Properties

Label 1512.2.c.f.757.12
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 757.12
Character \(\chi\) = 1512.757
Dual form 1512.2.c.f.757.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.174217 + 1.40344i) q^{2} +(-1.93930 - 0.489007i) q^{4} +1.26947i q^{5} +1.00000 q^{7} +(1.02415 - 2.63650i) q^{8} +O(q^{10})\) \(q+(-0.174217 + 1.40344i) q^{2} +(-1.93930 - 0.489007i) q^{4} +1.26947i q^{5} +1.00000 q^{7} +(1.02415 - 2.63650i) q^{8} +(-1.78162 - 0.221163i) q^{10} -2.02805i q^{11} +4.05339i q^{13} +(-0.174217 + 1.40344i) q^{14} +(3.52175 + 1.89666i) q^{16} -1.33658 q^{17} +3.28346i q^{19} +(0.620778 - 2.46188i) q^{20} +(2.84625 + 0.353321i) q^{22} +2.25680 q^{23} +3.38845 q^{25} +(-5.68870 - 0.706169i) q^{26} +(-1.93930 - 0.489007i) q^{28} -3.58798i q^{29} -0.464312 q^{31} +(-3.27540 + 4.61213i) q^{32} +(0.232854 - 1.87581i) q^{34} +1.26947i q^{35} +11.8743i q^{37} +(-4.60814 - 0.572034i) q^{38} +(3.34695 + 1.30013i) q^{40} -1.73758 q^{41} +1.70380i q^{43} +(-0.991730 + 3.93299i) q^{44} +(-0.393173 + 3.16729i) q^{46} -8.45083 q^{47} +1.00000 q^{49} +(-0.590326 + 4.75549i) q^{50} +(1.98213 - 7.86073i) q^{52} +11.7544i q^{53} +2.57454 q^{55} +(1.02415 - 2.63650i) q^{56} +(5.03553 + 0.625087i) q^{58} +5.49489i q^{59} +6.02150i q^{61} +(0.0808911 - 0.651635i) q^{62} +(-5.90223 - 5.40034i) q^{64} -5.14565 q^{65} +0.381481i q^{67} +(2.59202 + 0.653595i) q^{68} +(-1.78162 - 0.221163i) q^{70} +9.47622 q^{71} -10.0336 q^{73} +(-16.6648 - 2.06870i) q^{74} +(1.60563 - 6.36760i) q^{76} -2.02805i q^{77} +4.90442 q^{79} +(-2.40775 + 4.47074i) q^{80} +(0.302717 - 2.43860i) q^{82} -6.95800i q^{83} -1.69674i q^{85} +(-2.39118 - 0.296830i) q^{86} +(-5.34695 - 2.07703i) q^{88} -17.4322 q^{89} +4.05339i q^{91} +(-4.37661 - 1.10359i) q^{92} +(1.47228 - 11.8602i) q^{94} -4.16824 q^{95} +7.62794 q^{97} +(-0.174217 + 1.40344i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 24q^{7} + O(q^{10}) \) \( 24q + 24q^{7} + 20q^{10} - 4q^{16} + 4q^{22} - 24q^{25} - 16q^{31} + 4q^{34} + 12q^{40} - 52q^{46} + 24q^{49} + 12q^{52} - 8q^{55} - 28q^{58} + 24q^{64} + 20q^{70} - 24q^{76} + 32q^{79} + 44q^{82} - 60q^{88} + 12q^{94} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.174217 + 1.40344i −0.123190 + 0.992383i
\(3\) 0 0
\(4\) −1.93930 0.489007i −0.969648 0.244503i
\(5\) 1.26947i 0.567723i 0.958865 + 0.283862i \(0.0916156\pi\)
−0.958865 + 0.283862i \(0.908384\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.02415 2.63650i 0.362092 0.932142i
\(9\) 0 0
\(10\) −1.78162 0.221163i −0.563399 0.0699378i
\(11\) 2.02805i 0.611480i −0.952115 0.305740i \(-0.901096\pi\)
0.952115 0.305740i \(-0.0989039\pi\)
\(12\) 0 0
\(13\) 4.05339i 1.12421i 0.827066 + 0.562104i \(0.190008\pi\)
−0.827066 + 0.562104i \(0.809992\pi\)
\(14\) −0.174217 + 1.40344i −0.0465614 + 0.375086i
\(15\) 0 0
\(16\) 3.52175 + 1.89666i 0.880436 + 0.474164i
\(17\) −1.33658 −0.324167 −0.162084 0.986777i \(-0.551821\pi\)
−0.162084 + 0.986777i \(0.551821\pi\)
\(18\) 0 0
\(19\) 3.28346i 0.753277i 0.926360 + 0.376638i \(0.122920\pi\)
−0.926360 + 0.376638i \(0.877080\pi\)
\(20\) 0.620778 2.46188i 0.138810 0.550492i
\(21\) 0 0
\(22\) 2.84625 + 0.353321i 0.606823 + 0.0753282i
\(23\) 2.25680 0.470576 0.235288 0.971926i \(-0.424397\pi\)
0.235288 + 0.971926i \(0.424397\pi\)
\(24\) 0 0
\(25\) 3.38845 0.677690
\(26\) −5.68870 0.706169i −1.11565 0.138491i
\(27\) 0 0
\(28\) −1.93930 0.489007i −0.366493 0.0924136i
\(29\) 3.58798i 0.666272i −0.942879 0.333136i \(-0.891893\pi\)
0.942879 0.333136i \(-0.108107\pi\)
\(30\) 0 0
\(31\) −0.464312 −0.0833930 −0.0416965 0.999130i \(-0.513276\pi\)
−0.0416965 + 0.999130i \(0.513276\pi\)
\(32\) −3.27540 + 4.61213i −0.579014 + 0.815318i
\(33\) 0 0
\(34\) 0.232854 1.87581i 0.0399342 0.321698i
\(35\) 1.26947i 0.214579i
\(36\) 0 0
\(37\) 11.8743i 1.95212i 0.217507 + 0.976059i \(0.430207\pi\)
−0.217507 + 0.976059i \(0.569793\pi\)
\(38\) −4.60814 0.572034i −0.747539 0.0927962i
\(39\) 0 0
\(40\) 3.34695 + 1.30013i 0.529199 + 0.205568i
\(41\) −1.73758 −0.271365 −0.135683 0.990752i \(-0.543323\pi\)
−0.135683 + 0.990752i \(0.543323\pi\)
\(42\) 0 0
\(43\) 1.70380i 0.259827i 0.991525 + 0.129913i \(0.0414699\pi\)
−0.991525 + 0.129913i \(0.958530\pi\)
\(44\) −0.991730 + 3.93299i −0.149509 + 0.592921i
\(45\) 0 0
\(46\) −0.393173 + 3.16729i −0.0579702 + 0.466991i
