Properties

Label 460.2.g.c.459.4
Level $460$
Weight $2$
Character 460.459
Analytic conductor $3.673$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [460,2,Mod(459,460)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(460, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("460.459");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 460.g (of order \(2\), degree \(1\), 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: \(3.67311849298\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 459.4
Character \(\chi\) \(=\) 460.459
Dual form 460.2.g.c.459.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.35976 + 0.388659i) q^{2} +1.11016 q^{3} +(1.69789 - 1.05697i) q^{4} +(1.71804 + 1.43120i) q^{5} +(-1.50955 + 0.431474i) q^{6} -4.32159i q^{7} +(-1.89792 + 2.09712i) q^{8} -1.76755 q^{9} +O(q^{10})\) \(q+(-1.35976 + 0.388659i) q^{2} +1.11016 q^{3} +(1.69789 - 1.05697i) q^{4} +(1.71804 + 1.43120i) q^{5} +(-1.50955 + 0.431474i) q^{6} -4.32159i q^{7} +(-1.89792 + 2.09712i) q^{8} -1.76755 q^{9} +(-2.89237 - 1.27835i) q^{10} +4.83473 q^{11} +(1.88493 - 1.17340i) q^{12} -5.46176i q^{13} +(1.67963 + 5.87632i) q^{14} +(1.90730 + 1.58886i) q^{15} +(1.76565 - 3.58922i) q^{16} +1.74384 q^{17} +(2.40344 - 0.686973i) q^{18} -1.12597 q^{19} +(4.42977 + 0.614106i) q^{20} -4.79766i q^{21} +(-6.57406 + 1.87906i) q^{22} +(-4.61714 - 1.29694i) q^{23} +(-2.10699 + 2.32813i) q^{24} +(0.903337 + 4.91772i) q^{25} +(2.12276 + 7.42668i) q^{26} -5.29274 q^{27} +(-4.56777 - 7.33758i) q^{28} -2.64398 q^{29} +(-3.21099 - 1.41918i) q^{30} +3.01187i q^{31} +(-1.00587 + 5.56671i) q^{32} +5.36732 q^{33} +(-2.37120 + 0.677760i) q^{34} +(6.18506 - 7.42468i) q^{35} +(-3.00110 + 1.86824i) q^{36} +9.91265 q^{37} +(1.53105 - 0.437620i) q^{38} -6.06342i q^{39} +(-6.26210 + 0.886636i) q^{40} +10.3038 q^{41} +(1.86465 + 6.52365i) q^{42} +5.51134i q^{43} +(8.20883 - 5.11014i) q^{44} +(-3.03672 - 2.52971i) q^{45} +(6.78226 - 0.0309634i) q^{46} +0.335447 q^{47} +(1.96015 - 3.98460i) q^{48} -11.6762 q^{49} +(-3.13964 - 6.33582i) q^{50} +1.93594 q^{51} +(-5.77289 - 9.27346i) q^{52} +0.212290 q^{53} +(7.19684 - 2.05707i) q^{54} +(8.30627 + 6.91946i) q^{55} +(9.06289 + 8.20203i) q^{56} -1.25001 q^{57} +(3.59518 - 1.02761i) q^{58} -3.23125i q^{59} +(4.91775 + 0.681755i) q^{60} -2.94732i q^{61} +(-1.17059 - 4.09541i) q^{62} +7.63861i q^{63} +(-0.795805 - 7.96032i) q^{64} +(7.81687 - 9.38353i) q^{65} +(-7.29826 + 2.08606i) q^{66} +4.96759i q^{67} +(2.96085 - 1.84318i) q^{68} +(-5.12576 - 1.43981i) q^{69} +(-5.52452 + 12.4996i) q^{70} +12.4759i q^{71} +(3.35466 - 3.70675i) q^{72} +9.16159i q^{73} +(-13.4788 + 3.85264i) q^{74} +(1.00285 + 5.45945i) q^{75} +(-1.91178 + 1.19012i) q^{76} -20.8937i q^{77} +(2.35661 + 8.24480i) q^{78} +7.65531 q^{79} +(8.17034 - 3.63943i) q^{80} -0.573142 q^{81} +(-14.0106 + 4.00465i) q^{82} -7.95681i q^{83} +(-5.07096 - 8.14588i) q^{84} +(2.99599 + 2.49578i) q^{85} +(-2.14203 - 7.49409i) q^{86} -2.93524 q^{87} +(-9.17592 + 10.1390i) q^{88} +3.81527i q^{89} +(5.11240 + 2.25955i) q^{90} -23.6035 q^{91} +(-9.21020 + 2.67809i) q^{92} +3.34365i q^{93} +(-0.456127 + 0.130375i) q^{94} +(-1.93447 - 1.61149i) q^{95} +(-1.11668 + 6.17993i) q^{96} -14.6914 q^{97} +(15.8768 - 4.53804i) q^{98} -8.54560 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 8 q^{4} - 8 q^{6} + 16 q^{9} - 8 q^{16} - 100 q^{24} - 24 q^{25} - 24 q^{26} - 16 q^{29} + 104 q^{41} - 8 q^{46} + 32 q^{49} - 32 q^{50} + 52 q^{54} - 92 q^{64} + 32 q^{69} - 44 q^{70} + 24 q^{81} + 56 q^{85} + 28 q^{94} + 88 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(277\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35976 + 0.388659i −0.961495 + 0.274823i
\(3\) 1.11016 0.640951 0.320475 0.947257i \(-0.396157\pi\)
0.320475 + 0.947257i \(0.396157\pi\)
\(4\) 1.69789 1.05697i 0.848944 0.528483i
\(5\) 1.71804 + 1.43120i 0.768332 + 0.640052i
\(6\) −1.50955 + 0.431474i −0.616271 + 0.176148i
\(7\) 4.32159i 1.63341i −0.577057 0.816704i \(-0.695799\pi\)
0.577057 0.816704i \(-0.304201\pi\)
\(8\) −1.89792 + 2.09712i −0.671016 + 0.741443i
\(9\) −1.76755 −0.589182
\(10\) −2.89237 1.27835i −0.914648 0.404251i
\(11\) 4.83473 1.45773 0.728863 0.684660i \(-0.240049\pi\)
0.728863 + 0.684660i \(0.240049\pi\)
\(12\) 1.88493 1.17340i 0.544131 0.338731i
\(13\) 5.46176i 1.51482i −0.652940 0.757410i \(-0.726465\pi\)
0.652940 0.757410i \(-0.273535\pi\)
\(14\) 1.67963 + 5.87632i 0.448899 + 1.57051i
\(15\) 1.90730 + 1.58886i 0.492463 + 0.410242i
\(16\) 1.76565 3.58922i 0.441412 0.897304i
\(17\) 1.74384 0.422943 0.211472 0.977384i \(-0.432174\pi\)
0.211472 + 0.977384i \(0.432174\pi\)
\(18\) 2.40344 0.686973i 0.566495 0.161921i
\(19\) −1.12597 −0.258316 −0.129158 0.991624i \(-0.541227\pi\)
−0.129158 + 0.991624i \(0.541227\pi\)
\(20\) 4.42977 + 0.614106i 0.990527 + 0.137318i
\(21\) 4.79766i 1.04693i
\(22\) −6.57406 + 1.87906i −1.40160 + 0.400617i
\(23\) −4.61714 1.29694i −0.962739 0.270431i
\(24\) −2.10699 + 2.32813i −0.430088 + 0.475229i
\(25\) 0.903337 + 4.91772i 0.180667 + 0.983544i
\(26\) 2.12276 + 7.42668i 0.416308 + 1.45649i
\(27\) −5.29274 −1.01859
\(28\) −4.56777 7.33758i −0.863228 1.38667i
\(29\) −2.64398 −0.490975 −0.245488 0.969400i \(-0.578948\pi\)
−0.245488 + 0.969400i \(0.578948\pi\)
\(30\) −3.21099 1.41918i −0.586244 0.259105i
\(31\) 3.01187i 0.540947i 0.962727 + 0.270474i \(0.0871803\pi\)
−0.962727 + 0.270474i \(0.912820\pi\)
\(32\) −1.00587 + 5.56671i −0.177815 + 0.984064i
\(33\) 5.36732 0.934330
\(34\) −2.37120 + 0.677760i −0.406658 + 0.116235i
\(35\) 6.18506 7.42468i 1.04547 1.25500i
\(36\) −3.00110 + 1.86824i −0.500183 + 0.311373i
\(37\) 9.91265 1.62963 0.814815 0.579721i \(-0.196838\pi\)
0.814815 + 0.579721i \(0.196838\pi\)
\(38\) 1.53105 0.437620i 0.248370 0.0709914i
\(39\) 6.06342i 0.970925i
\(40\) −6.26210 + 0.886636i −0.990125 + 0.140189i
\(41\) 10.3038 1.60918 0.804588 0.593834i \(-0.202386\pi\)
0.804588 + 0.593834i \(0.202386\pi\)
\(42\) 1.86465 + 6.52365i 0.287722 + 1.00662i
\(43\) 5.51134i 0.840471i 0.907415 + 0.420236i \(0.138053\pi\)
−0.907415 + 0.420236i \(0.861947\pi\)
\(44\) 8.20883 5.11014i 1.23753 0.770383i
\(45\) −3.03672 2.52971i −0.452687 0.377107i
\(46\) 6.78226 0.0309634i 0.999990 0.00456531i
\(47\) 0.335447 0.0489300 0.0244650 0.999701i \(-0.492212\pi\)
0.0244650 + 0.999701i \(0.492212\pi\)
\(48\) 1.96015 3.98460i 0.282923 0.575128i
\(49\) −11.6762 −1.66802
\(50\) −3.13964 6.33582i −0.444012 0.896021i
\(51\) 1.93594 0.271086
\(52\) −5.77289 9.27346i −0.800556 1.28600i
\(53\) 0.212290 0.0291602 0.0145801 0.999894i \(-0.495359\pi\)
0.0145801 + 0.999894i \(0.495359\pi\)
\(54\) 7.19684 2.05707i 0.979367 0.279932i
\(55\) 8.30627 + 6.91946i 1.12002 + 0.933020i
\(56\) 9.06289 + 8.20203i 1.21108 + 1.09604i
\(57\) −1.25001 −0.165568
\(58\) 3.59518 1.02761i 0.472070 0.134931i
\(59\) 3.23125i 0.420673i −0.977629 0.210337i \(-0.932544\pi\)
0.977629 0.210337i \(-0.0674560\pi\)
\(60\) 4.91775 + 0.681755i 0.634879 + 0.0880142i
\(61\) 2.94732i 0.377366i −0.982038 0.188683i \(-0.939578\pi\)
