Properties

Label 845.2.e.m.146.1
Level $845$
Weight $2$
Character 845.146
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.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.74735897080\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 146.1
Root \(1.20036 + 0.747754i\) of defining polynomial
Character \(\chi\) \(=\) 845.146
Dual form 845.2.e.m.191.1

$q$-expansion

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

Character values

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

\(n\) \(171\) \(677\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.24775 2.16117i −0.882295 1.52818i −0.848783 0.528742i \(-0.822664\pi\)
−0.0335125 0.999438i \(-0.510669\pi\)
\(3\) 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
\(5\) −1.00000 −0.447214
\(6\) 3.52720 6.10929i 1.43997 2.49411i
\(7\) −0.952606 + 1.64996i −0.360051 + 0.623627i −0.987969 0.154653i \(-0.950574\pi\)
0.627918 + 0.778280i \(0.283907\pi\)
\(8\) 5.55889 1.96536
\(9\) −2.49551 + 4.32235i −0.831836 + 1.44078i
\(10\) 1.24775 + 2.16117i 0.394574 + 0.683423i
\(11\) −0.534695 0.926118i −0.161217 0.279235i 0.774089 0.633077i \(-0.218208\pi\)
−0.935305 + 0.353842i \(0.884875\pi\)
\(12\) −11.9506 −3.44985
\(13\) 0 0
\(14\) 4.75447 1.27069
\(15\) −1.41342 2.44811i −0.364943 0.632100i
\(16\) −2.70857 4.69138i −0.677142 1.17284i
\(17\) −0.318632 + 0.551886i −0.0772795 + 0.133852i −0.902075 0.431579i \(-0.857957\pi\)
0.824796 + 0.565431i \(0.191290\pi\)
\(18\) 12.4551 2.93570
\(19\) −2.86603 + 4.96410i −0.657511 + 1.13884i 0.323747 + 0.946144i \(0.395057\pi\)
−0.981258 + 0.192699i \(0.938276\pi\)
\(20\) 2.11378 3.66117i 0.472655 0.818663i
\(21\) −5.38573 −1.17526
\(22\) −1.33433 + 2.31114i −0.284481 + 0.492736i
\(23\) −1.90893 3.30636i −0.398039 0.689423i 0.595445 0.803396i \(-0.296976\pi\)
−0.993484 + 0.113973i \(0.963642\pi\)
\(24\) 7.85704 + 13.6088i 1.60381 + 2.77788i
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.62828 −1.08316
\(28\) −4.02720 6.97531i −0.761069 1.31821i
\(29\) −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
\(31\) −1.46410 −0.262960 −0.131480 0.991319i \(-0.541973\pi\)
−0.131480 + 0.991319i \(0.541973\pi\)
\(32\) −1.20036 + 2.07908i −0.212196 + 0.367534i
\(33\) 1.51150 2.61799i 0.263118 0.455733i
\(34\) 1.59030 0.272733
\(35\) 0.952606 1.64996i 0.161020 0.278895i
\(36\) −10.5499 18.2730i −1.75832 3.04550i
\(37\) −0.378725 0.655970i −0.0622619 0.107841i 0.833214 0.552950i \(-0.186498\pi\)
−0.895476 + 0.445110i \(0.853165\pi\)
\(38\) 14.3044 2.32048
\(39\) 0 0
\(40\) −5.55889 −0.878938
\(41\) −0.133975 0.232051i −0.0209233 0.0362402i 0.855374 0.518011i \(-0.173327\pi\)
−0.876297 + 0.481770i \(0.839994\pi\)
\(42\) 6.72006 + 11.6395i 1.03693 + 1.79601i
\(43\) −0.318632 + 0.551886i −0.0485909 + 0.0841618i −0.889298 0.457328i \(-0.848806\pi\)
0.840707 + 0.541490i \(0.182140\pi\)
\(44\) 4.52091 0.681552
\(45\) 2.49551 4.32235i 0.372008 0.644337i
\(46\) −4.76374 + 8.25104i −0.702375 + 1.21655i
\(47\) −9.44613 −1.37786 −0.688930 0.724828i \(-0.741919\pi\)
−0.688930 + 0.724828i \(0.741919\pi\)
\(48\) 7.65668 13.2618i 1.10515 1.91417i
\(49\) 1.68508 + 2.91865i 0.240726 + 0.416950i
\(50\) −1.24775 2.16117i −0.176459 0.305636i
\(51\) −1.80144 −0.252252
\(52\) 0 0
\(53\) −6.99102 −0.960290 −0.480145 0.877189i \(-0.659416\pi\)
−0.480145 + 0.877189i \(0.659416\pi\)
\(54\) 7.02271 + 12.1637i 0.955669 + 1.65527i
\(55\) 0.534695 + 0.926118i 0.0720982 + 0.124878i
\(56\) −5.29543 + 9.17196i −0.707632 + 1.22565i
\(57\) −16.2036 −2.14622
\(58\) −11.7977 + 20.4341i −1.54911 + 2.68313i
\(59\) −0.370518 + 0.641756i −0.0482373 + 0.0835495i −0.889136 0.457643i \(-0.848694\pi\)
0.840899 + 0.541193i \(0.182027\pi\)
\(60\) 11.9506 1.54282
\(61\) −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
\(63\) −4.75447 8.23499i −0.599007 1.03751i
\(64\) −4.84325 −0.605406
\(65\) 0 0
\(66\) −7.54390 −0.928589
\(67\) −4.04739 7.01029i −0.494468 0.856443i 0.505512 0.862820i \(-0.331304\pi\)
−0.999980 + 0.00637624i \(0.997970\pi\)
\(68\) −1.34703 2.33313i −0.163352 0.282934i
\(69\) 5.39623 9.34654i 0.649629 1.12519i
\(70\) −4.75447 −0.568268
\(71\) −4.88244 + 8.45663i −0.579439 + 1.00362i 0.416105 + 0.909317i \(0.363395\pi\)
−0.995544 + 0.0943010i \(0.969938\pi\)
\(72\) −13.8723 + 24.0274i −1.63486 + 2.83166i
\(73\) −3.71649 −0.434982 −0.217491 0.976062i \(-0.569787\pi\)
−0.217491 + 0.976062i \(0.569787\pi\)
\(74\) −0.945110 + 1.63698i −0.109867 + 0.190295i
\(75\) 1.41342 + 2.44811i 0.163208 + 0.282684i
\(76\) −12.1163 20.9860i −1.38983 2.40726i
\(77\) 2.03741 0.232185
\(78\) 0 0
\(79\) −9.31937 −1.04851 −0.524255 0.851561i \(-0.675656\pi\)
−0.524255 + 0.851561i \(0.675656\pi\)
\(80\) 2.70857 + 4.69138i 0.302827 + 0.524512i
\(81\) −0.468594 0.811629i −0.0520660 0.0901809i
