Properties

Label 630.2.be.a.341.3
Level 630
Weight 2
Character 630.341
Analytic conductor 5.031
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 630.be (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 341.3
Root \(0.965926 - 0.258819i\)
Character \(\chi\) = 630.341
Dual form 630.2.be.a.521.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.63896 - 0.189469i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-2.63896 - 0.189469i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{10} +(-4.67303 + 2.69798i) q^{11} +2.51764i q^{13} +(-2.19067 - 1.48356i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.24969 + 3.89658i) q^{17} +(-2.48004 - 1.43185i) q^{19} -1.00000 q^{20} -5.39595 q^{22} +(0.232051 + 0.133975i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-1.25882 + 2.18034i) q^{26} +(-1.15539 - 2.38014i) q^{28} +8.89898i q^{29} +(4.18154 - 2.41421i) q^{31} +(-0.866025 + 0.500000i) q^{32} +4.49938i q^{34} +(1.48356 - 2.19067i) q^{35} +(3.25882 - 5.64444i) q^{37} +(-1.43185 - 2.48004i) q^{38} +(-0.866025 - 0.500000i) q^{40} +0.760279 q^{41} -5.86370 q^{43} +(-4.67303 - 2.69798i) q^{44} +(0.133975 + 0.232051i) q^{46} +(3.99768 - 6.92418i) q^{47} +(6.92820 + 1.00000i) q^{49} -1.00000i q^{50} +(-2.18034 + 1.25882i) q^{52} +(-7.27319 + 4.19918i) q^{53} -5.39595i q^{55} +(0.189469 - 2.63896i) q^{56} +(-4.44949 + 7.70674i) q^{58} +(6.33573 + 10.9738i) q^{59} +(-2.27035 - 1.31079i) q^{61} +4.82843 q^{62} -1.00000 q^{64} +(-2.18034 - 1.25882i) q^{65} +(-4.91119 - 8.50643i) q^{67} +(-2.24969 + 3.89658i) q^{68} +(2.38014 - 1.15539i) q^{70} +4.76268i q^{71} +(10.0951 - 5.82843i) q^{73} +(5.64444 - 3.25882i) q^{74} -2.86370i q^{76} +(12.8431 - 6.23445i) q^{77} +(-4.29618 + 7.44120i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(0.658421 + 0.380139i) q^{82} +9.45001 q^{83} -4.49938 q^{85} +(-5.07812 - 2.93185i) q^{86} +(-2.69798 - 4.67303i) q^{88} +(-3.98502 + 6.90226i) q^{89} +(0.477014 - 6.64394i) q^{91} +0.267949i q^{92} +(6.92418 - 3.99768i) q^{94} +(2.48004 - 1.43185i) q^{95} +6.16353i q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} - 4q^{5} + O(q^{10}) \) \( 8q + 4q^{4} - 4q^{5} - 24q^{11} - 4q^{16} - 8q^{20} - 12q^{23} - 4q^{25} - 8q^{26} + 24q^{37} + 4q^{38} - 32q^{41} - 16q^{43} - 24q^{44} + 8q^{46} + 8q^{47} - 24q^{53} - 16q^{58} + 24q^{59} + 16q^{62} - 8q^{64} - 24q^{67} + 16q^{77} - 24q^{79} - 4q^{80} + 16q^{83} + 16q^{89} - 20q^{91} - 12q^{94} + 44q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −2.63896 0.189469i −0.997433 0.0716124i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −0.866025 + 0.500000i −0.273861 + 0.158114i
\(11\) −4.67303 + 2.69798i −1.40897 + 0.813471i −0.995289 0.0969504i \(-0.969091\pi\)
−0.413683 + 0.910421i \(0.635758\pi\)
\(12\) 0 0
\(13\) 2.51764i 0.698267i 0.937073 + 0.349134i \(0.113524\pi\)
−0.937073 + 0.349134i \(0.886476\pi\)
\(14\) −2.19067 1.48356i −0.585481 0.396499i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.24969 + 3.89658i 0.545630 + 0.945058i 0.998567 + 0.0535160i \(0.0170428\pi\)
−0.452937 + 0.891542i \(0.649624\pi\)
\(18\) 0 0
\(19\) −2.48004 1.43185i −0.568960 0.328489i 0.187774 0.982212i \(-0.439873\pi\)
−0.756734 + 0.653723i \(0.773206\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −5.39595 −1.15042
\(23\) 0.232051 + 0.133975i 0.0483859 + 0.0279356i 0.523998 0.851720i \(-0.324440\pi\)
−0.475612 + 0.879655i \(0.657773\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −1.25882 + 2.18034i −0.246875 + 0.427600i
\(27\) 0 0
\(28\) −1.15539 2.38014i −0.218349 0.449804i
\(29\) 8.89898i 1.65250i 0.563304 + 0.826250i \(0.309530\pi\)
−0.563304 + 0.826250i \(0.690470\pi\)
\(30\) 0 0
\(31\) 4.18154 2.41421i 0.751027 0.433606i −0.0750380 0.997181i \(-0.523908\pi\)
0.826065 + 0.563575i \(0.190574\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 4.49938i 0.771637i
\(35\) 1.48356 2.19067i 0.250768 0.370291i
\(36\) 0 0
\(37\) 3.25882 5.64444i 0.535747 0.927940i −0.463380 0.886160i \(-0.653364\pi\)
0.999127 0.0417807i \(-0.0133031\pi\)
\(38\) −1.43185 2.48004i −0.232277 0.402316i
\(39\) 0 0
\(40\) −0.866025 0.500000i −0.136931 0.0790569i
\(41\) 0.760279 0.118736 0.0593678 0.998236i \(-0.481092\pi\)
0.0593678 + 0.998236i \(0.481092\pi\)
\(42\) 0 0
\(43\) −5.86370 −0.894206 −0.447103 0.894482i \(-0.647544\pi\)
−0.447103 + 0.894482i \(0.647544\pi\)
\(44\) −4.67303 2.69798i −0.704486 0.406735i
\(45\) 0 0
\(46\) 0.133975 + 0.232051i 0.0197535 + 0.0342140i
\(47\) 3.99768 6.92418i 0.583121 1.01000i −0.411986 0.911190i \(-0.635165\pi\)
0.995107 0.0988053i \(-0.0315021\pi\)
\(48\) 0 0
\(49\) 6.92820 + 1.00000i 0.989743 + 0.142857i
\(50\) 1.00000i 0.141421i
\(51\) 0 0
