Properties

Label 3150.2.m.i.1457.2
Level 3150
Weight 2
Character 3150.1457
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 1457.2
Root \(-2.16053i\)
Character \(\chi\) = 3150.1457
Dual form 3150.2.m.i.2843.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(0.707107 + 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} -2.14860i q^{11} +(-2.16053 + 2.16053i) q^{13} -1.00000 q^{14} -1.00000 q^{16} +(-4.46967 + 4.46967i) q^{17} +(1.51929 + 1.51929i) q^{22} +(-6.32106 - 6.32106i) q^{23} -3.05545i q^{26} +(0.707107 - 0.707107i) q^{28} +8.20494 q^{29} -1.85140 q^{31} +(0.707107 - 0.707107i) q^{32} -6.32106i q^{34} +(5.13756 + 5.13756i) q^{37} -7.56282i q^{41} +(7.84035 - 7.84035i) q^{43} -2.14860 q^{44} +8.93933 q^{46} +(5.01193 - 5.01193i) q^{47} +1.00000i q^{49} +(2.16053 + 2.16053i) q^{52} +(-2.35876 - 2.35876i) q^{53} +1.00000i q^{56} +(-5.80177 + 5.80177i) q^{58} -9.35965 q^{59} -4.46967 q^{61} +(1.30913 - 1.30913i) q^{62} +1.00000i q^{64} +(3.84035 + 3.84035i) q^{67} +(4.46967 + 4.46967i) q^{68} -0.420314i q^{71} +(2.63020 - 2.63020i) q^{73} -7.26561 q^{74} +(1.51929 - 1.51929i) q^{77} -5.23654i q^{79} +(5.34772 + 5.34772i) q^{82} +(-10.6183 - 10.6183i) q^{83} +11.0879i q^{86} +(1.51929 - 1.51929i) q^{88} -14.5481 q^{89} -3.05545 q^{91} +(-6.32106 + 6.32106i) q^{92} +7.08794i q^{94} +(0.606342 + 0.606342i) q^{97} +(-0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + O(q^{10}) \) \( 8q + 4q^{13} - 8q^{14} - 8q^{16} + 4q^{22} - 8q^{23} - 24q^{29} - 8q^{31} + 4q^{37} + 12q^{43} - 24q^{44} + 12q^{47} - 4q^{52} - 32q^{53} - 12q^{58} - 16q^{59} - 4q^{62} - 20q^{67} - 36q^{73} - 40q^{74} + 4q^{77} + 12q^{82} - 56q^{83} + 4q^{88} - 72q^{89} - 8q^{92} + 4q^{97} + O(q^{100}) \)

Character values

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

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

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
\(11\) 2.14860i 0.647828i −0.946086 0.323914i \(-0.895001\pi\)
0.946086 0.323914i \(-0.104999\pi\)
\(12\) 0 0
\(13\) −2.16053 + 2.16053i −0.599224 + 0.599224i −0.940106 0.340882i \(-0.889274\pi\)
0.340882 + 0.940106i \(0.389274\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −4.46967 + 4.46967i −1.08405 + 1.08405i −0.0879263 + 0.996127i \(0.528024\pi\)
−0.996127 + 0.0879263i \(0.971976\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.51929 + 1.51929i 0.323914 + 0.323914i
\(23\) −6.32106 6.32106i −1.31803 1.31803i −0.915331 0.402701i \(-0.868071\pi\)
−0.402701 0.915331i \(-0.631929\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 3.05545i 0.599224i
\(27\) 0 0
\(28\) 0.707107 0.707107i 0.133631 0.133631i
\(29\) 8.20494 1.52362 0.761810 0.647801i \(-0.224311\pi\)
0.761810 + 0.647801i \(0.224311\pi\)
\(30\) 0 0
\(31\) −1.85140 −0.332521 −0.166260 0.986082i \(-0.553169\pi\)
−0.166260 + 0.986082i \(0.553169\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0 0
\(34\) 6.32106i 1.08405i
\(35\) 0 0
\(36\) 0 0
\(37\) 5.13756 + 5.13756i 0.844610 + 0.844610i 0.989454 0.144844i \(-0.0462682\pi\)
−0.144844 + 0.989454i \(0.546268\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7.56282i 1.18111i −0.806996 0.590557i \(-0.798908\pi\)
0.806996 0.590557i \(-0.201092\pi\)
\(42\) 0 0
\(43\) 7.84035 7.84035i 1.19564 1.19564i 0.220185 0.975458i \(-0.429334\pi\)
0.975458 0.220185i \(-0.0706660\pi\)
\(44\) −2.14860 −0.323914
\(45\) 0 0
\(46\) 8.93933 1.31803
\(47\) 5.01193 5.01193i 0.731065 0.731065i −0.239766 0.970831i \(-0.577071\pi\)
0.970831 + 0.239766i \(0.0770707\pi\)
\(48\) 0 0
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) 2.16053 + 2.16053i 0.299612 + 0.299612i
\(53\) −2.35876 2.35876i −0.324001 0.324001i 0.526299 0.850300i \(-0.323579\pi\)
−0.850300 + 0.526299i \(0.823579\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 0.133631i
\(57\) 0 0
\(58\) −5.80177 + 5.80177i −0.761810 + 0.761810i
\(59\) −9.35965 −1.21852 −0.609261 0.792970i \(-0.708534\pi\)
−0.609261 + 0.792970i \(0.708534\pi\)
\(60\) 0 0