\(82\) −0.334335 + 0.579085i −0.0369211 + 0.0639492i
\(83\) 5.11778 0.561749 0.280875 0.959744i \(-0.409376\pi\)
0.280875 + 0.959744i \(0.409376\pi\)
\(84\) 11.3842 19.7181i 1.24212 2.15142i
\(85\) 0.318632 0.551886i 0.0345605 0.0598605i
\(86\) 1.59030 0.171486
\(87\) 13.3640 23.1472i 1.43278 2.48164i
\(88\) −2.97231 5.14819i −0.316849 0.548799i
\(89\) 6.28917 + 10.8932i 0.666650 + 1.15467i 0.978835 + 0.204651i \(0.0656059\pi\)
−0.312185 + 0.950021i \(0.601061\pi\)
\(90\) −12.4551 −1.31288
\(91\) 0 0
\(92\) 16.1402 1.68273
\(93\) −2.06939 3.58429i −0.214586 0.371673i
\(94\) 11.7864 + 20.4147i 1.21568 + 2.10562i
\(95\) 2.86603 4.96410i 0.294048 0.509306i
\(96\) −6.78645 −0.692639
\(97\) 2.11078 3.65597i 0.214317 0.371208i −0.738744 0.673986i \(-0.764581\pi\)
0.953061 + 0.302778i \(0.0979142\pi\)
\(98\) 4.20514 7.28351i 0.424783 0.735746i
\(99\) 5.33734 0.536423
\(100\) −2.11378 + 3.66117i −0.211378 + 0.366117i
\(101\) 7.62379 + 13.2048i 0.758595 + 1.31393i 0.943567 + 0.331181i \(0.107447\pi\)
−0.184972 + 0.982744i \(0.559219\pi\)
\(102\) 2.24775 + 3.89322i 0.222561 + 0.385487i
\(103\) −13.5269 −1.33285 −0.666423 0.745574i \(-0.732176\pi\)
−0.666423 + 0.745574i \(0.732176\pi\)
\(104\) 0 0
\(105\) 5.38573 0.525593
\(106\) 8.72307 + 15.1088i 0.847259 + 1.46750i
\(107\) 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
\(109\) 10.0760 0.965103 0.482551 0.875868i \(-0.339710\pi\)
0.482551 + 0.875868i \(0.339710\pi\)
\(110\) 1.33433 2.31114i 0.127224 0.220358i
\(111\) 1.07059 1.85432i 0.101616 0.176004i
\(112\) 10.3208 0.975223
\(113\) 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
\(115\) 1.90893 + 3.30636i 0.178008 + 0.308320i
\(116\) 39.9721 3.71131
\(117\) 0 0
\(118\) 1.84926 0.170238
\(119\) −0.607061 1.05146i −0.0556492 0.0963872i
\(120\) −7.85704 13.6088i −0.717246 1.24231i
\(121\) 4.92820 8.53590i 0.448018 0.775991i
\(122\) 10.4775 0.948592
\(123\) 0.378725 0.655970i 0.0341484 0.0591468i
\(124\) 3.09479 5.36033i 0.277920 0.481372i
\(125\) −1.00000 −0.0894427
\(126\) −11.8648 + 20.5505i −1.05700 + 1.83078i
\(127\) −0.744750 1.28994i −0.0660859 0.114464i 0.831089 0.556139i \(-0.187718\pi\)
−0.897175 + 0.441675i \(0.854384\pi\)
\(128\) 8.44391 + 14.6253i 0.746343 + 1.29270i
\(129\) −1.80144 −0.158608
\(130\) 0 0
\(131\) 4.12676 0.360557 0.180278 0.983616i \(-0.442300\pi\)
0.180278 + 0.983616i \(0.442300\pi\)
\(132\) 6.38994 + 11.0677i 0.556172 + 0.963319i
\(133\) −5.46039 9.45767i −0.473476 0.820084i
\(134\) −10.1003 + 17.4942i −0.872533 + 1.51127i
\(135\) 5.62828 0.484405
\(136\) −1.77124 + 3.06787i −0.151882 + 0.263068i
\(137\) 10.0548 17.4155i 0.859041 1.48790i −0.0138029 0.999905i \(-0.504394\pi\)
0.872844 0.487999i \(-0.162273\pi\)
\(138\) −26.9327 −2.29266
\(139\) −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
\(141\) −13.3513 23.1252i −1.12439 1.94749i
\(142\) 24.3683 2.04494
\(143\) 0 0
\(144\) 27.0370 2.25308
\(145\) 4.72756 + 8.18837i 0.392602 + 0.680007i
\(146\) 4.63726 + 8.03198i 0.383783 + 0.664731i
\(147\) −4.76346 + 8.25055i −0.392883 + 0.680494i
\(148\) 3.20216 0.263216
\(149\) −6.68388 + 11.5768i −0.547565 + 0.948410i 0.450876 + 0.892587i \(0.351112\pi\)
−0.998441 + 0.0558233i \(0.982222\pi\)
\(150\) 3.52720 6.10929i 0.287995 0.498821i
\(151\) 18.2984 1.48910 0.744550 0.667567i \(-0.232664\pi\)
0.744550 + 0.667567i \(0.232664\pi\)
\(152\) −15.9319 + 27.5949i −1.29225 + 2.23824i
\(153\) −1.59030 2.75447i −0.128568 0.222686i
\(154\) −2.54219 4.40320i −0.204856 0.354820i
\(155\) 1.46410 0.117599
\(156\) 0 0
\(157\) 2.42229 0.193320 0.0966599 0.995317i \(-0.469184\pi\)
0.0966599 + 0.995317i \(0.469184\pi\)
\(158\) 11.6283 + 20.1408i 0.925096 + 1.60231i
\(159\) −9.88124 17.1148i −0.783633 1.35729i
\(160\) 1.20036 2.07908i 0.0948968 0.164366i
\(161\) 7.27382 0.573258
\(162\) −1.16938 + 2.02543i −0.0918752 + 0.159132i
\(163\) −7.99144 + 13.8416i −0.625938 + 1.08416i 0.362421 + 0.932015i \(0.381950\pi\)
−0.988359 + 0.152142i \(0.951383\pi\)
\(164\) 1.13277 0.0884545
\(165\) −1.51150 + 2.61799i −0.117670 + 0.203810i
\(166\) −6.38573 11.0604i −0.495629 0.858454i
\(167\) 7.19658 + 12.4648i 0.556888 + 0.964558i 0.997754 + 0.0669853i \(0.0213381\pi\)
−0.440866 + 0.897573i \(0.645329\pi\)
\(168\) −29.9387 −2.30982
\(169\) 0 0
\(170\) −1.59030 −0.121970
\(171\) −14.3044 24.7759i −1.09388 1.89466i
\(172\) −1.34703 2.33313i −0.102710 0.177900i
\(173\) 12.1745 21.0868i 0.925608 1.60320i 0.135027 0.990842i \(-0.456888\pi\)
0.790581 0.612358i \(-0.209779\pi\)
\(174\) −66.7001 −5.05653
\(175\) −0.952606 + 1.64996i −0.0720103 + 0.124725i
\(176\) −2.89651 + 5.01691i −0.218333 + 0.378164i
\(177\) −2.09479 −0.157454
\(178\) 15.6947 27.1840i 1.17636 2.03752i
\(179\) −1.89414 3.28075i −0.141575 0.245215i 0.786515 0.617571i \(-0.211883\pi\)
