Properties

Label 370.2.c.a.369.6
Level $370$
Weight $2$
Character 370.369
Analytic conductor $2.954$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
Defining polynomial: \(x^{10} + 19 x^{8} + 103 x^{6} + 210 x^{4} + 140 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 369.6
Root \(0.377861i\) of defining polynomial
Character \(\chi\) \(=\) 370.369
Dual form 370.2.c.a.369.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +0.377861i q^{3} +1.00000 q^{4} +(1.04797 + 1.97529i) q^{5} -0.377861i q^{6} +0.631751i q^{7} -1.00000 q^{8} +2.85722 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +0.377861i q^{3} +1.00000 q^{4} +(1.04797 + 1.97529i) q^{5} -0.377861i q^{6} +0.631751i q^{7} -1.00000 q^{8} +2.85722 q^{9} +(-1.04797 - 1.97529i) q^{10} +1.24789 q^{11} +0.377861i q^{12} -3.34999 q^{13} -0.631751i q^{14} +(-0.746385 + 0.395986i) q^{15} +1.00000 q^{16} -3.10511 q^{17} -2.85722 q^{18} +5.97327i q^{19} +(1.04797 + 1.97529i) q^{20} -0.238714 q^{21} -1.24789 q^{22} +7.60706 q^{23} -0.377861i q^{24} +(-2.80353 + 4.14008i) q^{25} +3.34999 q^{26} +2.21322i q^{27} +0.631751i q^{28} -9.57629i q^{29} +(0.746385 - 0.395986i) q^{30} +7.26707i q^{31} -1.00000 q^{32} +0.471529i q^{33} +3.10511 q^{34} +(-1.24789 + 0.662054i) q^{35} +2.85722 q^{36} +(4.10511 + 4.48866i) q^{37} -5.97327i q^{38} -1.26583i q^{39} +(-1.04797 - 1.97529i) q^{40} -8.45510 q^{41} +0.238714 q^{42} +4.86640 q^{43} +1.24789 q^{44} +(2.99427 + 5.64384i) q^{45} -7.60706 q^{46} +13.1187i q^{47} +0.377861i q^{48} +6.60089 q^{49} +(2.80353 - 4.14008i) q^{50} -1.17330i q^{51} -3.34999 q^{52} -7.17340i q^{53} -2.21322i q^{54} +(1.30775 + 2.46494i) q^{55} -0.631751i q^{56} -2.25707 q^{57} +9.57629i q^{58} -4.36469i q^{59} +(-0.746385 + 0.395986i) q^{60} -2.14666i q^{61} -7.26707i q^{62} +1.80505i q^{63} +1.00000 q^{64} +(-3.51068 - 6.61720i) q^{65} -0.471529i q^{66} -11.3451i q^{67} -3.10511 q^{68} +2.87441i q^{69} +(1.24789 - 0.662054i) q^{70} -12.7183 q^{71} -2.85722 q^{72} -4.45836i q^{73} +(-4.10511 - 4.48866i) q^{74} +(-1.56437 - 1.05934i) q^{75} +5.97327i q^{76} +0.788355i q^{77} +1.26583i q^{78} -8.78679i q^{79} +(1.04797 + 1.97529i) q^{80} +7.73537 q^{81} +8.45510 q^{82} -6.63185i q^{83} -0.238714 q^{84} +(-3.25406 - 6.13349i) q^{85} -4.86640 q^{86} +3.61851 q^{87} -1.24789 q^{88} -13.7784i q^{89} +(-2.99427 - 5.64384i) q^{90} -2.11636i q^{91} +7.60706 q^{92} -2.74594 q^{93} -13.1187i q^{94} +(-11.7989 + 6.25979i) q^{95} -0.377861i q^{96} -11.0583 q^{97} -6.60089 q^{98} +3.56550 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + 3q^{10} - 2q^{13} - 10q^{15} + 10q^{16} + 18q^{17} + 8q^{18} - 3q^{20} - 12q^{21} + 10q^{23} + 5q^{25} + 2q^{26} + 10q^{30} - 10q^{32} - 18q^{34} - 8q^{36} - 8q^{37} + 3q^{40} - 4q^{41} + 12q^{42} - 10q^{43} + 20q^{45} - 10q^{46} - 8q^{49} - 5q^{50} - 2q^{52} + 5q^{55} + 12q^{57} - 10q^{60} + 10q^{64} + 2q^{65} + 18q^{68} - 20q^{71} + 8q^{72} + 8q^{74} + 25q^{75} - 3q^{80} + 58q^{81} + 4q^{82} - 12q^{84} - 28q^{85} + 10q^{86} - 10q^{87} - 20q^{90} + 10q^{92} - 32q^{93} + 2q^{95} + 2q^{97} + 8q^{98} - 82q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.377861i 0.218158i 0.994033 + 0.109079i \(0.0347902\pi\)
−0.994033 + 0.109079i \(0.965210\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.04797 + 1.97529i 0.468665 + 0.883376i
\(6\) 0.377861i 0.154261i
\(7\) 0.631751i 0.238779i 0.992847 + 0.119390i \(0.0380938\pi\)
−0.992847 + 0.119390i \(0.961906\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.85722 0.952407
\(10\) −1.04797 1.97529i −0.331396 0.624641i
\(11\) 1.24789 0.376253 0.188126 0.982145i \(-0.439759\pi\)
0.188126 + 0.982145i \(0.439759\pi\)
\(12\) 0.377861i 0.109079i
\(13\) −3.34999 −0.929120 −0.464560 0.885542i \(-0.653788\pi\)
−0.464560 + 0.885542i \(0.653788\pi\)
\(14\) 0.631751i 0.168843i
\(15\) −0.746385 + 0.395986i −0.192716 + 0.102243i
\(16\) 1.00000 0.250000
\(17\) −3.10511 −0.753100 −0.376550 0.926396i \(-0.622890\pi\)
−0.376550 + 0.926396i \(0.622890\pi\)
\(18\) −2.85722 −0.673453
\(19\) 5.97327i 1.37036i 0.728373 + 0.685181i \(0.240277\pi\)
−0.728373 + 0.685181i \(0.759723\pi\)
\(20\) 1.04797 + 1.97529i 0.234333 + 0.441688i
\(21\) −0.238714 −0.0520917
\(22\) −1.24789 −0.266051
\(23\) 7.60706 1.58618 0.793090 0.609104i \(-0.208471\pi\)
0.793090 + 0.609104i \(0.208471\pi\)
\(24\) 0.377861i 0.0771306i
\(25\) −2.80353 + 4.14008i −0.560706 + 0.828015i
\(26\) 3.34999 0.656987
\(27\) 2.21322i 0.425934i
\(28\) 0.631751i 0.119390i
\(29\) 9.57629i 1.77827i −0.457643 0.889136i \(-0.651306\pi\)
0.457643 0.889136i \(-0.348694\pi\)
\(30\) 0.746385 0.395986i 0.136271 0.0722969i
\(31\) 7.26707i 1.30520i 0.757701 + 0.652602i \(0.226323\pi\)
