Properties

Label 1600.2.q.f.49.1
Level $1600$
Weight $2$
Character 1600.49
Analytic conductor $12.776$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.q (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.7760643234\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
Defining polynomial: \(x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 400)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 49.1
Root \(0.719139 + 1.21772i\) of defining polynomial
Character \(\chi\) \(=\) 1600.49
Dual form 1600.2.q.f.849.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.66783 - 1.66783i) q^{3} +1.87372 q^{7} +2.56332i q^{9} +O(q^{10})\) \(q+(-1.66783 - 1.66783i) q^{3} +1.87372 q^{7} +2.56332i q^{9} +(3.29695 + 3.29695i) q^{11} +(1.90022 + 1.90022i) q^{13} -2.57148i q^{17} +(-5.76636 + 5.76636i) q^{19} +(-3.12504 - 3.12504i) q^{21} -7.58574 q^{23} +(-0.728312 + 0.728312i) q^{27} +(-6.45786 + 6.45786i) q^{29} +0.799135 q^{31} -10.9975i q^{33} +(2.69652 - 2.69652i) q^{37} -6.33850i q^{39} +0.946984i q^{41} +(0.829986 - 0.829986i) q^{43} +1.52421i q^{47} -3.48919 q^{49} +(-4.28879 + 4.28879i) q^{51} +(-6.97225 + 6.97225i) q^{53} +19.2346 q^{57} +(6.84418 + 6.84418i) q^{59} +(-6.87247 + 6.87247i) q^{61} +4.80293i q^{63} +(-3.73647 - 3.73647i) q^{67} +(12.6517 + 12.6517i) q^{69} +9.34417i q^{71} +0.886316 q^{73} +(6.17755 + 6.17755i) q^{77} +3.07575 q^{79} +10.1194 q^{81} +(0.989393 + 0.989393i) q^{83} +21.5412 q^{87} -10.0942i q^{89} +(3.56048 + 3.56048i) q^{91} +(-1.33282 - 1.33282i) q^{93} +7.16829i q^{97} +(-8.45113 + 8.45113i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{3} - 12q^{7} + O(q^{10}) \) \( 12q + 2q^{3} - 12q^{7} + 2q^{11} + 4q^{13} - 14q^{19} - 20q^{21} - 12q^{23} - 10q^{27} + 4q^{31} - 8q^{37} - 4q^{49} - 10q^{51} - 16q^{53} - 16q^{57} + 20q^{59} + 4q^{61} - 50q^{67} + 40q^{73} - 8q^{77} + 12q^{79} - 8q^{81} - 2q^{83} + 64q^{87} + 44q^{93} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1151\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.66783 1.66783i −0.962922 0.962922i 0.0364144 0.999337i \(-0.488406\pi\)
−0.999337 + 0.0364144i \(0.988406\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.87372 0.708198 0.354099 0.935208i \(-0.384788\pi\)
0.354099 + 0.935208i \(0.384788\pi\)
\(8\) 0 0
\(9\) 2.56332i 0.854439i
\(10\) 0 0
\(11\) 3.29695 + 3.29695i 0.994068 + 0.994068i 0.999983 0.00591443i \(-0.00188263\pi\)
−0.00591443 + 0.999983i \(0.501883\pi\)
\(12\) 0 0
\(13\) 1.90022 + 1.90022i 0.527027 + 0.527027i 0.919685 0.392658i \(-0.128444\pi\)
−0.392658 + 0.919685i \(0.628444\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.57148i 0.623675i −0.950135 0.311838i \(-0.899056\pi\)
0.950135 0.311838i \(-0.100944\pi\)
\(18\) 0 0
\(19\) −5.76636 + 5.76636i −1.32289 + 1.32289i −0.411472 + 0.911422i \(0.634985\pi\)
−0.911422 + 0.411472i \(0.865015\pi\)
\(20\) 0 0
\(21\) −3.12504 3.12504i −0.681940 0.681940i
\(22\) 0 0
\(23\) −7.58574 −1.58174 −0.790868 0.611987i \(-0.790371\pi\)
−0.790868 + 0.611987i \(0.790371\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −0.728312 + 0.728312i −0.140164 + 0.140164i
\(28\) 0 0
\(29\) −6.45786 + 6.45786i −1.19919 + 1.19919i −0.224787 + 0.974408i \(0.572169\pi\)
−0.974408 + 0.224787i \(0.927831\pi\)
\(30\) 0 0
\(31\) 0.799135 0.143529 0.0717644 0.997422i \(-0.477137\pi\)
0.0717644 + 0.997422i \(0.477137\pi\)
\(32\) 0 0
\(33\) 10.9975i 1.91442i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.69652 2.69652i 0.443305 0.443305i −0.449816 0.893121i \(-0.648511\pi\)
0.893121 + 0.449816i \(0.148511\pi\)
\(38\) 0 0
\(39\) 6.33850i 1.01497i
\(40\) 0 0
\(41\) 0.946984i 0.147894i 0.997262 + 0.0739471i \(0.0235596\pi\)
−0.997262 + 0.0739471i \(0.976440\pi\)
\(42\) 0 0
\(43\) 0.829986 0.829986i 0.126572 0.126572i −0.640983 0.767555i \(-0.721473\pi\)
