Properties

Label 624.2.cn.f.305.5
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 305.5
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.19063 - 1.25794i) q^{3} +(2.36656 + 2.36656i) q^{5} +(0.332282 - 1.24009i) q^{7} +(-0.164807 + 2.99547i) q^{9} +O(q^{10})\) \(q+(-1.19063 - 1.25794i) q^{3} +(2.36656 + 2.36656i) q^{5} +(0.332282 - 1.24009i) q^{7} +(-0.164807 + 2.99547i) q^{9} +(1.52674 + 5.69787i) q^{11} +(-3.51077 + 0.821290i) q^{13} +(0.159288 - 5.79467i) q^{15} +(-1.04019 - 1.80167i) q^{17} +(-1.34634 - 0.360750i) q^{19} +(-1.95558 + 1.05850i) q^{21} +(-3.81352 + 6.60522i) q^{23} +6.20118i q^{25} +(3.96433 - 3.35917i) q^{27} +(6.87044 + 3.96665i) q^{29} +(-1.42567 + 1.42567i) q^{31} +(5.34977 - 8.70458i) q^{33} +(3.72111 - 2.14839i) q^{35} +(4.28784 - 1.14892i) q^{37} +(5.21315 + 3.43847i) q^{39} +(-0.985195 + 0.263982i) q^{41} +(8.68002 - 5.01141i) q^{43} +(-7.47898 + 6.69892i) q^{45} +(-2.59357 + 2.59357i) q^{47} +(4.63476 + 2.67588i) q^{49} +(-1.02790 + 3.45361i) q^{51} -7.08357i q^{53} +(-9.87121 + 17.0974i) q^{55} +(1.14919 + 2.12313i) q^{57} +(-1.48170 - 0.397021i) q^{59} +(3.39878 + 5.88685i) q^{61} +(3.65990 + 1.19972i) q^{63} +(-10.2521 - 6.36480i) q^{65} +(2.22473 + 8.30282i) q^{67} +(12.8494 - 3.06719i) q^{69} +(1.21596 - 4.53804i) q^{71} +(-9.61981 - 9.61981i) q^{73} +(7.80069 - 7.38331i) q^{75} +7.57319 q^{77} +11.7272 q^{79} +(-8.94568 - 0.987351i) q^{81} +(0.406364 + 0.406364i) q^{83} +(1.80207 - 6.72543i) q^{85} +(-3.19035 - 13.3654i) q^{87} +(-1.75705 - 6.55739i) q^{89} +(-0.148089 + 4.62658i) q^{91} +(3.49085 + 0.0959586i) q^{93} +(-2.33245 - 4.03992i) q^{95} +(-5.89119 - 1.57854i) q^{97} +(-17.3194 + 3.63425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

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
\(3\) −1.19063 1.25794i −0.687410 0.726270i
\(4\) 0 0
\(5\) 2.36656 + 2.36656i 1.05836 + 1.05836i 0.998188 + 0.0601682i \(0.0191637\pi\)
0.0601682 + 0.998188i \(0.480836\pi\)
\(6\) 0 0
\(7\) 0.332282 1.24009i 0.125591 0.468711i −0.874269 0.485441i \(-0.838659\pi\)
0.999860 + 0.0167303i \(0.00532566\pi\)
\(8\) 0 0
\(9\) −0.164807 + 2.99547i −0.0549358 + 0.998490i
\(10\) 0 0
\(11\) 1.52674 + 5.69787i 0.460329 + 1.71797i 0.671929 + 0.740615i \(0.265466\pi\)
−0.211600 + 0.977356i \(0.567867\pi\)
\(12\) 0 0
\(13\) −3.51077 + 0.821290i −0.973712 + 0.227785i
\(14\) 0 0
\(15\) 0.159288 5.79467i 0.0411279 1.49618i
\(16\) 0 0
\(17\) −1.04019 1.80167i −0.252284 0.436969i 0.711870 0.702311i \(-0.247848\pi\)
−0.964154 + 0.265342i \(0.914515\pi\)
\(18\) 0 0
\(19\) −1.34634 0.360750i −0.308871 0.0827618i 0.101054 0.994881i \(-0.467779\pi\)
−0.409925 + 0.912119i \(0.634445\pi\)
\(20\) 0 0
\(21\) −1.95558 + 1.05850i −0.426743 + 0.230984i
\(22\) 0 0
\(23\) −3.81352 + 6.60522i −0.795175 + 1.37728i 0.127553 + 0.991832i \(0.459288\pi\)
−0.922728 + 0.385452i \(0.874046\pi\)
\(24\) 0 0
\(25\) 6.20118i 1.24024i
\(26\) 0 0
\(27\) 3.96433 3.35917i 0.762936 0.646473i
\(28\) 0 0
\(29\) 6.87044 + 3.96665i 1.27581 + 0.736588i 0.976075 0.217435i \(-0.0697689\pi\)
0.299733 + 0.954023i \(0.403102\pi\)
\(30\) 0 0
\(31\) −1.42567 + 1.42567i −0.256058 + 0.256058i −0.823449 0.567391i \(-0.807953\pi\)
0.567391 + 0.823449i \(0.307953\pi\)
\(32\) 0 0
\(33\) 5.34977 8.70458i 0.931276 1.51527i
\(34\) 0 0
\(35\) 3.72111 2.14839i 0.628983 0.363143i
\(36\) 0 0
\(37\) 4.28784 1.14892i 0.704917 0.188882i 0.111485 0.993766i \(-0.464439\pi\)
0.593432 + 0.804884i \(0.297773\pi\)
\(38\) 0 0
\(39\) 5.21315 + 3.43847i 0.834772 + 0.550596i
\(40\) 0 0
\(41\) −0.985195 + 0.263982i −0.153862 + 0.0412271i −0.334928 0.942244i \(-0.608712\pi\)
0.181066 + 0.983471i \(0.442045\pi\)
\(42\) 0 0
\(43\) 8.68002 5.01141i 1.32369 0.764233i 0.339376 0.940651i \(-0.389784\pi\)
0.984315 + 0.176418i \(0.0564509\pi\)
\(44\) 0 0
\(45\) −7.47898 + 6.69892i −1.11490 + 0.998617i
\(46\) 0 0
\(47\) −2.59357 + 2.59357i −0.378312 + 0.378312i −0.870493 0.492181i \(-0.836200\pi\)
0.492181 + 0.870493i \(0.336200\pi\)
\(48\) 0 0
\(49\) 4.63476 + 2.67588i 0.662109 + 0.382269i
\(50\) 0 0
\(51\) −1.02790 + 3.45361i −0.143935 + 0.483603i
\(52\) 0 0
\(53\) 7.08357i 0.973003i −0.873680 0.486501i \(-0.838273\pi\)
0.873680 0.486501i \(-0.161727\pi\)
\(54\) 0 0
\(55\) −9.87121 + 17.0974i −1.33103 + 2.30542i
\(56\) 0 0
\(57\) 1.14919 + 2.12313i 0.152214 + 0.281215i
