Properties

Label 95.2.b.b.39.3
Level $95$
Weight $2$
Character 95.39
Analytic conductor $0.759$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.16516096.1
Defining polynomial: \(x^{6} + 9 x^{4} + 13 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 39.3
Root \(-0.285442i\) of defining polynomial
Character \(\chi\) \(=\) 95.39
Dual form 95.2.b.b.39.4

$q$-expansion

\(f(q)\) \(=\) \(q-0.906968i q^{2} -3.21789i q^{3} +1.17741 q^{4} +(-0.370556 + 2.20515i) q^{5} -2.91852 q^{6} +2.59637i q^{7} -2.88181i q^{8} -7.35482 q^{9} +O(q^{10})\) \(q-0.906968i q^{2} -3.21789i q^{3} +1.17741 q^{4} +(-0.370556 + 2.20515i) q^{5} -2.91852 q^{6} +2.59637i q^{7} -2.88181i q^{8} -7.35482 q^{9} +(2.00000 + 0.336083i) q^{10} +0.741113 q^{11} -3.78878i q^{12} +3.78878i q^{13} +2.35482 q^{14} +(7.09593 + 1.19241i) q^{15} -0.258887 q^{16} -3.16725i q^{17} +6.67058i q^{18} +1.00000 q^{19} +(-0.436297 + 2.59637i) q^{20} +8.35482 q^{21} -0.672165i q^{22} -0.570885i q^{23} -9.27334 q^{24} +(-4.72538 - 1.63427i) q^{25} +3.43630 q^{26} +14.0133i q^{27} +3.05699i q^{28} -6.00000 q^{29} +(1.08148 - 6.43578i) q^{30} +5.83705 q^{31} -5.52881i q^{32} -2.38482i q^{33} -2.87259 q^{34} +(-5.72538 - 0.962100i) q^{35} -8.65964 q^{36} -1.40396i q^{37} -0.906968i q^{38} +12.1919 q^{39} +(6.35482 + 1.06787i) q^{40} -3.83705 q^{41} -7.57755i q^{42} +2.59637i q^{43} +0.872594 q^{44} +(2.72538 - 16.2185i) q^{45} -0.517774 q^{46} +5.08247i q^{47} +0.833070i q^{48} +0.258887 q^{49} +(-1.48223 + 4.28576i) q^{50} -10.1919 q^{51} +4.46094i q^{52} +0.160905i q^{53} +12.7096 q^{54} +(-0.274624 + 1.63427i) q^{55} +7.48223 q^{56} -3.21789i q^{57} +5.44181i q^{58} -8.35482 q^{59} +(8.35482 + 1.40396i) q^{60} -8.57816 q^{61} -5.29401i q^{62} -19.0958i q^{63} -5.53223 q^{64} +(-8.35482 - 1.40396i) q^{65} -2.16295 q^{66} -14.8464i q^{67} -3.72915i q^{68} -1.83705 q^{69} +(-0.872594 + 5.19273i) q^{70} +3.64518 q^{71} +21.1952i q^{72} +10.8461i q^{73} -1.27334 q^{74} +(-5.25889 + 15.2057i) q^{75} +1.17741 q^{76} +1.92420i q^{77} -11.0576i q^{78} -1.83705 q^{79} +(0.0959323 - 0.570885i) q^{80} +23.0289 q^{81} +3.48008i q^{82} +4.19876i q^{83} +9.83705 q^{84} +(6.98426 + 1.17365i) q^{85} +2.35482 q^{86} +19.3073i q^{87} -2.13574i q^{88} +16.9015 q^{89} +(-14.7096 - 2.47183i) q^{90} -9.83705 q^{91} -0.672165i q^{92} -18.7830i q^{93} +4.60963 q^{94} +(-0.370556 + 2.20515i) q^{95} -17.7911 q^{96} -3.78878i q^{97} -0.234802i q^{98} -5.45075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 8 q^{4} - q^{5} - 14 q^{9} + O(q^{10}) \) \( 6 q - 8 q^{4} - q^{5} - 14 q^{9} + 12 q^{10} + 2 q^{11} - 16 q^{14} + 10 q^{15} - 4 q^{16} + 6 q^{19} + 10 q^{20} + 20 q^{21} - 8 q^{24} + 3 q^{25} + 8 q^{26} - 36 q^{29} + 24 q^{30} + 8 q^{34} - 3 q^{35} - 32 q^{36} + 8 q^{39} + 8 q^{40} + 12 q^{41} - 20 q^{44} - 15 q^{45} - 8 q^{46} + 4 q^{49} - 4 q^{50} + 4 q^{51} + 16 q^{54} - 33 q^{55} + 40 q^{56} - 20 q^{59} + 20 q^{60} - 14 q^{61} + 12 q^{64} - 20 q^{65} - 48 q^{66} + 24 q^{69} + 20 q^{70} + 52 q^{71} + 40 q^{74} - 34 q^{75} - 8 q^{76} + 24 q^{79} - 32 q^{80} + 38 q^{81} + 24 q^{84} + 13 q^{85} - 16 q^{86} - 24 q^{89} - 28 q^{90} - 24 q^{91} + 48 q^{94} - q^{95} - 64 q^{96} + 30 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.906968i 0.641323i −0.947194 0.320661i \(-0.896095\pi\)
0.947194 0.320661i \(-0.103905\pi\)
\(3\) 3.21789i 1.85785i −0.370268 0.928925i \(-0.620734\pi\)
0.370268 0.928925i \(-0.379266\pi\)
\(4\) 1.17741 0.588705
\(5\) −0.370556 + 2.20515i −0.165718 + 0.986173i
\(6\) −2.91852 −1.19148
\(7\) 2.59637i 0.981334i 0.871347 + 0.490667i \(0.163247\pi\)
−0.871347 + 0.490667i \(0.836753\pi\)
\(8\) 2.88181i 1.01887i
\(9\) −7.35482 −2.45161
\(10\) 2.00000 + 0.336083i 0.632456 + 0.106279i
\(11\) 0.741113 0.223454 0.111727 0.993739i \(-0.464362\pi\)
0.111727 + 0.993739i \(0.464362\pi\)
\(12\) 3.78878i 1.09373i
\(13\) 3.78878i 1.05082i 0.850850 + 0.525409i \(0.176088\pi\)
−0.850850 + 0.525409i \(0.823912\pi\)
\(14\) 2.35482 0.629352
\(15\) 7.09593 + 1.19241i 1.83216 + 0.307879i
\(16\) −0.258887 −0.0647218
\(17\) 3.16725i 0.768171i −0.923298 0.384086i \(-0.874517\pi\)
0.923298 0.384086i \(-0.125483\pi\)
\(18\) 6.67058i 1.57227i
\(19\) 1.00000 0.229416
\(20\) −0.436297 + 2.59637i −0.0975589 + 0.580565i
\(21\) 8.35482 1.82317
\(22\) 0.672165i 0.143306i
\(23\) 0.570885i 0.119038i −0.998227 0.0595189i \(-0.981043\pi\)
0.998227 0.0595189i \(-0.0189566\pi\)
\(24\) −9.27334 −1.89291
\(25\) −4.72538 1.63427i −0.945075 0.326853i
\(26\) 3.43630 0.673913
\(27\) 14.0133i 2.69687i
\(28\) 3.05699i 0.577716i
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 1.08148 6.43578i 0.197450 1.17501i
\(31\) 5.83705 1.04836 0.524182 0.851606i \(-0.324371\pi\)
