Properties

Label 3150.2.m.j.2843.3
Level 3150
Weight 2
Character 3150.2843
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.1698758656.6
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2843.3
Root \(3.16053i\)
Character \(\chi\) = 3150.2843
Dual form 3150.2.m.j.1457.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(0.707107 - 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} -5.26561i q^{11} +(3.16053 + 3.16053i) q^{13} +1.00000 q^{14} -1.00000 q^{16} +(-3.05545 - 3.05545i) q^{17} +(3.72335 - 3.72335i) q^{22} +(-4.32106 + 4.32106i) q^{23} +4.46967i q^{26} +(0.707107 + 0.707107i) q^{28} +9.96230 q^{29} +1.26561 q^{31} +(-0.707107 - 0.707107i) q^{32} -4.32106i q^{34} +(2.93351 - 2.93351i) q^{37} -10.6798i q^{41} +(-0.597714 - 0.597714i) q^{43} +5.26561 q^{44} -6.11091 q^{46} +(3.42614 + 3.42614i) q^{47} -1.00000i q^{49} +(-3.16053 + 3.16053i) q^{52} +(9.88388 - 9.88388i) q^{53} +1.00000i q^{56} +(7.04441 + 7.04441i) q^{58} +3.12563 q^{59} +3.05545 q^{61} +(0.894921 + 0.894921i) q^{62} -1.00000i q^{64} +(-4.59771 + 4.59771i) q^{67} +(3.05545 - 3.05545i) q^{68} -9.23654i q^{71} +(-10.2160 - 10.2160i) q^{73} +4.14860 q^{74} +(-3.72335 - 3.72335i) q^{77} -3.57969i q^{79} +(7.55178 - 7.55178i) q^{82} +(6.21016 - 6.21016i) q^{83} -0.845296i q^{86} +(3.72335 + 3.72335i) q^{88} -3.61916 q^{89} +4.46967 q^{91} +(-4.32106 - 4.32106i) q^{92} +4.84530i q^{94} +(4.63630 - 4.63630i) q^{97} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 4q^{13} + 8q^{14} - 8q^{16} + 4q^{22} + 8q^{23} + 24q^{29} - 8q^{31} + 4q^{37} + 12q^{43} + 24q^{44} - 12q^{47} - 4q^{52} + 32q^{53} - 12q^{58} + 16q^{59} + 4q^{62} - 20q^{67} - 36q^{73} + 40q^{74} - 4q^{77} + 12q^{82} + 56q^{83} + 4q^{88} + 72q^{89} + 8q^{92} + 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 0 0
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 0 0
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 0 0
\(10\) 0 0
\(11\) 5.26561i 1.58764i −0.608152 0.793821i \(-0.708089\pi\)
0.608152 0.793821i \(-0.291911\pi\)
\(12\) 0 0
\(13\) 3.16053 + 3.16053i 0.876574 + 0.876574i 0.993178 0.116605i \(-0.0372011\pi\)
−0.116605 + 0.993178i \(0.537201\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −3.05545 3.05545i −0.741056 0.741056i 0.231725 0.972781i \(-0.425563\pi\)
−0.972781 + 0.231725i \(0.925563\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 3.72335 3.72335i 0.793821 0.793821i
\(23\) −4.32106 + 4.32106i −0.901004 + 0.901004i −0.995523 0.0945192i \(-0.969869\pi\)
0.0945192 + 0.995523i \(0.469869\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 4.46967i 0.876574i
\(27\) 0 0
\(28\) 0.707107 + 0.707107i 0.133631 + 0.133631i
\(29\) 9.96230 1.84995 0.924977 0.380024i \(-0.124084\pi\)
0.924977 + 0.380024i \(0.124084\pi\)
\(30\) 0 0
\(31\) 1.26561 0.227310 0.113655 0.993520i \(-0.463744\pi\)
0.113655 + 0.993520i \(0.463744\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 0 0
\(34\) 4.32106i 0.741056i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.93351 2.93351i 0.482265 0.482265i −0.423589 0.905854i \(-0.639230\pi\)
0.905854 + 0.423589i \(0.139230\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 10.6798i 1.66791i −0.551834 0.833954i \(-0.686072\pi\)
0.551834 0.833954i \(-0.313928\pi\)
\(42\) 0 0
\(43\) −0.597714 0.597714i −0.0911506 0.0911506i 0.660061 0.751212i \(-0.270530\pi\)
−0.751212 + 0.660061i \(0.770530\pi\)
\(44\) 5.26561 0.793821
\(45\) 0 0
\(46\) −6.11091 −0.901004
\(47\) 3.42614 + 3.42614i 0.499754 + 0.499754i 0.911361 0.411607i \(-0.135032\pi\)
−0.411607 + 0.911361i \(0.635032\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −3.16053 + 3.16053i −0.438287 + 0.438287i
\(53\) 9.88388 9.88388i 1.35766 1.35766i 0.480855 0.876800i \(-0.340326\pi\)
0.876800 0.480855i \(-0.159674\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) 7.04441 + 7.04441i 0.924977 + 0.924977i
\(59\) 3.12563 0.406923 0.203461 0.979083i \(-0.434781\pi\)
0.203461 + 0.979083i \(0.434781\pi\)
\(60\) 0 0
