Properties

Label 3150.2.m.i.2843.1
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 2843.1
Root \(2.16053i\)
Character \(\chi\) = 3150.2843
Dual form 3150.2.m.i.1457.2

$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

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

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
\(11\) 2.14860i 0.647828i 0.946086 + 0.323914i \(0.104999\pi\)
−0.946086 + 0.323914i \(0.895001\pi\)
\(12\) 0 0
\(13\) −2.16053 2.16053i −0.599224 0.599224i 0.340882 0.940106i \(-0.389274\pi\)
−0.940106 + 0.340882i \(0.889274\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −4.46967 4.46967i −1.08405 1.08405i −0.996127 0.0879263i \(-0.971976\pi\)
−0.0879263 0.996127i \(-0.528024\pi\)
\(18\) 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 −0.402701 + 0.915331i \(0.631929\pi\)
−0.915331 + 0.402701i \(0.868071\pi\)
\(24\) 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 −0.144844 0.989454i \(-0.546268\pi\)
0.989454 + 0.144844i \(0.0462682\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7.56282i 1.18111i 0.806996 + 0.590557i \(0.201092\pi\)
−0.806996 + 0.590557i \(0.798908\pi\)
\(42\) 0 0
\(43\) 7.84035 + 7.84035i 1.19564 + 1.19564i 0.975458 + 0.220185i \(0.0706660\pi\)
0.220185 + 0.975458i \(0.429334\pi\)
\(44\) −2.14860 −0.323914
\(45\) 0 0
\(46\) 8.93933 1.31803
\(47\) 5.01193 + 5.01193i 0.731065 + 0.731065i 0.970831 0.239766i \(-0.0770707\pi\)
−0.239766 + 0.970831i \(0.577071\pi\)
\(48\) 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 −0.850300 0.526299i \(-0.823579\pi\)
0.526299 + 0.850300i \(0.323579\pi\)
\(54\) 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 −0.432473 0.901647i \(-0.642359\pi\)
0.901647 + 0.432473i \(0.142359\pi\)
\(68\) 4.46967 4.46967i 0.542027 0.542027i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.420314i 0.0498821i 0.999689 + 0.0249411i \(0.00793981\pi\)
−0.999689 + 0.0249411i \(0.992060\pi\)
\(72\) 0 0
\(73\) 2.63020 + 2.63020i 0.307841 + 0.307841i 0.844072 0.536230i \(-0.180152\pi\)
−0.536230 + 0.844072i \(0.680152\pi\)
\(74\) −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 \(0.0951792\pi\)
−0.955627 + 0.294578i \(0.904821\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 5.34772 5.34772i 0.590557 0.590557i
\(83\) −10.6183 + 10.6183i −1.16551 + 1.16551i −0.182255 + 0.983251i \(0.558340\pi\)
−0.983251 + 0.182255i \(0.941660\pi\)
\(84\) 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 −0.675654 0.737219i \(-0.736139\pi\)
0.737219 + 0.675654i \(0.236139\pi\)
\(98\) −0.707107 + 0.707107i −0.0714286 + 0.0714286i
\(99\) 0 0
\(100\) 0 0
\(101\) 5.39860i 0.537181i 0.963255 + 0.268590i \(0.0865578\pi\)
−0.963255 + 0.268590i \(0.913442\pi\)
\(102\) 0 0
\(103\) 7.80546 + 7.80546i 0.769095 + 0.769095i 0.977947 0.208853i \(-0.0669729\pi\)
−0.208853 + 0.977947i \(0.566973\pi\)
\(104\) −3.05545 −0.299612
\(105\) 0 0
\(106\) 3.33579 0.324001
\(107\) 2.40811 + 2.40811i 0.232801 + 0.232801i 0.813861 0.581060i \(-0.197362\pi\)
−0.581060 + 0.813861i \(0.697362\pi\)
\(108\) 0 0
\(109\) 9.90075i 0.948320i −0.880439 0.474160i \(-0.842752\pi\)
0.880439 0.474160i \(-0.157248\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.707107 + 0.707107i −0.0668153 + 0.0668153i
\(113\) −4.22703 + 4.22703i −0.397645 + 0.397645i −0.877402 0.479757i \(-0.840725\pi\)
0.479757 + 0.877402i \(0.340725\pi\)
\(114\) 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 −0.802548 0.596587i \(-0.796523\pi\)
0.596587 + 0.802548i \(0.296523\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 0 0
\(130\) 0 0
\(131\) 2.37438i 0.207450i −0.994606 0.103725i \(-0.966924\pi\)
0.994606 0.103725i \(-0.0330762\pi\)
\(132\) 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 0.989432 0.144995i \(-0.0463168\pi\)
−0.144995 + 0.989432i \(0.546317\pi\)
\(138\) 0 0
