Properties

Label 124.3.l.a.35.15
Level $124$
Weight $3$
Character 124.35
Analytic conductor $3.379$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [124,3,Mod(35,124)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(124, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 6]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("124.35");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 124 = 2^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 124.l (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.37875527807\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(30\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 35.15
Character \(\chi\) \(=\) 124.35
Dual form 124.3.l.a.39.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.316513 - 1.97480i) q^{2} +(1.26908 + 0.412350i) q^{3} +(-3.79964 + 1.25010i) q^{4} -3.39555 q^{5} +(0.412626 - 2.63670i) q^{6} +(-4.74424 - 6.52988i) q^{7} +(3.67133 + 7.10784i) q^{8} +(-5.84061 - 4.24345i) q^{9} +O(q^{10})\) \(q+(-0.316513 - 1.97480i) q^{2} +(1.26908 + 0.412350i) q^{3} +(-3.79964 + 1.25010i) q^{4} -3.39555 q^{5} +(0.412626 - 2.63670i) q^{6} +(-4.74424 - 6.52988i) q^{7} +(3.67133 + 7.10784i) q^{8} +(-5.84061 - 4.24345i) q^{9} +(1.07474 + 6.70552i) q^{10} +(-11.3616 - 15.6380i) q^{11} +(-5.33754 + 0.0196984i) q^{12} +(-1.03750 + 3.19309i) q^{13} +(-11.3936 + 11.4357i) q^{14} +(-4.30924 - 1.40016i) q^{15} +(12.8745 - 9.49985i) q^{16} +(16.9607 + 12.3227i) q^{17} +(-6.53132 + 12.8771i) q^{18} +(17.3206 - 5.62780i) q^{19} +(12.9019 - 4.24478i) q^{20} +(-3.32824 - 10.2433i) q^{21} +(-27.2857 + 27.3865i) q^{22} +(-5.79544 + 7.97674i) q^{23} +(1.72830 + 10.5343i) q^{24} -13.4702 q^{25} +(6.63409 + 1.03819i) q^{26} +(-12.7215 - 17.5096i) q^{27} +(26.1894 + 18.8804i) q^{28} +(11.5876 + 35.6630i) q^{29} +(-1.40109 + 8.95304i) q^{30} +(8.73751 - 29.7432i) q^{31} +(-22.8352 - 22.4177i) q^{32} +(-7.97056 - 24.5309i) q^{33} +(18.9665 - 37.3942i) q^{34} +(16.1093 + 22.1726i) q^{35} +(27.4969 + 8.82224i) q^{36} -2.06373 q^{37} +(-16.5960 - 32.4234i) q^{38} +(-2.63335 + 3.62449i) q^{39} +(-12.4662 - 24.1350i) q^{40} +(-15.8322 - 48.7264i) q^{41} +(-19.1749 + 9.81472i) q^{42} +(75.3810 - 24.4928i) q^{43} +(62.7191 + 45.2154i) q^{44} +(19.8321 + 14.4089i) q^{45} +(17.5868 + 8.92007i) q^{46} +(-19.5843 - 6.36333i) q^{47} +(20.2561 - 6.74730i) q^{48} +(-4.98975 + 15.3569i) q^{49} +(4.26351 + 26.6010i) q^{50} +(16.4433 + 22.6323i) q^{51} +(-0.0495625 - 13.4296i) q^{52} +(-43.2730 - 31.4397i) q^{53} +(-30.5514 + 30.6643i) q^{54} +(38.5790 + 53.0995i) q^{55} +(28.9957 - 57.6946i) q^{56} +24.3019 q^{57} +(66.7595 - 34.1710i) q^{58} +(-83.3220 - 27.0730i) q^{59} +(18.1239 - 0.0668870i) q^{60} +59.1013 q^{61} +(-61.5022 - 7.84068i) q^{62} +58.2705i q^{63} +(-37.0427 + 52.1904i) q^{64} +(3.52288 - 10.8423i) q^{65} +(-45.9206 + 23.5046i) q^{66} -53.1994i q^{67} +(-79.8491 - 25.6191i) q^{68} +(-10.6441 + 7.73340i) q^{69} +(38.6875 - 38.8305i) q^{70} +(-55.3694 + 76.2095i) q^{71} +(8.71897 - 57.0932i) q^{72} +(33.5930 - 24.4068i) q^{73} +(0.653200 + 4.07545i) q^{74} +(-17.0949 - 5.55445i) q^{75} +(-58.7767 + 43.0361i) q^{76} +(-48.2117 + 148.380i) q^{77} +(7.99112 + 4.05312i) q^{78} +(-57.0857 + 78.5717i) q^{79} +(-43.7160 + 32.2572i) q^{80} +(11.1537 + 34.3276i) q^{81} +(-91.2137 + 46.6879i) q^{82} +(9.23141 - 2.99947i) q^{83} +(25.4512 + 34.7601i) q^{84} +(-57.5909 - 41.8423i) q^{85} +(-72.2273 - 141.110i) q^{86} +50.0375i q^{87} +(69.4397 - 138.169i) q^{88} +(47.7459 - 34.6894i) q^{89} +(22.1774 - 43.7249i) q^{90} +(25.7727 - 8.37405i) q^{91} +(12.0489 - 37.5536i) q^{92} +(23.3532 - 34.1437i) q^{93} +(-6.36758 + 40.6891i) q^{94} +(-58.8130 + 19.1095i) q^{95} +(-19.7359 - 37.8660i) q^{96} +(-35.2198 + 25.5887i) q^{97} +(31.9060 + 4.99308i) q^{98} +139.548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q - 3 q^{2} + q^{4} - 16 q^{5} - 10 q^{6} + 27 q^{8} + 72 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 120 q - 3 q^{2} + q^{4} - 16 q^{5} - 10 q^{6} + 27 q^{8} + 72 q^{9} - 26 q^{10} - 66 q^{12} - 22 q^{13} - 34 q^{14} - 55 q^{16} - 6 q^{17} + 74 q^{18} - 47 q^{20} - 114 q^{21} - 56 q^{22} + 15 q^{24} + 440 q^{25} - 48 q^{26} - 8 q^{28} - 6 q^{29} - 254 q^{30} - 178 q^{32} - 90 q^{33} + 171 q^{34} - 8 q^{36} - 96 q^{37} - 42 q^{38} + 50 q^{40} - 6 q^{41} + 268 q^{42} + 196 q^{44} - 120 q^{45} - 231 q^{46} - 28 q^{48} + 48 q^{49} - 394 q^{50} - 7 q^{52} + 122 q^{53} - 126 q^{54} - 432 q^{56} - 196 q^{57} - 49 q^{58} - 163 q^{60} + 80 q^{61} + 200 q^{62} + 19 q^{64} - 156 q^{65} + 490 q^{66} + 266 q^{68} - 522 q^{69} + 65 q^{70} + 642 q^{72} + 122 q^{73} + 177 q^{74} + 517 q^{76} - 186 q^{77} + 303 q^{78} - 602 q^{80} - 168 q^{81} + 406 q^{82} + 769 q^{84} - 508 q^{85} - 677 q^{86} - 108 q^{88} - 30 q^{89} + 662 q^{90} + 910 q^{92} - 250 q^{93} + 354 q^{94} - 1230 q^{96} + 530 q^{97} + 76 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).

\(n\) \(63\) \(65\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.316513 1.97480i −0.158257 0.987398i
\(3\) 1.26908 + 0.412350i 0.423028 + 0.137450i 0.512792 0.858513i \(-0.328611\pi\)
−0.0897638 + 0.995963i \(0.528611\pi\)
\(4\) −3.79964 + 1.25010i −0.949910 + 0.312525i
\(5\) −3.39555 −0.679110 −0.339555 0.940586i \(-0.610277\pi\)
−0.339555 + 0.940586i \(0.610277\pi\)
\(6\) 0.412626 2.63670i 0.0687710 0.439449i
\(7\) −4.74424 6.52988i −0.677748 0.932840i 0.322156 0.946687i \(-0.395592\pi\)
−0.999904 + 0.0138462i \(0.995592\pi\)
\(8\) 3.67133 + 7.10784i 0.458916 + 0.888480i
\(9\) −5.84061 4.24345i −0.648957 0.471495i
\(10\) 1.07474 + 6.70552i 0.107474 + 0.670552i
\(11\) −11.3616 15.6380i −1.03288 1.42163i −0.902766 0.430132i \(-0.858467\pi\)
−0.130110 0.991500i \(-0.541533\pi\)
\(12\) −5.33754 + 0.0196984i −0.444795 + 0.00164154i
\(13\) −1.03750 + 3.19309i −0.0798076 + 0.245623i −0.982998 0.183618i \(-0.941219\pi\)
0.903190 + 0.429241i \(0.141219\pi\)
\(14\) −11.3936 + 11.4357i −0.813827 + 0.816836i
\(15\) −4.30924 1.40016i −0.287283 0.0933438i
\(16\) 12.8745 9.49985i 0.804657 0.593741i
\(17\) 16.9607 + 12.3227i 0.997688 + 0.724863i 0.961591 0.274485i \(-0.0885074\pi\)
0.0360971 + 0.999348i \(0.488507\pi\)
\(18\) −6.53132 + 12.8771i −0.362851 + 0.715396i
\(19\) 17.3206 5.62780i 0.911610 0.296200i 0.184590 0.982816i \(-0.440904\pi\)
0.727021 + 0.686616i \(0.240904\pi\)
\(20\) 12.9019 4.24478i 0.645093 0.212239i
\(21\) −3.32824 10.2433i −0.158487 0.487774i
\(22\) −27.2857 + 27.3865i −1.24026 + 1.24484i
\(23\) −5.79544 + 7.97674i −0.251976 + 0.346815i −0.916202 0.400717i \(-0.868761\pi\)
0.664226 + 0.747532i \(0.268761\pi\)
\(24\) 1.72830 + 10.5343i 0.0720127 + 0.438930i
\(25\) −13.4702 −0.538809
\(26\) 6.63409 + 1.03819i 0.255157 + 0.0399304i
\(27\) −12.7215 17.5096i −0.471166 0.648504i
\(28\) 26.1894 + 18.8804i 0.935335 + 0.674301i
\(29\) 11.5876 + 35.6630i 0.399573 + 1.22976i 0.925343 + 0.379132i \(0.123777\pi\)
−0.525770 + 0.850627i \(0.676223\pi\)
\(30\) −1.40109 + 8.95304i −0.0467031 + 0.298435i
\(31\) 8.73751 29.7432i 0.281855 0.959457i
\(32\) −22.8352 22.4177i −0.713601 0.700553i
\(33\) −7.97056 24.5309i −0.241532 0.743359i
\(34\) 18.9665 37.3942i 0.557837 1.09983i
\(35\) 16.1093 + 22.1726i 0.460266 + 0.633502i
\(36\) 27.4969 + 8.82224i 0.763804 + 0.245062i
\(37\) −2.06373 −0.0557766 −0.0278883 0.999611i \(-0.508878\pi\)
−0.0278883 + 0.999611i \(0.508878\pi\)
\(38\) −16.5960 32.4234i −0.436736 0.853246i
\(39\) −2.63335 + 3.62449i −0.0675217 + 0.0929357i
\(40\) −12.4662 24.1350i −0.311655 0.603376i
\(41\) −15.8322 48.7264i −0.386151 1.18845i −0.935642 0.352950i \(-0.885178\pi\)
0.549491 0.835499i \(-0.314822\pi\)
\(42\) −19.1749 + 9.81472i −0.456546 + 0.233684i
\(43\) 75.3810 24.4928i 1.75305 0.569599i 0.756604 0.653873i \(-0.226857\pi\)
0.996443 + 0.0842740i \(0.0268571\pi\)
\(44\) 62.7191 + 45.2154i 1.42543 + 1.02762i
\(45\) 19.8321 + 14.4089i 0.440713 + 0.320197i
\(46\) 17.5868 + 8.92007i 0.382321 + 0.193915i
