Properties

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

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.417332 - 1.35123i) q^{2} +(-1.65167 + 1.12783i) q^{4} -3.04340i q^{5} +1.00000 q^{7} +(2.21325 + 1.76111i) q^{8} +O(q^{10})\) \(q+(-0.417332 - 1.35123i) q^{2} +(-1.65167 + 1.12783i) q^{4} -3.04340i q^{5} +1.00000 q^{7} +(2.21325 + 1.76111i) q^{8} +(-4.11235 + 1.27011i) q^{10} -0.128573i q^{11} +6.30135i q^{13} +(-0.417332 - 1.35123i) q^{14} +(1.45602 - 3.72559i) q^{16} +5.32168 q^{17} -6.68215i q^{19} +(3.43243 + 5.02669i) q^{20} +(-0.173732 + 0.0536575i) q^{22} +5.18212 q^{23} -4.26229 q^{25} +(8.51460 - 2.62975i) q^{26} +(-1.65167 + 1.12783i) q^{28} -9.96821i q^{29} +3.27122 q^{31} +(-5.64179 - 0.412618i) q^{32} +(-2.22090 - 7.19083i) q^{34} -3.04340i q^{35} -0.796970i q^{37} +(-9.02915 + 2.78867i) q^{38} +(5.35978 - 6.73581i) q^{40} -2.96782 q^{41} +6.99100i q^{43} +(0.145008 + 0.212360i) q^{44} +(-2.16266 - 7.00226i) q^{46} +4.76595 q^{47} +1.00000 q^{49} +(1.77879 + 5.75936i) q^{50} +(-7.10682 - 10.4077i) q^{52} +1.14264i q^{53} -0.391299 q^{55} +(2.21325 + 1.76111i) q^{56} +(-13.4694 + 4.16005i) q^{58} +11.0999i q^{59} -14.6662i q^{61} +(-1.36518 - 4.42018i) q^{62} +(1.79695 + 7.79557i) q^{64} +19.1775 q^{65} -1.05725i q^{67} +(-8.78965 + 6.00192i) q^{68} +(-4.11235 + 1.27011i) q^{70} +1.10582 q^{71} -12.1019 q^{73} +(-1.07689 + 0.332601i) q^{74} +(7.53630 + 11.0367i) q^{76} -0.128573i q^{77} +2.62426 q^{79} +(-11.3385 - 4.43125i) q^{80} +(1.23856 + 4.01022i) q^{82} -6.46403i q^{83} -16.1960i q^{85} +(9.44648 - 2.91757i) q^{86} +(0.226432 - 0.284564i) q^{88} -2.23283 q^{89} +6.30135i q^{91} +(-8.55915 + 5.84453i) q^{92} +(-1.98898 - 6.43992i) q^{94} -20.3365 q^{95} -7.88097 q^{97} +(-0.417332 - 1.35123i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 6q^{4} + 24q^{7} + O(q^{10}) \) \( 24q + 6q^{4} + 24q^{7} - 16q^{10} + 2q^{16} + 16q^{22} - 24q^{25} + 6q^{28} + 8q^{31} + 22q^{34} + 26q^{46} + 24q^{49} - 6q^{52} + 16q^{55} - 58q^{58} + 6q^{64} - 16q^{70} + 60q^{76} + 8q^{79} - 28q^{82} + 12q^{88} + 36q^{94} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.417332 1.35123i −0.295098 0.955467i
\(3\) 0 0
\(4\) −1.65167 + 1.12783i −0.825834 + 0.563913i
\(5\) 3.04340i 1.36105i −0.732725 0.680525i \(-0.761752\pi\)
0.732725 0.680525i \(-0.238248\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.21325 + 1.76111i 0.782502 + 0.622648i
\(9\) 0 0
\(10\) −4.11235 + 1.27011i −1.30044 + 0.401643i
\(11\) 0.128573i 0.0387662i −0.999812 0.0193831i \(-0.993830\pi\)
0.999812 0.0193831i \(-0.00617022\pi\)
\(12\) 0 0
\(13\) 6.30135i 1.74768i 0.486214 + 0.873840i \(0.338378\pi\)
−0.486214 + 0.873840i \(0.661622\pi\)
\(14\) −0.417332 1.35123i −0.111537 0.361133i
\(15\) 0 0
\(16\) 1.45602 3.72559i 0.364005 0.931397i
\(17\) 5.32168 1.29070 0.645348 0.763889i \(-0.276712\pi\)
0.645348 + 0.763889i \(0.276712\pi\)
\(18\) 0 0
\(19\) 6.68215i 1.53299i −0.642250 0.766495i \(-0.721999\pi\)
0.642250 0.766495i \(-0.278001\pi\)
\(20\) 3.43243 + 5.02669i 0.767514 + 1.12400i
\(21\) 0 0
\(22\) −0.173732 + 0.0536575i −0.0370398 + 0.0114398i
\(23\) 5.18212 1.08055 0.540273 0.841490i \(-0.318321\pi\)
0.540273 + 0.841490i \(0.318321\pi\)
\(24\) 0 0
\(25\) −4.26229 −0.852459
\(26\) 8.51460 2.62975i 1.66985 0.515737i
\(27\) 0 0
\(28\) −1.65167 + 1.12783i −0.312136 + 0.213139i
\(29\) 9.96821i 1.85105i −0.378686 0.925525i \(-0.623624\pi\)
0.378686 0.925525i \(-0.376376\pi\)
\(30\) 0 0
\(31\) 3.27122 0.587528 0.293764 0.955878i \(-0.405092\pi\)
0.293764 + 0.955878i \(0.405092\pi\)
\(32\) −5.64179 0.412618i −0.997336 0.0729412i
\(33\) 0 0
\(34\) −2.22090 7.19083i −0.380882 1.23322i
\(35\) 3.04340i 0.514429i
\(36\) 0 0
\(37\) 0.796970i 0.131021i −0.997852 0.0655106i \(-0.979132\pi\)
0.997852 0.0655106i \(-0.0208676\pi\)
\(38\) −9.02915 + 2.78867i −1.46472 + 0.452382i
\(39\) 0 0
\(40\) 5.35978 6.73581i 0.847455 1.06502i
\(41\) −2.96782 −0.463496 −0.231748 0.972776i \(-0.574444\pi\)
−0.231748 + 0.972776i \(0.574444\pi\)
\(42\) 0 0
\(43\) 6.99100i 1.06612i 0.846078 + 0.533059i \(0.178958\pi\)
−0.846078 + 0.533059i \(0.821042\pi\)
\(44\) 0.145008 + 0.212360i 0.0218607 + 0.0320145i
\(45\) 0 0
\(46\) −2.16266 7.00226i −0.318867 1.03243i
\(47\) 4.76595 0.695186 0.347593 0.937646i \(-0.386999\pi\)
