Properties

Label 224.3.w.a.43.12
Level 224
Weight 3
Character 224.43
Analytic conductor 6.104
Analytic rank 0
Dimension 192
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(48\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 43.12
Character \(\chi\) \(=\) 224.43
Dual form 224.3.w.a.99.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.49125 - 1.33273i) q^{2} +(-1.51777 - 3.66421i) q^{3} +(0.447645 + 3.97487i) q^{4} +(2.18754 - 5.28118i) q^{5} +(-2.62005 + 7.48703i) q^{6} +(1.87083 - 1.87083i) q^{7} +(4.62989 - 6.52412i) q^{8} +(-4.75887 + 4.75887i) q^{9} +O(q^{10})\) \(q+(-1.49125 - 1.33273i) q^{2} +(-1.51777 - 3.66421i) q^{3} +(0.447645 + 3.97487i) q^{4} +(2.18754 - 5.28118i) q^{5} +(-2.62005 + 7.48703i) q^{6} +(1.87083 - 1.87083i) q^{7} +(4.62989 - 6.52412i) q^{8} +(-4.75887 + 4.75887i) q^{9} +(-10.3006 + 4.96015i) q^{10} +(7.75926 - 18.7325i) q^{11} +(13.8854 - 7.67319i) q^{12} +(-5.88041 - 14.1966i) q^{13} +(-5.28319 + 0.296556i) q^{14} -22.6715 q^{15} +(-15.5992 + 3.55867i) q^{16} +24.0748i q^{17} +(13.4390 - 0.754355i) q^{18} +(1.53905 - 0.637494i) q^{19} +(21.9712 + 6.33108i) q^{20} +(-9.69459 - 4.01563i) q^{21} +(-36.5364 + 17.5938i) q^{22} +(28.3097 + 28.3097i) q^{23} +(-30.9328 - 7.06283i) q^{24} +(-5.42785 - 5.42785i) q^{25} +(-10.1511 + 29.0076i) q^{26} +(-8.31756 - 3.44525i) q^{27} +(8.27377 + 6.59884i) q^{28} +(-13.0610 + 5.41004i) q^{29} +(33.8089 + 30.2151i) q^{30} -33.1552i q^{31} +(28.0051 + 15.4827i) q^{32} -80.4167 q^{33} +(32.0853 - 35.9015i) q^{34} +(-5.78767 - 13.9727i) q^{35} +(-21.0462 - 16.7856i) q^{36} +(-27.7286 + 66.9428i) q^{37} +(-3.14471 - 1.10048i) q^{38} +(-43.0941 + 43.0941i) q^{39} +(-24.3270 - 38.7230i) q^{40} +(-8.73947 + 8.73947i) q^{41} +(9.10528 + 18.9086i) q^{42} +(6.34896 - 15.3277i) q^{43} +(77.9328 + 22.4566i) q^{44} +(14.7222 + 35.5426i) q^{45} +(-4.48752 - 79.9459i) q^{46} +17.6271 q^{47} +(36.7157 + 51.7576i) q^{48} -7.00000i q^{49} +(0.860399 + 15.3281i) q^{50} +(88.2151 - 36.5399i) q^{51} +(53.7972 - 29.7289i) q^{52} +(0.509226 + 0.210928i) q^{53} +(7.81196 + 16.2228i) q^{54} +(-81.9561 - 81.9561i) q^{55} +(-3.54377 - 20.8672i) q^{56} +(-4.67182 - 4.67182i) q^{57} +(26.6873 + 9.33910i) q^{58} +(-71.9963 - 29.8218i) q^{59} +(-10.1488 - 90.1164i) q^{60} +(63.9474 - 26.4879i) q^{61} +(-44.1870 + 49.4426i) q^{62} +17.8061i q^{63} +(-21.1282 - 60.4119i) q^{64} -87.8382 q^{65} +(119.921 + 107.174i) q^{66} +(16.2654 + 39.2682i) q^{67} +(-95.6942 + 10.7770i) q^{68} +(60.7651 - 146.700i) q^{69} +(-9.99099 + 28.5502i) q^{70} +(73.2499 - 73.2499i) q^{71} +(9.01435 + 53.0805i) q^{72} +(9.82545 - 9.82545i) q^{73} +(130.567 - 62.8735i) q^{74} +(-11.6506 + 28.1270i) q^{75} +(3.22290 + 5.83214i) q^{76} +(-20.5291 - 49.5616i) q^{77} +(121.697 - 6.83109i) q^{78} +35.2139 q^{79} +(-15.3299 + 90.1670i) q^{80} +96.2769i q^{81} +(24.6801 - 1.38534i) q^{82} +(99.7432 - 41.3150i) q^{83} +(11.6219 - 40.3323i) q^{84} +(127.143 + 52.6644i) q^{85} +(-29.8957 + 14.3960i) q^{86} +(39.6471 + 39.6471i) q^{87} +(-86.2886 - 137.352i) q^{88} +(12.1938 + 12.1938i) q^{89} +(25.4143 - 72.6237i) q^{90} +(-37.5606 - 15.5581i) q^{91} +(-99.8546 + 125.200i) q^{92} +(-121.487 + 50.3218i) q^{93} +(-26.2864 - 23.4923i) q^{94} -9.52251i q^{95} +(14.2269 - 126.116i) q^{96} -67.1987 q^{97} +(-9.32913 + 10.4387i) q^{98} +(52.2203 + 126.071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192q + O(q^{10}) \) \( 192q + 80q^{10} + 96q^{12} - 20q^{16} - 60q^{18} - 260q^{22} + 64q^{23} - 144q^{24} - 200q^{26} + 192q^{27} - 40q^{30} + 40q^{32} + 120q^{34} + 464q^{36} + 504q^{38} - 384q^{39} + 360q^{40} - 96q^{43} + 52q^{44} + 64q^{46} - 104q^{48} - 312q^{50} - 384q^{51} - 320q^{52} + 160q^{53} - 576q^{54} - 512q^{55} - 196q^{56} - 360q^{58} - 872q^{60} + 128q^{61} - 408q^{62} + 832q^{66} + 160q^{67} + 856q^{68} - 384q^{69} + 336q^{70} + 1488q^{72} + 308q^{74} + 768q^{75} + 1024q^{76} - 224q^{77} - 408q^{78} + 1024q^{79} - 1040q^{80} - 240q^{82} - 1384q^{86} + 896q^{87} - 560q^{88} - 1320q^{90} - 380q^{92} - 936q^{94} - 1088q^{96} - 512q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.49125 1.33273i −0.745624 0.666367i
\(3\) −1.51777 3.66421i −0.505922 1.22140i −0.946212 0.323548i \(-0.895124\pi\)
0.440290 0.897856i \(-0.354876\pi\)
\(4\) 0.447645 + 3.97487i 0.111911 + 0.993718i
\(5\) 2.18754 5.28118i 0.437507 1.05624i −0.539300 0.842114i \(-0.681311\pi\)
0.976807 0.214122i \(-0.0686889\pi\)
\(6\) −2.62005 + 7.48703i −0.436675 + 1.24784i
\(7\) 1.87083 1.87083i 0.267261 0.267261i
\(8\) 4.62989 6.52412i 0.578737 0.815514i
\(9\) −4.75887 + 4.75887i −0.528763 + 0.528763i
\(10\) −10.3006 + 4.96015i −1.03006 + 0.496015i
\(11\) 7.75926 18.7325i 0.705388 1.70296i −0.00582822 0.999983i \(-0.501855\pi\)
0.711216 0.702974i \(-0.248145\pi\)
\(12\) 13.8854 7.67319i 1.15711 0.639433i
\(13\) −5.88041 14.1966i −0.452339 1.09204i −0.971430 0.237325i \(-0.923730\pi\)
0.519091 0.854719i \(-0.326270\pi\)
\(14\) −5.28319 + 0.296556i −0.377370 + 0.0211825i
\(15\) −22.6715 −1.51143
\(16\) −15.5992 + 3.55867i −0.974952 + 0.222417i
\(17\) 24.0748i 1.41616i 0.706130 + 0.708082i \(0.250439\pi\)
−0.706130 + 0.708082i \(0.749561\pi\)
\(18\) 13.4390 0.754355i 0.746609 0.0419086i
\(19\) 1.53905 0.637494i 0.0810024 0.0335523i −0.341814 0.939768i \(-0.611041\pi\)
0.422817 + 0.906215i \(0.361041\pi\)
\(20\) 21.9712 + 6.33108i 1.09856 + 0.316554i
\(21\) −9.69459 4.01563i −0.461647 0.191221i
\(22\) −36.5364 + 17.5938i −1.66075 + 0.799719i
\(23\) 28.3097 + 28.3097i 1.23085 + 1.23085i 0.963636 + 0.267218i \(0.0861045\pi\)
0.267218 + 0.963636i \(0.413895\pi\)
\(24\) −30.9328 7.06283i −1.28887 0.294284i
\(25\) −5.42785 5.42785i −0.217114 0.217114i
\(26\) −10.1511 + 29.0076i −0.390426 + 1.11568i
\(27\) −8.31756 3.44525i −0.308058 0.127602i
\(28\) 8.27377 + 6.59884i 0.295492 + 0.235673i
\(29\) −13.0610 + 5.41004i −0.450379 + 0.186553i −0.596331 0.802738i \(-0.703376\pi\)
0.145952 + 0.989292i \(0.453376\pi\)
\(30\) 33.8089 + 30.2151i 1.12696 + 1.00717i