\(61\) 3.05545 0.391211 0.195605 0.980683i \(-0.437333\pi\)
0.195605 + 0.980683i \(0.437333\pi\)
\(62\) 0.894921 + 0.894921i 0.113655 + 0.113655i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) −4.59771 + 4.59771i −0.561700 + 0.561700i −0.929790 0.368090i \(-0.880012\pi\)
0.368090 + 0.929790i \(0.380012\pi\)
\(68\) 3.05545 3.05545i 0.370528 0.370528i
\(69\) 0 0
\(70\) 0 0
\(71\) 9.23654i 1.09618i −0.836421 0.548088i \(-0.815356\pi\)
0.836421 0.548088i \(-0.184644\pi\)
\(72\) 0 0
\(73\) −10.2160 10.2160i −1.19569 1.19569i −0.975444 0.220246i \(-0.929314\pi\)
−0.220246 0.975444i \(-0.570686\pi\)
\(74\) 4.14860 0.482265
\(75\) 0 0
\(76\) 0 0
\(77\) −3.72335 3.72335i −0.424315 0.424315i
\(78\) 0 0
\(79\) 3.57969i 0.402746i −0.979515 0.201373i \(-0.935460\pi\)
0.979515 0.201373i \(-0.0645403\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 7.55178 7.55178i 0.833954 0.833954i
\(83\) 6.21016 6.21016i 0.681653 0.681653i −0.278719 0.960373i \(-0.589910\pi\)
0.960373 + 0.278719i \(0.0899099\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.845296i 0.0911506i
\(87\) 0 0
\(88\) 3.72335 + 3.72335i 0.396910 + 0.396910i
\(89\) −3.61916 −0.383630 −0.191815 0.981431i \(-0.561437\pi\)
−0.191815 + 0.981431i \(0.561437\pi\)
\(90\) 0 0
\(91\) 4.46967 0.468548
\(92\) −4.32106 4.32106i −0.450502 0.450502i
\(93\) 0 0
\(94\) 4.84530i 0.499754i
\(95\) 0 0
\(96\) 0 0
\(97\) 4.63630 4.63630i 0.470745 0.470745i −0.431411 0.902156i \(-0.641984\pi\)
0.902156 + 0.431411i \(0.141984\pi\)
\(98\) 0.707107 0.707107i 0.0714286 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 2.12652i 0.211597i 0.994388 + 0.105798i \(0.0337398\pi\)
−0.994388 + 0.105798i \(0.966260\pi\)
\(102\) 0 0
\(103\) 10.9225 + 10.9225i 1.07622 + 1.07622i 0.996845 + 0.0793778i \(0.0252933\pi\)
0.0793778 + 0.996845i \(0.474707\pi\)
\(104\) −4.46967 −0.438287
\(105\) 0 0
\(106\) 13.9779 1.35766
\(107\) 6.40811 + 6.40811i 0.619496 + 0.619496i 0.945402 0.325906i \(-0.105669\pi\)
−0.325906 + 0.945402i \(0.605669\pi\)
\(108\) 0 0
\(109\) 9.55760i 0.915452i 0.889093 + 0.457726i \(0.151336\pi\)
−0.889093 + 0.457726i \(0.848664\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.707107 + 0.707107i −0.0668153 + 0.0668153i
\(113\) −3.29809 + 3.29809i −0.310259 + 0.310259i −0.845010 0.534751i \(-0.820405\pi\)
0.534751 + 0.845010i \(0.320405\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 9.96230i 0.924977i
\(117\) 0 0
\(118\) 2.21016 + 2.21016i 0.203461 + 0.203461i
\(119\) −4.32106 −0.396111
\(120\) 0 0
\(121\) −16.7266 −1.52060
\(122\) 2.16053 + 2.16053i 0.195605 + 0.195605i
\(123\) 0 0
\(124\) 1.26561i 0.113655i
\(125\) 0 0
\(126\) 0 0
\(127\) 8.32106 8.32106i 0.738375 0.738375i −0.233889 0.972263i \(-0.575145\pi\)
0.972263 + 0.233889i \(0.0751451\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 17.4246i 1.52240i 0.648520 + 0.761198i \(0.275388\pi\)
−0.648520 + 0.761198i \(0.724612\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −6.50215 −0.561700
\(135\) 0 0
\(136\) 4.32106 0.370528
\(137\) −2.35876 2.35876i −0.201523 0.201523i 0.599130 0.800652i \(-0.295513\pi\)
−0.800652 + 0.599130i \(0.795513\pi\)
\(138\) 0 0
\(139\) 21.8449i 1.85286i 0.376464 + 0.926431i \(0.377140\pi\)
−0.376464 + 0.926431i \(0.622860\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.53122 6.53122i 0.548088 0.548088i
\(143\) 16.6421 16.6421i 1.39168 1.39168i
\(144\) 0 0
\(145\) 0 0
\(146\) 14.4476i 1.19569i
\(147\) 0 0
\(148\) 2.93351 + 2.93351i 0.241133 + 0.241133i
\(149\) 6.08541 0.498536 0.249268 0.968435i \(-0.419810\pi\)
0.249268 + 0.968435i \(0.419810\pi\)
\(150\) 0 0
\(151\) 22.7530 1.85162 0.925808 0.377995i \(-0.123386\pi\)
0.925808 + 0.377995i \(0.123386\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 5.26561i 0.424315i
\(155\) 0 0
\(156\) 0 0
\(157\) 10.7181 10.7181i 0.855400 0.855400i −0.135392 0.990792i \(-0.543229\pi\)
0.990792 + 0.135392i \(0.0432293\pi\)
\(158\) 2.53122 2.53122i 0.201373 0.201373i
\(159\) 0 0
\(160\) 0 0
\(161\) 6.11091i 0.481607i