0.982038 0.188683i \(-0.0604218\pi\)
\(62\) −1.17059 4.09541i −0.148665 0.520118i
\(63\) 7.63861i 0.962375i
\(64\) −0.795805 7.96032i −0.0994756 0.995040i
\(65\) 7.81687 9.38353i 0.969563 1.16388i
\(66\) −7.29826 + 2.08606i −0.898353 + 0.256776i
\(67\) 4.96759i 0.606888i 0.952849 + 0.303444i \(0.0981366\pi\)
−0.952849 + 0.303444i \(0.901863\pi\)
\(68\) 2.96085 1.84318i 0.359055 0.223518i
\(69\) −5.12576 1.43981i −0.617069 0.173333i
\(70\) −5.52452 + 12.4996i −0.660306 + 1.49399i
\(71\) 12.4759i 1.48062i 0.672268 + 0.740308i \(0.265320\pi\)
−0.672268 + 0.740308i \(0.734680\pi\)
\(72\) 3.35466 3.70675i 0.395350 0.436845i
\(73\) 9.16159i 1.07228i 0.844128 + 0.536142i \(0.180119\pi\)
−0.844128 + 0.536142i \(0.819881\pi\)
\(74\) −13.4788 + 3.85264i −1.56688 + 0.447861i
\(75\) 1.00285 + 5.45945i 0.115799 + 0.630403i
\(76\) −1.91178 + 1.19012i −0.219296 + 0.136516i
\(77\) 20.8937i 2.38106i
\(78\) 2.35661 + 8.24480i 0.266833 + 0.933539i
\(79\) 7.65531 0.861289 0.430645 0.902522i \(-0.358286\pi\)
0.430645 + 0.902522i \(0.358286\pi\)
\(80\) 8.17034 3.63943i 0.913472 0.406901i
\(81\) −0.573142 −0.0636824
\(82\) −14.0106 + 4.00465i −1.54721 + 0.442239i
\(83\) 7.95681i 0.873374i −0.899614 0.436687i \(-0.856152\pi\)
0.899614 0.436687i \(-0.143848\pi\)
\(84\) −5.07096 8.14588i −0.553287 0.888789i
\(85\) 2.99599 + 2.49578i 0.324961 + 0.270706i
\(86\) −2.14203 7.49409i −0.230981 0.808109i
\(87\) −2.93524 −0.314691
\(88\) −9.17592 + 10.1390i −0.978157 + 1.08082i
\(89\) 3.81527i 0.404418i 0.979342 + 0.202209i \(0.0648121\pi\)
−0.979342 + 0.202209i \(0.935188\pi\)
\(90\) 5.11240 + 2.25955i 0.538894 + 0.238177i
\(91\) −23.6035 −2.47432
\(92\) −9.21020 + 2.67809i −0.960230 + 0.279210i
\(93\) 3.34365i 0.346720i
\(94\) −0.456127 + 0.130375i −0.0470459 + 0.0134471i
\(95\) −1.93447 1.61149i −0.198473 0.165336i
\(96\) −1.11668 + 6.17993i −0.113971 + 0.630737i
\(97\) −14.6914 −1.49168 −0.745841 0.666124i \(-0.767952\pi\)
−0.745841 + 0.666124i \(0.767952\pi\)
\(98\) 15.8768 4.53804i 1.60379 0.458412i
\(99\) −8.54560 −0.858866
\(100\) 6.73163 + 7.39494i 0.673163 + 0.739494i
\(101\) −7.96306 −0.792354 −0.396177 0.918174i \(-0.629663\pi\)
−0.396177 + 0.918174i \(0.629663\pi\)
\(102\) −2.63241 + 0.752421i −0.260648 + 0.0745008i
\(103\) 6.72204i 0.662342i 0.943571 + 0.331171i \(0.107444\pi\)
−0.943571 + 0.331171i \(0.892556\pi\)
\(104\) 11.4540 + 10.3660i 1.12315 + 1.01647i
\(105\) 6.86640 8.24257i 0.670092 0.804393i
\(106\) −0.288663 + 0.0825083i −0.0280374 + 0.00801391i
\(107\) 15.6616i 1.51406i 0.653380 + 0.757030i \(0.273350\pi\)
−0.653380 + 0.757030i \(0.726650\pi\)
\(108\) −8.98647 + 5.59424i −0.864724 + 0.538306i
\(109\) 12.9565i 1.24101i −0.784202 0.620505i \(-0.786928\pi\)
0.784202 0.620505i \(-0.213072\pi\)
\(110\) −13.9838 6.18049i −1.33331 0.589287i
\(111\) 11.0046 1.04451
\(112\) −15.5111 7.63041i −1.46566 0.721006i
\(113\) −2.68622 −0.252698 −0.126349 0.991986i \(-0.540326\pi\)
−0.126349 + 0.991986i \(0.540326\pi\)
\(114\) 1.69971 0.485828i 0.159193 0.0455020i
\(115\) −6.07625 8.83624i −0.566613 0.823984i
\(116\) −4.48918 + 2.79460i −0.416810 + 0.259472i
\(117\) 9.65391i 0.892505i
\(118\) 1.25586 + 4.39373i 0.115611 + 0.404475i
\(119\) 7.53617i 0.690839i
\(120\) −6.95193 + 0.984307i −0.634621 + 0.0898545i
\(121\) 12.3746 1.12496
\(122\) 1.14550 + 4.00764i 0.103709 + 0.362835i
\(123\) 11.4388 1.03140
\(124\) 3.18344 + 5.11381i 0.285881 + 0.459234i
\(125\) −5.48627 + 9.74171i −0.490707 + 0.871325i
\(126\) −2.96882 10.3867i −0.264483 0.925318i
\(127\) −7.79228 −0.691453 −0.345727 0.938335i \(-0.612368\pi\)
−0.345727 + 0.938335i \(0.612368\pi\)
\(128\) 4.17595 + 10.5148i 0.369106 + 0.929387i
\(129\) 6.11846i 0.538701i
\(130\) −6.98206 + 15.7974i −0.612367 + 1.38553i
\(131\) 9.42434i 0.823408i −0.911318 0.411704i \(-0.864934\pi\)
0.911318 0.411704i \(-0.135066\pi\)
\(132\) 9.11311 5.67307i 0.793194 0.493777i
\(133\) 4.86600i 0.421936i
\(134\) −1.93070 6.75473i −0.166787 0.583520i
\(135\) −9.09314 7.57496i −0.782613 0.651949i
\(136\) −3.30967 + 3.65704i −0.283802 + 0.313588i
\(137\) −15.4923 −1.32359 −0.661797 0.749683i \(-0.730206\pi\)
−0.661797 + 0.749683i \(0.730206\pi\)
\(138\) 7.52939 0.0343744i 0.640944 0.00292614i
\(139\) 4.69573i 0.398287i 0.979970 + 0.199143i \(0.0638159\pi\)
−0.979970 + 0.199143i \(0.936184\pi\)
\(140\) 2.65391 19.1437i 0.224297 1.61793i
\(141\) 0.372400 0.0313617
\(142\) −4.84887 16.9642i −0.406908 1.42360i
\(143\) 26.4061i 2.20819i
\(144\) −3.12087 + 6.34411i −0.260072 + 0.528676i
\(145\) −4.54247 3.78406i −0.377232 0.314249i
\(146\) −3.56074 12.4576i −0.294689 1.03099i
\(147\) −12.9624 −1.06912
\(148\) 16.8306 10.4773i 1.38346 0.861231i
\(149\) 16.1954i 1.32678i 0.748275 + 0.663388i \(0.230882\pi\)
−0.748275 + 0.663388i \(0.769118\pi\)
\(150\) −3.48550 7.03378i −0.284590 0.574305i
\(151\) 9.24464i 0.752318i −0.926555 0.376159i \(-0.877245\pi\)
0.926555 0.376159i \(-0.122755\pi\)
\(152\) 2.13701 2.36130i 0.173334 0.191527i
\(153\) −3.08232 −0.249191
\(154\) 8.12053 + 28.4104i 0.654371 + 2.28938i
\(155\) −4.31058 + 5.17451i −0.346234 + 0.415627i
\(156\) −6.40883 10.2950i −0.513117 0.824261i
\(157\) −0.749867 −0.0598459 −0.0299229 0.999552i \(-0.509526\pi\)
−0.0299229 + 0.999552i \(0.509526\pi\)
\(158\) −10.4094 + 2.97530i −0.828125 + 0.236702i
\(159\) 0.235675 0.0186903
\(160\) −9.69520 + 8.12423i −0.766473 + 0.642277i
\(161\) −5.60485 + 19.9534i −0.441724 + 1.57255i
\(162\) 0.779335 0.222757i 0.0612303 0.0175014i
\(163\) −7.11782 −0.557510 −0.278755 0.960362i \(-0.589922\pi\)
−0.278755 + 0.960362i \(0.589922\pi\)
\(164\) 17.4946 10.8907i 1.36610 0.850421i
\(165\) 9.22128 + 7.68170i 0.717876 + 0.598020i
\(166\) 3.09249 + 10.8193i 0.240024 + 0.839744i
\(167\) −0.363102 −0.0280977 −0.0140488 0.999901i \(-0.504472\pi\)
−0.0140488 + 0.999901i \(0.504472\pi\)
\(168\) 10.0612 + 9.10556i 0.776242 + 0.702509i
\(169\) −16.8308 −1.29468
\(170\) −5.04383 2.22924i −0.386844 0.170975i
\(171\) 1.99021 0.152195
\(172\) 5.82529 + 9.35764i 0.444174 + 0.713513i
\(173\) 3.52247i 0.267808i 0.990994 + 0.133904i \(0.0427514\pi\)
−0.990994 + 0.133904i \(0.957249\pi\)
\(174\) 3.99122 1.14081i 0.302574 0.0864844i
\(175\) 21.2524 3.90385i 1.60653 0.295104i
\(176\) 8.53643 17.3529i 0.643458 1.30802i
\(177\) 3.58721i 0.269631i
\(178\) −1.48284 5.18785i −0.111144 0.388846i
\(179\) 21.0643i 1.57442i 0.616687 + 0.787209i \(0.288474\pi\)
−0.616687 + 0.787209i \(0.711526\pi\)
\(180\) −7.82983 1.08546i −0.583601 0.0809054i
\(181\) 18.9992i 1.41220i −0.708114 0.706098i \(-0.750454\pi\)
0.708114 0.706098i \(-0.249546\pi\)
\(182\) 32.0951 9.17371i 2.37904 0.680001i
\(183\) 3.27199i 0.241873i
\(184\) 11.4828 7.22119i 0.846523 0.532353i
\(185\) 17.0304 + 14.1870i 1.25210 + 1.04305i
\(186\) −1.29954 4.54656i −0.0952869 0.333370i
\(187\) 8.43099 0.616535
\(188\) 0.569552 0.354556i 0.0415388 0.0258586i
\(189\) 22.8730i 1.66377i
\(190\) 3.25674 + 1.43939i 0.236268 + 0.104425i
\(191\) 19.7883 1.43183 0.715916 0.698187i \(-0.246009\pi\)
