Properties

Label 624.2.cn.f.305.8
Level $624$
Weight $2$
Character 624.305
Analytic conductor $4.983$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.cn (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(14\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 312)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 305.8
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.121290 - 1.72780i) q^{3} +(-2.19967 - 2.19967i) q^{5} +(-1.17763 + 4.39498i) q^{7} +(-2.97058 - 0.419131i) q^{9} +O(q^{10})\) \(q+(0.121290 - 1.72780i) q^{3} +(-2.19967 - 2.19967i) q^{5} +(-1.17763 + 4.39498i) q^{7} +(-2.97058 - 0.419131i) q^{9} +(0.917595 + 3.42451i) q^{11} +(0.225112 + 3.59852i) q^{13} +(-4.06739 + 3.53380i) q^{15} +(-2.20507 - 3.81929i) q^{17} +(-1.06243 - 0.284677i) q^{19} +(7.45081 + 2.56778i) q^{21} +(-0.812870 + 1.40793i) q^{23} +4.67714i q^{25} +(-1.08448 + 5.08172i) q^{27} +(4.61533 + 2.66466i) q^{29} +(-3.28177 + 3.28177i) q^{31} +(6.02816 - 1.17006i) q^{33} +(12.2579 - 7.07712i) q^{35} +(2.75348 - 0.737792i) q^{37} +(6.24482 + 0.0475174i) q^{39} +(-9.76774 + 2.61726i) q^{41} +(6.07183 - 3.50557i) q^{43} +(5.61235 + 7.45626i) q^{45} +(-4.14895 + 4.14895i) q^{47} +(-11.8669 - 6.85134i) q^{49} +(-6.86643 + 3.34667i) q^{51} +8.33491i q^{53} +(5.51440 - 9.55122i) q^{55} +(-0.620727 + 1.80113i) q^{57} +(-1.97653 - 0.529610i) q^{59} +(-4.77501 - 8.27056i) q^{61} +(5.34032 - 12.5620i) q^{63} +(7.42039 - 8.41074i) q^{65} +(1.42966 + 5.33556i) q^{67} +(2.33403 + 1.57524i) q^{69} +(-1.43147 + 5.34234i) q^{71} +(2.99445 + 2.99445i) q^{73} +(8.08116 + 0.567292i) q^{75} -16.1312 q^{77} -15.4490 q^{79} +(8.64866 + 2.49012i) q^{81} +(-6.38106 - 6.38106i) q^{83} +(-3.55077 + 13.2516i) q^{85} +(5.16379 - 7.65116i) q^{87} +(1.98271 + 7.39957i) q^{89} +(-16.0805 - 3.24837i) q^{91} +(5.27219 + 6.06828i) q^{93} +(1.71080 + 2.96319i) q^{95} +(-8.75030 - 2.34464i) q^{97} +(-1.29047 - 10.5574i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(1\)

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 0
\(3\) 0.121290 1.72780i 0.0700270 0.997545i
\(4\) 0 0
\(5\) −2.19967 2.19967i −0.983725 0.983725i 0.0161451 0.999870i \(-0.494861\pi\)
−0.999870 + 0.0161451i \(0.994861\pi\)
\(6\) 0 0
\(7\) −1.17763 + 4.39498i −0.445103 + 1.66115i 0.270562 + 0.962703i \(0.412791\pi\)
−0.715665 + 0.698444i \(0.753876\pi\)
\(8\) 0 0
\(9\) −2.97058 0.419131i −0.990192 0.139710i
\(10\) 0 0
\(11\) 0.917595 + 3.42451i 0.276665 + 1.03253i 0.954717 + 0.297515i \(0.0961577\pi\)
−0.678052 + 0.735014i \(0.737176\pi\)
\(12\) 0 0
\(13\) 0.225112 + 3.59852i 0.0624348 + 0.998049i
\(14\) 0 0
\(15\) −4.06739 + 3.53380i −1.05020 + 0.912422i
\(16\) 0 0
\(17\) −2.20507 3.81929i −0.534808 0.926315i −0.999173 0.0406707i \(-0.987051\pi\)
0.464364 0.885644i \(-0.346283\pi\)
\(18\) 0 0
\(19\) −1.06243 0.284677i −0.243738 0.0653094i 0.134882 0.990862i \(-0.456935\pi\)
−0.378620 + 0.925552i \(0.623601\pi\)
\(20\) 0 0
\(21\) 7.45081 + 2.56778i 1.62590 + 0.560335i
\(22\) 0 0
\(23\) −0.812870 + 1.40793i −0.169495 + 0.293574i −0.938242 0.345978i \(-0.887547\pi\)
0.768747 + 0.639553i \(0.220880\pi\)
\(24\) 0 0
\(25\) 4.67714i 0.935428i
\(26\) 0 0
\(27\) −1.08448 + 5.08172i −0.208707 + 0.977978i
\(28\) 0 0
\(29\) 4.61533 + 2.66466i 0.857045 + 0.494815i 0.863022 0.505167i \(-0.168569\pi\)
−0.00597654 + 0.999982i \(0.501902\pi\)
\(30\) 0 0
\(31\) −3.28177 + 3.28177i −0.589423 + 0.589423i −0.937475 0.348052i \(-0.886843\pi\)
0.348052 + 0.937475i \(0.386843\pi\)
\(32\) 0 0
\(33\) 6.02816 1.17006i 1.04937 0.203681i
\(34\) 0 0
\(35\) 12.2579 7.07712i 2.07197 1.19625i
\(36\) 0 0
\(37\) 2.75348 0.737792i 0.452669 0.121292i −0.0252790 0.999680i \(-0.508047\pi\)
0.477948 + 0.878388i \(0.341381\pi\)
\(38\) 0 0
\(39\) 6.24482 + 0.0475174i 0.999971 + 0.00760887i
\(40\) 0 0
\(41\) −9.76774 + 2.61726i −1.52546 + 0.408747i −0.921536 0.388292i \(-0.873065\pi\)
−0.603928 + 0.797039i \(0.706398\pi\)
\(42\) 0 0
\(43\) 6.07183 3.50557i 0.925946 0.534595i 0.0404187 0.999183i \(-0.487131\pi\)
0.885527 + 0.464588i \(0.153797\pi\)
\(44\) 0 0
\(45\) 5.61235 + 7.45626i 0.836640 + 1.11151i
\(46\) 0 0
\(47\) −4.14895 + 4.14895i −0.605186 + 0.605186i −0.941684 0.336498i \(-0.890757\pi\)
0.336498 + 0.941684i \(0.390757\pi\)
\(48\) 0 0
\(49\) −11.8669 6.85134i −1.69527 0.978762i
\(50\) 0 0
\(51\) −6.86643 + 3.34667i −0.961492 + 0.468628i