−0.757701 + 0.652602i \(0.773677\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.471529i 0.0820827i
\(34\) 3.10511 0.532522
\(35\) −1.24789 + 0.662054i −0.210932 + 0.111908i
\(36\) 2.85722 0.476203
\(37\) 4.10511 + 4.48866i 0.674876 + 0.737931i
\(38\) 5.97327i 0.968992i
\(39\) 1.26583i 0.202695i
\(40\) −1.04797 1.97529i −0.165698 0.312321i
\(41\) −8.45510 −1.32046 −0.660232 0.751061i \(-0.729542\pi\)
−0.660232 + 0.751061i \(0.729542\pi\)
\(42\) 0.238714 0.0368344
\(43\) 4.86640 0.742119 0.371059 0.928609i \(-0.378995\pi\)
0.371059 + 0.928609i \(0.378995\pi\)
\(44\) 1.24789 0.188126
\(45\) 2.99427 + 5.64384i 0.446360 + 0.841333i
\(46\) −7.60706 −1.12160
\(47\) 13.1187i 1.91356i 0.290815 + 0.956779i \(0.406074\pi\)
−0.290815 + 0.956779i \(0.593926\pi\)
\(48\) 0.377861i 0.0545396i
\(49\) 6.60089 0.942984
\(50\) 2.80353 4.14008i 0.396479 0.585495i
\(51\) 1.17330i 0.164295i
\(52\) −3.34999 −0.464560
\(53\) 7.17340i 0.985343i −0.870215 0.492671i \(-0.836020\pi\)
0.870215 0.492671i \(-0.163980\pi\)
\(54\) 2.21322i 0.301181i
\(55\) 1.30775 + 2.46494i 0.176337 + 0.332373i
\(56\) 0.631751i 0.0844213i
\(57\) −2.25707 −0.298956
\(58\) 9.57629i 1.25743i
\(59\) 4.36469i 0.568234i −0.958790 0.284117i \(-0.908300\pi\)
0.958790 0.284117i \(-0.0917004\pi\)
\(60\) −0.746385 + 0.395986i −0.0963579 + 0.0511216i
\(61\) 2.14666i 0.274852i −0.990512 0.137426i \(-0.956117\pi\)
0.990512 0.137426i \(-0.0438829\pi\)
\(62\) 7.26707i 0.922919i
\(63\) 1.80505i 0.227415i
\(64\) 1.00000 0.125000
\(65\) −3.51068 6.61720i −0.435446 0.820762i
\(66\) 0.471529i 0.0580412i
\(67\) 11.3451i 1.38602i −0.720926 0.693012i \(-0.756283\pi\)
0.720926 0.693012i \(-0.243717\pi\)
\(68\) −3.10511 −0.376550
\(69\) 2.87441i 0.346038i
\(70\) 1.24789 0.662054i 0.149151 0.0791306i
\(71\) −12.7183 −1.50939 −0.754694 0.656077i \(-0.772215\pi\)
−0.754694 + 0.656077i \(0.772215\pi\)
\(72\) −2.85722 −0.336727
\(73\) 4.45836i 0.521811i −0.965364 0.260906i \(-0.915979\pi\)
0.965364 0.260906i \(-0.0840211\pi\)
\(74\) −4.10511 4.48866i −0.477209 0.521796i
\(75\) −1.56437 1.05934i −0.180638 0.122323i
\(76\) 5.97327i 0.685181i
\(77\) 0.788355i 0.0898414i
\(78\) 1.26583i 0.143327i
\(79\) 8.78679i 0.988592i −0.869294 0.494296i \(-0.835426\pi\)
0.869294 0.494296i \(-0.164574\pi\)
\(80\) 1.04797 + 1.97529i 0.117166 + 0.220844i
\(81\) 7.73537 0.859486
\(82\) 8.45510 0.933710
\(83\) 6.63185i 0.727941i −0.931411 0.363970i \(-0.881421\pi\)
0.931411 0.363970i \(-0.118579\pi\)
\(84\) −0.238714 −0.0260458
\(85\) −3.25406 6.13349i −0.352952 0.665270i
\(86\) −4.86640 −0.524757
\(87\) 3.61851 0.387945
\(88\) −1.24789 −0.133026
\(89\) 13.7784i 1.46051i −0.683175 0.730255i \(-0.739401\pi\)
0.683175 0.730255i \(-0.260599\pi\)
\(90\) −2.99427 5.64384i −0.315624 0.594912i
\(91\) 2.11636i 0.221855i
\(92\) 7.60706 0.793090
\(93\) −2.74594 −0.284741
\(94\) 13.1187i 1.35309i
\(95\) −11.7989 + 6.25979i −1.21054 + 0.642241i
\(96\) 0.377861i 0.0385653i
\(97\) −11.0583 −1.12280 −0.561398 0.827546i \(-0.689736\pi\)
−0.561398 + 0.827546i \(0.689736\pi\)
\(98\) −6.60089 −0.666791
\(99\) 3.56550 0.358346
\(100\) −2.80353 + 4.14008i −0.280353 + 0.414008i
\(101\) 8.65314 0.861019 0.430510 0.902586i \(-0.358334\pi\)
0.430510 + 0.902586i \(0.358334\pi\)
\(102\) 1.17330i 0.116174i
\(103\) 4.57336 0.450627 0.225313 0.974286i \(-0.427659\pi\)
0.225313 + 0.974286i \(0.427659\pi\)
\(104\) 3.34999 0.328494
\(105\) −0.250165 0.471529i −0.0244136 0.0460165i
\(106\) 7.17340i 0.696743i
\(107\) 11.4715i 1.10900i −0.832185 0.554498i \(-0.812910\pi\)
0.832185 0.554498i \(-0.187090\pi\)
\(108\) 2.21322i 0.212967i
\(109\) 0.727748i 0.0697057i 0.999392 + 0.0348528i \(0.0110962\pi\)
−0.999392 + 0.0348528i \(0.988904\pi\)
\(110\) −1.30775 2.46494i −0.124689 0.235023i
\(111\) −1.69609 + 1.55116i −0.160986 + 0.147230i
\(112\) 0.631751i 0.0596948i
\(113\) 17.9970 1.69301 0.846506 0.532379i \(-0.178702\pi\)
0.846506 + 0.532379i \(0.178702\pi\)
\(114\) 2.25707 0.211394
\(115\) 7.97195 + 15.0261i 0.743388 + 1.40119i
\(116\) 9.57629i 0.889136i
\(117\) −9.57166 −0.884901
\(118\) 4.36469i 0.401802i
\(119\) 1.96166i 0.179825i
\(120\) 0.746385 0.395986i 0.0681353 0.0361484i
\(121\) −9.44277 −0.858434
\(122\) 2.14666i 0.194350i
\(123\) 3.19485i 0.288070i
\(124\) 7.26707i 0.652602i
\(125\) −11.1159 1.19911i −0.994232 0.107252i
\(126\) 1.80505i 0.160807i
\(127\) 15.4830i 1.37389i 0.726707 + 0.686947i \(0.241050\pi\)
−0.726707 + 0.686947i \(0.758950\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.83882i 0.161899i
\(130\) 3.51068 + 6.61720i 0.307907 + 0.580367i
\(131\) 6.22121i 0.543550i −0.962361 0.271775i \(-0.912389\pi\)
0.962361 0.271775i \(-0.0876106\pi\)
\(132\) 0.471529i 0.0410413i
\(133\) −3.77362 −0.327214
\(134\) 11.3451i 0.980066i
\(135\) −4.37174 + 2.31938i −0.376260 + 0.199620i
