Properties

Label 315.2.p.e.307.4
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 307.4
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.118.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.540143 - 0.540143i) q^{2} -1.41649i q^{4} +(1.03649 - 1.98133i) q^{5} +(2.57351 + 0.614060i) q^{7} +(-1.84539 + 1.84539i) q^{8} +O(q^{10})\) \(q+(-0.540143 - 0.540143i) q^{2} -1.41649i q^{4} +(1.03649 - 1.98133i) q^{5} +(2.57351 + 0.614060i) q^{7} +(-1.84539 + 1.84539i) q^{8} +(-1.63006 + 0.510348i) q^{10} +3.85136 q^{11} +(-3.66816 - 3.66816i) q^{13} +(-1.05838 - 1.72174i) q^{14} -0.839427 q^{16} +(-1.49007 + 1.49007i) q^{17} +0.0697674 q^{19} +(-2.80654 - 1.46818i) q^{20} +(-2.08029 - 2.08029i) q^{22} +(0.534176 - 0.534176i) q^{23} +(-2.85136 - 4.10728i) q^{25} +3.96267i q^{26} +(0.869810 - 3.64535i) q^{28} -2.77107i q^{29} -2.39674i q^{31} +(4.14420 + 4.14420i) q^{32} +1.60970 q^{34} +(3.88408 - 4.46250i) q^{35} +(6.18757 + 6.18757i) q^{37} +(-0.0376844 - 0.0376844i) q^{38} +(1.74360 + 5.56908i) q^{40} -8.68077i q^{41} +(-2.77107 + 2.77107i) q^{43} -5.45542i q^{44} -0.577063 q^{46} +(-5.49042 + 5.49042i) q^{47} +(6.24586 + 3.16057i) q^{49} +(-0.678376 + 3.75866i) q^{50} +(-5.19592 + 5.19592i) q^{52} +(-6.13823 + 6.13823i) q^{53} +(3.99191 - 7.63083i) q^{55} +(-5.88231 + 3.61595i) q^{56} +(-1.49678 + 1.49678i) q^{58} +6.97440 q^{59} +14.3107i q^{61} +(-1.29458 + 1.29458i) q^{62} -2.79807i q^{64} +(-11.0699 + 3.46582i) q^{65} +(0.416491 + 0.416491i) q^{67} +(2.11067 + 2.11067i) q^{68} +(-4.50835 + 0.312431i) q^{70} +8.12783 q^{71} +(9.55210 + 9.55210i) q^{73} -6.68434i q^{74} -0.0988248i q^{76} +(9.91150 + 2.36497i) q^{77} -9.86329i q^{79} +(-0.870061 + 1.66319i) q^{80} +(-4.68886 + 4.68886i) q^{82} +(-1.63570 - 1.63570i) q^{83} +(1.40788 + 4.49678i) q^{85} +2.99355 q^{86} +(-7.10728 + 7.10728i) q^{88} +5.05313 q^{89} +(-7.18757 - 11.6925i) q^{91} +(-0.756656 - 0.756656i) q^{92} +5.93123 q^{94} +(0.0723134 - 0.138232i) q^{95} +(6.85851 - 6.85851i) q^{97} +(-1.66650 - 5.08082i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{7} - 24q^{8} + O(q^{10}) \) \( 16q - 8q^{7} - 24q^{8} + 16q^{11} - 48q^{16} - 16q^{22} + 40q^{23} + 24q^{28} - 48q^{32} + 8q^{35} + 32q^{37} - 16q^{43} + 64q^{46} + 72q^{50} - 24q^{53} - 24q^{56} + 32q^{58} - 40q^{65} - 32q^{67} - 40q^{70} - 64q^{71} + 24q^{77} + 48q^{85} - 64q^{86} - 64q^{88} - 48q^{91} + 40q^{92} + 72q^{95} + 96q^{98} + O(q^{100}) \)

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
\(7\) 2.57351 + 0.614060i 0.972694 + 0.232093i
\(8\) −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 \(-0.994423\pi\)
−0.0175187 0.999847i \(-0.505577\pi\)
\(14\) −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 \(-0.832255\pi\)
0.502931 + 0.864326i \(0.332255\pi\)
\(18\) 0 0
\(19\) 0.0697674 0.0160057 0.00800286 0.999968i \(-0.497453\pi\)
0.00800286 + 0.999968i \(0.497453\pi\)
\(20\) −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
\(28\) 0.869810 3.64535i 0.164379 0.688906i
\(29\) 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 \(-0.930949\pi\)
0.976563 0.215233i \(-0.0690512\pi\)
\(32\) 4.14420 + 4.14420i 0.732598 + 0.732598i
\(33\) 0 0
\(34\) 1.60970 0.276062
\(35\) 3.88408 4.46250i 0.656529 0.754301i
\(36\) 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 \(-0.762910\pi\)
0.735196 0.677854i \(-0.237090\pi\)
\(42\) 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 −0.983230 0.182370i \(-0.941623\pi\)
0.182370 + 0.983230i \(0.441623\pi\)
\(48\) 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 \(-0.349998\pi\)
0.453995 + 0.891004i \(0.349998\pi\)
\(60\) 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 0.732090 0.681208i \(-0.238545\pi\)