\(162\) 0 0
\(163\) 4.04441 + 4.04441i 0.316783 + 0.316783i 0.847530 0.530747i \(-0.178089\pi\)
−0.530747 + 0.847530i \(0.678089\pi\)
\(164\) 10.6798 0.833954
\(165\) 0 0
\(166\) 8.78249 0.681653
\(167\) −5.76929 5.76929i −0.446441 0.446441i 0.447729 0.894169i \(-0.352233\pi\)
−0.894169 + 0.447729i \(0.852233\pi\)
\(168\) 0 0
\(169\) 6.97792i 0.536763i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.597714 0.597714i 0.0455753 0.0455753i
\(173\) 6.14492 6.14492i 0.467189 0.467189i −0.433813 0.901003i \(-0.642832\pi\)
0.901003 + 0.433813i \(0.142832\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.26561i 0.396910i
\(177\) 0 0
\(178\) −2.55913 2.55913i −0.191815 0.191815i
\(179\) 0.391244 0.0292430 0.0146215 0.999893i \(-0.495346\pi\)
0.0146215 + 0.999893i \(0.495346\pi\)
\(180\) 0 0
\(181\) −15.0113 −1.11578 −0.557890 0.829915i \(-0.688389\pi\)
−0.557890 + 0.829915i \(0.688389\pi\)
\(182\) 3.16053 + 3.16053i 0.234274 + 0.234274i
\(183\) 0 0
\(184\) 6.11091i 0.450502i
\(185\) 0 0
\(186\) 0 0
\(187\) −16.0888 + 16.0888i −1.17653 + 1.17653i
\(188\) −3.42614 + 3.42614i −0.249877 + 0.249877i
\(189\) 0 0
\(190\) 0 0
\(191\) 23.3474i 1.68936i −0.535270 0.844681i \(-0.679790\pi\)
0.535270 0.844681i \(-0.320210\pi\)
\(192\) 0 0
\(193\) −6.69059 6.69059i −0.481599 0.481599i 0.424043 0.905642i \(-0.360611\pi\)
−0.905642 + 0.424043i \(0.860611\pi\)
\(194\) 6.55672 0.470745
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 0.375629 + 0.375629i 0.0267625 + 0.0267625i 0.720361 0.693599i \(-0.243976\pi\)
−0.693599 + 0.720361i \(0.743976\pi\)
\(198\) 0 0
\(199\) 18.0481i 1.27940i 0.768626 + 0.639698i \(0.220941\pi\)
−0.768626 + 0.639698i \(0.779059\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −1.50368 + 1.50368i −0.105798 + 0.105798i
\(203\) 7.04441 7.04441i 0.494421 0.494421i
\(204\) 0 0
\(205\) 0 0
\(206\) 15.4467i 1.07622i
\(207\) 0 0
\(208\) −3.16053 3.16053i −0.219143 0.219143i
\(209\) 0 0
\(210\) 0 0
\(211\) −8.22181 −0.566013 −0.283006 0.959118i \(-0.591332\pi\)
−0.283006 + 0.959118i \(0.591332\pi\)
\(212\) 9.88388 + 9.88388i 0.678828 + 0.678828i
\(213\) 0 0
\(214\) 9.06244i 0.619496i
\(215\) 0 0
\(216\) 0 0
\(217\) 0.894921 0.894921i 0.0607512 0.0607512i
\(218\) −6.75825 + 6.75825i −0.457726 + 0.457726i
\(219\) 0 0
\(220\) 0 0
\(221\) 19.3137i 1.29918i
\(222\) 0 0
\(223\) 13.2365 + 13.2365i 0.886384 + 0.886384i 0.994174 0.107789i \(-0.0343772\pi\)
−0.107789 + 0.994174i \(0.534377\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) −4.66421 −0.310259
\(227\) −5.46878 5.46878i −0.362976 0.362976i 0.501932 0.864907i \(-0.332623\pi\)
−0.864907 + 0.501932i \(0.832623\pi\)
\(228\) 0 0
\(229\) 13.0966i 0.865445i 0.901527 + 0.432723i \(0.142447\pi\)
−0.901527 + 0.432723i \(0.857553\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −7.04441 + 7.04441i −0.462488 + 0.462488i
\(233\) −0.642125 + 0.642125i −0.0420670 + 0.0420670i −0.727827 0.685760i \(-0.759470\pi\)
0.685760 + 0.727827i \(0.259470\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3.12563i 0.203461i
\(237\) 0 0
\(238\) −3.05545 3.05545i −0.198056 0.198056i
\(239\) −25.4246 −1.64458 −0.822291 0.569068i \(-0.807304\pi\)
−0.822291 + 0.569068i \(0.807304\pi\)
\(240\) 0 0
\(241\) −7.46878 −0.481106 −0.240553 0.970636i \(-0.577329\pi\)
−0.240553 + 0.970636i \(0.577329\pi\)
\(242\) −11.8275 11.8275i −0.760302 0.760302i
\(243\) 0 0
\(244\) 3.05545i 0.195605i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −0.894921 + 0.894921i −0.0568276 + 0.0568276i
\(249\) 0 0
\(250\) 0 0
\(251\) 1.23654i 0.0780497i −0.999238 0.0390249i \(-0.987575\pi\)
0.999238 0.0390249i \(-0.0124252\pi\)
\(252\) 0 0
\(253\) 22.7530 + 22.7530i 1.43047 + 1.43047i
\(254\) 11.7678 0.738375
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −10.8076 10.8076i −0.674159 0.674159i 0.284513 0.958672i \(-0.408168\pi\)
−0.958672 + 0.284513i \(0.908168\pi\)
\(258\) 0 0
\(259\) 4.14860i 0.257782i
\(260\) 0 0
\(261\) 0 0
\(262\) −12.3211 + 12.3211i −0.761198 + 0.761198i