\(47\) −19.5843 6.36333i −0.416688 0.135390i 0.0931671 0.995650i \(-0.470301\pi\)
−0.509855 + 0.860260i \(0.670301\pi\)
\(48\) 20.2561 6.74730i 0.422002 0.140569i
\(49\) −4.98975 + 15.3569i −0.101832 + 0.313406i
\(50\) 4.26351 + 26.6010i 0.0852702 + 0.532019i
\(51\) 16.4433 + 22.6323i 0.322418 + 0.443770i
\(52\) −0.0495625 13.4296i −0.000953124 0.258261i
\(53\) −43.2730 31.4397i −0.816472 0.593202i 0.0992274 0.995065i \(-0.468363\pi\)
−0.915700 + 0.401863i \(0.868363\pi\)
\(54\) −30.5514 + 30.6643i −0.565766 + 0.567858i
\(55\) 38.5790 + 53.0995i 0.701437 + 0.965445i
\(56\) 28.9957 57.6946i 0.517780 1.03026i
\(57\) 24.3019 0.426349
\(58\) 66.7595 34.1710i 1.15103 0.589155i
\(59\) −83.3220 27.0730i −1.41224 0.458864i −0.499110 0.866539i \(-0.666340\pi\)
−0.913127 + 0.407675i \(0.866340\pi\)
\(60\) 18.1239 0.0668870i 0.302065 0.00111478i
\(61\) 59.1013 0.968873 0.484437 0.874826i \(-0.339025\pi\)
0.484437 + 0.874826i \(0.339025\pi\)
\(62\) −61.5022 7.84068i −0.991971 0.126463i
\(63\) 58.2705i 0.924928i
\(64\) −37.0427 + 52.1904i −0.578792 + 0.815475i
\(65\) 3.52288 10.8423i 0.0541982 0.166805i
\(66\) −45.9206 + 23.5046i −0.695767 + 0.356130i
\(67\) 53.1994i 0.794021i −0.917814 0.397011i \(-0.870048\pi\)
0.917814 0.397011i \(-0.129952\pi\)
\(68\) −79.8491 25.6191i −1.17425 0.376752i
\(69\) −10.6441 + 7.73340i −0.154263 + 0.112078i
\(70\) 38.6875 38.8305i 0.552678 0.554722i
\(71\) −55.3694 + 76.2095i −0.779851 + 1.07337i 0.215447 + 0.976515i \(0.430879\pi\)
−0.995298 + 0.0968572i \(0.969121\pi\)
\(72\) 8.71897 57.0932i 0.121097 0.792961i
\(73\) 33.5930 24.4068i 0.460179 0.334339i −0.333423 0.942777i \(-0.608204\pi\)
0.793601 + 0.608438i \(0.208204\pi\)
\(74\) 0.653200 + 4.07545i 0.00882702 + 0.0550737i
\(75\) −17.0949 5.55445i −0.227931 0.0740594i
\(76\) −58.7767 + 43.0361i −0.773377 + 0.566264i
\(77\) −48.2117 + 148.380i −0.626126 + 1.92702i
\(78\) 7.99112 + 4.05312i 0.102450 + 0.0519631i
\(79\) −57.0857 + 78.5717i −0.722604 + 0.994579i 0.276830 + 0.960919i \(0.410716\pi\)
−0.999433 + 0.0336598i \(0.989284\pi\)
\(80\) −43.7160 + 32.2572i −0.546451 + 0.403215i
\(81\) 11.1537 + 34.3276i 0.137700 + 0.423797i
\(82\) −91.2137 + 46.6879i −1.11236 + 0.569365i
\(83\) 9.23141 2.99947i 0.111222 0.0361381i −0.252877 0.967498i \(-0.581377\pi\)
0.364099 + 0.931360i \(0.381377\pi\)
\(84\) 25.4512 + 34.7601i 0.302990 + 0.413810i
\(85\) −57.5909 41.8423i −0.677541 0.492262i
\(86\) −72.2273 141.110i −0.839853 1.64081i
\(87\) 50.0375i 0.575144i
\(88\) 69.4397 138.169i 0.789088 1.57010i
\(89\) 47.7459 34.6894i 0.536471 0.389769i −0.286302 0.958140i \(-0.592426\pi\)
0.822773 + 0.568370i \(0.192426\pi\)
\(90\) 22.1774 43.7249i 0.246416 0.485833i
\(91\) 25.7727 8.37405i 0.283216 0.0920225i
\(92\) 12.0489 37.5536i 0.130966 0.408191i
\(93\) 23.3532 34.1437i 0.251110 0.367136i
\(94\) −6.36758 + 40.6891i −0.0677402 + 0.432863i
\(95\) −58.8130 + 19.1095i −0.619084 + 0.201153i
\(96\) −19.7359 37.8660i −0.205582 0.394438i
\(97\) −35.2198 + 25.5887i −0.363091 + 0.263801i −0.754340 0.656484i \(-0.772043\pi\)
0.391249 + 0.920285i \(0.372043\pi\)
\(98\) 31.9060 + 4.99308i 0.325572 + 0.0509498i
\(99\) 139.548i 1.40957i
\(100\) 51.1820 16.8391i 0.511820 0.168391i
\(101\) 0.937819 + 0.681365i 0.00928534 + 0.00674619i 0.592418 0.805631i \(-0.298173\pi\)
−0.583133 + 0.812377i \(0.698173\pi\)
\(102\) 39.4896 39.6356i 0.387153 0.388584i
\(103\) 17.5722 5.70954i 0.170604 0.0554325i −0.222470 0.974940i \(-0.571412\pi\)
0.393073 + 0.919507i \(0.371412\pi\)
\(104\) −26.5050 + 4.34852i −0.254856 + 0.0418127i
\(105\) 11.3012 + 34.7815i 0.107630 + 0.331253i
\(106\) −48.3905 + 95.4065i −0.456514 + 0.900061i
\(107\) 70.2069 96.6314i 0.656139 0.903098i −0.343207 0.939260i \(-0.611513\pi\)
0.999346 + 0.0361621i \(0.0115133\pi\)
\(108\) 70.2257 + 50.6271i 0.650238 + 0.468769i
\(109\) 51.1725 157.493i 0.469473 1.44489i −0.383796 0.923418i \(-0.625383\pi\)
0.853269 0.521471i \(-0.174617\pi\)
\(110\) 92.6499 92.9924i 0.842271 0.845386i
\(111\) −2.61905 0.850982i −0.0235951 0.00766650i
\(112\) −123.113 38.9995i −1.09922 0.348210i
\(113\) −44.8104 + 32.5567i −0.396552 + 0.288112i −0.768135 0.640288i \(-0.778815\pi\)
0.371583 + 0.928400i \(0.378815\pi\)
\(114\) −7.69189 47.9913i −0.0674727 0.420977i
\(115\) 19.6787 27.0854i 0.171119 0.235526i
\(116\) −88.6110 121.021i −0.763888 1.04328i
\(117\) 19.6094 14.2470i 0.167601 0.121770i
\(118\) −27.0910 + 173.113i −0.229585 + 1.46706i
\(119\) 169.213i 1.42196i
\(120\) −5.86855 35.7698i −0.0489045 0.298082i
\(121\) −78.0677 + 240.268i −0.645188 + 1.98568i
\(122\) −18.7063 116.713i −0.153331 0.956663i
\(123\) 68.3664i 0.555824i
\(124\) 3.98254 + 123.936i 0.0321173 + 0.999484i
\(125\) 130.628 1.04502
\(126\) 115.072 18.4434i 0.913272 0.146376i
\(127\) −29.0431 9.43669i −0.228686 0.0743047i 0.192432 0.981310i \(-0.438362\pi\)
−0.421119 + 0.907006i \(0.638362\pi\)
\(128\) 114.790 + 56.6328i 0.896796 + 0.442444i
\(129\) 105.764 0.819879
\(130\) −22.5264 3.52523i −0.173280 0.0271172i
\(131\) −10.7868 14.8467i −0.0823417 0.113334i 0.765859 0.643008i \(-0.222314\pi\)
−0.848201 + 0.529675i \(0.822314\pi\)
\(132\) 60.9512 + 83.2444i 0.461752 + 0.630639i
\(133\) −118.922 86.4018i −0.894150 0.649638i
\(134\) −105.058 + 16.8383i −0.784015 + 0.125659i
\(135\) 43.1964 + 59.4548i 0.319973 + 0.440406i
\(136\) −25.3193 + 165.794i −0.186171 + 1.21908i
\(137\) 3.04768 9.37980i 0.0222458 0.0684657i −0.939317 0.343050i \(-0.888540\pi\)
0.961563 + 0.274584i \(0.0885401\pi\)
\(138\) 18.6409 + 18.5722i 0.135079 + 0.134581i
\(139\) 151.000 + 49.0629i 1.08633 + 0.352971i 0.796828 0.604206i \(-0.206510\pi\)
0.289504 + 0.957177i \(0.406510\pi\)
\(140\) −88.9274 64.1095i −0.635196 0.457925i
\(141\) −22.2302 16.1512i −0.157661 0.114548i
\(142\) 168.023 + 85.2220i 1.18326 + 0.600155i
\(143\) 61.7211 20.0544i 0.431616 0.140241i
\(144\) −115.507 + 0.852580i −0.802133 + 0.00592070i
\(145\) −39.3463 121.096i −0.271354 0.835142i
\(146\) −58.8310 58.6143i −0.402952 0.401468i
\(147\) −12.6648 + 17.4316i −0.0861553 + 0.118583i
\(148\) 7.84144 2.57987i 0.0529827 0.0174316i
\(149\) −162.013 −1.08734 −0.543669 0.839300i \(-0.682965\pi\)
−0.543669 + 0.839300i \(0.682965\pi\)
\(150\) −5.55816 + 35.5169i −0.0370544 + 0.236779i
\(151\) −12.4297 17.1080i −0.0823158 0.113298i 0.765873 0.642991i \(-0.222307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(152\) 103.591 + 102.450i 0.681520 + 0.674016i
\(153\) −46.7702 143.944i −0.305688 0.940810i
\(154\) 308.281 + 48.2439i 2.00182 + 0.313272i
\(155\) −29.6687 + 100.994i −0.191411 + 0.651577i
\(156\) 5.47479 17.0637i 0.0350948 0.109383i
\(157\) −43.9915 135.392i −0.280201 0.862369i −0.987796 0.155751i \(-0.950220\pi\)
0.707596 0.706618i \(-0.249780\pi\)
\(158\) 173.232 + 87.8636i 1.09640 + 0.556099i
\(159\) −41.9530 57.7433i −0.263855 0.363165i
\(160\) 77.5382 + 76.1204i 0.484614 + 0.475753i
\(161\) 79.5821 0.494299
\(162\) 64.2597 32.8914i 0.396665 0.203034i
\(163\) 94.6893 130.329i 0.580916 0.799562i −0.412879 0.910786i \(-0.635477\pi\)
0.993795 + 0.111223i \(0.0354769\pi\)
\(164\) 121.069 + 165.351i 0.738228 + 1.00824i
\(165\) 27.0644 + 83.2958i 0.164027 + 0.504823i
\(166\) −8.84520 17.2808i −0.0532843 0.104101i
\(167\) −87.1507 + 28.3170i −0.521860 + 0.169563i −0.558089 0.829781i \(-0.688465\pi\)
0.0362290 + 0.999344i \(0.488465\pi\)
\(168\) 60.5884 61.2629i 0.360645 0.364660i
\(169\) 127.604 + 92.7100i 0.755056 + 0.548580i
\(170\) −64.4016 + 126.974i −0.378833 + 0.746906i
\(171\) −125.044 40.6293i −0.731252 0.237598i
\(172\) −255.802 + 187.297i −1.48722 + 1.08894i
\(173\) −59.8985 + 184.349i −0.346234 + 1.06560i 0.614686 + 0.788772i \(0.289283\pi\)
−0.960920 + 0.276827i \(0.910717\pi\)
\(174\) 98.8138 15.8375i 0.567896 0.0910204i
\(175\) 63.9060 + 87.9590i 0.365177 + 0.502623i
\(176\) −294.834 93.3970i −1.67519 0.530665i
\(177\) −94.5791 68.7157i −0.534345 0.388224i
\(178\) −83.6168 83.3088i −0.469757 0.468027i
