Properties

Label 325.2.n.d.101.4
Level $325$
Weight $2$
Character 325.101
Analytic conductor $2.595$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.n (of order \(6\), degree \(2\), 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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.4
Root \(1.20036 - 0.747754i\) of defining polynomial
Character \(\chi\) \(=\) 325.101
Dual form 325.2.n.d.251.4

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 \(-0.862833\pi\)
0.0925423 0.995709i \(-0.470501\pi\)
\(4\) 2.11378 3.66117i 1.05689 1.83059i
\(5\) 0 0
\(6\) −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
\(10\) 0 0
\(11\) 0.926118 0.534695i 0.279235 0.161217i −0.353842 0.935305i \(-0.615125\pi\)
0.633077 + 0.774089i \(0.281792\pi\)
\(12\) −11.9506 −3.44985
\(13\) −1.40072 + 3.32235i −0.388490 + 0.921453i
\(14\) 4.75447 1.27069
\(15\) 0 0
\(16\) −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 \(0.191290\pi\)
\(18\) 12.4551i 2.93570i
\(19\) 4.96410 + 2.86603i 1.13884 + 0.657511i 0.946144 0.323747i \(-0.104943\pi\)
0.192699 + 0.981258i \(0.438276\pi\)
\(20\) 0 0
\(21\) 5.38573i 1.17526i
\(22\) 1.33433 2.31114i 0.284481 0.492736i
\(23\) −1.90893 3.30636i −0.398039 0.689423i 0.595445 0.803396i \(-0.296976\pi\)
−0.993484 + 0.113973i \(0.963642\pi\)
\(24\) −13.6088 + 7.85704i −2.77788 + 1.60381i
\(25\) 0 0
\(26\) 1.11827 + 8.92792i 0.219311 + 1.75091i
\(27\) 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 \(-0.507713\pi\)
\(30\) 0 0
\(31\) 1.46410i 0.262960i 0.991319 + 0.131480i \(0.0419730\pi\)
−0.991319 + 0.131480i \(0.958027\pi\)
\(32\) −2.07908 1.20036i −0.367534 0.212196i
\(33\) −2.61799 1.51150i −0.455733 0.263118i
\(34\) 1.59030i 0.272733i
\(35\) 0 0
\(36\) 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
\(39\) 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 \(0.339994\pi\)
\(42\) −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 \(0.182140\pi\)
\(44\) 4.52091i 0.681552i
\(45\) 0 0
\(46\) −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
\(50\) 0 0
\(51\) 1.80144 0.252252
\(52\) 9.20287 + 12.1510i 1.27621 + 1.68504i
\(53\) 6.99102 0.960290 0.480145 0.877189i \(-0.340584\pi\)
0.480145 + 0.877189i \(0.340584\pi\)
\(54\) 12.1637 7.02271i 1.65527 0.955669i
\(55\) 0 0
\(56\) 5.29543 9.17196i 0.707632 1.22565i
\(57\) 16.2036i 2.14622i
\(58\) −20.4341 11.7977i −2.68313 1.54911i
\(59\) −0.641756 0.370518i −0.0835495 0.0482373i 0.457643 0.889136i \(-0.348694\pi\)
−0.541193 + 0.840899i \(0.682027\pi\)
\(60\) 0 0
\(61\) −2.09928 + 3.63606i −0.268785 + 0.465550i −0.968548 0.248825i \(-0.919956\pi\)
0.699763 + 0.714375i \(0.253289\pi\)
\(62\) 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
\(70\) 0 0
\(71\) 8.45663 + 4.88244i 1.00362 + 0.579439i 0.909317 0.416105i \(-0.136605\pi\)
0.0943010 + 0.995544i \(0.469938\pi\)
\(72\) 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
\(75\) 0 0
\(76\) 20.9860 12.1163i 2.40726 1.38983i
\(77\) 2.03741 0.232185
\(78\) 20.2760 15.3565i 2.29580 1.73879i
\(79\) −9.31937 −1.04851 −0.524255 0.851561i \(-0.675656\pi\)
−0.524255 + 0.851561i \(0.675656\pi\)
\(80\) 0 0
\(81\) −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 0