\(263\) 6.99265 6.99265i 0.431185 0.431185i −0.457846 0.889031i \(-0.651379\pi\)
0.889031 + 0.457846i \(0.151379\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −4.59771 4.59771i −0.280850 0.280850i
\(269\) 21.7374 1.32535 0.662677 0.748905i \(-0.269420\pi\)
0.662677 + 0.748905i \(0.269420\pi\)
\(270\) 0 0
\(271\) −4.98566 −0.302857 −0.151429 0.988468i \(-0.548387\pi\)
−0.151429 + 0.988468i \(0.548387\pi\)
\(272\) 3.05545 + 3.05545i 0.185264 + 0.185264i
\(273\) 0 0
\(274\) 3.33579i 0.201523i
\(275\) 0 0
\(276\) 0 0
\(277\) −1.80787 + 1.80787i −0.108624 + 0.108624i −0.759330 0.650706i \(-0.774473\pi\)
0.650706 + 0.759330i \(0.274473\pi\)
\(278\) −15.4467 + 15.4467i −0.926431 + 0.926431i
\(279\) 0 0
\(280\) 0 0
\(281\) 8.66296i 0.516789i −0.966040 0.258394i \(-0.916807\pi\)
0.966040 0.258394i \(-0.0831934\pi\)
\(282\) 0 0
\(283\) 1.55760 + 1.55760i 0.0925899 + 0.0925899i 0.751885 0.659295i \(-0.229145\pi\)
−0.659295 + 0.751885i \(0.729145\pi\)
\(284\) 9.23654 0.548088
\(285\) 0 0
\(286\) 23.5355 1.39168
\(287\) −7.55178 7.55178i −0.445767 0.445767i
\(288\) 0 0
\(289\) 1.67158i 0.0983284i
\(290\) 0 0
\(291\) 0 0
\(292\) 10.2160 10.2160i 0.597845 0.597845i
\(293\) −5.39366 + 5.39366i −0.315101 + 0.315101i −0.846882 0.531781i \(-0.821523\pi\)
0.531781 + 0.846882i \(0.321523\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 4.14860i 0.241133i
\(297\) 0 0
\(298\) 4.30303 + 4.30303i 0.249268 + 0.249268i
\(299\) −27.3137 −1.57959
\(300\) 0 0
\(301\) −0.845296 −0.0487220
\(302\) 16.0888 + 16.0888i 0.925808 + 0.925808i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 1.46878 1.46878i 0.0838277 0.0838277i −0.663950 0.747777i \(-0.731121\pi\)
0.747777 + 0.663950i \(0.231121\pi\)
\(308\) 3.72335 3.72335i 0.212157 0.212157i
\(309\) 0 0
\(310\) 0 0
\(311\) 30.9822i 1.75684i 0.477889 + 0.878420i \(0.341402\pi\)
−0.477889 + 0.878420i \(0.658598\pi\)
\(312\) 0 0
\(313\) −6.74720 6.74720i −0.381375 0.381375i 0.490223 0.871597i \(-0.336915\pi\)
−0.871597 + 0.490223i \(0.836915\pi\)
\(314\) 15.1577 0.855400
\(315\) 0 0
\(316\) 3.57969 0.201373
\(317\) −20.4151 20.4151i −1.14663 1.14663i −0.987212 0.159415i \(-0.949039\pi\)
−0.159415 0.987212i \(-0.550961\pi\)
\(318\) 0 0
\(319\) 52.4576i 2.93706i
\(320\) 0 0
\(321\) 0 0
\(322\) −4.32106 + 4.32106i −0.240803 + 0.240803i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 5.71966i 0.316783i
\(327\) 0 0
\(328\) 7.55178 + 7.55178i 0.416977 + 0.416977i
\(329\) 4.84530 0.267130
\(330\) 0 0
\(331\) −18.2513 −1.00318 −0.501590 0.865105i \(-0.667251\pi\)
−0.501590 + 0.865105i \(0.667251\pi\)
\(332\) 6.21016 + 6.21016i 0.340827 + 0.340827i
\(333\) 0 0
\(334\) 8.15900i 0.446441i
\(335\) 0 0
\(336\) 0 0
\(337\) 7.21016 7.21016i 0.392762 0.392762i −0.482909 0.875671i \(-0.660420\pi\)
0.875671 + 0.482909i \(0.160420\pi\)
\(338\) −4.93413 + 4.93413i −0.268381 + 0.268381i
\(339\) 0 0
\(340\) 0 0
\(341\) 6.66421i 0.360887i
\(342\) 0 0
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 0.845296 0.0455753
\(345\) 0 0
\(346\) 8.69022 0.467189
\(347\) −10.8284 10.8284i −0.581300 0.581300i 0.353960 0.935261i \(-0.384835\pi\)
−0.935261 + 0.353960i \(0.884835\pi\)
\(348\) 0 0
\(349\) 16.0598i 0.859659i −0.902910 0.429829i \(-0.858574\pi\)
0.902910 0.429829i \(-0.141426\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.72335 + 3.72335i −0.198455 + 0.198455i
\(353\) −9.26561 + 9.26561i −0.493159 + 0.493159i −0.909300 0.416141i \(-0.863382\pi\)
0.416141 + 0.909300i \(0.363382\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 3.61916i 0.191815i
\(357\) 0 0
\(358\) 0.276651 + 0.276651i 0.0146215 + 0.0146215i
\(359\) −7.35787 −0.388334 −0.194167 0.980969i \(-0.562200\pi\)
−0.194167 + 0.980969i \(0.562200\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) −10.6146 10.6146i −0.557890 0.557890i
\(363\) 0 0
\(364\) 4.46967i 0.234274i
\(365\) 0 0
\(366\) 0 0
\(367\) −23.1443 + 23.1443i −1.20812 + 1.20812i −0.236487 + 0.971635i \(0.575996\pi\)
