Properties

Label 1155.2.i.b.76.3
Level $1155$
Weight $2$
Character 1155.76
Analytic conductor $9.223$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1155,2,Mod(76,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("1155.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.i (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: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.3
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1155.76
Dual form 1155.2.i.b.76.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.517638i q^{2} -1.00000i q^{3} +1.73205 q^{4} +1.00000i q^{5} -0.517638 q^{6} +(-2.63896 + 0.189469i) q^{7} -1.93185i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-0.517638i q^{2} -1.00000i q^{3} +1.73205 q^{4} +1.00000i q^{5} -0.517638 q^{6} +(-2.63896 + 0.189469i) q^{7} -1.93185i q^{8} -1.00000 q^{9} +0.517638 q^{10} +(-3.00000 - 1.41421i) q^{11} -1.73205i q^{12} -4.24264 q^{13} +(0.0980762 + 1.36603i) q^{14} +1.00000 q^{15} +2.46410 q^{16} -2.44949 q^{17} +0.517638i q^{18} -1.03528 q^{19} +1.73205i q^{20} +(0.189469 + 2.63896i) q^{21} +(-0.732051 + 1.55291i) q^{22} -4.00000 q^{23} -1.93185 q^{24} -1.00000 q^{25} +2.19615i q^{26} +1.00000i q^{27} +(-4.57081 + 0.328169i) q^{28} -1.03528i q^{29} -0.517638i q^{30} +2.92820i q^{31} -5.13922i q^{32} +(-1.41421 + 3.00000i) q^{33} +1.26795i q^{34} +(-0.189469 - 2.63896i) q^{35} -1.73205 q^{36} -0.535898 q^{37} +0.535898i q^{38} +4.24264i q^{39} +1.93185 q^{40} -6.69213 q^{41} +(1.36603 - 0.0980762i) q^{42} -2.44949i q^{43} +(-5.19615 - 2.44949i) q^{44} -1.00000i q^{45} +2.07055i q^{46} -2.92820i q^{47} -2.46410i q^{48} +(6.92820 - 1.00000i) q^{49} +0.517638i q^{50} +2.44949i q^{51} -7.34847 q^{52} -3.46410 q^{53} +0.517638 q^{54} +(1.41421 - 3.00000i) q^{55} +(0.366025 + 5.09808i) q^{56} +1.03528i q^{57} -0.535898 q^{58} -12.9282i q^{59} +1.73205 q^{60} +4.89898 q^{61} +1.51575 q^{62} +(2.63896 - 0.189469i) q^{63} +2.26795 q^{64} -4.24264i q^{65} +(1.55291 + 0.732051i) q^{66} -5.46410 q^{67} -4.24264 q^{68} +4.00000i q^{69} +(-1.36603 + 0.0980762i) q^{70} +6.92820 q^{71} +1.93185i q^{72} +0.656339 q^{73} +0.277401i q^{74} +1.00000i q^{75} -1.79315 q^{76} +(8.18482 + 3.16364i) q^{77} +2.19615 q^{78} +3.86370i q^{79} +2.46410i q^{80} +1.00000 q^{81} +3.46410i q^{82} -1.41421 q^{83} +(0.328169 + 4.57081i) q^{84} -2.44949i q^{85} -1.26795 q^{86} -1.03528 q^{87} +(-2.73205 + 5.79555i) q^{88} -4.92820i q^{89} -0.517638 q^{90} +(11.1962 - 0.803848i) q^{91} -6.92820 q^{92} +2.92820 q^{93} -1.51575 q^{94} -1.03528i q^{95} -5.13922 q^{96} +4.92820i q^{97} +(-0.517638 - 3.58630i) q^{98} +(3.00000 + 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{9} - 24 q^{11} - 20 q^{14} + 8 q^{15} - 8 q^{16} + 8 q^{22} - 32 q^{23} - 8 q^{25} - 32 q^{37} + 4 q^{42} - 4 q^{56} - 32 q^{58} + 32 q^{64} - 16 q^{67} - 4 q^{70} + 16 q^{77} - 24 q^{78} + 8 q^{81} - 24 q^{86} - 8 q^{88} + 48 q^{91} - 32 q^{93} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.517638i 0.366025i −0.983111 0.183013i \(-0.941415\pi\)
0.983111 0.183013i \(-0.0585849\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 1.73205 0.866025
\(5\) 1.00000i 0.447214i
\(6\) −0.517638 −0.211325
\(7\) −2.63896 + 0.189469i −0.997433 + 0.0716124i
\(8\) 1.93185i 0.683013i
\(9\) −1.00000 −0.333333
\(10\) 0.517638 0.163692
\(11\) −3.00000 1.41421i −0.904534 0.426401i
\(12\) 1.73205i 0.500000i
\(13\) −4.24264 −1.17670 −0.588348 0.808608i \(-0.700222\pi\)
−0.588348 + 0.808608i \(0.700222\pi\)
\(14\) 0.0980762 + 1.36603i 0.0262120 + 0.365086i
\(15\) 1.00000 0.258199
\(16\) 2.46410 0.616025
\(17\) −2.44949 −0.594089 −0.297044 0.954864i \(-0.596001\pi\)
−0.297044 + 0.954864i \(0.596001\pi\)
\(18\) 0.517638i 0.122008i
\(19\) −1.03528 −0.237509 −0.118754 0.992924i \(-0.537890\pi\)
−0.118754 + 0.992924i \(0.537890\pi\)
\(20\) 1.73205i 0.387298i
\(21\) 0.189469 + 2.63896i 0.0413455 + 0.575868i
\(22\) −0.732051 + 1.55291i −0.156074 + 0.331082i
\(23\) −4.00000 −0.834058 −0.417029 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) −1.93185 −0.394338
\(25\) −1.00000 −0.200000
\(26\) 2.19615i 0.430701i
\(27\) 1.00000i 0.192450i
\(28\) −4.57081 + 0.328169i −0.863802 + 0.0620182i
\(29\) 1.03528i 0.192246i −0.995369 0.0961230i \(-0.969356\pi\)
0.995369 0.0961230i \(-0.0306442\pi\)
\(30\) 0.517638i 0.0945074i
\(31\) 2.92820i 0.525921i 0.964807 + 0.262960i \(0.0846989\pi\)
−0.964807 + 0.262960i \(0.915301\pi\)
\(32\) 5.13922i 0.908494i
\(33\) −1.41421 + 3.00000i −0.246183 + 0.522233i
\(34\) 1.26795i 0.217451i
\(35\) −0.189469 2.63896i −0.0320261 0.446065i
\(36\) −1.73205 −0.288675
\(37\) −0.535898 −0.0881012 −0.0440506 0.999029i \(-0.514026\pi\)
−0.0440506 + 0.999029i \(0.514026\pi\)
\(38\) 0.535898i 0.0869342i
\(39\) 4.24264i 0.679366i
\(40\) 1.93185 0.305453
\(41\) −6.69213 −1.04514 −0.522568 0.852598i \(-0.675026\pi\)
−0.522568 + 0.852598i \(0.675026\pi\)
\(42\) 1.36603 0.0980762i 0.210782 0.0151335i
\(43\) 2.44949i 0.373544i −0.982403 0.186772i \(-0.940197\pi\)
0.982403 0.186772i \(-0.0598025\pi\)
\(44\) −5.19615 2.44949i −0.783349 0.369274i
\(45\) 1.00000i 0.149071i
\(46\) 2.07055i 0.305286i
\(47\) 2.92820i 0.427122i −0.976930 0.213561i \(-0.931494\pi\)
0.976930 0.213561i \(-0.0685063\pi\)
\(48\) 2.46410i 0.355662i
\(49\) 6.92820 1.00000i 0.989743 0.142857i
\(50\) 0.517638i 0.0732051i
\(51\) 2.44949i 0.342997i
\(52\) −7.34847 −1.01905
\(53\) −3.46410 −0.475831 −0.237915 0.971286i \(-0.576464\pi\)
−0.237915 + 0.971286i \(0.576464\pi\)
\(54\) 0.517638 0.0704416
\(55\) 1.41421 3.00000i 0.190693 0.404520i
\(56\) 0.366025 + 5.09808i 0.0489122 + 0.681259i
\(57\) 1.03528i 0.137126i
\(58\) −0.535898 −0.0703669
\(59\) 12.9282i 1.68311i −0.540172 0.841554i \(-0.681641\pi\)
0.540172 0.841554i \(-0.318359\pi\)
\(60\) 1.73205 0.223607
\(61\) 4.89898 0.627250 0.313625 0.949547i \(-0.398457\pi\)
0.313625 + 0.949547i \(0.398457\pi\)
