Properties

Label 624.2.cn.f.305.14
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 305.14
Character \(\chi\) \(=\) 624.305
Dual form 624.2.cn.f.401.14

$q$-expansion

\(f(q)\) \(=\) \(q+(1.68472 + 0.402146i) q^{3} +(-2.36656 - 2.36656i) q^{5} +(0.332282 - 1.24009i) q^{7} +(2.67656 + 1.35501i) q^{9} +O(q^{10})\) \(q+(1.68472 + 0.402146i) q^{3} +(-2.36656 - 2.36656i) q^{5} +(0.332282 - 1.24009i) q^{7} +(2.67656 + 1.35501i) q^{9} +(-1.52674 - 5.69787i) q^{11} +(-3.51077 + 0.821290i) q^{13} +(-3.03528 - 4.93869i) q^{15} +(1.04019 + 1.80167i) q^{17} +(-1.34634 - 0.360750i) q^{19} +(1.05850 - 1.95558i) q^{21} +(3.81352 - 6.60522i) q^{23} +6.20118i q^{25} +(3.96433 + 3.35917i) q^{27} +(-6.87044 - 3.96665i) q^{29} +(-1.42567 + 1.42567i) q^{31} +(-0.280749 - 10.2133i) q^{33} +(-3.72111 + 2.14839i) q^{35} +(4.28784 - 1.14892i) q^{37} +(-6.24493 - 0.0281999i) q^{39} +(0.985195 - 0.263982i) q^{41} +(8.68002 - 5.01141i) q^{43} +(-3.12752 - 9.54093i) q^{45} +(2.59357 - 2.59357i) q^{47} +(4.63476 + 2.67588i) q^{49} +(1.02790 + 3.45361i) q^{51} +7.08357i q^{53} +(-9.87121 + 17.0974i) q^{55} +(-2.12313 - 1.14919i) q^{57} +(1.48170 + 0.397021i) q^{59} +(3.39878 + 5.88685i) q^{61} +(2.56971 - 2.86893i) q^{63} +(10.2521 + 6.36480i) q^{65} +(2.22473 + 8.30282i) q^{67} +(9.08098 - 9.59434i) q^{69} +(-1.21596 + 4.53804i) q^{71} +(-9.61981 - 9.61981i) q^{73} +(-2.49378 + 10.4473i) q^{75} -7.57319 q^{77} +11.7272 q^{79} +(5.32791 + 7.25351i) q^{81} +(-0.406364 - 0.406364i) q^{83} +(1.80207 - 6.72543i) q^{85} +(-9.97958 - 9.44561i) q^{87} +(1.75705 + 6.55739i) q^{89} +(-0.148089 + 4.62658i) q^{91} +(-2.97518 + 1.82853i) q^{93} +(2.33245 + 4.03992i) q^{95} +(-5.89119 - 1.57854i) q^{97} +(3.63425 - 17.3194i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 4q^{7} + O(q^{10}) \) \( 56q - 4q^{7} + 8q^{13} + 8q^{15} - 4q^{19} + 16q^{21} - 24q^{27} + 36q^{31} + 28q^{33} + 20q^{37} - 16q^{39} + 84q^{43} + 12q^{45} - 12q^{49} + 24q^{55} - 36q^{57} - 24q^{61} + 12q^{63} + 32q^{67} - 36q^{69} - 20q^{73} + 60q^{75} + 32q^{79} - 88q^{85} + 16q^{87} - 28q^{91} - 88q^{93} - 36q^{97} - 44q^{99} + O(q^{100}) \)

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
\(3\) 1.68472 + 0.402146i 0.972673 + 0.232179i
\(4\) 0 0
\(5\) −2.36656 2.36656i −1.05836 1.05836i −0.998188 0.0601682i \(-0.980836\pi\)
−0.0601682 0.998188i \(-0.519164\pi\)
\(6\) 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
\(9\) 2.67656 + 1.35501i 0.892185 + 0.451669i
\(10\) 0 0
\(11\) −1.52674 5.69787i −0.460329 1.71797i −0.671929 0.740615i \(-0.734534\pi\)
0.211600 0.977356i \(-0.432133\pi\)
\(12\) 0 0
\(13\) −3.51077 + 0.821290i −0.973712 + 0.227785i
\(14\) 0 0
\(15\) −3.03528 4.93869i −0.783706 1.27516i
\(16\) 0 0
\(17\) 1.04019 + 1.80167i 0.252284 + 0.436969i 0.964154 0.265342i \(-0.0854850\pi\)
−0.711870 + 0.702311i \(0.752152\pi\)
\(18\) 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
\(21\) 1.05850 1.95558i 0.230984 0.426743i
\(22\) 0 0
