Properties

Label 483.2.h.b.160.3
Level $483$
Weight $2$
Character 483.160
Analytic conductor $3.857$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 14 x^{10} + 67 x^{8} + 141 x^{6} + 129 x^{4} + 39 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 160.3
Root \(-1.64421i\) of defining polynomial
Character \(\chi\) \(=\) 483.160
Dual form 483.2.h.b.160.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.11491 q^{2} +1.00000i q^{3} +2.47283 q^{4} -1.98969 q^{5} -2.11491i q^{6} +(2.62846 + 0.302029i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-2.11491 q^{2} +1.00000i q^{3} +2.47283 q^{4} -1.98969 q^{5} -2.11491i q^{6} +(2.62846 + 0.302029i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +4.20801 q^{10} +2.93048i q^{11} +2.47283i q^{12} -4.75698i q^{13} +(-5.55894 - 0.638764i) q^{14} -1.98969i q^{15} -2.83076 q^{16} +0.444839 q^{17} +2.11491 q^{18} +6.30581 q^{19} -4.92018 q^{20} +(-0.302029 + 2.62846i) q^{21} -6.19770i q^{22} +(4.70265 + 0.940794i) q^{23} -1.00000i q^{24} -1.04113 q^{25} +10.0606i q^{26} -1.00000i q^{27} +(6.49973 + 0.746868i) q^{28} -2.58774 q^{29} +4.20801i q^{30} +6.35793i q^{31} +7.98680 q^{32} -2.93048 q^{33} -0.940794 q^{34} +(-5.22982 - 0.600945i) q^{35} -2.47283 q^{36} +6.69366i q^{37} -13.3362 q^{38} +4.75698 q^{39} +1.98969 q^{40} -10.5877i q^{41} +(0.638764 - 5.55894i) q^{42} +12.6627i q^{43} +7.24660i q^{44} +1.98969 q^{45} +(-9.94567 - 1.98969i) q^{46} +5.66152i q^{47} -2.83076i q^{48} +(6.81756 + 1.58774i) q^{49} +2.20189 q^{50} +0.444839i q^{51} -11.7632i q^{52} +10.6219i q^{53} +2.11491i q^{54} -5.83076i q^{55} +(-2.62846 - 0.302029i) q^{56} +6.30581i q^{57} +5.47283 q^{58} +6.39905i q^{59} -4.92018i q^{60} +3.42644 q^{61} -13.4464i q^{62} +(-2.62846 - 0.302029i) q^{63} -11.2298 q^{64} +9.46492i q^{65} +6.19770 q^{66} +9.73225i q^{67} +1.10001 q^{68} +(-0.940794 + 4.70265i) q^{69} +(11.0606 + 1.27094i) q^{70} +8.75698 q^{71} +1.00000 q^{72} +0.926221i q^{73} -14.1565i q^{74} -1.04113i q^{75} +15.5932 q^{76} +(-0.885092 + 7.70265i) q^{77} -10.0606 q^{78} -8.86087i q^{79} +5.63234 q^{80} +1.00000 q^{81} +22.3921i q^{82} +4.81207 q^{83} +(-0.746868 + 6.49973i) q^{84} -0.885092 q^{85} -26.7805i q^{86} -2.58774i q^{87} -2.93048i q^{88} -0.0511154 q^{89} -4.20801 q^{90} +(1.43675 - 12.5035i) q^{91} +(11.6289 + 2.32643i) q^{92} -6.35793 q^{93} -11.9736i q^{94} -12.5466 q^{95} +7.98680i q^{96} -17.4237 q^{97} +(-14.4185 - 3.35793i) q^{98} -2.93048i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 8q^{4} - 12q^{8} - 12q^{9} + O(q^{10}) \) \( 12q + 8q^{4} - 12q^{8} - 12q^{9} - 16q^{16} - 16q^{23} + 24q^{25} + 16q^{29} + 16q^{32} - 12q^{35} - 8q^{36} + 28q^{39} - 76q^{46} - 16q^{49} + 92q^{50} + 44q^{58} - 84q^{64} + 64q^{70} + 76q^{71} + 12q^{72} - 36q^{77} - 52q^{78} + 12q^{81} - 36q^{85} + 56q^{92} - 80q^{93} - 140q^{95} - 108q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.11491 −1.49547 −0.747733 0.664000i \(-0.768858\pi\)
−0.747733 + 0.664000i \(0.768858\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 2.47283 1.23642
\(5\) −1.98969 −0.889817 −0.444909 0.895576i \(-0.646764\pi\)
−0.444909 + 0.895576i \(0.646764\pi\)
\(6\) 2.11491i 0.863407i
\(7\) 2.62846 + 0.302029i 0.993463 + 0.114156i
\(8\) −1.00000 −0.353553
\(9\) −1.00000 −0.333333
\(10\) 4.20801 1.33069
\(11\) 2.93048i 0.883574i 0.897120 + 0.441787i \(0.145655\pi\)
−0.897120 + 0.441787i \(0.854345\pi\)
\(12\) 2.47283i 0.713846i
\(13\) 4.75698i 1.31935i −0.751551 0.659675i \(-0.770694\pi\)
0.751551 0.659675i \(-0.229306\pi\)
\(14\) −5.55894 0.638764i −1.48569 0.170717i
\(15\) 1.98969i 0.513736i
\(16\) −2.83076 −0.707690
\(17\) 0.444839 0.107889 0.0539447 0.998544i \(-0.482821\pi\)
0.0539447 + 0.998544i \(0.482821\pi\)
\(18\) 2.11491 0.498488
\(19\) 6.30581 1.44665 0.723326 0.690507i \(-0.242612\pi\)
0.723326 + 0.690507i \(0.242612\pi\)
\(20\) −4.92018 −1.10018
\(21\) −0.302029 + 2.62846i −0.0659082 + 0.573576i
\(22\) 6.19770i 1.32136i
\(23\) 4.70265 + 0.940794i 0.980570 + 0.196169i
\(24\) 1.00000i 0.204124i
\(25\) −1.04113 −0.208226
\(26\) 10.0606i 1.97304i
\(27\) 1.00000i 0.192450i
\(28\) 6.49973 + 0.746868i 1.22833 + 0.141145i
\(29\) −2.58774 −0.480532 −0.240266 0.970707i \(-0.577235\pi\)
−0.240266 + 0.970707i \(0.577235\pi\)
\(30\) 4.20801i 0.768275i
\(31\) 6.35793i 1.14192i 0.820979 + 0.570959i \(0.193428\pi\)
−0.820979 + 0.570959i \(0.806572\pi\)
\(32\) 7.98680 1.41188
\(33\) −2.93048 −0.510132
\(34\) −0.940794 −0.161345
\(35\) −5.22982 0.600945i −0.884000 0.101578i
\(36\) −2.47283 −0.412139
\(37\) 6.69366i 1.10043i 0.835023 + 0.550215i \(0.185454\pi\)