\(86\) 1.59030i 0.171486i
\(87\) −13.3640 + 23.1472i −1.43278 + 2.48164i
\(88\) −2.97231 5.14819i −0.316849 0.548799i
\(89\) −10.8932 + 6.28917i −1.15467 + 0.666650i −0.950021 0.312185i \(-0.898939\pi\)
−0.204651 + 0.978835i \(0.565606\pi\)
\(90\) 0 0
\(91\) −5.47602 + 4.14741i −0.574043 + 0.434767i
\(92\) −16.1402 −1.68273
\(93\) 3.58429 2.06939i 0.371673 0.214586i
\(94\) 11.7864 + 20.4147i 1.21568 + 2.10562i
\(95\) 0 0
\(96\) 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
\(100\) 0 0
\(101\) −7.62379 13.2048i −0.758595 1.31393i −0.943567 0.331181i \(-0.892553\pi\)
0.184972 0.982744i \(-0.440781\pi\)
\(102\) 3.89322 2.24775i 0.385487 0.222561i
\(103\) −13.5269 −1.33285 −0.666423 0.745574i \(-0.732176\pi\)
−0.666423 + 0.745574i \(0.732176\pi\)
\(104\) 18.4686 + 7.78645i 1.81099 + 0.763524i
\(105\) 0 0
\(106\) 15.1088 8.72307i 1.46750 0.847259i
\(107\) −3.68137 6.37632i −0.355891 0.616422i 0.631379 0.775475i \(-0.282489\pi\)
−0.987270 + 0.159053i \(0.949156\pi\)
\(108\) 11.8969 20.6061i 1.14478 1.98282i
\(109\) 10.0760i 0.965103i −0.875868 0.482551i \(-0.839710\pi\)
0.875868 0.482551i \(-0.160290\pi\)
\(110\) 0 0
\(111\) 1.85432 + 1.07059i 0.176004 + 0.101616i
\(112\) 10.3208i 0.975223i
\(113\) −3.34403 + 5.79203i −0.314580 + 0.544868i −0.979348 0.202181i \(-0.935197\pi\)
0.664768 + 0.747050i \(0.268530\pi\)
\(114\) −20.2181 35.0187i −1.89360 3.27981i
\(115\) 0 0
\(116\) −39.9721 −3.71131
\(117\) −10.8648 14.3453i −1.00445 1.32623i
\(118\) −1.84926 −0.170238
\(119\) −1.05146 + 0.607061i −0.0963872 + 0.0556492i
\(120\) 0 0
\(121\) −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
\(125\) 0 0
\(126\) −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 \(0.854384\pi\)
\(128\) 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
\(135\) 0 0
\(136\) 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 \(0.822059\pi\)
\(140\) 0 0
\(141\) 23.1252 13.3513i 1.94749 1.12439i
\(142\) 24.3683 2.04494
\(143\) 0.479208 + 3.82584i 0.0400734 + 0.319933i
\(144\) 27.0370 2.25308
\(145\) 0 0
\(146\) 4.63726 + 8.03198i 0.383783 + 0.664731i
\(147\) −4.76346 + 8.25055i −0.392883 + 0.680494i
\(148\) 3.20216i 0.263216i
\(149\) 11.5768 + 6.68388i 0.948410 + 0.547565i 0.892587 0.450876i \(-0.148888\pi\)
0.0558233 + 0.998441i \(0.482222\pi\)
\(150\) 0 0
\(151\) 18.2984i 1.48910i 0.667567 + 0.744550i \(0.267336\pi\)
−0.667567 + 0.744550i \(0.732664\pi\)
\(152\) 15.9319 27.5949i 1.29225 2.23824i
\(153\) −1.59030 2.75447i −0.128568 0.222686i
\(154\) 4.40320 2.54219i 0.354820 0.204856i
\(155\) 0 0
\(156\) 16.7395 39.7041i 1.34023 3.17887i
\(157\) −2.42229 −0.193320 −0.0966599 0.995317i \(-0.530816\pi\)
−0.0966599 + 0.995317i \(0.530816\pi\)
\(158\) −20.1408 + 11.6283i −1.60231 + 0.925096i
\(159\) −9.88124 17.1148i −0.783633 1.35729i
\(160\) 0 0
\(161\) 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
\(165\) 0 0
\(166\) 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
\(169\) −9.07597 9.30735i −0.698151 0.715950i
\(170\) 0 0
\(171\) −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 \(-0.456888\pi\)
0.790581 0.612358i \(-0.209779\pi\)
\(174\) 66.7001i 5.05653i
