Properties

Label 325.2.m.b.49.1
Level $325$
Weight $2$
Character 325.49
Analytic conductor $2.595$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.59513806569\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Root \(1.20036 + 0.747754i\) of defining polynomial
Character \(\chi\) \(=\) 325.49
Dual form 325.2.m.b.199.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.24775 - 2.16117i) q^{2} +(2.44811 - 1.41342i) q^{3} +(-2.11378 + 3.66117i) q^{4} +(-6.10929 - 3.52720i) q^{6} +(0.952606 - 1.64996i) q^{7} +5.55889 q^{8} +(2.49551 - 4.32235i) q^{9} +O(q^{10})\) \(q+(-1.24775 - 2.16117i) q^{2} +(2.44811 - 1.41342i) q^{3} +(-2.11378 + 3.66117i) q^{4} +(-6.10929 - 3.52720i) q^{6} +(0.952606 - 1.64996i) q^{7} +5.55889 q^{8} +(2.49551 - 4.32235i) q^{9} +(0.926118 - 0.534695i) q^{11} +11.9506i q^{12} +(-3.32235 - 1.40072i) q^{13} -4.75447 q^{14} +(-2.70857 - 4.69138i) q^{16} +(0.551886 + 0.318632i) q^{17} -12.4551 q^{18} +(-4.96410 - 2.86603i) q^{19} -5.38573i q^{21} +(-2.31114 - 1.33433i) q^{22} +(3.30636 - 1.90893i) q^{23} +(13.6088 - 7.85704i) q^{24} +(1.11827 + 8.92792i) q^{26} -5.62828i q^{27} +(4.02720 + 6.97531i) q^{28} +(4.72756 + 8.18837i) q^{29} +1.46410i q^{31} +(-1.20036 + 2.07908i) q^{32} +(1.51150 - 2.61799i) q^{33} -1.59030i q^{34} +(10.5499 + 18.2730i) q^{36} +(0.378725 + 0.655970i) q^{37} +14.3044i q^{38} +(-10.1133 + 1.26675i) q^{39} +(-0.232051 + 0.133975i) q^{41} +(-11.6395 + 6.72006i) q^{42} +(-0.551886 - 0.318632i) q^{43} +4.52091i q^{44} +(-8.25104 - 4.76374i) q^{46} +9.44613 q^{47} +(-13.2618 - 7.65668i) q^{48} +(1.68508 + 2.91865i) q^{49} +1.80144 q^{51} +(12.1510 - 9.20287i) q^{52} +6.99102i q^{53} +(-12.1637 + 7.02271i) q^{54} +(5.29543 - 9.17196i) q^{56} -16.2036 q^{57} +(11.7977 - 20.4341i) q^{58} +(0.641756 + 0.370518i) q^{59} +(-2.09928 + 3.63606i) q^{61} +(3.16418 - 1.82684i) q^{62} +(-4.75447 - 8.23499i) q^{63} -4.84325 q^{64} -7.54390 q^{66} +(-4.04739 - 7.01029i) q^{67} +(-2.33313 + 1.34703i) q^{68} +(5.39623 - 9.34654i) q^{69} +(8.45663 + 4.88244i) q^{71} +(13.8723 - 24.0274i) q^{72} -3.71649 q^{73} +(0.945110 - 1.63698i) q^{74} +(20.9860 - 12.1163i) q^{76} -2.03741i q^{77} +(15.3565 + 20.2760i) q^{78} +9.31937 q^{79} +(-0.468594 - 0.811629i) q^{81} +(0.579085 + 0.334335i) q^{82} -5.11778 q^{83} +(19.7181 + 11.3842i) q^{84} +1.59030i q^{86} +(23.1472 + 13.3640i) q^{87} +(5.14819 - 2.97231i) q^{88} +(10.8932 - 6.28917i) q^{89} +(-5.47602 + 4.14741i) q^{91} +16.1402i q^{92} +(2.06939 + 3.58429i) q^{93} +(-11.7864 - 20.4147i) q^{94} +6.78645i q^{96} +(2.11078 - 3.65597i) q^{97} +(4.20514 - 7.28351i) q^{98} -5.33734i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 18 q^{6} + 10 q^{7} + 12 q^{8} + 4 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 18 q^{6} + 10 q^{7} + 12 q^{8} + 4 q^{9} + 8 q^{13} - 4 q^{14} - 2 q^{16} + 18 q^{17} - 40 q^{18} - 12 q^{19} + 6 q^{22} + 6 q^{23} + 12 q^{24} + 10 q^{26} + 8 q^{28} + 8 q^{29} - 4 q^{32} - 18 q^{33} + 20 q^{36} - 2 q^{37} + 12 q^{41} - 42 q^{42} - 18 q^{43} - 42 q^{46} - 16 q^{47} - 6 q^{48} - 12 q^{49} - 8 q^{51} + 16 q^{52} - 18 q^{54} + 12 q^{56} - 28 q^{57} + 22 q^{58} + 12 q^{59} - 28 q^{61} + 12 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} + 12 q^{68} + 16 q^{69} + 12 q^{72} - 16 q^{73} - 10 q^{74} + 54 q^{76} + 18 q^{78} + 16 q^{79} + 8 q^{81} - 6 q^{82} + 24 q^{83} + 30 q^{84} + 54 q^{87} + 42 q^{88} - 24 q^{89} + 28 q^{91} + 8 q^{93} - 32 q^{94} - 2 q^{97} + 24 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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 \(-0.510669\pi\)
\(3\) 2.44811 1.41342i 1.41342 0.816038i 0.417710 0.908580i \(-0.362833\pi\)
0.995709 + 0.0925423i \(0.0294993\pi\)
\(4\) −2.11378 + 3.66117i −1.05689 + 1.83059i
\(5\) 0 0
\(6\) −6.10929 3.52720i −2.49411 1.43997i
\(7\) 0.952606 1.64996i 0.360051 0.623627i −0.627918 0.778280i \(-0.716093\pi\)
0.987969 + 0.154653i \(0.0494259\pi\)
\(8\) 5.55889 1.96536
\(9\) 2.49551 4.32235i 0.831836 1.44078i
\(10\) 0 0
\(11\) 0.926118 0.534695i 0.279235 0.161217i −0.353842 0.935305i \(-0.615125\pi\)
0.633077 + 0.774089i \(0.281792\pi\)
\(12\) 11.9506i 3.44985i
\(13\) −3.32235 1.40072i −0.921453 0.388490i
\(14\) −4.75447 −1.27069
\(15\) 0 0
\(16\) −2.70857 4.69138i −0.677142 1.17284i
\(17\) 0.551886 + 0.318632i 0.133852 + 0.0772795i 0.565431 0.824796i \(-0.308710\pi\)
−0.431579 + 0.902075i \(0.642043\pi\)
\(18\) −12.4551 −2.93570
\(19\) −4.96410 2.86603i −1.13884 0.657511i −0.192699 0.981258i \(-0.561724\pi\)
−0.946144 + 0.323747i \(0.895057\pi\)
\(20\) 0 0
\(21\) 5.38573i 1.17526i
\(22\) −2.31114 1.33433i −0.492736 0.284481i
\(23\) 3.30636 1.90893i 0.689423 0.398039i −0.113973 0.993484i \(-0.536358\pi\)
0.803396 + 0.595445i \(0.203024\pi\)