−0.681208 + 0.732090i \(0.738545\pi\)
\(68\) 2.11067 + 2.11067i 0.255957 + 0.255957i
\(69\) 0 0
\(70\) −4.50835 + 0.312431i −0.538851 + 0.0373426i
\(71\) 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 \(0.0401987\pi\)
0.125953 + 0.992036i \(0.459801\pi\)
\(74\) 6.68434i 0.777039i
\(75\) 0 0
\(76\) 0.0988248i 0.0113360i
\(77\) 9.91150 + 2.36497i 1.12952 + 0.269513i
\(78\) 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 0.611615 0.791156i \(-0.290520\pi\)
−0.791156 + 0.611615i \(0.790520\pi\)
\(84\) 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 \(-0.413698\pi\)
0.267815 + 0.963470i \(0.413698\pi\)
\(90\) 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 \(-0.586115\pi\)
0.963627 + 0.267251i \(0.0861152\pi\)
\(98\) −1.66650 5.08082i −0.168342 0.513240i
\(99\) 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 \(-0.197911\pi\)
−0.582463 + 0.812857i \(0.697911\pi\)
\(104\) 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
\(112\) −2.16027 0.515459i −0.204126 0.0487063i
\(113\) 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 \(-0.990995\pi\)
0.999600 0.0282861i \(-0.00900495\pi\)
\(132\) 0 0
\(133\) 0.179547 + 0.0428413i 0.0155687 + 0.00371481i
\(134\) 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 \(-0.889231\pi\)
−0.940060 + 0.341009i \(0.889231\pi\)
\(140\) −6.32109 5.50176i −0.534230 0.464984i
\(141\) 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 −0.747762 0.663967i \(-0.768871\pi\)
0.663967 + 0.747762i \(0.268871\pi\)
\(158\) −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 −0.776431 0.630203i \(-0.782972\pi\)
0.630203 + 0.776431i \(0.282972\pi\)
\(168\) 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 \(-0.165014\pi\)
−0.495498 + 0.868609i \(0.665014\pi\)
\(174\) 0 0
\(175\) −4.81588 12.3210i −0.364046 0.931381i
\(176\) −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 \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) −2.43331 + 10.1979i −0.180369 + 0.755922i
\(183\) 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 \(-0.530181\pi\)
−0.0946750 + 0.995508i \(0.530181\pi\)
\(200\) 12.8414 + 2.31766i 0.908026 + 0.163884i
\(201\) 0 0
\(202\) 10.3682 10.3682i 0.729503 0.729503i
\(203\) 1.70161 7.13138i 0.119429 0.500524i
\(204\) 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
\(217\) 1.47174 6.16802i 0.0999082 0.418712i
\(218\) −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 \(-0.436768\pi\)
−0.980334 + 0.197346i \(0.936768\pi\)
\(224\) 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 \(-0.766518\pi\)
0.669478 + 0.742832i \(0.266518\pi\)
\(228\) 0 0
\(229\) 7.83309 0.517625 0.258812 0.965928i \(-0.416669\pi\)
0.258812 + 0.965928i \(0.416669\pi\)
\(230\) −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
\(238\) 4.14258 + 0.988454i 0.268524 + 0.0640720i
\(239\) 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 \(0.0284354\pi\)
−0.996013 + 0.0892136i \(0.971565\pi\)
\(242\) −2.07036 2.07036i −0.133088 0.133088i
\(243\) 0 0
\(244\) 20.2710 1.29772
\(245\) 12.7359 9.09922i 0.813670 0.581328i
\(246\) 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 \(-0.721624\pi\)
0.767252 + 0.641346i \(0.221624\pi\)
\(258\) 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 \(-0.771909\pi\)
−0.754064 + 0.656801i \(0.771909\pi\)
\(270\) 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 0.242393 0.970178i \(-0.422068\pi\)
−0.970178 + 0.242393i \(0.922068\pi\)
\(278\) 11.9730 + 11.9730i 0.718091 + 0.718091i
\(279\) 0 0
\(280\) 1.06742 + 15.4027i 0.0637904 + 0.920489i
\(281\) −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 \(-0.272326\pi\)
−0.754923 + 0.655813i \(0.772326\pi\)