0.524182 + 0.851606i \(0.324371\pi\)
\(32\) 5.52881i 0.977365i
\(33\) 2.38482i 0.415144i
\(34\) −2.87259 −0.492646
\(35\) −5.72538 0.962100i −0.967765 0.162625i
\(36\) −8.65964 −1.44327
\(37\) 1.40396i 0.230809i −0.993319 0.115404i \(-0.963184\pi\)
0.993319 0.115404i \(-0.0368164\pi\)
\(38\) 0.906968i 0.147130i
\(39\) 12.1919 1.95226
\(40\) 6.35482 + 1.06787i 1.00479 + 0.168845i
\(41\) −3.83705 −0.599246 −0.299623 0.954058i \(-0.596861\pi\)
−0.299623 + 0.954058i \(0.596861\pi\)
\(42\) 7.57755i 1.16924i
\(43\) 2.59637i 0.395942i 0.980208 + 0.197971i \(0.0634352\pi\)
−0.980208 + 0.197971i \(0.936565\pi\)
\(44\) 0.872594 0.131548
\(45\) 2.72538 16.2185i 0.406275 2.41771i
\(46\) −0.517774 −0.0763416
\(47\) 5.08247i 0.741354i 0.928762 + 0.370677i \(0.120874\pi\)
−0.928762 + 0.370677i \(0.879126\pi\)
\(48\) 0.833070i 0.120243i
\(49\) 0.258887 0.0369839
\(50\) −1.48223 + 4.28576i −0.209618 + 0.606098i
\(51\) −10.1919 −1.42715
\(52\) 4.46094i 0.618621i
\(53\) 0.160905i 0.0221020i 0.999939 + 0.0110510i \(0.00351771\pi\)
−0.999939 + 0.0110510i \(0.996482\pi\)
\(54\) 12.7096 1.72956
\(55\) −0.274624 + 1.63427i −0.0370303 + 0.220364i
\(56\) 7.48223 0.999854
\(57\) 3.21789i 0.426220i
\(58\) 5.44181i 0.714544i
\(59\) −8.35482 −1.08770 −0.543852 0.839181i \(-0.683035\pi\)
−0.543852 + 0.839181i \(0.683035\pi\)
\(60\) 8.35482 + 1.40396i 1.07860 + 0.181250i
\(61\) −8.57816 −1.09832 −0.549160 0.835717i \(-0.685052\pi\)
−0.549160 + 0.835717i \(0.685052\pi\)
\(62\) 5.29401i 0.672340i
\(63\) 19.0958i 2.40584i
\(64\) −5.53223 −0.691529
\(65\) −8.35482 1.40396i −1.03629 0.174139i
\(66\) −2.16295 −0.266241
\(67\) 14.8464i 1.81378i −0.421371 0.906888i \(-0.638451\pi\)
0.421371 0.906888i \(-0.361549\pi\)
\(68\) 3.72915i 0.452226i
\(69\) −1.83705 −0.221154
\(70\) −0.872594 + 5.19273i −0.104295 + 0.620650i
\(71\) 3.64518 0.432603 0.216302 0.976327i \(-0.430601\pi\)
0.216302 + 0.976327i \(0.430601\pi\)
\(72\) 21.1952i 2.49788i
\(73\) 10.8461i 1.26944i 0.772743 + 0.634719i \(0.218884\pi\)
−0.772743 + 0.634719i \(0.781116\pi\)
\(74\) −1.27334 −0.148023
\(75\) −5.25889 + 15.2057i −0.607244 + 1.75581i
\(76\) 1.17741 0.135058
\(77\) 1.92420i 0.219283i
\(78\) 11.0576i 1.25203i
\(79\) −1.83705 −0.206684 −0.103342 0.994646i \(-0.532954\pi\)
−0.103342 + 0.994646i \(0.532954\pi\)
\(80\) 0.0959323 0.570885i 0.0107256 0.0638269i
\(81\) 23.0289 2.55877
\(82\) 3.48008i 0.384310i
\(83\) 4.19876i 0.460873i 0.973087 + 0.230437i \(0.0740154\pi\)
−0.973087 + 0.230437i \(0.925985\pi\)
\(84\) 9.83705 1.07331
\(85\) 6.98426 + 1.17365i 0.757550 + 0.127300i
\(86\) 2.35482 0.253927
\(87\) 19.3073i 2.06996i
\(88\) 2.13574i 0.227671i
\(89\) 16.9015 1.79156 0.895778 0.444502i \(-0.146619\pi\)
0.895778 + 0.444502i \(0.146619\pi\)
\(90\) −14.7096 2.47183i −1.55053 0.260554i
\(91\) −9.83705 −1.03120
\(92\) 0.672165i 0.0700781i
\(93\) 18.7830i 1.94770i
\(94\) 4.60963 0.475447
\(95\) −0.370556 + 2.20515i −0.0380183 + 0.226244i
\(96\) −17.7911 −1.81580
\(97\) 3.78878i 0.384692i −0.981327 0.192346i \(-0.938390\pi\)
0.981327 0.192346i \(-0.0616096\pi\)
\(98\) 0.234802i 0.0237186i
\(99\) −5.45075 −0.547821
\(100\) −5.56370 1.92420i −0.556370 0.192420i
\(101\) 8.35482 0.831336 0.415668 0.909517i \(-0.363548\pi\)
0.415668 + 0.909517i \(0.363548\pi\)
\(102\) 9.24369i 0.915262i
\(103\) 2.07612i 0.204566i −0.994755 0.102283i \(-0.967385\pi\)
0.994755 0.102283i \(-0.0326148\pi\)
\(104\) 10.9185 1.07065
\(105\) −3.09593 + 18.4236i −0.302132 + 1.79796i
\(106\) 0.145935 0.0141745
\(107\) 5.70399i 0.551426i −0.961240 0.275713i \(-0.911086\pi\)
0.961240 0.275713i \(-0.0889139\pi\)
\(108\) 16.4994i 1.58766i
\(109\) −1.64518 −0.157580 −0.0787899 0.996891i \(-0.525106\pi\)
−0.0787899 + 0.996891i \(0.525106\pi\)
\(110\) 1.48223 + 0.249075i 0.141325 + 0.0237484i
\(111\) −4.51777 −0.428808
\(112\) 0.672165i 0.0635137i
\(113\) 3.89006i 0.365946i 0.983118 + 0.182973i \(0.0585720\pi\)
−0.983118 + 0.182973i \(0.941428\pi\)
\(114\) −2.91852 −0.273345
\(115\) 1.25889 + 0.211545i 0.117392 + 0.0197267i
\(116\) −7.06446 −0.655918
\(117\) 27.8658i 2.57619i
\(118\) 7.57755i 0.697570i
\(119\) 8.22334 0.753832
\(120\) 3.43630 20.4491i 0.313690 1.86674i
\(121\) −10.4508 −0.950068
\(122\) 7.78011i 0.704378i
\(123\) 12.3472i 1.11331i
\(124\) 6.87259 0.617177
\(125\) 5.35482 9.81458i 0.478950 0.877842i
\(126\) −17.3193 −1.54292
\(127\) 14.4233i 1.27986i −0.768432 0.639931i \(-0.778963\pi\)
0.768432 0.639931i \(-0.221037\pi\)
\(128\) 6.04007i 0.533872i
\(129\) 8.35482 0.735601
\(130\) −1.27334 + 7.57755i −0.111679 + 0.664595i
\(131\) 9.96853 0.870954 0.435477 0.900200i \(-0.356580\pi\)
0.435477 + 0.900200i \(0.356580\pi\)