\(47\) −8.45083 −1.23268 −0.616340 0.787480i \(-0.711385\pi\)
−0.616340 + 0.787480i \(0.711385\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −0.590326 + 4.75549i −0.0834846 + 0.672528i
\(51\) 0 0
\(52\) 1.98213 7.86073i 0.274873 1.09009i
\(53\) 11.7544i 1.61459i 0.590146 + 0.807296i \(0.299070\pi\)
−0.590146 + 0.807296i \(0.700930\pi\)
\(54\) 0 0
\(55\) 2.57454 0.347152
\(56\) 1.02415 2.63650i 0.136858 0.352317i
\(57\) 0 0
\(58\) 5.03553 + 0.625087i 0.661197 + 0.0820780i
\(59\) 5.49489i 0.715374i 0.933842 + 0.357687i \(0.116435\pi\)
−0.933842 + 0.357687i \(0.883565\pi\)
\(60\) 0 0
\(61\) 6.02150i 0.770975i 0.922713 + 0.385487i \(0.125967\pi\)
−0.922713 + 0.385487i \(0.874033\pi\)
\(62\) 0.0808911 0.651635i 0.0102732 0.0827578i
\(63\) 0 0
\(64\) −5.90223 5.40034i −0.737779 0.675042i
\(65\) −5.14565 −0.638239
\(66\) 0 0
\(67\) 0.381481i 0.0466054i 0.999728 + 0.0233027i \(0.00741815\pi\)
−0.999728 + 0.0233027i \(0.992582\pi\)
\(68\) 2.59202 + 0.653595i 0.314328 + 0.0792600i
\(69\) 0 0
\(70\) −1.78162 0.221163i −0.212945 0.0264340i
\(71\) 9.47622 1.12462 0.562310 0.826926i \(-0.309913\pi\)
0.562310 + 0.826926i \(0.309913\pi\)
\(72\) 0 0
\(73\) −10.0336 −1.17434 −0.587171 0.809463i \(-0.699759\pi\)
−0.587171 + 0.809463i \(0.699759\pi\)
\(74\) −16.6648 2.06870i −1.93725 0.240481i
\(75\) 0 0
\(76\) 1.60563 6.36760i 0.184179 0.730414i
\(77\) 2.02805i 0.231118i
\(78\) 0 0
\(79\) 4.90442 0.551791 0.275895 0.961188i \(-0.411026\pi\)
0.275895 + 0.961188i \(0.411026\pi\)
\(80\) −2.40775 + 4.47074i −0.269194 + 0.499844i
\(81\) 0 0
\(82\) 0.302717 2.43860i 0.0334295 0.269298i
\(83\) 6.95800i 0.763740i −0.924216 0.381870i \(-0.875280\pi\)
0.924216 0.381870i \(-0.124720\pi\)
\(84\) 0 0
\(85\) 1.69674i 0.184037i
\(86\) −2.39118 0.296830i −0.257848 0.0320080i
\(87\) 0 0
\(88\) −5.34695 2.07703i −0.569987 0.221412i
\(89\) −17.4322 −1.84781 −0.923903 0.382628i \(-0.875019\pi\)
−0.923903 + 0.382628i \(0.875019\pi\)
\(90\) 0 0
\(91\) 4.05339i 0.424911i
\(92\) −4.37661 1.10359i −0.456293 0.115057i
\(93\) 0 0
\(94\) 1.47228 11.8602i 0.151854 1.22329i
\(95\) −4.16824 −0.427653
\(96\) 0 0
\(97\) 7.62794 0.774500 0.387250 0.921975i \(-0.373425\pi\)
0.387250 + 0.921975i \(0.373425\pi\)
\(98\) −0.174217 + 1.40344i −0.0175986 + 0.141769i
\(99\) 0 0
\(100\) −6.57121 1.65697i −0.657121 0.165697i
\(101\) 5.27674i 0.525055i −0.964924 0.262528i \(-0.915444\pi\)
0.964924 0.262528i \(-0.0845561\pi\)
\(102\) 0 0
\(103\) −5.07253 −0.499812 −0.249906 0.968270i \(-0.580400\pi\)
−0.249906 + 0.968270i \(0.580400\pi\)
\(104\) 10.6868 + 4.15128i 1.04792 + 0.407067i
\(105\) 0 0
\(106\) −16.4966 2.04782i −1.60229 0.198902i
\(107\) 5.22269i 0.504896i 0.967610 + 0.252448i \(0.0812357\pi\)
−0.967610 + 0.252448i \(0.918764\pi\)
\(108\) 0 0
\(109\) 10.8354i 1.03784i −0.854822 0.518922i \(-0.826333\pi\)
0.854822 0.518922i \(-0.173667\pi\)
\(110\) −0.448529 + 3.61322i −0.0427656 + 0.344507i
\(111\) 0 0
\(112\) 3.52175 + 1.89666i 0.332774 + 0.179217i
\(113\) −10.8783 −1.02334 −0.511672 0.859181i \(-0.670974\pi\)
−0.511672 + 0.859181i \(0.670974\pi\)
\(114\) 0 0
\(115\) 2.86494i 0.267157i
\(116\) −1.75455 + 6.95817i −0.162906 + 0.646049i
\(117\) 0 0
\(118\) −7.71176 0.957303i −0.709925 0.0881269i
\(119\) −1.33658 −0.122524
\(120\) 0 0
\(121\) 6.88701 0.626092
\(122\) −8.45083 1.04905i −0.765102 0.0949763i
\(123\) 0 0
\(124\) 0.900440 + 0.227052i 0.0808619 + 0.0203899i
\(125\) 10.6489i 0.952464i
\(126\) 0 0
\(127\) 1.57175 0.139471 0.0697353 0.997566i \(-0.477785\pi\)
0.0697353 + 0.997566i \(0.477785\pi\)
\(128\) 8.60733 7.34261i 0.760788 0.649001i
\(129\) 0 0
\(130\) 0.896459 7.22162i 0.0786247 0.633378i
\(131\) 11.7947i 1.03051i 0.857037 + 0.515256i \(0.172303\pi\)
−0.857037 + 0.515256i \(0.827697\pi\)
\(132\) 0 0
\(133\) 3.28346i 0.284712i
\(134\) −0.535387 0.0664605i −0.0462504 0.00574131i
\(135\) 0 0
\(136\) −1.36886 + 3.52388i −0.117378 + 0.302170i
\(137\) −18.4006 −1.57207 −0.786033 0.618184i \(-0.787869\pi\)
−0.786033 + 0.618184i \(0.787869\pi\)
\(138\) 0 0
\(139\) 11.3851i 0.965674i 0.875710 + 0.482837i \(0.160394\pi\)
−0.875710 + 0.482837i \(0.839606\pi\)
\(140\) 0.620778 2.46188i 0.0524653 0.208066i
\(141\) 0 0
\(142\) −1.65092 + 13.2993i −0.138542 + 1.11605i
\(143\) 8.22048 0.687431
\(144\) 0 0
\(145\) 4.55483 0.378258
\(146\) 1.74802 14.0816i 0.144667 1.16540i
\(147\) 0 0
\(148\) 5.80659 23.0277i 0.477299 1.89287i