0.715916 + 0.698187i \(0.246009\pi\)
\(192\) −0.883470 8.83722i −0.0637590 0.637772i
\(193\) 17.5501i 1.26328i −0.775261 0.631641i \(-0.782382\pi\)
0.775261 0.631641i \(-0.217618\pi\)
\(194\) 19.9767 5.70993i 1.43424 0.409949i
\(195\) 8.67797 10.4172i 0.621442 0.745992i
\(196\) −19.8248 + 12.3413i −1.41606 + 0.881521i
\(197\) 13.3811i 0.953362i 0.879076 + 0.476681i \(0.158160\pi\)
−0.879076 + 0.476681i \(0.841840\pi\)
\(198\) 11.6200 3.32133i 0.825795 0.236036i
\(199\) −5.85698 −0.415190 −0.207595 0.978215i \(-0.566564\pi\)
−0.207595 + 0.978215i \(0.566564\pi\)
\(200\) −12.0275 7.43903i −0.850473 0.526019i
\(201\) 5.51482i 0.388986i
\(202\) 10.8278 3.09492i 0.761845 0.217758i
\(203\) 11.4262i 0.801963i
\(204\) 3.28701 2.04622i 0.230137 0.143264i
\(205\) 17.7023 + 14.7467i 1.23638 + 1.02996i
\(206\) −2.61258 9.14035i −0.182027 0.636838i
\(207\) 8.16100 + 2.29240i 0.567229 + 0.159333i
\(208\) −19.6034 9.64355i −1.35925 0.668660i
\(209\) −5.44378 −0.376554
\(210\) −6.13310 + 13.8766i −0.423224 + 0.957576i
\(211\) 17.0002i 1.17034i 0.810910 + 0.585171i \(0.198973\pi\)
−0.810910 + 0.585171i \(0.801027\pi\)
\(212\) 0.360444 0.224383i 0.0247554 0.0154107i
\(213\) 13.8502i 0.949002i
\(214\) −6.08701 21.2959i −0.416099 1.45576i
\(215\) −7.88782 + 9.46871i −0.537945 + 0.645761i
\(216\) 10.0452 11.0995i 0.683488 0.755225i
\(217\) 13.0161 0.883587
\(218\) 5.03567 + 17.6178i 0.341059 + 1.19322i
\(219\) 10.1708i 0.687281i
\(220\) 21.4167 + 2.96903i 1.44392 + 0.200172i
\(221\) 9.52444i 0.640683i
\(222\) −14.9636 + 4.27705i −1.00429 + 0.287057i
\(223\) −4.32099 −0.289355 −0.144677 0.989479i \(-0.546214\pi\)
−0.144677 + 0.989479i \(0.546214\pi\)
\(224\) 24.0570 + 4.34698i 1.60738 + 0.290445i
\(225\) −1.59669 8.69230i −0.106446 0.579487i
\(226\) 3.65261 1.04402i 0.242968 0.0694474i
\(227\) 2.12234i 0.140865i −0.997517 0.0704323i \(-0.977562\pi\)
0.997517 0.0704323i \(-0.0224379\pi\)
\(228\) −2.12238 + 1.32122i −0.140558 + 0.0874998i
\(229\) 4.12377i 0.272507i −0.990674 0.136253i \(-0.956494\pi\)
0.990674 0.136253i \(-0.0435061\pi\)
\(230\) 11.6965 + 9.65357i 0.771246 + 0.636537i
\(231\) 23.1954i 1.52614i
\(232\) 5.01806 5.54474i 0.329452 0.364030i
\(233\) 11.9095i 0.780216i −0.920769 0.390108i \(-0.872438\pi\)
0.920769 0.390108i \(-0.127562\pi\)
\(234\) −3.75208 13.1270i −0.245281 0.858138i
\(235\) 0.576312 + 0.480092i 0.0375945 + 0.0313177i
\(236\) −3.41532 5.48631i −0.222319 0.357128i
\(237\) 8.49861 0.552044
\(238\) 2.92900 + 10.2474i 0.189859 + 0.664238i
\(239\) 14.6042i 0.944667i −0.881420 0.472334i \(-0.843412\pi\)
0.881420 0.472334i \(-0.156588\pi\)
\(240\) 9.07038 4.04035i 0.585491 0.260803i
\(241\) 14.1752i 0.913104i 0.889697 + 0.456552i \(0.150916\pi\)
−0.889697 + 0.456552i \(0.849084\pi\)
\(242\) −16.8265 + 4.80950i −1.08165 + 0.309166i
\(243\) 15.2419 0.977770
\(244\) −3.11521 5.00422i −0.199431 0.320362i
\(245\) −20.0601 16.7109i −1.28159 1.06762i
\(246\) −15.5540 + 4.44580i −0.991688 + 0.283454i
\(247\) 6.14980i 0.391303i
\(248\) −6.31624 5.71628i −0.401081 0.362984i
\(249\) 8.83333i 0.559790i
\(250\) 3.67380 15.3787i 0.232351 0.972632i
\(251\) −7.03203 −0.443858 −0.221929 0.975063i \(-0.571235\pi\)
−0.221929 + 0.975063i \(0.571235\pi\)
\(252\) 8.07375 + 12.9695i 0.508598 + 0.817002i
\(253\) −22.3226 6.27036i −1.40341 0.394214i
\(254\) 10.5956 3.02854i 0.664829 0.190028i
\(255\) 3.32603 + 2.77072i 0.208284 + 0.173509i
\(256\) −9.76497 12.6746i −0.610311 0.792162i
\(257\) 2.46512i 0.153770i −0.997040 0.0768849i \(-0.975503\pi\)
0.997040 0.0768849i \(-0.0244974\pi\)
\(258\) −2.37800 8.31963i −0.148048 0.517958i
\(259\) 42.8384i 2.66185i
\(260\) 3.35410 24.1944i 0.208012 1.50047i
\(261\) 4.67336 0.289274
\(262\) 3.66285 + 12.8148i 0.226292 + 0.791702i
\(263\) 9.50506i 0.586107i −0.956096 0.293054i \(-0.905329\pi\)
0.956096 0.293054i \(-0.0946715\pi\)
\(264\) −10.1867 + 11.2559i −0.626950 + 0.692753i
\(265\) 0.364722 + 0.303829i 0.0224047 + 0.0186640i
\(266\) −1.89122 6.61659i −0.115958 0.405689i
\(267\) 4.23556i 0.259212i
\(268\) 5.25058 + 8.43442i 0.320730 + 0.515214i
\(269\) 3.29016 0.200605 0.100302 0.994957i \(-0.468019\pi\)
0.100302 + 0.994957i \(0.468019\pi\)
\(270\) 15.3086 + 6.76599i 0.931649 + 0.411765i
\(271\) 6.89939i 0.419108i 0.977797 + 0.209554i \(0.0672012\pi\)
−0.977797 + 0.209554i \(0.932799\pi\)
\(272\) 3.07901 6.25902i 0.186692 0.379509i
\(273\) −26.2036 −1.58592
\(274\) 21.0657 6.02121i 1.27263 0.363754i
\(275\) 4.36739 + 23.7758i 0.263363 + 1.43374i
\(276\) −10.2248 + 2.97311i −0.615460 + 0.178960i
\(277\) 16.1068i 0.967766i −0.875133 0.483883i \(-0.839226\pi\)
0.875133 0.483883i \(-0.160774\pi\)
\(278\) −1.82504 6.38506i −0.109458 0.382950i
\(279\) 5.32361i 0.318716i
\(280\) 3.83168 + 27.0622i 0.228986 + 1.61728i
\(281\) 6.79153i 0.405149i 0.979267 + 0.202574i \(0.0649308\pi\)
−0.979267 + 0.202574i \(0.935069\pi\)
\(282\) −0.506374 + 0.144737i −0.0301541 + 0.00861893i
\(283\) 7.20688i 0.428404i 0.976789 + 0.214202i \(0.0687151\pi\)
−0.976789 + 0.214202i \(0.931285\pi\)
\(284\) 13.1866 + 21.1827i 0.782480 + 1.25696i
\(285\) −2.14757 1.78901i −0.127211 0.105972i
\(286\) 10.2630 + 35.9060i 0.606863 + 2.12316i
\(287\) 44.5286i 2.62844i
\(288\) 1.77793 9.83941i 0.104765 0.579793i
\(289\) −13.9590 −0.821119
\(290\) 7.64738 + 3.37994i 0.449069 + 0.198477i
\(291\) −16.3097 −0.956094
\(292\) 9.68349 + 15.5554i 0.566683 + 0.910309i
\(293\) 25.1995 1.47217 0.736085 0.676889i \(-0.236672\pi\)
0.736085 + 0.676889i \(0.236672\pi\)
\(294\) 17.6257 5.03795i 1.02795 0.293819i
\(295\) 4.62457 5.55143i 0.269253 0.323217i
\(296\) −18.8134 + 20.7880i −1.09351 + 1.20828i
\(297\) −25.5889 −1.48482
\(298\) −6.29448 22.0218i −0.364629 1.27569i
\(299\) −7.08359 + 25.2177i −0.409654 + 1.45838i
\(300\) 7.47318 + 8.20957i 0.431464 + 0.473980i
\(301\) 23.8178 1.37283
\(302\) 3.59301 + 12.5705i 0.206755 + 0.723350i
\(303\) −8.84027 −0.507860
\(304\) −1.98807 + 4.04137i −0.114024 + 0.231788i
\(305\) 4.21820 5.06362i 0.241534 0.289942i
\(306\) 4.19121 1.19797i 0.239596 0.0684835i
\(307\) −9.88934 −0.564414 −0.282207 0.959354i \(-0.591067\pi\)
−0.282207 + 0.959354i \(0.591067\pi\)
\(308\) −22.0839 35.4752i −1.25835 2.02139i
\(309\) 7.46253i 0.424529i
\(310\) 3.85023 8.71144i 0.218678 0.494776i
\(311\) 26.2970i 1.49117i −0.666413 0.745583i \(-0.732171\pi\)
0.666413 0.745583i \(-0.267829\pi\)
\(312\) 12.7157 + 11.5079i 0.719886 + 0.651506i
\(313\) 29.2911 1.65563 0.827815 0.561001i \(-0.189584\pi\)
0.827815 + 0.561001i \(0.189584\pi\)
\(314\) 1.01964 0.291443i 0.0575415 0.0164471i
\(315\) −10.9324 + 13.1235i −0.615970 + 0.739423i
\(316\) 12.9979 8.09139i 0.731186 0.455176i
\(317\) 20.8716i 1.17227i 0.810215 + 0.586133i \(0.199350\pi\)
−0.810215 + 0.586133i \(0.800650\pi\)
\(318\) −0.320462 + 0.0915973i −0.0179706 + 0.00513652i
\(319\) −12.7829 −0.715707
\(320\) 10.0256 14.8151i 0.560447 0.828190i
\(321\) 17.3868i 0.970438i
\(322\) −0.133811 29.3102i −0.00745701 1.63339i
\(323\) −1.96352 −0.109253
\(324\) −0.973131 + 0.605791i −0.0540628 + 0.0336551i
