Properties

Label 1216.2.t.b.353.2
Level $1216$
Weight $2$
Character 1216.353
Analytic conductor $9.710$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1216 = 2^{6} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1216.t (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.70980888579\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.3317760000.2
Defining polynomial: \(x^{8} - 25 x^{4} + 625\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 353.2
Root \(0.578737 + 2.15988i\) of defining polynomial
Character \(\chi\) \(=\) 1216.353
Dual form 1216.2.t.b.1185.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.59808 - 1.50000i) q^{3} +(2.73861 + 1.58114i) q^{5} +3.16228 q^{7} +(3.00000 + 5.19615i) q^{9} +O(q^{10})\) \(q+(-2.59808 - 1.50000i) q^{3} +(2.73861 + 1.58114i) q^{5} +3.16228 q^{7} +(3.00000 + 5.19615i) q^{9} -3.00000i q^{11} +(5.47723 - 3.16228i) q^{13} +(-4.74342 - 8.21584i) q^{15} +(-2.00000 + 3.46410i) q^{17} +(-2.59808 + 3.50000i) q^{19} +(-8.21584 - 4.74342i) q^{21} +(4.74342 + 8.21584i) q^{23} +(2.50000 + 4.33013i) q^{25} -9.00000i q^{27} +(-2.73861 + 1.58114i) q^{29} +3.16228 q^{31} +(-4.50000 + 7.79423i) q^{33} +(8.66025 + 5.00000i) q^{35} +3.16228i q^{37} -18.9737 q^{39} +(1.50000 - 2.59808i) q^{41} +(-8.66025 - 5.00000i) q^{43} +18.9737i q^{45} +(1.58114 + 2.73861i) q^{47} +3.00000 q^{49} +(10.3923 - 6.00000i) q^{51} +(4.74342 - 8.21584i) q^{55} +(12.0000 - 5.19615i) q^{57} +(6.06218 + 3.50000i) q^{59} +(-2.73861 + 1.58114i) q^{61} +(9.48683 + 16.4317i) q^{63} +20.0000 q^{65} +(4.33013 - 2.50000i) q^{67} -28.4605i q^{69} +(3.50000 - 6.06218i) q^{73} -15.0000i q^{75} -9.48683i q^{77} +(3.16228 - 5.47723i) q^{79} +(-4.50000 + 7.79423i) q^{81} +7.00000i q^{83} +(-10.9545 + 6.32456i) q^{85} +9.48683 q^{87} +(-4.00000 - 6.92820i) q^{89} +(17.3205 - 10.0000i) q^{91} +(-8.21584 - 4.74342i) q^{93} +(-12.6491 + 5.47723i) q^{95} +(4.50000 - 7.79423i) q^{97} +(15.5885 - 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 24q^{9} + O(q^{10}) \) \( 8q + 24q^{9} - 16q^{17} + 20q^{25} - 36q^{33} + 12q^{41} + 24q^{49} + 96q^{57} + 160q^{65} + 28q^{73} - 36q^{81} - 32q^{89} + 36q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(705\) \(837\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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
\(3\) −2.59808 1.50000i −1.50000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
−1.00000 \(\pi\)
\(4\) 0 0
\(5\) 2.73861 + 1.58114i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(6\) 0 0
\(7\) 3.16228 1.19523 0.597614 0.801784i \(-0.296115\pi\)
0.597614 + 0.801784i \(0.296115\pi\)
\(8\) 0 0
\(9\) 3.00000 + 5.19615i 1.00000 + 1.73205i
\(10\) 0 0
\(11\) 3.00000i 0.904534i −0.891883 0.452267i \(-0.850615\pi\)
0.891883 0.452267i \(-0.149385\pi\)
\(12\) 0 0
\(13\) 5.47723 3.16228i 1.51911 0.877058i 0.519362 0.854554i \(-0.326170\pi\)
0.999747 0.0225039i \(-0.00716381\pi\)
\(14\) 0 0
\(15\) −4.74342 8.21584i −1.22474 2.12132i
\(16\) 0 0
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) −2.59808 + 3.50000i −0.596040 + 0.802955i
\(20\) 0 0
\(21\) −8.21584 4.74342i −1.79284 1.03510i
\(22\) 0 0
\(23\) 4.74342 + 8.21584i 0.989071 + 1.71312i 0.622224 + 0.782839i \(0.286229\pi\)
0.366847 + 0.930281i \(0.380437\pi\)
\(24\) 0 0
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 0 0
\(27\) 9.00000i 1.73205i
\(28\) 0 0
\(29\) −2.73861 + 1.58114i −0.508548 + 0.293610i −0.732236 0.681051i \(-0.761523\pi\)
0.223689 + 0.974661i \(0.428190\pi\)
\(30\) 0 0
\(31\) 3.16228 0.567962 0.283981 0.958830i \(-0.408345\pi\)
0.283981 + 0.958830i \(0.408345\pi\)
\(32\) 0 0
\(33\) −4.50000 + 7.79423i −0.783349 + 1.35680i
\(34\) 0 0
\(35\) 8.66025 + 5.00000i 1.46385 + 0.845154i
\(36\) 0 0
\(37\) 3.16228i 0.519875i 0.965625 + 0.259938i \(0.0837020\pi\)
−0.965625 + 0.259938i \(0.916298\pi\)
\(38\) 0 0
\(39\) −18.9737 −3.03822
\(40\) 0 0
\(41\) 1.50000 2.59808i 0.234261 0.405751i −0.724797 0.688963i \(-0.758066\pi\)
0.959058 + 0.283211i \(0.0913998\pi\)
\(42\) 0 0