−0.928090 + 0.372356i \(0.878550\pi\)
\(180\) 10.5499 + 18.2730i 0.786343 + 1.36199i
\(181\) −8.48794 −0.630904 −0.315452 0.948942i \(-0.602156\pi\)
−0.315452 + 0.948942i \(0.602156\pi\)
\(182\) 0 0
\(183\) −11.8687 −0.877356
\(184\) −10.6115 18.3797i −0.782291 1.35497i
\(185\) 0.378725 + 0.655970i 0.0278444 + 0.0482279i
\(186\) −5.16418 + 8.94462i −0.378656 + 0.655851i
\(187\) 0.681482 0.0498349
\(188\) 19.9670 34.5839i 1.45625 2.52229i
\(189\) 5.36153 9.28645i 0.389994 0.675490i
\(190\) −14.3044 −1.03775
\(191\) 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
\(193\) −6.07880 10.5288i −0.437562 0.757879i 0.559939 0.828534i \(-0.310824\pi\)
−0.997501 + 0.0706548i \(0.977491\pi\)
\(194\) −10.5349 −0.756363
\(195\) 0 0
\(196\) −14.2476 −1.01768
\(197\) 2.18915 + 3.79172i 0.155970 + 0.270149i 0.933412 0.358807i \(-0.116816\pi\)
−0.777442 + 0.628955i \(0.783483\pi\)
\(198\) −6.65968 11.5349i −0.473283 0.819751i
\(199\) −10.4186 + 18.0456i −0.738558 + 1.27922i 0.214586 + 0.976705i \(0.431160\pi\)
−0.953144 + 0.302516i \(0.902174\pi\)
\(200\) 5.55889 0.393073
\(201\) 11.4413 19.8170i 0.807009 1.39778i
\(202\) 19.0252 32.9526i 1.33861 2.31854i
\(203\) 18.0140 1.26434
\(204\) 3.80785 6.59538i 0.266603 0.461769i
\(205\) 0.133975 + 0.232051i 0.00935719 + 0.0162071i
\(206\) 16.8783 + 29.2340i 1.17596 + 2.03683i
\(207\) 19.0550 1.32441
\(208\) 0 0
\(209\) 6.12979 0.424007
\(210\) −6.72006 11.6395i −0.463728 0.803201i
\(211\) 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
\(213\) −27.6037 −1.89138
\(214\) 9.18688 15.9121i 0.628002 1.08773i
\(215\) 0.318632 0.551886i 0.0217305 0.0376383i
\(216\) −31.2870 −2.12881
\(217\) 1.39471 2.41571i 0.0946792 0.163989i
\(218\) −12.5723 21.7759i −0.851505 1.47485i
\(219\) −5.25296 9.09839i −0.354962 0.614812i
\(220\) −4.52091 −0.304799
\(221\) 0 0
\(222\) −5.34335 −0.358622
\(223\) −10.6697 18.4804i −0.714494 1.23754i −0.963155 0.268949i \(-0.913324\pi\)
0.248661 0.968591i \(-0.420010\pi\)
\(224\) −2.28694 3.96110i −0.152803 0.264662i
\(225\) −2.49551 + 4.32235i −0.166367 + 0.288156i
\(226\) −16.6901 −1.11021
\(227\) −7.84283 + 13.5842i −0.520547 + 0.901613i 0.479168 + 0.877723i \(0.340938\pi\)
−0.999715 + 0.0238900i \(0.992395\pi\)
\(228\) 34.2508 59.3241i 2.26831 3.92884i
\(229\) −7.62085 −0.503600 −0.251800 0.967779i \(-0.581023\pi\)
−0.251800 + 0.967779i \(0.581023\pi\)
\(230\) 4.76374 8.25104i 0.314112 0.544058i
\(231\) 2.87972 + 4.98782i 0.189472 + 0.328175i
\(232\) −26.2800 45.5182i −1.72536 2.98842i
\(233\) −19.0550 −1.24833 −0.624166 0.781292i \(-0.714561\pi\)
−0.624166 + 0.781292i \(0.714561\pi\)
\(234\) 0 0
\(235\) 9.44613 0.616198
\(236\) −1.56639 2.71306i −0.101963 0.176605i
\(237\) −13.1722 22.8149i −0.855625 1.48199i
\(238\) −1.51493 + 2.62393i −0.0981980 + 0.170084i
\(239\) 12.7535 0.824954 0.412477 0.910968i \(-0.364664\pi\)
0.412477 + 0.910968i \(0.364664\pi\)
\(240\) −7.65668 + 13.2618i −0.494237 + 0.856043i
\(241\) −12.9644 + 22.4550i −0.835111 + 1.44646i 0.0588285 + 0.998268i \(0.481263\pi\)
−0.893940 + 0.448187i \(0.852070\pi\)
\(242\) −24.5967 −1.58114
\(243\) −7.11778 + 12.3284i −0.456606 + 0.790864i
\(244\) −8.87483 15.3717i −0.568153 0.984069i
\(245\) −1.68508 2.91865i −0.107656 0.186466i
\(246\) −1.89022 −0.120516
\(247\) 0 0
\(248\) −8.13878 −0.516813
\(249\) 7.23357 + 12.5289i 0.458409 + 0.793987i
\(250\) 1.24775 + 2.16117i 0.0789149 + 0.136685i
\(251\) −3.80593 + 6.59207i −0.240228 + 0.416088i −0.960779 0.277314i \(-0.910556\pi\)
0.720551 + 0.693402i \(0.243889\pi\)
\(252\) 40.1996 2.53234
\(253\) −2.04139 + 3.53578i −0.128341 + 0.222293i
\(254\) −1.85853 + 3.21907i −0.116614 + 0.201982i
\(255\) 1.80144 0.112811
\(256\) 16.2286 28.1087i 1.01429 1.75680i
\(257\) −0.167891 0.290796i −0.0104728 0.0181394i 0.860742 0.509042i \(-0.170000\pi\)
−0.871214 + 0.490903i \(0.836667\pi\)
\(258\) 2.24775 + 3.89322i 0.139939 + 0.242382i
\(259\) 1.44310 0.0896700
\(260\) 0 0
\(261\) 47.1906 2.92103
\(262\) −5.14918 8.91865i −0.318118 0.550996i
\(263\) 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
\(265\) 6.99102 0.429455
\(266\) −13.6264 + 23.6017i −0.835491 + 1.44711i
\(267\) −17.7785 + 30.7932i −1.08802 + 1.88451i
\(268\) 34.2212 2.09039
\(269\) 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
\(271\) 5.82266 + 10.0851i 0.353701 + 0.612629i 0.986895 0.161365i \(-0.0515896\pi\)
−0.633194 + 0.773994i \(0.718256\pi\)
\(272\) 3.45214 0.209317
\(273\) 0 0
\(274\) −50.1838 −3.03171
\(275\) −0.534695 0.926118i −0.0322433 0.0558470i
\(276\) 22.8129 + 39.5130i 1.37317 + 2.37841i
\(277\) 10.1581 17.5943i 0.610338 1.05714i −0.380845 0.924639i \(-0.624367\pi\)
0.991183 0.132498i \(-0.0422999\pi\)
\(278\) 51.9697 3.11693
\(279\) 3.65368 6.32835i 0.218740 0.378869i
