Properties

Label 630.2.k.c.541.1
Level 630
Weight 2
Character 630.541
Analytic conductor 5.031
Analytic rank 0
Dimension 2
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.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.03057532734\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 630.541
Dual form 630.2.k.c.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} +(-0.500000 - 0.866025i) q^{11} +1.00000 q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{19} +1.00000 q^{20} +1.00000 q^{22} +(3.50000 - 6.06218i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(-2.50000 - 0.866025i) q^{28} +8.00000 q^{29} +(1.00000 + 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.500000 + 2.59808i) q^{35} +(-5.50000 + 9.52628i) q^{37} +(1.50000 + 2.59808i) q^{38} +(-0.500000 + 0.866025i) q^{40} +11.0000 q^{41} +8.00000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(3.50000 + 6.06218i) q^{46} +(-2.50000 + 4.33013i) q^{47} +(1.00000 - 6.92820i) q^{49} +1.00000 q^{50} +(-0.500000 - 0.866025i) q^{52} +(-5.50000 - 9.52628i) q^{53} +1.00000 q^{55} +(2.00000 - 1.73205i) q^{56} +(-4.00000 + 6.92820i) q^{58} +(2.00000 + 3.46410i) q^{59} -2.00000 q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-2.50000 - 0.866025i) q^{70} +6.00000 q^{71} +(3.00000 + 5.19615i) q^{73} +(-5.50000 - 9.52628i) q^{74} -3.00000 q^{76} +(-2.50000 - 0.866025i) q^{77} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-5.50000 + 9.52628i) q^{82} -8.00000 q^{83} +(-4.00000 + 6.92820i) q^{86} +(-0.500000 - 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(2.00000 - 1.73205i) q^{91} -7.00000 q^{92} +(-2.50000 - 4.33013i) q^{94} +(1.50000 + 2.59808i) q^{95} -16.0000 q^{97} +(5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} - q^{5} + 4q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - q^{5} + 4q^{7} + 2q^{8} - q^{10} - q^{11} + 2q^{13} + q^{14} - q^{16} + 3q^{19} + 2q^{20} + 2q^{22} + 7q^{23} - q^{25} - q^{26} - 5q^{28} + 16q^{29} + 2q^{31} - q^{32} + q^{35} - 11q^{37} + 3q^{38} - q^{40} + 22q^{41} + 16q^{43} - q^{44} + 7q^{46} - 5q^{47} + 2q^{49} + 2q^{50} - q^{52} - 11q^{53} + 2q^{55} + 4q^{56} - 8q^{58} + 4q^{59} - 4q^{62} + 2q^{64} - q^{65} - 5q^{70} + 12q^{71} + 6q^{73} - 11q^{74} - 6q^{76} - 5q^{77} + 8q^{79} - q^{80} - 11q^{82} - 16q^{83} - 8q^{86} - q^{88} - 10q^{89} + 4q^{91} - 14q^{92} - 5q^{94} + 3q^{95} - 32q^{97} + 11q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(281\) \(451\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0.500000 + 2.59808i 0.133631 + 0.694365i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 1.50000 2.59808i 0.344124 0.596040i −0.641071 0.767482i \(-0.721509\pi\)
0.985194 + 0.171442i \(0.0548427\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 3.50000 6.06218i 0.729800 1.26405i −0.227167 0.973856i \(-0.572946\pi\)
0.956967 0.290196i \(-0.0937204\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −0.500000 + 0.866025i −0.0980581 + 0.169842i
\(27\) 0 0
\(28\) −2.50000 0.866025i −0.472456 0.163663i
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) 1.00000 + 1.73205i 0.179605 + 0.311086i 0.941745 0.336327i \(-0.109185\pi\)
−0.762140 + 0.647412i \(0.775851\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.500000 + 2.59808i 0.0845154 + 0.439155i
\(36\) 0 0
\(37\) −5.50000 + 9.52628i −0.904194 + 1.56611i −0.0821995 + 0.996616i \(0.526194\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 1.50000 + 2.59808i 0.243332 + 0.421464i
\(39\) 0 0
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) 11.0000 1.71791 0.858956 0.512050i \(-0.171114\pi\)
0.858956 + 0.512050i \(0.171114\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) 0 0
\(46\) 3.50000 + 6.06218i 0.516047 + 0.893819i
\(47\) −2.50000 + 4.33013i −0.364662 + 0.631614i −0.988722 0.149763i \(-0.952149\pi\)
0.624059 + 0.781377i \(0.285482\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) −0.500000 0.866025i −0.0693375 0.120096i
\(53\) −5.50000 9.52628i −0.755483 1.30854i −0.945134 0.326683i \(-0.894069\pi\)
0.189651 0.981852i \(-0.439264\pi\)
\(54\) 0 0
\(55\) 1.00000 0.134840
\(56\) 2.00000 1.73205i 0.267261 0.231455i