−0.971635 + 0.236487i \(0.924004\pi\)
\(368\) 4.32106 4.32106i 0.225251 0.225251i
\(369\) 0 0
\(370\) 0 0
\(371\) 13.9779i 0.725697i
\(372\) 0 0
\(373\) −0.0812231 0.0812231i −0.00420557 0.00420557i 0.705001 0.709206i \(-0.250947\pi\)
−0.709206 + 0.705001i \(0.750947\pi\)
\(374\) −22.7530 −1.17653
\(375\) 0 0
\(376\) −4.84530 −0.249877
\(377\) 31.4862 + 31.4862i 1.62162 + 1.62162i
\(378\) 0 0
\(379\) 12.3548i 0.634623i −0.948321 0.317312i \(-0.897220\pi\)
0.948321 0.317312i \(-0.102780\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 16.5091 16.5091i 0.844681 0.844681i
\(383\) −11.7546 + 11.7546i −0.600631 + 0.600631i −0.940480 0.339849i \(-0.889624\pi\)
0.339849 + 0.940480i \(0.389624\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 9.46192i 0.481599i
\(387\) 0 0
\(388\) 4.63630 + 4.63630i 0.235372 + 0.235372i
\(389\) −11.4960 −0.582873 −0.291436 0.956590i \(-0.594133\pi\)
−0.291436 + 0.956590i \(0.594133\pi\)
\(390\) 0 0
\(391\) 26.4056 1.33539
\(392\) 0.707107 + 0.707107i 0.0357143 + 0.0357143i
\(393\) 0 0
\(394\) 0.531220i 0.0267625i
\(395\) 0 0
\(396\) 0 0
\(397\) 11.2424 11.2424i 0.564238 0.564238i −0.366270 0.930509i \(-0.619365\pi\)
0.930509 + 0.366270i \(0.119365\pi\)
\(398\) −12.7619 + 12.7619i −0.639698 + 0.639698i
\(399\) 0 0
\(400\) 0 0
\(401\) 29.5269i 1.47450i −0.675619 0.737251i \(-0.736123\pi\)
0.675619 0.737251i \(-0.263877\pi\)
\(402\) 0 0
\(403\) 4.00000 + 4.00000i 0.199254 + 0.199254i
\(404\) −2.12652 −0.105798
\(405\) 0 0
\(406\) 9.96230 0.494421
\(407\) −15.4467 15.4467i −0.765664 0.765664i
\(408\) 0 0
\(409\) 26.2916i 1.30004i 0.759919 + 0.650018i \(0.225239\pi\)
−0.759919 + 0.650018i \(0.774761\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −10.9225 + 10.9225i −0.538111 + 0.538111i
\(413\) 2.21016 2.21016i 0.108755 0.108755i
\(414\) 0 0
\(415\) 0 0
\(416\) 4.46967i 0.219143i
\(417\) 0 0
\(418\) 0 0
\(419\) 20.5980 1.00628 0.503138 0.864206i \(-0.332179\pi\)
0.503138 + 0.864206i \(0.332179\pi\)
\(420\) 0 0
\(421\) −1.73402 −0.0845111 −0.0422556 0.999107i \(-0.513454\pi\)
−0.0422556 + 0.999107i \(0.513454\pi\)
\(422\) −5.81370 5.81370i −0.283006 0.283006i
\(423\) 0 0
\(424\) 13.9779i 0.678828i
\(425\) 0 0
\(426\) 0 0
\(427\) 2.16053 2.16053i 0.104555 0.104555i
\(428\) −6.40811 + 6.40811i −0.309748 + 0.309748i
\(429\) 0 0
\(430\) 0 0
\(431\) 1.70102i 0.0819353i 0.999160 + 0.0409676i \(0.0130441\pi\)
−0.999160 + 0.0409676i \(0.986956\pi\)
\(432\) 0 0
\(433\) −2.88757 2.88757i −0.138768 0.138768i 0.634311 0.773078i \(-0.281284\pi\)
−0.773078 + 0.634311i \(0.781284\pi\)
\(434\) 1.26561 0.0607512
\(435\) 0 0
\(436\) −9.55760 −0.457726
\(437\) 0 0
\(438\) 0 0
\(439\) 32.8011i 1.56551i 0.622328 + 0.782756i \(0.286187\pi\)
−0.622328 + 0.782756i \(0.713813\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 13.6569 13.6569i 0.649590 0.649590i
\(443\) −20.0650 + 20.0650i −0.953315 + 0.953315i −0.998958 0.0456425i \(-0.985466\pi\)
0.0456425 + 0.998958i \(0.485466\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 18.7193i 0.886384i
\(447\) 0 0
\(448\) −0.707107 0.707107i −0.0334077 0.0334077i
\(449\) −11.9767 −0.565214 −0.282607 0.959236i \(-0.591199\pi\)
−0.282607 + 0.959236i \(0.591199\pi\)
\(450\) 0 0
\(451\) −56.2358 −2.64804
\(452\) −3.29809 3.29809i −0.155129 0.155129i
\(453\) 0 0
\(454\) 7.73402i 0.362976i
\(455\) 0 0
\(456\) 0 0
\(457\) −6.46878 + 6.46878i −0.302597 + 0.302597i −0.842029 0.539432i \(-0.818639\pi\)
0.539432 + 0.842029i \(0.318639\pi\)
\(458\) −9.26067 + 9.26067i −0.432723 + 0.432723i
\(459\) 0 0
\(460\) 0 0
\(461\) 37.0915i 1.72752i 0.503901 + 0.863761i \(0.331898\pi\)
−0.503901 + 0.863761i \(0.668102\pi\)
\(462\) 0 0
\(463\) 0.232240 + 0.232240i 0.0107931 + 0.0107931i 0.712483 0.701690i \(-0.247571\pi\)
−0.701690 + 0.712483i \(0.747571\pi\)
\(464\) −9.96230 −0.462488
\(465\) 0 0
\(466\) −0.908103 −0.0420670
\(467\) 22.1997 + 22.1997i 1.02728 + 1.02728i 0.999617 + 0.0276636i \(0.00880672\pi\)
0.0276636 + 0.999617i \(0.491193\pi\)
\(468\) 0 0