0.347593 + 0.937646i \(0.386999\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 1.77879 + 5.75936i 0.251559 + 0.814496i
\(51\) 0 0
\(52\) −7.10682 10.4077i −0.985539 1.44329i
\(53\) 1.14264i 0.156954i 0.996916 + 0.0784772i \(0.0250058\pi\)
−0.996916 + 0.0784772i \(0.974994\pi\)
\(54\) 0 0
\(55\) −0.391299 −0.0527627
\(56\) 2.21325 + 1.76111i 0.295758 + 0.235339i
\(57\) 0 0
\(58\) −13.4694 + 4.16005i −1.76862 + 0.546241i
\(59\) 11.0999i 1.44508i 0.691329 + 0.722540i \(0.257025\pi\)
−0.691329 + 0.722540i \(0.742975\pi\)
\(60\) 0 0
\(61\) 14.6662i 1.87782i −0.344165 0.938909i \(-0.611838\pi\)
0.344165 0.938909i \(-0.388162\pi\)
\(62\) −1.36518 4.42018i −0.173378 0.561364i
\(63\) 0 0
\(64\) 1.79695 + 7.79557i 0.224619 + 0.974447i
\(65\) 19.1775 2.37868
\(66\) 0 0
\(67\) 1.05725i 0.129163i −0.997912 0.0645816i \(-0.979429\pi\)
0.997912 0.0645816i \(-0.0205713\pi\)
\(68\) −8.78965 + 6.00192i −1.06590 + 0.727840i
\(69\) 0 0
\(70\) −4.11235 + 1.27011i −0.491520 + 0.151807i
\(71\) 1.10582 0.131237 0.0656185 0.997845i \(-0.479098\pi\)
0.0656185 + 0.997845i \(0.479098\pi\)
\(72\) 0 0
\(73\) −12.1019 −1.41642 −0.708212 0.706000i \(-0.750498\pi\)
−0.708212 + 0.706000i \(0.750498\pi\)
\(74\) −1.07689 + 0.332601i −0.125186 + 0.0386641i
\(75\) 0 0
\(76\) 7.53630 + 11.0367i 0.864473 + 1.26600i
\(77\) 0.128573i 0.0146522i
\(78\) 0 0
\(79\) 2.62426 0.295253 0.147626 0.989043i \(-0.452837\pi\)
0.147626 + 0.989043i \(0.452837\pi\)
\(80\) −11.3385 4.43125i −1.26768 0.495429i
\(81\) 0 0
\(82\) 1.23856 + 4.01022i 0.136777 + 0.442855i
\(83\) 6.46403i 0.709520i −0.934957 0.354760i \(-0.884563\pi\)
0.934957 0.354760i \(-0.115437\pi\)
\(84\) 0 0
\(85\) 16.1960i 1.75670i
\(86\) 9.44648 2.91757i 1.01864 0.314609i
\(87\) 0 0
\(88\) 0.226432 0.284564i 0.0241377 0.0303346i
\(89\) −2.23283 −0.236680 −0.118340 0.992973i \(-0.537757\pi\)
−0.118340 + 0.992973i \(0.537757\pi\)
\(90\) 0 0
\(91\) 6.30135i 0.660561i
\(92\) −8.55915 + 5.84453i −0.892353 + 0.609334i
\(93\) 0 0
\(94\) −1.98898 6.43992i −0.205148 0.664227i
\(95\) −20.3365 −2.08648
\(96\) 0 0
\(97\) −7.88097 −0.800192 −0.400096 0.916473i \(-0.631023\pi\)
−0.400096 + 0.916473i \(0.631023\pi\)
\(98\) −0.417332 1.35123i −0.0421569 0.136495i
\(99\) 0 0
\(100\) 7.03990 4.80712i 0.703990 0.480712i
\(101\) 16.9693i 1.68851i −0.535945 0.844253i \(-0.680045\pi\)
0.535945 0.844253i \(-0.319955\pi\)
\(102\) 0 0
\(103\) −10.7049 −1.05479 −0.527393 0.849621i \(-0.676830\pi\)
−0.527393 + 0.849621i \(0.676830\pi\)
\(104\) −11.0974 + 13.9465i −1.08819 + 1.36756i
\(105\) 0 0
\(106\) 1.54398 0.476862i 0.149965 0.0463169i
\(107\) 1.31462i 0.127089i −0.997979 0.0635445i \(-0.979760\pi\)
0.997979 0.0635445i \(-0.0202405\pi\)
\(108\) 0 0
\(109\) 10.2677i 0.983465i −0.870746 0.491732i \(-0.836364\pi\)
0.870746 0.491732i \(-0.163636\pi\)
\(110\) 0.163301 + 0.528737i 0.0155702 + 0.0504131i
\(111\) 0 0
\(112\) 1.45602 3.72559i 0.137581 0.352035i
\(113\) −13.1796 −1.23983 −0.619916 0.784668i \(-0.712834\pi\)
−0.619916 + 0.784668i \(0.712834\pi\)
\(114\) 0 0
\(115\) 15.7713i 1.47068i
\(116\) 11.2424 + 16.4642i 1.04383 + 1.52866i
\(117\) 0 0
\(118\) 14.9985 4.63232i 1.38073 0.426440i
\(119\) 5.32168 0.487837
\(120\) 0 0
\(121\) 10.9835 0.998497
\(122\) −19.8175 + 6.12068i −1.79419 + 0.554140i
\(123\) 0 0
\(124\) −5.40297 + 3.68936i −0.485201 + 0.331315i
\(125\) 2.24514i 0.200811i
\(126\) 0 0
\(127\) −0.840201 −0.0745558 −0.0372779 0.999305i \(-0.511869\pi\)
−0.0372779 + 0.999305i \(0.511869\pi\)
\(128\) 9.78372 5.68144i 0.864767 0.502173i
\(129\) 0 0
\(130\) −8.00339 25.9133i −0.701944 2.27275i
\(131\) 7.39979i 0.646523i −0.946310 0.323261i \(-0.895221\pi\)
0.946310 0.323261i \(-0.104779\pi\)
\(132\) 0 0
\(133\) 6.68215i 0.579416i
\(134\) −1.42859 + 0.441222i −0.123411 + 0.0381158i
\(135\) 0 0
\(136\) 11.7782 + 9.37208i 1.00997 + 0.803649i
\(137\) 5.61682 0.479877 0.239939 0.970788i \(-0.422873\pi\)
0.239939 + 0.970788i \(0.422873\pi\)
\(138\) 0 0
\(139\) 5.19553i 0.440679i −0.975423 0.220339i \(-0.929284\pi\)
0.975423 0.220339i \(-0.0707165\pi\)
\(140\) 3.43243 + 5.02669i 0.290093 + 0.424833i
\(141\) 0 0
\(142\) −0.461495 1.49423i −0.0387278 0.125393i
\(143\) 0.810183 0.0677509
\(144\) 0 0
\(145\) −30.3373 −2.51937
\(146\) 5.05052 + 16.3525i 0.417984 + 1.35335i
\(147\) 0 0
\(148\) 0.898844 + 1.31633i 0.0738845 + 0.108202i
\(149\) 11.6207i 0.952009i −0.879443 0.476004i \(-0.842085\pi\)