\(58\) 0 0
\(59\) −1.48170 0.397021i −0.192901 0.0516877i 0.161075 0.986942i \(-0.448504\pi\)
−0.353976 + 0.935254i \(0.615171\pi\)
\(60\) 0 0
\(61\) 3.39878 + 5.88685i 0.435169 + 0.753734i 0.997309 0.0733074i \(-0.0233554\pi\)
−0.562141 + 0.827042i \(0.690022\pi\)
\(62\) 0 0
\(63\) 3.65990 + 1.19972i 0.461104 + 0.151150i
\(64\) 0 0
\(65\) −10.2521 6.36480i −1.27161 0.789456i
\(66\) 0 0
\(67\) 2.22473 + 8.30282i 0.271794 + 1.01435i 0.957959 + 0.286904i \(0.0926262\pi\)
−0.686165 + 0.727446i \(0.740707\pi\)
\(68\) 0 0
\(69\) 12.8494 3.06719i 1.54689 0.369246i
\(70\) 0 0
\(71\) 1.21596 4.53804i 0.144308 0.538566i −0.855477 0.517841i \(-0.826736\pi\)
0.999785 0.0207249i \(-0.00659741\pi\)
\(72\) 0 0
\(73\) −9.61981 9.61981i −1.12591 1.12591i −0.990835 0.135079i \(-0.956871\pi\)
−0.135079 0.990835i \(-0.543129\pi\)
\(74\) 0 0
\(75\) 7.80069 7.38331i 0.900746 0.852551i
\(76\) 0 0
\(77\) 7.57319 0.863045
\(78\) 0 0
\(79\) 11.7272 1.31941 0.659706 0.751524i \(-0.270681\pi\)
0.659706 + 0.751524i \(0.270681\pi\)
\(80\) 0 0
\(81\) −8.94568 0.987351i −0.993964 0.109706i
\(82\) 0 0
\(83\) 0.406364 + 0.406364i 0.0446042 + 0.0446042i 0.729057 0.684453i \(-0.239959\pi\)
−0.684453 + 0.729057i \(0.739959\pi\)
\(84\) 0 0
\(85\) 1.80207 6.72543i 0.195462 0.729475i
\(86\) 0 0
\(87\) −3.19035 13.3654i −0.342041 1.43292i
\(88\) 0 0
\(89\) −1.75705 6.55739i −0.186247 0.695081i −0.994360 0.106055i \(-0.966178\pi\)
0.808114 0.589026i \(-0.200489\pi\)
\(90\) 0 0
\(91\) −0.148089 + 4.62658i −0.0155239 + 0.484997i
\(92\) 0 0
\(93\) 3.49085 + 0.0959586i 0.361984 + 0.00995045i
\(94\) 0 0
\(95\) −2.33245 4.03992i −0.239304 0.414487i
\(96\) 0 0
\(97\) −5.89119 1.57854i −0.598160 0.160276i −0.0529800 0.998596i \(-0.516872\pi\)
−0.545180 + 0.838319i \(0.683539\pi\)
\(98\) 0 0
\(99\) −17.3194 + 3.63425i −1.74067 + 0.365256i
\(100\) 0 0
\(101\) −5.42569 + 9.39757i −0.539876 + 0.935093i 0.459034 + 0.888419i \(0.348196\pi\)
−0.998910 + 0.0466743i \(0.985138\pi\)
\(102\) 0 0
\(103\) 5.53207i 0.545091i −0.962143 0.272546i \(-0.912134\pi\)
0.962143 0.272546i \(-0.0878656\pi\)
\(104\) 0 0
\(105\) −7.13300 2.12299i −0.696109 0.207183i
\(106\) 0 0
\(107\) 4.21782 + 2.43516i 0.407752 + 0.235416i 0.689823 0.723978i \(-0.257688\pi\)
−0.282071 + 0.959393i \(0.591022\pi\)
\(108\) 0 0
\(109\) 1.33269 1.33269i 0.127649 0.127649i −0.640396 0.768045i \(-0.721230\pi\)
0.768045 + 0.640396i \(0.221230\pi\)
\(110\) 0 0
\(111\) −6.55050 4.02589i −0.621746 0.382121i
\(112\) 0 0
\(113\) 8.42921 4.86661i 0.792954 0.457812i −0.0480476 0.998845i \(-0.515300\pi\)
0.841001 + 0.541033i \(0.181967\pi\)
\(114\) 0 0
\(115\) −24.6565 + 6.60670i −2.29924 + 0.616078i
\(116\) 0 0
\(117\) −1.88155 10.6517i −0.173949 0.984755i
\(118\) 0 0
\(119\) −2.57987 + 0.691275i −0.236496 + 0.0633690i
\(120\) 0 0
\(121\) −20.6085 + 11.8983i −1.87350 + 1.08166i
\(122\) 0 0
\(123\) 1.50507 + 0.925008i 0.135708 + 0.0834052i
\(124\) 0 0
\(125\) −2.84267 + 2.84267i −0.254256 + 0.254256i
\(126\) 0 0
\(127\) −3.90233 2.25301i −0.346276 0.199923i 0.316768 0.948503i \(-0.397402\pi\)
−0.663044 + 0.748581i \(0.730736\pi\)
\(128\) 0 0
\(129\) −16.6387 4.95218i −1.46496 0.436015i
\(130\) 0 0
\(131\) 6.24622i 0.545735i −0.962052 0.272867i \(-0.912028\pi\)
0.962052 0.272867i \(-0.0879721\pi\)
\(132\) 0 0
\(133\) −0.894727 + 1.54971i −0.0775827 + 0.134377i
\(134\) 0 0
\(135\) 17.3315 + 1.43214i 1.49166 + 0.123259i
\(136\) 0 0
\(137\) −22.2503 5.96195i −1.90097 0.509364i −0.996577 0.0826685i \(-0.973656\pi\)
−0.904395 0.426696i \(-0.859678\pi\)
\(138\) 0 0
\(139\) −9.56760 16.5716i −0.811513 1.40558i −0.911805 0.410624i \(-0.865311\pi\)
0.100292 0.994958i \(-0.468022\pi\)
\(140\) 0 0
\(141\) 6.35053 + 0.174568i 0.534811 + 0.0147012i
\(142\) 0 0
\(143\) −10.0396 18.7500i −0.839556 1.56795i
\(144\) 0 0
\(145\) 6.87198 + 25.6466i 0.570687 + 2.12983i
\(146\) 0 0
\(147\) −2.15219 9.01621i −0.177510 0.743645i
\(148\) 0 0
\(149\) 3.46420 12.9286i 0.283798 1.05915i −0.665915 0.746028i \(-0.731958\pi\)
0.949713 0.313122i \(-0.101375\pi\)
\(150\) 0 0
\(151\) 8.77938 + 8.77938i 0.714455 + 0.714455i 0.967464 0.253009i \(-0.0814201\pi\)
−0.253009 + 0.967464i \(0.581420\pi\)
\(152\) 0 0
\(153\) 5.56827 2.81894i 0.450168 0.227898i
\(154\) 0 0
\(155\) −6.74786 −0.542001
\(156\) 0 0
\(157\) 3.27714 0.261544 0.130772 0.991412i \(-0.458254\pi\)
