Properties

Label 768.2.n.b.289.2
Level $768$
Weight $2$
Character 768.289
Analytic conductor $6.133$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 768.n (of order \(8\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.13251087523\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 96)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 289.2
Character \(\chi\) \(=\) 768.289
Dual form 768.2.n.b.481.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.382683 + 0.923880i) q^{3} +(-1.60930 + 0.666593i) q^{5} +(0.589445 - 0.589445i) q^{7} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\) \(q+(-0.382683 + 0.923880i) q^{3} +(-1.60930 + 0.666593i) q^{5} +(0.589445 - 0.589445i) q^{7} +(-0.707107 - 0.707107i) q^{9} +(-0.657053 - 1.58627i) q^{11} +(-3.87213 - 1.60389i) q^{13} -1.74189i q^{15} -7.96502i q^{17} +(3.97306 + 1.64569i) q^{19} +(0.319006 + 0.770147i) q^{21} +(0.452012 + 0.452012i) q^{23} +(-1.39004 + 1.39004i) q^{25} +(0.923880 - 0.382683i) q^{27} +(1.69130 - 4.08316i) q^{29} +9.32808 q^{31} +1.71696 q^{33} +(-0.555673 + 1.34151i) q^{35} +(-0.810329 + 0.335649i) q^{37} +(2.96360 - 2.96360i) q^{39} +(-6.65023 - 6.65023i) q^{41} +(-2.22413 - 5.36952i) q^{43} +(1.60930 + 0.666593i) q^{45} -8.50500i q^{47} +6.30511i q^{49} +(7.35872 + 3.04808i) q^{51} +(-1.10759 - 2.67397i) q^{53} +(2.11479 + 2.11479i) q^{55} +(-3.04084 + 3.04084i) q^{57} +(-1.92200 + 0.796118i) q^{59} +(4.70435 - 11.3573i) q^{61} -0.833602 q^{63} +7.30055 q^{65} +(4.54765 - 10.9790i) q^{67} +(-0.590582 + 0.244627i) q^{69} +(-9.09946 + 9.09946i) q^{71} +(1.65052 + 1.65052i) q^{73} +(-0.752286 - 1.81618i) q^{75} +(-1.32231 - 0.547721i) q^{77} -0.580469i q^{79} +1.00000i q^{81} +(3.33576 + 1.38172i) q^{83} +(5.30942 + 12.8181i) q^{85} +(3.12512 + 3.12512i) q^{87} +(-4.91488 + 4.91488i) q^{89} +(-3.22782 + 1.33701i) q^{91} +(-3.56970 + 8.61802i) q^{93} -7.49083 q^{95} -3.30926 q^{97} +(-0.657053 + 1.58627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + O(q^{10}) \) \( 32q + 16q^{23} + 48q^{31} - 48q^{35} - 16q^{43} + 16q^{51} + 32q^{53} - 32q^{55} + 64q^{59} + 32q^{61} - 16q^{63} + 16q^{67} + 32q^{69} - 64q^{71} + 32q^{75} + 32q^{77} - 48q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\)

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
\(3\) −0.382683 + 0.923880i −0.220942 + 0.533402i
\(4\) 0 0
\(5\) −1.60930 + 0.666593i −0.719700 + 0.298109i −0.712312 0.701863i \(-0.752352\pi\)
−0.00738796 + 0.999973i \(0.502352\pi\)
\(6\) 0 0
\(7\) 0.589445 0.589445i 0.222789 0.222789i −0.586883 0.809672i \(-0.699645\pi\)
0.809672 + 0.586883i \(0.199645\pi\)
\(8\) 0 0
\(9\) −0.707107 0.707107i −0.235702 0.235702i
\(10\) 0 0
\(11\) −0.657053 1.58627i −0.198109 0.478277i 0.793339 0.608780i \(-0.208341\pi\)
−0.991448 + 0.130503i \(0.958341\pi\)
\(12\) 0 0
\(13\) −3.87213 1.60389i −1.07394 0.444839i −0.225558 0.974230i \(-0.572421\pi\)
−0.848378 + 0.529391i \(0.822421\pi\)
\(14\) 0 0
\(15\) 1.74189i 0.449754i
\(16\) 0 0
\(17\) 7.96502i 1.93180i −0.258913 0.965901i \(-0.583364\pi\)
0.258913 0.965901i \(-0.416636\pi\)
\(18\) 0 0
\(19\) 3.97306 + 1.64569i 0.911481 + 0.377548i 0.788624 0.614876i \(-0.210794\pi\)
0.122858 + 0.992424i \(0.460794\pi\)
\(20\) 0 0
\(21\) 0.319006 + 0.770147i 0.0696127 + 0.168060i
\(22\) 0 0
\(23\) 0.452012 + 0.452012i 0.0942511 + 0.0942511i 0.752660 0.658409i \(-0.228770\pi\)
−0.658409 + 0.752660i \(0.728770\pi\)
\(24\) 0 0
\(25\) −1.39004 + 1.39004i −0.278009 + 0.278009i
\(26\) 0 0
\(27\) 0.923880 0.382683i 0.177801 0.0736475i
\(28\) 0 0
\(29\) 1.69130 4.08316i 0.314067 0.758224i −0.685479 0.728092i \(-0.740407\pi\)
0.999546 0.0301318i \(-0.00959270\pi\)
\(30\) 0 0
\(31\) 9.32808 1.67537 0.837686 0.546152i \(-0.183908\pi\)
0.837686 + 0.546152i \(0.183908\pi\)
\(32\) 0 0
\(33\) 1.71696 0.298885
\(34\) 0 0
\(35\) −0.555673 + 1.34151i −0.0939258 + 0.226757i
\(36\) 0 0
\(37\) −0.810329 + 0.335649i −0.133217 + 0.0551804i −0.448296 0.893885i \(-0.647969\pi\)
0.315079 + 0.949065i \(0.397969\pi\)
\(38\) 0 0
\(39\) 2.96360 2.96360i 0.474556 0.474556i
\(40\) 0 0
\(41\) −6.65023 6.65023i −1.03859 1.03859i −0.999225 0.0393665i \(-0.987466\pi\)
−0.0393665 0.999225i \(-0.512534\pi\)
\(42\) 0 0
\(43\) −2.22413 5.36952i −0.339176 0.818844i −0.997795 0.0663675i \(-0.978859\pi\)
