Properties

Label 1170.2.cu.d.1151.1
Level $1170$
Weight $2$
Character 1170.1151
Analytic conductor $9.342$
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] = [1170,2,Mod(71,1170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1170, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1170.71");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.cu (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.34249703649\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{12})\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 1151.1
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1170.1151
Dual form 1170.2.cu.d.431.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.500000 + 0.133975i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.500000 + 0.133975i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{10} +(-5.01910 + 1.34486i) q^{11} +(0.232051 - 3.59808i) q^{13} -0.517638i q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.41421 - 2.44949i) q^{17} +(-0.232051 + 0.866025i) q^{19} +(-0.258819 + 0.965926i) q^{20} +(2.59808 + 4.50000i) q^{22} +(-1.22474 + 2.12132i) q^{23} -1.00000i q^{25} +(-3.53553 + 0.707107i) q^{26} +(-0.500000 + 0.133975i) q^{28} +(-6.69213 - 3.86370i) q^{29} +(0.732051 + 0.732051i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-2.00000 + 2.00000i) q^{34} +(0.448288 - 0.258819i) q^{35} +(-0.696152 - 2.59808i) q^{37} +0.896575 q^{38} +1.00000 q^{40} +(-2.31079 - 8.62398i) q^{41} +(-0.464102 + 0.267949i) q^{43} +(3.67423 - 3.67423i) q^{44} +(2.36603 + 0.633975i) q^{46} +(-4.57081 - 4.57081i) q^{47} +(-5.83013 - 3.36603i) q^{49} +(-0.965926 + 0.258819i) q^{50} +(1.59808 + 3.23205i) q^{52} -1.27551i q^{53} +(-2.59808 + 4.50000i) q^{55} +(0.258819 + 0.448288i) q^{56} +(-2.00000 + 7.46410i) q^{58} +(0.896575 - 3.34607i) q^{59} +(3.73205 + 6.46410i) q^{61} +(0.517638 - 0.896575i) q^{62} +1.00000i q^{64} +(-2.38014 - 2.70831i) q^{65} +(9.46410 - 2.53590i) q^{67} +(2.44949 + 1.41421i) q^{68} +(-0.366025 - 0.366025i) q^{70} +(1.93185 + 0.517638i) q^{71} +(-9.46410 + 9.46410i) q^{73} +(-2.32937 + 1.34486i) q^{74} +(-0.232051 - 0.866025i) q^{76} -2.68973 q^{77} -0.928203 q^{79} +(-0.258819 - 0.965926i) q^{80} +(-7.73205 + 4.46410i) q^{82} +(-8.48528 + 8.48528i) q^{83} +(-2.73205 - 0.732051i) q^{85} +(0.378937 + 0.378937i) q^{86} +(-4.50000 - 2.59808i) q^{88} +(-12.4183 + 3.32748i) q^{89} +(0.598076 - 1.76795i) q^{91} -2.44949i q^{92} +(-3.23205 + 5.59808i) q^{94} +(0.448288 + 0.776457i) q^{95} +(2.00000 - 7.46410i) q^{97} +(-1.74238 + 6.50266i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{7} - 12 q^{13} + 4 q^{16} + 12 q^{19} - 4 q^{28} - 8 q^{31} - 16 q^{34} + 36 q^{37} + 8 q^{40} + 24 q^{43} + 12 q^{46} - 12 q^{49} - 8 q^{52} - 16 q^{58} + 16 q^{61} + 48 q^{67} + 4 q^{70} - 48 q^{73} + 12 q^{76} + 48 q^{79} - 48 q^{82} - 8 q^{85} - 36 q^{88} - 16 q^{91} - 12 q^{94} + 16 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 0.965926i −0.183013 0.683013i
\(3\) 0 0
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 0.707107 0.707107i 0.316228 0.316228i
\(6\) 0 0
\(7\) 0.500000 + 0.133975i 0.188982 + 0.0506376i 0.352069 0.935974i \(-0.385478\pi\)
−0.163087 + 0.986612i \(0.552145\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0 0
\(10\) −0.866025 0.500000i −0.273861 0.158114i
\(11\) −5.01910 + 1.34486i −1.51331 + 0.405492i −0.917535 0.397656i \(-0.869824\pi\)
−0.595780 + 0.803147i \(0.703157\pi\)
\(12\) 0 0
\(13\) 0.232051 3.59808i 0.0643593 0.997927i
\(14\) 0.517638i 0.138345i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) −1.41421 2.44949i −0.342997 0.594089i 0.641991 0.766712i \(-0.278109\pi\)
−0.984988 + 0.172624i \(0.944775\pi\)
\(18\) 0 0
\(19\) −0.232051 + 0.866025i −0.0532361 + 0.198680i −0.987422 0.158107i \(-0.949461\pi\)
0.934186 + 0.356787i \(0.116128\pi\)
\(20\) −0.258819 + 0.965926i −0.0578737 + 0.215988i
\(21\) 0 0
\(22\) 2.59808 + 4.50000i 0.553912 + 0.959403i
\(23\) −1.22474 + 2.12132i −0.255377 + 0.442326i −0.964998 0.262258i \(-0.915533\pi\)
0.709621 + 0.704584i \(0.248866\pi\)
\(24\) 0 0
\(25\) 1.00000i 0.200000i
\(26\) −3.53553 + 0.707107i −0.693375 + 0.138675i
\(27\) 0 0
\(28\) −0.500000 + 0.133975i −0.0944911 + 0.0253188i
\(29\) −6.69213 3.86370i −1.24270 0.717472i −0.273055 0.961998i \(-0.588034\pi\)
−0.969643 + 0.244527i \(0.921367\pi\)
\(30\) 0 0
\(31\) 0.732051 + 0.732051i 0.131480 + 0.131480i 0.769784 0.638304i \(-0.220364\pi\)
−0.638304 + 0.769784i \(0.720364\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) 0 0
\(34\) −2.00000 + 2.00000i −0.342997 + 0.342997i
\(35\) 0.448288 0.258819i 0.0757745 0.0437484i
\(36\) 0 0
\(37\) −0.696152 2.59808i −0.114447 0.427121i 0.884798 0.465974i \(-0.154296\pi\)
−0.999245 + 0.0388534i \(0.987629\pi\)
\(38\) 0.896575 0.145444
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) −2.31079 8.62398i −0.360885 1.34684i −0.872915 0.487872i \(-0.837773\pi\)
0.512030 0.858967i \(-0.328894\pi\)
\(42\) 0 0
\(43\) −0.464102 + 0.267949i −0.0707748 + 0.0408619i −0.534970 0.844871i \(-0.679677\pi\)
0.464195 + 0.885733i \(0.346344\pi\)
\(44\) 3.67423 3.67423i 0.553912 0.553912i
\(45\) 0 0
\(46\) 2.36603 + 0.633975i 0.348851 + 0.0934745i
\(47\) −4.57081 4.57081i −0.666721 0.666721i 0.290234 0.956956i \(-0.406267\pi\)
−0.956956 + 0.290234i \(0.906267\pi\)
\(48\) 0 0
\(49\) −5.83013 3.36603i −0.832875 0.480861i
\(50\) −0.965926 + 0.258819i −0.136603 + 0.0366025i
\(51\) 0 0
\(52\) 1.59808 + 3.23205i 0.221613 + 0.448205i
\(53\) 1.27551i 0.175205i −0.996156 0.0876026i \(-0.972079\pi\)
0.996156 0.0876026i \(-0.0279206\pi\)
\(54\) 0 0
\(55\) −2.59808 + 4.50000i −0.350325 + 0.606780i
\(56\) 0.258819 + 0.448288i 0.0345861 + 0.0599050i
\(57\) 0 0
\(58\) −2.00000 + 7.46410i −0.262613 + 0.980085i
\(59\) 0.896575 3.34607i 0.116724 0.435621i −0.882686 0.469963i \(-0.844267\pi\)
0.999410 + 0.0343428i \(0.0109338\pi\)
\(60\) 0 0
\(61\) 3.73205 + 6.46410i 0.477840 + 0.827643i 0.999677 0.0254017i \(-0.00808648\pi\)
−0.521837 + 0.853045i \(0.674753\pi\)
\(62\) 0.517638 0.896575i 0.0657401 0.113865i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −2.38014 2.70831i −0.295220 0.335924i
\(66\) 0 0
\(67\) 9.46410 2.53590i 1.15622 0.309809i 0.370767 0.928726i \(-0.379095\pi\)