\(139\) 15.6109i 1.32410i 0.749459 + 0.662050i \(0.230313\pi\)
−0.749459 + 0.662050i \(0.769687\pi\)
\(140\) 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 −0.130804 + 0.991408i \(0.541756\pi\)
−0.991408 + 0.130804i \(0.958244\pi\)
\(158\) 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 0.272693 0.962101i \(-0.412086\pi\)
−0.962101 + 0.272693i \(0.912086\pi\)
\(164\) −7.56282 −0.590557
\(165\) 0 0
\(166\) 15.0165 1.16551
\(167\) −2.66878 2.66878i −0.206517 0.206517i 0.596269 0.802785i \(-0.296649\pi\)
−0.802785 + 0.596269i \(0.796649\pi\)
\(168\) 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 −0.404881 0.914369i \(-0.632687\pi\)
0.914369 + 0.404881i \(0.132687\pi\)
\(174\) 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 \(-0.994023\pi\)
0.999824 0.0187774i \(-0.00597739\pi\)
\(192\) 0 0
\(193\) 17.1759 + 17.1759i 1.23635 + 1.23635i 0.961483 + 0.274863i \(0.0886325\pi\)
0.274863 + 0.961483i \(0.411368\pi\)
\(194\) −0.857497 −0.0615647
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 4.03248 + 4.03248i 0.287303 + 0.287303i 0.836013 0.548710i \(-0.184881\pi\)
−0.548710 + 0.836013i \(0.684881\pi\)
\(198\) 0 0
\(199\) 21.1651i 1.50035i 0.661237 + 0.750177i \(0.270032\pi\)
−0.661237 + 0.750177i \(0.729968\pi\)
\(200\) 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 0.839447 0.543441i \(-0.182879\pi\)
−0.543441 + 0.839447i \(0.682879\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 5.97792 0.397645
\(227\) 11.7028 + 11.7028i 0.776742 + 0.776742i 0.979275 0.202534i \(-0.0649176\pi\)
−0.202534 + 0.979275i \(0.564918\pi\)
\(228\) 0 0
\(229\) 13.6314i 0.900785i 0.892831 + 0.450393i \(0.148716\pi\)
−0.892831 + 0.450393i \(0.851284\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 5.80177 5.80177i 0.380905 0.380905i
\(233\) −20.6421 + 20.6421i −1.35231 + 1.35231i −0.469240 + 0.883071i \(0.655472\pi\)
−0.883071 + 0.469240i \(0.844528\pi\)
\(234\) 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 \(-0.923111\pi\)
0.970967 0.239213i \(-0.0768893\pi\)
\(252\) 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 −0.973108 0.230349i \(-0.926013\pi\)
−0.230349 0.973108i \(-0.573987\pi\)
\(258\) 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 −0.0916118 + 0.995795i \(0.529202\pi\)
−0.995795 + 0.0916118i \(0.970798\pi\)
\(264\) 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 −0.637193 0.770705i \(-0.719904\pi\)
0.770705 + 0.637193i \(0.219904\pi\)
\(278\) 11.0386 11.0386i 0.662050 0.662050i
\(279\) 0 0
\(280\) 0 0
\(281\) 17.4792i 1.04272i 0.853337 + 0.521360i \(0.174575\pi\)
−0.853337 + 0.521360i \(0.825425\pi\)
\(282\) 0 0
\(283\) −17.9007 17.9007i −1.06409 1.06409i −0.997800 0.0662885i \(-0.978884\pi\)
−0.0662885 0.997800i \(-0.521116\pi\)
\(284\) −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 −0.666150 0.745818i \(-0.732059\pi\)
0.745818 + 0.666150i \(0.232059\pi\)
\(294\) 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 −0.452263 0.891885i \(-0.649383\pi\)
0.891885 + 0.452263i \(0.149383\pi\)
\(308\) −1.51929 + 1.51929i −0.0865697 + 0.0865697i
\(309\) 0 0
\(310\) 0 0
\(311\) 3.52637i 0.199962i 0.994989 + 0.0999811i \(0.0318782\pi\)
−0.994989 + 0.0999811i \(0.968122\pi\)
\(312\) 0 0
\(313\) 12.3330 + 12.3330i 0.697102 + 0.697102i 0.963784 0.266683i \(-0.0859275\pi\)
−0.266683 + 0.963784i \(0.585928\pi\)
\(314\) 19.8857 1.12221
\(315\) 0 0
\(316\) −5.23654 −0.294578
\(317\) 6.65597 + 6.65597i 0.373836 + 0.373836i 0.868872 0.495036i \(-0.164845\pi\)
−0.495036 + 0.868872i \(0.664845\pi\)
\(318\) 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 −0.315904 0.948791i \(-0.602308\pi\)
0.948791 + 0.315904i \(0.102308\pi\)
\(338\) −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 0.935261 0.353960i \(-0.115165\pi\)
−0.353960 + 0.935261i \(0.615165\pi\)
\(348\) 0 0