\(57\) 0 0
\(58\) −4.00000 + 6.92820i −0.525226 + 0.909718i
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 0 0
\(61\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) −2.00000 −0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −0.500000 + 0.866025i −0.0620174 + 0.107417i
\(66\) 0 0
\(67\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −2.50000 0.866025i −0.298807 0.103510i
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 3.00000 + 5.19615i 0.351123 + 0.608164i 0.986447 0.164083i \(-0.0524664\pi\)
−0.635323 + 0.772246i \(0.719133\pi\)
\(74\) −5.50000 9.52628i −0.639362 1.10741i
\(75\) 0 0
\(76\) −3.00000 −0.344124
\(77\) −2.50000 0.866025i −0.284901 0.0986928i
\(78\) 0 0
\(79\) 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i \(-0.684745\pi\)
0.998388 + 0.0567635i \(0.0180781\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) 0 0
\(82\) −5.50000 + 9.52628i −0.607373 + 1.05200i
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.00000 + 6.92820i −0.431331 + 0.747087i
\(87\) 0 0
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) −5.00000 + 8.66025i −0.529999 + 0.917985i 0.469389 + 0.882992i \(0.344474\pi\)
−0.999388 + 0.0349934i \(0.988859\pi\)
\(90\) 0 0
\(91\) 2.00000 1.73205i 0.209657 0.181568i
\(92\) −7.00000 −0.729800
\(93\) 0 0
\(94\) −2.50000 4.33013i −0.257855 0.446619i
\(95\) 1.50000 + 2.59808i 0.153897 + 0.266557i
\(96\) 0 0
\(97\) −16.0000 −1.62455 −0.812277 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) 5.50000 + 4.33013i 0.555584 + 0.437409i
\(99\) 0 0
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i \(-0.544314\pi\)
0.927030 0.374987i \(-0.122353\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) 11.0000 1.06841
\(107\) −5.00000 + 8.66025i −0.483368 + 0.837218i −0.999818 0.0190994i \(-0.993920\pi\)
0.516449 + 0.856318i \(0.327253\pi\)
\(108\) 0 0
\(109\) −3.00000 5.19615i −0.287348 0.497701i 0.685828 0.727764i \(-0.259440\pi\)
−0.973176 + 0.230063i \(0.926107\pi\)
\(110\) −0.500000 + 0.866025i −0.0476731 + 0.0825723i
\(111\) 0 0
\(112\) 0.500000 + 2.59808i 0.0472456 + 0.245495i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 3.50000 + 6.06218i 0.326377 + 0.565301i
\(116\) −4.00000 6.92820i −0.371391 0.643268i
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 0 0
\(123\) 0 0
\(124\) 1.00000 1.73205i 0.0898027 0.155543i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −17.0000 −1.50851 −0.754253 0.656584i \(-0.772001\pi\)
−0.754253 + 0.656584i \(0.772001\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −0.500000 0.866025i −0.0438529 0.0759555i
\(131\) −2.50000 + 4.33013i −0.218426 + 0.378325i −0.954327 0.298764i \(-0.903426\pi\)
0.735901 + 0.677089i \(0.236759\pi\)
\(132\) 0 0
\(133\) −1.50000 7.79423i −0.130066 0.675845i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.00000 15.5885i −0.768922 1.33181i −0.938148 0.346235i \(-0.887460\pi\)
0.169226 0.985577i \(-0.445873\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 2.00000 1.73205i 0.169031 0.146385i
\(141\) 0 0
\(142\) −3.00000 + 5.19615i −0.251754 + 0.436051i
\(143\) −0.500000 0.866025i −0.0418121 0.0724207i
\(144\) 0 0
\(145\) −4.00000 + 6.92820i −0.332182 + 0.575356i
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) 11.0000 0.904194
\(149\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) 0 0
\(151\) −3.00000 5.19615i −0.244137 0.422857i 0.717752 0.696299i \(-0.245171\pi\)
−0.961888 + 0.273442i \(0.911838\pi\)
\(152\) 1.50000 2.59808i 0.121666 0.210732i
\(153\) 0 0
\(154\) 2.00000 1.73205i 0.161165 0.139573i
\(155\) −2.00000 −0.160644
\(156\) 0 0
\(157\) 3.50000 + 6.06218i 0.279330 + 0.483814i 0.971219 0.238190i \(-0.0765542\pi\)
−0.691888 + 0.722005i \(0.743221\pi\)
\(158\) 4.00000 + 6.92820i 0.318223 + 0.551178i
\(159\) 0 0
\(160\) 1.00000 0.0790569
\(161\) −3.50000 18.1865i −0.275839 1.43330i
\(162\) 0 0
\(163\) −8.00000 + 13.8564i −0.626608 + 1.08532i 0.361619 + 0.932326i \(0.382224\pi\)
−0.988227 + 0.152992i \(0.951109\pi\)
\(164\) −5.50000 9.52628i −0.429478 0.743877i
\(165\) 0 0
\(166\) 4.00000 6.92820i 0.310460 0.537733i
\(167\) 3.00000 0.232147 0.116073 0.993241i \(-0.462969\pi\)