\(132\) 2.80791i 0.244397i
\(133\) 2.59637i 0.225133i
\(134\) −13.4652 −1.16322
\(135\) −30.9015 5.19273i −2.65958 0.446919i
\(136\) −9.12741 −0.782669
\(137\) 9.70431i 0.829095i −0.910028 0.414548i \(-0.863940\pi\)
0.910028 0.414548i \(-0.136060\pi\)
\(138\) 1.66614i 0.141831i
\(139\) 13.4508 1.14088 0.570439 0.821340i \(-0.306773\pi\)
0.570439 + 0.821340i \(0.306773\pi\)
\(140\) −6.74111 1.13279i −0.569728 0.0957379i
\(141\) 16.3548 1.37732
\(142\) 3.30606i 0.277438i
\(143\) 2.80791i 0.234809i
\(144\) 1.90407 0.158672
\(145\) 2.22334 13.2309i 0.184638 1.09877i
\(146\) 9.83705 0.814120
\(147\) 0.833070i 0.0687105i
\(148\) 1.65303i 0.135878i
\(149\) −15.0959 −1.23671 −0.618353 0.785900i \(-0.712200\pi\)
−0.618353 + 0.785900i \(0.712200\pi\)
\(150\) 13.7911 + 4.76964i 1.12604 + 0.389440i
\(151\) 14.1919 1.15492 0.577459 0.816420i \(-0.304044\pi\)
0.577459 + 0.816420i \(0.304044\pi\)
\(152\) 2.88181i 0.233745i
\(153\) 23.2946i 1.88325i
\(154\) 1.74519 0.140631
\(155\) −2.16295 + 12.8716i −0.173733 + 1.03387i
\(156\) 14.3548 1.14931
\(157\) 7.57755i 0.604754i −0.953188 0.302377i \(-0.902220\pi\)
0.953188 0.302377i \(-0.0977802\pi\)
\(158\) 1.66614i 0.132551i
\(159\) 0.517774 0.0410622
\(160\) 12.1919 + 2.04874i 0.963852 + 0.161967i
\(161\) 1.48223 0.116816
\(162\) 20.8865i 1.64100i
\(163\) 19.6757i 1.54112i −0.637369 0.770559i \(-0.719977\pi\)
0.637369 0.770559i \(-0.280023\pi\)
\(164\) −4.51777 −0.352779
\(165\) 5.25889 + 0.883711i 0.409404 + 0.0687968i
\(166\) 3.80814 0.295569
\(167\) 10.7954i 0.835376i 0.908590 + 0.417688i \(0.137160\pi\)
−0.908590 + 0.417688i \(0.862840\pi\)
\(168\) 24.0770i 1.85758i
\(169\) −1.35482 −0.104217
\(170\) 1.06446 6.33450i 0.0816402 0.485834i
\(171\) −7.35482 −0.562437
\(172\) 3.05699i 0.233093i
\(173\) 20.3895i 1.55018i 0.631848 + 0.775092i \(0.282297\pi\)
−0.631848 + 0.775092i \(0.717703\pi\)
\(174\) 17.5111 1.32752
\(175\) 4.24315 12.2688i 0.320752 0.927434i
\(176\) −0.191865 −0.0144623
\(177\) 26.8849i 2.02079i
\(178\) 15.3291i 1.14897i
\(179\) −25.0645 −1.87341 −0.936703 0.350126i \(-0.886139\pi\)
−0.936703 + 0.350126i \(0.886139\pi\)
\(180\) 3.20888 19.0958i 0.239176 1.42332i
\(181\) −19.4193 −1.44342 −0.721712 0.692194i \(-0.756644\pi\)
−0.721712 + 0.692194i \(0.756644\pi\)
\(182\) 8.92188i 0.661334i
\(183\) 27.6036i 2.04051i
\(184\) −1.64518 −0.121284
\(185\) 3.09593 + 0.520245i 0.227617 + 0.0382491i
\(186\) −17.0355 −1.24911
\(187\) 2.34729i 0.171651i
\(188\) 5.98414i 0.436439i
\(189\) −36.3837 −2.64653
\(190\) 2.00000 + 0.336083i 0.145095 + 0.0243820i
\(191\) 11.4508 0.828547 0.414274 0.910152i \(-0.364036\pi\)
0.414274 + 0.910152i \(0.364036\pi\)
\(192\) 17.8021i 1.28476i
\(193\) 3.78878i 0.272722i 0.990659 + 0.136361i \(0.0435407\pi\)
−0.990659 + 0.136361i \(0.956459\pi\)
\(194\) −3.43630 −0.246712
\(195\) −4.51777 + 26.8849i −0.323525 + 1.92527i
\(196\) 0.304816 0.0217726
\(197\) 2.28354i 0.162695i −0.996686 0.0813477i \(-0.974078\pi\)
0.996686 0.0813477i \(-0.0259224\pi\)
\(198\) 4.94366i 0.351330i
\(199\) 19.4508 1.37883 0.689414 0.724368i \(-0.257868\pi\)
0.689414 + 0.724368i \(0.257868\pi\)
\(200\) −4.70964 + 13.6176i −0.333022 + 0.962911i
\(201\) −47.7741 −3.36972
\(202\) 7.57755i 0.533155i
\(203\) 15.5782i 1.09337i
\(204\) −12.0000 −0.840168
\(205\) 1.42184 8.46126i 0.0993057 0.590960i
\(206\) −1.88297 −0.131193
\(207\) 4.19876i 0.291834i
\(208\) 0.980865i 0.0680108i
\(209\) 0.741113 0.0512639
\(210\) 16.7096 + 2.80791i 1.15307 + 0.193764i
\(211\) 11.2274 0.772927 0.386463 0.922305i \(-0.373697\pi\)
0.386463 + 0.922305i \(0.373697\pi\)
\(212\) 0.189451i 0.0130115i
\(213\) 11.7298i 0.803712i
\(214\) −5.17334 −0.353642
\(215\) −5.72538 0.962100i −0.390467 0.0656147i
\(216\) 40.3837 2.74776
\(217\) 15.1551i 1.02880i
\(218\) 1.49213i 0.101059i
\(219\) 34.9015 2.35843
\(220\) −0.323345 + 1.92420i −0.0217999 + 0.129730i
\(221\) 12.0000 0.807207
\(222\) 4.09748i 0.275005i
\(223\) 4.03785i 0.270394i −0.990819 0.135197i \(-0.956833\pi\)
0.990819 0.135197i \(-0.0431668\pi\)
\(224\) 14.3548 0.959122
\(225\) 34.7543 + 12.0197i 2.31695 + 0.801315i
\(226\) 3.52815 0.234689
\(227\) 11.2185i 0.744600i 0.928112 + 0.372300i \(0.121431\pi\)
−0.928112 + 0.372300i \(0.878569\pi\)
\(228\) 3.78878i 0.250918i
\(229\) −16.1315 −1.06600 −0.532999 0.846116i \(-0.678935\pi\)
−0.532999 + 0.846116i \(0.678935\pi\)
\(230\) 0.191865 1.14177i 0.0126512 0.0752861i
\(231\) 6.19186 0.407395
\(232\) 17.2908i 1.13520i
\(233\) 2.12676i 0.139329i −0.997570 0.0696644i \(-0.977807\pi\)
0.997570 0.0696644i \(-0.0221928\pi\)
\(234\) −25.2733 −1.65217
\(235\) −11.2076 1.88334i −0.731103 0.122856i
\(236\) −9.83705 −0.640337
\(237\) 5.91141i 0.383987i