\(31\) 33.1552i 1.06952i −0.845004 0.534761i \(-0.820402\pi\)
0.845004 0.534761i \(-0.179598\pi\)
\(32\) 28.0051 + 15.4827i 0.875159 + 0.483836i
\(33\) −80.4167 −2.43687
\(34\) 32.0853 35.9015i 0.943684 1.05593i
\(35\) −5.78767 13.9727i −0.165362 0.399219i
\(36\) −21.0462 16.7856i −0.584616 0.466267i
\(37\) −27.7286 + 66.9428i −0.749422 + 1.80926i −0.187111 + 0.982339i \(0.559912\pi\)
−0.562311 + 0.826926i \(0.690088\pi\)
\(38\) −3.14471 1.10048i −0.0827555 0.0289599i
\(39\) −43.0941 + 43.0941i −1.10498 + 1.10498i
\(40\) −24.3270 38.7230i −0.608174 0.968075i
\(41\) −8.73947 + 8.73947i −0.213158 + 0.213158i −0.805607 0.592450i \(-0.798161\pi\)
0.592450 + 0.805607i \(0.298161\pi\)
\(42\) 9.10528 + 18.9086i 0.216792 + 0.450205i
\(43\) 6.34896 15.3277i 0.147650 0.356459i −0.832700 0.553725i \(-0.813206\pi\)
0.980350 + 0.197265i \(0.0632060\pi\)
\(44\) 77.9328 + 22.4566i 1.77120 + 0.510376i
\(45\) 14.7222 + 35.5426i 0.327161 + 0.789836i
\(46\) −4.48752 79.9459i −0.0975549 1.73796i
\(47\) 17.6271 0.375046 0.187523 0.982260i \(-0.439954\pi\)
0.187523 + 0.982260i \(0.439954\pi\)
\(48\) 36.7157 + 51.7576i 0.764910 + 1.07828i
\(49\) 7.00000i 0.142857i
\(50\) 0.860399 + 15.3281i 0.0172080 + 0.306563i
\(51\) 88.2151 36.5399i 1.72971 0.716468i
\(52\) 53.7972 29.7289i 1.03456 0.571710i
\(53\) 0.509226 + 0.210928i 0.00960804 + 0.00397978i 0.387482 0.921877i \(-0.373345\pi\)
−0.377874 + 0.925857i \(0.623345\pi\)
\(54\) 7.81196 + 16.2228i 0.144666 + 0.300422i
\(55\) −81.9561 81.9561i −1.49011 1.49011i
\(56\) −3.54377 20.8672i −0.0632815 0.372629i
\(57\) −4.67182 4.67182i −0.0819618 0.0819618i
\(58\) 26.6873 + 9.33910i 0.460127 + 0.161019i
\(59\) −71.9963 29.8218i −1.22028 0.505455i −0.322779 0.946474i \(-0.604617\pi\)
−0.897498 + 0.441019i \(0.854617\pi\)
\(60\) −10.1488 90.1164i −0.169147 1.50194i
\(61\) 63.9474 26.4879i 1.04832 0.434228i 0.209027 0.977910i \(-0.432970\pi\)
0.839291 + 0.543682i \(0.182970\pi\)
\(62\) −44.1870 + 49.4426i −0.712693 + 0.797461i
\(63\) 17.8061i 0.282636i
\(64\) −21.1282 60.4119i −0.330128 0.943936i
\(65\) −87.8382 −1.35136
\(66\) 119.921 + 107.174i 1.81699 + 1.62385i
\(67\) 16.2654 + 39.2682i 0.242768 + 0.586093i 0.997556 0.0698759i \(-0.0222603\pi\)
−0.754788 + 0.655969i \(0.772260\pi\)
\(68\) −95.6942 + 10.7770i −1.40727 + 0.158485i
\(69\) 60.7651 146.700i 0.880654 2.12609i
\(70\) −9.99099 + 28.5502i −0.142728 + 0.407859i
\(71\) 73.2499 73.2499i 1.03169 1.03169i 0.0322080 0.999481i \(-0.489746\pi\)
0.999481 0.0322080i \(-0.0102539\pi\)
\(72\) 9.01435 + 53.0805i 0.125199 + 0.737228i
\(73\) 9.82545 9.82545i 0.134595 0.134595i −0.636599 0.771195i \(-0.719660\pi\)
0.771195 + 0.636599i \(0.219660\pi\)
\(74\) 130.567 62.8735i 1.76442 0.849642i
\(75\) −11.6506 + 28.1270i −0.155341 + 0.375026i
\(76\) 3.22290 + 5.83214i 0.0424066 + 0.0767387i
\(77\) −20.5291 49.5616i −0.266612 0.643657i
\(78\) 121.697 6.83109i 1.56022 0.0875781i
\(79\) 35.2139 0.445746 0.222873 0.974848i \(-0.428457\pi\)
0.222873 + 0.974848i \(0.428457\pi\)
\(80\) −15.3299 + 90.1670i −0.191624 + 1.12709i
\(81\) 96.2769i 1.18860i
\(82\) 24.6801 1.38534i 0.300977 0.0168944i
\(83\) 99.7432 41.3150i 1.20173 0.497771i 0.310169 0.950681i \(-0.399614\pi\)
0.891556 + 0.452911i \(0.149614\pi\)
\(84\) 11.6219 40.3323i 0.138356 0.480147i
\(85\) 127.143 + 52.6644i 1.49580 + 0.619581i
\(86\) −29.8957 + 14.3960i −0.347624 + 0.167396i
\(87\) 39.6471 + 39.6471i 0.455713 + 0.455713i
\(88\) −86.2886 137.352i −0.980552 1.56082i
\(89\) 12.1938 + 12.1938i 0.137009 + 0.137009i 0.772285 0.635276i \(-0.219114\pi\)
−0.635276 + 0.772285i \(0.719114\pi\)
\(90\) 25.4143 72.6237i 0.282381 0.806930i
\(91\) −37.5606 15.5581i −0.412754 0.170968i
\(92\) −99.8546 + 125.200i −1.08538 + 1.36087i
\(93\) −121.487 + 50.3218i −1.30632 + 0.541094i
\(94\) −26.2864 23.4923i −0.279643 0.249918i
\(95\) 9.52251i 0.100237i
\(96\) 14.2269 126.116i 0.148197 1.31371i
\(97\) −67.1987 −0.692770 −0.346385 0.938092i \(-0.612591\pi\)
−0.346385 + 0.938092i \(0.612591\pi\)
\(98\) −9.32913 + 10.4387i −0.0951952 + 0.106518i
\(99\) 52.2203 + 126.071i 0.527478 + 1.27344i
\(100\) 19.1453 24.0048i 0.191453 0.240048i
\(101\) 12.5523 30.3039i 0.124280 0.300039i −0.849478 0.527624i \(-0.823083\pi\)
0.973758 + 0.227585i \(0.0730831\pi\)
\(102\) −180.249 63.0771i −1.76714 0.618403i
\(103\) −4.85553 + 4.85553i −0.0471411 + 0.0471411i −0.730284 0.683143i \(-0.760612\pi\)
0.683143 + 0.730284i \(0.260612\pi\)
\(104\) −119.846 27.3641i −1.15236 0.263116i
\(105\) −42.4145 + 42.4145i −0.403948 + 0.403948i
\(106\) −0.478271 0.993209i −0.00451199 0.00936989i
\(107\) −74.9138 + 180.858i −0.700129 + 1.69026i 0.0231763 + 0.999731i \(0.492622\pi\)
−0.723305 + 0.690529i \(0.757378\pi\)
\(108\) 9.97110 34.6035i 0.0923250 0.320403i
\(109\) −43.2098 104.318i −0.396420 0.957042i −0.988508 0.151169i \(-0.951696\pi\)
0.592088 0.805873i \(-0.298304\pi\)
\(110\) 12.9913 + 231.443i 0.118103 + 2.10402i
\(111\) 287.378 2.58899
\(112\) −22.5258 + 35.8411i −0.201123 + 0.320010i
\(113\) 42.9776i 0.380333i 0.981752 + 0.190166i \(0.0609027\pi\)
−0.981752 + 0.190166i \(0.939097\pi\)
\(114\) 0.740557 + 13.1931i 0.00649612 + 0.115729i
\(115\) 211.437 87.5799i 1.83858 0.761565i
\(116\) −27.3509 49.4940i −0.235784 0.426673i
\(117\) 95.5437 + 39.5755i 0.816612 + 0.338252i
\(118\) 67.6198 + 140.424i 0.573049 + 1.19003i
\(119\) 45.0398 + 45.0398i 0.378486 + 0.378486i
\(120\) −104.967 + 147.912i −0.874722 + 1.23260i
\(121\) −205.141 205.141i −1.69538 1.69538i
\(122\) −130.663 45.7248i −1.07101 0.374793i
\(123\) 45.2877 + 18.7588i 0.368193 + 0.152510i
\(124\) 131.788 14.8418i 1.06280 0.119692i
\(125\) 91.4904 37.8966i 0.731923 0.303172i
\(126\) 23.7307 26.5533i 0.188339 0.210740i
\(127\) 70.4794i 0.554956i −0.960732 0.277478i \(-0.910501\pi\)
0.960732 0.277478i \(-0.0894986\pi\)
\(128\) −49.0056 + 118.247i −0.382856 + 0.923808i
\(129\) −65.8003 −0.510080
\(130\) 130.989 + 117.065i 1.00760 + 0.900499i
