Properties

Label 370.2.c.a.369.10
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 369.10
Root \(3.40359i\) of defining polynomial
Character \(\chi\) \(=\) 370.369
Dual form 370.2.c.a.369.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +3.40359i q^{3} +1.00000 q^{4} +(-1.28269 + 1.83159i) q^{5} -3.40359i q^{6} +2.06225i q^{7} -1.00000 q^{8} -8.58443 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +3.40359i q^{3} +1.00000 q^{4} +(-1.28269 + 1.83159i) q^{5} -3.40359i q^{6} +2.06225i q^{7} -1.00000 q^{8} -8.58443 q^{9} +(1.28269 - 1.83159i) q^{10} +3.77719 q^{11} +3.40359i q^{12} -2.88351 q^{13} -2.06225i q^{14} +(-6.23397 - 4.36575i) q^{15} +1.00000 q^{16} +5.80724 q^{17} +8.58443 q^{18} +0.157282i q^{19} +(-1.28269 + 1.83159i) q^{20} -7.01905 q^{21} -3.77719 q^{22} +5.41883 q^{23} -3.40359i q^{24} +(-1.70942 - 4.69871i) q^{25} +2.88351 q^{26} -19.0071i q^{27} +2.06225i q^{28} +4.29061i q^{29} +(6.23397 + 4.36575i) q^{30} -0.425694i q^{31} -1.00000 q^{32} +12.8560i q^{33} -5.80724 q^{34} +(-3.77719 - 2.64522i) q^{35} -8.58443 q^{36} +(-4.80724 - 3.72698i) q^{37} -0.157282i q^{38} -9.81429i q^{39} +(1.28269 - 1.83159i) q^{40} +0.923733 q^{41} +7.01905 q^{42} -10.8263 q^{43} +3.77719 q^{44} +(11.0112 - 15.7231i) q^{45} -5.41883 q^{46} +0.676445i q^{47} +3.40359i q^{48} +2.74713 q^{49} +(1.70942 + 4.69871i) q^{50} +19.7655i q^{51} -2.88351 q^{52} +9.87810i q^{53} +19.0071i q^{54} +(-4.84496 + 6.91824i) q^{55} -2.06225i q^{56} -0.535322 q^{57} -4.29061i q^{58} +8.47192i q^{59} +(-6.23397 - 4.36575i) q^{60} -1.23904i q^{61} +0.425694i q^{62} -17.7032i q^{63} +1.00000 q^{64} +(3.69865 - 5.28140i) q^{65} -12.8560i q^{66} +6.45516i q^{67} +5.80724 q^{68} +18.4435i q^{69} +(3.77719 + 2.64522i) q^{70} -3.28329 q^{71} +8.58443 q^{72} -0.980489i q^{73} +(4.80724 + 3.72698i) q^{74} +(15.9925 - 5.81815i) q^{75} +0.157282i q^{76} +7.78950i q^{77} +9.81429i q^{78} -8.04725i q^{79} +(-1.28269 + 1.83159i) q^{80} +38.9391 q^{81} -0.923733 q^{82} -11.9496i q^{83} -7.01905 q^{84} +(-7.44889 + 10.6365i) q^{85} +10.8263 q^{86} -14.6035 q^{87} -3.77719 q^{88} +7.65857i q^{89} +(-11.0112 + 15.7231i) q^{90} -5.94652i q^{91} +5.41883 q^{92} +1.44889 q^{93} -0.676445i q^{94} +(-0.288075 - 0.201743i) q^{95} -3.40359i q^{96} +13.9571 q^{97} -2.74713 q^{98} -32.4250 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + O(q^{10}) \) \( 10q - 10q^{2} + 10q^{4} - 3q^{5} - 10q^{8} - 8q^{9} + 3q^{10} - 2q^{13} - 10q^{15} + 10q^{16} + 18q^{17} + 8q^{18} - 3q^{20} - 12q^{21} + 10q^{23} + 5q^{25} + 2q^{26} + 10q^{30} - 10q^{32} - 18q^{34} - 8q^{36} - 8q^{37} + 3q^{40} - 4q^{41} + 12q^{42} - 10q^{43} + 20q^{45} - 10q^{46} - 8q^{49} - 5q^{50} - 2q^{52} + 5q^{55} + 12q^{57} - 10q^{60} + 10q^{64} + 2q^{65} + 18q^{68} - 20q^{71} + 8q^{72} + 8q^{74} + 25q^{75} - 3q^{80} + 58q^{81} + 4q^{82} - 12q^{84} - 28q^{85} + 10q^{86} - 10q^{87} - 20q^{90} + 10q^{92} - 32q^{93} + 2q^{95} + 2q^{97} + 8q^{98} - 82q^{99} + O(q^{100}) \)

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
\(3\) 3.40359i 1.96506i 0.186094 + 0.982532i \(0.440417\pi\)
−0.186094 + 0.982532i \(0.559583\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.28269 + 1.83159i −0.573636 + 0.819110i
\(6\) 3.40359i 1.38951i
\(7\) 2.06225i 0.779457i 0.920930 + 0.389728i \(0.127431\pi\)
−0.920930 + 0.389728i \(0.872569\pi\)
\(8\) −1.00000 −0.353553
\(9\) −8.58443 −2.86148
\(10\) 1.28269 1.83159i 0.405622 0.579198i
\(11\) 3.77719 1.13886 0.569432 0.822038i \(-0.307163\pi\)
0.569432 + 0.822038i \(0.307163\pi\)
\(12\) 3.40359i 0.982532i
\(13\) −2.88351 −0.799742 −0.399871 0.916571i \(-0.630945\pi\)
−0.399871 + 0.916571i \(0.630945\pi\)
\(14\) 2.06225i 0.551159i
\(15\) −6.23397 4.36575i −1.60960 1.12723i
\(16\) 1.00000 0.250000
\(17\) 5.80724 1.40846 0.704232 0.709970i \(-0.251292\pi\)
0.704232 + 0.709970i \(0.251292\pi\)
\(18\) 8.58443 2.02337
\(19\) 0.157282i 0.0360829i 0.999837 + 0.0180414i \(0.00574308\pi\)
−0.999837 + 0.0180414i \(0.994257\pi\)
\(20\) −1.28269 + 1.83159i −0.286818 + 0.409555i
\(21\) −7.01905 −1.53168
\(22\) −3.77719 −0.805299
\(23\) 5.41883 1.12990 0.564952 0.825124i \(-0.308895\pi\)
0.564952 + 0.825124i \(0.308895\pi\)
\(24\) 3.40359i 0.694755i
\(25\) −1.70942 4.69871i −0.341883 0.939742i
\(26\) 2.88351 0.565503
\(27\) 19.0071i 3.65792i
\(28\) 2.06225i 0.389728i
\(29\) 4.29061i 0.796746i 0.917223 + 0.398373i \(0.130425\pi\)
−0.917223 + 0.398373i \(0.869575\pi\)
\(30\) 6.23397 + 4.36575i 1.13816 + 0.797073i
\(31\) 0.425694i 0.0764569i −0.999269 0.0382285i \(-0.987829\pi\)
0.999269 0.0382285i \(-0.0121715\pi\)
\(32\) −1.00000 −0.176777
\(33\) 12.8560i 2.23794i
\(34\) −5.80724 −0.995934
\(35\) −3.77719 2.64522i −0.638461 0.447125i