\(238\) 7.45830i 0.483450i
\(239\) 14.4152 0.932442 0.466221 0.884668i \(-0.345615\pi\)
0.466221 + 0.884668i \(0.345615\pi\)
\(240\) −1.83705 0.308700i −0.118581 0.0199265i
\(241\) −0.162955 −0.0104968 −0.00524842 0.999986i \(-0.501671\pi\)
−0.00524842 + 0.999986i \(0.501671\pi\)
\(242\) 9.47849i 0.609301i
\(243\) 32.0645i 2.05694i
\(244\) −10.1000 −0.646587
\(245\) −0.0959323 + 0.570885i −0.00612889 + 0.0364725i
\(246\) 11.1985 0.713990
\(247\) 3.78878i 0.241074i
\(248\) 16.8212i 1.06815i
\(249\) 13.5111 0.856233
\(250\) −8.90150 4.85665i −0.562980 0.307161i
\(251\) 12.9330 0.816322 0.408161 0.912910i \(-0.366170\pi\)
0.408161 + 0.912910i \(0.366170\pi\)
\(252\) 22.4836i 1.41633i
\(253\) 0.423090i 0.0265995i
\(254\) −13.0815 −0.820805
\(255\) 3.77666 22.4746i 0.236504 1.40741i
\(256\) −16.5426 −1.03391
\(257\) 11.0445i 0.688938i 0.938798 + 0.344469i \(0.111941\pi\)
−0.938798 + 0.344469i \(0.888059\pi\)
\(258\) 7.57755i 0.471758i
\(259\) 3.64518 0.226501
\(260\) −9.83705 1.65303i −0.610068 0.102517i
\(261\) 44.1289 2.73151
\(262\) 9.04113i 0.558563i
\(263\) 17.8527i 1.10085i 0.834885 + 0.550424i \(0.185534\pi\)
−0.834885 + 0.550424i \(0.814466\pi\)
\(264\) −6.87259 −0.422979
\(265\) −0.354819 0.0596243i −0.0217964 0.00366269i
\(266\) 2.35482 0.144383
\(267\) 54.3872i 3.32844i
\(268\) 17.4803i 1.06778i
\(269\) −24.9934 −1.52387 −0.761936 0.647652i \(-0.775751\pi\)
−0.761936 + 0.647652i \(0.775751\pi\)
\(270\) −4.70964 + 28.0267i −0.286619 + 1.70565i
\(271\) −23.8660 −1.44975 −0.724877 0.688879i \(-0.758103\pi\)
−0.724877 + 0.688879i \(0.758103\pi\)
\(272\) 0.819960i 0.0497174i
\(273\) 31.6545i 1.91582i
\(274\) −8.80150 −0.531718
\(275\) −3.50204 1.21118i −0.211181 0.0730366i
\(276\) −2.16295 −0.130195
\(277\) 21.2315i 1.27568i 0.770169 + 0.637840i \(0.220172\pi\)
−0.770169 + 0.637840i \(0.779828\pi\)
\(278\) 12.1994i 0.731671i
\(279\) −42.9304 −2.57018
\(280\) −2.77259 + 16.4994i −0.165694 + 0.986030i
\(281\) 3.83705 0.228899 0.114449 0.993429i \(-0.463490\pi\)
0.114449 + 0.993429i \(0.463490\pi\)
\(282\) 14.8333i 0.883310i
\(283\) 0.211545i 0.0125751i 0.999980 + 0.00628753i \(0.00200139\pi\)
−0.999980 + 0.00628753i \(0.997999\pi\)
\(284\) 4.29187 0.254676
\(285\) 7.09593 + 1.19241i 0.420327 + 0.0706323i
\(286\) 2.54668 0.150589
\(287\) 9.96237i 0.588060i
\(288\) 40.6634i 2.39612i
\(289\) 6.96853 0.409913
\(290\) −12.0000 2.01650i −0.704664 0.118413i
\(291\) −12.1919 −0.714700
\(292\) 12.7703i 0.747324i
\(293\) 14.9942i 0.875970i −0.898982 0.437985i \(-0.855692\pi\)
0.898982 0.437985i \(-0.144308\pi\)
\(294\) −0.755568 −0.0440656
\(295\) 3.09593 18.4236i 0.180252 1.07267i
\(296\) −4.04593 −0.235165
\(297\) 10.3855i 0.602626i
\(298\) 13.6915i 0.793129i
\(299\) 2.16295 0.125087
\(300\) −6.19186 + 17.9034i −0.357487 + 1.03365i
\(301\) −6.74111 −0.388551
\(302\) 12.8716i 0.740675i
\(303\) 26.8849i 1.54450i
\(304\) −0.258887 −0.0148482
\(305\) 3.17869 18.9161i 0.182011 1.08313i
\(306\) 21.1274 1.20777
\(307\) 1.65303i 0.0943434i −0.998887 0.0471717i \(-0.984979\pi\)
0.998887 0.0471717i \(-0.0150208\pi\)
\(308\) 2.26557i 0.129093i
\(309\) −6.68073 −0.380053
\(310\) 11.6741 + 1.96173i 0.663044 + 0.111419i
\(311\) −0.741113 −0.0420247 −0.0210123 0.999779i \(-0.506689\pi\)
−0.0210123 + 0.999779i \(0.506689\pi\)
\(312\) 35.1346i 1.98911i
\(313\) 26.8849i 1.51962i −0.650143 0.759812i \(-0.725291\pi\)
0.650143 0.759812i \(-0.274709\pi\)
\(314\) −6.87259 −0.387843
\(315\) 42.1091 + 7.07607i 2.37258 + 0.398691i
\(316\) −2.16295 −0.121676
\(317\) 8.16155i 0.458398i 0.973380 + 0.229199i \(0.0736107\pi\)
−0.973380 + 0.229199i \(0.926389\pi\)
\(318\) 0.469604i 0.0263341i
\(319\) −4.44668 −0.248966
\(320\) 2.05000 12.1994i 0.114599 0.681967i
\(321\) −18.3548 −1.02447
\(322\) 1.34433i 0.0749166i
\(323\) 3.16725i 0.176231i
\(324\) 27.1145 1.50636
\(325\) 6.19186 17.9034i 0.343463 0.993101i
\(326\) −17.8452 −0.988354
\(327\) 5.29401i 0.292759i
\(328\) 11.0576i 0.610555i
\(329\) −13.1959 −0.727516
\(330\) 0.801497 4.76964i 0.0441210 0.262560i
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 4.94366i 0.271318i
\(333\) 10.3258i 0.565852i
\(334\) 9.79112 0.535746
\(335\) 32.7385 + 5.50143i 1.78870 + 0.300575i
\(336\) −2.16295 −0.117999
\(337\) 9.90275i 0.539437i 0.962939 + 0.269718i \(0.0869306\pi\)
−0.962939 + 0.269718i \(0.913069\pi\)
\(338\) 1.22878i 0.0668367i
\(339\) 12.5178 0.679872
\(340\) 8.22334 + 1.38186i 0.445973 + 0.0749419i
\(341\) 4.32591 0.234261
\(342\) 6.67058i 0.360704i
\(343\) 18.8467i 1.01763i
\(344\) 7.48223 0.403415
\(345\) 0.680729 4.05096i 0.0366492 0.218096i
\(346\) 18.4926 0.994169
\(347\) 21.2781i 1.14227i 0.820858 + 0.571133i \(0.193496\pi\)
