Properties

Label 196.2.f.a.31.1
Level $196$
Weight $2$
Character 196.31
Analytic conductor $1.565$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [196,2,Mod(19,196)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(196, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("196.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 196.f (of order \(6\), degree \(2\), not 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: \(1.56506787962\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 196.31
Dual form 196.2.f.a.19.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36603 - 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(1.50000 - 0.866025i) q^{5} +(1.73205 - 1.73205i) q^{6} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(-1.36603 - 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.73205 + 1.00000i) q^{4} +(1.50000 - 0.866025i) q^{5} +(1.73205 - 1.73205i) q^{6} +(-2.00000 - 2.00000i) q^{8} +(-2.36603 + 0.633975i) q^{10} +(0.866025 + 0.500000i) q^{11} +(-3.00000 + 1.73205i) q^{12} +3.46410i q^{13} +3.00000i q^{15} +(2.00000 + 3.46410i) q^{16} +(1.50000 + 0.866025i) q^{17} +(2.59808 + 4.50000i) q^{19} +3.46410 q^{20} +(-1.00000 - 1.00000i) q^{22} +(0.866025 - 0.500000i) q^{23} +(4.73205 - 1.26795i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(1.26795 - 4.73205i) q^{26} -5.19615 q^{27} +4.00000 q^{29} +(1.09808 - 4.09808i) q^{30} +(0.866025 - 1.50000i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(-1.50000 + 0.866025i) q^{33} +(-1.73205 - 1.73205i) q^{34} +(-1.50000 - 2.59808i) q^{37} +(-1.90192 - 7.09808i) q^{38} +(-5.19615 - 3.00000i) q^{39} +(-4.73205 - 1.26795i) q^{40} -3.46410i q^{41} +2.00000i q^{43} +(1.00000 + 1.73205i) q^{44} +(-1.36603 + 0.366025i) q^{46} +(-4.33013 - 7.50000i) q^{47} -6.92820 q^{48} +(2.00000 - 2.00000i) q^{50} +(-2.59808 + 1.50000i) q^{51} +(-3.46410 + 6.00000i) q^{52} +(0.500000 - 0.866025i) q^{53} +(7.09808 + 1.90192i) q^{54} +1.73205 q^{55} -9.00000 q^{57} +(-5.46410 - 1.46410i) q^{58} +(2.59808 - 4.50000i) q^{59} +(-3.00000 + 5.19615i) q^{60} +(4.50000 - 2.59808i) q^{61} +(-1.73205 + 1.73205i) q^{62} +8.00000i q^{64} +(3.00000 + 5.19615i) q^{65} +(2.36603 - 0.633975i) q^{66} +(2.59808 + 1.50000i) q^{67} +(1.73205 + 3.00000i) q^{68} +1.73205i q^{69} -14.0000i q^{71} +(-7.50000 - 4.33013i) q^{73} +(1.09808 + 4.09808i) q^{74} +(-1.73205 - 3.00000i) q^{75} +10.3923i q^{76} +(6.00000 + 6.00000i) q^{78} +(7.79423 - 4.50000i) q^{79} +(6.00000 + 3.46410i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-1.26795 + 4.73205i) q^{82} +13.8564 q^{83} +3.00000 q^{85} +(0.732051 - 2.73205i) q^{86} +(-3.46410 + 6.00000i) q^{87} +(-0.732051 - 2.73205i) q^{88} +(-13.5000 + 7.79423i) q^{89} +2.00000 q^{92} +(1.50000 + 2.59808i) q^{93} +(3.16987 + 11.8301i) q^{94} +(7.79423 + 4.50000i) q^{95} +(9.46410 + 2.53590i) q^{96} -17.3205i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 6 q^{5} - 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 6 q^{5} - 8 q^{8} - 6 q^{10} - 12 q^{12} + 8 q^{16} + 6 q^{17} - 4 q^{22} + 12 q^{24} - 4 q^{25} + 12 q^{26} + 16 q^{29} - 6 q^{30} + 8 q^{32} - 6 q^{33} - 6 q^{37} - 18 q^{38} - 12 q^{40} + 4 q^{44} - 2 q^{46} + 8 q^{50} + 2 q^{53} + 18 q^{54} - 36 q^{57} - 8 q^{58} - 12 q^{60} + 18 q^{61} + 12 q^{65} + 6 q^{66} - 30 q^{73} - 6 q^{74} + 24 q^{78} + 24 q^{80} + 18 q^{81} - 12 q^{82} + 12 q^{85} - 4 q^{86} + 4 q^{88} - 54 q^{89} + 8 q^{92} + 6 q^{93} + 30 q^{94} + 24 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).

\(n\) \(99\) \(101\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 0.366025i −0.965926 0.258819i
\(3\) −0.866025 + 1.50000i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) 1.50000 0.866025i 0.670820 0.387298i −0.125567 0.992085i \(-0.540075\pi\)
0.796387 + 0.604787i \(0.206742\pi\)
\(6\) 1.73205 1.73205i 0.707107 0.707107i
\(7\) 0 0
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) 0 0
\(10\) −2.36603 + 0.633975i −0.748203 + 0.200480i
\(11\) 0.866025 + 0.500000i 0.261116 + 0.150756i 0.624844 0.780750i \(-0.285163\pi\)
−0.363727 + 0.931505i \(0.618496\pi\)
\(12\) −3.00000 + 1.73205i −0.866025 + 0.500000i
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) 0 0
\(15\) 3.00000i 0.774597i
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 1.50000 + 0.866025i 0.363803 + 0.210042i 0.670748 0.741685i \(-0.265973\pi\)
−0.306944 + 0.951727i \(0.599307\pi\)
\(18\) 0 0
\(19\) 2.59808 + 4.50000i 0.596040 + 1.03237i 0.993399 + 0.114708i \(0.0365932\pi\)
−0.397360 + 0.917663i \(0.630073\pi\)
\(20\) 3.46410 0.774597
\(21\) 0 0
\(22\) −1.00000 1.00000i −0.213201 0.213201i
\(23\) 0.866025 0.500000i 0.180579 0.104257i −0.406986 0.913434i \(-0.633420\pi\)
0.587565 + 0.809177i \(0.300087\pi\)
\(24\) 4.73205 1.26795i 0.965926 0.258819i
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) 1.26795 4.73205i 0.248665 0.928032i
\(27\) −5.19615 −1.00000
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 1.09808 4.09808i 0.200480 0.748203i
\(31\) 0.866025 1.50000i 0.155543 0.269408i −0.777714 0.628619i \(-0.783621\pi\)
0.933257 + 0.359211i \(0.116954\pi\)
\(32\) −1.46410 5.46410i −0.258819 0.965926i
\(33\) −1.50000 + 0.866025i −0.261116 + 0.150756i
\(34\) −1.73205 1.73205i −0.297044 0.297044i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.50000 2.59808i −0.246598 0.427121i 0.715981 0.698119i \(-0.245980\pi\)
−0.962580 + 0.270998i \(0.912646\pi\)
\(38\) −1.90192 7.09808i −0.308533 1.15146i
\(39\) −5.19615 3.00000i −0.832050 0.480384i
\(40\) −4.73205 1.26795i −0.748203 0.200480i
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i 0.988304 + 0.152499i \(0.0487319\pi\)
−0.988304 + 0.152499i \(0.951268\pi\)
\(44\) 1.00000 + 1.73205i 0.150756 + 0.261116i
\(45\) 0 0
\(46\) −1.36603 + 0.366025i −0.201409 + 0.0539675i
\(47\) −4.33013 7.50000i −0.631614 1.09399i −0.987222 0.159352i \(-0.949059\pi\)
0.355608 0.934635i \(-0.384274\pi\)
\(48\) −6.92820 −1.00000
\(49\) 0 0
\(50\) 2.00000 2.00000i 0.282843 0.282843i
\(51\) −2.59808 + 1.50000i −0.363803 + 0.210042i
\(52\) −3.46410 + 6.00000i −0.480384 + 0.832050i
\(53\) 0.500000 0.866025i 0.0686803 0.118958i −0.829640 0.558298i \(-0.811454\pi\)
0.898321 + 0.439340i \(0.144788\pi\)
\(54\) 7.09808 + 1.90192i 0.965926 + 0.258819i
\(55\) 1.73205 0.233550
\(56\) 0 0
\(57\) −9.00000 −1.19208
\(58\) −5.46410 1.46410i −0.717472 0.192246i
\(59\) 2.59808 4.50000i 0.338241 0.585850i −0.645861 0.763455i \(-0.723502\pi\)
0.984102 + 0.177605i \(0.0568349\pi\)
\(60\) −3.00000 + 5.19615i −0.387298 + 0.670820i
\(61\) 4.50000 2.59808i 0.576166 0.332650i −0.183442 0.983030i \(-0.558724\pi\)
0.759608 + 0.650381i \(0.225391\pi\)
\(62\) −1.73205 + 1.73205i −0.219971 + 0.219971i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 3.00000 + 5.19615i 0.372104 + 0.644503i