\(23\) 3.81352 6.60522i 0.795175 1.37728i −0.127553 0.991832i \(-0.540712\pi\)
0.922728 0.385452i \(-0.125954\pi\)
\(24\) 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 −0.299733 0.954023i \(-0.596898\pi\)
−0.976075 + 0.217435i \(0.930231\pi\)
\(30\) 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
\(33\) −0.280749 10.2133i −0.0488721 1.77790i
\(34\) 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
\(39\) −6.24493 0.0281999i −0.999990 0.00451560i
\(40\) 0 0
\(41\) 0.985195 0.263982i 0.153862 0.0412271i −0.181066 0.983471i \(-0.557955\pi\)
0.334928 + 0.942244i \(0.391288\pi\)
\(42\) 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
\(45\) −3.12752 9.54093i −0.466223 1.42228i
\(46\) 0 0
\(47\) 2.59357 2.59357i 0.378312 0.378312i −0.492181 0.870493i \(-0.663800\pi\)
0.870493 + 0.492181i \(0.163800\pi\)
\(48\) 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 \(0.161727\pi\)
−0.873680 + 0.486501i \(0.838273\pi\)
\(54\) 0 0
\(55\) −9.87121 + 17.0974i −1.33103 + 2.30542i
\(56\) 0 0
\(57\) −2.12313 1.14919i −0.281215 0.152214i
\(58\) 0 0
\(59\) 1.48170 + 0.397021i 0.192901 + 0.0516877i 0.353976 0.935254i \(-0.384829\pi\)
−0.161075 + 0.986942i \(0.551496\pi\)
\(60\) 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
\(63\) 2.56971 2.86893i 0.323752 0.361452i
\(64\) 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
\(69\) 9.08098 9.59434i 1.09322 1.15502i
\(70\) 0 0
\(71\) −1.21596 + 4.53804i −0.144308 + 0.538566i 0.855477 + 0.517841i \(0.173264\pi\)
−0.999785 + 0.0207249i \(0.993403\pi\)
\(72\) 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
\(75\) −2.49378 + 10.4473i −0.287957 + 1.20634i
\(76\) 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
\(81\) 5.32791 + 7.25351i 0.591990 + 0.805945i
\(82\) 0 0
\(83\) −0.406364 0.406364i −0.0446042 0.0446042i 0.684453 0.729057i \(-0.260041\pi\)
−0.729057 + 0.684453i \(0.760041\pi\)
\(84\) 0 0
\(85\) 1.80207 6.72543i 0.195462 0.729475i
\(86\) 0 0
\(87\) −9.97958 9.44561i −1.06992 1.01268i
\(88\) 0 0
\(89\) 1.75705 + 6.55739i 0.186247 + 0.695081i 0.994360 + 0.106055i \(0.0338220\pi\)
−0.808114 + 0.589026i \(0.799511\pi\)
\(90\) 0 0
\(91\) −0.148089 + 4.62658i −0.0155239 + 0.484997i
\(92\) 0 0
\(93\) −2.97518 + 1.82853i −0.308512 + 0.189609i
\(94\) 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
\(99\) 3.63425 17.3194i 0.365256 1.74067i
\(100\) 0 0
\(101\) 5.42569 9.39757i 0.539876 0.935093i −0.459034 0.888419i \(-0.651804\pi\)
0.998910 0.0466743i \(-0.0148623\pi\)
\(102\) 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 0.282071 0.959393i \(-0.408978\pi\)
−0.689823 + 0.723978i \(0.742312\pi\)
\(108\) 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
\(111\) 7.68584 0.211273i 0.729508 0.0200532i
\(112\) 0 0
\(113\) −8.42921 + 4.86661i −0.792954 + 0.457812i −0.841001 0.541033i \(-0.818033\pi\)
0.0480476 + 0.998845i \(0.484700\pi\)
\(114\) 0 0
\(115\) −24.6565 + 6.60670i −2.29924 + 0.616078i
\(116\) 0 0
\(117\) −10.5096 2.55889i −0.971615 0.236569i