\(61\) −4.46967 −0.572282 −0.286141 0.958188i \(-0.592373\pi\)
−0.286141 + 0.958188i \(0.592373\pi\)
\(62\) 1.30913 1.30913i 0.166260 0.166260i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 0 0
\(67\) 3.84035 + 3.84035i 0.469174 + 0.469174i 0.901647 0.432473i \(-0.142359\pi\)
−0.432473 + 0.901647i \(0.642359\pi\)
\(68\) 4.46967 + 4.46967i 0.542027 + 0.542027i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.420314i 0.0498821i −0.999689 0.0249411i \(-0.992060\pi\)
0.999689 0.0249411i \(-0.00793981\pi\)
\(72\) 0 0
\(73\) 2.63020 2.63020i 0.307841 0.307841i −0.536230 0.844072i \(-0.680152\pi\)
0.844072 + 0.536230i \(0.180152\pi\)
\(74\) −7.26561 −0.844610
\(75\) 0 0
\(76\) 0 0
\(77\) 1.51929 1.51929i 0.173139 0.173139i
\(78\) 0 0
\(79\) 5.23654i 0.589157i −0.955627 0.294578i \(-0.904821\pi\)
0.955627 0.294578i \(-0.0951792\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 5.34772 + 5.34772i 0.590557 + 0.590557i
\(83\) −10.6183 10.6183i −1.16551 1.16551i −0.983251 0.182255i \(-0.941660\pi\)
−0.182255 0.983251i \(-0.558340\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 11.0879i 1.19564i
\(87\) 0 0
\(88\) 1.51929 1.51929i 0.161957 0.161957i
\(89\) −14.5481 −1.54209 −0.771047 0.636778i \(-0.780267\pi\)
−0.771047 + 0.636778i \(0.780267\pi\)
\(90\) 0 0
\(91\) −3.05545 −0.320298
\(92\) −6.32106 + 6.32106i −0.659016 + 0.659016i
\(93\) 0 0
\(94\) 7.08794i 0.731065i
\(95\) 0 0
\(96\) 0 0
\(97\) 0.606342 + 0.606342i 0.0615647 + 0.0615647i 0.737219 0.675654i \(-0.236139\pi\)
−0.675654 + 0.737219i \(0.736139\pi\)
\(98\) −0.707107 0.707107i −0.0714286 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 5.39860i 0.537181i −0.963255 0.268590i \(-0.913442\pi\)
0.963255 0.268590i \(-0.0865578\pi\)
\(102\) 0 0
\(103\) 7.80546 7.80546i 0.769095 0.769095i −0.208853 0.977947i \(-0.566973\pi\)
0.977947 + 0.208853i \(0.0669729\pi\)
\(104\) −3.05545 −0.299612
\(105\) 0 0
\(106\) 3.33579 0.324001
\(107\) 2.40811 2.40811i 0.232801 0.232801i −0.581060 0.813861i \(-0.697362\pi\)
0.813861 + 0.581060i \(0.197362\pi\)
\(108\) 0 0
\(109\) 9.90075i 0.948320i 0.880439 + 0.474160i \(0.157248\pi\)
−0.880439 + 0.474160i \(0.842752\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.707107 0.707107i −0.0668153 0.0668153i
\(113\) −4.22703 4.22703i −0.397645 0.397645i 0.479757 0.877402i \(-0.340725\pi\)
−0.877402 + 0.479757i \(0.840725\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 8.20494i 0.761810i
\(117\) 0 0
\(118\) 6.61827 6.61827i 0.609261 0.609261i
\(119\) −6.32106 −0.579451
\(120\) 0 0
\(121\) 6.38350 0.580318
\(122\) 3.16053 3.16053i 0.286141 0.286141i
\(123\) 0 0
\(124\) 1.85140i 0.166260i
\(125\) 0 0
\(126\) 0 0
\(127\) −2.32106 2.32106i −0.205961 0.205961i 0.596587 0.802548i \(-0.296523\pi\)
−0.802548 + 0.596587i \(0.796523\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 2.37438i 0.207450i 0.994606 + 0.103725i \(0.0330762\pi\)
−0.994606 + 0.103725i \(0.966924\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −5.43108 −0.469174
\(135\) 0 0
\(136\) −6.32106 −0.542027
\(137\) 9.88388 9.88388i 0.844437 0.844437i −0.144995 0.989432i \(-0.546317\pi\)
0.989432 + 0.144995i \(0.0463168\pi\)
\(138\) 0 0
\(139\) 15.6109i 1.32410i −0.749459 0.662050i \(-0.769687\pi\)
0.749459 0.662050i \(-0.230313\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.297207 + 0.297207i 0.0249411 + 0.0249411i
\(143\) 4.64213 + 4.64213i 0.388194 + 0.388194i
\(144\) 0 0
\(145\) 0 0
\(146\) 3.71966i 0.307841i
\(147\) 0 0
\(148\) 5.13756 5.13756i 0.422305 0.422305i
\(149\) 9.49962 0.778239 0.389120 0.921187i \(-0.372779\pi\)
0.389120 + 0.921187i \(0.372779\pi\)
\(150\) 0 0
\(151\) −13.5815 −1.10524 −0.552622 0.833432i \(-0.686373\pi\)
−0.552622 + 0.833432i \(0.686373\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 2.14860i 0.173139i
\(155\) 0 0
\(156\) 0 0
\(157\) −14.0613 14.0613i −1.12221 1.12221i −0.991408 0.130804i \(-0.958244\pi\)
−0.130804 0.991408i \(-0.541756\pi\)
\(158\) 3.70279 + 3.70279i 0.294578 + 0.294578i
\(159\) 0 0