0.130772 + 0.991412i \(0.458254\pi\)
\(158\) 0 0
\(159\) −8.91068 + 8.43390i −0.706663 + 0.668852i
\(160\) 0 0
\(161\) 6.92392 + 6.92392i 0.545681 + 0.545681i
\(162\) 0 0
\(163\) 1.17349 4.37951i 0.0919145 0.343030i −0.904619 0.426221i \(-0.859845\pi\)
0.996534 + 0.0831914i \(0.0265113\pi\)
\(164\) 0 0
\(165\) 33.2604 7.93935i 2.58932 0.618077i
\(166\) 0 0
\(167\) −2.16836 8.09242i −0.167793 0.626210i −0.997668 0.0682609i \(-0.978255\pi\)
0.829875 0.557949i \(-0.188412\pi\)
\(168\) 0 0
\(169\) 11.6510 5.76671i 0.896228 0.443593i
\(170\) 0 0
\(171\) 1.30250 3.97346i 0.0996049 0.303858i
\(172\) 0 0
\(173\) 7.39731 + 12.8125i 0.562407 + 0.974118i 0.997286 + 0.0736289i \(0.0234580\pi\)
−0.434878 + 0.900489i \(0.643209\pi\)
\(174\) 0 0
\(175\) 7.69004 + 2.06054i 0.581312 + 0.155762i
\(176\) 0 0
\(177\) 1.26473 + 2.33659i 0.0950629 + 0.175629i
\(178\) 0 0
\(179\) 0.299519 0.518782i 0.0223871 0.0387756i −0.854615 0.519262i \(-0.826207\pi\)
0.877002 + 0.480487i \(0.159540\pi\)
\(180\) 0 0
\(181\) 16.8056i 1.24915i 0.780964 + 0.624576i \(0.214728\pi\)
−0.780964 + 0.624576i \(0.785272\pi\)
\(182\) 0 0
\(183\) 3.35861 11.2845i 0.248275 0.834174i
\(184\) 0 0
\(185\) 12.8664 + 7.42843i 0.945958 + 0.546149i
\(186\) 0 0
\(187\) 8.67756 8.67756i 0.634566 0.634566i
\(188\) 0 0
\(189\) −2.84841 6.03233i −0.207191 0.438788i
\(190\) 0 0
\(191\) 4.19095 2.41964i 0.303246 0.175079i −0.340654 0.940189i \(-0.610648\pi\)
0.643900 + 0.765109i \(0.277315\pi\)
\(192\) 0 0
\(193\) 8.47201 2.27007i 0.609828 0.163403i 0.0593289 0.998238i \(-0.481104\pi\)
0.550500 + 0.834835i \(0.314437\pi\)
\(194\) 0 0
\(195\) 4.19988 + 20.4745i 0.300760 + 1.46621i
\(196\) 0 0
\(197\) −19.8579 + 5.32092i −1.41482 + 0.379100i −0.883643 0.468162i \(-0.844916\pi\)
−0.531176 + 0.847261i \(0.678250\pi\)
\(198\) 0 0
\(199\) −1.29567 + 0.748053i −0.0918473 + 0.0530281i −0.545220 0.838293i \(-0.683554\pi\)
0.453373 + 0.891321i \(0.350221\pi\)
\(200\) 0 0
\(201\) 7.79558 12.6841i 0.549858 0.894670i
\(202\) 0 0
\(203\) 7.20193 7.20193i 0.505477 0.505477i
\(204\) 0 0
\(205\) −2.95625 1.70679i −0.206473 0.119208i
\(206\) 0 0
\(207\) −19.1572 12.5119i −1.33152 0.869636i
\(208\) 0 0
\(209\) 8.22203i 0.568729i
\(210\) 0 0
\(211\) 7.74572 13.4160i 0.533237 0.923594i −0.466009 0.884780i \(-0.654309\pi\)
0.999246 0.0388139i \(-0.0123579\pi\)
\(212\) 0 0
\(213\) −7.15632 + 3.87351i −0.490343 + 0.265409i
\(214\) 0 0
\(215\) 32.4016 + 8.68197i 2.20977 + 0.592106i
\(216\) 0 0
\(217\) 1.29424 + 2.24169i 0.0878587 + 0.152176i
\(218\) 0 0
\(219\) −0.647487 + 23.5547i −0.0437531 + 1.59168i
\(220\) 0 0
\(221\) 5.13157 + 5.47093i 0.345187 + 0.368015i
\(222\) 0 0
\(223\) 4.86321 + 18.1498i 0.325665 + 1.21540i 0.913642 + 0.406520i \(0.133258\pi\)
−0.587977 + 0.808878i \(0.700075\pi\)
\(224\) 0 0
\(225\) −18.5755 1.02200i −1.23836 0.0681334i
\(226\) 0 0
\(227\) −0.273750 + 1.02165i −0.0181694 + 0.0678093i −0.974415 0.224755i \(-0.927842\pi\)
0.956246 + 0.292564i \(0.0945085\pi\)
\(228\) 0 0
\(229\) 5.97504 + 5.97504i 0.394842 + 0.394842i 0.876409 0.481567i \(-0.159932\pi\)
−0.481567 + 0.876409i \(0.659932\pi\)
\(230\) 0 0
\(231\) −9.01686 9.52659i −0.593266 0.626804i
\(232\) 0 0
\(233\) −2.30436 −0.150964 −0.0754820 0.997147i \(-0.524050\pi\)
−0.0754820 + 0.997147i \(0.524050\pi\)
\(234\) 0 0
\(235\) −12.2757 −0.800777
\(236\) 0 0
\(237\) −13.9627 14.7521i −0.906977 0.958249i
\(238\) 0 0
\(239\) −0.0131657 0.0131657i −0.000851621 0.000851621i 0.706681 0.707532i \(-0.250192\pi\)
−0.707532 + 0.706681i \(0.750192\pi\)
\(240\) 0 0
\(241\) 4.35079 16.2374i 0.280259 1.04594i −0.671976 0.740573i \(-0.734554\pi\)
0.952235 0.305367i \(-0.0987792\pi\)
\(242\) 0 0
\(243\) 9.40895 + 12.4287i 0.603585 + 0.797299i
\(244\) 0 0
\(245\) 4.63580 + 17.3010i 0.296170 + 1.10532i
\(246\) 0 0
\(247\) 5.02296 + 0.160776i 0.319603 + 0.0102299i
\(248\) 0 0
\(249\) 0.0273514 0.995008i 0.00173333 0.0630561i
\(250\) 0 0
\(251\) 6.88393 + 11.9233i 0.434510 + 0.752593i 0.997255 0.0740371i \(-0.0235883\pi\)
−0.562746 + 0.826630i \(0.690255\pi\)
\(252\) 0 0
\(253\) −43.4579 11.6445i −2.73218 0.732084i
\(254\) 0 0
\(255\) −10.6058 + 5.74059i −0.664158 + 0.359490i
\(256\) 0 0
\(257\) 5.82331 10.0863i 0.363248 0.629164i −0.625245 0.780428i \(-0.715001\pi\)
0.988493 + 0.151264i \(0.0483344\pi\)
\(258\) 0 0