−0.835023 + 0.550215i \(0.814546\pi\)
\(38\) −13.3362 −2.16342
\(39\) 4.75698 0.761727
\(40\) 1.98969 0.314598
\(41\) 10.5877i 1.65353i −0.562549 0.826764i \(-0.690179\pi\)
0.562549 0.826764i \(-0.309821\pi\)
\(42\) 0.638764 5.55894i 0.0985635 0.857763i
\(43\) 12.6627i 1.93105i 0.260313 + 0.965524i \(0.416174\pi\)
−0.260313 + 0.965524i \(0.583826\pi\)
\(44\) 7.24660i 1.09247i
\(45\) 1.98969 0.296606
\(46\) −9.94567 1.98969i −1.46641 0.293364i
\(47\) 5.66152i 0.825818i 0.910772 + 0.412909i \(0.135487\pi\)
−0.910772 + 0.412909i \(0.864513\pi\)
\(48\) 2.83076i 0.408585i
\(49\) 6.81756 + 1.58774i 0.973937 + 0.226820i
\(50\) 2.20189 0.311394
\(51\) 0.444839i 0.0622899i
\(52\) 11.7632i 1.63127i
\(53\) 10.6219i 1.45903i 0.683963 + 0.729517i \(0.260255\pi\)
−0.683963 + 0.729517i \(0.739745\pi\)
\(54\) 2.11491i 0.287802i
\(55\) 5.83076i 0.786220i
\(56\) −2.62846 0.302029i −0.351242 0.0403604i
\(57\) 6.30581i 0.835225i
\(58\) 5.47283 0.718618
\(59\) 6.39905i 0.833086i 0.909116 + 0.416543i \(0.136758\pi\)
−0.909116 + 0.416543i \(0.863242\pi\)
\(60\) 4.92018i 0.635192i
\(61\) 3.42644 0.438711 0.219355 0.975645i \(-0.429605\pi\)
0.219355 + 0.975645i \(0.429605\pi\)
\(62\) 13.4464i 1.70770i
\(63\) −2.62846 0.302029i −0.331154 0.0380521i
\(64\) −11.2298 −1.40373
\(65\) 9.46492i 1.17398i
\(66\) 6.19770 0.762885
\(67\) 9.73225i 1.18898i 0.804102 + 0.594492i \(0.202647\pi\)
−0.804102 + 0.594492i \(0.797353\pi\)
\(68\) 1.10001 0.133396
\(69\) −0.940794 + 4.70265i −0.113258 + 0.566132i
\(70\) 11.0606 + 1.27094i 1.32199 + 0.151907i
\(71\) 8.75698 1.03926 0.519631 0.854391i \(-0.326069\pi\)
0.519631 + 0.854391i \(0.326069\pi\)
\(72\) 1.00000 0.117851
\(73\) 0.926221i 0.108406i 0.998530 + 0.0542030i \(0.0172618\pi\)
−0.998530 + 0.0542030i \(0.982738\pi\)
\(74\) 14.1565i 1.64566i
\(75\) 1.04113i 0.120219i
\(76\) 15.5932 1.78866
\(77\) −0.885092 + 7.70265i −0.100866 + 0.877798i
\(78\) −10.0606 −1.13914
\(79\) 8.86087i 0.996925i −0.866911 0.498463i \(-0.833898\pi\)
0.866911 0.498463i \(-0.166102\pi\)
\(80\) 5.63234 0.629715
\(81\) 1.00000 0.111111
\(82\) 22.3921i 2.47279i
\(83\) 4.81207 0.528194 0.264097 0.964496i \(-0.414926\pi\)
0.264097 + 0.964496i \(0.414926\pi\)
\(84\) −0.746868 + 6.49973i −0.0814900 + 0.709179i
\(85\) −0.885092 −0.0960018
\(86\) 26.7805i 2.88782i
\(87\) 2.58774i 0.277435i
\(88\) 2.93048i 0.312391i
\(89\) −0.0511154 −0.00541822 −0.00270911 0.999996i \(-0.500862\pi\)
−0.00270911 + 0.999996i \(0.500862\pi\)
\(90\) −4.20801 −0.443564
\(91\) 1.43675 12.5035i 0.150612 1.31072i
\(92\) 11.6289 + 2.32643i 1.21239 + 0.242547i
\(93\) −6.35793 −0.659286
\(94\) 11.9736i 1.23498i
\(95\) −12.5466 −1.28726
\(96\) 7.98680i 0.815149i
\(97\) −17.4237 −1.76911 −0.884554 0.466438i \(-0.845537\pi\)
−0.884554 + 0.466438i \(0.845537\pi\)
\(98\) −14.4185 3.35793i −1.45649 0.339202i
\(99\) 2.93048i 0.294525i
\(100\) −2.57454 −0.257454
\(101\) 12.7500i 1.26867i −0.773056 0.634337i \(-0.781273\pi\)
0.773056 0.634337i \(-0.218727\pi\)
\(102\) 0.940794i 0.0931524i
\(103\) 6.46503 0.637018 0.318509 0.947920i \(-0.396818\pi\)
0.318509 + 0.947920i \(0.396818\pi\)
\(104\) 4.75698i 0.466460i
\(105\) 0.600945 5.22982i 0.0586462 0.510378i
\(106\) 22.4644i 2.18193i
\(107\) 13.0506i 1.26165i −0.775926 0.630824i \(-0.782717\pi\)
0.775926 0.630824i \(-0.217283\pi\)
\(108\) 2.47283i 0.237949i
\(109\) 9.80166i 0.938829i −0.882978 0.469414i \(-0.844465\pi\)
0.882978 0.469414i \(-0.155535\pi\)
\(110\) 12.3315i 1.17576i
\(111\) −6.69366 −0.635334
\(112\) −7.44053 0.854973i −0.703064 0.0807873i
\(113\) 12.2873i 1.15589i 0.816075 + 0.577946i \(0.196146\pi\)
−0.816075 + 0.577946i \(0.803854\pi\)
\(114\) 13.3362i 1.24905i
\(115\) −9.35682 1.87189i −0.872528 0.174555i
\(116\) −6.39905 −0.594137
\(117\) 4.75698i 0.439783i
\(118\) 13.5334i 1.24585i
\(119\) 1.16924 + 0.134354i 0.107184 + 0.0123163i
\(120\) 1.98969i 0.181633i
\(121\) 2.41226 0.219296
\(122\) −7.24660 −0.656077
\(123\) 10.5877 0.954664
\(124\) 15.7221i 1.41189i
\(125\) 12.0200 1.07510
\(126\) 5.55894 + 0.638764i 0.495230 + 0.0569056i
\(127\) −3.81131 −0.338199 −0.169100 0.985599i \(-0.554086\pi\)
−0.169100 + 0.985599i \(0.554086\pi\)
\(128\) 7.77643 0.687346
\(129\) −12.6627 −1.11489
\(130\) 20.0174i 1.75565i
\(131\) 7.87189i 0.687770i 0.939012 + 0.343885i \(0.111743\pi\)
−0.939012 + 0.343885i \(0.888257\pi\)
\(132\) −7.24660 −0.630736
\(133\) 16.5745 + 1.90454i 1.43719 + 0.165145i
\(134\) 20.5828i 1.77808i
\(135\) 1.98969i 0.171245i
\(136\) −0.444839 −0.0381446
\(137\) 17.8115i 1.52174i −0.648903 0.760871i \(-0.724772\pi\)
0.648903 0.760871i \(-0.275228\pi\)
\(138\) 1.98969 9.94567i 0.169374 0.846631i
