Properties

Label 315.2.p.e.307.3
Level 315
Weight 2
Character 315.307
Analytic conductor 2.515
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.3
Root \(-1.36166 - 0.381939i\) of \(x^{16} - 4 x^{14} + 6 x^{12} - 12 x^{10} + 33 x^{8} - 48 x^{6} + 96 x^{4} - 256 x^{2} + 256\)
Character \(\chi\) \(=\) 315.307
Dual form 315.2.p.e.118.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.540143 - 0.540143i) q^{2} -1.41649i q^{4} +(-1.03649 + 1.98133i) q^{5} +(0.614060 + 2.57351i) q^{7} +(-1.84539 + 1.84539i) q^{8} +O(q^{10})\) \(q+(-0.540143 - 0.540143i) q^{2} -1.41649i q^{4} +(-1.03649 + 1.98133i) q^{5} +(0.614060 + 2.57351i) q^{7} +(-1.84539 + 1.84539i) q^{8} +(1.63006 - 0.510348i) q^{10} +3.85136 q^{11} +(3.66816 + 3.66816i) q^{13} +(1.05838 - 1.72174i) q^{14} -0.839427 q^{16} +(1.49007 - 1.49007i) q^{17} -0.0697674 q^{19} +(2.80654 + 1.46818i) q^{20} +(-2.08029 - 2.08029i) q^{22} +(0.534176 - 0.534176i) q^{23} +(-2.85136 - 4.10728i) q^{25} -3.96267i q^{26} +(3.64535 - 0.869810i) q^{28} -2.77107i q^{29} +2.39674i q^{31} +(4.14420 + 4.14420i) q^{32} -1.60970 q^{34} +(-5.73544 - 1.45077i) q^{35} +(6.18757 + 6.18757i) q^{37} +(0.0376844 + 0.0376844i) q^{38} +(-1.74360 - 5.56908i) q^{40} +8.68077i q^{41} +(-2.77107 + 2.77107i) q^{43} -5.45542i q^{44} -0.577063 q^{46} +(5.49042 - 5.49042i) q^{47} +(-6.24586 + 3.16057i) q^{49} +(-0.678376 + 3.75866i) q^{50} +(5.19592 - 5.19592i) q^{52} +(-6.13823 + 6.13823i) q^{53} +(-3.99191 + 7.63083i) q^{55} +(-5.88231 - 3.61595i) q^{56} +(-1.49678 + 1.49678i) q^{58} -6.97440 q^{59} -14.3107i q^{61} +(1.29458 - 1.29458i) q^{62} -2.79807i q^{64} +(-11.0699 + 3.46582i) q^{65} +(0.416491 + 0.416491i) q^{67} +(-2.11067 - 2.11067i) q^{68} +(2.31434 + 3.88158i) q^{70} +8.12783 q^{71} +(-9.55210 - 9.55210i) q^{73} -6.68434i q^{74} +0.0988248i q^{76} +(2.36497 + 9.91150i) q^{77} -9.86329i q^{79} +(0.870061 - 1.66319i) q^{80} +(4.68886 - 4.68886i) q^{82} +(1.63570 + 1.63570i) q^{83} +(1.40788 + 4.49678i) q^{85} +2.99355 q^{86} +(-7.10728 + 7.10728i) q^{88} -5.05313 q^{89} +(-7.18757 + 11.6925i) q^{91} +(-0.756656 - 0.756656i) q^{92} -5.93123 q^{94} +(0.0723134 - 0.138232i) q^{95} +(-6.85851 + 6.85851i) q^{97} +(5.08082 + 1.66650i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} - 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} - 24q^{8} + 16q^{11} - 48q^{16} - 16q^{22} + 40q^{23} + 24q^{28} - 48q^{32} + 8q^{35} + 32q^{37} - 16q^{43} + 64q^{46} + 72q^{50} - 24q^{53} - 24q^{56} + 32q^{58} - 40q^{65} - 32q^{67} - 40q^{70} - 64q^{71} + 24q^{77} + 48q^{85} - 64q^{86} - 64q^{88} - 48q^{91} + 40q^{92} + 72q^{95} + 96q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.540143 0.540143i −0.381939 0.381939i 0.489861 0.871800i \(-0.337047\pi\)
−0.871800 + 0.489861i \(0.837047\pi\)
\(3\) 0 0
\(4\) 1.41649i 0.708245i
\(5\) −1.03649 + 1.98133i −0.463534 + 0.886079i
\(6\) 0 0
\(7\) 0.614060 + 2.57351i 0.232093 + 0.972694i
\(8\) −1.84539 + 1.84539i −0.652445 + 0.652445i
\(9\) 0 0
\(10\) 1.63006 0.510348i 0.515470 0.161386i
\(11\) 3.85136 1.16123 0.580615 0.814179i \(-0.302812\pi\)
0.580615 + 0.814179i \(0.302812\pi\)
\(12\) 0 0
\(13\) 3.66816 + 3.66816i 1.01737 + 1.01737i 0.999847 + 0.0175187i \(0.00557667\pi\)
0.0175187 + 0.999847i \(0.494423\pi\)
\(14\) 1.05838 1.72174i 0.282864 0.460155i
\(15\) 0 0
\(16\) −0.839427 −0.209857
\(17\) 1.49007 1.49007i 0.361395 0.361395i −0.502931 0.864326i \(-0.667745\pi\)
0.864326 + 0.502931i \(0.167745\pi\)
\(18\) 0 0
\(19\) −0.0697674 −0.0160057 −0.00800286 0.999968i \(-0.502547\pi\)
−0.00800286 + 0.999968i \(0.502547\pi\)
\(20\) 2.80654 + 1.46818i 0.627561 + 0.328296i
\(21\) 0 0
\(22\) −2.08029 2.08029i −0.443519 0.443519i
\(23\) 0.534176 0.534176i 0.111383 0.111383i −0.649218 0.760602i \(-0.724904\pi\)
0.760602 + 0.649218i \(0.224904\pi\)
\(24\) 0 0
\(25\) −2.85136 4.10728i −0.570272 0.821456i
\(26\) 3.96267i 0.777143i
\(27\) 0 0
\(28\) 3.64535 0.869810i 0.688906 0.164379i
\(29\) 2.77107i 0.514576i −0.966335 0.257288i \(-0.917171\pi\)
0.966335 0.257288i \(-0.0828288\pi\)
\(30\) 0 0
\(31\) 2.39674i 0.430467i 0.976563 + 0.215233i \(0.0690512\pi\)
−0.976563 + 0.215233i \(0.930949\pi\)
\(32\) 4.14420 + 4.14420i 0.732598 + 0.732598i
\(33\) 0 0
\(34\) −1.60970 −0.276062
\(35\) −5.73544 1.45077i −0.969466 0.245224i
\(36\) 0 0
\(37\) 6.18757 + 6.18757i 1.01723 + 1.01723i 0.999849 + 0.0173805i \(0.00553267\pi\)
0.0173805 + 0.999849i \(0.494467\pi\)
\(38\) 0.0376844 + 0.0376844i 0.00611321 + 0.00611321i
\(39\) 0 0
\(40\) −1.74360 5.56908i −0.275687 0.880549i
\(41\) 8.68077i 1.35571i 0.735196 + 0.677854i \(0.237090\pi\)
−0.735196 + 0.677854i \(0.762910\pi\)