0.767555 + 0.640983i \(0.221473\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.52421i 0.222329i 0.993802 + 0.111165i \(0.0354581\pi\)
−0.993802 + 0.111165i \(0.964542\pi\)
\(48\) 0 0
\(49\) −3.48919 −0.498456
\(50\) 0 0
\(51\) −4.28879 + 4.28879i −0.600551 + 0.600551i
\(52\) 0 0
\(53\) −6.97225 + 6.97225i −0.957712 + 0.957712i −0.999141 0.0414296i \(-0.986809\pi\)
0.0414296 + 0.999141i \(0.486809\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 19.2346 2.54769
\(58\) 0 0
\(59\) 6.84418 + 6.84418i 0.891036 + 0.891036i 0.994621 0.103585i \(-0.0330313\pi\)
−0.103585 + 0.994621i \(0.533031\pi\)
\(60\) 0 0
\(61\) −6.87247 + 6.87247i −0.879930 + 0.879930i −0.993527 0.113597i \(-0.963763\pi\)
0.113597 + 0.993527i \(0.463763\pi\)
\(62\) 0 0
\(63\) 4.80293i 0.605112i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −3.73647 3.73647i −0.456483 0.456483i 0.441016 0.897499i \(-0.354618\pi\)
−0.897499 + 0.441016i \(0.854618\pi\)
\(68\) 0 0
\(69\) 12.6517 + 12.6517i 1.52309 + 1.52309i
\(70\) 0 0
\(71\) 9.34417i 1.10895i 0.832201 + 0.554475i \(0.187081\pi\)
−0.832201 + 0.554475i \(0.812919\pi\)
\(72\) 0 0
\(73\) 0.886316 0.103735 0.0518677 0.998654i \(-0.483483\pi\)
0.0518677 + 0.998654i \(0.483483\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.17755 + 6.17755i 0.703997 + 0.703997i
\(78\) 0 0
\(79\) 3.07575 0.346049 0.173024 0.984918i \(-0.444646\pi\)
0.173024 + 0.984918i \(0.444646\pi\)
\(80\) 0 0
\(81\) 10.1194 1.12437
\(82\) 0 0
\(83\) 0.989393 + 0.989393i 0.108600 + 0.108600i 0.759319 0.650719i \(-0.225532\pi\)
−0.650719 + 0.759319i \(0.725532\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 21.5412 2.30946
\(88\) 0 0
\(89\) 10.0942i 1.06998i −0.844859 0.534990i \(-0.820316\pi\)
0.844859 0.534990i \(-0.179684\pi\)
\(90\) 0 0
\(91\) 3.56048 + 3.56048i 0.373239 + 0.373239i
\(92\) 0 0
\(93\) −1.33282 1.33282i −0.138207 0.138207i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.16829i 0.727830i 0.931432 + 0.363915i \(0.118560\pi\)
−0.931432 + 0.363915i \(0.881440\pi\)
\(98\) 0 0
\(99\) −8.45113 + 8.45113i −0.849371 + 0.849371i
\(100\) 0 0
\(101\) −1.05091 1.05091i −0.104570 0.104570i 0.652886 0.757456i \(-0.273558\pi\)
−0.757456 + 0.652886i \(0.773558\pi\)
\(102\) 0 0
\(103\) 8.20690 0.808649 0.404325 0.914616i \(-0.367507\pi\)
0.404325 + 0.914616i \(0.367507\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.85743 2.85743i 0.276238 0.276238i −0.555367 0.831605i \(-0.687422\pi\)
0.831605 + 0.555367i \(0.187422\pi\)
\(108\) 0 0
\(109\) 11.3735 11.3735i 1.08939 1.08939i 0.0937940 0.995592i \(-0.470100\pi\)
0.995592 0.0937940i \(-0.0298995\pi\)
\(110\) 0 0
\(111\) −8.99467 −0.853736
\(112\) 0 0
\(113\) 3.54221i 0.333223i −0.986023 0.166611i \(-0.946717\pi\)
0.986023 0.166611i \(-0.0532825\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −4.87088 + 4.87088i −0.450313 + 0.450313i
\(118\) 0 0
\(119\) 4.81822i 0.441685i
\(120\) 0 0
\(121\) 10.7398i 0.976343i
\(122\) 0 0
\(123\) 1.57941 1.57941i 0.142411 0.142411i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 18.0693i 1.60339i 0.597735 + 0.801693i \(0.296067\pi\)
−0.597735 + 0.801693i \(0.703933\pi\)
\(128\) 0 0
\(129\) −2.76855 −0.243757
\(130\) 0 0
\(131\) 6.39614 6.39614i 0.558834 0.558834i −0.370142 0.928975i \(-0.620691\pi\)
0.928975 + 0.370142i \(0.120691\pi\)
\(132\) 0 0
\(133\) −10.8045 + 10.8045i −0.936871 + 0.936871i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.7357 −0.917212 −0.458606 0.888640i \(-0.651651\pi\)
−0.458606 + 0.888640i \(0.651651\pi\)
\(138\) 0 0
\(139\) −2.31086 2.31086i −0.196005 0.196005i 0.602280 0.798285i \(-0.294259\pi\)
−0.798285 + 0.602280i \(0.794259\pi\)
\(140\) 0 0
\(141\) 2.54213 2.54213i 0.214086 0.214086i
\(142\) 0 0