0.785457 + 0.618917i \(0.212428\pi\)
\(68\) 2.44949 + 1.41421i 0.297044 + 0.171499i
\(69\) 0 0
\(70\) −0.366025 0.366025i −0.0437484 0.0437484i
\(71\) 1.93185 + 0.517638i 0.229269 + 0.0614323i 0.371624 0.928383i \(-0.378801\pi\)
−0.142356 + 0.989816i \(0.545468\pi\)
\(72\) 0 0
\(73\) −9.46410 + 9.46410i −1.10769 + 1.10769i −0.114236 + 0.993454i \(0.536442\pi\)
−0.993454 + 0.114236i \(0.963558\pi\)
\(74\) −2.32937 + 1.34486i −0.270784 + 0.156337i
\(75\) 0 0
\(76\) −0.232051 0.866025i −0.0266181 0.0993399i
\(77\) −2.68973 −0.306523
\(78\) 0 0
\(79\) −0.928203 −0.104431 −0.0522155 0.998636i \(-0.516628\pi\)
−0.0522155 + 0.998636i \(0.516628\pi\)
\(80\) −0.258819 0.965926i −0.0289368 0.107994i
\(81\) 0 0
\(82\) −7.73205 + 4.46410i −0.853862 + 0.492978i
\(83\) −8.48528 + 8.48528i −0.931381 + 0.931381i −0.997792 0.0664117i \(-0.978845\pi\)
0.0664117 + 0.997792i \(0.478845\pi\)
\(84\) 0 0
\(85\) −2.73205 0.732051i −0.296333 0.0794021i
\(86\) 0.378937 + 0.378937i 0.0408619 + 0.0408619i
\(87\) 0 0
\(88\) −4.50000 2.59808i −0.479702 0.276956i
\(89\) −12.4183 + 3.32748i −1.31634 + 0.352712i −0.847606 0.530626i \(-0.821957\pi\)
−0.468735 + 0.883339i \(0.655290\pi\)
\(90\) 0 0
\(91\) 0.598076 1.76795i 0.0626954 0.185331i
\(92\) 2.44949i 0.255377i
\(93\) 0 0
\(94\) −3.23205 + 5.59808i −0.333361 + 0.577397i
\(95\) 0.448288 + 0.776457i 0.0459934 + 0.0796628i
\(96\) 0 0
\(97\) 2.00000 7.46410i 0.203069 0.757865i −0.786960 0.617004i \(-0.788346\pi\)
0.990029 0.140861i \(-0.0449870\pi\)
\(98\) −1.74238 + 6.50266i −0.176007 + 0.656868i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −1.41421 + 2.44949i −0.140720 + 0.243733i −0.927768 0.373158i \(-0.878275\pi\)
0.787048 + 0.616891i \(0.211608\pi\)
\(102\) 0 0
\(103\) 3.53590i 0.348402i 0.984710 + 0.174201i \(0.0557343\pi\)
−0.984710 + 0.174201i \(0.944266\pi\)
\(104\) 2.70831 2.38014i 0.265572 0.233392i
\(105\) 0 0
\(106\) −1.23205 + 0.330127i −0.119667 + 0.0320648i
\(107\) 3.34607 + 1.93185i 0.323476 + 0.186759i 0.652941 0.757409i \(-0.273535\pi\)
−0.329465 + 0.944168i \(0.606868\pi\)
\(108\) 0 0
\(109\) −7.26795 7.26795i −0.696143 0.696143i 0.267433 0.963576i \(-0.413825\pi\)
−0.963576 + 0.267433i \(0.913825\pi\)
\(110\) 5.01910 + 1.34486i 0.478552 + 0.128228i
\(111\) 0 0
\(112\) 0.366025 0.366025i 0.0345861 0.0345861i
\(113\) −6.69213 + 3.86370i −0.629543 + 0.363467i −0.780575 0.625062i \(-0.785074\pi\)
0.151032 + 0.988529i \(0.451740\pi\)
\(114\) 0 0
\(115\) 0.633975 + 2.36603i 0.0591184 + 0.220633i
\(116\) 7.72741 0.717472
\(117\) 0 0
\(118\) −3.46410 −0.318896
\(119\) −0.378937 1.41421i −0.0347371 0.129641i
\(120\) 0 0
\(121\) 13.8564 8.00000i 1.25967 0.727273i
\(122\) 5.27792 5.27792i 0.477840 0.477840i
\(123\) 0 0
\(124\) −1.00000 0.267949i −0.0898027 0.0240625i
\(125\) −0.707107 0.707107i −0.0632456 0.0632456i
\(126\) 0 0
\(127\) −6.52628 3.76795i −0.579114 0.334351i 0.181667 0.983360i \(-0.441851\pi\)
−0.760781 + 0.649009i \(0.775184\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) 0 0
\(130\) −2.00000 + 3.00000i −0.175412 + 0.263117i
\(131\) 19.9377i 1.74196i −0.491315 0.870982i \(-0.663484\pi\)
0.491315 0.870982i \(-0.336516\pi\)
\(132\) 0 0
\(133\) −0.232051 + 0.401924i −0.0201214 + 0.0348512i
\(134\) −4.89898 8.48528i −0.423207 0.733017i
\(135\) 0 0
\(136\) 0.732051 2.73205i 0.0627728 0.234271i
\(137\) −1.41421 + 5.27792i −0.120824 + 0.450923i −0.999657 0.0262083i \(-0.991657\pi\)
0.878832 + 0.477131i \(0.158323\pi\)
\(138\) 0 0
\(139\) 5.13397 + 8.89230i 0.435458 + 0.754235i 0.997333 0.0729868i \(-0.0232531\pi\)
−0.561875 + 0.827222i \(0.689920\pi\)
\(140\) −0.258819 + 0.448288i −0.0218742 + 0.0378872i
\(141\) 0 0
\(142\) 2.00000i 0.167836i
\(143\) 3.67423 + 18.3712i 0.307255 + 1.53627i
\(144\) 0 0
\(145\) −7.46410 + 2.00000i −0.619860 + 0.166091i
\(146\) 11.5911 + 6.69213i 0.959287 + 0.553845i
\(147\) 0 0
\(148\) 1.90192 + 1.90192i 0.156337 + 0.156337i
\(149\) 16.7303 + 4.48288i 1.37060 + 0.367252i 0.867698 0.497091i \(-0.165599\pi\)
0.502903 + 0.864343i \(0.332265\pi\)
\(150\) 0 0
\(151\) −0.196152 + 0.196152i −0.0159627 + 0.0159627i −0.715043 0.699080i \(-0.753593\pi\)
0.699080 + 0.715043i \(0.253593\pi\)
\(152\) −0.776457 + 0.448288i −0.0629790 + 0.0363609i
\(153\) 0 0
\(154\) 0.696152 + 2.59808i 0.0560976 + 0.209359i
\(155\) 1.03528 0.0831554
\(156\) 0 0
\(157\) 18.3205 1.46214 0.731068 0.682305i \(-0.239022\pi\)
0.731068 + 0.682305i \(0.239022\pi\)
\(158\) 0.240237 + 0.896575i 0.0191122 + 0.0713277i
\(159\) 0 0
\(160\) −0.866025 + 0.500000i −0.0684653 + 0.0395285i
\(161\) −0.896575 + 0.896575i −0.0706600 + 0.0706600i
\(162\) 0 0
\(163\) −8.19615 2.19615i −0.641972 0.172016i −0.0768756 0.997041i \(-0.524494\pi\)
−0.565097 + 0.825025i \(0.691161\pi\)
\(164\) 6.31319 + 6.31319i 0.492978 + 0.492978i
\(165\) 0 0
\(166\) 10.3923 + 6.00000i 0.806599 + 0.465690i
\(167\) −0.258819 + 0.0693504i −0.0200280 + 0.00536649i −0.268819 0.963191i \(-0.586633\pi\)
0.248791 + 0.968557i \(0.419967\pi\)
\(168\) 0 0
\(169\) −12.8923 1.66987i −0.991716 0.128452i
\(170\) 2.82843i 0.216930i
\(171\) 0 0
\(172\) 0.267949 0.464102i 0.0204309 0.0353874i
\(173\) 11.9007 + 20.6126i 0.904793 + 1.56715i 0.821195 + 0.570648i \(0.193308\pi\)
0.0835987 + 0.996500i \(0.473359\pi\)
\(174\) 0 0
\(175\) 0.133975 0.500000i 0.0101275 0.0377964i
\(176\) −1.34486 + 5.01910i −0.101373 + 0.378329i
\(177\) 0 0
\(178\) 6.42820 + 11.1340i 0.481814 + 0.834527i
\(179\) 12.8159 22.1977i 0.957902 1.65913i 0.230319 0.973115i \(-0.426023\pi\)
0.727583 0.686020i \(-0.240644\pi\)
\(180\) 0 0
\(181\) 16.9282i 1.25826i −0.777299 0.629132i \(-0.783411\pi\)
0.777299 0.629132i \(-0.216589\pi\)
\(182\) −1.86250 0.120118i −0.138058 0.00890376i
\(183\) 0 0
\(184\) −2.36603 + 0.633975i −0.174426 + 0.0467372i
\(185\) −2.32937 1.34486i −0.171259 0.0988763i
\(186\) 0 0
\(187\) 10.3923 + 10.3923i 0.759961 + 0.759961i
\(188\) 6.24384 + 1.67303i 0.455379 + 0.122018i
\(189\) 0 0
\(190\) 0.633975 0.633975i 0.0459934 0.0459934i
\(191\) 0.416102 0.240237i 0.0301081 0.0173829i −0.484870 0.874586i \(-0.661133\pi\)
0.514978 + 0.857203i \(0.327800\pi\)
\(192\) 0 0
\(193\) −3.12436 11.6603i −0.224896 0.839323i −0.982446 0.186546i \(-0.940271\pi\)