\(43\) −8.66025 5.00000i −1.32068 0.762493i −0.336840 0.941562i \(-0.609358\pi\)
−0.983836 + 0.179069i \(0.942691\pi\)
\(44\) 0 0
\(45\) 18.9737i 2.82843i
\(46\) 0 0
\(47\) 1.58114 + 2.73861i 0.230633 + 0.399468i 0.957995 0.286787i \(-0.0925871\pi\)
−0.727362 + 0.686254i \(0.759254\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) 0 0
\(51\) 10.3923 6.00000i 1.45521 0.840168i
\(52\) 0 0
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 0 0
\(55\) 4.74342 8.21584i 0.639602 1.10782i
\(56\) 0 0
\(57\) 12.0000 5.19615i 1.58944 0.688247i
\(58\) 0 0
\(59\) 6.06218 + 3.50000i 0.789228 + 0.455661i 0.839691 0.543065i \(-0.182736\pi\)
−0.0504625 + 0.998726i \(0.516070\pi\)
\(60\) 0 0
\(61\) −2.73861 + 1.58114i −0.350643 + 0.202444i −0.664969 0.746871i \(-0.731555\pi\)
0.314325 + 0.949315i \(0.398222\pi\)
\(62\) 0 0
\(63\) 9.48683 + 16.4317i 1.19523 + 2.07020i
\(64\) 0 0
\(65\) 20.0000 2.48069
\(66\) 0 0
\(67\) 4.33013 2.50000i 0.529009 0.305424i −0.211604 0.977356i \(-0.567869\pi\)
0.740613 + 0.671932i \(0.234535\pi\)
\(68\) 0 0
\(69\) 28.4605i 3.42624i
\(70\) 0 0
\(71\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) 0 0
\(73\) 3.50000 6.06218i 0.409644 0.709524i −0.585206 0.810885i \(-0.698986\pi\)
0.994850 + 0.101361i \(0.0323196\pi\)
\(74\) 0 0
\(75\) 15.0000i 1.73205i
\(76\) 0 0
\(77\) 9.48683i 1.08112i
\(78\) 0 0
\(79\) 3.16228 5.47723i 0.355784 0.616236i −0.631468 0.775402i \(-0.717547\pi\)
0.987252 + 0.159166i \(0.0508805\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) 7.00000i 0.768350i 0.923260 + 0.384175i \(0.125514\pi\)
−0.923260 + 0.384175i \(0.874486\pi\)
\(84\) 0 0
\(85\) −10.9545 + 6.32456i −1.18818 + 0.685994i
\(86\) 0 0
\(87\) 9.48683 1.01710
\(88\) 0 0
\(89\) −4.00000 6.92820i −0.423999 0.734388i 0.572327 0.820025i \(-0.306041\pi\)
−0.996326 + 0.0856373i \(0.972707\pi\)
\(90\) 0 0
\(91\) 17.3205 10.0000i 1.81568 1.04828i
\(92\) 0 0
\(93\) −8.21584 4.74342i −0.851943 0.491869i
\(94\) 0 0
\(95\) −12.6491 + 5.47723i −1.29777 + 0.561951i
\(96\) 0 0
\(97\) 4.50000 7.79423i 0.456906 0.791384i −0.541890 0.840450i \(-0.682291\pi\)
0.998796 + 0.0490655i \(0.0156243\pi\)
\(98\) 0 0
\(99\) 15.5885 9.00000i 1.56670 0.904534i
\(100\) 0 0
\(101\) 8.21584 4.74342i 0.817506 0.471988i −0.0320494 0.999486i \(-0.510203\pi\)
0.849556 + 0.527499i \(0.176870\pi\)
\(102\) 0 0
\(103\) −6.32456 −0.623177 −0.311588 0.950217i \(-0.600861\pi\)
−0.311588 + 0.950217i \(0.600861\pi\)
\(104\) 0 0
\(105\) −15.0000 25.9808i −1.46385 2.53546i
\(106\) 0 0
\(107\) 6.00000i 0.580042i −0.957020 0.290021i \(-0.906338\pi\)
0.957020 0.290021i \(-0.0936623\pi\)
\(108\) 0 0
\(109\) 16.4317 + 9.48683i 1.57387 + 0.908674i 0.995688 + 0.0927654i \(0.0295707\pi\)
0.578181 + 0.815908i \(0.303763\pi\)
\(110\) 0 0
\(111\) 4.74342 8.21584i 0.450225 0.779813i
\(112\) 0 0
\(113\) −13.0000 −1.22294 −0.611469 0.791269i \(-0.709421\pi\)
−0.611469 + 0.791269i \(0.709421\pi\)
\(114\) 0 0
\(115\) 30.0000i 2.79751i
\(116\) 0 0
\(117\) 32.8634 + 18.9737i 3.03822 + 1.75412i
\(118\) 0 0
\(119\) −6.32456 + 10.9545i −0.579771 + 1.00419i
\(120\) 0 0
\(121\) 2.00000 0.181818
\(122\) 0 0
\(123\) −7.79423 + 4.50000i −0.702782 + 0.405751i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −3.16228 5.47723i −0.280607 0.486025i 0.690928 0.722924i \(-0.257202\pi\)
−0.971534 + 0.236899i \(0.923869\pi\)
\(128\) 0 0
\(129\) 15.0000 + 25.9808i 1.32068 + 2.28748i
\(130\) 0 0
\(131\) 7.79423 + 4.50000i 0.680985 + 0.393167i 0.800226 0.599699i \(-0.204713\pi\)
−0.119241 + 0.992865i \(0.538046\pi\)
\(132\) 0 0
\(133\) −8.21584 + 11.0680i −0.712404 + 0.959715i
\(134\) 0 0
\(135\) 14.2302 24.6475i 1.22474 2.12132i
\(136\) 0 0
\(137\) 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) 0 0
\(139\) −9.52628 + 5.50000i −0.808008 + 0.466504i −0.846264 0.532764i \(-0.821153\pi\)
0.0382553 + 0.999268i \(0.487820\pi\)
\(140\) 0 0
\(141\) 9.48683i 0.798935i
\(142\) 0 0
\(143\) −9.48683 16.4317i −0.793329 1.37409i
\(144\) 0 0
\(145\) −10.0000 −0.830455
\(146\) 0 0
\(147\) −7.79423 4.50000i −0.642857 0.371154i