\(280\) 5.29543 9.17196i 0.316463 0.548129i
\(281\) −11.8744 −0.708366 −0.354183 0.935176i \(-0.615241\pi\)
−0.354183 + 0.935176i \(0.615241\pi\)
\(282\) −33.3184 + 57.7091i −1.98408 + 3.43653i
\(283\) 11.3261 + 19.6173i 0.673264 + 1.16613i 0.976973 + 0.213363i \(0.0684418\pi\)
−0.303709 + 0.952765i \(0.598225\pi\)
\(284\) −20.6408 35.7509i −1.22481 2.12143i
\(285\) 16.2036 0.959817
\(286\) 0 0
\(287\) 0.510500 0.0301339
\(288\) −5.99102 10.3767i −0.353024 0.611455i
\(289\) 8.29695 + 14.3707i 0.488056 + 0.845337i
\(290\) 11.7977 20.4341i 0.692782 1.19993i
\(291\) 11.9336 0.699562
\(292\) 7.85584 13.6067i 0.459728 0.796272i
\(293\) −9.30636 + 16.1191i −0.543683 + 0.941687i 0.455005 + 0.890489i \(0.349637\pi\)
−0.998689 + 0.0511983i \(0.983696\pi\)
\(294\) 23.7745 1.38656
\(295\) 0.370518 0.641756i 0.0215724 0.0373645i
\(296\) −2.10529 3.64647i −0.122367 0.211946i
\(297\) 3.00941 + 5.21245i 0.174624 + 0.302457i
\(298\) 33.3593 1.93245
\(299\) 0 0
\(300\) −11.9506 −0.689970
\(301\) −0.607061 1.05146i −0.0349904 0.0606052i
\(302\) −22.8319 39.5459i −1.31383 2.27561i
\(303\) −21.5512 + 37.3278i −1.23808 + 2.14443i
\(304\) 31.0513 1.78091
\(305\) 2.09928 3.63606i 0.120204 0.208200i
\(306\) −3.96859 + 6.87381i −0.226869 + 0.392949i
\(307\) 3.14776 0.179652 0.0898262 0.995957i \(-0.471369\pi\)
0.0898262 + 0.995957i \(0.471369\pi\)
\(308\) −4.30664 + 7.45932i −0.245394 + 0.425034i
\(309\) −19.1192 33.1154i −1.08765 1.88387i
\(310\) −1.82684 3.16418i −0.103757 0.179713i
\(311\) −3.18059 −0.180355 −0.0901774 0.995926i \(-0.528743\pi\)
−0.0901774 + 0.995926i \(0.528743\pi\)
\(312\) 0 0
\(313\) 35.3533 1.99829 0.999144 0.0413596i \(-0.0131689\pi\)
0.999144 + 0.0413596i \(0.0131689\pi\)
\(314\) −3.02242 5.23499i −0.170565 0.295427i
\(315\) 4.75447 + 8.23499i 0.267884 + 0.463989i
\(316\) 19.6991 34.1198i 1.10816 1.91939i
\(317\) −13.6357 −0.765858 −0.382929 0.923778i \(-0.625085\pi\)
−0.382929 + 0.923778i \(0.625085\pi\)
\(318\) −24.6587 + 42.7101i −1.38279 + 2.39506i
\(319\) −5.05560 + 8.75656i −0.283059 + 0.490273i
\(320\) 4.84325 0.270746
\(321\) −10.4066 + 18.0248i −0.580842 + 1.00605i
\(322\) −9.07594 15.7200i −0.505782 0.876041i
\(323\) −1.82641 3.16344i −0.101624 0.176018i
\(324\) 3.96202 0.220112
\(325\) 0 0
\(326\) 39.8854 2.20905
\(327\) 14.2416 + 24.6671i 0.787560 + 1.36409i
\(328\) −0.744750 1.28994i −0.0411219 0.0712253i
\(329\) 8.99844 15.5858i 0.496100 0.859271i
\(330\) 7.54390 0.415278
\(331\) 14.3980 24.9380i 0.791383 1.37072i −0.133727 0.991018i \(-0.542695\pi\)
0.925110 0.379698i \(-0.123972\pi\)
\(332\) −10.8179 + 18.7371i −0.593707 + 1.02833i
\(333\) 3.78044 0.207167
\(334\) 17.9591 31.1061i 0.982679 1.70205i
\(335\) 4.04739 + 7.01029i 0.221133 + 0.383013i
\(336\) 14.5876 + 25.2665i 0.795819 + 1.37840i
\(337\) 11.7493 0.640026 0.320013 0.947413i \(-0.396313\pi\)
0.320013 + 0.947413i \(0.396313\pi\)
\(338\) 0 0
\(339\) 18.9061 1.02684
\(340\) 1.34703 + 2.33313i 0.0730532 + 0.126532i
\(341\) 0.782847 + 1.35593i 0.0423936 + 0.0734278i
\(342\) −35.6967 + 61.8285i −1.93026 + 3.34330i
\(343\) −19.7574 −1.06680
\(344\) −1.77124 + 3.06787i −0.0954987 + 0.165409i
\(345\) −5.39623 + 9.34654i −0.290523 + 0.503201i
\(346\) −60.7630 −3.26664
\(347\) −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
\(349\) 5.13454 + 8.89329i 0.274846 + 0.476047i 0.970096 0.242721i \(-0.0780398\pi\)
−0.695250 + 0.718768i \(0.744707\pi\)
\(350\) 4.75447 0.254137
\(351\) 0 0
\(352\) 2.56730 0.136838
\(353\) −0.400294 0.693330i −0.0213055 0.0369022i 0.855176 0.518338i \(-0.173449\pi\)
−0.876482 + 0.481435i \(0.840116\pi\)
\(354\) 2.61378 + 4.52720i 0.138921 + 0.240618i
\(355\) 4.88244 8.45663i 0.259133 0.448831i
\(356\) −53.1756 −2.81830
\(357\) 1.71606 2.97231i 0.0908237 0.157311i
\(358\) −4.72685 + 8.18714i −0.249822 + 0.432704i
\(359\) 8.13272 0.429228 0.214614 0.976699i \(-0.431151\pi\)
0.214614 + 0.976699i \(0.431151\pi\)
\(360\) 13.8723 24.0274i 0.731132 1.26636i
\(361\) −6.92820 12.0000i −0.364642 0.631579i
\(362\) 10.5909 + 18.3439i 0.556643 + 0.964135i
\(363\) 27.8625 1.46240
\(364\) 0 0
\(365\) 3.71649 0.194530
\(366\) 14.8092 + 25.6502i 0.774087 + 1.34076i
\(367\) 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
\(369\) 1.33734 0.0696191
\(370\) 0.945110 1.63698i 0.0491339 0.0851025i
\(371\) 6.65968 11.5349i 0.345754 0.598863i
\(372\) 17.4969 0.907173
\(373\) 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
\(375\) −1.41342 2.44811i −0.0729887 0.126420i
\(376\) −52.5100 −2.70800
\(377\) 0 0
\(378\) −26.7595 −1.37636
\(379\) −1.02277 1.77150i −0.0525363 0.0909956i 0.838561 0.544807i \(-0.183397\pi\)
−0.891098 + 0.453812i \(0.850064\pi\)
\(380\) 12.1163 + 20.9860i 0.621553 + 1.07656i
\(381\) 2.10529 3.64647i 0.107857 0.186814i