0.757550 0.652777i \(-0.226396\pi\)
\(194\) −7.72741 −0.554795
\(195\) 0 0
\(196\) 6.73205 0.480861
\(197\) 2.75908 + 10.2970i 0.196576 + 0.733632i 0.991853 + 0.127386i \(0.0406587\pi\)
−0.795277 + 0.606246i \(0.792675\pi\)
\(198\) 0 0
\(199\) 19.3923 11.1962i 1.37468 0.793674i 0.383170 0.923678i \(-0.374832\pi\)
0.991514 + 0.130003i \(0.0414988\pi\)
\(200\) 0.707107 0.707107i 0.0500000 0.0500000i
\(201\) 0 0
\(202\) 2.73205 + 0.732051i 0.192226 + 0.0515069i
\(203\) −2.82843 2.82843i −0.198517 0.198517i
\(204\) 0 0
\(205\) −7.73205 4.46410i −0.540030 0.311786i
\(206\) 3.41542 0.915158i 0.237963 0.0637621i
\(207\) 0 0
\(208\) −3.00000 2.00000i −0.208013 0.138675i
\(209\) 4.65874i 0.322252i
\(210\) 0 0
\(211\) 6.42820 11.1340i 0.442536 0.766494i −0.555341 0.831623i \(-0.687412\pi\)
0.997877 + 0.0651282i \(0.0207456\pi\)
\(212\) 0.637756 + 1.10463i 0.0438013 + 0.0758661i
\(213\) 0 0
\(214\) 1.00000 3.73205i 0.0683586 0.255118i
\(215\) −0.138701 + 0.517638i −0.00945931 + 0.0353026i
\(216\) 0 0
\(217\) 0.267949 + 0.464102i 0.0181896 + 0.0315053i
\(218\) −5.13922 + 8.90138i −0.348072 + 0.602878i
\(219\) 0 0
\(220\) 5.19615i 0.350325i
\(221\) −9.14162 + 4.52004i −0.614932 + 0.304051i
\(222\) 0 0
\(223\) −26.3564 + 7.06218i −1.76496 + 0.472918i −0.987712 0.156282i \(-0.950049\pi\)
−0.777243 + 0.629200i \(0.783382\pi\)
\(224\) −0.448288 0.258819i −0.0299525 0.0172931i
\(225\) 0 0
\(226\) 5.46410 + 5.46410i 0.363467 + 0.363467i
\(227\) 20.0764 + 5.37945i 1.33252 + 0.357047i 0.853653 0.520842i \(-0.174382\pi\)
0.478864 + 0.877889i \(0.341049\pi\)
\(228\) 0 0
\(229\) 5.12436 5.12436i 0.338627 0.338627i −0.517223 0.855850i \(-0.673034\pi\)
0.855850 + 0.517223i \(0.173034\pi\)
\(230\) 2.12132 1.22474i 0.139876 0.0807573i
\(231\) 0 0
\(232\) −2.00000 7.46410i −0.131306 0.490042i
\(233\) 18.7637 1.22925 0.614626 0.788819i \(-0.289307\pi\)
0.614626 + 0.788819i \(0.289307\pi\)
\(234\) 0 0
\(235\) −6.46410 −0.421671
\(236\) 0.896575 + 3.34607i 0.0583621 + 0.217810i
\(237\) 0 0
\(238\) −1.26795 + 0.732051i −0.0821889 + 0.0474518i
\(239\) 6.79367 6.79367i 0.439446 0.439446i −0.452380 0.891825i \(-0.649425\pi\)
0.891825 + 0.452380i \(0.149425\pi\)
\(240\) 0 0
\(241\) 1.96410 + 0.526279i 0.126519 + 0.0339006i 0.321523 0.946902i \(-0.395805\pi\)
−0.195004 + 0.980802i \(0.562472\pi\)
\(242\) −11.3137 11.3137i −0.727273 0.727273i
\(243\) 0 0
\(244\) −6.46410 3.73205i −0.413822 0.238920i
\(245\) −6.50266 + 1.74238i −0.415440 + 0.111317i
\(246\) 0 0
\(247\) 3.06218 + 1.03590i 0.194842 + 0.0659126i
\(248\) 1.03528i 0.0657401i
\(249\) 0 0
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) −8.17569 14.1607i −0.516045 0.893817i −0.999826 0.0186276i \(-0.994070\pi\)
0.483781 0.875189i \(-0.339263\pi\)
\(252\) 0 0
\(253\) 3.29423 12.2942i 0.207106 0.772932i
\(254\) −1.95043 + 7.27912i −0.122381 + 0.456733i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.41421 + 2.44949i −0.0882162 + 0.152795i −0.906757 0.421653i \(-0.861450\pi\)
0.818541 + 0.574448i \(0.194783\pi\)
\(258\) 0 0
\(259\) 1.39230i 0.0865136i
\(260\) 3.41542 + 1.15539i 0.211815 + 0.0716545i
\(261\) 0 0
\(262\) −19.2583 + 5.16025i −1.18978 + 0.318802i
\(263\) 25.0076 + 14.4381i 1.54203 + 0.890293i 0.998710 + 0.0507679i \(0.0161669\pi\)
0.543322 + 0.839525i \(0.317166\pi\)
\(264\) 0 0
\(265\) −0.901924 0.901924i −0.0554047 0.0554047i
\(266\) 0.448288 + 0.120118i 0.0274863 + 0.00736493i
\(267\) 0 0
\(268\) −6.92820 + 6.92820i −0.423207 + 0.423207i
\(269\) −17.1464 + 9.89949i −1.04544 + 0.603583i −0.921368 0.388691i \(-0.872927\pi\)
−0.124068 + 0.992274i \(0.539594\pi\)
\(270\) 0 0
\(271\) 1.26795 + 4.73205i 0.0770224 + 0.287452i 0.993684 0.112212i \(-0.0357936\pi\)
−0.916662 + 0.399664i \(0.869127\pi\)
\(272\) −2.82843 −0.171499
\(273\) 0 0
\(274\) 5.46410 0.330098
\(275\) 1.34486 + 5.01910i 0.0810983 + 0.302663i
\(276\) 0 0
\(277\) 20.5526 11.8660i 1.23488 0.712960i 0.266840 0.963741i \(-0.414021\pi\)
0.968044 + 0.250781i \(0.0806873\pi\)
\(278\) 7.26054 7.26054i 0.435458 0.435458i
\(279\) 0 0
\(280\) 0.500000 + 0.133975i 0.0298807 + 0.00800651i
\(281\) −19.7990 19.7990i −1.18111 1.18111i −0.979457 0.201651i \(-0.935369\pi\)
−0.201651 0.979457i \(-0.564631\pi\)
\(282\) 0 0
\(283\) 19.0526 + 11.0000i 1.13256 + 0.653882i 0.944577 0.328291i \(-0.106473\pi\)
0.187980 + 0.982173i \(0.439806\pi\)
\(284\) −1.93185 + 0.517638i −0.114634 + 0.0307162i
\(285\) 0 0
\(286\) 16.7942 8.30385i 0.993064 0.491017i
\(287\) 4.62158i 0.272803i
\(288\) 0 0
\(289\) 4.50000 7.79423i 0.264706 0.458484i
\(290\) 3.86370 + 6.69213i 0.226884 + 0.392975i
\(291\) 0 0
\(292\) 3.46410 12.9282i 0.202721 0.756566i
\(293\) 1.63587 6.10514i 0.0955684 0.356666i −0.901537 0.432703i \(-0.857560\pi\)
0.997105 + 0.0760366i \(0.0242266\pi\)
\(294\) 0 0
\(295\) −1.73205 3.00000i −0.100844 0.174667i
\(296\) 1.34486 2.32937i 0.0781686 0.135392i
\(297\) 0 0
\(298\) 17.3205i 1.00335i
\(299\) 7.34847 + 4.89898i 0.424973 + 0.283315i
\(300\) 0 0
\(301\) −0.267949 + 0.0717968i −0.0154443 + 0.00413830i
\(302\) 0.240237 + 0.138701i 0.0138241 + 0.00798133i
\(303\) 0 0
\(304\) 0.633975 + 0.633975i 0.0363609 + 0.0363609i
\(305\) 7.20977 + 1.93185i 0.412830 + 0.110618i
\(306\) 0 0
\(307\) −11.1244 + 11.1244i −0.634901 + 0.634901i −0.949293 0.314393i \(-0.898199\pi\)
0.314393 + 0.949293i \(0.398199\pi\)
\(308\) 2.32937 1.34486i 0.132728 0.0766307i
\(309\) 0 0
\(310\) −0.267949 1.00000i −0.0152185 0.0567962i
\(311\) −1.51575 −0.0859503 −0.0429751 0.999076i \(-0.513684\pi\)
−0.0429751 + 0.999076i \(0.513684\pi\)
\(312\) 0 0
\(313\) −7.46410 −0.421896 −0.210948 0.977497i \(-0.567655\pi\)
−0.210948 + 0.977497i \(0.567655\pi\)
\(314\) −4.74170 17.6963i −0.267589 0.998657i
\(315\) 0 0
\(316\) 0.803848 0.464102i 0.0452200 0.0261078i
\(317\) 19.2677 19.2677i 1.08218 1.08218i 0.0858790 0.996306i \(-0.472630\pi\)
0.996306 0.0858790i \(-0.0273698\pi\)
\(318\) 0 0
\(319\) 38.7846 + 10.3923i 2.17152 + 0.581857i
\(320\) 0.707107 + 0.707107i 0.0395285 + 0.0395285i
\(321\) 0 0
\(322\) 1.09808 + 0.633975i 0.0611934 + 0.0353300i
\(323\) 2.44949 0.656339i 0.136293 0.0365197i
\(324\) 0 0
\(325\) −3.59808 0.232051i −0.199585 0.0128719i