\(139\) 1.49228i 0.126574i −0.997995 0.0632868i \(-0.979842\pi\)
0.997995 0.0632868i \(-0.0201583\pi\)
\(140\) −12.9325 1.48604i −1.09299 0.125593i
\(141\) −5.66152 −0.476786
\(142\) −18.5202 −1.55418
\(143\) 13.9403 1.16574
\(144\) 2.83076 0.235897
\(145\) 5.14881 0.427585
\(146\) 1.95887i 0.162117i
\(147\) −1.58774 + 6.81756i −0.130955 + 0.562303i
\(148\) 16.5523i 1.36059i
\(149\) 4.15102i 0.340065i 0.985438 + 0.170033i \(0.0543873\pi\)
−0.985438 + 0.170033i \(0.945613\pi\)
\(150\) 2.20189i 0.179784i
\(151\) −4.08226 −0.332209 −0.166105 0.986108i \(-0.553119\pi\)
−0.166105 + 0.986108i \(0.553119\pi\)
\(152\) −6.30581 −0.511469
\(153\) −0.444839 −0.0359631
\(154\) 1.87189 16.2904i 0.150841 1.31272i
\(155\) 12.6503i 1.01610i
\(156\) 11.7632 0.941812
\(157\) 1.56315 0.124753 0.0623764 0.998053i \(-0.480132\pi\)
0.0623764 + 0.998053i \(0.480132\pi\)
\(158\) 18.7399i 1.49087i
\(159\) −10.6219 −0.842374
\(160\) −15.8913 −1.25631
\(161\) 12.0766 + 3.89317i 0.951766 + 0.306825i
\(162\) −2.11491 −0.166163
\(163\) −2.54661 −0.199466 −0.0997331 0.995014i \(-0.531799\pi\)
−0.0997331 + 0.995014i \(0.531799\pi\)
\(164\) 26.1817i 2.04445i
\(165\) 5.83076 0.453924
\(166\) −10.1771 −0.789895
\(167\) 3.07378i 0.237856i −0.992903 0.118928i \(-0.962054\pi\)
0.992903 0.118928i \(-0.0379458\pi\)
\(168\) 0.302029 2.62846i 0.0233021 0.202790i
\(169\) −9.62887 −0.740682
\(170\) 1.87189 0.143567
\(171\) −6.30581 −0.482217
\(172\) 31.3128i 2.38758i
\(173\) 6.24926i 0.475123i 0.971373 + 0.237561i \(0.0763481\pi\)
−0.971373 + 0.237561i \(0.923652\pi\)
\(174\) 5.47283i 0.414894i
\(175\) −2.73656 0.314451i −0.206864 0.0237703i
\(176\) 8.29550i 0.625297i
\(177\) −6.39905 −0.480982
\(178\) 0.108104 0.00810276
\(179\) −18.6678 −1.39529 −0.697647 0.716442i \(-0.745770\pi\)
−0.697647 + 0.716442i \(0.745770\pi\)
\(180\) 4.92018 0.366728
\(181\) 16.8890 1.25535 0.627676 0.778474i \(-0.284006\pi\)
0.627676 + 0.778474i \(0.284006\pi\)
\(182\) −3.03859 + 26.4438i −0.225235 + 1.96014i
\(183\) 3.42644i 0.253290i
\(184\) −4.70265 0.940794i −0.346684 0.0693562i
\(185\) 13.3183i 0.979182i
\(186\) 13.4464 0.985940
\(187\) 1.30359i 0.0953282i
\(188\) 14.0000i 1.02105i
\(189\) 0.302029 2.62846i 0.0219694 0.191192i
\(190\) 26.5349 1.92505
\(191\) 5.54253i 0.401043i 0.979689 + 0.200522i \(0.0642637\pi\)
−0.979689 + 0.200522i \(0.935736\pi\)
\(192\) 11.2298i 0.810442i
\(193\) −8.91926 −0.642022 −0.321011 0.947075i \(-0.604023\pi\)
−0.321011 + 0.947075i \(0.604023\pi\)
\(194\) 36.8495 2.64564
\(195\) −9.46492 −0.677797
\(196\) 16.8587 + 3.92622i 1.20419 + 0.280444i
\(197\) 24.1623 1.72149 0.860746 0.509035i \(-0.169998\pi\)
0.860746 + 0.509035i \(0.169998\pi\)
\(198\) 6.19770i 0.440452i
\(199\) 23.5520 1.66956 0.834778 0.550587i \(-0.185596\pi\)
0.834778 + 0.550587i \(0.185596\pi\)
\(200\) 1.04113 0.0736189
\(201\) −9.73225 −0.686460
\(202\) 26.9651i 1.89726i
\(203\) −6.80176 0.781574i −0.477390 0.0548557i
\(204\) 1.10001i 0.0770163i
\(205\) 21.0663i 1.47134i
\(206\) −13.6729 −0.952639
\(207\) −4.70265 0.940794i −0.326857 0.0653897i
\(208\) 13.4659i 0.933690i
\(209\) 18.4791i 1.27822i
\(210\) −1.27094 + 11.0606i −0.0877034 + 0.763252i
\(211\) −1.89830 −0.130684 −0.0653420 0.997863i \(-0.520814\pi\)
−0.0653420 + 0.997863i \(0.520814\pi\)
\(212\) 26.2663i 1.80397i
\(213\) 8.75698i 0.600018i
\(214\) 27.6008i 1.88675i
\(215\) 25.1949i 1.71828i
\(216\) 1.00000i 0.0680414i
\(217\) −1.92028 + 16.7115i −0.130357 + 1.13445i
\(218\) 20.7296i 1.40399i
\(219\) −0.926221 −0.0625882
\(220\) 14.4185i 0.972095i
\(221\) 2.11609i 0.142344i
\(222\) 14.1565 0.950120
\(223\) 5.19716i 0.348028i 0.984743 + 0.174014i \(0.0556738\pi\)
−0.984743 + 0.174014i \(0.944326\pi\)
\(224\) 20.9929 + 2.41225i 1.40265 + 0.161175i
\(225\) 1.04113 0.0694086
\(226\) 25.9865i 1.72860i
\(227\) −1.03060 −0.0684035 −0.0342017 0.999415i \(-0.510889\pi\)
−0.0342017 + 0.999415i \(0.510889\pi\)
\(228\) 15.5932i 1.03269i
\(229\) −12.8914 −0.851885 −0.425943 0.904750i \(-0.640057\pi\)
−0.425943 + 0.904750i \(0.640057\pi\)
\(230\) 19.7888 + 3.95887i 1.30484 + 0.261040i
\(231\) −7.70265 0.885092i −0.506797 0.0582348i
\(232\) 2.58774 0.169894
\(233\) 22.1817 1.45317 0.726587 0.687075i \(-0.241106\pi\)
0.726587 + 0.687075i \(0.241106\pi\)
\(234\) 10.0606i 0.657680i
\(235\) 11.2647i 0.734827i
\(236\) 15.8238i 1.03004i
\(237\) 8.86087 0.575575
\(238\) −2.47283 0.284147i −0.160290 0.0184185i
\(239\) 14.0995 0.912019 0.456009 0.889975i \(-0.349278\pi\)
0.456009 + 0.889975i \(0.349278\pi\)
\(240\) 5.63234i 0.363566i
\(241\) −15.9994 −1.03061 −0.515305 0.857007i \(-0.672321\pi\)