0.116073 + 0.993241i \(0.462969\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) −7.50000 + 12.9904i −0.570214 + 0.987640i 0.426329 + 0.904568i \(0.359807\pi\)
−0.996544 + 0.0830722i \(0.973527\pi\)
\(174\) 0 0
\(175\) −2.50000 0.866025i −0.188982 0.0654654i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −5.00000 8.66025i −0.374766 0.649113i
\(179\) −9.50000 16.4545i −0.710063 1.22987i −0.964833 0.262864i \(-0.915333\pi\)
0.254770 0.967002i \(-0.418000\pi\)
\(180\) 0 0
\(181\) −24.0000 −1.78391 −0.891953 0.452128i \(-0.850665\pi\)
−0.891953 + 0.452128i \(0.850665\pi\)
\(182\) 0.500000 + 2.59808i 0.0370625 + 0.192582i
\(183\) 0 0
\(184\) 3.50000 6.06218i 0.258023 0.446910i
\(185\) −5.50000 9.52628i −0.404368 0.700386i
\(186\) 0 0
\(187\) 0 0
\(188\) 5.00000 0.364662
\(189\) 0 0
\(190\) −3.00000 −0.217643
\(191\) −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) 0 0
\(193\) −11.0000 19.0526i −0.791797 1.37143i −0.924853 0.380325i \(-0.875812\pi\)
0.133056 0.991109i \(-0.457521\pi\)
\(194\) 8.00000 13.8564i 0.574367 0.994832i
\(195\) 0 0
\(196\) −6.50000 + 2.59808i −0.464286 + 0.185577i
\(197\) 1.00000 0.0712470 0.0356235 0.999365i \(-0.488658\pi\)
0.0356235 + 0.999365i \(0.488658\pi\)
\(198\) 0 0
\(199\) 12.0000 + 20.7846i 0.850657 + 1.47338i 0.880616 + 0.473831i \(0.157129\pi\)
−0.0299585 + 0.999551i \(0.509538\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 0 0
\(202\) 0 0
\(203\) 16.0000 13.8564i 1.12298 0.972529i
\(204\) 0 0
\(205\) −5.50000 + 9.52628i −0.384137 + 0.665344i
\(206\) 8.00000 + 13.8564i 0.557386 + 0.965422i
\(207\) 0 0
\(208\) −0.500000 + 0.866025i −0.0346688 + 0.0600481i
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) −5.50000 + 9.52628i −0.377742 + 0.654268i
\(213\) 0 0
\(214\) −5.00000 8.66025i −0.341793 0.592003i
\(215\) −4.00000 + 6.92820i −0.272798 + 0.472500i
\(216\) 0 0
\(217\) 5.00000 + 1.73205i 0.339422 + 0.117579i
\(218\) 6.00000 0.406371
\(219\) 0 0
\(220\) −0.500000 0.866025i −0.0337100 0.0583874i
\(221\) 0 0
\(222\) 0 0
\(223\) 12.0000 0.803579 0.401790 0.915732i \(-0.368388\pi\)
0.401790 + 0.915732i \(0.368388\pi\)
\(224\) −2.50000 0.866025i −0.167038 0.0578638i
\(225\) 0 0
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) 4.00000 + 6.92820i 0.265489 + 0.459841i 0.967692 0.252136i \(-0.0811332\pi\)
−0.702202 + 0.711977i \(0.747800\pi\)
\(228\) 0 0
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) −7.00000 −0.461566
\(231\) 0 0
\(232\) 8.00000 0.525226
\(233\) 9.00000 15.5885i 0.589610 1.02123i −0.404674 0.914461i \(-0.632615\pi\)
0.994283 0.106773i \(-0.0340517\pi\)
\(234\) 0 0
\(235\) −2.50000 4.33013i −0.163082 0.282466i
\(236\) 2.00000 3.46410i 0.130189 0.225494i
\(237\) 0 0
\(238\) 0 0
\(239\) 18.0000 1.16432 0.582162 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 0 0
\(241\) −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i \(-0.239053\pi\)
−0.956456 + 0.291877i \(0.905720\pi\)
\(242\) 5.00000 + 8.66025i 0.321412 + 0.556702i
\(243\) 0 0
\(244\) 0 0
\(245\) 5.50000 + 4.33013i 0.351382 + 0.276642i
\(246\) 0 0
\(247\) 1.50000 2.59808i 0.0954427 0.165312i
\(248\) 1.00000 + 1.73205i 0.0635001 + 0.109985i
\(249\) 0 0
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −13.0000 −0.820553 −0.410276 0.911961i \(-0.634568\pi\)
−0.410276 + 0.911961i \(0.634568\pi\)
\(252\) 0 0
\(253\) −7.00000 −0.440086
\(254\) 8.50000 14.7224i 0.533337 0.923768i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.0000 + 17.3205i −0.623783 + 1.08042i 0.364992 + 0.931011i \(0.381072\pi\)
−0.988775 + 0.149413i \(0.952262\pi\)
\(258\) 0 0
\(259\) 5.50000 + 28.5788i 0.341753 + 1.77580i
\(260\) 1.00000 0.0620174
\(261\) 0 0
\(262\) −2.50000 4.33013i −0.154451 0.267516i
\(263\) 12.0000 + 20.7846i 0.739952 + 1.28163i 0.952517 + 0.304487i \(0.0984850\pi\)
−0.212565 + 0.977147i \(0.568182\pi\)
\(264\) 0 0
\(265\) 11.0000 0.675725
\(266\) 7.50000 + 2.59808i 0.459855 + 0.159298i
\(267\) 0 0
\(268\) 0 0
\(269\) 10.0000 + 17.3205i 0.609711 + 1.05605i 0.991288 + 0.131713i \(0.0420477\pi\)
−0.381577 + 0.924337i \(0.624619\pi\)
\(270\) 0 0
\(271\) −16.0000 + 27.7128i −0.971931 + 1.68343i −0.282218 + 0.959350i \(0.591070\pi\)