\(143\) 12.5299i 1.04780i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.81938 + 5.81938i 0.479974 + 0.479974i
\(148\) 0 0
\(149\) −1.38743 1.38743i −0.113663 0.113663i 0.647988 0.761651i \(-0.275611\pi\)
−0.761651 + 0.647988i \(0.775611\pi\)
\(150\) 0 0
\(151\) 5.68590i 0.462712i 0.972869 + 0.231356i \(0.0743163\pi\)
−0.972869 + 0.231356i \(0.925684\pi\)
\(152\) 0 0
\(153\) 6.59152 0.532892
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2.48874 + 2.48874i 0.198623 + 0.198623i 0.799409 0.600787i \(-0.205146\pi\)
−0.600787 + 0.799409i \(0.705146\pi\)
\(158\) 0 0
\(159\) 23.2571 1.84440
\(160\) 0 0
\(161\) −14.2135 −1.12018
\(162\) 0 0
\(163\) −12.7091 12.7091i −0.995451 0.995451i 0.00453842 0.999990i \(-0.498555\pi\)
−0.999990 + 0.00453842i \(0.998555\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.00982 0.387672 0.193836 0.981034i \(-0.437907\pi\)
0.193836 + 0.981034i \(0.437907\pi\)
\(168\) 0 0
\(169\) 5.77830i 0.444485i
\(170\) 0 0
\(171\) −14.7810 14.7810i −1.13033 1.13033i
\(172\) 0 0
\(173\) 6.19546 + 6.19546i 0.471032 + 0.471032i 0.902249 0.431216i \(-0.141915\pi\)
−0.431216 + 0.902249i \(0.641915\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 22.8299i 1.71600i
\(178\) 0 0
\(179\) −5.51628 + 5.51628i −0.412306 + 0.412306i −0.882541 0.470235i \(-0.844169\pi\)
0.470235 + 0.882541i \(0.344169\pi\)
\(180\) 0 0
\(181\) 11.8993 + 11.8993i 0.884470 + 0.884470i 0.993985 0.109515i \(-0.0349298\pi\)
−0.109515 + 0.993985i \(0.534930\pi\)
\(182\) 0 0
\(183\) 22.9242 1.69461
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 8.47804 8.47804i 0.619976 0.619976i
\(188\) 0 0
\(189\) −1.36465 + 1.36465i −0.0992637 + 0.0992637i
\(190\) 0 0
\(191\) −11.1278 −0.805180 −0.402590 0.915380i \(-0.631890\pi\)
−0.402590 + 0.915380i \(0.631890\pi\)
\(192\) 0 0
\(193\) 20.7821i 1.49593i 0.663738 + 0.747965i \(0.268969\pi\)
−0.663738 + 0.747965i \(0.731031\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −14.0309 + 14.0309i −0.999663 + 0.999663i −1.00000 0.000337236i \(-0.999893\pi\)
0.000337236 1.00000i \(0.499893\pi\)
\(198\) 0 0
\(199\) 3.24727i 0.230193i −0.993354 0.115096i \(-0.963282\pi\)
0.993354 0.115096i \(-0.0367177\pi\)
\(200\) 0 0
\(201\) 12.4636i 0.879115i
\(202\) 0 0
\(203\) −12.1002 + 12.1002i −0.849267 + 0.849267i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 19.4447i 1.35150i
\(208\) 0 0
\(209\) −38.0228 −2.63009
\(210\) 0 0
\(211\) 10.1821 10.1821i 0.700964 0.700964i −0.263654 0.964617i \(-0.584928\pi\)
0.964617 + 0.263654i \(0.0849276\pi\)
\(212\) 0 0
\(213\) 15.5845 15.5845i 1.06783 1.06783i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 1.49735 0.101647
\(218\) 0 0
\(219\) −1.47822 1.47822i −0.0998892 0.0998892i
\(220\) 0 0
\(221\) 4.88638 4.88638i 0.328694 0.328694i
\(222\) 0 0
\(223\) 24.0469i 1.61030i −0.593070 0.805151i \(-0.702084\pi\)
0.593070 0.805151i \(-0.297916\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −11.9863 11.9863i −0.795562 0.795562i 0.186830 0.982392i \(-0.440179\pi\)
−0.982392 + 0.186830i \(0.940179\pi\)
\(228\) 0 0
\(229\) 20.1972 + 20.1972i 1.33467 + 1.33467i 0.901140 + 0.433529i \(0.142732\pi\)
0.433529 + 0.901140i \(0.357268\pi\)
\(230\) 0 0
\(231\) 20.6062i 1.35579i
\(232\) 0 0
\(233\) −10.0655 −0.659410 −0.329705 0.944084i \(-0.606949\pi\)
−0.329705 + 0.944084i \(0.606949\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −5.12983 5.12983i −0.333218 0.333218i
\(238\) 0 0
\(239\) 0.992801 0.0642189 0.0321095 0.999484i \(-0.489777\pi\)
0.0321095 + 0.999484i \(0.489777\pi\)
\(240\) 0 0
\(241\) 14.1229 0.909738 0.454869 0.890558i \(-0.349686\pi\)
0.454869 + 0.890558i \(0.349686\pi\)
\(242\) 0 0
\(243\) −14.6924 14.6924i −0.942520 0.942520i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −21.9148 −1.39440
\(248\) 0 0
\(249\) 3.30028i 0.209147i
\(250\) 0 0