\(149\) 14.6966i 1.20400i −0.798498 0.601998i \(-0.794372\pi\)
0.798498 0.601998i \(-0.205628\pi\)
\(150\) 0 0
\(151\) −0.220342 −0.0179312 −0.00896559 0.999960i \(-0.502854\pi\)
−0.00896559 + 0.999960i \(0.502854\pi\)
\(152\) 8.65683 + 3.36276i 0.702161 + 0.272755i
\(153\) 0 0
\(154\) 2.84625 + 0.353321i 0.229357 + 0.0284714i
\(155\) 0.589430i 0.0473441i
\(156\) 0 0
\(157\) 10.4367i 0.832941i 0.909149 + 0.416471i \(0.136733\pi\)
−0.909149 + 0.416471i \(0.863267\pi\)
\(158\) −0.854434 + 6.88307i −0.0679751 + 0.547588i
\(159\) 0 0
\(160\) −5.85496 4.15801i −0.462875 0.328720i
\(161\) 2.25680 0.177861
\(162\) 0 0
\(163\) 4.46955i 0.350082i 0.984561 + 0.175041i \(0.0560058\pi\)
−0.984561 + 0.175041i \(0.943994\pi\)
\(164\) 3.36969 + 0.849690i 0.263129 + 0.0663497i
\(165\) 0 0
\(166\) 9.76515 + 1.21220i 0.757923 + 0.0940851i
\(167\) 14.0617 1.08812 0.544062 0.839045i \(-0.316886\pi\)
0.544062 + 0.839045i \(0.316886\pi\)
\(168\) 0 0
\(169\) −3.42998 −0.263844
\(170\) 2.38128 + 0.295601i 0.182636 + 0.0226716i
\(171\) 0 0
\(172\) 0.833168 3.30417i 0.0635284 0.251940i
\(173\) 0.334570i 0.0254369i 0.999919 + 0.0127184i \(0.00404851\pi\)
−0.999919 + 0.0127184i \(0.995951\pi\)
\(174\) 0 0
\(175\) 3.38845 0.256143
\(176\) 3.84652 7.14228i 0.289942 0.538369i
\(177\) 0 0
\(178\) 3.03698 24.4650i 0.227631 1.83373i
\(179\) 1.85419i 0.138589i −0.997596 0.0692944i \(-0.977925\pi\)
0.997596 0.0692944i \(-0.0220748\pi\)
\(180\) 0 0
\(181\) 11.8864i 0.883512i 0.897135 + 0.441756i \(0.145644\pi\)
−0.897135 + 0.441756i \(0.854356\pi\)
\(182\) −5.68870 0.706169i −0.421674 0.0523447i
\(183\) 0 0
\(184\) 2.31130 5.95005i 0.170392 0.438643i
\(185\) −15.0740 −1.10826
\(186\) 0 0
\(187\) 2.71064i 0.198222i
\(188\) 16.3887 + 4.13251i 1.19527 + 0.301394i
\(189\) 0 0
\(190\) 0.726179 5.84989i 0.0526825 0.424396i
\(191\) 26.4777 1.91586 0.957928 0.287008i \(-0.0926607\pi\)
0.957928 + 0.287008i \(0.0926607\pi\)
\(192\) 0 0
\(193\) −17.6831 −1.27285 −0.636427 0.771337i \(-0.719588\pi\)
−0.636427 + 0.771337i \(0.719588\pi\)
\(194\) −1.32892 + 10.7054i −0.0954106 + 0.768600i
\(195\) 0 0
\(196\) −1.93930 0.489007i −0.138521 0.0349290i
\(197\) 9.22153i 0.657007i 0.944503 + 0.328504i \(0.106544\pi\)
−0.944503 + 0.328504i \(0.893456\pi\)
\(198\) 0 0
\(199\) −8.46365 −0.599973 −0.299986 0.953944i \(-0.596982\pi\)
−0.299986 + 0.953944i \(0.596982\pi\)
\(200\) 3.47028 8.93364i 0.245386 0.631704i
\(201\) 0 0
\(202\) 7.40560 + 0.919297i 0.521056 + 0.0646815i
\(203\) 3.58798i 0.251827i
\(204\) 0 0
\(205\) 2.20581i 0.154060i
\(206\) 0.883721 7.11900i 0.0615718 0.496005i
\(207\) 0 0
\(208\) −7.68790 + 14.2750i −0.533060 + 0.989794i
\(209\) 6.65902 0.460614
\(210\) 0 0
\(211\) 4.66745i 0.321321i 0.987010 + 0.160660i \(0.0513624\pi\)
−0.987010 + 0.160660i \(0.948638\pi\)
\(212\) 5.74798 22.7953i 0.394773 1.56559i
\(213\) 0 0
\(214\) −7.32974 0.909880i −0.501050 0.0621981i
\(215\) −2.16292 −0.147510
\(216\) 0 0
\(217\) −0.464312 −0.0315196
\(218\) 15.2069 + 1.88771i 1.02994 + 0.127852i
\(219\) 0 0
\(220\) −4.99281 1.25897i −0.336615 0.0848797i
\(221\) 5.41767i 0.364432i
\(222\) 0 0
\(223\) 7.85009 0.525681 0.262841 0.964839i \(-0.415341\pi\)
0.262841 + 0.964839i \(0.415341\pi\)
\(224\) −3.27540 + 4.61213i −0.218847 + 0.308161i
\(225\) 0 0
\(226\) 1.89518 15.2670i 0.126066 1.01555i
\(227\) 19.2857i 1.28004i −0.768360 0.640018i \(-0.778927\pi\)
0.768360 0.640018i \(-0.221073\pi\)
\(228\) 0 0
\(229\) 1.71588i 0.113389i −0.998392 0.0566944i \(-0.981944\pi\)
0.998392 0.0566944i \(-0.0180561\pi\)
\(230\) −4.02077 0.499120i −0.265122 0.0329110i
\(231\) 0 0
\(232\) −9.45971 3.67464i −0.621060 0.241252i
\(233\) 23.8734 1.56400 0.781999 0.623280i \(-0.214200\pi\)
0.781999 + 0.623280i \(0.214200\pi\)
\(234\) 0 0
\(235\) 10.7281i 0.699821i
\(236\) 2.68704 10.6562i 0.174911 0.693661i
\(237\) 0 0
\(238\) 0.232854 1.87581i 0.0150937 0.121591i
\(239\) 21.6697 1.40170 0.700848 0.713310i \(-0.252805\pi\)
0.700848 + 0.713310i \(0.252805\pi\)
\(240\) 0 0
\(241\) 27.8432 1.79354 0.896770 0.442497i \(-0.145907\pi\)
0.896770 + 0.442497i \(0.145907\pi\)
\(242\) −1.19983 + 9.66552i −0.0771283 + 0.621323i
\(243\) 0 0
\(244\) 2.94455 11.6775i 0.188506 0.747574i
\(245\) 1.26947i 0.0811033i
\(246\) 0 0
\(247\) −13.3091 −0.846840
\(248\) −0.475526 + 1.22416i −0.0301959 + 0.0777341i
\(249\) 0 0
\(250\) −14.9451 1.85521i −0.945209 0.117334i