\(36\) −8.58443 −1.43074
\(37\) −4.80724 3.72698i −0.790306 0.612713i
\(38\) 0.157282i 0.0255144i
\(39\) 9.81429i 1.57154i
\(40\) 1.28269 1.83159i 0.202811 0.289599i
\(41\) 0.923733 0.144263 0.0721314 0.997395i \(-0.477020\pi\)
0.0721314 + 0.997395i \(0.477020\pi\)
\(42\) 7.01905 1.08306
\(43\) −10.8263 −1.65099 −0.825497 0.564406i \(-0.809105\pi\)
−0.825497 + 0.564406i \(0.809105\pi\)
\(44\) 3.77719 0.569432
\(45\) 11.0112 15.7231i 1.64145 2.34386i
\(46\) −5.41883 −0.798963
\(47\) 0.676445i 0.0986697i 0.998782 + 0.0493348i \(0.0157101\pi\)
−0.998782 + 0.0493348i \(0.984290\pi\)
\(48\) 3.40359i 0.491266i
\(49\) 2.74713 0.392447
\(50\) 1.70942 + 4.69871i 0.241748 + 0.664498i
\(51\) 19.7655i 2.76772i
\(52\) −2.88351 −0.399871
\(53\) 9.87810i 1.35686i 0.734664 + 0.678431i \(0.237340\pi\)
−0.734664 + 0.678431i \(0.762660\pi\)
\(54\) 19.0071i 2.58654i
\(55\) −4.84496 + 6.91824i −0.653294 + 0.932856i
\(56\) 2.06225i 0.275580i
\(57\) −0.535322 −0.0709052
\(58\) 4.29061i 0.563385i
\(59\) 8.47192i 1.10295i 0.834192 + 0.551475i \(0.185935\pi\)
−0.834192 + 0.551475i \(0.814065\pi\)
\(60\) −6.23397 4.36575i −0.804802 0.563616i
\(61\) 1.23904i 0.158643i −0.996849 0.0793215i \(-0.974725\pi\)
0.996849 0.0793215i \(-0.0252754\pi\)
\(62\) 0.425694i 0.0540632i
\(63\) 17.7032i 2.23040i
\(64\) 1.00000 0.125000
\(65\) 3.69865 5.28140i 0.458761 0.655077i
\(66\) 12.8560i 1.58246i
\(67\) 6.45516i 0.788623i 0.918977 + 0.394312i \(0.129017\pi\)
−0.918977 + 0.394312i \(0.870983\pi\)
\(68\) 5.80724 0.704232
\(69\) 18.4435i 2.22033i
\(70\) 3.77719 + 2.64522i 0.451460 + 0.316165i
\(71\) −3.28329 −0.389655 −0.194828 0.980838i \(-0.562415\pi\)
−0.194828 + 0.980838i \(0.562415\pi\)
\(72\) 8.58443 1.01168
\(73\) 0.980489i 0.114758i −0.998352 0.0573788i \(-0.981726\pi\)
0.998352 0.0573788i \(-0.0182743\pi\)
\(74\) 4.80724 + 3.72698i 0.558831 + 0.433253i
\(75\) 15.9925 5.81815i 1.84665 0.671822i
\(76\) 0.157282i 0.0180414i
\(77\) 7.78950i 0.887696i
\(78\) 9.81429i 1.11125i
\(79\) 8.04725i 0.905387i −0.891666 0.452693i \(-0.850463\pi\)
0.891666 0.452693i \(-0.149537\pi\)
\(80\) −1.28269 + 1.83159i −0.143409 + 0.204778i
\(81\) 38.9391 4.32657
\(82\) −0.923733 −0.102009
\(83\) 11.9496i 1.31164i −0.754916 0.655821i \(-0.772323\pi\)
0.754916 0.655821i \(-0.227677\pi\)
\(84\) −7.01905 −0.765841
\(85\) −7.44889 + 10.6365i −0.807945 + 1.15369i
\(86\) 10.8263 1.16743
\(87\) −14.6035 −1.56566
\(88\) −3.77719 −0.402649
\(89\) 7.65857i 0.811807i 0.913916 + 0.405903i \(0.133043\pi\)
−0.913916 + 0.405903i \(0.866957\pi\)
\(90\) −11.0112 + 15.7231i −1.16068 + 1.65736i
\(91\) 5.94652i 0.623364i
\(92\) 5.41883 0.564952
\(93\) 1.44889 0.150243
\(94\) 0.676445i 0.0697700i
\(95\) −0.288075 0.201743i −0.0295558 0.0206984i
\(96\) 3.40359i 0.347378i
\(97\) 13.9571 1.41712 0.708562 0.705649i \(-0.249344\pi\)
0.708562 + 0.705649i \(0.249344\pi\)
\(98\) −2.74713 −0.277502
\(99\) −32.4250 −3.25883
\(100\) −1.70942 4.69871i −0.170942 0.469871i
\(101\) −8.38279 −0.834119 −0.417059 0.908879i \(-0.636939\pi\)
−0.417059 + 0.908879i \(0.636939\pi\)
\(102\) 19.7655i 1.95707i
\(103\) 13.4727 1.32751 0.663753 0.747951i \(-0.268962\pi\)
0.663753 + 0.747951i \(0.268962\pi\)
\(104\) 2.88351 0.282751
\(105\) 9.00326 12.8560i 0.878628 1.25462i
\(106\) 9.87810i 0.959446i
\(107\) 1.89614i 0.183306i −0.995791 0.0916532i \(-0.970785\pi\)
0.995791 0.0916532i \(-0.0292151\pi\)
\(108\) 19.0071i 1.82896i
\(109\) 17.2044i 1.64789i 0.566672 + 0.823943i \(0.308231\pi\)
−0.566672 + 0.823943i \(0.691769\pi\)
\(110\) 4.84496 6.91824i 0.461949 0.659629i
\(111\) 12.6851 16.3619i 1.20402 1.55300i
\(112\) 2.06225i 0.194864i
\(113\) −1.17098 −0.110157 −0.0550783 0.998482i \(-0.517541\pi\)
−0.0550783 + 0.998482i \(0.517541\pi\)
\(114\) 0.535322 0.0501375
\(115\) −6.95068 + 9.92506i −0.648154 + 0.925516i
\(116\) 4.29061i 0.398373i
\(117\) 24.7533 2.28844
\(118\) 8.47192i 0.779903i
\(119\) 11.9760i 1.09784i
\(120\) 6.23397 + 4.36575i 0.569081 + 0.398537i
\(121\) 3.26714 0.297012
\(122\) 1.23904i 0.112178i
\(123\) 3.14401i 0.283486i
\(124\) 0.425694i 0.0382285i
\(125\) 10.7987 + 2.89605i 0.965869 + 0.259030i
\(126\) 17.7032i 1.57713i
\(127\) 16.1128i 1.42978i 0.699236 + 0.714891i \(0.253524\pi\)
−0.699236 + 0.714891i \(0.746476\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 36.8483i 3.24431i
\(130\) −3.69865 + 5.28140i −0.324393 + 0.463209i
\(131\) 9.64715i 0.842875i −0.906857 0.421438i \(-0.861526\pi\)
0.906857 0.421438i \(-0.138474\pi\)
\(132\) 12.8560i 1.11897i
\(133\) −0.324354 −0.0281250
\(134\) 6.45516i 0.557641i
\(135\) 34.8132 + 24.3802i 2.99624 + 2.09832i
\(136\) −5.80724 −0.497967
\(137\) 2.53592i 0.216658i −0.994115 0.108329i \(-0.965450\pi\)