−0.515305 + 0.857007i \(0.672321\pi\)
\(242\) −5.10170 −0.327950
\(243\) 1.00000i 0.0641500i
\(244\) 8.47302 0.542429
\(245\) −13.5648 3.15912i −0.866625 0.201828i
\(246\) −22.3921 −1.42767
\(247\) 29.9966i 1.90864i
\(248\) 6.35793i 0.403729i
\(249\) 4.81207i 0.304953i
\(250\) −25.4211 −1.60777
\(251\) −15.3829 −0.970959 −0.485479 0.874248i \(-0.661355\pi\)
−0.485479 + 0.874248i \(0.661355\pi\)
\(252\) −6.49973 0.746868i −0.409445 0.0470483i
\(253\) −2.75698 + 13.7810i −0.173330 + 0.866407i
\(254\) 8.06058 0.505765
\(255\) 0.885092i 0.0554266i
\(256\) 6.01320 0.375825
\(257\) 9.74378i 0.607800i −0.952704 0.303900i \(-0.901711\pi\)
0.952704 0.303900i \(-0.0982889\pi\)
\(258\) 26.7805 1.66728
\(259\) −2.02168 + 17.5940i −0.125621 + 1.09324i
\(260\) 23.4052i 1.45153i
\(261\) 2.58774 0.160177
\(262\) 16.6483i 1.02854i
\(263\) 11.3465i 0.699656i 0.936814 + 0.349828i \(0.113760\pi\)
−0.936814 + 0.349828i \(0.886240\pi\)
\(264\) 2.93048 0.180359
\(265\) 21.1344i 1.29827i
\(266\) −35.0536 4.02792i −2.14928 0.246968i
\(267\) 0.0511154i 0.00312821i
\(268\) 24.0662i 1.47008i
\(269\) 8.79588i 0.536294i 0.963378 + 0.268147i \(0.0864113\pi\)
−0.963378 + 0.268147i \(0.913589\pi\)
\(270\) 4.20801i 0.256092i
\(271\) 32.1142i 1.95080i −0.220447 0.975399i \(-0.570751\pi\)
0.220447 0.975399i \(-0.429249\pi\)
\(272\) −1.25923 −0.0763522
\(273\) 12.5035 + 1.43675i 0.756747 + 0.0869559i
\(274\) 37.6698i 2.27571i
\(275\) 3.05101i 0.183983i
\(276\) −2.32643 + 11.6289i −0.140034 + 0.699976i
\(277\) −1.39058 −0.0835517 −0.0417758 0.999127i \(-0.513302\pi\)
−0.0417758 + 0.999127i \(0.513302\pi\)
\(278\) 3.15604i 0.189286i
\(279\) 6.35793i 0.380639i
\(280\) 5.22982 + 0.600945i 0.312541 + 0.0359133i
\(281\) 17.4361i 1.04015i −0.854120 0.520076i \(-0.825904\pi\)
0.854120 0.520076i \(-0.174096\pi\)
\(282\) 11.9736 0.713017
\(283\) 18.3645 1.09166 0.545828 0.837898i \(-0.316215\pi\)
0.545828 + 0.837898i \(0.316215\pi\)
\(284\) 21.6546 1.28496
\(285\) 12.5466i 0.743197i
\(286\) −29.4824 −1.74333
\(287\) 3.19781 27.8294i 0.188761 1.64272i
\(288\) −7.98680 −0.470626
\(289\) −16.8021 −0.988360
\(290\) −10.8893 −0.639439
\(291\) 17.4237i 1.02139i
\(292\) 2.29039i 0.134035i
\(293\) 1.70995 0.0998961 0.0499480 0.998752i \(-0.484094\pi\)
0.0499480 + 0.998752i \(0.484094\pi\)
\(294\) 3.35793 14.4185i 0.195838 0.840904i
\(295\) 12.7321i 0.741294i
\(296\) 6.69366i 0.389061i
\(297\) 2.93048 0.170044
\(298\) 8.77903i 0.508556i
\(299\) 4.47534 22.3704i 0.258815 1.29371i
\(300\) 2.57454i 0.148641i
\(301\) −3.82452 + 33.2834i −0.220442 + 1.91843i
\(302\) 8.63360 0.496808
\(303\) 12.7500 0.732470
\(304\) −17.8502 −1.02378
\(305\) −6.81756 −0.390372
\(306\) 0.940794 0.0537816
\(307\) 5.34696i 0.305167i −0.988291 0.152583i \(-0.951241\pi\)
0.988291 0.152583i \(-0.0487593\pi\)
\(308\) −2.18869 + 19.0474i −0.124712 + 1.08532i
\(309\) 6.46503i 0.367783i
\(310\) 26.7542i 1.51954i
\(311\) 1.72906i 0.0980458i 0.998798 + 0.0490229i \(0.0156107\pi\)
−0.998798 + 0.0490229i \(0.984389\pi\)
\(312\) −4.75698 −0.269311
\(313\) 5.54253 0.313282 0.156641 0.987656i \(-0.449933\pi\)
0.156641 + 0.987656i \(0.449933\pi\)
\(314\) −3.30591 −0.186563
\(315\) 5.22982 + 0.600945i 0.294667 + 0.0338594i
\(316\) 21.9114i 1.23262i
\(317\) −8.88509 −0.499037 −0.249518 0.968370i \(-0.580272\pi\)
−0.249518 + 0.968370i \(0.580272\pi\)
\(318\) 22.4644 1.25974
\(319\) 7.58334i 0.424585i
\(320\) 22.3439 1.24906
\(321\) 13.0506 0.728413
\(322\) −25.5408 8.23370i −1.42333 0.458846i
\(323\) 2.80507 0.156078
\(324\) 2.47283 0.137380
\(325\) 4.95263i 0.274722i
\(326\) 5.38585 0.298295
\(327\) 9.80166 0.542033
\(328\) 10.5877i 0.584610i
\(329\) −1.70995 + 14.8811i −0.0942723 + 0.820419i
\(330\) −12.3315 −0.678828
\(331\) −15.1491 −0.832668 −0.416334 0.909212i \(-0.636685\pi\)
−0.416334 + 0.909212i \(0.636685\pi\)
\(332\) 11.8995 0.653067
\(333\) 6.69366i 0.366810i
\(334\) 6.50076i 0.355706i
\(335\) 19.3642i 1.05798i
\(336\) 0.854973 7.44053i 0.0466426 0.405914i
\(337\) 14.8299i 0.807838i −0.914795 0.403919i \(-0.867648\pi\)
0.914795 0.403919i \(-0.132352\pi\)
\(338\) 20.3642 1.10766
\(339\) −12.2873 −0.667355
\(340\) −2.18869 −0.118698
\(341\) −18.6318 −1.00897
\(342\) 13.3362 0.721139
\(343\) 17.4401 + 6.23241i 0.941677 + 0.336519i
\(344\) 12.6627i 0.682729i
\(345\) 1.87189 9.35682i 0.100779 0.503754i
\(346\) 13.2166i 0.710529i
\(347\) −18.1017 −0.971750 −0.485875 0.874028i \(-0.661499\pi\)
−0.485875 + 0.874028i \(0.661499\pi\)
\(348\) 6.39905i 0.343025i
\(349\) 21.0062i 1.12444i 0.826988 + 0.562219i \(0.190052\pi\)
−0.826988 + 0.562219i \(0.809948\pi\)
\(350\) 5.78757 + 0.665036i 0.309359 + 0.0355476i