0.658619 0.752477i \(-0.271141\pi\)
\(44\) 0 0
\(45\) 1.60930 + 0.666593i 0.239900 + 0.0993698i
\(46\) 0 0
\(47\) 8.50500i 1.24058i −0.784372 0.620291i \(-0.787015\pi\)
0.784372 0.620291i \(-0.212985\pi\)
\(48\) 0 0
\(49\) 6.30511i 0.900730i
\(50\) 0 0
\(51\) 7.35872 + 3.04808i 1.03043 + 0.426817i
\(52\) 0 0
\(53\) −1.10759 2.67397i −0.152140 0.367298i 0.829373 0.558696i \(-0.188698\pi\)
−0.981513 + 0.191398i \(0.938698\pi\)
\(54\) 0 0
\(55\) 2.11479 + 2.11479i 0.285158 + 0.285158i
\(56\) 0 0
\(57\) −3.04084 + 3.04084i −0.402770 + 0.402770i
\(58\) 0 0
\(59\) −1.92200 + 0.796118i −0.250223 + 0.103646i −0.504270 0.863546i \(-0.668238\pi\)
0.254047 + 0.967192i \(0.418238\pi\)
\(60\) 0 0
\(61\) 4.70435 11.3573i 0.602331 1.45416i −0.268845 0.963183i \(-0.586642\pi\)
0.871176 0.490972i \(-0.163358\pi\)
\(62\) 0 0
\(63\) −0.833602 −0.105024
\(64\) 0 0
\(65\) 7.30055 0.905522
\(66\) 0 0
\(67\) 4.54765 10.9790i 0.555583 1.34130i −0.357648 0.933856i \(-0.616421\pi\)
0.913232 0.407441i \(-0.133579\pi\)
\(68\) 0 0
\(69\) −0.590582 + 0.244627i −0.0710978 + 0.0294497i
\(70\) 0 0
\(71\) −9.09946 + 9.09946i −1.07991 + 1.07991i −0.0833896 + 0.996517i \(0.526575\pi\)
−0.996517 + 0.0833896i \(0.973425\pi\)
\(72\) 0 0
\(73\) 1.65052 + 1.65052i 0.193179 + 0.193179i 0.797068 0.603889i \(-0.206383\pi\)
−0.603889 + 0.797068i \(0.706383\pi\)
\(74\) 0 0
\(75\) −0.752286 1.81618i −0.0868665 0.209714i
\(76\) 0 0
\(77\) −1.32231 0.547721i −0.150692 0.0624186i
\(78\) 0 0
\(79\) 0.580469i 0.0653079i −0.999467 0.0326540i \(-0.989604\pi\)
0.999467 0.0326540i \(-0.0103959\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) 0 0
\(83\) 3.33576 + 1.38172i 0.366147 + 0.151663i 0.558168 0.829728i \(-0.311504\pi\)
−0.192021 + 0.981391i \(0.561504\pi\)
\(84\) 0 0
\(85\) 5.30942 + 12.8181i 0.575888 + 1.39032i
\(86\) 0 0
\(87\) 3.12512 + 3.12512i 0.335048 + 0.335048i
\(88\) 0 0
\(89\) −4.91488 + 4.91488i −0.520976 + 0.520976i −0.917866 0.396890i \(-0.870089\pi\)
0.396890 + 0.917866i \(0.370089\pi\)
\(90\) 0 0
\(91\) −3.22782 + 1.33701i −0.338367 + 0.140156i
\(92\) 0 0
\(93\) −3.56970 + 8.61802i −0.370161 + 0.893647i
\(94\) 0 0
\(95\) −7.49083 −0.768543
\(96\) 0 0
\(97\) −3.30926 −0.336005 −0.168002 0.985787i \(-0.553732\pi\)
−0.168002 + 0.985787i \(0.553732\pi\)
\(98\) 0 0
\(99\) −0.657053 + 1.58627i −0.0660363 + 0.159426i
\(100\) 0 0
\(101\) 2.59134 1.07337i 0.257848 0.106804i −0.250015 0.968242i \(-0.580436\pi\)
0.507863 + 0.861438i \(0.330436\pi\)
\(102\) 0 0
\(103\) −12.7576 + 12.7576i −1.25705 + 1.25705i −0.304550 + 0.952496i \(0.598506\pi\)
−0.952496 + 0.304550i \(0.901494\pi\)
\(104\) 0 0
\(105\) −1.02675 1.02675i −0.100200 0.100200i
\(106\) 0 0
\(107\) −3.17275 7.65969i −0.306721 0.740490i −0.999807 0.0196351i \(-0.993750\pi\)
0.693086 0.720855i \(-0.256250\pi\)
\(108\) 0 0
\(109\) −10.8733 4.50386i −1.04147 0.431391i −0.204631 0.978839i \(-0.565599\pi\)
−0.836840 + 0.547448i \(0.815599\pi\)
\(110\) 0 0
\(111\) 0.877093i 0.0832500i
\(112\) 0 0
\(113\) 1.05718i 0.0994515i 0.998763 + 0.0497257i \(0.0158347\pi\)
−0.998763 + 0.0497257i \(0.984165\pi\)
\(114\) 0 0
\(115\) −1.02873 0.426114i −0.0959296 0.0397353i
\(116\) 0 0
\(117\) 1.60389 + 3.87213i 0.148280 + 0.357979i
\(118\) 0 0
\(119\) −4.69494 4.69494i −0.430385 0.430385i
\(120\) 0 0
\(121\) 5.69365 5.69365i 0.517605 0.517605i
\(122\) 0 0
\(123\) 8.68894 3.59908i 0.783456 0.324518i
\(124\) 0 0
\(125\) 4.64336 11.2101i 0.415315 1.00266i
\(126\) 0 0
\(127\) 7.93736 0.704327 0.352163 0.935939i \(-0.385446\pi\)
0.352163 + 0.935939i \(0.385446\pi\)
\(128\) 0 0
\(129\) 5.81193 0.511712
\(130\) 0 0
\(131\) −7.20756 + 17.4006i −0.629727 + 1.52030i 0.210234 + 0.977651i \(0.432577\pi\)
−0.839962 + 0.542645i \(0.817423\pi\)
\(132\) 0 0
\(133\) 3.31195 1.37185i 0.287182 0.118955i
\(134\) 0 0
\(135\) −1.23170 + 1.23170i −0.106008 + 0.106008i
\(136\) 0 0
\(137\) 0.305733 + 0.305733i 0.0261205 + 0.0261205i 0.720046 0.693926i \(-0.244120\pi\)
−0.693926 + 0.720046i \(0.744120\pi\)
\(138\) 0 0
\(139\) 6.72200 + 16.2283i 0.570153 + 1.37647i 0.901425 + 0.432935i \(0.142522\pi\)
−0.331273 + 0.943535i \(0.607478\pi\)
\(140\) 0 0
\(141\) 7.85759 + 3.25472i 0.661729 + 0.274097i
\(142\) 0 0
\(143\) 7.19608i 0.601766i
\(144\) 0 0
\(145\) 7.69843i 0.639320i
\(146\) 0 0
\(147\) −5.82516 2.41286i −0.480451 0.199009i
