Properties

Label 845.2.m.g.316.4
Level $845$
Weight $2$
Character 845.316
Analytic conductor $6.747$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 845 = 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 845.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \(x^{8} - 4 x^{7} + 5 x^{6} + 2 x^{5} - 11 x^{4} + 4 x^{3} + 20 x^{2} - 32 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 316.4
Root \(1.20036 + 0.747754i\) of defining polynomial
Character \(\chi\) \(=\) 845.316
Dual form 845.2.m.g.361.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.16117 + 1.24775i) q^{2} +(1.41342 - 2.44811i) q^{3} +(2.11378 + 3.66117i) q^{4} +1.00000i q^{5} +(6.10929 - 3.52720i) q^{6} +(1.64996 - 0.952606i) q^{7} +5.55889i q^{8} +(-2.49551 - 4.32235i) q^{9} +O(q^{10})\) \(q+(2.16117 + 1.24775i) q^{2} +(1.41342 - 2.44811i) q^{3} +(2.11378 + 3.66117i) q^{4} +1.00000i q^{5} +(6.10929 - 3.52720i) q^{6} +(1.64996 - 0.952606i) q^{7} +5.55889i q^{8} +(-2.49551 - 4.32235i) q^{9} +(-1.24775 + 2.16117i) q^{10} +(-0.926118 - 0.534695i) q^{11} +11.9506 q^{12} +4.75447 q^{14} +(2.44811 + 1.41342i) q^{15} +(-2.70857 + 4.69138i) q^{16} +(0.318632 + 0.551886i) q^{17} -12.4551i q^{18} +(-4.96410 + 2.86603i) q^{19} +(-3.66117 + 2.11378i) q^{20} -5.38573i q^{21} +(-1.33433 - 2.31114i) q^{22} +(1.90893 - 3.30636i) q^{23} +(13.6088 + 7.85704i) q^{24} -1.00000 q^{25} -5.62828 q^{27} +(6.97531 + 4.02720i) q^{28} +(-4.72756 + 8.18837i) q^{29} +(3.52720 + 6.10929i) q^{30} +1.46410i q^{31} +(-2.07908 + 1.20036i) q^{32} +(-2.61799 + 1.51150i) q^{33} +1.59030i q^{34} +(0.952606 + 1.64996i) q^{35} +(10.5499 - 18.2730i) q^{36} +(-0.655970 - 0.378725i) q^{37} -14.3044 q^{38} -5.55889 q^{40} +(0.232051 + 0.133975i) q^{41} +(6.72006 - 11.6395i) q^{42} +(0.318632 + 0.551886i) q^{43} -4.52091i q^{44} +(4.32235 - 2.49551i) q^{45} +(8.25104 - 4.76374i) q^{46} -9.44613i q^{47} +(7.65668 + 13.2618i) q^{48} +(-1.68508 + 2.91865i) q^{49} +(-2.16117 - 1.24775i) q^{50} +1.80144 q^{51} -6.99102 q^{53} +(-12.1637 - 7.02271i) q^{54} +(0.534695 - 0.926118i) q^{55} +(5.29543 + 9.17196i) q^{56} +16.2036i q^{57} +(-20.4341 + 11.7977i) q^{58} +(0.641756 - 0.370518i) q^{59} +11.9506i q^{60} +(-2.09928 - 3.63606i) q^{61} +(-1.82684 + 3.16418i) q^{62} +(-8.23499 - 4.75447i) q^{63} +4.84325 q^{64} -7.54390 q^{66} +(7.01029 + 4.04739i) q^{67} +(-1.34703 + 2.33313i) q^{68} +(-5.39623 - 9.34654i) q^{69} +4.75447i q^{70} +(-8.45663 + 4.88244i) q^{71} +(24.0274 - 13.8723i) q^{72} -3.71649i q^{73} +(-0.945110 - 1.63698i) q^{74} +(-1.41342 + 2.44811i) q^{75} +(-20.9860 - 12.1163i) q^{76} -2.03741 q^{77} -9.31937 q^{79} +(-4.69138 - 2.70857i) q^{80} +(-0.468594 + 0.811629i) q^{81} +(0.334335 + 0.579085i) q^{82} -5.11778i q^{83} +(19.7181 - 11.3842i) q^{84} +(-0.551886 + 0.318632i) q^{85} +1.59030i q^{86} +(13.3640 + 23.1472i) q^{87} +(2.97231 - 5.14819i) q^{88} +(10.8932 + 6.28917i) q^{89} +12.4551 q^{90} +16.1402 q^{92} +(3.58429 + 2.06939i) q^{93} +(11.7864 - 20.4147i) q^{94} +(-2.86603 - 4.96410i) q^{95} +6.78645i q^{96} +(3.65597 - 2.11078i) q^{97} +(-7.28351 + 4.20514i) q^{98} +5.33734i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{3} + 2q^{4} + 18q^{6} + 6q^{7} - 4q^{9} + O(q^{10}) \) \( 8q + 2q^{3} + 2q^{4} + 18q^{6} + 6q^{7} - 4q^{9} - 2q^{10} + 20q^{12} + 4q^{14} + 6q^{15} - 2q^{16} - 2q^{17} - 12q^{19} - 12q^{20} - 12q^{22} - 10q^{23} + 12q^{24} - 8q^{25} - 4q^{27} + 18q^{28} - 8q^{29} + 4q^{30} - 6q^{32} - 42q^{33} + 10q^{35} + 20q^{36} - 6q^{37} - 16q^{38} - 12q^{40} - 12q^{41} + 4q^{42} - 2q^{43} + 42q^{46} + 28q^{48} + 12q^{49} - 8q^{51} - 24q^{53} - 18q^{54} + 12q^{56} - 36q^{58} + 12q^{59} - 28q^{61} + 4q^{62} + 24q^{63} - 8q^{64} + 12q^{66} - 6q^{67} - 14q^{68} - 16q^{69} + 48q^{72} + 10q^{74} - 2q^{75} - 54q^{76} - 36q^{77} - 16q^{79} + 8q^{81} + 4q^{82} + 30q^{84} - 18q^{85} + 22q^{87} - 18q^{88} - 24q^{89} + 40q^{90} + 44q^{92} + 32q^{94} - 16q^{95} + 30q^{97} - 72q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.16117 + 1.24775i 1.52818 + 0.882295i 0.999438 + 0.0335125i \(0.0106693\pi\)
0.528742 + 0.848783i \(0.322664\pi\)
\(3\) 1.41342 2.44811i 0.816038 1.41342i −0.0925423 0.995709i \(-0.529499\pi\)
0.908580 0.417710i \(-0.137167\pi\)
\(4\) 2.11378 + 3.66117i 1.05689 + 1.83059i
\(5\) 1.00000i 0.447214i
\(6\) 6.10929 3.52720i 2.49411 1.43997i
\(7\) 1.64996 0.952606i 0.623627 0.360051i −0.154653 0.987969i \(-0.549426\pi\)
0.778280 + 0.627918i \(0.216093\pi\)
\(8\) 5.55889i 1.96536i
\(9\) −2.49551 4.32235i −0.831836 1.44078i
\(10\) −1.24775 + 2.16117i −0.394574 + 0.683423i
\(11\) −0.926118 0.534695i −0.279235 0.161217i 0.353842 0.935305i \(-0.384875\pi\)
−0.633077 + 0.774089i \(0.718208\pi\)
\(12\) 11.9506 3.44985
\(13\) 0 0
\(14\) 4.75447 1.27069
\(15\) 2.44811 + 1.41342i 0.632100 + 0.364943i
\(16\) −2.70857 + 4.69138i −0.677142 + 1.17284i
\(17\) 0.318632 + 0.551886i 0.0772795 + 0.133852i 0.902075 0.431579i \(-0.142043\pi\)
−0.824796 + 0.565431i \(0.808710\pi\)
\(18\) 12.4551i 2.93570i
\(19\) −4.96410 + 2.86603i −1.13884 + 0.657511i −0.946144 0.323747i \(-0.895057\pi\)
−0.192699 + 0.981258i \(0.561724\pi\)
\(20\) −3.66117 + 2.11378i −0.818663 + 0.472655i
\(21\) 5.38573i 1.17526i
\(22\) −1.33433 2.31114i −0.284481 0.492736i
\(23\) 1.90893 3.30636i 0.398039 0.689423i −0.595445 0.803396i \(-0.703024\pi\)
0.993484 + 0.113973i \(0.0363576\pi\)
\(24\) 13.6088 + 7.85704i 2.77788 + 1.60381i
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −5.62828 −1.08316