\(179\) 15.6768 + 21.5773i 0.0875800 + 0.120544i 0.850559 0.525880i \(-0.176264\pi\)
−0.762979 + 0.646424i \(0.776264\pi\)
\(180\) −93.3673 29.9564i −0.518707 0.166424i
\(181\) 324.182 1.79106 0.895529 0.445002i \(-0.146797\pi\)
0.895529 + 0.445002i \(0.146797\pi\)
\(182\) −24.6944 48.2453i −0.135684 0.265084i
\(183\) 75.0045 + 24.3704i 0.409861 + 0.133172i
\(184\) −77.9743 11.9078i −0.423774 0.0647165i
\(185\) 7.00752 0.0378785
\(186\) −74.8184 35.3110i −0.402249 0.189844i
\(187\) 405.236i 2.16704i
\(188\) 82.3681 0.303983i 0.438128 0.00161693i
\(189\) −53.9820 + 166.139i −0.285619 + 0.879045i
\(190\) 56.3525 + 110.095i 0.296592 + 0.579449i
\(191\) 59.5868i 0.311973i 0.987759 + 0.155987i \(0.0498556\pi\)
−0.987759 + 0.155987i \(0.950144\pi\)
\(192\) −68.5311 + 50.9594i −0.356933 + 0.265414i
\(193\) −30.2314 + 21.9644i −0.156640 + 0.113805i −0.663344 0.748314i \(-0.730863\pi\)
0.506705 + 0.862120i \(0.330863\pi\)
\(194\) 61.6800 + 61.4528i 0.317938 + 0.316767i
\(195\) 8.94167 12.3071i 0.0458547 0.0631136i
\(196\) −0.238366 64.5882i −0.00121615 0.329532i
\(197\) 116.581 84.7013i 0.591783 0.429956i −0.251170 0.967943i \(-0.580815\pi\)
0.842953 + 0.537987i \(0.180815\pi\)
\(198\) 275.578 44.1687i 1.39181 0.223074i
\(199\) −231.474 75.2104i −1.16319 0.377942i −0.337090 0.941472i \(-0.609443\pi\)
−0.826095 + 0.563531i \(0.809443\pi\)
\(200\) −49.4536 95.7442i −0.247268 0.478721i
\(201\) 21.9368 67.5145i 0.109138 0.335893i
\(202\) 1.04873 2.06766i 0.00519171 0.0102360i
\(203\) 177.901 244.859i 0.876359 1.20620i
\(204\) −90.7712 65.4387i −0.444957 0.320778i
\(205\) 53.7590 + 165.453i 0.262239 + 0.807088i
\(206\) −16.8370 32.8943i −0.0817331 0.159681i
\(207\) 67.6978 21.9964i 0.327043 0.106263i
\(208\) 16.9766 + 50.9656i 0.0816184 + 0.245027i
\(209\) −284.798 206.918i −1.36267 0.990036i
\(210\) 65.1094 33.3264i 0.310045 0.158697i
\(211\) 290.791i 1.37816i −0.724687 0.689078i \(-0.758016\pi\)
0.724687 0.689078i \(-0.241984\pi\)
\(212\) 203.725 + 65.3639i 0.960965 + 0.308320i
\(213\) −101.693 + 73.8846i −0.477434 + 0.346876i
\(214\) −213.049 108.059i −0.995555 0.504949i
\(215\) −255.960 + 83.1665i −1.19051 + 0.386821i
\(216\) 77.7507 154.706i 0.359957 0.716230i
\(217\) −235.672 + 84.0538i −1.08605 + 0.387345i
\(218\) −327.213 51.2067i −1.50098 0.234893i
\(219\) 52.6965 17.1221i 0.240623 0.0781833i
\(220\) −212.966 153.531i −0.968027 0.697869i
\(221\) −56.9442 + 41.3724i −0.257666 + 0.187205i
\(222\) −0.851550 + 5.44144i −0.00383581 + 0.0245110i
\(223\) 8.78854i 0.0394105i −0.999806 0.0197052i \(-0.993727\pi\)
0.999806 0.0197052i \(-0.00627278\pi\)
\(224\) −38.0492 + 255.466i −0.169862 + 1.14047i
\(225\) 78.6744 + 57.1603i 0.349664 + 0.254046i
\(226\) 78.4759 + 78.1868i 0.347238 + 0.345959i
\(227\) −122.718 + 39.8736i −0.540609 + 0.175654i −0.566578 0.824008i \(-0.691733\pi\)
0.0259689 + 0.999663i \(0.491733\pi\)
\(228\) −92.3385 + 30.3798i −0.404993 + 0.133245i
\(229\) 33.7541 + 103.884i 0.147398 + 0.453644i 0.997312 0.0732780i \(-0.0233460\pi\)
−0.849914 + 0.526922i \(0.823346\pi\)
\(230\) −59.7168 30.2886i −0.259638 0.131689i
\(231\) −122.369 + 168.427i −0.529738 + 0.729121i
\(232\) −210.945 + 213.293i −0.909245 + 0.919368i
\(233\) 125.302 385.640i 0.537776 1.65511i −0.199796 0.979837i \(-0.564028\pi\)
0.737573 0.675268i \(-0.235972\pi\)
\(234\) −34.3416 34.2151i −0.146759 0.146218i
\(235\) 66.4996 + 21.6070i 0.282977 + 0.0919448i
\(236\) 350.437 1.29330i 1.48490 0.00548010i
\(237\) −104.846 + 76.1748i −0.442387 + 0.321413i
\(238\) −334.161 + 53.5582i −1.40404 + 0.225035i
\(239\) −107.352 + 147.757i −0.449170 + 0.618229i −0.972219 0.234073i \(-0.924794\pi\)
0.523049 + 0.852302i \(0.324794\pi\)
\(240\) −68.7806 + 22.9108i −0.286586 + 0.0954617i
\(241\) −221.566 + 160.977i −0.919360 + 0.667954i −0.943365 0.331757i \(-0.892358\pi\)
0.0240043 + 0.999712i \(0.492358\pi\)
\(242\) 499.189 + 78.1198i 2.06276 + 0.322809i
\(243\) 242.951i 0.999800i
\(244\) −224.563 + 73.8824i −0.920342 + 0.302797i
\(245\) 16.9430 52.1451i 0.0691549 0.212837i
\(246\) −135.010 + 21.6389i −0.548820 + 0.0879629i
\(247\) 61.1451i 0.247551i
\(248\) 243.488 47.0921i 0.981806 0.189888i
\(249\) 12.9523 0.0520171
\(250\) −41.3454 257.963i −0.165382 1.03185i
\(251\) −23.9280 7.77469i −0.0953309 0.0309749i 0.260963 0.965349i \(-0.415960\pi\)
−0.356294 + 0.934374i \(0.615960\pi\)
\(252\) −72.8438 221.407i −0.289063 0.878598i
\(253\) 190.586 0.753303
\(254\) −9.44299 + 60.3411i −0.0371771 + 0.237564i
\(255\) −55.8341 76.8490i −0.218957 0.301369i
\(256\) 75.5057 244.612i 0.294944 0.955514i
\(257\) 375.690 + 272.955i 1.46183 + 1.06208i 0.982882 + 0.184237i \(0.0589812\pi\)
0.478947 + 0.877844i \(0.341019\pi\)
\(258\) −33.4759 208.863i −0.129751 0.809547i
\(259\) 9.79085 + 13.4759i 0.0378025 + 0.0520307i
\(260\) 0.168292 + 45.6008i 0.000647277 + 0.175388i
\(261\) 83.6555 257.465i 0.320519 0.986456i
\(262\) −25.9051 + 26.0008i −0.0988743 + 0.0992399i
\(263\) 308.301 + 100.173i 1.17225 + 0.380886i 0.829481 0.558535i \(-0.188636\pi\)
0.342765 + 0.939421i \(0.388636\pi\)
\(264\) 145.099 146.714i 0.549617 0.555736i
\(265\) 146.936 + 106.755i 0.554475 + 0.402850i
\(266\) −132.986 + 262.194i −0.499946 + 0.985691i
\(267\) 74.8978 24.3358i 0.280516 0.0911452i
\(268\) 66.5045 + 202.139i 0.248151 + 0.754248i
\(269\) −106.144 326.678i −0.394588 1.21442i −0.929282 0.369371i \(-0.879573\pi\)
0.534694 0.845046i \(-0.320427\pi\)
\(270\) 103.739 104.122i 0.384218 0.385638i
\(271\) −177.854 + 244.795i −0.656287 + 0.903302i −0.999351 0.0360102i \(-0.988535\pi\)
0.343064 + 0.939312i \(0.388535\pi\)
\(272\) 335.424 2.47583i 1.23318 0.00910231i
\(273\) 36.1607 0.132457
\(274\) −19.4878 3.04972i −0.0711234 0.0111303i
\(275\) 153.044 + 210.647i 0.556523 + 0.765988i
\(276\) 30.7763 42.6903i 0.111508 0.154675i
\(277\) −31.0948 95.6999i −0.112255 0.345487i 0.879109 0.476620i \(-0.158138\pi\)
−0.991365 + 0.131133i \(0.958138\pi\)
\(278\) 49.0957 313.724i 0.176603 1.12850i
\(279\) −177.246 + 136.641i −0.635291 + 0.489753i
\(280\) −98.4564 + 195.905i −0.351630 + 0.699661i
\(281\) −8.35541 25.7153i −0.0297346 0.0915135i 0.935088 0.354416i \(-0.115320\pi\)
−0.964822 + 0.262902i \(0.915320\pi\)
\(282\) −24.8592 + 49.0123i −0.0881531 + 0.173802i
\(283\) 27.7630 + 38.2125i 0.0981024 + 0.135026i 0.855246 0.518222i \(-0.173406\pi\)
−0.757144 + 0.653248i \(0.773406\pi\)
\(284\) 115.114 358.786i 0.405332 1.26333i
\(285\) −82.5184 −0.289538
\(286\) −59.1389 115.539i −0.206780 0.403983i
\(287\) −243.066 + 334.552i −0.846921 + 1.16569i
\(288\) 38.2432 + 227.833i 0.132789 + 0.791087i
\(289\) 46.5113 + 143.147i 0.160939 + 0.495318i
\(290\) −226.685 + 116.029i −0.781674 + 0.400101i
\(291\) −55.2484 + 17.9513i −0.189857 + 0.0616883i
\(292\) −97.1305 + 134.732i −0.332639 + 0.461409i
\(293\) 370.466 + 269.159i 1.26439 + 0.918633i 0.998964 0.0454989i \(-0.0144877\pi\)
0.265425 + 0.964132i \(0.414488\pi\)
\(294\) 38.4325 + 19.4931i 0.130723 + 0.0663031i
\(295\) 282.924 + 91.9276i 0.959065 + 0.311619i
\(296\) −7.57664 14.6687i −0.0255968 0.0495564i
\(297\) −129.278 + 397.876i −0.435278 + 1.33965i
\(298\) 51.2794 + 319.943i 0.172078 + 1.07363i
\(299\) −19.4577 26.7812i −0.0650760 0.0895694i
\(300\) 71.8979 0.265342i 0.239660 0.000884475i
\(301\) −517.560 376.030i −1.71947 1.24927i
\(302\) −29.8506 + 29.9610i −0.0988431 + 0.0992086i
\(303\) 0.909210 + 1.25142i 0.00300069 + 0.00413010i
\(304\) 169.531 236.998i 0.557667 0.779599i
\(305\) −200.681 −0.657972
\(306\) −269.456 + 137.922i −0.880576 + 0.450725i
\(307\) 168.115 + 54.6239i 0.547606 + 0.177928i 0.569737 0.821827i \(-0.307045\pi\)
−0.0221311 + 0.999755i \(0.507045\pi\)
\(308\) −2.30313 624.061i −0.00747768 2.02617i
\(309\) 24.6549 0.0797893
\(310\) 208.834 + 26.6234i 0.673658 + 0.0858820i
\(311\) 601.514i 1.93413i 0.254531 + 0.967065i \(0.418079\pi\)
−0.254531 + 0.967065i \(0.581921\pi\)
\(312\) −35.4302 5.41071i −0.113558 0.0173420i