\(351\) −4.75698 −0.253909
\(352\) 23.4052i 1.24750i
\(353\) 21.4945i 1.14404i 0.820241 + 0.572019i \(0.193840\pi\)
−0.820241 + 0.572019i \(0.806160\pi\)
\(354\) 13.5334 0.719293
\(355\) −17.4237 −0.924753
\(356\) −0.126400 −0.00669918
\(357\) −0.134354 + 1.16924i −0.00711079 + 0.0618827i
\(358\) 39.4806 2.08661
\(359\) 2.16133i 0.114071i 0.998372 + 0.0570354i \(0.0181648\pi\)
−0.998372 + 0.0570354i \(0.981835\pi\)
\(360\) −1.98969 −0.104866
\(361\) 20.7632 1.09280
\(362\) −35.7188 −1.87734
\(363\) 2.41226i 0.126611i
\(364\) 3.55284 30.9191i 0.186219 1.62060i
\(365\) 1.84289i 0.0964615i
\(366\) 7.24660i 0.378786i
\(367\) −16.5399 −0.863375 −0.431687 0.902023i \(-0.642082\pi\)
−0.431687 + 0.902023i \(0.642082\pi\)
\(368\) −13.3121 2.66316i −0.693940 0.138827i
\(369\) 10.5877i 0.551176i
\(370\) 28.1670i 1.46433i
\(371\) −3.20813 + 27.9193i −0.166558 + 1.44950i
\(372\) −15.7221 −0.815153
\(373\) 31.1660i 1.61372i 0.590745 + 0.806858i \(0.298834\pi\)
−0.590745 + 0.806858i \(0.701166\pi\)
\(374\) 2.75698i 0.142560i
\(375\) 12.0200i 0.620709i
\(376\) 5.66152i 0.291971i
\(377\) 12.3098i 0.633989i
\(378\) −0.638764 + 5.55894i −0.0328545 + 0.285921i
\(379\) 27.5949i 1.41745i −0.705482 0.708727i \(-0.749270\pi\)
0.705482 0.708727i \(-0.250730\pi\)
\(380\) −31.0257 −1.59158
\(381\) 3.81131i 0.195259i
\(382\) 11.7219i 0.599747i
\(383\) −12.9097 −0.659653 −0.329826 0.944042i \(-0.606990\pi\)
−0.329826 + 0.944042i \(0.606990\pi\)
\(384\) 7.77643i 0.396839i
\(385\) 1.76106 15.3259i 0.0897520 0.781080i
\(386\) 18.8634 0.960122
\(387\) 12.6627i 0.643683i
\(388\) −43.0859 −2.18735
\(389\) 15.8277i 0.802497i 0.915969 + 0.401249i \(0.131424\pi\)
−0.915969 + 0.401249i \(0.868576\pi\)
\(390\) 20.0174 1.01362
\(391\) 2.09192 + 0.418502i 0.105793 + 0.0211645i
\(392\) −6.81756 1.58774i −0.344339 0.0801931i
\(393\) −7.87189 −0.397084
\(394\) −51.1010 −2.57443
\(395\) 17.6304i 0.887081i
\(396\) 7.24660i 0.364155i
\(397\) 12.7159i 0.638190i −0.947723 0.319095i \(-0.896621\pi\)
0.947723 0.319095i \(-0.103379\pi\)
\(398\) −49.8103 −2.49676
\(399\) −1.90454 + 16.5745i −0.0953462 + 0.829765i
\(400\) 2.94719 0.147359
\(401\) 9.53434i 0.476122i −0.971250 0.238061i \(-0.923488\pi\)
0.971250 0.238061i \(-0.0765118\pi\)
\(402\) 20.5828 1.02658
\(403\) 30.2445 1.50659
\(404\) 31.5287i 1.56861i
\(405\) −1.98969 −0.0988686
\(406\) 14.3851 + 1.65296i 0.713921 + 0.0820349i
\(407\) −19.6157 −0.972312
\(408\) 0.444839i 0.0220228i
\(409\) 5.78963i 0.286279i −0.989703 0.143139i \(-0.954280\pi\)
0.989703 0.143139i \(-0.0457197\pi\)
\(410\) 44.5534i 2.20033i
\(411\) 17.8115 0.878578
\(412\) 15.9869 0.787620
\(413\) −1.93270 + 16.8196i −0.0951021 + 0.827640i
\(414\) 9.94567 + 1.98969i 0.488803 + 0.0977880i
\(415\) −9.57454 −0.469996
\(416\) 37.9930i 1.86276i
\(417\) 1.49228 0.0730773
\(418\) 39.0815i 1.91154i
\(419\) 4.01808 0.196296 0.0981479 0.995172i \(-0.468708\pi\)
0.0981479 + 0.995172i \(0.468708\pi\)
\(420\) 1.48604 12.9325i 0.0725112 0.631040i
\(421\) 11.8425i 0.577166i −0.957455 0.288583i \(-0.906816\pi\)
0.957455 0.288583i \(-0.0931842\pi\)
\(422\) 4.01472 0.195434
\(423\) 5.66152i 0.275273i
\(424\) 10.6219i 0.515846i
\(425\) −0.463135 −0.0224653
\(426\) 18.5202i 0.897307i
\(427\) 9.00624 + 1.03489i 0.435843 + 0.0500816i
\(428\) 32.2719i 1.55992i
\(429\) 13.9403i 0.673042i
\(430\) 53.2849i 2.56963i
\(431\) 26.8703i 1.29430i −0.762364 0.647149i \(-0.775961\pi\)
0.762364 0.647149i \(-0.224039\pi\)
\(432\) 2.83076i 0.136195i
\(433\) 3.76317 0.180847 0.0904233 0.995903i \(-0.471178\pi\)
0.0904233 + 0.995903i \(0.471178\pi\)
\(434\) 4.06122 35.3433i 0.194945 1.69653i
\(435\) 5.14881i 0.246866i
\(436\) 24.2379i 1.16078i
\(437\) 29.6540 + 5.93246i 1.41854 + 0.283788i
\(438\) 1.95887 0.0935985
\(439\) 40.1531i 1.91640i −0.286096 0.958201i \(-0.592358\pi\)
0.286096 0.958201i \(-0.407642\pi\)
\(440\) 5.83076i 0.277971i
\(441\) −6.81756 1.58774i −0.324646 0.0756067i
\(442\) 4.47534i 0.212870i
\(443\) 22.4985 1.06894 0.534469 0.845188i \(-0.320512\pi\)
0.534469 + 0.845188i \(0.320512\pi\)
\(444\) −16.5523 −0.785538
\(445\) 0.101704 0.00482122
\(446\) 10.9915i 0.520464i
\(447\) −4.15102 −0.196337
\(448\) −29.5171 3.39173i −1.39455 0.160244i
\(449\) 13.0885 0.617685 0.308842 0.951113i \(-0.400058\pi\)
0.308842 + 0.951113i \(0.400058\pi\)
\(450\) −2.20189 −0.103798
\(451\) 31.0272 1.46101
\(452\) 30.3845i 1.42916i
\(453\) 4.08226i 0.191801i
\(454\) 2.17963 0.102295
\(455\) −2.85868 + 24.8781i −0.134017 + 1.16630i
\(456\) 6.30581i 0.295297i
\(457\) 25.9354i 1.21321i −0.795005 0.606603i \(-0.792532\pi\)
0.795005 0.606603i \(-0.207468\pi\)