\(148\) 0 0
\(149\) −2.14465 5.17765i −0.175697 0.424170i 0.811359 0.584549i \(-0.198728\pi\)
−0.987056 + 0.160379i \(0.948728\pi\)
\(150\) 0 0
\(151\) −10.2384 10.2384i −0.833193 0.833193i 0.154759 0.987952i \(-0.450540\pi\)
−0.987952 + 0.154759i \(0.950540\pi\)
\(152\) 0 0
\(153\) −5.63212 + 5.63212i −0.455330 + 0.455330i
\(154\) 0 0
\(155\) −15.0116 + 6.21803i −1.20576 + 0.499444i
\(156\) 0 0
\(157\) −4.64097 + 11.2043i −0.370389 + 0.894199i 0.623295 + 0.781987i \(0.285794\pi\)
−0.993684 + 0.112212i \(0.964206\pi\)
\(158\) 0 0
\(159\) 2.89428 0.229532
\(160\) 0 0
\(161\) 0.532873 0.0419963
\(162\) 0 0
\(163\) 0.981891 2.37049i 0.0769076 0.185671i −0.880750 0.473582i \(-0.842961\pi\)
0.957657 + 0.287911i \(0.0929607\pi\)
\(164\) 0 0
\(165\) −2.76310 + 1.14451i −0.215107 + 0.0891004i
\(166\) 0 0
\(167\) 6.83087 6.83087i 0.528588 0.528588i −0.391563 0.920151i \(-0.628066\pi\)
0.920151 + 0.391563i \(0.128066\pi\)
\(168\) 0 0
\(169\) 3.22856 + 3.22856i 0.248351 + 0.248351i
\(170\) 0 0
\(171\) −1.64569 3.97306i −0.125849 0.303827i
\(172\) 0 0
\(173\) −2.76667 1.14599i −0.210346 0.0871282i 0.275023 0.961438i \(-0.411315\pi\)
−0.485369 + 0.874310i \(0.661315\pi\)
\(174\) 0 0
\(175\) 1.63871i 0.123875i
\(176\) 0 0
\(177\) 2.08036i 0.156369i
\(178\) 0 0
\(179\) −13.3854 5.54441i −1.00047 0.414409i −0.178501 0.983940i \(-0.557125\pi\)
−0.821970 + 0.569531i \(0.807125\pi\)
\(180\) 0 0
\(181\) 9.03488 + 21.8121i 0.671557 + 1.62128i 0.778965 + 0.627068i \(0.215745\pi\)
−0.107407 + 0.994215i \(0.534255\pi\)
\(182\) 0 0
\(183\) 8.69251 + 8.69251i 0.642569 + 0.642569i
\(184\) 0 0
\(185\) 1.08032 1.08032i 0.0794266 0.0794266i
\(186\) 0 0
\(187\) −12.6346 + 5.23344i −0.923937 + 0.382707i
\(188\) 0 0
\(189\) 0.319006 0.770147i 0.0232042 0.0560200i
\(190\) 0 0
\(191\) −15.9720 −1.15570 −0.577848 0.816144i \(-0.696107\pi\)
−0.577848 + 0.816144i \(0.696107\pi\)
\(192\) 0 0
\(193\) 0.411129 0.0295937 0.0147968 0.999891i \(-0.495290\pi\)
0.0147968 + 0.999891i \(0.495290\pi\)
\(194\) 0 0
\(195\) −2.79380 + 6.74483i −0.200068 + 0.483007i
\(196\) 0 0
\(197\) 4.09727 1.69715i 0.291919 0.120917i −0.231918 0.972735i \(-0.574500\pi\)
0.523837 + 0.851819i \(0.324500\pi\)
\(198\) 0 0
\(199\) 8.65705 8.65705i 0.613682 0.613682i −0.330221 0.943904i \(-0.607123\pi\)
0.943904 + 0.330221i \(0.107123\pi\)
\(200\) 0 0
\(201\) 8.40296 + 8.40296i 0.592699 + 0.592699i
\(202\) 0 0
\(203\) −1.40987 3.40373i −0.0989535 0.238895i
\(204\) 0 0
\(205\) 15.1352 + 6.26920i 1.05709 + 0.437860i
\(206\) 0 0
\(207\) 0.639242i 0.0444304i
\(208\) 0 0
\(209\) 7.38363i 0.510737i
\(210\) 0 0
\(211\) −4.51505 1.87019i −0.310829 0.128749i 0.221816 0.975089i \(-0.428802\pi\)
−0.532644 + 0.846339i \(0.678802\pi\)
\(212\) 0 0
\(213\) −4.92459 11.8890i −0.337427 0.814622i
\(214\) 0 0
\(215\) 7.15857 + 7.15857i 0.488210 + 0.488210i
\(216\) 0 0
\(217\) 5.49839 5.49839i 0.373255 0.373255i
\(218\) 0 0
\(219\) −2.15651 + 0.893256i −0.145723 + 0.0603606i
\(220\) 0 0
\(221\) −12.7750 + 30.8416i −0.859341 + 2.07463i
\(222\) 0 0
\(223\) 8.07183 0.540530 0.270265 0.962786i \(-0.412889\pi\)
0.270265 + 0.962786i \(0.412889\pi\)
\(224\) 0 0
\(225\) 1.96582 0.131054
\(226\) 0 0
\(227\) −0.993337 + 2.39813i −0.0659301 + 0.159169i −0.953410 0.301676i \(-0.902454\pi\)
0.887480 + 0.460846i \(0.152454\pi\)
\(228\) 0 0
\(229\) −9.46203 + 3.91930i −0.625269 + 0.258995i −0.672741 0.739878i \(-0.734883\pi\)
0.0474727 + 0.998873i \(0.484883\pi\)
\(230\) 0 0
\(231\) 1.01206 1.01206i 0.0665884 0.0665884i
\(232\) 0 0
\(233\) 5.94847 + 5.94847i 0.389698 + 0.389698i 0.874580 0.484882i \(-0.161137\pi\)
−0.484882 + 0.874580i \(0.661137\pi\)
\(234\) 0 0
\(235\) 5.66937 + 13.6871i 0.369829 + 0.892846i
\(236\) 0 0
\(237\) 0.536284 + 0.222136i 0.0348354 + 0.0144293i
\(238\) 0 0
\(239\) 2.07158i 0.134000i 0.997753 + 0.0669998i \(0.0213427\pi\)
−0.997753 + 0.0669998i \(0.978657\pi\)
\(240\) 0 0
\(241\) 5.10031i 0.328540i 0.986415 + 0.164270i \(0.0525268\pi\)
−0.986415 + 0.164270i \(0.947473\pi\)
\(242\) 0 0
\(243\) −0.923880 0.382683i −0.0592669 0.0245492i
\(244\) 0 0
\(245\) −4.20294 10.1468i −0.268516 0.648255i
\(246\) 0 0
\(247\) −12.7447 12.7447i −0.810925 0.810925i
\(248\) 0 0
\(249\) −2.55308 + 2.55308i −0.161795 + 0.161795i
\(250\) 0 0