\(28\) 6.97531 + 4.02720i 1.31821 + 0.761069i
\(29\) −4.72756 + 8.18837i −0.877886 + 1.52054i −0.0242288 + 0.999706i \(0.507713\pi\)
−0.853657 + 0.520836i \(0.825620\pi\)
\(30\) 3.52720 + 6.10929i 0.643975 + 1.11540i
\(31\) 1.46410i 0.262960i 0.991319 + 0.131480i \(0.0419730\pi\)
−0.991319 + 0.131480i \(0.958027\pi\)
\(32\) −2.07908 + 1.20036i −0.367534 + 0.212196i
\(33\) −2.61799 + 1.51150i −0.455733 + 0.263118i
\(34\) 1.59030i 0.272733i
\(35\) 0.952606 + 1.64996i 0.161020 + 0.278895i
\(36\) 10.5499 18.2730i 1.75832 3.04550i
\(37\) −0.655970 0.378725i −0.107841 0.0622619i 0.445110 0.895476i \(-0.353165\pi\)
−0.552950 + 0.833214i \(0.686498\pi\)
\(38\) −14.3044 −2.32048
\(39\) 0 0
\(40\) −5.55889 −0.878938
\(41\) 0.232051 + 0.133975i 0.0362402 + 0.0209233i 0.518011 0.855374i \(-0.326673\pi\)
−0.481770 + 0.876297i \(0.660006\pi\)
\(42\) 6.72006 11.6395i 1.03693 1.79601i
\(43\) 0.318632 + 0.551886i 0.0485909 + 0.0841618i 0.889298 0.457328i \(-0.151194\pi\)
−0.840707 + 0.541490i \(0.817860\pi\)
\(44\) 4.52091i 0.681552i
\(45\) 4.32235 2.49551i 0.644337 0.372008i
\(46\) 8.25104 4.76374i 1.21655 0.702375i
\(47\) 9.44613i 1.37786i −0.724828 0.688930i \(-0.758081\pi\)
0.724828 0.688930i \(-0.241919\pi\)
\(48\) 7.65668 + 13.2618i 1.10515 + 1.91417i
\(49\) −1.68508 + 2.91865i −0.240726 + 0.416950i
\(50\) −2.16117 1.24775i −0.305636 0.176459i
\(51\) 1.80144 0.252252
\(52\) 0 0
\(53\) −6.99102 −0.960290 −0.480145 0.877189i \(-0.659416\pi\)
−0.480145 + 0.877189i \(0.659416\pi\)
\(54\) −12.1637 7.02271i −1.65527 0.955669i
\(55\) 0.534695 0.926118i 0.0720982 0.124878i
\(56\) 5.29543 + 9.17196i 0.707632 + 1.22565i
\(57\) 16.2036i 2.14622i
\(58\) −20.4341 + 11.7977i −2.68313 + 1.54911i
\(59\) 0.641756 0.370518i 0.0835495 0.0482373i −0.457643 0.889136i \(-0.651306\pi\)
0.541193 + 0.840899i \(0.317973\pi\)
\(60\) 11.9506i 1.54282i
\(61\) −2.09928 3.63606i −0.268785 0.465550i 0.699763 0.714375i \(-0.253289\pi\)
−0.968548 + 0.248825i \(0.919956\pi\)
\(62\) −1.82684 + 3.16418i −0.232009 + 0.401851i
\(63\) −8.23499 4.75447i −1.03751 0.599007i
\(64\) 4.84325 0.605406
\(65\) 0 0
\(66\) −7.54390 −0.928589
\(67\) 7.01029 + 4.04739i 0.856443 + 0.494468i 0.862820 0.505512i \(-0.168696\pi\)
−0.00637624 + 0.999980i \(0.502030\pi\)
\(68\) −1.34703 + 2.33313i −0.163352 + 0.282934i
\(69\) −5.39623 9.34654i −0.649629 1.12519i
\(70\) 4.75447i 0.568268i
\(71\) −8.45663 + 4.88244i −1.00362 + 0.579439i −0.909317 0.416105i \(-0.863395\pi\)
−0.0943010 + 0.995544i \(0.530062\pi\)
\(72\) 24.0274 13.8723i 2.83166 1.63486i
\(73\) 3.71649i 0.434982i −0.976062 0.217491i \(-0.930213\pi\)
0.976062 0.217491i \(-0.0697873\pi\)
\(74\) −0.945110 1.63698i −0.109867 0.190295i
\(75\) −1.41342 + 2.44811i −0.163208 + 0.282684i
\(76\) −20.9860 12.1163i −2.40726 1.38983i
\(77\) −2.03741 −0.232185
\(78\) 0 0
\(79\) −9.31937 −1.04851 −0.524255 0.851561i \(-0.675656\pi\)
−0.524255 + 0.851561i \(0.675656\pi\)
\(80\) −4.69138 2.70857i −0.524512 0.302827i
\(81\) −0.468594 + 0.811629i −0.0520660 + 0.0901809i
\(82\) 0.334335 + 0.579085i 0.0369211 + 0.0639492i
\(83\) 5.11778i 0.561749i −0.959744 0.280875i \(-0.909376\pi\)
0.959744 0.280875i \(-0.0906245\pi\)
\(84\) 19.7181 11.3842i 2.15142 1.24212i
\(85\) −0.551886 + 0.318632i −0.0598605 + 0.0345605i
\(86\) 1.59030i 0.171486i
\(87\) 13.3640 + 23.1472i 1.43278 + 2.48164i
\(88\) 2.97231 5.14819i 0.316849 0.548799i
\(89\) 10.8932 + 6.28917i 1.15467 + 0.666650i 0.950021 0.312185i \(-0.101061\pi\)
0.204651 + 0.978835i \(0.434394\pi\)
\(90\) 12.4551 1.31288
\(91\) 0 0
\(92\) 16.1402 1.68273
\(93\) 3.58429 + 2.06939i 0.371673 + 0.214586i
\(94\) 11.7864 20.4147i 1.21568 2.10562i
\(95\) −2.86603 4.96410i −0.294048 0.509306i
\(96\) 6.78645i 0.692639i
\(97\) 3.65597 2.11078i 0.371208 0.214317i −0.302778 0.953061i \(-0.597914\pi\)
0.673986 + 0.738744i \(0.264581\pi\)
\(98\) −7.28351 + 4.20514i −0.735746 + 0.424783i
\(99\) 5.33734i 0.536423i
\(100\) −2.11378 3.66117i −0.211378 0.366117i
\(101\) −7.62379 + 13.2048i −0.758595 + 1.31393i 0.184972 + 0.982744i \(0.440781\pi\)
−0.943567 + 0.331181i \(0.892553\pi\)
\(102\) 3.89322 + 2.24775i 0.385487 + 0.222561i
\(103\) 13.5269 1.33285 0.666423 0.745574i \(-0.267824\pi\)
0.666423 + 0.745574i \(0.267824\pi\)
\(104\) 0 0
\(105\) 5.38573 0.525593
\(106\) −15.1088 8.72307i −1.46750 0.847259i
\(107\) 3.68137 6.37632i 0.355891 0.616422i −0.631379 0.775475i \(-0.717511\pi\)
0.987270 + 0.159053i \(0.0508440\pi\)
\(108\) −11.8969 20.6061i −1.14478 1.98282i
\(109\) 10.0760i 0.965103i −0.875868 0.482551i \(-0.839710\pi\)
0.875868 0.482551i \(-0.160290\pi\)
\(110\) 2.31114 1.33433i 0.220358 0.127224i
\(111\) −1.85432 + 1.07059i −0.176004 + 0.101616i
\(112\) 10.3208i 0.975223i
\(113\) 3.34403 + 5.79203i 0.314580 + 0.544868i 0.979348 0.202181i \(-0.0648030\pi\)
−0.664768 + 0.747050i \(0.731470\pi\)
\(114\) −20.2181 + 35.0187i −1.89360 + 3.27981i
\(115\) 3.30636 + 1.90893i 0.308320 + 0.178008i
\(116\) −39.9721 −3.71131
\(117\) 0 0
\(118\) 1.84926 0.170238
\(119\) 1.05146 + 0.607061i 0.0963872 + 0.0556492i
\(120\) −7.85704 + 13.6088i −0.717246 + 1.24231i
\(121\) −4.92820 8.53590i −0.448018 0.775991i
\(122\) 10.4775i 0.948592i
\(123\) 0.655970 0.378725i 0.0591468 0.0341484i
\(124\) −5.36033 + 3.09479i −0.481372 + 0.277920i
\(125\) 1.00000i 0.0894427i
\(126\) −11.8648 20.5505i −1.05700 1.83078i
\(127\) 0.744750 1.28994i 0.0660859 0.114464i −0.831089 0.556139i \(-0.812282\pi\)
0.897175 + 0.441675i \(0.145616\pi\)