−0.820858 + 0.571133i \(0.806504\pi\)
\(348\) 22.7327i 1.21860i
\(349\) 16.4152 0.878686 0.439343 0.898319i \(-0.355211\pi\)
0.439343 + 0.898319i \(0.355211\pi\)
\(350\) −11.1274 3.84840i −0.594785 0.205706i
\(351\) −53.0934 −2.83391
\(352\) 4.09748i 0.218396i
\(353\) 23.8744i 1.27071i 0.772221 + 0.635354i \(0.219146\pi\)
−0.772221 + 0.635354i \(0.780854\pi\)
\(354\) 24.3837 1.29598
\(355\) −1.35075 + 8.03817i −0.0716901 + 0.426622i
\(356\) 19.9000 1.05470
\(357\) 26.4618i 1.40051i
\(358\) 22.7327i 1.20146i
\(359\) −2.22334 −0.117343 −0.0586717 0.998277i \(-0.518687\pi\)
−0.0586717 + 0.998277i \(0.518687\pi\)
\(360\) −46.7385 7.85401i −2.46334 0.413943i
\(361\) 1.00000 0.0526316
\(362\) 17.6127i 0.925701i
\(363\) 33.6294i 1.76508i
\(364\) −11.5822 −0.607074
\(365\) −23.9172 4.01909i −1.25189 0.210369i
\(366\) 25.0355 1.30863
\(367\) 4.52057i 0.235972i 0.993015 + 0.117986i \(0.0376437\pi\)
−0.993015 + 0.117986i \(0.962356\pi\)
\(368\) 0.147795i 0.00770433i
\(369\) 28.2208 1.46911
\(370\) 0.471845 2.80791i 0.0245301 0.145976i
\(371\) −0.417768 −0.0216894
\(372\) 22.1153i 1.14662i
\(373\) 15.5186i 0.803521i 0.915745 + 0.401760i \(0.131602\pi\)
−0.915745 + 0.401760i \(0.868398\pi\)
\(374\) −2.12892 −0.110084
\(375\) −31.5822 17.2312i −1.63090 0.889817i
\(376\) 14.6467 0.755345
\(377\) 22.7327i 1.17079i
\(378\) 32.9989i 1.69728i
\(379\) 18.9015 0.970905 0.485453 0.874263i \(-0.338655\pi\)
0.485453 + 0.874263i \(0.338655\pi\)
\(380\) −0.436297 + 2.59637i −0.0223816 + 0.133191i
\(381\) −46.4126 −2.37779
\(382\) 10.3855i 0.531366i
\(383\) 13.7046i 0.700274i −0.936699 0.350137i \(-0.886135\pi\)
0.936699 0.350137i \(-0.113865\pi\)
\(384\) −19.4363 −0.991854
\(385\) −4.24315 0.713025i −0.216251 0.0363391i
\(386\) 3.43630 0.174903
\(387\) 19.0958i 0.970694i
\(388\) 4.46094i 0.226470i
\(389\) −12.7411 −0.646000 −0.323000 0.946399i \(-0.604691\pi\)
−0.323000 + 0.946399i \(0.604691\pi\)
\(390\) 24.3837 + 4.09748i 1.23472 + 0.207484i
\(391\) −1.80814 −0.0914413
\(392\) 0.746063i 0.0376819i
\(393\) 32.0776i 1.61810i
\(394\) −2.07110 −0.104340
\(395\) 0.680729 4.05096i 0.0342512 0.203826i
\(396\) −6.41777 −0.322505
\(397\) 38.6522i 1.93990i 0.243306 + 0.969950i \(0.421768\pi\)
−0.243306 + 0.969950i \(0.578232\pi\)
\(398\) 17.6412i 0.884274i
\(399\) 8.35482 0.418264
\(400\) 1.22334 + 0.423090i 0.0611669 + 0.0211545i
\(401\) 31.8660 1.59131 0.795655 0.605750i \(-0.207127\pi\)
0.795655 + 0.605750i \(0.207127\pi\)
\(402\) 43.3296i 2.16108i
\(403\) 22.1153i 1.10164i
\(404\) 9.83705 0.489411
\(405\) −8.53351 + 50.7822i −0.424034 + 2.52339i
\(406\) −14.1289 −0.701206
\(407\) 1.04049i 0.0515751i
\(408\) 29.3710i 1.45408i
\(409\) −11.0645 −0.547102 −0.273551 0.961857i \(-0.588198\pi\)
−0.273551 + 0.961857i \(0.588198\pi\)
\(410\) −7.67409 1.28956i −0.378996 0.0636871i
\(411\) −31.2274 −1.54033
\(412\) 2.44444i 0.120429i
\(413\) 21.6922i 1.06740i
\(414\) 3.80814 0.187160
\(415\) −9.25889 1.55588i −0.454501 0.0763749i
\(416\) 20.9474 1.02703
\(417\) 43.2830i 2.11958i
\(418\) 0.672165i 0.0328767i
\(419\) 25.7452 1.25773 0.628867 0.777513i \(-0.283519\pi\)
0.628867 + 0.777513i \(0.283519\pi\)
\(420\) −3.64518 + 21.6922i −0.177867 + 1.05847i
\(421\) 27.4482 1.33774 0.668871 0.743378i \(-0.266778\pi\)
0.668871 + 0.743378i \(0.266778\pi\)
\(422\) 10.1829i 0.495696i
\(423\) 37.3806i 1.81751i
\(424\) 0.463697 0.0225191
\(425\) −5.17613 + 14.9664i −0.251079 + 0.725979i
\(426\) −10.6385 −0.515439
\(427\) 22.2720i 1.07782i
\(428\) 6.71593i 0.324627i
\(429\) 9.03555 0.436240
\(430\) −0.872594 + 5.19273i −0.0420802 + 0.250416i
\(431\) 1.74519 0.0840627 0.0420314 0.999116i \(-0.486617\pi\)
0.0420314 + 0.999116i \(0.486617\pi\)
\(432\) 3.62787i 0.174546i
\(433\) 18.5208i 0.890052i −0.895518 0.445026i \(-0.853194\pi\)
0.895518 0.445026i \(-0.146806\pi\)
\(434\) 13.7452 0.659790
\(435\) −42.5756 7.15446i −2.04134 0.343030i
\(436\) −1.93705 −0.0927679
\(437\) 0.570885i 0.0273091i
\(438\) 31.6545i 1.51251i
\(439\) −29.4482 −1.40549 −0.702743 0.711444i \(-0.748041\pi\)
−0.702743 + 0.711444i \(0.748041\pi\)
\(440\) 4.70964 + 0.791414i 0.224523 + 0.0377292i
\(441\) −1.90407 −0.0906699
\(442\) 10.8836i 0.517681i
\(443\) 11.7388i 0.557726i 0.960331 + 0.278863i \(0.0899576\pi\)
−0.960331 + 0.278863i \(0.910042\pi\)
\(444\) −5.31927 −0.252441
\(445\) −6.26296 + 37.2704i −0.296893 + 1.76678i
\(446\) −3.66220 −0.173410
\(447\) 48.5771i 2.29762i
\(448\) 14.3637i 0.678620i
\(449\) 7.06446 0.333392 0.166696 0.986008i \(-0.446690\pi\)
0.166696 + 0.986008i \(0.446690\pi\)
\(450\) 10.9015 31.5210i 0.513902 1.48591i
\(451\) −2.84368 −0.133904
\(452\) 4.58019i 0.215434i
\(453\) 45.6679i 2.14566i
\(454\) 10.1748 0.477529