\(52\) −2.18034 + 1.25882i −0.302359 + 0.174567i
\(53\) −7.27319 + 4.19918i −0.999050 + 0.576802i −0.907967 0.419042i \(-0.862366\pi\)
−0.0910826 + 0.995843i \(0.529033\pi\)
\(54\) 0 0
\(55\) 5.39595i 0.727590i
\(56\) 0.189469 2.63896i 0.0253188 0.352646i
\(57\) 0 0
\(58\) −4.44949 + 7.70674i −0.584247 + 1.01194i
\(59\) 6.33573 + 10.9738i 0.824842 + 1.42867i 0.902040 + 0.431653i \(0.142069\pi\)
−0.0771977 + 0.997016i \(0.524597\pi\)
\(60\) 0 0
\(61\) −2.27035 1.31079i −0.290689 0.167829i 0.347564 0.937656i \(-0.387009\pi\)
−0.638253 + 0.769827i \(0.720342\pi\)
\(62\) 4.82843 0.613211
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −2.18034 1.25882i −0.270438 0.156137i
\(66\) 0 0
\(67\) −4.91119 8.50643i −0.599997 1.03923i −0.992821 0.119612i \(-0.961835\pi\)
0.392824 0.919614i \(-0.371498\pi\)
\(68\) −2.24969 + 3.89658i −0.272815 + 0.472529i
\(69\) 0 0
\(70\) 2.38014 1.15539i 0.284481 0.138096i
\(71\) 4.76268i 0.565226i 0.959234 + 0.282613i \(0.0912013\pi\)
−0.959234 + 0.282613i \(0.908799\pi\)
\(72\) 0 0
\(73\) 10.0951 5.82843i 1.18155 0.682166i 0.225174 0.974319i \(-0.427705\pi\)
0.956372 + 0.292153i \(0.0943716\pi\)
\(74\) 5.64444 3.25882i 0.656153 0.378830i
\(75\) 0 0
\(76\) 2.86370i 0.328489i
\(77\) 12.8431 6.23445i 1.46361 0.710482i
\(78\) 0 0
\(79\) −4.29618 + 7.44120i −0.483358 + 0.837200i −0.999817 0.0191114i \(-0.993916\pi\)
0.516460 + 0.856312i \(0.327250\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) 0 0
\(82\) 0.658421 + 0.380139i 0.0727104 + 0.0419794i
\(83\) 9.45001 1.03727 0.518636 0.854995i \(-0.326440\pi\)
0.518636 + 0.854995i \(0.326440\pi\)
\(84\) 0 0
\(85\) −4.49938 −0.488026
\(86\) −5.07812 2.93185i −0.547587 0.316150i
\(87\) 0 0
\(88\) −2.69798 4.67303i −0.287605 0.498147i
\(89\) −3.98502 + 6.90226i −0.422412 + 0.731638i −0.996175 0.0873828i \(-0.972150\pi\)
0.573763 + 0.819021i \(0.305483\pi\)
\(90\) 0 0
\(91\) 0.477014 6.64394i 0.0500046 0.696474i
\(92\) 0.267949i 0.0279356i
\(93\) 0 0
\(94\) 6.92418 3.99768i 0.714175 0.412329i
\(95\) 2.48004 1.43185i 0.254447 0.146905i
\(96\) 0 0
\(97\) 6.16353i 0.625812i 0.949784 + 0.312906i \(0.101302\pi\)
−0.949784 + 0.312906i \(0.898698\pi\)
\(98\) 5.50000 + 4.33013i 0.555584 + 0.437409i
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) −7.02458 12.1669i −0.698972 1.21065i −0.968823 0.247753i \(-0.920308\pi\)
0.269852 0.962902i \(-0.413025\pi\)
\(102\) 0 0
\(103\) 12.2776 + 7.08845i 1.20974 + 0.698446i 0.962703 0.270560i \(-0.0872088\pi\)
0.247040 + 0.969005i \(0.420542\pi\)
\(104\) −2.51764 −0.246875
\(105\) 0 0
\(106\) −8.39836 −0.815721
\(107\) −1.42178 0.820863i −0.137448 0.0793559i 0.429699 0.902972i \(-0.358620\pi\)
−0.567147 + 0.823616i \(0.691953\pi\)
\(108\) 0 0
\(109\) 9.94887 + 17.2319i 0.952929 + 1.65052i 0.739039 + 0.673663i \(0.235280\pi\)
0.213890 + 0.976858i \(0.431387\pi\)
\(110\) 2.69798 4.67303i 0.257242 0.445556i
\(111\) 0 0
\(112\) 1.48356 2.19067i 0.140184 0.206999i
\(113\) 5.95867i 0.560545i −0.959921 0.280272i \(-0.909575\pi\)
0.959921 0.280272i \(-0.0904248\pi\)
\(114\) 0 0
\(115\) −0.232051 + 0.133975i −0.0216388 + 0.0124932i
\(116\) −7.70674 + 4.44949i −0.715553 + 0.413125i
\(117\) 0 0
\(118\) 12.6715i 1.16650i
\(119\) −5.19856 10.7091i −0.476551 0.981706i
\(120\) 0 0
\(121\) 9.05816 15.6892i 0.823469 1.42629i
\(122\) −1.31079 2.27035i −0.118673 0.205548i
\(123\) 0 0
\(124\) 4.18154 + 2.41421i 0.375513 + 0.216803i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −14.5103 −1.28758 −0.643792 0.765200i \(-0.722640\pi\)
−0.643792 + 0.765200i \(0.722640\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −1.25882 2.18034i −0.110406 0.191228i
\(131\) 7.73325 13.3944i 0.675657 1.17027i −0.300619 0.953744i \(-0.597193\pi\)
0.976276 0.216529i \(-0.0694735\pi\)
\(132\) 0 0
\(133\) 6.27343 + 4.24849i 0.543975 + 0.368391i
\(134\) 9.82237i 0.848524i
\(135\) 0 0
\(136\) −3.89658 + 2.24969i −0.334129 + 0.192909i
\(137\) 7.46651 4.31079i 0.637907 0.368296i −0.145901 0.989299i \(-0.546608\pi\)
0.783808 + 0.621004i \(0.213275\pi\)
\(138\) 0 0
\(139\) 10.2512i 0.869495i 0.900552 + 0.434748i \(0.143162\pi\)
−0.900552 + 0.434748i \(0.856838\pi\)
\(140\) 2.63896 + 0.189469i 0.223033 + 0.0160130i
\(141\) 0 0
\(142\) −2.38134 + 4.12460i −0.199838 + 0.346129i
\(143\) −6.79253 11.7650i −0.568020 0.983839i
\(144\) 0 0
\(145\) −7.70674 4.44949i −0.640010 0.369510i
\(146\) 11.6569 0.964728
\(147\) 0 0
\(148\) 6.51764 0.535747
\(149\) −7.96640 4.59940i −0.652633 0.376798i 0.136831 0.990594i \(-0.456308\pi\)
−0.789464 + 0.613797i \(0.789641\pi\)
\(150\) 0 0
\(151\) 6.37429 + 11.0406i 0.518733 + 0.898471i 0.999763 + 0.0217674i \(0.00692931\pi\)
−0.481030 + 0.876704i \(0.659737\pi\)