\(251\) −1.56681 1.56681i −0.0988961 0.0988961i 0.655928 0.754824i \(-0.272278\pi\)
−0.754824 + 0.655928i \(0.772278\pi\)
\(252\) 0 0
\(253\) −25.0098 25.0098i −1.57235 1.57235i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 10.2593i 0.639960i −0.947424 0.319980i \(-0.896324\pi\)
0.947424 0.319980i \(-0.103676\pi\)
\(258\) 0 0
\(259\) 5.05251 5.05251i 0.313948 0.313948i
\(260\) 0 0
\(261\) −16.5535 16.5535i −1.02464 1.02464i
\(262\) 0 0
\(263\) 19.0630 1.17548 0.587739 0.809051i \(-0.300018\pi\)
0.587739 + 0.809051i \(0.300018\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −16.8354 + 16.8354i −1.03031 + 1.03031i
\(268\) 0 0
\(269\) −3.48459 + 3.48459i −0.212459 + 0.212459i −0.805311 0.592852i \(-0.798002\pi\)
0.592852 + 0.805311i \(0.298002\pi\)
\(270\) 0 0
\(271\) 30.0045 1.82264 0.911322 0.411695i \(-0.135063\pi\)
0.911322 + 0.411695i \(0.135063\pi\)
\(272\) 0 0
\(273\) 11.8765i 0.718801i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −8.43732 + 8.43732i −0.506949 + 0.506949i −0.913589 0.406639i \(-0.866701\pi\)
0.406639 + 0.913589i \(0.366701\pi\)
\(278\) 0 0
\(279\) 2.04844i 0.122637i
\(280\) 0 0
\(281\) 6.44714i 0.384604i −0.981336 0.192302i \(-0.938405\pi\)
0.981336 0.192302i \(-0.0615954\pi\)
\(282\) 0 0
\(283\) −2.61000 + 2.61000i −0.155148 + 0.155148i −0.780413 0.625264i \(-0.784991\pi\)
0.625264 + 0.780413i \(0.284991\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.77438i 0.104738i
\(288\) 0 0
\(289\) 10.3875 0.611029
\(290\) 0 0
\(291\) 11.9555 11.9555i 0.700844 0.700844i
\(292\) 0 0
\(293\) −7.52428 + 7.52428i −0.439573 + 0.439573i −0.891868 0.452295i \(-0.850605\pi\)
0.452295 + 0.891868i \(0.350605\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −4.80242 −0.278665
\(298\) 0 0
\(299\) −14.4146 14.4146i −0.833618 0.833618i
\(300\) 0 0
\(301\) 1.55516 1.55516i 0.0896377 0.0896377i
\(302\) 0 0
\(303\) 3.50549i 0.201385i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −12.7130 12.7130i −0.725571 0.725571i 0.244163 0.969734i \(-0.421487\pi\)
−0.969734 + 0.244163i \(0.921487\pi\)
\(308\) 0 0
\(309\) −13.6877 13.6877i −0.778667 0.778667i
\(310\) 0 0
\(311\) 11.9313i 0.676563i 0.941045 + 0.338281i \(0.109846\pi\)
−0.941045 + 0.338281i \(0.890154\pi\)
\(312\) 0 0
\(313\) 34.3458 1.94134 0.970670 0.240414i \(-0.0772832\pi\)
0.970670 + 0.240414i \(0.0772832\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −17.1112 17.1112i −0.961060 0.961060i 0.0382097 0.999270i \(-0.487835\pi\)
−0.999270 + 0.0382097i \(0.987835\pi\)
\(318\) 0 0
\(319\) −42.5825 −2.38416
\(320\) 0 0
\(321\) −9.53141 −0.531992
\(322\) 0 0
\(323\) 14.8281 + 14.8281i 0.825056 + 0.825056i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −37.9382 −2.09799
\(328\) 0 0
\(329\) 2.85594i 0.157453i
\(330\) 0 0
\(331\) −9.80246 9.80246i −0.538792 0.538792i 0.384382 0.923174i \(-0.374415\pi\)
−0.923174 + 0.384382i \(0.874415\pi\)
\(332\) 0 0
\(333\) 6.91203 + 6.91203i 0.378777 + 0.378777i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 6.07501i 0.330927i 0.986216 + 0.165463i \(0.0529120\pi\)
−0.986216 + 0.165463i \(0.947088\pi\)
\(338\) 0 0
\(339\) −5.90780 + 5.90780i −0.320868 + 0.320868i
\(340\) 0 0
\(341\) 2.63471 + 2.63471i 0.142677 + 0.142677i
\(342\) 0 0
\(343\) −19.6538 −1.06120
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5.77231 5.77231i 0.309874 0.309874i −0.534987 0.844860i \(-0.679683\pi\)
0.844860 + 0.534987i \(0.179683\pi\)
\(348\) 0 0
\(349\) 7.58851 7.58851i 0.406203 0.406203i −0.474209 0.880412i \(-0.657266\pi\)
0.880412 + 0.474209i \(0.157266\pi\)
\(350\) 0 0
\(351\) −2.76791 −0.147740
\(352\) 0 0
\(353\) 16.2285i 0.863753i 0.901933 + 0.431877i \(0.142148\pi\)
−0.901933 + 0.431877i \(0.857852\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −8.03597 + 8.03597i −0.425309 + 0.425309i
\(358\) 0 0