\(66\) 2.36603 0.633975i 0.291238 0.0780369i
\(67\) 2.59808 + 1.50000i 0.317406 + 0.183254i 0.650236 0.759733i \(-0.274670\pi\)
−0.332830 + 0.942987i \(0.608004\pi\)
\(68\) 1.73205 + 3.00000i 0.210042 + 0.363803i
\(69\) 1.73205i 0.208514i
\(70\) 0 0
\(71\) 14.0000i 1.66149i −0.556650 0.830747i \(-0.687914\pi\)
0.556650 0.830747i \(-0.312086\pi\)
\(72\) 0 0
\(73\) −7.50000 4.33013i −0.877809 0.506803i −0.00787336 0.999969i \(-0.502506\pi\)
−0.869935 + 0.493166i \(0.835840\pi\)
\(74\) 1.09808 + 4.09808i 0.127649 + 0.476392i
\(75\) −1.73205 3.00000i −0.200000 0.346410i
\(76\) 10.3923i 1.19208i
\(77\) 0 0
\(78\) 6.00000 + 6.00000i 0.679366 + 0.679366i
\(79\) 7.79423 4.50000i 0.876919 0.506290i 0.00727784 0.999974i \(-0.497683\pi\)
0.869641 + 0.493684i \(0.164350\pi\)
\(80\) 6.00000 + 3.46410i 0.670820 + 0.387298i
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) −1.26795 + 4.73205i −0.140022 + 0.522568i
\(83\) 13.8564 1.52094 0.760469 0.649374i \(-0.224969\pi\)
0.760469 + 0.649374i \(0.224969\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) 0.732051 2.73205i 0.0789391 0.294605i
\(87\) −3.46410 + 6.00000i −0.371391 + 0.643268i
\(88\) −0.732051 2.73205i −0.0780369 0.291238i
\(89\) −13.5000 + 7.79423i −1.43100 + 0.826187i −0.997197 0.0748225i \(-0.976161\pi\)
−0.433800 + 0.901009i \(0.642828\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 2.00000 0.208514
\(93\) 1.50000 + 2.59808i 0.155543 + 0.269408i
\(94\) 3.16987 + 11.8301i 0.326947 + 1.22018i
\(95\) 7.79423 + 4.50000i 0.799671 + 0.461690i
\(96\) 9.46410 + 2.53590i 0.965926 + 0.258819i
\(97\) 17.3205i 1.75863i −0.476240 0.879316i \(-0.658000\pi\)
0.476240 0.879316i \(-0.342000\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.46410 + 2.00000i −0.346410 + 0.200000i
\(101\) 7.50000 + 4.33013i 0.746278 + 0.430864i 0.824347 0.566084i \(-0.191542\pi\)
−0.0780696 + 0.996948i \(0.524876\pi\)
\(102\) 4.09808 1.09808i 0.405770 0.108726i
\(103\) 4.33013 + 7.50000i 0.426660 + 0.738997i 0.996574 0.0827075i \(-0.0263567\pi\)
−0.569914 + 0.821705i \(0.693023\pi\)
\(104\) 6.92820 6.92820i 0.679366 0.679366i
\(105\) 0 0
\(106\) −1.00000 + 1.00000i −0.0971286 + 0.0971286i
\(107\) −11.2583 + 6.50000i −1.08838 + 0.628379i −0.933146 0.359498i \(-0.882948\pi\)
−0.155238 + 0.987877i \(0.549614\pi\)
\(108\) −9.00000 5.19615i −0.866025 0.500000i
\(109\) −4.50000 + 7.79423i −0.431022 + 0.746552i −0.996962 0.0778949i \(-0.975180\pi\)
0.565940 + 0.824447i \(0.308513\pi\)
\(110\) −2.36603 0.633975i −0.225592 0.0604471i
\(111\) 5.19615 0.493197
\(112\) 0 0
\(113\) −16.0000 −1.50515 −0.752577 0.658505i \(-0.771189\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 12.2942 + 3.29423i 1.15146 + 0.308533i
\(115\) 0.866025 1.50000i 0.0807573 0.139876i
\(116\) 6.92820 + 4.00000i 0.643268 + 0.371391i
\(117\) 0 0
\(118\) −5.19615 + 5.19615i −0.478345 + 0.478345i
\(119\) 0 0
\(120\) 6.00000 6.00000i 0.547723 0.547723i
\(121\) −5.00000 8.66025i −0.454545 0.787296i
\(122\) −7.09808 + 1.90192i −0.642630 + 0.172192i
\(123\) 5.19615 + 3.00000i 0.468521 + 0.270501i
\(124\) 3.00000 1.73205i 0.269408 0.155543i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 6.00000i 0.532414i 0.963916 + 0.266207i \(0.0857705\pi\)
−0.963916 + 0.266207i \(0.914230\pi\)
\(128\) 2.92820 10.9282i 0.258819 0.965926i
\(129\) −3.00000 1.73205i −0.264135 0.152499i
\(130\) −2.19615 8.19615i −0.192615 0.718850i
\(131\) −2.59808 4.50000i −0.226995 0.393167i 0.729921 0.683531i \(-0.239557\pi\)
−0.956916 + 0.290365i \(0.906223\pi\)
\(132\) −3.46410 −0.301511
\(133\) 0 0
\(134\) −3.00000 3.00000i −0.259161 0.259161i
\(135\) −7.79423 + 4.50000i −0.670820 + 0.387298i
\(136\) −1.26795 4.73205i −0.108726 0.405770i
\(137\) −0.500000 + 0.866025i −0.0427179 + 0.0739895i −0.886594 0.462549i \(-0.846935\pi\)
0.843876 + 0.536538i \(0.180268\pi\)
\(138\) 0.633975 2.36603i 0.0539675 0.201409i
\(139\) −6.92820 −0.587643 −0.293821 0.955860i \(-0.594927\pi\)
−0.293821 + 0.955860i \(0.594927\pi\)
\(140\) 0 0
\(141\) 15.0000 1.26323
\(142\) −5.12436 + 19.1244i −0.430026 + 1.60488i
\(143\) −1.73205 + 3.00000i −0.144841 + 0.250873i
\(144\) 0 0
\(145\) 6.00000 3.46410i 0.498273 0.287678i
\(146\) 8.66025 + 8.66025i 0.716728 + 0.716728i
\(147\) 0 0
\(148\) 6.00000i 0.493197i
\(149\) −0.500000 0.866025i −0.0409616 0.0709476i 0.844818 0.535054i \(-0.179709\pi\)
−0.885779 + 0.464107i \(0.846375\pi\)
\(150\) 1.26795 + 4.73205i 0.103528 + 0.386370i
\(151\) −6.06218 3.50000i −0.493333 0.284826i 0.232623 0.972567i \(-0.425269\pi\)
−0.725956 + 0.687741i \(0.758602\pi\)
\(152\) 3.80385 14.1962i 0.308533 1.15146i
\(153\) 0 0
\(154\) 0 0
\(155\) 3.00000i 0.240966i
\(156\) −6.00000 10.3923i −0.480384 0.832050i
\(157\) −1.50000 0.866025i −0.119713 0.0691164i 0.438948 0.898513i \(-0.355351\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) −12.2942 + 3.29423i −0.978076 + 0.262075i
\(159\) 0.866025 + 1.50000i 0.0686803 + 0.118958i
\(160\) −6.92820 6.92820i −0.547723 0.547723i
\(161\) 0 0
\(162\) −9.00000 + 9.00000i −0.707107 + 0.707107i
\(163\) 18.1865 10.5000i 1.42448 0.822423i 0.427802 0.903873i \(-0.359288\pi\)
0.996678 + 0.0814491i \(0.0259548\pi\)
\(164\) 3.46410 6.00000i 0.270501 0.468521i
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) −18.9282 5.07180i −1.46911 0.393648i
\(167\) −17.3205 −1.34030 −0.670151 0.742225i \(-0.733770\pi\)
−0.670151 + 0.742225i \(0.733770\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −4.09808 1.09808i −0.314308 0.0842186i
\(171\) 0 0
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) 10.5000 6.06218i 0.798300 0.460899i −0.0445762 0.999006i \(-0.514194\pi\)
0.842876 + 0.538107i \(0.180860\pi\)
\(174\) 6.92820 6.92820i 0.525226 0.525226i
\(175\) 0 0
\(176\) 4.00000i 0.301511i
\(177\) 4.50000 + 7.79423i 0.338241 + 0.585850i
\(178\) 21.2942 5.70577i 1.59607 0.427666i
\(179\) −16.4545 9.50000i −1.22987 0.710063i −0.262864 0.964833i \(-0.584667\pi\)
−0.967002 + 0.254770i \(0.918000\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 0 0
\(183\) 9.00000i 0.665299i
\(184\) −2.73205 0.732051i −0.201409 0.0539675i
\(185\) −4.50000 2.59808i −0.330847 0.191014i
\(186\) −1.09808 4.09808i −0.0805149 0.300486i
\(187\) 0.866025 + 1.50000i 0.0633300 + 0.109691i
\(188\) 17.3205i 1.26323i
\(189\) 0 0
\(190\) −9.00000 9.00000i −0.652929 0.652929i
\(191\) −0.866025 + 0.500000i −0.0626634 + 0.0361787i −0.531004 0.847369i \(-0.678185\pi\)
0.468341 + 0.883548i \(0.344852\pi\)
\(192\) −12.0000 6.92820i −0.866025 0.500000i
\(193\) 7.50000 12.9904i 0.539862 0.935068i −0.459049 0.888411i \(-0.651810\pi\)
0.998911 0.0466572i \(-0.0148568\pi\)
\(194\) −6.33975 + 23.6603i −0.455167 + 1.69871i
\(195\) −10.3923 −0.744208
\(196\) 0 0
\(197\) 16.0000 1.13995 0.569976 0.821661i \(-0.306952\pi\)