\(325\) 26.8594 4.93381i 1.48989 0.273679i
\(326\) 9.67852 2.76640i 0.536043 0.153217i
\(327\) 14.3838i 0.795427i
\(328\) −19.5557 + 21.6082i −1.07978 + 1.19311i
\(329\) 1.44967i 0.0799226i
\(330\) −15.5243 6.86133i −0.854583 0.377704i
\(331\) 6.78902i 0.373158i 0.982440 + 0.186579i \(0.0597401\pi\)
−0.982440 + 0.186579i \(0.940260\pi\)
\(332\) −8.41007 13.5098i −0.461563 0.741445i
\(333\) −17.5211 −0.960149
\(334\) 0.493731 0.141123i 0.0270158 0.00772190i
\(335\) −7.10962 + 8.53454i −0.388440 + 0.466292i
\(336\) −17.2198 8.47097i −0.939419 0.462129i
\(337\) 11.8440 0.645183 0.322592 0.946538i \(-0.395446\pi\)
0.322592 + 0.946538i \(0.395446\pi\)
\(338\) 22.8859 6.54145i 1.24483 0.355808i
\(339\) −2.98213 −0.161967
\(340\) 7.72481 + 1.07090i 0.418937 + 0.0580778i
\(341\) 14.5616i 0.788552i
\(342\) −2.70621 + 0.773514i −0.146335 + 0.0418268i
\(343\) 20.2084i 1.09115i
\(344\) −11.5579 10.4601i −0.623162 0.563969i
\(345\) −6.74561 9.80964i −0.363171 0.528133i
\(346\) −1.36904 4.78971i −0.0736000 0.257496i
\(347\) −11.9606 −0.642077 −0.321039 0.947066i \(-0.604032\pi\)
−0.321039 + 0.947066i \(0.604032\pi\)
\(348\) −4.98371 + 3.10245i −0.267155 + 0.166309i
\(349\) −17.4732 −0.935318 −0.467659 0.883909i \(-0.654903\pi\)
−0.467659 + 0.883909i \(0.654903\pi\)
\(350\) −27.3808 + 13.5682i −1.46357 + 0.725252i
\(351\) 28.9077i 1.54298i
\(352\) −4.86313 + 26.9135i −0.259206 + 1.43449i
\(353\) 28.6864i 1.52682i 0.645912 + 0.763412i \(0.276477\pi\)
−0.645912 + 0.763412i \(0.723523\pi\)
\(354\) 1.39420 + 4.87774i 0.0741009 + 0.259249i
\(355\) −17.8555 + 21.4341i −0.947671 + 1.13760i
\(356\) 4.03261 + 6.47791i 0.213728 + 0.343329i
\(357\) 8.36635i 0.442794i
\(358\) −8.18682 28.6423i −0.432687 1.51379i
\(359\) 30.5812 1.61402 0.807008 0.590541i \(-0.201085\pi\)
0.807008 + 0.590541i \(0.201085\pi\)
\(360\) 11.0685 1.56717i 0.583364 0.0825971i
\(361\) −17.7322 −0.933273
\(362\) 7.38419 + 25.8343i 0.388105 + 1.35782i
\(363\) 13.7378 0.721046
\(364\) −40.0761 + 24.9481i −2.10056 + 1.30763i
\(365\) −13.1121 + 15.7400i −0.686317 + 0.823870i
\(366\) 1.27169 + 4.44912i 0.0664723 + 0.232559i
\(367\) 6.34724i 0.331323i 0.986183 + 0.165662i \(0.0529760\pi\)
−0.986183 + 0.165662i \(0.947024\pi\)
\(368\) −12.8072 + 14.2820i −0.667624 + 0.744499i
\(369\) −18.2124 −0.948097
\(370\) −28.6711 12.6719i −1.49054 0.658779i
\(371\) 0.917429i 0.0476305i
\(372\) 3.53412 + 5.67715i 0.183236 + 0.294346i
\(373\) 22.2449 1.15180 0.575899 0.817521i \(-0.304652\pi\)
0.575899 + 0.817521i \(0.304652\pi\)
\(374\) −11.4641 + 3.27678i −0.592795 + 0.169438i
\(375\) −6.09063 + 10.8148i −0.314519 + 0.558476i
\(376\) −0.636651 + 0.703472i −0.0328328 + 0.0362788i
\(377\) 14.4408i 0.743739i
\(378\) −8.88982 31.1018i −0.457243 1.59971i
\(379\) 12.5191 0.643062 0.321531 0.946899i \(-0.395803\pi\)
0.321531 + 0.946899i \(0.395803\pi\)
\(380\) −4.98781 0.691467i −0.255869 0.0354715i
\(381\) −8.65068 −0.443188
\(382\) −26.9073 + 7.69091i −1.37670 + 0.393501i
\(383\) 14.2978i 0.730583i −0.930893 0.365291i \(-0.880969\pi\)
0.930893 0.365291i \(-0.119031\pi\)
\(384\) 4.63597 + 11.6731i 0.236579 + 0.595692i
\(385\) 29.9031 35.8963i 1.52400 1.82944i
\(386\) 6.82099 + 23.8639i 0.347179 + 1.21464i
\(387\) 9.74154i 0.495191i
\(388\) −24.9443 + 15.5283i −1.26635 + 0.788328i
\(389\) 8.85964i 0.449201i 0.974451 + 0.224601i \(0.0721078\pi\)
−0.974451 + 0.224601i \(0.927892\pi\)
\(390\) −7.75120 + 17.5377i −0.392497 + 0.888055i
\(391\) −8.05155 2.26166i −0.407184 0.114377i
\(392\) 22.1604 24.4863i 1.11927 1.23674i
\(393\) 10.4625i 0.527764i
\(394\) −5.20068 18.1950i −0.262006 0.916652i
\(395\) 13.1521 + 10.9563i 0.661756 + 0.551270i
\(396\) −14.5095 + 9.03241i −0.729129 + 0.453896i
\(397\) 10.5297i 0.528472i −0.964458 0.264236i \(-0.914880\pi\)
0.964458 0.264236i \(-0.0851199\pi\)
\(398\) 7.96408 2.27637i 0.399203 0.114104i
\(399\) 5.40204i 0.270440i
\(400\) 19.2457 + 5.44069i 0.962287 + 0.272035i
\(401\) 33.5854i 1.67717i −0.544768 0.838587i \(-0.683382\pi\)
0.544768 0.838587i \(-0.316618\pi\)
\(402\) −2.14339 7.49883i −0.106902 0.374008i
\(403\) 16.4501 0.819437
\(404\) −13.5204 + 8.41668i −0.672665 + 0.418746i
\(405\) −0.984682 0.820280i −0.0489292 0.0407601i
\(406\) −4.44090 15.5369i −0.220398 0.771083i
\(407\) 47.9250 2.37555
\(408\) −3.67426 + 4.05990i −0.181903 + 0.200995i
\(409\) −27.7416 −1.37174 −0.685868 0.727726i \(-0.740577\pi\)
−0.685868 + 0.727726i \(0.740577\pi\)
\(410\) −29.8023 13.1718i −1.47183 0.650511i
\(411\) −17.1989 −0.848358
\(412\) 7.10496 + 11.4133i 0.350036 + 0.562291i
\(413\) −13.9642 −0.687131
\(414\) −11.9880 + 0.0547293i −0.589176 + 0.00268980i
\(415\) 11.3878 13.6701i 0.559004 0.671041i
\(416\) 30.4040 + 5.49384i 1.49068 + 0.269358i
\(417\) 5.21301i 0.255282i
\(418\) 7.40223 2.11577i 0.362055 0.103486i
\(419\) −0.289358 −0.0141361 −0.00706803 0.999975i \(-0.502250\pi\)
−0.00706803 + 0.999975i \(0.502250\pi\)
\(420\) 2.94627 21.2525i 0.143763 1.03702i
\(421\) 37.9107i 1.84765i −0.382809 0.923827i \(-0.625043\pi\)
0.382809 0.923827i \(-0.374957\pi\)
\(422\) −6.60728 23.1162i −0.321637 1.12528i
\(423\) −0.592918 −0.0288287
\(424\) −0.402908 + 0.445196i −0.0195670 + 0.0216206i
\(425\) 1.57528 + 8.57572i 0.0764121 + 0.415984i
\(426\) −5.38302 18.8330i −0.260808 0.912461i
\(427\) −12.7371 −0.616392
\(428\) 16.5537 + 26.5916i 0.800154 + 1.28535i
\(429\) 29.3150i 1.41534i
\(430\) 7.04544 15.9408i 0.339761 0.768735i
\(431\) −22.2740 −1.07290 −0.536450 0.843932i \(-0.680235\pi\)
−0.536450 + 0.843932i \(0.680235\pi\)
\(432\) −9.34511 + 18.9968i −0.449617 + 0.913983i
\(433\) 8.38264 0.402844 0.201422 0.979505i \(-0.435444\pi\)
0.201422 + 0.979505i \(0.435444\pi\)
\(434\) −17.6987 + 5.05881i −0.849565 + 0.242831i
\(435\) −5.04287 4.20091i −0.241787 0.201418i
\(436\) −13.6946 21.9987i −0.655853 1.05355i
\(437\) 5.19878 + 1.46032i 0.248691 + 0.0698567i
\(438\) −3.95299 13.8299i −0.188881 0.660817i
\(439\) 2.21723i 0.105822i −0.998599 0.0529112i \(-0.983150\pi\)
0.998599 0.0529112i \(-0.0168500\pi\)
\(440\) −30.2755 + 4.28664i −1.44333 + 0.204358i
\(441\) 20.6381 0.982768
\(442\) 3.70176 + 12.9509i 0.176075 + 0.616013i
\(443\) 11.6993 0.555852 0.277926 0.960603i \(-0.410353\pi\)
0.277926 + 0.960603i \(0.410353\pi\)
\(444\) 18.6846 11.6315i 0.886733 0.552007i
\(445\) −5.46042 + 6.55480i −0.258849 + 0.310727i
\(446\) 5.87550 1.67939i 0.278213 0.0795215i
\(447\) 17.9794i 0.850398i
\(448\) −34.4012 + 3.43914i −1.62531 + 0.162484i
\(449\) 31.2883 1.47658 0.738292 0.674481i \(-0.235633\pi\)
0.738292 + 0.674481i \(0.235633\pi\)
\(450\) 5.54945 + 11.1989i 0.261604 + 0.527919i
\(451\) 49.8158 2.34574
\(452\) −4.56090 + 2.83924i −0.214527 + 0.133547i
\(453\) 10.2630i 0.482199i
\(454\) 0.824866 + 2.88587i 0.0387129 + 0.135441i
\(455\) −40.5518 33.7813i −1.90110 1.58369i
\(456\) 2.37242 2.62142i 0.111099 0.122759i
\(457\) 26.9548 1.26089 0.630446 0.776233i \(-0.282872\pi\)
0.630446 + 0.776233i \(0.282872\pi\)
\(458\) 1.60274 + 5.60734i 0.0748912 + 0.262014i
\(459\) −9.22969 −0.430805