\(136\) 3.10511 0.266261
\(137\) 14.1258i 1.20685i −0.797419 0.603426i \(-0.793802\pi\)
0.797419 0.603426i \(-0.206198\pi\)
\(138\) 2.87441i 0.244686i
\(139\) 8.43675 0.715596 0.357798 0.933799i \(-0.383528\pi\)
0.357798 + 0.933799i \(0.383528\pi\)
\(140\) −1.24789 + 0.662054i −0.105466 + 0.0559538i
\(141\) −4.95705 −0.417459
\(142\) 12.7183 1.06730
\(143\) −4.18042 −0.349584
\(144\) 2.85722 0.238102
\(145\) 18.9159 10.0356i 1.57088 0.833414i
\(146\) 4.45836i 0.368976i
\(147\) 2.49422i 0.205720i
\(148\) 4.10511 + 4.48866i 0.337438 + 0.368966i
\(149\) 13.6447 1.11782 0.558909 0.829229i \(-0.311220\pi\)
0.558909 + 0.829229i \(0.311220\pi\)
\(150\) 1.56437 + 1.05934i 0.127731 + 0.0864951i
\(151\) −3.17741 −0.258574 −0.129287 0.991607i \(-0.541269\pi\)
−0.129287 + 0.991607i \(0.541269\pi\)
\(152\) 5.97327i 0.484496i
\(153\) −8.87199 −0.717258
\(154\) 0.788355i 0.0635275i
\(155\) −14.3546 + 7.61566i −1.15299 + 0.611704i
\(156\) 1.26583i 0.101348i
\(157\) 0.215310i 0.0171836i 0.999963 + 0.00859180i \(0.00273489\pi\)
−0.999963 + 0.00859180i \(0.997265\pi\)
\(158\) 8.78679i 0.699040i
\(159\) 2.71055 0.214961
\(160\) −1.04797 1.97529i −0.0828491 0.156160i
\(161\) 4.80576i 0.378747i
\(162\) −7.73537 −0.607748
\(163\) −1.66609 −0.130498 −0.0652490 0.997869i \(-0.520784\pi\)
−0.0652490 + 0.997869i \(0.520784\pi\)
\(164\) −8.45510 −0.660232
\(165\) −0.931406 + 0.494147i −0.0725099 + 0.0384693i
\(166\) 6.63185i 0.514732i
\(167\) 5.92242 0.458290 0.229145 0.973392i \(-0.426407\pi\)
0.229145 + 0.973392i \(0.426407\pi\)
\(168\) 0.238714 0.0184172
\(169\) −1.77756 −0.136736
\(170\) 3.25406 + 6.13349i 0.249575 + 0.470417i
\(171\) 17.0669i 1.30514i
\(172\) 4.86640 0.371059
\(173\) 2.88008i 0.218968i −0.993989 0.109484i \(-0.965080\pi\)
0.993989 0.109484i \(-0.0349199\pi\)
\(174\) −3.61851 −0.274318
\(175\) −2.61550 1.77113i −0.197713 0.133885i
\(176\) 1.24789 0.0940632
\(177\) 1.64925 0.123965
\(178\) 13.7784i 1.03274i
\(179\) 4.46182i 0.333492i 0.986000 + 0.166746i \(0.0533260\pi\)
−0.986000 + 0.166746i \(0.946674\pi\)
\(180\) 2.99427 + 5.64384i 0.223180 + 0.420667i
\(181\) 3.93480 0.292472 0.146236 0.989250i \(-0.453284\pi\)
0.146236 + 0.989250i \(0.453284\pi\)
\(182\) 2.11636i 0.156875i
\(183\) 0.811140 0.0599612
\(184\) −7.60706 −0.560800
\(185\) −4.56437 + 12.8127i −0.335579 + 0.942012i
\(186\) 2.74594 0.201342
\(187\) −3.87484 −0.283356
\(188\) 13.1187i 0.956779i
\(189\) −1.39820 −0.101704
\(190\) 11.7989 6.25979i 0.855984 0.454133i
\(191\) 7.76296i 0.561708i 0.959751 + 0.280854i \(0.0906177\pi\)
−0.959751 + 0.280854i \(0.909382\pi\)
\(192\) 0.377861i 0.0272698i
\(193\) −3.49189 −0.251352 −0.125676 0.992071i \(-0.540110\pi\)
−0.125676 + 0.992071i \(0.540110\pi\)
\(194\) 11.0583 0.793937
\(195\) 2.50038 1.32655i 0.179056 0.0949962i
\(196\) 6.60089 0.471492
\(197\) 1.07617i 0.0766736i 0.999265 + 0.0383368i \(0.0122060\pi\)
−0.999265 + 0.0383368i \(0.987794\pi\)
\(198\) −3.56550 −0.253389
\(199\) 5.71343i 0.405014i −0.979281 0.202507i \(-0.935091\pi\)
0.979281 0.202507i \(-0.0649090\pi\)
\(200\) 2.80353 4.14008i 0.198239 0.292748i
\(201\) 4.28687 0.302372
\(202\) −8.65314 −0.608833
\(203\) 6.04983 0.424615
\(204\) 1.17330i 0.0821475i
\(205\) −8.86067 16.7013i −0.618856 1.16647i
\(206\) −4.57336 −0.318641
\(207\) 21.7350 1.51069
\(208\) −3.34999 −0.232280
\(209\) 7.45398i 0.515603i
\(210\) 0.250165 + 0.471529i 0.0172630 + 0.0325386i
\(211\) 22.8397 1.57235 0.786176 0.618003i \(-0.212058\pi\)
0.786176 + 0.618003i \(0.212058\pi\)
\(212\) 7.17340i 0.492671i
\(213\) 4.80576i 0.329286i
\(214\) 11.4715i 0.784178i
\(215\) 5.09983 + 9.61254i 0.347805 + 0.655570i
\(216\) 2.21322i 0.150590i
\(217\) −4.59098 −0.311656
\(218\) 0.727748i 0.0492893i
\(219\) 1.68464 0.113837
\(220\) 1.30775 + 2.46494i 0.0881684 + 0.166186i
\(221\) 10.4021 0.699720
\(222\) 1.69609 1.55116i 0.113834 0.104107i
\(223\) 3.32116i 0.222401i −0.993798 0.111201i \(-0.964530\pi\)
0.993798 0.111201i \(-0.0354696\pi\)
\(224\) 0.631751i 0.0422106i
\(225\) −8.01030 + 11.8291i −0.534020 + 0.788607i
\(226\) −17.9970 −1.19714
\(227\) 5.62938 0.373635 0.186818 0.982395i \(-0.440183\pi\)
0.186818 + 0.982395i \(0.440183\pi\)
\(228\) −2.25707 −0.149478
\(229\) −0.973208 −0.0643114 −0.0321557 0.999483i \(-0.510237\pi\)
−0.0321557 + 0.999483i \(0.510237\pi\)
\(230\) −7.97195 15.0261i −0.525655 0.990794i
\(231\) −0.297889 −0.0195997
\(232\) 9.57629i 0.628714i
\(233\) 14.4150i 0.944357i −0.881503 0.472178i \(-0.843468\pi\)
0.881503 0.472178i \(-0.156532\pi\)
\(234\) 9.57166 0.625719
\(235\) −25.9132 + 13.7480i −1.69039 + 0.896819i
\(236\) 4.36469i 0.284117i
\(237\) 3.32019 0.215669
\(238\) 1.96166i 0.127155i
\(239\) 8.43344i 0.545514i 0.962083 + 0.272757i \(0.0879355\pi\)