\(458\) 27.2640 1.27397
\(459\) 0.444839i 0.0207633i
\(460\) −23.1379 4.62887i −1.07881 0.215822i
\(461\) 19.2361i 0.895913i −0.894055 0.447956i \(-0.852152\pi\)
0.894055 0.447956i \(-0.147848\pi\)
\(462\) 16.2904 + 1.87189i 0.757898 + 0.0870881i
\(463\) −23.6546 −1.09932 −0.549660 0.835388i \(-0.685243\pi\)
−0.549660 + 0.835388i \(0.685243\pi\)
\(464\) 7.32528 0.340067
\(465\) 12.6503 0.586644
\(466\) −46.9123 −2.17317
\(467\) −37.3454 −1.72814 −0.864071 0.503371i \(-0.832093\pi\)
−0.864071 + 0.503371i \(0.832093\pi\)
\(468\) 11.7632i 0.543755i
\(469\) −2.93942 + 25.5808i −0.135730 + 1.18121i
\(470\) 23.8238i 1.09891i
\(471\) 1.56315i 0.0720260i
\(472\) 6.39905i 0.294540i
\(473\) −37.1079 −1.70623
\(474\) −18.7399 −0.860753
\(475\) −6.56516 −0.301230
\(476\) 2.89134 + 0.332236i 0.132524 + 0.0152280i
\(477\) 10.6219i 0.486345i
\(478\) −29.8191 −1.36389
\(479\) −23.7419 −1.08480 −0.542398 0.840122i \(-0.682484\pi\)
−0.542398 + 0.840122i \(0.682484\pi\)
\(480\) 15.8913i 0.725333i
\(481\) 31.8416 1.45185
\(482\) 33.8372 1.54124
\(483\) −3.89317 + 12.0766i −0.177145 + 0.549502i
\(484\) 5.96511 0.271142
\(485\) 34.6678 1.57418
\(486\) 2.11491i 0.0959342i
\(487\) 34.2229 1.55079 0.775393 0.631479i \(-0.217552\pi\)
0.775393 + 0.631479i \(0.217552\pi\)
\(488\) −3.42644 −0.155108
\(489\) 2.54661i 0.115162i
\(490\) 28.6884 + 6.68124i 1.29601 + 0.301828i
\(491\) −4.30984 −0.194500 −0.0972501 0.995260i \(-0.531005\pi\)
−0.0972501 + 0.995260i \(0.531005\pi\)
\(492\) 26.1817 1.18036
\(493\) −1.15113 −0.0518442
\(494\) 63.4401i 2.85430i
\(495\) 5.83076i 0.262073i
\(496\) 17.9978i 0.808124i
\(497\) 23.0173 + 2.64487i 1.03247 + 0.118638i
\(498\) 10.1771i 0.456046i
\(499\) 30.5466 1.36745 0.683727 0.729738i \(-0.260358\pi\)
0.683727 + 0.729738i \(0.260358\pi\)
\(500\) 29.7234 1.32927
\(501\) 3.07378 0.137326
\(502\) 32.5334 1.45204
\(503\) −35.3433 −1.57588 −0.787941 0.615751i \(-0.788853\pi\)
−0.787941 + 0.615751i \(0.788853\pi\)
\(504\) 2.62846 + 0.302029i 0.117081 + 0.0134535i
\(505\) 25.3686i 1.12889i
\(506\) 5.83076 29.1456i 0.259209 1.29568i
\(507\) 9.62887i 0.427633i
\(508\) −9.42474 −0.418155
\(509\) 14.1212i 0.625909i −0.949768 0.312955i \(-0.898681\pi\)
0.949768 0.312955i \(-0.101319\pi\)
\(510\) 1.87189i 0.0828886i
\(511\) −0.279746 + 2.43453i −0.0123752 + 0.107697i
\(512\) −28.2702 −1.24938
\(513\) 6.30581i 0.278408i
\(514\) 20.6072i 0.908944i
\(515\) −12.8634 −0.566830
\(516\) −31.3128 −1.37847
\(517\) −16.5910 −0.729671
\(518\) 4.27567 37.2097i 0.187862 1.63490i
\(519\) −6.24926 −0.274312
\(520\) 9.46492i 0.415064i
\(521\) −13.3545 −0.585071 −0.292536 0.956255i \(-0.594499\pi\)
−0.292536 + 0.956255i \(0.594499\pi\)
\(522\) −5.47283 −0.239539
\(523\) 26.7170 1.16825 0.584126 0.811663i \(-0.301437\pi\)
0.584126 + 0.811663i \(0.301437\pi\)
\(524\) 19.4659i 0.850371i
\(525\) 0.314451 2.73656i 0.0137238 0.119433i
\(526\) 23.9968i 1.04631i
\(527\) 2.82825i 0.123201i
\(528\) 8.29550 0.361015
\(529\) 21.2298 + 8.84844i 0.923035 + 0.384715i
\(530\) 44.6972i 1.94152i
\(531\) 6.39905i 0.277695i
\(532\) 40.9861 + 4.70961i 1.77697 + 0.204187i
\(533\) −50.3657 −2.18158
\(534\) 0.108104i 0.00467813i
\(535\) 25.9666i 1.12264i
\(536\) 9.73225i 0.420369i
\(537\) 18.6678i 0.805573i
\(538\) 18.6025i 0.802009i
\(539\) −4.65285 + 19.9787i −0.200413 + 0.860546i
\(540\) 4.92018i 0.211731i
\(541\) −16.7159 −0.718671 −0.359335 0.933209i \(-0.616997\pi\)
−0.359335 + 0.933209i \(0.616997\pi\)
\(542\) 67.9185i 2.91735i
\(543\) 16.8890i 0.724778i
\(544\) 3.55284 0.152327
\(545\) 19.5023i 0.835386i
\(546\) −26.4438 3.03859i −1.13169 0.130040i
\(547\) 8.31680 0.355601 0.177800 0.984067i \(-0.443102\pi\)
0.177800 + 0.984067i \(0.443102\pi\)
\(548\) 44.0450i 1.88151i
\(549\) −3.42644 −0.146237
\(550\) 6.45261i 0.275140i
\(551\) −16.3178 −0.695162
\(552\) 0.940794 4.70265i 0.0400428 0.200158i
\(553\) 2.67624 23.2904i 0.113805 0.990408i
\(554\) 2.94094 0.124949
\(555\) 13.3183 0.565331
\(556\) 3.69016i 0.156498i
\(557\) 39.9903i 1.69444i 0.531239 + 0.847222i \(0.321727\pi\)
−0.531239 + 0.847222i \(0.678273\pi\)
\(558\) 13.4464i 0.569233i
\(559\) 60.2364 2.54773
\(560\) 14.8044 + 1.70113i 0.625598 + 0.0718859i
\(561\) −1.30359 −0.0550378
\(562\) 36.8758i 1.55551i
\(563\) −16.6093 −0.699998 −0.349999 0.936750i \(-0.613818\pi\)
−0.349999 + 0.936750i \(0.613818\pi\)
\(564\) −14.0000 −0.589506
\(565\) 24.4479i 1.02853i
\(566\) −38.8392 −1.63253
\(567\) 2.62846 + 0.302029i 0.110385 + 0.0126840i
\(568\) −8.75698 −0.367435
\(569\) 17.2973i 0.725140i −0.931957 0.362570i \(-0.881899\pi\)
0.931957 0.362570i \(-0.118101\pi\)
\(570\) 26.5349i 1.11143i
