Properties

Label 1274.2.n.c.753.1
Level $1274$
Weight $2$
Character 1274.753
Analytic conductor $10.173$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1274,2,Mod(753,1274)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1274.753");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1274.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(10.1729412175\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 753.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1274.753
Dual form 1274.2.n.c.961.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.59808 + 1.50000i) q^{5} -1.00000i q^{6} +1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.59808 + 1.50000i) q^{5} -1.00000i q^{6} +1.00000i q^{8} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{10} +(0.500000 + 0.866025i) q^{12} +(-2.00000 + 3.00000i) q^{13} -3.00000i q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.73205 - 1.00000i) q^{18} +(-5.19615 + 3.00000i) q^{19} +3.00000i q^{20} +(3.00000 + 5.19615i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(2.00000 - 3.46410i) q^{25} +(0.232051 - 3.59808i) q^{26} -5.00000 q^{27} +(1.50000 + 2.59808i) q^{30} +(0.866025 + 0.500000i) q^{32} +3.00000i q^{34} +2.00000 q^{36} +(-2.59808 + 1.50000i) q^{37} +(3.00000 - 5.19615i) q^{38} +(-1.59808 - 3.23205i) q^{39} +(-1.50000 - 2.59808i) q^{40} -1.00000 q^{43} +(-5.19615 - 3.00000i) q^{45} +(-5.19615 - 3.00000i) q^{46} +(2.59808 - 1.50000i) q^{47} +1.00000 q^{48} +4.00000i q^{50} +(1.50000 + 2.59808i) q^{51} +(1.59808 + 3.23205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(4.33013 - 2.50000i) q^{54} -6.00000i q^{57} +(5.19615 + 3.00000i) q^{59} +(-2.59808 - 1.50000i) q^{60} +(-4.00000 - 6.92820i) q^{61} -1.00000 q^{64} +(0.696152 - 10.7942i) q^{65} +(-10.3923 - 6.00000i) q^{67} +(-1.50000 - 2.59808i) q^{68} -6.00000 q^{69} -15.0000i q^{71} +(-1.73205 + 1.00000i) q^{72} +(-5.19615 - 3.00000i) q^{73} +(1.50000 - 2.59808i) q^{74} +(2.00000 + 3.46410i) q^{75} +6.00000i q^{76} +(3.00000 + 2.00000i) q^{78} +(-5.00000 - 8.66025i) q^{79} +(2.59808 + 1.50000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +6.00000i q^{83} +9.00000i q^{85} +(0.866025 - 0.500000i) q^{86} +(-5.19615 + 3.00000i) q^{89} +6.00000 q^{90} +6.00000 q^{92} +(-1.50000 + 2.59808i) q^{94} +(9.00000 - 15.5885i) q^{95} +(-0.866025 + 0.500000i) q^{96} -12.0000i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{4} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} + 2 q^{4} + 4 q^{9} + 6 q^{10} + 2 q^{12} - 8 q^{13} - 2 q^{16} + 6 q^{17} + 12 q^{23} + 8 q^{25} - 6 q^{26} - 20 q^{27} + 6 q^{30} + 8 q^{36} + 12 q^{38} + 4 q^{39} - 6 q^{40} - 4 q^{43} + 4 q^{48} + 6 q^{51} - 4 q^{52} + 12 q^{53} - 16 q^{61} - 4 q^{64} - 18 q^{65} - 6 q^{68} - 24 q^{69} + 6 q^{74} + 8 q^{75} + 12 q^{78} - 20 q^{79} - 2 q^{81} + 24 q^{90} + 24 q^{92} - 6 q^{94} + 36 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(885\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −2.59808 + 1.50000i −1.16190 + 0.670820i −0.951757 0.306851i \(-0.900725\pi\)
−0.210138 + 0.977672i \(0.567391\pi\)
\(6\) 1.00000i 0.408248i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 1.50000 2.59808i 0.474342 0.821584i
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −2.00000 + 3.00000i −0.554700 + 0.832050i
\(14\) 0 0
\(15\) 3.00000i 0.774597i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) −1.73205 1.00000i −0.408248 0.235702i
\(19\) −5.19615 + 3.00000i −1.19208 + 0.688247i −0.958778 0.284157i \(-0.908286\pi\)
−0.233301 + 0.972404i \(0.574953\pi\)
\(20\) 3.00000i 0.670820i
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0.232051 3.59808i 0.0455089 0.705641i
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 1.50000 + 2.59808i 0.273861 + 0.474342i
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 3.00000i 0.514496i
\(35\) 0 0
\(36\) 2.00000 0.333333
\(37\) −2.59808 + 1.50000i −0.427121 + 0.246598i −0.698119 0.715981i \(-0.745980\pi\)
0.270998 + 0.962580i \(0.412646\pi\)
