Properties

Label 315.2.p.e.118.3
Level 315
Weight 2
Character 315.118
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 118.3
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 \(\chi\) \(=\) 315.118
Dual form 315.2.p.e.307.3

$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.540143 + 0.540143i −0.381939 + 0.381939i −0.871800 0.489861i \(-0.837047\pi\)
0.489861 + 0.871800i \(0.337047\pi\)
\(3\) 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 0.0175187 0.999847i \(-0.494423\pi\)
0.999847 0.0175187i \(-0.00557667\pi\)
\(14\) 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 0.864326 0.502931i \(-0.167745\pi\)
−0.502931 + 0.864326i \(0.667745\pi\)
\(18\) 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 0.760602 0.649218i \(-0.224904\pi\)
−0.649218 + 0.760602i \(0.724904\pi\)
\(24\) 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 \(0.0828288\pi\)
−0.966335 + 0.257288i \(0.917171\pi\)
\(30\) 0 0
\(31\) 2.39674i 0.430467i −0.976563 0.215233i \(-0.930949\pi\)
0.976563 0.215233i \(-0.0690512\pi\)
\(32\) 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 0.0173805 0.999849i \(-0.494467\pi\)
0.999849 0.0173805i \(-0.00553267\pi\)
\(38\) 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 \(-0.762910\pi\)
0.735196 0.677854i \(-0.237090\pi\)
\(42\) 0 0
\(43\) −2.77107 2.77107i −0.422585 0.422585i 0.463508 0.886093i \(-0.346591\pi\)
−0.886093 + 0.463508i \(0.846591\pi\)
\(44\) 5.45542i 0.822435i
\(45\) 0 0
\(46\) −0.577063 −0.0850834
\(47\) 5.49042 + 5.49042i 0.800860 + 0.800860i 0.983230 0.182370i \(-0.0583768\pi\)
−0.182370 + 0.983230i \(0.558377\pi\)
\(48\) 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 0.146116 0.989267i \(-0.453323\pi\)
−0.989267 + 0.146116i \(0.953323\pi\)
\(54\) 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 \(0.368720\pi\)
−0.400835 + 0.916150i \(0.631280\pi\)
\(62\) 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 −0.681208 0.732090i \(-0.738545\pi\)
0.732090 + 0.681208i \(0.238545\pi\)
\(68\) −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 −0.125953 + 0.992036i \(0.540199\pi\)
−0.992036 + 0.125953i \(0.959801\pi\)
\(74\) 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 \(0.187226\pi\)
−0.831948 + 0.554854i \(0.812774\pi\)
\(80\) 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 −0.611615 0.791156i \(-0.709480\pi\)
0.791156 + 0.611615i \(0.209480\pi\)
\(84\) 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 0.267251 0.963627i \(-0.413885\pi\)
−0.963627 + 0.267251i \(0.913885\pi\)
\(98\) 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 \(0.404145\pi\)
−0.296605 + 0.955000i \(0.595855\pi\)
\(102\) 0 0
\(103\) −2.33825 + 2.33825i −0.230394 + 0.230394i −0.812857 0.582463i \(-0.802089\pi\)
0.582463 + 0.812857i \(0.302089\pi\)
\(104\) −13.5384 −1.32755
\(105\) 0 0
\(106\) 6.63105 0.644064
\(107\) 6.39747 6.39747i 0.618467 0.618467i −0.326671 0.945138i \(-0.605927\pi\)
0.945138 + 0.326671i \(0.105927\pi\)
\(108\) 0 0
\(109\) 2.16057i 0.206945i 0.994632 + 0.103473i \(0.0329954\pi\)
−0.994632 + 0.103473i \(0.967005\pi\)
\(110\) 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 0.874435 0.485143i \(-0.161232\pi\)
−0.485143 + 0.874435i \(0.661232\pi\)
\(114\) 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 −0.888239 0.459381i \(-0.848071\pi\)
0.459381 + 0.888239i \(0.348071\pi\)
\(128\) 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 \(-0.990995\pi\)
0.999600 0.0282861i \(-0.00900495\pi\)
\(132\) 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 −0.992969 0.118372i \(-0.962232\pi\)
0.118372 + 0.992969i \(0.462232\pi\)
\(138\) 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 \(-0.850523\pi\)
0.891752 0.452525i \(-0.149477\pi\)
\(150\) 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 0.747762 0.663967i \(-0.231129\pi\)
−0.663967 + 0.747762i \(0.731129\pi\)
\(158\) −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 0.889042 0.457826i \(-0.151372\pi\)
−0.457826 + 0.889042i \(0.651372\pi\)
\(164\) 12.2962 0.960174
\(165\) 0 0
\(166\) 1.76702i 0.137147i
\(167\) 1.88968 + 1.88968i 0.146228 + 0.146228i 0.776431 0.630203i \(-0.217028\pi\)
−0.630203 + 0.776431i \(0.717028\pi\)
\(168\) 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 −0.868609 0.495498i \(-0.834986\pi\)
0.495498 + 0.868609i \(0.334986\pi\)
\(174\) 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 \(0.244409\pi\)
−0.719416 + 0.694579i \(0.755591\pi\)
\(180\) 0 0
\(181\) 8.48528i 0.630706i 0.948974 + 0.315353i \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) 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 0.512653 0.858596i \(-0.328663\pi\)