\(455\) 3.64518 21.6922i 0.170889 1.01694i
\(456\) −9.27334 −0.434264
\(457\) 34.5000i 1.61384i 0.590660 + 0.806920i \(0.298867\pi\)
−0.590660 + 0.806920i \(0.701133\pi\)
\(458\) 14.6307i 0.683649i
\(459\) 44.3837 2.07166
\(460\) 1.48223 + 0.249075i 0.0691091 + 0.0116132i
\(461\) 8.03147 0.374063 0.187032 0.982354i \(-0.440113\pi\)
0.187032 + 0.982354i \(0.440113\pi\)
\(462\) 5.61582i 0.261272i
\(463\) 25.3290i 1.17714i −0.808447 0.588570i \(-0.799691\pi\)
0.808447 0.588570i \(-0.200309\pi\)
\(464\) 1.55332 0.0721112
\(465\) 41.4193 + 6.96015i 1.92077 + 0.322769i
\(466\) −1.92890 −0.0893547
\(467\) 26.8759i 1.24367i −0.783149 0.621834i \(-0.786388\pi\)
0.783149 0.621834i \(-0.213612\pi\)
\(468\) 32.8094i 1.51662i
\(469\) 38.5467 1.77992
\(470\) −1.70813 + 10.1649i −0.0787901 + 0.468873i
\(471\) −24.3837 −1.12354
\(472\) 24.0770i 1.10823i
\(473\) 1.92420i 0.0884748i
\(474\) 5.36146 0.246260
\(475\) −4.72538 1.63427i −0.216815 0.0749852i
\(476\) 9.68224 0.443785
\(477\) 1.18343i 0.0541854i
\(478\) 13.0741i 0.597996i
\(479\) 28.9015 1.32054 0.660272 0.751027i \(-0.270441\pi\)
0.660272 + 0.751027i \(0.270441\pi\)
\(480\) 6.59261 39.2321i 0.300910 1.79069i
\(481\) 5.31927 0.242538
\(482\) 0.147795i 0.00673187i
\(483\) 4.76964i 0.217026i
\(484\) −12.3048 −0.559310
\(485\) 8.35482 + 1.40396i 0.379373 + 0.0637503i
\(486\) −29.0815 −1.31916
\(487\) 17.7294i 0.803395i 0.915773 + 0.401697i \(0.131580\pi\)
−0.915773 + 0.401697i \(0.868420\pi\)
\(488\) 24.7206i 1.11905i
\(489\) −63.3141 −2.86316
\(490\) 0.517774 + 0.0870075i 0.0233907 + 0.00393060i
\(491\) −35.1645 −1.58695 −0.793475 0.608603i \(-0.791730\pi\)
−0.793475 + 0.608603i \(0.791730\pi\)
\(492\) 14.5377i 0.655410i
\(493\) 19.0035i 0.855875i
\(494\) 3.43630 0.154606
\(495\) 2.01981 12.0197i 0.0907838 0.540247i
\(496\) −1.51114 −0.0678520
\(497\) 9.46422i 0.424528i
\(498\) 12.2542i 0.549122i
\(499\) −21.4508 −0.960268 −0.480134 0.877195i \(-0.659412\pi\)
−0.480134 + 0.877195i \(0.659412\pi\)
\(500\) 6.30482 11.5558i 0.281960 0.516790i
\(501\) 34.7385 1.55200
\(502\) 11.7298i 0.523526i
\(503\) 5.34053i 0.238122i −0.992887 0.119061i \(-0.962012\pi\)
0.992887 0.119061i \(-0.0379884\pi\)
\(504\) −55.0304 −2.45125
\(505\) −3.09593 + 18.4236i −0.137767 + 0.819841i
\(506\) −0.383729 −0.0170588
\(507\) 4.35966i 0.193619i
\(508\) 16.9821i 0.753461i
\(509\) −36.1919 −1.60418 −0.802088 0.597206i \(-0.796278\pi\)
−0.802088 + 0.597206i \(0.796278\pi\)
\(510\) −20.3837 3.42531i −0.902607 0.151675i
\(511\) −28.1604 −1.24574
\(512\) 2.92346i 0.129200i
\(513\) 14.0133i 0.618704i
\(514\) 10.0170 0.441832
\(515\) 4.57816 + 0.769320i 0.201738 + 0.0339003i
\(516\) 9.83705 0.433052
\(517\) 3.76668i 0.165658i
\(518\) 3.30606i 0.145260i
\(519\) 65.6111 2.88001
\(520\) −4.04593 + 24.0770i −0.177426 + 1.05585i
\(521\) −2.77259 −0.121469 −0.0607346 0.998154i \(-0.519344\pi\)
−0.0607346 + 0.998154i \(0.519344\pi\)
\(522\) 40.0235i 1.75178i
\(523\) 20.5373i 0.898033i −0.893524 0.449016i \(-0.851774\pi\)
0.893524 0.449016i \(-0.148226\pi\)
\(524\) 11.7370 0.512735
\(525\) −39.4797 13.6540i −1.72303 0.595909i
\(526\) 16.1919 0.705999
\(527\) 18.4874i 0.805323i
\(528\) 0.617399i 0.0268688i
\(529\) 22.6741 0.985830
\(530\) −0.0540773 + 0.321810i −0.00234897 + 0.0139785i
\(531\) 61.4482 2.66662
\(532\) 3.05699i 0.132537i
\(533\) 14.5377i 0.629698i
\(534\) −49.3274 −2.13461
\(535\) 12.5782 + 2.11365i 0.543801 + 0.0913811i
\(536\) −42.7845 −1.84801
\(537\) 80.6547i 3.48051i
\(538\) 22.6682i 0.977294i
\(539\) 0.191865 0.00826419
\(540\) −36.3837 6.11397i −1.56571 0.263103i
\(541\) 35.4797 1.52539 0.762695 0.646758i \(-0.223876\pi\)
0.762695 + 0.646758i \(0.223876\pi\)
\(542\) 21.6456i 0.929760i
\(543\) 62.4891i 2.68166i
\(544\) −17.5111 −0.750784
\(545\) 0.609632 3.62787i 0.0261138 0.155401i
\(546\) 28.7096 1.22866
\(547\) 43.0756i 1.84178i −0.389822 0.920890i \(-0.627463\pi\)
0.389822 0.920890i \(-0.372537\pi\)
\(548\) 11.4260i 0.488092i
\(549\) 63.0908 2.69265
\(550\) −1.09850 + 3.17623i −0.0468401 + 0.135435i
\(551\) −6.00000 −0.255609
\(552\) 5.29401i 0.225328i
\(553\) 4.76964i 0.202826i
\(554\) 19.2563 0.818123
\(555\) 1.67409 9.96237i 0.0710612 0.422879i
\(556\) 15.8370 0.671640
\(557\) 40.4376i 1.71340i −0.515818 0.856698i \(-0.672512\pi\)
0.515818 0.856698i \(-0.327488\pi\)
\(558\) 38.9365i 1.64831i
\(559\) −9.83705 −0.416063
\(560\) 1.48223 + 0.249075i 0.0626355 + 0.0105254i
\(561\) −7.55332 −0.318902
\(562\) 3.48008i 0.146798i
\(563\) 19.7173i 0.830986i 0.909596 + 0.415493i \(0.136391\pi\)
−0.909596 + 0.415493i \(0.863609\pi\)
\(564\) 19.2563 0.810837
\(565\) −8.57816 1.44149i −0.360886 0.0606437i
\(566\) 0.191865 0.00806467
\(567\) 59.7915i 2.51101i