\(160\) 0 0
\(161\) 8.93933i 0.704518i
\(162\) 0 0
\(163\) −8.80177 + 8.80177i −0.689408 + 0.689408i −0.962101 0.272693i \(-0.912086\pi\)
0.272693 + 0.962101i \(0.412086\pi\)
\(164\) −7.56282 −0.590557
\(165\) 0 0
\(166\) 15.0165 1.16551
\(167\) −2.66878 + 2.66878i −0.206517 + 0.206517i −0.802785 0.596269i \(-0.796649\pi\)
0.596269 + 0.802785i \(0.296649\pi\)
\(168\) 0 0
\(169\) 3.66421i 0.281862i
\(170\) 0 0
\(171\) 0 0
\(172\) −7.84035 7.84035i −0.597821 0.597821i
\(173\) 6.70127 + 6.70127i 0.509488 + 0.509488i 0.914369 0.404881i \(-0.132687\pi\)
−0.404881 + 0.914369i \(0.632687\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.14860i 0.161957i
\(177\) 0 0
\(178\) 10.2871 10.2871i 0.771047 0.771047i
\(179\) −3.50825 −0.262219 −0.131109 0.991368i \(-0.541854\pi\)
−0.131109 + 0.991368i \(0.541854\pi\)
\(180\) 0 0
\(181\) 13.7981 1.02560 0.512802 0.858507i \(-0.328608\pi\)
0.512802 + 0.858507i \(0.328608\pi\)
\(182\) 2.16053 2.16053i 0.160149 0.160149i
\(183\) 0 0
\(184\) 8.93933i 0.659016i
\(185\) 0 0
\(186\) 0 0
\(187\) 9.60354 + 9.60354i 0.702280 + 0.702280i
\(188\) −5.01193 5.01193i −0.365532 0.365532i
\(189\) 0 0
\(190\) 0 0
\(191\) 0.519018i 0.0375548i 0.999824 + 0.0187774i \(0.00597739\pi\)
−0.999824 + 0.0187774i \(0.994023\pi\)
\(192\) 0 0
\(193\) 17.1759 17.1759i 1.23635 1.23635i 0.274863 0.961483i \(-0.411368\pi\)
0.961483 0.274863i \(-0.0886325\pi\)
\(194\) −0.857497 −0.0615647
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 4.03248 4.03248i 0.287303 0.287303i −0.548710 0.836013i \(-0.684881\pi\)
0.836013 + 0.548710i \(0.184881\pi\)
\(198\) 0 0
\(199\) 21.1651i 1.50035i −0.661237 0.750177i \(-0.729968\pi\)
0.661237 0.750177i \(-0.270032\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 3.81739 + 3.81739i 0.268590 + 0.268590i
\(203\) 5.80177 + 5.80177i 0.407204 + 0.407204i
\(204\) 0 0
\(205\) 0 0
\(206\) 11.0386i 0.769095i
\(207\) 0 0
\(208\) 2.16053 2.16053i 0.149806 0.149806i
\(209\) 0 0
\(210\) 0 0
\(211\) 21.8787 1.50619 0.753095 0.657912i \(-0.228560\pi\)
0.753095 + 0.657912i \(0.228560\pi\)
\(212\) −2.35876 + 2.35876i −0.162000 + 0.162000i
\(213\) 0 0
\(214\) 3.40559i 0.232801i
\(215\) 0 0
\(216\) 0 0
\(217\) −1.30913 1.30913i −0.0888699 0.0888699i
\(218\) −7.00089 7.00089i −0.474160 0.474160i
\(219\) 0 0
\(220\) 0 0
\(221\) 19.3137i 1.29918i
\(222\) 0 0
\(223\) 4.42031 4.42031i 0.296006 0.296006i −0.543441 0.839447i \(-0.682879\pi\)
0.839447 + 0.543441i \(0.182879\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 5.97792 0.397645
\(227\) 11.7028 11.7028i 0.776742 0.776742i −0.202534 0.979275i \(-0.564918\pi\)
0.979275 + 0.202534i \(0.0649176\pi\)
\(228\) 0 0
\(229\) 13.6314i 0.900785i −0.892831 0.450393i \(-0.851284\pi\)
0.892831 0.450393i \(-0.148716\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 5.80177 + 5.80177i 0.380905 + 0.380905i
\(233\) −20.6421 20.6421i −1.35231 1.35231i −0.883071 0.469240i \(-0.844528\pi\)
−0.469240 0.883071i \(-0.655472\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 9.35965i 0.609261i
\(237\) 0 0
\(238\) 4.46967 4.46967i 0.289725 0.289725i
\(239\) 10.3744 0.671063 0.335531 0.942029i \(-0.391084\pi\)
0.335531 + 0.942029i \(0.391084\pi\)
\(240\) 0 0
\(241\) −13.7028 −0.882674 −0.441337 0.897341i \(-0.645496\pi\)
−0.441337 + 0.897341i \(0.645496\pi\)
\(242\) −4.51382 + 4.51382i −0.290159 + 0.290159i
\(243\) 0 0
\(244\) 4.46967i 0.286141i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −1.30913 1.30913i −0.0831302 0.0831302i
\(249\) 0 0
\(250\) 0 0
\(251\) 7.57969i 0.478426i 0.970967 + 0.239213i \(0.0768893\pi\)
−0.970967 + 0.239213i \(0.923111\pi\)
\(252\) 0 0
\(253\) −13.5815 + 13.5815i −0.853859 + 0.853859i
\(254\) 3.28248 0.205961
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −19.2929 + 19.2929i −1.20346 + 1.20346i −0.230349 + 0.973108i \(0.573987\pi\)
−0.973108 + 0.230349i \(0.926013\pi\)
\(258\) 0 0
\(259\) 7.26561i 0.451463i
\(260\) 0 0
\(261\) 0 0
\(262\) −1.67894 1.67894i −0.103725 0.103725i