−0.962083 + 0.272757i \(0.912065\pi\)
\(240\) −0.746385 + 0.395986i −0.0481789 + 0.0255608i
\(241\) 18.6567i 1.20178i 0.799331 + 0.600891i \(0.205188\pi\)
−0.799331 + 0.600891i \(0.794812\pi\)
\(242\) 9.44277 0.607004
\(243\) 9.56255i 0.613438i
\(244\) 2.14666i 0.137426i
\(245\) 6.91752 + 13.0387i 0.441944 + 0.833010i
\(246\) 3.19485i 0.203696i
\(247\) 20.0104i 1.27323i
\(248\) 7.26707i 0.461460i
\(249\) 2.50592 0.158806
\(250\) 11.1159 + 1.19911i 0.703028 + 0.0758385i
\(251\) 25.1189i 1.58549i −0.609553 0.792746i \(-0.708651\pi\)
0.609553 0.792746i \(-0.291349\pi\)
\(252\) 1.80505i 0.113708i
\(253\) 9.49277 0.596805
\(254\) 15.4830i 0.971490i
\(255\) 2.31761 1.22958i 0.145134 0.0769994i
\(256\) 1.00000 0.0625000
\(257\) −20.3552 −1.26973 −0.634863 0.772625i \(-0.718943\pi\)
−0.634863 + 0.772625i \(0.718943\pi\)
\(258\) 1.83882i 0.114480i
\(259\) −2.83571 + 2.59341i −0.176203 + 0.161146i
\(260\) −3.51068 6.61720i −0.217723 0.410381i
\(261\) 27.3616i 1.69364i
\(262\) 6.22121i 0.384348i
\(263\) 22.2211i 1.37021i 0.728443 + 0.685107i \(0.240244\pi\)
−0.728443 + 0.685107i \(0.759756\pi\)
\(264\) 0.471529i 0.0290206i
\(265\) 14.1695 7.51750i 0.870428 0.461796i
\(266\) 3.77362 0.231375
\(267\) 5.20633 0.318622
\(268\) 11.3451i 0.693012i
\(269\) −15.8411 −0.965850 −0.482925 0.875662i \(-0.660426\pi\)
−0.482925 + 0.875662i \(0.660426\pi\)
\(270\) 4.37174 2.31938i 0.266056 0.141153i
\(271\) −2.00602 −0.121857 −0.0609285 0.998142i \(-0.519406\pi\)
−0.0609285 + 0.998142i \(0.519406\pi\)
\(272\) −3.10511 −0.188275
\(273\) 0.799690 0.0483994
\(274\) 14.1258i 0.853373i
\(275\) −3.49849 + 5.16636i −0.210967 + 0.311543i
\(276\) 2.87441i 0.173019i
\(277\) −11.5671 −0.695000 −0.347500 0.937680i \(-0.612969\pi\)
−0.347500 + 0.937680i \(0.612969\pi\)
\(278\) −8.43675 −0.506003
\(279\) 20.7636i 1.24309i
\(280\) 1.24789 0.662054i 0.0745757 0.0395653i
\(281\) 14.2909i 0.852521i −0.904600 0.426261i \(-0.859831\pi\)
0.904600 0.426261i \(-0.140169\pi\)
\(282\) 4.95705 0.295188
\(283\) −12.3837 −0.736137 −0.368068 0.929799i \(-0.619981\pi\)
−0.368068 + 0.929799i \(0.619981\pi\)
\(284\) −12.7183 −0.754694
\(285\) −2.36533 4.45836i −0.140110 0.264090i
\(286\) 4.18042 0.247193
\(287\) 5.34152i 0.315300i
\(288\) −2.85722 −0.168363
\(289\) −7.35829 −0.432840
\(290\) −18.9159 + 10.0356i −1.11078 + 0.589313i
\(291\) 4.17849i 0.244947i
\(292\) 4.45836i 0.260906i
\(293\) 27.8374i 1.62628i −0.582068 0.813140i \(-0.697756\pi\)
0.582068 0.813140i \(-0.302244\pi\)
\(294\) 2.49422i 0.145466i
\(295\) 8.62152 4.57405i 0.501964 0.266312i
\(296\) −4.10511 4.48866i −0.238605 0.260898i
\(297\) 2.76185i 0.160259i
\(298\) −13.6447 −0.790416
\(299\) −25.4836 −1.47375
\(300\) −1.56437 1.05934i −0.0903192 0.0611613i
\(301\) 3.07435i 0.177203i
\(302\) 3.17741 0.182839
\(303\) 3.26968i 0.187838i
\(304\) 5.97327i 0.342590i
\(305\) 4.24028 2.24963i 0.242798 0.128814i
\(306\) 8.87199 0.507178
\(307\) 19.9411i 1.13810i −0.822304 0.569049i \(-0.807312\pi\)
0.822304 0.569049i \(-0.192688\pi\)
\(308\) 0.788355i 0.0449207i
\(309\) 1.72810i 0.0983080i
\(310\) 14.3546 7.61566i 0.815284 0.432540i
\(311\) 4.96832i 0.281727i −0.990029 0.140864i \(-0.955012\pi\)
0.990029 0.140864i \(-0.0449879\pi\)
\(312\) 1.26583i 0.0716636i
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 0.215310i 0.0121506i
\(315\) −3.56550 + 1.89164i −0.200893 + 0.106582i
\(316\) 8.78679i 0.494296i
\(317\) 22.9198i 1.28730i 0.765319 + 0.643651i \(0.222581\pi\)
−0.765319 + 0.643651i \(0.777419\pi\)
\(318\) −2.71055 −0.152000
\(319\) 11.9502i 0.669080i
\(320\) 1.04797 + 1.97529i 0.0585832 + 0.110422i
\(321\) 4.33465 0.241937
\(322\) 4.80576i 0.267815i
\(323\) 18.5477i 1.03202i
\(324\) 7.73537 0.429743
\(325\) 9.39179 13.8692i 0.520963 0.769326i
\(326\) 1.66609 0.0922760
\(327\) −0.274988 −0.0152069
\(328\) 8.45510 0.466855
\(329\) −8.28775 −0.456918
\(330\) 0.931406 0.494147i 0.0512722 0.0272019i
\(331\) 5.54265i 0.304651i 0.988330 + 0.152326i \(0.0486763\pi\)
−0.988330 + 0.152326i \(0.951324\pi\)
\(332\) 6.63185i 0.363970i
\(333\) 11.7292 + 12.8251i 0.642757 + 0.702811i
\(334\) −5.92242 −0.324060
\(335\) 22.4098 11.8893i 1.22438 0.649581i
\(336\) −0.238714 −0.0130229
\(337\) 25.6348i 1.39642i 0.715894 + 0.698209i \(0.246019\pi\)
−0.715894 + 0.698209i \(0.753981\pi\)
\(338\) 1.77756 0.0966867
\(339\) 6.80035i 0.369344i
\(340\) −3.25406 6.13349i −0.176476 0.332635i
\(341\) 9.06851i 0.491087i
\(342\) 17.0669i 0.922875i
\(343\) 8.59237i 0.463945i
\(344\) −4.86640 −0.262379
\(345\) −5.67779 + 3.01229i −0.305682 + 0.162176i
\(346\) 2.88008i 0.154834i
\(347\) 19.6225 1.05339 0.526696 0.850054i \(-0.323431\pi\)
0.526696 + 0.850054i \(0.323431\pi\)
\(348\) 3.61851 0.193972