\(62\) 1.51575 0.192500
\(63\) 2.63896 0.189469i 0.332478 0.0238708i
\(64\) 2.26795 0.283494
\(65\) 4.24264i 0.526235i
\(66\) 1.55291 + 0.732051i 0.191151 + 0.0901092i
\(67\) −5.46410 −0.667546 −0.333773 0.942653i \(-0.608322\pi\)
−0.333773 + 0.942653i \(0.608322\pi\)
\(68\) −4.24264 −0.514496
\(69\) 4.00000i 0.481543i
\(70\) −1.36603 + 0.0980762i −0.163271 + 0.0117223i
\(71\) 6.92820 0.822226 0.411113 0.911584i \(-0.365140\pi\)
0.411113 + 0.911584i \(0.365140\pi\)
\(72\) 1.93185i 0.227671i
\(73\) 0.656339 0.0768186 0.0384093 0.999262i \(-0.487771\pi\)
0.0384093 + 0.999262i \(0.487771\pi\)
\(74\) 0.277401i 0.0322473i
\(75\) 1.00000i 0.115470i
\(76\) −1.79315 −0.205689
\(77\) 8.18482 + 3.16364i 0.932747 + 0.360531i
\(78\) 2.19615 0.248665
\(79\) 3.86370i 0.434701i 0.976094 + 0.217350i \(0.0697414\pi\)
−0.976094 + 0.217350i \(0.930259\pi\)
\(80\) 2.46410i 0.275495i
\(81\) 1.00000 0.111111
\(82\) 3.46410i 0.382546i
\(83\) −1.41421 −0.155230 −0.0776151 0.996983i \(-0.524731\pi\)
−0.0776151 + 0.996983i \(0.524731\pi\)
\(84\) 0.328169 + 4.57081i 0.0358062 + 0.498716i
\(85\) 2.44949i 0.265684i
\(86\) −1.26795 −0.136726
\(87\) −1.03528 −0.110993
\(88\) −2.73205 + 5.79555i −0.291238 + 0.617808i
\(89\) 4.92820i 0.522388i −0.965286 0.261194i \(-0.915884\pi\)
0.965286 0.261194i \(-0.0841163\pi\)
\(90\) −0.517638 −0.0545638
\(91\) 11.1962 0.803848i 1.17368 0.0842661i
\(92\) −6.92820 −0.722315
\(93\) 2.92820 0.303641
\(94\) −1.51575 −0.156338
\(95\) 1.03528i 0.106217i
\(96\) −5.13922 −0.524519
\(97\) 4.92820i 0.500383i 0.968196 + 0.250192i \(0.0804936\pi\)
−0.968196 + 0.250192i \(0.919506\pi\)
\(98\) −0.517638 3.58630i −0.0522893 0.362271i
\(99\) 3.00000 + 1.41421i 0.301511 + 0.142134i
\(100\) −1.73205 −0.173205
\(101\) −11.5911 −1.15336 −0.576679 0.816971i \(-0.695652\pi\)
−0.576679 + 0.816971i \(0.695652\pi\)
\(102\) 1.26795 0.125546
\(103\) 12.3923i 1.22105i 0.791997 + 0.610525i \(0.209042\pi\)
−0.791997 + 0.610525i \(0.790958\pi\)
\(104\) 8.19615i 0.803699i
\(105\) −2.63896 + 0.189469i −0.257536 + 0.0184903i
\(106\) 1.79315i 0.174166i
\(107\) 10.4543i 1.01066i −0.862928 0.505328i \(-0.831372\pi\)
0.862928 0.505328i \(-0.168628\pi\)
\(108\) 1.73205i 0.166667i
\(109\) 17.5254i 1.67863i 0.543649 + 0.839313i \(0.317042\pi\)
−0.543649 + 0.839313i \(0.682958\pi\)
\(110\) −1.55291 0.732051i −0.148065 0.0697983i
\(111\) 0.535898i 0.0508652i
\(112\) −6.50266 + 0.466870i −0.614444 + 0.0441151i
\(113\) 8.53590 0.802990 0.401495 0.915861i \(-0.368491\pi\)
0.401495 + 0.915861i \(0.368491\pi\)
\(114\) 0.535898 0.0501915
\(115\) 4.00000i 0.373002i
\(116\) 1.79315i 0.166490i
\(117\) 4.24264 0.392232
\(118\) −6.69213 −0.616061
\(119\) 6.46410 0.464102i 0.592563 0.0425441i
\(120\) 1.93185i 0.176353i
\(121\) 7.00000 + 8.48528i 0.636364 + 0.771389i
\(122\) 2.53590i 0.229589i
\(123\) 6.69213i 0.603409i
\(124\) 5.07180i 0.455461i
\(125\) 1.00000i 0.0894427i
\(126\) −0.0980762 1.36603i −0.00873732 0.121695i
\(127\) 12.2474i 1.08679i −0.839479 0.543393i \(-0.817139\pi\)
0.839479 0.543393i \(-0.182861\pi\)
\(128\) 11.4524i 1.01226i
\(129\) −2.44949 −0.215666
\(130\) −2.19615 −0.192615
\(131\) −4.89898 −0.428026 −0.214013 0.976831i \(-0.568653\pi\)
−0.214013 + 0.976831i \(0.568653\pi\)
\(132\) −2.44949 + 5.19615i −0.213201 + 0.452267i
\(133\) 2.73205 0.196152i 0.236899 0.0170086i
\(134\) 2.82843i 0.244339i
\(135\) −1.00000 −0.0860663
\(136\) 4.73205i 0.405770i
\(137\) −20.9282 −1.78802 −0.894009 0.448050i \(-0.852119\pi\)
−0.894009 + 0.448050i \(0.852119\pi\)
\(138\) 2.07055 0.176257
\(139\) 21.3891 1.81420 0.907099 0.420918i \(-0.138292\pi\)
0.907099 + 0.420918i \(0.138292\pi\)
\(140\) −0.328169 4.57081i −0.0277354 0.386304i
\(141\) −2.92820 −0.246599
\(142\) 3.58630i 0.300956i
\(143\) 12.7279 + 6.00000i 1.06436 + 0.501745i
\(144\) −2.46410 −0.205342
\(145\) 1.03528 0.0859750
\(146\) 0.339746i 0.0281176i
\(147\) −1.00000 6.92820i −0.0824786 0.571429i
\(148\) −0.928203 −0.0762978
\(149\) 18.7637i 1.53718i 0.639740 + 0.768592i \(0.279042\pi\)
−0.639740 + 0.768592i \(0.720958\pi\)
\(150\) 0.517638 0.0422650
\(151\) 5.93426i 0.482923i −0.970410 0.241461i \(-0.922373\pi\)
0.970410 0.241461i \(-0.0776267\pi\)
\(152\) 2.00000i 0.162221i
\(153\) 2.44949 0.198030
\(154\) 1.63762 4.23678i 0.131963 0.341409i
\(155\) −2.92820 −0.235199
\(156\) 7.34847i 0.588348i
\(157\) 6.39230i 0.510161i −0.966920 0.255081i \(-0.917898\pi\)
0.966920 0.255081i \(-0.0821021\pi\)
\(158\) 2.00000 0.159111
\(159\) 3.46410i 0.274721i
\(160\) 5.13922 0.406291
\(161\) 10.5558 0.757875i 0.831916 0.0597289i
\(162\) 0.517638i 0.0406695i
\(163\) −8.39230 −0.657336 −0.328668 0.944446i \(-0.606600\pi\)
−0.328668 + 0.944446i \(0.606600\pi\)
\(164\) −11.5911 −0.905114
\(165\) −3.00000 1.41421i −0.233550 0.110096i
\(166\) 0.732051i 0.0568182i
\(167\) 7.07107 0.547176 0.273588 0.961847i \(-0.411790\pi\)
0.273588 + 0.961847i \(0.411790\pi\)
\(168\) 5.09808 0.366025i 0.393325 0.0282395i
\(169\) 5.00000 0.384615
\(170\) −1.26795 −0.0972473
\(171\) 1.03528 0.0791695
\(172\) 4.24264i 0.323498i
\(173\) −2.44949 −0.186231 −0.0931156 0.995655i \(-0.529683\pi\)
−0.0931156 + 0.995655i \(0.529683\pi\)
\(174\) 0.535898i 0.0406264i
\(175\) 2.63896 0.189469i 0.199487 0.0143225i
\(176\) −7.39230 3.48477i −0.557216 0.262674i
\(177\) −12.9282 −0.971743
\(178\) −2.55103 −0.191207
\(179\) −4.92820 −0.368351 −0.184176 0.982893i \(-0.558962\pi\)
−0.184176 + 0.982893i \(0.558962\pi\)
\(180\) 1.73205i 0.129099i
\(181\) 16.9282i 1.25826i −0.777299 0.629132i \(-0.783411\pi\)
0.777299 0.629132i \(-0.216589\pi\)
\(182\) −0.416102 5.79555i −0.0308435 0.429595i
\(183\) 4.89898i 0.362143i
\(184\) 7.72741i 0.569672i
\(185\) 0.535898i 0.0394000i
\(186\) 1.51575i 0.111140i
\(187\) 7.34847 + 3.46410i 0.537373 + 0.253320i
\(188\) 5.07180i 0.369899i
\(189\) −0.189469 2.63896i −0.0137818 0.191956i
\(190\) −0.535898 −0.0388782