\(42\) 0 0
\(43\) −2.77107 + 2.77107i −0.422585 + 0.422585i −0.886093 0.463508i \(-0.846591\pi\)
0.463508 + 0.886093i \(0.346591\pi\)
\(44\) 5.45542i 0.822435i
\(45\) 0 0
\(46\) −0.577063 −0.0850834
\(47\) 5.49042 5.49042i 0.800860 0.800860i −0.182370 0.983230i \(-0.558377\pi\)
0.983230 + 0.182370i \(0.0583768\pi\)
\(48\) 0 0
\(49\) −6.24586 + 3.16057i −0.892266 + 0.451510i
\(50\) −0.678376 + 3.75866i −0.0959368 + 0.531555i
\(51\) 0 0
\(52\) 5.19592 5.19592i 0.720544 0.720544i
\(53\) −6.13823 + 6.13823i −0.843151 + 0.843151i −0.989267 0.146116i \(-0.953323\pi\)
0.146116 + 0.989267i \(0.453323\pi\)
\(54\) 0 0
\(55\) −3.99191 + 7.63083i −0.538269 + 1.02894i
\(56\) −5.88231 3.61595i −0.786057 0.483202i
\(57\) 0 0
\(58\) −1.49678 + 1.49678i −0.196536 + 0.196536i
\(59\) −6.97440 −0.907990 −0.453995 0.891004i \(-0.650002\pi\)
−0.453995 + 0.891004i \(0.650002\pi\)
\(60\) 0 0
\(61\) 14.3107i 1.83230i −0.400835 0.916150i \(-0.631280\pi\)
0.400835 0.916150i \(-0.368720\pi\)
\(62\) 1.29458 1.29458i 0.164412 0.164412i
\(63\) 0 0
\(64\) 2.79807i 0.349758i
\(65\) −11.0699 + 3.46582i −1.37305 + 0.429883i
\(66\) 0 0
\(67\) 0.416491 + 0.416491i 0.0508824 + 0.0508824i 0.732090 0.681208i \(-0.238545\pi\)
−0.681208 + 0.732090i \(0.738545\pi\)
\(68\) −2.11067 2.11067i −0.255957 0.255957i
\(69\) 0 0
\(70\) 2.31434 + 3.88158i 0.276616 + 0.463938i
\(71\) 8.12783 0.964595 0.482298 0.876007i \(-0.339802\pi\)
0.482298 + 0.876007i \(0.339802\pi\)
\(72\) 0 0
\(73\) −9.55210 9.55210i −1.11799 1.11799i −0.992036 0.125953i \(-0.959801\pi\)
−0.125953 0.992036i \(-0.540199\pi\)
\(74\) 6.68434i 0.777039i
\(75\) 0 0
\(76\) 0.0988248i 0.0113360i
\(77\) 2.36497 + 9.91150i 0.269513 + 1.12952i
\(78\) 0 0
\(79\) 9.86329i 1.10971i −0.831948 0.554854i \(-0.812774\pi\)
0.831948 0.554854i \(-0.187226\pi\)
\(80\) 0.870061 1.66319i 0.0972758 0.185950i
\(81\) 0 0
\(82\) 4.68886 4.68886i 0.517798 0.517798i
\(83\) 1.63570 + 1.63570i 0.179541 + 0.179541i 0.791156 0.611615i \(-0.209480\pi\)
−0.611615 + 0.791156i \(0.709480\pi\)
\(84\) 0 0
\(85\) 1.40788 + 4.49678i 0.152706 + 0.487744i
\(86\) 2.99355 0.322803
\(87\) 0 0
\(88\) −7.10728 + 7.10728i −0.757638 + 0.757638i
\(89\) −5.05313 −0.535631 −0.267815 0.963470i \(-0.586302\pi\)
−0.267815 + 0.963470i \(0.586302\pi\)
\(90\) 0 0
\(91\) −7.18757 + 11.6925i −0.753462 + 1.22571i
\(92\) −0.756656 0.756656i −0.0788868 0.0788868i
\(93\) 0 0
\(94\) −5.93123 −0.611759
\(95\) 0.0723134 0.138232i 0.00741920 0.0141823i
\(96\) 0 0
\(97\) −6.85851 + 6.85851i −0.696376 + 0.696376i −0.963627 0.267251i \(-0.913885\pi\)
0.267251 + 0.963627i \(0.413885\pi\)
\(98\) 5.08082 + 1.66650i 0.513240 + 0.168342i
\(99\) 0 0
\(100\) −5.81792 + 4.03893i −0.581792 + 0.403893i
\(101\) 19.1953i 1.91000i −0.296605 0.955000i \(-0.595855\pi\)
0.296605 0.955000i \(-0.404145\pi\)
\(102\) 0 0
\(103\) −2.33825 2.33825i −0.230394 0.230394i 0.582463 0.812857i \(-0.302089\pi\)
−0.812857 + 0.582463i \(0.802089\pi\)
\(104\) −13.5384 −1.32755
\(105\) 0 0
\(106\) 6.63105 0.644064
\(107\) 6.39747 + 6.39747i 0.618467 + 0.618467i 0.945138 0.326671i \(-0.105927\pi\)
−0.326671 + 0.945138i \(0.605927\pi\)
\(108\) 0 0
\(109\) 2.16057i 0.206945i −0.994632 0.103473i \(-0.967005\pi\)
0.994632 0.103473i \(-0.0329954\pi\)
\(110\) 6.27794 1.96554i 0.598578 0.187407i
\(111\) 0 0
\(112\) −0.515459 2.16027i −0.0487063 0.204126i
\(113\) 4.13823 4.13823i 0.389292 0.389292i −0.485143 0.874435i \(-0.661232\pi\)
0.874435 + 0.485143i \(0.161232\pi\)
\(114\) 0 0
\(115\) 0.504711 + 1.61205i 0.0470645 + 0.150325i
\(116\) −3.92520 −0.364446
\(117\) 0 0
\(118\) 3.76718 + 3.76718i 0.346797 + 0.346797i
\(119\) 4.74970 + 2.91971i 0.435404 + 0.267650i
\(120\) 0 0
\(121\) 3.83298 0.348453
\(122\) −7.72984 + 7.72984i −0.699827 + 0.699827i
\(123\) 0 0
\(124\) 3.39496 0.304876
\(125\) 11.0933 1.39233i 0.992215 0.124533i
\(126\) 0 0
\(127\) −4.83298 4.83298i −0.428858 0.428858i 0.459381 0.888239i \(-0.348071\pi\)
−0.888239 + 0.459381i \(0.848071\pi\)
\(128\) 6.77704 6.77704i 0.599011 0.599011i
\(129\) 0 0
\(130\) 7.85136 + 4.10728i 0.688610 + 0.360232i
\(131\) 0.647499i 0.0565722i 0.999600 + 0.0282861i \(0.00900495\pi\)
−0.999600 + 0.0282861i \(0.990995\pi\)
\(132\) 0 0
\(133\) −0.0428413 0.179547i −0.00371481 0.0155687i
\(134\) 0.449929i 0.0388680i
\(135\) 0 0
\(136\) 5.49954i 0.471581i
\(137\) −10.2369 10.2369i −0.874597 0.874597i 0.118372 0.992969i \(-0.462232\pi\)
−0.992969 + 0.118372i \(0.962232\pi\)
\(138\) 0 0
\(139\) 22.1663 1.88012 0.940060 0.341009i \(-0.110769\pi\)
0.940060 + 0.341009i \(0.110769\pi\)
\(140\) −2.05500 + 8.12420i −0.173679 + 0.686620i
\(141\) 0 0
