Properties

Label 845.2.m.g.361.4
Level $845$
Weight $2$
Character 845.361
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 361.4
Root \(1.20036 - 0.747754i\) of defining polynomial
Character \(\chi\) \(=\) 845.361
Dual form 845.2.m.g.316.4

$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 0.528742 0.848783i \(-0.322664\pi\)
0.999438 0.0335125i \(-0.0106693\pi\)
\(3\) 1.41342 + 2.44811i 0.816038 + 1.41342i 0.908580 + 0.417710i \(0.137167\pi\)
−0.0925423 + 0.995709i \(0.529499\pi\)
\(4\) 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 0.778280 0.627918i \(-0.216093\pi\)
−0.154653 + 0.987969i \(0.549426\pi\)
\(8\) 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 −0.633077 0.774089i \(-0.718208\pi\)
0.353842 + 0.935305i \(0.384875\pi\)
\(12\) 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 −0.824796 0.565431i \(-0.808710\pi\)
0.902075 + 0.431579i \(0.142043\pi\)
\(18\) 12.4551i 2.93570i
\(19\) −4.96410 2.86603i −1.13884 0.657511i −0.192699 0.981258i \(-0.561724\pi\)
−0.946144 + 0.323747i \(0.895057\pi\)
\(20\) −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 0.993484 0.113973i \(-0.0363576\pi\)
−0.595445 + 0.803396i \(0.703024\pi\)
\(24\) 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 −0.853657 0.520836i \(-0.825620\pi\)
−0.0242288 0.999706i \(-0.507713\pi\)
\(30\) 3.52720 6.10929i 0.643975 1.11540i
\(31\) 1.46410i 0.262960i −0.991319 0.131480i \(-0.958027\pi\)
0.991319 0.131480i \(-0.0419730\pi\)
\(32\) −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 −0.552950 0.833214i \(-0.686498\pi\)
0.445110 + 0.895476i \(0.353165\pi\)
\(38\) −14.3044 −2.32048
\(39\) 0 0
\(40\) −5.55889 −0.878938
\(41\) 0.232051 0.133975i 0.0362402 0.0209233i −0.481770 0.876297i \(-0.660006\pi\)
0.518011 + 0.855374i \(0.326673\pi\)
\(42\) 6.72006 + 11.6395i 1.03693 + 1.79601i
\(43\) 0.318632 0.551886i 0.0485909 0.0841618i −0.840707 0.541490i \(-0.817860\pi\)
0.889298 + 0.457328i \(0.151194\pi\)
\(44\) 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 \(0.241919\pi\)
−0.724828 + 0.688930i \(0.758081\pi\)
\(48\) 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 0.541193 0.840899i \(-0.317973\pi\)
−0.457643 + 0.889136i \(0.651306\pi\)
\(60\) 11.9506i 1.54282i
\(61\) −2.09928 + 3.63606i −0.268785 + 0.465550i −0.968548 0.248825i \(-0.919956\pi\)
0.699763 + 0.714375i \(0.253289\pi\)
\(62\) −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 −0.00637624 0.999980i \(-0.502030\pi\)
0.862820 + 0.505512i \(0.168696\pi\)
\(68\) −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 −0.0943010 0.995544i \(-0.530062\pi\)
−0.909317 + 0.416105i \(0.863395\pi\)
\(72\) 24.0274 + 13.8723i 2.83166 + 1.63486i
\(73\) 3.71649i 0.434982i 0.976062 + 0.217491i \(0.0697873\pi\)
−0.976062 + 0.217491i \(0.930213\pi\)
\(74\) −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 \(0.0906245\pi\)
−0.959744 + 0.280875i \(0.909376\pi\)
\(84\) 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 0.204651 0.978835i \(-0.434394\pi\)
0.950021 + 0.312185i \(0.101061\pi\)
\(90\) 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 0.673986 0.738744i \(-0.264581\pi\)
−0.302778 + 0.953061i \(0.597914\pi\)
\(98\) −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 −0.943567 0.331181i \(-0.892553\pi\)
0.184972 0.982744i \(-0.440781\pi\)