0.994115 0.108329i \(-0.0345501\pi\)
\(138\) 18.4435i 1.57001i
\(139\) 7.56000 0.641230 0.320615 0.947210i \(-0.396110\pi\)
0.320615 + 0.947210i \(0.396110\pi\)
\(140\) −3.77719 2.64522i −0.319231 0.223562i
\(141\) −2.30234 −0.193892
\(142\) 3.28329 0.275528
\(143\) −10.8916 −0.910798
\(144\) −8.58443 −0.715369
\(145\) −7.85862 5.50352i −0.652623 0.457042i
\(146\) 0.980489i 0.0811458i
\(147\) 9.35011i 0.771184i
\(148\) −4.80724 3.72698i −0.395153 0.306356i
\(149\) 6.72596 0.551012 0.275506 0.961299i \(-0.411155\pi\)
0.275506 + 0.961299i \(0.411155\pi\)
\(150\) −15.9925 + 5.81815i −1.30578 + 0.475050i
\(151\) −15.8051 −1.28620 −0.643101 0.765781i \(-0.722353\pi\)
−0.643101 + 0.765781i \(0.722353\pi\)
\(152\) 0.157282i 0.0127572i
\(153\) −49.8519 −4.03028
\(154\) 7.78950i 0.627696i
\(155\) 0.779696 + 0.546033i 0.0626267 + 0.0438585i
\(156\) 9.81429i 0.785772i
\(157\) 8.50755i 0.678976i 0.940610 + 0.339488i \(0.110254\pi\)
−0.940610 + 0.339488i \(0.889746\pi\)
\(158\) 8.04725i 0.640205i
\(159\) −33.6210 −2.66632
\(160\) 1.28269 1.83159i 0.101405 0.144800i
\(161\) 11.1750i 0.880712i
\(162\) −38.9391 −3.05935
\(163\) −5.41321 −0.423995 −0.211998 0.977270i \(-0.567997\pi\)
−0.211998 + 0.977270i \(0.567997\pi\)
\(164\) 0.923733 0.0721314
\(165\) −23.5469 16.4902i −1.83312 1.28376i
\(166\) 11.9496i 0.927471i
\(167\) 2.08165 0.161083 0.0805415 0.996751i \(-0.474335\pi\)
0.0805415 + 0.996751i \(0.474335\pi\)
\(168\) 7.01905 0.541532
\(169\) −4.68537 −0.360413
\(170\) 7.44889 10.6365i 0.571304 0.815780i
\(171\) 1.35017i 0.103250i
\(172\) −10.8263 −0.825497
\(173\) 12.3562i 0.939423i 0.882820 + 0.469712i \(0.155642\pi\)
−0.882820 + 0.469712i \(0.844358\pi\)
\(174\) 14.6035 1.10709
\(175\) 9.68991 3.52524i 0.732489 0.266483i
\(176\) 3.77719 0.284716
\(177\) −28.8349 −2.16737
\(178\) 7.65857i 0.574034i
\(179\) 13.4571i 1.00583i −0.864336 0.502915i \(-0.832261\pi\)
0.864336 0.502915i \(-0.167739\pi\)
\(180\) 11.0112 15.7231i 0.820723 1.17193i
\(181\) −3.66608 −0.272498 −0.136249 0.990675i \(-0.543505\pi\)
−0.136249 + 0.990675i \(0.543505\pi\)
\(182\) 5.94652i 0.440785i
\(183\) 4.21719 0.311744
\(184\) −5.41883 −0.399482
\(185\) 12.9925 4.02432i 0.955227 0.295874i
\(186\) −1.44889 −0.106238
\(187\) 21.9350 1.60405
\(188\) 0.676445i 0.0493348i
\(189\) 39.1974 2.85119
\(190\) 0.288075 + 0.201743i 0.0208991 + 0.0146360i
\(191\) 18.5540i 1.34252i 0.741221 + 0.671261i \(0.234247\pi\)
−0.741221 + 0.671261i \(0.765753\pi\)
\(192\) 3.40359i 0.245633i
\(193\) 4.89778 0.352550 0.176275 0.984341i \(-0.443595\pi\)
0.176275 + 0.984341i \(0.443595\pi\)
\(194\) −13.9571 −1.00206
\(195\) 17.9757 + 12.5887i 1.28727 + 0.901494i
\(196\) 2.74713 0.196224
\(197\) 14.7803i 1.05305i −0.850158 0.526527i \(-0.823494\pi\)
0.850158 0.526527i \(-0.176506\pi\)
\(198\) 32.4250 2.30434
\(199\) 12.3298i 0.874039i −0.899452 0.437019i \(-0.856034\pi\)
0.899452 0.437019i \(-0.143966\pi\)
\(200\) 1.70942 + 4.69871i 0.120874 + 0.332249i
\(201\) −21.9707 −1.54970
\(202\) 8.38279 0.589811
\(203\) −8.84831 −0.621029
\(204\) 19.7655i 1.38386i
\(205\) −1.18486 + 1.69190i −0.0827544 + 0.118167i
\(206\) −13.4727 −0.938689
\(207\) −46.5176 −3.23320
\(208\) −2.88351 −0.199935
\(209\) 0.594082i 0.0410935i
\(210\) −9.00326 + 12.8560i −0.621284 + 0.887148i
\(211\) 14.1805 0.976224 0.488112 0.872781i \(-0.337686\pi\)
0.488112 + 0.872781i \(0.337686\pi\)
\(212\) 9.87810i 0.678431i
\(213\) 11.1750i 0.765697i
\(214\) 1.89614i 0.129617i
\(215\) 13.8868 19.8293i 0.947070 1.35235i
\(216\) 19.0071i 1.29327i
\(217\) 0.877887 0.0595949
\(218\) 17.2044i 1.16523i
\(219\) 3.33718 0.225506
\(220\) −4.84496 + 6.91824i −0.326647 + 0.466428i
\(221\) −16.7452 −1.12641
\(222\) −12.6851 + 16.3619i −0.851370 + 1.09814i
\(223\) 7.29071i 0.488222i −0.969747 0.244111i \(-0.921504\pi\)
0.969747 0.244111i \(-0.0784962\pi\)
\(224\) 2.06225i 0.137790i
\(225\) 14.6744 + 40.3358i 0.978291 + 2.68905i
\(226\) 1.17098 0.0778925
\(227\) 26.3807 1.75095 0.875473 0.483267i \(-0.160550\pi\)
0.875473 + 0.483267i \(0.160550\pi\)
\(228\) −0.535322 −0.0354526
\(229\) −19.5925 −1.29471 −0.647354 0.762190i \(-0.724124\pi\)
−0.647354 + 0.762190i \(0.724124\pi\)
\(230\) 6.95068 9.92506i 0.458314 0.654439i
\(231\) −26.5123 −1.74438
\(232\) 4.29061i 0.281692i
\(233\) 3.69983i 0.242384i −0.992629 0.121192i \(-0.961328\pi\)
0.992629 0.121192i \(-0.0386717\pi\)
\(234\) −24.7533 −1.61817
\(235\) −1.23897 0.867669i −0.0808213 0.0566005i
\(236\) 8.47192i 0.551475i
\(237\) 27.3896 1.77914
\(238\) 11.9760i 0.776287i
\(239\) 8.68397i 0.561719i 0.959749 + 0.280860i \(0.0906195\pi\)
−0.959749 + 0.280860i \(0.909380\pi\)
\(240\) −6.23397 4.36575i −0.402401 0.281808i
\(241\) 27.5610i 1.77536i −0.460464 0.887678i \(-0.652317\pi\)