\(251\) 15.6741 6.49243i 0.989341 0.409798i 0.171463 0.985191i \(-0.445151\pi\)
0.817878 + 0.575392i \(0.195151\pi\)
\(252\) 0 0
\(253\) 0.420016 1.01401i 0.0264062 0.0637501i
\(254\) 0 0
\(255\) −13.8742 −0.868836
\(256\) 0 0
\(257\) 12.7920 0.797942 0.398971 0.916964i \(-0.369367\pi\)
0.398971 + 0.916964i \(0.369367\pi\)
\(258\) 0 0
\(259\) −0.279798 + 0.675491i −0.0173858 + 0.0419730i
\(260\) 0 0
\(261\) −4.08316 + 1.69130i −0.252741 + 0.104689i
\(262\) 0 0
\(263\) 5.06752 5.06752i 0.312477 0.312477i −0.533392 0.845868i \(-0.679083\pi\)
0.845868 + 0.533392i \(0.179083\pi\)
\(264\) 0 0
\(265\) 3.56490 + 3.56490i 0.218990 + 0.218990i
\(266\) 0 0
\(267\) −2.65991 6.42160i −0.162784 0.392995i
\(268\) 0 0
\(269\) 16.4527 + 6.81494i 1.00314 + 0.415514i 0.822948 0.568117i \(-0.192328\pi\)
0.180192 + 0.983631i \(0.442328\pi\)
\(270\) 0 0
\(271\) 6.40145i 0.388860i 0.980916 + 0.194430i \(0.0622857\pi\)
−0.980916 + 0.194430i \(0.937714\pi\)
\(272\) 0 0
\(273\) 3.49376i 0.211452i
\(274\) 0 0
\(275\) 3.11831 + 1.29165i 0.188041 + 0.0778892i
\(276\) 0 0
\(277\) −2.00777 4.84718i −0.120635 0.291239i 0.852014 0.523519i \(-0.175381\pi\)
−0.972649 + 0.232281i \(0.925381\pi\)
\(278\) 0 0
\(279\) −6.59595 6.59595i −0.394889 0.394889i
\(280\) 0 0
\(281\) 9.02739 9.02739i 0.538529 0.538529i −0.384568 0.923097i \(-0.625649\pi\)
0.923097 + 0.384568i \(0.125649\pi\)
\(282\) 0 0
\(283\) 7.91426 3.27819i 0.470454 0.194868i −0.134845 0.990867i \(-0.543054\pi\)
0.605299 + 0.795998i \(0.293054\pi\)
\(284\) 0 0
\(285\) 2.86662 6.92063i 0.169804 0.409943i
\(286\) 0 0
\(287\) −7.83989 −0.462774
\(288\) 0 0
\(289\) −46.4416 −2.73186
\(290\) 0 0
\(291\) 1.26640 3.05736i 0.0742377 0.179226i
\(292\) 0 0
\(293\) 1.10609 0.458156i 0.0646183 0.0267658i −0.350140 0.936697i \(-0.613866\pi\)
0.414758 + 0.909932i \(0.363866\pi\)
\(294\) 0 0
\(295\) 2.56238 2.56238i 0.149188 0.149188i
\(296\) 0 0
\(297\) −1.21408 1.21408i −0.0704478 0.0704478i
\(298\) 0 0
\(299\) −1.02527 2.47523i −0.0592931 0.143146i
\(300\) 0 0
\(301\) −4.47604 1.85404i −0.257995 0.106865i
\(302\) 0 0
\(303\) 2.80485i 0.161134i
\(304\) 0 0
\(305\) 21.4132i 1.22612i
\(306\) 0 0
\(307\) 10.0335 + 4.15602i 0.572643 + 0.237197i 0.650164 0.759794i \(-0.274700\pi\)
−0.0775205 + 0.996991i \(0.524700\pi\)
\(308\) 0 0
\(309\) −6.90438 16.6686i −0.392776 0.948246i
\(310\) 0 0
\(311\) 11.1912 + 11.1912i 0.634595 + 0.634595i 0.949217 0.314622i \(-0.101878\pi\)
−0.314622 + 0.949217i \(0.601878\pi\)
\(312\) 0 0
\(313\) 15.1491 15.1491i 0.856279 0.856279i −0.134619 0.990897i \(-0.542981\pi\)
0.990897 + 0.134619i \(0.0429809\pi\)
\(314\) 0 0
\(315\) 1.34151 0.555673i 0.0755857 0.0313086i
\(316\) 0 0
\(317\) 2.50910 6.05751i 0.140925 0.340223i −0.837621 0.546252i \(-0.816054\pi\)
0.978546 + 0.206029i \(0.0660540\pi\)
\(318\) 0 0
\(319\) −7.58826 −0.424861
\(320\) 0 0
\(321\) 8.29078 0.462746
\(322\) 0 0
\(323\) 13.1080 31.6455i 0.729348 1.76080i
\(324\) 0 0
\(325\) 7.61191 3.15295i 0.422233 0.174894i
\(326\) 0 0
\(327\) 8.32204 8.32204i 0.460210 0.460210i
\(328\) 0 0
\(329\) −5.01323 5.01323i −0.276388 0.276388i
\(330\) 0 0
\(331\) 7.52873 + 18.1760i 0.413817 + 0.999042i 0.984103 + 0.177596i \(0.0568321\pi\)
−0.570287 + 0.821446i \(0.693168\pi\)
\(332\) 0 0
\(333\) 0.810329 + 0.335649i 0.0444057 + 0.0183935i
\(334\) 0 0
\(335\) 20.6999i 1.13096i
\(336\) 0 0
\(337\) 29.9155i 1.62960i −0.579741 0.814801i \(-0.696846\pi\)
0.579741 0.814801i \(-0.303154\pi\)
\(338\) 0 0
\(339\) −0.976711 0.404567i −0.0530476 0.0219731i
\(340\) 0 0
\(341\) −6.12904 14.7968i −0.331906 0.801293i
\(342\) 0 0
\(343\) 7.84263 + 7.84263i 0.423462 + 0.423462i
\(344\) 0 0
\(345\) 0.787356 0.787356i 0.0423898 0.0423898i
\(346\) 0 0
\(347\) 18.9783 7.86106i 1.01881 0.422004i 0.190147 0.981756i \(-0.439103\pi\)
0.828660 + 0.559752i \(0.189103\pi\)
\(348\) 0 0
\(349\) 2.93498 7.08568i 0.157106 0.379288i −0.825653 0.564178i \(-0.809193\pi\)
0.982759 + 0.184891i \(0.0591931\pi\)
\(350\) 0 0
\(351\) −4.19117 −0.223708
\(352\) 0 0
\(353\) −28.6693 −1.52591 −0.762956 0.646450i \(-0.776253\pi\)
−0.762956 + 0.646450i \(0.776253\pi\)
\(354\) 0 0
\(355\) 8.57810 20.7094i 0.455278 1.09914i
\(356\) 0 0
\(357\) 6.13424 2.54089i 0.324658 0.134478i
\(358\) 0 0
\(359\) 13.9965 13.9965i 0.738709 0.738709i −0.233619 0.972328i \(-0.575057\pi\)