\(469\) 6.50215i 0.300241i
\(470\) 0 0
\(471\) 0 0
\(472\) −2.21016 + 2.21016i −0.101731 + 0.101731i
\(473\) −3.14733 + 3.14733i −0.144714 + 0.144714i
\(474\) 0 0
\(475\) 0 0
\(476\) 4.32106i 0.198056i
\(477\) 0 0
\(478\) −17.9779 17.9779i −0.822291 0.822291i
\(479\) −20.7751 −0.949239 −0.474620 0.880191i \(-0.657414\pi\)
−0.474620 + 0.880191i \(0.657414\pi\)
\(480\) 0 0
\(481\) 18.5429 0.845482
\(482\) −5.28123 5.28123i −0.240553 0.240553i
\(483\) 0 0
\(484\) 16.7266i 0.760302i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.00735 1.00735i 0.0456476 0.0456476i −0.683915 0.729562i \(-0.739724\pi\)
0.729562 + 0.683915i \(0.239724\pi\)
\(488\) −2.16053 + 2.16053i −0.0978027 + 0.0978027i
\(489\) 0 0
\(490\) 0 0
\(491\) 6.95620i 0.313929i 0.987604 + 0.156964i \(0.0501708\pi\)
−0.987604 + 0.156964i \(0.949829\pi\)
\(492\) 0 0
\(493\) −30.4393 30.4393i −1.37092 1.37092i
\(494\) 0 0
\(495\) 0 0
\(496\) −1.26561 −0.0568276
\(497\) −6.53122 6.53122i −0.292965 0.292965i
\(498\) 0 0
\(499\) 20.9969i 0.939951i 0.882679 + 0.469976i \(0.155737\pi\)
−0.882679 + 0.469976i \(0.844263\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.874366 0.874366i 0.0390249 0.0390249i
\(503\) 7.29315 7.29315i 0.325186 0.325186i −0.525567 0.850752i \(-0.676147\pi\)
0.850752 + 0.525567i \(0.176147\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 32.1776i 1.43047i
\(507\) 0 0
\(508\) 8.32106 + 8.32106i 0.369187 + 0.369187i
\(509\) −0.545062 −0.0241595 −0.0120797 0.999927i \(-0.503845\pi\)
−0.0120797 + 0.999927i \(0.503845\pi\)
\(510\) 0 0
\(511\) −14.4476 −0.639123
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 15.2843i 0.674159i
\(515\) 0 0
\(516\) 0 0
\(517\) 18.0407 18.0407i 0.793430 0.793430i
\(518\) 2.93351 2.93351i 0.128891 0.128891i
\(519\) 0 0
\(520\) 0 0
\(521\) 21.6963i 0.950533i 0.879842 + 0.475267i \(0.157648\pi\)
−0.879842 + 0.475267i \(0.842352\pi\)
\(522\) 0 0
\(523\) −26.9822 26.9822i −1.17985 1.17985i −0.979782 0.200068i \(-0.935884\pi\)
−0.200068 0.979782i \(-0.564116\pi\)
\(524\) −17.4246 −0.761198
\(525\) 0 0
\(526\) 9.88909 0.431185
\(527\) −3.86701 3.86701i −0.168450 0.168450i
\(528\) 0 0
\(529\) 14.3432i 0.623616i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 33.7539 33.7539i 1.46204 1.46204i
\(534\) 0 0
\(535\) 0 0
\(536\) 6.50215i 0.280850i
\(537\) 0 0
\(538\) 15.3707 + 15.3707i 0.662677 + 0.662677i
\(539\) −5.26561 −0.226806
\(540\) 0 0
\(541\) −15.2249 −0.654569 −0.327284 0.944926i \(-0.606134\pi\)
−0.327284 + 0.944926i \(0.606134\pi\)
\(542\) −3.52539 3.52539i −0.151429 0.151429i
\(543\) 0 0
\(544\) 4.32106i 0.185264i
\(545\) 0 0
\(546\) 0 0
\(547\) −6.84898 + 6.84898i −0.292841 + 0.292841i −0.838202 0.545360i \(-0.816393\pi\)
0.545360 + 0.838202i \(0.316393\pi\)
\(548\) 2.35876 2.35876i 0.100761 0.100761i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −2.53122 2.53122i −0.107638 0.107638i
\(554\) −2.55672 −0.108624
\(555\) 0 0
\(556\) −21.8449 −0.926431
\(557\) 25.8839 + 25.8839i 1.09674 + 1.09674i 0.994790 + 0.101945i \(0.0325066\pi\)
0.101945 + 0.994790i \(0.467493\pi\)
\(558\) 0 0
\(559\) 3.77819i 0.159800i
\(560\) 0 0
\(561\) 0 0
\(562\) 6.12563 6.12563i 0.258394 0.258394i
\(563\) −14.9926 + 14.9926i −0.631865 + 0.631865i −0.948535 0.316671i \(-0.897435\pi\)
0.316671 + 0.948535i \(0.397435\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 2.20278i 0.0925899i
\(567\) 0 0
\(568\) 6.53122 + 6.53122i 0.274044 + 0.274044i
\(569\) 4.97742 0.208664 0.104332 0.994543i \(-0.466730\pi\)
0.104332 + 0.994543i \(0.466730\pi\)
\(570\) 0 0
\(571\) 34.6949 1.45194 0.725968 0.687728i \(-0.241392\pi\)
0.725968 + 0.687728i \(0.241392\pi\)
\(572\) 16.6421 + 16.6421i 0.695842 + 0.695842i
\(573\) 0 0
\(574\) 10.6798i 0.445767i
\(575\) 0 0
\(576\) 0 0
\(577\) −32.5782 + 32.5782i −1.35625 + 1.35625i −0.477751 + 0.878495i \(0.658548\pi\)
−0.878495 + 0.477751i \(0.841452\pi\)
\(578\) −1.18199 + 1.18199i −0.0491642 + 0.0491642i
\(579\) 0 0
\(580\) 0 0
\(581\) 8.78249i 0.364359i
\(582\) 0 0