\(52\) 0 0
\(53\) 8.33491i 1.14489i 0.819944 + 0.572444i \(0.194005\pi\)
−0.819944 + 0.572444i \(0.805995\pi\)
\(54\) 0 0
\(55\) 5.51440 9.55122i 0.743561 1.28789i
\(56\) 0 0
\(57\) −0.620727 + 1.80113i −0.0822173 + 0.238566i
\(58\) 0 0
\(59\) −1.97653 0.529610i −0.257322 0.0689493i 0.127852 0.991793i \(-0.459192\pi\)
−0.385174 + 0.922844i \(0.625859\pi\)
\(60\) 0 0
\(61\) −4.77501 8.27056i −0.611378 1.05894i −0.991008 0.133799i \(-0.957282\pi\)
0.379631 0.925138i \(-0.376051\pi\)
\(62\) 0 0
\(63\) 5.34032 12.5620i 0.672817 1.58267i
\(64\) 0 0
\(65\) 7.42039 8.41074i 0.920387 1.04322i
\(66\) 0 0
\(67\) 1.42966 + 5.33556i 0.174661 + 0.651842i 0.996609 + 0.0822804i \(0.0262203\pi\)
−0.821949 + 0.569562i \(0.807113\pi\)
\(68\) 0 0
\(69\) 2.33403 + 1.57524i 0.280984 + 0.189637i
\(70\) 0 0
\(71\) −1.43147 + 5.34234i −0.169885 + 0.634019i 0.827482 + 0.561493i \(0.189773\pi\)
−0.997367 + 0.0725259i \(0.976894\pi\)
\(72\) 0 0
\(73\) 2.99445 + 2.99445i 0.350473 + 0.350473i 0.860286 0.509812i \(-0.170285\pi\)
−0.509812 + 0.860286i \(0.670285\pi\)
\(74\) 0 0
\(75\) 8.08116 + 0.567292i 0.933131 + 0.0655052i
\(76\) 0 0
\(77\) −16.1312 −1.83833
\(78\) 0 0
\(79\) −15.4490 −1.73815 −0.869077 0.494677i \(-0.835286\pi\)
−0.869077 + 0.494677i \(0.835286\pi\)
\(80\) 0 0
\(81\) 8.64866 + 2.49012i 0.960962 + 0.276680i
\(82\) 0 0
\(83\) −6.38106 6.38106i −0.700413 0.700413i 0.264086 0.964499i \(-0.414930\pi\)
−0.964499 + 0.264086i \(0.914930\pi\)
\(84\) 0 0
\(85\) −3.55077 + 13.2516i −0.385135 + 1.43734i
\(86\) 0 0
\(87\) 5.16379 7.65116i 0.553617 0.820291i
\(88\) 0 0
\(89\) 1.98271 + 7.39957i 0.210167 + 0.784353i 0.987812 + 0.155650i \(0.0497471\pi\)
−0.777646 + 0.628703i \(0.783586\pi\)
\(90\) 0 0
\(91\) −16.0805 3.24837i −1.68570 0.340521i
\(92\) 0 0
\(93\) 5.27219 + 6.06828i 0.546700 + 0.629251i
\(94\) 0 0
\(95\) 1.71080 + 2.96319i 0.175525 + 0.304017i
\(96\) 0 0
\(97\) −8.75030 2.34464i −0.888458 0.238062i −0.214405 0.976745i \(-0.568781\pi\)
−0.674053 + 0.738683i \(0.735448\pi\)
\(98\) 0 0
\(99\) −1.29047 10.5574i −0.129697 1.06106i
\(100\) 0 0
\(101\) −3.52149 + 6.09939i −0.350401 + 0.606912i −0.986320 0.164844i \(-0.947288\pi\)
0.635919 + 0.771756i \(0.280621\pi\)
\(102\) 0 0
\(103\) 7.10076i 0.699658i 0.936813 + 0.349829i \(0.113760\pi\)
−0.936813 + 0.349829i \(0.886240\pi\)
\(104\) 0 0
\(105\) −10.7411 22.0376i −1.04822 2.15065i
\(106\) 0 0
\(107\) −10.7690 6.21749i −1.04108 0.601068i −0.120941 0.992660i \(-0.538591\pi\)
−0.920139 + 0.391592i \(0.871924\pi\)
\(108\) 0 0
\(109\) 5.09377 5.09377i 0.487895 0.487895i −0.419746 0.907641i \(-0.637881\pi\)
0.907641 + 0.419746i \(0.137881\pi\)
\(110\) 0 0
\(111\) −0.940786 4.84694i −0.0892955 0.460051i
\(112\) 0 0
\(113\) 10.4784 6.04969i 0.985722 0.569107i 0.0817293 0.996655i \(-0.473956\pi\)
0.903993 + 0.427548i \(0.140622\pi\)
\(114\) 0 0
\(115\) 4.88504 1.30894i 0.455533 0.122060i
\(116\) 0 0
\(117\) 0.839536 10.7840i 0.0776152 0.996983i
\(118\) 0 0
\(119\) 19.3825 5.19352i 1.77679 0.476089i
\(120\) 0 0
\(121\) −1.35901 + 0.784625i −0.123546 + 0.0713296i
\(122\) 0 0
\(123\) 3.33736 + 17.1941i 0.300920 + 1.55034i
\(124\) 0 0
\(125\) −0.710189 + 0.710189i −0.0635212 + 0.0635212i
\(126\) 0 0
\(127\) −11.6158 6.70637i −1.03073 0.595094i −0.113539 0.993534i \(-0.536219\pi\)
−0.917195 + 0.398440i \(0.869552\pi\)
\(128\) 0 0
\(129\) −5.32047 10.9161i −0.468441 0.961109i
\(130\) 0 0
\(131\) 10.7616i 0.940244i 0.882601 + 0.470122i \(0.155790\pi\)
−0.882601 + 0.470122i \(0.844210\pi\)
\(132\) 0 0
\(133\) 2.50230 4.33411i 0.216977 0.375815i
\(134\) 0 0
\(135\) 13.5636 8.79265i 1.16737 0.756750i
\(136\) 0 0
\(137\) 18.9042 + 5.06536i 1.61509 + 0.432763i 0.949555 0.313600i \(-0.101535\pi\)
0.665539 + 0.746363i \(0.268202\pi\)
\(138\) 0 0
\(139\) −1.42992 2.47669i −0.121284 0.210070i 0.798990 0.601344i \(-0.205368\pi\)
−0.920274 + 0.391274i \(0.872034\pi\)
\(140\) 0 0
\(141\) 6.66532 + 7.67177i 0.561321 + 0.646080i
\(142\) 0 0
\(143\) −12.1166 + 4.07288i −1.01324 + 0.340591i
\(144\) 0 0
\(145\) −4.29083 16.0136i −0.356334 1.32986i
\(146\) 0 0
\(147\) −13.2771 + 19.6725i −1.09507 + 1.62256i
\(148\) 0 0
\(149\) 5.07006 18.9217i 0.415356 1.55013i −0.368766 0.929522i \(-0.620220\pi\)
0.784122 0.620607i \(-0.213114\pi\)
\(150\) 0 0
\(151\) 15.8267 + 15.8267i 1.28796 + 1.28796i 0.936023 + 0.351940i \(0.114478\pi\)