\(24\) 13.6088 7.85704i 2.77788 1.60381i
\(25\) 0 0
\(26\) 1.11827 + 8.92792i 0.219311 + 1.75091i
\(27\) 5.62828i 1.08316i
\(28\) 4.02720 + 6.97531i 0.761069 + 1.31821i
\(29\) 4.72756 + 8.18837i 0.877886 + 1.52054i 0.853657 + 0.520836i \(0.174380\pi\)
0.0242288 + 0.999706i \(0.492287\pi\)
\(30\) 0 0
\(31\) 1.46410i 0.262960i 0.991319 + 0.131480i \(0.0419730\pi\)
−0.991319 + 0.131480i \(0.958027\pi\)
\(32\) −1.20036 + 2.07908i −0.212196 + 0.367534i
\(33\) 1.51150 2.61799i 0.263118 0.455733i
\(34\) 1.59030i 0.272733i
\(35\) 0 0
\(36\) 10.5499 + 18.2730i 1.75832 + 3.04550i
\(37\) 0.378725 + 0.655970i 0.0622619 + 0.107841i 0.895476 0.445110i \(-0.146835\pi\)
−0.833214 + 0.552950i \(0.813502\pi\)
\(38\) 14.3044i 2.32048i
\(39\) −10.1133 + 1.26675i −1.61942 + 0.202842i
\(40\) 0 0
\(41\) −0.232051 + 0.133975i −0.0362402 + 0.0209233i −0.518011 0.855374i \(-0.673327\pi\)
0.481770 + 0.876297i \(0.339994\pi\)
\(42\) −11.6395 + 6.72006i −1.79601 + 1.03693i
\(43\) −0.551886 0.318632i −0.0841618 0.0485909i 0.457328 0.889298i \(-0.348806\pi\)
−0.541490 + 0.840707i \(0.682140\pi\)
\(44\) 4.52091i 0.681552i
\(45\) 0 0
\(46\) −8.25104 4.76374i −1.21655 0.702375i
\(47\) 9.44613 1.37786 0.688930 0.724828i \(-0.258081\pi\)
0.688930 + 0.724828i \(0.258081\pi\)
\(48\) −13.2618 7.65668i −1.91417 1.10515i
\(49\) 1.68508 + 2.91865i 0.240726 + 0.416950i
\(50\) 0 0
\(51\) 1.80144 0.252252
\(52\) 12.1510 9.20287i 1.68504 1.27621i
\(53\) 6.99102i 0.960290i 0.877189 + 0.480145i \(0.159416\pi\)
−0.877189 + 0.480145i \(0.840584\pi\)
\(54\) −12.1637 + 7.02271i −1.65527 + 0.955669i
\(55\) 0 0
\(56\) 5.29543 9.17196i 0.707632 1.22565i
\(57\) −16.2036 −2.14622
\(58\) 11.7977 20.4341i 1.54911 2.68313i
\(59\) 0.641756 + 0.370518i 0.0835495 + 0.0482373i 0.541193 0.840899i \(-0.317973\pi\)
−0.457643 + 0.889136i \(0.651306\pi\)
\(60\) 0 0
\(61\) −2.09928 + 3.63606i −0.268785 + 0.465550i −0.968548 0.248825i \(-0.919956\pi\)
0.699763 + 0.714375i \(0.253289\pi\)
\(62\) 3.16418 1.82684i 0.401851 0.232009i
\(63\) −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 \(0.997970\pi\)
\(68\) −2.33313 + 1.34703i −0.282934 + 0.163352i
\(69\) 5.39623 9.34654i 0.649629 1.12519i
\(70\) 0 0
\(71\) 8.45663 + 4.88244i 1.00362 + 0.579439i 0.909317 0.416105i \(-0.136605\pi\)
0.0943010 + 0.995544i \(0.469938\pi\)
\(72\) 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
\(75\) 0 0
\(76\) 20.9860 12.1163i 2.40726 1.38983i
\(77\) 2.03741i 0.232185i
\(78\) 15.3565 + 20.2760i 1.73879 + 2.29580i
\(79\) 9.31937 1.04851 0.524255 0.851561i \(-0.324344\pi\)
0.524255 + 0.851561i \(0.324344\pi\)
\(80\) 0 0
\(81\) −0.468594 0.811629i −0.0520660 0.0901809i
\(82\) 0.579085 + 0.334335i 0.0639492 + 0.0369211i
\(83\) −5.11778 −0.561749 −0.280875 0.959744i \(-0.590624\pi\)
−0.280875 + 0.959744i \(0.590624\pi\)
\(84\) 19.7181 + 11.3842i 2.15142 + 1.24212i
\(85\) 0 0
\(86\) 1.59030i 0.171486i
\(87\) 23.1472 + 13.3640i 2.48164 + 1.43278i
\(88\) 5.14819 2.97231i 0.548799 0.316849i
\(89\) 10.8932 6.28917i 1.15467 0.666650i 0.204651 0.978835i \(-0.434394\pi\)
0.950021 + 0.312185i \(0.101061\pi\)
\(90\) 0 0
\(91\) −5.47602 + 4.14741i −0.574043 + 0.434767i
\(92\) 16.1402i 1.68273i
\(93\) 2.06939 + 3.58429i 0.214586 + 0.371673i
\(94\) −11.7864 20.4147i −1.21568 2.10562i
\(95\) 0 0
\(96\) 6.78645i 0.692639i
\(97\) 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
\(99\) 5.33734i 0.536423i
\(100\) 0 0
\(101\) −7.62379 13.2048i −0.758595 1.31393i −0.943567 0.331181i \(-0.892553\pi\)
0.184972 0.982744i \(-0.440781\pi\)
\(102\) −2.24775 3.89322i −0.222561 0.385487i
\(103\) 13.5269i 1.33285i −0.745574 0.666423i \(-0.767824\pi\)
0.745574 0.666423i \(-0.232176\pi\)
\(104\) −18.4686 7.78645i −1.81099 0.763524i
\(105\) 0 0
\(106\) 15.1088 8.72307i 1.46750 0.847259i
\(107\) −6.37632 + 3.68137i −0.616422 + 0.355891i −0.775475 0.631379i \(-0.782489\pi\)
0.159053 + 0.987270i \(0.449156\pi\)
\(108\) 20.6061 + 11.8969i 1.98282 + 1.14478i
\(109\) 10.0760i 0.965103i 0.875868 + 0.482551i \(0.160290\pi\)
−0.875868 + 0.482551i \(0.839710\pi\)
\(110\) 0 0
\(111\) 1.85432 + 1.07059i 0.176004 + 0.101616i
\(112\) −10.3208 −0.975223
\(113\) −5.79203 3.34403i −0.544868 0.314580i 0.202181 0.979348i \(-0.435197\pi\)
−0.747050 + 0.664768i \(0.768530\pi\)
\(114\) 20.2181 + 35.0187i 1.89360 + 3.27981i
\(115\) 0 0
\(116\) −39.9721 −3.71131
\(117\) −14.3453 + 10.8648i −1.32623 + 1.00445i
\(118\) 1.84926i 0.170238i
\(119\) 1.05146 0.607061i 0.0963872 0.0556492i
\(120\) 0 0
\(121\) −4.92820 + 8.53590i −0.448018 + 0.775991i
\(122\) 10.4775 0.948592
\(123\) −0.378725 + 0.655970i −0.0341484 + 0.0591468i
\(124\) −5.36033 3.09479i −0.481372 0.277920i
\(125\) 0 0
\(126\) −11.8648 + 20.5505i −1.05700 + 1.83078i