\(349\) 15.3318i 0.820694i 0.911929 + 0.410347i \(0.134592\pi\)
−0.911929 + 0.410347i \(0.865408\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.51929 + 1.51929i −0.0809785 + 0.0809785i
\(353\) 6.14860 6.14860i 0.327257 0.327257i −0.524285 0.851543i \(-0.675668\pi\)
0.851543 + 0.524285i \(0.175668\pi\)
\(354\) 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 −0.393505 0.919322i \(-0.628738\pi\)
0.919322 + 0.393505i \(0.128738\pi\)
\(368\) 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 0.00782876 0.999969i \(-0.497508\pi\)
−0.999969 + 0.00782876i \(0.997508\pi\)
\(374\) −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 \(0.192663\pi\)
−0.822350 + 0.568982i \(0.807337\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −0.367001 + 0.367001i −0.0187774 + 0.0187774i
\(383\) 24.6008 24.6008i 1.25704 1.25704i 0.304541 0.952499i \(-0.401497\pi\)
0.952499 0.304541i \(-0.0985030\pi\)
\(384\) 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 −0.973384 0.229180i \(-0.926395\pi\)
0.229180 + 0.973384i \(0.426395\pi\)
\(398\) 14.9660 14.9660i 0.750177 0.750177i
\(399\) 0 0
\(400\) 0 0
\(401\) 13.0416i 0.651267i −0.945496 0.325633i \(-0.894422\pi\)
0.945496 0.325633i \(-0.105578\pi\)
\(402\) 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 \(-0.768206\pi\)
0.746371 0.665530i \(-0.231794\pi\)
\(410\) 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 \(-0.813261\pi\)
0.832795 0.553581i \(-0.186739\pi\)
\(432\) 0 0
\(433\) −11.3256 11.3256i −0.544275 0.544275i 0.380504 0.924779i \(-0.375751\pi\)
−0.924779 + 0.380504i \(0.875751\pi\)
\(434\) 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 \(-0.996837\pi\)
0.999951 0.00993573i \(-0.00316269\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 13.6569 13.6569i 0.649590 0.649590i
\(443\) 11.2487 11.2487i 0.534444 0.534444i −0.387448 0.921892i \(-0.626643\pi\)
0.921892 + 0.387448i \(0.126643\pi\)
\(444\) 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 −0.938766 0.344555i \(-0.888030\pi\)
0.344555 + 0.938766i \(0.388030\pi\)
\(458\) 9.63883 9.63883i 0.450393 0.450393i
\(459\) 0 0
\(460\) 0 0
\(461\) 29.8783i 1.39157i 0.718250 + 0.695785i \(0.244943\pi\)
−0.718250 + 0.695785i \(0.755057\pi\)
\(462\) 0 0
\(463\) 15.2825 + 15.2825i 0.710237 + 0.710237i 0.966585 0.256348i \(-0.0825192\pi\)
−0.256348 + 0.966585i \(0.582519\pi\)
\(464\) −8.20494 −0.380905
\(465\) 0 0
\(466\) 29.1924 1.35231
\(467\) 18.5429 + 18.5429i 0.858062 + 0.858062i 0.991110 0.133048i \(-0.0424764\pi\)
−0.133048 + 0.991110i \(0.542476\pi\)
\(468\) 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 −0.890864 0.454271i \(-0.849900\pi\)
0.454271 + 0.890864i \(0.349900\pi\)
\(488\) −3.16053 + 3.16053i −0.143071 + 0.143071i
\(489\) 0 0
\(490\) 0 0
\(491\) 20.0273i 0.903818i 0.892064 + 0.451909i \(0.149257\pi\)
−0.892064 + 0.451909i \(0.850743\pi\)
\(492\) 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 \(-0.715809\pi\)
0.627223 0.778840i \(-0.284191\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −5.35965 + 5.35965i −0.239213 + 0.239213i
\(503\) −3.26320 + 3.26320i −0.145499 + 0.145499i −0.776104 0.630605i \(-0.782807\pi\)
0.630605 + 0.776104i \(0.282807\pi\)
\(504\) 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 \(-0.912835\pi\)
0.962740 0.270429i \(-0.0871655\pi\)
\(522\) 0 0
\(523\) 7.52637 + 7.52637i 0.329105 + 0.329105i 0.852246 0.523141i \(-0.175240\pi\)
−0.523141 + 0.852246i \(0.675240\pi\)
\(524\) 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 −0.900339 0.435189i \(-0.856681\pi\)
0.435189 + 0.900339i \(0.356681\pi\)
\(548\) −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 0.201585 0.979471i \(-0.435391\pi\)
−0.979471 + 0.201585i \(0.935391\pi\)
\(558\) 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 0.0839029 0.996474i \(-0.473261\pi\)