\(263\) −17.6348 17.6348i −1.08741 1.08741i −0.995795 0.0916118i \(-0.970798\pi\)
−0.0916118 0.995795i \(-0.529202\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 3.84035 3.84035i 0.234587 0.234587i
\(269\) −20.4463 −1.24663 −0.623317 0.781969i \(-0.714216\pi\)
−0.623317 + 0.781969i \(0.714216\pi\)
\(270\) 0 0
\(271\) −20.5707 −1.24958 −0.624790 0.780793i \(-0.714816\pi\)
−0.624790 + 0.780793i \(0.714816\pi\)
\(272\) 4.46967 4.46967i 0.271013 0.271013i
\(273\) 0 0
\(274\) 13.9779i 0.844437i
\(275\) 0 0
\(276\) 0 0
\(277\) 2.22208 + 2.22208i 0.133512 + 0.133512i 0.770705 0.637193i \(-0.219904\pi\)
−0.637193 + 0.770705i \(0.719904\pi\)
\(278\) 11.0386 + 11.0386i 0.662050 + 0.662050i
\(279\) 0 0
\(280\) 0 0
\(281\) 17.4792i 1.04272i −0.853337 0.521360i \(-0.825425\pi\)
0.853337 0.521360i \(-0.174575\pi\)
\(282\) 0 0
\(283\) −17.9007 + 17.9007i −1.06409 + 1.06409i −0.0662885 + 0.997800i \(0.521116\pi\)
−0.997800 + 0.0662885i \(0.978884\pi\)
\(284\) −0.420314 −0.0249411
\(285\) 0 0
\(286\) −6.56496 −0.388194
\(287\) 5.34772 5.34772i 0.315666 0.315666i
\(288\) 0 0
\(289\) 22.9558i 1.35034i
\(290\) 0 0
\(291\) 0 0
\(292\) −2.63020 2.63020i −0.153921 0.153921i
\(293\) 1.36370 + 1.36370i 0.0796683 + 0.0796683i 0.745818 0.666150i \(-0.232059\pi\)
−0.666150 + 0.745818i \(0.732059\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 7.26561i 0.422305i
\(297\) 0 0
\(298\) −6.71725 + 6.71725i −0.389120 + 0.389120i
\(299\) 27.3137 1.57959
\(300\) 0 0
\(301\) 11.0879 0.639098
\(302\) 9.60354 9.60354i 0.552622 0.552622i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 7.70279 + 7.70279i 0.439622 + 0.439622i 0.891885 0.452263i \(-0.149383\pi\)
−0.452263 + 0.891885i \(0.649383\pi\)
\(308\) −1.51929 1.51929i −0.0865697 0.0865697i
\(309\) 0 0
\(310\) 0 0
\(311\) 3.52637i 0.199962i −0.994989 0.0999811i \(-0.968122\pi\)
0.994989 0.0999811i \(-0.0318782\pi\)
\(312\) 0 0
\(313\) 12.3330 12.3330i 0.697102 0.697102i −0.266683 0.963784i \(-0.585928\pi\)
0.963784 + 0.266683i \(0.0859275\pi\)
\(314\) 19.8857 1.12221
\(315\) 0 0
\(316\) −5.23654 −0.294578
\(317\) 6.65597 6.65597i 0.373836 0.373836i −0.495036 0.868872i \(-0.664845\pi\)
0.868872 + 0.495036i \(0.164845\pi\)
\(318\) 0 0
\(319\) 17.6292i 0.987044i
\(320\) 0 0
\(321\) 0 0
\(322\) 6.32106 + 6.32106i 0.352259 + 0.352259i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 12.4476i 0.689408i
\(327\) 0 0
\(328\) 5.34772 5.34772i 0.295278 0.295278i
\(329\) 7.08794 0.390771
\(330\) 0 0
\(331\) −30.7193 −1.68849 −0.844243 0.535961i \(-0.819949\pi\)
−0.844243 + 0.535961i \(0.819949\pi\)
\(332\) −10.6183 + 10.6183i −0.582753 + 0.582753i
\(333\) 0 0
\(334\) 3.77423i 0.206517i
\(335\) 0 0
\(336\) 0 0
\(337\) 11.6183 + 11.6183i 0.632887 + 0.632887i 0.948791 0.315904i \(-0.102308\pi\)
−0.315904 + 0.948791i \(0.602308\pi\)
\(338\) −2.59099 2.59099i −0.140931 0.140931i
\(339\) 0 0
\(340\) 0 0
\(341\) 3.97792i 0.215416i
\(342\) 0 0
\(343\) −0.707107 + 0.707107i −0.0381802 + 0.0381802i
\(344\) 11.0879 0.597821
\(345\) 0 0
\(346\) −9.47702 −0.509488
\(347\) 10.8284 10.8284i 0.581300 0.581300i −0.353960 0.935261i \(-0.615165\pi\)
0.935261 + 0.353960i \(0.115165\pi\)
\(348\) 0 0
\(349\) 15.3318i 0.820694i −0.911929 0.410347i \(-0.865408\pi\)
0.911929 0.410347i \(-0.134592\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.51929 1.51929i −0.0809785 0.0809785i
\(353\) 6.14860 + 6.14860i 0.327257 + 0.327257i 0.851543 0.524285i \(-0.175668\pi\)
−0.524285 + 0.851543i \(0.675668\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 14.5481i 0.771047i
\(357\) 0 0
\(358\) 2.48071 2.48071i 0.131109 0.131109i
\(359\) 28.6421 1.51167 0.755837 0.654760i \(-0.227230\pi\)
0.755837 + 0.654760i \(0.227230\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) −9.75672 + 9.75672i −0.512802 + 0.512802i
\(363\) 0 0
\(364\) 3.05545i 0.160149i
\(365\) 0 0
\(366\) 0 0
\(367\) 10.0732 + 10.0732i 0.525817 + 0.525817i 0.919322 0.393505i \(-0.128738\pi\)
−0.393505 + 0.919322i \(0.628738\pi\)