−0.689713 + 0.724083i \(0.742263\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 18.0000 1.08742
\(275\) −0.500000 + 0.866025i −0.0301511 + 0.0522233i
\(276\) 0 0
\(277\) 11.0000 + 19.0526i 0.660926 + 1.14476i 0.980373 + 0.197153i \(0.0631696\pi\)
−0.319447 + 0.947604i \(0.603497\pi\)
\(278\) −10.0000 + 17.3205i −0.599760 + 1.03882i
\(279\) 0 0
\(280\) 0.500000 + 2.59808i 0.0298807 + 0.155265i
\(281\) 1.00000 0.0596550 0.0298275 0.999555i \(-0.490504\pi\)
0.0298275 + 0.999555i \(0.490504\pi\)
\(282\) 0 0
\(283\) 7.00000 + 12.1244i 0.416107 + 0.720718i 0.995544 0.0942988i \(-0.0300609\pi\)
−0.579437 + 0.815017i \(0.696728\pi\)
\(284\) −3.00000 5.19615i −0.178017 0.308335i
\(285\) 0 0
\(286\) 1.00000 0.0591312
\(287\) 22.0000 19.0526i 1.29862 1.12464i
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) −4.00000 6.92820i −0.234888 0.406838i
\(291\) 0 0
\(292\) 3.00000 5.19615i 0.175562 0.304082i
\(293\) −27.0000 −1.57736 −0.788678 0.614806i \(-0.789234\pi\)
−0.788678 + 0.614806i \(0.789234\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) −5.50000 + 9.52628i −0.319681 + 0.553704i
\(297\) 0 0
\(298\) 0 0
\(299\) 3.50000 6.06218i 0.202410 0.350585i
\(300\) 0 0
\(301\) 16.0000 13.8564i 0.922225 0.798670i
\(302\) 6.00000 0.345261
\(303\) 0 0
\(304\) 1.50000 + 2.59808i 0.0860309 + 0.149010i
\(305\) 0 0
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0.500000 + 2.59808i 0.0284901 + 0.148039i
\(309\) 0 0
\(310\) 1.00000 1.73205i 0.0567962 0.0983739i
\(311\) 6.00000 + 10.3923i 0.340229 + 0.589294i 0.984475 0.175525i \(-0.0561621\pi\)
−0.644246 + 0.764818i \(0.722829\pi\)
\(312\) 0 0
\(313\) 6.00000 10.3923i 0.339140 0.587408i −0.645131 0.764072i \(-0.723197\pi\)
0.984271 + 0.176664i \(0.0565306\pi\)
\(314\) −7.00000 −0.395033
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 0 0
\(319\) −4.00000 6.92820i −0.223957 0.387905i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 17.5000 + 6.06218i 0.975237 + 0.337832i
\(323\) 0 0
\(324\) 0 0
\(325\) −0.500000 0.866025i −0.0277350 0.0480384i
\(326\) −8.00000 13.8564i −0.443079 0.767435i
\(327\) 0 0
\(328\) 11.0000 0.607373
\(329\) 2.50000 + 12.9904i 0.137829 + 0.716183i
\(330\) 0 0
\(331\) 6.50000 11.2583i 0.357272 0.618814i −0.630232 0.776407i \(-0.717040\pi\)
0.987504 + 0.157593i \(0.0503735\pi\)
\(332\) 4.00000 + 6.92820i 0.219529 + 0.380235i
\(333\) 0 0
\(334\) −1.50000 + 2.59808i −0.0820763 + 0.142160i
\(335\) 0 0
\(336\) 0 0
\(337\) −12.0000 −0.653682 −0.326841 0.945079i \(-0.605984\pi\)
−0.326841 + 0.945079i \(0.605984\pi\)
\(338\) 6.00000 10.3923i 0.326357 0.565267i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.00000 1.73205i 0.0541530 0.0937958i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) −7.50000 12.9904i −0.403202 0.698367i
\(347\) 7.00000 + 12.1244i 0.375780 + 0.650870i 0.990443 0.137920i \(-0.0440416\pi\)
−0.614664 + 0.788789i \(0.710708\pi\)
\(348\) 0 0
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) 2.00000 1.73205i 0.106904 0.0925820i
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 12.0000 + 20.7846i 0.638696 + 1.10625i 0.985719 + 0.168397i \(0.0538590\pi\)
−0.347024 + 0.937856i \(0.612808\pi\)
\(354\) 0 0
\(355\) −3.00000 + 5.19615i −0.159223 + 0.275783i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 19.0000 1.00418
\(359\) 2.00000 3.46410i 0.105556 0.182828i −0.808409 0.588621i \(-0.799671\pi\)
0.913965 + 0.405793i \(0.133004\pi\)
\(360\) 0 0
\(361\) 5.00000 + 8.66025i 0.263158 + 0.455803i
\(362\) 12.0000 20.7846i 0.630706 1.09241i
\(363\) 0 0
\(364\) −2.50000 0.866025i −0.131036 0.0453921i
\(365\) −6.00000 −0.314054
\(366\) 0 0
\(367\) −12.5000 21.6506i −0.652495 1.13015i −0.982516 0.186180i \(-0.940389\pi\)
0.330021 0.943974i \(-0.392944\pi\)
\(368\) 3.50000 + 6.06218i 0.182450 + 0.316013i
\(369\) 0 0
\(370\) 11.0000 0.571863
\(371\) −27.5000 9.52628i −1.42773 0.494580i
\(372\) 0 0
\(373\) −3.00000 + 5.19615i −0.155334 + 0.269047i −0.933181 0.359408i \(-0.882979\pi\)
0.777847 + 0.628454i \(0.216312\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −2.50000 + 4.33013i −0.128928 + 0.223309i