\(127\) −1.28994 + 0.744750i −0.114464 + 0.0660859i −0.556139 0.831089i \(-0.687718\pi\)
0.441675 + 0.897175i \(0.354384\pi\)
\(128\) 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
\(133\) −9.45767 + 5.46039i −0.820084 + 0.473476i
\(134\) −10.1003 + 17.4942i −0.872533 + 1.51127i
\(135\) 0 0
\(136\) 3.06787 + 1.77124i 0.263068 + 0.151882i
\(137\) −10.0548 + 17.4155i −0.859041 + 1.48790i 0.0138029 + 0.999905i \(0.495606\pi\)
−0.872844 + 0.487999i \(0.837727\pi\)
\(138\) −26.9327 −2.29266
\(139\) 10.4126 18.0352i 0.883189 1.52973i 0.0354130 0.999373i \(-0.488725\pi\)
0.847776 0.530355i \(-0.177941\pi\)
\(140\) 0 0
\(141\) 23.1252 13.3513i 1.94749 1.12439i
\(142\) 24.3683i 2.04494i
\(143\) −3.82584 + 0.479208i −0.319933 + 0.0400734i
\(144\) −27.0370 −2.25308
\(145\) 0 0
\(146\) 4.63726 + 8.03198i 0.383783 + 0.664731i
\(147\) 8.25055 + 4.76346i 0.680494 + 0.392883i
\(148\) −3.20216 −0.263216
\(149\) −11.5768 6.68388i −0.948410 0.547565i −0.0558233 0.998441i \(-0.517778\pi\)
−0.892587 + 0.450876i \(0.851112\pi\)
\(150\) 0 0
\(151\) 18.2984i 1.48910i 0.667567 + 0.744550i \(0.267336\pi\)
−0.667567 + 0.744550i \(0.732664\pi\)
\(152\) −27.5949 15.9319i −2.23824 1.29225i
\(153\) 2.75447 1.59030i 0.222686 0.128568i
\(154\) −4.40320 + 2.54219i −0.354820 + 0.204856i
\(155\) 0 0
\(156\) 16.7395 39.7041i 1.34023 3.17887i
\(157\) 2.42229i 0.193320i 0.995317 + 0.0966599i \(0.0308159\pi\)
−0.995317 + 0.0966599i \(0.969184\pi\)
\(158\) −11.6283 20.1408i −0.925096 1.60231i
\(159\) 9.88124 + 17.1148i 0.783633 + 1.35729i
\(160\) 0 0
\(161\) 7.27382i 0.573258i
\(162\) −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 \(0.951383\pi\)
\(164\) 1.13277i 0.0884545i
\(165\) 0 0
\(166\) 6.38573 + 11.0604i 0.495629 + 0.858454i
\(167\) −7.19658 12.4648i −0.556888 0.964558i −0.997754 0.0669853i \(-0.978662\pi\)
0.440866 0.897573i \(-0.354671\pi\)
\(168\) 29.9387i 2.30982i
\(169\) 9.07597 + 9.30735i 0.698151 + 0.715950i
\(170\) 0 0
\(171\) −24.7759 + 14.3044i −1.89466 + 1.09388i
\(172\) 2.33313 1.34703i 0.177900 0.102710i
\(173\) 21.0868 + 12.1745i 1.60320 + 0.925608i 0.990842 + 0.135027i \(0.0431121\pi\)
0.612358 + 0.790581i \(0.290221\pi\)
\(174\) 66.7001i 5.05653i
\(175\) 0 0
\(176\) −5.01691 2.89651i −0.378164 0.218333i
\(177\) 2.09479 0.157454
\(178\) −27.1840 15.6947i −2.03752 1.17636i
\(179\) −1.89414 3.28075i −0.141575 0.245215i 0.786515 0.617571i \(-0.211883\pi\)
−0.928090 + 0.372356i \(0.878550\pi\)
\(180\) 0 0
\(181\) 8.48794 0.630904 0.315452 0.948942i \(-0.397844\pi\)
0.315452 + 0.948942i \(0.397844\pi\)
\(182\) 15.7960 + 6.65968i 1.17088 + 0.493649i
\(183\) 11.8687i 0.877356i
\(184\) 18.3797 10.6115i 1.35497 0.782291i
\(185\) 0 0
\(186\) 5.16418 8.94462i 0.378656 0.655851i
\(187\) 0.681482 0.0498349
\(188\) −19.9670 + 34.5839i −1.45625 + 2.52229i
\(189\) −9.28645 5.36153i −0.675490 0.389994i
\(190\) 0 0
\(191\) 2.72155 4.71386i 0.196924 0.341083i −0.750605 0.660751i \(-0.770238\pi\)
0.947530 + 0.319668i \(0.103571\pi\)
\(192\) −11.8568 + 6.84555i −0.855693 + 0.494035i
\(193\) −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 \(0.783483\pi\)
\(198\) −11.5349 + 6.65968i −0.819751 + 0.473283i
\(199\) −10.4186 + 18.0456i −0.738558 + 1.27922i 0.214586 + 0.976705i \(0.431160\pi\)
−0.953144 + 0.302516i \(0.902174\pi\)
\(200\) 0 0
\(201\) −19.8170 11.4413i −1.39778 0.807009i
\(202\) −19.0252 + 32.9526i −1.33861 + 2.31854i
\(203\) 18.0140 1.26434
\(204\) −3.80785 + 6.59538i −0.266603 + 0.461769i
\(205\) 0 0
\(206\) −29.2340 + 16.8783i −2.03683 + 1.17596i
\(207\) 19.0550i 1.32441i
\(208\) 2.42749 + 19.3803i 0.168316 + 1.34378i
\(209\) −6.12979 −0.424007
\(210\) 0 0
\(211\) 5.32684 + 9.22635i 0.366715 + 0.635168i 0.989050 0.147583i \(-0.0471492\pi\)
−0.622335 + 0.782751i \(0.713816\pi\)
\(212\) −25.5953 14.7775i −1.75789 1.01492i
\(213\) 27.6037 1.89138
\(214\) 15.9121 + 9.18688i 1.08773 + 0.628002i
\(215\) 0 0
\(216\) 31.2870i 2.12881i
\(217\) 2.41571 + 1.39471i 0.163989 + 0.0946792i
\(218\) 21.7759 12.5723i 1.47485 0.851505i
\(219\) −9.09839 + 5.25296i −0.614812 + 0.354962i
\(220\) 0 0
\(221\) −1.38724 1.83164i −0.0933161 0.123210i
\(222\) 5.34335i 0.358622i
\(223\) 10.6697 + 18.4804i 0.714494 + 1.23754i 0.963155 + 0.268949i \(0.0866762\pi\)
−0.248661 + 0.968591i \(0.579990\pi\)
\(224\) 2.28694 + 3.96110i 0.152803 + 0.264662i
\(225\) 0 0
\(226\) 16.6901i 1.11021i
\(227\) −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
\(229\) 7.62085i 0.503600i 0.967779 + 0.251800i \(0.0810225\pi\)
−0.967779 + 0.251800i \(0.918977\pi\)
\(230\) 0 0
\(231\) −2.87972 4.98782i −0.189472 0.328175i
\(232\) 26.2800 + 45.5182i 1.72536 + 2.98842i
\(233\) 19.0550i 1.24833i −0.781292 0.624166i \(-0.785439\pi\)
0.781292 0.624166i \(-0.214561\pi\)
\(234\) 41.3802 + 17.4461i 2.70511 + 1.14049i