\(142\) −4.39019 4.39019i −0.368417 0.368417i
\(143\) 14.1274 + 14.1274i 1.18139 + 1.18139i
\(144\) 0 0
\(145\) 5.49042 + 2.87220i 0.455955 + 0.238523i
\(146\) 10.3190i 0.854007i
\(147\) 0 0
\(148\) 8.76463 8.76463i 0.720448 0.720448i
\(149\) 11.0475i 0.905050i 0.891752 + 0.452525i \(0.149477\pi\)
−0.891752 + 0.452525i \(0.850523\pi\)
\(150\) 0 0
\(151\) 18.3990 1.49729 0.748645 0.662972i \(-0.230705\pi\)
0.748645 + 0.662972i \(0.230705\pi\)
\(152\) 0.128748 0.128748i 0.0104429 0.0104429i
\(153\) 0 0
\(154\) 4.07621 6.63105i 0.328470 0.534345i
\(155\) −4.74873 2.48420i −0.381428 0.199536i
\(156\) 0 0
\(157\) 1.04994 1.04994i 0.0837946 0.0837946i −0.663967 0.747762i \(-0.731129\pi\)
0.747762 + 0.663967i \(0.231129\pi\)
\(158\) −5.32759 + 5.32759i −0.423840 + 0.423840i
\(159\) 0 0
\(160\) −12.5065 + 3.91560i −0.988724 + 0.309555i
\(161\) 1.70272 + 1.04669i 0.134193 + 0.0824907i
\(162\) 0 0
\(163\) 5.50539 5.50539i 0.431215 0.431215i −0.457826 0.889042i \(-0.651372\pi\)
0.889042 + 0.457826i \(0.151372\pi\)
\(164\) 12.2962 0.960174
\(165\) 0 0
\(166\) 1.76702i 0.137147i
\(167\) 1.88968 1.88968i 0.146228 0.146228i −0.630203 0.776431i \(-0.717028\pi\)
0.776431 + 0.630203i \(0.217028\pi\)
\(168\) 0 0
\(169\) 13.9108i 1.07006i
\(170\) 1.66845 3.18936i 0.127964 0.244613i
\(171\) 0 0
\(172\) 3.92520 + 3.92520i 0.299294 + 0.299294i
\(173\) −4.90751 4.90751i −0.373111 0.373111i 0.495498 0.868609i \(-0.334986\pi\)
−0.868609 + 0.495498i \(0.834986\pi\)
\(174\) 0 0
\(175\) 8.81920 9.86011i 0.666669 0.745354i
\(176\) −3.23294 −0.243692
\(177\) 0 0
\(178\) 2.72941 + 2.72941i 0.204578 + 0.204578i
\(179\) 18.5857i 1.38916i −0.719416 0.694579i \(-0.755591\pi\)
0.719416 0.694579i \(-0.244409\pi\)
\(180\) 0 0
\(181\) 8.48528i 0.630706i −0.948974 0.315353i \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) 10.1979 2.43331i 0.755922 0.180369i
\(183\) 0 0
\(184\) 1.97153i 0.145343i
\(185\) −18.6730 + 5.84625i −1.37287 + 0.429825i
\(186\) 0 0
\(187\) 5.73880 5.73880i 0.419663 0.419663i
\(188\) −7.77713 7.77713i −0.567206 0.567206i
\(189\) 0 0
\(190\) −0.113725 + 0.0356057i −0.00825047 + 0.00258311i
\(191\) 5.39351 0.390261 0.195130 0.980777i \(-0.437487\pi\)
0.195130 + 0.980777i \(0.437487\pi\)
\(192\) 0 0
\(193\) −4.80599 + 4.80599i −0.345943 + 0.345943i −0.858596 0.512653i \(-0.828663\pi\)
0.512653 + 0.858596i \(0.328663\pi\)
\(194\) 7.40916 0.531946
\(195\) 0 0
\(196\) 4.47692 + 8.84720i 0.319780 + 0.631943i
\(197\) −12.6739 12.6739i −0.902981 0.902981i 0.0927124 0.995693i \(-0.470446\pi\)
−0.995693 + 0.0927124i \(0.970446\pi\)
\(198\) 0 0
\(199\) 2.67111 0.189350 0.0946750 0.995508i \(-0.469819\pi\)
0.0946750 + 0.995508i \(0.469819\pi\)
\(200\) 12.8414 + 2.31766i 0.908026 + 0.163884i
\(201\) 0 0
\(202\) −10.3682 + 10.3682i −0.729503 + 0.729503i
\(203\) 7.13138 1.70161i 0.500524 0.119429i
\(204\) 0 0
\(205\) −17.1995 8.99757i −1.20127 0.628417i
\(206\) 2.52597i 0.175993i
\(207\) 0 0
\(208\) −3.07916 3.07916i −0.213501 0.213501i
\(209\) −0.268699 −0.0185863
\(210\) 0 0
\(211\) −12.0239 −0.827757 −0.413879 0.910332i \(-0.635826\pi\)
−0.413879 + 0.910332i \(0.635826\pi\)
\(212\) 8.69475 + 8.69475i 0.597158 + 0.597158i
\(213\) 0 0
\(214\) 6.91110i 0.472433i
\(215\) −2.61822 8.36262i −0.178561 0.570326i
\(216\) 0 0
\(217\) −6.16802 + 1.47174i −0.418712 + 0.0999082i
\(218\) −1.16702 + 1.16702i −0.0790405 + 0.0790405i
\(219\) 0 0
\(220\) 10.8090 + 5.65451i 0.728742 + 0.381227i
\(221\) 10.9316 0.735342
\(222\) 0 0
\(223\) 11.6925 + 11.6925i 0.782988 + 0.782988i 0.980334 0.197346i \(-0.0632321\pi\)
−0.197346 + 0.980334i \(0.563232\pi\)
\(224\) −8.12033 + 13.2099i −0.542563 + 0.882624i
\(225\) 0 0
\(226\) −4.47048 −0.297372
\(227\) 1.10518 1.10518i 0.0733535 0.0733535i −0.669478 0.742832i \(-0.733482\pi\)
0.742832 + 0.669478i \(0.233482\pi\)
\(228\) 0 0
\(229\) −7.83309 −0.517625 −0.258812 0.965928i \(-0.583331\pi\)
−0.258812 + 0.965928i \(0.583331\pi\)
\(230\) 0.598123 1.14335i 0.0394390 0.0753906i
\(231\) 0 0
\(232\) 5.11372 + 5.11372i 0.335732 + 0.335732i
\(233\) −1.00797 + 1.00797i −0.0660345 + 0.0660345i −0.739353 0.673318i \(-0.764868\pi\)
0.673318 + 0.739353i \(0.264868\pi\)
\(234\) 0 0
\(235\) 5.18757 + 16.5691i 0.338399 + 1.08085i
\(236\) 9.87918i 0.643080i
\(237\) 0 0
\(238\) −0.988454 4.14258i −0.0640720 0.268524i
\(239\) 20.2805i 1.31183i 0.754833 + 0.655917i \(0.227718\pi\)
−0.754833 + 0.655917i \(0.772282\pi\)
\(240\) 0 0
\(241\) 2.76994i 0.178427i −0.996013 0.0892136i \(-0.971565\pi\)
0.996013 0.0892136i \(-0.0284354\pi\)
\(242\) −2.07036 2.07036i −0.133088 0.133088i
\(243\) 0 0
\(244\) −20.2710 −1.29772
\(245\) 0.211650 15.6510i 0.0135218 0.999909i