0.879443 0.476004i \(-0.157915\pi\)
\(150\) 0 0
\(151\) 21.5154 1.75090 0.875448 0.483313i \(-0.160567\pi\)
0.875448 + 0.483313i \(0.160567\pi\)
\(152\) 11.7680 14.7893i 0.954514 1.19957i
\(153\) 0 0
\(154\) −0.173732 + 0.0536575i −0.0139997 + 0.00432385i
\(155\) 9.95563i 0.799655i
\(156\) 0 0
\(157\) 18.3001i 1.46050i 0.683178 + 0.730252i \(0.260597\pi\)
−0.683178 + 0.730252i \(0.739403\pi\)
\(158\) −1.09519 3.54599i −0.0871284 0.282104i
\(159\) 0 0
\(160\) −1.25576 + 17.1702i −0.0992767 + 1.35743i
\(161\) 5.18212 0.408408
\(162\) 0 0
\(163\) 18.8550i 1.47684i 0.674344 + 0.738418i \(0.264427\pi\)
−0.674344 + 0.738418i \(0.735573\pi\)
\(164\) 4.90185 3.34718i 0.382771 0.261371i
\(165\) 0 0
\(166\) −8.73442 + 2.69764i −0.677922 + 0.209378i
\(167\) 20.8283 1.61174 0.805872 0.592089i \(-0.201697\pi\)
0.805872 + 0.592089i \(0.201697\pi\)
\(168\) 0 0
\(169\) −26.7070 −2.05438
\(170\) −21.8846 + 6.75910i −1.67847 + 0.518399i
\(171\) 0 0
\(172\) −7.88463 11.5468i −0.601198 0.880437i
\(173\) 5.49174i 0.417529i −0.977966 0.208765i \(-0.933056\pi\)
0.977966 0.208765i \(-0.0669443\pi\)
\(174\) 0 0
\(175\) −4.26229 −0.322199
\(176\) −0.479010 0.187205i −0.0361067 0.0141111i
\(177\) 0 0
\(178\) 0.931830 + 3.01708i 0.0698436 + 0.226139i
\(179\) 7.62941i 0.570249i −0.958491 0.285124i \(-0.907965\pi\)
0.958491 0.285124i \(-0.0920349\pi\)
\(180\) 0 0
\(181\) 10.0176i 0.744600i 0.928113 + 0.372300i \(0.121431\pi\)
−0.928113 + 0.372300i \(0.878569\pi\)
\(182\) 8.51460 2.62975i 0.631144 0.194930i
\(183\) 0 0
\(184\) 11.4693 + 9.12631i 0.845530 + 0.672800i
\(185\) −2.42550 −0.178326
\(186\) 0 0
\(187\) 0.684223i 0.0500354i
\(188\) −7.87178 + 5.37516i −0.574108 + 0.392024i
\(189\) 0 0
\(190\) 8.48705 + 27.4793i 0.615715 + 1.99356i
\(191\) −6.25601 −0.452669 −0.226335 0.974050i \(-0.572674\pi\)
−0.226335 + 0.974050i \(0.572674\pi\)
\(192\) 0 0
\(193\) 2.46446 0.177396 0.0886980 0.996059i \(-0.471729\pi\)
0.0886980 + 0.996059i \(0.471729\pi\)
\(194\) 3.28898 + 10.6490i 0.236135 + 0.764557i
\(195\) 0 0
\(196\) −1.65167 + 1.12783i −0.117976 + 0.0805590i
\(197\) 23.8105i 1.69643i 0.529654 + 0.848214i \(0.322322\pi\)
−0.529654 + 0.848214i \(0.677678\pi\)
\(198\) 0 0
\(199\) 24.1296 1.71050 0.855252 0.518212i \(-0.173402\pi\)
0.855252 + 0.518212i \(0.173402\pi\)
\(200\) −9.43352 7.50639i −0.667051 0.530782i
\(201\) 0 0
\(202\) −22.9295 + 7.08181i −1.61331 + 0.498274i
\(203\) 9.96821i 0.699631i
\(204\) 0 0
\(205\) 9.03227i 0.630841i
\(206\) 4.46750 + 14.4648i 0.311265 + 1.00781i
\(207\) 0 0
\(208\) 23.4762 + 9.17488i 1.62778 + 0.636164i
\(209\) −0.859144 −0.0594282
\(210\) 0 0
\(211\) 14.9668i 1.03036i 0.857083 + 0.515179i \(0.172274\pi\)
−0.857083 + 0.515179i \(0.827726\pi\)
\(212\) −1.28870 1.88727i −0.0885085 0.129618i
\(213\) 0 0
\(214\) −1.77636 + 0.548632i −0.121429 + 0.0375037i
\(215\) 21.2764 1.45104
\(216\) 0 0
\(217\) 3.27122 0.222065
\(218\) −13.8740 + 4.28502i −0.939668 + 0.290218i
\(219\) 0 0
\(220\) 0.646296 0.441317i 0.0435733 0.0297536i
\(221\) 33.5337i 2.25572i
\(222\) 0 0
\(223\) 11.6108 0.777518 0.388759 0.921340i \(-0.372904\pi\)
0.388759 + 0.921340i \(0.372904\pi\)
\(224\) −5.64179 0.412618i −0.376958 0.0275692i
\(225\) 0 0
\(226\) 5.50026 + 17.8087i 0.365872 + 1.18462i
\(227\) 0.939445i 0.0623531i −0.999514 0.0311766i \(-0.990075\pi\)
0.999514 0.0311766i \(-0.00992542\pi\)
\(228\) 0 0
\(229\) 0.0137124i 0.000906143i 1.00000 0.000453071i \(0.000144217\pi\)
−1.00000 0.000453071i \(0.999856\pi\)
\(230\) −21.3107 + 6.58185i −1.40519 + 0.433994i
\(231\) 0 0
\(232\) 17.5552 22.0621i 1.15255 1.44845i
\(233\) −18.2195 −1.19360 −0.596800 0.802390i \(-0.703561\pi\)
−0.596800 + 0.802390i \(0.703561\pi\)
\(234\) 0 0
\(235\) 14.5047i 0.946183i
\(236\) −12.5187 18.3333i −0.814899 1.19340i
\(237\) 0 0
\(238\) −2.22090 7.19083i −0.143960 0.466112i
\(239\) 1.37153 0.0887169 0.0443585 0.999016i \(-0.485876\pi\)
0.0443585 + 0.999016i \(0.485876\pi\)
\(240\) 0 0
\(241\) −10.5054 −0.676711 −0.338355 0.941018i \(-0.609871\pi\)
−0.338355 + 0.941018i \(0.609871\pi\)
\(242\) −4.58375 14.8412i −0.294654 0.954031i
\(243\) 0 0
\(244\) 16.5409 + 24.2238i 1.05893 + 1.55077i
\(245\) 3.04340i 0.194436i
\(246\) 0 0
\(247\) 42.1066 2.67918
\(248\) 7.24002 + 5.76099i 0.459742 + 0.365823i
\(249\) 0 0
\(250\) −3.03371 + 0.936967i −0.191869 + 0.0592590i