\(382\) −13.5833 −0.694982
\(383\) 3.95261 6.84611i 0.201969 0.349820i −0.747194 0.664606i \(-0.768599\pi\)
0.949163 + 0.314786i \(0.101933\pi\)
\(384\) −23.8696 + 41.3433i −1.21809 + 2.10979i
\(385\) −2.03741 −0.103836
\(386\) −15.1697 + 26.2747i −0.772117 + 1.33735i
\(387\) −1.59030 2.75447i −0.0808393 0.140018i
\(388\) 8.92343 + 15.4558i 0.453018 + 0.784651i
\(389\) −9.21171 −0.467052 −0.233526 0.972351i \(-0.575026\pi\)
−0.233526 + 0.972351i \(0.575026\pi\)
\(390\) 0 0
\(391\) 2.43298 0.123041
\(392\) 9.36719 + 16.2244i 0.473114 + 0.819458i
\(393\) 5.83285 + 10.1028i 0.294228 + 0.509618i
\(394\) 5.46304 9.46226i 0.275224 0.476702i
\(395\) 9.31937 0.468908
\(396\) −11.2820 + 19.5409i −0.566940 + 0.981968i
\(397\) 3.17719 5.50305i 0.159458 0.276190i −0.775215 0.631697i \(-0.782359\pi\)
0.934674 + 0.355507i \(0.115692\pi\)
\(398\) 51.9996 2.60651
\(399\) 15.4356 26.7353i 0.772748 1.33844i
\(400\) −2.70857 4.69138i −0.135428 0.234569i
\(401\) −2.08460 3.61063i −0.104100 0.180306i 0.809270 0.587437i \(-0.199863\pi\)
−0.913370 + 0.407130i \(0.866530\pi\)
\(402\) −57.1038 −2.84808
\(403\) 0 0
\(404\) −64.4600 −3.20701
\(405\) 0.468594 + 0.811629i 0.0232846 + 0.0403301i
\(406\) −22.4770 38.9314i −1.11552 1.93213i
\(407\) −0.405004 + 0.701487i −0.0200753 + 0.0347714i
\(408\) −10.0140 −0.495767
\(409\) −5.08403 + 8.80580i −0.251389 + 0.435419i −0.963909 0.266234i \(-0.914221\pi\)
0.712519 + 0.701652i \(0.247554\pi\)
\(410\) 0.334335 0.579085i 0.0165116 0.0285989i
\(411\) 56.8467 2.80404
\(412\) 28.5929 49.5244i 1.40867 2.43989i
\(413\) −0.705915 1.22268i −0.0347358 0.0601642i
\(414\) −23.7759 41.1811i −1.16852 2.02394i
\(415\) −5.11778 −0.251222
\(416\) 0 0
\(417\) −58.8697 −2.88286
\(418\) −7.64847 13.2475i −0.374099 0.647959i
\(419\) −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
\(421\) 2.01797 0.0983498 0.0491749 0.998790i \(-0.484341\pi\)
0.0491749 + 0.998790i \(0.484341\pi\)
\(422\) 13.2932 23.0244i 0.647101 1.12081i
\(423\) 23.5729 40.8295i 1.14615 1.98520i
\(424\) −38.8623 −1.88732
\(425\) −0.318632 + 0.551886i −0.0154559 + 0.0267704i
\(426\) 34.4427 + 59.6564i 1.66875 + 2.89036i
\(427\) −3.99957 6.92747i −0.193553 0.335244i
\(428\) −31.1264 −1.50455
\(429\) 0 0
\(430\) −1.59030 −0.0766908
\(431\) 10.3061 + 17.8508i 0.496430 + 0.859842i 0.999992 0.00411765i \(-0.00131069\pi\)
−0.503562 + 0.863959i \(0.667977\pi\)
\(432\) 15.2446 + 26.4044i 0.733455 + 1.27038i
\(433\) −14.7178 + 25.4920i −0.707292 + 1.22507i 0.258566 + 0.965994i \(0.416750\pi\)
−0.965858 + 0.259072i \(0.916583\pi\)
\(434\) −6.96103 −0.334140
\(435\) −13.3640 + 23.1472i −0.640757 + 1.10982i
\(436\) −21.2984 + 36.8899i −1.02001 + 1.76670i
\(437\) 21.8841 1.04686
\(438\) −13.1088 + 22.7051i −0.626362 + 1.08489i
\(439\) −8.47602 14.6809i −0.404538 0.700681i 0.589729 0.807601i \(-0.299235\pi\)
−0.994268 + 0.106920i \(0.965901\pi\)
\(440\) 2.97231 + 5.14819i 0.141699 + 0.245430i
\(441\) −16.8205 −0.800978
\(442\) 0 0
\(443\) −24.1399 −1.14692 −0.573461 0.819233i \(-0.694400\pi\)
−0.573461 + 0.819233i \(0.694400\pi\)
\(444\) 4.52599 + 7.83925i 0.214794 + 0.372034i
\(445\) −6.28917 10.8932i −0.298135 0.516385i
\(446\) −26.6262 + 46.1180i −1.26079 + 2.18375i
\(447\) −37.7885 −1.78733
\(448\) 4.61371 7.99118i 0.217977 0.377548i
\(449\) 10.4315 18.0679i 0.492293 0.852676i −0.507668 0.861553i \(-0.669492\pi\)
0.999961 + 0.00887706i \(0.00282569\pi\)
\(450\) 12.4551 0.587140
\(451\) −0.143271 + 0.248153i −0.00674637 + 0.0116851i
\(452\) 14.1371 + 24.4861i 0.664952 + 1.15173i
\(453\) 25.8633 + 44.7965i 1.21516 + 2.10472i
\(454\) 39.1437 1.83710
\(455\) 0 0
\(456\) −90.0739 −4.21810
\(457\) 15.2830 + 26.4708i 0.714906 + 1.23825i 0.962996 + 0.269517i \(0.0868640\pi\)
−0.248089 + 0.968737i \(0.579803\pi\)
\(458\) 9.50894 + 16.4700i 0.444324 + 0.769591i
\(459\) 1.79335 3.10617i 0.0837063 0.144984i
\(460\) −16.1402 −0.752541
\(461\) −2.33911 + 4.05146i −0.108943 + 0.188695i −0.915342 0.402676i \(-0.868080\pi\)
0.806399 + 0.591372i \(0.201413\pi\)
\(462\) 7.18636 12.4471i 0.334340 0.579094i
\(463\) −14.0011 −0.650688 −0.325344 0.945596i \(-0.605480\pi\)
−0.325344 + 0.945596i \(0.605480\pi\)
\(464\) −25.6098 + 44.3575i −1.18891 + 2.05925i
\(465\) 2.06939 + 3.58429i 0.0959656 + 0.166217i
\(466\) 23.7759 + 41.1811i 1.10140 + 1.90768i
\(467\) −6.98506 −0.323230 −0.161615 0.986854i \(-0.551670\pi\)
−0.161615 + 0.986854i \(0.551670\pi\)
\(468\) 0 0
\(469\) 15.4223 0.712135
\(470\) −11.7864 20.4147i −0.543668 0.941661i
\(471\) 3.42371 + 5.93004i 0.157756 + 0.273242i
\(472\) −2.05967 + 3.56745i −0.0948039 + 0.164205i
\(473\) 0.681482 0.0313346
\(474\) −32.8713 + 56.9347i −1.50983 + 2.61510i
\(475\) −2.86603 + 4.96410i −0.131502 + 0.227769i
\(476\) 5.13277 0.235260