\(246\) 0 0
\(247\) −0.255918 0.255918i −0.0162837 0.0162837i
\(248\) −4.42292 4.42292i −0.280856 0.280856i
\(249\) 0 0
\(250\) −6.74403 5.23992i −0.426530 0.331401i
\(251\) 6.09982i 0.385017i −0.981295 0.192509i \(-0.938338\pi\)
0.981295 0.192509i \(-0.0616623\pi\)
\(252\) 0 0
\(253\) 2.05731 2.05731i 0.129342 0.129342i
\(254\) 5.22100i 0.327595i
\(255\) 0 0
\(256\) −12.9173 −0.807330
\(257\) −2.01843 + 2.01843i −0.125906 + 0.125906i −0.767252 0.641346i \(-0.778376\pi\)
0.641346 + 0.767252i \(0.278376\pi\)
\(258\) 0 0
\(259\) −12.1242 + 19.7233i −0.753361 + 1.22554i
\(260\) 4.90931 + 15.6804i 0.304462 + 0.972456i
\(261\) 0 0
\(262\) 0.349742 0.349742i 0.0216071 0.0216071i
\(263\) −16.7686 + 16.7686i −1.03400 + 1.03400i −0.0345941 + 0.999401i \(0.511014\pi\)
−0.999401 + 0.0345941i \(0.988986\pi\)
\(264\) 0 0
\(265\) −5.79964 18.5241i −0.356269 1.13793i
\(266\) −0.0738405 + 0.120121i −0.00452745 + 0.00736511i
\(267\) 0 0
\(268\) 0.589955 0.589955i 0.0360372 0.0360372i
\(269\) 24.7351 1.50813 0.754064 0.656801i \(-0.228091\pi\)
0.754064 + 0.656801i \(0.228091\pi\)
\(270\) 0 0
\(271\) 4.13470i 0.251165i −0.992083 0.125583i \(-0.959920\pi\)
0.992083 0.125583i \(-0.0400800\pi\)
\(272\) −1.25081 + 1.25081i −0.0758413 + 0.0758413i
\(273\) 0 0
\(274\) 11.0588i 0.668085i
\(275\) −10.9816 15.8186i −0.662217 0.953898i
\(276\) 0 0
\(277\) −12.1128 12.1128i −0.727786 0.727786i 0.242393 0.970178i \(-0.422068\pi\)
−0.970178 + 0.242393i \(0.922068\pi\)
\(278\) −11.9730 11.9730i −0.718091 0.718091i
\(279\) 0 0
\(280\) 13.2614 7.90691i 0.792519 0.472528i
\(281\) −5.25279 −0.313355 −0.156678 0.987650i \(-0.550078\pi\)
−0.156678 + 0.987650i \(0.550078\pi\)
\(282\) 0 0
\(283\) 1.66729 + 1.66729i 0.0991101 + 0.0991101i 0.754923 0.655813i \(-0.227674\pi\)
−0.655813 + 0.754923i \(0.727674\pi\)
\(284\) 11.5130i 0.683170i
\(285\) 0 0
\(286\) 15.2617i 0.902441i
\(287\) −22.3400 + 5.33051i −1.31869 + 0.314650i
\(288\) 0 0
\(289\) 12.5594i 0.738787i
\(290\) −1.41421 4.51701i −0.0830455 0.265248i
\(291\) 0 0
\(292\) −13.5305 + 13.5305i −0.791810 + 0.791810i
\(293\) −15.2556 15.2556i −0.891240 0.891240i 0.103400 0.994640i \(-0.467028\pi\)
−0.994640 + 0.103400i \(0.967028\pi\)
\(294\) 0 0
\(295\) 7.22893 13.8186i 0.420884 0.804551i
\(296\) −22.8370 −1.32737
\(297\) 0 0
\(298\) 5.96725 5.96725i 0.345674 0.345674i
\(299\) 3.91889 0.226635
\(300\) 0 0
\(301\) −8.83298 5.42977i −0.509125 0.312967i
\(302\) −9.93809 9.93809i −0.571873 0.571873i
\(303\) 0 0
\(304\) 0.0585646 0.00335891
\(305\) 28.3543 + 14.8330i 1.62356 + 0.849334i
\(306\) 0 0
\(307\) 14.6198 14.6198i 0.834394 0.834394i −0.153721 0.988114i \(-0.549126\pi\)
0.988114 + 0.153721i \(0.0491256\pi\)
\(308\) 14.0395 3.34995i 0.799977 0.190881i
\(309\) 0 0
\(310\) 1.22317 + 3.90682i 0.0694714 + 0.221893i
\(311\) 2.86218i 0.162299i 0.996702 + 0.0811497i \(0.0258592\pi\)
−0.996702 + 0.0811497i \(0.974141\pi\)
\(312\) 0 0
\(313\) 9.41824 + 9.41824i 0.532350 + 0.532350i 0.921271 0.388921i \(-0.127152\pi\)
−0.388921 + 0.921271i \(0.627152\pi\)
\(314\) −1.13424 −0.0640088
\(315\) 0 0
\(316\) −13.9713 −0.785945
\(317\) −7.38310 7.38310i −0.414676 0.414676i 0.468688 0.883364i \(-0.344727\pi\)
−0.883364 + 0.468688i \(0.844727\pi\)
\(318\) 0 0
\(319\) 10.6724i 0.597540i
\(320\) 5.54390 + 2.90018i 0.309914 + 0.162125i
\(321\) 0 0
\(322\) −0.354351 1.48508i −0.0197472 0.0827600i
\(323\) −0.103958 + 0.103958i −0.00578440 + 0.00578440i
\(324\) 0 0
\(325\) 4.60691 25.5254i 0.255545 1.41590i
\(326\) −5.94740 −0.329396
\(327\) 0 0
\(328\) −16.0194 16.0194i −0.884526 0.884526i
\(329\) 17.5011 + 10.7582i 0.964866 + 0.593118i
\(330\) 0 0
\(331\) 23.6200 1.29827 0.649136 0.760672i \(-0.275130\pi\)
0.649136 + 0.760672i \(0.275130\pi\)
\(332\) 2.31695 2.31695i 0.127159 0.127159i
\(333\) 0 0
\(334\) −2.04139 −0.111700
\(335\) −1.25690 + 0.393517i −0.0686716 + 0.0215001i
\(336\) 0 0
\(337\) −4.93809 4.93809i −0.268995 0.268995i 0.559700 0.828695i \(-0.310916\pi\)
−0.828695 + 0.559700i \(0.810916\pi\)
\(338\) 7.51384 7.51384i 0.408699 0.408699i
\(339\) 0 0
\(340\) 6.36964 1.99425i 0.345442 0.108153i
\(341\) 9.23070i 0.499870i
\(342\) 0 0
\(343\) −11.9691 14.1330i −0.646270 0.763109i
\(344\) 10.2274i 0.551427i
\(345\) 0 0
\(346\) 5.30151i 0.285011i
\(347\) −5.83694 5.83694i −0.313343 0.313343i 0.532860 0.846203i \(-0.321117\pi\)
−0.846203 + 0.532860i \(0.821117\pi\)
\(348\) 0 0
\(349\) 16.9121 0.905282 0.452641 0.891693i \(-0.350482\pi\)
0.452641 + 0.891693i \(0.350482\pi\)
\(350\) −10.0895 + 0.562240i −0.539306 + 0.0300530i
\(351\) 0 0
\(352\) 15.9608 + 15.9608i 0.850714 + 0.850714i