0.569976 + 0.821661i \(0.306952\pi\)
\(198\) 0 0
\(199\) 11.2583 19.5000i 0.798082 1.38232i −0.122782 0.992434i \(-0.539182\pi\)
0.920864 0.389885i \(-0.127485\pi\)
\(200\) 5.46410 1.46410i 0.386370 0.103528i
\(201\) −4.50000 + 2.59808i −0.317406 + 0.183254i
\(202\) −8.66025 8.66025i −0.609333 0.609333i
\(203\) 0 0
\(204\) −6.00000 −0.420084
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) −3.16987 11.8301i −0.220856 0.824244i
\(207\) 0 0
\(208\) −12.0000 + 6.92820i −0.832050 + 0.480384i
\(209\) 5.19615i 0.359425i
\(210\) 0 0
\(211\) 10.0000i 0.688428i 0.938891 + 0.344214i \(0.111855\pi\)
−0.938891 + 0.344214i \(0.888145\pi\)
\(212\) 1.73205 1.00000i 0.118958 0.0686803i
\(213\) 21.0000 + 12.1244i 1.43890 + 0.830747i
\(214\) 17.7583 4.75833i 1.21393 0.325273i
\(215\) 1.73205 + 3.00000i 0.118125 + 0.204598i
\(216\) 10.3923 + 10.3923i 0.707107 + 0.707107i
\(217\) 0 0
\(218\) 9.00000 9.00000i 0.609557 0.609557i
\(219\) 12.9904 7.50000i 0.877809 0.506803i
\(220\) 3.00000 + 1.73205i 0.202260 + 0.116775i
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) −7.09808 1.90192i −0.476392 0.127649i
\(223\) 6.92820 0.463947 0.231973 0.972722i \(-0.425482\pi\)
0.231973 + 0.972722i \(0.425482\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 21.8564 + 5.85641i 1.45387 + 0.389562i
\(227\) −9.52628 + 16.5000i −0.632281 + 1.09514i 0.354803 + 0.934941i \(0.384548\pi\)
−0.987084 + 0.160202i \(0.948785\pi\)
\(228\) −15.5885 9.00000i −1.03237 0.596040i
\(229\) 13.5000 7.79423i 0.892105 0.515057i 0.0174746 0.999847i \(-0.494437\pi\)
0.874630 + 0.484790i \(0.161104\pi\)
\(230\) −1.73205 + 1.73205i −0.114208 + 0.114208i
\(231\) 0 0
\(232\) −8.00000 8.00000i −0.525226 0.525226i
\(233\) 3.50000 + 6.06218i 0.229293 + 0.397146i 0.957599 0.288106i \(-0.0930254\pi\)
−0.728306 + 0.685252i \(0.759692\pi\)
\(234\) 0 0
\(235\) −12.9904 7.50000i −0.847399 0.489246i
\(236\) 9.00000 5.19615i 0.585850 0.338241i
\(237\) 15.5885i 1.01258i
\(238\) 0 0
\(239\) 20.0000i 1.29369i 0.762620 + 0.646846i \(0.223912\pi\)
−0.762620 + 0.646846i \(0.776088\pi\)
\(240\) −10.3923 + 6.00000i −0.670820 + 0.387298i
\(241\) 4.50000 + 2.59808i 0.289870 + 0.167357i 0.637883 0.770133i \(-0.279810\pi\)
−0.348013 + 0.937490i \(0.613143\pi\)
\(242\) 3.66025 + 13.6603i 0.235290 + 0.878114i
\(243\) 0 0
\(244\) 10.3923 0.665299
\(245\) 0 0
\(246\) −6.00000 6.00000i −0.382546 0.382546i
\(247\) −15.5885 + 9.00000i −0.991870 + 0.572656i
\(248\) −4.73205 + 1.26795i −0.300486 + 0.0805149i
\(249\) −12.0000 + 20.7846i −0.760469 + 1.31717i
\(250\) 4.43782 16.5622i 0.280673 1.04748i
\(251\) −3.46410 −0.218652 −0.109326 0.994006i \(-0.534869\pi\)
−0.109326 + 0.994006i \(0.534869\pi\)
\(252\) 0 0
\(253\) 1.00000 0.0628695
\(254\) 2.19615 8.19615i 0.137799 0.514272i
\(255\) −2.59808 + 4.50000i −0.162698 + 0.281801i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −4.50000 + 2.59808i −0.280702 + 0.162064i −0.633741 0.773545i \(-0.718482\pi\)
0.353039 + 0.935609i \(0.385148\pi\)
\(258\) 3.46410 + 3.46410i 0.215666 + 0.215666i
\(259\) 0 0
\(260\) 12.0000i 0.744208i
\(261\) 0 0
\(262\) 1.90192 + 7.09808i 0.117501 + 0.438521i
\(263\) 19.9186 + 11.5000i 1.22823 + 0.709120i 0.966660 0.256063i \(-0.0824256\pi\)
0.261573 + 0.965184i \(0.415759\pi\)
\(264\) 4.73205 + 1.26795i 0.291238 + 0.0780369i
\(265\) 1.73205i 0.106399i
\(266\) 0 0
\(267\) 27.0000i 1.65237i
\(268\) 3.00000 + 5.19615i 0.183254 + 0.317406i
\(269\) −19.5000 11.2583i −1.18894 0.686433i −0.230871 0.972984i \(-0.574158\pi\)
−0.958065 + 0.286552i \(0.907491\pi\)
\(270\) 12.2942 3.29423i 0.748203 0.200480i
\(271\) 7.79423 + 13.5000i 0.473466 + 0.820067i 0.999539 0.0303728i \(-0.00966946\pi\)
−0.526073 + 0.850439i \(0.676336\pi\)
\(272\) 6.92820i 0.420084i
\(273\) 0 0
\(274\) 1.00000 1.00000i 0.0604122 0.0604122i
\(275\) −1.73205 + 1.00000i −0.104447 + 0.0603023i
\(276\) −1.73205 + 3.00000i −0.104257 + 0.180579i
\(277\) 6.50000 11.2583i 0.390547 0.676448i −0.601975 0.798515i \(-0.705619\pi\)
0.992522 + 0.122068i \(0.0389525\pi\)
\(278\) 9.46410 + 2.53590i 0.567619 + 0.152093i
\(279\) 0 0
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) −20.4904 5.49038i −1.22018 0.326947i
\(283\) −6.06218 + 10.5000i −0.360359 + 0.624160i −0.988020 0.154327i \(-0.950679\pi\)
0.627661 + 0.778487i \(0.284012\pi\)
\(284\) 14.0000 24.2487i 0.830747 1.43890i
\(285\) −13.5000 + 7.79423i −0.799671 + 0.461690i
\(286\) 3.46410 3.46410i 0.204837 0.204837i
\(287\) 0 0
\(288\) 0 0
\(289\) −7.00000 12.1244i −0.411765 0.713197i
\(290\) −9.46410 + 2.53590i −0.555751 + 0.148913i
\(291\) 25.9808 + 15.0000i 1.52302 + 0.879316i
\(292\) −8.66025 15.0000i −0.506803 0.877809i
\(293\) 20.7846i 1.21425i −0.794606 0.607125i \(-0.792323\pi\)
0.794606 0.607125i \(-0.207677\pi\)
\(294\) 0 0
\(295\) 9.00000i 0.524000i
\(296\) −2.19615 + 8.19615i −0.127649 + 0.476392i
\(297\) −4.50000 2.59808i −0.261116 0.150756i
\(298\) 0.366025 + 1.36603i 0.0212033 + 0.0791317i
\(299\) 1.73205 + 3.00000i 0.100167 + 0.173494i
\(300\) 6.92820i 0.400000i
\(301\) 0 0
\(302\) 7.00000 + 7.00000i 0.402805 + 0.402805i
\(303\) −12.9904 + 7.50000i −0.746278 + 0.430864i
\(304\) −10.3923 + 18.0000i −0.596040 + 1.03237i
\(305\) 4.50000 7.79423i 0.257669 0.446296i
\(306\) 0 0
\(307\) 20.7846 1.18624 0.593120 0.805114i \(-0.297896\pi\)
0.593120 + 0.805114i \(0.297896\pi\)
\(308\) 0 0
\(309\) −15.0000 −0.853320
\(310\) −1.09808 + 4.09808i −0.0623665 + 0.232755i
\(311\) −4.33013 + 7.50000i −0.245539 + 0.425286i −0.962283 0.272050i \(-0.912298\pi\)
0.716744 + 0.697336i \(0.245632\pi\)
\(312\) 4.39230 + 16.3923i 0.248665 + 0.928032i
\(313\) −1.50000 + 0.866025i −0.0847850 + 0.0489506i −0.541793 0.840512i \(-0.682254\pi\)
0.457008 + 0.889463i \(0.348921\pi\)
\(314\) 1.73205 + 1.73205i 0.0977453 + 0.0977453i
\(315\) 0 0
\(316\) 18.0000 1.01258
\(317\) −5.50000 9.52628i −0.308911 0.535049i 0.669214 0.743070i \(-0.266631\pi\)
−0.978124 + 0.208021i \(0.933298\pi\)
\(318\) −0.633975 2.36603i −0.0355515 0.132680i
\(319\) 3.46410 + 2.00000i 0.193952 + 0.111979i
\(320\) 6.92820 + 12.0000i 0.387298 + 0.670820i
\(321\) 22.5167i 1.25676i
\(322\) 0 0
\(323\) 9.00000i 0.500773i
\(324\) 15.5885 9.00000i 0.866025 0.500000i
\(325\) −6.00000 3.46410i −0.332820 0.192154i
\(326\) −28.6865 + 7.68653i −1.58880 + 0.425718i
\(327\) −7.79423 13.5000i −0.431022 0.746552i
\(328\) −6.92820 + 6.92820i −0.382546 + 0.382546i
\(329\) 0 0
\(330\) 3.00000 3.00000i 0.165145 0.165145i
\(331\) −6.06218 + 3.50000i −0.333207 + 0.192377i −0.657264 0.753660i \(-0.728286\pi\)
0.324057 + 0.946038i \(0.394953\pi\)
\(332\) 24.0000 + 13.8564i 1.31717 + 0.760469i
\(333\) 0 0
\(334\) 23.6603 + 6.33975i 1.29463 + 0.346895i
\(335\) 5.19615 0.283896
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) −1.36603 0.366025i −0.0743020 0.0199092i