\(251\) 27.7106i 1.74908i −0.484957 0.874538i \(-0.661165\pi\)
0.484957 0.874538i \(-0.338835\pi\)
\(252\) 0 0
\(253\) 4.57691i 0.287748i
\(254\) −0.273826 + 2.20586i −0.0171814 + 0.138408i
\(255\) 0 0
\(256\) 8.80538 + 13.3591i 0.550336 + 0.834943i
\(257\) −1.90462 −0.118807 −0.0594035 0.998234i \(-0.518920\pi\)
−0.0594035 + 0.998234i \(0.518920\pi\)
\(258\) 0 0
\(259\) 11.8743i 0.737831i
\(260\) 9.97894 + 2.51626i 0.618868 + 0.156052i
\(261\) 0 0
\(262\) −16.5532 2.05484i −1.02266 0.126949i
\(263\) 19.2186 1.18507 0.592534 0.805545i \(-0.298128\pi\)
0.592534 + 0.805545i \(0.298128\pi\)
\(264\) 0 0
\(265\) −14.9218 −0.916642
\(266\) −4.60814 0.572034i −0.282543 0.0350737i
\(267\) 0 0
\(268\) 0.186547 0.739806i 0.0113952 0.0451908i
\(269\) 18.2931i 1.11535i 0.830059 + 0.557676i \(0.188307\pi\)
−0.830059 + 0.557676i \(0.811693\pi\)
\(270\) 0 0
\(271\) 19.1450 1.16297 0.581487 0.813555i \(-0.302471\pi\)
0.581487 + 0.813555i \(0.302471\pi\)
\(272\) −4.70708 2.53503i −0.285409 0.153709i
\(273\) 0 0
\(274\) 3.20569 25.8241i 0.193663 1.56009i
\(275\) 6.87195i 0.414394i
\(276\) 0 0
\(277\) 17.6288i 1.05921i −0.848244 0.529606i \(-0.822340\pi\)
0.848244 0.529606i \(-0.177660\pi\)
\(278\) −15.9784 1.98348i −0.958318 0.118961i
\(279\) 0 0
\(280\) 3.34695 + 1.30013i 0.200018 + 0.0776974i
\(281\) −12.3772 −0.738362 −0.369181 0.929358i \(-0.620362\pi\)
−0.369181 + 0.929358i \(0.620362\pi\)
\(282\) 0 0
\(283\) 2.56225i 0.152310i −0.997096 0.0761550i \(-0.975736\pi\)
0.997096 0.0761550i \(-0.0242644\pi\)
\(284\) −18.3772 4.63394i −1.09049 0.274973i
\(285\) 0 0
\(286\) −1.43215 + 11.5370i −0.0846846 + 0.682195i
\(287\) −1.73758 −0.102566
\(288\) 0 0
\(289\) −15.2136 −0.894916
\(290\) −0.793528 + 6.39244i −0.0465976 + 0.375377i
\(291\) 0 0
\(292\) 19.4581 + 4.90649i 1.13870 + 0.287131i
\(293\) 1.12608i 0.0657866i 0.999459 + 0.0328933i \(0.0104721\pi\)
−0.999459 + 0.0328933i \(0.989528\pi\)
\(294\) 0 0
\(295\) −6.97559 −0.406135
\(296\) 31.3065 + 12.1610i 1.81965 + 0.706846i
\(297\) 0 0
\(298\) 20.6259 + 2.56040i 1.19483 + 0.148320i
\(299\) 9.14770i 0.529025i
\(300\) 0 0
\(301\) 1.70380i 0.0982052i
\(302\) 0.0383873 0.309237i 0.00220894 0.0177946i
\(303\) 0 0
\(304\) −6.22760 + 11.5635i −0.357177 + 0.663212i
\(305\) −7.64411 −0.437700
\(306\) 0 0
\(307\) 24.9543i 1.42422i 0.702070 + 0.712108i \(0.252259\pi\)
−0.702070 + 0.712108i \(0.747741\pi\)
\(308\) −0.991730 + 3.93299i −0.0565091 + 0.224103i
\(309\) 0 0
\(310\) 0.827230 + 0.102689i 0.0469835 + 0.00583232i
\(311\) 20.4110 1.15740 0.578701 0.815540i \(-0.303560\pi\)
0.578701 + 0.815540i \(0.303560\pi\)
\(312\) 0 0
\(313\) 18.5902 1.05078 0.525389 0.850862i \(-0.323920\pi\)
0.525389 + 0.850862i \(0.323920\pi\)
\(314\) −14.6473 1.81825i −0.826597 0.102610i
\(315\) 0 0
\(316\) −9.51113 2.39830i −0.535043 0.134915i
\(317\) 1.68959i 0.0948970i −0.998874 0.0474485i \(-0.984891\pi\)
0.998874 0.0474485i \(-0.0151090\pi\)
\(318\) 0 0
\(319\) −7.27661 −0.407412
\(320\) 6.85556 7.49269i 0.383237 0.418854i
\(321\) 0 0
\(322\) −0.393173 + 3.16729i −0.0219107 + 0.176506i
\(323\) 4.38859i 0.244188i
\(324\) 0 0
\(325\) 13.7347i 0.761865i
\(326\) −6.27275 0.778671i −0.347416 0.0431266i
\(327\) 0 0
\(328\) −1.77955 + 4.58114i −0.0982591 + 0.252951i
\(329\) −8.45083 −0.465909
\(330\) 0 0
\(331\) 25.4187i 1.39714i −0.715542 0.698570i \(-0.753820\pi\)
0.715542 0.698570i \(-0.246180\pi\)
\(332\) −3.40251 + 13.4936i −0.186737 + 0.740559i
\(333\) 0 0
\(334\) −2.44978 + 19.7347i −0.134046 + 1.07984i
\(335\) −0.484278 −0.0264590
\(336\) 0 0
\(337\) −10.5368 −0.573979 −0.286989 0.957934i \(-0.592654\pi\)
−0.286989 + 0.957934i \(0.592654\pi\)
\(338\) 0.597560 4.81377i 0.0325030 0.261835i
\(339\) 0 0
\(340\) −0.829717 + 3.29048i −0.0449977 + 0.178452i
\(341\) 0.941649i 0.0509932i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 4.49206 + 1.74494i 0.242195 + 0.0940811i
\(345\) 0 0
\(346\) −0.469549 0.0582877i −0.0252431 0.00313356i
\(347\) 12.6098i 0.676930i 0.940979 + 0.338465i \(0.109908\pi\)
−0.940979 + 0.338465i \(0.890092\pi\)
\(348\) 0 0
\(349\) 10.3681i 0.554990i 0.960727 + 0.277495i \(0.0895043\pi\)
−0.960727 + 0.277495i \(0.910496\pi\)
\(350\) −0.590326 + 4.75549i −0.0315542 + 0.254192i
\(351\) 0 0
\(352\) 9.35364 + 6.64267i 0.498551 + 0.354055i
\(353\) −21.4319 −1.14071 −0.570353 0.821399i \(-0.693194\pi\)