\(118\) 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
\(123\) 1.76594 0.0485432i 0.159229 0.00437699i
\(124\) 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 \(0.0879721\pi\)
−0.962052 + 0.272867i \(0.912028\pi\)
\(132\) 0 0
\(133\) −0.894727 + 1.54971i −0.0775827 + 0.134377i
\(134\) 0 0
\(135\) −1.43214 17.3315i −0.123259 1.49166i
\(136\) 0 0
\(137\) 22.2503 + 5.96195i 1.90097 + 0.509364i 0.996577 + 0.0826685i \(0.0263443\pi\)
0.904395 + 0.426696i \(0.140322\pi\)
\(138\) 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
\(141\) 5.41244 3.32645i 0.455810 0.280137i
\(142\) 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
\(147\) 6.73217 + 6.37196i 0.555260 + 0.525550i
\(148\) 0 0
\(149\) −3.46420 + 12.9286i −0.283798 + 1.05915i 0.665915 + 0.746028i \(0.268042\pi\)
−0.949713 + 0.313122i \(0.898625\pi\)
\(150\) 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
\(153\) 0.342863 + 6.23173i 0.0277188 + 0.503806i
\(154\) 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
\(159\) −2.84863 + 11.9338i −0.225911 + 0.946414i
\(160\) 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
\(165\) −23.5059 + 24.8347i −1.82993 + 1.93338i
\(166\) 0 0
\(167\) 2.16836 + 8.09242i 0.167793 + 0.626210i 0.997668 + 0.0682609i \(0.0217450\pi\)
−0.829875 + 0.557949i \(0.811588\pi\)
\(168\) 0 0
\(169\) 11.6510 5.76671i 0.896228 0.443593i
\(170\) 0 0
\(171\) −3.11473 2.78987i −0.238189 0.213346i
\(172\) 0 0
\(173\) −7.39731 12.8125i −0.562407 0.974118i −0.997286 0.0736289i \(-0.976542\pi\)
0.434878 0.900489i \(-0.356791\pi\)
\(174\) 0 0
\(175\) 7.69004 + 2.06054i 0.581312 + 0.155762i
\(176\) 0 0
\(177\) 2.33659 + 1.26473i 0.175629 + 0.0950629i
\(178\) 0 0
\(179\) −0.299519 + 0.518782i −0.0223871 + 0.0387756i −0.877002 0.480487i \(-0.840460\pi\)
0.854615 + 0.519262i \(0.173793\pi\)
\(180\) 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
\(189\) 5.48296 3.79995i 0.398827 0.276406i
\(190\) 0 0
\(191\) −4.19095 + 2.41964i −0.303246 + 0.175079i −0.643900 0.765109i \(-0.722685\pi\)
0.340654 + 0.940189i \(0.389352\pi\)
\(192\) 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
\(195\) 14.7123 + 14.8457i 1.05357 + 1.06312i
\(196\) 0 0
\(197\) 19.8579 5.32092i 1.41482 0.379100i 0.531176 0.847261i \(-0.321750\pi\)
0.883643 + 0.468162i \(0.155084\pi\)
\(198\) 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
\(201\) 0.409102 + 14.8826i 0.0288558 + 1.04974i
\(202\) 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
\(213\) −3.87351 + 7.15632i −0.265409 + 0.490343i
\(214\) 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
\(219\) −12.3381 20.0752i −0.833732 1.35656i
\(220\) 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
\(225\) −8.40265 + 16.5978i −0.560177 + 1.10652i
\(226\) 0 0
\(227\) 0.273750 1.02165i 0.0181694 0.0678093i −0.956246 0.292564i \(-0.905491\pi\)
0.974415 + 0.224755i \(0.0721581\pi\)
\(228\) 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
\(231\) −12.7587 3.04553i −0.839461 0.200381i
\(232\) 0 0