\(377\) 8.00000 0.412021
\(378\) 0 0
\(379\) −19.0000 −0.975964 −0.487982 0.872854i \(-0.662267\pi\)
−0.487982 + 0.872854i \(0.662267\pi\)
\(380\) 1.50000 2.59808i 0.0769484 0.133278i
\(381\) 0 0
\(382\) −3.00000 5.19615i −0.153493 0.265858i
\(383\) 17.5000 30.3109i 0.894208 1.54881i 0.0594268 0.998233i \(-0.481073\pi\)
0.834781 0.550581i \(-0.185594\pi\)
\(384\) 0 0
\(385\) 2.00000 1.73205i 0.101929 0.0882735i
\(386\) 22.0000 1.11977
\(387\) 0 0
\(388\) 8.00000 + 13.8564i 0.406138 + 0.703452i
\(389\) 5.00000 + 8.66025i 0.253510 + 0.439092i 0.964490 0.264120i \(-0.0850816\pi\)
−0.710980 + 0.703213i \(0.751748\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.00000 6.92820i 0.0505076 0.349927i
\(393\) 0 0
\(394\) −0.500000 + 0.866025i −0.0251896 + 0.0436297i
\(395\) 4.00000 + 6.92820i 0.201262 + 0.348596i
\(396\) 0 0
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −2.50000 + 4.33013i −0.124844 + 0.216236i −0.921672 0.387970i \(-0.873176\pi\)
0.796828 + 0.604206i \(0.206510\pi\)
\(402\) 0 0
\(403\) 1.00000 + 1.73205i 0.0498135 + 0.0862796i
\(404\) 0 0
\(405\) 0 0
\(406\) 4.00000 + 20.7846i 0.198517 + 1.03152i
\(407\) 11.0000 0.545250
\(408\) 0 0
\(409\) −1.00000 1.73205i −0.0494468 0.0856444i 0.840243 0.542211i \(-0.182412\pi\)
−0.889689 + 0.456566i \(0.849079\pi\)
\(410\) −5.50000 9.52628i −0.271626 0.470469i
\(411\) 0 0
\(412\) −16.0000 −0.788263
\(413\) 10.0000 + 3.46410i 0.492068 + 0.170457i
\(414\) 0 0
\(415\) 4.00000 6.92820i 0.196352 0.340092i
\(416\) −0.500000 0.866025i −0.0245145 0.0424604i
\(417\) 0 0
\(418\) 1.50000 2.59808i 0.0733674 0.127076i
\(419\) 5.00000 0.244266 0.122133 0.992514i \(-0.461027\pi\)
0.122133 + 0.992514i \(0.461027\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) −2.50000 + 4.33013i −0.121698 + 0.210787i
\(423\) 0 0
\(424\) −5.50000 9.52628i −0.267104 0.462637i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 10.0000 0.483368
\(429\) 0 0
\(430\) −4.00000 6.92820i −0.192897 0.334108i
\(431\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0 0
\(433\) −32.0000 −1.53782 −0.768911 0.639356i \(-0.779201\pi\)
−0.768911 + 0.639356i \(0.779201\pi\)
\(434\) −4.00000 + 3.46410i −0.192006 + 0.166282i
\(435\) 0 0
\(436\) −3.00000 + 5.19615i −0.143674 + 0.248851i
\(437\) −10.5000 18.1865i −0.502283 0.869980i
\(438\) 0 0
\(439\) −16.0000 + 27.7128i −0.763638 + 1.32266i 0.177325 + 0.984152i \(0.443256\pi\)
−0.940963 + 0.338508i \(0.890078\pi\)
\(440\) 1.00000 0.0476731
\(441\) 0 0
\(442\) 0 0
\(443\) 8.00000 13.8564i 0.380091 0.658338i −0.610984 0.791643i \(-0.709226\pi\)
0.991075 + 0.133306i \(0.0425592\pi\)
\(444\) 0 0
\(445\) −5.00000 8.66025i −0.237023 0.410535i
\(446\) −6.00000 + 10.3923i −0.284108 + 0.492090i
\(447\) 0 0
\(448\) 2.00000 1.73205i 0.0944911 0.0818317i
\(449\) −11.0000 −0.519122 −0.259561 0.965727i \(-0.583578\pi\)
−0.259561 + 0.965727i \(0.583578\pi\)
\(450\) 0 0
\(451\) −5.50000 9.52628i −0.258985 0.448575i
\(452\) 3.00000 + 5.19615i 0.141108 + 0.244406i
\(453\) 0 0
\(454\) −8.00000 −0.375459
\(455\) 0.500000 + 2.59808i 0.0234404 + 0.121800i
\(456\) 0 0
\(457\) 9.00000 15.5885i 0.421002 0.729197i −0.575036 0.818128i \(-0.695012\pi\)
0.996038 + 0.0889312i \(0.0283451\pi\)
\(458\) −7.00000 12.1244i −0.327089 0.566534i
\(459\) 0 0
\(460\) 3.50000 6.06218i 0.163188 0.282650i
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) −13.0000 −0.604161 −0.302081 0.953282i \(-0.597681\pi\)
−0.302081 + 0.953282i \(0.597681\pi\)
\(464\) −4.00000 + 6.92820i −0.185695 + 0.321634i
\(465\) 0 0
\(466\) 9.00000 + 15.5885i 0.416917 + 0.722121i
\(467\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 5.00000 0.230633
\(471\) 0 0
\(472\) 2.00000 + 3.46410i 0.0920575 + 0.159448i
\(473\) −4.00000 6.92820i −0.183920 0.318559i
\(474\) 0 0
\(475\) −3.00000 −0.137649
\(476\) 0 0
\(477\) 0 0
\(478\) −9.00000 + 15.5885i −0.411650 + 0.712999i
\(479\) 11.0000 + 19.0526i 0.502603 + 0.870534i 0.999995 + 0.00300810i \(0.000957509\pi\)
−0.497393 + 0.867526i \(0.665709\pi\)
\(480\) 0 0
\(481\) −5.50000 + 9.52628i −0.250778 + 0.434361i
\(482\) 7.00000 0.318841