\(460\) −19.6564 8.58057i −0.916484 0.400071i
\(461\) −10.2640 −0.478043 −0.239022 0.971014i \(-0.576827\pi\)
−0.239022 + 0.971014i \(0.576827\pi\)
\(462\) 9.01509 + 31.5401i 0.419420 + 1.46738i
\(463\) −30.9103 −1.43653 −0.718263 0.695772i \(-0.755062\pi\)
−0.718263 + 0.695772i \(0.755062\pi\)
\(464\) −4.66834 + 9.48983i −0.216722 + 0.440554i
\(465\) −4.78543 + 5.74453i −0.221919 + 0.266396i
\(466\) 4.62873 + 16.1940i 0.214422 + 0.750174i
\(467\) 18.7363i 0.867013i 0.901150 + 0.433507i \(0.142724\pi\)
−0.901150 + 0.433507i \(0.857276\pi\)
\(468\) 10.2039 + 16.3913i 0.471673 + 0.757687i
\(469\) 21.4679 0.991296
\(470\) −0.970237 0.428820i −0.0447537 0.0197800i
\(471\) −0.832472 −0.0383583
\(472\) 6.77632 + 6.13266i 0.311905 + 0.282278i
\(473\) 26.6458i 1.22518i
\(474\) −11.5561 + 3.30306i −0.530787 + 0.151715i
\(475\) −1.01713 5.53723i −0.0466693 0.254065i
\(476\) −7.96547 12.7956i −0.365097 0.586484i
\(477\) −0.375232 −0.0171807
\(478\) 5.67606 + 19.8582i 0.259617 + 0.908293i
\(479\) 15.0861 0.689300 0.344650 0.938731i \(-0.387998\pi\)
0.344650 + 0.938731i \(0.387998\pi\)
\(480\) −10.7632 + 9.01919i −0.491271 + 0.411668i
\(481\) 54.1405i 2.46860i
\(482\) −5.50932 19.2748i −0.250943 0.877945i
\(483\) −6.22228 + 22.1514i −0.283124 + 1.00792i
\(484\) 21.0107 13.0795i 0.955031 0.594523i
\(485\) −25.2404 21.0263i −1.14611 0.954753i
\(486\) −20.7253 + 5.92391i −0.940121 + 0.268714i
\(487\) 37.0234 1.67769 0.838845 0.544370i \(-0.183231\pi\)
0.838845 + 0.544370i \(0.183231\pi\)
\(488\) 6.18088 + 5.59377i 0.279795 + 0.253218i
\(489\) −7.90191 −0.357337
\(490\) 33.7718 + 14.9262i 1.52565 + 0.674299i
\(491\) 2.39953i 0.108289i −0.998533 0.0541447i \(-0.982757\pi\)
0.998533 0.0541447i \(-0.0172432\pi\)
\(492\) 19.4218 12.0904i 0.875603 0.545078i
\(493\) −4.61068 −0.207655
\(494\) −2.39018 8.36225i −0.107539 0.376235i
\(495\) −14.6817 12.2305i −0.659894 0.549718i
\(496\) 10.8102 + 5.31790i 0.485394 + 0.238781i
\(497\) 53.9157 2.41845
\(498\) 3.43315 + 12.0112i 0.153843 + 0.538235i
\(499\) 16.5390i 0.740387i −0.928955 0.370193i \(-0.879291\pi\)
0.928955 0.370193i \(-0.120709\pi\)
\(500\) 0.981577 + 22.3391i 0.0438974 + 0.999036i
\(501\) −0.403101 −0.0180092
\(502\) 9.56186 2.73306i 0.426767 0.121983i
\(503\) 21.5112i 0.959137i 0.877504 + 0.479569i \(0.159207\pi\)
−0.877504 + 0.479569i \(0.840793\pi\)
\(504\) −16.0191 14.4975i −0.713546 0.645769i
\(505\) −13.6809 11.3967i −0.608791 0.507148i
\(506\) 32.7904 0.149700i 1.45771 0.00665497i
\(507\) −18.6849 −0.829826
\(508\) −13.2304 + 8.23617i −0.587005 + 0.365421i
\(509\) −19.5576 −0.866875 −0.433438 0.901184i \(-0.642700\pi\)
−0.433438 + 0.901184i \(0.642700\pi\)
\(510\) −5.59946 2.47482i −0.247948 0.109587i
\(511\) 39.5927 1.75148
\(512\) 18.2041 + 13.4391i 0.804515 + 0.593932i
\(513\) 5.95948 0.263118
\(514\) 0.958090 + 3.35196i 0.0422595 + 0.147849i
\(515\) −9.62058 + 11.5487i −0.423933 + 0.508899i
\(516\) 6.46700 + 10.3885i 0.284694 + 0.457327i
\(517\) 1.62180 0.0713265
\(518\) 16.6495 + 58.2499i 0.731539 + 2.55936i
\(519\) 3.91050i 0.171652i
\(520\) 4.84259 + 34.2021i 0.212362 + 1.49986i
\(521\) 40.5989i 1.77867i 0.457258 + 0.889334i \(0.348832\pi\)
−0.457258 + 0.889334i \(0.651168\pi\)
\(522\) −6.35464 + 1.81634i −0.278135 + 0.0794992i
\(523\) 32.4296i 1.41805i 0.705185 + 0.709024i \(0.250864\pi\)
−0.705185 + 0.709024i \(0.749136\pi\)
\(524\) −9.96120 16.0015i −0.435157 0.699027i
\(525\) 23.5935 4.33390i 1.02971 0.189147i
\(526\) 3.69423 + 12.9246i 0.161076 + 0.563539i
\(527\) 5.25221i 0.228790i
\(528\) 9.47680 19.2645i 0.412425 0.838379i
\(529\) 19.6359 + 11.9763i 0.853734 + 0.520709i
\(530\) −0.614020 0.271381i −0.0266713 0.0117880i
\(531\) 5.71139i 0.247853i
\(532\) 5.14319 + 8.26193i 0.222986 + 0.358200i
\(533\) 56.2766i 2.43761i
\(534\) −1.64619 5.75934i −0.0712376 0.249231i
\(535\) −22.4148 + 26.9072i −0.969077 + 1.16330i
\(536\) −10.4176 9.42809i −0.449973 0.407232i
\(537\) 23.3847i 1.00912i
\(538\) −4.47383 + 1.27875i −0.192880 + 0.0551309i
\(539\) −56.4510 −2.43152
\(540\) −23.4456 3.25030i −1.00894 0.139871i
\(541\) −16.1408 −0.693948 −0.346974 0.937875i \(-0.612791\pi\)
−0.346974 + 0.937875i \(0.612791\pi\)
\(542\) −2.68151 9.38151i −0.115181 0.402970i
\(543\) 21.0921i 0.905148i
\(544\) −1.75408 + 9.70745i −0.0752057 + 0.416203i
\(545\) 18.5434 22.2599i 0.794311 0.953508i
\(546\) 35.6306 10.1843i 1.52485 0.435847i
\(547\) 31.4175 1.34332 0.671658 0.740861i \(-0.265582\pi\)
0.671658 + 0.740861i \(0.265582\pi\)
\(548\) −26.3041 + 16.3748i −1.12366 + 0.699496i
\(549\) 5.20952i 0.222337i
\(550\) −15.1793 30.6320i −0.647247 1.30615i
\(551\) 2.97706 0.126827
\(552\) 12.7477 8.01667i 0.542579 0.341212i
\(553\) 33.0831i 1.40684i
\(554\) 6.26007 + 21.9014i 0.265965 + 0.930502i
\(555\) 18.9064 + 15.7498i 0.802532 + 0.668542i
\(556\) 4.96322 + 7.97282i 0.210488 + 0.338123i
\(557\) −34.8208 −1.47541 −0.737703 0.675125i \(-0.764090\pi\)
−0.737703 + 0.675125i \(0.764090\pi\)
\(558\) 2.06907 + 7.23883i 0.0875907 + 0.306444i
\(559\) 30.1016 1.27316
\(560\) −15.7281 35.3089i −0.664635 1.49207i
\(561\) 9.35975 0.395169
\(562\) −2.63959 9.23484i −0.111344 0.389548i
\(563\) 40.1892i 1.69377i −0.531773 0.846887i \(-0.678474\pi\)
0.531773 0.846887i \(-0.321526\pi\)
\(564\) 0.632293 0.393614i 0.0266243 0.0165741i
\(565\) −4.61503 3.84451i −0.194156 0.161740i
\(566\) −2.80102 9.79961i −0.117736 0.411908i
\(567\) 2.47689i 0.104019i
\(568\) −26.1634 23.6782i −1.09779 0.993517i
\(569\) 36.5494i 1.53223i −0.642703 0.766116i \(-0.722187\pi\)
0.642703 0.766116i \(-0.277813\pi\)
\(570\) 3.61550 + 1.59796i 0.151436 + 0.0669310i
\(571\) −13.2964 −0.556437 −0.278219 0.960518i \(-0.589744\pi\)
−0.278219 + 0.960518i \(0.589744\pi\)
\(572\) −27.9104 44.8346i −1.16699 1.87463i
\(573\) 21.9682 0.917734
\(574\) 17.3064 + 60.5482i 0.722357 + 2.52723i
\(575\) 2.20717 23.8774i 0.0920453 0.995755i
\(576\) 1.40662 + 14.0702i 0.0586093 + 0.586260i
\(577\) 18.2028i 0.757793i −0.925439 0.378897i \(-0.876304\pi\)
0.925439 0.378897i \(-0.123696\pi\)
\(578\) 18.9809 5.42530i 0.789501 0.225663i
\(579\) 19.4834i 0.809701i
\(580\) −11.7122 1.62368i −0.486324 0.0674198i
\(581\) −34.3861 −1.42658
\(582\) 22.1773 6.33893i 0.919280 0.262757i
\(583\) 1.02636 0.0425076
\(584\) −19.2129 17.3880i −0.795037 0.719519i
\(585\) −13.8167 + 16.5858i −0.571249 + 0.685740i
\(586\) −34.2652 + 9.79402i −1.41548 + 0.404587i
\(587\) −2.44585 −0.100951 −0.0504755 0.998725i \(-0.516074\pi\)
−0.0504755 + 0.998725i \(0.516074\pi\)
\(588\) −22.0087 + 13.7008i −0.907623 + 0.565011i
\(589\) 3.39128i 0.139735i
\(590\) −4.13068 + 9.34599i −0.170058 + 0.384768i
\(591\) 14.8551i 0.611058i
\(592\) 17.5023 35.5787i 0.719338 1.46227i
\(593\) 6.29249i 0.258401i 0.991618 + 0.129201i \(0.0412412\pi\)
−0.991618 + 0.129201i \(0.958759\pi\)
\(594\) 34.7948 9.94537i 1.42765 0.408064i
\(595\) 10.7858 12.9475i 0.442173 0.530794i
\(596\) 17.1179 + 27.4979i 0.701178 + 1.12636i
\(597\) −6.50218 −0.266116
\(598\) −0.169115 37.0431i −0.00691562 1.51480i