−0.570353 + 0.821399i \(0.693194\pi\)
\(354\) 0 0
\(355\) 12.0298i 0.638473i
\(356\) 33.8061 + 8.52444i 1.79172 + 0.451794i
\(357\) 0 0
\(358\) 2.60225 + 0.323031i 0.137533 + 0.0170727i
\(359\) 17.5414 0.925798 0.462899 0.886411i \(-0.346809\pi\)
0.462899 + 0.886411i \(0.346809\pi\)
\(360\) 0 0
\(361\) 8.21890 0.432574
\(362\) −16.6819 2.07082i −0.876783 0.108840i
\(363\) 0 0
\(364\) 1.98213 7.86073i 0.103892 0.412014i
\(365\) 12.7373i 0.666702i
\(366\) 0 0
\(367\) 28.4730 1.48628 0.743140 0.669136i \(-0.233335\pi\)
0.743140 + 0.669136i \(0.233335\pi\)
\(368\) 7.94788 + 4.28038i 0.414312 + 0.223130i
\(369\) 0 0
\(370\) 2.62615 21.1555i 0.136527 1.09982i
\(371\) 11.7544i 0.610259i
\(372\) 0 0
\(373\) 11.7775i 0.609818i 0.952382 + 0.304909i \(0.0986260\pi\)
−0.952382 + 0.304909i \(0.901374\pi\)
\(374\) −3.80423 0.472240i −0.196712 0.0244190i
\(375\) 0 0
\(376\) −8.65492 + 22.2806i −0.446343 + 1.14903i
\(377\) 14.5435 0.749028
\(378\) 0 0
\(379\) 14.4058i 0.739975i −0.929037 0.369988i \(-0.879362\pi\)
0.929037 0.369988i \(-0.120638\pi\)
\(380\) 8.08346 + 2.03830i 0.414673 + 0.104563i
\(381\) 0 0
\(382\) −4.61286 + 37.1599i −0.236014 + 1.90126i
\(383\) −11.8612 −0.606078 −0.303039 0.952978i \(-0.598001\pi\)
−0.303039 + 0.952978i \(0.598001\pi\)
\(384\) 0 0
\(385\) 2.57454 0.131211
\(386\) 3.08069 24.8171i 0.156803 1.26316i
\(387\) 0 0
\(388\) −14.7928 3.73011i −0.750992 0.189368i
\(389\) 16.3633i 0.829655i −0.909900 0.414827i \(-0.863842\pi\)
0.909900 0.414827i \(-0.136158\pi\)
\(390\) 0 0
\(391\) −3.01639 −0.152545
\(392\) 1.02415 2.63650i 0.0517274 0.133163i
\(393\) 0 0
\(394\) −12.9419 1.60655i −0.652003 0.0809367i
\(395\) 6.22601i 0.313265i
\(396\) 0 0
\(397\) 10.7133i 0.537685i −0.963184 0.268843i \(-0.913359\pi\)
0.963184 0.268843i \(-0.0866411\pi\)
\(398\) 1.47451 11.8782i 0.0739106 0.595403i
\(399\) 0 0
\(400\) 11.9333 + 6.42673i 0.596663 + 0.321337i
\(401\) 21.7286 1.08507 0.542536 0.840032i \(-0.317464\pi\)
0.542536 + 0.840032i \(0.317464\pi\)
\(402\) 0 0
\(403\) 1.88204i 0.0937511i
\(404\) −2.58036 + 10.2332i −0.128378 + 0.509119i
\(405\) 0 0
\(406\) 5.03553 + 0.625087i 0.249909 + 0.0310226i
\(407\) 24.0816 1.19368
\(408\) 0 0
\(409\) −14.3607 −0.710092 −0.355046 0.934849i \(-0.615535\pi\)
−0.355046 + 0.934849i \(0.615535\pi\)
\(410\) 3.09572 + 0.384289i 0.152887 + 0.0189787i
\(411\) 0 0
\(412\) 9.83715 + 2.48050i 0.484642 + 0.122206i
\(413\) 5.49489i 0.270386i
\(414\) 0 0
\(415\) 8.83296 0.433593
\(416\) −18.6948 13.2765i −0.916587 0.650932i
\(417\) 0 0
\(418\) −1.16011 + 9.34554i −0.0567430 + 0.457105i
\(419\) 33.7826i 1.65039i 0.564849 + 0.825194i \(0.308935\pi\)
−0.564849 + 0.825194i \(0.691065\pi\)
\(420\) 0 0
\(421\) 10.6036i 0.516788i −0.966040 0.258394i \(-0.916807\pi\)
0.966040 0.258394i \(-0.0831933\pi\)
\(422\) −6.55050 0.813149i −0.318873 0.0395835i
\(423\) 0 0
\(424\) 30.9905 + 12.0383i 1.50503 + 0.584631i
\(425\) −4.52892 −0.219685
\(426\) 0 0
\(427\) 6.02150i 0.291401i
\(428\) 2.55393 10.1283i 0.123449 0.489572i
\(429\) 0 0
\(430\) 0.376816 3.03553i 0.0181717 0.146386i
\(431\) 19.2155 0.925577 0.462788 0.886469i \(-0.346849\pi\)
0.462788 + 0.886469i \(0.346849\pi\)
\(432\) 0 0
\(433\) 39.8723 1.91614 0.958070 0.286534i \(-0.0925030\pi\)
0.958070 + 0.286534i \(0.0925030\pi\)
\(434\) 0.0808911 0.651635i 0.00388290 0.0312795i
\(435\) 0 0
\(436\) −5.29859 + 21.0131i −0.253756 + 1.00634i
\(437\) 7.41011i 0.354474i
\(438\) 0 0
\(439\) 2.96048 0.141296 0.0706481 0.997501i \(-0.477493\pi\)
0.0706481 + 0.997501i \(0.477493\pi\)
\(440\) 2.63672 6.78778i 0.125701 0.323595i
\(441\) 0 0
\(442\) 7.60338 + 0.943849i 0.361656 + 0.0448943i
\(443\) 12.7091i 0.603827i −0.953335 0.301914i \(-0.902375\pi\)
0.953335 0.301914i \(-0.0976254\pi\)
\(444\) 0 0
\(445\) 22.1296i 1.04904i
\(446\) −1.36762 + 11.0171i −0.0647586 + 0.521677i
\(447\) 0 0
\(448\) −5.90223 5.40034i −0.278854 0.255142i
\(449\) −27.4353 −1.29475 −0.647375 0.762171i \(-0.724133\pi\)
−0.647375 + 0.762171i \(0.724133\pi\)
\(450\) 0 0
\(451\) 3.52391i 0.165934i
\(452\) 21.0962 + 5.31955i 0.992283 + 0.250211i
\(453\) 0 0
\(454\) 27.0663 + 3.35989i 1.27029 + 0.157688i
\(455\) −5.14565 −0.241232
\(456\) 0 0
\(457\) 18.9049 0.884335 0.442168 0.896932i \(-0.354210\pi\)
0.442168 + 0.896932i \(0.354210\pi\)
\(458\) 2.40814 + 0.298936i 0.112525 + 0.0139684i
\(459\) 0 0
\(460\) 1.40097 5.55596i 0.0653207 0.259048i