\(359\) 6.77298i 0.357464i −0.983898 0.178732i \(-0.942800\pi\)
0.983898 0.178732i \(-0.0571996\pi\)
\(360\) 0 0
\(361\) 47.5019i 2.50010i
\(362\) 0 0
\(363\) 17.9121 17.9121i 0.940142 0.940142i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 6.35705i 0.331835i 0.986140 + 0.165918i \(0.0530586\pi\)
−0.986140 + 0.165918i \(0.946941\pi\)
\(368\) 0 0
\(369\) −2.42742 −0.126367
\(370\) 0 0
\(371\) −13.0640 + 13.0640i −0.678250 + 0.678250i
\(372\) 0 0
\(373\) 9.20937 9.20937i 0.476843 0.476843i −0.427278 0.904121i \(-0.640527\pi\)
0.904121 + 0.427278i \(0.140527\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −24.5428 −1.26402
\(378\) 0 0
\(379\) 5.41600 + 5.41600i 0.278201 + 0.278201i 0.832391 0.554189i \(-0.186972\pi\)
−0.554189 + 0.832391i \(0.686972\pi\)
\(380\) 0 0
\(381\) 30.1365 30.1365i 1.54394 1.54394i
\(382\) 0 0
\(383\) 28.1626i 1.43904i 0.694472 + 0.719520i \(0.255638\pi\)
−0.694472 + 0.719520i \(0.744362\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.12752 + 2.12752i 0.108148 + 0.108148i
\(388\) 0 0
\(389\) −9.59783 9.59783i −0.486629 0.486629i 0.420611 0.907241i \(-0.361816\pi\)
−0.907241 + 0.420611i \(0.861816\pi\)
\(390\) 0 0
\(391\) 19.5066i 0.986490i
\(392\) 0 0
\(393\) −21.3354 −1.07623
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 10.4884 + 10.4884i 0.526399 + 0.526399i 0.919497 0.393098i \(-0.128597\pi\)
−0.393098 + 0.919497i \(0.628597\pi\)
\(398\) 0 0
\(399\) 36.0402 1.80427
\(400\) 0 0
\(401\) −2.44221 −0.121958 −0.0609791 0.998139i \(-0.519422\pi\)
−0.0609791 + 0.998139i \(0.519422\pi\)
\(402\) 0 0
\(403\) 1.51853 + 1.51853i 0.0756436 + 0.0756436i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 17.7806 0.881350
\(408\) 0 0
\(409\) 24.6628i 1.21950i −0.792596 0.609748i \(-0.791271\pi\)
0.792596 0.609748i \(-0.208729\pi\)
\(410\) 0 0
\(411\) 17.9053 + 17.9053i 0.883204 + 0.883204i
\(412\) 0 0
\(413\) 12.8240 + 12.8240i 0.631030 + 0.631030i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 7.70826i 0.377475i
\(418\) 0 0
\(419\) 19.1661 19.1661i 0.936326 0.936326i −0.0617649 0.998091i \(-0.519673\pi\)
0.998091 + 0.0617649i \(0.0196729\pi\)
\(420\) 0 0
\(421\) −7.43469 7.43469i −0.362345 0.362345i 0.502331 0.864676i \(-0.332476\pi\)
−0.864676 + 0.502331i \(0.832476\pi\)
\(422\) 0 0
\(423\) −3.90704 −0.189967
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −12.8771 + 12.8771i −0.623164 + 0.623164i
\(428\) 0 0
\(429\) 20.8977 20.8977i 1.00895 1.00895i
\(430\) 0 0
\(431\) −22.5647 −1.08690 −0.543451 0.839441i \(-0.682883\pi\)
−0.543451 + 0.839441i \(0.682883\pi\)
\(432\) 0 0
\(433\) 26.4811i 1.27260i −0.771441 0.636301i \(-0.780464\pi\)
0.771441 0.636301i \(-0.219536\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 43.7421 43.7421i 2.09247 2.09247i
\(438\) 0 0
\(439\) 0.765288i 0.0365252i 0.999833 + 0.0182626i \(0.00581349\pi\)
−0.999833 + 0.0182626i \(0.994187\pi\)
\(440\) 0 0
\(441\) 8.94390i 0.425900i
\(442\) 0 0
\(443\) −20.2685 + 20.2685i −0.962985 + 0.962985i −0.999339 0.0363537i \(-0.988426\pi\)
0.0363537 + 0.999339i \(0.488426\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 4.62800i 0.218897i
\(448\) 0 0
\(449\) 35.2717 1.66457 0.832287 0.554345i \(-0.187031\pi\)
0.832287 + 0.554345i \(0.187031\pi\)
\(450\) 0 0
\(451\) −3.12216 + 3.12216i −0.147017 + 0.147017i
\(452\) 0 0
\(453\) 9.48312 9.48312i 0.445556 0.445556i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −9.01188 −0.421558 −0.210779 0.977534i \(-0.567600\pi\)
−0.210779 + 0.977534i \(0.567600\pi\)
\(458\) 0 0
\(459\) 1.87284 + 1.87284i 0.0874167 + 0.0874167i
\(460\) 0 0
\(461\) −22.8247 + 22.8247i −1.06305 + 1.06305i −0.0651807 + 0.997873i \(0.520762\pi\)
−0.997873 + 0.0651807i \(0.979238\pi\)
\(462\) 0 0
\(463\) 3.72721i 0.173218i 0.996242 + 0.0866090i \(0.0276031\pi\)