\(599\) 10.8781i 0.444466i 0.974994 + 0.222233i \(0.0713345\pi\)
−0.974994 + 0.222233i \(0.928665\pi\)
\(600\) −13.3524 8.25851i −0.545111 0.337152i
\(601\) 25.3031 1.03213 0.516067 0.856548i \(-0.327396\pi\)
0.516067 + 0.856548i \(0.327396\pi\)
\(602\) −32.3864 + 9.25699i −1.31997 + 0.377287i
\(603\) 8.78045i 0.357568i
\(604\) −9.77127 15.6964i −0.397587 0.638676i
\(605\) 21.2601 + 17.7105i 0.864345 + 0.720034i
\(606\) 12.0206 3.43585i 0.488305 0.139572i
\(607\) 32.1161 1.30355 0.651776 0.758411i \(-0.274024\pi\)
0.651776 + 0.758411i \(0.274024\pi\)
\(608\) 1.13259 6.26797i 0.0459325 0.254200i
\(609\) 12.6849i 0.514019i
\(610\) −3.76772 + 8.52474i −0.152550 + 0.345157i
\(611\) 1.83213i 0.0741201i
\(612\) −5.23343 + 3.25790i −0.211549 + 0.131693i
\(613\) 10.6896 0.431748 0.215874 0.976421i \(-0.430740\pi\)
0.215874 + 0.976421i \(0.430740\pi\)
\(614\) 13.4471 3.84358i 0.542681 0.155114i
\(615\) 19.6524 + 16.3712i 0.792459 + 0.660151i
\(616\) 43.8166 + 39.6546i 1.76542 + 1.59773i
\(617\) −21.7776 −0.876734 −0.438367 0.898796i \(-0.644443\pi\)
−0.438367 + 0.898796i \(0.644443\pi\)
\(618\) −2.90038 10.1472i −0.116670 0.408182i
\(619\) −22.0930 −0.887993 −0.443997 0.896029i \(-0.646440\pi\)
−0.443997 + 0.896029i \(0.646440\pi\)
\(620\) −1.84960 + 13.3419i −0.0742819 + 0.535823i
\(621\) 24.4373 + 6.86437i 0.980634 + 0.275458i
\(622\) 10.2206 + 35.7576i 0.409807 + 1.43375i
\(623\) 16.4881 0.660580
\(624\) −21.7630 10.7059i −0.871215 0.428578i
\(625\) −23.3680 + 8.88472i −0.934719 + 0.355389i
\(626\) −39.8288 + 11.3842i −1.59188 + 0.455006i
\(627\) −6.04346 −0.241353
\(628\) −1.27319 + 0.792583i −0.0508058 + 0.0316275i
\(629\) 17.2861 0.689241
\(630\) 9.76484 22.0937i 0.389041 0.880234i
\(631\) −21.0161 −0.836638 −0.418319 0.908300i \(-0.637381\pi\)
−0.418319 + 0.908300i \(0.637381\pi\)
\(632\) −14.5292 + 16.0541i −0.577939 + 0.638597i
\(633\) 18.8729i 0.750131i
\(634\) −8.11193 28.3803i −0.322166 1.12713i
\(635\) −13.3875 11.1523i −0.531265 0.442566i
\(636\) 0.400150 0.249101i 0.0158670 0.00987748i
\(637\) 63.7723i 2.52675i
\(638\) 17.3817 4.96820i 0.688148 0.196693i
\(639\) 22.0517i 0.872353i
\(640\) −7.87434 + 24.0415i −0.311260 + 0.950325i
\(641\) 18.6991i 0.738571i −0.929316 0.369286i \(-0.879602\pi\)
0.929316 0.369286i \(-0.120398\pi\)
\(642\) −6.75755 23.6419i −0.266699 0.933071i
\(643\) 30.5572i 1.20506i −0.798097 0.602529i \(-0.794160\pi\)
0.798097 0.602529i \(-0.205840\pi\)
\(644\) 11.5736 + 39.8027i 0.456064 + 1.56845i
\(645\) −8.75674 + 10.5118i −0.344796 + 0.413901i
\(646\) 2.66991 0.763140i 0.105046 0.0300253i
\(647\) −10.0344 −0.394493 −0.197247 0.980354i \(-0.563200\pi\)
−0.197247 + 0.980354i \(0.563200\pi\)
\(648\) 1.08778 1.20195i 0.0427319 0.0472169i
\(649\) 15.6222i 0.613226i
\(650\) −34.6048 + 17.1479i −1.35731 + 0.672598i
\(651\) 14.4499 0.566336
\(652\) −12.0853 + 7.52329i −0.473295 + 0.294635i
\(653\) 21.2536i 0.831719i 0.909429 + 0.415860i \(0.136519\pi\)
−0.909429 + 0.415860i \(0.863481\pi\)
\(654\) 5.59040 + 19.5585i 0.218602 + 0.764799i
\(655\) 13.4881 16.1914i 0.527024 0.632651i
\(656\) 18.1928 36.9824i 0.710310 1.44392i
\(657\) 16.1935i 0.631770i
\(658\) 0.563426 + 1.97119i 0.0219646 + 0.0768452i
\(659\) 19.6877 0.766923 0.383461 0.923557i \(-0.374732\pi\)
0.383461 + 0.923557i \(0.374732\pi\)
\(660\) 23.7760 + 3.29610i 0.925479 + 0.128301i
\(661\) 25.1207i 0.977081i 0.872541 + 0.488540i \(0.162470\pi\)
−0.872541 + 0.488540i \(0.837530\pi\)
\(662\) −2.63861 9.23143i −0.102553 0.358790i
\(663\) 10.5736i 0.410646i
\(664\) 16.6864 + 15.1014i 0.647557 + 0.586047i
\(665\) −6.96422 + 8.35999i −0.270061 + 0.324187i
\(666\) 23.8244 6.80972i 0.923178 0.263871i
\(667\) 12.2076 + 3.42909i 0.472681 + 0.132775i
\(668\) −0.616506 + 0.383786i −0.0238533 + 0.0148491i
\(669\) −4.79699 −0.185462
\(670\) 6.35034 14.3681i 0.245335 0.555089i
\(671\) 14.2495i 0.550095i
\(672\) 26.7071 + 4.82584i 1.03025 + 0.186161i
\(673\) 0.593638i 0.0228831i 0.999935 + 0.0114415i \(0.00364203\pi\)
−0.999935 + 0.0114415i \(0.996358\pi\)
\(674\) −16.1050 + 4.60328i −0.620340 + 0.177312i
\(675\) −4.78112 26.0282i −0.184026 1.00183i
\(676\) −28.5769 + 17.7896i −1.09911 + 0.684215i
\(677\) −27.1192 −1.04228 −0.521138 0.853472i \(-0.674492\pi\)
−0.521138 + 0.853472i \(0.674492\pi\)
\(678\) 4.05498 1.15903i 0.155730 0.0445123i
\(679\) 63.4900i 2.43652i
\(680\) −10.9201 + 1.54615i −0.418767 + 0.0592922i
\(681\) 2.35613i 0.0902873i
\(682\) −5.65948 19.8002i −0.216713 0.758189i
\(683\) −41.3849 −1.58355 −0.791775 0.610812i \(-0.790843\pi\)
−0.791775 + 0.610812i \(0.790843\pi\)
\(684\) 3.37916 2.10358i 0.129205 0.0804326i
\(685\) −26.6164 22.1725i −1.01696 0.847168i
\(686\) −7.85419 27.4786i −0.299874 1.04914i
\(687\) 4.57804i 0.174663i
\(688\) 19.7814 + 9.73109i 0.754159 + 0.370994i
\(689\) 1.15947i 0.0441725i
\(690\) 12.9850 + 10.7170i 0.494331 + 0.407989i
\(691\) 42.3136i 1.60968i 0.593489 + 0.804842i \(0.297750\pi\)
−0.593489 + 0.804842i \(0.702250\pi\)
\(692\) 3.72313 + 5.98076i 0.141532 + 0.227354i
\(693\) 36.9306i 1.40288i
\(694\) 16.2635 4.64859i 0.617354 0.176458i
\(695\) −6.72052 + 8.06746i −0.254924 + 0.306016i
\(696\) 5.57085 6.15555i 0.211163 0.233325i
\(697\) 17.9681 0.680590
\(698\) 23.7593 6.79111i 0.899304 0.257047i
\(699\) 13.2214i 0.500080i
\(700\) 31.9579 29.0913i 1.20790 1.09955i
\(701\) 37.1448i 1.40294i 0.712698 + 0.701471i \(0.247473\pi\)
−0.712698 + 0.701471i \(0.752527\pi\)
\(702\) −11.2352 39.3074i −0.424046 1.48356i
\(703\) −11.1614 −0.420960
\(704\) −3.84750 38.4860i −0.145008 1.45049i
\(705\) 0.639798 + 0.532978i 0.0240962 + 0.0200731i
\(706\) −11.1492 39.0066i −0.419607 1.46803i
\(707\) 34.4131i 1.29424i
\(708\) −3.79155 6.09067i −0.142495 0.228902i
\(709\) 0.657980i 0.0247109i −0.999924 0.0123555i \(-0.996067\pi\)
0.999924 0.0123555i \(-0.00393297\pi\)
\(710\) 15.9486 36.0849i 0.598540 1.35424i
\(711\) −13.5311 −0.507456
\(712\) −8.00108 7.24108i −0.299853 0.271371i
\(713\) 3.90622 13.9062i 0.146289 0.520791i
\(714\) 3.25166 + 11.3762i 0.121690 + 0.425744i
\(715\) 37.7924 45.3668i 1.41336 1.69662i
\(716\) 22.2642 + 35.7648i 0.832052 + 1.33659i
\(717\) 16.2130i 0.605485i
\(718\) −41.5831 + 11.8857i −1.55187 + 0.443569i
\(719\) 17.6047i 0.656544i 0.944583 + 0.328272i \(0.106466\pi\)
−0.944583 + 0.328272i \(0.893534\pi\)
\(720\) −14.4415 + 6.43286i −0.538201 + 0.239739i
\(721\) 29.0499 1.08188
\(722\) 24.1115 6.89177i 0.897337 0.256485i
\(723\) 15.7367i 0.585255i
\(724\) −20.0814 32.2584i −0.746321 1.19888i
\(725\) −2.38841 13.0024i −0.0887032 0.482896i
\(726\) −18.6801 + 5.33931i −0.693282 + 0.198160i
\(727\) 15.5188i 0.575562i −0.957696 0.287781i \(-0.907082\pi\)
0.957696 0.287781i \(-0.0929176\pi\)
\(728\) 44.7975 49.4993i 1.66031 1.83457i
\(729\) 18.6404 0.690385
\(730\) 11.7118 26.4987i 0.433471 0.980762i
\(731\) 9.61089i 0.355472i
\(732\) −3.45838 5.55548i −0.127826 0.205336i
\(733\) −10.9959 −0.406143 −0.203071 0.979164i \(-0.565092\pi\)
−0.203071 + 0.979164i \(0.565092\pi\)
\(734\) −2.46691 8.63072i −0.0910554 0.318566i
\(735\) −22.2699 18.5518i −0.821439 0.684292i