\(313\) 107.138 329.735i 0.342292 1.05347i −0.620725 0.784028i \(-0.713162\pi\)
0.963017 0.269439i \(-0.0868383\pi\)
\(314\) −253.448 + 129.728i −0.807158 + 0.413145i
\(315\) 197.860i 0.628128i
\(316\) 118.683 369.907i 0.375578 1.17059i
\(317\) 363.102 263.809i 1.14543 0.832206i 0.157566 0.987508i \(-0.449635\pi\)
0.987867 + 0.155302i \(0.0496352\pi\)
\(318\) −100.753 + 101.125i −0.316832 + 0.318003i
\(319\) 426.042 586.396i 1.33555 1.83823i
\(320\) 125.780 177.215i 0.393064 0.553798i
\(321\) 128.944 93.6836i 0.401696 0.291849i
\(322\) −25.1888 157.158i −0.0782261 0.488070i
\(323\) 363.119 + 117.985i 1.12421 + 0.365277i
\(324\) −85.2929 116.489i −0.263250 0.359534i
\(325\) 13.9753 43.0117i 0.0430011 0.132344i
\(326\) −287.343 145.741i −0.881420 0.447059i
\(327\) 129.885 178.771i 0.397200 0.546699i
\(328\) 288.214 291.423i 0.878703 0.888486i
\(329\) 51.3609 + 158.073i 0.156112 + 0.480464i
\(330\) 155.926 79.8110i 0.472503 0.241852i
\(331\) −156.879 + 50.9731i −0.473955 + 0.153997i −0.536248 0.844061i \(-0.680159\pi\)
0.0622928 + 0.998058i \(0.480159\pi\)
\(332\) −31.3264 + 22.9371i −0.0943566 + 0.0690875i
\(333\) 12.0535 + 8.75736i 0.0361966 + 0.0262984i
\(334\) 83.5046 + 163.142i 0.250014 + 0.488450i
\(335\) 180.641i 0.539228i
\(336\) −140.159 100.259i −0.417139 0.298390i
\(337\) 45.0078 32.7001i 0.133554 0.0970330i −0.519002 0.854773i \(-0.673696\pi\)
0.652557 + 0.757740i \(0.273696\pi\)
\(338\) 142.695 281.337i 0.422174 0.832357i
\(339\) −70.2929 + 22.8396i −0.207354 + 0.0673733i
\(340\) 271.132 + 86.9911i 0.797446 + 0.255856i
\(341\) −564.395 + 201.294i −1.65512 + 0.590306i
\(342\) −40.6564 + 259.796i −0.118878 + 0.759639i
\(343\) −252.189 + 81.9413i −0.735246 + 0.238896i
\(344\) 450.839 + 445.875i 1.31058 + 1.29615i
\(345\) 36.1426 26.2592i 0.104761 0.0761135i
\(346\) 383.009 + 59.9385i 1.10696 + 0.173233i
\(347\) 300.110i 0.864872i −0.901665 0.432436i \(-0.857654\pi\)
0.901665 0.432436i \(-0.142346\pi\)
\(348\) −62.5518 190.124i −0.179747 0.546334i
\(349\) −99.8351 72.5345i −0.286060 0.207835i 0.435496 0.900191i \(-0.356573\pi\)
−0.721557 + 0.692356i \(0.756573\pi\)
\(350\) 153.474 154.041i 0.438497 0.440118i
\(351\) 69.1083 22.4547i 0.196890 0.0639734i
\(352\) −91.1213 + 611.798i −0.258867 + 1.73806i
\(353\) 68.8064 + 211.764i 0.194919 + 0.599899i 0.999978 + 0.00670372i \(0.00213388\pi\)
−0.805058 + 0.593195i \(0.797866\pi\)
\(354\) −105.764 + 208.524i −0.298768 + 0.589050i
\(355\) 188.010 258.773i 0.529605 0.728939i
\(356\) −138.052 + 191.494i −0.387787 + 0.537906i
\(357\) 69.7751 214.746i 0.195448 0.601529i
\(358\) 37.6488 37.7880i 0.105164 0.105553i
\(359\) 105.336 + 34.2258i 0.293416 + 0.0953366i 0.452026 0.892005i \(-0.350701\pi\)
−0.158610 + 0.987341i \(0.550701\pi\)
\(360\) −29.6057 + 193.863i −0.0822381 + 0.538508i
\(361\) −23.7243 + 17.2367i −0.0657183 + 0.0477472i
\(362\) −102.608 640.193i −0.283447 1.76849i
\(363\) −198.149 + 272.729i −0.545865 + 0.751319i
\(364\) −87.4584 + 64.0367i −0.240270 + 0.175925i
\(365\) −114.067 + 82.8744i −0.312512 + 0.227053i
\(366\) 24.3867 155.832i 0.0666303 0.425771i
\(367\) 501.450i 1.36635i −0.730255 0.683175i \(-0.760599\pi\)
0.730255 0.683175i \(-0.239401\pi\)
\(368\) 1.16440 + 157.752i 0.00316413 + 0.428675i
\(369\) −114.299 + 351.775i −0.309753 + 0.953320i
\(370\) −2.21797 13.8384i −0.00599452 0.0374011i
\(371\) 431.725i 1.16368i
\(372\) −46.0509 + 158.927i −0.123793 + 0.427224i
\(373\) 252.906 0.678032 0.339016 0.940781i \(-0.389906\pi\)
0.339016 + 0.940781i \(0.389906\pi\)
\(374\) −800.259 + 128.263i −2.13973 + 0.342949i
\(375\) 165.777 + 53.8644i 0.442073 + 0.143638i
\(376\) −26.6709 162.564i −0.0709333 0.432351i
\(377\) −125.897 −0.333945
\(378\) 345.178 + 54.0180i 0.913168 + 0.142905i
\(379\) 287.483 + 395.686i 0.758529 + 1.04403i 0.997335 + 0.0729586i \(0.0232441\pi\)
−0.238806 + 0.971067i \(0.576756\pi\)
\(380\) 199.579 146.131i 0.525209 0.384556i
\(381\) −32.9670 23.9519i −0.0865275 0.0628659i
\(382\) 117.672 18.8600i 0.308042 0.0493718i
\(383\) −378.977 521.617i −0.989496 1.36192i −0.931553 0.363605i \(-0.881546\pi\)
−0.0579429 0.998320i \(-0.518454\pi\)
\(384\) 122.325 + 119.205i 0.318556 + 0.310431i
\(385\) 163.705 503.833i 0.425209 1.30866i
\(386\) 52.9439 + 52.7489i 0.137160 + 0.136655i
\(387\) −544.205 176.823i −1.40621 0.456907i
\(388\) 101.834 141.256i 0.262459 0.364062i
\(389\) 83.9351 + 60.9824i 0.215772 + 0.156767i 0.690421 0.723408i \(-0.257425\pi\)
−0.474650 + 0.880175i \(0.657425\pi\)
\(390\) −27.1343 13.7626i −0.0695750 0.0352887i
\(391\) −196.590 + 63.8758i −0.502786 + 0.163365i
\(392\) −127.473 + 20.9138i −0.325187 + 0.0533515i
\(393\) −7.56727 23.2897i −0.0192551 0.0592612i
\(394\) −204.167 203.415i −0.518191 0.516282i
\(395\) 193.837 266.794i 0.490728 0.675429i
\(396\) −174.449 530.231i −0.440527 1.33897i
\(397\) −106.602 −0.268519 −0.134260 0.990946i \(-0.542866\pi\)
−0.134260 + 0.990946i \(0.542866\pi\)
\(398\) −75.2606 + 480.919i −0.189097 + 1.20834i
\(399\) −115.294 158.689i −0.288958 0.397716i
\(400\) −173.423 + 127.965i −0.433556 + 0.319913i
\(401\) 134.274 + 413.254i 0.334849 + 1.03056i 0.966797 + 0.255547i \(0.0822557\pi\)
−0.631948 + 0.775011i \(0.717744\pi\)
\(402\) −140.271 21.9515i −0.348932 0.0546056i
\(403\) 85.9076 + 58.7582i 0.213170 + 0.145802i
\(404\) −4.41515 1.41658i −0.0109286 0.00350637i
\(405\) −37.8730 116.561i −0.0935136 0.287805i
\(406\) −539.855 273.816i −1.32969 0.674425i
\(407\) 23.4474 + 32.2726i 0.0576103 + 0.0792938i
\(408\) −100.498 + 199.967i −0.246318 + 0.490115i
\(409\) 156.052 0.381545 0.190772 0.981634i \(-0.438901\pi\)
0.190772 + 0.981634i \(0.438901\pi\)
\(410\) 309.721 158.531i 0.755416 0.386661i
\(411\) 7.73553 10.6470i 0.0188212 0.0259052i
\(412\) −59.6304 + 43.6611i −0.144734 + 0.105974i
\(413\) 218.516 + 672.523i 0.529095 + 1.62839i
\(414\) −64.8656 126.727i −0.156680 0.306105i
\(415\) −31.3457 + 10.1848i −0.0755319 + 0.0245418i
\(416\) 95.2733 49.6567i 0.229022 0.119367i
\(417\) 171.401 + 124.530i 0.411033 + 0.298633i
\(418\) −318.478 + 627.909i −0.761908 + 1.50218i
\(419\) −696.780 226.398i −1.66296 0.540328i −0.681471 0.731846i \(-0.738659\pi\)
−0.981489 + 0.191517i \(0.938659\pi\)
\(420\) −86.4208 118.030i −0.205764 0.281023i
\(421\) −32.6054 + 100.349i −0.0774475 + 0.238359i −0.982283 0.187402i \(-0.939993\pi\)
0.904836 + 0.425761i \(0.139993\pi\)
\(422\) −574.253 + 92.0393i −1.36079 + 0.218103i
\(423\) 87.3819 + 120.271i 0.206577 + 0.284328i
\(424\) 64.5988 423.003i 0.152356 0.997649i
\(425\) −228.465 165.989i −0.537564 0.390563i
\(426\) 178.094 + 177.438i 0.418062 + 0.416522i
\(427\) −280.390 385.924i −0.656652 0.903804i
\(428\) −145.962 + 454.930i −0.341032 + 1.06292i
\(429\) 86.5988 0.201862
\(430\) 245.252 + 479.146i 0.570353 + 1.11429i
\(431\) 76.9423 + 25.0001i 0.178521 + 0.0580048i 0.396913 0.917856i \(-0.370081\pi\)
−0.218393 + 0.975861i \(0.570081\pi\)
\(432\) −330.121 104.575i −0.764170 0.242073i
\(433\) −16.8576 −0.0389321 −0.0194661 0.999811i \(-0.506197\pi\)
−0.0194661 + 0.999811i \(0.506197\pi\)
\(434\) 240.582 + 438.800i 0.554338 + 1.01106i
\(435\) 169.905i 0.390586i
\(436\) 2.44457 + 662.387i 0.00560681 + 1.51924i
\(437\) −55.4890 + 170.777i −0.126977 + 0.390795i
\(438\) −50.4919 98.6455i −0.115278 0.225218i
\(439\) 556.353i 1.26732i −0.773612 0.633659i \(-0.781552\pi\)
0.773612 0.633659i \(-0.218448\pi\)
\(440\) −235.786 + 469.159i −0.535878 + 1.06627i
\(441\) 94.3093 68.5197i 0.213853 0.155374i
\(442\) 99.7255 + 99.3582i 0.225623 + 0.224792i
\(443\) −170.321 + 234.426i −0.384471 + 0.529179i −0.956762 0.290872i \(-0.906055\pi\)
0.572291 + 0.820051i \(0.306055\pi\)
\(444\) 11.0153 0.0406523i 0.0248092 9.15593e-5i
\(445\) −162.124 + 117.790i −0.364323 + 0.264696i
\(446\) −17.3556 + 2.78169i −0.0389138 + 0.00623697i
\(447\) −205.609 66.8063i −0.459974 0.149455i
\(448\) 516.537 5.71911i 1.15298 0.0127659i