0.972328 + 0.233619i \(0.0750569\pi\)
\(360\) 0 0
\(361\) −0.358168 0.358168i −0.0188510 0.0188510i
\(362\) 0 0
\(363\) 3.08138 + 7.43911i 0.161731 + 0.390452i
\(364\) 0 0
\(365\) −3.75641 1.55595i −0.196619 0.0814424i
\(366\) 0 0
\(367\) 11.6706i 0.609203i −0.952480 0.304601i \(-0.901477\pi\)
0.952480 0.304601i \(-0.0985232\pi\)
\(368\) 0 0
\(369\) 9.40484i 0.489597i
\(370\) 0 0
\(371\) −2.22902 0.923292i −0.115725 0.0479350i
\(372\) 0 0
\(373\) −10.5778 25.5370i −0.547697 1.32226i −0.919187 0.393820i \(-0.871153\pi\)
0.371491 0.928437i \(-0.378847\pi\)
\(374\) 0 0
\(375\) 8.57982 + 8.57982i 0.443060 + 0.443060i
\(376\) 0 0
\(377\) −13.0979 + 13.0979i −0.674575 + 0.674575i
\(378\) 0 0
\(379\) 11.2755 4.67048i 0.579185 0.239906i −0.0738049 0.997273i \(-0.523514\pi\)
0.652990 + 0.757366i \(0.273514\pi\)
\(380\) 0 0
\(381\) −3.03750 + 7.33317i −0.155616 + 0.375689i
\(382\) 0 0
\(383\) 14.2648 0.728897 0.364448 0.931224i \(-0.381258\pi\)
0.364448 + 0.931224i \(0.381258\pi\)
\(384\) 0 0
\(385\) 2.49310 0.127060
\(386\) 0 0
\(387\) −2.22413 + 5.36952i −0.113059 + 0.272948i
\(388\) 0 0
\(389\) −16.9675 + 7.02815i −0.860284 + 0.356341i −0.768819 0.639467i \(-0.779155\pi\)
−0.0914656 + 0.995808i \(0.529155\pi\)
\(390\) 0 0
\(391\) 3.60029 3.60029i 0.182074 0.182074i
\(392\) 0 0
\(393\) −13.3178 13.3178i −0.671796 0.671796i
\(394\) 0 0
\(395\) 0.386937 + 0.934148i 0.0194689 + 0.0470021i
\(396\) 0 0
\(397\) −12.7413 5.27761i −0.639466 0.264875i 0.0393030 0.999227i \(-0.487486\pi\)
−0.678769 + 0.734352i \(0.737486\pi\)
\(398\) 0 0
\(399\) 3.58482i 0.179466i
\(400\) 0 0
\(401\) 20.6525i 1.03134i −0.856788 0.515669i \(-0.827543\pi\)
0.856788 0.515669i \(-0.172457\pi\)
\(402\) 0 0
\(403\) −36.1196 14.9612i −1.79924 0.745271i
\(404\) 0 0
\(405\) −0.666593 1.60930i −0.0331233 0.0799666i
\(406\) 0 0
\(407\) 1.06486 + 1.06486i 0.0527831 + 0.0527831i
\(408\) 0 0
\(409\) 6.38072 6.38072i 0.315506 0.315506i −0.531532 0.847038i \(-0.678383\pi\)
0.847038 + 0.531532i \(0.178383\pi\)
\(410\) 0 0
\(411\) −0.399459 + 0.165462i −0.0197039 + 0.00816161i
\(412\) 0 0
\(413\) −0.663645 + 1.60218i −0.0326558 + 0.0788382i
\(414\) 0 0
\(415\) −6.28927 −0.308728
\(416\) 0 0
\(417\) −17.5654 −0.860183
\(418\) 0 0
\(419\) −8.46204 + 20.4292i −0.413398 + 0.998030i 0.570821 + 0.821075i \(0.306625\pi\)
−0.984219 + 0.176956i \(0.943375\pi\)
\(420\) 0 0
\(421\) 28.2742 11.7116i 1.37800 0.570786i 0.434054 0.900887i \(-0.357083\pi\)
0.943946 + 0.330100i \(0.107083\pi\)
\(422\) 0 0
\(423\) −6.01394 + 6.01394i −0.292408 + 0.292408i
\(424\) 0 0
\(425\) 11.0717 + 11.0717i 0.537057 + 0.537057i
\(426\) 0 0
\(427\) −3.92156 9.46748i −0.189777 0.458163i
\(428\) 0 0
\(429\) −6.64831 2.75382i −0.320983 0.132956i
\(430\) 0 0
\(431\) 8.30038i 0.399815i 0.979815 + 0.199908i \(0.0640642\pi\)
−0.979815 + 0.199908i \(0.935936\pi\)
\(432\) 0 0
\(433\) 29.4261i 1.41413i 0.707150 + 0.707063i \(0.249980\pi\)
−0.707150 + 0.707063i \(0.750020\pi\)
\(434\) 0 0
\(435\) −7.11242 2.94606i −0.341014 0.141253i
\(436\) 0 0
\(437\) 1.05200 + 2.53974i 0.0503238 + 0.121492i
\(438\) 0 0
\(439\) −20.3138 20.3138i −0.969524 0.969524i 0.0300252 0.999549i \(-0.490441\pi\)
−0.999549 + 0.0300252i \(0.990441\pi\)
\(440\) 0 0
\(441\) 4.45838 4.45838i 0.212304 0.212304i
\(442\) 0 0
\(443\) 18.1169 7.50428i 0.860762 0.356539i 0.0917565 0.995781i \(-0.470752\pi\)
0.769005 + 0.639242i \(0.220752\pi\)
\(444\) 0 0
\(445\) 4.63328 11.1857i 0.219638 0.530254i
\(446\) 0 0
\(447\) 5.60425 0.265072
\(448\) 0 0
\(449\) −8.20853 −0.387384 −0.193692 0.981062i \(-0.562046\pi\)
−0.193692 + 0.981062i \(0.562046\pi\)
\(450\) 0 0
\(451\) −6.17948 + 14.9186i −0.290981 + 0.702489i
\(452\) 0 0
\(453\) 13.3772 5.54101i 0.628514 0.260339i
\(454\) 0 0
\(455\) 4.30328 4.30328i 0.201741 0.201741i
\(456\) 0 0
\(457\) −12.2056 12.2056i −0.570953 0.570953i 0.361442 0.932395i \(-0.382285\pi\)
−0.932395 + 0.361442i \(0.882285\pi\)
\(458\) 0 0
\(459\) −3.04808 7.35872i −0.142272 0.343476i
\(460\) 0 0
\(461\) 28.6007 + 11.8468i 1.33207 + 0.551761i 0.931245 0.364394i \(-0.118724\pi\)
0.400824 + 0.916155i \(0.368724\pi\)
\(462\) 0 0
\(463\) 22.9354i 1.06590i 0.846148 + 0.532948i \(0.178916\pi\)
−0.846148 + 0.532948i \(0.821084\pi\)
\(464\) 0 0
\(465\) 16.2485i 0.753506i
\(466\) 0 0