\(568\) 10.5047i 0.440768i
\(569\) −18.6807 −0.783137 −0.391568 0.920149i \(-0.628067\pi\)
−0.391568 + 0.920149i \(0.628067\pi\)
\(570\) 1.08148 6.43578i 0.0452981 0.269565i
\(571\) −29.9371 −1.25283 −0.626413 0.779491i \(-0.715478\pi\)
−0.626413 + 0.779491i \(0.715478\pi\)
\(572\) 3.30606i 0.138233i
\(573\) 36.8473i 1.53932i
\(574\) −9.03555 −0.377137
\(575\) −0.932977 + 2.69765i −0.0389079 + 0.112500i
\(576\) 40.6885 1.69536
\(577\) 0.156779i 0.00652679i 0.999995 + 0.00326339i \(0.00103877\pi\)
−0.999995 + 0.00326339i \(0.998961\pi\)
\(578\) 6.32023i 0.262887i
\(579\) 12.1919 0.506677
\(580\) 2.61778 15.5782i 0.108697 0.646849i
\(581\) −10.9015 −0.452271
\(582\) 11.0576i 0.458353i
\(583\) 0.119249i 0.00493877i
\(584\) 31.2563 1.29340
\(585\) 61.4482 + 10.3258i 2.54057 + 0.426921i
\(586\) −13.5993 −0.561780
\(587\) 31.1474i 1.28559i −0.766038 0.642795i \(-0.777775\pi\)
0.766038 0.642795i \(-0.222225\pi\)
\(588\) 0.980865i 0.0404502i
\(589\) 5.83705 0.240511
\(590\) −16.7096 2.80791i −0.687925 0.115600i
\(591\) −7.34818 −0.302264
\(592\) 0.363466i 0.0149384i
\(593\) 28.8728i 1.18567i 0.805326 + 0.592833i \(0.201991\pi\)
−0.805326 + 0.592833i \(0.798009\pi\)
\(594\) 9.41928 0.386478
\(595\) −3.04721 + 18.1337i −0.124923 + 0.743409i
\(596\) −17.7741 −0.728055
\(597\) 62.5904i 2.56165i
\(598\) 1.96173i 0.0802211i
\(599\) −25.3274 −1.03485 −0.517425 0.855728i \(-0.673109\pi\)
−0.517425 + 0.855728i \(0.673109\pi\)
\(600\) 43.8200 + 15.1551i 1.78895 + 0.618704i
\(601\) −19.8370 −0.809170 −0.404585 0.914500i \(-0.632584\pi\)
−0.404585 + 0.914500i \(0.632584\pi\)
\(602\) 6.11397i 0.249187i
\(603\) 109.193i 4.44667i
\(604\) 16.7096 0.679906
\(605\) 3.87259 23.0455i 0.157443 0.936932i
\(606\) −24.3837 −0.990521
\(607\) 2.49921i 0.101440i 0.998713 + 0.0507199i \(0.0161516\pi\)
−0.998713 + 0.0507199i \(0.983848\pi\)
\(608\) 5.52881i 0.224223i
\(609\) −50.1289 −2.03133
\(610\) −17.1563 2.88297i −0.694639 0.116728i
\(611\) −19.2563 −0.779027
\(612\) 27.4272i 1.10868i
\(613\) 0.883711i 0.0356927i −0.999841 0.0178464i \(-0.994319\pi\)
0.999841 0.0178464i \(-0.00568098\pi\)
\(614\) −1.49925 −0.0605046
\(615\) −27.2274 4.57533i −1.09792 0.184495i
\(616\) 5.54517 0.223421
\(617\) 29.4085i 1.18394i 0.805959 + 0.591971i \(0.201650\pi\)
−0.805959 + 0.591971i \(0.798350\pi\)
\(618\) 6.05921i 0.243737i
\(619\) −30.3208 −1.21870 −0.609348 0.792903i \(-0.708569\pi\)
−0.609348 + 0.792903i \(0.708569\pi\)
\(620\) −2.54668 + 15.1551i −0.102277 + 0.608644i
\(621\) 8.00000 0.321029
\(622\) 0.672165i 0.0269514i
\(623\) 43.8825i 1.75811i
\(624\) −3.15632 −0.126354
\(625\) 19.6584 + 15.4450i 0.786334 + 0.617801i
\(626\) −24.3837 −0.974570
\(627\) 2.38482i 0.0952405i
\(628\) 8.92188i 0.356022i
\(629\) −4.44668 −0.177301
\(630\) 6.41777 38.1916i 0.255690 1.52159i
\(631\) 17.7767 0.707678 0.353839 0.935306i \(-0.384876\pi\)
0.353839 + 0.935306i \(0.384876\pi\)
\(632\) 5.29401i 0.210584i
\(633\) 36.1286i 1.43598i
\(634\) 7.40226 0.293981
\(635\) 31.8056 + 5.34465i 1.26217 + 0.212096i
\(636\) 0.609632 0.0241735
\(637\) 0.980865i 0.0388633i
\(638\) 4.03299i 0.159668i
\(639\) −26.8096 −1.06057
\(640\) 13.3193 + 2.23819i 0.526490 + 0.0884722i
\(641\) −32.6675 −1.29029 −0.645143 0.764062i \(-0.723202\pi\)
−0.645143 + 0.764062i \(0.723202\pi\)
\(642\) 16.6472i 0.657014i
\(643\) 31.8661i 1.25668i 0.777941 + 0.628338i \(0.216264\pi\)
−0.777941 + 0.628338i \(0.783736\pi\)
\(644\) 1.74519 0.0687700
\(645\) −3.09593 + 18.4236i −0.121902 + 0.725430i
\(646\) −2.87259 −0.113021
\(647\) 21.2601i 0.835820i −0.908488 0.417910i \(-0.862763\pi\)
0.908488 0.417910i \(-0.137237\pi\)
\(648\) 66.3649i 2.60706i
\(649\) −6.19186 −0.243052
\(650\) −16.2378 5.61582i −0.636899 0.220271i
\(651\) 48.7675 1.91135
\(652\) 23.1663i 0.907263i
\(653\) 12.8340i 0.502234i 0.967957 + 0.251117i \(0.0807980\pi\)
−0.967957 + 0.251117i \(0.919202\pi\)
\(654\) 4.80150 0.187753
\(655\) −3.69390 + 21.9821i −0.144333 + 0.858912i
\(656\) 0.993361 0.0387842
\(657\) 79.7710i 3.11216i
\(658\) 11.9683i 0.466573i
\(659\) −20.3548 −0.792911 −0.396456 0.918054i \(-0.629760\pi\)
−0.396456 + 0.918054i \(0.629760\pi\)
\(660\) 6.19186 + 1.04049i 0.241018 + 0.0405010i
\(661\) −30.7385 −1.19559 −0.597795 0.801649i \(-0.703957\pi\)
−0.597795 + 0.801649i \(0.703957\pi\)
\(662\) 7.25574i 0.282002i
\(663\) 38.6147i 1.49967i
\(664\) 12.1000 0.469571
\(665\) −5.72538 0.962100i −0.222021 0.0373086i
\(666\) 9.36520 0.362894
\(667\) 3.42531i 0.132629i
\(668\) 12.7107i 0.491790i
\(669\) −12.9934 −0.502352
\(670\) 4.98962 29.6928i 0.192766 1.14713i
\(671\) −6.35738 −0.245424
\(672\) 46.1922i 1.78190i
\(673\) 21.2094i 0.817564i 0.912632 + 0.408782i \(0.134046\pi\)