\(191\) −11.0718 −0.801127 −0.400564 0.916269i \(-0.631186\pi\)
−0.400564 + 0.916269i \(0.631186\pi\)
\(192\) 2.26795i 0.163675i
\(193\) 21.2132i 1.52696i 0.645832 + 0.763480i \(0.276511\pi\)
−0.645832 + 0.763480i \(0.723489\pi\)
\(194\) 2.55103 0.183153
\(195\) −4.24264 −0.303822
\(196\) 12.0000 1.73205i 0.857143 0.123718i
\(197\) 17.9043i 1.27563i −0.770190 0.637814i \(-0.779839\pi\)
0.770190 0.637814i \(-0.220161\pi\)
\(198\) 0.732051 1.55291i 0.0520246 0.110361i
\(199\) 19.4641i 1.37977i −0.723917 0.689887i \(-0.757660\pi\)
0.723917 0.689887i \(-0.242340\pi\)
\(200\) 1.93185i 0.136603i
\(201\) 5.46410i 0.385408i
\(202\) 6.00000i 0.422159i
\(203\) 0.196152 + 2.73205i 0.0137672 + 0.191752i
\(204\) 4.24264i 0.297044i
\(205\) 6.69213i 0.467399i
\(206\) 6.41473 0.446935
\(207\) 4.00000 0.278019
\(208\) −10.4543 −0.724875
\(209\) 3.10583 + 1.46410i 0.214835 + 0.101274i
\(210\) 0.0980762 + 1.36603i 0.00676790 + 0.0942647i
\(211\) 8.00481i 0.551074i −0.961291 0.275537i \(-0.911144\pi\)
0.961291 0.275537i \(-0.0888556\pi\)
\(212\) −6.00000 −0.412082
\(213\) 6.92820i 0.474713i
\(214\) −5.41154 −0.369925
\(215\) 2.44949 0.167054
\(216\) 1.93185 0.131446
\(217\) −0.554803 7.72741i −0.0376625 0.524571i
\(218\) 9.07180 0.614420
\(219\) 0.656339i 0.0443513i
\(220\) 2.44949 5.19615i 0.165145 0.350325i
\(221\) 10.3923 0.699062
\(222\) 0.277401 0.0186180
\(223\) 9.85641i 0.660034i −0.943975 0.330017i \(-0.892946\pi\)
0.943975 0.330017i \(-0.107054\pi\)
\(224\) 0.973721 + 13.5622i 0.0650594 + 0.906161i
\(225\) 1.00000 0.0666667
\(226\) 4.41851i 0.293915i
\(227\) 18.3848 1.22024 0.610120 0.792309i \(-0.291121\pi\)
0.610120 + 0.792309i \(0.291121\pi\)
\(228\) 1.79315i 0.118754i
\(229\) 17.8564i 1.17998i 0.807409 + 0.589992i \(0.200869\pi\)
−0.807409 + 0.589992i \(0.799131\pi\)
\(230\) −2.07055 −0.136528
\(231\) 3.16364 8.18482i 0.208153 0.538522i
\(232\) −2.00000 −0.131306
\(233\) 17.1464i 1.12330i 0.827375 + 0.561650i \(0.189833\pi\)
−0.827375 + 0.561650i \(0.810167\pi\)
\(234\) 2.19615i 0.143567i
\(235\) 2.92820 0.191015
\(236\) 22.3923i 1.45761i
\(237\) 3.86370 0.250974
\(238\) −0.240237 3.34607i −0.0155722 0.216893i
\(239\) 11.8685i 0.767710i −0.923393 0.383855i \(-0.874596\pi\)
0.923393 0.383855i \(-0.125404\pi\)
\(240\) 2.46410 0.159057
\(241\) 11.1106 0.715699 0.357850 0.933779i \(-0.383510\pi\)
0.357850 + 0.933779i \(0.383510\pi\)
\(242\) 4.39230 3.62347i 0.282348 0.232925i
\(243\) 1.00000i 0.0641500i
\(244\) 8.48528 0.543214
\(245\) 1.00000 + 6.92820i 0.0638877 + 0.442627i
\(246\) 3.46410 0.220863
\(247\) 4.39230 0.279476
\(248\) 5.65685 0.359211
\(249\) 1.41421i 0.0896221i
\(250\) −0.517638 −0.0327383
\(251\) 19.8564i 1.25333i −0.779291 0.626663i \(-0.784420\pi\)
0.779291 0.626663i \(-0.215580\pi\)
\(252\) 4.57081 0.328169i 0.287934 0.0206727i
\(253\) 12.0000 + 5.65685i 0.754434 + 0.355643i
\(254\) −6.33975 −0.397791
\(255\) −2.44949 −0.153393
\(256\) −1.39230 −0.0870191
\(257\) 14.0000i 0.873296i −0.899632 0.436648i \(-0.856166\pi\)
0.899632 0.436648i \(-0.143834\pi\)
\(258\) 1.26795i 0.0789391i
\(259\) 1.41421 0.101536i 0.0878750 0.00630914i
\(260\) 7.34847i 0.455733i
\(261\) 1.03528i 0.0640820i
\(262\) 2.53590i 0.156668i
\(263\) 6.31319i 0.389288i 0.980874 + 0.194644i \(0.0623552\pi\)
−0.980874 + 0.194644i \(0.937645\pi\)
\(264\) 5.79555 + 2.73205i 0.356692 + 0.168146i
\(265\) 3.46410i 0.212798i
\(266\) −0.101536 1.41421i −0.00622557 0.0867110i
\(267\) −4.92820 −0.301601
\(268\) −9.46410 −0.578112
\(269\) 2.53590i 0.154616i 0.997007 + 0.0773082i \(0.0246326\pi\)
−0.997007 + 0.0773082i \(0.975367\pi\)
\(270\) 0.517638i 0.0315025i
\(271\) 21.5921 1.31163 0.655815 0.754922i \(-0.272325\pi\)
0.655815 + 0.754922i \(0.272325\pi\)
\(272\) −6.03579 −0.365974
\(273\) −0.803848 11.1962i −0.0486511 0.677622i
\(274\) 10.8332i 0.654460i
\(275\) 3.00000 + 1.41421i 0.180907 + 0.0852803i
\(276\) 6.92820i 0.417029i
\(277\) 16.8690i 1.01356i −0.862075 0.506781i \(-0.830835\pi\)
0.862075 0.506781i \(-0.169165\pi\)
\(278\) 11.0718i 0.664042i
\(279\) 2.92820i 0.175307i
\(280\) −5.09808 + 0.366025i −0.304668 + 0.0218742i
\(281\) 12.3490i 0.736679i −0.929691 0.368339i \(-0.879926\pi\)
0.929691 0.368339i \(-0.120074\pi\)
\(282\) 1.51575i 0.0902616i
\(283\) 19.4201 1.15440 0.577201 0.816602i \(-0.304145\pi\)
0.577201 + 0.816602i \(0.304145\pi\)
\(284\) 12.0000 0.712069
\(285\) −1.03528 −0.0613245
\(286\) 3.10583 6.58846i 0.183651 0.389584i
\(287\) 17.6603 1.26795i 1.04245 0.0748447i
\(288\) 5.13922i 0.302831i
\(289\) −11.0000 −0.647059
\(290\) 0.535898i 0.0314690i
\(291\) 4.92820 0.288896
\(292\) 1.13681 0.0665269
\(293\) 16.3886 0.957430 0.478715 0.877970i \(-0.341103\pi\)
0.478715 + 0.877970i \(0.341103\pi\)
\(294\) −3.58630 + 0.517638i −0.209157 + 0.0301893i
\(295\) 12.9282 0.752709
\(296\) 1.03528i 0.0601742i
\(297\) 1.41421 3.00000i 0.0820610 0.174078i
\(298\) 9.71281 0.562648
\(299\) 16.9706 0.981433
\(300\) 1.73205i 0.100000i
\(301\) 0.464102 + 6.46410i 0.0267504 + 0.372585i
\(302\) −3.07180 −0.176762
\(303\) 11.5911i 0.665892i
\(304\) −2.55103 −0.146311
\(305\) 4.89898i 0.280515i
\(306\) 1.26795i 0.0724838i
\(307\) −15.0759 −0.860426 −0.430213 0.902727i \(-0.641561\pi\)
−0.430213 + 0.902727i \(0.641561\pi\)
\(308\) 14.1765 + 5.47959i 0.807783 + 0.312229i
\(309\) 12.3923 0.704974
\(310\) 1.51575i 0.0860888i
\(311\) 18.7846i 1.06518i 0.846374 + 0.532589i \(0.178781\pi\)
−0.846374 + 0.532589i \(0.821219\pi\)
\(312\) 8.19615 0.464016
\(313\) 31.8564i 1.80063i −0.435238 0.900315i \(-0.643336\pi\)
0.435238 0.900315i \(-0.356664\pi\)
\(314\) −3.30890 −0.186732
\(315\) 0.189469 + 2.63896i 0.0106754 + 0.148688i
\(316\) 6.69213i 0.376462i
\(317\) −28.2487 −1.58661 −0.793303 0.608827i \(-0.791640\pi\)
−0.793303 + 0.608827i \(0.791640\pi\)
\(318\) 1.79315 0.100555
\(319\) −1.46410 + 3.10583i −0.0819740 + 0.173893i
\(320\) 2.26795i 0.126782i
\(321\) −10.4543 −0.583502