\(284\) 11.5130i 0.683170i
\(285\) 0 0
\(286\) 15.2617i 0.902441i
\(287\) 5.33051 22.3400i 0.314650 1.31869i
\(288\) 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 \(-0.0329722\pi\)
−0.103400 + 0.994640i \(0.532972\pi\)
\(294\) 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 \(-0.950874\pi\)
0.153721 + 0.988114i \(0.450874\pi\)
\(308\) 3.34995 14.0395i 0.190881 0.799977i
\(309\) 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 \(-0.372848\pi\)
−0.921271 + 0.388921i \(0.872848\pi\)
\(314\) 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
\(322\) −1.48508 0.354351i −0.0827600 0.0197472i
\(323\) −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
\(343\) 14.1330 + 11.9691i 0.763109 + 0.646270i
\(344\) 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 \(-0.649518\pi\)
−0.452641 + 0.891693i \(0.649518\pi\)
\(350\) −4.05385 + 9.25637i −0.216687 + 0.494774i
\(351\) 0 0
\(352\) 15.9608 + 15.9608i 0.850714 + 0.850714i
\(353\) 11.1265 + 11.1265i 0.592202 + 0.592202i 0.938226 0.346024i \(-0.112468\pi\)
−0.346024 + 0.938226i \(0.612468\pi\)
\(354\) 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 −0.208238 0.978078i \(-0.566773\pi\)
0.978078 + 0.208238i \(0.0667728\pi\)
\(368\) −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 \(-0.976944\pi\)
−0.0723706 0.997378i \(-0.523056\pi\)
\(384\) 0 0
\(385\) 14.9590 17.1867i 0.762381 0.875916i
\(386\) 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
\(392\) −17.3586 + 5.69357i −0.876741 + 0.287569i
\(393\) 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 \(-0.673165\pi\)
0.855638 + 0.517575i \(0.173165\pi\)
\(398\) 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 \(-0.415918\pi\)
0.261090 + 0.965315i \(0.415918\pi\)
\(410\) 4.43022 + 14.1502i 0.218793 + 0.698827i
\(411\) 0 0
\(412\) 3.31210 3.31210i 0.163176 0.163176i
\(413\) 17.9487 + 4.28270i 0.883196 + 0.210738i
\(414\) 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 \(-0.623996\pi\)
−0.379766 + 0.925083i \(0.623996\pi\)
\(420\) 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
\(427\) −8.78764 + 36.8287i −0.425264 + 1.78227i
\(428\) 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 \(-0.268686\pi\)
−0.747374 + 0.664404i \(0.768686\pi\)
\(434\) −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 \(-0.724025\pi\)
−0.647116 + 0.762392i \(0.724025\pi\)
\(440\) 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
\(448\) 1.71818 7.20084i 0.0811764 0.340208i
\(449\) 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
\(455\) −30.6166 + 2.12175i −1.43533 + 0.0994691i
\(456\) 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 \(-0.993834\pi\)
0.999812 0.0193701i \(-0.00616607\pi\)
\(462\) 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 \(-0.474299\pi\)
0.996742 0.0806551i \(-0.0257012\pi\)
\(468\) 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 \(-0.125157\pi\)
0.923691 + 0.383138i \(0.125157\pi\)
\(480\) 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
\(490\) −11.7941 1.96435i −0.532804 0.0887404i
\(491\) −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
\(497\) 20.9170 + 4.99097i 0.938256 + 0.223876i
\(498\) 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 \(-0.944145\pi\)
−0.174573 0.984644i \(-0.555855\pi\)
\(504\) 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 \(-0.807598\pi\)
−0.822816 + 0.568309i \(0.807598\pi\)
\(510\) 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
\(518\) 4.10459 17.2022i 0.180345 0.755821i
\(519\) 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 \(-0.310283\pi\)
−0.827581 + 0.561347i \(0.810283\pi\)
\(524\) −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