\(467\) 20.6535 + 8.55495i 0.955729 + 0.395876i 0.805381 0.592757i \(-0.201961\pi\)
0.150348 + 0.988633i \(0.451961\pi\)
\(468\) 0 0
\(469\) −3.79093 9.15210i −0.175049 0.422605i
\(470\) 0 0
\(471\) −8.57539 8.57539i −0.395133 0.395133i
\(472\) 0 0
\(473\) −7.05612 + 7.05612i −0.324441 + 0.324441i
\(474\) 0 0
\(475\) −7.81030 + 3.23513i −0.358361 + 0.148438i
\(476\) 0 0
\(477\) −1.10759 + 2.67397i −0.0507133 + 0.122433i
\(478\) 0 0
\(479\) 41.8313 1.91132 0.955661 0.294468i \(-0.0951424\pi\)
0.955661 + 0.294468i \(0.0951424\pi\)
\(480\) 0 0
\(481\) 3.67604 0.167613
\(482\) 0 0
\(483\) −0.203922 + 0.492310i −0.00927876 + 0.0224009i
\(484\) 0 0
\(485\) 5.32559 2.20593i 0.241822 0.100166i
\(486\) 0 0
\(487\) −4.02796 + 4.02796i −0.182524 + 0.182524i −0.792455 0.609931i \(-0.791197\pi\)
0.609931 + 0.792455i \(0.291197\pi\)
\(488\) 0 0
\(489\) 1.81430 + 1.81430i 0.0820454 + 0.0820454i
\(490\) 0 0
\(491\) 15.7614 + 38.0514i 0.711301 + 1.71723i 0.696724 + 0.717340i \(0.254640\pi\)
0.0145778 + 0.999894i \(0.495360\pi\)
\(492\) 0 0
\(493\) −32.5225 13.4712i −1.46474 0.606714i
\(494\) 0 0
\(495\) 2.99076i 0.134425i
\(496\) 0 0
\(497\) 10.7273i 0.481184i
\(498\) 0 0
\(499\) 7.53276 + 3.12017i 0.337213 + 0.139678i 0.544863 0.838525i \(-0.316582\pi\)
−0.207650 + 0.978203i \(0.566582\pi\)
\(500\) 0 0
\(501\) 3.69684 + 8.92496i 0.165163 + 0.398738i
\(502\) 0 0
\(503\) −10.0612 10.0612i −0.448607 0.448607i 0.446284 0.894891i \(-0.352747\pi\)
−0.894891 + 0.446284i \(0.852747\pi\)
\(504\) 0 0
\(505\) −3.45474 + 3.45474i −0.153734 + 0.153734i
\(506\) 0 0
\(507\) −4.21832 + 1.74728i −0.187342 + 0.0775996i
\(508\) 0 0
\(509\) −5.89292 + 14.2268i −0.261199 + 0.630590i −0.999013 0.0444138i \(-0.985858\pi\)
0.737814 + 0.675004i \(0.235858\pi\)
\(510\) 0 0
\(511\) 1.94578 0.0860765
\(512\) 0 0
\(513\) 4.30040 0.189867
\(514\) 0 0
\(515\) 12.0267 29.0350i 0.529958 1.27943i
\(516\) 0 0
\(517\) −13.4912 + 5.58824i −0.593342 + 0.245770i
\(518\) 0 0
\(519\) 2.11752 2.11752i 0.0929487 0.0929487i
\(520\) 0 0
\(521\) 11.9481 + 11.9481i 0.523456 + 0.523456i 0.918613 0.395158i \(-0.129310\pi\)
−0.395158 + 0.918613i \(0.629310\pi\)
\(522\) 0 0
\(523\) −6.15336 14.8555i −0.269068 0.649587i 0.730372 0.683049i \(-0.239347\pi\)
−0.999440 + 0.0334625i \(0.989347\pi\)
\(524\) 0 0
\(525\) −1.51397 0.627107i −0.0660750 0.0273692i
\(526\) 0 0
\(527\) 74.2983i 3.23649i
\(528\) 0 0
\(529\) 22.5914i 0.982233i
\(530\) 0 0
\(531\) 1.92200 + 0.796118i 0.0834076 + 0.0345486i
\(532\) 0 0
\(533\) 15.0843 + 36.4168i 0.653375 + 1.57739i
\(534\) 0 0
\(535\) 10.2118 + 10.2118i 0.441494 + 0.441494i
\(536\) 0 0
\(537\) 10.2447 10.2447i 0.442093 0.442093i
\(538\) 0 0
\(539\) 10.0016 4.14279i 0.430799 0.178443i
\(540\) 0 0
\(541\) −8.64537 + 20.8718i −0.371693 + 0.897347i 0.621770 + 0.783200i \(0.286414\pi\)
−0.993464 + 0.114148i \(0.963586\pi\)
\(542\) 0 0
\(543\) −23.6093 −1.01317
\(544\) 0 0
\(545\) 20.5006 0.878148
\(546\) 0 0
\(547\) 10.1653 24.5412i 0.434637 1.04931i −0.543137 0.839644i \(-0.682764\pi\)
0.977774 0.209662i \(-0.0672363\pi\)
\(548\) 0 0
\(549\) −11.3573 + 4.70435i −0.484718 + 0.200777i
\(550\) 0 0
\(551\) 13.4393 13.4393i 0.572532 0.572532i
\(552\) 0 0
\(553\) −0.342155 0.342155i −0.0145499 0.0145499i
\(554\) 0 0
\(555\) 0.584664 + 1.41150i 0.0248176 + 0.0599150i
\(556\) 0 0
\(557\) −40.0425 16.5861i −1.69666 0.702778i −0.696761 0.717303i \(-0.745376\pi\)
−0.999894 + 0.0145256i \(0.995376\pi\)
\(558\) 0 0
\(559\) 24.3588i 1.03027i
\(560\) 0 0
\(561\) 13.6756i 0.577386i
\(562\) 0 0
\(563\) −18.6724 7.73435i −0.786947 0.325964i −0.0472316 0.998884i \(-0.515040\pi\)
−0.739715 + 0.672920i \(0.765040\pi\)
\(564\) 0 0
\(565\) −0.704711 1.70132i −0.0296474 0.0715752i
\(566\) 0 0
\(567\) 0.589445 + 0.589445i 0.0247544 + 0.0247544i
\(568\) 0 0
\(569\) 8.77986 8.77986i 0.368071 0.368071i −0.498702 0.866773i \(-0.666190\pi\)
0.866773 + 0.498702i \(0.166190\pi\)
\(570\) 0 0
\(571\) −23.2136 + 9.61539i −0.971459 + 0.402392i −0.811255 0.584692i \(-0.801215\pi\)
−0.160204 + 0.987084i \(0.551215\pi\)
\(572\) 0 0
\(573\) 6.11224 14.7562i 0.255342 0.616451i
\(574\) 0 0
\(575\) −1.25663 −0.0524052
\(576\) 0 0
\(577\) 32.9671 1.37244 0.686220 0.727394i \(-0.259269\pi\)
0.686220 + 0.727394i \(0.259269\pi\)
\(578\) 0 0