\(251\) 20.0556i 1.26590i −0.774192 0.632950i \(-0.781844\pi\)
0.774192 0.632950i \(-0.218156\pi\)
\(252\) 0 0
\(253\) 0.666280i 0.0418887i
\(254\) 0.350643 + 1.13531i 0.0220013 + 0.0712356i
\(255\) 0 0
\(256\) −11.7600 10.8491i −0.735001 0.678066i
\(257\) 24.6631 1.53844 0.769220 0.638984i \(-0.220645\pi\)
0.769220 + 0.638984i \(0.220645\pi\)
\(258\) 0 0
\(259\) 0.796970i 0.0495213i
\(260\) −31.6749 + 21.6289i −1.96440 + 1.34137i
\(261\) 0 0
\(262\) −9.99885 + 3.08817i −0.617731 + 0.190788i
\(263\) 14.0542 0.866616 0.433308 0.901246i \(-0.357346\pi\)
0.433308 + 0.901246i \(0.357346\pi\)
\(264\) 0 0
\(265\) 3.47753 0.213623
\(266\) −9.02915 + 2.78867i −0.553613 + 0.170984i
\(267\) 0 0
\(268\) 1.19239 + 1.74622i 0.0728368 + 0.106667i
\(269\) 13.1276i 0.800404i −0.916427 0.400202i \(-0.868940\pi\)
0.916427 0.400202i \(-0.131060\pi\)
\(270\) 0 0
\(271\) −15.4626 −0.939285 −0.469642 0.882857i \(-0.655617\pi\)
−0.469642 + 0.882857i \(0.655617\pi\)
\(272\) 7.74846 19.8264i 0.469820 1.20215i
\(273\) 0 0
\(274\) −2.34407 7.58964i −0.141611 0.458507i
\(275\) 0.548015i 0.0330466i
\(276\) 0 0
\(277\) 11.1880i 0.672223i 0.941822 + 0.336112i \(0.109112\pi\)
−0.941822 + 0.336112i \(0.890888\pi\)
\(278\) −7.02037 + 2.16826i −0.421054 + 0.130043i
\(279\) 0 0
\(280\) 5.35978 6.73581i 0.320308 0.402542i
\(281\) −0.179766 −0.0107240 −0.00536198 0.999986i \(-0.501707\pi\)
−0.00536198 + 0.999986i \(0.501707\pi\)
\(282\) 0 0
\(283\) 29.0480i 1.72673i 0.504583 + 0.863363i \(0.331646\pi\)
−0.504583 + 0.863363i \(0.668354\pi\)
\(284\) −1.82645 + 1.24717i −0.108380 + 0.0740062i
\(285\) 0 0
\(286\) −0.338115 1.09475i −0.0199931 0.0647337i
\(287\) −2.96782 −0.175185
\(288\) 0 0
\(289\) 11.3202 0.665897
\(290\) 12.6607 + 40.9928i 0.743462 + 2.40718i
\(291\) 0 0
\(292\) 19.9884 13.6489i 1.16973 0.798739i
\(293\) 4.42498i 0.258510i −0.991611 0.129255i \(-0.958741\pi\)
0.991611 0.129255i \(-0.0412586\pi\)
\(294\) 0 0
\(295\) 33.7813 1.96683
\(296\) 1.40356 1.76389i 0.0815800 0.102524i
\(297\) 0 0
\(298\) −15.7024 + 4.84970i −0.909613 + 0.280936i
\(299\) 32.6543i 1.88845i
\(300\) 0 0
\(301\) 6.99100i 0.402955i
\(302\) −8.97904 29.0723i −0.516686 1.67292i
\(303\) 0 0
\(304\) −24.8949 9.72934i −1.42782 0.558016i
\(305\) −44.6352 −2.55581
\(306\) 0 0
\(307\) 8.36831i 0.477605i −0.971068 0.238802i \(-0.923245\pi\)
0.971068 0.238802i \(-0.0767548\pi\)
\(308\) 0.145008 + 0.212360i 0.00826259 + 0.0121003i
\(309\) 0 0
\(310\) −13.4524 + 4.15480i −0.764044 + 0.235977i
\(311\) −28.1701 −1.59738 −0.798690 0.601743i \(-0.794473\pi\)
−0.798690 + 0.601743i \(0.794473\pi\)
\(312\) 0 0
\(313\) 14.0081 0.791784 0.395892 0.918297i \(-0.370435\pi\)
0.395892 + 0.918297i \(0.370435\pi\)
\(314\) 24.7277 7.63719i 1.39546 0.430992i
\(315\) 0 0
\(316\) −4.33441 + 2.95971i −0.243830 + 0.166497i
\(317\) 14.4390i 0.810974i −0.914101 0.405487i \(-0.867102\pi\)
0.914101 0.405487i \(-0.132898\pi\)
\(318\) 0 0
\(319\) −1.28164 −0.0717582
\(320\) 23.7251 5.46885i 1.32627 0.305718i
\(321\) 0 0
\(322\) −2.16266 7.00226i −0.120520 0.390221i
\(323\) 35.5603i 1.97863i
\(324\) 0 0
\(325\) 26.8582i 1.48982i
\(326\) 25.4775 7.86877i 1.41107 0.435811i
\(327\) 0 0
\(328\) −6.56853 5.22667i −0.362686 0.288595i
\(329\) 4.76595 0.262756
\(330\) 0 0
\(331\) 32.5738i 1.79042i 0.445648 + 0.895208i \(0.352973\pi\)
−0.445648 + 0.895208i \(0.647027\pi\)
\(332\) 7.29030 + 10.6764i 0.400107 + 0.585946i
\(333\) 0 0
\(334\) −8.69232 28.1440i −0.475623 1.53997i
\(335\) −3.21762 −0.175798
\(336\) 0 0
\(337\) −2.17181 −0.118306 −0.0591529 0.998249i \(-0.518840\pi\)
−0.0591529 + 0.998249i \(0.518840\pi\)
\(338\) 11.1457 + 36.0874i 0.606244 + 1.96290i
\(339\) 0 0
\(340\) 18.2663 + 26.7504i 0.990627 + 1.45075i
\(341\) 0.420590i 0.0227762i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −12.3120 + 15.4728i −0.663816 + 0.834240i
\(345\) 0 0
\(346\) −7.42063 + 2.29188i −0.398935 + 0.123212i
\(347\) 2.79477i 0.150031i 0.997182 + 0.0750157i \(0.0239007\pi\)
−0.997182 + 0.0750157i \(0.976099\pi\)
\(348\) 0 0
\(349\) 3.19085i 0.170802i 0.996347 + 0.0854011i \(0.0272172\pi\)
−0.996347 + 0.0854011i \(0.972783\pi\)
\(350\) 1.77879 + 5.75936i 0.0950803 + 0.307851i
\(351\) 0 0
\(352\) −0.0530515 + 0.725381i −0.00282765 + 0.0386629i
\(353\) 8.10245 0.431250 0.215625 0.976476i \(-0.430821\pi\)
0.215625 + 0.976476i \(0.430821\pi\)
\(354\) 0 0
\(355\) 3.36546i 0.178620i