\(353\) −11.1265 11.1265i −0.592202 0.592202i 0.346024 0.938226i \(-0.387532\pi\)
−0.938226 + 0.346024i \(0.887532\pi\)
\(354\) 0 0
\(355\) −8.42444 + 16.1039i −0.447123 + 0.854708i
\(356\) 7.15771i 0.379358i
\(357\) 0 0
\(358\) −10.0389 + 10.0389i −0.530574 + 0.530574i
\(359\) 8.14864i 0.430069i 0.976606 + 0.215034i \(0.0689864\pi\)
−0.976606 + 0.215034i \(0.931014\pi\)
\(360\) 0 0
\(361\) −18.9951 −0.999744
\(362\) −4.58327 + 4.58327i −0.240891 + 0.240891i
\(363\) 0 0
\(364\) 16.5623 + 10.1811i 0.868102 + 0.533636i
\(365\) 28.8266 9.02520i 1.50885 0.472401i
\(366\) 0 0
\(367\) −14.7480 + 14.7480i −0.769840 + 0.769840i −0.978078 0.208238i \(-0.933227\pi\)
0.208238 + 0.978078i \(0.433227\pi\)
\(368\) −0.448402 + 0.448402i −0.0233746 + 0.0233746i
\(369\) 0 0
\(370\) 13.2439 + 6.92828i 0.688518 + 0.360184i
\(371\) −19.5660 12.0275i −1.01582 0.624438i
\(372\) 0 0
\(373\) 1.49461 1.49461i 0.0773880 0.0773880i −0.667353 0.744741i \(-0.732573\pi\)
0.744741 + 0.667353i \(0.232573\pi\)
\(374\) −6.19955 −0.320571
\(375\) 0 0
\(376\) 20.2640i 1.04504i
\(377\) 10.1648 10.1648i 0.523511 0.523511i
\(378\) 0 0
\(379\) 18.7135i 0.961248i −0.876927 0.480624i \(-0.840410\pi\)
0.876927 0.480624i \(-0.159590\pi\)
\(380\) −0.195805 0.102431i −0.0100446 0.00525461i
\(381\) 0 0
\(382\) −2.91327 2.91327i −0.149056 0.149056i
\(383\) 20.9354 + 20.9354i 1.06975 + 1.06975i 0.997378 + 0.0723706i \(0.0230564\pi\)
0.0723706 + 0.997378i \(0.476944\pi\)
\(384\) 0 0
\(385\) −22.0893 5.58742i −1.12577 0.284761i
\(386\) 5.19184 0.264258
\(387\) 0 0
\(388\) 9.71502 + 9.71502i 0.493205 + 0.493205i
\(389\) 25.6611i 1.30107i 0.759477 + 0.650535i \(0.225455\pi\)
−0.759477 + 0.650535i \(0.774545\pi\)
\(390\) 0 0
\(391\) 1.59192i 0.0805069i
\(392\) 5.69357 17.3586i 0.287569 0.876741i
\(393\) 0 0
\(394\) 13.6915i 0.689767i
\(395\) 19.5425 + 10.2232i 0.983288 + 0.514387i
\(396\) 0 0
\(397\) −6.73585 + 6.73585i −0.338063 + 0.338063i −0.855638 0.517575i \(-0.826835\pi\)
0.517575 + 0.855638i \(0.326835\pi\)
\(398\) −1.44278 1.44278i −0.0723201 0.0723201i
\(399\) 0 0
\(400\) 2.39351 + 3.44776i 0.119676 + 0.172388i
\(401\) −14.7503 −0.736593 −0.368296 0.929708i \(-0.620059\pi\)
−0.368296 + 0.929708i \(0.620059\pi\)
\(402\) 0 0
\(403\) −8.79162 + 8.79162i −0.437942 + 0.437942i
\(404\) −27.1899 −1.35275
\(405\) 0 0
\(406\) −4.77107 2.93285i −0.236784 0.145555i
\(407\) 23.8305 + 23.8305i 1.18124 + 1.18124i
\(408\) 0 0
\(409\) −10.5604 −0.522180 −0.261090 0.965315i \(-0.584082\pi\)
−0.261090 + 0.965315i \(0.584082\pi\)
\(410\) 4.43022 + 14.1502i 0.218793 + 0.698827i
\(411\) 0 0
\(412\) −3.31210 + 3.31210i −0.163176 + 0.163176i
\(413\) −4.28270 17.9487i −0.210738 0.883196i
\(414\) 0 0
\(415\) −4.93625 + 1.54547i −0.242311 + 0.0758641i
\(416\) 30.4032i 1.49064i
\(417\) 0 0
\(418\) 0.145136 + 0.145136i 0.00709884 + 0.00709884i
\(419\) 15.5472 0.759532 0.379766 0.925083i \(-0.376004\pi\)
0.379766 + 0.925083i \(0.376004\pi\)
\(420\) 0 0
\(421\) 3.29886 0.160776 0.0803882 0.996764i \(-0.474384\pi\)
0.0803882 + 0.996764i \(0.474384\pi\)
\(422\) 6.49461 + 6.49461i 0.316153 + 0.316153i
\(423\) 0 0
\(424\) 22.6549i 1.10022i
\(425\) −10.3689 1.87141i −0.502964 0.0907766i
\(426\) 0 0
\(427\) 36.8287 8.78764i 1.78227 0.425264i
\(428\) 9.06196 9.06196i 0.438026 0.438026i
\(429\) 0 0
\(430\) −3.10280 + 5.93123i −0.149630 + 0.286029i
\(431\) 14.0911 0.678743 0.339371 0.940652i \(-0.389786\pi\)
0.339371 + 0.940652i \(0.389786\pi\)
\(432\) 0 0
\(433\) 1.72650 + 1.72650i 0.0829702 + 0.0829702i 0.747374 0.664404i \(-0.231314\pi\)
−0.664404 + 0.747374i \(0.731314\pi\)
\(434\) 4.12656 + 2.53666i 0.198081 + 0.121764i
\(435\) 0 0
\(436\) −3.06043 −0.146568
\(437\) −0.0372681 + 0.0372681i −0.00178277 + 0.00178277i
\(438\) 0 0
\(439\) 27.1172 1.29423 0.647116 0.762392i \(-0.275975\pi\)
0.647116 + 0.762392i \(0.275975\pi\)
\(440\) −6.71524 21.4485i −0.320136 1.02252i
\(441\) 0 0
\(442\) −5.90465 5.90465i −0.280856 0.280856i
\(443\) 24.1502 24.1502i 1.14741 1.14741i 0.160349 0.987060i \(-0.448738\pi\)
0.987060 0.160349i \(-0.0512618\pi\)
\(444\) 0 0
\(445\) 5.23754 10.0119i 0.248283 0.474611i
\(446\) 12.6313i 0.598107i
\(447\) 0 0
\(448\) 7.20084 1.71818i 0.340208 0.0811764i
\(449\) 9.80267i 0.462617i −0.972881 0.231308i \(-0.925699\pi\)
0.972881 0.231308i \(-0.0743006\pi\)
\(450\) 0 0
\(451\) 33.4328i 1.57429i
\(452\) −5.86177 5.86177i −0.275714 0.275714i
\(453\) 0 0
\(454\) −1.19391 −0.0560331
\(455\) −15.7169 26.3602i −0.736819 1.23578i
\(456\) 0 0
\(457\) 0.550071 + 0.550071i 0.0257312 + 0.0257312i 0.719855 0.694124i \(-0.244208\pi\)
−0.694124 + 0.719855i \(0.744208\pi\)