\(148\) 0 0
\(149\) 8.21584 + 4.74342i 0.673068 + 0.388596i 0.797238 0.603665i \(-0.206294\pi\)
−0.124170 + 0.992261i \(0.539627\pi\)
\(150\) 0 0
\(151\) 3.16228 0.257343 0.128671 0.991687i \(-0.458929\pi\)
0.128671 + 0.991687i \(0.458929\pi\)
\(152\) 0 0
\(153\) −24.0000 −1.94029
\(154\) 0 0
\(155\) 8.66025 + 5.00000i 0.695608 + 0.401610i
\(156\) 0 0
\(157\) −5.47723 3.16228i −0.437130 0.252377i 0.265249 0.964180i \(-0.414546\pi\)
−0.702380 + 0.711803i \(0.747879\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 15.0000 + 25.9808i 1.18217 + 2.04757i
\(162\) 0 0
\(163\) 5.00000i 0.391630i 0.980641 + 0.195815i \(0.0627352\pi\)
−0.980641 + 0.195815i \(0.937265\pi\)
\(164\) 0 0
\(165\) −24.6475 + 14.2302i −1.91881 + 1.10782i
\(166\) 0 0
\(167\) 3.16228 + 5.47723i 0.244704 + 0.423840i 0.962048 0.272879i \(-0.0879758\pi\)
−0.717344 + 0.696719i \(0.754642\pi\)
\(168\) 0 0
\(169\) 13.5000 23.3827i 1.03846 1.79867i
\(170\) 0 0
\(171\) −25.9808 3.00000i −1.98680 0.229416i
\(172\) 0 0
\(173\) −10.9545 6.32456i −0.832851 0.480847i 0.0219765 0.999758i \(-0.493004\pi\)
−0.854828 + 0.518911i \(0.826337\pi\)
\(174\) 0 0
\(175\) 7.90569 + 13.6931i 0.597614 + 1.03510i
\(176\) 0 0
\(177\) −10.5000 18.1865i −0.789228 1.36698i
\(178\) 0 0
\(179\) 3.00000i 0.224231i 0.993695 + 0.112115i \(0.0357626\pi\)
−0.993695 + 0.112115i \(0.964237\pi\)
\(180\) 0 0
\(181\) −8.21584 + 4.74342i −0.610678 + 0.352575i −0.773231 0.634125i \(-0.781361\pi\)
0.162552 + 0.986700i \(0.448027\pi\)
\(182\) 0 0
\(183\) 9.48683 0.701287
\(184\) 0 0
\(185\) −5.00000 + 8.66025i −0.367607 + 0.636715i
\(186\) 0 0
\(187\) 10.3923 + 6.00000i 0.759961 + 0.438763i
\(188\) 0 0
\(189\) 28.4605i 2.07020i
\(190\) 0 0
\(191\) −6.32456 −0.457629 −0.228814 0.973470i \(-0.573485\pi\)
−0.228814 + 0.973470i \(0.573485\pi\)
\(192\) 0 0
\(193\) −4.00000 + 6.92820i −0.287926 + 0.498703i −0.973315 0.229475i \(-0.926299\pi\)
0.685388 + 0.728178i \(0.259632\pi\)
\(194\) 0 0
\(195\) −51.9615 30.0000i −3.72104 2.14834i
\(196\) 0 0
\(197\) 22.1359i 1.57712i −0.614957 0.788560i \(-0.710827\pi\)
0.614957 0.788560i \(-0.289173\pi\)
\(198\) 0 0
\(199\) −3.16228 5.47723i −0.224168 0.388270i 0.731902 0.681410i \(-0.238633\pi\)
−0.956069 + 0.293140i \(0.905300\pi\)
\(200\) 0 0
\(201\) −15.0000 −1.05802
\(202\) 0 0
\(203\) −8.66025 + 5.00000i −0.607831 + 0.350931i
\(204\) 0 0
\(205\) 8.21584 4.74342i 0.573819 0.331295i
\(206\) 0 0
\(207\) −28.4605 + 49.2950i −1.97814 + 3.42624i
\(208\) 0 0
\(209\) 10.5000 + 7.79423i 0.726300 + 0.539138i
\(210\) 0 0
\(211\) −13.8564 8.00000i −0.953914 0.550743i −0.0596196 0.998221i \(-0.518989\pi\)
−0.894295 + 0.447478i \(0.852322\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −15.8114 27.3861i −1.07833 1.86772i
\(216\) 0 0
\(217\) 10.0000 0.678844
\(218\) 0 0
\(219\) −18.1865 + 10.5000i −1.22893 + 0.709524i
\(220\) 0 0
\(221\) 25.2982i 1.70174i
\(222\) 0 0
\(223\) 7.90569 13.6931i 0.529404 0.916955i −0.470007 0.882662i \(-0.655749\pi\)
0.999412 0.0342929i \(-0.0109179\pi\)
\(224\) 0 0
\(225\) −15.0000 + 25.9808i −1.00000 + 1.73205i
\(226\) 0 0
\(227\) 11.0000i 0.730096i 0.930989 + 0.365048i \(0.118947\pi\)
−0.930989 + 0.365048i \(0.881053\pi\)
\(228\) 0 0
\(229\) 25.2982i 1.67175i 0.548917 + 0.835877i \(0.315040\pi\)
−0.548917 + 0.835877i \(0.684960\pi\)
\(230\) 0 0
\(231\) −14.2302 + 24.6475i −0.936282 + 1.62169i
\(232\) 0 0
\(233\) 1.50000 2.59808i 0.0982683 0.170206i −0.812700 0.582683i \(-0.802003\pi\)
0.910968 + 0.412477i \(0.135336\pi\)
\(234\) 0 0
\(235\) 10.0000i 0.652328i
\(236\) 0 0
\(237\) −16.4317 + 9.48683i −1.06735 + 0.616236i
\(238\) 0 0
\(239\) 6.32456 0.409101 0.204551 0.978856i \(-0.434427\pi\)
0.204551 + 0.978856i \(0.434427\pi\)
\(240\) 0 0
\(241\) −6.50000 11.2583i −0.418702 0.725213i 0.577107 0.816668i \(-0.304181\pi\)
−0.995809 + 0.0914555i \(0.970848\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 8.21584 + 4.74342i 0.524891 + 0.303046i
\(246\) 0 0
\(247\) −3.16228 + 27.3861i −0.201211 + 1.74254i
\(248\) 0 0