\(356\) 3.68790 2.51824i 0.195458 0.133467i
\(357\) 0 0
\(358\) −10.3091 + 3.18399i −0.544854 + 0.168279i
\(359\) −17.2635 −0.911134 −0.455567 0.890202i \(-0.650563\pi\)
−0.455567 + 0.890202i \(0.650563\pi\)
\(360\) 0 0
\(361\) −25.6511 −1.35006
\(362\) 13.5361 4.18064i 0.711440 0.219730i
\(363\) 0 0
\(364\) −7.10682 10.4077i −0.372499 0.545514i
\(365\) 36.8310i 1.92782i
\(366\) 0 0
\(367\) −13.5508 −0.707348 −0.353674 0.935369i \(-0.615068\pi\)
−0.353674 + 0.935369i \(0.615068\pi\)
\(368\) 7.54527 19.3064i 0.393324 1.00642i
\(369\) 0 0
\(370\) 1.01224 + 3.27742i 0.0526238 + 0.170385i
\(371\) 1.14264i 0.0593232i
\(372\) 0 0
\(373\) 16.3399i 0.846048i 0.906118 + 0.423024i \(0.139031\pi\)
−0.906118 + 0.423024i \(0.860969\pi\)
\(374\) −0.924546 + 0.285548i −0.0478072 + 0.0147653i
\(375\) 0 0
\(376\) 10.5482 + 8.39339i 0.543984 + 0.432856i
\(377\) 62.8132 3.23504
\(378\) 0 0
\(379\) 2.37754i 0.122126i −0.998134 0.0610630i \(-0.980551\pi\)
0.998134 0.0610630i \(-0.0194491\pi\)
\(380\) 33.5891 22.9360i 1.72309 1.17659i
\(381\) 0 0
\(382\) 2.61083 + 8.45334i 0.133582 + 0.432511i
\(383\) −17.6210 −0.900389 −0.450194 0.892931i \(-0.648645\pi\)
−0.450194 + 0.892931i \(0.648645\pi\)
\(384\) 0 0
\(385\) −0.391299 −0.0199424
\(386\) −1.02850 3.33007i −0.0523492 0.169496i
\(387\) 0 0
\(388\) 13.0168 8.88836i 0.660826 0.451238i
\(389\) 12.6831i 0.643058i 0.946900 + 0.321529i \(0.104197\pi\)
−0.946900 + 0.321529i \(0.895803\pi\)
\(390\) 0 0
\(391\) 27.5776 1.39466
\(392\) 2.21325 + 1.76111i 0.111786 + 0.0889497i
\(393\) 0 0
\(394\) 32.1736 9.93687i 1.62088 0.500612i
\(395\) 7.98668i 0.401854i
\(396\) 0 0
\(397\) 34.3856i 1.72576i −0.505405 0.862882i \(-0.668657\pi\)
0.505405 0.862882i \(-0.331343\pi\)
\(398\) −10.0701 32.6048i −0.504767 1.63433i
\(399\) 0 0
\(400\) −6.20598 + 15.8795i −0.310299 + 0.793977i
\(401\) −3.75947 −0.187739 −0.0938696 0.995585i \(-0.529924\pi\)
−0.0938696 + 0.995585i \(0.529924\pi\)
\(402\) 0 0
\(403\) 20.6131i 1.02681i
\(404\) 19.1384 + 28.0276i 0.952170 + 1.39443i
\(405\) 0 0
\(406\) −13.4694 + 4.16005i −0.668475 + 0.206460i
\(407\) −0.102469 −0.00507919
\(408\) 0 0
\(409\) 13.0996 0.647731 0.323866 0.946103i \(-0.395017\pi\)
0.323866 + 0.946103i \(0.395017\pi\)
\(410\) 12.2047 3.76945i 0.602748 0.186160i
\(411\) 0 0
\(412\) 17.6810 12.0733i 0.871079 0.594807i
\(413\) 11.0999i 0.546189i
\(414\) 0 0
\(415\) −19.6726 −0.965692
\(416\) 2.60005 35.5509i 0.127478 1.74302i
\(417\) 0 0
\(418\) 0.358548 + 1.16090i 0.0175371 + 0.0567817i
\(419\) 24.4344i 1.19370i −0.802353 0.596849i \(-0.796419\pi\)
0.802353 0.596849i \(-0.203581\pi\)
\(420\) 0 0
\(421\) 26.3907i 1.28620i 0.765781 + 0.643101i \(0.222353\pi\)
−0.765781 + 0.643101i \(0.777647\pi\)
\(422\) 20.2237 6.24612i 0.984472 0.304056i
\(423\) 0 0
\(424\) −2.01233 + 2.52896i −0.0977273 + 0.122817i
\(425\) −22.6825 −1.10027
\(426\) 0 0
\(427\) 14.6662i 0.709749i
\(428\) 1.48266 + 2.17132i 0.0716671 + 0.104954i
\(429\) 0 0
\(430\) −8.87933 28.7494i −0.428199 1.38642i
\(431\) 32.7161 1.57588 0.787940 0.615751i \(-0.211147\pi\)
0.787940 + 0.615751i \(0.211147\pi\)
\(432\) 0 0
\(433\) 12.3235 0.592228 0.296114 0.955153i \(-0.404309\pi\)
0.296114 + 0.955153i \(0.404309\pi\)
\(434\) −1.36518 4.42018i −0.0655308 0.212176i
\(435\) 0 0
\(436\) 11.5801 + 16.9588i 0.554588 + 0.812179i
\(437\) 34.6277i 1.65647i
\(438\) 0 0
\(439\) 4.67878 0.223306 0.111653 0.993747i \(-0.464385\pi\)
0.111653 + 0.993747i \(0.464385\pi\)
\(440\) −0.866043 0.689122i −0.0412870 0.0328526i
\(441\) 0 0
\(442\) 45.3119 13.9947i 2.15527 0.665659i
\(443\) 35.6471i 1.69364i 0.531877 + 0.846821i \(0.321487\pi\)
−0.531877 + 0.846821i \(0.678513\pi\)
\(444\) 0 0
\(445\) 6.79540i 0.322133i
\(446\) −4.84556 15.6889i −0.229444 0.742892i
\(447\) 0 0
\(448\) 1.79695 + 7.79557i 0.0848980 + 0.368306i
\(449\) 6.02786 0.284472 0.142236 0.989833i \(-0.454571\pi\)
0.142236 + 0.989833i \(0.454571\pi\)
\(450\) 0 0
\(451\) 0.381581i 0.0179680i
\(452\) 21.7683 14.8643i 1.02390 0.699158i
\(453\) 0 0
\(454\) −1.26941 + 0.392060i −0.0595764 + 0.0184003i
\(455\) 19.1775 0.899057
\(456\) 0 0
\(457\) 4.88761 0.228633 0.114316 0.993444i \(-0.463532\pi\)
0.114316 + 0.993444i \(0.463532\pi\)
\(458\) 0.0185287 0.00572263i 0.000865789 0.000267401i
\(459\) 0 0
\(460\) 17.7872 + 26.0489i 0.829335 + 1.21454i