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) 8.00000 13.8564i 0.363261 0.629187i
\(486\) 0 0
\(487\) 8.00000 + 13.8564i 0.362515 + 0.627894i 0.988374 0.152042i \(-0.0485850\pi\)
−0.625859 + 0.779936i \(0.715252\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −6.50000 + 2.59808i −0.293640 + 0.117369i
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 1.50000 + 2.59808i 0.0674882 + 0.116893i
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) 12.0000 10.3923i 0.538274 0.466159i
\(498\) 0 0
\(499\) 16.0000 27.7128i 0.716258 1.24060i −0.246214 0.969216i \(-0.579187\pi\)
0.962472 0.271380i \(-0.0874801\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 0 0
\(502\) 6.50000 11.2583i 0.290109 0.502484i
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 3.50000 6.06218i 0.155594 0.269497i
\(507\) 0 0
\(508\) 8.50000 + 14.7224i 0.377127 + 0.653202i
\(509\) −17.0000 + 29.4449i −0.753512 + 1.30512i 0.192599 + 0.981278i \(0.438308\pi\)
−0.946111 + 0.323843i \(0.895025\pi\)
\(510\) 0 0
\(511\) 15.0000 + 5.19615i 0.663561 + 0.229864i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −10.0000 17.3205i −0.441081 0.763975i
\(515\) 8.00000 + 13.8564i 0.352522 + 0.610586i
\(516\) 0 0
\(517\) 5.00000 0.219900
\(518\) −27.5000 9.52628i −1.20828 0.418561i
\(519\) 0 0
\(520\) −0.500000 + 0.866025i −0.0219265 + 0.0379777i
\(521\) −16.5000 28.5788i −0.722878 1.25206i −0.959841 0.280543i \(-0.909485\pi\)
0.236963 0.971519i \(-0.423848\pi\)
\(522\) 0 0
\(523\) −1.00000 + 1.73205i −0.0437269 + 0.0757373i −0.887061 0.461653i \(-0.847256\pi\)
0.843334 + 0.537390i \(0.180590\pi\)
\(524\) 5.00000 0.218426
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) −13.0000 22.5167i −0.565217 0.978985i
\(530\) −5.50000 + 9.52628i −0.238905 + 0.413795i
\(531\) 0 0
\(532\) −6.00000 + 5.19615i −0.260133 + 0.225282i
\(533\) 11.0000 0.476463
\(534\) 0 0
\(535\) −5.00000 8.66025i −0.216169 0.374415i
\(536\) 0 0
\(537\) 0 0
\(538\) −20.0000 −0.862261
\(539\) −6.50000 + 2.59808i −0.279975 + 0.111907i
\(540\) 0 0
\(541\) 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i \(-0.764369\pi\)
0.953262 + 0.302144i \(0.0977023\pi\)
\(542\) −16.0000 27.7128i −0.687259 1.19037i
\(543\) 0 0
\(544\) 0 0
\(545\) 6.00000 0.257012
\(546\) 0 0
\(547\) 16.0000 0.684111 0.342055 0.939680i \(-0.388877\pi\)
0.342055 + 0.939680i \(0.388877\pi\)
\(548\) −9.00000 + 15.5885i −0.384461 + 0.665906i
\(549\) 0 0
\(550\) −0.500000 0.866025i −0.0213201 0.0369274i
\(551\) 12.0000 20.7846i 0.511217 0.885454i
\(552\) 0 0
\(553\) −4.00000 20.7846i −0.170097 0.883852i
\(554\) −22.0000 −0.934690
\(555\) 0 0
\(556\) −10.0000 17.3205i −0.424094 0.734553i
\(557\) −16.5000 28.5788i −0.699127 1.21092i −0.968769 0.247964i \(-0.920239\pi\)
0.269642 0.962961i \(-0.413095\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) −2.50000 0.866025i −0.105644 0.0365963i
\(561\) 0 0
\(562\) −0.500000 + 0.866025i −0.0210912 + 0.0365311i
\(563\) −19.0000 32.9090i −0.800755 1.38695i −0.919120 0.393977i \(-0.871099\pi\)
0.118366 0.992970i \(-0.462235\pi\)
\(564\) 0 0
\(565\) 3.00000 5.19615i 0.126211 0.218604i
\(566\) −14.0000 −0.588464
\(567\) 0 0
\(568\) 6.00000 0.251754
\(569\) −4.50000 + 7.79423i −0.188650 + 0.326751i −0.944800 0.327647i \(-0.893744\pi\)
0.756151 + 0.654398i \(0.227078\pi\)
\(570\) 0 0
\(571\) 16.0000 + 27.7128i 0.669579 + 1.15975i 0.978022 + 0.208502i \(0.0668588\pi\)
−0.308443 + 0.951243i \(0.599808\pi\)
\(572\) −0.500000 + 0.866025i −0.0209061 + 0.0362103i
\(573\) 0 0
\(574\) 5.50000 + 28.5788i 0.229566 + 1.19286i
\(575\) −7.00000 −0.291920
\(576\) 0 0
\(577\) 7.00000 + 12.1244i 0.291414 + 0.504744i 0.974144 0.225927i \(-0.0725410\pi\)
−0.682730 + 0.730670i \(0.739208\pi\)
\(578\) 8.50000 + 14.7224i 0.353553 + 0.612372i
\(579\) 0 0
\(580\) 8.00000 0.332182
\(581\) −16.0000 + 13.8564i −0.663792 + 0.574861i
\(582\) 0 0
\(583\) −5.50000 + 9.52628i −0.227787 + 0.394538i
\(584\) 3.00000 + 5.19615i 0.124141 + 0.215018i
\(585\) 0 0
\(586\) 13.5000 23.3827i 0.557680 0.965930i
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) 2.00000 3.46410i 0.0823387 0.142615i
\(591\) 0 0
\(592\) −5.50000 9.52628i −0.226049 0.391528i