\(233\) 2.30436 0.150964 0.0754820 0.997147i \(-0.475950\pi\)
0.0754820 + 0.997147i \(0.475950\pi\)
\(234\) 0 0
\(235\) −12.2757 −0.800777
\(236\) 0 0
\(237\) 19.7570 + 4.71605i 1.28336 + 0.306340i
\(238\) 0 0
\(239\) 0.0131657 + 0.0131657i 0.000851621 + 0.000851621i 0.707532 0.706681i \(-0.249808\pi\)
−0.706681 + 0.707532i \(0.749808\pi\)
\(240\) 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
\(243\) 6.05906 + 14.3627i 0.388689 + 0.921369i
\(244\) 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
\(249\) −0.521191 0.848026i −0.0330291 0.0537415i
\(250\) 0 0
\(251\) −6.88393 11.9233i −0.434510 0.752593i 0.562746 0.826630i \(-0.309745\pi\)
−0.997255 + 0.0740371i \(0.976412\pi\)
\(252\) 0 0
\(253\) −43.4579 11.6445i −2.73218 0.732084i
\(254\) 0 0
\(255\) 5.74059 10.6058i 0.359490 0.664158i
\(256\) 0 0
\(257\) −5.82331 + 10.0863i −0.363248 + 0.629164i −0.988493 0.151264i \(-0.951666\pi\)
0.625245 + 0.780428i \(0.284999\pi\)
\(258\) 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 −0.330170 0.943922i \(-0.607106\pi\)
−0.982545 + 0.186025i \(0.940439\pi\)
\(264\) 0 0
\(265\) 16.7637 16.7637i 1.02978 1.02978i
\(266\) 0 0
\(267\) 0.323100 + 11.7539i 0.0197734 + 0.719330i
\(268\) 0 0
\(269\) −1.83996 + 1.06230i −0.112184 + 0.0647697i −0.555042 0.831822i \(-0.687298\pi\)
0.442858 + 0.896592i \(0.353965\pi\)
\(270\) 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
\(273\) −2.11005 + 7.73493i −0.127706 + 0.468139i
\(274\) 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
\(279\) −5.74768 + 1.88409i −0.344105 + 0.112798i
\(280\) 0 0
\(281\) 21.9749 21.9749i 1.31091 1.31091i 0.390172 0.920742i \(-0.372415\pi\)
0.920742 0.390172i \(-0.127585\pi\)
\(282\) 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
\(291\) −9.29020 5.02852i −0.544601 0.294777i
\(292\) 0 0
\(293\) −6.05925 1.62357i −0.353985 0.0948500i 0.0774445 0.996997i \(-0.475324\pi\)
−0.431429 + 0.902147i \(0.641991\pi\)
\(294\) 0 0
\(295\) −2.56696 4.44610i −0.149454 0.258862i
\(296\) 0 0
\(297\) 13.0876 27.7168i 0.759421 1.60829i
\(298\) 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
\(303\) 12.9200 13.6503i 0.742232 0.784192i
\(304\) 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
\(309\) 2.22470 9.31999i 0.126559 0.530196i
\(310\) 0 0
\(311\) 20.8546 1.18255 0.591277 0.806469i \(-0.298624\pi\)
0.591277 + 0.806469i \(0.298624\pi\)
\(312\) 0 0
\(313\) −22.0202 −1.24465 −0.622327 0.782757i \(-0.713813\pi\)
−0.622327 + 0.782757i \(0.713813\pi\)
\(314\) 0 0
\(315\) −12.8708 + 0.708139i −0.725190 + 0.0398991i
\(316\) 0 0
\(317\) −12.4092 12.4092i −0.696968 0.696968i 0.266787 0.963755i \(-0.414038\pi\)
−0.963755 + 0.266787i \(0.914038\pi\)
\(318\) 0 0
\(319\) −12.1121 + 45.2029i −0.678146 + 2.53088i
\(320\) 0 0
\(321\) −6.12655 5.79874i −0.341951 0.323654i
\(322\) 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
\(327\) 2.78114 1.70927i 0.153798 0.0945229i
\(328\) 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