\(322\) −0.392305 5.46410i −0.0218623 0.304502i
\(323\) 2.53590 0.141101
\(324\) 1.73205 0.0962250
\(325\) 4.24264 0.235339
\(326\) 4.34418i 0.240602i
\(327\) 17.5254 0.969155
\(328\) 12.9282i 0.713841i
\(329\) 0.554803 + 7.72741i 0.0305873 + 0.426026i
\(330\) −0.732051 + 1.55291i −0.0402981 + 0.0854851i
\(331\) −32.2487 −1.77255 −0.886275 0.463160i \(-0.846716\pi\)
−0.886275 + 0.463160i \(0.846716\pi\)
\(332\) −2.44949 −0.134433
\(333\) 0.535898 0.0293671
\(334\) 3.66025i 0.200280i
\(335\) 5.46410i 0.298536i
\(336\) 0.466870 + 6.50266i 0.0254699 + 0.354749i
\(337\) 6.31319i 0.343902i −0.985106 0.171951i \(-0.944993\pi\)
0.985106 0.171951i \(-0.0550070\pi\)
\(338\) 2.58819i 0.140779i
\(339\) 8.53590i 0.463606i
\(340\) 4.24264i 0.230089i
\(341\) 4.14110 8.78461i 0.224253 0.475713i
\(342\) 0.535898i 0.0289781i
\(343\) −18.0938 + 3.95164i −0.976972 + 0.213368i
\(344\) −4.73205 −0.255135
\(345\) −4.00000 −0.215353
\(346\) 1.26795i 0.0681654i
\(347\) 9.14162i 0.490748i −0.969429 0.245374i \(-0.921089\pi\)
0.969429 0.245374i \(-0.0789107\pi\)
\(348\) −1.79315 −0.0961230
\(349\) −8.48528 −0.454207 −0.227103 0.973871i \(-0.572926\pi\)
−0.227103 + 0.973871i \(0.572926\pi\)
\(350\) −0.0980762 1.36603i −0.00524239 0.0730171i
\(351\) 4.24264i 0.226455i
\(352\) −7.26795 + 15.4176i −0.387383 + 0.821763i
\(353\) 19.4641i 1.03597i 0.855390 + 0.517985i \(0.173318\pi\)
−0.855390 + 0.517985i \(0.826682\pi\)
\(354\) 6.69213i 0.355683i
\(355\) 6.92820i 0.367711i
\(356\) 8.53590i 0.452402i
\(357\) −0.464102 6.46410i −0.0245629 0.342117i
\(358\) 2.55103i 0.134826i
\(359\) 14.9000i 0.786392i 0.919455 + 0.393196i \(0.128631\pi\)
−0.919455 + 0.393196i \(0.871369\pi\)
\(360\) −1.93185 −0.101818
\(361\) −17.9282 −0.943590
\(362\) −8.76268 −0.460556
\(363\) 8.48528 7.00000i 0.445362 0.367405i
\(364\) 19.3923 1.39230i 1.01643 0.0729766i
\(365\) 0.656339i 0.0343543i
\(366\) −2.53590 −0.132554
\(367\) 16.7846i 0.876149i −0.898939 0.438075i \(-0.855661\pi\)
0.898939 0.438075i \(-0.144339\pi\)
\(368\) −9.85641 −0.513801
\(369\) 6.69213 0.348378
\(370\) −0.277401 −0.0144214
\(371\) 9.14162 0.656339i 0.474609 0.0340754i
\(372\) 5.07180 0.262960
\(373\) 35.9101i 1.85936i 0.368372 + 0.929678i \(0.379915\pi\)
−0.368372 + 0.929678i \(0.620085\pi\)
\(374\) 1.79315 3.80385i 0.0927216 0.196692i
\(375\) −1.00000 −0.0516398
\(376\) −5.65685 −0.291730
\(377\) 4.39230i 0.226215i
\(378\) −1.36603 + 0.0980762i −0.0702608 + 0.00504450i
\(379\) 6.14359 0.315575 0.157788 0.987473i \(-0.449564\pi\)
0.157788 + 0.987473i \(0.449564\pi\)
\(380\) 1.79315i 0.0919867i
\(381\) −12.2474 −0.627456
\(382\) 5.73118i 0.293233i
\(383\) 3.60770i 0.184345i 0.995743 + 0.0921723i \(0.0293811\pi\)
−0.995743 + 0.0921723i \(0.970619\pi\)
\(384\) −11.4524 −0.584428
\(385\) −3.16364 + 8.18482i −0.161234 + 0.417137i
\(386\) 10.9808 0.558906
\(387\) 2.44949i 0.124515i
\(388\) 8.53590i 0.433345i
\(389\) 30.7846 1.56084 0.780421 0.625255i \(-0.215005\pi\)
0.780421 + 0.625255i \(0.215005\pi\)
\(390\) 2.19615i 0.111207i
\(391\) 9.79796 0.495504
\(392\) −1.93185 13.3843i −0.0975732 0.676007i
\(393\) 4.89898i 0.247121i
\(394\) −9.26795 −0.466913
\(395\) −3.86370 −0.194404
\(396\) 5.19615 + 2.44949i 0.261116 + 0.123091i
\(397\) 4.92820i 0.247339i 0.992323 + 0.123670i \(0.0394663\pi\)
−0.992323 + 0.123670i \(0.960534\pi\)
\(398\) −10.0754 −0.505032
\(399\) −0.196152 2.73205i −0.00981990 0.136774i
\(400\) −2.46410 −0.123205
\(401\) −17.4641 −0.872116 −0.436058 0.899919i \(-0.643626\pi\)
−0.436058 + 0.899919i \(0.643626\pi\)
\(402\) 2.82843 0.141069
\(403\) 12.4233i 0.618849i
\(404\) −20.0764 −0.998838
\(405\) 1.00000i 0.0496904i
\(406\) 1.41421 0.101536i 0.0701862 0.00503915i
\(407\) 1.60770 + 0.757875i 0.0796905 + 0.0375665i
\(408\) 4.73205 0.234271
\(409\) −30.3548 −1.50095 −0.750475 0.660899i \(-0.770175\pi\)
−0.750475 + 0.660899i \(0.770175\pi\)
\(410\) −3.46410 −0.171080
\(411\) 20.9282i 1.03231i
\(412\) 21.4641i 1.05746i
\(413\) 2.44949 + 34.1170i 0.120532 + 1.67879i
\(414\) 2.07055i 0.101762i
\(415\) 1.41421i 0.0694210i
\(416\) 21.8038i 1.06902i
\(417\) 21.3891i 1.04743i
\(418\) 0.757875 1.60770i 0.0370689 0.0786349i
\(419\) 17.0718i 0.834012i −0.908904 0.417006i \(-0.863079\pi\)
0.908904 0.417006i \(-0.136921\pi\)
\(420\) −4.57081 + 0.328169i −0.223033 + 0.0160130i
\(421\) −1.85641 −0.0904757 −0.0452379 0.998976i \(-0.514405\pi\)
−0.0452379 + 0.998976i \(0.514405\pi\)
\(422\) −4.14359 −0.201707
\(423\) 2.92820i 0.142374i
\(424\) 6.69213i 0.324999i
\(425\) 2.44949 0.118818
\(426\) −3.58630 −0.173757
\(427\) −12.9282 + 0.928203i −0.625640 + 0.0449189i
\(428\) 18.1074i 0.875253i
\(429\) 6.00000 12.7279i 0.289683 0.614510i
\(430\) 1.26795i 0.0611459i
\(431\) 24.4949i 1.17988i −0.807448 0.589939i \(-0.799152\pi\)
0.807448 0.589939i \(-0.200848\pi\)
\(432\) 2.46410i 0.118554i
\(433\) 16.9282i 0.813518i 0.913536 + 0.406759i \(0.133341\pi\)
−0.913536 + 0.406759i \(0.866659\pi\)
\(434\) −4.00000 + 0.287187i −0.192006 + 0.0137854i
\(435\) 1.03528i 0.0496377i
\(436\) 30.3548i 1.45373i
\(437\) 4.14110 0.198096
\(438\) −0.339746 −0.0162337
\(439\) −38.3596 −1.83081 −0.915403 0.402539i \(-0.868128\pi\)
−0.915403 + 0.402539i \(0.868128\pi\)
\(440\) −5.79555 2.73205i −0.276292 0.130245i
\(441\) −6.92820 + 1.00000i −0.329914 + 0.0476190i
\(442\) 5.37945i 0.255874i
\(443\) −4.78461 −0.227324 −0.113662 0.993519i \(-0.536258\pi\)
−0.113662 + 0.993519i \(0.536258\pi\)
\(444\) 0.928203i 0.0440506i
\(445\) 4.92820 0.233619
\(446\) −5.10205 −0.241589
\(447\) 18.7637 0.887493
\(448\) −5.98502 + 0.429705i −0.282766 + 0.0203017i
\(449\) 23.3205 1.10056 0.550281 0.834979i \(-0.314520\pi\)
0.550281 + 0.834979i \(0.314520\pi\)
\(450\) 0.517638i 0.0244017i
\(451\) 20.0764 + 9.46410i 0.945360 + 0.445647i
\(452\) 14.7846 0.695410
\(453\) −5.93426 −0.278816
\(454\) 9.51666i 0.446639i
\(455\) 0.803848 + 11.1962i 0.0376850 + 0.524884i
\(456\) 2.00000 0.0936586