\(339\) 13.8564 24.0000i 0.752577 1.30350i
\(340\) 5.19615 + 3.00000i 0.281801 + 0.162698i
\(341\) 1.50000 0.866025i 0.0812296 0.0468979i
\(342\) 0 0
\(343\) 0 0
\(344\) 4.00000 4.00000i 0.215666 0.215666i
\(345\) 1.50000 + 2.59808i 0.0807573 + 0.139876i
\(346\) −16.5622 + 4.43782i −0.890388 + 0.238579i
\(347\) −11.2583 6.50000i −0.604379 0.348938i 0.166383 0.986061i \(-0.446791\pi\)
−0.770762 + 0.637123i \(0.780124\pi\)
\(348\) −12.0000 + 6.92820i −0.643268 + 0.371391i
\(349\) 10.3923i 0.556287i 0.960539 + 0.278144i \(0.0897191\pi\)
−0.960539 + 0.278144i \(0.910281\pi\)
\(350\) 0 0
\(351\) 18.0000i 0.960769i
\(352\) 1.46410 5.46410i 0.0780369 0.291238i
\(353\) 25.5000 + 14.7224i 1.35723 + 0.783596i 0.989249 0.146238i \(-0.0467166\pi\)
0.367979 + 0.929834i \(0.380050\pi\)
\(354\) −3.29423 12.2942i −0.175086 0.653431i
\(355\) −12.1244 21.0000i −0.643494 1.11456i
\(356\) −31.1769 −1.65237
\(357\) 0 0
\(358\) 19.0000 + 19.0000i 1.00418 + 1.00418i
\(359\) 19.9186 11.5000i 1.05126 0.606947i 0.128260 0.991741i \(-0.459061\pi\)
0.923003 + 0.384794i \(0.125727\pi\)
\(360\) 0 0
\(361\) −4.00000 + 6.92820i −0.210526 + 0.364642i
\(362\) 2.53590 9.46410i 0.133284 0.497422i
\(363\) 17.3205 0.909091
\(364\) 0 0
\(365\) −15.0000 −0.785136
\(366\) 3.29423 12.2942i 0.172192 0.642630i
\(367\) −0.866025 + 1.50000i −0.0452062 + 0.0782994i −0.887743 0.460339i \(-0.847728\pi\)
0.842537 + 0.538639i \(0.181061\pi\)
\(368\) 3.46410 + 2.00000i 0.180579 + 0.104257i
\(369\) 0 0
\(370\) 5.19615 + 5.19615i 0.270135 + 0.270135i
\(371\) 0 0
\(372\) 6.00000i 0.311086i
\(373\) 14.5000 + 25.1147i 0.750782 + 1.30039i 0.947444 + 0.319921i \(0.103656\pi\)
−0.196663 + 0.980471i \(0.563010\pi\)
\(374\) −0.633975 2.36603i −0.0327820 0.122344i
\(375\) −18.1865 10.5000i −0.939149 0.542218i
\(376\) −6.33975 + 23.6603i −0.326947 + 1.22018i
\(377\) 13.8564i 0.713641i
\(378\) 0 0
\(379\) 8.00000i 0.410932i −0.978664 0.205466i \(-0.934129\pi\)
0.978664 0.205466i \(-0.0658711\pi\)
\(380\) 9.00000 + 15.5885i 0.461690 + 0.799671i
\(381\) −9.00000 5.19615i −0.461084 0.266207i
\(382\) 1.36603 0.366025i 0.0698919 0.0187275i
\(383\) 2.59808 + 4.50000i 0.132755 + 0.229939i 0.924738 0.380605i \(-0.124284\pi\)
−0.791982 + 0.610544i \(0.790951\pi\)
\(384\) 13.8564 + 13.8564i 0.707107 + 0.707107i
\(385\) 0 0
\(386\) −15.0000 + 15.0000i −0.763480 + 0.763480i
\(387\) 0 0
\(388\) 17.3205 30.0000i 0.879316 1.52302i
\(389\) 9.50000 16.4545i 0.481669 0.834275i −0.518110 0.855314i \(-0.673364\pi\)
0.999779 + 0.0210389i \(0.00669738\pi\)
\(390\) 14.1962 + 3.80385i 0.718850 + 0.192615i
\(391\) 1.73205 0.0875936
\(392\) 0 0
\(393\) 9.00000 0.453990
\(394\) −21.8564 5.85641i −1.10111 0.295041i
\(395\) 7.79423 13.5000i 0.392170 0.679259i
\(396\) 0 0
\(397\) −16.5000 + 9.52628i −0.828111 + 0.478110i −0.853206 0.521575i \(-0.825345\pi\)
0.0250943 + 0.999685i \(0.492011\pi\)
\(398\) −22.5167 + 22.5167i −1.12866 + 1.12866i
\(399\) 0 0
\(400\) −8.00000 −0.400000
\(401\) 11.5000 + 19.9186i 0.574283 + 0.994687i 0.996119 + 0.0880147i \(0.0280523\pi\)
−0.421837 + 0.906672i \(0.638614\pi\)
\(402\) 7.09808 1.90192i 0.354020 0.0948593i
\(403\) 5.19615 + 3.00000i 0.258839 + 0.149441i
\(404\) 8.66025 + 15.0000i 0.430864 + 0.746278i
\(405\) 15.5885i 0.774597i
\(406\) 0 0
\(407\) 3.00000i 0.148704i
\(408\) 8.19615 + 2.19615i 0.405770 + 0.108726i
\(409\) −22.5000 12.9904i −1.11255 0.642333i −0.173064 0.984911i \(-0.555367\pi\)
−0.939490 + 0.342578i \(0.888700\pi\)
\(410\) 2.19615 + 8.19615i 0.108460 + 0.404779i
\(411\) −0.866025 1.50000i −0.0427179 0.0739895i
\(412\) 17.3205i 0.853320i
\(413\) 0 0
\(414\) 0 0
\(415\) 20.7846 12.0000i 1.02028 0.589057i
\(416\) 18.9282 5.07180i 0.928032 0.248665i
\(417\) 6.00000 10.3923i 0.293821 0.508913i
\(418\) 1.90192 7.09808i 0.0930261 0.347178i
\(419\) −20.7846 −1.01539 −0.507697 0.861536i \(-0.669503\pi\)
−0.507697 + 0.861536i \(0.669503\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 3.66025 13.6603i 0.178178 0.664971i
\(423\) 0 0
\(424\) −2.73205 + 0.732051i −0.132680 + 0.0355515i
\(425\) −3.00000 + 1.73205i −0.145521 + 0.0840168i
\(426\) −24.2487 24.2487i −1.17485 1.17485i
\(427\) 0 0
\(428\) −26.0000 −1.25676
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) −1.26795 4.73205i −0.0611459 0.228200i
\(431\) −19.9186 11.5000i −0.959444 0.553936i −0.0634424 0.997985i \(-0.520208\pi\)
−0.896002 + 0.444050i \(0.853541\pi\)
\(432\) −10.3923 18.0000i −0.500000 0.866025i
\(433\) 10.3923i 0.499422i −0.968320 0.249711i \(-0.919664\pi\)
0.968320 0.249711i \(-0.0803357\pi\)
\(434\) 0 0
\(435\) 12.0000i 0.575356i
\(436\) −15.5885 + 9.00000i −0.746552 + 0.431022i
\(437\) 4.50000 + 2.59808i 0.215264 + 0.124283i
\(438\) −20.4904 + 5.49038i −0.979068 + 0.262341i
\(439\) −11.2583 19.5000i −0.537331 0.930684i −0.999047 0.0436563i \(-0.986099\pi\)
0.461716 0.887028i \(-0.347234\pi\)
\(440\) −3.46410 3.46410i −0.165145 0.165145i
\(441\) 0 0
\(442\) 6.00000 6.00000i 0.285391 0.285391i
\(443\) −14.7224 + 8.50000i −0.699484 + 0.403847i −0.807155 0.590339i \(-0.798994\pi\)
0.107671 + 0.994187i \(0.465661\pi\)
\(444\) 9.00000 + 5.19615i 0.427121 + 0.246598i
\(445\) −13.5000 + 23.3827i −0.639961 + 1.10845i
\(446\) −9.46410 2.53590i −0.448138 0.120078i
\(447\) 1.73205 0.0819232
\(448\) 0 0
\(449\) 8.00000 0.377543 0.188772 0.982021i \(-0.439549\pi\)
0.188772 + 0.982021i \(0.439549\pi\)
\(450\) 0 0
\(451\) 1.73205 3.00000i 0.0815591 0.141264i
\(452\) −27.7128 16.0000i −1.30350 0.752577i
\(453\) 10.5000 6.06218i 0.493333 0.284826i
\(454\) 19.0526 19.0526i 0.894181 0.894181i
\(455\) 0 0
\(456\) 18.0000 + 18.0000i 0.842927 + 0.842927i
\(457\) −7.50000 12.9904i −0.350835 0.607664i 0.635561 0.772051i \(-0.280769\pi\)
−0.986396 + 0.164386i \(0.947436\pi\)
\(458\) −21.2942 + 5.70577i −0.995014 + 0.266613i
\(459\) −7.79423 4.50000i −0.363803 0.210042i
\(460\) 3.00000 1.73205i 0.139876 0.0807573i
\(461\) 17.3205i 0.806696i −0.915047 0.403348i \(-0.867846\pi\)
0.915047 0.403348i \(-0.132154\pi\)
\(462\) 0 0
\(463\) 30.0000i 1.39422i −0.716965 0.697109i \(-0.754469\pi\)
0.716965 0.697109i \(-0.245531\pi\)
\(464\) 8.00000 + 13.8564i 0.371391 + 0.643268i
\(465\) 4.50000 + 2.59808i 0.208683 + 0.120483i
\(466\) −2.56218 9.56218i −0.118691 0.442959i
\(467\) 4.33013 + 7.50000i 0.200374 + 0.347059i 0.948649 0.316330i \(-0.102451\pi\)
−0.748275 + 0.663389i \(0.769117\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 15.0000 + 15.0000i 0.691898 + 0.691898i
\(471\) 2.59808 1.50000i 0.119713 0.0691164i
\(472\) −14.1962 + 3.80385i −0.653431 + 0.175086i
\(473\) −1.00000 + 1.73205i −0.0459800 + 0.0796398i
\(474\) 5.70577 21.2942i 0.262075 0.978076i
\(475\) −10.3923 −0.476832
\(476\) 0 0
\(477\) 0 0
\(478\) 7.32051 27.3205i 0.334832 1.24961i