\(152\) 1.43185 2.48004i 0.116139 0.201158i
\(153\) 0 0
\(154\) 14.2397 + 1.02236i 1.14747 + 0.0823845i
\(155\) 4.82843i 0.387829i
\(156\) 0 0
\(157\) 11.9899 6.92236i 0.956896 0.552464i 0.0616798 0.998096i \(-0.480354\pi\)
0.895216 + 0.445632i \(0.147021\pi\)
\(158\) −7.44120 + 4.29618i −0.591990 + 0.341786i
\(159\) 0 0
\(160\) 1.00000i 0.0790569i
\(161\) −0.586988 0.397520i −0.0462612 0.0313289i
\(162\) 0 0
\(163\) 10.3025 17.8444i 0.806954 1.39768i −0.108010 0.994150i \(-0.534448\pi\)
0.914964 0.403535i \(-0.132219\pi\)
\(164\) 0.380139 + 0.658421i 0.0296839 + 0.0514140i
\(165\) 0 0
\(166\) 8.18394 + 4.72500i 0.635197 + 0.366731i
\(167\) 6.84961 0.530038 0.265019 0.964243i \(-0.414622\pi\)
0.265019 + 0.964243i \(0.414622\pi\)
\(168\) 0 0
\(169\) 6.66150 0.512423
\(170\) −3.89658 2.24969i −0.298854 0.172543i
\(171\) 0 0
\(172\) −2.93185 5.07812i −0.223552 0.387203i
\(173\) −6.37902 + 11.0488i −0.484988 + 0.840024i −0.999851 0.0172486i \(-0.994509\pi\)
0.514863 + 0.857272i \(0.327843\pi\)
\(174\) 0 0
\(175\) 1.15539 + 2.38014i 0.0873396 + 0.179922i
\(176\) 5.39595i 0.406735i
\(177\) 0 0
\(178\) −6.90226 + 3.98502i −0.517347 + 0.298690i
\(179\) −16.3390 + 9.43331i −1.22123 + 0.705079i −0.965181 0.261584i \(-0.915755\pi\)
−0.256052 + 0.966663i \(0.582422\pi\)
\(180\) 0 0
\(181\) 25.5498i 1.89910i 0.313615 + 0.949550i \(0.398460\pi\)
−0.313615 + 0.949550i \(0.601540\pi\)
\(182\) 3.73508 5.51532i 0.276862 0.408822i
\(183\) 0 0
\(184\) −0.133975 + 0.232051i −0.00987674 + 0.0171070i
\(185\) 3.25882 + 5.64444i 0.239593 + 0.414987i
\(186\) 0 0
\(187\) −21.0257 12.1392i −1.53755 0.887707i
\(188\) 7.99536 0.583121
\(189\) 0 0
\(190\) 2.86370 0.207755
\(191\) −7.00657 4.04524i −0.506977 0.292704i 0.224613 0.974448i \(-0.427888\pi\)
−0.731590 + 0.681745i \(0.761222\pi\)
\(192\) 0 0
\(193\) 7.06350 + 12.2343i 0.508442 + 0.880648i 0.999952 + 0.00977575i \(0.00311177\pi\)
−0.491510 + 0.870872i \(0.663555\pi\)
\(194\) −3.08176 + 5.33777i −0.221258 + 0.383230i
\(195\) 0 0
\(196\) 2.59808 + 6.50000i 0.185577 + 0.464286i
\(197\) 14.2738i 1.01697i 0.861072 + 0.508483i \(0.169793\pi\)
−0.861072 + 0.508483i \(0.830207\pi\)
\(198\) 0 0
\(199\) 3.06742 1.77098i 0.217444 0.125541i −0.387322 0.921944i \(-0.626600\pi\)
0.604766 + 0.796403i \(0.293267\pi\)
\(200\) 0.866025 0.500000i 0.0612372 0.0353553i
\(201\) 0 0
\(202\) 14.0492i 0.988495i
\(203\) 1.68608 23.4840i 0.118339 1.64826i
\(204\) 0 0
\(205\) −0.380139 + 0.658421i −0.0265501 + 0.0459861i
\(206\) 7.08845 + 12.2776i 0.493876 + 0.855418i
\(207\) 0 0
\(208\) −2.18034 1.25882i −0.151179 0.0872834i
\(209\) 15.4524 1.06887
\(210\) 0 0
\(211\) −3.92340 −0.270098 −0.135049 0.990839i \(-0.543119\pi\)
−0.135049 + 0.990839i \(0.543119\pi\)
\(212\) −7.27319 4.19918i −0.499525 0.288401i
\(213\) 0 0
\(214\) −0.820863 1.42178i −0.0561131 0.0971907i
\(215\) 2.93185 5.07812i 0.199951 0.346325i
\(216\) 0 0
\(217\) −11.4923 + 5.57874i −0.780150 + 0.378709i
\(218\) 19.8977i 1.34764i
\(219\) 0 0
\(220\) 4.67303 2.69798i 0.315056 0.181898i
\(221\) −9.81017 + 5.66390i −0.659903 + 0.380995i
\(222\) 0 0
\(223\) 14.6904i 0.983740i 0.870669 + 0.491870i \(0.163686\pi\)
−0.870669 + 0.491870i \(0.836314\pi\)
\(224\) 2.38014 1.15539i 0.159030 0.0771980i
\(225\) 0 0
\(226\) 2.97934 5.16036i 0.198182 0.343262i
\(227\) −11.3913 19.7303i −0.756068 1.30955i −0.944842 0.327527i \(-0.893785\pi\)
0.188774 0.982021i \(-0.439549\pi\)
\(228\) 0 0
\(229\) −17.5089 10.1087i −1.15702 0.668005i −0.206431 0.978461i \(-0.566185\pi\)
−0.950588 + 0.310456i \(0.899518\pi\)
\(230\) −0.267949 −0.0176680
\(231\) 0 0
\(232\) −8.89898 −0.584247
\(233\) 2.27840 + 1.31543i 0.149263 + 0.0861769i 0.572771 0.819715i \(-0.305868\pi\)
−0.423509 + 0.905892i \(0.639202\pi\)
\(234\) 0 0
\(235\) 3.99768 + 6.92418i 0.260780 + 0.451684i
\(236\) −6.33573 + 10.9738i −0.412421 + 0.714334i
\(237\) 0 0
\(238\) 0.852491 11.8737i 0.0552588 0.769656i
\(239\) 16.8766i 1.09165i 0.837898 + 0.545827i \(0.183784\pi\)
−0.837898 + 0.545827i \(0.816216\pi\)
\(240\) 0 0
\(241\) −12.5793 + 7.26268i −0.810306 + 0.467831i −0.847062 0.531494i \(-0.821631\pi\)
0.0367560 + 0.999324i \(0.488298\pi\)
\(242\) 15.6892 9.05816i 1.00854 0.582280i
\(243\) 0 0
\(244\) 2.62158i 0.167829i
\(245\) −4.33013 + 5.50000i −0.276642 + 0.351382i
\(246\) 0 0
\(247\) 3.60488 6.24384i 0.229373 0.397286i
\(248\) 2.41421 + 4.18154i 0.153303 + 0.265528i
\(249\) 0 0
\(250\) 0.866025 + 0.500000i 0.0547723 + 0.0316228i
\(251\) 15.7243 0.992507 0.496254 0.868178i \(-0.334709\pi\)
0.496254 + 0.868178i \(0.334709\pi\)
\(252\) 0 0
\(253\) −1.44584 −0.0908993