\(333\) 13.0334 + 2.73490i 0.714229 + 0.149871i
\(334\) 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
\(345\) −44.1962 + 1.21489i −2.37944 + 0.0654077i
\(346\) 0 0
\(347\) −9.61214 + 5.54957i −0.516007 + 0.297917i −0.735299 0.677742i \(-0.762958\pi\)
0.219293 + 0.975659i \(0.429625\pi\)
\(348\) 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
\(351\) −16.6767 8.53741i −0.890137 0.455693i
\(352\) 0 0
\(353\) −17.4311 + 4.67065i −0.927765 + 0.248594i −0.690901 0.722949i \(-0.742786\pi\)
−0.236863 + 0.971543i \(0.576119\pi\)
\(354\) 0 0
\(355\) 13.6172 7.86187i 0.722724 0.417265i
\(356\) 0 0
\(357\) 4.62435 0.127117i 0.244747 0.00672775i
\(358\) 0 0
\(359\) −10.6950 + 10.6950i −0.564462 + 0.564462i −0.930572 0.366110i \(-0.880689\pi\)
0.366110 + 0.930572i \(0.380689\pi\)
\(360\) 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
\(369\) 2.99463 + 0.628384i 0.155894 + 0.0327123i
\(370\) 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
\(375\) 5.93227 3.64593i 0.306341 0.188275i
\(376\) 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
\(381\) −5.66829 5.36500i −0.290396 0.274857i
\(382\) 0 0
\(383\) −1.45165 + 5.41763i −0.0741758 + 0.276828i −0.993045 0.117734i \(-0.962437\pi\)
0.918869 + 0.394562i \(0.129104\pi\)
\(384\) 0 0
\(385\) 17.9224 + 17.9224i 0.913409 + 0.913409i
\(386\) 0 0
\(387\) 30.0231 1.65183i 1.52616 0.0839675i
\(388\) 0 0
\(389\) 14.1875 0.719336 0.359668 0.933080i \(-0.382890\pi\)
0.359668 + 0.933080i \(0.382890\pi\)
\(390\) 0 0
\(391\) 15.8672 0.802439
\(392\) 0 0
\(393\) −2.51190 + 10.5231i −0.126708 + 0.530822i
\(394\) 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
\(399\) −2.13058 + 2.25102i −0.106662 + 0.112692i
\(400\) 0 0
\(401\) 2.47565 + 9.23926i 0.123628 + 0.461387i 0.999787 0.0206358i \(-0.00656905\pi\)
−0.876159 + 0.482022i \(0.839902\pi\)
\(402\) 0 0
\(403\) 3.83431 6.17609i 0.191001 0.307653i
\(404\) 0 0
\(405\) 4.55704 29.7746i 0.226441 1.47951i
\(406\) 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
\(411\) 35.0879 + 18.9921i 1.73076 + 0.936811i
\(412\) 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 0.999455 0.0330044i \(-0.0105075\pi\)
0.471145 + 0.882056i \(0.343841\pi\)
\(420\) 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
\(423\) 10.4562 3.42753i 0.508396 0.166652i
\(424\) 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
\(429\) 9.37370 + 35.6259i 0.452567 + 1.72003i
\(430\) 0 0
\(431\) 13.0403 3.49414i 0.628129 0.168307i 0.0693083 0.997595i \(-0.477921\pi\)
0.558820 + 0.829289i \(0.311254\pi\)
\(432\) 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
\(435\) 1.26368 + 45.9708i 0.0605886 + 2.20413i
\(436\) 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 \(0.0911404\pi\)
−0.959288 + 0.282430i \(0.908860\pi\)
\(444\) 0 0
\(445\) 11.3603 19.6766i 0.538529 0.932759i
\(446\) 0 0
\(447\) −11.0354 + 20.3879i −0.521956 + 0.964315i
\(448\) 0 0
\(449\) −28.5028 7.63730i −1.34513 0.360427i −0.486795 0.873516i \(-0.661834\pi\)