\(175\) 0 0
\(176\) −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 \(0.788117\pi\)
\(180\) 0 0
\(181\) 8.48794 0.630904 0.315452 0.948942i \(-0.397844\pi\)
0.315452 + 0.948942i \(0.397844\pi\)
\(182\) −6.65968 + 15.7960i −0.493649 + 1.17088i
\(183\) 11.8687 0.877356
\(184\) −18.3797 + 10.6115i −1.35497 + 0.782291i
\(185\) 0 0
\(186\) 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
\(190\) 0 0
\(191\) 2.72155 4.71386i 0.196924 0.341083i −0.750605 0.660751i \(-0.770238\pi\)
0.947530 + 0.319668i \(0.103571\pi\)
\(192\) −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 \(-0.0978265\pi\)
\(200\) 0 0
\(201\) −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 0
\(206\) −29.2340 + 16.8783i −2.03683 + 1.17596i
\(207\) 19.0550 1.32441
\(208\) 19.3803 2.42749i 1.34378 0.168316i
\(209\) 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 \(0.713816\pi\)
\(212\) 14.7775 25.5953i 1.01492 1.75789i
\(213\) 27.6037i 1.89138i
\(214\) −15.9121 9.18688i −1.08773 0.628002i
\(215\) 0 0
\(216\) 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
\(220\) 0 0
\(221\) −1.38724 1.83164i −0.0933161 0.123210i
\(222\) 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
\(225\) 0 0
\(226\) 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 \(-0.918977\pi\)
0.967779 0.251800i \(-0.0810225\pi\)
\(230\) 0 0
\(231\) −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 \(-0.714561\pi\)
−0.624166 + 0.781292i \(0.714561\pi\)
\(234\) −41.3802 17.4461i −2.70511 1.14049i
\(235\) 0 0
\(236\) −2.71306 + 1.56639i −0.176605 + 0.101963i
\(237\) 13.1722 + 22.8149i 0.855625 + 1.48199i
\(238\) −1.51493 + 2.62393i −0.0981980 + 0.170084i
\(239\) 12.7535i 0.824954i −0.910968 0.412477i \(-0.864664\pi\)
0.910968 0.412477i \(-0.135336\pi\)
\(240\) 0 0
\(241\) −22.4550 12.9644i −1.44646 0.835111i −0.448187 0.893940i \(-0.647930\pi\)
−0.998268 + 0.0588285i \(0.981263\pi\)
\(242\) 24.5967i 1.58114i
\(243\) 7.11778 12.3284i 0.456606 0.790864i
\(244\) 8.87483 + 15.3717i 0.568153 + 0.984069i
\(245\) 0 0
\(246\) 1.89022 0.120516
\(247\) −16.4752 + 12.4780i −1.04829 + 0.793954i
\(248\) 8.13878 0.516813
\(249\) 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 \(0.0894444\pi\)
\(252\) 40.1996i 2.53234i
\(253\) −3.53578 2.04139i −0.222293 0.128341i
\(254\) −3.21907 1.85853i −0.201982 0.116614i
\(255\) 0 0
\(256\) 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 \(0.836667\pi\)
\(258\) 3.89322 2.24775i 0.242382 0.139939i
\(259\) −1.44310 −0.0896700
\(260\) 0 0
\(261\) 47.1906 2.92103
\(262\) 8.91865 5.14918i 0.550996 0.318118i
\(263\) −2.68795 4.65566i −0.165746 0.287080i 0.771174 0.636624i \(-0.219670\pi\)
−0.936920 + 0.349544i \(0.886336\pi\)
\(264\) −8.40224 + 14.5531i −0.517122 + 0.895681i
\(265\) 0 0
\(266\) 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 \(0.153948\pi\)
\(270\) 0 0
\(271\) −10.0851 + 5.82266i −0.612629 + 0.353701i −0.773994 0.633194i \(-0.781744\pi\)
0.161365 + 0.986895i \(0.448410\pi\)
\(272\) 3.45214 0.209317
\(273\) 17.8933 + 7.54390i 1.08295 + 0.456577i
\(274\) −50.1838 −3.03171
\(275\) 0 0
\(276\) 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 \(-0.0422999\pi\)