\(593\) 8.00000 13.8564i 0.328521 0.569014i −0.653698 0.756756i \(-0.726783\pi\)
0.982219 + 0.187741i \(0.0601166\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 3.50000 + 6.06218i 0.143126 + 0.247901i
\(599\) 1.00000 + 1.73205i 0.0408589 + 0.0707697i 0.885732 0.464198i \(-0.153657\pi\)
−0.844873 + 0.534967i \(0.820324\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 4.00000 + 20.7846i 0.163028 + 0.847117i
\(603\) 0 0
\(604\) −3.00000 + 5.19615i −0.122068 + 0.211428i
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 0 0
\(607\) 18.5000 32.0429i 0.750892 1.30058i −0.196499 0.980504i \(-0.562957\pi\)
0.947391 0.320079i \(-0.103709\pi\)
\(608\) −3.00000 −0.121666
\(609\) 0 0
\(610\) 0 0
\(611\) −2.50000 + 4.33013i −0.101139 + 0.175178i
\(612\) 0 0
\(613\) 20.5000 + 35.5070i 0.827987 + 1.43412i 0.899615 + 0.436684i \(0.143847\pi\)
−0.0716275 + 0.997431i \(0.522819\pi\)
\(614\) −10.0000 + 17.3205i −0.403567 + 0.698999i
\(615\) 0 0
\(616\) −2.50000 0.866025i −0.100728 0.0348932i
\(617\) −28.0000 −1.12724 −0.563619 0.826035i \(-0.690591\pi\)
−0.563619 + 0.826035i \(0.690591\pi\)
\(618\) 0 0
\(619\) −14.5000 25.1147i −0.582804 1.00945i −0.995145 0.0984169i \(-0.968622\pi\)
0.412341 0.911030i \(-0.364711\pi\)
\(620\) 1.00000 + 1.73205i 0.0401610 + 0.0695608i
\(621\) 0 0
\(622\) −12.0000 −0.481156
\(623\) 5.00000 + 25.9808i 0.200321 + 1.04090i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 6.00000 + 10.3923i 0.239808 + 0.415360i
\(627\) 0 0
\(628\) 3.50000 6.06218i 0.139665 0.241907i
\(629\) 0 0
\(630\) 0 0
\(631\) −26.0000 −1.03504 −0.517522 0.855670i \(-0.673145\pi\)
−0.517522 + 0.855670i \(0.673145\pi\)
\(632\) 4.00000 6.92820i 0.159111 0.275589i
\(633\) 0 0
\(634\) −9.00000 15.5885i −0.357436 0.619097i
\(635\) 8.50000 14.7224i 0.337312 0.584242i
\(636\) 0 0
\(637\) 1.00000 6.92820i 0.0396214 0.274505i
\(638\) 8.00000 0.316723
\(639\) 0 0
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −1.50000 2.59808i −0.0592464 0.102618i 0.834881 0.550431i \(-0.185536\pi\)
−0.894127 + 0.447813i \(0.852203\pi\)
\(642\) 0 0
\(643\) −10.0000 −0.394362 −0.197181 0.980367i \(-0.563179\pi\)
−0.197181 + 0.980367i \(0.563179\pi\)
\(644\) −14.0000 + 12.1244i −0.551677 + 0.477767i
\(645\) 0 0
\(646\) 0 0
\(647\) −8.50000 14.7224i −0.334169 0.578799i 0.649155 0.760656i \(-0.275122\pi\)
−0.983325 + 0.181857i \(0.941789\pi\)
\(648\) 0 0
\(649\) 2.00000 3.46410i 0.0785069 0.135978i
\(650\) 1.00000 0.0392232
\(651\) 0 0
\(652\) 16.0000 0.626608
\(653\) 3.50000 6.06218i 0.136966 0.237231i −0.789381 0.613904i \(-0.789598\pi\)
0.926347 + 0.376672i \(0.122932\pi\)
\(654\) 0 0
\(655\) −2.50000 4.33013i −0.0976831 0.169192i
\(656\) −5.50000 + 9.52628i −0.214739 + 0.371939i
\(657\) 0 0
\(658\) −12.5000 4.33013i −0.487301 0.168806i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) 12.0000 + 20.7846i 0.466746 + 0.808428i 0.999278 0.0379819i \(-0.0120929\pi\)
−0.532533 + 0.846410i \(0.678760\pi\)
\(662\) 6.50000 + 11.2583i 0.252630 + 0.437567i
\(663\) 0 0
\(664\) −8.00000 −0.310460
\(665\) 7.50000 + 2.59808i 0.290838 + 0.100749i
\(666\) 0 0
\(667\) 28.0000 48.4974i 1.08416 1.87783i
\(668\) −1.50000 2.59808i −0.0580367 0.100523i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 28.0000 1.07932 0.539660 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) 6.00000 10.3923i 0.231111 0.400297i
\(675\) 0 0
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) −6.50000 + 11.2583i −0.249815 + 0.432693i −0.963474 0.267800i \(-0.913703\pi\)
0.713659 + 0.700493i \(0.247037\pi\)
\(678\) 0 0
\(679\) −32.0000 + 27.7128i −1.22805 + 1.06352i
\(680\) 0 0
\(681\) 0 0
\(682\) 1.00000 + 1.73205i 0.0382920 + 0.0663237i
\(683\) 2.00000 + 3.46410i 0.0765279 + 0.132550i 0.901750 0.432259i \(-0.142283\pi\)
−0.825222 + 0.564809i \(0.808950\pi\)
\(684\) 0 0
\(685\) 18.0000 0.687745
\(686\) 18.5000 0.866025i 0.706333 0.0330650i
\(687\) 0 0
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) −5.50000 9.52628i −0.209533 0.362922i
\(690\) 0 0
\(691\) 6.00000 10.3923i 0.228251 0.395342i −0.729039 0.684472i \(-0.760033\pi\)
0.957290 + 0.289130i \(0.0933661\pi\)
\(692\) 15.0000 0.570214