\(368\) 6.32106 + 6.32106i 0.329508 + 0.329508i
\(369\) 0 0
\(370\) 0 0
\(371\) 3.33579i 0.173186i
\(372\) 0 0
\(373\) −19.1614 + 19.1614i −0.992141 + 0.992141i −0.999969 0.00782876i \(-0.997508\pi\)
0.00782876 + 0.999969i \(0.497508\pi\)
\(374\) −13.5815 −0.702280
\(375\) 0 0
\(376\) 7.08794 0.365532
\(377\) −17.7270 + 17.7270i −0.912989 + 0.912989i
\(378\) 0 0
\(379\) 22.1538i 1.13796i −0.822350 0.568982i \(-0.807337\pi\)
0.822350 0.568982i \(-0.192663\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −0.367001 0.367001i −0.0187774 0.0187774i
\(383\) 24.6008 + 24.6008i 1.25704 + 1.25704i 0.952499 + 0.304541i \(0.0985030\pi\)
0.304541 + 0.952499i \(0.401497\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 24.2904i 1.23635i
\(387\) 0 0
\(388\) 0.606342 0.606342i 0.0307824 0.0307824i
\(389\) −9.25341 −0.469166 −0.234583 0.972096i \(-0.575373\pi\)
−0.234583 + 0.972096i \(0.575373\pi\)
\(390\) 0 0
\(391\) 56.5061 2.85764
\(392\) −0.707107 + 0.707107i −0.0357143 + 0.0357143i
\(393\) 0 0
\(394\) 5.70279i 0.287303i
\(395\) 0 0
\(396\) 0 0
\(397\) −14.8282 14.8282i −0.744204 0.744204i 0.229180 0.973384i \(-0.426395\pi\)
−0.973384 + 0.229180i \(0.926395\pi\)
\(398\) 14.9660 + 14.9660i 0.750177 + 0.750177i
\(399\) 0 0
\(400\) 0 0
\(401\) 13.0416i 0.651267i 0.945496 + 0.325633i \(0.105578\pi\)
−0.945496 + 0.325633i \(0.894422\pi\)
\(402\) 0 0
\(403\) 4.00000 4.00000i 0.199254 0.199254i
\(404\) −5.39860 −0.268590
\(405\) 0 0
\(406\) −8.20494 −0.407204
\(407\) 11.0386 11.0386i 0.547162 0.547162i
\(408\) 0 0
\(409\) 26.9190i 1.33106i 0.746371 + 0.665530i \(0.231794\pi\)
−0.746371 + 0.665530i \(0.768206\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −7.80546 7.80546i −0.384547 0.384547i
\(413\) −6.61827 6.61827i −0.325664 0.325664i
\(414\) 0 0
\(415\) 0 0
\(416\) 3.05545i 0.149806i
\(417\) 0 0
\(418\) 0 0
\(419\) 21.9705 1.07333 0.536666 0.843795i \(-0.319684\pi\)
0.536666 + 0.843795i \(0.319684\pi\)
\(420\) 0 0
\(421\) −10.5502 −0.514188 −0.257094 0.966386i \(-0.582765\pi\)
−0.257094 + 0.966386i \(0.582765\pi\)
\(422\) −15.4706 + 15.4706i −0.753095 + 0.753095i
\(423\) 0 0
\(424\) 3.33579i 0.162000i
\(425\) 0 0
\(426\) 0 0
\(427\) −3.16053 3.16053i −0.152949 0.152949i
\(428\) −2.40811 2.40811i −0.116401 0.116401i
\(429\) 0 0
\(430\) 0 0
\(431\) 22.9853i 1.10716i 0.832795 + 0.553581i \(0.186739\pi\)
−0.832795 + 0.553581i \(0.813261\pi\)
\(432\) 0 0
\(433\) −11.3256 + 11.3256i −0.544275 + 0.544275i −0.924779 0.380504i \(-0.875751\pi\)
0.380504 + 0.924779i \(0.375751\pi\)
\(434\) 1.85140 0.0888699
\(435\) 0 0
\(436\) 9.90075 0.474160
\(437\) 0 0
\(438\) 0 0
\(439\) 0.416353i 0.0198715i 0.999951 + 0.00993573i \(0.00316269\pi\)
−0.999951 + 0.00993573i \(0.996837\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 13.6569 + 13.6569i 0.649590 + 0.649590i
\(443\) 11.2487 + 11.2487i 0.534444 + 0.534444i 0.921892 0.387448i \(-0.126643\pi\)
−0.387448 + 0.921892i \(0.626643\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 6.25127i 0.296006i
\(447\) 0 0
\(448\) −0.707107 + 0.707107i −0.0334077 + 0.0334077i
\(449\) 20.7929 0.981277 0.490639 0.871363i \(-0.336764\pi\)
0.490639 + 0.871363i \(0.336764\pi\)
\(450\) 0 0
\(451\) −16.2495 −0.765159
\(452\) −4.22703 + 4.22703i −0.198823 + 0.198823i
\(453\) 0 0
\(454\) 16.5502i 0.776742i
\(455\) 0 0
\(456\) 0 0
\(457\) −12.7028 12.7028i −0.594212 0.594212i 0.344555 0.938766i \(-0.388030\pi\)
−0.938766 + 0.344555i \(0.888030\pi\)
\(458\) 9.63883 + 9.63883i 0.450393 + 0.450393i
\(459\) 0 0
\(460\) 0 0
\(461\) 29.8783i 1.39157i −0.718250 0.695785i \(-0.755057\pi\)
0.718250 0.695785i \(-0.244943\pi\)
\(462\) 0 0
\(463\) 15.2825 15.2825i 0.710237 0.710237i −0.256348 0.966585i \(-0.582519\pi\)
0.966585 + 0.256348i \(0.0825192\pi\)
\(464\) −8.20494 −0.380905
\(465\) 0 0
\(466\) 29.1924 1.35231
\(467\) 18.5429 18.5429i 0.858062 0.858062i −0.133048 0.991110i \(-0.542476\pi\)
0.991110 + 0.133048i \(0.0424764\pi\)
\(468\) 0 0
\(469\) 5.43108i 0.250784i
\(470\) 0 0
\(471\) 0 0