\(479\) 6.06218 10.5000i 0.276988 0.479757i −0.693647 0.720315i \(-0.743997\pi\)
0.970635 + 0.240558i \(0.0773304\pi\)
\(480\) 16.3923 4.39230i 0.748203 0.200480i
\(481\) 9.00000 5.19615i 0.410365 0.236924i
\(482\) −5.19615 5.19615i −0.236678 0.236678i
\(483\) 0 0
\(484\) 20.0000i 0.909091i
\(485\) −15.0000 25.9808i −0.681115 1.17973i
\(486\) 0 0
\(487\) 26.8468 + 15.5000i 1.21654 + 0.702372i 0.964177 0.265260i \(-0.0854576\pi\)
0.252367 + 0.967632i \(0.418791\pi\)
\(488\) −14.1962 3.80385i −0.642630 0.172192i
\(489\) 36.3731i 1.64485i
\(490\) 0 0
\(491\) 32.0000i 1.44414i 0.691820 + 0.722070i \(0.256809\pi\)
−0.691820 + 0.722070i \(0.743191\pi\)
\(492\) 6.00000 + 10.3923i 0.270501 + 0.468521i
\(493\) 6.00000 + 3.46410i 0.270226 + 0.156015i
\(494\) 24.5885 6.58846i 1.10629 0.296429i
\(495\) 0 0
\(496\) 6.92820 0.311086
\(497\) 0 0
\(498\) 24.0000 24.0000i 1.07547 1.07547i
\(499\) −30.3109 + 17.5000i −1.35690 + 0.783408i −0.989205 0.146538i \(-0.953187\pi\)
−0.367697 + 0.929946i \(0.619854\pi\)
\(500\) −12.1244 + 21.0000i −0.542218 + 0.939149i
\(501\) 15.0000 25.9808i 0.670151 1.16073i
\(502\) 4.73205 + 1.26795i 0.211202 + 0.0565913i
\(503\) −6.92820 −0.308913 −0.154457 0.988000i \(-0.549363\pi\)
−0.154457 + 0.988000i \(0.549363\pi\)
\(504\) 0 0
\(505\) 15.0000 0.667491
\(506\) −1.36603 0.366025i −0.0607272 0.0162718i
\(507\) −0.866025 + 1.50000i −0.0384615 + 0.0666173i
\(508\) −6.00000 + 10.3923i −0.266207 + 0.461084i
\(509\) −10.5000 + 6.06218i −0.465404 + 0.268701i −0.714314 0.699825i \(-0.753261\pi\)
0.248910 + 0.968527i \(0.419928\pi\)
\(510\) 5.19615 5.19615i 0.230089 0.230089i
\(511\) 0 0
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) −13.5000 23.3827i −0.596040 1.03237i
\(514\) 7.09808 1.90192i 0.313083 0.0838903i
\(515\) 12.9904 + 7.50000i 0.572425 + 0.330489i
\(516\) −3.46410 6.00000i −0.152499 0.264135i
\(517\) 8.66025i 0.380878i
\(518\) 0 0
\(519\) 21.0000i 0.921798i
\(520\) 4.39230 16.3923i 0.192615 0.718850i
\(521\) −1.50000 0.866025i −0.0657162 0.0379413i 0.466782 0.884372i \(-0.345413\pi\)
−0.532498 + 0.846431i \(0.678747\pi\)
\(522\) 0 0
\(523\) 12.9904 + 22.5000i 0.568030 + 0.983856i 0.996761 + 0.0804241i \(0.0256275\pi\)
−0.428731 + 0.903432i \(0.641039\pi\)
\(524\) 10.3923i 0.453990i
\(525\) 0 0
\(526\) −23.0000 23.0000i −1.00285 1.00285i
\(527\) 2.59808 1.50000i 0.113174 0.0653410i
\(528\) −6.00000 3.46410i −0.261116 0.150756i
\(529\) −11.0000 + 19.0526i −0.478261 + 0.828372i
\(530\) −0.633975 + 2.36603i −0.0275381 + 0.102774i
\(531\) 0 0
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) −9.88269 + 36.8827i −0.427666 + 1.59607i
\(535\) −11.2583 + 19.5000i −0.486740 + 0.843059i
\(536\) −2.19615 8.19615i −0.0948593 0.354020i
\(537\) 28.5000 16.4545i 1.22987 0.710063i
\(538\) 22.5167 + 22.5167i 0.970762 + 0.970762i
\(539\) 0 0
\(540\) −18.0000 −0.774597
\(541\) 9.50000 + 16.4545i 0.408437 + 0.707433i 0.994715 0.102677i \(-0.0327407\pi\)
−0.586278 + 0.810110i \(0.699407\pi\)
\(542\) −5.70577 21.2942i −0.245084 0.914665i
\(543\) −10.3923 6.00000i −0.445976 0.257485i
\(544\) 2.53590 9.46410i 0.108726 0.405770i
\(545\) 15.5885i 0.667736i
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −1.73205 + 1.00000i −0.0739895 + 0.0427179i
\(549\) 0 0
\(550\) 2.73205 0.732051i 0.116495 0.0312148i
\(551\) 10.3923 + 18.0000i 0.442727 + 0.766826i
\(552\) 3.46410 3.46410i 0.147442 0.147442i
\(553\) 0 0
\(554\) −13.0000 + 13.0000i −0.552317 + 0.552317i
\(555\) 7.79423 4.50000i 0.330847 0.191014i
\(556\) −12.0000 6.92820i −0.508913 0.293821i
\(557\) −18.5000 + 32.0429i −0.783870 + 1.35770i 0.145802 + 0.989314i \(0.453424\pi\)
−0.929672 + 0.368389i \(0.879909\pi\)
\(558\) 0 0
\(559\) −6.92820 −0.293032
\(560\) 0 0
\(561\) −3.00000 −0.126660
\(562\) 5.46410 + 1.46410i 0.230489 + 0.0617594i
\(563\) −11.2583 + 19.5000i −0.474482 + 0.821827i −0.999573 0.0292191i \(-0.990698\pi\)
0.525091 + 0.851046i \(0.324031\pi\)
\(564\) 25.9808 + 15.0000i 1.09399 + 0.631614i
\(565\) −24.0000 + 13.8564i −1.00969 + 0.582943i
\(566\) 12.1244 12.1244i 0.509625 0.509625i
\(567\) 0 0
\(568\) −28.0000 + 28.0000i −1.17485 + 1.17485i
\(569\) 6.50000 + 11.2583i 0.272494 + 0.471974i 0.969500 0.245092i \(-0.0788181\pi\)
−0.697006 + 0.717066i \(0.745485\pi\)
\(570\) 21.2942 5.70577i 0.891917 0.238988i
\(571\) 18.1865 + 10.5000i 0.761083 + 0.439411i 0.829684 0.558233i \(-0.188520\pi\)
−0.0686016 + 0.997644i \(0.521854\pi\)
\(572\) −6.00000 + 3.46410i −0.250873 + 0.144841i
\(573\) 1.73205i 0.0723575i
\(574\) 0 0
\(575\) 2.00000i 0.0834058i
\(576\) 0 0
\(577\) 28.5000 + 16.4545i 1.18647 + 0.685009i 0.957503 0.288425i \(-0.0931316\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 5.12436 + 19.1244i 0.213145 + 0.795468i
\(579\) 12.9904 + 22.5000i 0.539862 + 0.935068i
\(580\) 13.8564 0.575356
\(581\) 0 0
\(582\) −30.0000 30.0000i −1.24354 1.24354i
\(583\) 0.866025 0.500000i 0.0358671 0.0207079i
\(584\) 6.33975 + 23.6603i 0.262341 + 0.979068i
\(585\) 0 0
\(586\) −7.60770 + 28.3923i −0.314271 + 1.17288i
\(587\) 6.92820 0.285958 0.142979 0.989726i \(-0.454332\pi\)
0.142979 + 0.989726i \(0.454332\pi\)
\(588\) 0 0
\(589\) 9.00000 0.370839
\(590\) −3.29423 + 12.2942i −0.135621 + 0.506145i
\(591\) −13.8564 + 24.0000i −0.569976 + 0.987228i
\(592\) 6.00000 10.3923i 0.246598 0.427121i
\(593\) 13.5000 7.79423i 0.554379 0.320071i −0.196508 0.980502i \(-0.562960\pi\)
0.750886 + 0.660432i \(0.229627\pi\)
\(594\) 5.19615 + 5.19615i 0.213201 + 0.213201i
\(595\) 0 0
\(596\) 2.00000i 0.0819232i
\(597\) 19.5000 + 33.7750i 0.798082 + 1.38232i
\(598\) −1.26795 4.73205i −0.0518503 0.193508i
\(599\) −14.7224 8.50000i −0.601542 0.347301i 0.168106 0.985769i \(-0.446235\pi\)
−0.769648 + 0.638468i \(0.779568\pi\)
\(600\) −2.53590 + 9.46410i −0.103528 + 0.386370i
\(601\) 38.1051i 1.55434i 0.629291 + 0.777170i \(0.283346\pi\)
−0.629291 + 0.777170i \(0.716654\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −7.00000 12.1244i −0.284826 0.493333i
\(605\) −15.0000 8.66025i −0.609837 0.352089i
\(606\) 20.4904 5.49038i 0.832365 0.223031i
\(607\) −7.79423 13.5000i −0.316358 0.547948i 0.663367 0.748294i \(-0.269127\pi\)
−0.979725 + 0.200346i \(0.935793\pi\)
\(608\) 20.7846 20.7846i 0.842927 0.842927i
\(609\) 0 0
\(610\) −9.00000 + 9.00000i −0.364399 + 0.364399i
\(611\) 25.9808 15.0000i 1.05107 0.606835i
\(612\) 0 0
\(613\) 15.5000 26.8468i 0.626039 1.08433i −0.362300 0.932062i \(-0.618008\pi\)
0.988339 0.152270i \(-0.0486583\pi\)
\(614\) −28.3923 7.60770i −1.14582 0.307022i
\(615\) 10.3923 0.419058
\(616\) 0 0
\(617\) 20.0000 0.805170 0.402585 0.915383i \(-0.368112\pi\)
0.402585 + 0.915383i \(0.368112\pi\)
\(618\) 20.4904 + 5.49038i 0.824244 + 0.220856i
\(619\) −7.79423 + 13.5000i −0.313276 + 0.542611i −0.979070 0.203526i \(-0.934760\pi\)