\(349\) −15.6263 −0.836459 −0.418230 0.908341i \(-0.637349\pi\)
−0.418230 + 0.908341i \(0.637349\pi\)
\(350\) 2.61550 + 1.77113i 0.139804 + 0.0946709i
\(351\) 7.41425i 0.395744i
\(352\) −1.24789 −0.0665128
\(353\) 23.5724 1.25463 0.627316 0.778765i \(-0.284153\pi\)
0.627316 + 0.778765i \(0.284153\pi\)
\(354\) −1.64925 −0.0876564
\(355\) −13.3284 25.1224i −0.707398 1.33336i
\(356\) 13.7784i 0.730255i
\(357\) 0.741234 0.0392302
\(358\) 4.46182i 0.235815i
\(359\) −9.34905 −0.493424 −0.246712 0.969089i \(-0.579350\pi\)
−0.246712 + 0.969089i \(0.579350\pi\)
\(360\) −2.99427 5.64384i −0.157812 0.297456i
\(361\) −16.6799 −0.877891
\(362\) −3.93480 −0.206809
\(363\) 3.56806i 0.187274i
\(364\) 2.11636i 0.110927i
\(365\) 8.80654 4.67221i 0.460955 0.244555i
\(366\) −0.811140 −0.0423990
\(367\) 12.2379i 0.638811i −0.947618 0.319406i \(-0.896517\pi\)
0.947618 0.319406i \(-0.103483\pi\)
\(368\) 7.60706 0.396545
\(369\) −24.1581 −1.25762
\(370\) 4.56437 12.8127i 0.237291 0.666103i
\(371\) 4.53180 0.235280
\(372\) −2.74594 −0.142371
\(373\) 10.1918i 0.527712i 0.964562 + 0.263856i \(0.0849943\pi\)
−0.964562 + 0.263856i \(0.915006\pi\)
\(374\) 3.87484 0.200363
\(375\) 0.453098 4.20025i 0.0233979 0.216900i
\(376\) 13.1187i 0.676545i
\(377\) 32.0805i 1.65223i
\(378\) 1.39820 0.0719157
\(379\) 20.7538 1.06605 0.533025 0.846099i \(-0.321055\pi\)
0.533025 + 0.846099i \(0.321055\pi\)
\(380\) −11.7989 + 6.25979i −0.605272 + 0.321120i
\(381\) −5.85042 −0.299726
\(382\) 7.76296i 0.397188i
\(383\) 17.7328 0.906103 0.453052 0.891484i \(-0.350335\pi\)
0.453052 + 0.891484i \(0.350335\pi\)
\(384\) 0.377861i 0.0192826i
\(385\) −1.55723 + 0.826171i −0.0793638 + 0.0421056i
\(386\) 3.49189 0.177732
\(387\) 13.9044 0.706799
\(388\) −11.0583 −0.561398
\(389\) 10.9054i 0.552923i 0.961025 + 0.276462i \(0.0891619\pi\)
−0.961025 + 0.276462i \(0.910838\pi\)
\(390\) −2.50038 + 1.32655i −0.126612 + 0.0671725i
\(391\) −23.6208 −1.19455
\(392\) −6.60089 −0.333395
\(393\) 2.35075 0.118580
\(394\) 1.07617i 0.0542164i
\(395\) 17.3565 9.20827i 0.873298 0.463319i
\(396\) 3.56550 0.179173
\(397\) 23.0106i 1.15487i −0.816437 0.577435i \(-0.804054\pi\)
0.816437 0.577435i \(-0.195946\pi\)
\(398\) 5.71343i 0.286388i
\(399\) 1.42590i 0.0713844i
\(400\) −2.80353 + 4.14008i −0.140176 + 0.207004i
\(401\) 16.5769i 0.827809i −0.910320 0.413904i \(-0.864165\pi\)
0.910320 0.413904i \(-0.135835\pi\)
\(402\) −4.28687 −0.213810
\(403\) 24.3446i 1.21269i
\(404\) 8.65314 0.430510
\(405\) 8.10642 + 15.2796i 0.402811 + 0.759249i
\(406\) −6.04983 −0.300248
\(407\) 5.12273 + 5.60135i 0.253924 + 0.277649i
\(408\) 1.17330i 0.0580870i
\(409\) 5.05401i 0.249905i 0.992163 + 0.124952i \(0.0398778\pi\)
−0.992163 + 0.124952i \(0.960122\pi\)
\(410\) 8.86067 + 16.7013i 0.437597 + 0.824817i
\(411\) 5.33760 0.263285
\(412\) 4.57336 0.225313
\(413\) 2.75740 0.135683
\(414\) −21.7350 −1.06822
\(415\) 13.0998 6.94997i 0.643045 0.341161i
\(416\) 3.34999 0.164247
\(417\) 3.18792i 0.156113i
\(418\) 7.45398i 0.364586i
\(419\) −24.2194 −1.18319 −0.591597 0.806234i \(-0.701502\pi\)
−0.591597 + 0.806234i \(0.701502\pi\)
\(420\) −0.250165 0.471529i −0.0122068 0.0230083i
\(421\) 20.8487i 1.01611i 0.861326 + 0.508053i \(0.169635\pi\)
−0.861326 + 0.508053i \(0.830365\pi\)
\(422\) −22.8397 −1.11182
\(423\) 37.4830i 1.82249i
\(424\) 7.17340i 0.348371i
\(425\) 8.70527 12.8554i 0.422267 0.623578i
\(426\) 4.80576i 0.232840i
\(427\) 1.35616 0.0656290
\(428\) 11.4715i 0.554498i
\(429\) 1.57962i 0.0762647i
\(430\) −5.09983 9.61254i −0.245935 0.463558i
\(431\) 28.2298i 1.35978i 0.733314 + 0.679890i \(0.237973\pi\)
−0.733314 + 0.679890i \(0.762027\pi\)
\(432\) 2.21322i 0.106483i
\(433\) 30.3997i 1.46091i −0.682958 0.730457i \(-0.739307\pi\)
0.682958 0.730457i \(-0.260693\pi\)
\(434\) 4.59098 0.220374
\(435\) 3.79208 + 7.14759i 0.181816 + 0.342701i
\(436\) 0.727748i 0.0348528i
\(437\) 45.4390i 2.17364i
\(438\) −1.68464 −0.0804952
\(439\) 33.7591i 1.61123i 0.592438 + 0.805616i \(0.298166\pi\)
−0.592438 + 0.805616i \(0.701834\pi\)
\(440\) −1.30775 2.46494i −0.0623444 0.117512i
\(441\) 18.8602 0.898105
\(442\) −10.4021 −0.494777
\(443\) 15.5413i 0.738388i 0.929352 + 0.369194i \(0.120366\pi\)
−0.929352 + 0.369194i \(0.879634\pi\)
\(444\) −1.69609 + 1.55116i −0.0804929 + 0.0736149i
\(445\) 27.2164 14.4393i 1.29018 0.684490i
\(446\) 3.32116i 0.157261i
\(447\) 5.15580i 0.243861i
\(448\) 0.631751i 0.0298474i
\(449\) 14.2184i 0.671006i 0.942039 + 0.335503i \(0.108906\pi\)
−0.942039 + 0.335503i \(0.891094\pi\)
\(450\) 8.01030 11.8291i 0.377609 0.557630i
\(451\) −10.5510 −0.496829
\(452\) 17.9970 0.846506
\(453\) 1.20062i 0.0564100i
\(454\) −5.62938 −0.264200
\(455\) 4.18042 2.21788i 0.195981 0.103976i
\(456\) 2.25707 0.105697