0.351940 + 0.936023i \(0.385522\pi\)
\(152\) 0 0
\(153\) 4.94955 + 12.2697i 0.400147 + 0.991948i
\(154\) 0 0
\(155\) 14.4376 1.15966
\(156\) 0 0
\(157\) 1.15713 0.0923494 0.0461747 0.998933i \(-0.485297\pi\)
0.0461747 + 0.998933i \(0.485297\pi\)
\(158\) 0 0
\(159\) 14.4010 + 1.01094i 1.14208 + 0.0801731i
\(160\) 0 0
\(161\) −5.23057 5.23057i −0.412227 0.412227i
\(162\) 0 0
\(163\) 3.58002 13.3608i 0.280409 1.04650i −0.671720 0.740805i \(-0.734444\pi\)
0.952129 0.305696i \(-0.0988891\pi\)
\(164\) 0 0
\(165\) −15.8337 10.6862i −1.23266 0.831923i
\(166\) 0 0
\(167\) −2.53415 9.45758i −0.196098 0.731849i −0.991980 0.126397i \(-0.959659\pi\)
0.795881 0.605453i \(-0.207008\pi\)
\(168\) 0 0
\(169\) −12.8986 + 1.62014i −0.992204 + 0.124626i
\(170\) 0 0
\(171\) 3.03671 + 1.29095i 0.232223 + 0.0987215i
\(172\) 0 0
\(173\) −2.36780 4.10115i −0.180020 0.311804i 0.761867 0.647734i \(-0.224283\pi\)
−0.941887 + 0.335929i \(0.890950\pi\)
\(174\) 0 0
\(175\) −20.5559 5.50795i −1.55388 0.416362i
\(176\) 0 0
\(177\) −1.15479 + 3.35081i −0.0867995 + 0.251862i
\(178\) 0 0
\(179\) 4.29215 7.43422i 0.320810 0.555660i −0.659845 0.751402i \(-0.729378\pi\)
0.980655 + 0.195742i \(0.0627115\pi\)
\(180\) 0 0
\(181\) 6.64164i 0.493670i 0.969058 + 0.246835i \(0.0793905\pi\)
−0.969058 + 0.246835i \(0.920610\pi\)
\(182\) 0 0
\(183\) −14.8690 + 7.24712i −1.09915 + 0.535723i
\(184\) 0 0
\(185\) −7.67966 4.43385i −0.564620 0.325983i
\(186\) 0 0
\(187\) 11.0559 11.0559i 0.808484 0.808484i
\(188\) 0 0
\(189\) −21.0570 10.7506i −1.53167 0.781994i
\(190\) 0 0
\(191\) 6.75249 3.89855i 0.488593 0.282089i −0.235398 0.971899i \(-0.575639\pi\)
0.723991 + 0.689810i \(0.242306\pi\)
\(192\) 0 0
\(193\) −2.57872 + 0.690967i −0.185621 + 0.0497369i −0.350432 0.936588i \(-0.613965\pi\)
0.164811 + 0.986325i \(0.447299\pi\)
\(194\) 0 0
\(195\) −13.6320 13.8411i −0.976211 0.991181i
\(196\) 0 0
\(197\) 18.6823 5.00590i 1.33106 0.356655i 0.477947 0.878388i \(-0.341381\pi\)
0.853109 + 0.521733i \(0.174714\pi\)
\(198\) 0 0
\(199\) −6.95427 + 4.01505i −0.492975 + 0.284619i −0.725808 0.687898i \(-0.758534\pi\)
0.232833 + 0.972517i \(0.425200\pi\)
\(200\) 0 0
\(201\) 9.39217 1.82301i 0.662473 0.128585i
\(202\) 0 0
\(203\) −17.1463 + 17.1463i −1.20343 + 1.20343i
\(204\) 0 0
\(205\) 27.2430 + 15.7287i 1.90273 + 1.09854i
\(206\) 0 0
\(207\) 3.00480 3.84167i 0.208848 0.267015i
\(208\) 0 0
\(209\) 3.89952i 0.269735i
\(210\) 0 0
\(211\) −2.69364 + 4.66552i −0.185438 + 0.321187i −0.943724 0.330734i \(-0.892704\pi\)
0.758286 + 0.651922i \(0.226037\pi\)
\(212\) 0 0
\(213\) 9.05686 + 3.12127i 0.620566 + 0.213866i
\(214\) 0 0
\(215\) −21.0672 5.64493i −1.43677 0.384981i
\(216\) 0 0
\(217\) −10.5586 18.2880i −0.716764 1.24147i
\(218\) 0 0
\(219\) 5.53700 4.81060i 0.374156 0.325070i
\(220\) 0 0
\(221\) 13.2474 8.79475i 0.891117 0.591599i
\(222\) 0 0
\(223\) −2.18490 8.15417i −0.146312 0.546044i −0.999693 0.0247569i \(-0.992119\pi\)
0.853381 0.521287i \(-0.174548\pi\)
\(224\) 0 0
\(225\) 1.96033 13.8938i 0.130689 0.926254i
\(226\) 0 0
\(227\) −0.237467 + 0.886239i −0.0157612 + 0.0588217i −0.973359 0.229288i \(-0.926360\pi\)
0.957597 + 0.288110i \(0.0930268\pi\)
\(228\) 0 0
\(229\) −2.28432 2.28432i −0.150952 0.150952i 0.627591 0.778543i \(-0.284041\pi\)
−0.778543 + 0.627591i \(0.784041\pi\)
\(230\) 0 0
\(231\) −1.95656 + 27.8715i −0.128732 + 1.83381i
\(232\) 0 0
\(233\) 9.30420 0.609538 0.304769 0.952426i \(-0.401421\pi\)
0.304769 + 0.952426i \(0.401421\pi\)
\(234\) 0 0
\(235\) 18.2527 1.19067
\(236\) 0 0
\(237\) −1.87382 + 26.6928i −0.121718 + 1.73389i
\(238\) 0 0
\(239\) 18.5336 + 18.5336i 1.19884 + 1.19884i 0.974515 + 0.224323i \(0.0720171\pi\)
0.224323 + 0.974515i \(0.427983\pi\)
\(240\) 0 0
\(241\) −3.15760 + 11.7843i −0.203399 + 0.759094i 0.786533 + 0.617548i \(0.211874\pi\)
−0.989932 + 0.141546i \(0.954793\pi\)
\(242\) 0 0
\(243\) 5.35142 14.6411i 0.343294 0.939228i
\(244\) 0 0
\(245\) 11.0325 + 41.1740i 0.704842 + 2.63051i
\(246\) 0 0
\(247\) 0.785250 3.88725i 0.0499642 0.247340i
\(248\) 0 0
\(249\) −11.7992 + 10.2512i −0.747741 + 0.649646i
\(250\) 0 0
\(251\) −4.56257 7.90260i −0.287987 0.498808i 0.685342 0.728221i \(-0.259653\pi\)
−0.973329 + 0.229413i \(0.926319\pi\)
\(252\) 0 0
\(253\) −5.56736 1.49177i −0.350017 0.0937868i
\(254\) 0 0
\(255\) 22.4655 + 7.74231i 1.40684 + 0.484842i
\(256\) 0 0