\(457\) 40.2543i 1.88302i −0.336988 0.941509i \(-0.609408\pi\)
0.336988 0.941509i \(-0.390592\pi\)
\(458\) 9.24316 0.431904
\(459\) 2.44949i 0.114332i
\(460\) 6.92820i 0.323029i
\(461\) −36.8439 −1.71599 −0.857995 0.513657i \(-0.828290\pi\)
−0.857995 + 0.513657i \(0.828290\pi\)
\(462\) −4.23678 1.63762i −0.197113 0.0761891i
\(463\) 31.7128 1.47382 0.736910 0.675991i \(-0.236284\pi\)
0.736910 + 0.675991i \(0.236284\pi\)
\(464\) 2.55103i 0.118428i
\(465\) 2.92820i 0.135792i
\(466\) 8.87564 0.411156
\(467\) 26.2487i 1.21465i −0.794455 0.607323i \(-0.792243\pi\)
0.794455 0.607323i \(-0.207757\pi\)
\(468\) 7.34847 0.339683
\(469\) 14.4195 1.03528i 0.665832 0.0478046i
\(470\) 1.51575i 0.0699163i
\(471\) −6.39230 −0.294542
\(472\) −24.9754 −1.14958
\(473\) −3.46410 + 7.34847i −0.159280 + 0.337883i
\(474\) 2.00000i 0.0918630i
\(475\) 1.03528 0.0475017
\(476\) 11.1962 0.803848i 0.513175 0.0368443i
\(477\) 3.46410 0.158610
\(478\) −6.14359 −0.281001
\(479\) −2.82843 −0.129234 −0.0646171 0.997910i \(-0.520583\pi\)
−0.0646171 + 0.997910i \(0.520583\pi\)
\(480\) 5.13922i 0.234572i
\(481\) 2.27362 0.103668
\(482\) 5.75129i 0.261964i
\(483\) −0.757875 10.5558i −0.0344845 0.480307i
\(484\) 12.1244 + 14.6969i 0.551107 + 0.668043i
\(485\) −4.92820 −0.223778
\(486\) −0.517638 −0.0234805
\(487\) −15.3205 −0.694238 −0.347119 0.937821i \(-0.612840\pi\)
−0.347119 + 0.937821i \(0.612840\pi\)
\(488\) 9.46410i 0.428420i
\(489\) 8.39230i 0.379513i
\(490\) 3.58630 0.517638i 0.162013 0.0233845i
\(491\) 2.82843i 0.127645i 0.997961 + 0.0638226i \(0.0203292\pi\)
−0.997961 + 0.0638226i \(0.979671\pi\)
\(492\) 11.5911i 0.522568i
\(493\) 2.53590i 0.114211i
\(494\) 2.27362i 0.102295i
\(495\) −1.41421 + 3.00000i −0.0635642 + 0.134840i
\(496\) 7.21539i 0.323981i
\(497\) −18.2832 + 1.31268i −0.820115 + 0.0588816i
\(498\) 0.732051 0.0328040
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 1.73205i 0.0774597i
\(501\) 7.07107i 0.315912i
\(502\) −10.2784 −0.458749
\(503\) 19.4944 0.869212 0.434606 0.900621i \(-0.356888\pi\)
0.434606 + 0.900621i \(0.356888\pi\)
\(504\) −0.366025 5.09808i −0.0163041 0.227086i
\(505\) 11.5911i 0.515798i
\(506\) 2.92820 6.21166i 0.130175 0.276142i
\(507\) 5.00000i 0.222058i
\(508\) 21.2132i 0.941184i
\(509\) 18.2487i 0.808860i 0.914569 + 0.404430i \(0.132530\pi\)
−0.914569 + 0.404430i \(0.867470\pi\)
\(510\) 1.26795i 0.0561457i
\(511\) −1.73205 + 0.124356i −0.0766214 + 0.00550117i
\(512\) 22.1841i 0.980408i
\(513\) 1.03528i 0.0457086i
\(514\) −7.24693 −0.319649
\(515\) −12.3923 −0.546070
\(516\) −4.24264 −0.186772
\(517\) −4.14110 + 8.78461i −0.182126 + 0.386347i
\(518\) −0.0525589 0.732051i −0.00230930 0.0321645i
\(519\) 2.44949i 0.107521i
\(520\) −8.19615 −0.359425
\(521\) 31.8564i 1.39565i 0.716266 + 0.697827i \(0.245850\pi\)
−0.716266 + 0.697827i \(0.754150\pi\)
\(522\) 0.535898 0.0234556
\(523\) 1.13681 0.0497093 0.0248547 0.999691i \(-0.492088\pi\)
0.0248547 + 0.999691i \(0.492088\pi\)
\(524\) −8.48528 −0.370681
\(525\) −0.189469 2.63896i −0.00826909 0.115174i
\(526\) 3.26795 0.142489
\(527\) 7.17260i 0.312444i
\(528\) −3.48477 + 7.39230i −0.151655 + 0.321709i
\(529\) −7.00000 −0.304348
\(530\) −1.79315 −0.0778895
\(531\) 12.9282i 0.561036i
\(532\) 4.73205 0.339746i 0.205160 0.0147299i
\(533\) 28.3923 1.22981
\(534\) 2.55103i 0.110394i
\(535\) 10.4543 0.451979
\(536\) 10.5558i 0.455943i
\(537\) 4.92820i 0.212668i
\(538\) 1.31268 0.0565935
\(539\) −22.1988 6.79796i −0.956171 0.292809i
\(540\) −1.73205 −0.0745356
\(541\) 33.9411i 1.45924i −0.683851 0.729621i \(-0.739696\pi\)
0.683851 0.729621i \(-0.260304\pi\)
\(542\) 11.1769i 0.480090i
\(543\) −16.9282 −0.726459
\(544\) 12.5885i 0.539726i
\(545\) −17.5254 −0.750704
\(546\) −5.79555 + 0.416102i −0.248027 + 0.0178075i
\(547\) 3.76217i 0.160859i 0.996760 + 0.0804293i \(0.0256291\pi\)
−0.996760 + 0.0804293i \(0.974371\pi\)
\(548\) −36.2487 −1.54847
\(549\) −4.89898 −0.209083
\(550\) 0.732051 1.55291i 0.0312148 0.0662165i
\(551\) 1.07180i 0.0456601i
\(552\) 7.72741 0.328900
\(553\) −0.732051 10.1962i −0.0311300 0.433585i
\(554\) −8.73205 −0.370989
\(555\) −0.535898 −0.0227476
\(556\) 37.0470 1.57114
\(557\) 17.3495i 0.735122i 0.929999 + 0.367561i \(0.119807\pi\)
−0.929999 + 0.367561i \(0.880193\pi\)
\(558\) −1.51575 −0.0641668
\(559\) 10.3923i 0.439548i
\(560\) −0.466870 6.50266i −0.0197289 0.274788i
\(561\) 3.46410 7.34847i 0.146254 0.310253i
\(562\) −6.39230 −0.269643
\(563\) −21.7680 −0.917412 −0.458706 0.888588i \(-0.651687\pi\)
−0.458706 + 0.888588i \(0.651687\pi\)
\(564\) −5.07180 −0.213561
\(565\) 8.53590i 0.359108i
\(566\) 10.0526i 0.422541i
\(567\) −2.63896 + 0.189469i −0.110826 + 0.00795694i
\(568\) 13.3843i 0.561591i
\(569\) 23.4596i 0.983478i 0.870743 + 0.491739i \(0.163639\pi\)
−0.870743 + 0.491739i \(0.836361\pi\)
\(570\) 0.535898i 0.0224463i
\(571\) 43.2586i 1.81032i 0.425075 + 0.905158i \(0.360248\pi\)
−0.425075 + 0.905158i \(0.639752\pi\)
\(572\) 22.0454 + 10.3923i 0.921765 + 0.434524i
\(573\) 11.0718i 0.462531i
\(574\) −0.656339 9.14162i −0.0273951 0.381564i
\(575\) 4.00000 0.166812
\(576\) −2.26795 −0.0944979
\(577\) 35.1769i 1.46443i 0.681071 + 0.732217i \(0.261514\pi\)
−0.681071 + 0.732217i \(0.738486\pi\)
\(578\) 5.69402i 0.236840i
\(579\) 21.2132 0.881591
\(580\) 1.79315 0.0744565
\(581\) 3.73205 0.267949i 0.154832 0.0111164i
\(582\) 2.55103i 0.105743i
\(583\) 10.3923 + 4.89898i 0.430405 + 0.202895i
\(584\) 1.26795i 0.0524681i
\(585\) 4.24264i 0.175412i
\(586\) 8.48334i 0.350444i
\(587\) 15.6077i 0.644199i −0.946706 0.322099i \(-0.895612\pi\)
0.946706 0.322099i \(-0.104388\pi\)
\(588\) −1.73205 12.0000i −0.0714286 0.494872i
\(589\) 3.03150i 0.124911i
\(590\) 6.69213i 0.275511i
\(591\) −17.9043 −0.736485
\(592\) −1.32051 −0.0542725
\(593\) −39.2190 −1.61053 −0.805267 0.592913i \(-0.797978\pi\)
−0.805267 + 0.592913i \(0.797978\pi\)
\(594\) −1.55291 0.732051i −0.0637168 0.0300364i