0.665793 + 0.746136i \(0.268093\pi\)
\(620\) 3.00000 5.19615i 0.120483 0.208683i
\(621\) −4.50000 + 2.59808i −0.180579 + 0.104257i
\(622\) 8.66025 8.66025i 0.347245 0.347245i
\(623\) 0 0
\(624\) 24.0000i 0.960769i
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) 2.36603 0.633975i 0.0945654 0.0253387i
\(627\) −7.79423 4.50000i −0.311272 0.179713i
\(628\) −1.73205 3.00000i −0.0691164 0.119713i
\(629\) 5.19615i 0.207184i
\(630\) 0 0
\(631\) 30.0000i 1.19428i 0.802137 + 0.597141i \(0.203697\pi\)
−0.802137 + 0.597141i \(0.796303\pi\)
\(632\) −24.5885 6.58846i −0.978076 0.262075i
\(633\) −15.0000 8.66025i −0.596196 0.344214i
\(634\) 4.02628 + 15.0263i 0.159904 + 0.596770i
\(635\) 5.19615 + 9.00000i 0.206203 + 0.357154i
\(636\) 3.46410i 0.137361i
\(637\) 0 0
\(638\) −4.00000 4.00000i −0.158362 0.158362i
\(639\) 0 0
\(640\) −5.07180 18.9282i −0.200480 0.748203i
\(641\) 6.50000 11.2583i 0.256735 0.444677i −0.708631 0.705580i \(-0.750687\pi\)
0.965365 + 0.260902i \(0.0840201\pi\)
\(642\) −8.24167 + 30.7583i −0.325273 + 1.21393i
\(643\) −13.8564 −0.546443 −0.273222 0.961951i \(-0.588089\pi\)
−0.273222 + 0.961951i \(0.588089\pi\)
\(644\) 0 0
\(645\) −6.00000 −0.236250
\(646\) 3.29423 12.2942i 0.129610 0.483710i
\(647\) 16.4545 28.5000i 0.646892 1.12045i −0.336968 0.941516i \(-0.609402\pi\)
0.983861 0.178935i \(-0.0572651\pi\)
\(648\) −24.5885 + 6.58846i −0.965926 + 0.258819i
\(649\) 4.50000 2.59808i 0.176640 0.101983i
\(650\) 6.92820 + 6.92820i 0.271746 + 0.271746i
\(651\) 0 0
\(652\) 42.0000 1.64485
\(653\) −15.5000 26.8468i −0.606562 1.05060i −0.991803 0.127780i \(-0.959215\pi\)
0.385241 0.922816i \(-0.374118\pi\)
\(654\) 5.70577 + 21.2942i 0.223113 + 0.832670i
\(655\) −7.79423 4.50000i −0.304546 0.175830i
\(656\) 12.0000 6.92820i 0.468521 0.270501i
\(657\) 0 0
\(658\) 0 0
\(659\) 38.0000i 1.48027i −0.672458 0.740135i \(-0.734762\pi\)
0.672458 0.740135i \(-0.265238\pi\)
\(660\) −5.19615 + 3.00000i −0.202260 + 0.116775i
\(661\) 34.5000 + 19.9186i 1.34189 + 0.774743i 0.987085 0.160196i \(-0.0512125\pi\)
0.354809 + 0.934939i \(0.384546\pi\)
\(662\) 9.56218 2.56218i 0.371645 0.0995819i
\(663\) −5.19615 9.00000i −0.201802 0.349531i
\(664\) −27.7128 27.7128i −1.07547 1.07547i
\(665\) 0 0
\(666\) 0 0
\(667\) 3.46410 2.00000i 0.134131 0.0774403i
\(668\) −30.0000 17.3205i −1.16073 0.670151i
\(669\) −6.00000 + 10.3923i −0.231973 + 0.401790i
\(670\) −7.09808 1.90192i −0.274223 0.0734777i
\(671\) 5.19615 0.200595
\(672\) 0 0
\(673\) 24.0000 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) 0 0
\(675\) 5.19615 9.00000i 0.200000 0.346410i
\(676\) 1.73205 + 1.00000i 0.0666173 + 0.0384615i
\(677\) 37.5000 21.6506i 1.44124 0.832102i 0.443309 0.896369i \(-0.353804\pi\)
0.997933 + 0.0642672i \(0.0204710\pi\)
\(678\) −27.7128 + 27.7128i −1.06430 + 1.06430i
\(679\) 0 0
\(680\) −6.00000 6.00000i −0.230089 0.230089i
\(681\) −16.5000 28.5788i −0.632281 1.09514i
\(682\) −2.36603 + 0.633975i −0.0905998 + 0.0242761i
\(683\) 21.6506 + 12.5000i 0.828439 + 0.478299i 0.853318 0.521391i \(-0.174587\pi\)
−0.0248792 + 0.999690i \(0.507920\pi\)
\(684\) 0 0
\(685\) 1.73205i 0.0661783i
\(686\) 0 0
\(687\) 27.0000i 1.03011i
\(688\) −6.92820 + 4.00000i −0.264135 + 0.152499i
\(689\) 3.00000 + 1.73205i 0.114291 + 0.0659859i
\(690\) −1.09808 4.09808i −0.0418030 0.156011i
\(691\) −6.06218 10.5000i −0.230616 0.399439i 0.727373 0.686242i \(-0.240741\pi\)
−0.957990 + 0.286803i \(0.907407\pi\)
\(692\) 24.2487 0.921798
\(693\) 0 0
\(694\) 13.0000 + 13.0000i 0.493473 + 0.493473i
\(695\) −10.3923 + 6.00000i −0.394203 + 0.227593i
\(696\) 18.9282 5.07180i 0.717472 0.192246i
\(697\) 3.00000 5.19615i 0.113633 0.196818i
\(698\) 3.80385 14.1962i 0.143978 0.537332i
\(699\) −12.1244 −0.458585
\(700\) 0 0
\(701\) −26.0000 −0.982006 −0.491003 0.871158i \(-0.663370\pi\)
−0.491003 + 0.871158i \(0.663370\pi\)
\(702\) −6.58846 + 24.5885i −0.248665 + 0.928032i
\(703\) 7.79423 13.5000i 0.293965 0.509162i
\(704\) −4.00000 + 6.92820i −0.150756 + 0.261116i
\(705\) 22.5000 12.9904i 0.847399 0.489246i
\(706\) −29.4449 29.4449i −1.10817 1.10817i
\(707\) 0 0
\(708\) 18.0000i 0.676481i
\(709\) 4.50000 + 7.79423i 0.169001 + 0.292718i 0.938069 0.346449i \(-0.112613\pi\)
−0.769068 + 0.639167i \(0.779279\pi\)
\(710\) 8.87564 + 33.1244i 0.333097 + 1.24313i
\(711\) 0 0
\(712\) 42.5885 + 11.4115i 1.59607 + 0.427666i
\(713\) 1.73205i 0.0648658i
\(714\) 0 0
\(715\) 6.00000i 0.224387i
\(716\) −19.0000 32.9090i −0.710063 1.22987i
\(717\) −30.0000 17.3205i −1.12037 0.646846i
\(718\) −31.4186 + 8.41858i −1.17253 + 0.314179i
\(719\) −12.9904 22.5000i −0.484459 0.839108i 0.515381 0.856961i \(-0.327650\pi\)
−0.999841 + 0.0178527i \(0.994317\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 8.00000 8.00000i 0.297729 0.297729i
\(723\) −7.79423 + 4.50000i −0.289870 + 0.167357i
\(724\) −6.92820 + 12.0000i −0.257485 + 0.445976i
\(725\) −4.00000 + 6.92820i −0.148556 + 0.257307i
\(726\) −23.6603 6.33975i −0.878114 0.235290i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 20.4904 + 5.49038i 0.758383 + 0.203208i
\(731\) −1.73205 + 3.00000i −0.0640622 + 0.110959i
\(732\) −9.00000 + 15.5885i −0.332650 + 0.576166i
\(733\) −37.5000 + 21.6506i −1.38509 + 0.799684i −0.992757 0.120137i \(-0.961667\pi\)
−0.392337 + 0.919822i \(0.628333\pi\)
\(734\) 1.73205 1.73205i 0.0639312 0.0639312i
\(735\) 0 0
\(736\) −4.00000 4.00000i −0.147442 0.147442i
\(737\) 1.50000 + 2.59808i 0.0552532 + 0.0957014i
\(738\) 0 0
\(739\) −44.1673 25.5000i −1.62472 0.938033i −0.985634 0.168898i \(-0.945979\pi\)
−0.639087 0.769135i \(-0.720687\pi\)
\(740\) −5.19615 9.00000i −0.191014 0.330847i
\(741\) 31.1769i 1.14531i
\(742\) 0 0
\(743\) 34.0000i 1.24734i −0.781688 0.623670i \(-0.785641\pi\)
0.781688 0.623670i \(-0.214359\pi\)
\(744\) 2.19615 8.19615i 0.0805149 0.300486i
\(745\) −1.50000 0.866025i −0.0549557 0.0317287i
\(746\) −10.6147 39.6147i −0.388633 1.45040i
\(747\) 0 0
\(748\) 3.46410i 0.126660i
\(749\) 0 0
\(750\) 21.0000 + 21.0000i 0.766812 + 0.766812i
\(751\) −21.6506 + 12.5000i −0.790043 + 0.456131i −0.839978 0.542621i \(-0.817432\pi\)
0.0499348 + 0.998752i \(0.484099\pi\)
\(752\) 17.3205 30.0000i 0.631614 1.09399i
\(753\) 3.00000 5.19615i 0.109326 0.189358i
\(754\) 5.07180 18.9282i 0.184704 0.689325i
\(755\) −12.1244 −0.441250
\(756\) 0 0
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) −2.92820 + 10.9282i −0.106357 + 0.396930i
\(759\) −0.866025 + 1.50000i −0.0314347 + 0.0544466i
\(760\) −6.58846 24.5885i −0.238988 0.891917i
\(761\) −16.5000 + 9.52628i −0.598125 + 0.345327i −0.768303 0.640086i \(-0.778899\pi\)
0.170179 + 0.985413i \(0.445565\pi\)
\(762\) 10.3923 + 10.3923i 0.376473 + 0.376473i
\(763\) 0 0
\(764\) −2.00000 −0.0723575
\(765\) 0 0
\(766\) −1.90192 7.09808i −0.0687193 0.256464i