\(128\) 14.6253 + 8.44391i 1.29270 + 0.746343i
\(129\) 1.80144 0.158608
\(130\) 0 0
\(131\) 4.12676 0.360557 0.180278 0.983616i \(-0.442300\pi\)
0.180278 + 0.983616i \(0.442300\pi\)
\(132\) −11.0677 6.38994i −0.963319 0.556172i
\(133\) −5.46039 + 9.45767i −0.473476 + 0.820084i
\(134\) 10.1003 + 17.4942i 0.872533 + 1.51127i
\(135\) 5.62828i 0.484405i
\(136\) −3.06787 + 1.77124i −0.263068 + 0.151882i
\(137\) −17.4155 + 10.0548i −1.48790 + 0.859041i −0.999905 0.0138029i \(-0.995606\pi\)
−0.487999 + 0.872844i \(0.662273\pi\)
\(138\) 26.9327i 2.29266i
\(139\) −10.4126 18.0352i −0.883189 1.52973i −0.847776 0.530355i \(-0.822059\pi\)
−0.0354130 0.999373i \(-0.511275\pi\)
\(140\) −4.02720 + 6.97531i −0.340360 + 0.589521i
\(141\) −23.1252 13.3513i −1.94749 1.12439i
\(142\) −24.3683 −2.04494
\(143\) 0 0
\(144\) 27.0370 2.25308
\(145\) −8.18837 4.72756i −0.680007 0.392602i
\(146\) 4.63726 8.03198i 0.383783 0.664731i
\(147\) 4.76346 + 8.25055i 0.392883 + 0.680494i
\(148\) 3.20216i 0.263216i
\(149\) −11.5768 + 6.68388i −0.948410 + 0.547565i −0.892587 0.450876i \(-0.851112\pi\)
−0.0558233 + 0.998441i \(0.517778\pi\)
\(150\) −6.10929 + 3.52720i −0.498821 + 0.287995i
\(151\) 18.2984i 1.48910i 0.667567 + 0.744550i \(0.267336\pi\)
−0.667567 + 0.744550i \(0.732664\pi\)
\(152\) −15.9319 27.5949i −1.29225 2.23824i
\(153\) 1.59030 2.75447i 0.128568 0.222686i
\(154\) −4.40320 2.54219i −0.354820 0.204856i
\(155\) −1.46410 −0.117599
\(156\) 0 0
\(157\) 2.42229 0.193320 0.0966599 0.995317i \(-0.469184\pi\)
0.0966599 + 0.995317i \(0.469184\pi\)
\(158\) −20.1408 11.6283i −1.60231 0.925096i
\(159\) −9.88124 + 17.1148i −0.783633 + 1.35729i
\(160\) −1.20036 2.07908i −0.0948968 0.164366i
\(161\) 7.27382i 0.573258i
\(162\) −2.02543 + 1.16938i −0.159132 + 0.0918752i
\(163\) 13.8416 7.99144i 1.08416 0.625938i 0.152142 0.988359i \(-0.451383\pi\)
0.932015 + 0.362421i \(0.118050\pi\)
\(164\) 1.13277i 0.0884545i
\(165\) −1.51150 2.61799i −0.117670 0.203810i
\(166\) 6.38573 11.0604i 0.495629 0.858454i
\(167\) 12.4648 + 7.19658i 0.964558 + 0.556888i 0.897573 0.440866i \(-0.145329\pi\)
0.0669853 + 0.997754i \(0.478662\pi\)
\(168\) 29.9387 2.30982
\(169\) 0 0
\(170\) −1.59030 −0.121970
\(171\) 24.7759 + 14.3044i 1.89466 + 1.09388i
\(172\) −1.34703 + 2.33313i −0.102710 + 0.177900i
\(173\) −12.1745 21.0868i −0.925608 1.60320i −0.790581 0.612358i \(-0.790221\pi\)
−0.135027 0.990842i \(-0.543112\pi\)
\(174\) 66.7001i 5.05653i
\(175\) −1.64996 + 0.952606i −0.124725 + 0.0720103i
\(176\) 5.01691 2.89651i 0.378164 0.218333i
\(177\) 2.09479i 0.157454i
\(178\) 15.6947 + 27.1840i 1.17636 + 2.03752i
\(179\) 1.89414 3.28075i 0.141575 0.245215i −0.786515 0.617571i \(-0.788117\pi\)
0.928090 + 0.372356i \(0.121450\pi\)
\(180\) 18.2730 + 10.5499i 1.36199 + 0.786343i
\(181\) 8.48794 0.630904 0.315452 0.948942i \(-0.397844\pi\)
0.315452 + 0.948942i \(0.397844\pi\)
\(182\) 0 0
\(183\) −11.8687 −0.877356
\(184\) 18.3797 + 10.6115i 1.35497 + 0.782291i
\(185\) 0.378725 0.655970i 0.0278444 0.0482279i
\(186\) 5.16418 + 8.94462i 0.378656 + 0.655851i
\(187\) 0.681482i 0.0498349i
\(188\) 34.5839 19.9670i 2.52229 1.45625i
\(189\) −9.28645 + 5.36153i −0.675490 + 0.389994i
\(190\) 14.3044i 1.03775i
\(191\) 2.72155 + 4.71386i 0.196924 + 0.341083i 0.947530 0.319668i \(-0.103571\pi\)
−0.750605 + 0.660751i \(0.770238\pi\)
\(192\) 6.84555 11.8568i 0.494035 0.855693i
\(193\) −10.5288 6.07880i −0.757879 0.437562i 0.0706548 0.997501i \(-0.477491\pi\)
−0.828534 + 0.559939i \(0.810824\pi\)
\(194\) 10.5349 0.756363
\(195\) 0 0
\(196\) −14.2476 −1.01768
\(197\) −3.79172 2.18915i −0.270149 0.155970i 0.358807 0.933412i \(-0.383184\pi\)
−0.628955 + 0.777442i \(0.716517\pi\)
\(198\) −6.65968 + 11.5349i −0.473283 + 0.819751i
\(199\) 10.4186 + 18.0456i 0.738558 + 1.27922i 0.953144 + 0.302516i \(0.0978265\pi\)
−0.214586 + 0.976705i \(0.568840\pi\)
\(200\) 5.55889i 0.393073i
\(201\) 19.8170 11.4413i 1.39778 0.807009i
\(202\) −32.9526 + 19.0252i −2.31854 + 1.33861i
\(203\) 18.0140i 1.26434i
\(204\) 3.80785 + 6.59538i 0.266603 + 0.461769i
\(205\) −0.133975 + 0.232051i −0.00935719 + 0.0162071i
\(206\) 29.2340 + 16.8783i 2.03683 + 1.17596i
\(207\) −19.0550 −1.32441
\(208\) 0 0
\(209\) 6.12979 0.424007
\(210\) 11.6395 + 6.72006i 0.803201 + 0.463728i
\(211\) 5.32684 9.22635i 0.366715 0.635168i −0.622335 0.782751i \(-0.713816\pi\)
0.989050 + 0.147583i \(0.0471492\pi\)
\(212\) −14.7775 25.5953i −1.01492 1.75789i
\(213\) 27.6037i 1.89138i
\(214\) 15.9121 9.18688i 1.08773 0.628002i
\(215\) −0.551886 + 0.318632i −0.0376383 + 0.0217305i
\(216\) 31.2870i 2.12881i
\(217\) 1.39471 + 2.41571i 0.0946792 + 0.163989i
\(218\) 12.5723 21.7759i 0.851505 1.47485i
\(219\) −9.09839 5.25296i −0.614812 0.354962i
\(220\) 4.52091 0.304799
\(221\) 0 0
\(222\) −5.34335 −0.358622
\(223\) 18.4804 + 10.6697i 1.23754 + 0.714494i 0.968591 0.248661i \(-0.0799905\pi\)
0.268949 + 0.963155i \(0.413324\pi\)
\(224\) −2.28694 + 3.96110i −0.152803 + 0.264662i
\(225\) 2.49551 + 4.32235i 0.166367 + 0.288156i
\(226\) 16.6901i 1.11021i
\(227\) −13.5842 + 7.84283i −0.901613 + 0.520547i −0.877723 0.479168i \(-0.840938\pi\)
−0.0238900 + 0.999715i \(0.507605\pi\)
\(228\) −59.3241 + 34.2508i −3.92884 + 2.26831i
\(229\) 7.62085i 0.503600i −0.967779 0.251800i \(-0.918977\pi\)
0.967779 0.251800i \(-0.0810225\pi\)
\(230\) 4.76374 + 8.25104i 0.314112 + 0.544058i
\(231\) −2.87972 + 4.98782i −0.189472 + 0.328175i
\(232\) −45.5182 26.2800i −2.98842 1.72536i