\(571\) 13.3749i 0.559722i 0.960041 + 0.279861i \(0.0902884\pi\)
−0.960041 + 0.279861i \(0.909712\pi\)
\(572\) 34.4720 1.44134
\(573\) −5.54253 −0.231543
\(574\) −6.76307 + 58.8566i −0.282285 + 2.45663i
\(575\) −4.89606 0.979487i −0.204180 0.0408474i
\(576\) 11.2298 0.467909
\(577\) 38.9193i 1.62023i −0.586271 0.810115i \(-0.699405\pi\)
0.586271 0.810115i \(-0.300595\pi\)
\(578\) 35.5349 1.47806
\(579\) 8.91926i 0.370672i
\(580\) 12.7321 0.528673
\(581\) 12.6483 + 1.45339i 0.524741 + 0.0602967i
\(582\) 36.8495i 1.52746i
\(583\) −31.1274 −1.28916
\(584\) 0.926221i 0.0383273i
\(585\) 9.46492i 0.391326i
\(586\) −3.61638 −0.149391
\(587\) 19.7974i 0.817126i −0.912730 0.408563i \(-0.866030\pi\)
0.912730 0.408563i \(-0.133970\pi\)
\(588\) −3.92622 + 16.8587i −0.161915 + 0.695240i
\(589\) 40.0919i 1.65196i
\(590\) 26.9273i 1.10858i
\(591\) 24.1623i 0.993903i
\(592\) 18.9481i 0.778764i
\(593\) 40.3370i 1.65644i −0.560400 0.828222i \(-0.689353\pi\)
0.560400 0.828222i \(-0.310647\pi\)
\(594\) −6.19770 −0.254295
\(595\) −2.32643 0.267324i −0.0953742 0.0109592i
\(596\) 10.2648i 0.420462i
\(597\) 23.5520i 0.963918i
\(598\) −9.46492 + 47.3114i −0.387050 + 1.93471i
\(599\) 16.2012 0.661962 0.330981 0.943637i \(-0.392620\pi\)
0.330981 + 0.943637i \(0.392620\pi\)
\(600\) 1.04113i 0.0425039i
\(601\) 0.750021i 0.0305940i 0.999883 + 0.0152970i \(0.00486937\pi\)
−0.999883 + 0.0152970i \(0.995131\pi\)
\(602\) 8.08850 70.3914i 0.329663 2.86894i
\(603\) 9.73225i 0.396328i
\(604\) −10.0947 −0.410749
\(605\) −4.79965 −0.195134
\(606\) −26.9651 −1.09538
\(607\) 21.0691i 0.855166i 0.903976 + 0.427583i \(0.140635\pi\)
−0.903976 + 0.427583i \(0.859365\pi\)
\(608\) 50.3632 2.04250
\(609\) 0.781574 6.80176i 0.0316710 0.275621i
\(610\) 14.4185 0.583788
\(611\) 26.9317 1.08954
\(612\) −1.10001 −0.0444654
\(613\) 2.93048i 0.118361i −0.998247 0.0591806i \(-0.981151\pi\)
0.998247 0.0591806i \(-0.0188488\pi\)
\(614\) 11.3083i 0.456367i
\(615\) −21.0663 −0.849477
\(616\) 0.885092 7.70265i 0.0356614 0.310349i
\(617\) 7.33641i 0.295353i 0.989036 + 0.147676i \(0.0471794\pi\)
−0.989036 + 0.147676i \(0.952821\pi\)
\(618\) 13.6729i 0.550006i
\(619\) −23.2905 −0.936126 −0.468063 0.883695i \(-0.655048\pi\)
−0.468063 + 0.883695i \(0.655048\pi\)
\(620\) 31.2821i 1.25632i
\(621\) 0.940794 4.70265i 0.0377527 0.188711i
\(622\) 3.65679i 0.146624i
\(623\) −0.134354 0.0154383i −0.00538280 0.000618524i
\(624\) −13.4659 −0.539066
\(625\) −18.7104 −0.748416
\(626\) −11.7219 −0.468503
\(627\) −18.4791 −0.737983
\(628\) 3.86540 0.154246
\(629\) 2.97760i 0.118725i
\(630\) −11.0606 1.27094i −0.440664 0.0506356i
\(631\) 21.1540i 0.842129i −0.907031 0.421065i \(-0.861657\pi\)
0.907031 0.421065i \(-0.138343\pi\)
\(632\) 8.86087i 0.352466i
\(633\) 1.89830i 0.0754505i
\(634\) 18.7911 0.746292
\(635\) 7.58334 0.300936
\(636\) −26.2663 −1.04152
\(637\) 7.55286 32.4310i 0.299255 1.28496i
\(638\) 16.0381i 0.634953i
\(639\) −8.75698 −0.346421
\(640\) −15.4727 −0.611612
\(641\) 10.3487i 0.408750i −0.978893 0.204375i \(-0.934484\pi\)
0.978893 0.204375i \(-0.0655162\pi\)
\(642\) −27.6008 −1.08932
\(643\) −21.9318 −0.864908 −0.432454 0.901656i \(-0.642352\pi\)
−0.432454 + 0.901656i \(0.642352\pi\)
\(644\) 29.8633 + 9.62717i 1.17678 + 0.379364i
\(645\) 25.1949 0.992049
\(646\) −5.93246 −0.233410
\(647\) 11.5356i 0.453513i −0.973951 0.226756i \(-0.927188\pi\)
0.973951 0.226756i \(-0.0728121\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −18.7523 −0.736093
\(650\) 10.4744i 0.410838i
\(651\) −16.7115 1.92028i −0.654976 0.0752617i
\(652\) −6.29735 −0.246623
\(653\) 40.3726 1.57990 0.789952 0.613169i \(-0.210105\pi\)
0.789952 + 0.613169i \(0.210105\pi\)
\(654\) −20.7296 −0.810592
\(655\) 15.6626i 0.611990i
\(656\) 29.9714i 1.17018i
\(657\) 0.926221i 0.0361353i
\(658\) 3.61638 31.4721i 0.140981 1.22691i
\(659\) 40.0145i 1.55874i 0.626562 + 0.779371i \(0.284461\pi\)
−0.626562 + 0.779371i \(0.715539\pi\)
\(660\) 14.4185 0.561239
\(661\) −0.159220 −0.00619293 −0.00309646 0.999995i \(-0.500986\pi\)
−0.00309646 + 0.999995i \(0.500986\pi\)
\(662\) 32.0389 1.24523
\(663\) 2.11609 0.0821822
\(664\) −4.81207 −0.186745
\(665\) −32.9782 3.78945i −1.27884 0.146948i
\(666\) 14.1565i 0.548552i
\(667\) −12.1692 2.43453i −0.471195 0.0942654i
\(668\) 7.60095i 0.294089i
\(669\) −5.19716 −0.200934
\(670\) 40.9534i 1.58217i
\(671\) 10.0411i 0.387633i
\(672\) −2.41225 + 20.9929i −0.0930544 + 0.809820i
\(673\) 37.5459 1.44729 0.723644 0.690173i \(-0.242466\pi\)
0.723644 + 0.690173i \(0.242466\pi\)
\(674\) 31.3640i 1.20809i
\(675\) 1.04113i 0.0400731i
\(676\) −23.8106 −0.915792