\(457\) 9.17031 0.428969 0.214484 0.976727i \(-0.431193\pi\)
0.214484 + 0.976727i \(0.431193\pi\)
\(458\) 0.973208 0.0454750
\(459\) 6.87228i 0.320771i
\(460\) 7.97195 + 15.0261i 0.371694 + 0.700597i
\(461\) 10.3300i 0.481114i 0.970635 + 0.240557i \(0.0773301\pi\)
−0.970635 + 0.240557i \(0.922670\pi\)
\(462\) 0.297889 0.0138590
\(463\) −25.8049 −1.19926 −0.599629 0.800278i \(-0.704685\pi\)
−0.599629 + 0.800278i \(0.704685\pi\)
\(464\) 9.57629i 0.444568i
\(465\) −2.87766 5.42403i −0.133448 0.251533i
\(466\) 14.4150i 0.667761i
\(467\) −34.4582 −1.59454 −0.797268 0.603625i \(-0.793722\pi\)
−0.797268 + 0.603625i \(0.793722\pi\)
\(468\) −9.57166 −0.442450
\(469\) 7.16727 0.330954
\(470\) 25.9132 13.7480i 1.19529 0.634147i
\(471\) −0.0813572 −0.00374874
\(472\) 4.36469i 0.200901i
\(473\) 6.07273 0.279224
\(474\) −3.32019 −0.152501
\(475\) −24.7298 16.7462i −1.13468 0.768369i
\(476\) 1.96166i 0.0899124i
\(477\) 20.4960i 0.938448i
\(478\) 8.43344i 0.385737i
\(479\) 29.6039i 1.35264i 0.736610 + 0.676318i \(0.236426\pi\)
−0.736610 + 0.676318i \(0.763574\pi\)
\(480\) 0.746385 0.395986i 0.0340676 0.0180742i
\(481\) −13.7521 15.0370i −0.627041 0.685627i
\(482\) 18.6567i 0.849789i
\(483\) −1.81591 −0.0826268
\(484\) −9.44277 −0.429217
\(485\) −11.5887 21.8433i −0.526216 0.991852i
\(486\) 9.56255i 0.433766i
\(487\) −27.0961 −1.22784 −0.613920 0.789369i \(-0.710408\pi\)
−0.613920 + 0.789369i \(0.710408\pi\)
\(488\) 2.14666i 0.0971749i
\(489\) 0.629549i 0.0284692i
\(490\) −6.91752 13.0387i −0.312502 0.589027i
\(491\) 2.46033 0.111033 0.0555166 0.998458i \(-0.482319\pi\)
0.0555166 + 0.998458i \(0.482319\pi\)
\(492\) 3.19485i 0.144035i
\(493\) 29.7354i 1.33922i
\(494\) 20.0104i 0.900310i
\(495\) 3.73653 + 7.04289i 0.167944 + 0.316554i
\(496\) 7.26707i 0.326301i
\(497\) 8.03482i 0.360411i
\(498\) −2.50592 −0.112293
\(499\) 31.4091i 1.40606i −0.711158 0.703032i \(-0.751829\pi\)
0.711158 0.703032i \(-0.248171\pi\)
\(500\) −11.1159 1.19911i −0.497116 0.0536259i
\(501\) 2.23785i 0.0999798i
\(502\) 25.1189i 1.12111i
\(503\) 1.78145 0.0794311 0.0397156 0.999211i \(-0.487355\pi\)
0.0397156 + 0.999211i \(0.487355\pi\)
\(504\) 1.80505i 0.0804034i
\(505\) 9.06821 + 17.0924i 0.403530 + 0.760604i
\(506\) −9.49277 −0.422005
\(507\) 0.671672i 0.0298300i
\(508\) 15.4830i 0.686947i
\(509\) 21.2370 0.941314 0.470657 0.882316i \(-0.344017\pi\)
0.470657 + 0.882316i \(0.344017\pi\)
\(510\) −2.31761 + 1.22958i −0.102625 + 0.0544468i
\(511\) 2.81657 0.124598
\(512\) −1.00000 −0.0441942
\(513\) −13.2201 −0.583683
\(514\) 20.3552 0.897831
\(515\) 4.79274 + 9.03371i 0.211193 + 0.398073i
\(516\) 1.83882i 0.0809496i
\(517\) 16.3707i 0.719982i
\(518\) 2.83571 2.59341i 0.124594 0.113948i
\(519\) 1.08827 0.0477698
\(520\) 3.51068 + 6.61720i 0.153954 + 0.290183i
\(521\) 2.52950 0.110819 0.0554097 0.998464i \(-0.482354\pi\)
0.0554097 + 0.998464i \(0.482354\pi\)
\(522\) 27.3616i 1.19758i
\(523\) −1.60848 −0.0703338 −0.0351669 0.999381i \(-0.511196\pi\)
−0.0351669 + 0.999381i \(0.511196\pi\)
\(524\) 6.22121i 0.271775i
\(525\) 0.669242 0.988294i 0.0292081 0.0431327i
\(526\) 22.2211i 0.968887i
\(527\) 22.5651i 0.982950i
\(528\) 0.471529i 0.0205207i
\(529\) 34.8673 1.51597
\(530\) −14.1695 + 7.51750i −0.615486 + 0.326539i
\(531\) 12.4709i 0.541190i
\(532\) −3.77362 −0.163607
\(533\) 28.3245 1.22687
\(534\) −5.20633 −0.225300
\(535\) 22.6596 12.0218i 0.979660 0.519748i
\(536\) 11.3451i 0.490033i
\(537\) −1.68595 −0.0727541
\(538\) 15.8411 0.682959
\(539\) 8.23719 0.354801
\(540\) −4.37174 + 2.31938i −0.188130 + 0.0998102i
\(541\) 3.12463i 0.134338i −0.997742 0.0671692i \(-0.978603\pi\)
0.997742 0.0671692i \(-0.0213967\pi\)
\(542\) 2.00602 0.0861660
\(543\) 1.48681i 0.0638051i
\(544\) 3.10511 0.133131
\(545\) −1.43751 + 0.762657i −0.0615763 + 0.0326686i
\(546\) −0.799690 −0.0342236
\(547\) 5.44201 0.232683 0.116342 0.993209i \(-0.462883\pi\)
0.116342 + 0.993209i \(0.462883\pi\)
\(548\) 14.1258i 0.603426i
\(549\) 6.13349i 0.261771i
\(550\) 3.49849 5.16636i 0.149176 0.220294i
\(551\) 57.2017 2.43688
\(552\) 2.87441i 0.122343i
\(553\) 5.55106 0.236055
\(554\) 11.5671 0.491440
\(555\) −4.84144 1.72470i −0.205508 0.0732094i
\(556\) 8.43675 0.357798
\(557\) −36.3451 −1.53999 −0.769995 0.638050i \(-0.779741\pi\)
−0.769995 + 0.638050i \(0.779741\pi\)
\(558\) 20.7636i 0.878995i
\(559\) −16.3024 −0.689517
\(560\) −1.24789 + 0.662054i −0.0527330 + 0.0279769i
\(561\) 1.46415i 0.0618165i
\(562\) 14.2909i 0.602824i
\(563\) −38.4949 −1.62237 −0.811184 0.584791i \(-0.801177\pi\)
−0.811184 + 0.584791i \(0.801177\pi\)
\(564\) −4.95705 −0.208729
\(565\) 18.8602 + 35.5492i 0.793456 + 1.49557i
\(566\) 12.3837 0.520527
\(567\) 4.88683i 0.205228i
\(568\) 12.7183 0.533649
\(569\) 41.2793i 1.73052i 0.501324 + 0.865260i \(0.332846\pi\)