\(259\) 5.69909i 0.354124i
\(260\) 0 0
\(261\) −13.0143 + 19.9265i −0.805563 + 1.23342i
\(262\) 0 0
\(263\) 21.2887 + 12.2910i 1.31271 + 0.757896i 0.982545 0.186025i \(-0.0595606\pi\)
0.330170 + 0.943922i \(0.392894\pi\)
\(264\) 0 0
\(265\) 16.7637 16.7637i 1.02978 1.02978i
\(266\) 0 0
\(267\) −6.15678 + 10.0177i −0.376789 + 0.613071i
\(268\) 0 0
\(269\) 1.83996 1.06230i 0.112184 0.0647697i −0.442858 0.896592i \(-0.646035\pi\)
0.555042 + 0.831822i \(0.312702\pi\)
\(270\) 0 0
\(271\) −2.53449 + 0.679116i −0.153960 + 0.0412533i −0.334976 0.942227i \(-0.608728\pi\)
0.181016 + 0.983480i \(0.442061\pi\)
\(272\) 0 0
\(273\) 5.99626 5.32225i 0.362910 0.322117i
\(274\) 0 0
\(275\) −35.3335 + 9.46759i −2.13069 + 0.570917i
\(276\) 0 0
\(277\) 17.6137 10.1693i 1.05831 0.611013i 0.133342 0.991070i \(-0.457429\pi\)
0.924963 + 0.380057i \(0.124096\pi\)
\(278\) 0 0
\(279\) −4.03559 4.50551i −0.241605 0.269738i
\(280\) 0 0
\(281\) −21.9749 + 21.9749i −1.31091 + 1.31091i −0.390172 + 0.920742i \(0.627585\pi\)
−0.920742 + 0.390172i \(0.872415\pi\)
\(282\) 0 0
\(283\) 2.14892 + 1.24068i 0.127740 + 0.0737508i 0.562508 0.826792i \(-0.309836\pi\)
−0.434768 + 0.900542i \(0.643170\pi\)
\(284\) 0 0
\(285\) −2.30488 + 7.74412i −0.136529 + 0.458722i
\(286\) 0 0
\(287\) 1.30945i 0.0772944i
\(288\) 0 0
\(289\) 6.33600 10.9743i 0.372706 0.645545i
\(290\) 0 0
\(291\) 5.02852 + 9.29020i 0.294777 + 0.544601i
\(292\) 0 0
\(293\) 6.05925 + 1.62357i 0.353985 + 0.0948500i 0.431429 0.902147i \(-0.358009\pi\)
−0.0774445 + 0.996997i \(0.524676\pi\)
\(294\) 0 0
\(295\) −2.56696 4.44610i −0.149454 0.258862i
\(296\) 0 0
\(297\) 25.1926 + 17.4597i 1.46182 + 1.01311i
\(298\) 0 0
\(299\) 7.96360 26.3214i 0.460547 1.52221i
\(300\) 0 0
\(301\) −3.33040 12.4292i −0.191961 0.716409i
\(302\) 0 0
\(303\) 18.2815 4.36384i 1.05025 0.250696i
\(304\) 0 0
\(305\) −5.88817 + 21.9750i −0.337156 + 1.25828i
\(306\) 0 0
\(307\) 3.38970 + 3.38970i 0.193461 + 0.193461i 0.797190 0.603729i \(-0.206319\pi\)
−0.603729 + 0.797190i \(0.706319\pi\)
\(308\) 0 0
\(309\) −6.95899 + 6.58664i −0.395883 + 0.374701i
\(310\) 0 0
\(311\) −20.8546 −1.18255 −0.591277 0.806469i \(-0.701376\pi\)
−0.591277 + 0.806469i \(0.701376\pi\)
\(312\) 0 0
\(313\) −22.0202 −1.24465 −0.622327 0.782757i \(-0.713813\pi\)
−0.622327 + 0.782757i \(0.713813\pi\)
\(314\) 0 0
\(315\) 5.82216 + 11.5006i 0.328041 + 0.647983i
\(316\) 0 0
\(317\) 12.4092 + 12.4092i 0.696968 + 0.696968i 0.963755 0.266787i \(-0.0859621\pi\)
−0.266787 + 0.963755i \(0.585962\pi\)
\(318\) 0 0
\(319\) −12.1121 + 45.2029i −0.678146 + 2.53088i
\(320\) 0 0
\(321\) −1.95858 8.20512i −0.109317 0.457965i
\(322\) 0 0
\(323\) 0.750500 + 2.80090i 0.0417589 + 0.155846i
\(324\) 0 0
\(325\) −5.09297 21.7709i −0.282507 1.20763i
\(326\) 0 0
\(327\) −3.26318 0.0897003i −0.180454 0.00496044i
\(328\) 0 0
\(329\) 2.35447 + 4.07807i 0.129806 + 0.224831i
\(330\) 0 0
\(331\) −10.7039 2.86810i −0.588340 0.157645i −0.0476456 0.998864i \(-0.515172\pi\)
−0.540694 + 0.841219i \(0.681838\pi\)
\(332\) 0 0
\(333\) 2.73490 + 13.0334i 0.149871 + 0.714229i
\(334\) 0 0
\(335\) −14.3841 + 24.9140i −0.785889 + 1.36120i
\(336\) 0 0
\(337\) 13.4976i 0.735259i −0.929972 0.367630i \(-0.880169\pi\)
0.929972 0.367630i \(-0.119831\pi\)
\(338\) 0 0
\(339\) −16.1579 4.80909i −0.877579 0.261194i
\(340\) 0 0
\(341\) −10.2999 5.94666i −0.557771 0.322029i
\(342\) 0 0
\(343\) 11.2131 11.2131i 0.605448 0.605448i
\(344\) 0 0
\(345\) 37.6676 + 23.1502i 2.02796 + 1.24637i
\(346\) 0 0
\(347\) 9.61214 5.54957i 0.516007 0.297917i −0.219293 0.975659i \(-0.570375\pi\)
0.735299 + 0.677742i \(0.237042\pi\)
\(348\) 0 0
\(349\) 20.6033 5.52063i 1.10287 0.295512i 0.338936 0.940810i \(-0.389933\pi\)
0.763932 + 0.645297i \(0.223266\pi\)
\(350\) 0 0
\(351\) −11.1590 + 15.0491i −0.595623 + 0.803264i
\(352\) 0 0
\(353\) 17.4311 4.67065i 0.927765 0.248594i 0.236863 0.971543i \(-0.423881\pi\)
0.690901 + 0.722949i \(0.257214\pi\)
\(354\) 0 0
\(355\) 13.6172 7.86187i 0.722724 0.417265i
\(356\) 0 0
\(357\) 3.94125 + 2.42226i 0.208593 + 0.128200i
\(358\) 0 0
\(359\) 10.6950 10.6950i 0.564462 0.564462i −0.366110 0.930572i \(-0.619311\pi\)
0.930572 + 0.366110i \(0.119311\pi\)
\(360\) 0 0
\(361\) −14.7720 8.52862i −0.777474 0.448875i
\(362\) 0 0
\(363\) 39.5044 + 11.7577i 2.07344 + 0.617118i
\(364\) 0 0
\(365\) 45.5317i 2.38324i