\(278\) 51.9697i 3.11693i
\(279\) −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 \(-0.115241\pi\)
\(282\) 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 \(0.598225\pi\)
\(284\) 35.7509 20.6408i 2.12143 1.22481i
\(285\) 0 0
\(286\) 5.80936 + 7.67038i 0.343515 + 0.453559i
\(287\) −0.510500 −0.0301339
\(288\) 10.3767 5.99102i 0.611455 0.353024i
\(289\) 8.29695 + 14.3707i 0.488056 + 0.845337i
\(290\) 0 0
\(291\) 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 0
\(296\) 2.10529 + 3.64647i 0.122367 + 0.211946i
\(297\) 5.21245 3.00941i 0.302457 0.174624i
\(298\) 33.3593 1.93245
\(299\) 13.6587 1.71083i 0.789905 0.0989400i
\(300\) 0 0
\(301\) −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
\(305\) 0 0
\(306\) −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
\(310\) 0 0
\(311\) 3.18059 0.180355 0.0901774 0.995926i \(-0.471257\pi\)
0.0901774 + 0.995926i \(0.471257\pi\)
\(312\) −7.04170 56.2186i −0.398658 3.18275i
\(313\) −35.3533 −1.99829 −0.999144 0.0413596i \(-0.986831\pi\)
−0.999144 + 0.0413596i \(0.986831\pi\)
\(314\) −5.23499 + 3.02242i −0.295427 + 0.170565i
\(315\) 0 0
\(316\) −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
\(320\) 0 0
\(321\) −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
\(330\) 0 0
\(331\) −24.9380 14.3980i −1.37072 0.791383i −0.379698 0.925110i \(-0.623972\pi\)
−0.991018 + 0.133727i \(0.957305\pi\)
\(332\) 18.7371 + 10.8179i 1.02833 + 0.593707i
\(333\) 3.78044i 0.207167i
\(334\) 17.9591 31.1061i 0.982679 1.70205i
\(335\) 0 0
\(336\) −25.2665 + 14.5876i −1.37840 + 0.795819i
\(337\) 11.7493 0.640026 0.320013 0.947413i \(-0.396313\pi\)
0.320013 + 0.947413i \(0.396313\pi\)
\(338\) −31.2280 8.79023i −1.69858 0.478125i
\(339\) 18.9061 1.02684
\(340\) 0 0
\(341\) 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
\(345\) 0 0
\(346\) 60.7630i 3.26664i
\(347\) 0.949887 1.64525i 0.0509926 0.0883218i −0.839402 0.543510i \(-0.817095\pi\)
0.890395 + 0.455189i \(0.150428\pi\)
\(348\) 56.4973 + 97.8562i 3.02857 + 5.24564i
\(349\) −8.89329 + 5.13454i −0.476047 + 0.274846i −0.718768 0.695250i \(-0.755293\pi\)
0.242721 + 0.970096i \(0.421960\pi\)
\(350\) 0 0
\(351\) −7.88364 + 18.6991i −0.420798 + 0.998084i
\(352\) −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
\(355\) 0 0
\(356\) 53.1756i 2.81830i
\(357\) 2.97231 + 1.71606i 0.157311 + 0.0908237i
\(358\) 8.18714 + 4.72685i 0.432704 + 0.249822i
\(359\) 8.13272i 0.429228i 0.976699 + 0.214614i \(0.0688494\pi\)
−0.976699 + 0.214614i \(0.931151\pi\)
\(360\) 0 0
\(361\) 6.92820 + 12.0000i 0.364642 + 0.631579i
\(362\) 18.3439 10.5909i 0.964135 0.556643i
\(363\) 27.8625 1.46240
\(364\) 3.60929 + 28.8154i 0.189178 + 1.51034i
\(365\) 0 0
\(366\) 25.6502 14.8092i 1.34076 0.774087i
\(367\) −10.2632 17.7765i −0.535737 0.927924i −0.999127 0.0417696i \(-0.986700\pi\)
0.463390 0.886154i \(-0.346633\pi\)
\(368\) −10.3409 + 17.9110i −0.539057 + 0.933675i
\(369\) 1.33734i 0.0696191i
\(370\) 0 0
\(371\) 11.5349 + 6.65968i 0.598863 + 0.345754i
\(372\) 17.4969i 0.907173i
\(373\) −8.90292 + 15.4203i −0.460976 + 0.798433i −0.999010 0.0444897i \(-0.985834\pi\)
0.538034 + 0.842923i \(0.319167\pi\)