−0.501324 + 0.865260i \(0.667154\pi\)
\(570\) 2.36533 + 4.45836i 0.0990728 + 0.186740i
\(571\) −26.0635 −1.09072 −0.545362 0.838200i \(-0.683608\pi\)
−0.545362 + 0.838200i \(0.683608\pi\)
\(572\) −4.18042 −0.174792
\(573\) −2.93332 −0.122541
\(574\) 5.34152i 0.222951i
\(575\) −21.3266 + 31.4938i −0.889381 + 1.31338i
\(576\) 2.85722 0.119051
\(577\) 11.8411 0.492952 0.246476 0.969149i \(-0.420727\pi\)
0.246476 + 0.969149i \(0.420727\pi\)
\(578\) 7.35829 0.306064
\(579\) 1.31945i 0.0548344i
\(580\) 18.9159 10.0356i 0.785441 0.416707i
\(581\) 4.18968 0.173817
\(582\) 4.17849i 0.173204i
\(583\) 8.95162i 0.370738i
\(584\) 4.45836i 0.184488i
\(585\) −10.0308 18.9068i −0.414722 0.781700i
\(586\) 27.8374i 1.14995i
\(587\) −26.7315 −1.10333 −0.551663 0.834067i \(-0.686006\pi\)
−0.551663 + 0.834067i \(0.686006\pi\)
\(588\) 2.49422i 0.102860i
\(589\) −43.4082 −1.78860
\(590\) −8.62152 + 4.57405i −0.354942 + 0.188311i
\(591\) −0.406641 −0.0167270
\(592\) 4.10511 + 4.48866i 0.168719 + 0.184483i
\(593\) 22.6119i 0.928560i −0.885688 0.464280i \(-0.846313\pi\)
0.885688 0.464280i \(-0.153687\pi\)
\(594\) 2.76185i 0.113320i
\(595\) 3.87484 2.05575i 0.158853 0.0842776i
\(596\) 13.6447 0.558909
\(597\) 2.15888 0.0883572
\(598\) 25.4836 1.04210
\(599\) 14.3406 0.585942 0.292971 0.956121i \(-0.405356\pi\)
0.292971 + 0.956121i \(0.405356\pi\)
\(600\) 1.56437 + 1.05934i 0.0638653 + 0.0432476i
\(601\) 15.0845 0.615308 0.307654 0.951498i \(-0.400456\pi\)
0.307654 + 0.951498i \(0.400456\pi\)
\(602\) 3.07435i 0.125301i
\(603\) 32.4154i 1.32006i
\(604\) −3.17741 −0.129287
\(605\) −9.89572 18.6522i −0.402318 0.758320i
\(606\) 3.26968i 0.132822i
\(607\) 41.5964 1.68835 0.844174 0.536070i \(-0.180092\pi\)
0.844174 + 0.536070i \(0.180092\pi\)
\(608\) 5.97327i 0.242248i
\(609\) 2.28599i 0.0926332i
\(610\) −4.24028 + 2.24963i −0.171684 + 0.0910850i
\(611\) 43.9475i 1.77793i
\(612\) −8.87199 −0.358629
\(613\) 30.4369i 1.22934i 0.788786 + 0.614668i \(0.210710\pi\)
−0.788786 + 0.614668i \(0.789290\pi\)
\(614\) 19.9411i 0.804756i
\(615\) 6.31076 3.34810i 0.254474 0.135009i
\(616\) 0.788355i 0.0317637i
\(617\) 39.8195i 1.60307i 0.597946 + 0.801536i \(0.295984\pi\)
−0.597946 + 0.801536i \(0.704016\pi\)
\(618\) 1.72810i 0.0695142i
\(619\) 39.4011 1.58367 0.791833 0.610738i \(-0.209127\pi\)
0.791833 + 0.610738i \(0.209127\pi\)
\(620\) −14.3546 + 7.61566i −0.576493 + 0.305852i
\(621\) 16.8361i 0.675608i
\(622\) 4.96832i 0.199211i
\(623\) 8.70453 0.348740
\(624\) 1.26583i 0.0506738i
\(625\) −9.28046 23.2136i −0.371218 0.928546i
\(626\) 10.0000 0.399680
\(627\) −2.81657 −0.112483
\(628\) 0.215310i 0.00859180i
\(629\) −12.7468 13.9378i −0.508249 0.555736i
\(630\) 3.56550 1.89164i 0.142053 0.0753646i
\(631\) 0.114985i 0.00457750i −0.999997 0.00228875i \(-0.999271\pi\)
0.999997 0.00228875i \(-0.000728532\pi\)
\(632\) 8.78679i 0.349520i
\(633\) 8.63024i 0.343021i
\(634\) 22.9198i 0.910260i
\(635\) −30.5834 + 16.2257i −1.21366 + 0.643897i
\(636\) 2.71055 0.107480
\(637\) −22.1129 −0.876146
\(638\) 11.9502i 0.473111i
\(639\) −36.3391 −1.43755
\(640\) −1.04797 1.97529i −0.0414246 0.0780801i
\(641\) 34.9774 1.38153 0.690763 0.723081i \(-0.257275\pi\)
0.690763 + 0.723081i \(0.257275\pi\)
\(642\) −4.33465 −0.171075
\(643\) −25.2868 −0.997216 −0.498608 0.866828i \(-0.666155\pi\)
−0.498608 + 0.866828i \(0.666155\pi\)
\(644\) 4.80576i 0.189374i
\(645\) −3.63220 + 1.92703i −0.143018 + 0.0758766i
\(646\) 18.5477i 0.729748i
\(647\) 23.5824 0.927120 0.463560 0.886066i \(-0.346572\pi\)
0.463560 + 0.886066i \(0.346572\pi\)
\(648\) −7.73537 −0.303874
\(649\) 5.44665i 0.213800i
\(650\) −9.39179 + 13.8692i −0.368376 + 0.543995i
\(651\) 1.73475i 0.0679903i
\(652\) −1.66609 −0.0652490
\(653\) −9.89261 −0.387128 −0.193564 0.981088i \(-0.562005\pi\)
−0.193564 + 0.981088i \(0.562005\pi\)
\(654\) 0.274988 0.0107529
\(655\) 12.2887 6.51963i 0.480159 0.254743i
\(656\) −8.45510 −0.330116
\(657\) 12.7385i 0.496977i
\(658\) 8.28775 0.323090
\(659\) −25.4137 −0.989976 −0.494988 0.868900i \(-0.664827\pi\)
−0.494988 + 0.868900i \(0.664827\pi\)
\(660\) −0.931406 + 0.494147i −0.0362549 + 0.0192347i
\(661\) 28.4574i 1.10687i 0.832894 + 0.553433i \(0.186682\pi\)
−0.832894 + 0.553433i \(0.813318\pi\)
\(662\) 5.54265i 0.215421i
\(663\) 3.93055i 0.152650i
\(664\) 6.63185i 0.257366i
\(665\) −3.95463 7.45398i −0.153354 0.289053i
\(666\) −11.7292 12.8251i −0.454498 0.496962i
\(667\) 72.8474i 2.82066i
\(668\) 5.92242 0.229145
\(669\) 1.25494 0.0485186
\(670\) −22.4098 + 11.8893i −0.865767 + 0.459323i
\(671\) 2.67880i 0.103414i
\(672\) 0.238714 0.00920860
\(673\) 20.4187i 0.787082i 0.919307 + 0.393541i \(0.128750\pi\)
−0.919307 + 0.393541i \(0.871250\pi\)
\(674\) 25.6348i 0.987416i