0.460464 0.887678i \(-0.347683\pi\)
\(242\) −3.26714 −0.210020
\(243\) 75.5116i 4.84407i
\(244\) 1.23904i 0.0793215i
\(245\) −3.52371 + 5.03161i −0.225122 + 0.321457i
\(246\) 3.14401i 0.200455i
\(247\) 0.453523i 0.0288570i
\(248\) 0.425694i 0.0270316i
\(249\) 40.6716 2.57746
\(250\) −10.7987 2.89605i −0.682973 0.183162i
\(251\) 20.4512i 1.29087i −0.763816 0.645434i \(-0.776676\pi\)
0.763816 0.645434i \(-0.223324\pi\)
\(252\) 17.7032i 1.11520i
\(253\) 20.4679 1.28681
\(254\) 16.1128i 1.01101i
\(255\) −36.2022 25.3530i −2.26707 1.58766i
\(256\) 1.00000 0.0625000
\(257\) 22.8951 1.42815 0.714077 0.700067i \(-0.246847\pi\)
0.714077 + 0.700067i \(0.246847\pi\)
\(258\) 36.8483i 2.29407i
\(259\) 7.68597 9.91373i 0.477583 0.616009i
\(260\) 3.69865 5.28140i 0.229380 0.327538i
\(261\) 36.8324i 2.27987i
\(262\) 9.64715i 0.596003i
\(263\) 22.1600i 1.36644i −0.730212 0.683221i \(-0.760579\pi\)
0.730212 0.683221i \(-0.239421\pi\)
\(264\) 12.8560i 0.791232i
\(265\) −18.0926 12.6705i −1.11142 0.778345i
\(266\) 0.324354 0.0198874
\(267\) −26.0666 −1.59525
\(268\) 6.45516i 0.394312i
\(269\) 23.9657 1.46121 0.730607 0.682798i \(-0.239237\pi\)
0.730607 + 0.682798i \(0.239237\pi\)
\(270\) −34.8132 24.3802i −2.11866 1.48373i
\(271\) 9.82713 0.596956 0.298478 0.954417i \(-0.403521\pi\)
0.298478 + 0.954417i \(0.403521\pi\)
\(272\) 5.80724 0.352116
\(273\) 20.2395 1.22495
\(274\) 2.53592i 0.153201i
\(275\) −6.45678 17.7479i −0.389359 1.07024i
\(276\) 18.4435i 1.11017i
\(277\) −0.807608 −0.0485245 −0.0242622 0.999706i \(-0.507724\pi\)
−0.0242622 + 0.999706i \(0.507724\pi\)
\(278\) −7.56000 −0.453418
\(279\) 3.65434i 0.218780i
\(280\) 3.77719 + 2.64522i 0.225730 + 0.158082i
\(281\) 1.03833i 0.0619414i −0.999520 0.0309707i \(-0.990140\pi\)
0.999520 0.0309707i \(-0.00985986\pi\)
\(282\) 2.30234 0.137102
\(283\) 6.26151 0.372208 0.186104 0.982530i \(-0.440414\pi\)
0.186104 + 0.982530i \(0.440414\pi\)
\(284\) −3.28329 −0.194828
\(285\) 0.686652 0.980489i 0.0406738 0.0580791i
\(286\) 10.8916 0.644031
\(287\) 1.90497i 0.112447i
\(288\) 8.58443 0.505842
\(289\) 16.7241 0.983769
\(290\) 7.85862 + 5.50352i 0.461474 + 0.323178i
\(291\) 47.5041i 2.78474i
\(292\) 0.980489i 0.0573788i
\(293\) 4.84496i 0.283045i 0.989935 + 0.141523i \(0.0451998\pi\)
−0.989935 + 0.141523i \(0.954800\pi\)
\(294\) 9.35011i 0.545309i
\(295\) −15.5170 10.8668i −0.903437 0.632692i
\(296\) 4.80724 + 3.72698i 0.279415 + 0.216627i
\(297\) 71.7934i 4.16588i
\(298\) −6.72596 −0.389624
\(299\) −15.6253 −0.903632
\(300\) 15.9925 5.81815i 0.923327 0.335911i
\(301\) 22.3265i 1.28688i
\(302\) 15.8051 0.909483
\(303\) 28.5316i 1.63910i
\(304\) 0.157282i 0.00902072i
\(305\) 2.26941 + 1.58931i 0.129946 + 0.0910034i
\(306\) 49.8519 2.84984
\(307\) 2.87515i 0.164093i 0.996628 + 0.0820467i \(0.0261457\pi\)
−0.996628 + 0.0820467i \(0.973854\pi\)
\(308\) 7.78950i 0.443848i
\(309\) 45.8556i 2.60864i
\(310\) −0.779696 0.546033i −0.0442837 0.0310126i
\(311\) 6.07102i 0.344256i −0.985075 0.172128i \(-0.944936\pi\)
0.985075 0.172128i \(-0.0550643\pi\)
\(312\) 9.81429i 0.555625i
\(313\) −10.0000 −0.565233 −0.282617 0.959233i \(-0.591202\pi\)
−0.282617 + 0.959233i \(0.591202\pi\)
\(314\) 8.50755i 0.480109i
\(315\) 32.4250 + 22.7077i 1.82694 + 1.27944i
\(316\) 8.04725i 0.452693i
\(317\) 25.5691i 1.43610i 0.695989 + 0.718052i \(0.254966\pi\)
−0.695989 + 0.718052i \(0.745034\pi\)
\(318\) 33.6210 1.88537
\(319\) 16.2064i 0.907386i
\(320\) −1.28269 + 1.83159i −0.0717045 + 0.102389i
\(321\) 6.45367 0.360209
\(322\) 11.1750i 0.622757i
\(323\) 0.913372i 0.0508214i
\(324\) 38.9391 2.16329
\(325\) 4.92912 + 13.5488i 0.273418 + 0.751551i
\(326\) 5.41321 0.299810
\(327\) −58.5569 −3.23820
\(328\) −0.923733 −0.0510046
\(329\) −1.39500 −0.0769087
\(330\) 23.5469 + 16.4902i 1.29621 + 0.907758i
\(331\) 16.8578i 0.926589i −0.886204 0.463295i \(-0.846667\pi\)
0.886204 0.463295i \(-0.153333\pi\)
\(332\) 11.9496i 0.655821i
\(333\) 41.2674 + 31.9940i 2.26144 + 1.75326i
\(334\) −2.08165 −0.113903
\(335\) −11.8232 8.27996i −0.645969 0.452383i
\(336\) −7.01905 −0.382921
\(337\) 14.7105i 0.801334i 0.916224 + 0.400667i \(0.131221\pi\)
−0.916224 + 0.400667i \(0.868779\pi\)
\(338\) 4.68537 0.254851
\(339\) 3.98554i 0.216465i
\(340\) −7.44889 + 10.6365i −0.403973 + 0.576843i
\(341\) 1.60793i 0.0870741i
\(342\) 1.35017i 0.0730090i
\(343\) 20.1010i 1.08535i
\(344\) 10.8263 0.583715
\(345\) −33.7808 23.6573i −1.81870 1.27366i
\(346\) 12.3562i 0.664273i
\(347\) 3.26296 0.175165 0.0875824 0.996157i \(-0.472086\pi\)
0.0875824 + 0.996157i \(0.472086\pi\)
\(348\) −14.6035 −0.782829
\(349\) −17.2097 −0.921213 −0.460607 0.887604i \(-0.652368\pi\)
−0.460607 + 0.887604i \(0.652368\pi\)