\(458\) 4.23099 + 4.23099i 0.197701 + 0.197701i
\(459\) 0 0
\(460\) 2.28346 0.714918i 0.106467 0.0333332i
\(461\) 0.831786i 0.0387401i 0.999812 + 0.0193701i \(0.00616607\pi\)
−0.999812 + 0.0193701i \(0.993834\pi\)
\(462\) 0 0
\(463\) 5.45140 5.45140i 0.253348 0.253348i −0.568994 0.822342i \(-0.692667\pi\)
0.822342 + 0.568994i \(0.192667\pi\)
\(464\) 2.32612i 0.107987i
\(465\) 0 0
\(466\) 1.08890 0.0504423
\(467\) −23.2827 + 23.2827i −1.07740 + 1.07740i −0.0806551 + 0.996742i \(0.525701\pi\)
−0.996742 + 0.0806551i \(0.974299\pi\)
\(468\) 0 0
\(469\) −0.816091 + 1.32759i −0.0376836 + 0.0613025i
\(470\) 6.14768 11.7517i 0.283571 0.542067i
\(471\) 0 0
\(472\) 12.8705 12.8705i 0.592414 0.592414i
\(473\) −10.6724 + 10.6724i −0.490718 + 0.490718i
\(474\) 0 0
\(475\) 0.198932 + 0.286554i 0.00912762 + 0.0131480i
\(476\) 4.13575 6.72791i 0.189562 0.308373i
\(477\) 0 0
\(478\) 10.9544 10.9544i 0.501041 0.501041i
\(479\) −40.4319 −1.84738 −0.923691 0.383138i \(-0.874843\pi\)
−0.923691 + 0.383138i \(0.874843\pi\)
\(480\) 0 0
\(481\) 45.3940i 2.06979i
\(482\) −1.49616 + 1.49616i −0.0681483 + 0.0681483i
\(483\) 0 0
\(484\) 5.42938i 0.246790i
\(485\) −6.48019 20.6978i −0.294250 0.939839i
\(486\) 0 0
\(487\) −7.22893 7.22893i −0.327574 0.327574i 0.524089 0.851663i \(-0.324406\pi\)
−0.851663 + 0.524089i \(0.824406\pi\)
\(488\) 26.4089 + 26.4089i 1.19548 + 1.19548i
\(489\) 0 0
\(490\) −8.56813 + 8.33948i −0.387068 + 0.376739i
\(491\) −20.1040 −0.907279 −0.453639 0.891185i \(-0.649875\pi\)
−0.453639 + 0.891185i \(0.649875\pi\)
\(492\) 0 0
\(493\) −4.12910 4.12910i −0.185965 0.185965i
\(494\) 0.276465i 0.0124387i
\(495\) 0 0
\(496\) 2.01189i 0.0903364i
\(497\) 4.99097 + 20.9170i 0.223876 + 0.938256i
\(498\) 0 0
\(499\) 15.4227i 0.690414i −0.938527 0.345207i \(-0.887809\pi\)
0.938527 0.345207i \(-0.112191\pi\)
\(500\) −1.97222 15.7136i −0.0882002 0.702732i
\(501\) 0 0
\(502\) −3.29478 + 3.29478i −0.147053 + 0.147053i
\(503\) 25.9985 + 25.9985i 1.15922 + 1.15922i 0.984644 + 0.174573i \(0.0558546\pi\)
0.174573 + 0.984644i \(0.444145\pi\)
\(504\) 0 0
\(505\) 38.0322 + 19.8958i 1.69241 + 0.885350i
\(506\) −2.22248 −0.0988013
\(507\) 0 0
\(508\) −6.84587 + 6.84587i −0.303737 + 0.303737i
\(509\) 37.1271 1.64563 0.822816 0.568309i \(-0.192402\pi\)
0.822816 + 0.568309i \(0.192402\pi\)
\(510\) 0 0
\(511\) 18.7168 30.4479i 0.827983 1.34694i
\(512\) −6.57690 6.57690i −0.290661 0.290661i
\(513\) 0 0
\(514\) 2.18048 0.0961768
\(515\) 7.05642 2.20927i 0.310943 0.0973519i
\(516\) 0 0
\(517\) 21.1456 21.1456i 0.929982 0.929982i
\(518\) 17.2022 4.10459i 0.755821 0.180345i
\(519\) 0 0
\(520\) 14.0325 26.8241i 0.615365 1.17631i
\(521\) 2.59132i 0.113528i −0.998388 0.0567639i \(-0.981922\pi\)
0.998388 0.0567639i \(-0.0180782\pi\)
\(522\) 0 0
\(523\) 6.08854 + 6.08854i 0.266233 + 0.266233i 0.827581 0.561347i \(-0.189717\pi\)
−0.561347 + 0.827581i \(0.689717\pi\)
\(524\) 0.917176 0.0400670
\(525\) 0 0
\(526\) 18.1149 0.789846
\(527\) 3.57131 + 3.57131i 0.155569 + 0.155569i
\(528\) 0 0
\(529\) 22.4293i 0.975187i
\(530\) −6.87304 + 13.1383i −0.298546 + 0.570692i
\(531\) 0 0
\(532\) −0.254326 + 0.0606843i −0.0110264 + 0.00263100i
\(533\) −31.8425 + 31.8425i −1.37925 + 1.37925i
\(534\) 0 0
\(535\) −19.3065 + 6.04458i −0.834691 + 0.261330i
\(536\) −1.53718 −0.0663960
\(537\) 0 0
\(538\) −13.3605 13.3605i −0.576013 0.576013i
\(539\) −24.0551 + 12.1725i −1.03613 + 0.524307i
\(540\) 0 0
\(541\) −33.4638 −1.43872 −0.719360 0.694638i \(-0.755565\pi\)
−0.719360 + 0.694638i \(0.755565\pi\)
\(542\) −2.23333 + 2.23333i −0.0959297 + 0.0959297i
\(543\) 0 0
\(544\) 12.3503 0.529515
\(545\) 4.28081 + 2.23942i 0.183370 + 0.0959262i
\(546\) 0 0
\(547\) −0.828381 0.828381i −0.0354190 0.0354190i 0.689175 0.724594i \(-0.257973\pi\)
−0.724594 + 0.689175i \(0.757973\pi\)
\(548\) −14.5005 + 14.5005i −0.619429 + 0.619429i
\(549\) 0 0
\(550\) −2.61267 + 14.4760i −0.111405 + 0.617257i
\(551\) 0.193331i 0.00823616i
\(552\) 0 0
\(553\) 25.3832 6.05665i 1.07941 0.257555i
\(554\) 13.0853i 0.555939i
\(555\) 0 0
\(556\) 31.3983i 1.33159i
\(557\) −14.7120 14.7120i −0.623366 0.623366i 0.323024 0.946391i \(-0.395300\pi\)
−0.946391 + 0.323024i \(0.895300\pi\)
\(558\) 0 0
\(559\) −20.3295 −0.859846
\(560\) 4.81449 + 1.21781i 0.203449 + 0.0514620i
\(561\) 0 0
\(562\) 2.83726 + 2.83726i 0.119683 + 0.119683i
\(563\) −23.9693 23.9693i −1.01019 1.01019i −0.999948 0.0102391i \(-0.996741\pi\)
−0.0102391 0.999948i \(-0.503259\pi\)
\(564\) 0 0
\(565\) 3.90996 + 12.4885i 0.164493 + 0.525394i
\(566\) 1.80115i 0.0757080i
\(567\) 0 0
\(568\) −14.9990 + 14.9990i −0.629346 + 0.629346i