\(532\) 0.0606843 0.254326i 0.00263100 0.0110264i
\(533\) −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
\(553\) 6.05665 25.3832i 0.257555 1.07941i
\(554\) 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
\(560\) −3.26040 + 3.74595i −0.137777 + 0.158295i
\(561\) 0 0
\(562\) 2.83726 + 2.83726i 0.119683 + 0.119683i
\(563\) 23.9693 + 23.9693i 1.01019 + 1.01019i 0.999948 + 0.0102391i \(0.00325926\pi\)
0.0102391 + 0.999948i \(0.496741\pi\)
\(564\) 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 −0.304724 0.952441i \(-0.598564\pi\)
0.952441 + 0.304724i \(0.0985641\pi\)
\(578\) 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 \(-0.598374\pi\)
0.952623 + 0.304155i \(0.0983740\pi\)
\(588\) 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 \(-0.232874\pi\)
−0.668057 + 0.744110i \(0.732874\pi\)
\(594\) 0 0
\(595\) 0.861891 + 12.4370i 0.0353341 + 0.509867i
\(596\) 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 \(-0.927428\pi\)
0.974123 0.226021i \(-0.0725717\pi\)
\(602\) 7.70393 + 1.83822i 0.313989 + 0.0749203i
\(603\) 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 \(-0.680507\pi\)
0.843474 + 0.537170i \(0.180507\pi\)
\(608\) 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 \(-0.558332\pi\)
−0.182231 + 0.983256i \(0.558332\pi\)
\(620\) −3.51885 + 6.72654i −0.141320 + 0.270144i
\(621\) 0 0
\(622\) −1.54599 + 1.54599i −0.0619884 + 0.0619884i
\(623\) 13.0043 + 3.10292i 0.521005 + 0.124316i
\(624\) 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
\(637\) −11.3173 34.5043i −0.448409 1.36711i
\(638\) −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 \(-0.215355\pi\)
−0.626112 + 0.779733i \(0.715355\pi\)
\(644\) −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 \(-0.905089\pi\)
0.293772 + 0.955876i \(0.405089\pi\)
\(648\) 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
\(658\) 15.2640 + 3.64213i 0.595054 + 0.141985i
\(659\) 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 \(0.217926\pi\)
−0.774650 + 0.632391i \(0.782074\pi\)
\(662\) −12.7582 12.7582i −0.495861 0.495861i
\(663\) 0 0
\(664\) 6.03701 0.234281
\(665\) 0.270982 0.311337i 0.0105082 0.0120731i
\(666\) 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 −0.562983 0.826468i \(-0.690346\pi\)
0.826468 + 0.562983i \(0.190346\pi\)
\(678\) 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 \(0.299366\pi\)
−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
\(700\) −17.4526 + 6.82165i −0.659646 + 0.257834i
\(701\) −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
\(707\) −11.7870 + 49.3991i −0.443297 + 1.85785i
\(708\) 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 \(-0.382659\pi\)
0.360346 + 0.932819i \(0.382659\pi\)
\(720\) 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 \(-0.727292\pi\)
0.755710 + 0.654907i \(0.227292\pi\)
\(728\) 34.8412 + 8.31339i 1.29130 + 0.308115i
\(729\) 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 \(-0.269835\pi\)
−0.749769 + 0.661700i \(0.769835\pi\)
\(734\) −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
\(742\) 17.0650 + 4.07186i 0.626477 + 0.149483i
\(743\) −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 \(-0.829783\pi\)
0.860395 0.509629i \(-0.170217\pi\)
\(762\) 0 0
\(763\) 1.32672 5.56025i 0.0480305 0.201294i
\(764\) 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 \(-0.461959\pi\)
0.119226 + 0.992867i \(0.461959\pi\)
\(770\) −17.3633 + 1.20328i −0.625729 + 0.0433634i
\(771\) 0 0
\(772\) 6.80764 + 6.80764i 0.245012 + 0.245012i
\(773\) −31.7247 31.7247i −1.14106 1.14106i −0.988257 0.152800i \(-0.951171\pi\)
−0.152800 0.988257i \(-0.548829\pi\)
\(774\) 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