\(449\) 180.770 556.353i 0.402606 1.23909i −0.520272 0.854001i \(-0.674169\pi\)
0.922878 0.385093i \(-0.125831\pi\)
\(450\) 87.9784 173.458i 0.195507 0.385462i
\(451\) −582.102 + 801.195i −1.29069 + 1.77649i
\(452\) 129.564 179.721i 0.286647 0.397613i
\(453\) −8.71983 26.8369i −0.0192491 0.0592425i
\(454\) 117.584 + 229.723i 0.258996 + 0.505998i
\(455\) −87.5124 + 28.4345i −0.192335 + 0.0624934i
\(456\) 89.2203 + 172.734i 0.195659 + 0.378803i
\(457\) −663.600 482.133i −1.45208 1.05500i −0.985340 0.170601i \(-0.945429\pi\)
−0.466738 0.884396i \(-0.654571\pi\)
\(458\) 194.467 99.5383i 0.424600 0.217333i
\(459\) 453.738i 0.988535i
\(460\) −40.9125 + 127.515i −0.0889403 + 0.277207i
\(461\) 301.239 218.863i 0.653447 0.474757i −0.210997 0.977487i \(-0.567671\pi\)
0.864443 + 0.502730i \(0.167671\pi\)
\(462\) 371.341 + 188.345i 0.803768 + 0.407674i
\(463\) 752.029 244.349i 1.62425 0.527752i 0.651313 0.758809i \(-0.274218\pi\)
0.972940 + 0.231057i \(0.0742185\pi\)
\(464\) 487.978 + 349.063i 1.05168 + 0.752290i
\(465\) −79.2971 + 115.937i −0.170531 + 0.249326i
\(466\) −801.219 125.386i −1.71935 0.269068i
\(467\) 662.756 215.342i 1.41918 0.461118i 0.503836 0.863799i \(-0.331921\pi\)
0.915341 + 0.402681i \(0.131921\pi\)
\(468\) −56.6983 + 78.6473i −0.121150 + 0.168050i
\(469\) −347.386 + 252.391i −0.740695 + 0.538146i
\(470\) 21.6215 138.162i 0.0460031 0.293962i
\(471\) 189.964i 0.403320i
\(472\) −113.472 691.633i −0.240407 1.46532i
\(473\) −1239.47 900.527i −2.62044 1.90386i
\(474\) 183.615 + 182.938i 0.387373 + 0.385946i
\(475\) −233.312 + 75.8078i −0.491184 + 0.159595i
\(476\) 211.533 + 642.949i 0.444397 + 1.35073i
\(477\) 119.328 + 367.254i 0.250164 + 0.769925i
\(478\) 325.768 + 165.230i 0.681522 + 0.345670i
\(479\) 466.311 641.822i 0.973509 1.33992i 0.0332553 0.999447i \(-0.489413\pi\)
0.940254 0.340474i \(-0.110587\pi\)
\(480\) 67.0142 + 128.576i 0.139613 + 0.267867i
\(481\) 2.14112 6.58970i 0.00445140 0.0137000i
\(482\) 388.025 + 386.596i 0.805032 + 0.802066i
\(483\) 100.996 + 32.8157i 0.209102 + 0.0679415i
\(484\) −3.72938 1010.52i −0.00770533 2.08786i
\(485\) 119.591 86.8877i 0.246579 0.179150i
\(486\) 479.779 76.8974i 0.987200 0.158225i
\(487\) 133.384 183.587i 0.273889 0.376976i −0.649809 0.760098i \(-0.725151\pi\)
0.923698 + 0.383122i \(0.125151\pi\)
\(488\) 216.980 + 420.082i 0.444631 + 0.860824i
\(489\) 173.910 126.353i 0.355644 0.258390i
\(490\) −108.339 16.9543i −0.221099 0.0346005i
\(491\) 248.654i 0.506425i 0.967411 + 0.253212i \(0.0814871\pi\)
−0.967411 + 0.253212i \(0.918513\pi\)
\(492\) 85.4647 + 259.767i 0.173709 + 0.527983i
\(493\) −242.929 + 747.660i −0.492757 + 1.51655i
\(494\) 120.749 19.3533i 0.244431 0.0391766i
\(495\) 473.842i 0.957256i
\(496\) −170.065 465.934i −0.342872 0.939382i
\(497\) 760.325 1.52983
\(498\) −4.09957 25.5781i −0.00823206 0.0513616i
\(499\) −84.6319 27.4986i −0.169603 0.0551074i 0.222985 0.974822i \(-0.428420\pi\)
−0.392588 + 0.919715i \(0.628420\pi\)
\(500\) −496.338 + 163.298i −0.992676 + 0.326595i
\(501\) −122.278 −0.244068
\(502\) −7.77989 + 49.7138i −0.0154978 + 0.0990315i
\(503\) −80.8438 111.272i −0.160723 0.221216i 0.721059 0.692874i \(-0.243656\pi\)
−0.881782 + 0.471658i \(0.843656\pi\)
\(504\) −414.177 + 213.930i −0.821780 + 0.424464i
\(505\) −3.18441 2.31361i −0.00630577 0.00458141i
\(506\) −60.3229 376.368i −0.119215 0.743810i
\(507\) 123.712 + 170.275i 0.244007 + 0.335847i
\(508\) 122.150 0.450801i 0.240453 0.000887404i
\(509\) 247.049 760.338i 0.485361 1.49379i −0.346097 0.938199i \(-0.612493\pi\)
0.831457 0.555588i \(-0.187507\pi\)
\(510\) −134.089 + 134.585i −0.262919 + 0.263892i
\(511\) −318.747 103.567i −0.623770 0.202675i
\(512\) −506.957 71.6855i −0.990150 0.140011i
\(513\) −318.884 231.683i −0.621606 0.451623i
\(514\) 420.119 828.305i 0.817352 1.61149i
\(515\) −59.6672 + 19.3870i −0.115859 + 0.0376448i
\(516\) −401.867 + 132.216i −0.778811 + 0.256233i
\(517\) 123.000 + 378.557i 0.237912 + 0.732218i
\(518\) 23.5133 23.6002i 0.0453925 0.0455603i
\(519\) −152.032 + 209.255i −0.292933 + 0.403188i
\(520\) 89.9991 14.7656i 0.173075 0.0283954i
\(521\) 566.494 1.08732 0.543660 0.839306i \(-0.317038\pi\)
0.543660 + 0.839306i \(0.317038\pi\)
\(522\) −534.919 83.7113i −1.02475 0.160367i
\(523\) −102.918 141.654i −0.196783 0.270849i 0.699210 0.714916i \(-0.253535\pi\)
−0.895993 + 0.444067i \(0.853535\pi\)
\(524\) 59.5457 + 42.9276i 0.113637 + 0.0819229i
\(525\) 44.8321 + 137.979i 0.0853945 + 0.262817i
\(526\) 100.240 640.537i 0.190570 1.21775i
\(527\) 514.710 396.796i 0.976678 0.752933i
\(528\) −335.656 240.104i −0.635713 0.454741i
\(529\) 133.429 + 410.651i 0.252228 + 0.776279i
\(530\) 164.312 323.958i 0.310024 0.611241i
\(531\) 371.768 + 511.695i 0.700129 + 0.963645i
\(532\) 559.871 + 179.632i 1.05239 + 0.337653i
\(533\) 172.014 0.322728
\(534\) −71.7644 140.205i −0.134390 0.262557i
\(535\) −238.391 + 328.117i −0.445591 + 0.613303i
\(536\) 378.133 195.312i 0.705472 0.364389i
\(537\) 10.9978 + 33.8478i 0.0204801 + 0.0630312i
\(538\) −611.526 + 313.011i −1.13667 + 0.581805i
\(539\) 296.842 96.4497i 0.550727 0.178942i
\(540\) −238.455 171.907i −0.441584 0.318346i
\(541\) 662.911 + 481.633i 1.22534 + 0.890264i 0.996532 0.0832069i \(-0.0265162\pi\)
0.228811 + 0.973471i \(0.426516\pi\)
\(542\) 539.713 + 273.744i 0.995780 + 0.505063i
\(543\) 411.414 + 133.676i 0.757668 + 0.246181i
\(544\) −111.056 661.611i −0.204146 1.21620i
\(545\) −173.759 + 534.775i −0.318824 + 0.981239i
\(546\) −11.4454 71.4101i −0.0209622 0.130788i
\(547\) 80.9626 + 111.435i 0.148012 + 0.203721i 0.876585 0.481247i \(-0.159816\pi\)
−0.728573 + 0.684968i \(0.759816\pi\)
\(548\) 0.145591 + 39.4497i 0.000265677 + 0.0719886i
\(549\) −345.188 250.793i −0.628757 0.456819i
\(550\) 367.544 368.903i 0.668262 0.670733i
\(551\) 401.408 + 552.491i 0.728509 + 1.00271i
\(552\) −94.0458 47.2648i −0.170373 0.0856246i
\(553\) 783.892 1.41753
\(554\) −179.146 + 91.6961i −0.323368 + 0.165516i
\(555\) 8.89313 + 2.88955i 0.0160237 + 0.00520640i
\(556\) −635.079 + 2.34379i −1.14223 + 0.00421545i
\(557\) −597.655 −1.07299 −0.536495 0.843904i \(-0.680252\pi\)
−0.536495 + 0.843904i \(0.680252\pi\)
\(558\) 325.939 + 306.776i 0.584120 + 0.549778i
\(559\) 266.110i 0.476046i
\(560\) 418.035 + 132.425i 0.746492 + 0.236473i
\(561\) 167.099 514.279i 0.297860 0.916719i
\(562\) −48.1379 + 24.6395i −0.0856546 + 0.0438425i
\(563\) 804.116i 1.42827i 0.700008 + 0.714135i \(0.253180\pi\)
−0.700008 + 0.714135i \(0.746820\pi\)
\(564\) 104.657 + 33.5788i 0.185563 + 0.0595368i
\(565\) 152.156 110.548i 0.269303 0.195660i
\(566\) 66.6745 66.9210i 0.117799 0.118235i
\(567\) 171.239 235.691i 0.302009 0.415680i
\(568\) −744.964 113.767i −1.31156 0.200294i
\(569\) −774.798 + 562.924i −1.36168 + 0.989321i −0.363348 + 0.931654i \(0.618366\pi\)
−0.998336 + 0.0576675i \(0.981634\pi\)
\(570\) 26.1182 + 162.957i 0.0458214 + 0.285890i
\(571\) −88.0958 28.6240i −0.154283 0.0501297i 0.230857 0.972988i \(-0.425847\pi\)
−0.385140 + 0.922858i \(0.625847\pi\)
\(572\) −209.448 + 153.357i −0.366168 + 0.268107i
\(573\) −24.5707 + 75.6207i −0.0428807 + 0.131973i
\(574\) 737.606 + 374.116i 1.28503 + 0.651770i
\(575\) 78.0659 107.449i 0.135767 0.186867i
\(576\) 437.820 147.635i 0.760103 0.256311i
\(577\) −182.117 560.500i −0.315628 0.971403i −0.975495 0.220021i \(-0.929387\pi\)
0.659867 0.751382i \(-0.270613\pi\)
\(578\) 267.965 137.158i 0.463607 0.237298i
\(579\) −47.4233 + 15.4088i −0.0819055 + 0.0266127i
\(580\) 300.883 + 410.932i 0.518764 + 0.708504i
\(581\) −63.3822 46.0498i −0.109091 0.0792596i
\(582\) 52.9370 + 103.423i 0.0909571 + 0.177702i
\(583\) 1033.91i 1.77343i
\(584\) 296.810 + 149.169i 0.508237 + 0.255426i
\(585\) −66.5846 + 48.3766i −0.113820 + 0.0826950i
\(586\) 414.277 816.788i 0.706958 1.39384i
\(587\) −642.960 + 208.910i −1.09533 + 0.355895i −0.800304 0.599594i \(-0.795329\pi\)
−0.295027 + 0.955489i \(0.595329\pi\)
\(588\) 26.3305 82.0662i 0.0447797 0.139568i