\(233\) 19.0550 1.24833 0.624166 0.781292i \(-0.285439\pi\)
0.624166 + 0.781292i \(0.285439\pi\)
\(234\) 0 0
\(235\) 9.44613 0.616198
\(236\) 2.71306 + 1.56639i 0.176605 + 0.101963i
\(237\) −13.1722 + 22.8149i −0.855625 + 1.48199i
\(238\) 1.51493 + 2.62393i 0.0981980 + 0.170084i
\(239\) 12.7535i 0.824954i −0.910968 0.412477i \(-0.864664\pi\)
0.910968 0.412477i \(-0.135336\pi\)
\(240\) −13.2618 + 7.65668i −0.856043 + 0.494237i
\(241\) 22.4550 12.9644i 1.44646 0.835111i 0.448187 0.893940i \(-0.352070\pi\)
0.998268 + 0.0588285i \(0.0187365\pi\)
\(242\) 24.5967i 1.58114i
\(243\) −7.11778 12.3284i −0.456606 0.790864i
\(244\) 8.87483 15.3717i 0.568153 0.984069i
\(245\) −2.91865 1.68508i −0.186466 0.107656i
\(246\) 1.89022 0.120516
\(247\) 0 0
\(248\) −8.13878 −0.516813
\(249\) −12.5289 7.23357i −0.793987 0.458409i
\(250\) 1.24775 2.16117i 0.0789149 0.136685i
\(251\) 3.80593 + 6.59207i 0.240228 + 0.416088i 0.960779 0.277314i \(-0.0894444\pi\)
−0.720551 + 0.693402i \(0.756111\pi\)
\(252\) 40.1996i 2.53234i
\(253\) −3.53578 + 2.04139i −0.222293 + 0.128341i
\(254\) 3.21907 1.85853i 0.201982 0.116614i
\(255\) 1.80144i 0.112811i
\(256\) 16.2286 + 28.1087i 1.01429 + 1.75680i
\(257\) 0.167891 0.290796i 0.0104728 0.0181394i −0.860742 0.509042i \(-0.830000\pi\)
0.871214 + 0.490903i \(0.163333\pi\)
\(258\) 3.89322 + 2.24775i 0.242382 + 0.139939i
\(259\) −1.44310 −0.0896700
\(260\) 0 0
\(261\) 47.1906 2.92103
\(262\) 8.91865 + 5.14918i 0.550996 + 0.318118i
\(263\) 2.68795 4.65566i 0.165746 0.287080i −0.771174 0.636624i \(-0.780330\pi\)
0.936920 + 0.349544i \(0.113664\pi\)
\(264\) −8.40224 14.5531i −0.517122 0.895681i
\(265\) 6.99102i 0.429455i
\(266\) −23.6017 + 13.6264i −1.44711 + 0.835491i
\(267\) 30.7932 17.7785i 1.88451 1.08802i
\(268\) 34.2212i 2.09039i
\(269\) 0.655192 + 1.13483i 0.0399478 + 0.0691916i 0.885308 0.465005i \(-0.153948\pi\)
−0.845360 + 0.534197i \(0.820614\pi\)
\(270\) 7.02271 12.1637i 0.427388 0.740258i
\(271\) 10.0851 + 5.82266i 0.612629 + 0.353701i 0.773994 0.633194i \(-0.218256\pi\)
−0.161365 + 0.986895i \(0.551590\pi\)
\(272\) −3.45214 −0.209317
\(273\) 0 0
\(274\) −50.1838 −3.03171
\(275\) 0.926118 + 0.534695i 0.0558470 + 0.0322433i
\(276\) 22.8129 39.5130i 1.37317 2.37841i
\(277\) −10.1581 17.5943i −0.610338 1.05714i −0.991183 0.132498i \(-0.957700\pi\)
0.380845 0.924639i \(-0.375633\pi\)
\(278\) 51.9697i 3.11693i
\(279\) 6.32835 3.65368i 0.378869 0.218740i
\(280\) −9.17196 + 5.29543i −0.548129 + 0.316463i
\(281\) 11.8744i 0.708366i −0.935176 0.354183i \(-0.884759\pi\)
0.935176 0.354183i \(-0.115241\pi\)
\(282\) −33.3184 57.7091i −1.98408 3.43653i
\(283\) −11.3261 + 19.6173i −0.673264 + 1.16613i 0.303709 + 0.952765i \(0.401775\pi\)
−0.976973 + 0.213363i \(0.931558\pi\)
\(284\) −35.7509 20.6408i −2.12143 1.22481i
\(285\) −16.2036 −0.959817
\(286\) 0 0
\(287\) 0.510500 0.0301339
\(288\) 10.3767 + 5.99102i 0.611455 + 0.353024i
\(289\) 8.29695 14.3707i 0.488056 0.845337i
\(290\) −11.7977 20.4341i −0.692782 1.19993i
\(291\) 11.9336i 0.699562i
\(292\) 13.6067 7.85584i 0.796272 0.459728i
\(293\) 16.1191 9.30636i 0.941687 0.543683i 0.0511983 0.998689i \(-0.483696\pi\)
0.890489 + 0.455005i \(0.150363\pi\)
\(294\) 23.7745i 1.38656i
\(295\) 0.370518 + 0.641756i 0.0215724 + 0.0373645i
\(296\) 2.10529 3.64647i 0.122367 0.211946i
\(297\) 5.21245 + 3.00941i 0.302457 + 0.174624i
\(298\) −33.3593 −1.93245
\(299\) 0 0
\(300\) −11.9506 −0.689970
\(301\) 1.05146 + 0.607061i 0.0606052 + 0.0349904i
\(302\) −22.8319 + 39.5459i −1.31383 + 2.27561i
\(303\) 21.5512 + 37.3278i 1.23808 + 2.14443i
\(304\) 31.0513i 1.78091i
\(305\) 3.63606 2.09928i 0.208200 0.120204i
\(306\) 6.87381 3.96859i 0.392949 0.226869i
\(307\) 3.14776i 0.179652i 0.995957 + 0.0898262i \(0.0286311\pi\)
−0.995957 + 0.0898262i \(0.971369\pi\)
\(308\) −4.30664 7.45932i −0.245394 0.425034i
\(309\) 19.1192 33.1154i 1.08765 1.88387i
\(310\) −3.16418 1.82684i −0.179713 0.103757i
\(311\) 3.18059 0.180355 0.0901774 0.995926i \(-0.471257\pi\)
0.0901774 + 0.995926i \(0.471257\pi\)
\(312\) 0 0
\(313\) 35.3533 1.99829 0.999144 0.0413596i \(-0.0131689\pi\)
0.999144 + 0.0413596i \(0.0131689\pi\)
\(314\) 5.23499 + 3.02242i 0.295427 + 0.170565i
\(315\) 4.75447 8.23499i 0.267884 0.463989i
\(316\) −19.6991 34.1198i −1.10816 1.91939i
\(317\) 13.6357i 0.765858i 0.923778 + 0.382929i \(0.125085\pi\)
−0.923778 + 0.382929i \(0.874915\pi\)
\(318\) −42.7101 + 24.6587i −2.39506 + 1.38279i
\(319\) 8.75656 5.05560i 0.490273 0.283059i
\(320\) 4.84325i 0.270746i
\(321\) −10.4066 18.0248i −0.580842 1.00605i
\(322\) 9.07594 15.7200i 0.505782 0.876041i
\(323\) −3.16344 1.82641i −0.176018 0.101624i
\(324\) −3.96202 −0.220112
\(325\) 0 0
\(326\) 39.8854 2.20905
\(327\) −24.6671 14.2416i −1.36409 0.787560i
\(328\) −0.744750 + 1.28994i −0.0411219 + 0.0712253i
\(329\) −8.99844 15.5858i −0.496100 0.859271i
\(330\) 7.54390i 0.415278i
\(331\) 24.9380 14.3980i 1.37072 0.791383i 0.379698 0.925110i \(-0.376028\pi\)
0.991018 + 0.133727i \(0.0426945\pi\)
\(332\) 18.7371 10.8179i 1.02833 0.593707i
\(333\) 3.78044i 0.207167i
\(334\) 17.9591 + 31.1061i 0.982679 + 1.70205i
\(335\) −4.04739 + 7.01029i −0.221133 + 0.383013i
\(336\) 25.2665 + 14.5876i 1.37840 + 0.795819i
\(337\) −11.7493 −0.640026 −0.320013 0.947413i \(-0.603687\pi\)
−0.320013 + 0.947413i \(0.603687\pi\)
\(338\) 0 0
\(339\) 18.9061 1.02684
\(340\) −2.33313 1.34703i −0.126532 0.0730532i
\(341\) 0.782847 1.35593i 0.0423936 0.0734278i
\(342\) 35.6967 + 61.8285i 1.93026 + 3.34330i