\(254\) −12.5663 7.25517i −0.788481 0.455230i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 9.83083 17.0275i 0.613230 1.06215i −0.377462 0.926025i \(-0.623203\pi\)
0.990692 0.136121i \(-0.0434636\pi\)
\(258\) 0 0
\(259\) −9.66933 + 14.2780i −0.600823 + 0.887192i
\(260\) 2.51764i 0.156137i
\(261\) 0 0
\(262\) 13.3944 7.73325i 0.827508 0.477762i
\(263\) −3.74275 + 2.16088i −0.230788 + 0.133245i −0.610935 0.791680i \(-0.709206\pi\)
0.380148 + 0.924926i \(0.375873\pi\)
\(264\) 0 0
\(265\) 8.39836i 0.515907i
\(266\) 3.30871 + 6.81601i 0.202870 + 0.417917i
\(267\) 0 0
\(268\) 4.91119 8.50643i 0.299999 0.519613i
\(269\) 8.79895 + 15.2402i 0.536482 + 0.929214i 0.999090 + 0.0426509i \(0.0135803\pi\)
−0.462608 + 0.886563i \(0.653086\pi\)
\(270\) 0 0
\(271\) −9.12436 5.26795i −0.554265 0.320005i 0.196575 0.980489i \(-0.437018\pi\)
−0.750840 + 0.660484i \(0.770351\pi\)
\(272\) −4.49938 −0.272815
\(273\) 0 0
\(274\) 8.62158 0.520849
\(275\) 4.67303 + 2.69798i 0.281794 + 0.162694i
\(276\) 0 0
\(277\) −1.50971 2.61489i −0.0907097 0.157114i 0.817100 0.576496i \(-0.195580\pi\)
−0.907810 + 0.419382i \(0.862247\pi\)
\(278\) −5.12560 + 8.87780i −0.307413 + 0.532455i
\(279\) 0 0
\(280\) 2.19067 + 1.48356i 0.130918 + 0.0886599i
\(281\) 10.6880i 0.637591i 0.947824 + 0.318795i \(0.103278\pi\)
−0.947824 + 0.318795i \(0.896722\pi\)
\(282\) 0 0
\(283\) −15.2149 + 8.78434i −0.904434 + 0.522175i −0.878636 0.477492i \(-0.841546\pi\)
−0.0257976 + 0.999667i \(0.508213\pi\)
\(284\) −4.12460 + 2.38134i −0.244750 + 0.141307i
\(285\) 0 0
\(286\) 13.5851i 0.803301i
\(287\) −2.00634 0.144049i −0.118431 0.00850295i
\(288\) 0 0
\(289\) −1.62220 + 2.80973i −0.0954235 + 0.165278i
\(290\) −4.44949 7.70674i −0.261283 0.452555i
\(291\) 0 0
\(292\) 10.0951 + 5.82843i 0.590773 + 0.341083i
\(293\) −14.6710 −0.857086 −0.428543 0.903521i \(-0.640973\pi\)
−0.428543 + 0.903521i \(0.640973\pi\)
\(294\) 0 0
\(295\) −12.6715 −0.737761
\(296\) 5.64444 + 3.25882i 0.328076 + 0.189415i
\(297\) 0 0
\(298\) −4.59940 7.96640i −0.266436 0.461481i
\(299\) −0.337300 + 0.584220i −0.0195065 + 0.0337863i
\(300\) 0 0
\(301\) 15.4741 + 1.11099i 0.891911 + 0.0640363i
\(302\) 12.7486i 0.733599i
\(303\) 0 0
\(304\) 2.48004 1.43185i 0.142240 0.0821223i
\(305\) 2.27035 1.31079i 0.130000 0.0750556i
\(306\) 0 0
\(307\) 21.2772i 1.21435i −0.794567 0.607177i \(-0.792302\pi\)
0.794567 0.607177i \(-0.207698\pi\)
\(308\) 11.8208 + 8.00524i 0.673550 + 0.456141i
\(309\) 0 0
\(310\) −2.41421 + 4.18154i −0.137118 + 0.237496i
\(311\) −5.91724 10.2490i −0.335536 0.581165i 0.648052 0.761596i \(-0.275584\pi\)
−0.983588 + 0.180431i \(0.942251\pi\)
\(312\) 0 0
\(313\) −3.90551 2.25485i −0.220753 0.127452i 0.385546 0.922689i \(-0.374013\pi\)
−0.606299 + 0.795237i \(0.707346\pi\)
\(314\) 13.8447 0.781302
\(315\) 0 0
\(316\) −8.59235 −0.483358
\(317\) −15.9202 9.19151i −0.894165 0.516247i −0.0188626 0.999822i \(-0.506005\pi\)
−0.875303 + 0.483576i \(0.839338\pi\)
\(318\) 0 0
\(319\) −24.0092 41.5852i −1.34426 2.32833i
\(320\) 0.500000 0.866025i 0.0279508 0.0484123i
\(321\) 0 0
\(322\) −0.309587 0.637756i −0.0172526 0.0355408i
\(323\) 12.8849i 0.716934i
\(324\) 0 0
\(325\) 2.18034 1.25882i 0.120943 0.0698267i
\(326\) 17.8444 10.3025i 0.988313 0.570603i
\(327\) 0 0
\(328\) 0.760279i 0.0419794i
\(329\) −11.8616 + 17.5152i −0.653952 + 0.965644i
\(330\) 0 0
\(331\) −3.98066 + 6.89471i −0.218797 + 0.378967i −0.954440 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(332\) 4.72500 + 8.18394i 0.259318 + 0.449152i
\(333\) 0 0
\(334\) 5.93193 + 3.42480i 0.324581 + 0.187397i
\(335\) 9.82237 0.536654
\(336\) 0 0
\(337\) −6.89417 −0.375549 −0.187775 0.982212i \(-0.560127\pi\)
−0.187775 + 0.982212i \(0.560127\pi\)
\(338\) 5.76903 + 3.33075i 0.313794 + 0.181169i
\(339\) 0 0
\(340\) −2.24969 3.89658i −0.122007 0.211321i
\(341\) −13.0270 + 22.5634i −0.705451 + 1.22188i
\(342\) 0 0
\(343\) −18.0938 3.95164i −0.976972 0.213368i
\(344\) 5.86370i 0.316150i
\(345\) 0 0
\(346\) −11.0488 + 6.37902i −0.593986 + 0.342938i
\(347\) −14.1645 + 8.17789i −0.760392 + 0.439012i −0.829436 0.558601i \(-0.811338\pi\)
0.0690448 + 0.997614i \(0.478005\pi\)
\(348\) 0 0
\(349\) 24.5851i 1.31601i 0.753014 + 0.658004i \(0.228599\pi\)
−0.753014 + 0.658004i \(0.771401\pi\)
\(350\) −0.189469 + 2.63896i −0.0101275 + 0.141058i
\(351\) 0 0
\(352\) 2.69798 4.67303i 0.143803 0.249073i
\(353\) 6.85906 + 11.8802i 0.365071 + 0.632321i 0.988788 0.149329i \(-0.0477114\pi\)
−0.623717 + 0.781651i \(0.714378\pi\)
\(354\) 0 0
\(355\) −4.12460 2.38134i −0.218911 0.126388i
\(356\) −7.97005 −0.422412
\(357\) 0 0
\(358\) −18.8666 −0.997132
\(359\) −10.3059 5.95011i −0.543924 0.314035i 0.202744 0.979232i \(-0.435014\pi\)
−0.746668 + 0.665197i \(0.768348\pi\)
\(360\) 0 0