−0.996242 + 0.0866090i \(0.972397\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.23477 + 3.23477i 0.149687 + 0.149687i 0.777978 0.628291i \(-0.216245\pi\)
−0.628291 + 0.777978i \(0.716245\pi\)
\(468\) 0 0
\(469\) −7.00109 7.00109i −0.323280 0.323280i
\(470\) 0 0
\(471\) 8.30158i 0.382517i
\(472\) 0 0
\(473\) 5.47284 0.251642
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −17.8721 17.8721i −0.818307 0.818307i
\(478\) 0 0
\(479\) −11.0636 −0.505508 −0.252754 0.967531i \(-0.581336\pi\)
−0.252754 + 0.967531i \(0.581336\pi\)
\(480\) 0 0
\(481\) 10.2480 0.467267
\(482\) 0 0
\(483\) 23.7057 + 23.7057i 1.07865 + 1.07865i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −6.68176 −0.302779 −0.151390 0.988474i \(-0.548375\pi\)
−0.151390 + 0.988474i \(0.548375\pi\)
\(488\) 0 0
\(489\) 42.3932i 1.91708i
\(490\) 0 0
\(491\) 18.4274 + 18.4274i 0.831618 + 0.831618i 0.987738 0.156120i \(-0.0498986\pi\)
−0.156120 + 0.987738i \(0.549899\pi\)
\(492\) 0 0
\(493\) 16.6063 + 16.6063i 0.747908 + 0.747908i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 17.5083i 0.785356i
\(498\) 0 0
\(499\) 8.84615 8.84615i 0.396008 0.396008i −0.480814 0.876822i \(-0.659659\pi\)
0.876822 + 0.480814i \(0.159659\pi\)
\(500\) 0 0
\(501\) −8.35554 8.35554i −0.373298 0.373298i
\(502\) 0 0
\(503\) −16.8746 −0.752401 −0.376201 0.926538i \(-0.622770\pi\)
−0.376201 + 0.926538i \(0.622770\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −9.63723 + 9.63723i −0.428004 + 0.428004i
\(508\) 0 0
\(509\) −20.5691 + 20.5691i −0.911707 + 0.911707i −0.996407 0.0846994i \(-0.973007\pi\)
0.0846994 + 0.996407i \(0.473007\pi\)
\(510\) 0 0
\(511\) 1.66070 0.0734652
\(512\) 0 0
\(513\) 8.39943i 0.370844i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −5.02526 + 5.02526i −0.221011 + 0.221011i
\(518\) 0 0
\(519\) 20.6660i 0.907135i
\(520\) 0 0
\(521\) 12.6708i 0.555118i 0.960709 + 0.277559i \(0.0895253\pi\)
−0.960709 + 0.277559i \(0.910475\pi\)
\(522\) 0 0
\(523\) 27.8509 27.8509i 1.21784 1.21784i 0.249448 0.968388i \(-0.419751\pi\)
0.968388 0.249448i \(-0.0802491\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.05496i 0.0895154i
\(528\) 0 0
\(529\) 34.5435 1.50189
\(530\) 0 0
\(531\) −17.5438 + 17.5438i −0.761336 + 0.761336i
\(532\) 0 0
\(533\) −1.79948 + 1.79948i −0.0779442 + 0.0779442i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 18.4005 0.794038
\(538\) 0 0
\(539\) −11.5037 11.5037i −0.495499 0.495499i
\(540\) 0 0
\(541\) −23.4122 + 23.4122i −1.00657 + 1.00657i −0.00659048 + 0.999978i \(0.502098\pi\)
−0.999978 + 0.00659048i \(0.997902\pi\)
\(542\) 0 0
\(543\) 39.6921i 1.70335i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −17.3745 17.3745i −0.742878 0.742878i 0.230253 0.973131i \(-0.426045\pi\)
−0.973131 + 0.230253i \(0.926045\pi\)
\(548\) 0 0
\(549\) −17.6163 17.6163i −0.751846 0.751846i
\(550\) 0 0
\(551\) 74.4767i 3.17282i
\(552\) 0 0
\(553\) 5.76308 0.245071
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 22.8889 + 22.8889i 0.969832 + 0.969832i 0.999558 0.0297261i \(-0.00946351\pi\)
−0.0297261 + 0.999558i \(0.509464\pi\)
\(558\) 0 0
\(559\) 3.15432 0.133413
\(560\) 0 0
\(561\) −28.2799 −1.19398
\(562\) 0 0
\(563\) 19.2489 + 19.2489i 0.811246 + 0.811246i 0.984821 0.173574i \(-0.0555317\pi\)
−0.173574 + 0.984821i \(0.555532\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 18.9608 0.796278
\(568\) 0 0
\(569\) 34.4274i 1.44327i −0.692273 0.721635i \(-0.743391\pi\)
0.692273 0.721635i \(-0.256609\pi\)
\(570\) 0 0
\(571\) −5.85059 5.85059i −0.244840 0.244840i 0.574009 0.818849i \(-0.305387\pi\)
−0.818849 + 0.574009i \(0.805387\pi\)
\(572\) 0 0
\(573\) 18.5593 + 18.5593i 0.775326 + 0.775326i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 32.5042i 1.35317i 0.736365 + 0.676585i \(0.236541\pi\)
−0.736365 + 0.676585i \(0.763459\pi\)