\(461\) 30.3182i 1.41206i −0.708181 0.706030i \(-0.750484\pi\)
0.708181 0.706030i \(-0.249516\pi\)
\(462\) 0 0
\(463\) −29.2518 −1.35944 −0.679722 0.733470i \(-0.737900\pi\)
−0.679722 + 0.733470i \(0.737900\pi\)
\(464\) 6.80518 12.6360i 0.315922 0.586610i
\(465\) 0 0
\(466\) −4.15915 + 33.5049i −0.192669 + 1.55208i
\(467\) 32.7692i 1.51638i −0.652036 0.758188i \(-0.726085\pi\)
0.652036 0.758188i \(-0.273915\pi\)
\(468\) 0 0
\(469\) 0.381481i 0.0176152i
\(470\) 15.0562 + 1.86901i 0.694491 + 0.0862109i
\(471\) 0 0
\(472\) 14.4873 + 5.62760i 0.666831 + 0.259031i
\(473\) 3.45539 0.158879
\(474\) 0 0
\(475\) 11.1258i 0.510488i
\(476\) 2.59202 + 0.653595i 0.118805 + 0.0299575i
\(477\) 0 0
\(478\) −3.77523 + 30.4122i −0.172675 + 1.39102i
\(479\) −25.8900 −1.18294 −0.591472 0.806326i \(-0.701453\pi\)
−0.591472 + 0.806326i \(0.701453\pi\)
\(480\) 0 0
\(481\) −48.1310 −2.19459
\(482\) −4.85076 + 39.0763i −0.220946 + 1.77988i
\(483\) 0 0
\(484\) −13.3560 3.36779i −0.607089 0.153082i
\(485\) 9.68342i 0.439701i
\(486\) 0 0
\(487\) −5.94127 −0.269225 −0.134612 0.990898i \(-0.542979\pi\)
−0.134612 + 0.990898i \(0.542979\pi\)
\(488\) 15.8757 + 6.16693i 0.718658 + 0.279164i
\(489\) 0 0
\(490\) −1.78162 0.221163i −0.0804856 0.00999112i
\(491\) 3.77413i 0.170324i −0.996367 0.0851621i \(-0.972859\pi\)
0.996367 0.0851621i \(-0.0271408\pi\)
\(492\) 0 0
\(493\) 4.79561i 0.215984i
\(494\) 2.31868 18.6786i 0.104322 0.840390i
\(495\) 0 0
\(496\) −1.63519 0.880642i −0.0734222 0.0395420i
\(497\) 9.47622 0.425067
\(498\) 0 0
\(499\) 7.66921i 0.343321i −0.985156 0.171661i \(-0.945087\pi\)
0.985156 0.171661i \(-0.0549132\pi\)
\(500\) 5.20737 20.6513i 0.232881 0.923555i
\(501\) 0 0
\(502\) 38.8902 + 4.82765i 1.73575 + 0.215469i
\(503\) −7.29637 −0.325329 −0.162664 0.986681i \(-0.552009\pi\)
−0.162664 + 0.986681i \(0.552009\pi\)
\(504\) 0 0
\(505\) 6.69865 0.298086
\(506\) 6.42342 + 0.797374i 0.285556 + 0.0354476i
\(507\) 0 0
\(508\) −3.04810 0.768597i −0.135237 0.0341010i
\(509\) 7.32231i 0.324556i −0.986745 0.162278i \(-0.948116\pi\)
0.986745 0.162278i \(-0.0518841\pi\)
\(510\) 0 0
\(511\) −10.0336 −0.443860
\(512\) −20.2828 + 10.0305i −0.896379 + 0.443288i
\(513\) 0 0
\(514\) 0.331817 2.67302i 0.0146358 0.117902i
\(515\) 6.43942i 0.283755i
\(516\) 0 0
\(517\) 17.1387i 0.753759i
\(518\) −16.6648 2.06870i −0.732211 0.0908934i
\(519\) 0 0
\(520\) −5.26992 + 13.5665i −0.231101 + 0.594930i
\(521\) −29.2300 −1.28059 −0.640295 0.768129i \(-0.721188\pi\)
−0.640295 + 0.768129i \(0.721188\pi\)
\(522\) 0 0
\(523\) 37.4676i 1.63835i −0.573547 0.819173i \(-0.694433\pi\)
0.573547 0.819173i \(-0.305567\pi\)
\(524\) 5.76770 22.8735i 0.251963 0.999234i
\(525\) 0 0
\(526\) −3.34820 + 26.9721i −0.145988 + 1.17604i
\(527\) 0.620589 0.0270333
\(528\) 0 0
\(529\) −17.9068 −0.778559
\(530\) 2.59964 20.9419i 0.112921 0.909660i
\(531\) 0 0
\(532\) 1.60563 6.36760i 0.0696130 0.276070i
\(533\) 7.04311i 0.305071i
\(534\) 0 0
\(535\) −6.63003 −0.286641
\(536\) 1.00577 + 0.390694i 0.0434428 + 0.0168754i
\(537\) 0 0
\(538\) −25.6733 3.18697i −1.10686 0.137400i
\(539\) 2.02805i 0.0873543i
\(540\) 0 0
\(541\) 22.9143i 0.985164i −0.870266 0.492582i \(-0.836053\pi\)
0.870266 0.492582i \(-0.163947\pi\)
\(542\) −3.33538 + 26.8689i −0.143267 + 1.15412i
\(543\) 0 0
\(544\) 4.37782 6.16447i 0.187697 0.264299i
\(545\) 13.7552 0.589208
\(546\) 0 0
\(547\) 14.0319i 0.599959i 0.953946 + 0.299979i \(0.0969798\pi\)
−0.953946 + 0.299979i \(0.903020\pi\)
\(548\) 35.6842 + 8.99800i 1.52435 + 0.384375i
\(549\) 0 0
\(550\) 9.64438 + 1.19721i 0.411238 + 0.0510492i
\(551\) 11.7810 0.501887
\(552\) 0 0
\(553\) 4.90442 0.208557
\(554\) 24.7410 + 3.07123i 1.05114 + 0.130484i
\(555\) 0 0
\(556\) 5.56740 22.0791i 0.236110 0.936364i
\(557\) 29.1958i 1.23706i 0.785760 + 0.618532i \(0.212272\pi\)
−0.785760 + 0.618532i \(0.787728\pi\)
\(558\) 0 0
\(559\) −6.90615 −0.292099
\(560\) −2.40775 + 4.47074i −0.101746 + 0.188923i
\(561\) 0 0
\(562\) 2.15632 17.3707i 0.0909587 0.732738i
\(563\) 29.5633i 1.24594i 0.782245 + 0.622971i \(0.214075\pi\)
−0.782245 + 0.622971i \(0.785925\pi\)
\(564\) 0 0
\(565\) 13.8096i 0.580976i
\(566\) 3.59597 + 0.446387i 0.151150 + 0.0187631i
\(567\) 0 0
\(568\) 9.70508 24.9840i 0.407216 1.04831i
\(569\) 28.2748 1.18534 0.592672 0.805444i \(-0.298073\pi\)
0.592672 + 0.805444i \(0.298073\pi\)
\(570\) 0 0