\(350\) −9.68991 + 3.52524i −0.517948 + 0.188432i
\(351\) 54.8072i 2.92539i
\(352\) −3.77719 −0.201325
\(353\) −4.88641 −0.260077 −0.130039 0.991509i \(-0.541510\pi\)
−0.130039 + 0.991509i \(0.541510\pi\)
\(354\) 28.8349 1.53256
\(355\) 4.21144 6.01363i 0.223520 0.319170i
\(356\) 7.65857i 0.405903i
\(357\) −40.7613 −2.15732
\(358\) 13.4571i 0.711229i
\(359\) 3.39107 0.178974 0.0894870 0.995988i \(-0.471477\pi\)
0.0894870 + 0.995988i \(0.471477\pi\)
\(360\) −11.0112 + 15.7231i −0.580339 + 0.828681i
\(361\) 18.9753 0.998698
\(362\) 3.66608 0.192685
\(363\) 11.1200i 0.583649i
\(364\) 5.94652i 0.311682i
\(365\) 1.79585 + 1.25766i 0.0939991 + 0.0658291i
\(366\) −4.21719 −0.220436
\(367\) 9.25169i 0.482934i −0.970409 0.241467i \(-0.922371\pi\)
0.970409 0.241467i \(-0.0776286\pi\)
\(368\) 5.41883 0.282476
\(369\) −7.92972 −0.412805
\(370\) −12.9925 + 4.02432i −0.675448 + 0.209214i
\(371\) −20.3711 −1.05761
\(372\) 1.44889 0.0751214
\(373\) 11.4101i 0.590792i −0.955375 0.295396i \(-0.904548\pi\)
0.955375 0.295396i \(-0.0954515\pi\)
\(374\) −21.9350 −1.13423
\(375\) −9.85695 + 36.7545i −0.509011 + 1.89799i
\(376\) 0.676445i 0.0348850i
\(377\) 12.3720i 0.637191i
\(378\) −39.1974 −2.01610
\(379\) 36.3643 1.86791 0.933954 0.357394i \(-0.116335\pi\)
0.933954 + 0.357394i \(0.116335\pi\)
\(380\) −0.288075 0.201743i −0.0147779 0.0103492i
\(381\) −54.8415 −2.80961
\(382\) 18.5540i 0.949307i
\(383\) −13.6526 −0.697615 −0.348807 0.937194i \(-0.613413\pi\)
−0.348807 + 0.937194i \(0.613413\pi\)
\(384\) 3.40359i 0.173689i
\(385\) −14.2671 9.99151i −0.727121 0.509214i
\(386\) −4.89778 −0.249290
\(387\) 92.9376 4.72428
\(388\) 13.9571 0.708562
\(389\) 2.36833i 0.120079i −0.998196 0.0600396i \(-0.980877\pi\)
0.998196 0.0600396i \(-0.0191227\pi\)
\(390\) −17.9757 12.5887i −0.910236 0.637453i
\(391\) 31.4685 1.59143
\(392\) −2.74713 −0.138751
\(393\) 32.8349 1.65630
\(394\) 14.7803i 0.744621i
\(395\) 14.7392 + 10.3221i 0.741611 + 0.519362i
\(396\) −32.4250 −1.62942
\(397\) 34.4978i 1.73140i 0.500567 + 0.865698i \(0.333125\pi\)
−0.500567 + 0.865698i \(0.666875\pi\)
\(398\) 12.3298i 0.618039i
\(399\) 1.10397i 0.0552675i
\(400\) −1.70942 4.69871i −0.0854708 0.234936i
\(401\) 29.0777i 1.45207i 0.687658 + 0.726035i \(0.258639\pi\)
−0.687658 + 0.726035i \(0.741361\pi\)
\(402\) 21.9707 1.09580
\(403\) 1.22749i 0.0611458i
\(404\) −8.38279 −0.417059
\(405\) −49.9468 + 71.3204i −2.48188 + 3.54394i
\(406\) 8.84831 0.439134
\(407\) −18.1579 14.0775i −0.900051 0.697797i
\(408\) 19.7655i 0.978537i
\(409\) 16.4980i 0.815773i 0.913033 + 0.407887i \(0.133734\pi\)
−0.913033 + 0.407887i \(0.866266\pi\)
\(410\) 1.18486 1.69190i 0.0585162 0.0835568i
\(411\) 8.63124 0.425748
\(412\) 13.4727 0.663753
\(413\) −17.4712 −0.859702
\(414\) 46.5176 2.28621
\(415\) 21.8868 + 15.3277i 1.07438 + 0.752405i
\(416\) 2.88351 0.141376
\(417\) 25.7311i 1.26006i
\(418\) 0.594082i 0.0290575i
\(419\) 22.9409 1.12074 0.560368 0.828244i \(-0.310660\pi\)
0.560368 + 0.828244i \(0.310660\pi\)
\(420\) 9.00326 12.8560i 0.439314 0.627308i
\(421\) 1.72030i 0.0838422i −0.999121 0.0419211i \(-0.986652\pi\)
0.999121 0.0419211i \(-0.0133478\pi\)
\(422\) −14.1805 −0.690294
\(423\) 5.80690i 0.282341i
\(424\) 9.87810i 0.479723i
\(425\) −9.92699 27.2866i −0.481530 1.32359i
\(426\) 11.1750i 0.541430i
\(427\) 2.55521 0.123655
\(428\) 1.89614i 0.0916532i
\(429\) 37.0704i 1.78978i
\(430\) −13.8868 + 19.8293i −0.669680 + 0.956253i
\(431\) 2.55447i 0.123045i 0.998106 + 0.0615223i \(0.0195955\pi\)
−0.998106 + 0.0615223i \(0.980404\pi\)
\(432\) 19.0071i 0.914480i
\(433\) 30.0446i 1.44385i −0.691970 0.721926i \(-0.743257\pi\)
0.691970 0.721926i \(-0.256743\pi\)
\(434\) −0.877887 −0.0421399
\(435\) 18.7317 26.7475i 0.898118 1.28245i
\(436\) 17.2044i 0.823943i
\(437\) 0.852283i 0.0407702i
\(438\) −3.33718 −0.159457
\(439\) 38.4265i 1.83400i −0.398889 0.916999i \(-0.630604\pi\)
0.398889 0.916999i \(-0.369396\pi\)
\(440\) 4.84496 6.91824i 0.230974 0.329814i
\(441\) −23.5825 −1.12298
\(442\) 16.7452 0.796490
\(443\) 1.00809i 0.0478957i 0.999713 + 0.0239479i \(0.00762357\pi\)
−0.999713 + 0.0239479i \(0.992376\pi\)
\(444\) 12.6851 16.3619i 0.602010 0.776501i
\(445\) −14.0273 9.82357i −0.664959 0.465682i
\(446\) 7.29071i 0.345225i
\(447\) 22.8924i 1.08277i
\(448\) 2.06225i 0.0974321i
\(449\) 32.1157i 1.51563i 0.652468 + 0.757817i \(0.273734\pi\)
−0.652468 + 0.757817i \(0.726266\pi\)
\(450\) −14.6744 40.3358i −0.691756 1.90145i
\(451\) 3.48911 0.164296
\(452\) −1.17098 −0.0550783
\(453\) 53.7942i 2.52747i
\(454\) −26.3807 −1.23811
\(455\) 10.8916 + 7.62753i 0.510604 + 0.357584i
\(456\) 0.535322 0.0250688
\(457\) 7.85884 0.367621 0.183810 0.982962i \(-0.441157\pi\)