\(326\) 8.48528i 0.469956i
\(327\) 0 0
\(328\) 4.46410 7.73205i 0.246489 0.426931i
\(329\) −1.67303 2.89778i −0.0922373 0.159760i
\(330\) 0 0
\(331\) −0.973721 + 3.63397i −0.0535205 + 0.199741i −0.987509 0.157561i \(-0.949637\pi\)
0.933989 + 0.357303i \(0.116303\pi\)
\(332\) 3.10583 11.5911i 0.170454 0.636145i
\(333\) 0 0
\(334\) 0.133975 + 0.232051i 0.00733076 + 0.0126973i
\(335\) 4.89898 8.48528i 0.267660 0.463600i
\(336\) 0 0
\(337\) 21.7128i 1.18277i −0.806389 0.591386i \(-0.798581\pi\)
0.806389 0.591386i \(-0.201419\pi\)
\(338\) 1.72380 + 12.8852i 0.0937624 + 0.700863i
\(339\) 0 0
\(340\) 2.73205 0.732051i 0.148166 0.0397010i
\(341\) −4.65874 2.68973i −0.252285 0.145657i
\(342\) 0 0
\(343\) −5.02628 5.02628i −0.271394 0.271394i
\(344\) −0.517638 0.138701i −0.0279092 0.00747824i
\(345\) 0 0
\(346\) 16.8301 16.8301i 0.904793 0.904793i
\(347\) −13.3843 + 7.72741i −0.718505 + 0.414829i −0.814202 0.580582i \(-0.802825\pi\)
0.0956973 + 0.995410i \(0.469492\pi\)
\(348\) 0 0
\(349\) 1.80385 + 6.73205i 0.0965577 + 0.360358i 0.997251 0.0740971i \(-0.0236075\pi\)
−0.900693 + 0.434456i \(0.856941\pi\)
\(350\) −0.517638 −0.0276689
\(351\) 0 0
\(352\) 5.19615 0.276956
\(353\) 2.55103 + 9.52056i 0.135777 + 0.506728i 0.999993 + 0.00360735i \(0.00114826\pi\)
−0.864216 + 0.503121i \(0.832185\pi\)
\(354\) 0 0
\(355\) 1.73205 1.00000i 0.0919277 0.0530745i
\(356\) 9.09085 9.09085i 0.481814 0.481814i
\(357\) 0 0
\(358\) −24.7583 6.63397i −1.30852 0.350616i
\(359\) 22.8033 + 22.8033i 1.20351 + 1.20351i 0.973091 + 0.230420i \(0.0740100\pi\)
0.230420 + 0.973091i \(0.425990\pi\)
\(360\) 0 0
\(361\) 15.7583 + 9.09808i 0.829386 + 0.478846i
\(362\) −16.3514 + 4.38134i −0.859410 + 0.230278i
\(363\) 0 0
\(364\) 0.366025 + 1.83013i 0.0191849 + 0.0959247i
\(365\) 13.3843i 0.700564i
\(366\) 0 0
\(367\) 4.00000 6.92820i 0.208798 0.361649i −0.742538 0.669804i \(-0.766378\pi\)
0.951336 + 0.308155i \(0.0997115\pi\)
\(368\) 1.22474 + 2.12132i 0.0638442 + 0.110581i
\(369\) 0 0
\(370\) −0.696152 + 2.59808i −0.0361912 + 0.135068i
\(371\) 0.170886 0.637756i 0.00887198 0.0331107i
\(372\) 0 0
\(373\) −2.07180 3.58846i −0.107274 0.185803i 0.807391 0.590016i \(-0.200879\pi\)
−0.914665 + 0.404213i \(0.867545\pi\)
\(374\) 7.34847 12.7279i 0.379980 0.658145i
\(375\) 0 0
\(376\) 6.46410i 0.333361i
\(377\) −15.4548 + 23.1822i −0.795963 + 1.19395i
\(378\) 0 0
\(379\) −26.0885 + 6.99038i −1.34007 + 0.359072i −0.856462 0.516211i \(-0.827342\pi\)
−0.483612 + 0.875282i \(0.660676\pi\)
\(380\) −0.776457 0.448288i −0.0398314 0.0229967i
\(381\) 0 0
\(382\) −0.339746 0.339746i −0.0173829 0.0173829i
\(383\) −11.0735 2.96713i −0.565828 0.151613i −0.0354455 0.999372i \(-0.511285\pi\)
−0.530382 + 0.847758i \(0.677952\pi\)
\(384\) 0 0
\(385\) −1.90192 + 1.90192i −0.0969310 + 0.0969310i
\(386\) −10.4543 + 6.03579i −0.532110 + 0.307214i
\(387\) 0 0
\(388\) 2.00000 + 7.46410i 0.101535 + 0.378932i
\(389\) −19.7990 −1.00385 −0.501924 0.864912i \(-0.667374\pi\)
−0.501924 + 0.864912i \(0.667374\pi\)
\(390\) 0 0
\(391\) 6.92820 0.350374
\(392\) −1.74238 6.50266i −0.0880036 0.328434i
\(393\) 0 0
\(394\) 9.23205 5.33013i 0.465104 0.268528i
\(395\) −0.656339 + 0.656339i −0.0330240 + 0.0330240i
\(396\) 0 0
\(397\) −16.3301 4.37564i −0.819586 0.219607i −0.175420 0.984494i \(-0.556128\pi\)
−0.644165 + 0.764886i \(0.722795\pi\)
\(398\) −15.8338 15.8338i −0.793674 0.793674i
\(399\) 0 0
\(400\) −0.866025 0.500000i −0.0433013 0.0250000i
\(401\) 17.1278 4.58939i 0.855324 0.229183i 0.195593 0.980685i \(-0.437337\pi\)
0.659731 + 0.751502i \(0.270670\pi\)
\(402\) 0 0
\(403\) 2.80385 2.46410i 0.139670 0.122746i
\(404\) 2.82843i 0.140720i
\(405\) 0 0
\(406\) −2.00000 + 3.46410i −0.0992583 + 0.171920i
\(407\) 6.98811 + 12.1038i 0.346388 + 0.599962i
\(408\) 0 0
\(409\) 0.892305 3.33013i 0.0441216 0.164664i −0.940350 0.340209i \(-0.889502\pi\)
0.984471 + 0.175545i \(0.0561688\pi\)
\(410\) −2.31079 + 8.62398i −0.114122 + 0.425908i
\(411\) 0 0
\(412\) −1.76795 3.06218i −0.0871006 0.150863i
\(413\) 0.896575 1.55291i 0.0441176 0.0764139i
\(414\) 0 0
\(415\) 12.0000i 0.589057i
\(416\) −1.15539 + 3.41542i −0.0566479 + 0.167455i
\(417\) 0 0
\(418\) −4.50000 + 1.20577i −0.220102 + 0.0589762i
\(419\) 27.0967 + 15.6443i 1.32376 + 0.764273i 0.984326 0.176357i \(-0.0564313\pi\)
0.339434 + 0.940630i \(0.389765\pi\)
\(420\) 0 0
\(421\) −18.9282 18.9282i −0.922504 0.922504i 0.0747017 0.997206i \(-0.476200\pi\)
−0.997206 + 0.0747017i \(0.976200\pi\)
\(422\) −12.4183 3.32748i −0.604515 0.161979i
\(423\) 0 0
\(424\) 0.901924 0.901924i 0.0438013 0.0438013i
\(425\) −2.44949 + 1.41421i −0.118818 + 0.0685994i
\(426\) 0 0
\(427\) 1.00000 + 3.73205i 0.0483934 + 0.180607i
\(428\) −3.86370 −0.186759
\(429\) 0 0
\(430\) 0.535898 0.0258433
\(431\) −3.76217 14.0406i −0.181217 0.676312i −0.995409 0.0957155i \(-0.969486\pi\)
0.814192 0.580596i \(-0.197181\pi\)
\(432\) 0 0
\(433\) −1.26795 + 0.732051i −0.0609337 + 0.0351801i −0.530157 0.847899i \(-0.677867\pi\)
0.469224 + 0.883079i \(0.344534\pi\)
\(434\) 0.378937 0.378937i 0.0181896 0.0181896i
\(435\) 0 0
\(436\) 9.92820 + 2.66025i 0.475475 + 0.127403i
\(437\) −1.55291 1.55291i −0.0742860 0.0742860i
\(438\) 0 0
\(439\) −22.8564 13.1962i −1.09088 0.629818i −0.157067 0.987588i \(-0.550204\pi\)
−0.933810 + 0.357770i \(0.883537\pi\)
\(440\) −5.01910 + 1.34486i −0.239276 + 0.0641138i
\(441\) 0 0
\(442\) 6.73205 + 7.66025i 0.320211 + 0.364361i
\(443\) 15.7322i 0.747460i −0.927538 0.373730i \(-0.878079\pi\)
0.927538 0.373730i \(-0.121921\pi\)
\(444\) 0 0
\(445\) −6.42820 + 11.1340i −0.304726 + 0.527801i
\(446\) 13.6431 + 23.6305i 0.646019 + 1.11894i
\(447\) 0 0
\(448\) −0.133975 + 0.500000i −0.00632970 + 0.0236228i
\(449\) −1.57150 + 5.86491i −0.0741635 + 0.276782i −0.993042 0.117758i \(-0.962429\pi\)
0.918879 + 0.394540i \(0.129096\pi\)
\(450\) 0 0
\(451\) 23.1962 + 40.1769i 1.09226 + 1.89186i
\(452\) 3.86370 6.69213i 0.181733 0.314771i
\(453\) 0 0
\(454\) 20.7846i 0.975470i
\(455\) −0.827225 1.67303i −0.0387809 0.0784330i
\(456\) 0 0
\(457\) −11.1962 + 3.00000i −0.523734 + 0.140334i −0.510993 0.859585i \(-0.670722\pi\)
−0.0127407 + 0.999919i \(0.504056\pi\)
\(458\) −6.27603 3.62347i −0.293260 0.169313i
\(459\) 0 0