\(102\) 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 0.987270 0.159053i \(-0.0508440\pi\)
−0.631379 + 0.775475i \(0.717511\pi\)
\(108\) −11.8969 + 20.6061i −1.14478 + 1.98282i
\(109\) 10.0760i 0.965103i 0.875868 + 0.482551i \(0.160290\pi\)
−0.875868 + 0.482551i \(0.839710\pi\)
\(110\) 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 −0.664768 0.747050i \(-0.731470\pi\)
0.979348 + 0.202181i \(0.0648030\pi\)
\(114\) −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 0.897175 0.441675i \(-0.145616\pi\)
−0.831089 + 0.556139i \(0.812282\pi\)
\(128\) 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 −0.487999 0.872844i \(-0.662273\pi\)
−0.999905 + 0.0138029i \(0.995606\pi\)
\(138\) 26.9327i 2.29266i
\(139\) −10.4126 + 18.0352i −0.883189 + 1.52973i −0.0354130 + 0.999373i \(0.511275\pi\)
−0.847776 + 0.530355i \(0.822059\pi\)
\(140\) −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 −0.0558233 0.998441i \(-0.517778\pi\)
−0.892587 + 0.450876i \(0.851112\pi\)
\(150\) −6.10929 3.52720i −0.498821 0.287995i
\(151\) 18.2984i 1.48910i −0.667567 0.744550i \(-0.732664\pi\)
0.667567 0.744550i \(-0.267336\pi\)
\(152\) −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 0.932015 0.362421i \(-0.118050\pi\)
0.152142 + 0.988359i \(0.451383\pi\)
\(164\) 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 0.0669853 0.997754i \(-0.478662\pi\)
0.897573 + 0.440866i \(0.145329\pi\)
\(168\) 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 −0.135027 + 0.990842i \(0.543112\pi\)
−0.790581 + 0.612358i \(0.790221\pi\)
\(174\) 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 0.928090 0.372356i \(-0.121450\pi\)
−0.786515 + 0.617571i \(0.788117\pi\)
\(180\) 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 −0.750605 0.660751i \(-0.770238\pi\)
0.947530 + 0.319668i \(0.103571\pi\)
\(192\) 6.84555 + 11.8568i 0.494035 + 0.855693i
\(193\) −10.5288 + 6.07880i −0.757879 + 0.437562i −0.828534 0.559939i \(-0.810824\pi\)
0.0706548 + 0.997501i \(0.477491\pi\)
\(194\) 10.5349 0.756363
\(195\) 0 0
\(196\) −14.2476 −1.01768
\(197\) −3.79172 + 2.18915i −0.270149 + 0.155970i −0.628955 0.777442i \(-0.716517\pi\)
0.358807 + 0.933412i \(0.383184\pi\)
\(198\) −6.65968 11.5349i −0.473283 0.819751i
\(199\) 10.4186 18.0456i 0.738558 1.27922i −0.214586 0.976705i \(-0.568840\pi\)
0.953144 0.302516i \(-0.0978265\pi\)
\(200\) 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 0.989050 0.147583i \(-0.0471492\pi\)
−0.622335 + 0.782751i \(0.713816\pi\)
\(212\) −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 0.268949 0.963155i \(-0.413324\pi\)
0.968591 + 0.248661i \(0.0799905\pi\)
\(224\) −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 −0.0238900 0.999715i \(-0.507605\pi\)
−0.877723 + 0.479168i \(0.840938\pi\)
\(228\) −59.3241 34.2508i −3.92884 2.26831i
\(229\) 7.62085i 0.503600i 0.967779 + 0.251800i \(0.0810225\pi\)
−0.967779 + 0.251800i \(0.918977\pi\)
\(230\) 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 \(0.135336\pi\)
−0.910968 + 0.412477i \(0.864664\pi\)
\(240\) −13.2618 7.65668i −0.856043 0.494237i
\(241\) 22.4550 + 12.9644i 1.44646 + 0.835111i 0.998268 0.0588285i \(-0.0187365\pi\)
0.448187 + 0.893940i \(0.352070\pi\)
\(242\) 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 −0.720551 0.693402i \(-0.756111\pi\)