−0.858335 + 0.513089i \(0.828501\pi\)
\(450\) 0 0
\(451\) −3.00827 5.21048i −0.141654 0.245352i
\(452\) 0 0
\(453\) 11.2602 + 18.3214i 0.529050 + 0.860813i
\(454\) 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
\(459\) −1.92844 + 10.6366i −0.0900120 + 0.496474i
\(460\) 0 0
\(461\) −6.56519 + 24.5016i −0.305771 + 1.14115i 0.626508 + 0.779415i \(0.284484\pi\)
−0.932279 + 0.361739i \(0.882183\pi\)
\(462\) 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
\(465\) 11.3683 + 2.71363i 0.527190 + 0.125842i
\(466\) 0 0
\(467\) 33.4165 1.54633 0.773166 0.634204i \(-0.218672\pi\)
0.773166 + 0.634204i \(0.218672\pi\)
\(468\) 0 0
\(469\) 11.0355 0.509572
\(470\) 0 0
\(471\) 5.52105 + 1.31789i 0.254397 + 0.0607251i
\(472\) 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
\(477\) −9.59829 + 18.9596i −0.439475 + 0.868099i
\(478\) 0 0
\(479\) −4.90851 18.3188i −0.224275 0.837007i −0.982693 0.185239i \(-0.940694\pi\)
0.758418 0.651768i \(-0.225973\pi\)
\(480\) 0 0
\(481\) −14.1100 + 7.55516i −0.643361 + 0.344486i
\(482\) 0 0
\(483\) −8.88043 14.4493i −0.404073 0.657465i
\(484\) 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
\(489\) 3.73820 6.90633i 0.169047 0.312315i
\(490\) 0 0
\(491\) 6.52793 11.3067i 0.294601 0.510265i −0.680291 0.732942i \(-0.738146\pi\)
0.974892 + 0.222678i \(0.0714798\pi\)
\(492\) 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
\(501\) 0.398735 + 14.5055i 0.0178142 + 0.648056i
\(502\) 0 0
\(503\) −37.3942 + 21.5895i −1.66732 + 0.962630i −0.698251 + 0.715853i \(0.746038\pi\)
−0.969072 + 0.246777i \(0.920629\pi\)
\(504\) 0 0
\(505\) −35.0801 + 9.39968i −1.56104 + 0.418280i
\(506\) 0 0
\(507\) 21.9477 5.02990i 0.974730 0.223386i
\(508\) 0 0
\(509\) 10.6268 2.84743i 0.471023 0.126210i −0.0154964 0.999880i \(-0.504933\pi\)
0.486520 + 0.873670i \(0.338266\pi\)
\(510\) 0 0
\(511\) −15.1259 + 8.73297i −0.669132 + 0.386324i
\(512\) 0 0
\(513\) −4.12551 5.95272i −0.182146 0.262819i
\(514\) 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 \(0.0431692\pi\)
−0.990818 + 0.135205i \(0.956831\pi\)
\(522\) 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
\(525\) 12.1269 + 6.56395i 0.529262 + 0.286474i
\(526\) 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
\(531\) 3.42789 + 3.07036i 0.148758 + 0.133242i
\(532\) 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
\(537\) −0.713231 + 0.753551i −0.0307782 + 0.0325181i
\(538\) 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
\(543\) −6.75832 + 28.3127i −0.290027 + 1.21502i
\(544\) 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
\(549\) 1.12029 + 20.3619i 0.0478126 + 0.869023i
\(550\) 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
\(555\) −18.6890 17.6890i −0.793303 0.750856i
\(556\) 0 0
\(557\) −3.48270 12.9976i −0.147567 0.550726i −0.999628 0.0272837i \(-0.991314\pi\)
0.852061 0.523442i \(-0.175352\pi\)
\(558\) 0 0
\(559\) −26.3577 + 24.7227i −1.11481 + 1.04566i
\(560\) 0 0
\(561\) 18.1089 11.1296i 0.764558 0.469892i
\(562\) 0 0