\(767\) 15.5885 + 9.00000i 0.562867 + 0.324971i
\(768\) −13.8564 24.0000i −0.500000 0.866025i
\(769\) 3.46410i 0.124919i −0.998048 0.0624593i \(-0.980106\pi\)
0.998048 0.0624593i \(-0.0198944\pi\)
\(770\) 0 0
\(771\) 9.00000i 0.324127i
\(772\) 25.9808 15.0000i 0.935068 0.539862i
\(773\) −22.5000 12.9904i −0.809269 0.467232i 0.0374331 0.999299i \(-0.488082\pi\)
−0.846702 + 0.532068i \(0.821415\pi\)
\(774\) 0 0
\(775\) 1.73205 + 3.00000i 0.0622171 + 0.107763i
\(776\) −34.6410 + 34.6410i −1.24354 + 1.24354i
\(777\) 0 0
\(778\) −19.0000 + 19.0000i −0.681183 + 0.681183i
\(779\) 15.5885 9.00000i 0.558514 0.322458i
\(780\) −18.0000 10.3923i −0.644503 0.372104i
\(781\) 7.00000 12.1244i 0.250480 0.433844i
\(782\) −2.36603 0.633975i −0.0846089 0.0226709i
\(783\) −20.7846 −0.742781
\(784\) 0 0
\(785\) −3.00000 −0.107075
\(786\) −12.2942 3.29423i −0.438521 0.117501i
\(787\) 2.59808 4.50000i 0.0926114 0.160408i −0.815998 0.578055i \(-0.803812\pi\)
0.908609 + 0.417647i \(0.137145\pi\)
\(788\) 27.7128 + 16.0000i 0.987228 + 0.569976i
\(789\) −34.5000 + 19.9186i −1.22823 + 0.709120i
\(790\) −15.5885 + 15.5885i −0.554612 + 0.554612i
\(791\) 0 0
\(792\) 0 0
\(793\) 9.00000 + 15.5885i 0.319599 + 0.553562i
\(794\) 26.0263 6.97372i 0.923638 0.247488i
\(795\) 2.59808 + 1.50000i 0.0921443 + 0.0531995i
\(796\) 39.0000 22.5167i 1.38232 0.798082i
\(797\) 10.3923i 0.368114i −0.982916 0.184057i \(-0.941077\pi\)
0.982916 0.184057i \(-0.0589232\pi\)
\(798\) 0 0
\(799\) 15.0000i 0.530662i
\(800\) 10.9282 + 2.92820i 0.386370 + 0.103528i
\(801\) 0 0
\(802\) −8.41858 31.4186i −0.297271 1.10943i
\(803\) −4.33013 7.50000i −0.152807 0.264669i
\(804\) −10.3923 −0.366508
\(805\) 0 0
\(806\) −6.00000 6.00000i −0.211341 0.211341i
\(807\) 33.7750 19.5000i 1.18894 0.686433i
\(808\) −6.33975 23.6603i −0.223031 0.832365i
\(809\) −21.5000 + 37.2391i −0.755900 + 1.30926i 0.189026 + 0.981972i \(0.439467\pi\)
−0.944926 + 0.327285i \(0.893866\pi\)
\(810\) −5.70577 + 21.2942i −0.200480 + 0.748203i
\(811\) 13.8564 0.486564 0.243282 0.969956i \(-0.421776\pi\)
0.243282 + 0.969956i \(0.421776\pi\)
\(812\) 0 0
\(813\) −27.0000 −0.946931
\(814\) −1.09808 + 4.09808i −0.0384876 + 0.143637i
\(815\) 18.1865 31.5000i 0.637046 1.10340i
\(816\) −10.3923 6.00000i −0.363803 0.210042i
\(817\) −9.00000 + 5.19615i −0.314870 + 0.181790i
\(818\) 25.9808 + 25.9808i 0.908396 + 0.908396i
\(819\) 0 0
\(820\) 12.0000i 0.419058i
\(821\) 5.50000 + 9.52628i 0.191951 + 0.332469i 0.945897 0.324468i \(-0.105185\pi\)
−0.753946 + 0.656937i \(0.771852\pi\)
\(822\) 0.633975 + 2.36603i 0.0221124 + 0.0825246i
\(823\) −7.79423 4.50000i −0.271690 0.156860i 0.357966 0.933735i \(-0.383471\pi\)
−0.629655 + 0.776875i \(0.716804\pi\)
\(824\) 6.33975 23.6603i 0.220856 0.824244i
\(825\) 3.46410i 0.120605i
\(826\) 0 0
\(827\) 22.0000i 0.765015i 0.923952 + 0.382507i \(0.124939\pi\)
−0.923952 + 0.382507i \(0.875061\pi\)
\(828\) 0 0
\(829\) 7.50000 + 4.33013i 0.260486 + 0.150392i 0.624556 0.780980i \(-0.285280\pi\)
−0.364070 + 0.931371i \(0.618613\pi\)
\(830\) −32.7846 + 8.78461i −1.13797 + 0.304918i
\(831\) 11.2583 + 19.5000i 0.390547 + 0.676448i
\(832\) −27.7128 −0.960769
\(833\) 0 0
\(834\) −12.0000 + 12.0000i −0.415526 + 0.415526i
\(835\) −25.9808 + 15.0000i −0.899101 + 0.519096i
\(836\) −5.19615 + 9.00000i −0.179713 + 0.311272i
\(837\) −4.50000 + 7.79423i −0.155543 + 0.269408i
\(838\) 28.3923 + 7.60770i 0.980796 + 0.262803i
\(839\) 48.4974 1.67432 0.837158 0.546960i \(-0.184215\pi\)
0.837158 + 0.546960i \(0.184215\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 27.3205 + 7.32051i 0.941527 + 0.252281i
\(843\) 3.46410 6.00000i 0.119310 0.206651i
\(844\) −10.0000 + 17.3205i −0.344214 + 0.596196i
\(845\) 1.50000 0.866025i 0.0516016 0.0297922i
\(846\) 0 0
\(847\) 0 0
\(848\) 4.00000 0.137361
\(849\) −10.5000 18.1865i −0.360359 0.624160i
\(850\) 4.73205 1.26795i 0.162308 0.0434903i
\(851\) −2.59808 1.50000i −0.0890609 0.0514193i
\(852\) 24.2487 + 42.0000i 0.830747 + 1.43890i
\(853\) 24.2487i 0.830260i −0.909762 0.415130i \(-0.863736\pi\)
0.909762 0.415130i \(-0.136264\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 35.5167 + 9.51666i 1.21393 + 0.325273i
\(857\) 22.5000 + 12.9904i 0.768585 + 0.443743i 0.832370 0.554221i \(-0.186984\pi\)
−0.0637844 + 0.997964i \(0.520317\pi\)
\(858\) 2.19615 + 8.19615i 0.0749754 + 0.279812i
\(859\) −25.1147 43.5000i −0.856904 1.48420i −0.874868 0.484362i \(-0.839052\pi\)
0.0179638 0.999839i \(-0.494282\pi\)
\(860\) 6.92820i 0.236250i
\(861\) 0 0
\(862\) 23.0000 + 23.0000i 0.783383 + 0.783383i
\(863\) −30.3109 + 17.5000i −1.03179 + 0.595707i −0.917498 0.397740i \(-0.869795\pi\)
−0.114296 + 0.993447i \(0.536461\pi\)
\(864\) 7.60770 + 28.3923i 0.258819 + 0.965926i
\(865\) 10.5000 18.1865i 0.357011 0.618361i
\(866\) −3.80385 + 14.1962i −0.129260 + 0.482405i
\(867\) 24.2487 0.823529
\(868\) 0 0
\(869\) 9.00000 0.305304
\(870\) 4.39230 16.3923i 0.148913 0.555751i
\(871\) −5.19615 + 9.00000i −0.176065 + 0.304953i
\(872\) 24.5885 6.58846i 0.832670 0.223113i
\(873\) 0 0
\(874\) −5.19615 5.19615i −0.175762 0.175762i
\(875\) 0 0
\(876\) 30.0000 1.01361
\(877\) −0.500000 0.866025i −0.0168838 0.0292436i 0.857460 0.514551i \(-0.172041\pi\)
−0.874344 + 0.485307i \(0.838708\pi\)
\(878\) 8.24167 + 30.7583i 0.278143 + 1.03804i
\(879\) 31.1769 + 18.0000i 1.05157 + 0.607125i
\(880\) 3.46410 + 6.00000i 0.116775 + 0.202260i
\(881\) 13.8564i 0.466834i 0.972377 + 0.233417i \(0.0749907\pi\)
−0.972377 + 0.233417i \(0.925009\pi\)
\(882\) 0 0
\(883\) 10.0000i 0.336527i −0.985742 0.168263i \(-0.946184\pi\)
0.985742 0.168263i \(-0.0538159\pi\)
\(884\) −10.3923 + 6.00000i −0.349531 + 0.201802i
\(885\) 13.5000 + 7.79423i 0.453798 + 0.262000i
\(886\) 23.2224 6.22243i 0.780173 0.209047i
\(887\) 12.9904 + 22.5000i 0.436174 + 0.755476i 0.997391 0.0721931i \(-0.0229998\pi\)
−0.561216 + 0.827669i \(0.689666\pi\)
\(888\) −10.3923 10.3923i −0.348743 0.348743i
\(889\) 0 0
\(890\) 27.0000 27.0000i 0.905042 0.905042i
\(891\) 7.79423 4.50000i 0.261116 0.150756i
\(892\) 12.0000 + 6.92820i 0.401790 + 0.231973i
\(893\) 22.5000 38.9711i 0.752934 1.30412i
\(894\) −2.36603 0.633975i −0.0791317 0.0212033i
\(895\) −32.9090 −1.10003
\(896\) 0 0
\(897\) −6.00000 −0.200334
\(898\) −10.9282 2.92820i −0.364679 0.0977154i
\(899\) 3.46410 6.00000i 0.115534 0.200111i
\(900\) 0 0
\(901\) 1.50000 0.866025i 0.0499722 0.0288515i
\(902\) −3.46410 + 3.46410i −0.115342 + 0.115342i
\(903\) 0 0
\(904\) 32.0000 + 32.0000i 1.06430 + 1.06430i
\(905\) 6.00000 + 10.3923i 0.199447 + 0.345452i
\(906\) −16.5622 + 4.43782i −0.550242 + 0.147437i
\(907\) 6.06218 + 3.50000i 0.201291 + 0.116216i 0.597258 0.802049i \(-0.296257\pi\)
−0.395966 + 0.918265i \(0.629590\pi\)
\(908\) −33.0000 + 19.0526i −1.09514 + 0.632281i