\(571\) 40.3483i 1.68852i −0.535932 0.844261i \(-0.680040\pi\)
0.535932 0.844261i \(-0.319960\pi\)
\(572\) −15.9420 4.01987i −0.666567 0.168079i
\(573\) 0 0
\(574\) 0.302717 2.43860i 0.0126351 0.101785i
\(575\) 7.64706 0.318904
\(576\) 0 0
\(577\) −0.0318593 −0.00132632 −0.000663161 1.00000i \(-0.500211\pi\)
−0.000663161 1.00000i \(0.500211\pi\)
\(578\) 2.65046 21.3513i 0.110245 0.888099i
\(579\) 0 0
\(580\) −8.83317 2.22734i −0.366777 0.0924853i
\(581\) 6.95800i 0.288667i
\(582\) 0 0
\(583\) 23.8385 0.987291
\(584\) −10.2759 + 26.4535i −0.425220 + 1.09465i
\(585\) 0 0
\(586\) −1.58039 0.196183i −0.0652855 0.00810424i
\(587\) 22.9245i 0.946195i 0.881010 + 0.473098i \(0.156864\pi\)
−0.881010 + 0.473098i \(0.843136\pi\)
\(588\) 0 0
\(589\) 1.52455i 0.0628180i
\(590\) 1.21527 9.78983i 0.0500317 0.403041i
\(591\) 0 0
\(592\) −22.5214 + 41.8181i −0.925625 + 1.71872i
\(593\) 19.8895 0.816764 0.408382 0.912811i \(-0.366093\pi\)
0.408382 + 0.912811i \(0.366093\pi\)
\(594\) 0 0
\(595\) 1.69674i 0.0695596i
\(596\) −7.18675 + 28.5012i −0.294381 + 1.16745i
\(597\) 0 0
\(598\) −12.8383 1.59368i −0.524995 0.0651706i
\(599\) −9.01493 −0.368340 −0.184170 0.982894i \(-0.558960\pi\)
−0.184170 + 0.982894i \(0.558960\pi\)
\(600\) 0 0
\(601\) −30.3934 −1.23977 −0.619886 0.784692i \(-0.712821\pi\)
−0.619886 + 0.784692i \(0.712821\pi\)
\(602\) −2.39118 0.296830i −0.0974572 0.0120979i
\(603\) 0 0
\(604\) 0.427308 + 0.107749i 0.0173869 + 0.00438423i
\(605\) 8.74284i 0.355447i
\(606\) 0 0
\(607\) −35.5668 −1.44361 −0.721807 0.692095i \(-0.756688\pi\)
−0.721807 + 0.692095i \(0.756688\pi\)
\(608\) −15.1437 10.7546i −0.614160 0.436158i
\(609\) 0 0
\(610\) 1.33173 10.7281i 0.0539203 0.434366i
\(611\) 34.2545i 1.38579i
\(612\) 0 0
\(613\) 36.1874i 1.46159i −0.682595 0.730797i \(-0.739149\pi\)
0.682595 0.730797i \(-0.260851\pi\)
\(614\) −35.0219 4.34746i −1.41337 0.175449i
\(615\) 0 0
\(616\) −5.34695 2.07703i −0.215435 0.0836859i
\(617\) −27.7558 −1.11741 −0.558704 0.829367i \(-0.688701\pi\)
−0.558704 + 0.829367i \(0.688701\pi\)
\(618\) 0 0
\(619\) 30.0187i 1.20656i −0.797531 0.603278i \(-0.793861\pi\)
0.797531 0.603278i \(-0.206139\pi\)
\(620\) −0.288235 + 1.14308i −0.0115758 + 0.0459072i
\(621\) 0 0
\(622\) −3.55594 + 28.6457i −0.142580 + 1.14859i
\(623\) −17.4322 −0.698405
\(624\) 0 0
\(625\) 3.42386 0.136954
\(626\) −3.23872 + 26.0902i −0.129445 + 1.04277i
\(627\) 0 0
\(628\) 5.10363 20.2399i 0.203657 0.807660i
\(629\) 15.8709i 0.632813i
\(630\) 0 0
\(631\) 46.3724 1.84606 0.923028 0.384732i \(-0.125706\pi\)
0.923028 + 0.384732i \(0.125706\pi\)
\(632\) 5.02287 12.9305i 0.199799 0.514348i
\(633\) 0 0
\(634\) 2.37124 + 0.294356i 0.0941741 + 0.0116904i
\(635\) 1.99529i 0.0791807i
\(636\) 0 0
\(637\) 4.05339i 0.160601i
\(638\) 1.26771 10.2123i 0.0501891 0.404309i
\(639\) 0 0
\(640\) 9.32120 + 10.9267i 0.368453 + 0.431917i
\(641\) −16.0590 −0.634294 −0.317147 0.948376i \(-0.602725\pi\)
−0.317147 + 0.948376i \(0.602725\pi\)
\(642\) 0 0
\(643\) 11.8356i 0.466752i 0.972387 + 0.233376i \(0.0749774\pi\)
−0.972387 + 0.233376i \(0.925023\pi\)
\(644\) −4.37661 1.10359i −0.172462 0.0434876i
\(645\) 0 0
\(646\) 6.15913 + 0.764567i 0.242328 + 0.0300815i
\(647\) −5.05582 −0.198765 −0.0993824 0.995049i \(-0.531687\pi\)
−0.0993824 + 0.995049i \(0.531687\pi\)
\(648\) 0 0
\(649\) 11.1439 0.437437
\(650\) −19.2759 2.39282i −0.756062 0.0938541i
\(651\) 0 0
\(652\) 2.18564 8.66779i 0.0855963 0.339457i
\(653\) 21.1804i 0.828851i −0.910083 0.414426i \(-0.863982\pi\)
0.910083 0.414426i \(-0.136018\pi\)
\(654\) 0 0
\(655\) −14.9730 −0.585045
\(656\) −6.11933 3.29560i −0.238920 0.128672i
\(657\) 0 0
\(658\) 1.47228 11.8602i 0.0573953 0.462360i
\(659\) 18.6255i 0.725548i 0.931877 + 0.362774i \(0.118170\pi\)
−0.931877 + 0.362774i \(0.881830\pi\)
\(660\) 0 0
\(661\) 8.43660i 0.328146i 0.986448 + 0.164073i \(0.0524632\pi\)
−0.986448 + 0.164073i \(0.947537\pi\)
\(662\) 35.6737 + 4.42837i 1.38650 + 0.172114i
\(663\) 0 0
\(664\) −18.3448 7.12604i −0.711915 0.276544i
\(665\) −4.16824 −0.161638
\(666\) 0 0
\(667\) 8.09736i 0.313531i
\(668\) −27.2697 6.87624i −1.05510 0.266050i
\(669\) 0 0
\(670\) 0.0843695 0.679657i 0.00325948 0.0262574i
\(671\) 12.2119 0.471436
\(672\) 0 0
\(673\) −11.6372 −0.448581 −0.224291 0.974522i \(-0.572006\pi\)
−0.224291 + 0.974522i \(0.572006\pi\)
\(674\) 1.83570 14.7878i 0.0707084 0.569607i