\(257\) −0.0791658 + 0.137119i −0.00493823 + 0.00855326i −0.868484 0.495717i \(-0.834905\pi\)
0.863546 + 0.504271i \(0.168239\pi\)
\(258\) 0 0
\(259\) 12.9703i 0.805937i
\(260\) 0 0
\(261\) −12.5934 9.85001i −0.779509 0.609700i
\(262\) 0 0
\(263\) 3.05457 + 1.76356i 0.188353 + 0.108746i 0.591211 0.806517i \(-0.298650\pi\)
−0.402858 + 0.915262i \(0.631983\pi\)
\(264\) 0 0
\(265\) 18.3341 18.3341i 1.12625 1.12625i
\(266\) 0 0
\(267\) 13.0254 2.52822i 0.797144 0.154725i
\(268\) 0 0
\(269\) −16.2959 + 9.40842i −0.993576 + 0.573641i −0.906341 0.422546i \(-0.861136\pi\)
−0.0872346 + 0.996188i \(0.527803\pi\)
\(270\) 0 0
\(271\) −1.95323 + 0.523366i −0.118650 + 0.0317922i −0.317656 0.948206i \(-0.602896\pi\)
0.199005 + 0.979998i \(0.436229\pi\)
\(272\) 0 0
\(273\) −7.56293 + 27.3899i −0.457729 + 1.65771i
\(274\) 0 0
\(275\) −16.0169 + 4.29172i −0.965856 + 0.258800i
\(276\) 0 0
\(277\) 15.1882 8.76890i 0.912569 0.526872i 0.0313123 0.999510i \(-0.490031\pi\)
0.881257 + 0.472638i \(0.156698\pi\)
\(278\) 0 0
\(279\) 11.1242 8.37325i 0.665990 0.501294i
\(280\) 0 0
\(281\) −13.8319 + 13.8319i −0.825142 + 0.825142i −0.986840 0.161698i \(-0.948303\pi\)
0.161698 + 0.986840i \(0.448303\pi\)
\(282\) 0 0
\(283\) 15.2851 + 8.82488i 0.908607 + 0.524585i 0.879983 0.475006i \(-0.157554\pi\)
0.0286245 + 0.999590i \(0.490887\pi\)
\(284\) 0 0
\(285\) 5.32731 2.59651i 0.315562 0.153804i
\(286\) 0 0
\(287\) 46.0112i 2.71595i
\(288\) 0 0
\(289\) −1.22467 + 2.12120i −0.0720396 + 0.124776i
\(290\) 0 0
\(291\) −5.11239 + 14.8344i −0.299693 + 0.869607i
\(292\) 0 0
\(293\) 12.2454 + 3.28114i 0.715383 + 0.191686i 0.598111 0.801414i \(-0.295918\pi\)
0.117272 + 0.993100i \(0.462585\pi\)
\(294\) 0 0
\(295\) 3.18275 + 5.51269i 0.185307 + 0.320961i
\(296\) 0 0
\(297\) −18.3975 + 0.949165i −1.06753 + 0.0550762i
\(298\) 0 0
\(299\) −5.24945 2.60818i −0.303584 0.150835i
\(300\) 0 0
\(301\) 8.25655 + 30.8139i 0.475900 + 1.77608i
\(302\) 0 0
\(303\) 10.1114 + 6.82422i 0.580885 + 0.392041i
\(304\) 0 0
\(305\) −7.68908 + 28.6960i −0.440275 + 1.64313i
\(306\) 0 0
\(307\) 6.09233 + 6.09233i 0.347707 + 0.347707i 0.859255 0.511548i \(-0.170928\pi\)
−0.511548 + 0.859255i \(0.670928\pi\)
\(308\) 0 0
\(309\) 12.2687 + 0.861253i 0.697941 + 0.0489950i
\(310\) 0 0
\(311\) −9.87859 −0.560164 −0.280082 0.959976i \(-0.590362\pi\)
−0.280082 + 0.959976i \(0.590362\pi\)
\(312\) 0 0
\(313\) 17.2222 0.973456 0.486728 0.873554i \(-0.338190\pi\)
0.486728 + 0.873554i \(0.338190\pi\)
\(314\) 0 0
\(315\) −39.3794 + 15.8855i −2.21878 + 0.895045i
\(316\) 0 0
\(317\) −0.00884596 0.00884596i −0.000496839 0.000496839i 0.706858 0.707355i \(-0.250112\pi\)
−0.707355 + 0.706858i \(0.750112\pi\)
\(318\) 0 0
\(319\) −4.89016 + 18.2503i −0.273796 + 1.02182i
\(320\) 0 0
\(321\) −12.0488 + 17.8526i −0.672496 + 0.996433i
\(322\) 0 0
\(323\) 1.25547 + 4.68546i 0.0698560 + 0.260706i
\(324\) 0 0
\(325\) −16.8308 + 1.05288i −0.933603 + 0.0584032i
\(326\) 0 0
\(327\) −8.18319 9.41884i −0.452531 0.520863i
\(328\) 0 0
\(329\) −13.3486 23.1205i −0.735933 1.27467i
\(330\) 0 0
\(331\) −0.360355 0.0965567i −0.0198069 0.00530724i 0.248902 0.968529i \(-0.419930\pi\)
−0.268709 + 0.963221i \(0.586597\pi\)
\(332\) 0 0
\(333\) −8.48865 + 1.03760i −0.465175 + 0.0568602i
\(334\) 0 0
\(335\) 8.59171 14.8813i 0.469415 0.813051i
\(336\) 0 0
\(337\) 22.3015i 1.21484i 0.794381 + 0.607420i \(0.207796\pi\)
−0.794381 + 0.607420i \(0.792204\pi\)
\(338\) 0 0
\(339\) −9.18172 18.8383i −0.498683 1.02316i
\(340\) 0 0
\(341\) −14.2498 8.22711i −0.771669 0.445523i
\(342\) 0 0
\(343\) 21.5648 21.5648i 1.16439 1.16439i
\(344\) 0 0
\(345\) −1.66908 8.59913i −0.0898604 0.462962i
\(346\) 0 0
\(347\) 0.801179 0.462561i 0.0430095 0.0248316i −0.478341 0.878174i \(-0.658762\pi\)
0.521351 + 0.853343i \(0.325428\pi\)
\(348\) 0 0
\(349\) −16.4270 + 4.40159i −0.879315 + 0.235612i −0.670112 0.742260i \(-0.733754\pi\)
−0.209204 + 0.977872i \(0.567087\pi\)
\(350\) 0 0
\(351\) −18.5308 2.75855i −0.989101 0.147240i
\(352\) 0 0
\(353\) −1.31686 + 0.352851i −0.0700893 + 0.0187804i −0.293693 0.955900i \(-0.594884\pi\)
0.223604 + 0.974680i \(0.428218\pi\)
\(354\) 0 0
\(355\) 14.9002 8.60262i 0.790819 0.456580i
\(356\) 0 0
\(357\) −6.62245 34.1190i −0.350497 1.80577i
\(358\) 0 0
\(359\) −23.2669 + 23.2669i −1.22798 + 1.22798i −0.263256 + 0.964726i \(0.584796\pi\)
−0.964726 + 0.263256i \(0.915204\pi\)