\(131\) 38.4674 + 92.8686i 0.293645 + 0.708921i 0.999999 + 0.00106291i \(0.000338336\pi\)
−0.706355 + 0.707858i \(0.749662\pi\)
\(132\) −35.9981 319.646i −0.272713 2.42156i
\(133\) 1.68665 4.07193i 0.0126816 0.0306160i
\(134\) 28.0783 80.2361i 0.209539 0.598777i
\(135\) −36.3899 + 36.3899i −0.269555 + 0.269555i
\(136\) 157.067 + 111.464i 1.15490 + 0.819586i
\(137\) 49.4925 49.4925i 0.361259 0.361259i −0.503017 0.864276i \(-0.667777\pi\)
0.864276 + 0.503017i \(0.167777\pi\)
\(138\) −286.128 + 137.782i −2.07339 + 0.998424i
\(139\) −43.3287 + 104.605i −0.311718 + 0.752553i 0.687924 + 0.725783i \(0.258522\pi\)
−0.999642 + 0.0267701i \(0.991478\pi\)
\(140\) 52.9488 29.2601i 0.378206 0.209001i
\(141\) −26.7539 64.5896i −0.189744 0.458082i
\(142\) −206.856 + 11.6113i −1.45674 + 0.0817695i
\(143\) −311.565 −2.17878
\(144\) 57.2994 91.1699i 0.397913 0.633124i
\(145\) 80.8121i 0.557325i
\(146\) −27.7469 + 1.55749i −0.190047 + 0.0106677i
\(147\) −25.6495 + 10.6244i −0.174486 + 0.0722746i
\(148\) −278.502 80.2511i −1.88177 0.542237i
\(149\) 157.582 + 65.2724i 1.05759 + 0.438070i 0.842597 0.538545i \(-0.181026\pi\)
0.214997 + 0.976615i \(0.431026\pi\)
\(150\) 54.8597 26.4172i 0.365731 0.176115i
\(151\) −98.5245 98.5245i −0.652480 0.652480i 0.301110 0.953590i \(-0.402643\pi\)
−0.953590 + 0.301110i \(0.902643\pi\)
\(152\) 2.96654 12.9924i 0.0195167 0.0854766i
\(153\) −114.569 114.569i −0.748815 0.748815i
\(154\) −35.4384 + 101.268i −0.230120 + 0.657587i
\(155\) −175.098 72.5281i −1.12967 0.467923i
\(156\) −190.585 152.003i −1.22170 0.974377i
\(157\) 70.0191 29.0029i 0.445981 0.184732i −0.148379 0.988931i \(-0.547405\pi\)
0.594360 + 0.804199i \(0.297405\pi\)
\(158\) −52.5127 46.9308i −0.332359 0.297030i
\(159\) 2.18605i 0.0137487i
\(160\) 143.029 114.031i 0.893933 0.712692i
\(161\) 105.925 0.657919
\(162\) 128.311 143.573i 0.792045 0.886251i
\(163\) −1.04564 2.52439i −0.00641494 0.0154870i 0.920640 0.390414i \(-0.127668\pi\)
−0.927055 + 0.374926i \(0.877668\pi\)
\(164\) −38.6504 30.8261i −0.235673 0.187964i
\(165\) −175.914 + 424.695i −1.06615 + 2.57391i
\(166\) −203.804 71.3201i −1.22773 0.429639i
\(167\) 205.131 205.131i 1.22833 1.22833i 0.263730 0.964596i \(-0.415047\pi\)
0.964596 0.263730i \(-0.0849529\pi\)
\(168\) −71.0834 + 44.6567i −0.423115 + 0.265814i
\(169\) −47.4622 + 47.4622i −0.280841 + 0.280841i
\(170\) −119.414 247.984i −0.702438 1.45873i
\(171\) −4.29037 + 10.3579i −0.0250899 + 0.0605723i
\(172\) 63.7679 + 18.3749i 0.370744 + 0.106831i
\(173\) 24.7655 + 59.7892i 0.143153 + 0.345602i 0.979152 0.203129i \(-0.0651111\pi\)
−0.835999 + 0.548731i \(0.815111\pi\)
\(174\) −6.28468 111.963i −0.0361189 0.643463i
\(175\) −20.3091 −0.116052
\(176\) −54.3757 + 319.826i −0.308953 + 1.81719i
\(177\) 309.072i 1.74617i
\(178\) −1.93290 34.4350i −0.0108590 0.193455i
\(179\) −69.3636 + 28.7314i −0.387506 + 0.160510i −0.567927 0.823079i \(-0.692254\pi\)
0.180420 + 0.983590i \(0.442254\pi\)
\(180\) −134.687 + 74.4295i −0.748261 + 0.413497i
\(181\) −193.451 80.1302i −1.06879 0.442708i −0.222228 0.974995i \(-0.571333\pi\)
−0.846564 + 0.532287i \(0.821333\pi\)
\(182\) 35.2774 + 73.2592i 0.193832 + 0.402523i
\(183\) −194.114 194.114i −1.06073 1.06073i
\(184\) 315.766 53.6248i 1.71612 0.291439i
\(185\) 292.879 + 292.879i 1.58313 + 1.58313i
\(186\) 248.234 + 86.8681i 1.33459 + 0.467033i
\(187\) 450.981 + 186.803i 2.41166 + 0.998944i
\(188\) 7.89071 + 70.0656i 0.0419719 + 0.372690i
\(189\) −22.0062 + 9.11526i −0.116435 + 0.0482289i
\(190\) −12.6910 + 14.2004i −0.0667946 + 0.0747391i
\(191\) 176.285i 0.922959i −0.887151 0.461479i \(-0.847319\pi\)
0.887151 0.461479i \(-0.152681\pi\)
\(192\) −189.294 + 169.109i −0.985908 + 0.880777i
\(193\) 271.897 1.40879 0.704395 0.709808i \(-0.251218\pi\)
0.704395 + 0.709808i \(0.251218\pi\)
\(194\) 100.210 + 89.5579i 0.516546 + 0.461639i
\(195\) 133.318 + 321.858i 0.683681 + 1.65055i
\(196\) 27.8241 3.13352i 0.141960 0.0159873i
\(197\) −46.5896 + 112.477i −0.236495 + 0.570950i −0.996916 0.0784811i \(-0.974993\pi\)
0.760420 + 0.649431i \(0.224993\pi\)
\(198\) 90.1454 257.599i 0.455280 1.30100i
\(199\) 36.5908 36.5908i 0.183873 0.183873i −0.609168 0.793041i \(-0.708496\pi\)
0.793041 + 0.609168i \(0.208496\pi\)
\(200\) −60.5423 + 10.2815i −0.302711 + 0.0514077i
\(201\) 119.200 119.200i 0.593034 0.593034i
\(202\) −59.1056 + 28.4618i −0.292602 + 0.140900i
\(203\) −14.3136 + 34.5562i −0.0705105 + 0.170227i
\(204\) 184.730 + 334.287i 0.905541 + 1.63866i
\(205\) 27.0368 + 65.2725i 0.131887 + 0.318403i
\(206\) 13.7119 0.769678i 0.0665628 0.00373630i
\(207\) −269.444 −1.30166
\(208\) 142.251 + 200.529i 0.683898 + 0.964082i
\(209\) 33.7767i 0.161611i
\(210\) 119.778 6.72337i 0.570371 0.0320160i
\(211\) −223.782 + 92.6934i −1.06058 + 0.439305i −0.843656 0.536884i \(-0.819601\pi\)
−0.216921 + 0.976189i \(0.569601\pi\)
\(212\) −0.610460 + 2.11853i −0.00287953 + 0.00999306i
\(213\) −379.579 157.227i −1.78206 0.738155i
\(214\) 352.750 169.864i 1.64837 0.793757i
\(215\) −67.0600 67.0600i −0.311907 0.311907i
\(216\) −60.9866 + 38.3136i −0.282345 + 0.177378i
\(217\) −62.0276 62.0276i −0.285842 0.285842i
\(218\) −74.5910 + 213.151i −0.342161 + 0.977755i
\(219\) −50.9152 21.0898i −0.232490 0.0963004i
\(220\) 289.078 362.452i 1.31399 1.64751i
\(221\) 341.779 141.570i 1.54651 0.640586i
\(222\) −428.552 382.998i −1.93042 1.72522i
\(223\) 120.728i 0.541379i −0.962667 0.270689i \(-0.912748\pi\)
0.962667 0.270689i \(-0.0872517\pi\)
\(224\) 81.3583 23.4271i 0.363207 0.104585i
\(225\) 51.6608 0.229604
\(226\) 57.2776 64.0903i 0.253441 0.283585i
\(227\) −47.0858 113.675i −0.207427 0.500772i 0.785590 0.618747i \(-0.212360\pi\)
−0.993017 + 0.117976i \(0.962360\pi\)
\(228\) 16.4786 20.6612i 0.0722745 0.0906194i
\(229\) 69.6857 168.236i 0.304304 0.734655i −0.695565 0.718463i \(-0.744846\pi\)
0.999869 0.0161919i \(-0.00515425\pi\)
\(230\) −432.025 151.185i −1.87837 0.657327i
\(231\) −150.446 + 150.446i −0.651281 + 0.651281i
\(232\) −25.1753 + 110.259i −0.108514 + 0.475256i