0.996474 0.0839029i \(-0.0267385\pi\)
\(564\) 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 −0.967360 0.253406i \(-0.918449\pi\)
0.253406 + 0.967360i \(0.418449\pi\)
\(578\) 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 0.541215 0.840884i \(-0.317964\pi\)
−0.840884 + 0.541215i \(0.817964\pi\)
\(588\) 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 −0.851698 0.524033i \(-0.824427\pi\)
0.524033 + 0.851698i \(0.324427\pi\)
\(594\) 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 −0.630718 0.776012i \(-0.717239\pi\)
0.776012 + 0.630718i \(0.217239\pi\)
\(608\) 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 0.557031 0.830492i \(-0.311940\pi\)
−0.830492 + 0.557031i \(0.811940\pi\)
\(614\) −10.8934 −0.439622
\(615\) 0 0
\(616\) 2.14860 0.0865697
\(617\) 0.889981 + 0.889981i 0.0358293 + 0.0358293i 0.724794 0.688965i \(-0.241935\pi\)
−0.688965 + 0.724794i \(0.741935\pi\)
\(618\) 0 0
\(619\) 40.4436i 1.62557i 0.582566 + 0.812783i \(0.302049\pi\)
−0.582566 + 0.812783i \(0.697951\pi\)
\(620\) 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 \(-0.866042\pi\)
0.912745 0.408529i \(-0.133958\pi\)
\(642\) 0 0
\(643\) −1.55583 1.55583i −0.0613559 0.0613559i 0.675763 0.737119i \(-0.263814\pi\)
−0.737119 + 0.675763i \(0.763814\pi\)
\(644\) −8.93933 −0.352259
\(645\) 0 0
\(646\) 0 0
\(647\) −31.9053 31.9053i −1.25433 1.25433i −0.953761 0.300567i \(-0.902824\pi\)
−0.300567 0.953761i \(-0.597176\pi\)
\(648\) 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 −0.315569 0.948903i \(-0.602195\pi\)
0.948903 + 0.315569i \(0.102195\pi\)
\(654\) 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 0.915853 0.401513i \(-0.131516\pi\)
−0.401513 + 0.915853i \(0.631516\pi\)
\(674\) −16.4307 −0.632887
\(675\) 0 0
\(676\) 3.66421 0.140931
\(677\) −1.38289 1.38289i −0.0531488 0.0531488i 0.680033 0.733182i \(-0.261965\pi\)
−0.733182 + 0.680033i \(0.761965\pi\)
\(678\) 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 −0.997671 0.0682116i \(-0.978271\pi\)
0.0682116 + 0.997671i \(0.478271\pi\)
\(684\) 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 \(0.00985986\pi\)
−0.999520 + 0.0309707i \(0.990140\pi\)
\(702\) 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 \(0.0501746\pi\)
−0.987602 + 0.156976i \(0.949825\pi\)
\(710\) 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 −0.711208 0.702982i \(-0.751852\pi\)
0.702982 + 0.711208i \(0.251852\pi\)
\(728\) −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 0.623487 0.781833i \(-0.285715\pi\)
−0.781833 + 0.623487i \(0.785715\pi\)
\(734\) −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 \(-0.931451\pi\)
0.976901 0.213692i \(-0.0685489\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2.35876 2.35876i 0.0865928 0.0865928i
\(743\) 7.65508 7.65508i 0.280838 0.280838i −0.552605 0.833443i \(-0.686366\pi\)
0.833443 + 0.552605i \(0.186366\pi\)
\(744\) 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 0.156586 0.987664i \(-0.449951\pi\)
0.987664 0.156586i \(-0.0500488\pi\)
\(758\) 15.6651 15.6651i 0.568982 0.568982i
\(759\) 0 0
\(760\) 0 0
\(761\) 19.2552i 0.698000i −0.937123 0.349000i \(-0.886521\pi\)
0.937123 0.349000i \(-0.113479\pi\)
\(762\) 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 \(-0.607061\pi\)
0.330037 0.943968i \(-0.392939\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −17.1759 + 17.1759i −0.618173 + 0.618173i
\(773\) −24.6410 + 24.6410i −0.886274 + 0.886274i −0.994163 0.107889i \(-0.965591\pi\)
0.107889 + 0.994163i \(0.465591\pi\)
\(774\) 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 −0.238105 + 0.971239i \(0.576526\pi\)
−0.971239 + 0.238105i \(0.923474\pi\)
\(788\) −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 0.418461 0.908235i \(-0.362570\pi\)
−0.908235 + 0.418461i \(0.862570\pi\)
\(798\) 0 0
\(799\) 44.8033i 1.58503i