\(360\) 0 0
\(361\) −15.4068 8.89510i −0.810883 0.468163i
\(362\) 0 0
\(363\) 1.19084 + 2.44326i 0.0625029 + 0.128238i
\(364\) 0 0
\(365\) 13.1736i 0.689539i
\(366\) 0 0
\(367\) −8.66640 + 15.0106i −0.452382 + 0.783549i −0.998533 0.0541374i \(-0.982759\pi\)
0.546151 + 0.837687i \(0.316092\pi\)
\(368\) 0 0
\(369\) 30.1128 3.68081i 1.56761 0.191615i
\(370\) 0 0
\(371\) −36.6318 9.81545i −1.90183 0.509593i
\(372\) 0 0
\(373\) 1.40911 + 2.44066i 0.0729611 + 0.126372i 0.900198 0.435481i \(-0.143422\pi\)
−0.827237 + 0.561854i \(0.810088\pi\)
\(374\) 0 0
\(375\) 1.14092 + 1.31320i 0.0589171 + 0.0678135i
\(376\) 0 0
\(377\) −8.54986 + 17.2082i −0.440340 + 0.886267i
\(378\) 0 0
\(379\) 7.23342 + 26.9955i 0.371556 + 1.38667i 0.858312 + 0.513128i \(0.171513\pi\)
−0.486756 + 0.873538i \(0.661820\pi\)
\(380\) 0 0
\(381\) −12.9961 + 19.2563i −0.665812 + 0.986530i
\(382\) 0 0
\(383\) 1.58764 5.92516i 0.0811248 0.302762i −0.913427 0.407002i \(-0.866574\pi\)
0.994552 + 0.104240i \(0.0332410\pi\)
\(384\) 0 0
\(385\) 35.4835 + 35.4835i 1.80841 + 1.80841i
\(386\) 0 0
\(387\) −19.5061 + 7.86869i −0.991553 + 0.399988i
\(388\) 0 0
\(389\) −34.3070 −1.73943 −0.869717 0.493550i \(-0.835699\pi\)
−0.869717 + 0.493550i \(0.835699\pi\)
\(390\) 0 0
\(391\) 7.16974 0.362589
\(392\) 0 0
\(393\) 18.5939 + 1.30528i 0.937936 + 0.0658425i
\(394\) 0 0
\(395\) 33.9829 + 33.9829i 1.70986 + 1.70986i
\(396\) 0 0
\(397\) 2.44015 9.10677i 0.122468 0.457056i −0.877269 0.479999i \(-0.840637\pi\)
0.999737 + 0.0229433i \(0.00730371\pi\)
\(398\) 0 0
\(399\) −7.18496 4.84916i −0.359698 0.242761i
\(400\) 0 0
\(401\) −7.09363 26.4738i −0.354239 1.32204i −0.881440 0.472297i \(-0.843425\pi\)
0.527201 0.849741i \(-0.323242\pi\)
\(402\) 0 0
\(403\) −12.5483 11.0707i −0.625073 0.551472i
\(404\) 0 0
\(405\) −13.5468 24.5017i −0.673145 1.21750i
\(406\) 0 0
\(407\) 5.05315 + 8.75232i 0.250476 + 0.433836i
\(408\) 0 0
\(409\) 13.8641 + 3.71487i 0.685535 + 0.183689i 0.584743 0.811219i \(-0.301195\pi\)
0.100793 + 0.994907i \(0.467862\pi\)
\(410\) 0 0
\(411\) 11.0448 32.0483i 0.544801 1.58082i
\(412\) 0 0
\(413\) 4.65525 8.06313i 0.229070 0.396761i
\(414\) 0 0
\(415\) 28.0725i 1.37803i
\(416\) 0 0
\(417\) −4.45265 + 2.17021i −0.218047 + 0.106276i
\(418\) 0 0
\(419\) 27.2181 + 15.7144i 1.32969 + 0.767697i 0.985252 0.171112i \(-0.0547361\pi\)
0.344438 + 0.938809i \(0.388069\pi\)
\(420\) 0 0
\(421\) 15.8765 15.8765i 0.773773 0.773773i −0.204991 0.978764i \(-0.565717\pi\)
0.978764 + 0.204991i \(0.0657165\pi\)
\(422\) 0 0
\(423\) 14.0637 10.5858i 0.683801 0.514700i
\(424\) 0 0
\(425\) 17.8634 10.3134i 0.866501 0.500274i
\(426\) 0 0
\(427\) 41.9722 11.2464i 2.03118 0.544252i
\(428\) 0 0
\(429\) 5.56749 + 21.4290i 0.268801 + 1.03460i
\(430\) 0 0
\(431\) −12.3582 + 3.31137i −0.595274 + 0.159503i −0.543862 0.839174i \(-0.683039\pi\)
−0.0514116 + 0.998678i \(0.516372\pi\)
\(432\) 0 0
\(433\) 14.1339 8.16020i 0.679231 0.392154i −0.120335 0.992733i \(-0.538397\pi\)
0.799565 + 0.600579i \(0.205063\pi\)
\(434\) 0 0
\(435\) −28.1887 + 5.47140i −1.35155 + 0.262334i
\(436\) 0 0
\(437\) 1.26442 1.26442i 0.0604855 0.0604855i
\(438\) 0 0
\(439\) 20.2300 + 11.6798i 0.965525 + 0.557446i 0.897869 0.440262i \(-0.145115\pi\)
0.0676563 + 0.997709i \(0.478448\pi\)
\(440\) 0 0
\(441\) 32.3798 + 25.3262i 1.54190 + 1.20601i
\(442\) 0 0
\(443\) 19.6001i 0.931228i 0.884988 + 0.465614i \(0.154166\pi\)
−0.884988 + 0.465614i \(0.845834\pi\)
\(444\) 0 0
\(445\) 11.9153 20.6380i 0.564841 0.978333i
\(446\) 0 0
\(447\) −32.0780 11.0551i −1.51724 0.522887i
\(448\) 0 0
\(449\) 11.4364 + 3.06438i 0.539717 + 0.144617i 0.518372 0.855155i \(-0.326538\pi\)
0.0213456 + 0.999772i \(0.493205\pi\)
\(450\) 0 0
\(451\) −17.9256 31.0481i −0.844086 1.46200i
\(452\) 0 0
\(453\) 29.2651 25.4258i 1.37499 1.19461i
\(454\) 0 0
\(455\) 28.2266 + 42.5172i 1.32328 + 1.99324i
\(456\) 0 0
\(457\) 8.92124 + 33.2945i 0.417318 + 1.55745i 0.780147 + 0.625596i \(0.215144\pi\)
−0.362830 + 0.931856i \(0.618189\pi\)
\(458\) 0 0
\(459\) 21.7999 7.06363i 1.01753 0.329702i
\(460\) 0 0
\(461\) 4.84992 18.1002i 0.225883 0.843008i −0.756165 0.654381i \(-0.772929\pi\)
0.982049 0.188628i \(-0.0604039\pi\)
\(462\) 0 0
\(463\) −16.7806 16.7806i −0.779860 0.779860i 0.199947 0.979807i \(-0.435923\pi\)
−0.979807 + 0.199947i \(0.935923\pi\)
\(464\) 0 0
\(465\) 1.75115 24.9453i 0.0812074 1.15681i