\(233\) −4.88688 + 4.88688i −0.0209737 + 0.0209737i −0.717516 0.696542i \(-0.754721\pi\)
0.696542 + 0.717516i \(0.254721\pi\)
\(234\) −89.7358 186.351i −0.383486 0.796372i
\(235\) 38.5600 93.0920i 0.164085 0.396136i
\(236\) 86.3092 299.526i 0.365717 1.26918i
\(237\) −53.4465 129.031i −0.225513 0.544436i
\(238\) −7.13951 127.192i −0.0299980 0.534418i
\(239\) 128.146 0.536176 0.268088 0.963394i \(-0.413608\pi\)
0.268088 + 0.963394i \(0.413608\pi\)
\(240\) 353.658 80.6804i 1.47358 0.336168i
\(241\) 210.011i 0.871416i 0.900088 + 0.435708i \(0.143502\pi\)
−0.900088 + 0.435708i \(0.856498\pi\)
\(242\) 32.5181 + 579.315i 0.134372 + 2.39386i
\(243\) 277.921 115.119i 1.14371 0.473739i
\(244\) 133.912 + 242.326i 0.548818 + 0.993138i
\(245\) −36.9682 15.3127i −0.150891 0.0625010i
\(246\) −42.5348 88.3304i −0.172906 0.359067i
\(247\) −18.1004 18.1004i −0.0732811 0.0732811i
\(248\) −216.308 153.505i −0.872210 0.618971i
\(249\) −302.774 302.774i −1.21596 1.21596i
\(250\) −186.941 65.4191i −0.747764 0.261676i
\(251\) −253.863 105.154i −1.01141 0.418939i −0.185439 0.982656i \(-0.559371\pi\)
−0.825968 + 0.563717i \(0.809371\pi\)
\(252\) −70.7768 + 7.97080i −0.280860 + 0.0316301i
\(253\) 749.973 310.649i 2.96432 1.22786i
\(254\) −93.9302 + 105.102i −0.369804 + 0.413789i
\(255\) 545.812i 2.14044i
\(256\) 230.672 111.025i 0.901062 0.433691i
\(257\) 259.740 1.01066 0.505331 0.862926i \(-0.331371\pi\)
0.505331 + 0.862926i \(0.331371\pi\)
\(258\) 98.1247 + 87.6943i 0.380328 + 0.339900i
\(259\) 73.3630 + 177.114i 0.283255 + 0.683838i
\(260\) −39.3204 349.146i −0.151232 1.34287i
\(261\) 36.4099 87.9012i 0.139501 0.336786i
\(262\) 66.4046 189.757i 0.253453 0.724264i
\(263\) −180.123 + 180.123i −0.684880 + 0.684880i −0.961096 0.276216i \(-0.910919\pi\)
0.276216 + 0.961096i \(0.410919\pi\)
\(264\) −372.321 + 524.648i −1.41031 + 1.98730i
\(265\) 2.22790 2.22790i 0.00840717 0.00840717i
\(266\) −7.94201 + 3.82441i −0.0298572 + 0.0143775i
\(267\) 26.1732 63.1878i 0.0980271 0.236658i
\(268\) −148.805 + 82.2312i −0.555243 + 0.306833i
\(269\) 84.4320 + 203.837i 0.313874 + 0.757758i 0.999554 + 0.0298556i \(0.00950475\pi\)
−0.685680 + 0.727903i \(0.740495\pi\)
\(270\) 102.764 5.76837i 0.380609 0.0213643i
\(271\) 106.984 0.394775 0.197388 0.980326i \(-0.436754\pi\)
0.197388 + 0.980326i \(0.436754\pi\)
\(272\) −85.6741 375.548i −0.314978 1.38069i
\(273\) 161.243i 0.590635i
\(274\) −139.766 + 7.84533i −0.510094 + 0.0286326i
\(275\) −143.793 + 59.5612i −0.522885 + 0.216586i
\(276\) 610.315 + 175.864i 2.21129 + 0.637189i
\(277\) −77.4208 32.0688i −0.279498 0.115772i 0.238531 0.971135i \(-0.423334\pi\)
−0.518029 + 0.855363i \(0.673334\pi\)
\(278\) 204.024 98.2462i 0.733900 0.353404i
\(279\) 157.781 + 157.781i 0.565523 + 0.565523i
\(280\) −117.956 26.9326i −0.421270 0.0961878i
\(281\) 223.879 + 223.879i 0.796724 + 0.796724i 0.982577 0.185854i \(-0.0595050\pi\)
−0.185854 + 0.982577i \(0.559505\pi\)
\(282\) −46.1840 + 131.975i −0.163773 + 0.467996i
\(283\) −499.979 207.098i −1.76671 0.731795i −0.995451 0.0952711i \(-0.969628\pi\)
−0.771257 0.636524i \(-0.780372\pi\)
\(284\) 323.949 + 258.369i 1.14067 + 0.909751i
\(285\) −34.8925 + 14.4529i −0.122430 + 0.0507121i
\(286\) 464.621 + 415.233i 1.62455 + 1.45186i
\(287\) 32.7001i 0.113938i
\(288\) −206.953 + 59.5921i −0.718586 + 0.206917i
\(289\) −290.595 −1.00552
\(290\) 107.701 120.511i 0.371383 0.415555i
\(291\) 101.992 + 246.230i 0.350487 + 0.846152i
\(292\) 43.4532 + 34.6566i 0.148812 + 0.118687i
\(293\) −26.7148 + 64.4952i −0.0911768 + 0.220120i −0.962889 0.269898i \(-0.913010\pi\)
0.871712 + 0.490018i \(0.163010\pi\)
\(294\) 52.4092 + 18.3403i 0.178263 + 0.0623821i
\(295\) −314.989 + 314.989i −1.06776 + 1.06776i
\(296\) 308.362 + 490.843i 1.04176 + 1.65825i
\(297\) −129.076 + 129.076i −0.434600 + 0.434600i
\(298\) −148.003 307.352i −0.496653 1.03138i
\(299\) 235.427 568.372i 0.787383 1.90091i
\(300\) −117.017 33.7187i −0.390055 0.112396i
\(301\) −16.7978 40.5534i −0.0558066 0.134729i
\(302\) 15.6177 + 278.231i 0.0517142 + 0.921296i
\(303\) −130.091 −0.429344
\(304\) −21.7393 + 15.4214i −0.0715109 + 0.0507282i
\(305\) 395.661i 1.29725i
\(306\) 18.1609 + 323.540i 0.0593495 + 1.05732i
\(307\) −227.384 + 94.1854i −0.740663 + 0.306793i −0.720926 0.693012i \(-0.756283\pi\)
−0.0197376 + 0.999805i \(0.506283\pi\)
\(308\) 187.811 103.787i 0.609777 0.336969i
\(309\) 25.1613 + 10.4221i 0.0814280 + 0.0337286i
\(310\) 164.454 + 341.517i 0.530498 + 1.10167i
\(311\) 185.286 + 185.286i 0.595774 + 0.595774i 0.939185 0.343411i \(-0.111582\pi\)
−0.343411 + 0.939185i \(0.611582\pi\)
\(312\) 81.6298 + 480.672i 0.261634 + 1.54062i
\(313\) −244.886 244.886i −0.782384 0.782384i 0.197849 0.980233i \(-0.436604\pi\)
−0.980233 + 0.197849i \(0.936604\pi\)
\(314\) −143.069 50.0663i −0.455634 0.159447i
\(315\) 94.0369 + 38.9514i 0.298530 + 0.123655i
\(316\) 15.7633 + 139.971i 0.0498840 + 0.442946i
\(317\) 280.654 116.251i 0.885344 0.366722i 0.106777 0.994283i \(-0.465947\pi\)
0.778567 + 0.627561i \(0.215947\pi\)
\(318\) −2.91342 + 3.25995i −0.00916171 + 0.0102514i
\(319\) 286.643i 0.898569i
\(320\) −365.265 20.5716i −1.14145 0.0642862i
\(321\) 776.403 2.41870
\(322\) −157.961 141.170i −0.490561 0.438415i
\(323\) 15.3475 + 37.0522i 0.0475155 + 0.114713i
\(324\) −382.688 + 43.0979i −1.18114 + 0.133018i
\(325\) −45.1388 + 108.975i −0.138889 + 0.335307i
\(326\) −1.80503 + 5.15804i −0.00553691 + 0.0158222i
\(327\) −316.659 + 316.659i −0.968377 + 0.968377i
\(328\) 16.5545 + 97.4801i 0.0504710 + 0.297195i
\(329\) 32.9774 32.9774i 0.100235 0.100235i
\(330\) 828.336 398.879i 2.51011 1.20872i
\(331\) −102.501 + 247.458i −0.309669 + 0.747608i 0.690046 + 0.723765i \(0.257590\pi\)
−0.999716 + 0.0238430i \(0.992410\pi\)
\(332\) 208.871 + 377.972i 0.629131 + 1.13847i
\(333\) −186.615 450.529i −0.560406 1.35294i
\(334\) −579.285 + 32.5164i −1.73439 + 0.0973545i
\(335\) 242.964 0.725264
\(336\) 165.518 + 28.1409i 0.492614 + 0.0837527i