\(249\) 10.5000 18.1865i 0.665410 1.15252i
\(250\) 0 0
\(251\) 6.06218 3.50000i 0.382641 0.220918i −0.296326 0.955087i \(-0.595761\pi\)
0.678967 + 0.734169i \(0.262428\pi\)
\(252\) 0 0
\(253\) 24.6475 14.2302i 1.54958 0.894648i
\(254\) 0 0
\(255\) 37.9473 2.37635
\(256\) 0 0
\(257\) −10.5000 18.1865i −0.654972 1.13444i −0.981901 0.189396i \(-0.939347\pi\)
0.326929 0.945049i \(-0.393986\pi\)
\(258\) 0 0
\(259\) 10.0000i 0.621370i
\(260\) 0 0
\(261\) −16.4317 9.48683i −1.01710 0.587220i
\(262\) 0 0
\(263\) 4.74342 8.21584i 0.292492 0.506610i −0.681907 0.731439i \(-0.738849\pi\)
0.974398 + 0.224829i \(0.0721823\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 24.0000i 1.46878i
\(268\) 0 0
\(269\) −21.9089 12.6491i −1.33581 0.771230i −0.349626 0.936889i \(-0.613691\pi\)
−0.986183 + 0.165659i \(0.947025\pi\)
\(270\) 0 0
\(271\) 11.0680 19.1703i 0.672331 1.16451i −0.304910 0.952381i \(-0.598626\pi\)
0.977241 0.212131i \(-0.0680403\pi\)
\(272\) 0 0
\(273\) −60.0000 −3.63137
\(274\) 0 0
\(275\) 12.9904 7.50000i 0.783349 0.452267i
\(276\) 0 0
\(277\) 28.4605i 1.71003i −0.518607 0.855013i \(-0.673549\pi\)
0.518607 0.855013i \(-0.326451\pi\)
\(278\) 0 0
\(279\) 9.48683 + 16.4317i 0.567962 + 0.983739i
\(280\) 0 0
\(281\) 9.50000 + 16.4545i 0.566722 + 0.981592i 0.996887 + 0.0788417i \(0.0251222\pi\)
−0.430165 + 0.902750i \(0.641545\pi\)
\(282\) 0 0
\(283\) −12.9904 7.50000i −0.772198 0.445829i 0.0614601 0.998110i \(-0.480424\pi\)
−0.833658 + 0.552281i \(0.813758\pi\)
\(284\) 0 0
\(285\) 41.0792 + 4.74342i 2.43332 + 0.280976i
\(286\) 0 0
\(287\) 4.74342 8.21584i 0.279995 0.484966i
\(288\) 0 0
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) −23.3827 + 13.5000i −1.37072 + 0.791384i
\(292\) 0 0
\(293\) 15.8114i 0.923711i 0.886955 + 0.461856i \(0.152816\pi\)
−0.886955 + 0.461856i \(0.847184\pi\)
\(294\) 0 0
\(295\) 11.0680 + 19.1703i 0.644402 + 1.11614i
\(296\) 0 0
\(297\) −27.0000 −1.56670
\(298\) 0 0
\(299\) 51.9615 + 30.0000i 3.00501 + 1.73494i
\(300\) 0 0
\(301\) −27.3861 15.8114i −1.57851 0.911353i
\(302\) 0 0
\(303\) −28.4605 −1.63501
\(304\) 0 0
\(305\) −10.0000 −0.572598
\(306\) 0 0
\(307\) −18.1865 10.5000i −1.03796 0.599267i −0.118705 0.992930i \(-0.537874\pi\)
−0.919255 + 0.393663i \(0.871208\pi\)
\(308\) 0 0
\(309\) 16.4317 + 9.48683i 0.934765 + 0.539687i
\(310\) 0 0
\(311\) 22.1359 1.25521 0.627607 0.778530i \(-0.284034\pi\)
0.627607 + 0.778530i \(0.284034\pi\)
\(312\) 0 0
\(313\) 1.50000 + 2.59808i 0.0847850 + 0.146852i 0.905300 0.424774i \(-0.139646\pi\)
−0.820515 + 0.571626i \(0.806313\pi\)
\(314\) 0 0
\(315\) 60.0000i 3.38062i
\(316\) 0 0
\(317\) −27.3861 + 15.8114i −1.53816 + 0.888056i −0.539211 + 0.842170i \(0.681278\pi\)
−0.998947 + 0.0458856i \(0.985389\pi\)
\(318\) 0 0
\(319\) 4.74342 + 8.21584i 0.265580 + 0.459999i
\(320\) 0 0
\(321\) −9.00000 + 15.5885i −0.502331 + 0.870063i
\(322\) 0 0
\(323\) −6.92820 16.0000i −0.385496 0.890264i
\(324\) 0 0
\(325\) 27.3861 + 15.8114i 1.51911 + 0.877058i
\(326\) 0 0
\(327\) −28.4605 49.2950i −1.57387 2.72602i
\(328\) 0 0
\(329\) 5.00000 + 8.66025i 0.275659 + 0.477455i
\(330\) 0 0
\(331\) 29.0000i 1.59398i −0.603990 0.796992i \(-0.706423\pi\)
0.603990 0.796992i \(-0.293577\pi\)
\(332\) 0 0
\(333\) −16.4317 + 9.48683i −0.900450 + 0.519875i
\(334\) 0 0
\(335\) 15.8114 0.863868
\(336\) 0 0
\(337\) 12.5000 21.6506i 0.680918 1.17939i −0.293783 0.955872i \(-0.594914\pi\)
0.974701 0.223513i \(-0.0717525\pi\)
\(338\) 0 0
\(339\) 33.7750 + 19.5000i 1.83441 + 1.05909i
\(340\) 0 0
\(341\) 9.48683i 0.513741i
\(342\) 0 0
\(343\) −12.6491 −0.682988
\(344\) 0 0
\(345\) 45.0000 77.9423i 2.42272 4.19627i
\(346\) 0 0
\(347\) −4.33013 2.50000i −0.232453 0.134207i 0.379250 0.925294i \(-0.376182\pi\)
−0.611703 + 0.791087i \(0.709515\pi\)
\(348\) 0 0
\(349\) 12.6491i 0.677091i −0.940950 0.338546i \(-0.890065\pi\)
0.940950 0.338546i \(-0.109935\pi\)
\(350\) 0 0
\(351\) −28.4605 49.2950i −1.51911 2.63117i
\(352\) 0 0
\(353\) −13.0000 −0.691920 −0.345960 0.938249i \(-0.612447\pi\)