\(578\) 0 0
\(579\) 34.6611 34.6611i 1.44047 1.44047i
\(580\) 0 0
\(581\) 1.85384 + 1.85384i 0.0769103 + 0.0769103i
\(582\) 0 0
\(583\) −45.9743 −1.90406
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14.7519 + 14.7519i −0.608875 + 0.608875i −0.942652 0.333777i \(-0.891677\pi\)
0.333777 + 0.942652i \(0.391677\pi\)
\(588\) 0 0
\(589\) −4.60810 + 4.60810i −0.189873 + 0.189873i
\(590\) 0 0
\(591\) 46.8024 1.92520
\(592\) 0 0
\(593\) 20.5310i 0.843108i 0.906803 + 0.421554i \(0.138515\pi\)
−0.906803 + 0.421554i \(0.861485\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −5.41590 + 5.41590i −0.221658 + 0.221658i
\(598\) 0 0
\(599\) 12.3998i 0.506644i 0.967382 + 0.253322i \(0.0815232\pi\)
−0.967382 + 0.253322i \(0.918477\pi\)
\(600\) 0 0
\(601\) 12.3980i 0.505723i 0.967502 + 0.252862i \(0.0813718\pi\)
−0.967502 + 0.252862i \(0.918628\pi\)
\(602\) 0 0
\(603\) 9.57777 9.57777i 0.390037 0.390037i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 4.90398i 0.199046i −0.995035 0.0995232i \(-0.968268\pi\)
0.995035 0.0995232i \(-0.0317318\pi\)
\(608\) 0 0
\(609\) 40.3621 1.63556
\(610\) 0 0
\(611\) −2.89635 + 2.89635i −0.117174 + 0.117174i
\(612\) 0 0
\(613\) −0.408547 + 0.408547i −0.0165011 + 0.0165011i −0.715309 0.698808i \(-0.753714\pi\)
0.698808 + 0.715309i \(0.253714\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.17186 0.248470 0.124235 0.992253i \(-0.460352\pi\)
0.124235 + 0.992253i \(0.460352\pi\)
\(618\) 0 0
\(619\) 18.5138 + 18.5138i 0.744132 + 0.744132i 0.973370 0.229238i \(-0.0736234\pi\)
−0.229238 + 0.973370i \(0.573623\pi\)
\(620\) 0 0
\(621\) 5.52479 5.52479i 0.221702 0.221702i
\(622\) 0 0
\(623\) 18.9136i 0.757757i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 63.4156 + 63.4156i 2.53258 + 2.53258i
\(628\) 0 0
\(629\) −6.93404 6.93404i −0.276478 0.276478i
\(630\) 0 0
\(631\) 20.7940i 0.827795i 0.910323 + 0.413897i \(0.135833\pi\)
−0.910323 + 0.413897i \(0.864167\pi\)
\(632\) 0 0
\(633\) −33.9640 −1.34995
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −6.63024 6.63024i −0.262700 0.262700i
\(638\) 0 0
\(639\) −23.9521 −0.947530
\(640\) 0 0
\(641\) 16.1179 0.636620 0.318310 0.947987i \(-0.396885\pi\)
0.318310 + 0.947987i \(0.396885\pi\)
\(642\) 0 0
\(643\) 10.3733 + 10.3733i 0.409082 + 0.409082i 0.881419 0.472336i \(-0.156589\pi\)
−0.472336 + 0.881419i \(0.656589\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −32.5724 −1.28055 −0.640276 0.768145i \(-0.721180\pi\)
−0.640276 + 0.768145i \(0.721180\pi\)
\(648\) 0 0
\(649\) 45.1298i 1.77150i
\(650\) 0 0
\(651\) −2.49733 2.49733i −0.0978780 0.0978780i
\(652\) 0 0
\(653\) −4.31962 4.31962i −0.169040 0.169040i 0.617517 0.786557i \(-0.288139\pi\)
−0.786557 + 0.617517i \(0.788139\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.27191i 0.0886356i
\(658\) 0 0
\(659\) −4.19711 + 4.19711i −0.163496 + 0.163496i −0.784114 0.620617i \(-0.786882\pi\)
0.620617 + 0.784114i \(0.286882\pi\)
\(660\) 0 0
\(661\) 21.2310 + 21.2310i 0.825790 + 0.825790i 0.986931 0.161141i \(-0.0515175\pi\)
−0.161141 + 0.986931i \(0.551518\pi\)
\(662\) 0 0
\(663\) −16.2993 −0.633013
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 48.9877 48.9877i 1.89681 1.89681i
\(668\) 0 0
\(669\) −40.1062 + 40.1062i −1.55060 + 1.55060i
\(670\) 0 0
\(671\) −45.3164 −1.74942
\(672\) 0 0
\(673\) 6.08317i 0.234489i 0.993103 + 0.117244i \(0.0374061\pi\)
−0.993103 + 0.117244i \(0.962594\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8.42443 8.42443i 0.323777 0.323777i −0.526437 0.850214i \(-0.676472\pi\)
0.850214 + 0.526437i \(0.176472\pi\)
\(678\) 0 0
\(679\) 13.4313i 0.515447i
\(680\) 0 0
\(681\) 39.9824i 1.53213i
\(682\) 0 0
\(683\) −14.7609 + 14.7609i −0.564812 + 0.564812i −0.930670 0.365859i \(-0.880775\pi\)