\(563\) −1.92896 3.34105i −0.0812959 0.140809i 0.822511 0.568749i \(-0.192573\pi\)
−0.903807 + 0.427941i \(0.859239\pi\)
\(564\) 0 0
\(565\) 31.4653 + 8.43111i 1.32376 + 0.354699i
\(566\) 0 0
\(567\) 10.7654 4.19689i 0.452104 0.176253i
\(568\) 0 0
\(569\) −21.1796 + 36.6841i −0.887895 + 1.53788i −0.0455351 + 0.998963i \(0.514499\pi\)
−0.842360 + 0.538916i \(0.818834\pi\)
\(570\) 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
\(579\) 15.1859 0.417438i 0.631103 0.0173481i
\(580\) 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
\(585\) 18.8159 + 30.9274i 0.777940 + 1.27869i
\(586\) 0 0
\(587\) −31.4131 + 8.41711i −1.29656 + 0.347411i −0.840147 0.542358i \(-0.817532\pi\)
−0.456410 + 0.889770i \(0.650865\pi\)
\(588\) 0 0
\(589\) 2.43375 1.40512i 0.100281 0.0578971i
\(590\) 0 0
\(591\) 35.5948 0.978453i 1.46418 0.0402482i
\(592\) 0 0
\(593\) −2.50934 + 2.50934i −0.103046 + 0.103046i −0.756750 0.653704i \(-0.773214\pi\)
0.653704 + 0.756750i \(0.273214\pi\)
\(594\) 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 \(-0.827854\pi\)
0.857291 0.514833i \(-0.172146\pi\)
\(600\) 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
\(603\) −5.29575 + 25.2375i −0.215660 + 1.02775i
\(604\) 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
\(609\) −15.0295 + 9.23700i −0.609025 + 0.374302i
\(610\) 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
\(615\) −4.29407 4.06431i −0.173154 0.163889i
\(616\) 0 0
\(617\) −3.71774 + 13.8748i −0.149671 + 0.558579i 0.849832 + 0.527053i \(0.176703\pi\)
−0.999503 + 0.0315255i \(0.989963\pi\)
\(618\) 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
\(621\) 37.3062 13.3750i 1.49704 0.536720i
\(622\) 0 0
\(623\) 8.71560 0.349183
\(624\) 0 0
\(625\) 17.5512 0.702050
\(626\) 0 0
\(627\) −3.30646 + 13.8518i −0.132047 + 0.553188i
\(628\) 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
\(633\) 18.4445 19.4872i 0.733105 0.774548i
\(634\) 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
\(639\) −9.40367 + 10.4987i −0.372003 + 0.415321i
\(640\) 0 0
\(641\) −12.6100 21.8411i −0.498063 0.862671i 0.501934 0.864906i \(-0.332622\pi\)
−0.999998 + 0.00223486i \(0.999289\pi\)
\(642\) 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
\(645\) −51.0961 27.6569i −2.01191 1.08899i
\(646\) 0 0
\(647\) −2.88978 + 5.00524i −0.113609 + 0.196776i −0.917223 0.398375i \(-0.869574\pi\)
0.803614 + 0.595151i \(0.202908\pi\)
\(648\) 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 0.391330 0.920250i \(-0.372015\pi\)
−0.601295 + 0.799027i \(0.705348\pi\)
\(654\) 0 0
\(655\) 14.7820 14.7820i 0.577582 0.577582i
\(656\) 0 0
\(657\) −12.7130 38.7829i −0.495983 1.51306i
\(658\) 0 0
\(659\) 17.8116 10.2836i 0.693843 0.400590i −0.111207 0.993797i \(-0.535472\pi\)
0.805050 + 0.593207i \(0.202138\pi\)
\(660\) 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
\(663\) −6.44513 11.2806i −0.250308 0.438103i
\(664\) 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
\(669\) 0.894287 + 32.5330i 0.0345751 + 1.25780i