\(677\) 37.0329 1.42329 0.711645 0.702540i \(-0.247951\pi\)
0.711645 + 0.702540i \(0.247951\pi\)
\(678\) 25.9865 0.998006
\(679\) −45.7974 5.26247i −1.75754 0.201955i
\(680\) 0.885092 0.0339417
\(681\) 1.03060i 0.0394928i
\(682\) 39.4045 1.50888
\(683\) −45.1421 −1.72732 −0.863658 0.504079i \(-0.831832\pi\)
−0.863658 + 0.504079i \(0.831832\pi\)
\(684\) −15.5932 −0.596222
\(685\) 35.4395i 1.35407i
\(686\) −36.8842 13.1810i −1.40825 0.503252i
\(687\) 12.8914i 0.491836i
\(688\) 35.8452i 1.36658i
\(689\) 50.5283 1.92498
\(690\) −3.95887 + 19.7888i −0.150712 + 0.753347i
\(691\) 29.1902i 1.11045i 0.831701 + 0.555224i \(0.187367\pi\)
−0.831701 + 0.555224i \(0.812633\pi\)
\(692\) 15.4534i 0.587450i
\(693\) 0.885092 7.70265i 0.0336219 0.292599i
\(694\) 38.2834 1.45322
\(695\) 2.96918i 0.112627i
\(696\) 2.58774i 0.0980881i
\(697\) 4.70984i 0.178398i
\(698\) 44.4263i 1.68156i
\(699\) 22.1817i 0.838990i
\(700\) −6.76706 0.777586i −0.255771 0.0293900i
\(701\) 22.0254i 0.831889i −0.909390 0.415944i \(-0.863451\pi\)
0.909390 0.415944i \(-0.136549\pi\)
\(702\) 10.0606 0.379712
\(703\) 42.2089i 1.59194i
\(704\) 32.9088i 1.24030i
\(705\) 11.2647 0.424252
\(706\) 45.4589i 1.71087i
\(707\) 3.85088 33.5129i 0.144827 1.26038i
\(708\) −15.8238 −0.594695
\(709\) 14.9322i 0.560789i 0.959885 + 0.280395i \(0.0904654\pi\)
−0.959885 + 0.280395i \(0.909535\pi\)
\(710\) 36.8495 1.38294
\(711\) 8.86087i 0.332308i
\(712\) 0.0511154 0.00191563
\(713\) −5.98150 + 29.8991i −0.224009 + 1.11973i
\(714\) 0.284147 2.47283i 0.0106339 0.0925435i
\(715\) −27.7368 −1.03730
\(716\) −46.1623 −1.72517
\(717\) 14.0995i 0.526554i
\(718\) 4.57102i 0.170589i
\(719\) 18.0070i 0.671546i 0.941943 + 0.335773i \(0.108998\pi\)
−0.941943 + 0.335773i \(0.891002\pi\)
\(720\) −5.63234 −0.209905
\(721\) 16.9930 + 1.95263i 0.632854 + 0.0727197i
\(722\) −43.9123 −1.63425
\(723\) 15.9994i 0.595023i
\(724\) 41.7638 1.55214
\(725\) 2.69417 0.100059
\(726\) 5.10170i 0.189342i
\(727\) 24.9172 0.924128 0.462064 0.886846i \(-0.347109\pi\)
0.462064 + 0.886846i \(0.347109\pi\)
\(728\) −1.43675 + 12.5035i −0.0532494 + 0.463411i
\(729\) −1.00000 −0.0370370
\(730\) 3.89755i 0.144255i
\(731\) 5.63288i 0.208340i
\(732\) 8.47302i 0.313172i
\(733\) −37.5821 −1.38812 −0.694062 0.719915i \(-0.744181\pi\)
−0.694062 + 0.719915i \(0.744181\pi\)
\(734\) 34.9803 1.29115
\(735\) 3.15912 13.5648i 0.116526 0.500346i
\(736\) 37.5591 + 7.51393i 1.38445 + 0.276967i
\(737\) −28.5202 −1.05056
\(738\) 22.3921i 0.824264i
\(739\) 23.3983 0.860722 0.430361 0.902657i \(-0.358386\pi\)
0.430361 + 0.902657i \(0.358386\pi\)
\(740\) 32.9340i 1.21068i
\(741\) 29.9966 1.10195
\(742\) 6.78491 59.0467i 0.249082 2.16767i
\(743\) 0.254902i 0.00935144i 0.999989 + 0.00467572i \(0.00148833\pi\)
−0.999989 + 0.00467572i \(0.998512\pi\)
\(744\) 6.35793 0.233093
\(745\) 8.25926i 0.302596i
\(746\) 65.9133i 2.41326i
\(747\) −4.81207 −0.176065
\(748\) 3.22357i 0.117865i
\(749\) 3.94166 34.3029i 0.144025 1.25340i
\(750\) 25.4211i 0.928249i
\(751\) 1.20224i 0.0438705i 0.999759 + 0.0219353i \(0.00698277\pi\)
−0.999759 + 0.0219353i \(0.993017\pi\)
\(752\) 16.0264i 0.584423i
\(753\) 15.3829i 0.560583i
\(754\) 26.0342i 0.948108i
\(755\) 8.12243 0.295606
\(756\) 0.746868 6.49973i 0.0271633 0.236393i
\(757\) 3.06931i 0.111556i −0.998443 0.0557779i \(-0.982236\pi\)
0.998443 0.0557779i \(-0.0177639\pi\)
\(758\) 58.3607i 2.11975i
\(759\) −13.7810 2.75698i −0.500220 0.100072i
\(760\) 12.5466 0.455113
\(761\) 0.186452i 0.00675888i −0.999994 0.00337944i \(-0.998924\pi\)
0.999994 0.00337944i \(-0.00107571\pi\)
\(762\) 8.06058i 0.292004i
\(763\) 2.96039 25.7632i 0.107173 0.932691i
\(764\) 13.7058i 0.495857i
\(765\) 0.885092 0.0320006
\(766\) 27.3027 0.986488
\(767\) 30.4402 1.09913
\(768\) 6.01320i 0.216983i
\(769\) −45.8185 −1.65226 −0.826128 0.563483i \(-0.809461\pi\)
−0.826128 + 0.563483i \(0.809461\pi\)
\(770\) −3.72448 + 32.4128i −0.134221 + 1.16808i
\(771\) 9.74378 0.350914
\(772\) −22.0558 −0.793807
\(773\) −40.5819 −1.45963 −0.729816 0.683644i \(-0.760394\pi\)
−0.729816 + 0.683644i \(0.760394\pi\)
\(774\) 26.7805i 0.962606i
\(775\) 6.61942i 0.237777i
\(776\) 17.4237 0.625474
\(777\) −17.5940 2.02168i −0.631181 0.0725274i
\(778\) 33.4742i 1.20011i
\(779\) 66.7643i 2.39208i
\(780\) −23.4052 −0.838040
\(781\) 25.6622i 0.918266i
\(782\) −4.42422 0.885092i −0.158210 0.0316508i
\(783\) 2.58774i 0.0924783i
\(784\) −19.2989 4.49452i −0.689245 0.160518i
\(785\) −3.11018 −0.111007
\(786\) 16.6483 0.593826
\(787\) −42.9391 −1.53061 −0.765307 0.643666i \(-0.777413\pi\)
−0.765307 + 0.643666i \(0.777413\pi\)
\(788\) 59.7493 2.12848
\(789\)