\(472\) −6.61827 6.61827i −0.304631 0.304631i
\(473\) −16.8458 16.8458i −0.774571 0.774571i
\(474\) 0 0
\(475\) 0 0
\(476\) 6.32106i 0.289725i
\(477\) 0 0
\(478\) −7.33579 + 7.33579i −0.335531 + 0.335531i
\(479\) −4.91725 −0.224675 −0.112337 0.993670i \(-0.535834\pi\)
−0.112337 + 0.993670i \(0.535834\pi\)
\(480\) 0 0
\(481\) −22.1997 −1.01222
\(482\) 9.68934 9.68934i 0.441337 0.441337i
\(483\) 0 0
\(484\) 6.38350i 0.290159i
\(485\) 0 0
\(486\) 0 0
\(487\) −9.63477 9.63477i −0.436593 0.436593i 0.454271 0.890864i \(-0.349900\pi\)
−0.890864 + 0.454271i \(0.849900\pi\)
\(488\) −3.16053 3.16053i −0.143071 0.143071i
\(489\) 0 0
\(490\) 0 0
\(491\) 20.0273i 0.903818i −0.892064 0.451909i \(-0.850743\pi\)
0.892064 0.451909i \(-0.149257\pi\)
\(492\) 0 0
\(493\) −36.6734 + 36.6734i −1.65168 + 1.65168i
\(494\) 0 0
\(495\) 0 0
\(496\) 1.85140 0.0831302
\(497\) 0.297207 0.297207i 0.0133316 0.0133316i
\(498\) 0 0
\(499\) 34.7959i 1.55768i 0.627223 + 0.778840i \(0.284191\pi\)
−0.627223 + 0.778840i \(0.715809\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −5.35965 5.35965i −0.239213 0.239213i
\(503\) −3.26320 3.26320i −0.145499 0.145499i 0.630605 0.776104i \(-0.282807\pi\)
−0.776104 + 0.630605i \(0.782807\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 19.2071i 0.853859i
\(507\) 0 0
\(508\) −2.32106 + 2.32106i −0.102981 + 0.102981i
\(509\) 29.3544 1.30111 0.650556 0.759458i \(-0.274536\pi\)
0.650556 + 0.759458i \(0.274536\pi\)
\(510\) 0 0
\(511\) 3.71966 0.164548
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 27.2843i 1.20346i
\(515\) 0 0
\(516\) 0 0
\(517\) −10.7686 10.7686i −0.473605 0.473605i
\(518\) −5.13756 5.13756i −0.225732 0.225732i
\(519\) 0 0
\(520\) 0 0
\(521\) 12.3453i 0.540858i 0.962740 + 0.270429i \(0.0871655\pi\)
−0.962740 + 0.270429i \(0.912835\pi\)
\(522\) 0 0
\(523\) 7.52637 7.52637i 0.329105 0.329105i −0.523141 0.852246i \(-0.675240\pi\)
0.852246 + 0.523141i \(0.175240\pi\)
\(524\) 2.37438 0.103725
\(525\) 0 0
\(526\) 24.9393 1.08741
\(527\) 8.27512 8.27512i 0.360470 0.360470i
\(528\) 0 0
\(529\) 56.9117i 2.47442i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 16.3397 + 16.3397i 0.707751 + 0.707751i
\(534\) 0 0
\(535\) 0 0
\(536\) 5.43108i 0.234587i
\(537\) 0 0
\(538\) 14.4577 14.4577i 0.623317 0.623317i
\(539\) 2.14860 0.0925469
\(540\) 0 0
\(541\) −40.9172 −1.75917 −0.879585 0.475742i \(-0.842180\pi\)
−0.879585 + 0.475742i \(0.842180\pi\)
\(542\) 14.5457 14.5457i 0.624790 0.624790i
\(543\) 0 0
\(544\) 6.32106i 0.271013i
\(545\) 0 0
\(546\) 0 0
\(547\) −10.8789 10.8789i −0.465150 0.465150i 0.435189 0.900339i \(-0.356681\pi\)
−0.900339 + 0.435189i \(0.856681\pi\)
\(548\) −9.88388 9.88388i −0.422218 0.422218i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 3.70279 3.70279i 0.157459 0.157459i
\(554\) −3.14250 −0.133512
\(555\) 0 0
\(556\) −15.6109 −0.662050
\(557\) −18.3588 + 18.3588i −0.777886 + 0.777886i −0.979471 0.201585i \(-0.935391\pi\)
0.201585 + 0.979471i \(0.435391\pi\)
\(558\) 0 0
\(559\) 33.8787i 1.43291i
\(560\) 0 0
\(561\) 0 0
\(562\) 12.3596 + 12.3596i 0.521360 + 0.521360i
\(563\) 25.6348 + 25.6348i 1.08038 + 1.08038i 0.996474 + 0.0839029i \(0.0267385\pi\)
0.0839029 + 0.996474i \(0.473261\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 25.3155i 1.06409i
\(567\) 0 0
\(568\) 0.297207 0.297207i 0.0124705 0.0124705i
\(569\) −44.9637 −1.88498 −0.942488 0.334239i \(-0.891521\pi\)
−0.942488 + 0.334239i \(0.891521\pi\)
\(570\) 0 0
\(571\) −13.0380 −0.545625 −0.272812 0.962067i \(-0.587954\pi\)
−0.272812 + 0.962067i \(0.587954\pi\)
\(572\) 4.64213 4.64213i 0.194097 0.194097i
\(573\) 0 0
\(574\) 7.56282i 0.315666i
\(575\) 0 0
\(576\) 0 0
\(577\) −17.1498 17.1498i −0.713954 0.713954i 0.253406 0.967360i \(-0.418449\pi\)
−0.967360 + 0.253406i \(0.918449\pi\)
\(578\) 16.2322 + 16.2322i 0.675172 + 0.675172i
\(579\) 0 0
\(580\) 0 0
\(581\) 15.0165i 0.622989i
\(582\) 0 0
\(583\) −5.06804 + 5.06804i −0.209897 + 0.209897i
\(584\) 3.71966 0.153921
\(585\) 0 0