\(374\) 0.850322 + 1.47280i 0.0439691 + 0.0761568i
\(375\) 0 0
\(376\) 52.5100 2.70800
\(377\) 33.8266 4.23697i 1.74216 0.218215i
\(378\) 26.7595 1.37636
\(379\) −1.77150 + 1.02277i −0.0909956 + 0.0525363i −0.544807 0.838561i \(-0.683397\pi\)
0.453812 + 0.891098i \(0.350064\pi\)
\(380\) 0 0
\(381\) −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
\(385\) 0 0
\(386\) −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
\(395\) 0 0
\(396\) 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
\(400\) 0 0
\(401\) 3.61063 2.08460i 0.180306 0.104100i −0.407130 0.913370i \(-0.633470\pi\)
0.587437 + 0.809270i \(0.300137\pi\)
\(402\) −57.1038 −2.84808
\(403\) −4.86425 2.05080i −0.242306 0.102157i
\(404\) −64.4600 −3.20701
\(405\) 0 0
\(406\) −22.4770 38.9314i −1.11552 1.93213i
\(407\) −0.405004 + 0.701487i −0.0200753 + 0.0347714i
\(408\) 10.0140i 0.495767i
\(409\) 8.80580 + 5.08403i 0.435419 + 0.251389i 0.701652 0.712519i \(-0.252446\pi\)
−0.266234 + 0.963909i \(0.585779\pi\)
\(410\) 0 0
\(411\) 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
\(415\) 0 0
\(416\) 6.90023 5.22607i 0.338311 0.256229i
\(417\) 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 \(-0.412761\pi\)
\(420\) 0 0
\(421\) 2.01797i 0.0983498i −0.998790 0.0491749i \(-0.984341\pi\)
0.998790 0.0491749i \(-0.0156592\pi\)
\(422\) 23.0244 + 13.2932i 1.12081 + 0.647101i
\(423\) −40.8295 23.5729i −1.98520 1.14615i
\(424\) 38.8623i 1.88732i
\(425\) 0 0
\(426\) −34.4427 59.6564i −1.66875 2.89036i
\(427\) −6.92747 + 3.99957i −0.335244 + 0.193553i
\(428\) −31.1264 −1.50455
\(429\) 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 \(0.167977\pi\)
\(432\) −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 \(0.916583\pi\)
\(434\) 6.96103i 0.334140i
\(435\) 0 0
\(436\) −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 \(0.700765\pi\)
\(440\) 0 0
\(441\) 16.8205 0.800978
\(442\) −5.28351 2.22756i −0.251311 0.105954i
\(443\) 24.1399 1.14692 0.573461 0.819233i \(-0.305600\pi\)
0.573461 + 0.819233i \(0.305600\pi\)
\(444\) 7.83925 4.52599i 0.372034 0.214794i
\(445\) 0 0
\(446\) 26.6262 46.1180i 1.26079 2.18375i
\(447\) 37.7885i 1.78733i
\(448\) 7.99118 + 4.61371i 0.377548 + 0.217977i
\(449\) 18.0679 + 10.4315i 0.852676 + 0.492293i 0.861553 0.507668i \(-0.169492\pi\)
−0.00887706 + 0.999961i \(0.502826\pi\)
\(450\) 0 0
\(451\) −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
\(460\) 0 0
\(461\) 4.05146 + 2.33911i 0.188695 + 0.108943i 0.591372 0.806399i \(-0.298587\pi\)
−0.402676 + 0.915342i \(0.631920\pi\)
\(462\) −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
\(465\) 0 0
\(466\) −41.1811 + 23.7759i −1.90768 + 1.10140i
\(467\) −6.98506 −0.323230 −0.161615 0.986854i \(-0.551670\pi\)
−0.161615 + 0.986854i \(0.551670\pi\)
\(468\) −75.4866 + 9.45512i −3.48937 + 0.437063i
\(469\) 15.4223 0.712135
\(470\) 0 0
\(471\) 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
\(475\) 0 0
\(476\) 5.13277i 0.235260i
\(477\) −17.4461 + 30.2176i −0.798804 + 1.38357i
\(478\) −15.9132 27.5625i −0.727853 1.26068i
\(479\) −14.1065 + 8.14438i −0.644542 + 0.372126i −0.786362 0.617766i \(-0.788038\pi\)
0.141820 + 0.989892i \(0.454704\pi\)