0.183810 + 0.982962i \(0.441157\pi\)
\(458\) 19.5925 0.915496
\(459\) 110.379i 5.15205i
\(460\) −6.95068 + 9.92506i −0.324077 + 0.462758i
\(461\) 16.7952i 0.782233i 0.920341 + 0.391116i \(0.127911\pi\)
−0.920341 + 0.391116i \(0.872089\pi\)
\(462\) 26.5123 1.23346
\(463\) −2.46094 −0.114370 −0.0571848 0.998364i \(-0.518212\pi\)
−0.0571848 + 0.998364i \(0.518212\pi\)
\(464\) 4.29061i 0.199187i
\(465\) −1.85847 + 2.65376i −0.0861847 + 0.123065i
\(466\) 3.69983i 0.171391i
\(467\) −7.57699 −0.350621 −0.175311 0.984513i \(-0.556093\pi\)
−0.175311 + 0.984513i \(0.556093\pi\)
\(468\) 24.7533 1.14422
\(469\) −13.3121 −0.614698
\(470\) 1.23897 + 0.867669i 0.0571493 + 0.0400226i
\(471\) −28.9562 −1.33423
\(472\) 8.47192i 0.389952i
\(473\) −40.8929 −1.88026
\(474\) −27.3896 −1.25804
\(475\) 0.739021 0.268860i 0.0339086 0.0123361i
\(476\) 11.9760i 0.548918i
\(477\) 84.7979i 3.88263i
\(478\) 8.68397i 0.397195i
\(479\) 12.6993i 0.580246i −0.956989 0.290123i \(-0.906304\pi\)
0.956989 0.290123i \(-0.0936962\pi\)
\(480\) 6.23397 + 4.36575i 0.284540 + 0.199268i
\(481\) 13.8617 + 10.7468i 0.632041 + 0.490012i
\(482\) 27.5610i 1.25537i
\(483\) −38.0351 −1.73066
\(484\) 3.26714 0.148506
\(485\) −17.9026 + 25.5635i −0.812913 + 1.16078i
\(486\) 75.5116i 3.42527i
\(487\) −10.8489 −0.491611 −0.245806 0.969319i \(-0.579052\pi\)
−0.245806 + 0.969319i \(0.579052\pi\)
\(488\) 1.23904i 0.0560888i
\(489\) 18.4243i 0.833178i
\(490\) 3.52371 5.03161i 0.159185 0.227305i
\(491\) −17.5266 −0.790965 −0.395482 0.918474i \(-0.629423\pi\)
−0.395482 + 0.918474i \(0.629423\pi\)
\(492\) 3.14401i 0.141743i
\(493\) 24.9166i 1.12219i
\(494\) 0.453523i 0.0204050i
\(495\) 41.5912 59.3892i 1.86938 2.66934i
\(496\) 0.425694i 0.0191142i
\(497\) 6.77096i 0.303719i
\(498\) −40.6716 −1.82254
\(499\) 32.4860i 1.45427i 0.686494 + 0.727135i \(0.259149\pi\)
−0.686494 + 0.727135i \(0.740851\pi\)
\(500\) 10.7987 + 2.89605i 0.482935 + 0.129515i
\(501\) 7.08508i 0.316538i
\(502\) 20.4512i 0.912782i
\(503\) 18.1375 0.808712 0.404356 0.914602i \(-0.367496\pi\)
0.404356 + 0.914602i \(0.367496\pi\)
\(504\) 17.7032i 0.788565i
\(505\) 10.7525 15.3538i 0.478481 0.683235i
\(506\) −20.4679 −0.909911
\(507\) 15.9471i 0.708235i
\(508\) 16.1128i 0.714891i
\(509\) −15.2070 −0.674037 −0.337018 0.941498i \(-0.609418\pi\)
−0.337018 + 0.941498i \(0.609418\pi\)
\(510\) 36.2022 + 25.3530i 1.60306 + 1.12265i
\(511\) 2.02201 0.0894485
\(512\) −1.00000 −0.0441942
\(513\) 2.98947 0.131988
\(514\) −22.8951 −1.00986
\(515\) −17.2813 + 24.6765i −0.761506 + 1.08737i
\(516\) 36.8483i 1.62215i
\(517\) 2.55506i 0.112371i
\(518\) −7.68597 + 9.91373i −0.337702 + 0.435584i
\(519\) −42.0554 −1.84603
\(520\) −3.69865 + 5.28140i −0.162196 + 0.231605i
\(521\) 21.5850 0.945657 0.472829 0.881154i \(-0.343233\pi\)
0.472829 + 0.881154i \(0.343233\pi\)
\(522\) 36.8324i 1.61211i
\(523\) 6.64279 0.290469 0.145234 0.989397i \(-0.453606\pi\)
0.145234 + 0.989397i \(0.453606\pi\)
\(524\) 9.64715i 0.421438i
\(525\) 11.9985 + 32.9805i 0.523657 + 1.43939i
\(526\) 22.1600i 0.966220i
\(527\) 2.47211i 0.107687i
\(528\) 12.8560i 0.559485i
\(529\) 6.36374 0.276684
\(530\) 18.0926 + 12.6705i 0.785892 + 0.550373i
\(531\) 72.7266i 3.15606i
\(532\) −0.324354 −0.0140625
\(533\) −2.66359 −0.115373
\(534\) 26.0666 1.12801
\(535\) 3.47294 + 2.43215i 0.150148 + 0.105151i
\(536\) 6.45516i 0.278820i
\(537\) 45.8024 1.97652
\(538\) −23.9657 −1.03323
\(539\) 10.3764 0.446944
\(540\) 34.8132 + 24.3802i 1.49812 + 1.04916i
\(541\) 12.3214i 0.529737i 0.964285 + 0.264868i \(0.0853286\pi\)
−0.964285 + 0.264868i \(0.914671\pi\)
\(542\) −9.82713 −0.422112
\(543\) 12.4778i 0.535475i
\(544\) −5.80724 −0.248983
\(545\) −31.5114 22.0680i −1.34980 0.945287i
\(546\) −20.2395 −0.866171
\(547\) −38.2186 −1.63411 −0.817054 0.576561i \(-0.804394\pi\)
−0.817054 + 0.576561i \(0.804394\pi\)
\(548\) 2.53592i 0.108329i
\(549\) 10.6365i 0.453953i
\(550\) 6.45678 + 17.7479i 0.275318 + 0.756774i
\(551\) −0.674834 −0.0287489
\(552\) 18.4435i 0.785007i
\(553\) 16.5954 0.705710
\(554\) 0.807608 0.0343120
\(555\) 13.6971 + 44.2211i 0.581411 + 1.87708i
\(556\) 7.56000 0.320615
\(557\) 32.9212 1.39492 0.697458 0.716626i \(-0.254315\pi\)
0.697458 + 0.716626i \(0.254315\pi\)
\(558\) 3.65434i 0.154701i
\(559\) 31.2177 1.32037
\(560\) −3.77719 2.64522i −0.159615 0.111781i
\(561\) 74.6579i 3.15206i
\(562\) 1.03833i 0.0437992i
\(563\) 5.39047 0.227181 0.113591 0.993528i \(-0.463765\pi\)
0.113591 + 0.993528i \(0.463765\pi\)
\(564\) −2.30234 −0.0969461
\(565\) 1.50200 2.14475i 0.0631898 0.0902304i
\(566\) −6.26151 −0.263191
\(567\) 80.3022i 3.37238i
\(568\) 3.28329 0.137764
\(569\) 2.18118i 0.0914399i −0.998954 0.0457200i \(-0.985442\pi\)