\(583\) −52.0447 52.0447i −2.15547 2.15547i
\(584\) 14.4476 0.597845
\(585\) 0 0
\(586\) −7.62778 −0.315101
\(587\) −18.4320 18.4320i −0.760769 0.760769i 0.215693 0.976461i \(-0.430799\pi\)
−0.976461 + 0.215693i \(0.930799\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −2.93351 + 2.93351i −0.120566 + 0.120566i
\(593\) −22.1213 + 22.1213i −0.908413 + 0.908413i −0.996144 0.0877310i \(-0.972038\pi\)
0.0877310 + 0.996144i \(0.472038\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.08541i 0.249268i
\(597\) 0 0
\(598\) −19.3137 19.3137i −0.789796 0.789796i
\(599\) −17.6906 −0.722818 −0.361409 0.932407i \(-0.617704\pi\)
−0.361409 + 0.932407i \(0.617704\pi\)
\(600\) 0 0
\(601\) 18.6979 0.762705 0.381353 0.924430i \(-0.375458\pi\)
0.381353 + 0.924430i \(0.375458\pi\)
\(602\) −0.597714 0.597714i −0.0243610 0.0243610i
\(603\) 0 0
\(604\) 22.7530i 0.925808i
\(605\) 0 0
\(606\) 0 0
\(607\) −5.23654 + 5.23654i −0.212545 + 0.212545i −0.805348 0.592803i \(-0.798021\pi\)
0.592803 + 0.805348i \(0.298021\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 21.6569i 0.876143i
\(612\) 0 0
\(613\) −21.4426 21.4426i −0.866060 0.866060i 0.125973 0.992034i \(-0.459795\pi\)
−0.992034 + 0.125973i \(0.959795\pi\)
\(614\) 2.07717 0.0838277
\(615\) 0 0
\(616\) 5.26561 0.212157
\(617\) −2.18109 2.18109i −0.0878073 0.0878073i 0.661839 0.749646i \(-0.269776\pi\)
−0.749646 + 0.661839i \(0.769776\pi\)
\(618\) 0 0
\(619\) 19.7573i 0.794114i −0.917794 0.397057i \(-0.870031\pi\)
0.917794 0.397057i \(-0.129969\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −21.9077 + 21.9077i −0.878420 + 0.878420i
\(623\) −2.55913 + 2.55913i −0.102529 + 0.102529i
\(624\) 0 0
\(625\) 0 0
\(626\) 9.54199i 0.381375i
\(627\) 0 0
\(628\) 10.7181 + 10.7181i 0.427700 + 0.427700i
\(629\) −17.9264 −0.714771
\(630\) 0 0
\(631\) 2.15507 0.0857920 0.0428960 0.999080i \(-0.486342\pi\)
0.0428960 + 0.999080i \(0.486342\pi\)
\(632\) 2.53122 + 2.53122i 0.100687 + 0.100687i
\(633\) 0 0
\(634\) 28.8713i 1.14663i
\(635\) 0 0
\(636\) 0 0
\(637\) 3.16053 3.16053i 0.125225 0.125225i
\(638\) 37.0931 37.0931i 1.46853 1.46853i
\(639\) 0 0
\(640\) 0 0
\(641\) 39.5147i 1.56074i −0.625320 0.780368i \(-0.715032\pi\)
0.625320 0.780368i \(-0.284968\pi\)
\(642\) 0 0
\(643\) −9.61574 9.61574i −0.379208 0.379208i 0.491608 0.870816i \(-0.336409\pi\)
−0.870816 + 0.491608i \(0.836409\pi\)
\(644\) −6.11091 −0.240803
\(645\) 0 0
\(646\) 0 0
\(647\) 14.6510 + 14.6510i 0.575991 + 0.575991i 0.933796 0.357805i \(-0.116475\pi\)
−0.357805 + 0.933796i \(0.616475\pi\)
\(648\) 0 0
\(649\) 16.4584i 0.646048i
\(650\) 0 0
\(651\) 0 0
\(652\) −4.04441 + 4.04441i −0.158391 + 0.158391i
\(653\) 32.0836 32.0836i 1.25553 1.25553i 0.302323 0.953206i \(-0.402238\pi\)
0.953206 0.302323i \(-0.0977621\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 10.6798i 0.416977i
\(657\) 0 0
\(658\) 3.42614 + 3.42614i 0.133565 + 0.133565i
\(659\) −38.5499 −1.50169 −0.750845 0.660479i \(-0.770353\pi\)
−0.750845 + 0.660479i \(0.770353\pi\)
\(660\) 0 0
\(661\) −39.4176 −1.53317 −0.766584 0.642144i \(-0.778045\pi\)
−0.766584 + 0.642144i \(0.778045\pi\)
\(662\) −12.9056 12.9056i −0.501590 0.501590i
\(663\) 0 0
\(664\) 8.78249i 0.340827i
\(665\) 0 0
\(666\) 0 0
\(667\) −43.0477 + 43.0477i −1.66681 + 1.66681i
\(668\) 5.76929 5.76929i 0.223220 0.223220i
\(669\) 0 0
\(670\) 0 0
\(671\) 16.0888i 0.621102i
\(672\) 0 0
\(673\) 13.3431 + 13.3431i 0.514340 + 0.514340i 0.915853 0.401513i \(-0.131516\pi\)
−0.401513 + 0.915853i \(0.631516\pi\)
\(674\) 10.1967 0.392762
\(675\) 0 0
\(676\) −6.97792 −0.268381
\(677\) 18.1024 + 18.1024i 0.695731 + 0.695731i 0.963487 0.267755i \(-0.0862819\pi\)
−0.267755 + 0.963487i \(0.586282\pi\)
\(678\) 0 0
\(679\) 6.55672i 0.251624i
\(680\) 0 0
\(681\) 0 0
\(682\) 4.71231 4.71231i 0.180444 0.180444i
\(683\) 27.4077 27.4077i 1.04873 1.04873i 0.0499779 0.998750i \(-0.484085\pi\)
0.998750 0.0499779i \(-0.0159151\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) 0.597714 + 0.597714i 0.0227876 + 0.0227876i