\(337\) 15.2508i 0.0452546i −0.999744 0.0226273i \(-0.992797\pi\)
0.999744 0.0226273i \(-0.00720310\pi\)
\(338\) 134.032 7.52350i 0.396545 0.0222589i
\(339\) 157.479 65.2299i 0.464540 0.192419i
\(340\) −152.419 + 528.953i −0.448292 + 1.55574i
\(341\) −621.080 257.260i −1.82135 0.754427i
\(342\) 20.2023 9.72824i 0.0590710 0.0284451i
\(343\) −13.0958 13.0958i −0.0381802 0.0381802i
\(344\) −70.6050 112.387i −0.205247 0.326707i
\(345\) −641.823 641.823i −1.86036 1.86036i
\(346\) 42.7515 122.166i 0.123559 0.353082i
\(347\) 134.982 + 55.9114i 0.388997 + 0.161128i 0.568606 0.822610i \(-0.307483\pi\)
−0.179609 + 0.983738i \(0.557483\pi\)
\(348\) −139.844 + 175.340i −0.401851 + 0.503850i
\(349\) −81.0202 + 33.5596i −0.232149 + 0.0961595i −0.495726 0.868479i \(-0.665098\pi\)
0.263576 + 0.964639i \(0.415098\pi\)
\(350\) 30.2860 + 27.0667i 0.0865314 + 0.0773333i
\(351\) 138.340i 0.394132i
\(352\) 507.330 404.471i 1.44128 1.14907i
\(353\) −386.116 −1.09381 −0.546906 0.837194i \(-0.684195\pi\)
−0.546906 + 0.837194i \(0.684195\pi\)
\(354\) 411.911 460.904i 1.16359 1.30199i
\(355\) −226.609 547.083i −0.638335 1.54108i
\(356\) −43.0102 + 53.9271i −0.120815 + 0.151481i
\(357\) 96.6754 233.395i 0.270800 0.653768i
\(358\) 141.730 + 49.5976i 0.395893 + 0.138541i
\(359\) 143.589 143.589i 0.399970 0.399970i −0.478253 0.878222i \(-0.658730\pi\)
0.878222 + 0.478253i \(0.158730\pi\)
\(360\) 300.046 + 68.5090i 0.833462 + 0.190303i
\(361\) −253.303 + 253.303i −0.701671 + 0.701671i
\(362\) 181.692 + 377.313i 0.501912 + 1.04230i
\(363\) −440.325 + 1063.04i −1.21302 + 2.92848i
\(364\) 45.0277 156.263i 0.123702 0.429294i
\(365\) −30.3964 73.3834i −0.0832779 0.201051i
\(366\) 30.7702 + 548.175i 0.0840715 + 1.49775i
\(367\) 43.6619 0.118970 0.0594849 0.998229i \(-0.481054\pi\)
0.0594849 + 0.998229i \(0.481054\pi\)
\(368\) −542.353 340.864i −1.47379 0.926261i
\(369\) 83.1799i 0.225420i
\(370\) −46.4260 827.086i −0.125476 2.23537i
\(371\) 1.34729 0.558064i 0.00363150 0.00150422i
\(372\) −254.406 460.371i −0.683887 1.23756i
\(373\) 306.743 + 127.057i 0.822368 + 0.340636i 0.753877 0.657016i \(-0.228182\pi\)
0.0684910 + 0.997652i \(0.478182\pi\)
\(374\) −423.567 879.607i −1.13253 2.35189i
\(375\) −277.722 277.722i −0.740592 0.740592i
\(376\) 81.6118 115.001i 0.217053 0.305855i
\(377\) 153.608 + 153.608i 0.407448 + 0.407448i
\(378\) 44.9649 + 15.7353i 0.118955 + 0.0416277i
\(379\) −217.916 90.2639i −0.574977 0.238163i 0.0761958 0.997093i \(-0.475723\pi\)
−0.651173 + 0.758930i \(0.725723\pi\)
\(380\) 37.8508 4.26271i 0.0996073 0.0112177i
\(381\) −258.251 + 106.971i −0.677825 + 0.280764i
\(382\) −234.941 + 262.885i −0.615029 + 0.688180i
\(383\) 31.0189i 0.0809892i −0.999180 0.0404946i \(-0.987107\pi\)
0.999180 0.0404946i \(-0.0128934\pi\)
\(384\) 507.662 + 0.0949962i 1.32204 + 0.000247386i
\(385\) −306.652 −0.796498
\(386\) −405.465 362.366i −1.05043 0.938771i
\(387\) 42.7289 + 103.157i 0.110410 + 0.266555i
\(388\) −30.0812 267.106i −0.0775288 0.688418i
\(389\) 15.7473 38.0173i 0.0404814 0.0977308i −0.902346 0.431013i \(-0.858156\pi\)
0.942827 + 0.333282i \(0.108156\pi\)
\(390\) 230.140 657.647i 0.590103 1.68627i
\(391\) −681.549 + 681.549i −1.74309 + 1.74309i
\(392\) −45.6688 32.4093i −0.116502 0.0826767i
\(393\) 281.906 281.906i 0.717317 0.717317i
\(394\) 219.379 105.640i 0.556799 0.268122i
\(395\) 77.0317 185.971i 0.195017 0.470812i
\(396\) −477.740 + 264.004i −1.20641 + 0.666677i
\(397\) −53.6931 129.627i −0.135247 0.326515i 0.841717 0.539919i \(-0.181545\pi\)
−0.976964 + 0.213404i \(0.931545\pi\)
\(398\) −103.332 + 5.80022i −0.259628 + 0.0145734i
\(399\) −17.4804 −0.0438104
\(400\) 103.986 + 65.3543i 0.259965 + 0.163386i
\(401\) 98.7401i 0.246235i −0.992392 0.123117i \(-0.960711\pi\)
0.992392 0.123117i \(-0.0392891\pi\)
\(402\) −336.618 + 18.8951i −0.837359 + 0.0470026i
\(403\) −470.689 + 194.966i −1.16796 + 0.483786i
\(404\) 126.073 + 36.3283i 0.312062 + 0.0899216i
\(405\) 508.455 + 210.609i 1.25544 + 0.520022i
\(406\) 67.3993 32.4556i 0.166008 0.0799398i
\(407\) 1038.85 + 1038.85i 2.55247 + 2.55247i
\(408\) 170.036 744.701i 0.416755 1.82525i
\(409\) 156.599 + 156.599i 0.382882 + 0.382882i 0.872140 0.489257i \(-0.162732\pi\)
−0.489257 + 0.872140i \(0.662732\pi\)
\(410\) 46.6723 133.370i 0.113835 0.325294i
\(411\) −256.469 106.233i −0.624012 0.258474i
\(412\) −21.4737 17.1266i −0.0521206 0.0415693i
\(413\) −190.484 + 78.9012i −0.461221 + 0.191044i
\(414\) 401.808 + 359.097i 0.970550 + 0.867383i
\(415\) 617.139i 1.48708i
\(416\) 55.1205 488.621i 0.132501 1.17457i
\(417\) 449.057 1.07688
\(418\) −45.0153 + 50.3695i −0.107692 + 0.120501i
\(419\) −213.878 516.346i −0.510448 1.23233i −0.943624 0.331020i \(-0.892607\pi\)
0.433176 0.901309i \(-0.357393\pi\)
\(420\) −187.579 149.606i −0.446617 0.356204i
\(421\) 11.2856 27.2460i 0.0268068 0.0647172i −0.909909 0.414807i \(-0.863849\pi\)
0.936716 + 0.350090i \(0.113849\pi\)
\(422\) 457.250 + 160.012i 1.08353 + 0.379176i
\(423\) −83.8852 + 83.8852i −0.198310 + 0.198310i
\(424\) 3.73378 2.34567i 0.00880609 0.00553225i
\(425\) 130.674 130.674i 0.307469 0.307469i
\(426\) 356.506 + 740.343i 0.836868 + 1.73789i
\(427\) 70.0803 169.189i 0.164123 0.396227i
\(428\) −752.422 216.813i −1.75799 0.506571i
\(429\) 472.883 + 1141.64i 1.10229 + 2.66117i
\(430\) 10.6301 + 189.376i 0.0247211 + 0.440410i
\(431\) −304.575 −0.706671 −0.353335 0.935497i \(-0.614953\pi\)
−0.353335 + 0.935497i \(0.614953\pi\)
\(432\) 142.008 + 24.1437i 0.328722 + 0.0558883i
\(433\) 291.352i 0.672869i −0.941707 0.336434i \(-0.890779\pi\)
0.941707 0.336434i \(-0.109221\pi\)
\(434\) 9.83235 + 175.165i 0.0226552 + 0.403606i
\(435\) 296.113 122.654i 0.680719 0.281963i
\(436\) 395.307 218.451i 0.906667 0.501034i
\(437\) 61.6171 + 25.5226i 0.141000 + 0.0584042i
\(438\) 47.8202 + 99.3065i 0.109179 + 0.226727i
\(439\) 269.998 + 269.998i 0.615030 + 0.615030i 0.944252 0.329222i \(-0.106787\pi\)
−0.329222 + 0.944252i \(0.606787\pi\)
\(440\) −914.139 + 155.243i −2.07759 + 0.352825i