\(670\) 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 \(0.257621\pi\)
−0.689977 + 0.723831i \(0.742379\pi\)
\(678\) 0 0
\(679\) −3.91507 + 6.78110i −0.150247 + 0.260235i
\(680\) 0 0
\(681\) 0.872045 1.61111i 0.0334168 0.0617377i
\(682\) 0 0
\(683\) −44.1988 11.8430i −1.69122 0.453161i −0.720517 0.693438i \(-0.756095\pi\)
−0.970705 + 0.240276i \(0.922762\pi\)
\(684\) 0 0
\(685\) −38.5473 66.7659i −1.47282 2.55100i
\(686\) 0 0
\(687\) 7.66342 + 12.4691i 0.292378 + 0.475726i
\(688\) 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
\(693\) −20.2701 10.2617i −0.769996 0.389811i
\(694\) 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
\(699\) 3.88221 + 0.926692i 0.146839 + 0.0350507i
\(700\) 0 0
\(701\) 8.75126 0.330531 0.165265 0.986249i \(-0.447152\pi\)
0.165265 + 0.986249i \(0.447152\pi\)
\(702\) 0 0
\(703\) −6.18736 −0.233361
\(704\) 0 0
\(705\) −20.6811 4.93662i −0.778894 0.185924i
\(706\) 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
\(711\) 31.3885 + 15.8904i 1.17716 + 0.595938i
\(712\) 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
\(717\) 0.0168860 + 0.0274751i 0.000630620 + 0.00102608i
\(718\) 0 0
\(719\) 17.9675 + 31.1206i 0.670075 + 1.16060i 0.977882 + 0.209155i \(0.0670714\pi\)
−0.307807 + 0.951449i \(0.599595\pi\)
\(720\) 0 0
\(721\) −6.86028 1.83821i −0.255490 0.0684584i
\(722\) 0 0
\(723\) 13.8597 25.6057i 0.515446 0.952288i
\(724\) 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
\(735\) −0.852469 31.0117i −0.0314438 1.14388i
\(736\) 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
\(741\) 8.39762 + 2.29083i 0.308494 + 0.0841557i
\(742\) 0 0
\(743\) 2.74994 0.736843i 0.100885 0.0270321i −0.208023 0.978124i \(-0.566703\pi\)
0.308909 + 0.951092i \(0.400036\pi\)
\(744\) 0 0
\(745\) 38.7944 22.3980i 1.42132 0.820598i
\(746\) 0 0
\(747\) −0.537030 1.63828i −0.0196489 0.0599416i
\(748\) 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
\(759\) −68.5316 37.0942i −2.48754 1.34643i
\(760\) 0 0
\(761\) −12.2935 3.29404i −0.445640 0.119409i 0.0290184 0.999579i \(-0.490762\pi\)
−0.474659 + 0.880170i \(0.657429\pi\)
\(762\) 0 0
\(763\) −1.20983 2.09549i −0.0437988 0.0758617i
\(764\) 0 0
\(765\) 13.9364 15.5592i 0.503870 0.562543i
\(766\) 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
\(771\) −13.8668 + 14.6507i −0.499401 + 0.527632i
\(772\) 0 0
\(773\) −6.75254 + 25.2008i −0.242872 + 0.906410i 0.731569 + 0.681767i \(0.238788\pi\)
−0.974441 + 0.224643i \(0.927878\pi\)
\(774\) 0 0
\(775\) −8.84085 8.84085i −0.317573 0.317573i
\(776\) 0 0
\(777\) 2.29187 9.60136i 0.0822203 0.344447i
\(778\) 0 0
\(779\) −1.42164 −0.0509355
\(780\) 0 0
\(781\) 27.7136 0.991670
\(782\) 0 0
\(783\) −13.9120 38.8041i −0.497176 1.38675i
\(784\) 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
\(789\) −30.9226 29.2681i −1.10087 1.04197i
\(790\) 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
\(795\) 34.9835 21.5006i 1.24074 0.762548i
\(796\) 0 0
\(797\) −0.895558