\(235\) 0 0
\(236\) −2.71306 + 1.56639i −0.176605 + 0.101963i
\(237\) 22.8149 13.1722i 1.48199 0.855625i
\(238\) −2.62393 1.51493i −0.170084 0.0981980i
\(239\) 12.7535i 0.824954i 0.910968 + 0.412477i \(0.135336\pi\)
−0.910968 + 0.412477i \(0.864664\pi\)
\(240\) 0 0
\(241\) −22.4550 12.9644i −1.44646 0.835111i −0.448187 0.893940i \(-0.647930\pi\)
−0.998268 + 0.0588285i \(0.981263\pi\)
\(242\) 24.5967 1.58114
\(243\) 12.3284 + 7.11778i 0.790864 + 0.456606i
\(244\) −8.87483 15.3717i −0.568153 0.984069i
\(245\) 0 0
\(246\) 1.89022 0.120516
\(247\) 12.4780 + 16.4752i 0.793954 + 1.04829i
\(248\) 8.13878i 0.516813i
\(249\) −12.5289 + 7.23357i −0.793987 + 0.458409i
\(250\) 0 0
\(251\) 3.80593 6.59207i 0.240228 0.416088i −0.720551 0.693402i \(-0.756111\pi\)
0.960779 + 0.277314i \(0.0894444\pi\)
\(252\) 40.1996 2.53234
\(253\) 2.04139 3.53578i 0.128341 0.222293i
\(254\) 3.21907 + 1.85853i 0.201982 + 0.116614i
\(255\) 0 0
\(256\) 16.2286 28.1087i 1.01429 1.75680i
\(257\) −0.290796 + 0.167891i −0.0181394 + 0.0104728i −0.509042 0.860742i \(-0.670000\pi\)
0.490903 + 0.871214i \(0.336667\pi\)
\(258\) 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
\(263\) 4.65566 2.68795i 0.287080 0.165746i −0.349544 0.936920i \(-0.613664\pi\)
0.636624 + 0.771174i \(0.280330\pi\)
\(264\) 8.40224 14.5531i 0.517122 0.895681i
\(265\) 0 0
\(266\) 23.6017 + 13.6264i 1.44711 + 0.835491i
\(267\) 17.7785 30.7932i 1.08802 1.88451i
\(268\) 34.2212 2.09039
\(269\) −0.655192 + 1.13483i −0.0399478 + 0.0691916i −0.885308 0.465005i \(-0.846052\pi\)
0.845360 + 0.534197i \(0.179386\pi\)
\(270\) 0 0
\(271\) −10.0851 + 5.82266i −0.612629 + 0.353701i −0.773994 0.633194i \(-0.781744\pi\)
0.161365 + 0.986895i \(0.448410\pi\)
\(272\) 3.45214i 0.209317i
\(273\) −7.54390 + 17.8933i −0.456577 + 1.08295i
\(274\) 50.1838 3.03171
\(275\) 0 0
\(276\) 22.8129 + 39.5130i 1.37317 + 2.37841i
\(277\) −17.5943 10.1581i −1.05714 0.610338i −0.132498 0.991183i \(-0.542300\pi\)
−0.924639 + 0.380845i \(0.875633\pi\)
\(278\) −51.9697 −3.11693
\(279\) 6.32835 + 3.65368i 0.378869 + 0.218740i
\(280\) 0 0
\(281\) 11.8744i 0.708366i −0.935176 0.354183i \(-0.884759\pi\)
0.935176 0.354183i \(-0.115241\pi\)
\(282\) −57.7091 33.3184i −3.43653 1.98408i
\(283\) −19.6173 + 11.3261i −1.16613 + 0.673264i −0.952765 0.303709i \(-0.901775\pi\)
−0.213363 + 0.976973i \(0.568442\pi\)
\(284\) −35.7509 + 20.6408i −2.12143 + 1.22481i
\(285\) 0 0
\(286\) 5.80936 + 7.67038i 0.343515 + 0.453559i
\(287\) 0.510500i 0.0301339i
\(288\) 5.99102 + 10.3767i 0.353024 + 0.611455i
\(289\) −8.29695 14.3707i −0.488056 0.845337i
\(290\) 0 0
\(291\) 11.9336i 0.699562i
\(292\) 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 \(0.983696\pi\)
\(294\) 23.7745i 1.38656i
\(295\) 0 0
\(296\) 2.10529 + 3.64647i 0.122367 + 0.211946i
\(297\) −3.00941 5.21245i −0.174624 0.302457i
\(298\) 33.3593i 1.93245i
\(299\) −13.6587 + 1.71083i −0.789905 + 0.0989400i
\(300\) 0 0
\(301\) −1.05146 + 0.607061i −0.0606052 + 0.0349904i
\(302\) 39.5459 22.8319i 2.27561 1.31383i
\(303\) −37.3278 21.5512i −2.14443 1.23808i
\(304\) 31.0513i 1.78091i
\(305\) 0 0
\(306\) −6.87381 3.96859i −0.392949 0.226869i
\(307\) −3.14776 −0.179652 −0.0898262 0.995957i \(-0.528631\pi\)
−0.0898262 + 0.995957i \(0.528631\pi\)
\(308\) 7.45932 + 4.30664i 0.425034 + 0.245394i
\(309\) −19.1192 33.1154i −1.08765 1.88387i
\(310\) 0 0
\(311\) 3.18059 0.180355 0.0901774 0.995926i \(-0.471257\pi\)
0.0901774 + 0.995926i \(0.471257\pi\)
\(312\) −56.2186 + 7.04170i −3.18275 + 0.398658i
\(313\) 35.3533i 1.99829i −0.0413596 0.999144i \(-0.513169\pi\)
0.0413596 0.999144i \(-0.486831\pi\)
\(314\) 5.23499 3.02242i 0.295427 0.170565i
\(315\) 0 0
\(316\) −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
\(319\) 8.75656 + 5.05560i 0.490273 + 0.283059i
\(320\) 0 0
\(321\) −10.4066 + 18.0248i −0.580842 + 1.00605i
\(322\) −15.7200 + 9.07594i −0.876041 + 0.505782i
\(323\) −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
\(328\) −1.28994 + 0.744750i −0.0712253 + 0.0411219i
\(329\) 8.99844 15.5858i 0.496100 0.859271i
\(330\) 0 0
\(331\) −24.9380 14.3980i −1.37072 0.791383i −0.379698 0.925110i \(-0.623972\pi\)
−0.991018 + 0.133727i \(0.957305\pi\)
\(332\) 10.8179 18.7371i 0.593707 1.02833i
\(333\) 3.78044 0.207167
\(334\) −17.9591 + 31.1061i −0.982679 + 1.70205i
\(335\) 0 0
\(336\) −25.2665 + 14.5876i −1.37840 + 0.795819i
\(337\) 11.7493i 0.640026i −0.947413 0.320013i \(-0.896313\pi\)
0.947413 0.320013i \(-0.103687\pi\)
\(338\) 8.79023 31.2280i 0.478125 1.69858i
\(339\) −18.9061 −1.02684
\(340\) 0 0
\(341\) 0.782847 + 1.35593i 0.0423936 + 0.0734278i
\(342\) 61.8285 + 35.6967i 3.34330 + 1.93026i
\(343\) 19.7574 1.06680
\(344\) −3.06787 1.77124i −0.165409 0.0954987i
\(345\) 0 0