\(460\) −1.73205 1.73205i −0.0807573 0.0807573i
\(461\) 4.62158 + 1.23835i 0.215248 + 0.0576756i 0.364832 0.931074i \(-0.381127\pi\)
−0.149583 + 0.988749i \(0.547793\pi\)
\(462\) 0 0
\(463\) −29.0526 + 29.0526i −1.35019 + 1.35019i −0.464739 + 0.885448i \(0.653852\pi\)
−0.885448 + 0.464739i \(0.846148\pi\)
\(464\) −6.69213 + 3.86370i −0.310674 + 0.179368i
\(465\) 0 0
\(466\) −4.85641 18.1244i −0.224969 0.839595i
\(467\) 28.0812 1.29944 0.649721 0.760172i \(-0.274886\pi\)
0.649721 + 0.760172i \(0.274886\pi\)
\(468\) 0 0
\(469\) 5.07180 0.234194
\(470\) 1.67303 + 6.24384i 0.0771712 + 0.288007i
\(471\) 0 0
\(472\) 3.00000 1.73205i 0.138086 0.0797241i
\(473\) 1.96902 1.96902i 0.0905355 0.0905355i
\(474\) 0 0
\(475\) 0.866025 + 0.232051i 0.0397360 + 0.0106472i
\(476\) 1.03528 + 1.03528i 0.0474518 + 0.0474518i
\(477\) 0 0
\(478\) −8.32051 4.80385i −0.380571 0.219723i
\(479\) −29.8744 + 8.00481i −1.36499 + 0.365749i −0.865648 0.500654i \(-0.833093\pi\)
−0.499346 + 0.866403i \(0.666426\pi\)
\(480\) 0 0
\(481\) −9.50962 + 1.90192i −0.433601 + 0.0867203i
\(482\) 2.03339i 0.0926183i
\(483\) 0 0
\(484\) −8.00000 + 13.8564i −0.363636 + 0.629837i
\(485\) −3.86370 6.69213i −0.175442 0.303874i
\(486\) 0 0
\(487\) 3.17949 11.8660i 0.144077 0.537701i −0.855718 0.517442i \(-0.826884\pi\)
0.999795 0.0202589i \(-0.00644904\pi\)
\(488\) −1.93185 + 7.20977i −0.0874508 + 0.326371i
\(489\) 0 0
\(490\) 3.36603 + 5.83013i 0.152062 + 0.263378i
\(491\) 19.0089 32.9244i 0.857861 1.48586i −0.0161042 0.999870i \(-0.505126\pi\)
0.873965 0.485988i \(-0.161540\pi\)
\(492\) 0 0
\(493\) 21.8564i 0.984363i
\(494\) 0.208051 3.22595i 0.00936066 0.145142i
\(495\) 0 0
\(496\) 1.00000 0.267949i 0.0449013 0.0120313i
\(497\) 0.896575 + 0.517638i 0.0402169 + 0.0232192i
\(498\) 0 0
\(499\) 19.7321 + 19.7321i 0.883328 + 0.883328i 0.993871 0.110543i \(-0.0352591\pi\)
−0.110543 + 0.993871i \(0.535259\pi\)
\(500\) 0.965926 + 0.258819i 0.0431975 + 0.0115747i
\(501\) 0 0
\(502\) −11.5622 + 11.5622i −0.516045 + 0.516045i
\(503\) −16.9384 + 9.77938i −0.755245 + 0.436041i −0.827586 0.561339i \(-0.810286\pi\)
0.0723410 + 0.997380i \(0.476953\pi\)
\(504\) 0 0
\(505\) 0.732051 + 2.73205i 0.0325758 + 0.121575i
\(506\) −12.7279 −0.565825
\(507\) 0 0
\(508\) 7.53590 0.334351
\(509\) −8.72552 32.5641i −0.386752 1.44338i −0.835387 0.549662i \(-0.814756\pi\)
0.448635 0.893715i \(-0.351910\pi\)
\(510\) 0 0
\(511\) −6.00000 + 3.46410i −0.265424 + 0.153243i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 2.73205 + 0.732051i 0.120506 + 0.0322894i
\(515\) 2.50026 + 2.50026i 0.110175 + 0.110175i
\(516\) 0 0
\(517\) 29.0885 + 16.7942i 1.27931 + 0.738609i
\(518\) −1.34486 + 0.360355i −0.0590899 + 0.0158331i
\(519\) 0 0
\(520\) 0.232051 3.59808i 0.0101761 0.157786i
\(521\) 15.9725i 0.699766i −0.936793 0.349883i \(-0.886221\pi\)
0.936793 0.349883i \(-0.113779\pi\)
\(522\) 0 0
\(523\) −15.9282 + 27.5885i −0.696492 + 1.20636i 0.273184 + 0.961962i \(0.411923\pi\)
−0.969675 + 0.244397i \(0.921410\pi\)
\(524\) 9.96885 + 17.2665i 0.435491 + 0.754293i
\(525\) 0 0
\(526\) 7.47372 27.8923i 0.325870 1.21616i
\(527\) 0.757875 2.82843i 0.0330135 0.123208i
\(528\) 0 0
\(529\) 8.50000 + 14.7224i 0.369565 + 0.640106i
\(530\) −0.637756 + 1.10463i −0.0277024 + 0.0479819i
\(531\) 0 0
\(532\) 0.464102i 0.0201214i
\(533\) −31.5660 + 6.31319i −1.36727 + 0.273455i
\(534\) 0 0
\(535\) 3.73205 1.00000i 0.161351 0.0432338i
\(536\) 8.48528 + 4.89898i 0.366508 + 0.211604i
\(537\) 0 0
\(538\) 14.0000 + 14.0000i 0.603583 + 0.603583i
\(539\) 33.7888 + 9.05369i 1.45539 + 0.389970i
\(540\) 0 0
\(541\) −23.6603 + 23.6603i −1.01723 + 1.01723i −0.0173849 + 0.999849i \(0.505534\pi\)
−0.999849 + 0.0173849i \(0.994466\pi\)
\(542\) 4.24264 2.44949i 0.182237 0.105215i
\(543\) 0 0
\(544\) 0.732051 + 2.73205i 0.0313864 + 0.117136i
\(545\) −10.2784 −0.440280
\(546\) 0 0
\(547\) 13.6077 0.581823 0.290912 0.956750i \(-0.406041\pi\)
0.290912 + 0.956750i \(0.406041\pi\)
\(548\) −1.41421 5.27792i −0.0604122 0.225461i
\(549\) 0 0
\(550\) 4.50000 2.59808i 0.191881 0.110782i
\(551\) 4.89898 4.89898i 0.208704 0.208704i
\(552\) 0 0
\(553\) −0.464102 0.124356i −0.0197356 0.00528814i
\(554\) −16.7811 16.7811i −0.712960 0.712960i
\(555\) 0 0
\(556\) −8.89230 5.13397i −0.377118 0.217729i
\(557\) −4.88040 + 1.30770i −0.206789 + 0.0554090i −0.360727 0.932672i \(-0.617471\pi\)
0.153937 + 0.988081i \(0.450805\pi\)
\(558\) 0 0
\(559\) 0.856406 + 1.73205i 0.0362221 + 0.0732579i
\(560\) 0.517638i 0.0218742i
\(561\) 0 0
\(562\) −14.0000 + 24.2487i −0.590554 + 1.02287i
\(563\) 2.72689 + 4.72311i 0.114925 + 0.199056i 0.917750 0.397159i \(-0.130004\pi\)
−0.802825 + 0.596215i \(0.796671\pi\)
\(564\) 0 0
\(565\) −2.00000 + 7.46410i −0.0841406 + 0.314017i
\(566\) 5.69402 21.2504i 0.239337 0.893220i
\(567\) 0 0
\(568\) 1.00000 + 1.73205i 0.0419591 + 0.0726752i
\(569\) −13.3149 + 23.0621i −0.558190 + 0.966814i 0.439458 + 0.898263i \(0.355171\pi\)
−0.997648 + 0.0685502i \(0.978163\pi\)
\(570\) 0 0
\(571\) 43.5885i 1.82412i 0.410057 + 0.912060i \(0.365509\pi\)
−0.410057 + 0.912060i \(0.634491\pi\)
\(572\) −12.3676 14.0728i −0.517114 0.588413i
\(573\) 0 0
\(574\) −4.46410 + 1.19615i −0.186328 + 0.0499264i
\(575\) 2.12132 + 1.22474i 0.0884652 + 0.0510754i
\(576\) 0 0
\(577\) −26.5885 26.5885i −1.10689 1.10689i −0.993557 0.113335i \(-0.963847\pi\)
−0.113335 0.993557i \(-0.536153\pi\)
\(578\) −8.69333 2.32937i −0.361595 0.0968891i
\(579\) 0 0
\(580\) 5.46410 5.46410i 0.226884 0.226884i
\(581\) −5.37945 + 3.10583i −0.223177 + 0.128851i
\(582\) 0 0
\(583\) 1.71539 + 6.40192i 0.0710442 + 0.265141i
\(584\) −13.3843 −0.553845
\(585\) 0 0
\(586\) −6.32051 −0.261098
\(587\) −8.79985 32.8415i −0.363209 1.35551i −0.869833 0.493346i \(-0.835774\pi\)
0.506625 0.862167i \(-0.330893\pi\)
\(588\) 0 0
\(589\) −0.803848 + 0.464102i −0.0331220 + 0.0191230i
\(590\) −2.44949 + 2.44949i −0.100844 + 0.100844i
\(591\) 0 0
\(592\) −2.59808 0.696152i −0.106780 0.0286117i
\(593\) 6.96953 + 6.96953i 0.286204 + 0.286204i 0.835577 0.549373i \(-0.185133\pi\)
−0.549373 + 0.835577i \(0.685133\pi\)
\(594\) 0 0
\(595\) −1.26795 0.732051i −0.0519808 0.0300112i
\(596\) −16.7303 + 4.48288i −0.685301 + 0.183626i
\(597\) 0 0