\(589\) −16.0499 564.342i −0.0272493 0.958136i
\(590\) 91.9890 587.814i 0.155914 0.996294i
\(591\) 182.878 59.4207i 0.309438 0.100543i
\(592\) −26.5696 + 19.6052i −0.0448810 + 0.0331168i
\(593\) 78.5153 57.0447i 0.132403 0.0961968i −0.519612 0.854402i \(-0.673924\pi\)
0.652016 + 0.758205i \(0.273924\pi\)
\(594\) 826.641 + 129.364i 1.39165 + 0.217784i
\(595\) 574.572i 0.965667i
\(596\) 615.592 202.533i 1.03287 0.339820i
\(597\) −262.747 190.897i −0.440112 0.319760i
\(598\) −46.7289 + 46.9016i −0.0781419 + 0.0784308i
\(599\) 388.249 126.150i 0.648162 0.210601i 0.0335584 0.999437i \(-0.489316\pi\)
0.614604 + 0.788836i \(0.289316\pi\)
\(600\) −23.2806 141.900i −0.0388011 0.236499i
\(601\) 185.310 + 570.325i 0.308336 + 0.948960i 0.978411 + 0.206667i \(0.0662617\pi\)
−0.670076 + 0.742293i \(0.733738\pi\)
\(602\) −578.767 + 1141.09i −0.961407 + 1.89551i
\(603\) −225.749 + 310.717i −0.374377 + 0.515285i
\(604\) 68.6150 + 49.4658i 0.113601 + 0.0818971i
\(605\) 265.083 815.841i 0.438154 1.34850i
\(606\) 2.18352 2.19160i 0.00360317 0.00361649i
\(607\) −1011.86 328.773i −1.66698 0.541635i −0.684665 0.728858i \(-0.740051\pi\)
−0.982318 + 0.187222i \(0.940051\pi\)
\(608\) −521.682 259.776i −0.858029 0.427263i
\(609\) 326.739 237.390i 0.536517 0.389803i
\(610\) 63.5184 + 396.305i 0.104128 + 0.649680i
\(611\) 40.6374 55.9326i 0.0665097 0.0915428i
\(612\) 357.654 + 488.467i 0.584402 + 0.798149i
\(613\) −74.3019 + 53.9835i −0.121210 + 0.0880645i −0.646739 0.762712i \(-0.723868\pi\)
0.525528 + 0.850776i \(0.323868\pi\)
\(614\) 54.6603 349.282i 0.0890234 0.568863i
\(615\) 232.142i 0.377466i
\(616\) −1231.66 + 202.072i −1.99945 + 0.328039i
\(617\) −99.0609 + 304.878i −0.160553 + 0.494130i −0.998681 0.0513429i \(-0.983650\pi\)
0.838129 + 0.545473i \(0.183650\pi\)
\(618\) −7.80361 48.6884i −0.0126272 0.0787838i
\(619\) 186.724i 0.301654i 0.988560 + 0.150827i \(0.0481936\pi\)
−0.988560 + 0.150827i \(0.951806\pi\)
\(620\) −13.5229 420.831i −0.0218112 0.678760i
\(621\) 213.396 0.343633
\(622\) 1187.87 190.387i 1.90976 0.306089i
\(623\) −453.036 147.200i −0.727185 0.236277i
\(624\) 0.529083 + 71.6799i 0.000847890 + 0.114872i
\(625\) −106.797 −0.170876
\(626\) −685.070 107.209i −1.09436 0.171260i
\(627\) −276.110 380.032i −0.440366 0.606112i
\(628\) 336.405 + 459.447i 0.535677 + 0.731603i
\(629\) −35.0024 25.4307i −0.0556477 0.0404304i
\(630\) −390.734 + 62.6255i −0.620212 + 0.0994055i
\(631\) 629.251 + 866.089i 0.997228 + 1.37257i 0.927011 + 0.375035i \(0.122369\pi\)
0.0702170 + 0.997532i \(0.477631\pi\)
\(632\) −768.055 117.293i −1.21528 0.185591i
\(633\) 119.908 369.038i 0.189428 0.582999i
\(634\) −635.896 633.554i −1.00299 0.999296i
\(635\) 98.6175 + 32.0428i 0.155303 + 0.0504611i
\(636\) 231.591 + 166.958i 0.364137 + 0.262513i
\(637\) −43.8591 31.8655i −0.0688525 0.0500243i
\(638\) −1292.86 655.744i −2.02643 1.02781i
\(639\) 646.782 210.152i 1.01218 0.328877i
\(640\) −389.775 192.300i −0.609024 0.300468i
\(641\) 259.106 + 797.448i 0.404222 + 1.24407i 0.921543 + 0.388277i \(0.126929\pi\)
−0.517321 + 0.855792i \(0.673071\pi\)
\(642\) −225.819 224.987i −0.351743 0.350447i
\(643\) −174.595 + 240.310i −0.271533 + 0.373732i −0.922906 0.385024i \(-0.874193\pi\)
0.651374 + 0.758757i \(0.274193\pi\)
\(644\) −302.383 + 99.4856i −0.469539 + 0.154481i
\(645\) −359.129 −0.556789
\(646\) 118.063 754.430i 0.182761 1.16785i
\(647\) −73.6604 101.385i −0.113849 0.156700i 0.748290 0.663372i \(-0.230875\pi\)
−0.862139 + 0.506672i \(0.830875\pi\)
\(648\) −203.046 + 205.307i −0.313343 + 0.316831i
\(649\) 523.309 + 1610.58i 0.806331 + 2.48163i
\(650\) −89.3627 13.9847i −0.137481 0.0215149i
\(651\) −333.748 + 9.49176i −0.512669 + 0.0145803i
\(652\) −196.861 + 613.573i −0.301935 + 0.941063i
\(653\) 29.0527 + 89.4151i 0.0444912 + 0.136930i 0.970835 0.239750i \(-0.0770656\pi\)
−0.926343 + 0.376680i \(0.877066\pi\)
\(654\) −394.146 199.912i −0.602670 0.305676i
\(655\) 36.6270 + 50.4128i 0.0559191 + 0.0769661i
\(656\) −666.725 476.925i −1.01635 0.727020i
\(657\) −299.773 −0.456275
\(658\) 295.905 151.459i 0.449703 0.230181i
\(659\) −46.2771 + 63.6949i −0.0702232 + 0.0966539i −0.842684 0.538409i \(-0.819026\pi\)
0.772461 + 0.635063i \(0.219026\pi\)
\(660\) −206.963 282.661i −0.313580 0.428274i
\(661\) 38.9223 + 119.791i 0.0588840 + 0.181226i 0.976172 0.216998i \(-0.0696266\pi\)
−0.917288 + 0.398224i \(0.869627\pi\)
\(662\) 150.316 + 293.670i 0.227063 + 0.443611i
\(663\) −89.3268 + 29.0240i −0.134731 + 0.0437768i
\(664\) 55.2112 + 54.6033i 0.0831495 + 0.0822339i
\(665\) 403.806 + 293.382i 0.607226 + 0.441176i
\(666\) 13.4789 26.5750i 0.0202386 0.0399023i
\(667\) −351.630 114.251i −0.527181 0.171291i
\(668\) 295.742 216.541i 0.442728 0.324164i
\(669\) 3.62396 11.1534i 0.00541698 0.0166717i
\(670\) 356.730 57.1754i 0.532433 0.0853365i
\(671\) −671.487 924.223i −1.00073 1.37738i
\(672\) −153.629 + 308.518i −0.228615 + 0.459105i
\(673\) −1038.52 754.531i −1.54312 1.12115i −0.948338 0.317263i \(-0.897236\pi\)
−0.594787 0.803883i \(-0.702764\pi\)
\(674\) −78.8216 78.5313i −0.116946 0.116515i
\(675\) 171.361 + 235.858i 0.253868 + 0.349420i
\(676\) −600.747 192.746i −0.888680 0.285128i
\(677\) −513.431 −0.758392 −0.379196 0.925316i \(-0.623799\pi\)
−0.379196 + 0.925316i \(0.623799\pi\)
\(678\) 67.3521 + 131.585i 0.0993394 + 0.194078i
\(679\) 334.182 + 108.582i 0.492168 + 0.159915i
\(680\) 85.9728 562.964i 0.126431 0.827888i
\(681\) −172.182 −0.252836
\(682\) 576.154 + 1050.85i 0.844800 + 1.54084i
\(683\) 1151.65i 1.68616i −0.537791 0.843078i \(-0.680741\pi\)
0.537791 0.843078i \(-0.319259\pi\)
\(684\) 525.913 1.94091i 0.768879 0.00283758i
\(685\) −10.3486 + 31.8496i −0.0151074 + 0.0464957i
\(686\) 241.639 + 472.087i 0.352243 + 0.688174i
\(687\) 145.757i 0.212164i
\(688\) 737.815 1031.44i 1.07241 1.49919i
\(689\) 145.286 105.556i 0.210865 0.153202i
\(690\) −63.2961 63.0630i −0.0917335 0.0913956i
\(691\) −713.489 + 982.033i −1.03255 + 1.42118i −0.129527 + 0.991576i \(0.541346\pi\)
−0.903019 + 0.429601i \(0.858654\pi\)
\(692\) −2.86142 775.337i −0.00413499 1.12043i
\(693\) 911.231 662.048i 1.31491 0.955336i
\(694\) −592.657 + 94.9890i −0.853973 + 0.136872i
\(695\) −512.729 166.596i −0.737739 0.239706i
\(696\) −355.658 + 183.704i −0.511003 + 0.263943i
\(697\) 331.915 1021.53i 0.476205 1.46561i
\(698\) −111.642 + 220.112i −0.159945 + 0.315347i
\(699\) 318.037 437.741i 0.454989 0.626239i
\(700\) −352.777 254.324i −0.503967 0.363320i
\(701\) −32.2430 99.2337i −0.0459957 0.141560i 0.925421 0.378940i \(-0.123711\pi\)
−0.971417 + 0.237380i \(0.923711\pi\)
\(702\) −66.2171 129.368i −0.0943263 0.184284i
\(703\) −35.7451 + 11.6143i −0.0508465 + 0.0165210i
\(704\) 1237.02 13.6963i 1.75713 0.0194550i
\(705\) 75.4839 + 54.8423i 0.107069 + 0.0777905i
\(706\) 396.413 202.905i 0.561492 0.287401i
\(707\) 9.35641i 0.0132340i
\(708\) 445.268 + 142.862i 0.628909 + 0.201782i
\(709\) 208.334 151.363i 0.293842 0.213489i −0.431090 0.902309i \(-0.641871\pi\)
0.724932 + 0.688820i \(0.241871\pi\)
\(710\) −570.532 289.376i −0.803566 0.407571i
\(711\) 666.831 216.666i 0.937877 0.304735i
\(712\) 421.858 + 212.014i 0.592497 + 0.297772i
\(713\) 186.616 + 242.072i 0.261733 + 0.339511i
\(714\) −446.164 69.8217i −0.624879 0.0977895i
\(715\) −209.577 + 68.0958i −0.293115 + 0.0952389i
\(716\) −86.5400 62.3883i −0.120866 0.0871346i
\(717\) −197.166 + 143.249i −0.274987 + 0.199790i
\(718\) 34.2487 218.851i 0.0477001 0.304806i
\(719\) 404.409i 0.562461i −0.959640 0.281230i \(-0.909258\pi\)
0.959640 0.281230i \(-0.0907425\pi\)
\(720\) 392.210 2.89498i 0.544737 0.00402081i
\(721\) −120.649 87.6568i −0.167336 0.121577i
\(722\) 41.5481 + 41.3950i 0.0575458 + 0.0573338i
\(723\) −347.565 + 112.931i −0.480726 + 0.156197i
\(724\) −1231.77 + 405.259i −1.70134 + 0.559750i
\(725\) −156.088 480.389i −0.215293 0.662605i
\(726\) 601.300 + 304.981i 0.828237 + 0.420085i