\(343\) 19.7574i 1.06680i
\(344\) −3.06787 + 1.77124i −0.165409 + 0.0954987i
\(345\) 9.34654 5.39623i 0.503201 0.290523i
\(346\) 60.7630i 3.26664i
\(347\) −0.949887 1.64525i −0.0509926 0.0883218i 0.839402 0.543510i \(-0.182905\pi\)
−0.890395 + 0.455189i \(0.849572\pi\)
\(348\) −56.4973 + 97.8562i −3.02857 + 5.24564i
\(349\) 8.89329 + 5.13454i 0.476047 + 0.274846i 0.718768 0.695250i \(-0.244707\pi\)
−0.242721 + 0.970096i \(0.578040\pi\)
\(350\) −4.75447 −0.254137
\(351\) 0 0
\(352\) 2.56730 0.136838
\(353\) 0.693330 + 0.400294i 0.0369022 + 0.0213055i 0.518338 0.855176i \(-0.326551\pi\)
−0.481435 + 0.876482i \(0.659884\pi\)
\(354\) 2.61378 4.52720i 0.138921 0.240618i
\(355\) −4.88244 8.45663i −0.259133 0.448831i
\(356\) 53.1756i 2.81830i
\(357\) 2.97231 1.71606i 0.157311 0.0908237i
\(358\) 8.18714 4.72685i 0.432704 0.249822i
\(359\) 8.13272i 0.429228i 0.976699 + 0.214614i \(0.0688494\pi\)
−0.976699 + 0.214614i \(0.931151\pi\)
\(360\) 13.8723 + 24.0274i 0.731132 + 1.26636i
\(361\) 6.92820 12.0000i 0.364642 0.631579i
\(362\) 18.3439 + 10.5909i 0.964135 + 0.556643i
\(363\) −27.8625 −1.46240
\(364\) 0 0
\(365\) 3.71649 0.194530
\(366\) −25.6502 14.8092i −1.34076 0.774087i
\(367\) 10.2632 17.7765i 0.535737 0.927924i −0.463390 0.886154i \(-0.653367\pi\)
0.999127 0.0417696i \(-0.0132996\pi\)
\(368\) 10.3409 + 17.9110i 0.539057 + 0.933675i
\(369\) 1.33734i 0.0696191i
\(370\) 1.63698 0.945110i 0.0851025 0.0491339i
\(371\) −11.5349 + 6.65968i −0.598863 + 0.345754i
\(372\) 17.4969i 0.907173i
\(373\) 8.90292 + 15.4203i 0.460976 + 0.798433i 0.999010 0.0444897i \(-0.0141662\pi\)
−0.538034 + 0.842923i \(0.680833\pi\)
\(374\) 0.850322 1.47280i 0.0439691 0.0761568i
\(375\) −2.44811 1.41342i −0.126420 0.0729887i
\(376\) 52.5100 2.70800
\(377\) 0 0
\(378\) −26.7595 −1.37636
\(379\) 1.77150 + 1.02277i 0.0909956 + 0.0525363i 0.544807 0.838561i \(-0.316603\pi\)
−0.453812 + 0.891098i \(0.649936\pi\)
\(380\) 12.1163 20.9860i 0.621553 1.07656i
\(381\) −2.10529 3.64647i −0.107857 0.186814i
\(382\) 13.5833i 0.694982i
\(383\) 6.84611 3.95261i 0.349820 0.201969i −0.314786 0.949163i \(-0.601933\pi\)
0.664606 + 0.747194i \(0.268599\pi\)
\(384\) 41.3433 23.8696i 2.10979 1.21809i
\(385\) 2.03741i 0.103836i
\(386\) −15.1697 26.2747i −0.772117 1.33735i
\(387\) 1.59030 2.75447i 0.0808393 0.140018i
\(388\) 15.4558 + 8.92343i 0.784651 + 0.453018i
\(389\) 9.21171 0.467052 0.233526 0.972351i \(-0.424974\pi\)
0.233526 + 0.972351i \(0.424974\pi\)
\(390\) 0 0
\(391\) 2.43298 0.123041
\(392\) −16.2244 9.36719i −0.819458 0.473114i
\(393\) 5.83285 10.1028i 0.294228 0.509618i
\(394\) −5.46304 9.46226i −0.275224 0.476702i
\(395\) 9.31937i 0.468908i
\(396\) −19.5409 + 11.2820i −0.981968 + 0.566940i
\(397\) −5.50305 + 3.17719i −0.276190 + 0.159458i −0.631697 0.775215i \(-0.717641\pi\)
0.355507 + 0.934674i \(0.384308\pi\)
\(398\) 51.9996i 2.60651i
\(399\) 15.4356 + 26.7353i 0.772748 + 1.33844i
\(400\) 2.70857 4.69138i 0.135428 0.234569i
\(401\) −3.61063 2.08460i −0.180306 0.104100i 0.407130 0.913370i \(-0.366530\pi\)
−0.587437 + 0.809270i \(0.699863\pi\)
\(402\) 57.1038 2.84808
\(403\) 0 0
\(404\) −64.4600 −3.20701
\(405\) −0.811629 0.468594i −0.0403301 0.0232846i
\(406\) −22.4770 + 38.9314i −1.11552 + 1.93213i
\(407\) 0.405004 + 0.701487i 0.0200753 + 0.0347714i
\(408\) 10.0140i 0.495767i
\(409\) −8.80580 + 5.08403i −0.435419 + 0.251389i −0.701652 0.712519i \(-0.747554\pi\)
0.266234 + 0.963909i \(0.414221\pi\)
\(410\) −0.579085 + 0.334335i −0.0285989 + 0.0165116i
\(411\) 56.8467i 2.80404i
\(412\) 28.5929 + 49.5244i 1.40867 + 2.43989i
\(413\) 0.705915 1.22268i 0.0347358 0.0601642i
\(414\) −41.1811 23.7759i −2.02394 1.16852i
\(415\) 5.11778 0.251222
\(416\) 0 0
\(417\) −58.8697 −2.88286
\(418\) 13.2475 + 7.64847i 0.647959 + 0.374099i
\(419\) −14.2954 + 24.7604i −0.698378 + 1.20963i 0.270651 + 0.962677i \(0.412761\pi\)
−0.969029 + 0.246948i \(0.920572\pi\)
\(420\) 11.3842 + 19.7181i 0.555494 + 0.962144i
\(421\) 2.01797i 0.0983498i −0.998790 0.0491749i \(-0.984341\pi\)
0.998790 0.0491749i \(-0.0156592\pi\)
\(422\) 23.0244 13.2932i 1.12081 0.647101i
\(423\) −40.8295 + 23.5729i −1.98520 + 1.14615i
\(424\) 38.8623i 1.88732i
\(425\) −0.318632 0.551886i −0.0154559 0.0267704i
\(426\) −34.4427 + 59.6564i −1.66875 + 2.89036i
\(427\) −6.92747 3.99957i −0.335244 0.193553i
\(428\) 31.1264 1.50455
\(429\) 0 0
\(430\) −1.59030 −0.0766908
\(431\) −17.8508 10.3061i −0.859842 0.496430i 0.00411765 0.999992i \(-0.498689\pi\)
−0.863959 + 0.503562i \(0.832023\pi\)
\(432\) 15.2446 26.4044i 0.733455 1.27038i
\(433\) 14.7178 + 25.4920i 0.707292 + 1.22507i 0.965858 + 0.259072i \(0.0834168\pi\)
−0.258566 + 0.965994i \(0.583250\pi\)
\(434\) 6.96103i 0.334140i
\(435\) −23.1472 + 13.3640i −1.10982 + 0.640757i
\(436\) 36.8899 21.2984i 1.76670 1.02001i
\(437\) 21.8841i 1.04686i
\(438\) −13.1088 22.7051i −0.626362 1.08489i
\(439\) 8.47602 14.6809i 0.404538 0.700681i −0.589729 0.807601i \(-0.700765\pi\)
0.994268 + 0.106920i \(0.0340988\pi\)
\(440\) 5.14819 + 2.97231i 0.245430 + 0.141699i
\(441\) 16.8205 0.800978
\(442\) 0 0
\(443\) −24.1399 −1.14692 −0.573461 0.819233i \(-0.694400\pi\)
−0.573461 + 0.819233i \(0.694400\pi\)
\(444\) −7.83925 4.52599i −0.372034 0.214794i
\(445\) −6.28917 + 10.8932i −0.298135 + 0.516385i
\(446\) 26.6262 + 46.1180i 1.26079 + 2.18375i
\(447\) 37.7885i 1.78733i
\(448\) 7.99118 4.61371i 0.377548 0.217977i
\(449\) −18.0679 + 10.4315i −0.852676 + 0.492293i −0.861553 0.507668i \(-0.830508\pi\)