\(598\) 2.83013 8.36603i 0.115733 0.342112i
\(599\) 17.4510i 0.713030i 0.934290 + 0.356515i \(0.116035\pi\)
−0.934290 + 0.356515i \(0.883965\pi\)
\(600\) 0 0
\(601\) 2.89230 5.00962i 0.117980 0.204347i −0.800987 0.598681i \(-0.795692\pi\)
0.918967 + 0.394335i \(0.129025\pi\)
\(602\) 0.138701 + 0.240237i 0.00565302 + 0.00979132i
\(603\) 0 0
\(604\) 0.0717968 0.267949i 0.00292137 0.0109027i
\(605\) 4.14110 15.4548i 0.168360 0.628328i
\(606\) 0 0
\(607\) 5.69615 + 9.86603i 0.231200 + 0.400450i 0.958161 0.286228i \(-0.0924016\pi\)
−0.726962 + 0.686678i \(0.759068\pi\)
\(608\) 0.448288 0.776457i 0.0181805 0.0314895i
\(609\) 0 0
\(610\) 7.46410i 0.302213i
\(611\) −17.5068 + 15.3855i −0.708249 + 0.622429i
\(612\) 0 0
\(613\) −26.1865 + 7.01666i −1.05766 + 0.283400i −0.745415 0.666600i \(-0.767749\pi\)
−0.312249 + 0.950000i \(0.601082\pi\)
\(614\) 13.6245 + 7.86611i 0.549840 + 0.317450i
\(615\) 0 0
\(616\) −1.90192 1.90192i −0.0766307 0.0766307i
\(617\) 26.9072 + 7.20977i 1.08324 + 0.290254i 0.755924 0.654659i \(-0.227188\pi\)
0.327320 + 0.944914i \(0.393855\pi\)
\(618\) 0 0
\(619\) 3.95448 3.95448i 0.158944 0.158944i −0.623155 0.782099i \(-0.714149\pi\)
0.782099 + 0.623155i \(0.214149\pi\)
\(620\) −0.896575 + 0.517638i −0.0360073 + 0.0207888i
\(621\) 0 0
\(622\) 0.392305 + 1.46410i 0.0157300 + 0.0587051i
\(623\) −6.65497 −0.266626
\(624\) 0 0
\(625\) −1.00000 −0.0400000
\(626\) 1.93185 + 7.20977i 0.0772123 + 0.288160i
\(627\) 0 0
\(628\) −15.8660 + 9.16025i −0.633123 + 0.365534i
\(629\) −5.37945 + 5.37945i −0.214493 + 0.214493i
\(630\) 0 0
\(631\) −19.1244 5.12436i −0.761329 0.203997i −0.142791 0.989753i \(-0.545608\pi\)
−0.618537 + 0.785755i \(0.712274\pi\)
\(632\) −0.656339 0.656339i −0.0261078 0.0261078i
\(633\) 0 0
\(634\) −23.5981 13.6244i −0.937199 0.541092i
\(635\) −7.27912 + 1.95043i −0.288863 + 0.0774006i
\(636\) 0 0
\(637\) −13.4641 + 20.1962i −0.533467 + 0.800201i
\(638\) 40.1528i 1.58966i
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) −7.98623 13.8325i −0.315437 0.546353i 0.664093 0.747650i \(-0.268818\pi\)
−0.979530 + 0.201297i \(0.935484\pi\)
\(642\) 0 0
\(643\) 3.66025 13.6603i 0.144346 0.538708i −0.855437 0.517906i \(-0.826712\pi\)
0.999784 0.0208014i \(-0.00662178\pi\)
\(644\) 0.328169 1.22474i 0.0129317 0.0482617i
\(645\) 0 0
\(646\) −1.26795 2.19615i −0.0498868 0.0864065i
\(647\) −10.2091 + 17.6826i −0.401360 + 0.695177i −0.993890 0.110372i \(-0.964796\pi\)
0.592530 + 0.805548i \(0.298129\pi\)
\(648\) 0 0
\(649\) 18.0000i 0.706562i
\(650\) 0.707107 + 3.53553i 0.0277350 + 0.138675i
\(651\) 0 0
\(652\) 8.19615 2.19615i 0.320986 0.0860080i
\(653\) 12.3676 + 7.14042i 0.483980 + 0.279426i 0.722074 0.691816i \(-0.243189\pi\)
−0.238093 + 0.971242i \(0.576522\pi\)
\(654\) 0 0
\(655\) −14.0981 14.0981i −0.550857 0.550857i
\(656\) −8.62398 2.31079i −0.336710 0.0902212i
\(657\) 0 0
\(658\) −2.36603 + 2.36603i −0.0922373 + 0.0922373i
\(659\) −11.0871 + 6.40113i −0.431891 + 0.249352i −0.700152 0.713994i \(-0.746884\pi\)
0.268261 + 0.963346i \(0.413551\pi\)
\(660\) 0 0
\(661\) −6.12436 22.8564i −0.238210 0.889011i −0.976676 0.214720i \(-0.931116\pi\)
0.738466 0.674291i \(-0.235551\pi\)
\(662\) 3.76217 0.146221
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0.120118 + 0.448288i 0.00465799 + 0.0173839i
\(666\) 0 0
\(667\) 16.3923 9.46410i 0.634713 0.366451i
\(668\) 0.189469 0.189469i 0.00733076 0.00733076i
\(669\) 0 0
\(670\) −9.46410 2.53590i −0.365630 0.0979703i
\(671\) −27.4249 27.4249i −1.05872 1.05872i
\(672\) 0 0
\(673\) −11.0718 6.39230i −0.426786 0.246405i 0.271190 0.962526i \(-0.412583\pi\)
−0.697977 + 0.716121i \(0.745916\pi\)
\(674\) −20.9730 + 5.61969i −0.807848 + 0.216462i
\(675\) 0 0
\(676\) 12.0000 5.00000i 0.461538 0.192308i
\(677\) 13.2827i 0.510497i −0.966876 0.255248i \(-0.917843\pi\)
0.966876 0.255248i \(-0.0821572\pi\)
\(678\) 0 0
\(679\) 2.00000 3.46410i 0.0767530 0.132940i
\(680\) −1.41421 2.44949i −0.0542326 0.0939336i
\(681\) 0 0
\(682\) −1.39230 + 5.19615i −0.0533141 + 0.198971i
\(683\) 8.72552 32.5641i 0.333873 1.24603i −0.571213 0.820802i \(-0.693527\pi\)
0.905086 0.425228i \(-0.139806\pi\)
\(684\) 0 0
\(685\) 2.73205 + 4.73205i 0.104386 + 0.180802i
\(686\) −3.55412 + 6.15591i −0.135697 + 0.235034i
\(687\) 0 0
\(688\) 0.535898i 0.0204309i
\(689\) −4.58939 0.295984i −0.174842 0.0112761i
\(690\) 0 0
\(691\) −46.0167 + 12.3301i −1.75056 + 0.469060i −0.984745 0.174005i \(-0.944329\pi\)
−0.765811 + 0.643065i \(0.777662\pi\)
\(692\) −20.6126 11.9007i −0.783574 0.452397i
\(693\) 0 0
\(694\) 10.9282 + 10.9282i 0.414829 + 0.414829i
\(695\) 9.91808 + 2.65754i 0.376214 + 0.100806i
\(696\) 0 0
\(697\) −17.8564 + 17.8564i −0.676360 + 0.676360i
\(698\) 6.03579 3.48477i 0.228458 0.131900i
\(699\) 0 0
\(700\) 0.133975 + 0.500000i 0.00506376 + 0.0188982i
\(701\) −1.31268 −0.0495791 −0.0247896 0.999693i \(-0.507892\pi\)
−0.0247896 + 0.999693i \(0.507892\pi\)
\(702\) 0 0
\(703\) 2.41154 0.0909531
\(704\) −1.34486 5.01910i −0.0506864 0.189164i
\(705\) 0 0
\(706\) 8.53590 4.92820i 0.321253 0.185475i
\(707\) −1.03528 + 1.03528i −0.0389356 + 0.0389356i
\(708\) 0 0
\(709\) 15.4641 + 4.14359i 0.580767 + 0.155616i 0.537230 0.843436i \(-0.319471\pi\)
0.0435367 + 0.999052i \(0.486137\pi\)
\(710\) −1.41421 1.41421i −0.0530745 0.0530745i
\(711\) 0 0
\(712\) −11.1340 6.42820i −0.417263 0.240907i
\(713\) −2.44949 + 0.656339i −0.0917341 + 0.0245801i
\(714\) 0 0
\(715\) 15.5885 + 10.3923i 0.582975 + 0.388650i
\(716\) 25.6317i 0.957902i
\(717\) 0 0
\(718\) 16.1244 27.9282i 0.601756 1.04227i
\(719\) 8.86422 + 15.3533i 0.330580 + 0.572581i 0.982626 0.185599i \(-0.0594225\pi\)
−0.652046 + 0.758179i \(0.726089\pi\)
\(720\) 0 0
\(721\) −0.473721 + 1.76795i −0.0176423 + 0.0658419i
\(722\) 4.70951 17.5761i 0.175270 0.654116i
\(723\) 0 0
\(724\) 8.46410 + 14.6603i 0.314566 + 0.544844i
\(725\) −3.86370 + 6.69213i −0.143494 + 0.248539i
\(726\) 0 0
\(727\) 45.5885i 1.69078i 0.534148 + 0.845391i \(0.320633\pi\)
−0.534148 + 0.845391i \(0.679367\pi\)
\(728\) 1.67303 0.827225i 0.0620067 0.0306590i
\(729\) 0 0
\(730\) 12.9282 3.46410i 0.478494 0.128212i
\(731\) 1.31268 + 0.757875i 0.0485511 + 0.0280310i
\(732\) 0 0