\(466\) 0 0
\(467\) 30.7628 1.42353 0.711767 0.702416i \(-0.247895\pi\)
0.711767 + 0.702416i \(0.247895\pi\)
\(468\) 0 0
\(469\) −25.1333 −1.16055
\(470\) 0 0
\(471\) 0.140349 1.99930i 0.00646695 0.0921227i
\(472\) 0 0
\(473\) 17.5764 + 17.5764i 0.808162 + 0.808162i
\(474\) 0 0
\(475\) 1.33147 4.96913i 0.0610922 0.227999i
\(476\) 0 0
\(477\) 3.49342 24.7595i 0.159953 1.13366i
\(478\) 0 0
\(479\) −4.38660 16.3710i −0.200429 0.748010i −0.990794 0.135375i \(-0.956776\pi\)
0.790366 0.612635i \(-0.209891\pi\)
\(480\) 0 0
\(481\) 3.27480 + 9.74235i 0.149318 + 0.444213i
\(482\) 0 0
\(483\) −9.67179 + 8.40296i −0.440082 + 0.382348i
\(484\) 0 0
\(485\) 14.0904 + 24.4053i 0.639811 + 1.10819i
\(486\) 0 0
\(487\) −27.0620 7.25125i −1.22630 0.328585i −0.413161 0.910658i \(-0.635575\pi\)
−0.813137 + 0.582073i \(0.802242\pi\)
\(488\) 0 0
\(489\) −22.6506 7.80610i −1.02430 0.353004i
\(490\) 0 0
\(491\) 6.45173 11.1747i 0.291162 0.504308i −0.682922 0.730491i \(-0.739291\pi\)
0.974085 + 0.226183i \(0.0726247\pi\)
\(492\) 0 0
\(493\) 23.5031i 1.05852i
\(494\) 0 0
\(495\) −20.3842 + 26.0614i −0.916200 + 1.17137i
\(496\) 0 0
\(497\) −21.7937 12.5826i −0.977582 0.564407i
\(498\) 0 0
\(499\) 2.22600 2.22600i 0.0996495 0.0996495i −0.655524 0.755174i \(-0.727552\pi\)
0.755174 + 0.655524i \(0.227552\pi\)
\(500\) 0 0
\(501\) −16.6482 + 3.23139i −0.743785 + 0.144368i
\(502\) 0 0
\(503\) 3.89079 2.24635i 0.173482 0.100160i −0.410745 0.911750i \(-0.634731\pi\)
0.584226 + 0.811591i \(0.301398\pi\)
\(504\) 0 0
\(505\) 21.1628 5.67056i 0.941733 0.252336i
\(506\) 0 0
\(507\) 1.23479 + 22.4828i 0.0548389 + 0.998495i
\(508\) 0 0
\(509\) −22.9448 + 6.14805i −1.01701 + 0.272508i −0.728556 0.684986i \(-0.759808\pi\)
−0.288456 + 0.957493i \(0.593142\pi\)
\(510\) 0 0
\(511\) −16.6869 + 9.63418i −0.738185 + 0.426191i
\(512\) 0 0
\(513\) 2.59883 5.09024i 0.114741 0.224740i
\(514\) 0 0
\(515\) 15.6194 15.6194i 0.688271 0.688271i
\(516\) 0 0
\(517\) −18.0152 10.4011i −0.792306 0.457438i
\(518\) 0 0
\(519\) −7.37314 + 3.59365i −0.323645 + 0.157744i
\(520\) 0 0
\(521\) 9.05417i 0.396670i 0.980134 + 0.198335i \(0.0635534\pi\)
−0.980134 + 0.198335i \(0.936447\pi\)
\(522\) 0 0
\(523\) 14.6521 25.3781i 0.640691 1.10971i −0.344588 0.938754i \(-0.611981\pi\)
0.985279 0.170955i \(-0.0546852\pi\)
\(524\) 0 0
\(525\) −12.0099 + 34.8485i −0.524153 + 1.52091i
\(526\) 0 0
\(527\) 19.7706 + 5.29751i 0.861219 + 0.230763i
\(528\) 0 0
\(529\) 10.1785 + 17.6297i 0.442543 + 0.766507i
\(530\) 0 0
\(531\) 5.64946 + 2.40167i 0.245166 + 0.104224i
\(532\) 0 0
\(533\) −11.6171 34.5602i −0.503191 1.49697i
\(534\) 0 0
\(535\) 10.0119 + 37.3648i 0.432851 + 1.61542i
\(536\) 0 0
\(537\) −12.3242 8.31767i −0.531830 0.358934i
\(538\) 0 0
\(539\) 12.5735 46.9249i 0.541579 2.02120i
\(540\) 0 0
\(541\) −29.7524 29.7524i −1.27916 1.27916i −0.941141 0.338015i \(-0.890244\pi\)
−0.338015 0.941141i \(-0.609756\pi\)
\(542\) 0 0
\(543\) 11.4754 + 0.805567i 0.492458 + 0.0345702i
\(544\) 0 0
\(545\) −22.4093 −0.959909
\(546\) 0 0
\(547\) 9.72797 0.415938 0.207969 0.978135i \(-0.433315\pi\)
0.207969 + 0.978135i \(0.433315\pi\)
\(548\) 0 0
\(549\) 10.7181 + 26.5697i 0.457437 + 1.13397i
\(550\) 0 0
\(551\) −4.14489 4.14489i −0.176578 0.176578i
\(552\) 0 0
\(553\) 18.1933 67.8983i 0.773657 2.88733i
\(554\) 0 0
\(555\) −8.59228 + 12.7311i −0.364722 + 0.540406i
\(556\) 0 0
\(557\) −2.30023 8.58457i −0.0974638 0.363740i 0.899918 0.436060i \(-0.143626\pi\)
−0.997381 + 0.0723199i \(0.976960\pi\)
\(558\) 0 0
\(559\) 13.9817 + 21.0604i 0.591363 + 0.890762i
\(560\) 0 0
\(561\) −17.7613 20.4433i −0.749883 0.863115i
\(562\) 0 0
\(563\) −0.952635 1.65001i −0.0401488 0.0695398i 0.845253 0.534367i \(-0.179450\pi\)
−0.885402 + 0.464827i \(0.846117\pi\)
\(564\) 0 0
\(565\) −36.3564 9.74166i −1.52952 0.409835i
\(566\) 0 0
\(567\) −21.1290 + 35.0782i −0.887333 + 1.47315i
\(568\) 0 0
\(569\) −5.02931 + 8.71103i −0.210840 + 0.365185i −0.951978 0.306168i \(-0.900953\pi\)
0.741138 + 0.671353i \(0.234287\pi\)
\(570\) 0 0
\(571\) 20.2231i 0.846309i −0.906057 0.423155i \(-0.860923\pi\)
0.906057 0.423155i \(-0.139077\pi\)
\(572\) 0 0
\(573\) −5.91690 12.1398i −0.247182 0.507147i
\(574\) 0 0
\(575\) −6.58509 3.80191i −0.274617 0.158550i
\(576\) 0 0
\(577\) −7.71564 + 7.71564i −0.321206 + 0.321206i −0.849230 0.528024i \(-0.822933\pi\)
0.528024 + 0.849230i \(0.322933\pi\)