0.998954 0.0457200i \(-0.0145582\pi\)
\(570\) −0.686652 + 0.980489i −0.0287607 + 0.0410682i
\(571\) 41.7356 1.74658 0.873291 0.487200i \(-0.161982\pi\)
0.873291 + 0.487200i \(0.161982\pi\)
\(572\) −10.8916 −0.455399
\(573\) −63.1503 −2.63814
\(574\) 1.90497i 0.0795118i
\(575\) −9.26304 25.4615i −0.386295 1.06182i
\(576\) −8.58443 −0.357685
\(577\) −27.9657 −1.16423 −0.582114 0.813107i \(-0.697774\pi\)
−0.582114 + 0.813107i \(0.697774\pi\)
\(578\) −16.7241 −0.695630
\(579\) 16.6700i 0.692783i
\(580\) −7.85862 5.50352i −0.326312 0.228521i
\(581\) 24.6431 1.02237
\(582\) 47.5041i 1.96911i
\(583\) 37.3114i 1.54528i
\(584\) 0.980489i 0.0405729i
\(585\) −31.7508 + 45.3378i −1.31273 + 1.87449i
\(586\) 4.84496i 0.200143i
\(587\) −19.4024 −0.800825 −0.400412 0.916335i \(-0.631133\pi\)
−0.400412 + 0.916335i \(0.631133\pi\)
\(588\) 9.35011i 0.385592i
\(589\) 0.0669539 0.00275879
\(590\) 15.5170 + 10.8668i 0.638827 + 0.447381i
\(591\) 50.3061 2.06932
\(592\) −4.80724 3.72698i −0.197576 0.153178i
\(593\) 12.5182i 0.514061i 0.966403 + 0.257030i \(0.0827440\pi\)
−0.966403 + 0.257030i \(0.917256\pi\)
\(594\) 71.7934i 2.94572i
\(595\) −21.9350 15.3615i −0.899249 0.629759i
\(596\) 6.72596 0.275506
\(597\) 41.9657 1.71754
\(598\) 15.6253 0.638964
\(599\) 11.7177 0.478771 0.239386 0.970925i \(-0.423054\pi\)
0.239386 + 0.970925i \(0.423054\pi\)
\(600\) −15.9925 + 5.81815i −0.652891 + 0.237525i
\(601\) 1.37239 0.0559808 0.0279904 0.999608i \(-0.491089\pi\)
0.0279904 + 0.999608i \(0.491089\pi\)
\(602\) 22.3265i 0.909961i
\(603\) 55.4139i 2.25663i
\(604\) −15.8051 −0.643101
\(605\) −4.19072 + 5.98404i −0.170377 + 0.243286i
\(606\) 28.5316i 1.15902i
\(607\) 24.6378 1.00002 0.500008 0.866021i \(-0.333330\pi\)
0.500008 + 0.866021i \(0.333330\pi\)
\(608\) 0.157282i 0.00637861i
\(609\) 30.1160i 1.22036i
\(610\) −2.26941 1.58931i −0.0918858 0.0643491i
\(611\) 1.95054i 0.0789102i
\(612\) −49.8519 −2.01514
\(613\) 27.6733i 1.11771i −0.829264 0.558857i \(-0.811240\pi\)
0.829264 0.558857i \(-0.188760\pi\)
\(614\) 2.87515i 0.116032i
\(615\) −5.75852 4.03279i −0.232206 0.162618i
\(616\) 7.78950i 0.313848i
\(617\) 17.9433i 0.722371i 0.932494 + 0.361185i \(0.117628\pi\)
−0.932494 + 0.361185i \(0.882372\pi\)
\(618\) 45.8556i 1.84458i
\(619\) −25.1044 −1.00903 −0.504515 0.863403i \(-0.668329\pi\)
−0.504515 + 0.863403i \(0.668329\pi\)
\(620\) 0.779696 + 0.546033i 0.0313133 + 0.0219292i
\(621\) 102.996i 4.13310i
\(622\) 6.07102i 0.243426i
\(623\) −15.7939 −0.632768
\(624\) 9.81429i 0.392886i
\(625\) −19.1558 + 16.0641i −0.766232 + 0.642564i
\(626\) 10.0000 0.399680
\(627\) −2.02201 −0.0807514
\(628\) 8.50755i 0.339488i
\(629\) −27.9168 21.6435i −1.11312 0.862983i
\(630\) −32.4250 22.7077i −1.29184 0.904698i
\(631\) 47.8987i 1.90682i −0.301679 0.953409i \(-0.597547\pi\)
0.301679 0.953409i \(-0.402453\pi\)
\(632\) 8.04725i 0.320102i
\(633\) 48.2645i 1.91834i
\(634\) 25.5691i 1.01548i
\(635\) −29.5120 20.6677i −1.17115 0.820175i
\(636\) −33.6210 −1.33316
\(637\) −7.92138 −0.313856
\(638\) 16.2064i 0.641619i
\(639\) 28.1852 1.11499
\(640\) 1.28269 1.83159i 0.0507027 0.0723998i
\(641\) −19.4541 −0.768390 −0.384195 0.923252i \(-0.625521\pi\)
−0.384195 + 0.923252i \(0.625521\pi\)
\(642\) −6.45367 −0.254706
\(643\) 26.0553 1.02752 0.513760 0.857934i \(-0.328252\pi\)
0.513760 + 0.857934i \(0.328252\pi\)
\(644\) 11.1750i 0.440356i
\(645\) 67.4908 + 47.2649i 2.65745 + 1.86105i
\(646\) 0.913372i 0.0359362i
\(647\) 14.7320 0.579176 0.289588 0.957151i \(-0.406482\pi\)
0.289588 + 0.957151i \(0.406482\pi\)
\(648\) −38.9391 −1.52967
\(649\) 32.0000i 1.25611i
\(650\) −4.92912 13.5488i −0.193336 0.531427i
\(651\) 2.98797i 0.117108i
\(652\) −5.41321 −0.211998
\(653\) −30.5877 −1.19699 −0.598494 0.801127i \(-0.704234\pi\)
−0.598494 + 0.801127i \(0.704234\pi\)
\(654\) 58.5569 2.28976
\(655\) 17.6696 + 12.3743i 0.690408 + 0.483504i
\(656\) 0.923733 0.0360657
\(657\) 8.41694i 0.328376i
\(658\) 1.39500 0.0543827
\(659\) 29.3533 1.14344 0.571720 0.820448i \(-0.306276\pi\)
0.571720 + 0.820448i \(0.306276\pi\)
\(660\) −23.5469 16.4902i −0.916561 0.641882i
\(661\) 16.7963i 0.653299i 0.945145 + 0.326650i \(0.105920\pi\)
−0.945145 + 0.326650i \(0.894080\pi\)
\(662\) 16.8578i 0.655198i
\(663\) 56.9940i 2.21346i
\(664\) 11.9496i 0.463735i
\(665\) 0.416045 0.594082i 0.0161335 0.0230375i
\(666\) −41.2674 31.9940i −1.59908 1.23974i
\(667\) 23.2501i 0.900247i
\(668\) 2.08165 0.0805415
\(669\) 24.8146 0.959388
\(670\) 11.8232 + 8.27996i 0.456769 + 0.319883i
\(671\) 4.68009i 0.180673i
\(672\) 7.01905 0.270766
\(673\) 21.2015i 0.817259i 0.912700 + 0.408629i \(0.133993\pi\)
−0.912700 + 0.408629i \(0.866007\pi\)
\(674\) 14.7105i 0.566628i