\(366\) 0 0
\(367\) 14.7893 25.6158i 0.771995 1.33713i −0.164473 0.986382i \(-0.552592\pi\)
0.936468 0.350753i \(-0.114074\pi\)
\(368\) 0 0
\(369\) −0.628384 2.99463i −0.0327123 0.155894i
\(370\) 0 0
\(371\) −8.78428 2.35374i −0.456057 0.122200i
\(372\) 0 0
\(373\) 9.76737 + 16.9176i 0.505735 + 0.875959i 0.999978 + 0.00663494i \(0.00211198\pi\)
−0.494243 + 0.869324i \(0.664555\pi\)
\(374\) 0 0
\(375\) 6.96046 + 0.191334i 0.359437 + 0.00988042i
\(376\) 0 0
\(377\) −27.3783 8.28336i −1.41005 0.426615i
\(378\) 0 0
\(379\) −8.69053 32.4335i −0.446402 1.66600i −0.712207 0.701970i \(-0.752304\pi\)
0.265804 0.964027i \(-0.414363\pi\)
\(380\) 0 0
\(381\) 1.81208 + 7.59139i 0.0928358 + 0.388919i
\(382\) 0 0
\(383\) 1.45165 5.41763i 0.0741758 0.276828i −0.918869 0.394562i \(-0.870896\pi\)
0.993045 + 0.117734i \(0.0375630\pi\)
\(384\) 0 0
\(385\) 17.9224 + 17.9224i 0.913409 + 0.913409i
\(386\) 0 0
\(387\) 13.5810 + 26.8267i 0.690361 + 1.36368i
\(388\) 0 0
\(389\) −14.1875 −0.719336 −0.359668 0.933080i \(-0.617110\pi\)
−0.359668 + 0.933080i \(0.617110\pi\)
\(390\) 0 0
\(391\) 15.8672 0.802439
\(392\) 0 0
\(393\) −7.85735 + 7.43693i −0.396351 + 0.375144i
\(394\) 0 0
\(395\) 27.7531 + 27.7531i 1.39641 + 1.39641i
\(396\) 0 0
\(397\) −10.0364 + 37.4565i −0.503714 + 1.87989i −0.0293274 + 0.999570i \(0.509337\pi\)
−0.474387 + 0.880317i \(0.657330\pi\)
\(398\) 0 0
\(399\) 3.01473 0.719623i 0.150925 0.0360262i
\(400\) 0 0
\(401\) −2.47565 9.23926i −0.123628 0.461387i 0.876159 0.482022i \(-0.160098\pi\)
−0.999787 + 0.0206358i \(0.993431\pi\)
\(402\) 0 0
\(403\) 3.83431 6.17609i 0.191001 0.307653i
\(404\) 0 0
\(405\) −18.8338 23.5071i −0.935861 1.16808i
\(406\) 0 0
\(407\) 13.0928 + 22.6774i 0.648987 + 1.12408i
\(408\) 0 0
\(409\) 29.7151 + 7.96215i 1.46932 + 0.393703i 0.902698 0.430275i \(-0.141583\pi\)
0.566622 + 0.823978i \(0.308250\pi\)
\(410\) 0 0
\(411\) 18.9921 + 35.0879i 0.936811 + 1.73076i
\(412\) 0 0
\(413\) −0.984685 + 1.70552i −0.0484532 + 0.0839234i
\(414\) 0 0
\(415\) 1.92337i 0.0944143i
\(416\) 0 0
\(417\) −9.45452 + 31.7660i −0.462990 + 1.55559i
\(418\) 0 0
\(419\) −30.1024 17.3796i −1.47060 0.849051i −0.471145 0.882056i \(-0.656159\pi\)
−0.999455 + 0.0330044i \(0.989492\pi\)
\(420\) 0 0
\(421\) −2.85119 + 2.85119i −0.138959 + 0.138959i −0.773164 0.634206i \(-0.781327\pi\)
0.634206 + 0.773164i \(0.281327\pi\)
\(422\) 0 0
\(423\) −7.34153 8.19641i −0.356957 0.398523i
\(424\) 0 0
\(425\) 11.1725 6.45043i 0.541944 0.312892i
\(426\) 0 0
\(427\) 8.42959 2.25870i 0.407937 0.109306i
\(428\) 0 0
\(429\) −11.6328 + 34.9535i −0.561638 + 1.68757i
\(430\) 0 0
\(431\) −13.0403 + 3.49414i −0.628129 + 0.168307i −0.558820 0.829289i \(-0.688746\pi\)
−0.0693083 + 0.997595i \(0.522079\pi\)
\(432\) 0 0
\(433\) −7.21603 + 4.16618i −0.346781 + 0.200214i −0.663266 0.748383i \(-0.730830\pi\)
0.316486 + 0.948597i \(0.397497\pi\)
\(434\) 0 0
\(435\) 24.0798 39.1801i 1.15454 1.87854i
\(436\) 0 0
\(437\) 7.51713 7.51713i 0.359593 0.359593i
\(438\) 0 0
\(439\) −18.5522 10.7111i −0.885447 0.511213i −0.0129962 0.999916i \(-0.504137\pi\)
−0.872450 + 0.488703i \(0.837470\pi\)
\(440\) 0 0
\(441\) −8.77936 + 13.4423i −0.418065 + 0.640108i
\(442\) 0 0
\(443\) 11.8889i 0.564859i −0.959288 0.282430i \(-0.908860\pi\)
0.959288 0.282430i \(-0.0911404\pi\)
\(444\) 0 0
\(445\) 11.3603 19.6766i 0.538529 0.932759i
\(446\) 0 0
\(447\) −20.3879 + 11.0354i −0.964315 + 0.521956i
\(448\) 0 0
\(449\) 28.5028 + 7.63730i 1.34513 + 0.360427i 0.858335 0.513089i \(-0.171499\pi\)
0.486795 + 0.873516i \(0.338166\pi\)
\(450\) 0 0
\(451\) −3.00827 5.21048i −0.141654 0.245352i
\(452\) 0 0
\(453\) 0.590920 21.4969i 0.0277638 1.01001i
\(454\) 0 0
\(455\) −11.2995 + 10.5986i −0.529729 + 0.496870i
\(456\) 0 0
\(457\) 0.778148 + 2.90409i 0.0364002 + 0.135848i 0.981735 0.190255i \(-0.0609313\pi\)
−0.945335 + 0.326102i \(0.894265\pi\)
\(458\) 0 0
\(459\) −10.1758 3.64822i −0.474965 0.170284i
\(460\) 0 0
\(461\) 6.56519 24.5016i 0.305771 1.14115i −0.626508 0.779415i \(-0.715516\pi\)
0.932279 0.361739i \(-0.117817\pi\)
\(462\) 0 0
\(463\) −24.1905 24.1905i −1.12423 1.12423i −0.991098 0.133132i \(-0.957497\pi\)
−0.133132 0.991098i \(-0.542503\pi\)
\(464\) 0 0
\(465\) 8.03420 + 8.48838i 0.372577 + 0.393639i
\(466\) 0 0
\(467\) −33.4165 −1.54633 −0.773166 0.634204i \(-0.781328\pi\)