−0.345960 + 0.938249i \(0.612447\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 32.8634 18.9737i 1.73931 1.00419i
\(358\) 0 0
\(359\) 4.74342 8.21584i 0.250348 0.433615i −0.713274 0.700886i \(-0.752788\pi\)
0.963622 + 0.267270i \(0.0861217\pi\)
\(360\) 0 0
\(361\) −5.50000 18.1865i −0.289474 0.957186i
\(362\) 0 0
\(363\) −5.19615 3.00000i −0.272727 0.157459i
\(364\) 0 0
\(365\) 19.1703 11.0680i 1.00342 0.579324i
\(366\) 0 0
\(367\) 1.58114 + 2.73861i 0.0825348 + 0.142954i 0.904338 0.426817i \(-0.140365\pi\)
−0.821803 + 0.569771i \(0.807032\pi\)
\(368\) 0 0
\(369\) 18.0000 0.937043
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −10.0000 + 17.3205i −0.515026 + 0.892052i
\(378\) 0 0
\(379\) 32.0000i 1.64373i 0.569683 + 0.821865i \(0.307066\pi\)
−0.569683 + 0.821865i \(0.692934\pi\)
\(380\) 0 0
\(381\) 18.9737i 0.972050i
\(382\) 0 0
\(383\) −14.2302 + 24.6475i −0.727132 + 1.25943i 0.230959 + 0.972964i \(0.425814\pi\)
−0.958091 + 0.286466i \(0.907520\pi\)
\(384\) 0 0
\(385\) 15.0000 25.9808i 0.764471 1.32410i
\(386\) 0 0
\(387\) 60.0000i 3.04997i
\(388\) 0 0
\(389\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(390\) 0 0
\(391\) −37.9473 −1.91908
\(392\) 0 0
\(393\) −13.5000 23.3827i −0.680985 1.17950i
\(394\) 0 0
\(395\) 17.3205 10.0000i 0.871489 0.503155i
\(396\) 0 0
\(397\) 13.6931 + 7.90569i 0.687235 + 0.396775i 0.802575 0.596551i \(-0.203463\pi\)
−0.115340 + 0.993326i \(0.536796\pi\)
\(398\) 0 0
\(399\) 37.9473 16.4317i 1.89974 0.822613i
\(400\) 0 0
\(401\) 6.50000 11.2583i 0.324595 0.562214i −0.656836 0.754034i \(-0.728105\pi\)
0.981430 + 0.191820i \(0.0614388\pi\)
\(402\) 0 0
\(403\) 17.3205 10.0000i 0.862796 0.498135i
\(404\) 0 0
\(405\) −24.6475 + 14.2302i −1.22474 + 0.707107i
\(406\) 0 0
\(407\) 9.48683 0.470245
\(408\) 0 0
\(409\) −4.50000 7.79423i −0.222511 0.385400i 0.733059 0.680165i \(-0.238092\pi\)
−0.955570 + 0.294765i \(0.904759\pi\)
\(410\) 0 0
\(411\) 27.0000i 1.33181i
\(412\) 0 0
\(413\) 19.1703 + 11.0680i 0.943308 + 0.544619i
\(414\) 0 0
\(415\) −11.0680 + 19.1703i −0.543305 + 0.941033i
\(416\) 0 0
\(417\) 33.0000 1.61602
\(418\) 0 0
\(419\) 18.0000i 0.879358i 0.898155 + 0.439679i \(0.144908\pi\)
−0.898155 + 0.439679i \(0.855092\pi\)
\(420\) 0 0
\(421\) −24.6475 14.2302i −1.20125 0.693540i −0.240414 0.970670i \(-0.577283\pi\)
−0.960832 + 0.277130i \(0.910617\pi\)
\(422\) 0 0
\(423\) −9.48683 + 16.4317i −0.461266 + 0.798935i
\(424\) 0 0
\(425\) −20.0000 −0.970143
\(426\) 0 0
\(427\) −8.66025 + 5.00000i −0.419099 + 0.241967i
\(428\) 0 0
\(429\) 56.9210i 2.74817i
\(430\) 0 0
\(431\) −6.32456 10.9545i −0.304643 0.527657i 0.672539 0.740062i \(-0.265204\pi\)
−0.977182 + 0.212405i \(0.931871\pi\)
\(432\) 0 0
\(433\) 14.0000 + 24.2487i 0.672797 + 1.16532i 0.977108 + 0.212746i \(0.0682406\pi\)
−0.304311 + 0.952573i \(0.598426\pi\)
\(434\) 0 0
\(435\) 25.9808 + 15.0000i 1.24568 + 0.719195i
\(436\) 0 0
\(437\) −41.0792 4.74342i −1.96508 0.226908i
\(438\) 0 0
\(439\) −7.90569 + 13.6931i −0.377318 + 0.653534i −0.990671 0.136275i \(-0.956487\pi\)
0.613353 + 0.789809i \(0.289820\pi\)
\(440\) 0 0
\(441\) 9.00000 + 15.5885i 0.428571 + 0.742307i
\(442\) 0 0
\(443\) 30.3109 17.5000i 1.44011 0.831450i 0.442257 0.896888i \(-0.354178\pi\)
0.997857 + 0.0654382i \(0.0208445\pi\)
\(444\) 0 0
\(445\) 25.2982i 1.19925i
\(446\) 0 0
\(447\) −14.2302 24.6475i −0.673068 1.16579i
\(448\) 0 0
\(449\) 17.0000 0.802280 0.401140 0.916017i \(-0.368614\pi\)
0.401140 + 0.916017i \(0.368614\pi\)
\(450\) 0 0
\(451\) −7.79423 4.50000i −0.367016 0.211897i
\(452\) 0 0
\(453\) −8.21584 4.74342i −0.386014 0.222865i
\(454\) 0 0
\(455\) 63.2456 2.96500
\(456\) 0 0
\(457\) −31.0000 −1.45012 −0.725059 0.688686i \(-0.758188\pi\)
−0.725059 + 0.688686i \(0.758188\pi\)
\(458\) 0 0
\(459\) 31.1769 + 18.0000i 1.45521 + 0.840168i
\(460\) 0 0
\(461\) 27.3861 + 15.8114i 1.27550 + 0.736410i 0.976017 0.217692i \(-0.0698529\pi\)
0.299482 + 0.954102i \(0.403186\pi\)
\(462\) 0 0
\(463\) −31.6228 −1.46964 −0.734818 0.678265i \(-0.762732\pi\)
−0.734818 + 0.678265i \(0.762732\pi\)
\(464\) 0 0