\(441\) 33.3121 + 33.3121i 0.0755376 + 0.0755376i
\(442\) −698.352 244.385i −1.57998 0.552907i
\(443\) −118.626 49.1365i −0.267779 0.110918i 0.244754 0.969585i \(-0.421293\pi\)
−0.512533 + 0.858668i \(0.671293\pi\)
\(444\) 128.643 + 1142.29i 0.289738 + 2.57273i
\(445\) 91.0717 37.7231i 0.204655 0.0847711i
\(446\) −160.898 + 180.035i −0.360757 + 0.403665i
\(447\) 676.480i 1.51338i
\(448\) −152.548 73.4932i −0.340508 0.164047i
\(449\) −666.767 −1.48500 −0.742502 0.669844i \(-0.766361\pi\)
−0.742502 + 0.669844i \(0.766361\pi\)
\(450\) −77.0391 68.8501i −0.171198 0.153000i
\(451\) 95.9004 + 231.524i 0.212639 + 0.513357i
\(452\) −170.830 + 19.2387i −0.377943 + 0.0425635i
\(453\) −211.477 + 510.552i −0.466838 + 1.12705i
\(454\) −81.2821 + 232.271i −0.179035 + 0.511610i
\(455\) −164.330 + 164.330i −0.361165 + 0.361165i
\(456\) −52.1096 + 8.84947i −0.114275 + 0.0194067i
\(457\) −102.929 + 102.929i −0.225227 + 0.225227i −0.810695 0.585468i \(-0.800911\pi\)
0.585468 + 0.810695i \(0.300911\pi\)
\(458\) −328.132 + 158.009i −0.716446 + 0.344999i
\(459\) 82.9435 200.243i 0.180705 0.436260i
\(460\) 442.768 + 801.229i 0.962538 + 1.74180i
\(461\) 193.859 + 468.016i 0.420518 + 1.01522i 0.982195 + 0.187863i \(0.0601561\pi\)
−0.561678 + 0.827356i \(0.689844\pi\)
\(462\) 424.856 23.8480i 0.919602 0.0516191i
\(463\) −553.943 −1.19642 −0.598211 0.801339i \(-0.704121\pi\)
−0.598211 + 0.801339i \(0.704121\pi\)
\(464\) 184.489 130.872i 0.397605 0.282052i
\(465\) 751.677i 1.61651i
\(466\) 13.8005 0.774647i 0.0296147 0.00166233i
\(467\) 835.194 345.949i 1.78842 0.740790i 0.798013 0.602640i \(-0.205884\pi\)
0.990411 0.138150i \(-0.0441155\pi\)
\(468\) −114.538 + 397.490i −0.244739 + 0.849337i
\(469\) 103.894 + 43.0343i 0.221522 + 0.0917575i
\(470\) −181.569 + 87.4332i −0.386318 + 0.186028i
\(471\) −212.545 212.545i −0.451264 0.451264i
\(472\) −527.896 + 331.640i −1.11842 + 0.702628i
\(473\) −237.864 237.864i −0.502884 0.502884i
\(474\) −92.2622 + 263.648i −0.194646 + 0.556218i
\(475\) −11.8139 4.89349i −0.0248714 0.0103021i
\(476\) −158.866 + 199.189i −0.333751 + 0.418465i
\(477\) −3.42712 + 1.41956i −0.00718473 + 0.00297601i
\(478\) −191.098 170.784i −0.399786 0.357290i
\(479\) 245.020i 0.511525i −0.966740 0.255762i \(-0.917674\pi\)
0.966740 0.255762i \(-0.0823265\pi\)
\(480\) −634.917 351.017i −1.32274 0.731286i
\(481\) 1113.41 2.31479
\(482\) 279.889 313.179i 0.580683 0.649749i
\(483\) −160.769 388.132i −0.332856 0.803585i
\(484\) 723.580 907.241i 1.49500 1.87447i
\(485\) −146.999 + 354.888i −0.303092 + 0.731728i
\(486\) −567.871 198.724i −1.16846 0.408897i
\(487\) 539.203 539.203i 1.10719 1.10719i 0.113676 0.993518i \(-0.463737\pi\)
0.993518 0.113676i \(-0.0362626\pi\)
\(488\) 123.260 539.836i 0.252581 1.10622i
\(489\) −7.66286 + 7.66286i −0.0156705 + 0.0156705i
\(490\) 34.7210 + 72.1039i 0.0708593 + 0.147151i
\(491\) 305.018 736.379i 0.621218 1.49975i −0.229056 0.973413i \(-0.573564\pi\)
0.850274 0.526340i \(-0.176436\pi\)
\(492\) −54.2909 + 188.410i −0.110347 + 0.382947i
\(493\) −130.246 314.441i −0.264190 0.637811i
\(494\) 2.86920 + 51.1153i 0.00580811 + 0.103472i
\(495\) 780.036 1.57583
\(496\) 117.988 + 517.195i 0.237879 + 1.04273i
\(497\) 274.076i 0.551461i
\(498\) 47.9944 + 855.027i 0.0963742 + 1.71692i
\(499\) −799.885 + 331.323i −1.60298 + 0.663975i −0.991833 0.127545i \(-0.959290\pi\)
−0.611144 + 0.791520i \(0.709290\pi\)
\(500\) 191.589 + 346.698i 0.383178 + 0.693397i
\(501\) −1062.98 440.302i −2.12172 0.878845i
\(502\) 238.432 + 495.142i 0.474963 + 0.986339i
\(503\) −42.8278 42.8278i −0.0851447 0.0851447i 0.663252 0.748396i \(-0.269176\pi\)
−0.748396 + 0.663252i \(0.769176\pi\)
\(504\) 116.169 + 82.4401i 0.230494 + 0.163572i
\(505\) −132.582 132.582i −0.262538 0.262538i
\(506\) −1532.41 536.259i −3.02848 1.05980i
\(507\) 245.948 + 101.875i 0.485104 + 0.200937i
\(508\) 280.147 31.5498i 0.551470 0.0621059i
\(509\) 835.958 346.265i 1.64235 0.680285i 0.645821 0.763489i \(-0.276515\pi\)
0.996533 + 0.0832038i \(0.0265152\pi\)
\(510\) −727.421 + 813.941i −1.42632 + 1.59596i
\(511\) 36.7635i 0.0719442i
\(512\) −491.956 141.858i −0.960851 0.277067i
\(513\) −14.9974 −0.0292348
\(514\) −387.337 346.164i −0.753574 0.673471i
\(515\) 15.0213 + 36.2646i 0.0291675 + 0.0704166i
\(516\) −29.4552 261.548i −0.0570838 0.506876i
\(517\) 136.774 330.201i 0.264553 0.638686i
\(518\) 126.643 361.894i 0.244485 0.698638i
\(519\) 181.492 181.492i 0.349695 0.349695i
\(520\) −406.681 + 573.066i −0.782080 + 1.10205i
\(521\) −372.130 + 372.130i −0.714261 + 0.714261i −0.967424 0.253163i \(-0.918529\pi\)
0.253163 + 0.967424i \(0.418529\pi\)
\(522\) −171.445 + 82.5579i −0.328439 + 0.158157i
\(523\) −182.500 + 440.595i −0.348949 + 0.842437i 0.647796 + 0.761814i \(0.275691\pi\)
−0.996745 + 0.0806233i \(0.974309\pi\)
\(524\) −351.921 + 194.475i −0.671605 + 0.371136i
\(525\) 30.8245 + 74.4170i 0.0587134 + 0.141747i
\(526\) 508.665 28.5524i 0.967044 0.0542821i
\(527\) 798.203 1.51462
\(528\) 1254.44 286.176i 2.37583 0.542000i
\(529\) 1073.87i 2.03001i
\(530\) −6.29155 + 0.353157i −0.0118708 + 0.000666334i
\(531\) 484.539 200.703i 0.912503 0.377971i
\(532\) 16.9404 + 4.88144i 0.0318429 + 0.00917563i
\(533\) 175.462 + 72.6787i 0.329197 + 0.136358i
\(534\) −123.243 + 59.3468i −0.230793 + 0.111136i
\(535\) 791.266 + 791.266i 1.47900 + 1.47900i
\(536\) 331.498 + 75.6901i 0.618466 + 0.141213i
\(537\) 210.555 + 210.555i 0.392096 + 0.392096i
\(538\) 145.751 416.497i 0.270913 0.774158i
\(539\) −131.128 54.3149i −0.243280 0.100770i
\(540\) −160.935 128.355i −0.298028 0.237695i
\(541\) 381.203 157.900i 0.704627 0.291866i −0.00145217 0.999999i \(-0.500462\pi\)
0.706079 + 0.708133i \(0.250462\pi\)
\(542\) −159.540 142.581i −0.294354 0.263065i
\(543\) 830.465i 1.52940i
\(544\) −372.744 + 674.216i −0.685191 + 1.23937i
\(545\) −645.443 −1.18430
\(546\) 214.894 240.454i 0.393580 0.440392i
\(547\) 363.427 + 877.389i 0.664399 + 1.60400i 0.790836 + 0.612028i \(0.209646\pi\)