\(578\) 0 0
\(579\) 0.881078 + 4.53932i 0.0366163 + 0.188648i
\(580\) 0 0
\(581\) 35.5592 20.5301i 1.47524 0.851733i
\(582\) 0 0
\(583\) −28.5430 + 7.64807i −1.18213 + 0.316751i
\(584\) 0 0
\(585\) −25.5681 + 21.8746i −1.05711 + 0.904405i
\(586\) 0 0
\(587\) 1.87678 0.502881i 0.0774630 0.0207561i −0.219879 0.975527i \(-0.570566\pi\)
0.297342 + 0.954771i \(0.403900\pi\)
\(588\) 0 0
\(589\) 4.42089 2.55240i 0.182159 0.105170i
\(590\) 0 0
\(591\) −6.38321 32.8864i −0.262570 1.35276i
\(592\) 0 0
\(593\) 23.1037 23.1037i 0.948756 0.948756i −0.0499940 0.998750i \(-0.515920\pi\)
0.998750 + 0.0499940i \(0.0159202\pi\)
\(594\) 0 0
\(595\) −54.0592 31.2111i −2.21621 1.27953i
\(596\) 0 0
\(597\) 6.09371 + 12.5026i 0.249399 + 0.511696i
\(598\) 0 0
\(599\) 8.98472i 0.367106i −0.983010 0.183553i \(-0.941240\pi\)
0.983010 0.183553i \(-0.0587598\pi\)
\(600\) 0 0
\(601\) −16.6602 + 28.8563i −0.679583 + 1.17707i 0.295523 + 0.955336i \(0.404506\pi\)
−0.975107 + 0.221737i \(0.928827\pi\)
\(602\) 0 0
\(603\) −2.01062 16.4489i −0.0818786 0.669851i
\(604\) 0 0
\(605\) 4.71530 + 1.26346i 0.191704 + 0.0513670i
\(606\) 0 0
\(607\) −22.1672 38.3948i −0.899740 1.55840i −0.827826 0.560984i \(-0.810423\pi\)
−0.0719135 0.997411i \(-0.522911\pi\)
\(608\) 0 0
\(609\) 27.5457 + 31.7050i 1.11621 + 1.28475i
\(610\) 0 0
\(611\) −15.8640 13.9961i −0.641790 0.566221i
\(612\) 0 0
\(613\) 11.5021 + 42.9265i 0.464566 + 1.73379i 0.658323 + 0.752736i \(0.271266\pi\)
−0.193756 + 0.981050i \(0.562067\pi\)
\(614\) 0 0
\(615\) 30.4804 45.1626i 1.22909 1.82113i
\(616\) 0 0
\(617\) 2.01395 7.51616i 0.0810785 0.302589i −0.913464 0.406919i \(-0.866603\pi\)
0.994543 + 0.104330i \(0.0332698\pi\)
\(618\) 0 0
\(619\) 3.82416 + 3.82416i 0.153706 + 0.153706i 0.779771 0.626065i \(-0.215336\pi\)
−0.626065 + 0.779771i \(0.715336\pi\)
\(620\) 0 0
\(621\) −6.27318 5.65765i −0.251734 0.227034i
\(622\) 0 0
\(623\) −34.8559 −1.39647
\(624\) 0 0
\(625\) 26.5101 1.06040
\(626\) 0 0
\(627\) −6.73758 0.472974i −0.269073 0.0188887i
\(628\) 0 0
\(629\) −8.88946 8.88946i −0.354446 0.354446i
\(630\) 0 0
\(631\) 4.24796 15.8536i 0.169109 0.631122i −0.828372 0.560179i \(-0.810732\pi\)
0.997480 0.0709434i \(-0.0226010\pi\)
\(632\) 0 0
\(633\) 7.73436 + 5.21994i 0.307413 + 0.207474i
\(634\) 0 0
\(635\) 10.7991 + 40.3028i 0.428549 + 1.59937i
\(636\) 0 0
\(637\) 21.9833 44.2454i 0.871009 1.75307i
\(638\) 0 0
\(639\) 6.49144 15.2698i 0.256797 0.604066i
\(640\) 0 0
\(641\) 24.3557 + 42.1853i 0.961993 + 1.66622i 0.717487 + 0.696572i \(0.245292\pi\)
0.244506 + 0.969648i \(0.421374\pi\)
\(642\) 0 0
\(643\) 16.3066 + 4.36934i 0.643069 + 0.172310i 0.565593 0.824684i \(-0.308647\pi\)
0.0774759 + 0.996994i \(0.475314\pi\)
\(644\) 0 0
\(645\) −12.3086 + 35.7152i −0.484649 + 1.40628i
\(646\) 0 0
\(647\) 10.9410 18.9504i 0.430137 0.745018i −0.566748 0.823891i \(-0.691799\pi\)
0.996885 + 0.0788727i \(0.0251321\pi\)
\(648\) 0 0
\(649\) 7.25461i 0.284769i
\(650\) 0 0
\(651\) −32.8787 + 16.0250i −1.28862 + 0.628068i
\(652\) 0 0
\(653\) −19.2265 11.1004i −0.752392 0.434393i 0.0741658 0.997246i \(-0.476371\pi\)
−0.826557 + 0.562852i \(0.809704\pi\)
\(654\) 0 0
\(655\) 23.6720 23.6720i 0.924941 0.924941i
\(656\) 0 0
\(657\) −7.64017 10.1503i −0.298071 0.396001i
\(658\) 0 0
\(659\) −37.6857 + 21.7578i −1.46803 + 0.847565i −0.999359 0.0358100i \(-0.988599\pi\)
−0.468667 + 0.883375i \(0.655266\pi\)
\(660\) 0 0
\(661\) −5.55235 + 1.48775i −0.215961 + 0.0578667i −0.365177 0.930938i \(-0.618992\pi\)
0.149216 + 0.988805i \(0.452325\pi\)
\(662\) 0 0
\(663\) −13.5888 23.9556i −0.527744 0.930357i
\(664\) 0 0
\(665\) −15.0379 + 4.02939i −0.583144 + 0.156253i
\(666\) 0 0
\(667\) −7.50332 + 4.33205i −0.290530 + 0.167738i
\(668\) 0 0
\(669\) −14.3538 + 2.78605i −0.554949 + 0.107715i
\(670\) 0 0
\(671\) 23.9411 23.9411i 0.924236 0.924236i
\(672\) 0 0
\(673\) −19.1318 11.0458i −0.737478 0.425783i 0.0836738 0.996493i \(-0.473335\pi\)
−0.821152 + 0.570710i \(0.806668\pi\)
\(674\) 0 0
\(675\) −23.7679 5.07224i −0.914828 0.195231i
\(676\) 0 0
\(677\) 29.1088i 1.11874i 0.828917 + 0.559371i \(0.188957\pi\)
−0.828917 + 0.559371i \(0.811043\pi\)
\(678\) 0 0
\(679\) 20.6093 35.6963i 0.790911 1.36990i
\(680\) 0 0
\(681\) 1.50244 + 0.517787i 0.0575736 + 0.0198416i
\(682\) 0 0
\(683\) 19.8514 + 5.31917i 0.759593 + 0.203532i 0.617769 0.786360i \(-0.288037\pi\)