\(727\) −382.717 + 526.765i −0.526433 + 0.724573i −0.986582 0.163269i \(-0.947796\pi\)
0.460148 + 0.887842i \(0.347796\pi\)
\(728\) 154.141 + 152.444i 0.211733 + 0.209401i
\(729\) 0.202247 0.622451i 0.000277430 0.000853843i
\(730\) 199.764 + 199.028i 0.273649 + 0.272641i
\(731\) 1580.33 + 513.481i 2.16188 + 0.702436i
\(732\) −315.455 + 1.16420i −0.430950 + 0.00159044i
\(733\) −1.55060 + 1.12658i −0.00211542 + 0.00153694i −0.588842 0.808248i \(-0.700416\pi\)
0.586727 + 0.809785i \(0.300416\pi\)
\(734\) −990.262 + 158.716i −1.34913 + 0.216234i
\(735\) 43.0041 59.1900i 0.0585089 0.0805307i
\(736\) 311.160 52.2302i 0.422772 0.0709650i
\(737\) −831.930 + 604.433i −1.12881 + 0.820126i
\(738\) 730.861 + 114.375i 0.990327 + 0.154980i
\(739\) 868.687i 1.17549i 0.809046 + 0.587745i \(0.199984\pi\)
−0.809046 + 0.587745i \(0.800016\pi\)
\(740\) −26.6260 + 8.76009i −0.0359811 + 0.0118380i
\(741\) −25.2132 + 77.5983i −0.0340259 + 0.104721i
\(742\) 852.569 136.647i 1.14902 0.184160i
\(743\) 819.871i 1.10346i −0.834023 0.551730i \(-0.813968\pi\)
0.834023 0.551730i \(-0.186032\pi\)
\(744\) 328.425 + 40.6384i 0.441432 + 0.0546216i
\(745\) 550.125 0.738422
\(746\) −80.0482 499.438i −0.107303 0.669488i
\(747\) −66.6452 21.6543i −0.0892171 0.0289884i
\(748\) 506.586 + 1539.75i 0.677254 + 2.05849i
\(749\) −964.070 −1.28714
\(750\) 53.9003 344.426i 0.0718671 0.459234i
\(751\) −275.787 379.588i −0.367226 0.505443i 0.584918 0.811092i \(-0.301127\pi\)
−0.952144 + 0.305649i \(0.901127\pi\)
\(752\) −312.589 + 104.123i −0.415677 + 0.138462i
\(753\) −27.1608 19.7335i −0.0360701 0.0262065i
\(754\) 39.8482 + 248.622i 0.0528491 + 0.329737i
\(755\) 42.2056 + 58.0911i 0.0559015 + 0.0769418i
\(756\) −2.57878 698.753i −0.00341108 0.924276i
\(757\) 4.86327 14.9676i 0.00642440 0.0197723i −0.947793 0.318886i \(-0.896691\pi\)
0.954217 + 0.299114i \(0.0966911\pi\)
\(758\) 690.407 692.959i 0.910827 0.914194i
\(759\) 241.869 + 78.5881i 0.318668 + 0.103542i
\(760\) −351.749 347.876i −0.462827 0.457731i
\(761\) 98.1508 + 71.3107i 0.128976 + 0.0937066i 0.650403 0.759589i \(-0.274600\pi\)
−0.521427 + 0.853296i \(0.674600\pi\)
\(762\) −36.8656 + 72.6842i −0.0483801 + 0.0953860i
\(763\) −1271.18 + 413.033i −1.66604 + 0.541328i
\(764\) −74.4895 226.408i −0.0974993 0.296346i
\(765\) 158.811 + 488.769i 0.207596 + 0.638914i
\(766\) −910.136 + 913.501i −1.18817 + 1.19256i
\(767\) 172.893 237.967i 0.225415 0.310256i
\(768\) 196.689 279.298i 0.256105 0.363669i
\(769\) −1133.84 −1.47443 −0.737216 0.675658i \(-0.763860\pi\)
−0.737216 + 0.675658i \(0.763860\pi\)
\(770\) −1046.78 163.815i −1.35946 0.212746i
\(771\) 364.229 + 501.318i 0.472411 + 0.650218i
\(772\) 87.4108 121.249i 0.113226 0.157058i
\(773\) 145.151 + 446.728i 0.187776 + 0.577915i 0.999985 0.00545140i \(-0.00173524\pi\)
−0.812209 + 0.583366i \(0.801735\pi\)
\(774\) −176.941 + 1130.66i −0.228606 + 1.46080i
\(775\) −117.696 + 400.647i −0.151866 + 0.516964i
\(776\) −311.184 156.392i −0.401010 0.201536i
\(777\) 6.86860 + 21.1394i 0.00883989 + 0.0272064i
\(778\) 93.8613 185.057i 0.120644 0.237862i
\(779\) −548.445 754.870i −0.704038 0.969025i
\(780\) −18.5899 + 57.9407i −0.0238333 + 0.0742829i
\(781\) 1820.85 2.33143
\(782\) 188.365 + 368.007i 0.240876 + 0.470597i
\(783\) 477.033 656.580i 0.609238 0.838544i
\(784\) 81.6474 + 245.114i 0.104142 + 0.312645i
\(785\) 149.375 + 459.730i 0.190287 + 0.585644i
\(786\) −43.5972 + 22.3153i −0.0554671 + 0.0283910i
\(787\) 847.027 275.216i 1.07627 0.349703i 0.283346 0.959018i \(-0.408556\pi\)
0.792928 + 0.609315i \(0.208556\pi\)
\(788\) −337.082 + 467.572i −0.427769 + 0.593366i
\(789\) 349.953 + 254.256i 0.443540 + 0.322251i
\(790\) −588.217 298.345i −0.744578 0.377652i
\(791\) 425.182 + 138.150i 0.537525 + 0.174653i
\(792\) −991.883 + 512.326i −1.25238 + 0.646876i
\(793\) −61.3175 + 188.716i −0.0773235 + 0.237977i
\(794\) 33.7410 + 210.518i 0.0424950 + 0.265136i
\(795\) 142.453 + 196.070i 0.179187 + 0.246629i
\(796\) 973.538 3.59288i 1.22304 0.00451367i
\(797\) −49.7487 36.1445i −0.0624199 0.0453507i 0.556138 0.831090i \(-0.312283\pi\)
−0.618558 + 0.785739i \(0.712283\pi\)
\(798\) −276.886 + 277.909i −0.346975 + 0.348257i
\(799\) −253.751 349.258i −0.317585 0.437119i
\(800\) 307.596 + 301.971i 0.384494 + 0.377464i
\(801\) −426.068 −0.531921
\(802\) 773.592 395.965i 0.964579 0.493722i
\(803\) −763.344 248.025i −0.950615 0.308874i
\(804\) 1.04795 + 283.954i 0.00130341 + 0.353177i
\(805\) −270.225 −0.335684
\(806\) 88.8445 188.248i 0.110229 0.233558i
\(807\) 458.350i 0.567968i
\(808\) −1.39999 + 9.16738i −0.00173267 + 0.0113458i
\(809\) 93.7547 288.547i 0.115890 0.356672i −0.876242 0.481872i \(-0.839957\pi\)
0.992132 + 0.125200i \(0.0399572\pi\)
\(810\) −218.197 + 111.685i −0.269379 + 0.137882i
\(811\) 287.487i 0.354484i −0.984167 0.177242i \(-0.943282\pi\)
0.984167 0.177242i \(-0.0567176\pi\)
\(812\) −369.860 + 1152.77i −0.455493 + 1.41967i
\(813\) −326.653 + 237.327i −0.401787 + 0.291915i
\(814\) 56.3103 56.5185i 0.0691773 0.0694331i
\(815\) −321.523 + 442.538i −0.394506 + 0.542991i
\(816\) 426.702 + 135.170i 0.522920 + 0.165650i
\(817\) 1167.80 848.459i 1.42938 1.03851i
\(818\) −49.3925 308.170i −0.0603820 0.376736i
\(819\) −186.063 60.4555i −0.227183 0.0738163i
\(820\) −411.098 561.458i −0.501338 0.684705i
\(821\) 269.145 828.342i 0.327825 1.00894i −0.642324 0.766434i \(-0.722029\pi\)
0.970149 0.242510i \(-0.0779706\pi\)
\(822\) −23.4741 11.9062i −0.0285573 0.0144844i
\(823\) 574.273 790.420i 0.697781 0.960413i −0.302194 0.953247i \(-0.597719\pi\)
0.999974 0.00716608i \(-0.00228105\pi\)
\(824\) 105.096 + 103.938i 0.127543 + 0.126139i
\(825\) 107.365 + 330.436i 0.130140 + 0.400529i
\(826\) 1258.93 644.387i 1.52413 0.780130i
\(827\) 1140.54 370.583i 1.37913 0.448105i 0.476744 0.879042i \(-0.341817\pi\)
0.902382 + 0.430937i \(0.141817\pi\)
\(828\) −229.730 + 168.207i −0.277451 + 0.203149i
\(829\) −587.618 426.930i −0.708828 0.514993i 0.173968 0.984751i \(-0.444341\pi\)
−0.882795 + 0.469758i \(0.844341\pi\)
\(830\) 30.0343 + 58.6778i 0.0361859 + 0.0706961i
\(831\) 134.273i 0.161580i
\(832\) −128.217 172.428i −0.154107 0.207246i
\(833\) −273.867 + 198.976i −0.328772 + 0.238867i
\(834\) 191.671 377.897i 0.229821 0.453114i
\(835\) 295.925 96.1518i 0.354401 0.115152i
\(836\) 1340.80 + 430.187i 1.60382 + 0.514577i
\(837\) −631.945 + 225.387i −0.755012 + 0.269279i
\(838\) −226.549 + 1447.66i −0.270345 + 1.72751i
\(839\) −1476.64 + 479.789i −1.76000 + 0.571858i −0.997200 0.0747808i \(-0.976174\pi\)
−0.762797 + 0.646638i \(0.776174\pi\)
\(840\) −205.731 + 208.021i −0.244918 + 0.247645i
\(841\) −457.193 + 332.170i −0.543630 + 0.394970i
\(842\) 208.489 + 32.6272i 0.247612 + 0.0387496i
\(843\) 36.0802i 0.0427998i
\(844\) 363.518 + 1104.90i 0.430708 + 1.30912i
\(845\) −433.287 314.802i −0.512766 0.372546i
\(846\) 209.853 210.629i 0.248053 0.248970i
\(847\) 1939.29 630.114i 2.28960 0.743936i
\(848\) −855.791 + 6.31676i −1.00919 + 0.00744901i
\(849\) 19.4766 + 59.9429i 0.0229407 + 0.0706042i
\(850\) −255.483 + 503.709i −0.300568 + 0.592598i
\(851\) 11.9603 16.4619i 0.0140543 0.0193442i
\(852\) 294.035 407.862i 0.345112 0.478711i
\(853\) −415.732 + 1279.49i −0.487377 + 1.49999i 0.341132 + 0.940015i \(0.389190\pi\)
−0.828509 + 0.559976i \(0.810810\pi\)
\(854\) −673.375 + 675.864i −0.788495 + 0.791410i
\(855\) 424.594 + 137.959i 0.496601 + 0.161355i
\(856\) 944.593 + 144.253i 1.10350 + 0.168520i
\(857\) 894.050 649.566i 1.04323 0.757953i 0.0723186 0.997382i \(-0.476960\pi\)
0.970914 + 0.239429i \(0.0769601\pi\)
\(858\) −27.4097 171.015i −0.0319460 0.199318i
\(859\) −437.193 + 601.745i −0.508956 + 0.700518i −0.983743 0.179583i \(-0.942525\pi\)
0.474787 + 0.880101i \(0.342525\pi\)
\(860\) 868.590 635.978i 1.00999 0.739509i
\(861\) −446.424 + 324.346i −0.518495 + 0.376709i
\(862\) 25.0168 159.858i 0.0290218 0.185450i
\(863\) 1109.84i 1.28602i −0.765857 0.643011i \(-0.777685\pi\)
0.765857 0.643011i \(-0.222315\pi\)