\(477\) 17.4461 30.2176i 0.798804 1.38357i
\(478\) −15.9132 27.5625i −0.727853 1.26068i
\(479\) 8.14438 + 14.1065i 0.372126 + 0.644542i 0.989892 0.141820i \(-0.0452955\pi\)
−0.617766 + 0.786362i \(0.711962\pi\)
\(480\) 6.78645 0.309758
\(481\) 0 0
\(482\) 64.7056 2.94726
\(483\) 10.2810 + 17.8071i 0.467800 + 0.810253i
\(484\) 20.8343 + 36.0860i 0.947012 + 1.64027i
\(485\) −2.11078 + 3.65597i −0.0958454 + 0.166009i
\(486\) 35.5249 1.61144
\(487\) −10.0204 + 17.3559i −0.454069 + 0.786471i −0.998634 0.0522474i \(-0.983362\pi\)
0.544565 + 0.838719i \(0.316695\pi\)
\(488\) −11.6697 + 20.2125i −0.528261 + 0.914975i
\(489\) −45.1810 −2.04316
\(490\) −4.20514 + 7.28351i −0.189969 + 0.329035i
\(491\) 7.89916 + 13.6818i 0.356484 + 0.617449i 0.987371 0.158426i \(-0.0506420\pi\)
−0.630887 + 0.775875i \(0.717309\pi\)
\(492\) 1.60108 + 2.77315i 0.0721823 + 0.125023i
\(493\) 6.02540 0.271370
\(494\) 0 0
\(495\) −5.33734 −0.239896
\(496\) 3.96562 + 6.86865i 0.178061 + 0.308411i
\(497\) −9.30208 16.1117i −0.417255 0.722708i
\(498\) 18.0514 31.2660i 0.808903 1.40106i
\(499\) 1.24651 0.0558016 0.0279008 0.999611i \(-0.491118\pi\)
0.0279008 + 0.999611i \(0.491118\pi\)
\(500\) 2.11378 3.66117i 0.0945311 0.163733i
\(501\) −20.3436 + 35.2361i −0.908883 + 1.57423i
\(502\) 18.9955 0.847809
\(503\) 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
\(505\) −7.62379 13.2048i −0.339254 0.587605i
\(506\) 10.1886 0.452938
\(507\) 0 0
\(508\) 6.29695 0.279382
\(509\) −12.8621 22.2777i −0.570101 0.987444i −0.996555 0.0829345i \(-0.973571\pi\)
0.426454 0.904509i \(-0.359763\pi\)
\(510\) −2.24775 3.89322i −0.0995322 0.172395i
\(511\) 3.54035 6.13207i 0.156616 0.271267i
\(512\) −47.2215 −2.08691
\(513\) 16.1308 27.9393i 0.712192 1.23355i
\(514\) −0.418974 + 0.725685i −0.0184802 + 0.0320086i
\(515\) 13.5269 0.596067
\(516\) 3.80785 6.59538i 0.167631 0.290346i
\(517\) 5.05080 + 8.74824i 0.222134 + 0.384747i
\(518\) −1.80064 3.11879i −0.0791154 0.137032i
\(519\) 68.8305 3.02132
\(520\) 0 0
\(521\) −30.1519 −1.32098 −0.660490 0.750835i \(-0.729651\pi\)
−0.660490 + 0.750835i \(0.729651\pi\)
\(522\) −58.8823 101.987i −2.57721 4.46386i
\(523\) −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
\(525\) −5.38573 −0.235052
\(526\) 6.70779 11.6182i 0.292473 0.506579i
\(527\) 0.466509 0.808017i 0.0203215 0.0351978i
\(528\) −16.3759 −0.712672
\(529\) 4.21200 7.29539i 0.183130 0.317191i
\(530\) −8.72307 15.1088i −0.378906 0.656284i
\(531\) −1.84926 3.20301i −0.0802510 0.138999i
\(532\) 46.1682 2.00165
\(533\) 0 0
\(534\) 88.7326 3.83983
\(535\) −3.68137 6.37632i −0.159159 0.275672i
\(536\) −22.4990 38.9694i −0.971809 1.68322i
\(537\) 5.35444 9.27415i 0.231061 0.400209i
\(538\) −3.27007 −0.140983
\(539\) 1.80201 3.12117i 0.0776180 0.134438i
\(540\) −11.8969 + 20.6061i −0.511963 + 0.886745i
\(541\) −15.8881 −0.683083 −0.341541 0.939867i \(-0.610949\pi\)
−0.341541 + 0.939867i \(0.610949\pi\)
\(542\) 14.5305 25.1675i 0.624138 1.08104i
\(543\) −11.9970 20.7795i −0.514842 0.891732i
\(544\) −0.764945 1.32492i −0.0327968 0.0568057i
\(545\) −10.0760 −0.431607
\(546\) 0 0
\(547\) −6.56107 −0.280531 −0.140266 0.990114i \(-0.544796\pi\)
−0.140266 + 0.990114i \(0.544796\pi\)
\(548\) 42.5074 + 73.6249i 1.81582 + 3.14510i
\(549\) −10.4775 18.1476i −0.447170 0.774522i
\(550\) −1.33433 + 2.31114i −0.0568962 + 0.0985471i
\(551\) 54.1972 2.30888
\(552\) 29.9970 51.9564i 1.27676 2.21141i
\(553\) 8.87769 15.3766i 0.377518 0.653880i
\(554\) −50.6990 −2.15399
\(555\) −1.07059 + 1.85432i −0.0454441 + 0.0787116i
\(556\) −44.0200 76.2450i −1.86687 3.23351i
\(557\) −3.92503 6.79835i −0.166309 0.288055i 0.770810 0.637065i \(-0.219852\pi\)
−0.937119 + 0.349009i \(0.886518\pi\)
\(558\) −18.2356 −0.771973
\(559\) 0 0
\(560\) −10.3208 −0.436133
\(561\) 0.963220 + 1.66835i 0.0406672 + 0.0704377i
\(562\) 14.8163 + 25.6626i 0.624988 + 1.08251i
\(563\) 7.77976 13.4749i 0.327878 0.567901i −0.654213 0.756310i \(-0.727000\pi\)
0.982091 + 0.188410i \(0.0603333\pi\)
\(564\) 112.887 4.75341
\(565\) −3.34403 + 5.79203i −0.140684 + 0.243673i
\(566\) 28.2643 48.9552i 1.18804 2.05774i
\(567\) 1.78554 0.0749857
\(568\) −27.1409 + 47.0095i −1.13881 + 1.97247i
\(569\) −1.73957 3.01303i −0.0729267 0.126313i 0.827256 0.561825i \(-0.189901\pi\)
−0.900183 + 0.435512i \(0.856567\pi\)
\(570\) −20.2181 35.0187i −0.846842 1.46677i
\(571\) −21.5118 −0.900240 −0.450120 0.892968i \(-0.648619\pi\)
−0.450120 + 0.892968i \(0.648619\pi\)
\(572\) 0 0
\(573\) 15.3868 0.642791
\(574\) −0.636978 1.10328i −0.0265870 0.0460500i
\(575\) −1.90893 3.30636i −0.0796078 0.137885i
\(576\) 12.0864 20.9342i 0.503599 0.872259i
\(577\) 9.97608 0.415310 0.207655 0.978202i \(-0.433417\pi\)
0.207655 + 0.978202i \(0.433417\pi\)
\(578\) 20.7051 35.8623i 0.861218 1.49167i