\(586\) −1.92857 −0.0796683
\(587\) −7.26040 + 7.26040i −0.299669 + 0.299669i −0.840884 0.541215i \(-0.817964\pi\)
0.541215 + 0.840884i \(0.317964\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −5.13756 5.13756i −0.211153 0.211153i
\(593\) −7.97917 7.97917i −0.327665 0.327665i 0.524033 0.851698i \(-0.324427\pi\)
−0.851698 + 0.524033i \(0.824427\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 9.49962i 0.389120i
\(597\) 0 0
\(598\) −19.3137 + 19.3137i −0.789796 + 0.789796i
\(599\) −6.17587 −0.252339 −0.126170 0.992009i \(-0.540268\pi\)
−0.126170 + 0.992009i \(0.540268\pi\)
\(600\) 0 0
\(601\) −15.8106 −0.644930 −0.322465 0.946581i \(-0.604511\pi\)
−0.322465 + 0.946581i \(0.604511\pi\)
\(602\) −7.84035 + 7.84035i −0.319549 + 0.319549i
\(603\) 0 0
\(604\) 13.5815i 0.552622i
\(605\) 0 0
\(606\) 0 0
\(607\) 3.57969 + 3.57969i 0.145295 + 0.145295i 0.776012 0.630718i \(-0.217239\pi\)
−0.630718 + 0.776012i \(0.717239\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 21.6569i 0.876143i
\(612\) 0 0
\(613\) −6.77056 + 6.77056i −0.273460 + 0.273460i −0.830492 0.557031i \(-0.811940\pi\)
0.557031 + 0.830492i \(0.311940\pi\)
\(614\) −10.8934 −0.439622
\(615\) 0 0
\(616\) 2.14860 0.0865697
\(617\) 0.889981 0.889981i 0.0358293 0.0358293i −0.688965 0.724794i \(-0.741935\pi\)
0.724794 + 0.688965i \(0.241935\pi\)
\(618\) 0 0
\(619\) 40.4436i 1.62557i −0.582566 0.812783i \(-0.697951\pi\)
0.582566 0.812783i \(-0.302049\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 2.49352 + 2.49352i 0.0999811 + 0.0999811i
\(623\) −10.2871 10.2871i −0.412142 0.412142i
\(624\) 0 0
\(625\) 0 0
\(626\) 17.4415i 0.697102i
\(627\) 0 0
\(628\) −14.0613 + 14.0613i −0.561106 + 0.561106i
\(629\) −45.9264 −1.83120
\(630\) 0 0
\(631\) 8.38908 0.333964 0.166982 0.985960i \(-0.446598\pi\)
0.166982 + 0.985960i \(0.446598\pi\)
\(632\) 3.70279 3.70279i 0.147289 0.147289i
\(633\) 0 0
\(634\) 9.41296i 0.373836i
\(635\) 0 0
\(636\) 0 0
\(637\) −2.16053 2.16053i −0.0856034 0.0856034i
\(638\) 12.4657 + 12.4657i 0.493522 + 0.493522i
\(639\) 0 0
\(640\) 0 0
\(641\) 20.6863i 0.817058i 0.912745 + 0.408529i \(0.133958\pi\)
−0.912745 + 0.408529i \(0.866042\pi\)
\(642\) 0 0
\(643\) −1.55583 + 1.55583i −0.0613559 + 0.0613559i −0.737119 0.675763i \(-0.763814\pi\)
0.675763 + 0.737119i \(0.263814\pi\)
\(644\) −8.93933 −0.352259
\(645\) 0 0
\(646\) 0 0
\(647\) −31.9053 + 31.9053i −1.25433 + 1.25433i −0.300567 + 0.953761i \(0.597176\pi\)
−0.953761 + 0.300567i \(0.902824\pi\)
\(648\) 0 0
\(649\) 20.1102i 0.789393i
\(650\) 0 0
\(651\) 0 0
\(652\) 8.80177 + 8.80177i 0.344704 + 0.344704i
\(653\) 16.1841 + 16.1841i 0.633333 + 0.633333i 0.948903 0.315569i \(-0.102195\pi\)
−0.315569 + 0.948903i \(0.602195\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 7.56282i 0.295278i
\(657\) 0 0
\(658\) −5.01193 + 5.01193i −0.195385 + 0.195385i
\(659\) −7.13565 −0.277965 −0.138983 0.990295i \(-0.544383\pi\)
−0.138983 + 0.990295i \(0.544383\pi\)
\(660\) 0 0
\(661\) −29.3103 −1.14004 −0.570019 0.821631i \(-0.693064\pi\)
−0.570019 + 0.821631i \(0.693064\pi\)
\(662\) 21.7218 21.7218i 0.844243 0.844243i
\(663\) 0 0
\(664\) 15.0165i 0.582753i
\(665\) 0 0
\(666\) 0 0
\(667\) −51.8640 51.8640i −2.00818 2.00818i
\(668\) 2.66878 + 2.66878i 0.103258 + 0.103258i
\(669\) 0 0
\(670\) 0 0
\(671\) 9.60354i 0.370741i
\(672\) 0 0
\(673\) 13.3431 13.3431i 0.514340 0.514340i −0.401513 0.915853i \(-0.631516\pi\)
0.915853 + 0.401513i \(0.131516\pi\)
\(674\) −16.4307 −0.632887
\(675\) 0 0
\(676\) 3.66421 0.140931
\(677\) −1.38289 + 1.38289i −0.0531488 + 0.0531488i −0.733182 0.680033i \(-0.761965\pi\)
0.680033 + 0.733182i \(0.261965\pi\)
\(678\) 0 0
\(679\) 0.857497i 0.0329077i
\(680\) 0 0
\(681\) 0 0
\(682\) −2.81281 2.81281i −0.107708 0.107708i
\(683\) −24.2907 24.2907i −0.929459 0.929459i 0.0682116 0.997671i \(-0.478271\pi\)
−0.997671 + 0.0682116i \(0.978271\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000i 0.0381802i
\(687\) 0 0
\(688\) −7.84035 + 7.84035i −0.298911 + 0.298911i