\(465\) −15.0000 25.9808i −0.695608 1.20483i
\(466\) 0 0
\(467\) 21.0000i 0.971764i 0.874024 + 0.485882i \(0.161502\pi\)
−0.874024 + 0.485882i \(0.838498\pi\)
\(468\) 0 0
\(469\) 13.6931 7.90569i 0.632287 0.365051i
\(470\) 0 0
\(471\) 9.48683 + 16.4317i 0.437130 + 0.757132i
\(472\) 0 0
\(473\) −15.0000 + 25.9808i −0.689701 + 1.19460i
\(474\) 0 0
\(475\) −21.6506 2.50000i −0.993399 0.114708i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9.48683 + 16.4317i 0.433464 + 0.750782i 0.997169 0.0751941i \(-0.0239576\pi\)
−0.563704 + 0.825977i \(0.690624\pi\)
\(480\) 0 0
\(481\) 10.0000 + 17.3205i 0.455961 + 0.789747i
\(482\) 0 0
\(483\) 90.0000i 4.09514i
\(484\) 0 0
\(485\) 24.6475 14.2302i 1.11919 0.646162i
\(486\) 0 0
\(487\) −9.48683 −0.429889 −0.214945 0.976626i \(-0.568957\pi\)
−0.214945 + 0.976626i \(0.568957\pi\)
\(488\) 0 0
\(489\) 7.50000 12.9904i 0.339162 0.587445i
\(490\) 0 0
\(491\) 15.5885 + 9.00000i 0.703497 + 0.406164i 0.808649 0.588292i \(-0.200199\pi\)
−0.105151 + 0.994456i \(0.533533\pi\)
\(492\) 0 0
\(493\) 12.6491i 0.569687i
\(494\) 0 0
\(495\) 56.9210 2.55841
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 11.2583 + 6.50000i 0.503992 + 0.290980i 0.730361 0.683062i \(-0.239352\pi\)
−0.226369 + 0.974042i \(0.572685\pi\)
\(500\) 0 0
\(501\) 18.9737i 0.847681i
\(502\) 0 0
\(503\) 1.58114 + 2.73861i 0.0704995 + 0.122109i 0.899120 0.437702i \(-0.144207\pi\)
−0.828621 + 0.559810i \(0.810874\pi\)
\(504\) 0 0
\(505\) 30.0000 1.33498
\(506\) 0 0
\(507\) −70.1481 + 40.5000i −3.11538 + 1.79867i
\(508\) 0 0
\(509\) −27.3861 + 15.8114i −1.21387 + 0.700827i −0.963600 0.267349i \(-0.913852\pi\)
−0.250269 + 0.968176i \(0.580519\pi\)
\(510\) 0 0
\(511\) 11.0680 19.1703i 0.489618 0.848044i
\(512\) 0 0
\(513\) 31.5000 + 23.3827i 1.39076 + 1.03237i
\(514\) 0 0
\(515\) −17.3205 10.0000i −0.763233 0.440653i
\(516\) 0 0
\(517\) 8.21584 4.74342i 0.361332 0.208615i
\(518\) 0 0
\(519\) 18.9737 + 32.8634i 0.832851 + 1.44254i
\(520\) 0 0
\(521\) −33.0000 −1.44576 −0.722878 0.690976i \(-0.757181\pi\)
−0.722878 + 0.690976i \(0.757181\pi\)
\(522\) 0 0
\(523\) 19.0526 11.0000i 0.833110 0.480996i −0.0218062 0.999762i \(-0.506942\pi\)
0.854916 + 0.518766i \(0.173608\pi\)
\(524\) 0 0
\(525\) 47.4342i 2.07020i
\(526\) 0 0
\(527\) −6.32456 + 10.9545i −0.275502 + 0.477183i
\(528\) 0 0
\(529\) −33.5000 + 58.0237i −1.45652 + 2.52277i
\(530\) 0 0
\(531\) 42.0000i 1.82264i
\(532\) 0 0
\(533\) 18.9737i 0.821841i
\(534\) 0 0
\(535\) 9.48683 16.4317i 0.410152 0.710403i
\(536\) 0 0
\(537\) 4.50000 7.79423i 0.194189 0.336346i
\(538\) 0 0
\(539\) 9.00000i 0.387657i
\(540\) 0 0
\(541\) −21.9089 + 12.6491i −0.941937 + 0.543828i −0.890567 0.454852i \(-0.849692\pi\)
−0.0513702 + 0.998680i \(0.516359\pi\)
\(542\) 0 0
\(543\) 28.4605 1.22136
\(544\) 0 0
\(545\) 30.0000 + 51.9615i 1.28506 + 2.22579i
\(546\) 0 0
\(547\) −22.5167 + 13.0000i −0.962743 + 0.555840i −0.897016 0.441998i \(-0.854270\pi\)
−0.0657267 + 0.997838i \(0.520937\pi\)
\(548\) 0 0
\(549\) −16.4317 9.48683i −0.701287 0.404888i
\(550\) 0 0
\(551\) 1.58114 13.6931i 0.0673588 0.583344i
\(552\) 0 0
\(553\) 10.0000 17.3205i 0.425243 0.736543i
\(554\) 0 0
\(555\) 25.9808 15.0000i 1.10282 0.636715i
\(556\) 0 0
\(557\) −16.4317 + 9.48683i −0.696232 + 0.401970i −0.805943 0.591994i \(-0.798341\pi\)
0.109710 + 0.993964i \(0.465008\pi\)
\(558\) 0 0
\(559\) −63.2456 −2.67500
\(560\) 0 0
\(561\) −18.0000 31.1769i −0.759961 1.31629i
\(562\) 0 0
\(563\) 3.00000i 0.126435i 0.998000 + 0.0632175i \(0.0201362\pi\)
−0.998000 + 0.0632175i \(0.979864\pi\)
\(564\) 0 0
\(565\) −35.6020 20.5548i −1.49779 0.864747i
\(566\) 0 0
\(567\) −14.2302 + 24.6475i −0.597614 + 1.03510i
\(568\) 0 0
\(569\) 12.0000 0.503066 0.251533 0.967849i \(-0.419065\pi\)
0.251533 + 0.967849i \(0.419065\pi\)
\(570\) 0 0
\(571\) 29.0000i 1.21361i −0.794850 0.606806i \(-0.792450\pi\)
0.794850 0.606806i \(-0.207550\pi\)
\(572\) 0 0
\(573\) 16.4317 + 9.48683i 0.686443 + 0.396318i
\(574\) 0 0
\(575\) −23.7171 + 41.0792i −0.989071 + 1.71312i
\(576\) 0 0