\(480\) 0 0
\(481\) −0.339423 2.70985i −0.0154764 0.123558i
\(482\) −64.7056 −2.94726
\(483\) −17.8071 + 10.2810i −0.810253 + 0.467800i
\(484\) 20.8343 + 36.0860i 0.947012 + 1.64027i
\(485\) 0 0
\(486\) 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
\(490\) 0 0
\(491\) −7.89916 13.6818i −0.356484 0.617449i 0.630887 0.775875i \(-0.282691\pi\)
−0.987371 + 0.158426i \(0.949358\pi\)
\(492\) 2.77315 1.60108i 0.125023 0.0721823i
\(493\) 6.02540 0.271370
\(494\) −20.0364 + 47.5241i −0.901481 + 2.13821i
\(495\) 0 0
\(496\) 6.86865 3.96562i 0.308411 0.178061i
\(497\) 9.30208 + 16.1117i 0.417255 + 0.722708i
\(498\) 18.0514 31.2660i 0.808903 1.40106i
\(499\) 1.24651i 0.0558016i −0.999611 0.0279008i \(-0.991118\pi\)
0.999611 0.0279008i \(-0.00888226\pi\)
\(500\) 0 0
\(501\) −35.2361 20.3436i −1.57423 0.908883i
\(502\) 18.9955i 0.847809i
\(503\) −3.82672 + 6.62808i −0.170625 + 0.295532i −0.938639 0.344902i \(-0.887912\pi\)
0.768013 + 0.640434i \(0.221245\pi\)
\(504\) 26.4296 + 45.7774i 1.17727 + 2.03909i
\(505\) 0 0
\(506\) −10.1886 −0.452938
\(507\) −9.95732 + 35.3742i −0.442220 + 1.57102i
\(508\) −6.29695 −0.279382
\(509\) −22.2777 + 12.8621i −0.987444 + 0.570101i −0.904509 0.426454i \(-0.859763\pi\)
−0.0829345 + 0.996555i \(0.526429\pi\)
\(510\) 0 0
\(511\) −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
\(515\) 0 0
\(516\) 3.80785 6.59538i 0.167631 0.290346i
\(517\) 5.05080 + 8.74824i 0.222134 + 0.384747i
\(518\) −3.11879 + 1.80064i −0.137032 + 0.0791154i
\(519\) −68.8305 −3.02132
\(520\) 0 0
\(521\) −30.1519 −1.32098 −0.660490 0.750835i \(-0.729651\pi\)
−0.660490 + 0.750835i \(0.729651\pi\)
\(522\) 101.987 58.8823i 4.46386 2.57721i
\(523\) 1.96876 + 3.41000i 0.0860880 + 0.149109i 0.905854 0.423589i \(-0.139230\pi\)
−0.819766 + 0.572698i \(0.805897\pi\)
\(524\) 8.72307 15.1088i 0.381069 0.660031i
\(525\) 0 0
\(526\) −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
\(530\) 0 0
\(531\) 3.20301 1.84926i 0.138999 0.0802510i
\(532\) 46.1682 2.00165
\(533\) −0.120072 0.958614i −0.00520088 0.0415222i
\(534\) 88.7326 3.83983
\(535\) 0 0
\(536\) −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
\(540\) 0 0
\(541\) 15.8881i 0.683083i −0.939867 0.341541i \(-0.889051\pi\)
0.939867 0.341541i \(-0.110949\pi\)
\(542\) −14.5305 + 25.1675i −0.624138 + 1.08104i
\(543\) −11.9970 20.7795i −0.514842 0.891732i
\(544\) 1.32492 0.764945i 0.0568057 0.0327968i
\(545\) 0 0
\(546\) 48.0833 6.02271i 2.05778 0.257748i
\(547\) 6.56107 0.280531 0.140266 0.990114i \(-0.455204\pi\)
0.140266 + 0.990114i \(0.455204\pi\)
\(548\) −73.6249 + 42.5074i −3.14510 + 1.81582i
\(549\) −10.4775 18.1476i −0.447170 0.774522i
\(550\) 0 0
\(551\) 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
\(555\) 0 0
\(556\) 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
\(559\) −1.38724 1.83164i −0.0586741 0.0774702i
\(560\) 0 0
\(561\) 1.66835 0.963220i 0.0704377 0.0406672i
\(562\) −14.8163 25.6626i −0.624988 1.08251i
\(563\) 7.77976 13.4749i 0.327878 0.567901i −0.654213 0.756310i \(-0.727000\pi\)
0.982091 + 0.188410i \(0.0603333\pi\)
\(564\) 112.887i 4.75341i
\(565\) 0 0
\(566\) 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 \(0.810099\pi\)