\(461\) 9.16306i 0.426766i −0.976969 0.213383i \(-0.931552\pi\)
0.976969 0.213383i \(-0.0684483\pi\)
\(462\) 0 0
\(463\) 32.8412 1.52626 0.763130 0.646245i \(-0.223662\pi\)
0.763130 + 0.646245i \(0.223662\pi\)
\(464\) −37.1374 14.5139i −1.72406 0.673791i
\(465\) 0 0
\(466\) 7.60358 + 24.6188i 0.352229 + 1.14045i
\(467\) 6.40559i 0.296415i 0.988956 + 0.148208i \(0.0473504\pi\)
−0.988956 + 0.148208i \(0.952650\pi\)
\(468\) 0 0
\(469\) 1.05725i 0.0488191i
\(470\) −19.5993 + 6.05327i −0.904047 + 0.279217i
\(471\) 0 0
\(472\) −19.5481 + 24.5668i −0.899776 + 1.13078i
\(473\) 0.898854 0.0413293
\(474\) 0 0
\(475\) 28.4813i 1.30681i
\(476\) −8.78965 + 6.00192i −0.402873 + 0.275098i
\(477\) 0 0
\(478\) −0.572383 1.85326i −0.0261802 0.0847661i
\(479\) 27.3218 1.24837 0.624184 0.781278i \(-0.285432\pi\)
0.624184 + 0.781278i \(0.285432\pi\)
\(480\) 0 0
\(481\) 5.02199 0.228983
\(482\) 4.38423 + 14.1952i 0.199696 + 0.646575i
\(483\) 0 0
\(484\) −18.1411 + 12.3874i −0.824593 + 0.563065i
\(485\) 23.9850i 1.08910i
\(486\) 0 0
\(487\) 9.05264 0.410214 0.205107 0.978740i \(-0.434246\pi\)
0.205107 + 0.978740i \(0.434246\pi\)
\(488\) 25.8289 32.4600i 1.16922 1.46940i
\(489\) 0 0
\(490\) −4.11235 + 1.27011i −0.185777 + 0.0573776i
\(491\) 10.1183i 0.456632i 0.973587 + 0.228316i \(0.0733219\pi\)
−0.973587 + 0.228316i \(0.926678\pi\)
\(492\) 0 0
\(493\) 53.0476i 2.38914i
\(494\) −17.5724 56.8958i −0.790619 2.55986i
\(495\) 0 0
\(496\) 4.76296 12.1872i 0.213863 0.547222i
\(497\) 1.10582 0.0496029
\(498\) 0 0
\(499\) 19.9396i 0.892621i 0.894878 + 0.446310i \(0.147262\pi\)
−0.894878 + 0.446310i \(0.852738\pi\)
\(500\) 2.53212 + 3.70823i 0.113240 + 0.165837i
\(501\) 0 0
\(502\) −27.0999 + 8.36985i −1.20953 + 0.373565i
\(503\) 24.3936 1.08766 0.543828 0.839197i \(-0.316974\pi\)
0.543828 + 0.839197i \(0.316974\pi\)
\(504\) 0 0
\(505\) −51.6443 −2.29814
\(506\) −0.900301 + 0.278060i −0.0400233 + 0.0123613i
\(507\) 0 0
\(508\) 1.38773 0.947601i 0.0615708 0.0420430i
\(509\) 7.20394i 0.319309i 0.987173 + 0.159655i \(0.0510381\pi\)
−0.987173 + 0.159655i \(0.948962\pi\)
\(510\) 0 0
\(511\) −12.1019 −0.535358
\(512\) −9.75179 + 20.4182i −0.430972 + 0.902365i
\(513\) 0 0
\(514\) −10.2927 33.3256i −0.453991 1.46993i
\(515\) 32.5793i 1.43562i
\(516\) 0 0
\(517\) 0.612773i 0.0269497i
\(518\) −1.07689 + 0.332601i −0.0473160 + 0.0146136i
\(519\) 0 0
\(520\) 42.4447 + 33.7738i 1.86132 + 1.48108i
\(521\) 14.8648 0.651240 0.325620 0.945501i \(-0.394427\pi\)
0.325620 + 0.945501i \(0.394427\pi\)
\(522\) 0 0
\(523\) 32.1286i 1.40489i −0.711740 0.702443i \(-0.752093\pi\)
0.711740 0.702443i \(-0.247907\pi\)
\(524\) 8.34567 + 12.2220i 0.364582 + 0.533921i
\(525\) 0 0
\(526\) −5.86524 18.9905i −0.255737 0.828023i
\(527\) 17.4084 0.758320
\(528\) 0 0
\(529\) 3.85438 0.167582
\(530\) −1.45128 4.69895i −0.0630396 0.204109i
\(531\) 0 0
\(532\) 7.53630 + 11.0367i 0.326740 + 0.478502i
\(533\) 18.7013i 0.810042i
\(534\) 0 0
\(535\) −4.00091 −0.172975
\(536\) 1.86193 2.33995i 0.0804232 0.101070i
\(537\) 0 0
\(538\) −17.7385 + 5.47856i −0.764760 + 0.236198i
\(539\) 0.128573i 0.00553803i
\(540\) 0 0
\(541\) 30.6123i 1.31612i 0.752964 + 0.658062i \(0.228624\pi\)
−0.752964 + 0.658062i \(0.771376\pi\)
\(542\) 6.45302 + 20.8936i 0.277181 + 0.897456i
\(543\) 0 0
\(544\) −30.0238 2.19582i −1.28726 0.0941449i
\(545\) −31.2487 −1.33855
\(546\) 0 0
\(547\) 7.64518i 0.326884i −0.986553 0.163442i \(-0.947740\pi\)
0.986553 0.163442i \(-0.0522597\pi\)
\(548\) −9.27712 + 6.33479i −0.396299 + 0.270609i
\(549\) 0 0
\(550\) 0.740497 0.228704i 0.0315749 0.00975198i
\(551\) −66.6091 −2.83764
\(552\) 0 0
\(553\) 2.62426 0.111595
\(554\) 15.1176 4.66911i 0.642287 0.198372i
\(555\) 0 0
\(556\) 5.85965 + 8.58129i 0.248504 + 0.363928i
\(557\) 24.9682i 1.05794i 0.848641 + 0.528969i \(0.177421\pi\)
−0.848641 + 0.528969i \(0.822579\pi\)
\(558\) 0 0
\(559\) −44.0527 −1.86323
\(560\) −11.3385 4.43125i −0.479137 0.187255i
\(561\) 0 0
\(562\) 0.0750222 + 0.242907i 0.00316462 + 0.0102464i
\(563\) 33.1836i 1.39852i 0.714865 + 0.699262i \(0.246488\pi\)
−0.714865 + 0.699262i \(0.753512\pi\)
\(564\) 0 0
\(565\) 40.1108i 1.68748i
\(566\) 39.2507 12.1227i 1.64983 0.509553i
\(567\) 0 0
\(568\) 2.44746 + 1.94748i 0.102693 + 0.0817144i
\(569\) −17.0679 −0.715523 −0.357761 0.933813i \(-0.616460\pi\)
−0.357761 + 0.933813i \(0.616460\pi\)
\(570\) 0 0