0.960779 + 0.277314i \(0.0894444\pi\)
\(252\) 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 0.871214 0.490903i \(-0.163333\pi\)
−0.860742 + 0.509042i \(0.830000\pi\)
\(258\) 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 0.936920 0.349544i \(-0.113664\pi\)
−0.771174 + 0.636624i \(0.780330\pi\)
\(264\) −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 −0.845360 0.534197i \(-0.820614\pi\)
0.885308 + 0.465005i \(0.153948\pi\)
\(270\) 7.02271 + 12.1637i 0.427388 + 0.740258i
\(271\) 10.0851 5.82266i 0.612629 0.353701i −0.161365 0.986895i \(-0.551590\pi\)
0.773994 + 0.633194i \(0.218256\pi\)
\(272\) −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 0.380845 + 0.924639i \(0.375633\pi\)
−0.991183 + 0.132498i \(0.957700\pi\)
\(278\) 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 \(0.115241\pi\)
−0.935176 + 0.354183i \(0.884759\pi\)
\(282\) −33.3184 + 57.7091i −1.98408 + 3.43653i
\(283\) −11.3261 19.6173i −0.673264 1.16613i −0.976973 0.213363i \(-0.931558\pi\)
0.303709 0.952765i \(-0.401775\pi\)
\(284\) −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 0.890489 0.455005i \(-0.150363\pi\)
0.0511983 + 0.998689i \(0.483696\pi\)
\(294\) 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 \(-0.971369\pi\)
0.995957 0.0898262i \(-0.0286311\pi\)
\(308\) −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 \(-0.874915\pi\)
0.923778 0.382929i \(-0.125085\pi\)
\(318\) −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 0.991018 0.133727i \(-0.0426945\pi\)
0.379698 + 0.925110i \(0.376028\pi\)
\(332\) 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 −0.890395 0.455189i \(-0.849572\pi\)
0.839402 + 0.543510i \(0.182905\pi\)
\(348\) −56.4973 97.8562i −3.02857 5.24564i
\(349\) 8.89329 5.13454i 0.476047 0.274846i −0.242721 0.970096i \(-0.578040\pi\)
0.718768 + 0.695250i \(0.244707\pi\)
\(350\) −4.75447 −0.254137
\(351\) 0 0
\(352\) 2.56730 0.136838
\(353\) 0.693330 0.400294i 0.0369022 0.0213055i −0.481435 0.876482i \(-0.659884\pi\)
0.518338 + 0.855176i \(0.326551\pi\)
\(354\) 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 \(-0.931151\pi\)
0.976699 0.214614i \(-0.0688494\pi\)
\(360\) 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 0.999127 + 0.0417696i \(0.0132996\pi\)
−0.463390 + 0.886154i \(0.653367\pi\)
\(368\) 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 −0.538034 0.842923i \(-0.680833\pi\)
0.999010 + 0.0444897i \(0.0141662\pi\)
\(374\) 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 −0.453812 0.891098i \(-0.649936\pi\)
0.544807 + 0.838561i \(0.316603\pi\)
\(380\) 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 0.664606 0.747194i \(-0.268599\pi\)
−0.314786 + 0.949163i \(0.601933\pi\)
\(384\) 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 0.355507 0.934674i \(-0.384308\pi\)
−0.631697 + 0.775215i \(0.717641\pi\)
\(398\) 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 −0.587437 0.809270i \(-0.699863\pi\)
0.407130 + 0.913370i \(0.366530\pi\)
\(402\) 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 0.266234 0.963909i \(-0.414221\pi\)
−0.701652 + 0.712519i \(0.747554\pi\)
\(410\) −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 −0.969029 0.246948i \(-0.920572\pi\)
0.270651 0.962677i \(-0.412761\pi\)