\(570\) 0 0
\(571\) 21.5118 0.900240 0.450120 0.892968i \(-0.351381\pi\)
0.450120 + 0.892968i \(0.351381\pi\)
\(572\) 15.0200 + 6.33252i 0.628018 + 0.264776i
\(573\) −15.3868 −0.642791
\(574\) −1.10328 + 0.636978i −0.0460500 + 0.0265870i
\(575\) 0 0
\(576\) −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
\(580\) 0 0
\(581\) −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
\(590\) 0 0
\(591\) 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 0
\(596\) 48.9417 28.2565i 2.00473 1.15743i
\(597\) −58.9037 −2.41077
\(598\) 27.3842 20.7401i 1.11982 0.848128i
\(599\) −11.4270 −0.466896 −0.233448 0.972369i \(-0.575001\pi\)
−0.233448 + 0.972369i \(0.575001\pi\)
\(600\) 0 0
\(601\) 18.0215 + 31.2142i 0.735114 + 1.27325i 0.954674 + 0.297655i \(0.0962045\pi\)
−0.219560 + 0.975599i \(0.570462\pi\)
\(602\) −1.51493 + 2.62393i −0.0617437 + 0.106943i
\(603\) 40.4012i 1.64526i
\(604\) 66.9935 + 38.6787i 2.72593 + 1.57381i
\(605\) 0 0
\(606\) 107.562i 4.36942i
\(607\) 19.9454 34.5464i 0.809557 1.40219i −0.103614 0.994618i \(-0.533041\pi\)
0.913171 0.407576i \(-0.133626\pi\)
\(608\) −6.88052 11.9174i −0.279042 0.483315i
\(609\) −44.1003 + 25.4613i −1.78704 + 1.03175i
\(610\) 0 0
\(611\) −31.3833 13.2314i −1.26963 0.535285i
\(612\) −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 0
\(616\) 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 \(0.0967805\pi\)
−0.954133 + 0.299382i \(0.903219\pi\)
\(620\) 0 0
\(621\) −10.7440 18.6091i −0.431141 0.746758i
\(622\) 6.87381 3.96859i 0.275615 0.159126i
\(623\) −23.9644 −0.960113
\(624\) −33.3353 44.0142i −1.33448 1.76198i
\(625\) 0 0
\(626\) −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
\(630\) 0 0
\(631\) 33.6408 + 19.4225i 1.33922 + 0.773198i 0.986691 0.162604i \(-0.0519893\pi\)
0.352526 + 0.935802i \(0.385323\pi\)
\(632\) 51.8053i 2.06071i
\(633\) 15.0581 26.0814i 0.598506 1.03664i
\(634\) −17.0140 29.4691i −0.675713 1.17037i
\(635\) 0 0
\(636\) −83.5470 −3.31285
\(637\) 12.0571 1.51022i 0.477719 0.0598370i
\(638\) −25.2326 −0.998967
\(639\) −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 \(-0.0958197\pi\)
\(642\) 51.9397i 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
\(645\) 0 0
\(646\) −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 \(0.710671\pi\)
\(648\) −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 \(0.0703289\pi\)
−0.298055 + 0.954549i \(0.596338\pi\)
\(654\) −35.5399 + 61.5570i −1.38972 + 2.40707i
\(655\) 0 0
\(656\) 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 \(0.125018\pi\)
\(660\) 0 0
\(661\) 5.22004 3.01379i 0.203036 0.117223i −0.395035 0.918666i \(-0.629268\pi\)
0.598071 + 0.801443i \(0.295934\pi\)
\(662\) −71.8604 −2.79294
\(663\) −2.52331 + 5.98501i −0.0979974 + 0.232438i
\(664\) 28.4492 1.10404
\(665\) 0 0
\(666\) −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
\(670\) 0 0
\(671\) 4.48990i 0.173330i
\(672\) −6.46481 + 11.1974i −0.249386 + 0.431948i
\(673\) −11.6784 20.2276i −0.450169 0.779715i 0.548227 0.836329i \(-0.315303\pi\)
−0.998396 + 0.0566140i \(0.981970\pi\)
\(674\) 25.3923 14.6603i 0.978075 0.564692i
\(675\) 0 0