\(579\) 17.1838 29.7632i 0.714134 1.23692i
\(580\) −39.9721 −1.65975
\(581\) −4.87523 + 8.44414i −0.202259 + 0.350322i
\(582\) −14.8902 25.7907i −0.617221 1.06906i
\(583\) 3.73806 + 6.47451i 0.154815 + 0.268147i
\(584\) −20.6595 −0.854898
\(585\) 0 0
\(586\) 46.4482 1.91876
\(587\) 12.0286 + 20.8341i 0.496472 + 0.859915i 0.999992 0.00406862i \(-0.00129509\pi\)
−0.503519 + 0.863984i \(0.667962\pi\)
\(588\) −20.1378 34.8797i −0.830469 1.43841i
\(589\) 4.19615 7.26795i 0.172899 0.299471i
\(590\) −1.84926 −0.0761328
\(591\) −6.18837 + 10.7186i −0.254556 + 0.440903i
\(592\) −2.05160 + 3.55348i −0.0843203 + 0.146047i
\(593\) 0.940219 0.0386102 0.0193051 0.999814i \(-0.493855\pi\)
0.0193051 + 0.999814i \(0.493855\pi\)
\(594\) 7.51001 13.0077i 0.308139 0.533713i
\(595\) 0.607061 + 1.05146i 0.0248871 + 0.0431057i
\(596\) −28.2565 48.9417i −1.15743 2.00473i
\(597\) −58.9037 −2.41077
\(598\) 0 0
\(599\) −11.4270 −0.466896 −0.233448 0.972369i \(-0.575001\pi\)
−0.233448 + 0.972369i \(0.575001\pi\)
\(600\) 7.85704 + 13.6088i 0.320762 + 0.555577i
\(601\) 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
\(603\) 40.4012 1.64526
\(604\) −38.6787 + 66.9935i −1.57381 + 2.72593i
\(605\) −4.92820 + 8.53590i −0.200360 + 0.347034i
\(606\) 107.562 4.36942
\(607\) −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
\(609\) 25.4613 + 44.1003i 1.03175 + 1.78704i
\(610\) −10.4775 −0.424223
\(611\) 0 0
\(612\) 13.4461 0.543528
\(613\) 0.172736 + 0.299187i 0.00697673 + 0.0120841i 0.869493 0.493946i \(-0.164446\pi\)
−0.862516 + 0.506030i \(0.831113\pi\)
\(614\) −3.92763 6.80286i −0.158506 0.274541i
\(615\) −0.378725 + 0.655970i −0.0152716 + 0.0264513i
\(616\) 11.3258 0.456328
\(617\) −19.3425 + 33.5022i −0.778700 + 1.34875i 0.153991 + 0.988072i \(0.450787\pi\)
−0.932691 + 0.360676i \(0.882546\pi\)
\(618\) −47.7121 + 82.6398i −1.91926 + 3.32426i
\(619\) 14.8971 0.598764 0.299382 0.954133i \(-0.403219\pi\)
0.299382 + 0.954133i \(0.403219\pi\)
\(620\) −3.09479 + 5.36033i −0.124290 + 0.215276i
\(621\) 10.7440 + 18.6091i 0.431141 + 0.746758i
\(622\) 3.96859 + 6.87381i 0.159126 + 0.275615i
\(623\) −23.9644 −0.960113
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −44.1123 76.4047i −1.76308 3.05374i
\(627\) 8.66397 + 15.0064i 0.346006 + 0.599299i
\(628\) −5.12019 + 8.86842i −0.204318 + 0.353889i
\(629\) 0.482694 0.0192463
\(630\) 11.8648 20.5505i 0.472706 0.818750i
\(631\) 19.4225 33.6408i 0.773198 1.33922i −0.162604 0.986691i \(-0.551989\pi\)
0.935802 0.352526i \(-0.114677\pi\)
\(632\) −51.8053 −2.06071
\(633\) −15.0581 + 26.0814i −0.598506 + 1.03664i
\(634\) 17.0140 + 29.4691i 0.675713 + 1.17037i
\(635\) 0.744750 + 1.28994i 0.0295545 + 0.0511899i
\(636\) 83.5470 3.31285
\(637\) 0 0
\(638\) 25.2326 0.998967
\(639\) −24.3683 42.2072i −0.963996 1.66969i
\(640\) −8.44391 14.6253i −0.333775 0.578115i
\(641\) −18.5908 + 32.2003i −0.734293 + 1.27183i 0.220739 + 0.975333i \(0.429153\pi\)
−0.955033 + 0.296501i \(0.904180\pi\)
\(642\) 51.9397 2.04990
\(643\) −4.55189 + 7.88410i −0.179509 + 0.310918i −0.941712 0.336419i \(-0.890784\pi\)
0.762204 + 0.647337i \(0.224118\pi\)
\(644\) −15.3753 + 26.6307i −0.605870 + 1.04940i
\(645\) 1.80144 0.0709316
\(646\) −4.55783 + 7.89439i −0.179325 + 0.310601i
\(647\) 9.56118 + 16.5605i 0.375889 + 0.651059i 0.990460 0.137803i \(-0.0440041\pi\)
−0.614571 + 0.788862i \(0.710671\pi\)
\(648\) −2.60486 4.51175i −0.102329 0.177238i
\(649\) 0.792455 0.0311066
\(650\) 0 0
\(651\) 7.88525 0.309047
\(652\) −33.7843 58.5161i −1.32309 2.29167i
\(653\) −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
\(655\) −4.12676 −0.161246
\(656\) −0.725758 + 1.25705i −0.0283361 + 0.0490796i
\(657\) 9.27453 16.0640i 0.361834 0.626714i
\(658\) −44.9114 −1.75083
\(659\) 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
\(661\) −3.01379 5.22004i −0.117223 0.203036i 0.801443 0.598071i \(-0.204066\pi\)
−0.918666 + 0.395035i \(0.870732\pi\)
\(662\) −71.8604 −2.79294
\(663\) 0 0
\(664\) 28.4492 1.10404
\(665\) 5.46039 + 9.45767i 0.211745 + 0.366753i
\(666\) −4.71706 8.17018i −0.182782 0.316588i
\(667\) −18.0491 + 31.2620i −0.698865 + 1.21047i
\(668\) −60.8479 −2.35428
\(669\) 30.1614 52.2411i 1.16611 2.01976i
\(670\) 10.1003 17.4942i 0.390209 0.675861i
\(671\) 4.48990 0.173330
\(672\) 6.46481 11.1974i 0.249386 0.431948i
\(673\) −11.6784 20.2276i −0.450169 0.779715i 0.548227 0.836329i \(-0.315303\pi\)
−0.998396 + 0.0566140i \(0.981970\pi\)
\(674\) −14.6603 25.3923i −0.564692 0.978075i
\(675\) −5.62828 −0.216633
\(676\) 0 0
\(677\) −45.4042 −1.74503 −0.872513 0.488590i \(-0.837511\pi\)
−0.872513 + 0.488590i \(0.837511\pi\)
\(678\) −23.5901 40.8593i −0.905973 1.56919i
\(679\) 4.02148 + 6.96540i 0.154330 + 0.267308i
\(680\) 1.77124 3.06787i 0.0679239 0.117648i