−0.858596 + 0.512653i \(0.828663\pi\)
\(194\) 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 −0.995693 0.0927124i \(-0.970446\pi\)
0.0927124 + 0.995693i \(0.470446\pi\)
\(198\) 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 −0.197346 0.980334i \(-0.563232\pi\)
0.980334 + 0.197346i \(0.0632321\pi\)
\(224\) −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 0.742832 0.669478i \(-0.233482\pi\)
−0.669478 + 0.742832i \(0.733482\pi\)
\(228\) 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 0.673318 0.739353i \(-0.264868\pi\)
−0.739353 + 0.673318i \(0.764868\pi\)
\(234\) 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 \(-0.772282\pi\)
0.754833 0.655917i \(-0.227718\pi\)
\(240\) 0 0
\(241\) 2.76994i 0.178427i 0.996013 + 0.0892136i \(0.0284354\pi\)
−0.996013 + 0.0892136i \(0.971565\pi\)
\(242\) −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 \(0.0616623\pi\)
−0.981295 + 0.192509i \(0.938338\pi\)
\(252\) 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 0.641346 0.767252i \(-0.278376\pi\)
−0.767252 + 0.641346i \(0.778376\pi\)
\(258\) 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 −0.999401 0.0345941i \(-0.988986\pi\)
−0.0345941 0.999401i \(-0.511014\pi\)
\(264\) 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 \(0.0400800\pi\)
−0.992083 + 0.125583i \(0.959920\pi\)
\(272\) −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 −0.970178 0.242393i \(-0.922068\pi\)
0.242393 + 0.970178i \(0.422068\pi\)
\(278\) −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 −0.655813 0.754923i \(-0.727674\pi\)
0.754923 + 0.655813i \(0.227674\pi\)
\(284\) 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 −0.994640 0.103400i \(-0.967028\pi\)
0.103400 + 0.994640i \(0.467028\pi\)
\(294\) 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 0.988114 0.153721i \(-0.0491256\pi\)
−0.153721 + 0.988114i \(0.549126\pi\)
\(308\) 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 \(-0.974141\pi\)
0.996702 0.0811497i \(-0.0258592\pi\)
\(312\) 0 0
\(313\) 9.41824 9.41824i 0.532350 0.532350i −0.388921 0.921271i \(-0.627152\pi\)
0.921271 + 0.388921i \(0.127152\pi\)
\(314\) −1.13424 −0.0640088
\(315\) 0 0
\(316\) −13.9713 −0.785945
\(317\) −7.38310 + 7.38310i −0.414676 + 0.414676i −0.883364 0.468688i \(-0.844727\pi\)
0.468688 + 0.883364i \(0.344727\pi\)
\(318\) 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 −0.828695 0.559700i \(-0.810916\pi\)
0.559700 + 0.828695i \(0.310916\pi\)
\(338\) 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 −0.846203 0.532860i \(-0.821117\pi\)
0.532860 + 0.846203i \(0.321117\pi\)
\(348\) 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 −0.938226 0.346024i \(-0.887532\pi\)
0.346024 + 0.938226i \(0.387532\pi\)
\(354\) 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 \(-0.931014\pi\)
0.976606 0.215034i \(-0.0689864\pi\)
\(360\) 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 0.208238 0.978078i \(-0.433227\pi\)
−0.978078 + 0.208238i \(0.933227\pi\)
\(368\) −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 0.744741 0.667353i \(-0.232573\pi\)
−0.667353 + 0.744741i \(0.732573\pi\)
\(374\) −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 \(0.159590\pi\)
−0.876927 + 0.480624i \(0.840410\pi\)
\(380\) −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 0.0723706 0.997378i \(-0.476944\pi\)
0.997378 0.0723706i \(-0.0230564\pi\)
\(384\) 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 \(-0.774545\pi\)
0.759477 0.650535i \(-0.225455\pi\)
\(390\) 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 0.517575 0.855638i \(-0.326835\pi\)
−0.855638 + 0.517575i \(0.826835\pi\)
\(398\) −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 −0.664404 0.747374i \(-0.731314\pi\)
0.747374 + 0.664404i \(0.231314\pi\)
\(434\) 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 0.987060 + 0.160349i \(0.0512618\pi\)
0.160349 + 0.987060i \(0.448738\pi\)
\(444\) 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 \(0.0743006\pi\)
−0.972881 + 0.231308i \(0.925699\pi\)
\(450\) 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 −0.694124 0.719855i \(-0.744208\pi\)
0.719855 + 0.694124i \(0.244208\pi\)
\(458\) 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 \(-0.993834\pi\)
0.999812 0.0193701i \(-0.00616607\pi\)
\(462\) 0 0
\(463\) 5.45140 + 5.45140i 0.253348 + 0.253348i 0.822342 0.568994i \(-0.192667\pi\)
−0.568994 + 0.822342i \(0.692667\pi\)
\(464\) 2.32612i 0.107987i
\(465\) 0 0
\(466\) 1.08890 0.0504423
\(467\) −23.2827 23.2827i −1.07740 1.07740i −0.996742 0.0806551i \(-0.974299\pi\)