\(675\) 0 0
\(676\) 6.65175 + 1.67728i 0.255836 + 0.0645108i
\(677\) 42.4251i 1.63053i 0.579089 + 0.815264i \(0.303408\pi\)
−0.579089 + 0.815264i \(0.696592\pi\)
\(678\) 0 0
\(679\) 7.62794 0.292733
\(680\) −4.47345 1.73772i −0.171549 0.0666384i
\(681\) 0 0
\(682\) −1.32155 0.164051i −0.0506047 0.00628184i
\(683\) 26.8253i 1.02644i −0.858257 0.513221i \(-0.828452\pi\)
0.858257 0.513221i \(-0.171548\pi\)
\(684\) 0 0
\(685\) 23.3589i 0.892499i
\(686\) −0.174217 + 1.40344i −0.00665163 + 0.0535837i
\(687\) 0 0
\(688\) −3.23152 + 6.00034i −0.123201 + 0.228761i
\(689\) −47.6452 −1.81514
\(690\) 0 0
\(691\) 49.9065i 1.89853i −0.314476 0.949265i \(-0.601829\pi\)
0.314476 0.949265i \(-0.398171\pi\)
\(692\) 0.163607 0.648830i 0.00621939 0.0246648i
\(693\) 0 0
\(694\) −17.6971 2.19684i −0.671774 0.0833910i
\(695\) −14.4530 −0.548235
\(696\) 0 0
\(697\) 2.32241 0.0879677
\(698\) −14.5510 1.80629i −0.550763 0.0683693i
\(699\) 0 0
\(700\) −6.57121 1.65697i −0.248369 0.0626278i
\(701\) 47.6375i 1.79924i 0.436671 + 0.899621i \(0.356157\pi\)
−0.436671 + 0.899621i \(0.643843\pi\)
\(702\) 0 0
\(703\) −38.9887 −1.47049
\(704\) −10.9522 + 11.9700i −0.412775 + 0.451137i
\(705\) 0 0
\(706\) 3.73381 30.0785i 0.140524 1.13202i
\(707\) 5.27674i 0.198452i
\(708\) 0 0
\(709\) 24.0726i 0.904064i −0.892002 0.452032i \(-0.850699\pi\)
0.892002 0.452032i \(-0.149301\pi\)
\(710\) −16.8831 2.09579i −0.633610 0.0786535i
\(711\) 0 0
\(712\) −17.8532 + 45.9598i −0.669075 + 1.72242i
\(713\) −1.04786 −0.0392427
\(714\) 0 0
\(715\) 10.4356i 0.390271i
\(716\) −0.906712 + 3.59583i −0.0338854 + 0.134382i
\(717\) 0 0
\(718\) −3.05600 + 24.6183i −0.114049 + 0.918746i
\(719\) −49.0237 −1.82827 −0.914137 0.405406i \(-0.867130\pi\)
−0.914137 + 0.405406i \(0.867130\pi\)
\(720\) 0 0
\(721\) −5.07253 −0.188911
\(722\) −1.43187 + 11.5347i −0.0532887 + 0.429279i
\(723\) 0 0
\(724\) 5.81255 23.0513i 0.216022 0.856696i
\(725\) 12.1577i 0.451526i
\(726\) 0 0
\(727\) 18.0843 0.670710 0.335355 0.942092i \(-0.391144\pi\)
0.335355 + 0.942092i \(0.391144\pi\)
\(728\) 10.6868 + 4.15128i 0.396077 + 0.153857i
\(729\) 0 0
\(730\) 17.8761 + 2.21906i 0.661624 + 0.0821310i
\(731\) 2.27725i 0.0842273i
\(732\) 0 0
\(733\) 2.54526i 0.0940114i −0.998895 0.0470057i \(-0.985032\pi\)
0.998895 0.0470057i \(-0.0149679\pi\)
\(734\) −4.96049 + 39.9603i −0.183095 + 1.47496i
\(735\) 0 0
\(736\) −7.39192 + 10.4087i −0.272470 + 0.383669i
\(737\) 0.773664 0.0284983
\(738\) 0 0
\(739\) 36.7876i 1.35326i −0.736325 0.676628i \(-0.763441\pi\)
0.736325 0.676628i \(-0.236559\pi\)
\(740\) 29.2330 + 7.37129i 1.07463 + 0.270974i
\(741\) 0 0
\(742\) −16.4966 2.04782i −0.605610 0.0751777i
\(743\) 27.1051 0.994391 0.497196 0.867638i \(-0.334363\pi\)
0.497196 + 0.867638i \(0.334363\pi\)
\(744\) 0 0
\(745\) 18.6569 0.683537
\(746\) −16.5291 2.05185i −0.605173 0.0751234i
\(747\) 0 0
\(748\) 1.32552 5.25674i 0.0484659 0.192206i
\(749\) 5.22269i 0.190833i
\(750\) 0 0
\(751\) −35.3786 −1.29098 −0.645491 0.763768i \(-0.723347\pi\)
−0.645491 + 0.763768i \(0.723347\pi\)
\(752\) −29.7617 16.0283i −1.08530 0.584493i
\(753\) 0 0
\(754\) −2.53372 + 20.4110i −0.0922728 + 0.743323i
\(755\) 0.279717i 0.0101799i
\(756\) 0 0
\(757\) 0.340328i 0.0123694i −0.999981 0.00618471i \(-0.998031\pi\)
0.999981 0.00618471i \(-0.00196867\pi\)
\(758\) 20.2177 + 2.50973i 0.734339 + 0.0911575i
\(759\) 0 0
\(760\) −4.26891 + 10.9896i −0.154850 + 0.398633i
\(761\) 30.2601 1.09693 0.548464 0.836174i \(-0.315213\pi\)
0.548464 + 0.836174i \(0.315213\pi\)
\(762\) 0 0
\(763\) 10.8354i 0.392268i
\(764\) −51.3480 12.9477i −1.85771 0.468433i
\(765\) 0 0
\(766\) 2.06642 16.6465i 0.0746627 0.601461i
\(767\) −22.2729 −0.804230
\(768\) 0 0
\(769\) 18.0636 0.651389 0.325695 0.945475i \(-0.394402\pi\)
0.325695 + 0.945475i \(0.394402\pi\)
\(770\) −0.448529 + 3.61322i −0.0161639 + 0.130212i
\(771\) 0 0
\(772\) 34.2927 + 8.64713i 1.23422 + 0.311217i
\(773\) 3.29847i 0.118638i −0.998239 0.0593188i \(-0.981107\pi\)
0.998239 0.0593188i \(-0.0188929\pi\)
\(774\) 0 0
\(775\) −1.57330 −0.0565146
\(776\) 7.81215 20.1110i 0.280440 0.721944i
\(777\) 0 0
\(778\) 22.9650 + 2.85077i 0.823335 + 0.102205i
\(779\) 5.70529i 0.204413i
\(780\) 0 0
\(781\) 19.2183i 0.687683i
\(782\) 0.525506 4.23332i 0.0187920 0.151383i
\(783\) 0 0
\(784\) 3.52175 + 1.89666i 0.125777 + 0.0677378i
\(785\) −13.2491 −0.472880
\(786\)