\(361\) −5.39960 9.35238i −0.284190 0.492231i
\(362\) −12.7749 + 22.1268i −0.671433 + 1.16296i
\(363\) 0 0
\(364\) 5.99233 2.90887i 0.314083 0.152466i
\(365\) 11.6569i 0.610148i
\(366\) 0 0
\(367\) −10.9026 + 6.29461i −0.569110 + 0.328576i −0.756794 0.653654i \(-0.773235\pi\)
0.187684 + 0.982230i \(0.439902\pi\)
\(368\) −0.232051 + 0.133975i −0.0120965 + 0.00698391i
\(369\) 0 0
\(370\) 6.51764i 0.338836i
\(371\) 19.9893 9.70342i 1.03779 0.503776i
\(372\) 0 0
\(373\) 13.5868 23.5331i 0.703499 1.21850i −0.263731 0.964596i \(-0.584953\pi\)
0.967230 0.253900i \(-0.0817136\pi\)
\(374\) −12.1392 21.0257i −0.627704 1.08722i
\(375\) 0 0
\(376\) 6.92418 + 3.99768i 0.357087 + 0.206164i
\(377\) −22.4044 −1.15389
\(378\) 0 0
\(379\) 15.7335 0.808174 0.404087 0.914721i \(-0.367589\pi\)
0.404087 + 0.914721i \(0.367589\pi\)
\(380\) 2.48004 + 1.43185i 0.127223 + 0.0734524i
\(381\) 0 0
\(382\) −4.04524 7.00657i −0.206973 0.358487i
\(383\) −7.89060 + 13.6669i −0.403191 + 0.698347i −0.994109 0.108384i \(-0.965432\pi\)
0.590918 + 0.806732i \(0.298766\pi\)
\(384\) 0 0
\(385\) −1.02236 + 14.2397i −0.0521045 + 0.725722i
\(386\) 14.1270i 0.719046i
\(387\) 0 0
\(388\) −5.33777 + 3.08176i −0.270984 + 0.156453i
\(389\) −13.7556 + 7.94182i −0.697438 + 0.402666i −0.806393 0.591381i \(-0.798583\pi\)
0.108954 + 0.994047i \(0.465250\pi\)
\(390\) 0 0
\(391\) 1.20560i 0.0609700i
\(392\) −1.00000 + 6.92820i −0.0505076 + 0.349927i
\(393\) 0 0
\(394\) −7.13689 + 12.3615i −0.359552 + 0.622762i
\(395\) −4.29618 7.44120i −0.216164 0.374407i
\(396\) 0 0
\(397\) 32.3557 + 18.6806i 1.62388 + 0.937550i 0.985867 + 0.167528i \(0.0535784\pi\)
0.638017 + 0.770022i \(0.279755\pi\)
\(398\) 3.54195 0.177542
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 24.4856 + 14.1368i 1.22275 + 0.705957i 0.965504 0.260389i \(-0.0838507\pi\)
0.257249 + 0.966345i \(0.417184\pi\)
\(402\) 0 0
\(403\) 6.07812 + 10.5276i 0.302773 + 0.524417i
\(404\) 7.02458 12.1669i 0.349486 0.605327i
\(405\) 0 0
\(406\) 13.2022 19.4947i 0.655214 0.967507i
\(407\) 35.1689i 1.74326i
\(408\) 0 0
\(409\) 13.8647 8.00481i 0.685567 0.395812i −0.116382 0.993204i \(-0.537130\pi\)
0.801949 + 0.597392i \(0.203796\pi\)
\(410\) −0.658421 + 0.380139i −0.0325171 + 0.0187737i
\(411\) 0 0
\(412\) 14.1769i 0.698446i
\(413\) −14.6405 30.1599i −0.720414 1.48407i
\(414\) 0 0
\(415\) −4.72500 + 8.18394i −0.231941 + 0.401734i
\(416\) −1.25882 2.18034i −0.0617187 0.106900i
\(417\) 0 0
\(418\) 13.3822 + 7.72620i 0.654544 + 0.377901i
\(419\) 29.5137 1.44184 0.720919 0.693020i \(-0.243720\pi\)
0.720919 + 0.693020i \(0.243720\pi\)
\(420\) 0 0
\(421\) 0.309114 0.0150653 0.00753265 0.999972i \(-0.497602\pi\)
0.00753265 + 0.999972i \(0.497602\pi\)
\(422\) −3.39776 1.96170i −0.165400 0.0954939i
\(423\) 0 0
\(424\) −4.19918 7.27319i −0.203930 0.353217i
\(425\) 2.24969 3.89658i 0.109126 0.189012i
\(426\) 0 0
\(427\) 5.74301 + 3.88928i 0.277924 + 0.188215i
\(428\) 1.64173i 0.0793559i
\(429\) 0 0
\(430\) 5.07812 2.93185i 0.244889 0.141386i
\(431\) 7.63843 4.41005i 0.367930 0.212425i −0.304624 0.952473i \(-0.598531\pi\)
0.672554 + 0.740048i \(0.265197\pi\)
\(432\) 0 0
\(433\) 9.56388i 0.459611i −0.973237 0.229805i \(-0.926191\pi\)
0.973237 0.229805i \(-0.0738089\pi\)
\(434\) −12.7420 0.914836i −0.611636 0.0439135i
\(435\) 0 0
\(436\) −9.94887 + 17.2319i −0.476464 + 0.825260i
\(437\) −0.383663 0.664525i −0.0183531 0.0317885i
\(438\) 0 0
\(439\) −31.3336 18.0905i −1.49547 0.863412i −0.495487 0.868615i \(-0.665010\pi\)
−0.999986 + 0.00520362i \(0.998344\pi\)
\(440\) 5.39595 0.257242
\(441\) 0 0
\(442\) −11.3278 −0.538809
\(443\) −3.53830 2.04284i −0.168110 0.0970582i 0.413584 0.910466i \(-0.364277\pi\)
−0.581694 + 0.813408i \(0.697610\pi\)
\(444\) 0 0
\(445\) −3.98502 6.90226i −0.188908 0.327199i
\(446\) −7.34519 + 12.7222i −0.347805 + 0.602415i
\(447\) 0 0
\(448\) 2.63896 + 0.189469i 0.124679 + 0.00895155i
\(449\) 19.9377i 0.940918i −0.882422 0.470459i \(-0.844088\pi\)
0.882422 0.470459i \(-0.155912\pi\)
\(450\) 0 0
\(451\) −3.55281 + 2.05121i −0.167295 + 0.0965879i
\(452\) 5.16036 2.97934i 0.242723 0.140136i
\(453\) 0 0
\(454\) 22.7826i 1.06924i
\(455\) 5.51532 + 3.73508i 0.258562 + 0.175103i
\(456\) 0 0
\(457\) 10.0623 17.4283i 0.470693 0.815264i −0.528745 0.848780i \(-0.677337\pi\)
0.999438 + 0.0335168i \(0.0106707\pi\)
\(458\) −10.1087 17.5089i −0.472351 0.818136i
\(459\) 0 0
\(460\) −0.232051 0.133975i −0.0108194 0.00624660i
\(461\) −0.909299 −0.0423503 −0.0211751 0.999776i \(-0.506741\pi\)
−0.0211751 + 0.999776i \(0.506741\pi\)
\(462\) 0 0
\(463\) 21.4280 0.995843 0.497922 0.867222i \(-0.334097\pi\)
0.497922 + 0.867222i \(0.334097\pi\)
