 0.0873363i
\(566\) 5.44783 0.228990
\(567\) 0 0
\(568\) −5.96254 −0.250182
\(569\) 6.38311i 0.267594i −0.991009 0.133797i \(-0.957283\pi\)
0.991009 0.133797i \(-0.0427170\pi\)
\(570\) 0 0
\(571\) −7.82375 −0.327414 −0.163707 0.986509i \(-0.552345\pi\)
−0.163707 + 0.986509i \(0.552345\pi\)
\(572\) 11.7465 0.491148
\(573\) 0 0
\(574\) 10.8407 18.4308i 0.452482 0.769289i
\(575\) 6.75933i 0.281884i
\(576\) 0 0
\(577\) 14.3197i 0.596138i 0.954544 + 0.298069i \(0.0963425\pi\)
−0.954544 + 0.298069i \(0.903657\pi\)
\(578\) 3.57023i 0.148502i
\(579\) 0 0
\(580\) 11.7465i 0.487749i
\(581\) −31.9395 18.7863i −1.32508 0.779387i
\(582\) 0 0
\(583\) 0 0
\(584\) −12.3814 −0.512346
\(585\) 0 0
\(586\) 24.4622i 1.01053i
\(587\) −4.75150 −0.196115 −0.0980577 0.995181i \(-0.531263\pi\)
−0.0980577 + 0.995181i \(0.531263\pi\)
\(588\) 0 0
\(589\) 14.0189 0.577637
\(590\) 26.1212i 1.07539i
\(591\) 0 0
\(592\) 9.36404 0.384860
\(593\) −3.58070 −0.147042 −0.0735208 0.997294i \(-0.523424\pi\)
−0.0735208 + 0.997294i \(0.523424\pi\)
\(594\) 0 0
\(595\) 14.9625 + 8.80071i 0.613404 + 0.360794i
\(596\) 17.3640i 0.711259i
\(597\) 0 0
\(598\) 18.4226i 0.753357i
\(599\) 15.0655i 0.615561i 0.951457 + 0.307780i \(0.0995862\pi\)
−0.951457 + 0.307780i \(0.900414\pi\)
\(600\) 0 0
\(601\) 22.9444i 0.935920i 0.883750 + 0.467960i \(0.155011\pi\)
−0.883750 + 0.467960i \(0.844989\pi\)
\(602\) −9.33927 + 15.8782i −0.380640 + 0.647146i
\(603\) 0 0
\(604\) 11.2328 0.457055
\(605\) −9.36850 −0.380884
\(606\) 0 0
\(607\) 24.4832i 0.993741i 0.867825 + 0.496870i \(0.165518\pi\)
−0.867825 + 0.496870i \(0.834482\pi\)
\(608\) −3.01701 −0.122356
\(609\) 0 0
\(610\) −20.2816 −0.821178
\(611\) 25.1221i 1.01633i
\(612\) 0 0
\(613\) −0.880086 −0.0355463 −0.0177732 0.999842i \(-0.505658\pi\)
−0.0177732 + 0.999842i \(0.505658\pi\)
\(614\) 31.2223 1.26003
\(615\) 0 0
\(616\) −5.47667 3.22128i −0.220661 0.129789i
\(617\) 13.5801i 0.546714i 0.961913 + 0.273357i \(0.0881341\pi\)
−0.961913 + 0.273357i \(0.911866\pi\)
\(618\) 0 0
\(619\) 35.4869i 1.42634i 0.700992 + 0.713169i \(0.252741\pi\)
−0.700992 + 0.713169i \(0.747259\pi\)
\(620\) 8.31905i 0.334101i
\(621\) 0 0
\(622\) 10.9100i 0.437452i
\(623\) 8.54881 + 5.02826i 0.342501 + 0.201453i
\(624\) 0 0
\(625\) −12.8060 −0.512240
\(626\) 3.42405 0.136853
\(627\) 0 0
\(628\) 13.8431i 0.552399i
\(629\) −34.3161 −1.36827
\(630\) 0 0
\(631\) 26.9822 1.07415 0.537073 0.843536i \(-0.319530\pi\)
0.537073 + 0.843536i \(0.319530\pi\)
\(632\) 3.03663i 0.120790i
\(633\) 0 0
\(634\) −19.0471 −0.756458
\(635\) −2.50918 −0.0995739
\(636\) 0 0
\(637\) 29.9251 16.6379i 1.18567 0.659216i
\(638\) 15.7563i 0.623800i
\(639\) 0 0
\(640\) 1.79035i 0.0707698i
\(641\) 1.07708i 0.0425420i 0.999774 + 0.0212710i \(0.00677128\pi\)