−0.773166 + 0.634204i \(0.781328\pi\)
\(468\) 0 0
\(469\) 11.0355 0.509572
\(470\) 0 0
\(471\) −3.90185 4.12243i −0.179788 0.189952i
\(472\) 0 0
\(473\) 41.8065 + 41.8065i 1.92226 + 1.92226i
\(474\) 0 0
\(475\) 2.23708 8.34889i 0.102644 0.383073i
\(476\) 0 0
\(477\) 21.2186 + 1.16742i 0.971534 + 0.0534527i
\(478\) 0 0
\(479\) 4.90851 + 18.3188i 0.224275 + 0.837007i 0.982693 + 0.185239i \(0.0593059\pi\)
−0.758418 + 0.651768i \(0.774027\pi\)
\(480\) 0 0
\(481\) −14.1100 + 7.55516i −0.643361 + 0.344486i
\(482\) 0 0
\(483\) 0.466033 16.9537i 0.0212052 0.771418i
\(484\) 0 0
\(485\) −10.2061 17.6775i −0.463437 0.802696i
\(486\) 0 0
\(487\) 1.74563 + 0.467740i 0.0791021 + 0.0211953i 0.298153 0.954518i \(-0.403629\pi\)
−0.219051 + 0.975713i \(0.570296\pi\)
\(488\) 0 0
\(489\) −6.90633 + 3.73820i −0.312315 + 0.169047i
\(490\) 0 0
\(491\) −6.52793 + 11.3067i −0.294601 + 0.510265i −0.974892 0.222678i \(-0.928520\pi\)
0.680291 + 0.732942i \(0.261854\pi\)
\(492\) 0 0
\(493\) 16.5043i 0.743317i
\(494\) 0 0
\(495\) −49.5880 32.3867i −2.22882 1.45567i
\(496\) 0 0
\(497\) −5.22354 3.01581i −0.234308 0.135278i
\(498\) 0 0
\(499\) 10.7768 10.7768i 0.482436 0.482436i −0.423473 0.905909i \(-0.639189\pi\)
0.905909 + 0.423473i \(0.139189\pi\)
\(500\) 0 0
\(501\) −7.59804 + 12.3627i −0.339455 + 0.552326i
\(502\) 0 0
\(503\) 37.3942 21.5895i 1.66732 0.962630i 0.698251 0.715853i \(-0.253962\pi\)
0.969072 0.246777i \(-0.0793714\pi\)
\(504\) 0 0
\(505\) −35.0801 + 9.39968i −1.56104 + 0.418280i
\(506\) 0 0
\(507\) −21.1261 7.79016i −0.938244 0.345973i
\(508\) 0 0
\(509\) −10.6268 + 2.84743i −0.471023 + 0.126210i −0.486520 0.873670i \(-0.661734\pi\)
0.0154964 + 0.999880i \(0.495067\pi\)
\(510\) 0 0
\(511\) −15.1259 + 8.73297i −0.669132 + 0.386324i
\(512\) 0 0
\(513\) −6.54916 + 3.09245i −0.289152 + 0.136535i
\(514\) 0 0
\(515\) 13.0920 13.0920i 0.576901 0.576901i
\(516\) 0 0
\(517\) −18.7375 10.8181i −0.824076 0.475781i
\(518\) 0 0
\(519\) 7.30989 24.5603i 0.320868 1.07808i
\(520\) 0 0
\(521\) 6.17222i 0.270410i −0.990818 0.135205i \(-0.956831\pi\)
0.990818 0.135205i \(-0.0431692\pi\)
\(522\) 0 0
\(523\) 0.876655 1.51841i 0.0383334 0.0663954i −0.846222 0.532830i \(-0.821128\pi\)
0.884556 + 0.466435i \(0.154462\pi\)
\(524\) 0 0
\(525\) −6.56395 12.1269i −0.286474 0.529262i
\(526\) 0 0
\(527\) 4.05156 + 1.08561i 0.176489 + 0.0472900i
\(528\) 0 0
\(529\) −17.5859 30.4597i −0.764606 1.32434i
\(530\) 0 0
\(531\) 1.43346 4.37296i 0.0622068 0.189770i
\(532\) 0 0
\(533\) 3.24199 1.73591i 0.140426 0.0751907i
\(534\) 0 0
\(535\) 4.21877 + 15.7446i 0.182393 + 0.680701i
\(536\) 0 0
\(537\) −1.00921 + 0.240901i −0.0435506 + 0.0103956i
\(538\) 0 0
\(539\) −8.17074 + 30.4936i −0.351939 + 1.31345i
\(540\) 0 0
\(541\) 13.8540 + 13.8540i 0.595630 + 0.595630i 0.939147 0.343517i \(-0.111618\pi\)
−0.343517 + 0.939147i \(0.611618\pi\)
\(542\) 0 0
\(543\) 21.1404 20.0092i 0.907221 0.858679i
\(544\) 0 0
\(545\) 6.30777 0.270195
\(546\) 0 0
\(547\) 13.1018 0.560192 0.280096 0.959972i \(-0.409634\pi\)
0.280096 + 0.959972i \(0.409634\pi\)
\(548\) 0 0
\(549\) −18.1940 + 9.21073i −0.776502 + 0.393104i
\(550\) 0 0
\(551\) −7.81896 7.81896i −0.333099 0.333099i
\(552\) 0 0
\(553\) 3.89673 14.5428i 0.165706 0.618423i
\(554\) 0 0
\(555\) −5.97463 25.0296i −0.253609 1.06245i
\(556\) 0 0
\(557\) 3.48270 + 12.9976i 0.147567 + 0.550726i 0.999628 + 0.0272837i \(0.00868574\pi\)
−0.852061 + 0.523442i \(0.824648\pi\)
\(558\) 0 0
\(559\) −26.3577 + 24.7227i −1.11481 + 1.04566i
\(560\) 0 0
\(561\) −21.2476 0.584067i −0.897073 0.0246593i
\(562\) 0 0
\(563\) 1.92896 + 3.34105i 0.0812959 + 0.140809i 0.903807 0.427941i \(-0.140761\pi\)
−0.822511 + 0.568749i \(0.807427\pi\)
\(564\) 0 0
\(565\) 31.4653 + 8.43111i 1.32376 + 0.354699i
\(566\) 0 0
\(567\) −4.19689 + 10.7654i −0.176253 + 0.452104i
\(568\) 0 0
\(569\) 21.1796 36.6841i 0.887895 1.53788i 0.0455351 0.998963i \(-0.485501\pi\)
0.842360 0.538916i \(-0.181166\pi\)
\(570\) 0 0
\(571\) 17.5465i 0.734300i 0.930162 + 0.367150i \(0.119666\pi\)
−0.930162 + 0.367150i \(0.880334\pi\)
\(572\) 0 0
\(573\) −8.03362 2.39105i −0.335609 0.0998874i
\(574\) 0 0
\(575\) −40.9602 23.6484i −1.70816 0.986205i
\(576\) 0 0
\(577\) −7.37810 + 7.37810i −0.307154 + 0.307154i −0.843805 0.536650i \(-0.819689\pi\)
0.536650 + 0.843805i \(0.319689\pi\)
\(578\) 0 0