\(579\) −0.157332 + 0.379833i −0.00653850 + 0.0157853i
\(580\) 0 0
\(581\) 2.78069 1.15180i 0.115363 0.0477848i
\(582\) 0 0
\(583\) −3.51388 + 3.51388i −0.145530 + 0.145530i
\(584\) 0 0
\(585\) −5.16227 5.16227i −0.213434 0.213434i
\(586\) 0 0
\(587\) 6.05934 + 14.6285i 0.250096 + 0.603785i 0.998211 0.0597837i \(-0.0190411\pi\)
−0.748115 + 0.663569i \(0.769041\pi\)
\(588\) 0 0
\(589\) 37.0610 + 15.3512i 1.52707 + 0.632533i
\(590\) 0 0
\(591\) 4.43486i 0.182426i
\(592\) 0 0
\(593\) 21.5942i 0.886767i 0.896332 + 0.443384i \(0.146222\pi\)
−0.896332 + 0.443384i \(0.853778\pi\)
\(594\) 0 0
\(595\) 10.6852 + 4.42595i 0.438050 + 0.181446i
\(596\) 0 0
\(597\) 4.68516 + 11.3110i 0.191751 + 0.462928i
\(598\) 0 0
\(599\) 16.6522 + 16.6522i 0.680392 + 0.680392i 0.960089 0.279696i \(-0.0902338\pi\)
−0.279696 + 0.960089i \(0.590234\pi\)
\(600\) 0 0
\(601\) 17.8090 17.8090i 0.726445 0.726445i −0.243465 0.969910i \(-0.578284\pi\)
0.969910 + 0.243465i \(0.0782840\pi\)
\(602\) 0 0
\(603\) −10.9790 + 4.54765i −0.447099 + 0.185194i
\(604\) 0 0
\(605\) −5.36743 + 12.9581i −0.218217 + 0.526823i
\(606\) 0 0
\(607\) 2.08575 0.0846579 0.0423289 0.999104i \(-0.486522\pi\)
0.0423289 + 0.999104i \(0.486522\pi\)
\(608\) 0 0
\(609\) 3.68417 0.149290
\(610\) 0 0
\(611\) −13.6411 + 32.9325i −0.551859 + 1.33231i
\(612\) 0 0
\(613\) −23.3947 + 9.69039i −0.944902 + 0.391391i −0.801312 0.598246i \(-0.795865\pi\)
−0.143590 + 0.989637i \(0.545865\pi\)
\(614\) 0 0
\(615\) −11.5840 + 11.5840i −0.467111 + 0.467111i
\(616\) 0 0
\(617\) −3.94760 3.94760i −0.158924 0.158924i 0.623166 0.782090i \(-0.285846\pi\)
−0.782090 + 0.623166i \(0.785846\pi\)
\(618\) 0 0
\(619\) −13.7586 33.2161i −0.553004 1.33507i −0.915212 0.402972i \(-0.867977\pi\)
0.362208 0.932097i \(-0.382023\pi\)
\(620\) 0 0
\(621\) 0.590582 + 0.244627i 0.0236993 + 0.00981655i
\(622\) 0 0
\(623\) 5.79410i 0.232136i
\(624\) 0 0
\(625\) 11.3065i 0.452259i
\(626\) 0 0
\(627\) 6.82159 + 2.82559i 0.272428 + 0.112843i
\(628\) 0 0
\(629\) 2.67345 + 6.45428i 0.106598 + 0.257349i
\(630\) 0 0
\(631\) 28.2524 + 28.2524i 1.12471 + 1.12471i 0.991024 + 0.133687i \(0.0426817\pi\)
0.133687 + 0.991024i \(0.457318\pi\)
\(632\) 0 0
\(633\) 3.45567 3.45567i 0.137350 0.137350i
\(634\) 0 0
\(635\) −12.7736 + 5.29099i −0.506904 + 0.209966i
\(636\) 0 0
\(637\) 10.1127 24.4142i 0.400680 0.967326i
\(638\) 0 0
\(639\) 12.8686 0.509073
\(640\) 0 0
\(641\) 9.34587 0.369140 0.184570 0.982819i \(-0.440911\pi\)
0.184570 + 0.982819i \(0.440911\pi\)
\(642\) 0 0
\(643\) −14.3013 + 34.5265i −0.563989 + 1.36159i 0.342562 + 0.939495i \(0.388705\pi\)
−0.906551 + 0.422096i \(0.861295\pi\)
\(644\) 0 0
\(645\) −9.35312 + 3.87419i −0.368279 + 0.152546i
\(646\) 0 0
\(647\) −29.8159 + 29.8159i −1.17218 + 1.17218i −0.190496 + 0.981688i \(0.561010\pi\)
−0.981688 + 0.190496i \(0.938990\pi\)
\(648\) 0 0
\(649\) 2.52571 + 2.52571i 0.0991428 + 0.0991428i
\(650\) 0 0
\(651\) 2.97571 + 7.18400i 0.116627 + 0.281563i
\(652\) 0 0
\(653\) 30.3070 + 12.5536i 1.18600 + 0.491259i 0.886452 0.462821i \(-0.153163\pi\)
0.299552 + 0.954080i \(0.403163\pi\)
\(654\) 0 0
\(655\) 32.8072i 1.28188i
\(656\) 0 0
\(657\) 2.33419i 0.0910654i
\(658\) 0 0
\(659\) 23.8281 + 9.86994i 0.928212 + 0.384478i 0.795000 0.606609i \(-0.207471\pi\)
0.133212 + 0.991088i \(0.457471\pi\)
\(660\) 0 0
\(661\) 1.40604 + 3.39448i 0.0546886 + 0.132030i 0.948862 0.315690i \(-0.102236\pi\)
−0.894174 + 0.447720i \(0.852236\pi\)
\(662\) 0 0
\(663\) −23.6052 23.6052i −0.916748 0.916748i
\(664\) 0 0
\(665\) −4.41544 + 4.41544i −0.171223 + 0.171223i
\(666\) 0 0
\(667\) 2.61013 1.08115i 0.101065 0.0418623i
\(668\) 0 0
\(669\) −3.08896 + 7.45740i −0.119426 + 0.288320i
\(670\) 0 0
\(671\) −21.1067 −0.814817
\(672\) 0 0
\(673\) 19.4796 0.750885 0.375442 0.926846i \(-0.377491\pi\)
0.375442 + 0.926846i \(0.377491\pi\)
\(674\) 0 0
\(675\) −0.752286 + 1.81618i −0.0289555 + 0.0699047i
\(676\) 0 0
\(677\) −19.1189 + 7.91933i −0.734801 + 0.304364i −0.718523 0.695503i \(-0.755182\pi\)
−0.0162777 + 0.999868i \(0.505182\pi\)
\(678\) 0 0
\(679\) −1.95063 + 1.95063i −0.0748583 + 0.0748583i
\(680\) 0 0
\(681\) −1.83545 1.83545i −0.0703345 0.0703345i
\(682\) 0 0
\(683\) −8.46056 20.4256i −0.323734 0.781564i −0.999031 0.0440175i \(-0.985984\pi\)
0.675296 0.737547i \(-0.264016\pi\)
\(684\) 0 0