\(681\) −44.3408 −1.69914
\(682\) 1.95360 3.38374i 0.0748073 0.129570i
\(683\) 12.7489 22.0817i 0.487823 0.844934i −0.512079 0.858938i \(-0.671125\pi\)
0.999902 + 0.0140045i \(0.00445791\pi\)
\(684\) 120.945 4.62445
\(685\) −10.0548 + 17.4155i −0.384175 + 0.665411i
\(686\) 24.6523 + 42.6991i 0.941230 + 1.63026i
\(687\) −10.7715 18.6567i −0.410957 0.711798i
\(688\) 3.45214 0.131612
\(689\) 0 0
\(690\) 26.9327 1.02531
\(691\) 3.29815 + 5.71257i 0.125468 + 0.217316i 0.921916 0.387391i \(-0.126624\pi\)
−0.796448 + 0.604707i \(0.793290\pi\)
\(692\) 51.4683 + 89.1457i 1.95653 + 3.38881i
\(693\) −5.08438 + 8.80641i −0.193140 + 0.334528i
\(694\) 4.74090 0.179962
\(695\) 10.4126 18.0352i 0.394974 0.684115i
\(696\) 74.2892 128.673i 2.81593 4.87733i
\(697\) 0.170754 0.00646778
\(698\) 12.8133 22.1933i 0.484990 0.840028i
\(699\) −26.9327 46.6487i −1.01869 1.76442i
\(700\) −4.02720 6.97531i −0.152214 0.263642i
\(701\) 29.2474 1.10466 0.552329 0.833626i \(-0.313739\pi\)
0.552329 + 0.833626i \(0.313739\pi\)
\(702\) 0 0
\(703\) 4.34174 0.163752
\(704\) 2.58966 + 4.48542i 0.0976015 + 0.169051i
\(705\) 13.3513 + 23.1252i 0.502841 + 0.870946i
\(706\) −0.998937 + 1.73021i −0.0375955 + 0.0651173i
\(707\) −29.0499 −1.09253
\(708\) 4.42792 7.66938i 0.166411 0.288233i
\(709\) −5.46673 + 9.46865i −0.205307 + 0.355603i −0.950231 0.311548i \(-0.899153\pi\)
0.744923 + 0.667150i \(0.232486\pi\)
\(710\) −24.3683 −0.914527
\(711\) 23.2566 40.2815i 0.872189 1.51068i
\(712\) 34.9608 + 60.5538i 1.31021 + 2.26935i
\(713\) 2.79486 + 4.84084i 0.104668 + 0.181291i
\(714\) −8.56490 −0.320533
\(715\) 0 0
\(716\) 16.0152 0.598516
\(717\) 18.0260 + 31.2220i 0.673194 + 1.16601i
\(718\) −10.1476 17.5762i −0.378706 0.655938i
\(719\) −8.02989 + 13.9082i −0.299464 + 0.518688i −0.976014 0.217710i \(-0.930141\pi\)
0.676549 + 0.736398i \(0.263475\pi\)
\(720\) −27.0370 −1.00761
\(721\) 12.8858 22.3189i 0.479893 0.831199i
\(722\) −17.2894 + 29.9461i −0.643444 + 1.11448i
\(723\) −73.2966 −2.72593
\(724\) 17.9416 31.0758i 0.666796 1.15492i
\(725\) −4.72756 8.18837i −0.175577 0.304108i
\(726\) −34.7655 60.2156i −1.29027 2.23481i
\(727\) 51.3754 1.90541 0.952704 0.303900i \(-0.0982889\pi\)
0.952704 + 0.303900i \(0.0982889\pi\)
\(728\) 0 0
\(729\) −43.0532 −1.59456
\(730\) −4.63726 8.03198i −0.171633 0.297277i
\(731\) −0.203052 0.351697i −0.00751016 0.0130080i
\(732\) 25.0877 43.4532i 0.927268 1.60608i
\(733\) −9.82358 −0.362842 −0.181421 0.983406i \(-0.558070\pi\)
−0.181421 + 0.983406i \(0.558070\pi\)
\(734\) 25.6120 44.3613i 0.945357 1.63741i
\(735\) 4.76346 8.25055i 0.175703 0.304326i
\(736\) 9.16560 0.337848
\(737\) −4.32824 + 7.49673i −0.159433 + 0.276146i
\(738\) −1.66867 2.89022i −0.0614246 0.106390i
\(739\) −24.5421 42.5082i −0.902797 1.56369i −0.823848 0.566811i \(-0.808177\pi\)
−0.0789487 0.996879i \(-0.525156\pi\)
\(740\) −3.20216 −0.117714
\(741\) 0 0
\(742\) −33.2386 −1.22023
\(743\) −20.4188 35.3663i −0.749091 1.29746i −0.948259 0.317499i \(-0.897157\pi\)
0.199167 0.979966i \(-0.436176\pi\)
\(744\) −11.5035 19.9247i −0.421739 0.730473i
\(745\) 6.68388 11.5768i 0.244878 0.424142i
\(746\) −44.4346 −1.62687
\(747\) −12.7715 + 22.1208i −0.467283 + 0.809358i
\(748\) −1.44050 + 2.49503i −0.0526700 + 0.0912272i
\(749\) −14.0276 −0.512557
\(750\) −3.52720 + 6.10929i −0.128795 + 0.223080i
\(751\) 1.36340 + 2.36148i 0.0497512 + 0.0861716i 0.889829 0.456295i \(-0.150824\pi\)
−0.840077 + 0.542467i \(0.817490\pi\)
\(752\) 25.5855 + 44.3154i 0.933006 + 1.61601i
\(753\) −21.5175 −0.784142
\(754\) 0 0
\(755\) −18.2984 −0.665946
\(756\) 22.6662 + 39.2590i 0.824362 + 1.42784i
\(757\) −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
\(759\) −11.5413 −0.418924
\(760\) 15.9319 27.5949i 0.577911 1.00097i
\(761\) 5.68445 9.84575i 0.206061 0.356908i −0.744409 0.667724i \(-0.767269\pi\)
0.950470 + 0.310815i \(0.100602\pi\)
\(762\) −10.5075 −0.380647
\(763\) −9.59843 + 16.6250i −0.347486 + 0.601864i
\(764\) 11.5055 + 19.9281i 0.416255 + 0.720975i
\(765\) 1.59030 + 2.75447i 0.0574972 + 0.0995882i
\(766\) −19.7275 −0.712784
\(767\) 0 0
\(768\) 91.7512 3.31078
\(769\) 10.5281 + 18.2352i 0.379654 + 0.657579i 0.991012 0.133775i \(-0.0427098\pi\)
−0.611358 + 0.791354i \(0.709377\pi\)
\(770\) 2.54219 + 4.40320i 0.0916142 + 0.158680i
\(771\) 0.474602 0.822034i 0.0170924 0.0296048i
\(772\) 51.3970 1.84982
\(773\) −7.04144 + 12.1961i −0.253263 + 0.438664i −0.964422 0.264367i \(-0.914837\pi\)
0.711159 + 0.703031i \(0.248170\pi\)
\(774\) −3.96859 + 6.87381i −0.142648 + 0.247074i
\(775\) −1.46410 −0.0525921
\(776\) 11.7336 20.3231i 0.421210 0.729558i
\(777\) 2.03971 + 3.53288i 0.0731741 + 0.126741i
\(778\) 11.4940 + 19.9081i 0.412078 + 0.713740i
\(779\) 1.53590 0.0550293
\(780\) 0 0
\(781\) 10.4425