0.141824 + 0.989892i \(0.454703\pi\)
\(684\) 0 0
\(685\) −30.4409 52.7252i −1.16309 2.01453i
\(686\) 0 0
\(687\) −4.22391 + 3.66978i −0.161152 + 0.140011i
\(688\) 0 0
\(689\) −29.9933 + 1.87629i −1.14265 + 0.0714808i
\(690\) 0 0
\(691\) 7.53183 + 28.1092i 0.286524 + 1.06932i 0.947718 + 0.319109i \(0.103383\pi\)
−0.661194 + 0.750215i \(0.729950\pi\)
\(692\) 0 0
\(693\) 47.9191 + 6.76110i 1.82030 + 0.256833i
\(694\) 0 0
\(695\) −2.30256 + 8.59325i −0.0873409 + 0.325961i
\(696\) 0 0
\(697\) 31.5346 + 31.5346i 1.19446 + 1.19446i
\(698\) 0 0
\(699\) 1.12851 16.0758i 0.0426841 0.608042i
\(700\) 0 0
\(701\) 47.9676 1.81171 0.905855 0.423588i \(-0.139230\pi\)
0.905855 + 0.423588i \(0.139230\pi\)
\(702\) 0 0
\(703\) −3.13541 −0.118254
\(704\) 0 0
\(705\) 2.21387 31.5369i 0.0833792 1.18775i
\(706\) 0 0
\(707\) −22.6597 22.6597i −0.852206 0.852206i
\(708\) 0 0
\(709\) −13.0177 + 48.5829i −0.488891 + 1.82457i 0.0729667 + 0.997334i \(0.476753\pi\)
−0.561858 + 0.827234i \(0.689913\pi\)
\(710\) 0 0
\(711\) 45.8926 + 6.47517i 1.72111 + 0.242838i
\(712\) 0 0
\(713\) −1.95285 7.28815i −0.0731350 0.272943i
\(714\) 0 0
\(715\) 35.6116 + 17.6936i 1.33180 + 0.661702i
\(716\) 0 0
\(717\) 34.2703 29.7744i 1.27985 1.11194i
\(718\) 0 0
\(719\) 4.43706 + 7.68521i 0.165474 + 0.286610i 0.936824 0.349802i \(-0.113751\pi\)
−0.771349 + 0.636412i \(0.780418\pi\)
\(720\) 0 0
\(721\) −31.2077 8.36208i −1.16224 0.311420i
\(722\) 0 0
\(723\) 19.9779 + 6.88501i 0.742987 + 0.256056i
\(724\) 0 0
\(725\) −12.4630 + 21.5865i −0.462864 + 0.801704i
\(726\) 0 0
\(727\) 11.4138i 0.423315i 0.977344 + 0.211658i \(0.0678861\pi\)
−0.977344 + 0.211658i \(0.932114\pi\)
\(728\) 0 0
\(729\) −24.6478 11.0220i −0.912882 0.408223i
\(730\) 0 0
\(731\) −26.7776 15.4601i −0.990407 0.571812i
\(732\) 0 0
\(733\) −14.4825 + 14.4825i −0.534923 + 0.534923i −0.922033 0.387110i \(-0.873473\pi\)
0.387110 + 0.922033i \(0.373473\pi\)
\(734\) 0 0
\(735\) 72.4784 14.0680i 2.67341 0.518905i
\(736\) 0 0
\(737\) −16.9598 + 9.79176i −0.624723 + 0.360684i
\(738\) 0 0
\(739\) −35.8764 + 9.61305i −1.31973 + 0.353622i −0.848879 0.528588i \(-0.822722\pi\)
−0.470856 + 0.882210i \(0.656055\pi\)
\(740\) 0 0
\(741\) −6.62115 1.82824i −0.243234 0.0671620i
\(742\) 0 0
\(743\) 12.1935 3.26724i 0.447337 0.119864i −0.0281161 0.999605i \(-0.508951\pi\)
0.475453 + 0.879741i \(0.342284\pi\)
\(744\) 0 0
\(745\) −52.7741 + 30.4692i −1.93350 + 1.11630i
\(746\) 0 0
\(747\) 16.2809 + 21.6299i 0.595689 + 0.791398i
\(748\) 0 0
\(749\) 40.0077 40.0077i 1.46185 1.46185i
\(750\) 0 0
\(751\) 2.30561 + 1.33114i 0.0841328 + 0.0485741i 0.541476 0.840716i \(-0.317866\pi\)
−0.457343 + 0.889290i \(0.651199\pi\)
\(752\) 0 0
\(753\) −14.2075 + 6.92469i −0.517750 + 0.252350i
\(754\) 0 0
\(755\) 69.6274i 2.53400i
\(756\) 0 0
\(757\) −4.12709 + 7.14833i −0.150002 + 0.259810i −0.931228 0.364438i \(-0.881261\pi\)
0.781226 + 0.624248i \(0.214595\pi\)
\(758\) 0 0
\(759\) −3.25275 + 9.43834i −0.118067 + 0.342590i
\(760\) 0 0
\(761\) 17.6088 + 4.71825i 0.638317 + 0.171037i 0.563441 0.826156i \(-0.309477\pi\)
0.0748761 + 0.997193i \(0.476144\pi\)
\(762\) 0 0
\(763\) 16.3884 + 28.3856i 0.593302 + 1.02763i
\(764\) 0 0
\(765\) 16.1020 37.8768i 0.582169 1.36944i
\(766\) 0 0
\(767\) 1.46087 7.23180i 0.0527489 0.261125i
\(768\) 0 0
\(769\) 1.20203 + 4.48602i 0.0433462 + 0.161770i 0.984206 0.177025i \(-0.0566473\pi\)
−0.940860 + 0.338795i \(0.889981\pi\)
\(770\) 0 0
\(771\) 0.227312 + 0.153414i 0.00818645 + 0.00552506i
\(772\) 0 0
\(773\) −4.06155 + 15.1579i −0.146084 + 0.545193i 0.853621 + 0.520895i \(0.174402\pi\)
−0.999705 + 0.0242978i \(0.992265\pi\)
\(774\) 0 0
\(775\) −15.3493 15.3493i −0.551362 0.551362i
\(776\) 0 0
\(777\) 22.4101 + 1.57318i 0.803959 + 0.0564374i
\(778\) 0 0
\(779\) 11.1226 0.398508
\(780\) 0 0
\(781\) −19.6084 −0.701644
\(782\) 0 0
\(783\) −18.5463 + 20.5641i −0.662790 + 0.734900i
\(784\) 0 0
\(785\) −2.54532 2.54532i −0.0908464 0.0908464i
\(786\) 0 0
\(787\) −12.6603 + 47.2487i −0.451290 + 1.68424i 0.247483 + 0.968892i \(0.420396\pi\)
−0.698773 + 0.715343i \(0.746270\pi\)
\(788\) 0 0
\(789\) 3.41756 5.06378i 0.121668 0.180275i
\(790\) 0 0
\(791\) 14.2486 + 53.1765i 0.506622 + 1.89074i
\(792\) 0 0
\(793\) 28.6869 19.0448i 1.01870 0.676299i
\(794\) 0 0
\(795\) −29.4539 33.9014i −1.04462 1.20236i
\(796\) 0 0
\(797\) 22.4830 + 38.9417i