\(675\) −9.16288 6.20481i −0.352680 0.238823i
\(676\) −1.77756 −0.0683678
\(677\) 18.5163i 0.711641i −0.934554 0.355821i \(-0.884201\pi\)
0.934554 0.355821i \(-0.115799\pi\)
\(678\) 6.80035i 0.261166i
\(679\) 6.98607i 0.268101i
\(680\) 3.25406 + 6.13349i 0.124787 + 0.235209i
\(681\) 2.12713i 0.0815116i
\(682\) 9.06851i 0.347251i
\(683\) −32.0667 −1.22700 −0.613499 0.789695i \(-0.710239\pi\)
−0.613499 + 0.789695i \(0.710239\pi\)
\(684\) 17.0669i 0.652571i
\(685\) 27.9026 14.8034i 1.06610 0.565609i
\(686\) 8.59237i 0.328058i
\(687\) 0.367738i 0.0140301i
\(688\) 4.86640 0.185530
\(689\) 24.0308i 0.915502i
\(690\) 5.67779 3.01229i 0.216150 0.114676i
\(691\) −6.57629 −0.250174 −0.125087 0.992146i \(-0.539921\pi\)
−0.125087 + 0.992146i \(0.539921\pi\)
\(692\) 2.88008i 0.109484i
\(693\) 2.25251i 0.0855656i
\(694\) −19.6225 −0.744860
\(695\) 8.84144 + 16.6650i 0.335375 + 0.632140i
\(696\) −3.61851 −0.137159
\(697\) 26.2540 0.994442
\(698\) 15.6263 0.591466
\(699\) 5.44686 0.206019
\(700\) −2.61550 1.77113i −0.0988565 0.0669425i
\(701\) 9.62168i 0.363406i −0.983353 0.181703i \(-0.941839\pi\)
0.983353 0.181703i \(-0.0581609\pi\)
\(702\) 7.41425i 0.279833i
\(703\) −26.8120 + 24.5209i −1.01123 + 0.924824i
\(704\) 1.24789 0.0470316
\(705\) −5.19482 9.79160i −0.195648 0.368773i
\(706\) −23.5724 −0.887159
\(707\) 5.46663i 0.205594i
\(708\) 1.64925 0.0619825
\(709\) 8.65759i 0.325142i −0.986697 0.162571i \(-0.948021\pi\)
0.986697 0.162571i \(-0.0519787\pi\)
\(710\) 13.3284 + 25.1224i 0.500206 + 0.942826i
\(711\) 25.1058i 0.941541i
\(712\) 13.7784i 0.516368i
\(713\) 55.2810i 2.07029i
\(714\) −0.741234 −0.0277400
\(715\) −4.38094 8.25753i −0.163838 0.308814i
\(716\) 4.46182i 0.166746i
\(717\) −3.18667 −0.119008
\(718\) 9.34905 0.348904
\(719\) 51.5303 1.92176 0.960878 0.276972i \(-0.0893310\pi\)
0.960878 + 0.276972i \(0.0893310\pi\)
\(720\) 2.99427 + 5.64384i 0.111590 + 0.210333i
\(721\) 2.88923i 0.107600i
\(722\) 16.6799 0.620763
\(723\) −7.04964 −0.262179
\(724\) 3.93480 0.146236
\(725\) 39.6466 + 26.8474i 1.47244 + 0.997087i
\(726\) 3.56806i 0.132423i
\(727\) 11.3224 0.419924 0.209962 0.977710i \(-0.432666\pi\)
0.209962 + 0.977710i \(0.432666\pi\)
\(728\) 2.11636i 0.0784375i
\(729\) 19.5928 0.725660
\(730\) −8.80654 + 4.67221i −0.325945 + 0.172926i
\(731\) −15.1107 −0.558890
\(732\) 0.811140 0.0299806
\(733\) 2.74231i 0.101290i −0.998717 0.0506448i \(-0.983872\pi\)
0.998717 0.0506448i \(-0.0161276\pi\)
\(734\) 12.2379i 0.451708i
\(735\) −4.92680 + 2.61386i −0.181728 + 0.0964137i
\(736\) −7.60706 −0.280400
\(737\) 14.1574i 0.521495i
\(738\) 24.1581 0.889272
\(739\) 8.18878 0.301229 0.150614 0.988593i \(-0.451875\pi\)
0.150614 + 0.988593i \(0.451875\pi\)
\(740\) −4.56437 + 12.8127i −0.167790 + 0.471006i
\(741\) 7.56115 0.277766
\(742\) −4.53180 −0.166368
\(743\) 22.1217i 0.811567i 0.913969 + 0.405784i \(0.133001\pi\)
−0.913969 + 0.405784i \(0.866999\pi\)
\(744\) 2.74594 0.100671
\(745\) 14.2992 + 26.9522i 0.523882 + 0.987453i
\(746\) 10.1918i 0.373149i
\(747\) 18.9487i 0.693296i
\(748\) −3.87484 −0.141678
\(749\) 7.24715 0.264805
\(750\) −0.453098 + 4.20025i −0.0165448 + 0.153371i
\(751\) −19.0818 −0.696306 −0.348153 0.937438i \(-0.613191\pi\)
−0.348153 + 0.937438i \(0.613191\pi\)
\(752\) 13.1187i 0.478390i
\(753\) 9.49146 0.345888
\(754\) 32.0805i 1.16830i
\(755\) −3.32982 6.27630i −0.121185 0.228418i
\(756\) −1.39820 −0.0508521
\(757\) 31.2209 1.13474 0.567372 0.823462i \(-0.307960\pi\)
0.567372 + 0.823462i \(0.307960\pi\)
\(758\) −20.7538 −0.753811
\(759\) 3.58695i 0.130198i
\(760\) 11.7989 6.25979i 0.427992 0.227066i
\(761\) −29.3163 −1.06271 −0.531357 0.847148i \(-0.678318\pi\)
−0.531357 + 0.847148i \(0.678318\pi\)
\(762\) 5.85042 0.211939
\(763\) −0.459756 −0.0166443
\(764\) 7.76296i 0.280854i
\(765\) −9.29756 17.5247i −0.336154 0.633608i
\(766\) −17.7328 −0.640712
\(767\) 14.6217i 0.527958i
\(768\) 0.377861i 0.0136349i
\(769\) 29.0289i 1.04681i −0.852084 0.523404i \(-0.824662\pi\)
0.852084 0.523404i \(-0.175338\pi\)
\(770\) 1.55723 0.826171i 0.0561187 0.0297731i
\(771\) 7.69146i 0.277001i
\(772\) −3.49189 −0.125676
\(773\) 43.4153i 1.56154i −0.624819 0.780769i \(-0.714827\pi\)
0.624819 0.780769i \(-0.285173\pi\)
\(774\) −13.9044 −0.499782
\(775\) −30.0862 20.3734i −1.08073 0.731836i
\(776\) 11.0583 0.396969
\(777\) −0.979948 1.07151i −0.0351554 0.0384401i
\(778\) 10.9054i 0.390976i
\(779\) 50.5046i 1.80951i
\(780\) 2.50038 1.32655i 0.0895280 0.0474981i
\(781\) −15.8711 −0.567912
\(782\) 23.6208 0.844676
\(783\) 21.1944 0.757426
\(784\) 6.60089 0.235746
\(785\) −0.425299 + 0.225638i −0.0151796 + 0.00805336i
\(786\) −2.35075 −0.0838486
\(787\) 18.9119i 0.674136i −0.941480 0.337068i \(-0.890565\pi\)
0.941480