−0.999774 + 0.0212710i \(0.993229\pi\)
\(642\) 0 0
\(643\) 38.4661i 1.51695i 0.651700 + 0.758477i \(0.274056\pi\)
−0.651700 + 0.758477i \(0.725944\pi\)
\(644\) −5.05208 + 8.58930i −0.199080 + 0.338466i
\(645\) 0 0
\(646\) 11.0563 0.435006
\(647\) 8.95210 0.351943 0.175972 0.984395i \(-0.443693\pi\)
0.175972 + 0.984395i \(0.443693\pi\)
\(648\) 0 0
\(649\) 35.0380i 1.37536i
\(650\) −8.77821 −0.344310
\(651\) 0 0
\(652\) 4.33577 0.169802
\(653\) 11.3846i 0.445513i 0.974874 + 0.222757i \(0.0715055\pi\)
−0.974874 + 0.222757i \(0.928494\pi\)
\(654\) 0 0
\(655\) 18.7839 0.733949
\(656\) −8.08188 −0.315544
\(657\) 0 0
\(658\) −6.88929 + 11.7128i −0.268572 + 0.456614i
\(659\) 36.3007i 1.41407i 0.707177 + 0.707036i \(0.249968\pi\)
−0.707177 + 0.707036i \(0.750032\pi\)
\(660\) 0 0
\(661\) 36.0758i 1.40319i −0.712578 0.701593i \(-0.752473\pi\)
0.712578 0.701593i \(-0.247527\pi\)
\(662\) 0.0732502i 0.00284695i
\(663\) 0 0
\(664\) 14.0054i 0.543515i
\(665\) 7.24536 12.3182i 0.280963 0.477680i
\(666\) 0 0
\(667\) −24.7114 −0.956828
\(668\) 12.4151 0.480355
\(669\) 0 0
\(670\) 1.02091i 0.0394413i
\(671\) −27.2049 −1.05023
\(672\) 0 0
\(673\) −9.57023 −0.368905 −0.184453 0.982841i \(-0.559051\pi\)
−0.184453 + 0.982841i \(0.559051\pi\)
\(674\) 2.23278i 0.0860034i
\(675\) 0 0
\(676\) 10.9251 0.420195
\(677\) 15.6282 0.600639 0.300320 0.953839i \(-0.402907\pi\)
0.300320 + 0.953839i \(0.402907\pi\)
\(678\) 0 0
\(679\) 7.39207 12.5676i 0.283682 0.482302i
\(680\) 6.56103i 0.251604i
\(681\) 0 0
\(682\) 11.1589i 0.427294i
\(683\) 11.1313i 0.425926i 0.977060 + 0.212963i \(0.0683114\pi\)
−0.977060 + 0.212963i \(0.931689\pi\)
\(684\) 0 0
\(685\) 8.45145i 0.322913i
\(686\) −18.5148 0.449242i −0.706899 0.0171522i
\(687\) 0 0
\(688\) 6.96254 0.265444
\(689\) 0 0
\(690\) 0 0
\(691\) 3.02419i 0.115046i −0.998344 0.0575228i \(-0.981680\pi\)
0.998344 0.0575228i \(-0.0183202\pi\)
\(692\) −17.4182 −0.662139
\(693\) 0 0
\(694\) 31.8409 1.20867
\(695\) 4.23194i 0.160527i
\(696\) 0 0
\(697\) 29.6174 1.12184
\(698\) −14.7354 −0.557745
\(699\) 0 0
\(700\) 4.09272 + 2.40727i 0.154690 + 0.0909863i
\(701\) 50.1486i 1.89409i 0.321103 + 0.947044i \(0.395946\pi\)
−0.321103 + 0.947044i \(0.604054\pi\)
\(702\) 0 0
\(703\) 28.2514i 1.06552i
\(704\) 2.40150i 0.0905101i
\(705\) 0 0
\(706\) 2.15957i 0.0812766i
\(707\) −0.570868 0.335775i −0.0214697 0.0126281i
\(708\) 0 0
\(709\) −3.60770 −0.135490 −0.0677449 0.997703i \(-0.521580\pi\)
−0.0677449 + 0.997703i \(0.521580\pi\)
\(710\) −10.6750 −0.400626
\(711\) 0 0
\(712\) 3.74863i 0.140486i
\(713\) −17.5009 −0.655414
\(714\) 0 0
\(715\) 21.0304 0.786493
\(716\) 13.1221i 0.490395i
\(717\) 0 0
\(718\) −32.6448 −1.21829
\(719\) 34.3161 1.27977 0.639887 0.768469i \(-0.278981\pi\)