0.00887706 + 0.999961i \(0.497174\pi\)
\(450\) 12.4551i 0.587140i
\(451\) −0.143271 0.248153i −0.00674637 0.0116851i
\(452\) −14.1371 + 24.4861i −0.664952 + 1.15173i
\(453\) 44.7965 + 25.8633i 2.10472 + 1.21516i
\(454\) −39.1437 −1.83710
\(455\) 0 0
\(456\) −90.0739 −4.21810
\(457\) −26.4708 15.2830i −1.23825 0.714906i −0.269517 0.962996i \(-0.586864\pi\)
−0.968737 + 0.248089i \(0.920197\pi\)
\(458\) 9.50894 16.4700i 0.444324 0.769591i
\(459\) −1.79335 3.10617i −0.0837063 0.144984i
\(460\) 16.1402i 0.752541i
\(461\) −4.05146 + 2.33911i −0.188695 + 0.108943i −0.591372 0.806399i \(-0.701413\pi\)
0.402676 + 0.915342i \(0.368080\pi\)
\(462\) −12.4471 + 7.18636i −0.579094 + 0.334340i
\(463\) 14.0011i 0.650688i −0.945596 0.325344i \(-0.894520\pi\)
0.945596 0.325344i \(-0.105480\pi\)
\(464\) −25.6098 44.3575i −1.18891 2.05925i
\(465\) −2.06939 + 3.58429i −0.0959656 + 0.166217i
\(466\) 41.1811 + 23.7759i 1.90768 + 1.10140i
\(467\) 6.98506 0.323230 0.161615 0.986854i \(-0.448330\pi\)
0.161615 + 0.986854i \(0.448330\pi\)
\(468\) 0 0
\(469\) 15.4223 0.712135
\(470\) 20.4147 + 11.7864i 0.941661 + 0.543668i
\(471\) 3.42371 5.93004i 0.157756 0.273242i
\(472\) 2.05967 + 3.56745i 0.0948039 + 0.164205i
\(473\) 0.681482i 0.0313346i
\(474\) −56.9347 + 32.8713i −2.61510 + 1.50983i
\(475\) 4.96410 2.86603i 0.227769 0.131502i
\(476\) 5.13277i 0.235260i
\(477\) 17.4461 + 30.2176i 0.798804 + 1.38357i
\(478\) 15.9132 27.5625i 0.727853 1.26068i
\(479\) 14.1065 + 8.14438i 0.644542 + 0.372126i 0.786362 0.617766i \(-0.211962\pi\)
−0.141820 + 0.989892i \(0.545296\pi\)
\(480\) −6.78645 −0.309758
\(481\) 0 0
\(482\) 64.7056 2.94726
\(483\) −17.8071 10.2810i −0.810253 0.467800i
\(484\) 20.8343 36.0860i 0.947012 1.64027i
\(485\) 2.11078 + 3.65597i 0.0958454 + 0.166009i
\(486\) 35.5249i 1.61144i
\(487\) −17.3559 + 10.0204i −0.786471 + 0.454069i −0.838719 0.544565i \(-0.816695\pi\)
0.0522474 + 0.998634i \(0.483362\pi\)
\(488\) 20.2125 11.6697i 0.914975 0.528261i
\(489\) 45.1810i 2.04316i
\(490\) −4.20514 7.28351i −0.189969 0.329035i
\(491\) −7.89916 + 13.6818i −0.356484 + 0.617449i −0.987371 0.158426i \(-0.949358\pi\)
0.630887 + 0.775875i \(0.282691\pi\)
\(492\) 2.77315 + 1.60108i 0.125023 + 0.0721823i
\(493\) −6.02540 −0.271370
\(494\) 0 0
\(495\) −5.33734 −0.239896
\(496\) −6.86865 3.96562i −0.308411 0.178061i
\(497\) −9.30208 + 16.1117i −0.417255 + 0.722708i
\(498\) −18.0514 31.2660i −0.808903 1.40106i
\(499\) 1.24651i 0.0558016i −0.999611 0.0279008i \(-0.991118\pi\)
0.999611 0.0279008i \(-0.00888226\pi\)
\(500\) 3.66117 2.11378i 0.163733 0.0945311i
\(501\) 35.2361 20.3436i 1.57423 0.908883i
\(502\) 18.9955i 0.847809i
\(503\) 3.82672 + 6.62808i 0.170625 + 0.295532i 0.938639 0.344902i \(-0.112088\pi\)
−0.768013 + 0.640434i \(0.778755\pi\)
\(504\) 26.4296 45.7774i 1.17727 2.03909i
\(505\) −13.2048 7.62379i −0.587605 0.339254i
\(506\) −10.1886 −0.452938
\(507\) 0 0
\(508\) 6.29695 0.279382
\(509\) 22.2777 + 12.8621i 0.987444 + 0.570101i 0.904509 0.426454i \(-0.140237\pi\)
0.0829345 + 0.996555i \(0.473571\pi\)
\(510\) −2.24775 + 3.89322i −0.0995322 + 0.172395i
\(511\) −3.54035 6.13207i −0.156616 0.271267i
\(512\) 47.2215i 2.08691i
\(513\) 27.9393 16.1308i 1.23355 0.712192i
\(514\) 0.725685 0.418974i 0.0320086 0.0184802i
\(515\) 13.5269i 0.596067i
\(516\) 3.80785 + 6.59538i 0.167631 + 0.290346i
\(517\) −5.05080 + 8.74824i −0.222134 + 0.384747i
\(518\) −3.11879 1.80064i −0.137032 0.0791154i
\(519\) −68.8305 −3.02132
\(520\) 0 0
\(521\) −30.1519 −1.32098 −0.660490 0.750835i \(-0.729651\pi\)
−0.660490 + 0.750835i \(0.729651\pi\)
\(522\) 101.987 + 58.8823i 4.46386 + 2.57721i
\(523\) −1.96876 + 3.41000i −0.0860880 + 0.149109i −0.905854 0.423589i \(-0.860770\pi\)
0.819766 + 0.572698i \(0.194103\pi\)
\(524\) 8.72307 + 15.1088i 0.381069 + 0.660031i
\(525\) 5.38573i 0.235052i
\(526\) 11.6182 6.70779i 0.506579 0.292473i
\(527\) −0.808017 + 0.466509i −0.0351978 + 0.0203215i
\(528\) 16.3759i 0.712672i
\(529\) 4.21200 + 7.29539i 0.183130 + 0.317191i
\(530\) 8.72307 15.1088i 0.378906 0.656284i
\(531\) −3.20301 1.84926i −0.138999 0.0802510i
\(532\) −46.1682 −2.00165
\(533\) 0 0
\(534\) 88.7326 3.83983
\(535\) 6.37632 + 3.68137i 0.275672 + 0.159159i
\(536\) −22.4990 + 38.9694i −0.971809 + 1.68322i
\(537\) −5.35444 9.27415i −0.231061 0.400209i
\(538\) 3.27007i 0.140983i
\(539\) 3.12117 1.80201i 0.134438 0.0776180i
\(540\) 20.6061 11.8969i 0.886745 0.511963i
\(541\) 15.8881i 0.683083i −0.939867 0.341541i \(-0.889051\pi\)
0.939867 0.341541i \(-0.110949\pi\)
\(542\) 14.5305 + 25.1675i 0.624138 + 1.08104i
\(543\) 11.9970 20.7795i 0.514842 0.891732i
\(544\) −1.32492 0.764945i −0.0568057 0.0327968i
\(545\) 10.0760 0.431607
\(546\) 0 0
\(547\) −6.56107 −0.280531 −0.140266 0.990114i \(-0.544796\pi\)
−0.140266 + 0.990114i \(0.544796\pi\)
\(548\) −73.6249 42.5074i −3.14510 1.81582i
\(549\) −10.4775 + 18.1476i −0.447170 + 0.774522i
\(550\) 1.33433 + 2.31114i 0.0568962 + 0.0985471i
\(551\) 54.1972i 2.30888i
\(552\) 51.9564 29.9970i 2.21141 1.27676i
\(553\) −15.3766 + 8.87769i −0.653880 + 0.377518i
\(554\) 50.6990i 2.15399i
\(555\) −1.07059 1.85432i −0.0454441 0.0787116i
\(556\) 44.0200 76.2450i 1.86687 3.23351i
\(557\) −6.79835 3.92503i −0.288055 0.166309i 0.349009 0.937119i \(-0.386518\pi\)
−0.637065 + 0.770810i \(0.719852\pi\)
\(558\) 18.2356 0.771973
\(559\) 0 0
\(560\) −10.3208 −0.436133
\(561\) −1.66835 0.963220i −0.0704377 0.0406672i
\(562\) 14.8163 25.6626i 0.624988 1.08251i