\(685\) −0.695815 0.288216i −0.0265857 0.0110122i
\(686\) 0 0
\(687\) 10.2416i 0.390743i
\(688\) 0 0
\(689\) 12.1304i 0.462132i
\(690\) 0 0
\(691\) −14.6182 6.05507i −0.556104 0.230346i 0.0868889 0.996218i \(-0.472307\pi\)
−0.642993 + 0.765872i \(0.722307\pi\)
\(692\) 0 0
\(693\) 0.547721 + 1.32231i 0.0208062 + 0.0502306i
\(694\) 0 0
\(695\) −21.6354 21.6354i −0.820677 0.820677i
\(696\) 0 0
\(697\) −52.9692 + 52.9692i −2.00635 + 2.00635i
\(698\) 0 0
\(699\) −7.77206 + 3.21929i −0.293966 + 0.121765i
\(700\) 0 0
\(701\) 9.53654 23.0232i 0.360190 0.869576i −0.635082 0.772445i \(-0.719034\pi\)
0.995272 0.0971307i \(-0.0309665\pi\)
\(702\) 0 0
\(703\) −3.77186 −0.142258
\(704\) 0 0
\(705\) −14.8148 −0.557957
\(706\) 0 0
\(707\) 0.894763 2.16015i 0.0336510 0.0812407i
\(708\) 0 0
\(709\) 4.53151 1.87701i 0.170184 0.0704927i −0.295965 0.955199i \(-0.595641\pi\)
0.466149 + 0.884706i \(0.345641\pi\)
\(710\) 0 0
\(711\) −0.410454 + 0.410454i −0.0153932 + 0.0153932i
\(712\) 0 0
\(713\) 4.21641 + 4.21641i 0.157906 + 0.157906i
\(714\) 0 0
\(715\) −4.79685 11.5806i −0.179392 0.433091i
\(716\) 0 0
\(717\) −1.91389 0.792761i −0.0714757 0.0296062i
\(718\) 0 0
\(719\) 39.7315i 1.48173i 0.671652 + 0.740867i \(0.265585\pi\)
−0.671652 + 0.740867i \(0.734415\pi\)
\(720\) 0 0
\(721\) 15.0398i 0.560113i
\(722\) 0 0
\(723\) −4.71207 1.95180i −0.175244 0.0725883i
\(724\) 0 0
\(725\) 3.32479 + 8.02675i 0.123480 + 0.298106i
\(726\) 0 0
\(727\) 6.99691 + 6.99691i 0.259501 + 0.259501i 0.824851 0.565350i \(-0.191259\pi\)
−0.565350 + 0.824851i \(0.691259\pi\)
\(728\) 0 0
\(729\) 0.707107 0.707107i 0.0261891 0.0261891i
\(730\) 0 0
\(731\) −42.7683 + 17.7152i −1.58184 + 0.655221i
\(732\) 0 0
\(733\) −1.40532 + 3.39275i −0.0519068 + 0.125314i −0.947706 0.319145i \(-0.896604\pi\)
0.895799 + 0.444459i \(0.146604\pi\)
\(734\) 0 0
\(735\) 10.9828 0.405107
\(736\) 0 0
\(737\) −20.4037 −0.751578
\(738\) 0 0
\(739\) −8.11566 + 19.5929i −0.298539 + 0.720738i 0.701429 + 0.712740i \(0.252546\pi\)
−0.999968 + 0.00799797i \(0.997454\pi\)
\(740\) 0 0
\(741\) 16.6517 6.89737i 0.611717 0.253381i
\(742\) 0 0
\(743\) −5.67248 + 5.67248i −0.208103 + 0.208103i −0.803461 0.595358i \(-0.797010\pi\)
0.595358 + 0.803461i \(0.297010\pi\)
\(744\) 0 0
\(745\) 6.90277 + 6.90277i 0.252898 + 0.252898i
\(746\) 0 0
\(747\) −1.38172 3.33576i −0.0505544 0.122049i
\(748\) 0 0
\(749\) −6.38513 2.64481i −0.233307 0.0966391i
\(750\) 0 0
\(751\) 14.2209i 0.518930i −0.965753 0.259465i \(-0.916454\pi\)
0.965753 0.259465i \(-0.0835462\pi\)
\(752\) 0 0
\(753\) 16.9655i 0.618258i
\(754\) 0 0
\(755\) 23.3016 + 9.65183i 0.848031 + 0.351266i
\(756\) 0 0
\(757\) 6.45206 + 15.5767i 0.234504 + 0.566143i 0.996697 0.0812065i \(-0.0258773\pi\)
−0.762193 + 0.647350i \(0.775877\pi\)
\(758\) 0 0
\(759\) 0.776088 + 0.776088i 0.0281702 + 0.0281702i
\(760\) 0 0
\(761\) −8.62429 + 8.62429i −0.312630 + 0.312630i −0.845928 0.533298i \(-0.820953\pi\)
0.533298 + 0.845928i \(0.320953\pi\)
\(762\) 0 0
\(763\) −9.06398 + 3.75442i −0.328138 + 0.135919i
\(764\) 0 0
\(765\) 5.30942 12.8181i 0.191963 0.463439i
\(766\) 0 0
\(767\) 8.71912 0.314829
\(768\) 0 0
\(769\) 13.1949 0.475821 0.237911 0.971287i \(-0.423537\pi\)
0.237911 + 0.971287i \(0.423537\pi\)
\(770\) 0 0
\(771\) −4.89528 + 11.8183i −0.176299 + 0.425624i
\(772\) 0 0
\(773\) 23.3275 9.66257i 0.839032 0.347538i 0.0785601 0.996909i \(-0.474968\pi\)
0.760472 + 0.649371i \(0.224968\pi\)
\(774\) 0 0
\(775\) −12.9664 + 12.9664i −0.465768 + 0.465768i
\(776\) 0 0
\(777\) −0.516999 0.516999i −0.0185472 0.0185472i
\(778\) 0 0
\(779\) −15.4775 37.3660i −0.554539 1.33877i
\(780\) 0 0
\(781\) 20.4130 + 8.45534i 0.730434 + 0.302556i
\(782\) 0 0
\(783\) 4.41958i 0.157943i
\(784\) 0 0
\(785\) 21.1247i 0.753971i
\(786\) 0 0
\(787\) 12.3210 + 5.10352i 0.439196 + 0.181921i 0.591314 0.806442i \(-0.298609\pi\)
−0.152118 + 0.988362i \(0.548609\pi\)
\(788\) 0 0
\(789\) 2.74252 + 6.62104i 0.0976364 + 0.235715i
\(790\) 0 0
\(791\) 0.623152 + 0.623152i 0.0221567 + 0.0221567i
\(792\) 0 0
\(793\) −36.4318 + 36.4318i −1.29373 + 1.29373i
\(794\) 0 0
\(795\) −4.65776 + 1.92931i −0.165194 + 0.0684255i
\(796\) 0 0
\(797\) 0.0303911 0.0733705i 0.00107651 0.00259892i −0.923340 0.383983i \(-0.874552\pi\)
0.924417 + 0.381384i \(0.124552\pi\)
\(798\) 0