0.639887 + 0.768469i \(0.278981\pi\)
\(720\) 0 0
\(721\) −0.225257 + 0.382970i −0.00838899 + 0.0142626i
\(722\) 9.89765i 0.368352i
\(723\) 0 0
\(724\) 13.3577i 0.496437i
\(725\) 11.7747i 0.437303i
\(726\) 0 0
\(727\) 22.4886i 0.834057i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(728\) −11.1547 6.56103i −0.413422 0.243168i
\(729\) 0 0
\(730\) −22.1670 −0.820439
\(731\) −25.5154 −0.943720
\(732\) 0 0
\(733\) 31.1845i 1.15182i 0.817512 + 0.575912i \(0.195353\pi\)
−0.817512 + 0.575912i \(0.804647\pi\)
\(734\) 29.7003 1.09626
\(735\) 0 0
\(736\) 3.76638 0.138831
\(737\) 1.36941i 0.0504429i
\(738\) 0 0
\(739\) 4.08628 0.150316 0.0751581 0.997172i \(-0.476054\pi\)
0.0751581 + 0.997172i \(0.476054\pi\)
\(740\) 16.7649 0.616290
\(741\) 0 0
\(742\) 0 0
\(743\) 2.05821i 0.0755083i 0.999287 + 0.0377542i \(0.0120204\pi\)
−0.999287 + 0.0377542i \(0.987980\pi\)
\(744\) 0 0
\(745\) 31.0877i 1.13897i
\(746\) 2.01672i 0.0738374i
\(747\) 0 0
\(748\) 8.80071i 0.321786i
\(749\) −10.7185 + 18.2231i −0.391647 + 0.665859i
\(750\) 0 0
\(751\) 23.8105 0.868859 0.434429 0.900706i \(-0.356950\pi\)
0.434429 + 0.900706i \(0.356950\pi\)
\(752\) 5.13604 0.187292
\(753\) 0 0
\(754\) 32.0921i 1.16873i
\(755\) 20.1106 0.731900
\(756\) 0 0
\(757\) 10.0754 0.366197 0.183098 0.983095i \(-0.441387\pi\)
0.183098 + 0.983095i \(0.441387\pi\)
\(758\) 18.8709i 0.685421i
\(759\) 0 0
\(760\) −5.40150 −0.195933
\(761\) 27.8735 1.01041 0.505207 0.862998i \(-0.331416\pi\)
0.505207 + 0.862998i \(0.331416\pi\)
\(762\) 0 0
\(763\) −43.2234 25.4233i −1.56479 0.920384i
\(764\) 9.25333i 0.334774i
\(765\) 0 0
\(766\) 0.836511i 0.0302244i
\(767\) 71.3645i 2.57682i
\(768\) 0 0
\(769\) 7.17261i 0.258651i −0.991602 0.129326i \(-0.958719\pi\)
0.991602 0.129326i \(-0.0412812\pi\)
\(770\) −9.80515 5.76722i −0.353353 0.207836i
\(771\) 0 0
\(772\) 24.5602 0.883941
\(773\) 2.14153 0.0770255 0.0385128 0.999258i \(-0.487738\pi\)
0.0385128 + 0.999258i \(0.487738\pi\)
\(774\) 0 0
\(775\) 8.33903i 0.299547i
\(776\) −5.51087 −0.197829
\(777\) 0 0
\(778\) −24.8219 −0.889907
\(779\) 24.3831i 0.873615i
\(780\) 0 0
\(781\) −14.3191 −0.512376
\(782\) −13.8025 −0.493578
\(783\) 0 0
\(784\) 3.40150 + 6.11799i 0.121482 + 0.218500i
\(785\) 24.7839i 0.884577i
\(786\) 0 0
\(787\) 18.3552i 0.654292i 0.944974 + 0.327146i \(0.106087\pi\)
−0.944974 + 0.327146i \(0.893913\pi\)
\(788\) 12.4861i 0.444799i
\(789\) 0 0
\(790\) 5.43662i 0.193426i
\(791\) −1.55534 + 2.64432i −0.0553017 + 0.0940212i
\(792\) 0 0
\(793\) −55.4103 −1.96768
\(794\) 3.03390 0.107669
\(795\) 0 0
\(796\) 0.179145i 0.00634964i
\(797\) 24.8452 0.880062 0.440031 0.897982i \(-0.354967\pi\)
0.440031 + 0.897982i \(0.354967\pi\)
\(798\) 0 0
\(799\) −18.8219 −0.665870