\(733\) −16.9019 16.9019i −0.624287 0.624287i 0.322338 0.946625i \(-0.395531\pi\)
−0.946625 + 0.322338i \(0.895531\pi\)
\(734\) −7.72741 2.07055i −0.285224 0.0764255i
\(735\) 0 0
\(736\) 1.73205 1.73205i 0.0638442 0.0638442i
\(737\) −44.0908 + 25.4558i −1.62411 + 0.937678i
\(738\) 0 0
\(739\) −4.59808 17.1603i −0.169143 0.631250i −0.997475 0.0710132i \(-0.977377\pi\)
0.828332 0.560237i \(-0.189290\pi\)
\(740\) 2.68973 0.0988763
\(741\) 0 0
\(742\) −0.660254 −0.0242387
\(743\) −13.3199 49.7105i −0.488659 1.82370i −0.562984 0.826467i \(-0.690347\pi\)
0.0743251 0.997234i \(-0.476320\pi\)
\(744\) 0 0
\(745\) 15.0000 8.66025i 0.549557 0.317287i
\(746\) −2.92996 + 2.92996i −0.107274 + 0.107274i
\(747\) 0 0
\(748\) −14.1962 3.80385i −0.519063 0.139082i
\(749\) 1.41421 + 1.41421i 0.0516742 + 0.0516742i
\(750\) 0 0
\(751\) −5.66025 3.26795i −0.206546 0.119249i 0.393159 0.919470i \(-0.371382\pi\)
−0.599705 + 0.800221i \(0.704715\pi\)
\(752\) −6.24384 + 1.67303i −0.227690 + 0.0610092i
\(753\) 0 0
\(754\) 26.3923 + 8.92820i 0.961151 + 0.325146i
\(755\) 0.277401i 0.0100957i
\(756\) 0 0
\(757\) 9.59808 16.6244i 0.348848 0.604222i −0.637197 0.770701i \(-0.719906\pi\)
0.986045 + 0.166478i \(0.0532396\pi\)
\(758\) 13.5044 + 23.3903i 0.490501 + 0.849573i
\(759\) 0 0
\(760\) −0.232051 + 0.866025i −0.00841737 + 0.0314140i
\(761\) −5.67544 + 21.1810i −0.205734 + 0.767811i 0.783490 + 0.621404i \(0.213438\pi\)
−0.989224 + 0.146407i \(0.953229\pi\)
\(762\) 0 0
\(763\) −2.66025 4.60770i −0.0963077 0.166810i
\(764\) −0.240237 + 0.416102i −0.00869146 + 0.0150540i
\(765\) 0 0
\(766\) 11.4641i 0.414215i
\(767\) −11.8313 4.00240i −0.427205 0.144518i
\(768\) 0 0
\(769\) 25.0263 6.70577i 0.902471 0.241816i 0.222394 0.974957i \(-0.428613\pi\)
0.680077 + 0.733141i \(0.261946\pi\)
\(770\) 2.32937 + 1.34486i 0.0839447 + 0.0484655i
\(771\) 0 0
\(772\) 8.53590 + 8.53590i 0.307214 + 0.307214i
\(773\) 6.10514 + 1.63587i 0.219587 + 0.0588381i 0.366935 0.930247i \(-0.380407\pi\)
−0.147348 + 0.989085i \(0.547074\pi\)
\(774\) 0 0
\(775\) 0.732051 0.732051i 0.0262960 0.0262960i
\(776\) 6.69213 3.86370i 0.240233 0.138699i
\(777\) 0 0
\(778\) 5.12436 + 19.1244i 0.183717 + 0.685641i
\(779\) 8.00481 0.286802
\(780\) 0 0
\(781\) −10.3923 −0.371866
\(782\) −1.79315 6.69213i −0.0641229 0.239310i
\(783\) 0 0
\(784\) −5.83013 + 3.36603i −0.208219 + 0.120215i
\(785\) 12.9546 12.9546i 0.462368 0.462368i
\(786\) 0 0
\(787\) 39.8564 + 10.6795i 1.42073 + 0.380683i 0.885742 0.464178i \(-0.153650\pi\)
0.534986 + 0.844861i \(0.320317\pi\)
\(788\) −7.53794 7.53794i −0.268528 0.268528i
\(789\) 0 0
\(790\) 0.803848 + 0.464102i 0.0285996 + 0.0165120i
\(791\) −3.86370 + 1.03528i −0.137377 + 0.0368102i
\(792\) 0 0
\(793\) 24.1244 11.9282i 0.856681 0.423583i
\(794\) 16.9062i 0.599978i
\(795\) 0 0
\(796\) −11.1962 + 19.3923i −0.396837 + 0.687342i
\(797\) 3.15660 + 5.46739i 0.111812 + 0.193665i 0.916501 0.400032i \(-0.131001\pi\)
−0.804689 + 0.593697i \(0.797668\pi\)
\(798\) 0 0
\(799\) −4.73205 + 17.6603i −0.167408 + 0.624775i
\(800\) −0.258819 + 0.965926i −0.00915064 + 0.0341506i
\(801\) 0 0
\(802\) −8.86603 15.3564i −0.313070 0.542254i
\(803\) 34.7733 60.2292i 1.22712 2.12544i
\(804\) 0 0
\(805\) 1.26795i 0.0446893i
\(806\) −3.10583 2.07055i −0.109398 0.0729321i
\(807\) 0 0
\(808\) −2.73205 + 0.732051i −0.0961132 + 0.0257535i
\(809\) 6.60420 + 3.81294i 0.232191 + 0.134056i 0.611583 0.791181i \(-0.290533\pi\)
−0.379391 + 0.925236i \(0.623867\pi\)
\(810\) 0 0
\(811\) 1.97372 + 1.97372i 0.0693067 + 0.0693067i 0.740910 0.671604i \(-0.234394\pi\)
−0.671604 + 0.740910i \(0.734394\pi\)
\(812\) 3.86370 + 1.03528i 0.135589 + 0.0363311i
\(813\) 0 0
\(814\) 9.88269 9.88269i 0.346388 0.346388i
\(815\) −7.34847 + 4.24264i −0.257406 + 0.148613i
\(816\) 0 0
\(817\) −0.124356 0.464102i −0.00435065 0.0162369i
\(818\) −3.44760 −0.120543
\(819\) 0 0
\(820\) 8.92820 0.311786
\(821\) −8.52245 31.8062i −0.297435 1.11004i −0.939264 0.343196i \(-0.888491\pi\)
0.641828 0.766848i \(-0.278176\pi\)
\(822\) 0 0
\(823\) 16.7942 9.69615i 0.585410 0.337987i −0.177870 0.984054i \(-0.556921\pi\)
0.763280 + 0.646067i \(0.223587\pi\)
\(824\) −2.50026 + 2.50026i −0.0871006 + 0.0871006i
\(825\) 0 0
\(826\) −1.73205 0.464102i −0.0602658 0.0161482i
\(827\) 29.2180 + 29.2180i 1.01601 + 1.01601i 0.999870 + 0.0161401i \(0.00513777\pi\)
0.0161401 + 0.999870i \(0.494862\pi\)
\(828\) 0 0
\(829\) −40.6410 23.4641i −1.41152 0.814942i −0.415989 0.909370i \(-0.636565\pi\)
−0.995532 + 0.0944277i \(0.969898\pi\)
\(830\) 11.5911 3.10583i 0.402333 0.107805i
\(831\) 0 0
\(832\) 3.59808 + 0.232051i 0.124741 + 0.00804491i
\(833\) 19.0411i 0.659736i
\(834\) 0 0
\(835\) −0.133975 + 0.232051i −0.00463638 + 0.00803045i
\(836\) 2.32937 + 4.03459i 0.0805630 + 0.139539i
\(837\) 0 0
\(838\) 8.09808 30.2224i 0.279743 1.04402i
\(839\) −2.86559 + 10.6945i −0.0989312 + 0.369216i −0.997586 0.0694400i \(-0.977879\pi\)
0.898655 + 0.438656i \(0.144545\pi\)
\(840\) 0 0
\(841\) 15.3564 + 26.5981i 0.529531 + 0.917175i
\(842\) −13.3843 + 23.1822i −0.461252 + 0.798912i
\(843\) 0 0
\(844\) 12.8564i 0.442536i
\(845\) −10.2970 + 7.93546i −0.354228 + 0.272988i
\(846\) 0 0
\(847\) 8.00000 2.14359i 0.274883 0.0736547i
\(848\) −1.10463 0.637756i −0.0379330 0.0219006i
\(849\) 0 0
\(850\) 2.00000 + 2.00000i 0.0685994 + 0.0685994i
\(851\) 6.36396 + 1.70522i 0.218154 + 0.0584541i
\(852\) 0 0
\(853\) 26.3205 26.3205i 0.901197 0.901197i −0.0943427 0.995540i \(-0.530075\pi\)
0.995540 + 0.0943427i \(0.0300750\pi\)
\(854\) 3.34607 1.93185i 0.114500 0.0661066i
\(855\) 0 0
\(856\) 1.00000 + 3.73205i 0.0341793 + 0.127559i
\(857\) 38.9144 1.32929 0.664646 0.747159i \(-0.268582\pi\)
0.664646 + 0.747159i \(0.268582\pi\)
\(858\) 0 0
\(859\) −10.2154 −0.348545 −0.174272 0.984697i \(-0.555757\pi\)
−0.174272 + 0.984697i \(0.555757\pi\)
\(860\) −0.138701 0.517638i −0.00472965 0.0176513i
\(861\) 0 0
\(862\) −12.5885 + 7.26795i −0.428765 + 0.247547i
\(863\) −11.6926 + 11.6926i −0.398022 + 0.398022i −0.877535 0.479513i \(-0.840813\pi\)
0.479513 + 0.877535i \(0.340813\pi\)
\(864\) 0 0
\(865\) 22.9904 + 6.16025i 0.781696 + 0.209455i
\(866\) 1.03528 + 1.03528i 0.0351801 + 0.0351801i
\(867\) 0 0
\(868\) −0.464102 0.267949i −0.0157526 0.00909479i