\(909\) 0 0
\(910\) 0 0
\(911\) 26.0000i 0.861418i −0.902491 0.430709i \(-0.858263\pi\)
0.902491 0.430709i \(-0.141737\pi\)
\(912\) −18.0000 31.1769i −0.596040 1.03237i
\(913\) 12.0000 + 6.92820i 0.397142 + 0.229290i
\(914\) 5.49038 + 20.4904i 0.181606 + 0.677762i
\(915\) 7.79423 + 13.5000i 0.257669 + 0.446296i
\(916\) 31.1769 1.03011
\(917\) 0 0
\(918\) 9.00000 + 9.00000i 0.297044 + 0.297044i
\(919\) −0.866025 + 0.500000i −0.0285675 + 0.0164935i −0.514216 0.857661i \(-0.671917\pi\)
0.485648 + 0.874154i \(0.338584\pi\)
\(920\) −4.73205 + 1.26795i −0.156011 + 0.0418030i
\(921\) −18.0000 + 31.1769i −0.593120 + 1.02731i
\(922\) −6.33975 + 23.6603i −0.208788 + 0.779209i
\(923\) 48.4974 1.59631
\(924\) 0 0
\(925\) 6.00000 0.197279
\(926\) −10.9808 + 40.9808i −0.360850 + 1.34671i
\(927\) 0 0
\(928\) −5.85641 21.8564i −0.192246 0.717472i
\(929\) −7.50000 + 4.33013i −0.246067 + 0.142067i −0.617962 0.786208i \(-0.712041\pi\)
0.371895 + 0.928275i \(0.378708\pi\)
\(930\) −5.19615 5.19615i −0.170389 0.170389i
\(931\) 0 0
\(932\) 14.0000i 0.458585i
\(933\) −7.50000 12.9904i −0.245539 0.425286i
\(934\) −3.16987 11.8301i −0.103721 0.387094i
\(935\) 2.59808 + 1.50000i 0.0849662 + 0.0490552i
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 3.00000i 0.0979013i
\(940\) −15.0000 25.9808i −0.489246 0.847399i
\(941\) −49.5000 28.5788i −1.61365 0.931644i −0.988514 0.151131i \(-0.951708\pi\)
−0.625140 0.780513i \(-0.714958\pi\)
\(942\) −4.09808 + 1.09808i −0.133523 + 0.0357773i
\(943\) −1.73205 3.00000i −0.0564033 0.0976934i
\(944\) 20.7846 0.676481
\(945\) 0 0
\(946\) 2.00000 2.00000i 0.0650256 0.0650256i
\(947\) 25.1147 14.5000i 0.816119 0.471187i −0.0329571 0.999457i \(-0.510492\pi\)
0.849076 + 0.528270i \(0.177159\pi\)
\(948\) −15.5885 + 27.0000i −0.506290 + 0.876919i
\(949\) 15.0000 25.9808i 0.486921 0.843371i
\(950\) 14.1962 + 3.80385i 0.460584 + 0.123413i
\(951\) 19.0526 0.617822
\(952\) 0 0
\(953\) −8.00000 −0.259145 −0.129573 0.991570i \(-0.541361\pi\)
−0.129573 + 0.991570i \(0.541361\pi\)
\(954\) 0 0
\(955\) −0.866025 + 1.50000i −0.0280239 + 0.0485389i
\(956\) −20.0000 + 34.6410i −0.646846 + 1.12037i
\(957\) −6.00000 + 3.46410i −0.193952 + 0.111979i
\(958\) −12.1244 + 12.1244i −0.391720 + 0.391720i
\(959\) 0 0
\(960\) −24.0000 −0.774597
\(961\) 14.0000 + 24.2487i 0.451613 + 0.782216i
\(962\) −14.1962 + 3.80385i −0.457702 + 0.122641i
\(963\) 0 0
\(964\) 5.19615 + 9.00000i 0.167357 + 0.289870i
\(965\) 25.9808i 0.836350i
\(966\) 0 0
\(967\) 6.00000i 0.192947i −0.995336 0.0964735i \(-0.969244\pi\)
0.995336 0.0964735i \(-0.0307563\pi\)
\(968\) −7.32051 + 27.3205i −0.235290 + 0.878114i
\(969\) −13.5000 7.79423i −0.433682 0.250387i
\(970\) 10.9808 + 40.9808i 0.352571 + 1.31581i
\(971\) −30.3109 52.5000i −0.972723 1.68481i −0.687254 0.726417i \(-0.741184\pi\)
−0.285469 0.958388i \(-0.592149\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −31.0000 31.0000i −0.993304 0.993304i
\(975\) 10.3923 6.00000i 0.332820 0.192154i
\(976\) 18.0000 + 10.3923i 0.576166 + 0.332650i
\(977\) 15.5000 26.8468i 0.495889 0.858905i −0.504100 0.863645i \(-0.668176\pi\)
0.999989 + 0.00474056i \(0.00150897\pi\)
\(978\) 13.3135 49.6865i 0.425718 1.58880i
\(979\) −15.5885 −0.498209
\(980\) 0 0
\(981\) 0 0
\(982\) 11.7128 43.7128i 0.373771 1.39493i
\(983\) −30.3109 + 52.5000i −0.966767 + 1.67449i −0.261977 + 0.965074i \(0.584374\pi\)
−0.704790 + 0.709416i \(0.748959\pi\)
\(984\) −4.39230 16.3923i −0.140022 0.522568i
\(985\) 24.0000 13.8564i 0.764704 0.441502i
\(986\) −6.92820 6.92820i −0.220639 0.220639i
\(987\) 0 0
\(988\) −36.0000 −1.14531
\(989\) 1.00000 + 1.73205i 0.0317982 + 0.0550760i
\(990\) 0 0
\(991\) 19.9186 + 11.5000i 0.632735 + 0.365310i 0.781810 0.623516i \(-0.214296\pi\)
−0.149076 + 0.988826i \(0.547630\pi\)
\(992\) −9.46410 2.53590i −0.300486 0.0805149i
\(993\) 12.1244i 0.384755i
\(994\) 0 0
\(995\) 39.0000i 1.23638i
\(996\) −41.5692 + 24.0000i −1.31717 + 0.760469i
\(997\) −19.5000 11.2583i −0.617571 0.356555i 0.158352 0.987383i \(-0.449382\pi\)
−0.775923 + 0.630828i \(0.782715\pi\)
\(998\) 47.8109 12.8109i 1.51343 0.405522i
\(999\) 7.79423 + 13.5000i 0.246598 + 0.427121i
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 196.2.f.a.31.1 4
4.3 odd 2 inner 196.2.f.a.31.2 4
7.2 even 3 28.2.f.a.19.2 yes 4
7.3 odd 6 196.2.d.b.195.1 4
7.4 even 3 196.2.d.b.195.2 4
7.5 odd 6 inner 196.2.f.a.19.2 4
7.6 odd 2 28.2.f.a.3.1 4
21.2 odd 6 252.2.bf.e.19.1 4
21.11 odd 6 1764.2.b.a.1567.3 4
21.17 even 6 1764.2.b.a.1567.4 4
21.20 even 2 252.2.bf.e.199.2 4
28.3 even 6 196.2.d.b.195.4 4
28.11 odd 6 196.2.d.b.195.3 4
28.19 even 6 inner 196.2.f.a.19.1 4
28.23 odd 6 28.2.f.a.19.1 yes 4
28.27 even 2 28.2.f.a.3.2 yes 4
35.2 odd 12 700.2.t.a.299.1 4
35.9 even 6 700.2.p.a.551.1 4
35.13 even 4 700.2.t.b.199.1 4
35.23 odd 12 700.2.t.b.299.2 4
35.27 even 4 700.2.t.a.199.2 4
35.34 odd 2 700.2.p.a.451.2 4
56.3 even 6 3136.2.f.e.3135.2 4
56.11 odd 6 3136.2.f.e.3135.3 4
56.13 odd 2 448.2.p.d.255.1 4
56.27 even 2 448.2.p.d.255.2 4
56.37 even 6 448.2.p.d.383.2 4
56.45 odd 6 3136.2.f.e.3135.4 4
56.51 odd 6 448.2.p.d.383.1 4
56.53 even 6 3136.2.f.e.3135.1 4
84.11 even 6 1764.2.b.a.1567.1 4
84.23 even 6 252.2.bf.e.19.2 4
84.59 odd 6 1764.2.b.a.1567.2 4
84.83 odd 2 252.2.bf.e.199.1 4
140.23 even 12 700.2.t.a.299.2 4
140.27 odd 4 700.2.t.b.199.2 4
140.79 odd 6 700.2.p.a.551.2 4
140.83 odd 4 700.2.t.a.199.1 4
140.107 even 12 700.2.t.b.299.1 4
140.139 even 2 700.2.p.a.451.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.2.f.a.3.1 4 7.6 odd 2
28.2.f.a.3.2 yes 4 28.27 even 2
28.2.f.a.19.1 yes 4 28.23 odd 6
28.2.f.a.19.2 yes 4 7.2 even 3
196.2.d.b.195.1 4 7.3 odd 6
196.2.d.b.195.2 4 7.4 even 3
196.2.d.b.195.3 4 28.11 odd 6
196.2.d.b.195.4 4 28.3 even 6
196.2.f.a.19.1 4 28.19 even 6 inner
196.2.f.a.19.2 4 7.5 odd 6 inner
196.2.f.a.31.1 4 1.1 even 1 trivial
196.2.f.a.31.2 4 4.3 odd 2 inner
252.2.bf.e.19.1 4 21.2 odd 6
252.2.bf.e.19.2 4 84.23 even 6
252.2.bf.e.199.1 4 84.83 odd 2
252.2.bf.e.199.2 4 21.20 even 2
448.2.p.d.255.1 4 56.13 odd 2
448.2.p.d.255.2 4 56.27 even 2
448.2.p.d.383.1 4 56.51 odd 6
448.2.p.d.383.2 4 56.37 even 6
700.2.p.a.451.1 4 140.139 even 2
700.2.p.a.451.2 4 35.34 odd 2
700.2.p.a.551.1 4 35.9 even 6
700.2.p.a.551.2 4 140.79 odd 6
700.2.t.a.199.1 4 140.83 odd 4
700.2.t.a.199.2 4 35.27 even 4
700.2.t.a.299.1 4 35.2 odd 12
700.2.t.a.299.2 4 140.23 even 12
700.2.t.b.199.1 4 35.13 even 4
700.2.t.b.199.2 4 140.27 odd 4
700.2.t.b.299.1 4 140.107 even 12
700.2.t.b.299.2 4 35.23 odd 12
1764.2.b.a.1567.1 4 84.11 even 6
1764.2.b.a.1567.2 4 84.59 odd 6
1764.2.b.a.1567.3 4 21.11 odd 6
1764.2.b.a.1567.4 4 21.17 even 6
3136.2.f.e.3135.1 4 56.53 even 6
3136.2.f.e.3135.2 4 56.3 even 6
3136.2.f.e.3135.3 4 56.11 odd 6
3136.2.f.e.3135.4 4 56.45 odd 6