\(595\) 0.464102 + 6.46410i 0.0190263 + 0.265002i
\(596\) 32.4997i 1.33124i
\(597\) −19.4641 −0.796613
\(598\) 8.78461i 0.359229i
\(599\) 7.85641 0.321004 0.160502 0.987036i \(-0.448689\pi\)
0.160502 + 0.987036i \(0.448689\pi\)
\(600\) 1.93185 0.0788675
\(601\) 13.5873 0.554239 0.277119 0.960835i \(-0.410620\pi\)
0.277119 + 0.960835i \(0.410620\pi\)
\(602\) 3.34607 0.240237i 0.136375 0.00979132i
\(603\) 5.46410 0.222515
\(604\) 10.2784i 0.418223i
\(605\) −8.48528 + 7.00000i −0.344976 + 0.284590i
\(606\) 6.00000 0.243733
\(607\) −21.6937 −0.880519 −0.440260 0.897871i \(-0.645114\pi\)
−0.440260 + 0.897871i \(0.645114\pi\)
\(608\) 5.32051i 0.215775i
\(609\) 2.73205 0.196152i 0.110708 0.00794850i
\(610\) 2.53590 0.102676
\(611\) 12.4233i 0.502593i
\(612\) 4.24264 0.171499
\(613\) 35.9101i 1.45040i −0.688540 0.725198i \(-0.741748\pi\)
0.688540 0.725198i \(-0.258252\pi\)
\(614\) 7.80385i 0.314938i
\(615\) −6.69213 −0.269853
\(616\) 6.11169 15.8119i 0.246247 0.637078i
\(617\) 20.5359 0.826744 0.413372 0.910562i \(-0.364351\pi\)
0.413372 + 0.910562i \(0.364351\pi\)
\(618\) 6.41473i 0.258038i
\(619\) 9.85641i 0.396162i 0.980186 + 0.198081i \(0.0634710\pi\)
−0.980186 + 0.198081i \(0.936529\pi\)
\(620\) −5.07180 −0.203688
\(621\) 4.00000i 0.160514i
\(622\) 9.72363 0.389882
\(623\) 0.933740 + 13.0053i 0.0374095 + 0.521047i
\(624\) 10.4543i 0.418507i
\(625\) 1.00000 0.0400000
\(626\) −16.4901 −0.659077
\(627\) 1.46410 3.10583i 0.0584706 0.124035i
\(628\) 11.0718i 0.441813i
\(629\) 1.31268 0.0523399
\(630\) 1.36603 0.0980762i 0.0544238 0.00390745i
\(631\) −43.7128 −1.74018 −0.870090 0.492893i \(-0.835939\pi\)
−0.870090 + 0.492893i \(0.835939\pi\)
\(632\) 7.46410 0.296906
\(633\) −8.00481 −0.318163
\(634\) 14.6226i 0.580738i
\(635\) 12.2474 0.486025
\(636\) 6.00000i 0.237915i
\(637\) −29.3939 + 4.24264i −1.16463 + 0.168100i
\(638\) 1.60770 + 0.757875i 0.0636493 + 0.0300045i
\(639\) −6.92820 −0.274075
\(640\) 11.4524 0.452696
\(641\) 11.3205 0.447133 0.223567 0.974689i \(-0.428230\pi\)
0.223567 + 0.974689i \(0.428230\pi\)
\(642\) 5.41154i 0.213577i
\(643\) 22.5359i 0.888729i 0.895846 + 0.444365i \(0.146570\pi\)
−0.895846 + 0.444365i \(0.853430\pi\)
\(644\) 18.2832 1.31268i 0.720461 0.0517267i
\(645\) 2.44949i 0.0964486i
\(646\) 1.31268i 0.0516466i
\(647\) 19.6077i 0.770858i 0.922737 + 0.385429i \(0.125947\pi\)
−0.922737 + 0.385429i \(0.874053\pi\)
\(648\) 1.93185i 0.0758903i
\(649\) −18.2832 + 38.7846i −0.717680 + 1.52243i
\(650\) 2.19615i 0.0861402i
\(651\) −7.72741 + 0.554803i −0.302861 + 0.0217444i
\(652\) −14.5359 −0.569270
\(653\) 39.5692 1.54846 0.774232 0.632902i \(-0.218137\pi\)
0.774232 + 0.632902i \(0.218137\pi\)
\(654\) 9.07180i 0.354735i
\(655\) 4.89898i 0.191419i
\(656\) −16.4901 −0.643830
\(657\) −0.656339 −0.0256062
\(658\) 4.00000 0.287187i 0.155936 0.0111957i
\(659\) 5.45378i 0.212449i 0.994342 + 0.106225i \(0.0338763\pi\)
−0.994342 + 0.106225i \(0.966124\pi\)
\(660\) −5.19615 2.44949i −0.202260 0.0953463i
\(661\) 41.5692i 1.61686i −0.588596 0.808428i \(-0.700319\pi\)
0.588596 0.808428i \(-0.299681\pi\)
\(662\) 16.6932i 0.648798i
\(663\) 10.3923i 0.403604i
\(664\) 2.73205i 0.106024i
\(665\) 0.196152 + 2.73205i 0.00760646 + 0.105944i
\(666\) 0.277401i 0.0107491i
\(667\) 4.14110i 0.160344i
\(668\) 12.2474 0.473868
\(669\) −9.85641 −0.381071
\(670\) −2.82843 −0.109272
\(671\) −14.6969 6.92820i −0.567369 0.267460i
\(672\) 13.5622 0.973721i 0.523172 0.0375621i
\(673\) 31.2142i 1.20322i −0.798790 0.601610i \(-0.794526\pi\)
0.798790 0.601610i \(-0.205474\pi\)
\(674\) −3.26795 −0.125877
\(675\) 1.00000i 0.0384900i
\(676\) 8.66025 0.333087
\(677\) 29.0149 1.11513 0.557567 0.830132i \(-0.311735\pi\)
0.557567 + 0.830132i \(0.311735\pi\)
\(678\) −4.41851 −0.169692
\(679\) −0.933740 13.0053i −0.0358337 0.499099i
\(680\) −4.73205 −0.181466
\(681\) 18.3848i 0.704506i
\(682\) −4.54725 2.14359i −0.174123 0.0820824i
\(683\) −44.1051 −1.68764 −0.843818 0.536630i \(-0.819697\pi\)
−0.843818 + 0.536630i \(0.819697\pi\)
\(684\) 1.79315 0.0685628
\(685\) 20.9282i 0.799626i
\(686\) 2.04552 + 9.36603i 0.0780982 + 0.357597i
\(687\) 17.8564 0.681264
\(688\) 6.03579i 0.230112i
\(689\) 14.6969 0.559909
\(690\) 2.07055i 0.0788246i
\(691\) 23.1769i 0.881691i −0.897583 0.440846i \(-0.854679\pi\)
0.897583 0.440846i \(-0.145321\pi\)
\(692\) −4.24264 −0.161281
\(693\) −8.18482 3.16364i −0.310916 0.120177i
\(694\) −4.73205 −0.179626
\(695\) 21.3891i 0.811334i
\(696\) 2.00000i 0.0758098i
\(697\) 16.3923 0.620903
\(698\) 4.39230i 0.166251i
\(699\) 17.1464 0.648537
\(700\) 4.57081 0.328169i 0.172760 0.0124036i
\(701\) 34.5703i 1.30570i 0.757487 + 0.652850i \(0.226427\pi\)
−0.757487 + 0.652850i \(0.773573\pi\)
\(702\) −2.19615 −0.0828884
\(703\) 0.554803 0.0209248
\(704\) −6.80385 3.20736i −0.256430 0.120882i
\(705\) 2.92820i 0.110283i
\(706\) 10.0754 0.379191
\(707\) 30.5885 2.19615i 1.15040 0.0825948i
\(708\) −22.3923 −0.841554
\(709\) −10.9282 −0.410417 −0.205209 0.978718i \(-0.565787\pi\)
−0.205209 + 0.978718i \(0.565787\pi\)
\(710\) 3.58630 0.134592
\(711\) 3.86370i 0.144900i
\(712\) −9.52056 −0.356798
\(713\) 11.7128i 0.438648i
\(714\) −3.34607 + 0.240237i −0.125223 + 0.00899063i
\(715\) −6.00000 + 12.7279i −0.224387 + 0.475997i
\(716\) −8.53590 −0.319002
\(717\) −11.8685 −0.443238
\(718\) 7.71281 0.287840
\(719\) 5.85641i 0.218407i 0.994019 + 0.109204i \(0.0348300\pi\)
−0.994019 + 0.109204i \(0.965170\pi\)
\(720\) 2.46410i 0.0918316i
\(721\) −2.34795 32.7028i −0.0874424 1.21792i
\(722\) 9.28032i 0.345378i
\(723\) 11.1106i 0.413209i
\(724\) 29.3205i 1.08969i
\(725\) 1.03528i 0.0384492i
\(726\) −3.62347 4.39230i −0.134479 0.163014i
\(727\) 45.5692i 1.69007i 0.534712 + 0.845034i \(0.320420\pi\)
−0.534712 + 0.845034i \(0.679580\pi\)
\(728\) −1.55291 21.6293i −0.0575548 0.801635i
\(729\) −1.00000 −0.0370370
\(730\) 0.339746 0.0125746