\(569\) 15.6660i 0.656751i 0.944547 + 0.328376i \(0.106501\pi\)
−0.944547 + 0.328376i \(0.893499\pi\)
\(570\) 0 0
\(571\) 36.9887 1.54793 0.773964 0.633229i \(-0.218271\pi\)
0.773964 + 0.633229i \(0.218271\pi\)
\(572\) 20.0114 20.0114i 0.836717 0.836717i
\(573\) 0 0
\(574\) 14.9460 + 9.18757i 0.623836 + 0.383482i
\(575\) −3.71714 0.670882i −0.155015 0.0279777i
\(576\) 0 0
\(577\) −15.5587 + 15.5587i −0.647717 + 0.647717i −0.952441 0.304724i \(-0.901436\pi\)
0.304724 + 0.952441i \(0.401436\pi\)
\(578\) 6.78386 6.78386i 0.282171 0.282171i
\(579\) 0 0
\(580\) 4.06845 7.77713i 0.168933 0.322928i
\(581\) −3.20506 + 5.21389i −0.132968 + 0.216309i
\(582\) 0 0
\(583\) −23.6405 + 23.6405i −0.979091 + 0.979091i
\(584\) 35.2548 1.45885
\(585\) 0 0
\(586\) 16.4804i 0.680798i
\(587\) −15.7111 + 15.7111i −0.648468 + 0.648468i −0.952623 0.304155i \(-0.901626\pi\)
0.304155 + 0.952623i \(0.401626\pi\)
\(588\) 0 0
\(589\) 0.167214i 0.00688993i
\(590\) −11.3687 + 3.55938i −0.468041 + 0.146537i
\(591\) 0 0
\(592\) −5.19401 5.19401i −0.213473 0.213473i
\(593\) −1.85199 1.85199i −0.0760523 0.0760523i 0.668057 0.744110i \(-0.267126\pi\)
−0.744110 + 0.668057i \(0.767126\pi\)
\(594\) 0 0
\(595\) −10.7080 + 6.38447i −0.438984 + 0.261738i
\(596\) 15.6487 0.640997
\(597\) 0 0
\(598\) −2.11676 2.11676i −0.0865609 0.0865609i
\(599\) 47.3151i 1.93324i −0.256208 0.966622i \(-0.582473\pi\)
0.256208 0.966622i \(-0.417527\pi\)
\(600\) 0 0
\(601\) 11.0819i 0.452041i 0.974123 + 0.226021i \(0.0725717\pi\)
−0.974123 + 0.226021i \(0.927428\pi\)
\(602\) 1.83822 + 7.70393i 0.0749203 + 0.313989i
\(603\) 0 0
\(604\) 26.0620i 1.06045i
\(605\) −3.97286 + 7.59441i −0.161520 + 0.308757i
\(606\) 0 0
\(607\) −7.54653 + 7.54653i −0.306304 + 0.306304i −0.843474 0.537170i \(-0.819493\pi\)
0.537170 + 0.843474i \(0.319493\pi\)
\(608\) −0.289130 0.289130i −0.0117258 0.0117258i
\(609\) 0 0
\(610\) −7.30346 23.3273i −0.295708 0.944496i
\(611\) 40.2795 1.62953
\(612\) 0 0
\(613\) −2.62487 + 2.62487i −0.106017 + 0.106017i −0.758126 0.652108i \(-0.773885\pi\)
0.652108 + 0.758126i \(0.273885\pi\)
\(614\) −15.7935 −0.637375
\(615\) 0 0
\(616\) −22.6549 13.9263i −0.912793 0.561108i
\(617\) −11.3212 11.3212i −0.455774 0.455774i 0.441491 0.897266i \(-0.354450\pi\)
−0.897266 + 0.441491i \(0.854450\pi\)
\(618\) 0 0
\(619\) 9.06771 0.364462 0.182231 0.983256i \(-0.441668\pi\)
0.182231 + 0.983256i \(0.441668\pi\)
\(620\) −3.51885 + 6.72654i −0.141320 + 0.270144i
\(621\) 0 0
\(622\) 1.54599 1.54599i 0.0619884 0.0619884i
\(623\) −3.10292 13.0043i −0.124316 0.521005i
\(624\) 0 0
\(625\) −8.73948 + 23.4227i −0.349579 + 0.936907i
\(626\) 10.1744i 0.406651i
\(627\) 0 0
\(628\) −1.48723 1.48723i −0.0593471 0.0593471i
\(629\) 18.4398 0.735244
\(630\) 0 0
\(631\) −9.67260 −0.385060 −0.192530 0.981291i \(-0.561669\pi\)
−0.192530 + 0.981291i \(0.561669\pi\)
\(632\) 18.2017 + 18.2017i 0.724023 + 0.724023i
\(633\) 0 0
\(634\) 7.97587i 0.316762i
\(635\) 14.5851 4.56639i 0.578792 0.181212i
\(636\) 0 0
\(637\) −34.5043 11.3173i −1.36711 0.448409i
\(638\) −5.76463 + 5.76463i −0.228224 + 0.228224i
\(639\) 0 0
\(640\) 6.40321 + 20.4519i 0.253109 + 0.808434i
\(641\) 40.5847 1.60300 0.801500 0.597995i \(-0.204036\pi\)
0.801500 + 0.597995i \(0.204036\pi\)
\(642\) 0 0
\(643\) −3.89544 3.89544i −0.153621 0.153621i 0.626112 0.779733i \(-0.284645\pi\)
−0.779733 + 0.626112i \(0.784645\pi\)
\(644\) 1.48263 2.41189i 0.0584236 0.0950418i
\(645\) 0 0
\(646\) 0.112305 0.00441857
\(647\) 16.8414 16.8414i 0.662104 0.662104i −0.293772 0.955876i \(-0.594911\pi\)
0.955876 + 0.293772i \(0.0949106\pi\)
\(648\) 0 0
\(649\) −26.8609 −1.05438
\(650\) −16.2758 + 11.2990i −0.638388 + 0.443183i
\(651\) 0 0
\(652\) −7.79833 7.79833i −0.305406 0.305406i
\(653\) 22.9951 22.9951i 0.899867 0.899867i −0.0955569 0.995424i \(-0.530463\pi\)
0.995424 + 0.0955569i \(0.0304632\pi\)
\(654\) 0 0
\(655\) −1.28291 0.671128i −0.0501275 0.0262232i
\(656\) 7.28688i 0.284505i
\(657\) 0 0
\(658\) −3.64213 15.2640i −0.141985 0.595054i
\(659\) 32.7543i 1.27593i −0.770067 0.637963i \(-0.779777\pi\)
0.770067 0.637963i \(-0.220223\pi\)
\(660\) 0 0
\(661\) 32.5174i 1.26478i −0.774650 0.632391i \(-0.782074\pi\)
0.774650 0.632391i \(-0.217926\pi\)
\(662\) −12.7582 12.7582i −0.495861 0.495861i
\(663\) 0 0
\(664\) −6.03701 −0.234281
\(665\) 0.400147 + 0.101216i 0.0155170 + 0.00392499i
\(666\) 0 0
\(667\) −1.48024 1.48024i −0.0573152 0.0573152i
\(668\) −2.67671 2.67671i −0.103565 0.103565i
\(669\) 0 0
\(670\) 0.891460 + 0.466349i 0.0344401 + 0.0180166i
\(671\) 55.1158i 2.12772i
\(672\) 0 0
\(673\) −16.7534 + 16.7534i −0.645796 + 0.645796i −0.951974 0.306179i \(-0.900950\pi\)