\(346\) 60.7630i 3.26664i
\(347\) −1.64525 0.949887i −0.0883218 0.0509926i 0.455189 0.890395i \(-0.349572\pi\)
−0.543510 + 0.839402i \(0.682905\pi\)
\(348\) −97.8562 + 56.4973i −5.24564 + 3.02857i
\(349\) 8.89329 5.13454i 0.476047 0.274846i −0.242721 0.970096i \(-0.578040\pi\)
0.718768 + 0.695250i \(0.244707\pi\)
\(350\) 0 0
\(351\) −7.88364 + 18.6991i −0.420798 + 0.998084i
\(352\) 2.56730i 0.136838i
\(353\) 0.400294 + 0.693330i 0.0213055 + 0.0369022i 0.876482 0.481435i \(-0.159884\pi\)
−0.855176 + 0.518338i \(0.826551\pi\)
\(354\) −2.61378 4.52720i −0.138921 0.240618i
\(355\) 0 0
\(356\) 53.1756i 2.81830i
\(357\) 1.71606 2.97231i 0.0908237 0.157311i
\(358\) −4.72685 + 8.18714i −0.249822 + 0.432704i
\(359\) 8.13272i 0.429228i −0.976699 0.214614i \(-0.931151\pi\)
0.976699 0.214614i \(-0.0688494\pi\)
\(360\) 0 0
\(361\) 6.92820 + 12.0000i 0.364642 + 0.631579i
\(362\) −10.5909 18.3439i −0.556643 0.964135i
\(363\) 27.8625i 1.46240i
\(364\) −3.60929 28.8154i −0.189178 1.51034i
\(365\) 0 0
\(366\) 25.6502 14.8092i 1.34076 0.774087i
\(367\) −17.7765 + 10.2632i −0.927924 + 0.535737i −0.886154 0.463390i \(-0.846633\pi\)
−0.0417696 + 0.999127i \(0.513300\pi\)
\(368\) −17.9110 10.3409i −0.933675 0.539057i
\(369\) 1.33734i 0.0696191i
\(370\) 0 0
\(371\) 11.5349 + 6.65968i 0.598863 + 0.345754i
\(372\) −17.4969 −0.907173
\(373\) −15.4203 8.90292i −0.798433 0.460976i 0.0444897 0.999010i \(-0.485834\pi\)
−0.842923 + 0.538034i \(0.819167\pi\)
\(374\) −0.850322 1.47280i −0.0439691 0.0761568i
\(375\) 0 0
\(376\) 52.5100 2.70800
\(377\) −4.23697 33.8266i −0.218215 1.74216i
\(378\) 26.7595i 1.37636i
\(379\) 1.77150 1.02277i 0.0909956 0.0525363i −0.453812 0.891098i \(-0.649936\pi\)
0.544807 + 0.838561i \(0.316603\pi\)
\(380\) 0 0
\(381\) −2.10529 + 3.64647i −0.107857 + 0.186814i
\(382\) −13.5833 −0.694982
\(383\) −3.95261 + 6.84611i −0.201969 + 0.349820i −0.949163 0.314786i \(-0.898067\pi\)
0.747194 + 0.664606i \(0.231401\pi\)
\(384\) 41.3433 + 23.8696i 2.10979 + 1.21809i
\(385\) 0 0
\(386\) −15.1697 + 26.2747i −0.772117 + 1.33735i
\(387\) −2.75447 + 1.59030i −0.140018 + 0.0808393i
\(388\) 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
\(393\) 10.1028 5.83285i 0.509618 0.294228i
\(394\) 5.46304 9.46226i 0.275224 0.476702i
\(395\) 0 0
\(396\) 19.5409 + 11.2820i 0.981968 + 0.566940i
\(397\) −3.17719 + 5.50305i −0.159458 + 0.276190i −0.934674 0.355507i \(-0.884308\pi\)
0.775215 + 0.631697i \(0.217641\pi\)
\(398\) 51.9996 2.60651
\(399\) −15.4356 + 26.7353i −0.772748 + 1.33844i
\(400\) 0 0
\(401\) 3.61063 2.08460i 0.180306 0.104100i −0.407130 0.913370i \(-0.633470\pi\)
0.587437 + 0.809270i \(0.300137\pi\)
\(402\) 57.1038i 2.84808i
\(403\) 2.05080 4.86425i 0.102157 0.242306i
\(404\) 64.4600 3.20701
\(405\) 0 0
\(406\) −22.4770 38.9314i −1.11552 1.93213i
\(407\) 0.701487 + 0.405004i 0.0347714 + 0.0200753i
\(408\) 10.0140 0.495767
\(409\) −8.80580 5.08403i −0.435419 0.251389i 0.266234 0.963909i \(-0.414221\pi\)
−0.701652 + 0.712519i \(0.747554\pi\)
\(410\) 0 0
\(411\) 56.8467i 2.80404i
\(412\) 49.5244 + 28.5929i 2.43989 + 1.40867i
\(413\) 1.22268 0.705915i 0.0601642 0.0347358i
\(414\) −41.1811 + 23.7759i −2.02394 + 1.16852i
\(415\) 0 0
\(416\) 6.90023 5.22607i 0.338311 0.256229i
\(417\) 58.8697i 2.88286i
\(418\) 7.64847 + 13.2475i 0.374099 + 0.647959i
\(419\) 14.2954 + 24.7604i 0.698378 + 1.20963i 0.969029 + 0.246948i \(0.0794277\pi\)
−0.270651 + 0.962677i \(0.587239\pi\)
\(420\) 0 0
\(421\) 2.01797i 0.0983498i −0.998790 0.0491749i \(-0.984341\pi\)
0.998790 0.0491749i \(-0.0156592\pi\)
\(422\) 13.2932 23.0244i 0.647101 1.12081i
\(423\) 23.5729 40.8295i 1.14615 1.98520i
\(424\) 38.8623i 1.88732i
\(425\) 0 0
\(426\) −34.4427 59.6564i −1.66875 2.89036i
\(427\) 3.99957 + 6.92747i 0.193553 + 0.335244i
\(428\) 31.1264i 1.50455i
\(429\) −8.68878 + 6.58068i −0.419498 + 0.317718i
\(430\) 0 0
\(431\) 17.8508 10.3061i 0.859842 0.496430i −0.00411765 0.999992i \(-0.501311\pi\)
0.863959 + 0.503562i \(0.167977\pi\)
\(432\) −26.4044 + 15.2446i −1.27038 + 0.733455i
\(433\) −25.4920 14.7178i −1.22507 0.707292i −0.259072 0.965858i \(-0.583417\pi\)
−0.965994 + 0.258566i \(0.916750\pi\)
\(434\) 6.96103i 0.334140i
\(435\) 0 0
\(436\) −36.8899 21.2984i −1.76670 1.02001i
\(437\) −21.8841 −1.04686
\(438\) 22.7051 + 13.1088i 1.08489 + 0.626362i
\(439\) −8.47602 14.6809i −0.404538 0.700681i 0.589729 0.807601i \(-0.299235\pi\)
−0.994268 + 0.106920i \(0.965901\pi\)
\(440\) 0 0
\(441\) 16.8205 0.800978
\(442\) −2.22756 + 5.28351i −0.105954 + 0.251311i
\(443\) 24.1399i 1.14692i 0.819233 + 0.573461i \(0.194400\pi\)
−0.819233 + 0.573461i \(0.805600\pi\)
\(444\) −7.83925 + 4.52599i −0.372034 + 0.214794i
\(445\) 0 0
\(446\) 26.6262 46.1180i 1.26079 2.18375i
\(447\) −37.7885 −1.78733