\(731\) 6.00000i 0.221918i
\(732\) 8.48528i 0.313625i
\(733\) −0.101536 −0.00375032 −0.00187516 0.999998i \(-0.500597\pi\)
−0.00187516 + 0.999998i \(0.500597\pi\)
\(734\) −8.68835 −0.320693
\(735\) 6.92820 1.00000i 0.255551 0.0368856i
\(736\) 20.5569i 0.757736i
\(737\) 16.3923 + 7.72741i 0.603818 + 0.284643i
\(738\) 3.46410i 0.127515i
\(739\) 51.5408i 1.89596i −0.318330 0.947980i \(-0.603122\pi\)
0.318330 0.947980i \(-0.396878\pi\)
\(740\) 0.928203i 0.0341214i
\(741\) 4.39230i 0.161355i
\(742\) −0.339746 4.73205i −0.0124725 0.173719i
\(743\) 32.3238i 1.18585i 0.805259 + 0.592923i \(0.202026\pi\)
−0.805259 + 0.592923i \(0.797974\pi\)
\(744\) 5.65685i 0.207390i
\(745\) −18.7637 −0.687449
\(746\) 18.5885 0.680572
\(747\) 1.41421 0.0517434
\(748\) 12.7279 + 6.00000i 0.465379 + 0.219382i
\(749\) 1.98076 + 27.5885i 0.0723755 + 1.00806i
\(750\) 0.517638i 0.0189015i
\(751\) 18.9282 0.690700 0.345350 0.938474i \(-0.387760\pi\)
0.345350 + 0.938474i \(0.387760\pi\)
\(752\) 7.21539i 0.263118i
\(753\) −19.8564 −0.723608
\(754\) 2.27362 0.0828005
\(755\) 5.93426 0.215970
\(756\) −0.328169 4.57081i −0.0119354 0.166239i
\(757\) 20.6410 0.750210 0.375105 0.926982i \(-0.377607\pi\)
0.375105 + 0.926982i \(0.377607\pi\)
\(758\) 3.18016i 0.115509i
\(759\) 5.65685 12.0000i 0.205331 0.435572i
\(760\) −2.00000 −0.0725476
\(761\) −52.8535 −1.91594 −0.957969 0.286872i \(-0.907385\pi\)
−0.957969 + 0.286872i \(0.907385\pi\)
\(762\) 6.33975i 0.229665i
\(763\) −3.32051 46.2487i −0.120210 1.67432i
\(764\) −19.1769 −0.693796
\(765\) 2.44949i 0.0885615i
\(766\) 1.86748 0.0674748
\(767\) 54.8497i 1.98051i
\(768\) 1.39230i 0.0502405i
\(769\) −46.5675 −1.67927 −0.839634 0.543153i \(-0.817230\pi\)
−0.839634 + 0.543153i \(0.817230\pi\)
\(770\) 4.23678 + 1.63762i 0.152683 + 0.0590158i
\(771\) −14.0000 −0.504198
\(772\) 36.7423i 1.32239i
\(773\) 42.0000i 1.51064i 0.655359 + 0.755318i \(0.272517\pi\)
−0.655359 + 0.755318i \(0.727483\pi\)
\(774\) 1.26795 0.0455755
\(775\) 2.92820i 0.105184i
\(776\) 9.52056 0.341768
\(777\) −0.101536 1.41421i −0.00364258 0.0507346i
\(778\) 15.9353i 0.571308i
\(779\) 6.92820 0.248229
\(780\) −7.34847 −0.263117
\(781\) −20.7846 9.79796i −0.743732 0.350599i
\(782\) 5.07180i 0.181367i
\(783\) 1.03528 0.0369978
\(784\) 17.0718 2.46410i 0.609707 0.0880036i
\(785\) 6.39230 0.228151
\(786\) 2.53590 0.0904525
\(787\) −3.96524 −0.141346 −0.0706728 0.997500i \(-0.522515\pi\)
−0.0706728 + 0.997500i \(0.522515\pi\)
\(788\) 31.0112i 1.10473i
\(789\) 6.31319 0.224756
\(790\) 2.00000i 0.0711568i
\(791\) −22.5259 + 1.61729i −0.800928 + 0.0575041i
\(792\) 2.73205 5.79555i 0.0970792 0.205936i
\(793\) −20.7846 −0.738083
\(794\) 2.55103 0.0905325
\(795\) −3.46410 −0.122859
\(796\) 33.7128i 1.19492i
\(797\) 18.3923i 0.651489i 0.945458 + 0.325744i \(0.105615\pi\)
−0.945458 + 0.325744i \(0.894385\pi\)
\(798\) −1.41421 + 0.101536i −0.0500626 + 0.00359433i
\(799\) 7.17260i 0.253748i
\(800\) 5.13922i 0.181699i
\(801\) 4.92820i 0.174129i
\(802\) 9.04008i 0.319216i
\(803\) −1.96902 0.928203i −0.0694851 0.0327556i
\(804\) 9.46410i 0.333773i
\(805\) 0.757875 + 10.5558i 0.0267116 + 0.372044i
\(806\) −6.43078 −0.226515
\(807\) 2.53590 0.0892679
\(808\) 22.3923i 0.787759i
\(809\) 31.3901i 1.10362i 0.833971 + 0.551809i \(0.186062\pi\)
−0.833971 + 0.551809i \(0.813938\pi\)
\(810\) 0.517638 0.0181879
\(811\) 28.0069 0.983454 0.491727 0.870749i \(-0.336366\pi\)
0.491727 + 0.870749i \(0.336366\pi\)
\(812\) 0.339746 + 4.73205i 0.0119227 + 0.166062i
\(813\) 21.5921i 0.757269i
\(814\) 0.392305 0.832204i 0.0137503 0.0291687i
\(815\) 8.39230i 0.293970i
\(816\) 6.03579i 0.211295i
\(817\) 2.53590i 0.0887199i
\(818\) 15.7128i 0.549386i
\(819\) −11.1962 + 0.803848i −0.391225 + 0.0280887i
\(820\) 11.5911i 0.404779i
\(821\) 42.7038i 1.49037i 0.666856 + 0.745187i \(0.267640\pi\)
−0.666856 + 0.745187i \(0.732360\pi\)
\(822\) 10.8332 0.377852
\(823\) 13.1769 0.459318 0.229659 0.973271i \(-0.426239\pi\)
0.229659 + 0.973271i \(0.426239\pi\)
\(824\) 23.9401 0.833993
\(825\) 1.41421 3.00000i 0.0492366 0.104447i
\(826\) 17.6603 1.26795i 0.614479 0.0441176i
\(827\) 37.4259i 1.30143i 0.759324 + 0.650713i \(0.225530\pi\)
−0.759324 + 0.650713i \(0.774470\pi\)
\(828\) 6.92820 0.240772
\(829\) 12.1436i 0.421764i −0.977511 0.210882i \(-0.932366\pi\)
0.977511 0.210882i \(-0.0676337\pi\)
\(830\) −0.732051 −0.0254099
\(831\) −16.8690 −0.585180
\(832\) −9.62209 −0.333586
\(833\) −16.9706 + 2.44949i −0.587995 + 0.0848698i
\(834\) −11.0718 −0.383385
\(835\) 7.07107i 0.244704i
\(836\) 5.37945 + 2.53590i 0.186052 + 0.0877059i
\(837\) −2.92820 −0.101214
\(838\) −8.83701 −0.305270
\(839\) 46.7846i 1.61518i −0.589742 0.807592i \(-0.700770\pi\)
0.589742 0.807592i \(-0.299230\pi\)
\(840\) 0.366025 + 5.09808i 0.0126291 + 0.175900i
\(841\) 27.9282 0.963041
\(842\) 0.960947i 0.0331164i
\(843\) −12.3490 −0.425322
\(844\) 13.8647i 0.477244i
\(845\) 5.00000i 0.172005i
\(846\) 1.51575 0.0521125
\(847\) −20.0804 21.0660i −0.689971 0.723837i
\(848\) −8.53590 −0.293124
\(849\) 19.4201i 0.666494i
\(850\) 1.26795i 0.0434903i
\(851\) 2.14359 0.0734814
\(852\) 12.0000i 0.411113i
\(853\) 3.48477 0.119316 0.0596581 0.998219i \(-0.480999\pi\)
0.0596581 + 0.998219i \(0.480999\pi\)
\(854\) 0.480473 + 6.69213i 0.0164415 + 0.229000i
\(855\) 1.03528i 0.0354057i
\(856\) −20.1962 −0.690290
\(857\) 9.62209 0.328684 0.164342 0.986403i \(-0.447450\pi\)
0.164342 + 0.986403i \(0.447450\pi\)
\(858\) −6.58846 3.10583i −0.224926 0.106031i
\(859\) 26.6410i 0.908980i 0.890752 + 0.454490i \(0.150178\pi\)
−0.890752 + 0.454490i \(0.849822\pi\)
\(860\) 4.24264 0.144673
\(861\) −1.26795 17.6603i −0.0432116 0.601860i
\(862\) −12.6795 −0.431865
\(863\) 16.7846 0.571355 0.285677 0.958326i \(-0.407781\pi\)
0.285677 + 0.958326i \(0.407781\pi\)
\(864\) 5.13922 0.174840
\(865\) 2.44949i 0.0832851i
\(866\) 8.76268 0.297768
\(867\) 11.0000i 0.373580i