−0.0806551 0.996742i \(-0.525701\pi\)
\(468\) 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 −0.851663 0.524089i \(-0.824406\pi\)
0.524089 + 0.851663i \(0.324406\pi\)
\(488\) 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 \(0.112191\pi\)
−0.938527 + 0.345207i \(0.887809\pi\)
\(500\) −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 0.174573 0.984644i \(-0.444145\pi\)
0.984644 0.174573i \(-0.0558546\pi\)
\(504\) 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 \(0.0180782\pi\)
−0.998388 + 0.0567639i \(0.981922\pi\)
\(522\) 0 0
\(523\) 6.08854 6.08854i 0.266233 0.266233i −0.561347 0.827581i \(-0.689717\pi\)
0.827581 + 0.561347i \(0.189717\pi\)
\(524\) 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 −0.724594 0.689175i \(-0.757973\pi\)
0.689175 + 0.724594i \(0.257973\pi\)
\(548\) −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 −0.946391 0.323024i \(-0.895300\pi\)
0.323024 + 0.946391i \(0.395300\pi\)
\(558\) 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 −0.0102391 + 0.999948i \(0.503259\pi\)
−0.999948 + 0.0102391i \(0.996741\pi\)
\(564\) 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 \(-0.893499\pi\)
0.944547 0.328376i \(-0.106501\pi\)
\(570\) 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 0.304724 0.952441i \(-0.401436\pi\)
−0.952441 + 0.304724i \(0.901436\pi\)
\(578\) 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 0.304155 0.952623i \(-0.401626\pi\)
−0.952623 + 0.304155i \(0.901626\pi\)
\(588\) 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 −0.744110 0.668057i \(-0.767126\pi\)
0.668057 + 0.744110i \(0.267126\pi\)
\(594\) 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 \(0.417527\pi\)
−0.256208 + 0.966622i \(0.582473\pi\)
\(600\) 0 0
\(601\) 11.0819i 0.452041i −0.974123 0.226021i \(-0.927428\pi\)
0.974123 0.226021i \(-0.0725717\pi\)
\(602\) 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 0.537170 0.843474i \(-0.319493\pi\)
−0.843474 + 0.537170i \(0.819493\pi\)
\(608\) −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 0.652108 0.758126i \(-0.273885\pi\)
−0.758126 + 0.652108i \(0.773885\pi\)
\(614\) −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 −0.897266 0.441491i \(-0.854450\pi\)
0.441491 + 0.897266i \(0.354450\pi\)
\(618\) 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 −0.779733 0.626112i \(-0.784645\pi\)
0.626112 + 0.779733i \(0.284645\pi\)
\(644\) 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 0.955876 0.293772i \(-0.0949106\pi\)
−0.293772 + 0.955876i \(0.594911\pi\)
\(648\) 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 0.995424 0.0955569i \(-0.0304632\pi\)
−0.0955569 + 0.995424i \(0.530463\pi\)
\(654\) 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 \(0.220223\pi\)
−0.770067 + 0.637963i \(0.779777\pi\)
\(660\) 0 0
\(661\) 32.5174i 1.26478i 0.774650 + 0.632391i \(0.217926\pi\)
−0.774650 + 0.632391i \(0.782074\pi\)
\(662\) −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 0.306179 0.951974i \(-0.400950\pi\)
−0.951974 + 0.306179i \(0.900950\pi\)
\(674\) 5.33455i 0.205479i
\(675\) 0 0
\(676\) 19.7046 0.757868
\(677\) −6.85568 6.85568i −0.263485 0.263485i 0.562983 0.826468i \(-0.309654\pi\)
−0.826468 + 0.562983i \(0.809654\pi\)
\(678\) 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 0.105389 0.994431i \(-0.466391\pi\)
−0.994431 + 0.105389i \(0.966391\pi\)
\(684\) 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 \(0.299366\pi\)
−0.589395 + 0.807845i \(0.700634\pi\)
\(692\) −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 \(-0.789740\pi\)
0.789654 0.613552i \(-0.210260\pi\)
\(710\) 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 0.654907 0.755710i \(-0.272708\pi\)
−0.755710 + 0.654907i \(0.772708\pi\)
\(728\) −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 −0.661700 0.749769i \(-0.730165\pi\)
0.749769 + 0.661700i \(0.230165\pi\)
\(734\) 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 \(-0.970940\pi\)
0.995835 0.0911693i \(-0.0290605\pi\)
\(740\) 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 0.358993 0.933340i \(-0.383120\pi\)
−0.933340 + 0.358993i \(0.883120\pi\)
\(744\) 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 0.0749214 0.997189i \(-0.476129\pi\)
0.997189 0.0749214i \(-0.0238706\pi\)
\(758\) −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 \(-0.829783\pi\)
0.860395 0.509629i \(-0.170217\pi\)
\(762\) 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 0.152800 0.988257i \(-0.451171\pi\)
0.988257 0.152800i \(-0.0488290\pi\)
\(774\) 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 3.16855i