−0.912632 + 0.408782i \(0.865954\pi\)
\(674\) 8.98147 0.345953
\(675\) 22.9015 66.2183i 0.881479 2.54874i
\(676\) −1.59518 −0.0613530
\(677\) 11.2650i 0.432951i −0.976288 0.216475i \(-0.930544\pi\)
0.976288 0.216475i \(-0.0694561\pi\)
\(678\) 11.3532i 0.436018i
\(679\) 9.83705 0.377511
\(680\) 3.38222 20.1273i 0.129702 0.771847i
\(681\) 36.1000 1.38336
\(682\) 3.92346i 0.150237i
\(683\) 12.3603i 0.472954i −0.971637 0.236477i \(-0.924007\pi\)
0.971637 0.236477i \(-0.0759928\pi\)
\(684\) −8.65964 −0.331109
\(685\) 21.3995 + 3.59600i 0.817632 + 0.137396i
\(686\) 17.0934 0.652628
\(687\) 51.9093i 1.98046i
\(688\) 0.672165i 0.0256261i
\(689\) −0.609632 −0.0232251
\(690\) −3.67409 0.617399i −0.139870 0.0235040i
\(691\) 22.7493 0.865423 0.432711 0.901533i \(-0.357557\pi\)
0.432711 + 0.901533i \(0.357557\pi\)
\(692\) 24.0068i 0.912601i
\(693\) 14.1521i 0.537595i
\(694\) 19.2985 0.732561
\(695\) −4.98426 + 29.6609i −0.189064 + 1.12510i
\(696\) 55.6401 2.10903
\(697\) 12.1529i 0.460323i
\(698\) 14.8881i 0.563521i
\(699\) −6.84368 −0.258852
\(700\) 4.99593 14.4454i 0.188828 0.545985i
\(701\) −16.0289 −0.605404 −0.302702 0.953085i \(-0.597889\pi\)
−0.302702 + 0.953085i \(0.597889\pi\)
\(702\) 48.1540i 1.81745i
\(703\) 1.40396i 0.0529512i
\(704\) −4.10001 −0.154525
\(705\) −6.06038 + 36.0648i −0.228247 + 1.35828i
\(706\) 21.6533 0.814934
\(707\) 21.6922i 0.815818i
\(708\) 31.6545i 1.18965i
\(709\) −31.4193 −1.17998 −0.589988 0.807412i \(-0.700867\pi\)
−0.589988 + 0.807412i \(0.700867\pi\)
\(710\) 7.29036 + 1.22508i 0.273602 + 0.0459765i
\(711\) 13.5111 0.506707
\(712\) 48.7069i 1.82537i
\(713\) 3.33228i 0.124795i
\(714\) −24.0000 −0.898177
\(715\) −6.19186 1.04049i −0.231563 0.0389121i
\(716\) −29.5111 −1.10288
\(717\) 46.3865i 1.73234i
\(718\) 2.01650i 0.0752550i
\(719\) −11.2589 −0.419886 −0.209943 0.977714i \(-0.567328\pi\)
−0.209943 + 0.977714i \(0.567328\pi\)
\(720\) −0.705565 + 4.19876i −0.0262948 + 0.156478i
\(721\) 5.39037 0.200748
\(722\) 0.906968i 0.0337538i
\(723\) 0.524371i 0.0195016i
\(724\) −22.8644 −0.849750
\(725\) 28.3523 + 9.80559i 1.05298 + 0.364171i
\(726\) 30.5008 1.13199
\(727\) 48.9829i 1.81668i −0.418237 0.908338i \(-0.637352\pi\)
0.418237 0.908338i \(-0.362648\pi\)
\(728\) 28.3485i 1.05066i
\(729\) −34.0934 −1.26272
\(730\) −3.64518 + 21.6922i −0.134914 + 0.802863i
\(731\) 8.22334 0.304151
\(732\) 32.5007i 1.20126i
\(733\) 35.9260i 1.32696i −0.748195 0.663479i \(-0.769079\pi\)
0.748195 0.663479i \(-0.230921\pi\)
\(734\) 4.10001 0.151334
\(735\) 1.83705 + 0.308700i 0.0677604 + 0.0113866i
\(736\) −3.15632 −0.116343
\(737\) 11.0029i 0.405296i
\(738\) 25.5953i 0.942177i
\(739\) −14.3523 −0.527956 −0.263978 0.964529i \(-0.585035\pi\)
−0.263978 + 0.964529i \(0.585035\pi\)
\(740\) 3.64518 + 0.612541i 0.134000 + 0.0225175i
\(741\) 12.1919 0.447879
\(742\) 0.378902i 0.0139099i
\(743\) 12.5629i 0.460887i 0.973086 + 0.230443i \(0.0740176\pi\)
−0.973086 + 0.230443i \(0.925982\pi\)
\(744\) −54.1289 −1.98446
\(745\) 5.59390 33.2888i 0.204944 1.21961i
\(746\) 14.0748 0.515316
\(747\) 30.8811i 1.12988i
\(748\) 2.76372i 0.101052i
\(749\) 14.8096 0.541133
\(750\) −15.6282 + 28.6441i −0.570660 + 1.04593i
\(751\) 26.4548 0.965350 0.482675 0.875799i \(-0.339665\pi\)
0.482675 + 0.875799i \(0.339665\pi\)
\(752\) 1.31578i 0.0479817i
\(753\) 41.6169i 1.51660i
\(754\) −20.6178 −0.750855
\(755\) −5.25889 + 31.2952i −0.191390 + 1.13895i
\(756\) −42.8386 −1.55802
\(757\) 15.7350i 0.571897i 0.958245 + 0.285949i \(0.0923087\pi\)
−0.958245 + 0.285949i \(0.907691\pi\)
\(758\) 17.1431i 0.622664i
\(759\) −1.36146 −0.0494178
\(760\) 6.35482 + 1.06787i 0.230514 + 0.0387358i
\(761\) 16.9619 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(762\) 42.0948i 1.52493i
\(763\) 4.27149i 0.154638i
\(764\) 13.4822 0.487770
\(765\) −51.3680 8.63195i −1.85721 0.312089i
\(766\) −12.4297 −0.449102
\(767\) 31.6545i 1.14298i
\(768\) 53.2323i 1.92086i
\(769\) −41.9974 −1.51447 −0.757233 0.653145i \(-0.773449\pi\)
−0.757233 + 0.653145i \(0.773449\pi\)
\(770\) −0.646690 + 3.84840i −0.0233051 + 0.138687i
\(771\) 35.5400 1.27994
\(772\) 4.46094i 0.160553i
\(773\) 40.9579i 1.47315i −0.676355 0.736576i \(-0.736441\pi\)
0.676355 0.736576i \(-0.263559\pi\)
\(774\) −17.3193 −0.622528
\(775\) −27.5822 9.53928i −0.990783 0.342661i
\(776\) −10.9185 −0.391952
\(777\) 11.7298i 0.420804i
\(778\) 11.5558i 0.414295i
\(779\) −3.83705 −0.137476
\(780\) −5.31927 + 31.6545i −0.190460 + 1.13341i
\(781\) 2.70149 0.0966669
\(782\) 1.63992i 0.0586434i
\(783\) 84.0800i 3.00477i
\(784\) −0.0670225 −0.00239366
\(785\) 16.7096 + 2.80791i 0.596393 + 0.100219i
\(786\) −29.0934 −1.03773
\(787\) 28.5379i 1.01727i 0.860983 +