\(464\) −7.70674 4.44949i −0.357777 0.206562i
\(465\) 0 0
\(466\) 1.31543 + 2.27840i 0.0609363 + 0.105545i
\(467\) −6.34607 + 10.9917i −0.293661 + 0.508636i −0.974672 0.223637i \(-0.928207\pi\)
0.681012 + 0.732273i \(0.261540\pi\)
\(468\) 0 0
\(469\) 11.3487 + 23.3786i 0.524035 + 1.07952i
\(470\) 7.99536i 0.368798i
\(471\) 0 0
\(472\) −10.9738 + 6.33573i −0.505111 + 0.291626i
\(473\) 27.4013 15.8201i 1.25991 0.727411i
\(474\) 0 0
\(475\) 2.86370i 0.131396i
\(476\) 6.67511 9.85666i 0.305953 0.451779i
\(477\) 0 0
\(478\) −8.43828 + 14.6155i −0.385958 + 0.668499i
\(479\) 6.43828 + 11.1514i 0.294172 + 0.509522i 0.974792 0.223115i \(-0.0716227\pi\)
−0.680620 + 0.732637i \(0.738289\pi\)
\(480\) 0 0
\(481\) 14.2107 + 8.20453i 0.647950 + 0.374094i
\(482\) −14.5254 −0.661612
\(483\) 0 0
\(484\) 18.1163 0.823469
\(485\) −5.33777 3.08176i −0.242376 0.139936i
\(486\) 0 0
\(487\) 10.4097 + 18.0301i 0.471708 + 0.817022i 0.999476 0.0323665i \(-0.0103044\pi\)
−0.527768 + 0.849388i \(0.676971\pi\)
\(488\) 1.31079 2.27035i 0.0593366 0.102774i
\(489\) 0 0
\(490\) −6.50000 + 2.59808i −0.293640 + 0.117369i
\(491\) 27.3271i 1.23325i −0.787256 0.616627i \(-0.788499\pi\)
0.787256 0.616627i \(-0.211501\pi\)
\(492\) 0 0
\(493\) −34.6755 + 20.0199i −1.56171 + 0.901653i
\(494\) 6.24384 3.60488i 0.280924 0.162191i
\(495\) 0 0
\(496\) 4.82843i 0.216803i
\(497\) 0.902379 12.5685i 0.0404772 0.563775i
\(498\) 0 0
\(499\) −16.6802 + 28.8909i −0.746708 + 1.29334i 0.202685 + 0.979244i \(0.435033\pi\)
−0.949393 + 0.314092i \(0.898300\pi\)
\(500\) 0.500000 + 0.866025i 0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) 13.6176 + 7.86214i 0.607784 + 0.350904i
\(503\) −16.2936 −0.726494 −0.363247 0.931693i \(-0.618332\pi\)
−0.363247 + 0.931693i \(0.618332\pi\)
\(504\) 0 0
\(505\) 14.0492 0.625179
\(506\) −1.25214 0.722921i −0.0556642 0.0321377i
\(507\) 0 0
\(508\) −7.25517 12.5663i −0.321896 0.557540i
\(509\) 12.3400 21.3735i 0.546961 0.947365i −0.451519 0.892261i \(-0.649118\pi\)
0.998481 0.0551036i \(-0.0175489\pi\)
\(510\) 0 0
\(511\) −27.7449 + 13.4683i −1.22736 + 0.595801i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 17.0275 9.83083i 0.751051 0.433619i
\(515\) −12.2776 + 7.08845i −0.541014 + 0.312354i
\(516\) 0 0
\(517\) 43.1426i 1.89741i
\(518\) −15.5129 + 7.53044i −0.681597 + 0.330869i
\(519\) 0 0
\(520\) 1.25882 2.18034i 0.0552029 0.0956142i
\(521\) 0.141663 + 0.245367i 0.00620635 + 0.0107497i 0.869112 0.494616i \(-0.164691\pi\)
−0.862906 + 0.505365i \(0.831358\pi\)
\(522\) 0 0
\(523\) −9.77021 5.64083i −0.427222 0.246656i 0.270941 0.962596i \(-0.412665\pi\)
−0.698162 + 0.715940i \(0.745999\pi\)
\(524\) 15.4665 0.675657
\(525\) 0 0
\(526\) −4.32175 −0.188437
\(527\) 18.8143 + 10.8625i 0.819565 + 0.473176i
\(528\) 0 0
\(529\) −11.4641 19.8564i −0.498439 0.863322i
\(530\) 4.19918 7.27319i 0.182401 0.315927i
\(531\) 0 0
\(532\) −0.542582 + 7.55719i −0.0235239 + 0.327646i
\(533\) 1.91411i 0.0829092i
\(534\) 0 0
\(535\) 1.42178 0.820863i 0.0614688 0.0354890i
\(536\) 8.50643 4.91119i 0.367422 0.212131i
\(537\) 0 0
\(538\) 17.5979i 0.758700i
\(539\) −35.0737 + 14.0191i −1.51073 + 0.603845i
\(540\) 0 0
\(541\) 17.4125 30.1593i 0.748621 1.29665i −0.199862 0.979824i \(-0.564049\pi\)
0.948484 0.316826i \(-0.102617\pi\)
\(542\) −5.26795 9.12436i −0.226278 0.391925i
\(543\) 0 0
\(544\) −3.89658 2.24969i −0.167064 0.0964546i
\(545\) −19.8977 −0.852325
\(546\) 0 0
\(547\) 35.4261 1.51471 0.757356 0.653002i \(-0.226491\pi\)
0.757356 + 0.653002i \(0.226491\pi\)
\(548\) 7.46651 + 4.31079i 0.318953 + 0.184148i
\(549\) 0 0
\(550\) 2.69798 + 4.67303i 0.115042 + 0.199259i
\(551\) 12.7420 22.0698i 0.542828 0.940206i
\(552\) 0 0
\(553\) 12.7473 18.8230i 0.542071 0.800436i
\(554\) 3.01942i 0.128283i
\(555\) 0 0
\(556\) −8.87780 + 5.12560i −0.376503 + 0.217374i
\(557\) 7.05105 4.07093i 0.298763 0.172491i −0.343124 0.939290i \(-0.611485\pi\)
0.641887 + 0.766799i \(0.278152\pi\)
\(558\) 0 0
\(559\) 14.7627i 0.624395i
\(560\) 1.15539 + 2.38014i 0.0488243 + 0.100579i
\(561\) 0 0
\(562\) −5.34398 + 9.25605i −0.225422 + 0.390443i
\(563\) 10.2088 + 17.6821i 0.430248 + 0.745212i 0.996894 0.0787491i \(-0.0250926\pi\)
−0.566646 + 0.823961i \(0.691759\pi\)
\(564\) 0 0
\(565\) 5.16036 + 2.97934i 0.217098 + 0.125342i
\(566\) −17.5687 −0.738467
\(567\) 0 0
\(568\) −4.76268 −0.199838
\(569\) 22.5542 + 13.0217i 0.945520 + 0.545896i 0.891686 0.452654i \(-0.149523\pi\)
0.0538334 + 0.998550i \(0.482856\pi\)
\(570\) 0 0
\(571\) 6.18811 + 10.7181i 0.258964 + 0.448539i 0.965965 0.258674i \(-0.0832855\pi\)
−0.707000 + 0.707213i \(0.749952\pi\)
\(572\) 6.79253 11.7650i 0.284010 0.491920i
\(573\) 0 0
\(574\) −1.66552 1.12792i −0.0695175 0.0470786i