\(864\) −102.027 + 685.022i −0.118087 + 0.792849i
\(865\) 203.388 625.965i 0.235131 0.723659i
\(866\) 5.33566 + 33.2904i 0.00616127 + 0.0384415i
\(867\) 200.845i 0.231655i
\(868\) 790.394 613.988i 0.910592 0.707359i
\(869\) 1877.29 2.16029
\(870\) −335.528 + 53.7772i −0.385664 + 0.0618129i
\(871\) 169.871 + 55.1943i 0.195030 + 0.0633689i
\(872\) 1307.31 214.482i 1.49920 0.245965i
\(873\) 314.290 0.360011
\(874\) 354.814 + 55.5260i 0.405965 + 0.0635309i
\(875\) −619.729 852.983i −0.708261 0.974838i
\(876\) −178.823 + 130.934i −0.204136 + 0.149468i
\(877\) −347.368 252.378i −0.396087 0.287774i 0.371858 0.928289i \(-0.378721\pi\)
−0.767945 + 0.640516i \(0.778721\pi\)
\(878\) −1098.68 + 176.093i −1.25135 + 0.200562i
\(879\) 359.165 + 494.348i 0.408606 + 0.562398i
\(880\) 1001.12 + 317.134i 1.13764 + 0.360380i
\(881\) 220.040 677.215i 0.249762 0.768689i −0.745054 0.667004i \(-0.767577\pi\)
0.994817 0.101685i \(-0.0324235\pi\)
\(882\) −165.163 164.554i −0.187259 0.186569i
\(883\) 31.7991 + 10.3322i 0.0360126 + 0.0117012i 0.326968 0.945035i \(-0.393973\pi\)
−0.290955 + 0.956737i \(0.593973\pi\)
\(884\) 164.648 228.386i 0.186253 0.258355i
\(885\) 321.148 + 233.328i 0.362879 + 0.263647i
\(886\) 516.853 + 262.149i 0.583355 + 0.295880i
\(887\) 159.980 51.9807i 0.180361 0.0586029i −0.217444 0.976073i \(-0.569772\pi\)
0.397805 + 0.917470i \(0.369772\pi\)
\(888\) −3.56676 21.7400i −0.00401662 0.0244820i
\(889\) 76.1671 + 234.418i 0.0856773 + 0.263688i
\(890\) 283.925 + 282.879i 0.319017 + 0.317842i
\(891\) 410.089 564.439i 0.460257 0.633489i
\(892\) 10.9865 + 33.3933i 0.0123168 + 0.0374364i
\(893\) −375.024 −0.419959
\(894\) −66.8509 + 427.180i −0.0747772 + 0.477830i
\(895\) −53.2315 73.2668i −0.0594765 0.0818624i
\(896\) −174.785 1018.24i −0.195072 1.13643i
\(897\) −13.6502 42.0111i −0.0152176 0.0468351i
\(898\) −1155.90 180.891i −1.28719 0.201437i
\(899\) 1161.98 33.0466i 1.29252 0.0367592i
\(900\) −370.390 118.838i −0.411545 0.132042i
\(901\) −346.520 1066.48i −0.384595 1.18366i
\(902\) 1766.44 + 895.944i 1.95836 + 0.993286i
\(903\) −501.772 690.630i −0.555672 0.764817i
\(904\) −395.921 198.979i −0.437966 0.220109i
\(905\) −1100.78 −1.21633
\(906\) −50.2374 + 25.7141i −0.0554497 + 0.0283820i
\(907\) 171.296 235.769i 0.188860 0.259944i −0.704078 0.710122i \(-0.748640\pi\)
0.892939 + 0.450178i \(0.148640\pi\)
\(908\) 416.439 304.915i 0.458633 0.335810i
\(909\) −2.58609 7.95918i −0.00284499 0.00875597i
\(910\) 83.8512 + 163.819i 0.0921442 + 0.180021i
\(911\) −865.996 + 281.379i −0.950599 + 0.308868i −0.742959 0.669337i \(-0.766578\pi\)
−0.207640 + 0.978205i \(0.566578\pi\)
\(912\) 312.875 230.865i 0.343065 0.253141i
\(913\) −151.789 110.281i −0.166253 0.120790i
\(914\) −742.077 + 1463.08i −0.811900 + 1.60074i
\(915\) −254.682 82.7511i −0.278341 0.0904383i
\(916\) −258.119 352.527i −0.281790 0.384855i
\(917\) −45.7723 + 140.873i −0.0499153 + 0.153623i
\(918\) −896.039 + 143.614i −0.976078 + 0.156442i
\(919\) −269.693 371.200i −0.293463 0.403918i 0.636672 0.771135i \(-0.280311\pi\)
−0.930135 + 0.367217i \(0.880311\pi\)
\(920\) 264.766 + 40.4336i 0.287789 + 0.0439496i
\(921\) 190.828 + 138.645i 0.207196 + 0.150537i
\(922\) −527.556 525.612i −0.572186 0.570078i
\(923\) −185.898 255.867i −0.201407 0.277212i
\(924\) 254.409 792.936i 0.275334 0.858156i
\(925\) 27.7990 0.0300529
\(926\) −720.567 1407.76i −0.778150 1.52026i
\(927\) −126.860 41.2194i −0.136850 0.0444654i
\(928\) 534.876 1074.14i 0.576375 1.15748i
\(929\) −1534.96 −1.65227 −0.826137 0.563469i \(-0.809467\pi\)
−0.826137 + 0.563469i \(0.809467\pi\)
\(930\) 254.050 + 119.900i 0.273172 + 0.128925i
\(931\) 294.071i 0.315866i
\(932\) 5.98581 + 1621.93i 0.00642254 + 1.74027i
\(933\) −248.035 + 763.372i −0.265846 + 0.818191i
\(934\) −635.028 1240.65i −0.679902 1.32832i
\(935\) 1376.00i 1.47166i
\(936\) 173.258 + 87.0747i 0.185105 + 0.0930285i
\(937\) −464.604 + 337.554i −0.495842 + 0.360250i −0.807426 0.589968i \(-0.799140\pi\)
0.311585 + 0.950218i \(0.399140\pi\)
\(938\) 608.373 + 606.131i 0.648585 + 0.646196i
\(939\) 271.933 374.284i 0.289599 0.398598i
\(940\) −279.685 + 1.03219i −0.297538 + 0.00109808i
\(941\) 638.412 463.833i 0.678440 0.492915i −0.194400 0.980922i \(-0.562276\pi\)
0.872840 + 0.488007i \(0.162276\pi\)
\(942\) −375.140 + 60.1261i −0.398237 + 0.0638281i
\(943\) 480.433 + 156.102i 0.509473 + 0.165538i
\(944\) −1329.92 + 442.995i −1.40881 + 0.469275i
\(945\) 183.299 564.135i 0.193967 0.596968i
\(946\) −1386.05 + 2732.73i −1.46517 + 2.88872i
\(947\) −504.439 + 694.300i −0.532670 + 0.733158i −0.987534 0.157403i \(-0.949688\pi\)
0.454864 + 0.890561i \(0.349688\pi\)
\(948\) 303.149 420.504i 0.319778 0.443570i
\(949\) 43.0804 + 132.588i 0.0453955 + 0.139713i
\(950\) 223.551 + 436.750i 0.235317 + 0.459737i
\(951\) 569.589 185.071i 0.598937 0.194607i
\(952\) 1202.74 621.237i 1.26338 0.652560i
\(953\) 812.977 + 590.662i 0.853071 + 0.619793i 0.925991 0.377545i \(-0.123232\pi\)
−0.0729199 + 0.997338i \(0.523232\pi\)
\(954\) 687.483 351.890i 0.720632 0.368857i
\(955\) 202.330i 0.211864i
\(956\) 223.187 695.622i 0.233459 0.727638i
\(957\) 782.484 568.508i 0.817643 0.594052i
\(958\) −1415.06 717.724i −1.47710 0.749190i
\(959\) −75.7079 + 24.5990i −0.0789446 + 0.0256507i
\(960\) 232.701 173.035i 0.242397 0.180245i
\(961\) −808.312 519.762i −0.841115 0.540856i
\(962\) −13.6910 2.14255i −0.0142318 0.00222718i
\(963\) −820.102 + 266.467i −0.851612 + 0.276705i
\(964\) 640.633 888.634i 0.664557 0.921819i
\(965\) 102.652 74.5813i 0.106376 0.0772864i
\(966\) 32.8376 209.834i 0.0339934 0.217219i
\(967\) 507.531i 0.524851i 0.964952 + 0.262425i \(0.0845224\pi\)
−0.964952 + 0.262425i \(0.915478\pi\)
\(968\) −1994.40 + 327.209i −2.06033 + 0.338026i
\(969\) 412.178 + 299.465i 0.425364 + 0.309045i
\(970\) −209.438 208.666i −0.215915 0.215120i
\(971\) −392.109 + 127.404i −0.403819 + 0.131209i −0.503882 0.863772i \(-0.668096\pi\)
0.100063 + 0.994981i \(0.468096\pi\)
\(972\) −303.713 923.127i −0.312462 0.949720i
\(973\) −396.005 1218.78i −0.406994 1.25260i
\(974\) −404.765 205.298i −0.415570 0.210778i
\(975\) 35.4718 48.8227i 0.0363813 0.0500746i
\(976\) 760.899 561.453i 0.779610 0.575259i
\(977\) 38.1628 117.453i 0.0390612 0.120218i −0.929624 0.368508i \(-0.879869\pi\)
0.968686 + 0.248290i \(0.0798686\pi\)
\(978\) −304.566 303.444i −0.311417 0.310270i
\(979\) −1084.94 352.520i −1.10822 0.360081i
\(980\) 0.809383 + 219.313i 0.000825901 + 0.223789i
\(981\) −967.192 + 702.706i −0.985925 + 0.716316i
\(982\) 491.042 78.7025i 0.500043 0.0801451i
\(983\) 264.202 363.643i 0.268771 0.369932i −0.653203 0.757183i \(-0.726575\pi\)
0.921974 + 0.387251i \(0.126575\pi\)
\(984\) 485.937 250.995i 0.493838 0.255077i
\(985\) −395.858 + 287.608i −0.401886 + 0.291987i
\(986\) 1553.37 + 243.092i 1.57542 + 0.246543i
\(987\) 221.786i 0.224707i
\(988\) −76.4375 232.329i −0.0773658 0.235151i
\(989\) −241.494 + 743.241i −0.244180 + 0.751508i
\(990\) −935.741 + 149.977i −0.945193 + 0.151492i
\(991\) 804.782i 0.812091i 0.913853 + 0.406045i \(0.133092\pi\)
−0.913853 + 0.406045i \(0.866908\pi\)
\(992\) −866.296 + 483.317i −0.873282 + 0.487215i
\(993\) −220.112 −0.221663
\(994\) −240.653 1501.49i −0.242106 1.51055i
\(995\) 785.982 + 255.381i 0.789931 + 0.256664i
\(996\) −49.2139 + 16.1916i −0.0494116 + 0.0162566i
\(997\) 777.454 0.779793 0.389897 0.920859i \(-0.372511\pi\)
0.389897 + 0.920859i \(0.372511\pi\)
\(998\) −27.5169 + 175.834i −0.0275721 + 0.176187i
\(999\) 26.2537 + 36.1352i 0.0262800 + 0.0361713i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 124.3.l.a.35.15 yes 120
4.3 odd 2 inner 124.3.l.a.35.11 120
31.8 even 5 inner 124.3.l.a.39.11 yes 120
124.39 odd 10 inner 124.3.l.a.39.15 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
124.3.l.a.35.11 120 4.3 odd 2 inner
124.3.l.a.35.15 yes 120 1.1 even 1 trivial
124.3.l.a.39.11 yes 120 31.8 even 5 inner
124.3.l.a.39.15 yes 120 124.39 odd 10 inner