\(420\) 11.3842 19.7181i 0.555494 0.962144i
\(421\) 2.01797i 0.0983498i 0.998790 + 0.0491749i \(0.0156592\pi\)
−0.998790 + 0.0491749i \(0.984341\pi\)
\(422\) 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 −0.863959 0.503562i \(-0.832023\pi\)
0.00411765 + 0.999992i \(0.498689\pi\)
\(432\) 15.2446 + 26.4044i 0.733455 + 1.27038i
\(433\) 14.7178 25.4920i 0.707292 1.22507i −0.258566 0.965994i \(-0.583250\pi\)
0.965858 0.259072i \(-0.0834168\pi\)
\(434\) 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 0.994268 0.106920i \(-0.0340988\pi\)
−0.589729 + 0.807601i \(0.700765\pi\)
\(440\) 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 0.00887706 0.999961i \(-0.497174\pi\)
−0.861553 + 0.507668i \(0.830508\pi\)
\(450\) 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 −0.968737 0.248089i \(-0.920197\pi\)
−0.269517 + 0.962996i \(0.586864\pi\)
\(458\) 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 0.402676 0.915342i \(-0.368080\pi\)
−0.591372 + 0.806399i \(0.701413\pi\)
\(462\) −12.4471 7.18636i −0.579094 0.334340i
\(463\) 14.0011i 0.650688i 0.945596 + 0.325344i \(0.105480\pi\)
−0.945596 + 0.325344i \(0.894520\pi\)
\(464\) −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 −0.141820 0.989892i \(-0.545296\pi\)
0.786362 + 0.617766i \(0.211962\pi\)
\(480\) −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 0.0522474 0.998634i \(-0.483362\pi\)
−0.838719 + 0.544565i \(0.816695\pi\)
\(488\) 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 0.630887 0.775875i \(-0.282691\pi\)
−0.987371 + 0.158426i \(0.949358\pi\)
\(492\) 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 \(0.00888226\pi\)
−0.999611 + 0.0279008i \(0.991118\pi\)
\(500\) 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 −0.768013 0.640434i \(-0.778755\pi\)
0.938639 + 0.344902i \(0.112088\pi\)
\(504\) 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 0.0829345 0.996555i \(-0.473571\pi\)
0.904509 + 0.426454i \(0.140237\pi\)
\(510\) −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 0.819766 0.572698i \(-0.194103\pi\)
−0.905854 + 0.423589i \(0.860770\pi\)
\(524\) 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 \(0.110949\pi\)
−0.939867 + 0.341541i \(0.889051\pi\)
\(542\) 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 −0.637065 0.770810i \(-0.719852\pi\)
0.349009 + 0.937119i \(0.386518\pi\)
\(558\) 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 −0.982091 0.188410i \(-0.939667\pi\)
0.654213 + 0.756310i \(0.273000\pi\)
\(564\) 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 0.900183 0.435512i \(-0.143433\pi\)
−0.827256 + 0.561825i \(0.810099\pi\)
\(570\) −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 \(0.0665831\pi\)
−0.978202 + 0.207655i \(0.933417\pi\)
\(578\) 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 −0.863984 0.503519i \(-0.832038\pi\)
0.00406862 + 0.999992i \(0.498705\pi\)
\(588\) −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 \(-0.993855\pi\)
0.999814 0.0193051i \(-0.00614538\pi\)
\(594\) 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 0.954674 + 0.297655i \(0.0962045\pi\)
−0.219560 + 0.975599i \(0.570462\pi\)
\(602\) 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 0.103614 + 0.994618i \(0.466959\pi\)
−0.913171 + 0.407576i \(0.866374\pi\)