\(579\) −12.9426 7.95444i −0.537877 0.330575i
\(580\) 0 0
\(581\) 0.638956 0.368901i 0.0265084 0.0153046i
\(582\) 0 0
\(583\) 40.3612 10.8148i 1.67159 0.447902i
\(584\) 0 0
\(585\) 20.7552 29.6608i 0.858121 1.22632i
\(586\) 0 0
\(587\) 31.4131 8.41711i 1.29656 0.347411i 0.456410 0.889770i \(-0.349135\pi\)
0.840147 + 0.542358i \(0.182468\pi\)
\(588\) 0 0
\(589\) 2.43375 1.40512i 0.100281 0.0578971i
\(590\) 0 0
\(591\) 30.3368 + 18.6448i 1.24789 + 0.766944i
\(592\) 0 0
\(593\) 2.50934 2.50934i 0.103046 0.103046i −0.653704 0.756750i \(-0.726786\pi\)
0.756750 + 0.653704i \(0.226786\pi\)
\(594\) 0 0
\(595\) −7.74135 4.46947i −0.317365 0.183231i
\(596\) 0 0
\(597\) 2.48366 + 0.739212i 0.101649 + 0.0302539i
\(598\) 0 0
\(599\) 25.2005i 1.02967i 0.857291 + 0.514833i \(0.172146\pi\)
−0.857291 + 0.514833i \(0.827854\pi\)
\(600\) 0 0
\(601\) 10.3583 17.9411i 0.422525 0.731834i −0.573661 0.819093i \(-0.694477\pi\)
0.996186 + 0.0872588i \(0.0278107\pi\)
\(602\) 0 0
\(603\) −25.2375 + 5.29575i −1.02775 + 0.215660i
\(604\) 0 0
\(605\) −76.9292 20.6131i −3.12762 0.838042i
\(606\) 0 0
\(607\) 2.69471 + 4.66737i 0.109375 + 0.189443i 0.915517 0.402279i \(-0.131782\pi\)
−0.806142 + 0.591722i \(0.798448\pi\)
\(608\) 0 0
\(609\) −17.6344 0.484746i −0.714582 0.0196429i
\(610\) 0 0
\(611\) 6.97536 11.2355i 0.282193 0.454540i
\(612\) 0 0
\(613\) 4.44016 + 16.5709i 0.179336 + 0.669292i 0.995772 + 0.0918561i \(0.0292800\pi\)
−0.816436 + 0.577436i \(0.804053\pi\)
\(614\) 0 0
\(615\) 1.37276 + 5.75093i 0.0553550 + 0.231900i
\(616\) 0 0
\(617\) 3.71774 13.8748i 0.149671 0.558579i −0.849832 0.527053i \(-0.823297\pi\)
0.999503 0.0315255i \(-0.0100365\pi\)
\(618\) 0 0
\(619\) 26.5212 + 26.5212i 1.06598 + 1.06598i 0.997664 + 0.0683140i \(0.0217620\pi\)
0.0683140 + 0.997664i \(0.478238\pi\)
\(620\) 0 0
\(621\) 7.07000 + 38.9956i 0.283709 + 1.56484i
\(622\) 0 0
\(623\) −8.71560 −0.349183
\(624\) 0 0
\(625\) 17.5512 0.702050
\(626\) 0 0
\(627\) −10.3428 + 9.78938i −0.413051 + 0.390950i
\(628\) 0 0
\(629\) −6.53016 6.53016i −0.260375 0.260375i
\(630\) 0 0
\(631\) 3.01788 11.2629i 0.120140 0.448369i −0.879480 0.475936i \(-0.842109\pi\)
0.999620 + 0.0275672i \(0.00877604\pi\)
\(632\) 0 0
\(633\) −26.0987 + 6.22982i −1.03733 + 0.247613i
\(634\) 0 0
\(635\) −3.90321 14.5670i −0.154894 0.578073i
\(636\) 0 0
\(637\) −18.4692 5.58791i −0.731778 0.221401i
\(638\) 0 0
\(639\) 13.3932 + 4.39028i 0.529825 + 0.173677i
\(640\) 0 0
\(641\) 12.6100 + 21.8411i 0.498063 + 0.862671i 0.999998 0.00223486i \(-0.000711379\pi\)
−0.501934 + 0.864906i \(0.667378\pi\)
\(642\) 0 0
\(643\) −39.7951 10.6631i −1.56937 0.420511i −0.633753 0.773535i \(-0.718486\pi\)
−0.935614 + 0.353025i \(0.885153\pi\)
\(644\) 0 0
\(645\) −27.6569 51.0961i −1.08899 2.01191i
\(646\) 0 0
\(647\) 2.88978 5.00524i 0.113609 0.196776i −0.803614 0.595151i \(-0.797092\pi\)
0.917223 + 0.398375i \(0.130426\pi\)
\(648\) 0 0
\(649\) 9.04868i 0.355192i
\(650\) 0 0
\(651\) 1.27894 4.29709i 0.0501257 0.168416i
\(652\) 0 0
\(653\) 5.36540 + 3.09771i 0.209964 + 0.121223i 0.601295 0.799027i \(-0.294652\pi\)
−0.391330 + 0.920250i \(0.627985\pi\)
\(654\) 0 0
\(655\) 14.7820 14.7820i 0.577582 0.577582i
\(656\) 0 0
\(657\) 30.4013 27.2304i 1.18607 1.06236i
\(658\) 0 0
\(659\) −17.8116 + 10.2836i −0.693843 + 0.400590i −0.805050 0.593207i \(-0.797862\pi\)
0.111207 + 0.993797i \(0.464528\pi\)
\(660\) 0 0
\(661\) −41.1745 + 11.0327i −1.60150 + 0.429121i −0.945496 0.325634i \(-0.894422\pi\)
−0.656007 + 0.754755i \(0.727756\pi\)
\(662\) 0 0
\(663\) 0.772297 12.9690i 0.0299935 0.503676i
\(664\) 0 0
\(665\) −5.78491 + 1.55006i −0.224329 + 0.0601088i
\(666\) 0 0
\(667\) −52.4012 + 30.2538i −2.02898 + 1.17143i
\(668\) 0 0
\(669\) 17.0410 27.7272i 0.658842 1.07200i
\(670\) 0 0
\(671\) −28.3535 + 28.3535i −1.09457 + 1.09457i
\(672\) 0 0
\(673\) 27.9181 + 16.1185i 1.07616 + 0.621323i 0.929859 0.367917i \(-0.119929\pi\)
0.146304 + 0.989240i \(0.453262\pi\)
\(674\) 0 0
\(675\) 20.8309 + 24.5836i 0.801780 + 0.946222i
\(676\) 0 0
\(677\) 37.6671i 1.44766i −0.689977 0.723831i \(-0.742379\pi\)
0.689977 0.723831i \(-0.257621\pi\)
\(678\) 0 0
\(679\) −3.91507 + 6.78110i −0.150247 + 0.260235i
\(680\) 0 0
\(681\) 1.61111 0.872045i 0.0617377 0.0334168i
\(682\) 0 0
\(683\) 44.1988 + 11.8430i 1.69122 + 0.453161i 0.970705 0.240276i \(-0.0772381\pi\)