\(575\) 0.267949i 0.0111743i
\(576\) 0 0
\(577\) 23.3399 13.4753i 0.971654 0.560985i 0.0719139 0.997411i \(-0.477089\pi\)
0.899740 + 0.436426i \(0.143756\pi\)
\(578\) −2.80973 + 1.62220i −0.116869 + 0.0674746i
\(579\) 0 0
\(580\) 8.89898i 0.369510i
\(581\) −24.9382 1.79048i −1.03461 0.0742816i
\(582\) 0 0
\(583\) 22.6586 39.2458i 0.938422 1.62539i
\(584\) 5.82843 + 10.0951i 0.241182 + 0.417740i
\(585\) 0 0
\(586\) −12.7054 7.33548i −0.524856 0.303026i
\(587\) −35.3511 −1.45910 −0.729548 0.683930i \(-0.760269\pi\)
−0.729548 + 0.683930i \(0.760269\pi\)
\(588\) 0 0
\(589\) −13.8272 −0.569739
\(590\) −10.9738 6.33573i −0.451785 0.260838i
\(591\) 0 0
\(592\) 3.25882 + 5.64444i 0.133937 + 0.231985i
\(593\) 14.7057 25.4711i 0.603893 1.04597i −0.388333 0.921519i \(-0.626949\pi\)
0.992225 0.124454i \(-0.0397178\pi\)
\(594\) 0 0
\(595\) 11.8737 + 0.852491i 0.486773 + 0.0349487i
\(596\) 9.19881i 0.376798i
\(597\) 0 0
\(598\) −0.584220 + 0.337300i −0.0238905 + 0.0137932i
\(599\) 26.5494 15.3283i 1.08478 0.626298i 0.152598 0.988288i \(-0.451236\pi\)
0.932182 + 0.361990i \(0.117903\pi\)
\(600\) 0 0
\(601\) 34.3407i 1.40078i −0.713758 0.700392i \(-0.753008\pi\)
0.713758 0.700392i \(-0.246992\pi\)
\(602\) 12.8454 + 8.69918i 0.523541 + 0.354552i
\(603\) 0 0
\(604\) −6.37429 + 11.0406i −0.259366 + 0.449236i
\(605\) 9.05816 + 15.6892i 0.368266 + 0.637856i
\(606\) 0 0
\(607\) 28.2475 + 16.3087i 1.14653 + 0.661950i 0.948040 0.318153i \(-0.103062\pi\)
0.198492 + 0.980103i \(0.436396\pi\)
\(608\) 2.86370 0.116139
\(609\) 0 0
\(610\) 2.62158 0.106145
\(611\) 17.4326 + 10.0647i 0.705247 + 0.407174i
\(612\) 0 0
\(613\) 7.99843 + 13.8537i 0.323054 + 0.559545i 0.981117 0.193418i \(-0.0619572\pi\)
−0.658063 + 0.752963i \(0.728624\pi\)
\(614\) 10.6386 18.4266i 0.429339 0.743636i
\(615\) 0 0
\(616\) 6.23445 + 12.8431i 0.251193 + 0.517464i
\(617\) 25.1429i 1.01221i −0.862471 0.506107i \(-0.831084\pi\)
0.862471 0.506107i \(-0.168916\pi\)
\(618\) 0 0
\(619\) 32.3379 18.6703i 1.29977 0.750423i 0.319406 0.947618i \(-0.396517\pi\)
0.980364 + 0.197195i \(0.0631832\pi\)
\(620\) −4.18154 + 2.41421i −0.167935 + 0.0969571i
\(621\) 0 0
\(622\) 11.8345i 0.474519i
\(623\) 11.8241 17.4597i 0.473722 0.699510i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −2.25485 3.90551i −0.0901219 0.156096i
\(627\) 0 0
\(628\) 11.9899 + 6.92236i 0.478448 + 0.276232i
\(629\) 29.3253 1.16928
\(630\) 0 0
\(631\) 49.5015 1.97062 0.985311 0.170767i \(-0.0546245\pi\)
0.985311 + 0.170767i \(0.0546245\pi\)
\(632\) −7.44120 4.29618i −0.295995 0.170893i
\(633\) 0 0
\(634\) −9.19151 15.9202i −0.365041 0.632270i
\(635\) 7.25517 12.5663i 0.287913 0.498679i
\(636\) 0 0
\(637\) −2.51764 + 17.4427i −0.0997525 + 0.691105i
\(638\) 48.0185i 1.90107i
\(639\) 0 0
\(640\) 0.866025 0.500000i 0.0342327 0.0197642i
\(641\) −31.4439 + 18.1542i −1.24196 + 0.717046i −0.969493 0.245119i \(-0.921173\pi\)
−0.272467 + 0.962165i \(0.587840\pi\)
\(642\) 0 0
\(643\) 10.2653i 0.404824i −0.979300 0.202412i \(-0.935122\pi\)
0.979300 0.202412i \(-0.0648780\pi\)
\(644\) 0.0507680 0.707107i 0.00200054 0.0278639i
\(645\) 0 0
\(646\) 6.44244 11.1586i 0.253474 0.439031i
\(647\) −10.9108 18.8980i −0.428946 0.742956i 0.567834 0.823143i \(-0.307782\pi\)
−0.996780 + 0.0801869i \(0.974448\pi\)
\(648\) 0 0
\(649\) −59.2142 34.1873i −2.32436 1.34197i
\(650\) 2.51764 0.0987499
\(651\) 0 0
\(652\) 20.6050 0.806954
\(653\) 40.9556 + 23.6457i 1.60272 + 0.925329i 0.990941 + 0.134297i \(0.0428776\pi\)
0.611775 + 0.791032i \(0.290456\pi\)
\(654\) 0 0
\(655\) 7.73325 + 13.3944i 0.302163 + 0.523362i
\(656\) −0.380139 + 0.658421i −0.0148419 + 0.0257070i
\(657\) 0 0
\(658\) −19.0301 + 9.23779i −0.741869 + 0.360127i
\(659\) 3.58255i 0.139556i −0.997563 0.0697782i \(-0.977771\pi\)
0.997563 0.0697782i \(-0.0222291\pi\)
\(660\) 0 0
\(661\) −1.41761 + 0.818459i −0.0551388 + 0.0318344i −0.527316 0.849669i \(-0.676802\pi\)
0.472177 + 0.881504i \(0.343468\pi\)
\(662\) −6.89471 + 3.98066i −0.267970 + 0.154713i
\(663\) 0 0
\(664\) 9.45001i 0.366731i
\(665\) −6.81601 + 3.30871i −0.264314 + 0.128306i
\(666\) 0 0
\(667\) −1.19224 + 2.06502i −0.0461636 + 0.0799577i
\(668\) 3.42480 + 5.93193i 0.132510 + 0.229513i
\(669\) 0 0
\(670\) 8.50643 + 4.91119i 0.328632 + 0.189736i
\(671\) 14.1459 0.546097
\(672\) 0 0
\(673\) −2.02242 −0.0779587 −0.0389794 0.999240i \(-0.512411\pi\)
−0.0389794 + 0.999240i \(0.512411\pi\)
\(674\) −5.97053 3.44709i −0.229976 0.132777i
\(675\) 0 0
\(676\) 3.33075 + 5.76903i 0.128106 + 0.221886i
\(677\) 11.4413 19.8169i 0.439725 0.761626i −0.557943 0.829879i \(-0.688409\pi\)
0.997668 + 0.0682532i \(0.0217426\pi\)
\(678\) 0 0
\(679\) 1.16780 16.2653i 0.0448159 0.624205i