\(448\) −4.61371 + 7.99118i −0.217977 + 0.377548i
\(449\) −18.0679 10.4315i −0.852676 0.492293i 0.00887706 0.999961i \(-0.497174\pi\)
−0.861553 + 0.507668i \(0.830508\pi\)
\(450\) 0 0
\(451\) −0.143271 + 0.248153i −0.00674637 + 0.0116851i
\(452\) 24.4861 14.1371i 1.15173 0.664952i
\(453\) 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 \(0.579803\pi\)
\(458\) 16.4700 9.50894i 0.769591 0.444324i
\(459\) 1.79335 3.10617i 0.0837063 0.144984i
\(460\) 0 0
\(461\) 4.05146 + 2.33911i 0.188695 + 0.108943i 0.591372 0.806399i \(-0.298587\pi\)
−0.402676 + 0.915342i \(0.631920\pi\)
\(462\) −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
\(465\) 0 0
\(466\) −41.1811 + 23.7759i −1.90768 + 1.10140i
\(467\) 6.98506i 0.323230i 0.986854 + 0.161615i \(0.0516703\pi\)
−0.986854 + 0.161615i \(0.948330\pi\)
\(468\) −9.45512 75.4866i −0.437063 3.48937i
\(469\) −15.4223 −0.712135
\(470\) 0 0
\(471\) 3.42371 + 5.93004i 0.157756 + 0.273242i
\(472\) 3.56745 + 2.05967i 0.164205 + 0.0948039i
\(473\) −0.681482 −0.0313346
\(474\) −56.9347 32.8713i −2.61510 1.50983i
\(475\) 0 0
\(476\) 5.13277i 0.235260i
\(477\) 30.2176 + 17.4461i 1.38357 + 0.798804i
\(478\) 27.5625 15.9132i 1.26068 0.727853i
\(479\) 14.1065 8.14438i 0.644542 0.372126i −0.141820 0.989892i \(-0.545296\pi\)
0.786362 + 0.617766i \(0.211962\pi\)
\(480\) 0 0
\(481\) −0.339423 2.70985i −0.0154764 0.123558i
\(482\) 64.7056i 2.94726i
\(483\) −10.2810 17.8071i −0.467800 0.810253i
\(484\) −20.8343 36.0860i −0.947012 1.64027i
\(485\) 0 0
\(486\) 35.5249i 1.61144i
\(487\) −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
\(489\) 45.1810i 2.04316i
\(490\) 0 0
\(491\) −7.89916 13.6818i −0.356484 0.617449i 0.630887 0.775875i \(-0.282691\pi\)
−0.987371 + 0.158426i \(0.949358\pi\)
\(492\) −1.60108 2.77315i −0.0721823 0.125023i
\(493\) 6.02540i 0.271370i
\(494\) 20.0364 47.5241i 0.901481 2.13821i
\(495\) 0 0
\(496\) 6.86865 3.96562i 0.308411 0.178061i
\(497\) 16.1117 9.30208i 0.722708 0.417255i
\(498\) 31.2660 + 18.0514i 1.40106 + 0.808903i
\(499\) 1.24651i 0.0558016i 0.999611 + 0.0279008i \(0.00888226\pi\)
−0.999611 + 0.0279008i \(0.991118\pi\)
\(500\) 0 0
\(501\) −35.2361 20.3436i −1.57423 0.908883i
\(502\) −18.9955 −0.847809
\(503\) −6.62808 3.82672i −0.295532 0.170625i 0.344902 0.938639i \(-0.387912\pi\)
−0.640434 + 0.768013i \(0.721245\pi\)
\(504\) −26.4296 45.7774i −1.17727 2.03909i
\(505\) 0 0
\(506\) −10.1886 −0.452938
\(507\) 35.3742 + 9.95732i 1.57102 + 0.442220i
\(508\) 6.29695i 0.279382i
\(509\) 22.2777 12.8621i 0.987444 0.570101i 0.0829345 0.996555i \(-0.473571\pi\)
0.904509 + 0.426454i \(0.140237\pi\)
\(510\) 0 0
\(511\) −3.54035 + 6.13207i −0.156616 + 0.271267i
\(512\) −47.2215 −2.08691
\(513\) −16.1308 + 27.9393i −0.712192 + 1.23355i
\(514\) 0.725685 + 0.418974i 0.0320086 + 0.0184802i
\(515\) 0 0
\(516\) 3.80785 6.59538i 0.167631 0.290346i
\(517\) 8.74824 5.05080i 0.384747 0.222134i
\(518\) −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
\(523\) −3.41000 + 1.96876i −0.149109 + 0.0860880i −0.572698 0.819766i \(-0.694103\pi\)
0.423589 + 0.905854i \(0.360770\pi\)
\(524\) −8.72307 + 15.1088i −0.381069 + 0.660031i
\(525\) 0 0
\(526\) −11.6182 6.70779i −0.506579 0.292473i
\(527\) −0.466509 + 0.808017i −0.0203215 + 0.0351978i
\(528\) −16.3759 −0.712672
\(529\) −4.21200 + 7.29539i −0.183130 + 0.317191i
\(530\) 0 0
\(531\) 3.20301 1.84926i 0.138999 0.0802510i
\(532\) 46.1682i 2.00165i
\(533\) 0.958614 0.120072i 0.0415222 0.00520088i
\(534\) −88.7326 −3.83983
\(535\) 0 0
\(536\) −22.4990 38.9694i −0.971809 1.68322i
\(537\) −9.27415 5.35444i −0.400209 0.231061i
\(538\) 3.27007 0.140983
\(539\) 3.12117 + 1.80201i 0.134438 + 0.0776180i
\(540\) 0 0
\(541\) 15.8881i 0.683083i −0.939867 0.341541i \(-0.889051\pi\)
0.939867 0.341541i \(-0.110949\pi\)
\(542\) 25.1675 + 14.5305i 1.08104 + 0.624138i
\(543\) 20.7795 11.9970i 0.891732 0.514842i
\(544\) −1.32492 + 0.764945i −0.0568057 + 0.0327968i
\(545\) 0 0
\(546\) 48.0833 6.02271i 2.05778 0.257748i
\(547\) 6.56107i 0.280531i −0.990114 0.140266i \(-0.955204\pi\)
0.990114 0.140266i \(-0.0447956\pi\)
\(548\) −42.5074 73.6249i −1.81582 3.14510i
\(549\) 10.4775 + 18.1476i 0.447170 + 0.774522i
\(550\) 0 0
\(551\) 54.1972i 2.30888i
\(552\) 29.9970 51.9564i 1.27676 2.21141i
\(553\) 8.87769 15.3766i 0.377518 0.653880i
\(554\) 50.6990i 2.15399i
\(555\) 0 0
\(556\) 44.0200 + 76.2450i 1.86687 + 3.23351i
\(557\) 3.92503 + 6.79835i 0.166309 + 0.288055i 0.937119 0.349009i \(-0.113482\pi\)
−0.770810 + 0.637065i \(0.780148\pi\)
\(558\) 18.2356i 0.771973i
\(559\) 1.38724 + 1.83164i 0.0586741 + 0.0774702i
\(560\) 0 0
\(561\) 1.66835 0.963220i 0.0704377 0.0406672i
\(562\) −25.6626 + 14.8163i −1.08251 + 0.624988i