\(563\) −7.77976 13.4749i −0.327878 0.567901i 0.654213 0.756310i \(-0.273000\pi\)
−0.982091 + 0.188410i \(0.939667\pi\)
\(564\) 112.887i 4.75341i
\(565\) −5.79203 + 3.34403i −0.243673 + 0.140684i
\(566\) −48.9552 + 28.2643i −2.05774 + 1.18804i
\(567\) 1.78554i 0.0749857i
\(568\) −27.1409 47.0095i −1.13881 1.97247i
\(569\) 1.73957 3.01303i 0.0729267 0.126313i −0.827256 0.561825i \(-0.810099\pi\)
0.900183 + 0.435512i \(0.143433\pi\)
\(570\) −35.0187 20.2181i −1.46677 0.846842i
\(571\) 21.5118 0.900240 0.450120 0.892968i \(-0.351381\pi\)
0.450120 + 0.892968i \(0.351381\pi\)
\(572\) 0 0
\(573\) 15.3868 0.642791
\(574\) 1.10328 + 0.636978i 0.0460500 + 0.0265870i
\(575\) −1.90893 + 3.30636i −0.0796078 + 0.137885i
\(576\) −12.0864 20.9342i −0.503599 0.872259i
\(577\) 9.97608i 0.415310i −0.978202 0.207655i \(-0.933417\pi\)
0.978202 0.207655i \(-0.0665831\pi\)
\(578\) 35.8623 20.7051i 1.49167 0.861218i
\(579\) −29.7632 + 17.1838i −1.23692 + 0.714134i
\(580\) 39.9721i 1.65975i
\(581\) −4.87523 8.44414i −0.202259 0.350322i
\(582\) 14.8902 25.7907i 0.617221 1.06906i
\(583\) 6.47451 + 3.73806i 0.268147 + 0.154815i
\(584\) 20.6595 0.854898
\(585\) 0 0
\(586\) 46.4482 1.91876
\(587\) −20.8341 12.0286i −0.859915 0.496472i 0.00406862 0.999992i \(-0.498705\pi\)
−0.863984 + 0.503519i \(0.832038\pi\)
\(588\) −20.1378 + 34.8797i −0.830469 + 1.43841i
\(589\) −4.19615 7.26795i −0.172899 0.299471i
\(590\) 1.84926i 0.0761328i
\(591\) −10.7186 + 6.18837i −0.440903 + 0.254556i
\(592\) 3.55348 2.05160i 0.146047 0.0843203i
\(593\) 0.940219i 0.0386102i 0.999814 + 0.0193051i \(0.00614538\pi\)
−0.999814 + 0.0193051i \(0.993855\pi\)
\(594\) 7.51001 + 13.0077i 0.308139 + 0.533713i
\(595\) −0.607061 + 1.05146i −0.0248871 + 0.0431057i
\(596\) −48.9417 28.2565i −2.00473 1.15743i
\(597\) 58.9037 2.41077
\(598\) 0 0
\(599\) −11.4270 −0.466896 −0.233448 0.972369i \(-0.575001\pi\)
−0.233448 + 0.972369i \(0.575001\pi\)
\(600\) −13.6088 7.85704i −0.555577 0.320762i
\(601\) 18.0215 31.2142i 0.735114 1.27325i −0.219560 0.975599i \(-0.570462\pi\)
0.954674 0.297655i \(-0.0962045\pi\)
\(602\) 1.51493 + 2.62393i 0.0617437 + 0.106943i
\(603\) 40.4012i 1.64526i
\(604\) −66.9935 + 38.6787i −2.72593 + 1.57381i
\(605\) 8.53590 4.92820i 0.347034 0.200360i
\(606\) 107.562i 4.36942i
\(607\) −19.9454 34.5464i −0.809557 1.40219i −0.913171 0.407576i \(-0.866374\pi\)
0.103614 0.994618i \(-0.466959\pi\)
\(608\) 6.88052 11.9174i 0.279042 0.483315i
\(609\) 44.1003 + 25.4613i 1.78704 + 1.03175i
\(610\) 10.4775 0.424223
\(611\) 0 0
\(612\) 13.4461 0.543528
\(613\) −0.299187 0.172736i −0.0120841 0.00697673i 0.493946 0.869493i \(-0.335554\pi\)
−0.506030 + 0.862516i \(0.668887\pi\)
\(614\) −3.92763 + 6.80286i −0.158506 + 0.274541i
\(615\) 0.378725 + 0.655970i 0.0152716 + 0.0264513i
\(616\) 11.3258i 0.456328i
\(617\) −33.5022 + 19.3425i −1.34875 + 0.778700i −0.988072 0.153991i \(-0.950787\pi\)
−0.360676 + 0.932691i \(0.617454\pi\)
\(618\) 82.6398 47.7121i 3.32426 1.91926i
\(619\) 14.8971i 0.598764i 0.954133 + 0.299382i \(0.0967805\pi\)
−0.954133 + 0.299382i \(0.903219\pi\)
\(620\) −3.09479 5.36033i −0.124290 0.215276i
\(621\) −10.7440 + 18.6091i −0.431141 + 0.746758i
\(622\) 6.87381 + 3.96859i 0.275615 + 0.159126i
\(623\) 23.9644 0.960113
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 76.4047 + 44.1123i 3.05374 + 1.76308i
\(627\) 8.66397 15.0064i 0.346006 0.599299i
\(628\) 5.12019 + 8.86842i 0.204318 + 0.353889i
\(629\) 0.482694i 0.0192463i
\(630\) 20.5505 11.8648i 0.818750 0.472706i
\(631\) −33.6408 + 19.4225i −1.33922 + 0.773198i −0.986691 0.162604i \(-0.948011\pi\)
−0.352526 + 0.935802i \(0.614677\pi\)
\(632\) 51.8053i 2.06071i
\(633\) −15.0581 26.0814i −0.598506 1.03664i
\(634\) −17.0140 + 29.4691i −0.675713 + 1.17037i
\(635\) 1.28994 + 0.744750i 0.0511899 + 0.0295545i
\(636\) −83.5470 −3.31285
\(637\) 0 0
\(638\) 25.2326 0.998967
\(639\) 42.2072 + 24.3683i 1.66969 + 0.963996i
\(640\) −8.44391 + 14.6253i −0.333775 + 0.578115i
\(641\) 18.5908 + 32.2003i 0.734293 + 1.27183i 0.955033 + 0.296501i \(0.0958197\pi\)
−0.220739 + 0.975333i \(0.570847\pi\)
\(642\) 51.9397i 2.04990i
\(643\) −7.88410 + 4.55189i −0.310918 + 0.179509i −0.647337 0.762204i \(-0.724118\pi\)
0.336419 + 0.941712i \(0.390784\pi\)
\(644\) 26.6307 15.3753i 1.04940 0.605870i
\(645\) 1.80144i 0.0709316i
\(646\) −4.55783 7.89439i −0.179325 0.310601i
\(647\) −9.56118 + 16.5605i −0.375889 + 0.651059i −0.990460 0.137803i \(-0.955996\pi\)
0.614571 + 0.788862i \(0.289329\pi\)
\(648\) −4.51175 2.60486i −0.177238 0.102329i
\(649\) −0.792455 −0.0311066
\(650\) 0 0
\(651\) 7.88525 0.309047
\(652\) 58.5161 + 33.7843i 2.29167 + 1.32309i
\(653\) −17.3162 + 29.9926i −0.677636 + 1.17370i 0.298055 + 0.954549i \(0.403662\pi\)
−0.975691 + 0.219152i \(0.929671\pi\)
\(654\) −35.5399 61.5570i −1.38972 2.40707i
\(655\) 4.12676i 0.161246i
\(656\) −1.25705 + 0.725758i −0.0490796 + 0.0283361i
\(657\) −16.0640 + 9.27453i −0.626714 + 0.361834i
\(658\) 44.9114i 1.75083i
\(659\) 3.34926 + 5.80109i 0.130469 + 0.225978i 0.923857 0.382737i \(-0.125018\pi\)
−0.793389 + 0.608715i \(0.791685\pi\)
\(660\) 6.38994 11.0677i 0.248728 0.430809i
\(661\) −5.22004 3.01379i −0.203036 0.117223i 0.395035 0.918666i \(-0.370732\pi\)
−0.598071 + 0.801443i \(0.704066\pi\)
\(662\) 71.8604 2.79294
\(663\) 0 0
\(664\) 28.4492 1.10404
\(665\) −9.45767 5.46039i −0.366753 0.211745i
\(666\) −4.71706 + 8.17018i −0.182782 + 0.316588i
\(667\) 18.0491 + 31.2620i 0.698865 + 1.21047i