\(577\) −45.0000 −1.87337 −0.936687 0.350167i \(-0.886125\pi\)
−0.936687 + 0.350167i \(0.886125\pi\)
\(578\) 0 0
\(579\) 20.7846 12.0000i 0.863779 0.498703i
\(580\) 0 0
\(581\) 22.1359i 0.918354i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 60.0000 + 103.923i 2.48069 + 4.29669i
\(586\) 0 0
\(587\) −29.4449 17.0000i −1.21532 0.701665i −0.251406 0.967882i \(-0.580893\pi\)
−0.963913 + 0.266217i \(0.914226\pi\)
\(588\) 0 0
\(589\) −8.21584 + 11.0680i −0.338528 + 0.456048i
\(590\) 0 0
\(591\) −33.2039 + 57.5109i −1.36583 + 2.36568i
\(592\) 0 0
\(593\) 17.5000 + 30.3109i 0.718639 + 1.24472i 0.961539 + 0.274668i \(0.0885679\pi\)
−0.242900 + 0.970051i \(0.578099\pi\)
\(594\) 0 0
\(595\) −34.6410 + 20.0000i −1.42014 + 0.819920i
\(596\) 0 0
\(597\) 18.9737i 0.776540i
\(598\) 0 0
\(599\) −14.2302 24.6475i −0.581432 1.00707i −0.995310 0.0967377i \(-0.969159\pi\)
0.413878 0.910333i \(-0.364174\pi\)
\(600\) 0 0
\(601\) −31.0000 −1.26452 −0.632258 0.774758i \(-0.717872\pi\)
−0.632258 + 0.774758i \(0.717872\pi\)
\(602\) 0 0
\(603\) 25.9808 + 15.0000i 1.05802 + 0.610847i
\(604\) 0 0
\(605\) 5.47723 + 3.16228i 0.222681 + 0.128565i
\(606\) 0 0
\(607\) 22.1359 0.898470 0.449235 0.893414i \(-0.351697\pi\)
0.449235 + 0.893414i \(0.351697\pi\)
\(608\) 0 0
\(609\) 30.0000 1.21566
\(610\) 0 0
\(611\) 17.3205 + 10.0000i 0.700713 + 0.404557i
\(612\) 0 0
\(613\) −16.4317 9.48683i −0.663669 0.383170i 0.130004 0.991513i \(-0.458501\pi\)
−0.793674 + 0.608344i \(0.791834\pi\)
\(614\) 0 0
\(615\) −28.4605 −1.14764
\(616\) 0 0
\(617\) 10.5000 + 18.1865i 0.422714 + 0.732162i 0.996204 0.0870504i \(-0.0277441\pi\)
−0.573490 + 0.819213i \(0.694411\pi\)
\(618\) 0 0
\(619\) 14.0000i 0.562708i −0.959604 0.281354i \(-0.909217\pi\)
0.959604 0.281354i \(-0.0907834\pi\)
\(620\) 0 0
\(621\) 73.9425 42.6907i 2.96721 1.71312i
\(622\) 0 0
\(623\) −12.6491 21.9089i −0.506776 0.877762i
\(624\) 0 0
\(625\) 12.5000 21.6506i 0.500000 0.866025i
\(626\) 0 0
\(627\) −15.5885 36.0000i −0.622543 1.43770i
\(628\) 0 0
\(629\) −10.9545 6.32456i −0.436783 0.252177i
\(630\) 0 0
\(631\) 1.58114 + 2.73861i 0.0629441 + 0.109022i 0.895780 0.444497i \(-0.146618\pi\)
−0.832836 + 0.553520i \(0.813284\pi\)
\(632\) 0 0
\(633\) 24.0000 + 41.5692i 0.953914 + 1.65223i
\(634\) 0 0
\(635\) 20.0000i 0.793676i
\(636\) 0 0
\(637\) 16.4317 9.48683i 0.651047 0.375882i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.50000 9.52628i 0.217237 0.376265i −0.736725 0.676192i \(-0.763629\pi\)
0.953962 + 0.299927i \(0.0969622\pi\)
\(642\) 0 0
\(643\) −37.2391 21.5000i −1.46857 0.847877i −0.469187 0.883099i \(-0.655453\pi\)
−0.999380 + 0.0352216i \(0.988786\pi\)
\(644\) 0 0
\(645\) 94.8683i 3.73544i
\(646\) 0 0
\(647\) −25.2982 −0.994576 −0.497288 0.867586i \(-0.665671\pi\)
−0.497288 + 0.867586i \(0.665671\pi\)
\(648\) 0 0
\(649\) 10.5000 18.1865i 0.412161 0.713884i
\(650\) 0 0
\(651\) −25.9808 15.0000i −1.01827 0.587896i
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 14.2302 + 24.6475i 0.556022 + 0.963058i
\(656\) 0 0
\(657\) 42.0000 1.63858
\(658\) 0 0
\(659\) 15.5885 9.00000i 0.607240 0.350590i −0.164644 0.986353i \(-0.552648\pi\)
0.771885 + 0.635763i \(0.219314\pi\)
\(660\) 0 0
\(661\) −13.6931 + 7.90569i −0.532598 + 0.307496i −0.742074 0.670318i \(-0.766158\pi\)
0.209475 + 0.977814i \(0.432824\pi\)
\(662\) 0 0
\(663\) 37.9473 65.7267i 1.47375 2.55261i
\(664\) 0 0
\(665\) −40.0000 + 17.3205i −1.55113 + 0.671660i
\(666\) 0 0
\(667\) −25.9808 15.0000i −1.00598 0.580802i
\(668\) 0 0
\(669\) −41.0792 + 23.7171i −1.58821 + 0.916955i
\(670\) 0 0
\(671\) 4.74342 + 8.21584i 0.183118 + 0.317169i
\(672\) 0 0
\(673\) −20.0000 −0.770943 −0.385472 0.922720i \(-0.625961\pi\)
−0.385472 + 0.922720i \(0.625961\pi\)
\(674\) 0 0
\(675\) 38.9711 22.5000i 1.50000 0.866025i
\(676\) 0 0
\(677\) 31.6228i 1.21536i 0.794181 + 0.607681i \(0.207900\pi\)
−0.794181 + 0.607681i \(0.792100\pi\)
\(678\) 0 0
\(679\) 14.2302 24.6475i 0.546107 0.945885i
\(680\) 0 0
\(681\) 16.5000 28.5788i 0.632281 1.09514i
\(682\) 0 0