\(571\) 5.13058i 0.214708i −0.994221 0.107354i \(-0.965762\pi\)
0.994221 0.107354i \(-0.0342378\pi\)
\(572\) −1.33815 + 0.913745i −0.0559510 + 0.0382056i
\(573\) 0 0
\(574\) 1.23856 + 4.01022i 0.0516967 + 0.167383i
\(575\) −22.0877 −0.921121
\(576\) 0 0
\(577\) −47.5819 −1.98086 −0.990429 0.138021i \(-0.955926\pi\)
−0.990429 + 0.138021i \(0.955926\pi\)
\(578\) −4.72430 15.2963i −0.196505 0.636242i
\(579\) 0 0
\(580\) 50.1071 34.2151i 2.08058 1.42071i
\(581\) 6.46403i 0.268173i
\(582\) 0 0
\(583\) 0.146913 0.00608452
\(584\) −26.7846 21.3129i −1.10835 0.881933i
\(585\) 0 0
\(586\) −5.97919 + 1.84668i −0.246998 + 0.0762858i
\(587\) 23.6803i 0.977390i 0.872455 + 0.488695i \(0.162527\pi\)
−0.872455 + 0.488695i \(0.837473\pi\)
\(588\) 0 0
\(589\) 21.8588i 0.900675i
\(590\) −14.0980 45.6465i −0.580406 1.87924i
\(591\) 0 0
\(592\) −2.96918 1.16040i −0.122033 0.0476923i
\(593\) −17.8919 −0.734734 −0.367367 0.930076i \(-0.619741\pi\)
−0.367367 + 0.930076i \(0.619741\pi\)
\(594\) 0 0
\(595\) 16.1960i 0.663971i
\(596\) 13.1062 + 19.1936i 0.536850 + 0.786201i
\(597\) 0 0
\(598\) 44.1237 13.6277i 1.80435 0.557278i
\(599\) −32.0167 −1.30817 −0.654083 0.756423i \(-0.726945\pi\)
−0.654083 + 0.756423i \(0.726945\pi\)
\(600\) 0 0
\(601\) 23.7187 0.967507 0.483754 0.875204i \(-0.339273\pi\)
0.483754 + 0.875204i \(0.339273\pi\)
\(602\) 9.44648 2.91757i 0.385010 0.118911i
\(603\) 0 0
\(604\) −35.5362 + 24.2656i −1.44595 + 0.987352i
\(605\) 33.4271i 1.35901i
\(606\) 0 0
\(607\) −14.4444 −0.586281 −0.293141 0.956069i \(-0.594700\pi\)
−0.293141 + 0.956069i \(0.594700\pi\)
\(608\) −2.75717 + 37.6993i −0.111818 + 1.52891i
\(609\) 0 0
\(610\) 18.6277 + 60.3127i 0.754213 + 2.44199i
\(611\) 30.0319i 1.21496i
\(612\) 0 0
\(613\) 16.2817i 0.657610i −0.944398 0.328805i \(-0.893354\pi\)
0.944398 0.328805i \(-0.106646\pi\)
\(614\) −11.3076 + 3.49236i −0.456336 + 0.140940i
\(615\) 0 0
\(616\) 0.226432 0.284564i 0.00912319 0.0114654i
\(617\) −28.7753 −1.15845 −0.579225 0.815167i \(-0.696645\pi\)
−0.579225 + 0.815167i \(0.696645\pi\)
\(618\) 0 0
\(619\) 36.0871i 1.45046i −0.688506 0.725231i \(-0.741733\pi\)
0.688506 0.725231i \(-0.258267\pi\)
\(620\) 11.2282 + 16.4434i 0.450936 + 0.660383i
\(621\) 0 0
\(622\) 11.7563 + 38.0644i 0.471383 + 1.52624i
\(623\) −2.23283 −0.0894564
\(624\) 0 0
\(625\) −28.1443 −1.12577
\(626\) −5.84602 18.9282i −0.233654 0.756524i
\(627\) 0 0
\(628\) −20.6393 30.2256i −0.823596 1.20613i
\(629\) 4.24122i 0.169108i
\(630\) 0 0
\(631\) 18.0509 0.718595 0.359297 0.933223i \(-0.383016\pi\)
0.359297 + 0.933223i \(0.383016\pi\)
\(632\) 5.80815 + 4.62163i 0.231036 + 0.183838i
\(633\) 0 0
\(634\) −19.5104 + 6.02584i −0.774859 + 0.239317i
\(635\) 2.55707i 0.101474i
\(636\) 0 0
\(637\) 6.30135i 0.249668i
\(638\) 0.534870 + 1.73180i 0.0211757 + 0.0685626i
\(639\) 0 0
\(640\) −17.2909 29.7758i −0.683483 1.17699i
\(641\) −12.0253 −0.474971 −0.237486 0.971391i \(-0.576323\pi\)
−0.237486 + 0.971391i \(0.576323\pi\)
\(642\) 0 0
\(643\) 9.54316i 0.376345i 0.982136 + 0.188173i \(0.0602565\pi\)
−0.982136 + 0.188173i \(0.939744\pi\)
\(644\) −8.55915 + 5.84453i −0.337278 + 0.230307i
\(645\) 0 0
\(646\) −48.0502 + 14.8404i −1.89051 + 0.583888i
\(647\) −32.2201 −1.26670 −0.633351 0.773865i \(-0.718321\pi\)
−0.633351 + 0.773865i \(0.718321\pi\)
\(648\) 0 0
\(649\) 1.42714 0.0560202
\(650\) −36.2917 + 11.2088i −1.42348 + 0.439644i
\(651\) 0 0
\(652\) −21.2651 31.1422i −0.832806 1.21962i
\(653\) 14.5245i 0.568388i −0.958767 0.284194i \(-0.908274\pi\)
0.958767 0.284194i \(-0.0917259\pi\)
\(654\) 0 0
\(655\) −22.5205 −0.879950
\(656\) −4.32120 + 11.0569i −0.168715 + 0.431698i
\(657\) 0 0
\(658\) −1.98898 6.43992i −0.0775386 0.251054i
\(659\) 10.5726i 0.411849i 0.978568 + 0.205924i \(0.0660201\pi\)
−0.978568 + 0.205924i \(0.933980\pi\)
\(660\) 0 0
\(661\) 27.0965i 1.05393i −0.849887 0.526965i \(-0.823330\pi\)
0.849887 0.526965i \(-0.176670\pi\)
\(662\) 44.0148 13.5941i 1.71068 0.528348i
\(663\) 0 0
\(664\) 11.3839 14.3065i 0.441781 0.555200i
\(665\) −20.3365 −0.788614
\(666\) 0 0
\(667\) 51.6565i 2.00015i
\(668\) −34.4015 + 23.4907i −1.33103 + 0.908883i
\(669\) 0 0
\(670\) 1.34282 + 4.34777i 0.0518775 + 0.167969i
\(671\) −1.88568 −0.0727959
\(672\) 0 0
\(673\) 38.2417 1.47411 0.737055 0.675833i \(-0.236216\pi\)
0.737055 + 0.675833i \(0.236216\pi\)
\(674\) 0.906363 + 2.93462i 0.0349118 + 0.113037i