0.365859 + 0.930670i \(0.380775\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 67.3710i 2.57036i
\(688\) 0 0
\(689\) −26.4977 −1.00948
\(690\) 0 0
\(691\) 4.06268 4.06268i 0.154552 0.154552i −0.625596 0.780147i \(-0.715144\pi\)
0.780147 + 0.625596i \(0.215144\pi\)
\(692\) 0 0
\(693\) −15.8350 + 15.8350i −0.601523 + 0.601523i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 2.43515 0.0922379
\(698\) 0 0
\(699\) 16.7875 + 16.7875i 0.634961 + 0.634961i
\(700\) 0 0
\(701\) 11.1049 11.1049i 0.419428 0.419428i −0.465578 0.885007i \(-0.654154\pi\)
0.885007 + 0.465578i \(0.154154\pi\)
\(702\) 0 0
\(703\) 31.0982i 1.17289i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.96911 1.96911i −0.0740561 0.0740561i
\(708\) 0 0
\(709\) −13.0114 13.0114i −0.488652 0.488652i 0.419229 0.907881i \(-0.362300\pi\)
−0.907881 + 0.419229i \(0.862300\pi\)
\(710\) 0 0
\(711\) 7.88412i 0.295678i
\(712\) 0 0
\(713\) −6.06203 −0.227025
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −1.65582 1.65582i −0.0618378 0.0618378i
\(718\) 0 0
\(719\) −50.0570 −1.86681 −0.933406 0.358821i \(-0.883179\pi\)
−0.933406 + 0.358821i \(0.883179\pi\)
\(720\) 0 0
\(721\) 15.3774 0.572684
\(722\) 0 0
\(723\) −23.5547 23.5547i −0.876007 0.876007i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 27.7141 1.02786 0.513930 0.857832i \(-0.328189\pi\)
0.513930 + 0.857832i \(0.328189\pi\)
\(728\) 0 0
\(729\) 18.6509i 0.690775i
\(730\) 0 0
\(731\) −2.13429 2.13429i −0.0789396 0.0789396i
\(732\) 0 0
\(733\) −16.8860 16.8860i −0.623698 0.623698i 0.322777 0.946475i \(-0.395384\pi\)
−0.946475 + 0.322777i \(0.895384\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24.6379i 0.907550i
\(738\) 0 0
\(739\) −23.6286 + 23.6286i −0.869193 + 0.869193i −0.992383 0.123190i \(-0.960688\pi\)
0.123190 + 0.992383i \(0.460688\pi\)
\(740\) 0 0
\(741\) 36.5501 + 36.5501i 1.34270 + 1.34270i
\(742\) 0 0
\(743\) 6.53356 0.239693 0.119846 0.992792i \(-0.461760\pi\)
0.119846 + 0.992792i \(0.461760\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −2.53613 + 2.53613i −0.0927921 + 0.0927921i
\(748\) 0 0
\(749\) 5.35401 5.35401i 0.195631 0.195631i
\(750\) 0 0
\(751\) 22.8483 0.833746 0.416873 0.908965i \(-0.363126\pi\)
0.416873 + 0.908965i \(0.363126\pi\)
\(752\) 0 0
\(753\) 5.22634i 0.190459i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 24.0190 24.0190i 0.872985 0.872985i −0.119811 0.992797i \(-0.538229\pi\)
0.992797 + 0.119811i \(0.0382290\pi\)
\(758\) 0 0
\(759\) 83.4243i 3.02811i
\(760\) 0 0
\(761\) 5.51772i 0.200017i −0.994987 0.100009i \(-0.968113\pi\)
0.994987 0.100009i \(-0.0318871\pi\)
\(762\) 0 0
\(763\) 21.3107 21.3107i 0.771501 0.771501i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 26.0109i 0.939200i
\(768\) 0 0
\(769\) −14.0124 −0.505299 −0.252649 0.967558i \(-0.581302\pi\)
−0.252649 + 0.967558i \(0.581302\pi\)
\(770\) 0 0
\(771\) −17.1108 + 17.1108i −0.616231 + 0.616231i
\(772\) 0 0
\(773\) 0.753043 0.753043i 0.0270851 0.0270851i −0.693435 0.720520i \(-0.743903\pi\)
0.720520 + 0.693435i \(0.243903\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −16.8535 −0.604614
\(778\) 0 0
\(779\) −5.46066 5.46066i −0.195648 0.195648i
\(780\) 0 0
\(781\) −30.8073 + 30.8073i −1.10237 + 1.10237i
\(782\) 0 0
\(783\) 9.40668i 0.336167i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 29.2752 + 29.2752i 1.04355 + 1.04355i 0.999008 + 0.0445395i \(0.0141821\pi\)
0.0445395 + 0.999008i \(0.485818\pi\)
\(788\) 0 0
\(789\) −31.7939 31.7939i −1.13189 1.13189i
\(790\) 0 0
\(791\) 6.63709i 0.235988i
\(792\) 0 0
\(793\) −26.1185 −0.927494
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −6.09658 6.09658i −0.215952 0.215952i 0.590838 0.806790i \(-0.298797\pi\)
−0.806790 + 0.590838i \(0.798797\pi\)
\(798\) 0 0
\(799\) 3.91948 0.138661
\(800\) 0 0
\(801\) 25.8745 0.914232
\(802\) 0 0