\(736\) 11.8640 24.3977i 0.437311 0.899310i
\(737\) 24.0170i 0.884676i
\(738\) 24.7644 7.07840i 0.911591 0.260559i
\(739\) 14.0735i 0.517702i 0.965917 + 0.258851i \(0.0833439\pi\)
−0.965917 + 0.258851i \(0.916656\pi\)
\(740\) 43.9108 + 6.08741i 1.61419 + 0.223778i
\(741\) 6.82726i 0.250806i
\(742\) 0.356567 + 1.24748i 0.0130900 + 0.0457965i
\(743\) 3.97256i 0.145739i −0.997341 0.0728695i \(-0.976784\pi\)
0.997341 0.0728695i \(-0.0232157\pi\)
\(744\) −7.01203 6.34598i −0.257073 0.232655i
\(745\) −23.1788 + 27.8243i −0.849206 + 1.01940i
\(746\) −30.2477 + 8.64568i −1.10745 + 0.316541i
\(747\) 14.0640i 0.514576i
\(748\) 14.3149 8.91127i 0.523404 0.325828i
\(749\) 67.6828 2.47308
\(750\) 4.07850 17.0728i 0.148926 0.623409i
\(751\) 19.1625 0.699248 0.349624 0.936890i \(-0.386309\pi\)
0.349624 + 0.936890i \(0.386309\pi\)
\(752\) 0.592282 1.20399i 0.0215983 0.0439051i
\(753\) −7.80667 −0.284491
\(754\) −5.61255 19.6360i −0.204397 0.715101i
\(755\) 13.2309 15.8827i 0.481523 0.578030i
\(756\) 24.1760 + 38.8359i 0.879273 + 1.41245i
\(757\) −11.1132 −0.403917 −0.201959 0.979394i \(-0.564731\pi\)
−0.201959 + 0.979394i \(0.564731\pi\)
\(758\) −17.0229 + 4.86566i −0.618301 + 0.176729i
\(759\) −24.7816 6.96110i −0.899516 0.252672i
\(760\) 7.05096 0.998329i 0.255765 0.0362132i
\(761\) −11.4048 −0.413422 −0.206711 0.978402i \(-0.566276\pi\)
−0.206711 + 0.978402i \(0.566276\pi\)
\(762\) 11.7628 3.36216i 0.426122 0.121798i
\(763\) −55.9928 −2.02708
\(764\) 33.5983 20.9156i 1.21555 0.756698i
\(765\) −5.29555 4.41141i −0.191461 0.159495i
\(766\) 5.55697 + 19.4415i 0.200781 + 0.702451i
\(767\) −17.6483 −0.637244
\(768\) −10.8407 14.0708i −0.391179 0.507737i
\(769\) 23.6281i 0.852049i 0.904712 + 0.426025i \(0.140086\pi\)
−0.904712 + 0.426025i \(0.859914\pi\)
\(770\) −26.7096 + 60.4324i −0.962545 + 2.17783i
\(771\) 2.73667i 0.0985588i
\(772\) −18.5498 29.7980i −0.667622 1.07246i
\(773\) −30.7686 −1.10667 −0.553335 0.832959i \(-0.686645\pi\)
−0.553335 + 0.832959i \(0.686645\pi\)
\(774\) 3.78614 + 13.2462i 0.136090 + 0.476123i
\(775\) −14.8115 + 2.72073i −0.532045 + 0.0977315i
\(776\) 27.8830 30.8095i 1.00094 1.10600i
\(777\) 47.5575i 1.70612i
\(778\) −3.44338 12.0470i −0.123451 0.431905i
\(779\) −11.6018 −0.415676
\(780\) 3.72358 26.8596i 0.133326 0.961727i
\(781\) 60.3176i 2.15833i
\(782\) 11.8272 0.0539953i 0.422939 0.00193087i
\(783\) 13.9939 0.500101
\(784\) −20.6160 + 41.9083i −0.736285 + 1.49672i
\(785\) −1.28830 1.07321i −0.0459815 0.0383045i
\(786\) 4.06635 + 14.2265i 0.145042 + 0.507442i
\(787\) 27.7205i 0.988129i −0.869425 0.494065i \(-0.835511\pi\)
0.869425 0.494065i \(-0.164489\pi\)
\(788\) 14.1433 + 22.7196i 0.503835 + 0.809351i
\(789\) 10.5521i 0.375666i
\(790\) −22.1420 9.78618i −0.787777 0.348177i
\(791\) 11.6087i 0.412759i
\(792\) 16.2189 17.9211i 0.576312 0.636800i
\(793\) −16.0976 −0.571641
\(794\) 4.09248 + 14.3179i 0.145237 + 0.508123i
\(795\) 0.404900 + 0.337298i 0.0143603 + 0.0119627i
\(796\) −9.94449 + 6.19062i −0.352473 + 0.219421i
\(797\) 30.0790 1.06545 0.532726 0.846288i \(-0.321168\pi\)
0.532726 + 0.846288i \(0.321168\pi\)
\(798\) −2.09955 7.34547i −0.0743233 0.260027i
\(799\) 0.584966 0.0206946
\(800\) −28.2842 + 0.0820039i −0.999996 + 0.00289928i
\(801\) 6.74367i 0.238276i
\(802\) 13.0533 + 45.6680i 0.460927 + 1.61259i
\(803\) 44.2938i 1.56309i
\(804\) 5.82898 + 9.36355i 0.205572 + 0.330227i
\(805\) −38.1866 + 26.2591i −1.34590 + 0.925511i
\(806\) −22.3682 + 6.39348i −0.787885 + 0.225201i
\(807\) 3.65261 0.128578
\(808\) 15.1133 16.6995i 0.531682 0.587486i
\(809\) −14.2873 −0.502316 −0.251158 0.967946i \(-0.580811\pi\)
−0.251158 + 0.967946i \(0.580811\pi\)
\(810\) 1.65774 + 0.732678i 0.0582470 + 0.0257437i
\(811\) 50.5206i 1.77402i −0.461752 0.887009i \(-0.652779\pi\)
0.461752 0.887009i \(-0.347221\pi\)
\(812\) 12.0771 + 19.4004i 0.423823 + 0.680821i
\(813\) 7.65942i 0.268628i
\(814\) −65.1664 + 18.6265i −2.28408 + 0.652858i
\(815\) −12.2287 10.1870i −0.428353 0.356836i
\(816\) 3.41819 6.94851i 0.119661 0.243247i
\(817\) 6.20563i 0.217107i
\(818\) 37.7219 10.7820i 1.31892 0.376985i
\(819\) 41.7203 1.45782
\(820\) 45.6433 + 6.32759i 1.59393 + 0.220969i
\(821\) −15.7791 −0.550695 −0.275348 0.961345i \(-0.588793\pi\)
−0.275348 + 0.961345i \(0.588793\pi\)
\(822\) 23.3863 6.68450i 0.815692 0.233149i
\(823\) 3.65484 0.127400 0.0636998 0.997969i \(-0.479710\pi\)
0.0636998 + 0.997969i \(0.479710\pi\)
\(824\) −14.0969 12.7579i −0.491089 0.444442i
\(825\) 4.84850 + 26.3950i 0.168803 + 0.918955i
\(826\) 18.9879 5.42730i 0.660673 0.188840i
\(827\) 14.3902i 0.500397i −0.968195 0.250199i \(-0.919504\pi\)
0.968195 0.250199i \(-0.0804959\pi\)
\(828\) 16.2795 4.73365i 0.565750 0.164506i
\(829\) 12.9284 0.449023 0.224511 0.974471i \(-0.427921\pi\)
0.224511 + 0.974471i \(0.427921\pi\)
\(830\) −10.1716 + 23.0141i −0.353062 + 0.798830i
\(831\) 17.8812i 0.620290i
\(832\) −43.4774 + 4.34650i −1.50731 + 0.150688i
\(833\) −20.3613 −0.705479
\(834\) −2.02608 7.08843i −0.0701575 0.245452i
\(835\) −0.623824 0.519671i −0.0215883 0.0179840i
\(836\) −9.24293 + 5.75389i −0.319673 + 0.199002i
\(837\) 15.9410i 0.551002i
\(838\) 0.393457 0.112462i 0.0135917 0.00388492i
\(839\) 43.2349 1.49264 0.746318 0.665590i \(-0.231820\pi\)
0.746318 + 0.665590i \(0.231820\pi\)
\(840\) 4.25377 + 30.0434i 0.146769 + 1.03660i
\(841\) −22.0094 −0.758944
\(842\) 14.7343 + 51.5494i 0.507779 + 1.77651i
\(843\) 7.53968i 0.259680i
\(844\) 17.9686 + 28.8644i 0.618505 + 0.993555i
\(845\) −28.9161 24.0883i −0.994743 0.828662i
\(846\) 0.806226 0.230443i 0.0277186 0.00792279i
\(847\) 53.4779i 1.83752i
\(848\) 0.374829 0.761954i 0.0128717 0.0261656i
\(849\) 8.00078i 0.274586i
\(850\) −5.47503 11.0487i −0.187792 0.378966i
\(851\) −45.7681 12.8561i −1.56891 0.440703i
\(852\) 14.6392 + 23.5161i 0.501531 + 0.805650i
\(853\) 6.61354i 0.226443i −0.993570 0.113222i \(-0.963883\pi\)
0.993570 0.113222i \(-0.0361170\pi\)
\(854\) 17.3194 4.95039i 0.592658 0.169399i
\(855\) 3.41927 + 2.84839i 0.116936 + 0.0974129i
\(856\) −32.8441 29.7244i −1.12259 1.01596i
\(857\) 7.39107i 0.252474i −0.992000 0.126237i \(-0.959710\pi\)
0.992000 0.126237i \(-0.0402900\pi\)
\(858\) 11.3935 + 39.8613i 0.388969 + 1.36084i
\(859\) 25.9916i 0.886821i −0.896319 0.443411i \(-0.853768\pi\)
0.896319 0.443411i \(-0.146232\pi\)
\(860\) −3.38454 + 24.4140i −0.115412 + 0.832509i
\(861\) 49.4338i 1.68470i
\(862\) 30.2873 8.65699i 1.03159 0.294858i
\(863\) −23.5099 −0.800285 −0.400142 0.916453i \(-0.631039\pi\)
−0.400142 + 0.916453i \(0.631039\pi\)
\(864\) 5.32383 29.4631i 0.181120 1.00236i
\(865\) −5.04136 + 6.05175i −0.171411 + 0.205766i
\(866\) −11.3984 + 3.25799i −0.387332 + 0.110711i
\(867\) −15.4967 −0.526297
\(868\) 22.0998 13.7575i 0.750116 0.466961i
\(869\) 37.0113 1.25552
\(870\) 8.48981 + 3.75227i 0.287831 + 0.127214i
\(871\) 27.1318 0.919326
\(872\) 27.1714 + 24.5904i 0.920139 + 0.832738i
\(873\) 25.9677 0.878872
\(874\) −7.63665 + 0.0348640i −0.258314 + 0.00117929i