\(869\) 4.65874 1.24831i 0.158037 0.0423459i
\(870\) 0 0
\(871\) −6.92820 34.6410i −0.234753 1.17377i
\(872\) 10.2784i 0.348072i
\(873\) 0 0
\(874\) −1.09808 + 1.90192i −0.0371430 + 0.0643335i
\(875\) −0.258819 0.448288i −0.00874968 0.0151549i
\(876\) 0 0
\(877\) 3.09808 11.5622i 0.104615 0.390427i −0.893687 0.448692i \(-0.851890\pi\)
0.998301 + 0.0582648i \(0.0185568\pi\)
\(878\) −6.83083 + 25.4930i −0.230529 + 0.860347i
\(879\) 0 0
\(880\) 2.59808 + 4.50000i 0.0875811 + 0.151695i
\(881\) 7.74599 13.4164i 0.260969 0.452012i −0.705531 0.708679i \(-0.749291\pi\)
0.966500 + 0.256668i \(0.0826246\pi\)
\(882\) 0 0
\(883\) 29.7128i 0.999916i 0.866050 + 0.499958i \(0.166651\pi\)
−0.866050 + 0.499958i \(0.833349\pi\)
\(884\) 5.65685 8.48528i 0.190261 0.285391i
\(885\) 0 0
\(886\) −15.1962 + 4.07180i −0.510525 + 0.136795i
\(887\) −39.3120 22.6968i −1.31997 0.762083i −0.336243 0.941775i \(-0.609156\pi\)
−0.983723 + 0.179692i \(0.942490\pi\)
\(888\) 0 0
\(889\) −2.75833 2.75833i −0.0925114 0.0925114i
\(890\) 12.4183 + 3.32748i 0.416264 + 0.111537i
\(891\) 0 0
\(892\) 19.2942 19.2942i 0.646019 0.646019i
\(893\) 5.01910 2.89778i 0.167958 0.0969704i
\(894\) 0 0
\(895\) −6.63397 24.7583i −0.221749 0.827580i
\(896\) 0.517638 0.0172931
\(897\) 0 0
\(898\) 6.07180 0.202618
\(899\) −2.07055 7.72741i −0.0690568 0.257723i
\(900\) 0 0
\(901\) −3.12436 + 1.80385i −0.104087 + 0.0600949i
\(902\) 32.8043 32.8043i 1.09226 1.09226i
\(903\) 0 0
\(904\) −7.46410 2.00000i −0.248252 0.0665190i
\(905\) −11.9700 11.9700i −0.397898 0.397898i
\(906\) 0 0
\(907\) −6.46410 3.73205i −0.214637 0.123921i 0.388828 0.921311i \(-0.372880\pi\)
−0.603465 + 0.797390i \(0.706214\pi\)
\(908\) −20.0764 + 5.37945i −0.666258 + 0.178523i
\(909\) 0 0
\(910\) −1.40192 + 1.23205i −0.0464733 + 0.0408421i
\(911\) 23.7370i 0.786443i 0.919444 + 0.393221i \(0.128639\pi\)
−0.919444 + 0.393221i \(0.871361\pi\)
\(912\) 0 0
\(913\) 31.1769 54.0000i 1.03181 1.78714i
\(914\) 5.79555 + 10.0382i 0.191700 + 0.332034i
\(915\) 0 0
\(916\) −1.87564 + 7.00000i −0.0619730 + 0.231287i
\(917\) 2.67114 9.96885i 0.0882089 0.329200i
\(918\) 0 0
\(919\) −21.7846 37.7321i −0.718608 1.24467i −0.961551 0.274625i \(-0.911446\pi\)
0.242943 0.970040i \(-0.421887\pi\)
\(920\) −1.22474 + 2.12132i −0.0403786 + 0.0699379i
\(921\) 0 0
\(922\) 4.78461i 0.157573i
\(923\) 2.31079 6.83083i 0.0760605 0.224840i
\(924\) 0 0
\(925\) −2.59808 + 0.696152i −0.0854242 + 0.0228894i
\(926\) 35.5820 + 20.5433i 1.16930 + 0.675093i
\(927\) 0 0
\(928\) 5.46410 + 5.46410i 0.179368 + 0.179368i
\(929\) 5.93426 + 1.59008i 0.194697 + 0.0521688i 0.354850 0.934923i \(-0.384532\pi\)
−0.160153 + 0.987092i \(0.551199\pi\)
\(930\) 0 0
\(931\) 4.26795 4.26795i 0.139876 0.139876i
\(932\) −16.2499 + 9.38186i −0.532282 + 0.307313i
\(933\) 0 0
\(934\) −7.26795 27.1244i −0.237815 0.887536i
\(935\) 14.6969 0.480641
\(936\) 0 0
\(937\) 31.5692 1.03132 0.515661 0.856793i \(-0.327547\pi\)
0.515661 + 0.856793i \(0.327547\pi\)
\(938\) −1.31268 4.89898i −0.0428604 0.159957i
\(939\) 0 0
\(940\) 5.59808 3.23205i 0.182589 0.105418i
\(941\) −4.41851 + 4.41851i −0.144039 + 0.144039i −0.775449 0.631410i \(-0.782477\pi\)
0.631410 + 0.775449i \(0.282477\pi\)
\(942\) 0 0
\(943\) 21.1244 + 5.66025i 0.687904 + 0.184323i
\(944\) −2.44949 2.44949i −0.0797241 0.0797241i
\(945\) 0 0
\(946\) −2.41154 1.39230i −0.0784060 0.0452677i
\(947\) 12.1087 3.24453i 0.393481 0.105433i −0.0566528 0.998394i \(-0.518043\pi\)
0.450134 + 0.892961i \(0.351376\pi\)
\(948\) 0 0
\(949\) 31.8564 + 36.2487i 1.03410 + 1.17668i
\(950\) 0.896575i 0.0290887i
\(951\) 0 0
\(952\) 0.732051 1.26795i 0.0237259 0.0410945i
\(953\) 2.68973 + 4.65874i 0.0871288 + 0.150911i 0.906296 0.422643i \(-0.138898\pi\)
−0.819168 + 0.573554i \(0.805564\pi\)
\(954\) 0 0
\(955\) 0.124356 0.464102i 0.00402405 0.0150180i
\(956\) −2.48665 + 9.28032i −0.0804242 + 0.300147i
\(957\) 0 0
\(958\) 15.4641 + 26.7846i 0.499622 + 0.865371i
\(959\) −1.41421 + 2.44949i −0.0456673 + 0.0790981i
\(960\) 0 0
\(961\) 29.9282i 0.965426i
\(962\) 4.29839 + 8.69333i 0.138586 + 0.280284i
\(963\) 0 0
\(964\) −1.96410 + 0.526279i −0.0632595 + 0.0169503i
\(965\) −10.4543 6.03579i −0.336536 0.194299i
\(966\) 0 0
\(967\) −42.3468 42.3468i −1.36178 1.36178i −0.871647 0.490134i \(-0.836948\pi\)
−0.490134 0.871647i \(-0.663052\pi\)
\(968\) 15.4548 + 4.14110i 0.496737 + 0.133100i
\(969\) 0 0
\(970\) −5.46410 + 5.46410i −0.175442 + 0.175442i
\(971\) −28.6174 + 16.5223i −0.918377 + 0.530225i −0.883117 0.469153i \(-0.844559\pi\)
−0.0352599 + 0.999378i \(0.511226\pi\)
\(972\) 0 0
\(973\) 1.37564 + 5.13397i 0.0441011 + 0.164588i
\(974\) −12.2846 −0.393624
\(975\) 0 0
\(976\) 7.46410 0.238920
\(977\) 10.4543 + 39.0160i 0.334463 + 1.24823i 0.904451 + 0.426578i \(0.140281\pi\)
−0.569988 + 0.821653i \(0.693052\pi\)
\(978\) 0 0
\(979\) 57.8538 33.4019i 1.84902 1.06753i
\(980\) 4.76028 4.76028i 0.152062 0.152062i
\(981\) 0 0
\(982\) −36.7224 9.83975i −1.17186 0.313999i
\(983\) −2.84203 2.84203i −0.0906467 0.0906467i 0.660329 0.750976i \(-0.270417\pi\)
−0.750976 + 0.660329i \(0.770417\pi\)
\(984\) 0 0
\(985\) 9.23205 + 5.33013i 0.294158 + 0.169832i
\(986\) 21.1117 5.65685i 0.672332 0.180151i
\(987\) 0 0
\(988\) −3.16987 + 0.633975i −0.100847 + 0.0201694i
\(989\) 1.31268i 0.0417407i
\(990\) 0 0
\(991\) −3.92820 + 6.80385i −0.124783 + 0.216131i −0.921648 0.388026i \(-0.873157\pi\)
0.796865 + 0.604158i \(0.206490\pi\)
\(992\) −0.517638 0.896575i −0.0164350 0.0284663i
\(993\) 0 0
\(994\) 0.267949 1.00000i 0.00849883 0.0317181i
\(995\) 5.79555 21.6293i 0.183731 0.685695i
\(996\) 0 0
\(997\) −1.33013 2.30385i −0.0421255 0.0729636i 0.844194 0.536038i \(-0.180080\pi\)
−0.886319 + 0.463074i \(0.846746\pi\)
\(998\) 13.9527 24.1667i 0.441664 0.764984i
\(999\) 0 0
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 1170.2.cu.d.1151.1 yes 8
3.2 odd 2 inner 1170.2.cu.d.1151.2 yes 8
13.2 odd 12 inner 1170.2.cu.d.431.2 yes 8
39.2 even 12 inner 1170.2.cu.d.431.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1170.2.cu.d.431.1 8 39.2 even 12 inner
1170.2.cu.d.431.2 yes 8 13.2 odd 12 inner
1170.2.cu.d.1151.1 yes 8 1.1 even 1 trivial
1170.2.cu.d.1151.2 yes 8 3.2 odd 2 inner