−0.126437 + 0.991975i \(0.540354\pi\)
\(548\) 218.881 + 174.571i 0.399419 + 0.318561i
\(549\) −178.265 + 430.370i −0.324708 + 0.783915i
\(550\) 293.811 + 102.818i 0.534202 + 0.186941i
\(551\) −16.6526 + 16.6526i −0.0302225 + 0.0302225i
\(552\) −675.751 1075.64i −1.22419 1.94863i
\(553\) 65.8792 65.8792i 0.119131 0.119131i
\(554\) 72.7146 + 151.004i 0.131254 + 0.272570i
\(555\) 628.650 1517.69i 1.13270 2.73458i
\(556\) −435.187 125.400i −0.782710 0.225540i
\(557\) 282.771 + 682.669i 0.507668 + 1.22562i 0.945223 + 0.326426i \(0.105844\pi\)
−0.437555 + 0.899192i \(0.644156\pi\)
\(558\) −25.0108 445.571i −0.0448221 0.798514i
\(559\) −254.936 −0.456057
\(560\) 140.007 + 197.367i 0.250013 + 0.352440i
\(561\) 1936.01i 3.45100i
\(562\) −35.4884 632.231i −0.0631466 1.12497i
\(563\) 412.762 170.972i 0.733148 0.303680i 0.0153030 0.999883i \(-0.495129\pi\)
0.717845 + 0.696203i \(0.245129\pi\)
\(564\) 244.759 135.256i 0.433970 0.239816i
\(565\) 226.972 + 94.0150i 0.401721 + 0.166398i
\(566\) 469.586 + 975.172i 0.829658 + 1.72292i
\(567\) 180.118 + 180.118i 0.317668 + 0.317668i
\(568\) −138.752 817.030i −0.244281 1.43843i
\(569\) 377.422 + 377.422i 0.663308 + 0.663308i 0.956158 0.292850i \(-0.0946037\pi\)
−0.292850 + 0.956158i \(0.594604\pi\)
\(570\) 71.2953 + 24.9495i 0.125080 + 0.0437710i
\(571\) 192.899 + 79.9015i 0.337827 + 0.139933i 0.545147 0.838341i \(-0.316474\pi\)
−0.207319 + 0.978273i \(0.566474\pi\)
\(572\) −139.471 1238.43i −0.243830 2.16509i
\(573\) −645.946 + 267.559i −1.12730 + 0.466945i
\(574\) 43.5805 48.7640i 0.0759242 0.0849546i
\(575\) 307.321i 0.534471i
\(576\) 388.038 + 186.946i 0.673678 + 0.324559i
\(577\) 442.603 0.767077 0.383538 0.923525i \(-0.374705\pi\)
0.383538 + 0.923525i \(0.374705\pi\)
\(578\) 433.349 + 387.286i 0.749739 + 0.670044i
\(579\) −412.675 996.286i −0.712738 1.72070i
\(580\) −321.218 + 36.1752i −0.553824 + 0.0623710i
\(581\) 109.309 263.896i 0.188140 0.454209i
\(582\) 176.064 503.118i 0.302515 0.864464i
\(583\) 7.90244 7.90244i 0.0135548 0.0135548i
\(584\) −18.6116 109.593i −0.0318691 0.187660i
\(585\) 418.010 418.010i 0.714547 0.714547i
\(586\) 125.793 60.5747i 0.214664 0.103370i
\(587\) −244.570 + 590.444i −0.416644 + 1.00587i 0.566669 + 0.823946i \(0.308232\pi\)
−0.983313 + 0.181922i \(0.941768\pi\)
\(588\) −53.7124 97.1975i −0.0913475 0.165302i
\(589\) −21.1362 51.0273i −0.0358849 0.0866338i
\(590\) 889.523 49.9307i 1.50767 0.0846283i
\(591\) 482.852 0.817009
\(592\) 194.318 1142.93i 0.328240 1.93063i
\(593\) 871.740i 1.47005i 0.678040 + 0.735025i \(0.262830\pi\)
−0.678040 + 0.735025i \(0.737170\pi\)
\(594\) 364.509 20.4606i 0.613652 0.0344455i
\(595\) 336.389 139.337i 0.565360 0.234180i
\(596\) −188.909 + 655.585i −0.316961 + 1.09998i
\(597\) −189.613 78.5401i −0.317609 0.131558i
\(598\) −1108.57 + 533.822i −1.85379 + 0.892679i
\(599\) 276.926 + 276.926i 0.462313 + 0.462313i 0.899413 0.437100i \(-0.143994\pi\)
−0.437100 + 0.899413i \(0.643994\pi\)
\(600\) 129.563 + 206.235i 0.215938 + 0.343724i
\(601\) 559.839 + 559.839i 0.931513 + 0.931513i 0.997801 0.0662876i \(-0.0211155\pi\)
−0.0662876 + 0.997801i \(0.521115\pi\)
\(602\) −28.9972 + 82.8622i −0.0481681 + 0.137645i
\(603\) −264.277 109.467i −0.438271 0.181538i
\(604\) 347.518 435.726i 0.575361 0.721401i
\(605\) −1532.14 + 634.634i −2.53246 + 1.04898i
\(606\) 193.998 + 173.377i 0.320129 + 0.286101i
\(607\) 756.139i 1.24570i 0.782342 + 0.622849i \(0.214025\pi\)
−0.782342 + 0.622849i \(0.785975\pi\)
\(608\) 52.9713 + 5.97560i 0.0871238 + 0.00982829i
\(609\) 148.346 0.243589
\(610\) −527.310 + 590.028i −0.864443 + 0.967260i
\(611\) −103.655 250.245i −0.169648 0.409566i
\(612\) 404.110 506.682i 0.660310 0.827912i
\(613\) 93.4814 225.684i 0.152498 0.368163i −0.829106 0.559092i \(-0.811150\pi\)
0.981604 + 0.190929i \(0.0611499\pi\)
\(614\) 464.609 + 162.588i 0.756693 + 0.264801i
\(615\) 198.137 198.137i 0.322174 0.322174i
\(616\) −418.393 95.5308i −0.679210 0.155082i
\(617\) 558.283 558.283i 0.904835 0.904835i −0.0910146 0.995850i \(-0.529011\pi\)
0.995850 + 0.0910146i \(0.0290110\pi\)
\(618\) −23.6318 49.0752i −0.0382391 0.0794097i
\(619\) 385.549 930.799i 0.622858 1.50371i −0.225474 0.974249i \(-0.572393\pi\)
0.848332 0.529464i \(-0.177607\pi\)
\(620\) 209.908 728.460i 0.338561 1.17494i
\(621\) −137.933 333.001i −0.222115 0.536233i
\(622\) −29.3707 523.243i −0.0472197 0.841227i
\(623\) 45.6249 0.0732342
\(624\) 518.877 825.593i 0.831534 1.32307i
\(625\) 757.980i 1.21277i
\(626\) 38.8183 + 691.554i 0.0620100 + 1.10472i
\(627\) −123.765 + 51.2651i −0.197392 + 0.0817626i
\(628\) 146.626 + 265.334i 0.233482 + 0.422506i
\(629\) −1611.63 667.560i −2.56221 1.06130i
\(630\) −88.3206 183.412i −0.140192 0.291131i
\(631\) 180.106 + 180.106i 0.285430 + 0.285430i 0.835270 0.549840i \(-0.185311\pi\)
−0.549840 + 0.835270i \(0.685311\pi\)
\(632\) 163.037 229.740i 0.257969 0.363512i
\(633\) 679.296 + 679.296i 1.07314 + 1.07314i
\(634\) −573.456 200.678i −0.904505 0.316527i
\(635\) −372.214 154.176i −0.586164 0.242797i
\(636\) 8.68927 0.978576i 0.0136624 0.00153864i
\(637\) −99.3760 + 41.1629i −0.156006 + 0.0646199i
\(638\) 382.019 427.457i 0.598776 0.669995i
\(639\) 697.173i 1.09104i
\(640\) 517.284 + 517.478i 0.808256 + 0.808559i
\(641\) 643.970 1.00463 0.502317 0.864684i \(-0.332481\pi\)
0.502317 + 0.864684i \(0.332481\pi\)
\(642\) −1157.81 1034.74i −1.80344 1.61174i
\(643\) 352.151 + 850.169i 0.547669 + 1.32219i 0.919208 + 0.393773i \(0.128830\pi\)
−0.371538 + 0.928418i \(0.621170\pi\)
\(644\) 47.4168 + 421.038i 0.0736286 + 0.653786i
\(645\) −143.941 + 347.503i −0.223164 + 0.538765i
\(646\) 26.4937 75.7082i 0.0410119 0.117195i
\(647\) 225.721 225.721i 0.348873 0.348873i −0.510817 0.859690i \(-0.670657\pi\)
0.859690 + 0.510817i \(0.170657\pi\)
\(648\) 628.121 + 445.752i 0.969323 + 0.687888i
\(649\) −1117.28 + 1117.28i −1.72154 + 1.72154i
\(650\) 212.547 102.350i 0.326996 0.157462i
\(651\) −133.139 + 321.426i −0.204514 + 0.493741i