\(563\) 13.4749 + 7.77976i 0.567901 + 0.327878i 0.756310 0.654213i \(-0.227000\pi\)
−0.188410 + 0.982091i \(0.560333\pi\)
\(564\) 112.887i 4.75341i
\(565\) 0 0
\(566\) 48.9552 + 28.2643i 2.05774 + 1.18804i
\(567\) −1.78554 −0.0749857
\(568\) 47.0095 + 27.1409i 1.97247 + 1.13881i
\(569\) −1.73957 3.01303i −0.0729267 0.126313i 0.827256 0.561825i \(-0.189901\pi\)
−0.900183 + 0.435512i \(0.856567\pi\)
\(570\) 0 0
\(571\) 21.5118 0.900240 0.450120 0.892968i \(-0.351381\pi\)
0.450120 + 0.892968i \(0.351381\pi\)
\(572\) 6.33252 15.0200i 0.264776 0.628018i
\(573\) 15.3868i 0.642791i
\(574\) 1.10328 0.636978i 0.0460500 0.0265870i
\(575\) 0 0
\(576\) −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
\(579\) −29.7632 17.1838i −1.23692 0.714134i
\(580\) 0 0
\(581\) −4.87523 + 8.44414i −0.202259 + 0.350322i
\(582\) −25.7907 + 14.8902i −1.06906 + 0.617221i
\(583\) 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 \(0.667962\pi\)
\(588\) −34.8797 + 20.1378i −1.43841 + 0.830469i
\(589\) 4.19615 7.26795i 0.172899 0.299471i
\(590\) 0 0
\(591\) 10.7186 + 6.18837i 0.440903 + 0.254556i
\(592\) 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 0
\(596\) 48.9417 28.2565i 2.00473 1.15743i
\(597\) 58.9037i 2.41077i
\(598\) 20.7401 + 27.3842i 0.848128 + 1.11982i
\(599\) 11.4270 0.466896 0.233448 0.972369i \(-0.424999\pi\)
0.233448 + 0.972369i \(0.424999\pi\)
\(600\) 0 0
\(601\) 18.0215 + 31.2142i 0.735114 + 1.27325i 0.954674 + 0.297655i \(0.0962045\pi\)
−0.219560 + 0.975599i \(0.570462\pi\)
\(602\) 2.62393 + 1.51493i 0.106943 + 0.0617437i
\(603\) −40.4012 −1.64526
\(604\) −66.9935 38.6787i −2.72593 1.57381i
\(605\) 0 0
\(606\) 107.562i 4.36942i
\(607\) −34.5464 19.9454i −1.40219 0.809557i −0.407576 0.913171i \(-0.633626\pi\)
−0.994618 + 0.103614i \(0.966959\pi\)
\(608\) 11.9174 6.88052i 0.483315 0.279042i
\(609\) 44.1003 25.4613i 1.78704 1.03175i
\(610\) 0 0
\(611\) −31.3833 13.2314i −1.26963 0.535285i
\(612\) 13.4461i 0.543528i
\(613\) −0.172736 0.299187i −0.00697673 0.0120841i 0.862516 0.506030i \(-0.168887\pi\)
−0.869493 + 0.493946i \(0.835554\pi\)
\(614\) 3.92763 + 6.80286i 0.158506 + 0.274541i
\(615\) 0 0
\(616\) 11.3258i 0.456328i
\(617\) −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
\(619\) 14.8971i 0.598764i −0.954133 0.299382i \(-0.903219\pi\)
0.954133 0.299382i \(-0.0967805\pi\)
\(620\) 0 0
\(621\) −10.7440 18.6091i −0.431141 0.746758i
\(622\) −3.96859 6.87381i −0.159126 0.275615i
\(623\) 23.9644i 0.960113i
\(624\) 33.3353 + 44.0142i 1.33448 + 1.76198i
\(625\) 0 0
\(626\) −76.4047 + 44.1123i −3.05374 + 1.76308i
\(627\) −15.0064 + 8.66397i −0.599299 + 0.346006i
\(628\) −8.86842 5.12019i −0.353889 0.204318i
\(629\) 0.482694i 0.0192463i
\(630\) 0 0
\(631\) 33.6408 + 19.4225i 1.33922 + 0.773198i 0.986691 0.162604i \(-0.0519893\pi\)
0.352526 + 0.935802i \(0.385323\pi\)
\(632\) 51.8053 2.06071
\(633\) 26.0814 + 15.0581i 1.03664 + 0.598506i
\(634\) 17.0140 + 29.4691i 0.675713 + 1.17037i
\(635\) 0 0
\(636\) −83.5470 −3.31285
\(637\) −1.51022 12.0571i −0.0598370 0.477719i
\(638\) 25.2326i 0.998967i
\(639\) 42.2072 24.3683i 1.66969 0.963996i
\(640\) 0 0
\(641\) 18.5908 32.2003i 0.734293 1.27183i −0.220739 0.975333i \(-0.570847\pi\)
0.955033 0.296501i \(-0.0958197\pi\)
\(642\) 51.9397 2.04990
\(643\) 4.55189 7.88410i 0.179509 0.310918i −0.762204 0.647337i \(-0.775882\pi\)
0.941712 + 0.336419i \(0.109216\pi\)
\(644\) 26.6307 + 15.3753i 1.04940 + 0.605870i
\(645\) 0 0
\(646\) −4.55783 + 7.89439i −0.179325 + 0.310601i
\(647\) 16.5605 9.56118i 0.651059 0.375889i −0.137803 0.990460i \(-0.544004\pi\)
0.788862 + 0.614571i \(0.210671\pi\)
\(648\) −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
\(653\) −29.9926 + 17.3162i −1.17370 + 0.677636i −0.954549 0.298055i \(-0.903662\pi\)
−0.219152 + 0.975691i \(0.570329\pi\)
\(654\) 35.5399 61.5570i 1.38972 2.40707i
\(655\) 0 0
\(656\) 1.25705 + 0.725758i 0.0490796 + 0.0283361i
\(657\) −9.27453 + 16.0640i −0.361834 + 0.626714i
\(658\) −44.9114 −1.75083
\(659\) −3.34926 + 5.80109i −0.130469 + 0.225978i −0.923857 0.382737i \(-0.874982\pi\)
0.793389 + 0.608715i \(0.208315\pi\)
\(660\) 0 0
\(661\) 5.22004 3.01379i 0.203036 0.117223i −0.395035 0.918666i \(-0.629268\pi\)
0.598071 + 0.801443i \(0.295934\pi\)
\(662\) 71.8604i 2.79294i
\(663\) −5.98501 2.52331i −0.232438 0.0979974i
\(664\) −28.4492 −1.10404
\(665\) 0 0
\(666\) −4.71706 8.17018i −0.182782 0.316588i
\(667\) 31.2620 + 18.0491i 1.21047 + 0.698865i
\(668\) 60.8479 2.35428
\(669\) 52.2411 + 30.1614i 2.01976 + 1.16611i
\(670\) 0 0
\(671\) 4.48990i 0.173330i
\(672\) 11.1974 + 6.46481i 0.431948 + 0.249386i
\(673\) 20.2276 11.6784i 0.779715 0.450169i −0.0566140 0.998396i \(-0.518030\pi\)
0.836329 + 0.548227i \(0.184697\pi\)
\(674\) −25.3923 + 14.6603i −0.978075 + 0.564692i