\(689\) 10.1924 0.388298
\(690\) 0 0
\(691\) 27.0642 1.02957 0.514786 0.857319i \(-0.327872\pi\)
0.514786 + 0.857319i \(0.327872\pi\)
\(692\) 6.70127 6.70127i 0.254744 0.254744i
\(693\) 0 0
\(694\) 15.3137i 0.581300i
\(695\) 0 0
\(696\) 0 0
\(697\) 33.8033 + 33.8033i 1.28039 + 1.28039i
\(698\) 10.8412 + 10.8412i 0.410347 + 0.410347i
\(699\) 0 0
\(700\) 0 0
\(701\) 1.63999i 0.0619414i −0.999520 0.0309707i \(-0.990140\pi\)
0.999520 0.0309707i \(-0.00985986\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 2.14860 0.0809785
\(705\) 0 0
\(706\) −8.69544 −0.327257
\(707\) 3.81739 3.81739i 0.143568 0.143568i
\(708\) 0 0
\(709\) 8.35963i 0.313952i −0.987602 0.156976i \(-0.949825\pi\)
0.987602 0.156976i \(-0.0501746\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −10.2871 10.2871i −0.385524 0.385524i
\(713\) 11.7028 + 11.7028i 0.438273 + 0.438273i
\(714\) 0 0
\(715\) 0 0
\(716\) 3.50825i 0.131109i
\(717\) 0 0
\(718\) −20.2530 + 20.2530i −0.755837 + 0.755837i
\(719\) 16.9706 0.632895 0.316448 0.948610i \(-0.397510\pi\)
0.316448 + 0.948610i \(0.397510\pi\)
\(720\) 0 0
\(721\) 11.0386 0.411098
\(722\) −13.4350 + 13.4350i −0.500000 + 0.500000i
\(723\) 0 0
\(724\) 13.7981i 0.512802i
\(725\) 0 0
\(726\) 0 0
\(727\) −0.221811 0.221811i −0.00822652 0.00822652i 0.702982 0.711208i \(-0.251852\pi\)
−0.711208 + 0.702982i \(0.751852\pi\)
\(728\) −2.16053 2.16053i −0.0800746 0.0800746i
\(729\) 0 0
\(730\) 0 0
\(731\) 70.0875i 2.59228i
\(732\) 0 0
\(733\) −4.28705 + 4.28705i −0.158346 + 0.158346i −0.781833 0.623487i \(-0.785715\pi\)
0.623487 + 0.781833i \(0.285715\pi\)
\(734\) −14.2457 −0.525817
\(735\) 0 0
\(736\) −8.93933 −0.329508
\(737\) 8.25140 8.25140i 0.303944 0.303944i
\(738\) 0 0
\(739\) 11.6182i 0.427384i 0.976901 + 0.213692i \(0.0685489\pi\)
−0.976901 + 0.213692i \(0.931451\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2.35876 + 2.35876i 0.0865928 + 0.0865928i
\(743\) 7.65508 + 7.65508i 0.280838 + 0.280838i 0.833443 0.552605i \(-0.186366\pi\)
−0.552605 + 0.833443i \(0.686366\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 27.0983i 0.992141i
\(747\) 0 0
\(748\) 9.60354 9.60354i 0.351140 0.351140i
\(749\) 3.40559 0.124437
\(750\) 0 0
\(751\) −23.7505 −0.866668 −0.433334 0.901233i \(-0.642663\pi\)
−0.433334 + 0.901233i \(0.642663\pi\)
\(752\) −5.01193 + 5.01193i −0.182766 + 0.182766i
\(753\) 0 0
\(754\) 25.0698i 0.912989i
\(755\) 0 0
\(756\) 0 0
\(757\) 31.4825 + 31.4825i 1.14425 + 1.14425i 0.987664 + 0.156586i \(0.0500488\pi\)
0.156586 + 0.987664i \(0.449951\pi\)
\(758\) 15.6651 + 15.6651i 0.568982 + 0.568982i
\(759\) 0 0
\(760\) 0 0
\(761\) 19.2552i 0.698000i 0.937123 + 0.349000i \(0.113479\pi\)
−0.937123 + 0.349000i \(0.886521\pi\)
\(762\) 0 0
\(763\) −7.00089 + 7.00089i −0.253449 + 0.253449i
\(764\) 0.519018 0.0187774
\(765\) 0 0
\(766\) −34.7907 −1.25704
\(767\) 20.2218 20.2218i 0.730167 0.730167i
\(768\) 0 0
\(769\) 52.3541i 1.88794i 0.330037 + 0.943968i \(0.392939\pi\)
−0.330037 + 0.943968i \(0.607061\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −17.1759 17.1759i −0.618173 0.618173i
\(773\) −24.6410 24.6410i −0.886274 0.886274i 0.107889 0.994163i \(-0.465591\pi\)
−0.994163 + 0.107889i \(0.965591\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0.857497i 0.0307824i
\(777\) 0 0
\(778\) 6.54315 6.54315i 0.234583 0.234583i
\(779\) 0 0
\(780\) 0 0
\(781\) −0.903089 −0.0323151
\(782\) −39.9558 + 39.9558i −1.42882 + 1.42882i
\(783\) 0 0
\(784\) 1.00000i 0.0357143i
\(785\) 0 0
\(786\) 0 0
\(787\) −33.9264 33.9264i −1.20934 1.20934i −0.971239 0.238105i \(-0.923474\pi\)
−0.238105 0.971239i \(-0.576526\pi\)
\(788\) −4.03248 4.03248i −0.143651 0.143651i
\(789\) 0 0
\(790\) 0 0
\(791\) 5.97792i 0.212550i
\(792\) 0 0
\(793\) 9.65685 9.65685i 0.342925 0.342925i
\(794\) 20.9702 0.744204
\(795\) 0 0
\(796\) −21.1651 −0.750177
\(797\) −13.8269 + 13.8269i −0.489774 + 0.489774i −0.908235 0.418461i \(-0.862570\pi\)
0.418461 + 0.908235i \(0.362570\pi\)
\(798\) 0 0
\(799\) 44.8033i 1.58503i