\(676\) −53.2604 + 13.5550i −2.04848 + 0.521346i
\(677\) 45.4042 1.74503 0.872513 0.488590i \(-0.162489\pi\)
0.872513 + 0.488590i \(0.162489\pi\)
\(678\) 40.8593 23.5901i 1.56919 0.905973i
\(679\) 4.02148 + 6.96540i 0.154330 + 0.267308i
\(680\) 0 0
\(681\) 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
\(685\) 0 0
\(686\) −24.6523 42.6991i −0.941230 1.63026i
\(687\) −18.6567 + 10.7715i −0.711798 + 0.410957i
\(688\) 3.45214 0.131612
\(689\) −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 \(0.293290\pi\)
\(692\) −51.4683 89.1457i −1.95653 3.38881i
\(693\) −5.08438 + 8.80641i −0.193140 + 0.334528i
\(694\) 4.74090i 0.179962i
\(695\) 0 0
\(696\) 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
\(700\) 0 0
\(701\) −29.2474 −1.10466 −0.552329 0.833626i \(-0.686261\pi\)
−0.552329 + 0.833626i \(0.686261\pi\)
\(702\) 6.29394 + 50.2488i 0.237550 + 1.89652i
\(703\) −4.34174 −0.163752
\(704\) 4.48542 2.58966i 0.169051 0.0976015i
\(705\) 0 0
\(706\) 0.998937 1.73021i 0.0375955 0.0651173i
\(707\) 29.0499i 1.09253i
\(708\) 7.66938 + 4.42792i 0.288233 + 0.166411i
\(709\) −9.46865 5.46673i −0.355603 0.205307i 0.311548 0.950231i \(-0.399153\pi\)
−0.667150 + 0.744923i \(0.732486\pi\)
\(710\) 0 0
\(711\) 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 \(0.0698587\pi\)
\(720\) 0 0
\(721\) −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
\(725\) 0 0
\(726\) 60.2156 34.7655i 2.23481 1.29027i
\(727\) 51.3754 1.90541 0.952704 0.303900i \(-0.0982889\pi\)
0.952704 + 0.303900i \(0.0982889\pi\)
\(728\) 23.0550 + 30.4406i 0.854475 + 1.12820i
\(729\) −43.0532 −1.59456
\(730\) 0 0
\(731\) −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
\(735\) 0 0
\(736\) 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 \(-0.308177\pi\)
0.996879 0.0789487i \(-0.0251563\pi\)
\(740\) 0 0
\(741\) 53.8339 + 22.6967i 1.97764 + 0.833783i
\(742\) 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
\(745\) 0 0
\(746\) 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
\(750\) 0 0
\(751\) −1.36340 2.36148i −0.0497512 0.0861716i 0.840077 0.542467i \(-0.182510\pi\)
−0.889829 + 0.456295i \(0.849176\pi\)
\(752\) 44.3154 25.5855i 1.61601 0.933006i
\(753\) −21.5175 −0.784142
\(754\) 67.8184 51.3641i 2.46980 1.87057i
\(755\) 0 0
\(756\) 39.2590 22.6662i 1.42784 0.824362i
\(757\) 7.40301 + 12.8224i 0.269067 + 0.466038i 0.968621 0.248542i \(-0.0799513\pi\)
−0.699554 + 0.714580i \(0.746618\pi\)
\(758\) −2.55234 + 4.42078i −0.0927051 + 0.160570i
\(759\) 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 \(0.600602\pi\)
\(762\) 10.5075i 0.380647i
\(763\) 9.59843 16.6250i 0.347486 0.601864i
\(764\) −11.5055 19.9281i −0.416255 0.720975i
\(765\) 0 0
\(766\) 19.7275 0.712784
\(767\) 2.12991 1.61314i 0.0769065 0.0582472i
\(768\) −91.7512 −3.31078
\(769\) 18.2352 10.5281i 0.657579 0.379654i −0.133775 0.991012i \(-0.542710\pi\)
0.791354 + 0.611358i \(0.209377\pi\)
\(770\) 0 0
\(771\) −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
\(775\) 0 0
\(776\) 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 −0.0550293
\(780\) 0 0
\(781\) 10.4425 0.373660
\(782\) 5.25809 3.03576i 0.188029 0.108558i
\(783\) −26.6080