\(608\) 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 −0.506030 0.862516i \(-0.668887\pi\)
0.493946 + 0.869493i \(0.335554\pi\)
\(614\) −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 −0.360676 0.932691i \(-0.617454\pi\)
−0.988072 + 0.153991i \(0.950787\pi\)
\(618\) 82.6398 + 47.7121i 3.32426 + 1.91926i
\(619\) 14.8971i 0.598764i −0.954133 0.299382i \(-0.903219\pi\)
0.954133 0.299382i \(-0.0967805\pi\)
\(620\) −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 −0.352526 0.935802i \(-0.614677\pi\)
−0.986691 + 0.162604i \(0.948011\pi\)
\(632\) 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 −0.220739 0.975333i \(-0.570847\pi\)
0.955033 0.296501i \(-0.0958197\pi\)
\(642\) 51.9397i 2.04990i
\(643\) −7.88410 4.55189i −0.310918 0.179509i 0.336419 0.941712i \(-0.390784\pi\)
−0.647337 + 0.762204i \(0.724118\pi\)
\(644\) 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 0.614571 0.788862i \(-0.289329\pi\)
−0.990460 + 0.137803i \(0.955996\pi\)
\(648\) −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 −0.975691 0.219152i \(-0.929671\pi\)
0.298055 0.954549i \(-0.403662\pi\)
\(654\) −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 −0.793389 0.608715i \(-0.791685\pi\)
0.923857 + 0.382737i \(0.125018\pi\)
\(660\) 6.38994 + 11.0677i 0.248728 + 0.430809i
\(661\) −5.22004 + 3.01379i −0.203036 + 0.117223i −0.598071 0.801443i \(-0.704066\pi\)
0.395035 + 0.918666i \(0.370732\pi\)
\(662\) 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 0.998396 0.0566140i \(-0.0180304\pi\)
−0.548227 + 0.836329i \(0.684697\pi\)
\(674\) −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 0.0140045 0.999902i \(-0.495542\pi\)
−0.858938 + 0.512079i \(0.828875\pi\)
\(684\) 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 −0.604707 0.796448i \(-0.706710\pi\)
0.387391 + 0.921916i \(0.373376\pi\)
\(692\) 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 0.667150 0.744923i \(-0.267514\pi\)
−0.311548 + 0.950231i \(0.600847\pi\)
\(710\) 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 −0.676549 0.736398i \(-0.736525\pi\)
0.976014 + 0.217710i \(0.0698587\pi\)
\(720\) 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 \(-0.941930\pi\)
0.983406 0.181421i \(-0.0580697\pi\)
\(734\) 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 −0.566811 + 0.823848i \(0.691823\pi\)
−0.996879 + 0.0789487i \(0.974844\pi\)
\(740\) 3.20216 0.117714
\(741\) 0 0
\(742\) −33.2386 −1.22023
\(743\) 35.3663 20.4188i 1.29746 0.749091i 0.317499 0.948259i \(-0.397157\pi\)
0.979966 + 0.199167i \(0.0638237\pi\)
\(744\) −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 0.840077 0.542467i \(-0.182510\pi\)
−0.889829 + 0.456295i \(0.849176\pi\)
\(752\) 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 0.699554 0.714580i \(-0.253382\pi\)
−0.968621 + 0.248542i \(0.920049\pi\)
\(758\) 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 0.310815 0.950470i \(-0.399398\pi\)
−0.667724 + 0.744409i \(0.732731\pi\)
\(762\) 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 −0.791354 0.611358i \(-0.790623\pi\)
0.133775 + 0.991012i \(0.457290\pi\)
\(770\) 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 0.264367 0.964422i \(-0.414837\pi\)
−0.703031 + 0.711159i \(0.748170\pi\)
\(774\) 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
\(779\) −1.53590