\(868\) −0.960947 13.3843i −0.0326167 0.454291i
\(869\) 5.46410 11.5911i 0.185357 0.393201i
\(870\) −0.535898 −0.0181687
\(871\) 23.1822 0.785500
\(872\) 33.8564 1.14652
\(873\) 4.92820i 0.166794i
\(874\) 2.14359i 0.0725081i
\(875\) 0.189469 + 2.63896i 0.00640521 + 0.0892131i
\(876\) 1.13681i 0.0384093i
\(877\) 1.96902i 0.0664890i −0.999447 0.0332445i \(-0.989416\pi\)
0.999447 0.0332445i \(-0.0105840\pi\)
\(878\) 19.8564i 0.670121i
\(879\) 16.3886i 0.552772i
\(880\) 3.48477 7.39230i 0.117471 0.249195i
\(881\) 6.24871i 0.210524i −0.994445 0.105262i \(-0.966432\pi\)
0.994445 0.105262i \(-0.0335682\pi\)
\(882\) 0.517638 + 3.58630i 0.0174298 + 0.120757i
\(883\) 6.92820 0.233153 0.116576 0.993182i \(-0.462808\pi\)
0.116576 + 0.993182i \(0.462808\pi\)
\(884\) 18.0000 0.605406
\(885\) 12.9282i 0.434577i
\(886\) 2.47670i 0.0832062i
\(887\) 15.9081 0.534141 0.267071 0.963677i \(-0.413944\pi\)
0.267071 + 0.963677i \(0.413944\pi\)
\(888\) 1.03528 0.0347416
\(889\) 2.32051 + 32.3205i 0.0778273 + 1.08400i
\(890\) 2.55103i 0.0855106i
\(891\) −3.00000 1.41421i −0.100504 0.0473779i
\(892\) 17.0718i 0.571606i
\(893\) 3.03150i 0.101445i
\(894\) 9.71281i 0.324845i
\(895\) 4.92820i 0.164732i
\(896\) 2.16987 + 30.2224i 0.0724904 + 1.00966i
\(897\) 16.9706i 0.566631i
\(898\) 12.0716i 0.402834i
\(899\) 3.03150 0.101106
\(900\) 1.73205 0.0577350
\(901\) 8.48528 0.282686
\(902\) 4.89898 10.3923i 0.163118 0.346026i
\(903\) 6.46410 0.464102i 0.215112 0.0154443i
\(904\) 16.4901i 0.548452i
\(905\) 16.9282 0.562713
\(906\) 3.07180i 0.102054i
\(907\) −4.00000 −0.132818 −0.0664089 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) 31.8434 1.05676
\(909\) 11.5911 0.384453
\(910\) 5.79555 0.416102i 0.192121 0.0137937i
\(911\) 20.9282 0.693382 0.346691 0.937979i \(-0.387305\pi\)
0.346691 + 0.937979i \(0.387305\pi\)
\(912\) 2.55103i 0.0844729i
\(913\) 4.24264 + 2.00000i 0.140411 + 0.0661903i
\(914\) −20.8372 −0.689232
\(915\) 4.89898 0.161955
\(916\) 30.9282i 1.02190i
\(917\) 12.9282 0.928203i 0.426927 0.0306520i
\(918\) −1.26795 −0.0418486
\(919\) 22.1469i 0.730560i −0.930898 0.365280i \(-0.880973\pi\)
0.930898 0.365280i \(-0.119027\pi\)
\(920\) −7.72741 −0.254765
\(921\) 15.0759i 0.496767i
\(922\) 19.0718i 0.628096i
\(923\) −29.3939 −0.967511
\(924\) 5.47959 14.1765i 0.180265 0.466374i
\(925\) 0.535898 0.0176202
\(926\) 16.4158i 0.539455i
\(927\) 12.3923i 0.407017i
\(928\) −5.32051 −0.174654
\(929\) 9.46410i 0.310507i −0.987875 0.155254i \(-0.950381\pi\)
0.987875 0.155254i \(-0.0496195\pi\)
\(930\) 1.51575 0.0497034
\(931\) −7.17260 + 1.03528i −0.235073 + 0.0339298i
\(932\) 29.6985i 0.972806i
\(933\) 18.7846 0.614981
\(934\) −13.5873 −0.444591
\(935\) −3.46410 + 7.34847i −0.113288 + 0.240321i
\(936\) 8.19615i 0.267900i
\(937\) −43.6375 −1.42558 −0.712788 0.701379i \(-0.752568\pi\)
−0.712788 + 0.701379i \(0.752568\pi\)
\(938\) −0.535898 7.46410i −0.0174977 0.243712i
\(939\) −31.8564 −1.03959
\(940\) 5.07180 0.165424
\(941\) −22.3500 −0.728590 −0.364295 0.931284i \(-0.618690\pi\)
−0.364295 + 0.931284i \(0.618690\pi\)
\(942\) 3.30890i 0.107810i
\(943\) 26.7685 0.871703
\(944\) 31.8564i 1.03684i
\(945\) 2.63896 0.189469i 0.0858453 0.00616342i
\(946\) 3.80385 + 1.79315i 0.123674 + 0.0583004i
\(947\) −4.39230 −0.142731 −0.0713654 0.997450i \(-0.522736\pi\)
−0.0713654 + 0.997450i \(0.522736\pi\)
\(948\) 6.69213 0.217350
\(949\) −2.78461 −0.0903923
\(950\) 0.535898i 0.0173868i
\(951\) 28.2487i 0.916027i
\(952\) −0.896575 12.4877i −0.0290582 0.404728i
\(953\) 15.0759i 0.488356i 0.969730 + 0.244178i \(0.0785180\pi\)
−0.969730 + 0.244178i \(0.921482\pi\)
\(954\) 1.79315i 0.0580554i
\(955\) 11.0718i 0.358275i
\(956\) 20.5569i 0.664857i
\(957\) 3.10583 + 1.46410i 0.100397 + 0.0473277i
\(958\) 1.46410i 0.0473030i
\(959\) 55.2287 3.96524i 1.78343 0.128044i
\(960\) 2.26795 0.0731977
\(961\) 22.4256 0.723407
\(962\) 1.17691i 0.0379452i
\(963\) 10.4543i 0.336885i
\(964\) 19.2442 0.619814
\(965\) −21.2132 −0.682877
\(966\) −5.46410 + 0.392305i −0.175805 + 0.0126222i
\(967\) 36.7423i 1.18155i 0.806835 + 0.590777i \(0.201179\pi\)
−0.806835 + 0.590777i \(0.798821\pi\)
\(968\) 16.3923 13.5230i 0.526869 0.434644i
\(969\) 2.53590i 0.0814648i
\(970\) 2.55103i 0.0819085i
\(971\) 10.1436i 0.325523i −0.986665 0.162762i \(-0.947960\pi\)
0.986665 0.162762i \(-0.0520402\pi\)
\(972\) 1.73205i 0.0555556i
\(973\) −56.4449 + 4.05256i −1.80954 + 0.129919i
\(974\) 7.93048i 0.254109i
\(975\) 4.24264i 0.135873i
\(976\) 12.0716 0.386402
\(977\) −23.0718 −0.738132 −0.369066 0.929403i \(-0.620322\pi\)
−0.369066 + 0.929403i \(0.620322\pi\)
\(978\) 4.34418 0.138911
\(979\) −6.96953 + 14.7846i −0.222747 + 0.472518i
\(980\) 1.73205 + 12.0000i 0.0553283 + 0.383326i
\(981\) 17.5254i 0.559542i
\(982\) 1.46410 0.0467214
\(983\) 16.3923i 0.522833i 0.965226 + 0.261417i \(0.0841897\pi\)
−0.965226 + 0.261417i \(0.915810\pi\)
\(984\) 12.9282 0.412136
\(985\) 17.9043 0.570479
\(986\) 1.31268 0.0418042
\(987\) 7.72741 0.554803i 0.245966 0.0176596i
\(988\) 7.60770 0.242033
\(989\) 9.79796i 0.311557i
\(990\) 1.55291 + 0.732051i 0.0493549 + 0.0232661i
\(991\) −18.1051 −0.575128 −0.287564 0.957761i \(-0.592845\pi\)
−0.287564 + 0.957761i \(0.592845\pi\)
\(992\) 15.0487 0.477796
\(993\) 32.2487i 1.02338i
\(994\) 0.679492 + 9.46410i 0.0215522 + 0.300183i
\(995\) 19.4641 0.617054
\(996\) 2.44949i 0.0776151i
\(997\) 26.1122 0.826981 0.413491 0.910508i \(-0.364309\pi\)
0.413491 + 0.910508i \(0.364309\pi\)
\(998\) 2.07055i 0.0655422i
\(999\) 0.535898i 0.0169551i
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 1155.2.i.b.76.3 8
7.6 odd 2 inner 1155.2.i.b.76.4 yes 8
11.10 odd 2 inner 1155.2.i.b.76.5 yes 8
77.76 even 2 inner 1155.2.i.b.76.6 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.i.b.76.3 8 1.1 even 1 trivial
1155.2.i.b.76.4 yes 8 7.6 odd 2 inner
1155.2.i.b.76.5 yes 8 11.10 odd 2 inner
1155.2.i.b.76.6 yes 8 77.76 even 2 inner