\(675\) 0 0
\(676\) 44.1111 30.1208i 1.69658 1.15849i
\(677\) 14.2289i 0.546860i 0.961892 + 0.273430i \(0.0881582\pi\)
−0.961892 + 0.273430i \(0.911842\pi\)
\(678\) 0 0
\(679\) −7.88097 −0.302444
\(680\) 28.5230 35.8458i 1.09381 1.37462i
\(681\) 0 0
\(682\) −0.568316 + 0.175525i −0.0217619 + 0.00672122i
\(683\) 39.0552i 1.49441i 0.664596 + 0.747203i \(0.268603\pi\)
−0.664596 + 0.747203i \(0.731397\pi\)
\(684\) 0 0
\(685\) 17.0942i 0.653137i
\(686\) −0.417332 1.35123i −0.0159338 0.0515904i
\(687\) 0 0
\(688\) 26.0456 + 10.1790i 0.992979 + 0.388072i
\(689\) −7.20020 −0.274306
\(690\) 0 0
\(691\) 20.1602i 0.766929i 0.923556 + 0.383464i \(0.125269\pi\)
−0.923556 + 0.383464i \(0.874731\pi\)
\(692\) 6.19373 + 9.07054i 0.235450 + 0.344810i
\(693\) 0 0
\(694\) 3.77639 1.16635i 0.143350 0.0442739i
\(695\) −15.8121 −0.599786
\(696\) 0 0
\(697\) −15.7938 −0.598232
\(698\) 4.31159 1.33164i 0.163196 0.0504034i
\(699\) 0 0
\(700\) 7.03990 4.80712i 0.266083 0.181692i
\(701\) 22.4760i 0.848908i −0.905449 0.424454i \(-0.860466\pi\)
0.905449 0.424454i \(-0.139534\pi\)
\(702\) 0 0
\(703\) −5.32548 −0.200854
\(704\) 1.00230 0.231039i 0.0377756 0.00870762i
\(705\) 0 0
\(706\) −3.38141 10.9483i −0.127261 0.412045i
\(707\) 16.9693i 0.638195i
\(708\) 0 0
\(709\) 20.2609i 0.760915i −0.924798 0.380458i \(-0.875767\pi\)
0.924798 0.380458i \(-0.124233\pi\)
\(710\) −4.54753 + 1.40451i −0.170666 + 0.0527104i
\(711\) 0 0
\(712\) −4.94181 3.93227i −0.185202 0.147368i
\(713\) 16.9518 0.634852
\(714\) 0 0
\(715\) 2.46571i 0.0922124i
\(716\) 8.60464 + 12.6013i 0.321571 + 0.470931i
\(717\) 0 0
\(718\) 7.20461 + 23.3271i 0.268874 + 0.870558i
\(719\) −21.2440 −0.792269 −0.396134 0.918193i \(-0.629649\pi\)
−0.396134 + 0.918193i \(0.629649\pi\)
\(720\) 0 0
\(721\) −10.7049 −0.398672
\(722\) 10.7050 + 34.6607i 0.398400 + 1.28994i
\(723\) 0 0
\(724\) −11.2981 16.5457i −0.419889 0.614916i
\(725\) 42.4874i 1.57794i
\(726\) 0 0
\(727\) −32.9048 −1.22037 −0.610185 0.792259i \(-0.708905\pi\)
−0.610185 + 0.792259i \(0.708905\pi\)
\(728\) −11.0974 + 13.9465i −0.411297 + 0.516890i
\(729\) 0 0
\(730\) 49.7674 15.3708i 1.84197 0.568897i
\(731\) 37.2039i 1.37603i
\(732\) 0 0
\(733\) 32.0598i 1.18415i 0.805881 + 0.592077i \(0.201692\pi\)
−0.805881 + 0.592077i \(0.798308\pi\)
\(734\) 5.65519 + 18.3104i 0.208737 + 0.675847i
\(735\) 0 0
\(736\) −29.2364 2.13823i −1.07767 0.0788164i
\(737\) −0.135933 −0.00500716
\(738\) 0 0
\(739\) 46.3826i 1.70621i 0.521738 + 0.853106i \(0.325284\pi\)
−0.521738 + 0.853106i \(0.674716\pi\)
\(740\) 4.00612 2.73554i 0.147268 0.100561i
\(741\) 0 0
\(742\) 1.54398 0.476862i 0.0566813 0.0175061i
\(743\) 12.1782 0.446777 0.223388 0.974730i \(-0.428288\pi\)
0.223388 + 0.974730i \(0.428288\pi\)
\(744\) 0 0
\(745\) −35.3666 −1.29573
\(746\) 22.0790 6.81916i 0.808371 0.249667i
\(747\) 0 0
\(748\) 0.771685 + 1.13011i 0.0282156 + 0.0413209i
\(749\) 1.31462i 0.0480351i
\(750\) 0 0
\(751\) 24.4371 0.891723 0.445862 0.895102i \(-0.352897\pi\)
0.445862 + 0.895102i \(0.352897\pi\)
\(752\) 6.93932 17.7560i 0.253051 0.647494i
\(753\) 0 0
\(754\) −26.2139 84.8753i −0.954655 3.09098i
\(755\) 65.4799i 2.38306i
\(756\) 0 0
\(757\) 7.15224i 0.259953i 0.991517 + 0.129976i \(0.0414902\pi\)
−0.991517 + 0.129976i \(0.958510\pi\)
\(758\) −3.21261 + 0.992223i −0.116687 + 0.0360391i
\(759\) 0 0
\(760\) −45.0097 35.8148i −1.63267 1.29914i
\(761\) 14.7809 0.535806 0.267903 0.963446i \(-0.413669\pi\)
0.267903 + 0.963446i \(0.413669\pi\)
\(762\) 0 0
\(763\) 10.2677i 0.371715i
\(764\) 10.3329 7.05569i 0.373830 0.255266i
\(765\) 0 0
\(766\) 7.35378 + 23.8100i 0.265703 + 0.860292i
\(767\) −69.9441 −2.52554
\(768\) 0 0
\(769\) −1.90576 −0.0687235 −0.0343618 0.999409i \(-0.510940\pi\)
−0.0343618 + 0.999409i \(0.510940\pi\)
\(770\) 0.163301 + 0.528737i 0.00588497 + 0.0190543i
\(771\) 0 0
\(772\) −4.07048 + 2.77948i −0.146500 + 0.100036i
\(773\) 6.63435i 0.238621i 0.992857 + 0.119310i \(0.0380684\pi\)
−0.992857 + 0.119310i \(0.961932\pi\)
\(774\) 0 0
\(775\) −13.9429 −0.500843
\(776\) −17.4426 13.8793i −0.626152 0.498238i
\(777\) 0 0
\(778\) 17.1378 5.29305i 0.614421 0.189765i
\(779\) 19.8314i 0.710534i
\(780\) 0 0
\(781\) 0.142179i 0.00508756i
\(782\) −11.5090 37.2638i −0.411561 1.33255i
\(783\) 0 0
\(784\) 1.45602 3.72559i 0.0520007 0.133057i
\(785\) 55.6944 1.98782
\(786\) 0 0