\(652\) 9.56605 5.28630i 0.0146719 0.00810782i
\(653\) −195.806 472.718i −0.299857 0.723918i −0.999951 0.00986790i \(-0.996859\pi\)
0.700095 0.714050i \(-0.253141\pi\)
\(654\) 894.240 50.1955i 1.36734 0.0767515i
\(655\) 574.605 0.877259
\(656\) 105.228 167.430i 0.160409 0.255228i
\(657\) 93.5160i 0.142338i
\(658\) −93.1275 + 5.22743i −0.141531 + 0.00794442i
\(659\) 656.103 271.767i 0.995604 0.412393i 0.175421 0.984494i \(-0.443871\pi\)
0.820183 + 0.572101i \(0.193871\pi\)
\(660\) −1766.85 509.124i −2.67705 0.771400i
\(661\) −442.685 183.366i −0.669721 0.277407i 0.0218017 0.999762i \(-0.493060\pi\)
−0.691523 + 0.722355i \(0.743060\pi\)
\(662\) 482.650 232.416i 0.729078 0.351082i
\(663\) −1037.48 1037.48i −1.56483 1.56483i
\(664\) 192.257 842.020i 0.289543 1.26810i
\(665\) −17.8150 17.8150i −0.0267895 0.0267895i
\(666\) −322.145 + 920.558i −0.483701 + 1.38222i
\(667\) −522.909 216.596i −0.783971 0.324731i
\(668\) 907.194 + 723.542i 1.35807 + 1.08315i
\(669\) −442.371 + 183.236i −0.661242 + 0.273896i
\(670\) −362.319 323.806i −0.540775 0.483292i
\(671\) 1403.42i 2.09154i
\(672\) −209.325 262.557i −0.311495 0.390710i
\(673\) −303.397 −0.450812 −0.225406 0.974265i \(-0.572371\pi\)
−0.225406 + 0.974265i \(0.572371\pi\)
\(674\) −20.3252 + 22.7427i −0.0301561 + 0.0337429i
\(675\) 26.4462 + 63.8467i 0.0391795 + 0.0945877i
\(676\) −209.902 167.410i −0.310506 0.247648i
\(677\) −408.017 + 985.041i −0.602684 + 1.45501i 0.268123 + 0.963385i \(0.413597\pi\)
−0.870807 + 0.491624i \(0.836403\pi\)
\(678\) −321.774 112.603i −0.474593 0.166082i
\(679\) −125.717 + 125.717i −0.185151 + 0.185151i
\(680\) 932.248 585.666i 1.37095 0.861274i
\(681\) −345.065 + 345.065i −0.506703 + 0.506703i
\(682\) 583.326 + 1211.37i 0.855316 + 1.77620i
\(683\) −34.2714 + 82.7384i −0.0501777 + 0.121140i −0.946981 0.321290i \(-0.895883\pi\)
0.896803 + 0.442430i \(0.145883\pi\)
\(684\) −43.0918 12.4170i −0.0629996 0.0181535i
\(685\) −153.112 369.645i −0.223521 0.539628i
\(686\) 2.07589 + 36.9823i 0.00302608 + 0.0539101i
\(687\) −722.219 −1.05126
\(688\) −44.4925 + 261.695i −0.0646694 + 0.380370i
\(689\) 8.46960i 0.0122926i
\(690\) 101.739 + 1812.50i 0.147448 + 2.62680i
\(691\) −175.152 + 72.5503i −0.253476 + 0.104993i −0.505804 0.862649i \(-0.668804\pi\)
0.252328 + 0.967642i \(0.418804\pi\)
\(692\) −226.568 + 125.204i −0.327411 + 0.180931i
\(693\) 333.552 + 138.162i 0.481316 + 0.199368i
\(694\) −126.777 263.273i −0.182675 0.379355i
\(695\) 457.654 + 457.654i 0.658494 + 0.658494i
\(696\) 442.224 75.1004i 0.635379 0.107903i
\(697\) −210.401 210.401i −0.301866 0.301866i
\(698\) 165.547 + 57.9325i 0.237174 + 0.0829978i
\(699\) 25.3237 + 10.4894i 0.0362285 + 0.0150063i
\(700\) −9.09130 80.7263i −0.0129876 0.115323i
\(701\) 83.5729 34.6170i 0.119219 0.0493823i −0.322276 0.946646i \(-0.604448\pi\)
0.441496 + 0.897263i \(0.354448\pi\)
\(702\) 184.371 206.300i 0.262636 0.293874i
\(703\) 120.705i 0.171700i
\(704\) −1295.61 72.9682i −1.84035 0.103648i
\(705\) −399.634 −0.566857
\(706\) 575.795 + 514.589i 0.815573 + 0.728880i
\(707\) −33.2102 80.1766i −0.0469734 0.113404i
\(708\) −1228.52 + 138.355i −1.73520 + 0.195416i
\(709\) −259.787 + 627.182i −0.366414 + 0.884601i 0.627918 + 0.778279i \(0.283907\pi\)
−0.994332 + 0.106321i \(0.966093\pi\)
\(710\) −391.185 + 1117.85i −0.550964 + 1.57443i
\(711\) −167.578 + 167.578i −0.235694 + 0.235694i
\(712\) 136.009 23.0977i 0.191024 0.0324406i
\(713\) 938.611 938.611i 1.31642 1.31642i
\(714\) −455.221 + 219.208i −0.637564 + 0.307014i
\(715\) −681.560 + 1645.43i −0.953230 + 2.30130i
\(716\) −145.254 262.850i −0.202868 0.367109i
\(717\) −194.496 469.554i −0.271263 0.654887i
\(718\) −405.493 + 22.7611i −0.564753 + 0.0317007i
\(719\) 428.661 0.596191 0.298095 0.954536i \(-0.403649\pi\)
0.298095 + 0.954536i \(0.403649\pi\)
\(720\) −356.140 502.046i −0.494639 0.697286i
\(721\) 18.1677i 0.0251980i
\(722\) 715.324 40.1525i 0.990753 0.0556129i
\(723\) 769.526 318.748i 1.06435 0.440869i
\(724\) 231.910 804.814i 0.320317 1.11162i
\(725\) 100.258 + 41.5282i 0.138287 + 0.0572803i
\(726\) 2073.38 998.418i 2.85589 1.37523i
\(727\) 366.325 + 366.325i 0.503886 + 0.503886i 0.912643 0.408757i \(-0.134038\pi\)
−0.408757 + 0.912643i \(0.634038\pi\)
\(728\) −275.404 + 173.017i −0.378303 + 0.237661i
\(729\) −230.935 230.935i −0.316783 0.316783i
\(730\) −52.4719 + 149.943i −0.0718793 + 0.205402i
\(731\) 369.012 + 152.850i 0.504805 + 0.209097i
\(732\) 684.685 858.474i 0.935363 1.17278i
\(733\) −146.181 + 60.5501i −0.199428 + 0.0826058i −0.480162 0.877180i \(-0.659422\pi\)
0.280734 + 0.959786i \(0.409422\pi\)
\(734\) −65.1108 58.1897i −0.0887068 0.0792775i
\(735\) 158.701i 0.215919i
\(736\) 354.503 + 1231.13i 0.481662 + 1.67272i
\(737\) 861.801 1.16934
\(738\) −110.857 + 124.042i −0.150212 + 0.168079i
\(739\) 429.198 + 1036.18i 0.580782 + 1.40213i 0.892105 + 0.451827i \(0.149228\pi\)
−0.311324 + 0.950304i \(0.600772\pi\)
\(740\) −1033.05 + 1295.26i −1.39602 + 1.75036i
\(741\) −38.8516 + 93.7961i −0.0524313 + 0.126580i
\(742\) −2.75289 0.963360i −0.00371009 0.00129833i
\(743\) −384.156 + 384.156i −0.517034 + 0.517034i −0.916673 0.399639i \(-0.869135\pi\)
0.399639 + 0.916673i \(0.369135\pi\)
\(744\) −234.169 + 1025.58i −0.314743 + 1.37847i
\(745\) 689.430 689.430i 0.925410 0.925410i
\(746\) −288.097 598.281i −0.386189 0.801985i
\(747\) −278.052 + 671.277i −0.372225 + 0.898631i
\(748\) −540.637 + 1876.21i −0.722776 + 2.50831i
\(749\) 198.203 + 478.505i 0.264624 + 0.638858i
\(750\) 44.0233 + 784.282i 0.0586977 + 1.04571i
\(751\) −707.917 −0.942633 −0.471316 0.881964i \(-0.656221\pi\)
−0.471316 + 0.881964i \(0.656221\pi\)
\(752\) −274.970 + 62.7291i −0.365651 + 0.0834164i
\(753\) 1089.81i 1.44729i
\(754\) −24.3493 433.786i −0.0322935 0.575313i
\(755\) −735.851 + 304.799i −0.974637 + 0.403708i
\(756\) −46.0830 83.3914i −0.0609563 0.110306i
\(757\) −1139.90 472.163i −1.50582 0.623729i −0.531126 0.847293i \(-0.678231\pi\)
−0.974689 + 0.223564i \(0.928231\pi\)