\(680\) 4.49938i 0.172543i
\(681\) 0 0
\(682\) −22.5634 + 13.0270i −0.863997 + 0.498829i
\(683\) 27.1977 15.7026i 1.04069 0.600844i 0.120663 0.992694i \(-0.461498\pi\)
0.920029 + 0.391850i \(0.128165\pi\)
\(684\) 0 0
\(685\) 8.62158i 0.329414i
\(686\) −13.6938 12.4691i −0.522834 0.476073i
\(687\) 0 0
\(688\) 2.93185 5.07812i 0.111776 0.193601i
\(689\) −10.5720 18.3113i −0.402762 0.697604i
\(690\) 0 0
\(691\) 29.3677 + 16.9554i 1.11720 + 0.645015i 0.940684 0.339283i \(-0.110184\pi\)
0.176515 + 0.984298i \(0.443518\pi\)
\(692\) −12.7580 −0.484988
\(693\) 0 0
\(694\) −16.3558 −0.620857
\(695\) −8.87780 5.12560i −0.336754 0.194425i
\(696\) 0 0
\(697\) 1.71039 + 2.96248i 0.0647857 + 0.112212i
\(698\) −12.2925 + 21.2913i −0.465279 + 0.805887i
\(699\) 0 0
\(700\) −1.48356 + 2.19067i −0.0560734 + 0.0827996i
\(701\) 10.5296i 0.397699i 0.980030 + 0.198849i \(0.0637205\pi\)
−0.980030 + 0.198849i \(0.936280\pi\)
\(702\) 0 0
\(703\) −16.1640 + 9.33229i −0.609637 + 0.351974i
\(704\) 4.67303 2.69798i 0.176122 0.101684i
\(705\) 0 0
\(706\) 13.7181i 0.516288i
\(707\) 16.2323 + 33.4390i 0.610479 + 1.25760i
\(708\) 0 0
\(709\) −7.52572 + 13.0349i −0.282634 + 0.489537i −0.972033 0.234845i \(-0.924542\pi\)
0.689398 + 0.724382i \(0.257875\pi\)
\(710\) −2.38134 4.12460i −0.0893702 0.154794i
\(711\) 0 0
\(712\) −6.90226 3.98502i −0.258673 0.149345i
\(713\) 1.29377 0.0484522
\(714\) 0 0
\(715\) 13.5851 0.508052
\(716\) −16.3390 9.43331i −0.610616 0.352539i
\(717\) 0 0
\(718\) −5.95011 10.3059i −0.222056 0.384613i
\(719\) 12.2137 21.1547i 0.455494 0.788938i −0.543223 0.839589i \(-0.682796\pi\)
0.998716 + 0.0506506i \(0.0161295\pi\)
\(720\) 0 0
\(721\) −31.0569 21.0323i −1.15662 0.783285i
\(722\) 10.7992i 0.401905i
\(723\) 0 0
\(724\) −22.1268 + 12.7749i −0.822335 + 0.474775i
\(725\) 7.70674 4.44949i 0.286221 0.165250i
\(726\) 0 0
\(727\) 43.7349i 1.62204i −0.585020 0.811019i \(-0.698913\pi\)
0.585020 0.811019i \(-0.301087\pi\)
\(728\) 6.64394 + 0.477014i 0.246241 + 0.0176793i
\(729\) 0 0
\(730\) −5.82843 + 10.0951i −0.215720 + 0.373638i
\(731\) −13.1915 22.8484i −0.487906 0.845077i
\(732\) 0 0
\(733\) 38.7280 + 22.3596i 1.43045 + 0.825872i 0.997155 0.0753789i \(-0.0240166\pi\)
0.433297 + 0.901251i \(0.357350\pi\)
\(734\) −12.5892 −0.464677
\(735\) 0 0
\(736\) −0.267949 −0.00987674
\(737\) 45.9003 + 26.5005i 1.69076 + 0.976160i
\(738\) 0 0
\(739\) 10.7360 + 18.5954i 0.394932 + 0.684042i 0.993092 0.117334i \(-0.0374348\pi\)
−0.598161 + 0.801376i \(0.704102\pi\)
\(740\) −3.25882 + 5.64444i −0.119797 + 0.207494i
\(741\) 0 0
\(742\) 22.1629 + 1.59123i 0.813626 + 0.0584157i
\(743\) 29.5637i 1.08459i 0.840190 + 0.542293i \(0.182444\pi\)
−0.840190 + 0.542293i \(0.817556\pi\)
\(744\) 0 0
\(745\) 7.96640 4.59940i 0.291866 0.168509i
\(746\) 23.5331 13.5868i 0.861607 0.497449i
\(747\) 0 0
\(748\) 24.2784i 0.887707i
\(749\) 3.59648 + 2.43561i 0.131413 + 0.0889951i
\(750\) 0 0
\(751\) −0.596750 + 1.03360i −0.0217757 + 0.0377166i −0.876708 0.481023i \(-0.840265\pi\)
0.854932 + 0.518740i \(0.173599\pi\)
\(752\) 3.99768 + 6.92418i 0.145780 + 0.252499i
\(753\) 0 0
\(754\) −19.4028 11.2022i −0.706608 0.407960i
\(755\) −12.7486 −0.463969
\(756\) 0 0
\(757\) −26.8915 −0.977386 −0.488693 0.872456i \(-0.662526\pi\)
−0.488693 + 0.872456i \(0.662526\pi\)
\(758\) 13.6256 + 7.86673i 0.494903 + 0.285732i
\(759\) 0 0
\(760\) 1.43185 + 2.48004i 0.0519387 + 0.0899605i
\(761\) −0.939574 + 1.62739i −0.0340595 + 0.0589928i −0.882553 0.470213i \(-0.844177\pi\)
0.848493 + 0.529206i \(0.177510\pi\)
\(762\) 0 0
\(763\) −22.9897 47.3594i −0.832284 1.71452i
\(764\) 8.09049i 0.292704i
\(765\) 0 0
\(766\) −13.6669 + 7.89060i −0.493806 + 0.285099i
\(767\) −27.6281 + 15.9511i −0.997592 + 0.575960i
\(768\) 0 0
\(769\) 50.6544i 1.82664i −0.407239 0.913322i \(-0.633508\pi\)
0.407239 0.913322i \(-0.366492\pi\)
\(770\) −8.00524 + 11.8208i −0.288489 + 0.425991i
\(771\) 0 0
\(772\) −7.06350 + 12.2343i −0.254221 + 0.440324i
\(773\) −24.3353 42.1499i −0.875279 1.51603i −0.856466 0.516204i \(-0.827345\pi\)
−0.0188128 0.999823i \(-0.505989\pi\)
\(774\) 0 0
\(775\) −4.18154 2.41421i −0.150205 0.0867211i
\(776\) −6.16353 −0.221258
\(777\) 0 0
\(778\) −15.8836 −0.569456
\(779\) −1.88552 1.08861i −0.0675558 0.0390034i
\(780\) 0 0
\(781\) −12.8496 22.2562i −0.459795 0.796388i
\(782\) −0.602802 + 1.04408i −0.0215562 + 0.0373364i
\(783\) 0 0
\(784\) −4.33013 + 5.50000i −0.154647 + 0.196429i
\(785\) 13.8447i 0.494139i
\(786\) 0 0
\(787\) −12.9437 + 7.47307i −0.461395 + 0.266386i −0.712630 0.701540i \(-0.752496\pi\)
0.251236 + 0.967926i \(0.419163\pi\)
\(788\) −12.3615 + 7.13689i −0.440359 + 0.254241i
\(789\) 0 0
\(790\) 8.59235i