\(693\) 0 0
\(694\) −14.0000 −0.531433
\(695\) −10.0000 + 17.3205i −0.379322 + 0.657004i
\(696\) 0 0
\(697\) 0 0
\(698\) −6.00000 + 10.3923i −0.227103 + 0.393355i
\(699\) 0 0
\(700\) 0.500000 + 2.59808i 0.0188982 + 0.0981981i
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 16.5000 + 28.5788i 0.622309 + 1.07787i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) 0 0
\(708\) 0 0
\(709\) −22.0000 + 38.1051i −0.826227 + 1.43107i 0.0747503 + 0.997202i \(0.476184\pi\)
−0.900978 + 0.433865i \(0.857149\pi\)
\(710\) −3.00000 5.19615i −0.112588 0.195008i
\(711\) 0 0
\(712\) −5.00000 + 8.66025i −0.187383 + 0.324557i
\(713\) 14.0000 0.524304
\(714\) 0 0
\(715\) 1.00000 0.0373979
\(716\) −9.50000 + 16.4545i −0.355032 + 0.614933i
\(717\) 0 0
\(718\) 2.00000 + 3.46410i 0.0746393 + 0.129279i
\(719\) 1.00000 1.73205i 0.0372937 0.0645946i −0.846776 0.531949i \(-0.821460\pi\)
0.884070 + 0.467355i \(0.154793\pi\)
\(720\) 0 0
\(721\) −8.00000 41.5692i −0.297936 1.54812i
\(722\) −10.0000 −0.372161
\(723\) 0 0
\(724\) 12.0000 + 20.7846i 0.445976 + 0.772454i
\(725\) −4.00000 6.92820i −0.148556 0.257307i
\(726\) 0 0
\(727\) 11.0000 0.407967 0.203984 0.978974i \(-0.434611\pi\)
0.203984 + 0.978974i \(0.434611\pi\)
\(728\) 2.00000 1.73205i 0.0741249 0.0641941i
\(729\) 0 0
\(730\) 3.00000 5.19615i 0.111035 0.192318i
\(731\) 0 0
\(732\) 0 0
\(733\) −5.50000 + 9.52628i −0.203147 + 0.351861i −0.949541 0.313644i \(-0.898450\pi\)
0.746394 + 0.665505i \(0.231784\pi\)
\(734\) 25.0000 0.922767
\(735\) 0 0
\(736\) −7.00000 −0.258023
\(737\) 0 0
\(738\) 0 0
\(739\) 9.50000 + 16.4545i 0.349463 + 0.605288i 0.986154 0.165831i \(-0.0530307\pi\)
−0.636691 + 0.771119i \(0.719697\pi\)
\(740\) −5.50000 + 9.52628i −0.202184 + 0.350193i
\(741\) 0 0
\(742\) 22.0000 19.0526i 0.807645 0.699441i
\(743\) −49.0000 −1.79764 −0.898818 0.438322i \(-0.855573\pi\)
−0.898818 + 0.438322i \(0.855573\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −3.00000 5.19615i −0.109838 0.190245i
\(747\) 0 0
\(748\) 0 0
\(749\) 5.00000 + 25.9808i 0.182696 + 0.949316i
\(750\) 0 0
\(751\) −13.0000 + 22.5167i −0.474377 + 0.821645i −0.999570 0.0293387i \(-0.990660\pi\)
0.525193 + 0.850983i \(0.323993\pi\)
\(752\) −2.50000 4.33013i −0.0911656 0.157903i
\(753\) 0 0
\(754\) −4.00000 + 6.92820i −0.145671 + 0.252310i
\(755\) 6.00000 0.218362
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 9.50000 16.4545i 0.345056 0.597654i
\(759\) 0 0
\(760\) 1.50000 + 2.59808i 0.0544107 + 0.0942421i
\(761\) 13.5000 23.3827i 0.489375 0.847622i −0.510551 0.859848i \(-0.670558\pi\)
0.999925 + 0.0122260i \(0.00389175\pi\)
\(762\) 0 0
\(763\) −15.0000 5.19615i −0.543036 0.188113i
\(764\) 6.00000 0.217072
\(765\) 0 0
\(766\) 17.5000 + 30.3109i 0.632301 + 1.09518i
\(767\) 2.00000 + 3.46410i 0.0722158 + 0.125081i
\(768\) 0 0
\(769\) −5.00000 −0.180305 −0.0901523 0.995928i \(-0.528735\pi\)
−0.0901523 + 0.995928i \(0.528735\pi\)
\(770\) 0.500000 + 2.59808i 0.0180187 + 0.0936282i
\(771\) 0 0
\(772\) −11.0000 + 19.0526i −0.395899 + 0.685717i
\(773\) 16.5000 + 28.5788i 0.593464 + 1.02791i 0.993762 + 0.111524i \(0.0355733\pi\)
−0.400298 + 0.916385i \(0.631093\pi\)
\(774\) 0 0
\(775\) 1.00000 1.73205i 0.0359211 0.0622171i
\(776\) −16.0000 −0.574367
\(777\) 0 0
\(778\) −10.0000 −0.358517
\(779\) 16.5000 28.5788i 0.591174 1.02394i
\(780\) 0 0
\(781\) −3.00000 5.19615i −0.107348 0.185933i
\(782\) 0 0
\(783\) 0 0
\(784\) 5.50000 + 4.33013i 0.196429 + 0.154647i
\(785\) −7.00000 −0.249841
\(786\) 0 0
\(787\) −11.0000 19.0526i −0.392108 0.679150i 0.600620 0.799535i \(-0.294921\pi\)
−0.992727 + 0.120384i \(0.961587\pi\)
\(788\) −0.500000 0.866025i −0.0178118 0.0308509i
\(789\) 0 0
\(790\) −8.00000 −0.284627
\(791\) −12.0000 + 10.3923i −0.426671 + 0.369508i
\(792\) 0 0
\(793\) 0 0
\(794\) −7.00000 12.1244i −0.248421 0.430277i
\(795\) 0 0
\(796\) 12.0000 20.7846i 0.425329 0.736691i
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.500000 + 0.866025i −0.0176777 + 0.0306186i
\(801\) 0 0
\(802\) −2.50000 4.33013i −0.0882781 0.152902i
\(803\) 3.00000 5.19615i 0.105868 0.183368i
\(804\) 0 0
\(805\) 17.5000 + 6.06218i 0.616794 + 0.213664i