\(683\) 38.0000i 1.45403i −0.686622 0.727015i \(-0.740907\pi\)
0.686622 0.727015i \(-0.259093\pi\)
\(684\) 0 0
\(685\) 28.4605i 1.08742i
\(686\) 0 0
\(687\) 37.9473 65.7267i 1.44778 2.50763i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 6.00000i 0.228251i −0.993466 0.114125i \(-0.963593\pi\)
0.993466 0.114125i \(-0.0364066\pi\)
\(692\) 0 0
\(693\) 49.2950 28.4605i 1.87256 1.08112i
\(694\) 0 0
\(695\) −34.7851 −1.31947
\(696\) 0 0
\(697\) 6.00000 + 10.3923i 0.227266 + 0.393637i
\(698\) 0 0
\(699\) −7.79423 + 4.50000i −0.294805 + 0.170206i
\(700\) 0 0
\(701\) 35.6020 + 20.5548i 1.34467 + 0.776344i 0.987488 0.157692i \(-0.0504052\pi\)
0.357179 + 0.934036i \(0.383739\pi\)
\(702\) 0 0
\(703\) −11.0680 8.21584i −0.417436 0.309866i
\(704\) 0 0
\(705\) 15.0000 25.9808i 0.564933 0.978492i
\(706\) 0 0
\(707\) 25.9808 15.0000i 0.977107 0.564133i
\(708\) 0 0
\(709\) 13.6931 7.90569i 0.514254 0.296905i −0.220327 0.975426i \(-0.570712\pi\)
0.734580 + 0.678522i \(0.237379\pi\)
\(710\) 0 0
\(711\) 37.9473 1.42314
\(712\) 0 0
\(713\) 15.0000 + 25.9808i 0.561754 + 0.972987i
\(714\) 0 0
\(715\) 60.0000i 2.24387i
\(716\) 0 0
\(717\) −16.4317 9.48683i −0.613652 0.354292i
\(718\) 0 0
\(719\) 18.9737 32.8634i 0.707598 1.22560i −0.258147 0.966106i \(-0.583112\pi\)
0.965746 0.259491i \(-0.0835547\pi\)
\(720\) 0 0
\(721\) −20.0000 −0.744839
\(722\) 0 0
\(723\) 39.0000i 1.45043i
\(724\) 0 0
\(725\) −13.6931 7.90569i −0.508548 0.293610i
\(726\) 0 0
\(727\) 22.1359 38.3406i 0.820977 1.42197i −0.0839790 0.996468i \(-0.526763\pi\)
0.904956 0.425506i \(-0.139904\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 34.6410 20.0000i 1.28124 0.739727i
\(732\) 0 0
\(733\) 41.1096i 1.51842i −0.650847 0.759209i \(-0.725586\pi\)
0.650847 0.759209i \(-0.274414\pi\)
\(734\) 0 0
\(735\) −14.2302 24.6475i −0.524891 0.909137i
\(736\) 0 0
\(737\) −7.50000 12.9904i −0.276266 0.478507i
\(738\) 0 0
\(739\) −11.2583 6.50000i −0.414144 0.239106i 0.278425 0.960458i \(-0.410188\pi\)
−0.692569 + 0.721352i \(0.743521\pi\)
\(740\) 0 0
\(741\) 49.2950 66.4078i 1.81090 2.43955i
\(742\) 0 0
\(743\) 14.2302 24.6475i 0.522057 0.904230i −0.477614 0.878570i \(-0.658498\pi\)
0.999671 0.0256596i \(-0.00816860\pi\)
\(744\) 0 0
\(745\) 15.0000 + 25.9808i 0.549557 + 0.951861i
\(746\) 0 0
\(747\) −36.3731 + 21.0000i −1.33082 + 0.768350i
\(748\) 0 0
\(749\) 18.9737i 0.693283i
\(750\) 0 0
\(751\) 25.2982 + 43.8178i 0.923145 + 1.59893i 0.794517 + 0.607241i \(0.207724\pi\)
0.128628 + 0.991693i \(0.458943\pi\)
\(752\) 0 0
\(753\) −21.0000 −0.765283
\(754\) 0 0
\(755\) 8.66025 + 5.00000i 0.315179 + 0.181969i
\(756\) 0 0
\(757\) 21.9089 + 12.6491i 0.796293 + 0.459740i 0.842173 0.539207i \(-0.181276\pi\)
−0.0458805 + 0.998947i \(0.514609\pi\)
\(758\) 0 0
\(759\) −85.3815 −3.09915
\(760\) 0 0
\(761\) −17.0000 −0.616250 −0.308125 0.951346i \(-0.599701\pi\)
−0.308125 + 0.951346i \(0.599701\pi\)
\(762\) 0 0
\(763\) 51.9615 + 30.0000i 1.88113 + 1.08607i
\(764\) 0 0
\(765\) −65.7267 37.9473i −2.37635 1.37199i
\(766\) 0 0
\(767\) 44.2719 1.59857
\(768\) 0 0
\(769\) −4.00000 6.92820i −0.144244 0.249837i 0.784847 0.619690i \(-0.212742\pi\)
−0.929091 + 0.369852i \(0.879408\pi\)
\(770\) 0 0
\(771\) 63.0000i 2.26889i
\(772\) 0 0
\(773\) 30.1247 17.3925i 1.08351 0.625566i 0.151670 0.988431i \(-0.451535\pi\)
0.931842 + 0.362865i \(0.118202\pi\)
\(774\) 0 0
\(775\) 7.90569 + 13.6931i 0.283981 + 0.491869i
\(776\) 0 0
\(777\) 15.0000 25.9808i 0.538122 0.932055i
\(778\) 0 0
\(779\) 5.19615 + 12.0000i 0.186171 + 0.429945i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 14.2302 + 24.6475i 0.508548 + 0.880830i
\(784\) 0 0
\(785\) −10.0000 17.3205i −0.356915 0.618195i
\(786\) 0 0
\(787\) 31.0000i 1.10503i 0.833503 + 0.552515i \(0.186332\pi\)
−0.833503 + 0.552515i \(0.813668\pi\)
\(788\) 0 0
\(789\) −24.6475 + 14.2302i −0.877475 + 0.506610i
\(790\) 0 0
\(791\) −41.1096 −1.46169
\(792\) 0 0
\(793\) −10.0000 + 17.3205i −0.355110 + 0.615069i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 28.4605i 1.00812i 0.863668 +