\(675\) 0 0
\(676\) −53.2604 + 13.5550i −2.04848 + 0.521346i
\(677\) 45.4042i 1.74503i −0.488590 0.872513i \(-0.662489\pi\)
0.488590 0.872513i \(-0.337511\pi\)
\(678\) 23.5901 + 40.8593i 0.905973 + 1.56919i
\(679\) −4.02148 6.96540i −0.154330 0.267308i
\(680\) 0 0
\(681\) 44.3408i 1.69914i
\(682\) 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 \(0.00445791\pi\)
\(684\) 120.945i 4.62445i
\(685\) 0 0
\(686\) −24.6523 42.6991i −0.941230 1.63026i
\(687\) 10.7715 + 18.6567i 0.410957 + 0.711798i
\(688\) 3.45214i 0.131612i
\(689\) 9.79246 23.2266i 0.373063 0.884862i
\(690\) 0 0
\(691\) 5.71257 3.29815i 0.217316 0.125468i −0.387391 0.921916i \(-0.626624\pi\)
0.604707 + 0.796448i \(0.293290\pi\)
\(692\) −89.1457 + 51.4683i −3.38881 + 1.95653i
\(693\) −8.80641 5.08438i −0.334528 0.193140i
\(694\) 4.74090i 0.179962i
\(695\) 0 0
\(696\) 128.673 + 74.2892i 4.87733 + 2.81593i
\(697\) −0.170754 −0.00646778
\(698\) −22.1933 12.8133i −0.840028 0.484990i
\(699\) −26.9327 46.6487i −1.01869 1.76442i
\(700\) 0 0
\(701\) −29.2474 −1.10466 −0.552329 0.833626i \(-0.686261\pi\)
−0.552329 + 0.833626i \(0.686261\pi\)
\(702\) 50.2488 6.29394i 1.89652 0.237550i
\(703\) 4.34174i 0.163752i
\(704\) −4.48542 + 2.58966i −0.169051 + 0.0976015i
\(705\) 0 0
\(706\) 0.998937 1.73021i 0.0375955 0.0651173i
\(707\) −29.0499 −1.09253
\(708\) −4.42792 + 7.66938i −0.166411 + 0.288233i
\(709\) 9.46865 + 5.46673i 0.355603 + 0.205307i 0.667150 0.744923i \(-0.267514\pi\)
−0.311548 + 0.950231i \(0.600847\pi\)
\(710\) 0 0
\(711\) 23.2566 40.2815i 0.872189 1.51068i
\(712\) 60.5538 34.9608i 2.26935 1.31021i
\(713\) 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
\(718\) −17.5762 + 10.1476i −0.655938 + 0.378706i
\(719\) −8.02989 + 13.9082i −0.299464 + 0.518688i −0.976014 0.217710i \(-0.930141\pi\)
0.676549 + 0.736398i \(0.263475\pi\)
\(720\) 0 0
\(721\) −22.3189 12.8858i −0.831199 0.479893i
\(722\) 17.2894 29.9461i 0.643444 1.11448i
\(723\) −73.2966 −2.72593
\(724\) −17.9416 + 31.0758i −0.666796 + 1.15492i
\(725\) 0 0
\(726\) 60.2156 34.7655i 2.23481 1.29027i
\(727\) 51.3754i 1.90541i −0.303900 0.952704i \(-0.598289\pi\)
0.303900 0.952704i \(-0.401711\pi\)
\(728\) −30.4406 + 23.0550i −1.12820 + 0.854475i
\(729\) 43.0532 1.59456
\(730\) 0 0
\(731\) −0.203052 0.351697i −0.00751016 0.0130080i
\(732\) −43.4532 25.0877i −1.60608 0.927268i
\(733\) 9.82358 0.362842 0.181421 0.983406i \(-0.441930\pi\)
0.181421 + 0.983406i \(0.441930\pi\)
\(734\) 44.3613 + 25.6120i 1.63741 + 0.945357i
\(735\) 0 0
\(736\) 9.16560i 0.337848i
\(737\) −7.49673 4.32824i −0.276146 0.159433i
\(738\) 2.89022 1.66867i 0.106390 0.0614246i
\(739\) −42.5082 + 24.5421i −1.56369 + 0.902797i −0.566811 + 0.823848i \(0.691823\pi\)
−0.996879 + 0.0789487i \(0.974844\pi\)
\(740\) 0 0
\(741\) 53.8339 + 22.6967i 1.97764 + 0.833783i
\(742\) 33.2386i 1.22023i
\(743\) 20.4188 + 35.3663i 0.749091 + 1.29746i 0.948259 + 0.317499i \(0.102843\pi\)
−0.199167 + 0.979966i \(0.563824\pi\)
\(744\) 11.5035 + 19.9247i 0.421739 + 0.730473i
\(745\) 0 0
\(746\) 44.4346i 1.62687i
\(747\) −12.7715 + 22.1208i −0.467283 + 0.809358i
\(748\) −1.44050 + 2.49503i −0.0526700 + 0.0912272i
\(749\) 14.0276i 0.512557i
\(750\) 0 0
\(751\) −1.36340 2.36148i −0.0497512 0.0861716i 0.840077 0.542467i \(-0.182510\pi\)
−0.889829 + 0.456295i \(0.849176\pi\)
\(752\) −25.5855 44.3154i −0.933006 1.61601i
\(753\) 21.5175i 0.784142i
\(754\) −67.8184 + 51.3641i −2.46980 + 1.87057i
\(755\) 0 0
\(756\) 39.2590 22.6662i 1.42784 0.824362i
\(757\) 12.8224 7.40301i 0.466038 0.269067i −0.248542 0.968621i \(-0.579951\pi\)
0.714580 + 0.699554i \(0.246618\pi\)
\(758\) −4.42078 2.55234i −0.160570 0.0927051i
\(759\) 11.5413i 0.418924i
\(760\) 0 0
\(761\) 9.84575 + 5.68445i 0.356908 + 0.206061i 0.667724 0.744409i \(-0.267269\pi\)
−0.310815 + 0.950470i \(0.600602\pi\)
\(762\) 10.5075 0.380647
\(763\) 16.6250 + 9.59843i 0.601864 + 0.347486i
\(764\) 11.5055 + 19.9281i 0.416255 + 0.720975i
\(765\) 0 0
\(766\) 19.7275 0.712784
\(767\) −1.61314 2.12991i −0.0582472 0.0769065i
\(768\) 91.7512i 3.31078i
\(769\) −18.2352 + 10.5281i −0.657579 + 0.379654i −0.791354 0.611358i \(-0.790623\pi\)
0.133775 + 0.991012i \(0.457290\pi\)
\(770\) 0 0
\(771\) −0.474602 + 0.822034i −0.0170924 + 0.0296048i
\(772\) 51.3970 1.84982
\(773\) 7.04144 12.1961i 0.253263 0.438664i −0.711159 0.703031i \(-0.751830\pi\)
0.964422 + 0.264367i \(0.0851629\pi\)
\(774\) 6.87381 + 3.96859i 0.247074 + 0.142648i
\(775\) 0 0
\(776\) 11.7336 20.3231i 0.421210 0.729558i
\(777\) 3.53288 2.03971i 0.126741 0.0731741i
\(778\) 11.4940 + 19.9081i 0.412078 + 0.713740i
\(779\) 1.53590 0.0550293
\(780\) 0 0
\(781\) 10.4425 0.373660
\(782\) −3.03576 5.25809i −0.108558 0.188029i
\(783\) 46.0864 26.6080i 1.64699 0.950893