0.306179 + 0.951974i \(0.400950\pi\)
\(674\) 5.33455i 0.205479i
\(675\) 0 0
\(676\) 19.7046 0.757868
\(677\) −6.85568 + 6.85568i −0.263485 + 0.263485i −0.826468 0.562983i \(-0.809654\pi\)
0.562983 + 0.826468i \(0.309654\pi\)
\(678\) 0 0
\(679\) −21.8620 13.4389i −0.838985 0.515737i
\(680\) −10.8964 5.70024i −0.417858 0.218594i
\(681\) 0 0
\(682\) 4.98590 4.98590i 0.190920 0.190920i
\(683\) −23.2345 + 23.2345i −0.889042 + 0.889042i −0.994431 0.105389i \(-0.966391\pi\)
0.105389 + 0.994431i \(0.466391\pi\)
\(684\) 0 0
\(685\) 30.8932 9.67222i 1.18037 0.369557i
\(686\) −1.16881 + 14.0988i −0.0446255 + 0.538297i
\(687\) 0 0
\(688\) 2.32612 2.32612i 0.0886823 0.0886823i
\(689\) −45.0321 −1.71559
\(690\) 0 0
\(691\) 42.4714i 1.61569i −0.589395 0.807845i \(-0.700634\pi\)
0.589395 0.807845i \(-0.299366\pi\)
\(692\) −6.95144 + 6.95144i −0.264254 + 0.264254i
\(693\) 0 0
\(694\) 6.30557i 0.239356i
\(695\) −22.9752 + 43.9188i −0.871500 + 1.66594i
\(696\) 0 0
\(697\) 12.9350 + 12.9350i 0.489947 + 0.489947i
\(698\) −9.13494 9.13494i −0.345763 0.345763i
\(699\) 0 0
\(700\) −13.9668 12.4923i −0.527894 0.472165i
\(701\) −17.0793 −0.645077 −0.322539 0.946556i \(-0.604536\pi\)
−0.322539 + 0.946556i \(0.604536\pi\)
\(702\) 0 0
\(703\) −0.431690 0.431690i −0.0162815 0.0162815i
\(704\) 10.7764i 0.406150i
\(705\) 0 0
\(706\) 12.0198i 0.452370i
\(707\) 49.3991 11.7870i 1.85785 0.443297i
\(708\) 0 0
\(709\) 32.6742i 1.22710i 0.789654 + 0.613552i \(0.210260\pi\)
−0.789654 + 0.613552i \(0.789740\pi\)
\(710\) 13.2488 4.14802i 0.497220 0.155673i
\(711\) 0 0
\(712\) 9.32502 9.32502i 0.349470 0.349470i
\(713\) 1.28028 + 1.28028i 0.0479469 + 0.0479469i
\(714\) 0 0
\(715\) −42.6341 + 13.3481i −1.59443 + 0.499192i
\(716\) −26.3264 −0.983865
\(717\) 0 0
\(718\) 4.40143 4.40143i 0.164260 0.164260i
\(719\) −19.3248 −0.720693 −0.360346 0.932819i \(-0.617341\pi\)
−0.360346 + 0.932819i \(0.617341\pi\)
\(720\) 0 0
\(721\) 4.58166 7.45331i 0.170630 0.277576i
\(722\) 10.2601 + 10.2601i 0.381841 + 0.381841i
\(723\) 0 0
\(724\) −12.0193 −0.446695
\(725\) −11.3816 + 7.90133i −0.422701 + 0.293448i
\(726\) 0 0
\(727\) −2.71795 + 2.71795i −0.100803 + 0.100803i −0.755710 0.654907i \(-0.772708\pi\)
0.654907 + 0.755710i \(0.272708\pi\)
\(728\) −8.31339 34.8412i −0.308115 1.29130i
\(729\) 0 0
\(730\) −20.4454 10.6956i −0.756718 0.395861i
\(731\) 8.25820i 0.305440i
\(732\) 0 0
\(733\) 2.38437 + 2.38437i 0.0880686 + 0.0880686i 0.749769 0.661700i \(-0.230165\pi\)
−0.661700 + 0.749769i \(0.730165\pi\)
\(734\) 15.9321 0.588064
\(735\) 0 0
\(736\) 4.42747 0.163199
\(737\) 1.60406 + 1.60406i 0.0590862 + 0.0590862i
\(738\) 0 0
\(739\) 4.95679i 0.182339i 0.995835 + 0.0911693i \(0.0290605\pi\)
−0.995835 + 0.0911693i \(0.970940\pi\)
\(740\) 8.28116 + 26.4501i 0.304422 + 0.972326i
\(741\) 0 0
\(742\) 4.07186 + 17.0650i 0.149483 + 0.626477i
\(743\) −15.6556 + 15.6556i −0.574347 + 0.574347i −0.933340 0.358993i \(-0.883120\pi\)
0.358993 + 0.933340i \(0.383120\pi\)
\(744\) 0 0
\(745\) −21.8889 11.4507i −0.801946 0.419521i
\(746\) −1.61461 −0.0591150
\(747\) 0 0
\(748\) −8.12896 8.12896i −0.297224 0.297224i
\(749\) −12.5355 + 20.3924i −0.458037 + 0.745120i
\(750\) 0 0
\(751\) −11.1909 −0.408361 −0.204181 0.978933i \(-0.565453\pi\)
−0.204181 + 0.978933i \(0.565453\pi\)
\(752\) −4.60881 + 4.60881i −0.168066 + 0.168066i
\(753\) 0 0
\(754\) −10.9808 −0.399899
\(755\) −19.0704 + 36.4545i −0.694045 + 1.32672i
\(756\) 0 0
\(757\) 29.4977 + 29.4977i 1.07211 + 1.07211i 0.997189 + 0.0749214i \(0.0238706\pi\)
0.0749214 + 0.997189i \(0.476129\pi\)
\(758\) −10.1080 + 10.1080i −0.367138 + 0.367138i
\(759\) 0 0
\(760\) 0.121646 + 0.388540i 0.00441258 + 0.0140938i
\(761\) 28.1175i 1.01926i 0.860395 + 0.509629i \(0.170217\pi\)
−0.860395 + 0.509629i \(0.829783\pi\)
\(762\) 0 0
\(763\) 5.56025 1.32672i 0.201294 0.0480305i
\(764\) 7.63986i 0.276400i
\(765\) 0 0
\(766\) 22.6162i 0.817157i
\(767\) −25.5832 25.5832i −0.923757 0.923757i
\(768\) 0 0
\(769\) −6.61248 −0.238452 −0.119226 0.992867i \(-0.538041\pi\)
−0.119226 + 0.992867i \(0.538041\pi\)
\(770\) 8.91335 + 14.9494i 0.321215 + 0.538738i
\(771\) 0 0
\(772\) 6.80764 + 6.80764i 0.245012 + 0.245012i
\(773\) 31.7247 + 31.7247i 1.14106 + 1.14106i 0.988257 + 0.152800i \(0.0488290\pi\)
0.152800 + 0.988257i \(0.451171\pi\)
\(774\) 0 0
\(775\) 9.84407 6.83396i 0.353609 0.245483i
\(776\) 25.3133i 0.908695i
\(777\) 0 0
\(778\) 13.8607 13.8607i 0.496929 0.496929i
\(779\) 0.605634i 0.0216991i
\(780\) 0 0
\(781\) 31.3032 1.12012
\(782\) −0.859866 + 0.859866i −0.0307487 + 0.0307487i
\(783\) 0 0
\(784\) 5.24295 2.65307i 0.187248 0.0947525i
\(785\) 0.992027 +