\(875\) 42.0997 + 23.7094i 1.42323 + 0.801524i
\(876\) 10.7502 + 17.2689i 0.363216 + 0.583463i
\(877\) 26.7427i 0.903038i 0.892262 + 0.451519i \(0.149118\pi\)
−0.892262 + 0.451519i \(0.850882\pi\)
\(878\) 0.861745 + 3.01489i 0.0290825 + 0.101748i
\(879\) 27.9755 0.943589
\(880\) 39.5014 17.5957i 1.33159 0.593150i
\(881\) 1.75131i 0.0590030i −0.999565 0.0295015i \(-0.990608\pi\)
0.999565 0.0295015i \(-0.00939198\pi\)
\(882\) −28.0629 + 8.02120i −0.944927 + 0.270088i
\(883\) −17.6978 −0.595577 −0.297789 0.954632i \(-0.596249\pi\)
−0.297789 + 0.954632i \(0.596249\pi\)
\(884\) −10.0670 16.1714i −0.338590 0.543904i
\(885\) 5.13401 6.16297i 0.172578 0.207166i
\(886\) −15.9083 + 4.54705i −0.534449 + 0.152761i
\(887\) 16.7977 0.564011 0.282006 0.959413i \(-0.409000\pi\)
0.282006 + 0.959413i \(0.409000\pi\)
\(888\) −20.8859 + 23.0780i −0.700884 + 0.774447i
\(889\) 33.6751i 1.12943i
\(890\) 4.87727 11.0352i 0.163486 0.369900i
\(891\) −2.77099 −0.0928315
\(892\) −7.33656 + 4.56714i −0.245646 + 0.152919i
\(893\) −0.377705 −0.0126394
\(894\) −6.98787 24.4477i −0.233709 0.817653i
\(895\) −30.1472 + 36.1893i −1.00771 + 1.20967i
\(896\) 45.4407 18.0468i 1.51807 0.602900i
\(897\) −7.86391 + 27.9957i −0.262568 + 0.934748i
\(898\) −42.5445 + 12.1605i −1.41973 + 0.405800i
\(899\) 7.96332i 0.265592i
\(900\) −11.8985 13.0709i −0.396615 0.435697i
\(901\) 0.370199 0.0123331
\(902\) −67.7375 + 19.3614i −2.25541 + 0.644663i
\(903\) 26.4415 0.879918
\(904\) 5.09822 5.63331i 0.169564 0.187361i
\(905\) 27.1916 32.6413i 0.903878 1.08503i
\(906\) 3.98882 + 13.9552i 0.132520 + 0.463632i
\(907\) 40.6854i 1.35094i 0.737389 + 0.675469i \(0.236059\pi\)
−0.737389 + 0.675469i \(0.763941\pi\)
\(908\) −2.24324 3.60349i −0.0744445 0.119586i
\(909\) 14.0751 0.466841
\(910\) 68.2701 + 30.1736i 2.26313 + 1.00025i
\(911\) −10.5511 −0.349574 −0.174787 0.984606i \(-0.555924\pi\)
−0.174787 + 0.984606i \(0.555924\pi\)
\(912\) −2.20708 + 4.48656i −0.0730837 + 0.148565i
\(913\) 38.4690i 1.27314i
\(914\) −36.6520 + 10.4762i −1.21234 + 0.346523i
\(915\) 4.68288 5.62142i 0.154811 0.185839i
\(916\) −4.35868 7.00170i −0.144015 0.231343i
\(917\) −40.7281 −1.34496
\(918\) 12.5501 3.58720i 0.414217 0.118395i
\(919\) −50.5889 −1.66877 −0.834387 0.551179i \(-0.814178\pi\)
−0.834387 + 0.551179i \(0.814178\pi\)
\(920\) 30.0629 + 4.02786i 0.991144 + 0.132795i
\(921\) −10.9787 −0.361762
\(922\) 13.9566 3.98921i 0.459636 0.131378i
\(923\) 68.1403 2.24287
\(924\) −24.5167 39.3831i −0.806540 1.29561i
\(925\) 8.95447 + 48.7477i 0.294421 + 1.60281i
\(926\) 42.0306 12.0136i 1.38121 0.394791i
\(927\) 11.8815i 0.390240i
\(928\) 2.65951 14.7183i 0.0873028 0.483151i
\(929\) 24.3910 0.800243 0.400122 0.916462i \(-0.368968\pi\)
0.400122 + 0.916462i \(0.368968\pi\)
\(930\) 4.27437 9.67108i 0.140162 0.317127i
\(931\) 13.1470 0.430877
\(932\) −12.5879 20.2210i −0.412331 0.662360i
\(933\) 29.1939i 0.955764i
\(934\) −7.28204 25.4769i −0.238276 0.833629i
\(935\) 14.4848 + 12.0664i 0.473704 + 0.394615i
\(936\) −20.2454 18.3223i −0.661741 0.598885i
\(937\) 5.60780 0.183199 0.0915994 0.995796i \(-0.470802\pi\)
0.0915994 + 0.995796i \(0.470802\pi\)
\(938\) −29.1912 + 8.34370i −0.953126 + 0.272431i
\(939\) 32.5178 1.06118
\(940\) 1.48595 + 0.206000i 0.0484665 + 0.00671898i
\(941\) 22.1204i 0.721105i −0.932739 0.360553i \(-0.882588\pi\)
0.932739 0.360553i \(-0.117412\pi\)
\(942\) 1.13196 0.323548i 0.0368813 0.0105418i
\(943\) −47.5738 13.3634i −1.54922 0.435171i
\(944\) −11.5977 5.70526i −0.377472 0.185690i
\(945\) −32.7359 + 39.2968i −1.06490 + 1.27833i
\(946\) −10.3561 36.2319i −0.336707 1.17800i
\(947\) −9.04206 −0.293828 −0.146914 0.989149i \(-0.546934\pi\)
−0.146914 + 0.989149i \(0.546934\pi\)
\(948\) 14.4297 8.98273i 0.468654 0.291746i
\(949\) 50.0384 1.62432
\(950\) 3.53515 + 7.13398i 0.114695 + 0.231457i
\(951\) 23.1708i 0.751364i
\(952\) 15.8042 + 14.3030i 0.512218 + 0.463564i
\(953\) −36.5931 −1.18537 −0.592683 0.805436i \(-0.701931\pi\)
−0.592683 + 0.805436i \(0.701931\pi\)
\(954\) 0.510225 0.145837i 0.0165191 0.00472165i
\(955\) 33.9971 + 28.3210i 1.10012 + 0.916446i
\(956\) −15.4361 24.7963i −0.499240 0.801970i
\(957\) −14.1911 −0.458733
\(958\) −20.5134 + 5.86334i −0.662759 + 0.189436i
\(959\) 66.9512i 2.16197i
\(960\) 11.1300 16.4471i 0.359219 0.530829i
\(961\) 21.9287 0.707376
\(962\) 21.0422 + 73.6181i 0.678428 + 2.37354i
\(963\) 27.6825i 0.892057i
\(964\) 14.9827 + 24.0679i 0.482560 + 0.775175i
\(965\) 25.1176 30.1518i 0.808566 0.970619i
\(966\) −0.148552 32.5389i −0.00477958 1.04692i
\(967\) −32.8759 −1.05722 −0.528608 0.848866i \(-0.677286\pi\)
−0.528608 + 0.848866i \(0.677286\pi\)
\(968\) −23.4860 + 25.9510i −0.754868 + 0.834096i
\(969\) −2.17982 −0.0700259
\(970\) 42.4929 + 18.7807i 1.36436 + 0.603013i
\(971\) −25.9741 −0.833548 −0.416774 0.909010i \(-0.636839\pi\)
−0.416774 + 0.909010i \(0.636839\pi\)
\(972\) 25.8791 16.1102i 0.830072 0.516735i
\(973\) 20.2930 0.650564
\(974\) −50.3429 + 14.3895i −1.61309 + 0.461069i
\(975\) 29.8182 5.47732i 0.954948 0.175414i
\(976\) −10.5786 5.20393i −0.338612 0.166574i
\(977\) −15.7214 −0.502972 −0.251486 0.967861i \(-0.580919\pi\)
−0.251486 + 0.967861i \(0.580919\pi\)
\(978\) 10.7447 3.07115i 0.343577 0.0982045i
\(979\) 18.4458i 0.589531i
\(980\) −51.7227 7.17039i −1.65222 0.229050i
\(981\) 22.9013i 0.731181i
\(982\) 0.932601 + 3.26279i 0.0297605 + 0.104120i
\(983\) 26.5632i 0.847235i 0.905841 + 0.423618i \(0.139240\pi\)
−0.905841 + 0.423618i \(0.860760\pi\)
\(984\) −21.7099 + 23.9885i −0.692087 + 0.764726i
\(985\) −19.1510 + 22.9892i −0.610201 + 0.732498i
\(986\) 6.26942 1.79198i 0.199659 0.0570684i
\(987\) 1.60936i 0.0512265i
\(988\) 6.50013 + 10.4417i 0.206797 + 0.332194i
\(989\) 7.14789 25.4466i 0.227290 0.809155i
\(990\) 24.7171 + 10.9243i 0.785560 + 0.347197i
\(991\) 7.50012i 0.238249i −0.992879 0.119125i \(-0.961991\pi\)
0.992879 0.119125i \(-0.0380088\pi\)
\(992\) −16.7662 3.02956i −0.532327 0.0961886i
\(993\) 7.53689i 0.239176i
\(994\) −73.3124 + 20.9548i −2.32533 + 0.664647i
\(995\) −10.0625 8.38250i −0.319004 0.265743i
\(996\) −9.33652 14.9980i −0.295839 0.475230i
\(997\) 15.8439i 0.501780i −0.968016 0.250890i \(-0.919277\pi\)
0.968016 0.250890i \(-0.0807233\pi\)
\(998\) 6.42803 + 22.4890i 0.203476 + 0.711878i
\(999\) −52.4651 −1.65992
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 460.2.g.c.459.4 yes 56
4.3 odd 2 inner 460.2.g.c.459.56 yes 56
5.4 even 2 inner 460.2.g.c.459.53 yes 56
20.19 odd 2 inner 460.2.g.c.459.1 56
23.22 odd 2 inner 460.2.g.c.459.3 yes 56
92.91 even 2 inner 460.2.g.c.459.55 yes 56
115.114 odd 2 inner 460.2.g.c.459.54 yes 56
460.459 even 2 inner 460.2.g.c.459.2 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.g.c.459.1 56 20.19 odd 2 inner
460.2.g.c.459.2 yes 56 460.459 even 2 inner
460.2.g.c.459.3 yes 56 23.22 odd 2 inner
460.2.g.c.459.4 yes 56 1.1 even 1 trivial
460.2.g.c.459.53 yes 56 5.4 even 2 inner
460.2.g.c.459.54 yes 56 115.114 odd 2 inner
460.2.g.c.459.55 yes 56 92.91 even 2 inner
460.2.g.c.459.56 yes 56 4.3 odd 2 inner