\(675\) −89.3089 + 32.4911i −3.43750 + 1.25058i
\(676\) −4.68537 −0.180207
\(677\) 45.9734i 1.76690i −0.468526 0.883450i \(-0.655215\pi\)
0.468526 0.883450i \(-0.344785\pi\)
\(678\) 3.98554i 0.153064i
\(679\) 28.7829i 1.10459i
\(680\) 7.44889 10.6365i 0.285652 0.407890i
\(681\) 89.7890i 3.44072i
\(682\) 1.60793i 0.0615707i
\(683\) 3.06580 0.117309 0.0586547 0.998278i \(-0.481319\pi\)
0.0586547 + 0.998278i \(0.481319\pi\)
\(684\) 1.35017i 0.0516251i
\(685\) 4.64476 + 3.25280i 0.177467 + 0.124283i
\(686\) 20.1010i 0.767460i
\(687\) 66.6848i 2.54418i
\(688\) −10.8263 −0.412749
\(689\) 28.4836i 1.08514i
\(690\) 33.7808 + 23.6573i 1.28601 + 0.900617i
\(691\) 8.43426 0.320854 0.160427 0.987048i \(-0.448713\pi\)
0.160427 + 0.987048i \(0.448713\pi\)
\(692\) 12.3562i 0.469712i
\(693\) 66.8684i 2.54012i
\(694\) −3.26296 −0.123860
\(695\) −9.69713 + 13.8468i −0.367833 + 0.525238i
\(696\) 14.6035 0.553543
\(697\) 5.36434 0.203189
\(698\) 17.2097 0.651396
\(699\) 12.5927 0.476300
\(700\) 9.68991 3.52524i 0.366244 0.133242i
\(701\) 20.3110i 0.767136i −0.923513 0.383568i \(-0.874695\pi\)
0.923513 0.383568i \(-0.125305\pi\)
\(702\) 54.8072i 2.06856i
\(703\) 0.586186 0.756091i 0.0221084 0.0285165i
\(704\) 3.77719 0.142358
\(705\) 2.95319 4.21694i 0.111224 0.158819i
\(706\) 4.88641 0.183902
\(707\) 17.2874i 0.650159i
\(708\) −28.8349 −1.08368
\(709\) 23.8789i 0.896790i 0.893836 + 0.448395i \(0.148004\pi\)
−0.893836 + 0.448395i \(0.851996\pi\)
\(710\) −4.21144 + 6.01363i −0.158053 + 0.225688i
\(711\) 69.0811i 2.59074i
\(712\) 7.65857i 0.287017i
\(713\) 2.30677i 0.0863890i
\(714\) 40.7613 1.52545
\(715\) 13.9705 19.9488i 0.522466 0.746044i
\(716\) 13.4571i 0.502915i
\(717\) −29.5567 −1.10381
\(718\) −3.39107 −0.126554
\(719\) 14.6971 0.548110 0.274055 0.961714i \(-0.411635\pi\)
0.274055 + 0.961714i \(0.411635\pi\)
\(720\) 11.0112 15.7231i 0.410362 0.585966i
\(721\) 27.7841i 1.03473i
\(722\) −18.9753 −0.706186
\(723\) 93.8062 3.48869
\(724\) −3.66608 −0.136249
\(725\) 20.1603 7.33444i 0.748736 0.272394i
\(726\) 11.1200i 0.412702i
\(727\) 5.61569 0.208274 0.104137 0.994563i \(-0.466792\pi\)
0.104137 + 0.994563i \(0.466792\pi\)
\(728\) 5.94652i 0.220393i
\(729\) −140.193 −5.19233
\(730\) −1.79585 1.25766i −0.0664674 0.0465482i
\(731\) −62.8709 −2.32536
\(732\) 4.21719 0.155872
\(733\) 16.7565i 0.618917i −0.950913 0.309459i \(-0.899852\pi\)
0.950913 0.309459i \(-0.100148\pi\)
\(734\) 9.25169i 0.341486i
\(735\) −17.1255 11.9933i −0.631684 0.442379i
\(736\) −5.41883 −0.199741
\(737\) 24.3823i 0.898135i
\(738\) 7.92972 0.291897
\(739\) −13.2106 −0.485960 −0.242980 0.970031i \(-0.578125\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(740\) 12.9925 4.02432i 0.477614 0.147937i
\(741\) 1.54361 0.0567058
\(742\) 20.3711 0.747847
\(743\) 23.0799i 0.846721i 0.905961 + 0.423360i \(0.139150\pi\)
−0.905961 + 0.423360i \(0.860850\pi\)
\(744\) −1.44889 −0.0531188
\(745\) −8.62731 + 12.3192i −0.316080 + 0.451340i
\(746\) 11.4101i 0.417753i
\(747\) 102.581i 3.75323i
\(748\) 21.9350 0.802024
\(749\) 3.91030 0.142879
\(750\) 9.85695 36.7545i 0.359925 1.34209i
\(751\) 25.0437 0.913856 0.456928 0.889504i \(-0.348950\pi\)
0.456928 + 0.889504i \(0.348950\pi\)
\(752\) 0.676445i 0.0246674i
\(753\) 69.6075 2.53664
\(754\) 12.3720i 0.450562i
\(755\) 20.2731 28.9484i 0.737812 1.05354i
\(756\) 39.1974 1.42560
\(757\) −33.5882 −1.22078 −0.610392 0.792099i \(-0.708988\pi\)
−0.610392 + 0.792099i \(0.708988\pi\)
\(758\) −36.3643 −1.32081
\(759\) 69.6645i 2.52866i
\(760\) 0.288075 + 0.201743i 0.0104496 + 0.00731800i
\(761\) −14.8529 −0.538416 −0.269208 0.963082i \(-0.586762\pi\)
−0.269208 + 0.963082i \(0.586762\pi\)
\(762\) 54.8415 1.98670
\(763\) −35.4798 −1.28446
\(764\) 18.5540i 0.671261i
\(765\) 63.9445 91.3080i 2.31192 3.30125i
\(766\) 13.6526 0.493288
\(767\) 24.4289i 0.882075i
\(768\) 3.40359i 0.122816i
\(769\) 8.80892i 0.317658i −0.987306 0.158829i \(-0.949228\pi\)
0.987306 0.158829i \(-0.0507718\pi\)
\(770\) 14.2671 + 9.99151i 0.514152 + 0.360069i
\(771\) 77.9254i 2.80641i
\(772\) 4.89778 0.176275
\(773\) 38.8401i 1.39698i 0.715619 + 0.698491i \(0.246145\pi\)
−0.715619 + 0.698491i \(0.753855\pi\)
\(774\) −92.9376 −3.34057
\(775\) −2.00021 + 0.727688i −0.0718498 + 0.0261393i
\(776\) −13.9571 −0.501029
\(777\) 33.7423 + 26.1599i 1.21050 + 0.938481i
\(778\) 2.36833i 0.0849089i
\(779\) 0.145286i 0.00520542i
\(780\) 17.9757 + 12.5887i 0.643634 + 0.450747i
\(781\) −12.4016 −0.443764
\(782\) −31.4685 −1.12531
\(783\) 81.5521 2.91443
\(784\) 2.74713 0.0981118
\(785\) −15.5823 10.9125i −0.556156 0.389485i
\(786\) −32.8349 −1.17118
\(787\) 34.2645i 1.22140i −0.791864 0.610698i \(-0.790889\pi\)
0.791864 0.610698i \(-0.209111\pi\)