\(689\) 62.4766 2.38017
\(690\) 0 0
\(691\) −12.9221 −0.491579 −0.245789 0.969323i \(-0.579047\pi\)
−0.245789 + 0.969323i \(0.579047\pi\)
\(692\) 6.14492 + 6.14492i 0.233595 + 0.233595i
\(693\) 0 0
\(694\) 15.3137i 0.581300i
\(695\) 0 0
\(696\) 0 0
\(697\) −32.6317 + 32.6317i −1.23601 + 1.23601i
\(698\) 11.3560 11.3560i 0.429829 0.429829i
\(699\) 0 0
\(700\) 0 0
\(701\) 13.5732i 0.512653i −0.966590 0.256327i \(-0.917488\pi\)
0.966590 0.256327i \(-0.0825123\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −5.26561 −0.198455
\(705\) 0 0
\(706\) −13.1036 −0.493159
\(707\) 1.50368 + 1.50368i 0.0565516 + 0.0565516i
\(708\) 0 0
\(709\) 40.4429i 1.51886i −0.650586 0.759432i \(-0.725477\pi\)
0.650586 0.759432i \(-0.274523\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 2.55913 2.55913i 0.0959074 0.0959074i
\(713\) −5.46878 + 5.46878i −0.204807 + 0.204807i
\(714\) 0 0
\(715\) 0 0
\(716\) 0.391244i 0.0146215i
\(717\) 0 0
\(718\) −5.20280 5.20280i −0.194167 0.194167i
\(719\) −16.9706 −0.632895 −0.316448 0.948610i \(-0.602490\pi\)
−0.316448 + 0.948610i \(0.602490\pi\)
\(720\) 0 0
\(721\) 15.4467 0.575265
\(722\) 13.4350 + 13.4350i 0.500000 + 0.500000i
\(723\) 0 0
\(724\) 15.0113i 0.557890i
\(725\) 0 0
\(726\) 0 0
\(727\) 29.8787 29.8787i 1.10814 1.10814i 0.114743 0.993395i \(-0.463395\pi\)
0.993395 0.114743i \(-0.0366045\pi\)
\(728\) −3.16053 + 3.16053i −0.117137 + 0.117137i
\(729\) 0 0
\(730\) 0 0
\(731\) 3.65258i 0.135095i
\(732\) 0 0
\(733\) 8.55913 + 8.55913i 0.316139 + 0.316139i 0.847282 0.531143i \(-0.178237\pi\)
−0.531143 + 0.847282i \(0.678237\pi\)
\(734\) −32.7309 −1.20812
\(735\) 0 0
\(736\) 6.11091 0.225251
\(737\) 24.2098 + 24.2098i 0.891778 + 0.891778i
\(738\) 0 0
\(739\) 35.3584i 1.30068i 0.759644 + 0.650339i \(0.225373\pi\)
−0.759644 + 0.650339i \(0.774627\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 9.88388 9.88388i 0.362849 0.362849i
\(743\) −35.1733 + 35.1733i −1.29038 + 1.29038i −0.355837 + 0.934548i \(0.615804\pi\)
−0.934548 + 0.355837i \(0.884196\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.114867i 0.00420557i
\(747\) 0 0
\(748\) −16.0888 16.0888i −0.588266 0.588266i
\(749\) 9.06244 0.331134
\(750\) 0 0
\(751\) 16.2358 0.592452 0.296226 0.955118i \(-0.404272\pi\)
0.296226 + 0.955118i \(0.404272\pi\)
\(752\) −3.42614 3.42614i −0.124939 0.124939i
\(753\) 0 0
\(754\) 44.5282i 1.62162i
\(755\) 0 0
\(756\) 0 0
\(757\) 1.76016 1.76016i 0.0639741 0.0639741i −0.674396 0.738370i \(-0.735596\pi\)
0.738370 + 0.674396i \(0.235596\pi\)
\(758\) 8.73616 8.73616i 0.317312 0.317312i
\(759\) 0 0
\(760\) 0 0
\(761\) 29.0125i 1.05170i −0.850576 0.525852i \(-0.823747\pi\)
0.850576 0.525852i \(-0.176253\pi\)
\(762\) 0 0
\(763\) 6.75825 + 6.75825i 0.244665 + 0.244665i
\(764\) 23.3474 0.844681
\(765\) 0 0
\(766\) −16.6235 −0.600631
\(767\) 9.87867 + 9.87867i 0.356698 + 0.356698i
\(768\) 0 0
\(769\) 29.2439i 1.05456i −0.849691 0.527281i \(-0.823211\pi\)
0.849691 0.527281i \(-0.176789\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.69059 6.69059i 0.240800 0.240800i
\(773\) −8.95467 + 8.95467i −0.322077 + 0.322077i −0.849564 0.527486i \(-0.823135\pi\)
0.527486 + 0.849564i \(0.323135\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 6.55672i 0.235372i
\(777\) 0 0
\(778\) −8.12893 8.12893i −0.291436 0.291436i
\(779\) 0 0
\(780\) 0 0
\(781\) −48.6360 −1.74033
\(782\) 18.6716 + 18.6716i 0.667694 + 0.667694i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) 29.9264 29.9264i 1.06676 1.06676i 0.0691541 0.997606i \(-0.477970\pi\)
0.997606 0.0691541i \(-0.0220300\pi\)
\(788\) −0.375629 + 0.375629i −0.0133812 + 0.0133812i
\(789\) 0 0
\(790\) 0 0
\(791\) 4.66421i 0.165840i
\(792\) 0 0
\(793\) 9.65685 + 9.65685i 0.342925 + 0.342925i
\(794\) 15.8991 0.564238
\(795\) 0 0
\(796\) −18.0481 −0.639698
\(797\) 7.21473 + 7.21473i 0.255559 + 0.255559i 0.823245 0.567686i \(-0.192161\pi\)
−0.567686 + 0.823245i \(0.692161\pi\)
\(798\) 0 0
\(799\) 20.9368i 0.740692i