\(668\) 60.8479i 2.35428i
\(669\) 52.2411 30.1614i 2.01976 1.16611i
\(670\) −17.4942 + 10.1003i −0.675861 + 0.390209i
\(671\) 4.48990i 0.173330i
\(672\) 6.46481 + 11.1974i 0.249386 + 0.431948i
\(673\) 11.6784 20.2276i 0.450169 0.779715i −0.548227 0.836329i \(-0.684697\pi\)
0.998396 + 0.0566140i \(0.0180304\pi\)
\(674\) −25.3923 14.6603i −0.978075 0.564692i
\(675\) 5.62828 0.216633
\(676\) 0 0
\(677\) −45.4042 −1.74503 −0.872513 0.488590i \(-0.837511\pi\)
−0.872513 + 0.488590i \(0.837511\pi\)
\(678\) 40.8593 + 23.5901i 1.56919 + 0.905973i
\(679\) 4.02148 6.96540i 0.154330 0.267308i
\(680\) −1.77124 3.06787i −0.0679239 0.117648i
\(681\) 44.3408i 1.69914i
\(682\) 3.38374 1.95360i 0.129570 0.0748073i
\(683\) −22.0817 + 12.7489i −0.844934 + 0.487823i −0.858938 0.512079i \(-0.828875\pi\)
0.0140045 + 0.999902i \(0.495542\pi\)
\(684\) 120.945i 4.62445i
\(685\) −10.0548 17.4155i −0.384175 0.665411i
\(686\) −24.6523 + 42.6991i −0.941230 + 1.63026i
\(687\) −18.6567 10.7715i −0.711798 0.410957i
\(688\) −3.45214 −0.131612
\(689\) 0 0
\(690\) 26.9327 1.02531
\(691\) −5.71257 3.29815i −0.217316 0.125468i 0.387391 0.921916i \(-0.373376\pi\)
−0.604707 + 0.796448i \(0.706710\pi\)
\(692\) 51.4683 89.1457i 1.95653 3.38881i
\(693\) 5.08438 + 8.80641i 0.193140 + 0.334528i
\(694\) 4.74090i 0.179962i
\(695\) 18.0352 10.4126i 0.684115 0.394974i
\(696\) −128.673 + 74.2892i −4.87733 + 2.81593i
\(697\) 0.170754i 0.00646778i
\(698\) 12.8133 + 22.1933i 0.484990 + 0.840028i
\(699\) 26.9327 46.6487i 1.01869 1.76442i
\(700\) −6.97531 4.02720i −0.263642 0.152214i
\(701\) −29.2474 −1.10466 −0.552329 0.833626i \(-0.686261\pi\)
−0.552329 + 0.833626i \(0.686261\pi\)
\(702\) 0 0
\(703\) 4.34174 0.163752
\(704\) −4.48542 2.58966i −0.169051 0.0976015i
\(705\) 13.3513 23.1252i 0.502841 0.870946i
\(706\) 0.998937 + 1.73021i 0.0375955 + 0.0651173i
\(707\) 29.0499i 1.09253i
\(708\) 7.66938 4.42792i 0.288233 0.166411i
\(709\) 9.46865 5.46673i 0.355603 0.205307i −0.311548 0.950231i \(-0.600847\pi\)
0.667150 + 0.744923i \(0.267514\pi\)
\(710\) 24.3683i 0.914527i
\(711\) 23.2566 + 40.2815i 0.872189 + 1.51068i
\(712\) −34.9608 + 60.5538i −1.31021 + 2.26935i
\(713\) 4.84084 + 2.79486i 0.181291 + 0.104668i
\(714\) 8.56490 0.320533
\(715\) 0 0
\(716\) 16.0152 0.598516
\(717\) −31.2220 18.0260i −1.16601 0.673194i
\(718\) −10.1476 + 17.5762i −0.378706 + 0.655938i
\(719\) 8.02989 + 13.9082i 0.299464 + 0.518688i 0.976014 0.217710i \(-0.0698587\pi\)
−0.676549 + 0.736398i \(0.736525\pi\)
\(720\) 27.0370i 1.00761i
\(721\) 22.3189 12.8858i 0.831199 0.479893i
\(722\) 29.9461 17.2894i 1.11448 0.643444i
\(723\) 73.2966i 2.72593i
\(724\) 17.9416 + 31.0758i 0.666796 + 1.15492i
\(725\) 4.72756 8.18837i 0.175577 0.304108i
\(726\) −60.2156 34.7655i −2.23481 1.29027i
\(727\) −51.3754 −1.90541 −0.952704 0.303900i \(-0.901711\pi\)
−0.952704 + 0.303900i \(0.901711\pi\)
\(728\) 0 0
\(729\) −43.0532 −1.59456
\(730\) 8.03198 + 4.63726i 0.297277 + 0.171633i
\(731\) −0.203052 + 0.351697i −0.00751016 + 0.0130080i
\(732\) −25.0877 43.4532i −0.927268 1.60608i
\(733\) 9.82358i 0.362842i 0.983406 + 0.181421i \(0.0580697\pi\)
−0.983406 + 0.181421i \(0.941930\pi\)
\(734\) 44.3613 25.6120i 1.63741 0.945357i
\(735\) −8.25055 + 4.76346i −0.304326 + 0.175703i
\(736\) 9.16560i 0.337848i
\(737\) −4.32824 7.49673i −0.159433 0.276146i
\(738\) 1.66867 2.89022i 0.0614246 0.106390i
\(739\) −42.5082 24.5421i −1.56369 0.902797i −0.996879 0.0789487i \(-0.974844\pi\)
−0.566811 0.823848i \(-0.691823\pi\)
\(740\) 3.20216 0.117714
\(741\) 0 0
\(742\) −33.2386 −1.22023
\(743\) 35.3663 + 20.4188i 1.29746 + 0.749091i 0.979966 0.199167i \(-0.0638237\pi\)
0.317499 + 0.948259i \(0.397157\pi\)
\(744\) −11.5035 + 19.9247i −0.421739 + 0.730473i
\(745\) −6.68388 11.5768i −0.244878 0.424142i
\(746\) 44.4346i 1.62687i
\(747\) −22.1208 + 12.7715i −0.809358 + 0.467283i
\(748\) 2.49503 1.44050i 0.0912272 0.0526700i
\(749\) 14.0276i 0.512557i
\(750\) −3.52720 6.10929i −0.128795 0.223080i
\(751\) −1.36340 + 2.36148i −0.0497512 + 0.0861716i −0.889829 0.456295i \(-0.849176\pi\)
0.840077 + 0.542467i \(0.182510\pi\)
\(752\) 44.3154 + 25.5855i 1.61601 + 0.933006i
\(753\) 21.5175 0.784142
\(754\) 0 0
\(755\) −18.2984 −0.665946
\(756\) −39.2590 22.6662i −1.42784 0.824362i
\(757\) −7.40301 + 12.8224i −0.269067 + 0.466038i −0.968621 0.248542i \(-0.920049\pi\)
0.699554 + 0.714580i \(0.253382\pi\)
\(758\) 2.55234 + 4.42078i 0.0927051 + 0.160570i
\(759\) 11.5413i 0.418924i
\(760\) 27.5949 15.9319i 1.00097 0.577911i
\(761\) −9.84575 + 5.68445i −0.356908 + 0.206061i −0.667724 0.744409i \(-0.732731\pi\)
0.310815 + 0.950470i \(0.399398\pi\)
\(762\) 10.5075i 0.380647i
\(763\) −9.59843 16.6250i −0.347486 0.601864i
\(764\) −11.5055 + 19.9281i −0.416255 + 0.720975i
\(765\) 2.75447 + 1.59030i 0.0995882 + 0.0574972i
\(766\) 19.7275 0.712784
\(767\) 0 0
\(768\) 91.7512 3.31078
\(769\) −18.2352 10.5281i −0.657579 0.379654i 0.133775 0.991012i \(-0.457290\pi\)
−0.791354 + 0.611358i \(0.790623\pi\)
\(770\) 2.54219 4.40320i 0.0916142 0.158680i
\(771\) −0.474602 0.822034i −0.0170924 0.0296048i
\(772\) 51.3970i 1.84982i
\(773\) −12.1961 + 7.04144i −0.438664 + 0.253263i −0.703031 0.711159i \(-0.748170\pi\)
0.264367 + 0.964422i \(0.414837\pi\)
\(774\) 6.87381 3.96859i 0.247074 0.142648i
\(775\) 1.46410i 0.0525921i
\(776\) 11.7336 + 20.3231i 0.421210 + 0.729558i
\(777\) −2.03971 + 3.53288i −0.0731741 + 0.126741i
\(778\) 19.9081 + 11.4940i 0.713740 + 0.412078i
\(779\)