0.720517 + 0.693438i \(0.243905\pi\)
\(684\) 0 0
\(685\) −38.5473 66.7659i −1.47282 2.55100i
\(686\) 0 0
\(687\) 0.402166 14.6303i 0.0153436 0.558180i
\(688\) 0 0
\(689\) 5.81766 + 24.8688i 0.221635 + 0.947424i
\(690\) 0 0
\(691\) 7.42504 + 27.7106i 0.282462 + 1.05416i 0.950674 + 0.310191i \(0.100393\pi\)
−0.668212 + 0.743971i \(0.732940\pi\)
\(692\) 0 0
\(693\) −1.24812 + 22.6853i −0.0474120 + 0.861742i
\(694\) 0 0
\(695\) 16.5753 61.8598i 0.628736 2.34648i
\(696\) 0 0
\(697\) 1.50040 + 1.50040i 0.0568318 + 0.0568318i
\(698\) 0 0
\(699\) 2.74364 + 2.89874i 0.103774 + 0.109641i
\(700\) 0 0
\(701\) −8.75126 −0.330531 −0.165265 0.986249i \(-0.552848\pi\)
−0.165265 + 0.986249i \(0.552848\pi\)
\(702\) 0 0
\(703\) −6.18736 −0.233361
\(704\) 0 0
\(705\) 14.6158 + 15.4420i 0.550462 + 0.581580i
\(706\) 0 0
\(707\) 9.85100 + 9.85100i 0.370485 + 0.370485i
\(708\) 0 0
\(709\) −6.73251 + 25.1261i −0.252845 + 0.943629i 0.716432 + 0.697657i \(0.245774\pi\)
−0.969277 + 0.245972i \(0.920893\pi\)
\(710\) 0 0
\(711\) −1.93273 + 35.1285i −0.0724829 + 1.31742i
\(712\) 0 0
\(713\) −3.98004 14.8537i −0.149054 0.556275i
\(714\) 0 0
\(715\) 20.6136 68.1323i 0.770904 2.54800i
\(716\) 0 0
\(717\) −0.000886156 0.0322372i −3.30941e−5 0.00120392i
\(718\) 0 0
\(719\) −17.9675 31.1206i −0.670075 1.16060i −0.977882 0.209155i \(-0.932929\pi\)
0.307807 0.951449i \(-0.400405\pi\)
\(720\) 0 0
\(721\) −6.86028 1.83821i −0.255490 0.0684584i
\(722\) 0 0
\(723\) −25.6057 + 13.8597i −0.952288 + 0.515446i
\(724\) 0 0
\(725\) −24.5979 + 42.6048i −0.913544 + 1.58230i
\(726\) 0 0
\(727\) 29.2791i 1.08590i 0.839764 + 0.542951i \(0.182693\pi\)
−0.839764 + 0.542951i \(0.817307\pi\)
\(728\) 0 0
\(729\) 4.43189 26.6338i 0.164144 0.986436i
\(730\) 0 0
\(731\) −18.0578 10.4257i −0.667892 0.385608i
\(732\) 0 0
\(733\) 0.720934 0.720934i 0.0266283 0.0266283i −0.693667 0.720296i \(-0.744006\pi\)
0.720296 + 0.693667i \(0.244006\pi\)
\(734\) 0 0
\(735\) 16.2441 26.4307i 0.599172 0.974910i
\(736\) 0 0
\(737\) −43.9118 + 25.3525i −1.61751 + 0.933870i
\(738\) 0 0
\(739\) −24.3751 + 6.53128i −0.896652 + 0.240257i −0.677578 0.735451i \(-0.736970\pi\)
−0.219074 + 0.975708i \(0.570304\pi\)
\(740\) 0 0
\(741\) −5.77823 6.50999i −0.212269 0.239150i
\(742\) 0 0
\(743\) −2.74994 + 0.736843i −0.100885 + 0.0270321i −0.308909 0.951092i \(-0.599964\pi\)
0.208023 + 0.978124i \(0.433297\pi\)
\(744\) 0 0
\(745\) 38.7944 22.3980i 1.42132 0.820598i
\(746\) 0 0
\(747\) −1.28422 + 1.15028i −0.0469872 + 0.0420865i
\(748\) 0 0
\(749\) 4.42133 4.42133i 0.161552 0.161552i
\(750\) 0 0
\(751\) 39.7116 + 22.9275i 1.44910 + 0.836636i 0.998428 0.0560550i \(-0.0178522\pi\)
0.450669 + 0.892691i \(0.351186\pi\)
\(752\) 0 0
\(753\) 6.80257 22.8558i 0.247899 0.832911i
\(754\) 0 0
\(755\) 41.5538i 1.51230i
\(756\) 0 0
\(757\) −9.99976 + 17.3201i −0.363448 + 0.629510i −0.988526 0.151052i \(-0.951734\pi\)
0.625078 + 0.780562i \(0.285067\pi\)
\(758\) 0 0
\(759\) 37.0942 + 68.5316i 1.34643 + 2.48754i
\(760\) 0 0
\(761\) 12.2935 + 3.29404i 0.445640 + 0.119409i 0.474659 0.880170i \(-0.342571\pi\)
−0.0290184 + 0.999579i \(0.509238\pi\)
\(762\) 0 0
\(763\) −1.20983 2.09549i −0.0437988 0.0758617i
\(764\) 0 0
\(765\) 19.8488 + 6.50645i 0.717635 + 0.235241i
\(766\) 0 0
\(767\) 5.52798 + 0.176941i 0.199604 + 0.00638897i
\(768\) 0 0
\(769\) 5.98953 + 22.3532i 0.215988 + 0.806078i 0.985816 + 0.167827i \(0.0536751\pi\)
−0.769828 + 0.638251i \(0.779658\pi\)
\(770\) 0 0
\(771\) −19.6213 + 4.68365i −0.706643 + 0.168677i
\(772\) 0 0
\(773\) 6.75254 25.2008i 0.242872 0.906410i −0.731569 0.681767i \(-0.761212\pi\)
0.974441 0.224643i \(-0.0721216\pi\)
\(774\) 0 0
\(775\) −8.84085 8.84085i −0.317573 0.317573i
\(776\) 0 0
\(777\) −7.16909 + 6.78549i −0.257190 + 0.243428i
\(778\) 0 0
\(779\) 1.42164 0.0509355
\(780\) 0 0
\(781\) 27.7136 0.991670
\(782\) 0 0
\(783\) 40.5614 7.35388i 1.44955 0.262806i
\(784\) 0 0
\(785\) 7.75553 + 7.75553i 0.276807 + 0.276807i
\(786\) 0 0
\(787\) 3.78032 14.1083i 0.134754 0.502908i −0.865245 0.501349i \(-0.832837\pi\)
0.999999 0.00155884i \(-0.000496195\pi\)
\(788\) 0 0
\(789\) −9.88557 41.4138i −0.351936 1.47437i
\(790\) 0 0
\(791\) −3.23417 12.0701i −0.114994 0.429163i
\(792\) 0 0
\(793\) −16.7671 17.8760i −0.595418 0.634795i
\(794\) 0 0
\(795\) −41.0469 1.12832i −1.45578 0.0400175i
\(796\) 0 0
\(797\) 0.895558 +