\(38\) 3.00000 5.19615i 0.486664 0.842927i
\(39\) −1.59808 3.23205i −0.255897 0.517542i
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) −5.19615 3.00000i −0.774597 0.447214i
\(46\) −5.19615 3.00000i −0.766131 0.442326i
\(47\) 2.59808 1.50000i 0.378968 0.218797i −0.298401 0.954441i \(-0.596453\pi\)
0.677369 + 0.735643i \(0.263120\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) 4.00000i 0.565685i
\(51\) 1.50000 + 2.59808i 0.210042 + 0.363803i
\(52\) 1.59808 + 3.23205i 0.221613 + 0.448205i
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) 4.33013 2.50000i 0.589256 0.340207i
\(55\) 0 0
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) 0 0
\(59\) 5.19615 + 3.00000i 0.676481 + 0.390567i 0.798528 0.601958i \(-0.205612\pi\)
−0.122047 + 0.992524i \(0.538946\pi\)
\(60\) −2.59808 1.50000i −0.335410 0.193649i
\(61\) −4.00000 6.92820i −0.512148 0.887066i −0.999901 0.0140840i \(-0.995517\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.696152 10.7942i 0.0863471 1.33886i
\(66\) 0 0
\(67\) −10.3923 6.00000i −1.26962 0.733017i −0.294706 0.955588i \(-0.595222\pi\)
−0.974916 + 0.222571i \(0.928555\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 15.0000i 1.78017i −0.455792 0.890086i \(-0.650644\pi\)
0.455792 0.890086i \(-0.349356\pi\)
\(72\) −1.73205 + 1.00000i −0.204124 + 0.117851i
\(73\) −5.19615 3.00000i −0.608164 0.351123i 0.164083 0.986447i \(-0.447534\pi\)
−0.772246 + 0.635323i \(0.780867\pi\)
\(74\) 1.50000 2.59808i 0.174371 0.302020i
\(75\) 2.00000 + 3.46410i 0.230940 + 0.400000i
\(76\) 6.00000i 0.688247i
\(77\) 0 0
\(78\) 3.00000 + 2.00000i 0.339683 + 0.226455i
\(79\) −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i \(-0.976489\pi\)
0.434730 0.900561i \(-0.356844\pi\)
\(80\) 2.59808 + 1.50000i 0.290474 + 0.167705i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) 0 0
\(85\) 9.00000i 0.976187i
\(86\) 0.866025 0.500000i 0.0933859 0.0539164i
\(87\) 0 0
\(88\) 0 0
\(89\) −5.19615 + 3.00000i −0.550791 + 0.317999i −0.749441 0.662071i \(-0.769678\pi\)
0.198650 + 0.980071i \(0.436344\pi\)
\(90\) 6.00000 0.632456
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) −1.50000 + 2.59808i −0.154713 + 0.267971i
\(95\) 9.00000 15.5885i 0.923381 1.59934i
\(96\) −0.866025 + 0.500000i −0.0883883 + 0.0510310i
\(97\) 12.0000i 1.21842i −0.793011 0.609208i \(-0.791488\pi\)
0.793011 0.609208i \(-0.208512\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 3.46410i −0.200000 0.346410i
\(101\) 6.00000 10.3923i 0.597022 1.03407i −0.396236 0.918149i \(-0.629684\pi\)
0.993258 0.115924i \(-0.0369830\pi\)
\(102\) −2.59808 1.50000i −0.257248 0.148522i
\(103\) 7.00000 + 12.1244i 0.689730 + 1.19465i 0.971925 + 0.235291i \(0.0756043\pi\)
−0.282194 + 0.959357i \(0.591062\pi\)
\(104\) −3.00000 2.00000i −0.294174 0.196116i
\(105\) 0 0
\(106\) 6.00000i 0.582772i
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) −2.50000 + 4.33013i −0.240563 + 0.416667i
\(109\) 7.79423 + 4.50000i 0.746552 + 0.431022i 0.824447 0.565940i \(-0.191487\pi\)
−0.0778949 + 0.996962i \(0.524820\pi\)
\(110\) 0 0
\(111\) 3.00000i 0.284747i
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 3.00000 + 5.19615i 0.280976 + 0.486664i
\(115\) −15.5885 9.00000i −1.45363 0.839254i
\(116\) 0 0
\(117\) −7.19615 0.464102i −0.665285 0.0429062i
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) 3.00000 0.273861
\(121\) −5.50000 9.52628i −0.500000 0.866025i
\(122\) 6.92820 + 4.00000i 0.627250 + 0.362143i
\(123\) 0 0
\(124\) 0 0
\(125\) 3.00000i 0.268328i
\(126\) 0 0
\(127\) −2.00000 −0.177471 −0.0887357 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0.500000 0.866025i 0.0440225 0.0762493i
\(130\) 4.79423 + 9.69615i 0.420482 + 0.850409i
\(131\) −1.50000 2.59808i −0.131056 0.226995i 0.793028 0.609185i \(-0.208503\pi\)
−0.924084 + 0.382190i \(0.875170\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 12.0000 1.03664
\(135\) 12.9904 7.50000i 1.11803 0.645497i
\(136\) 2.59808 + 1.50000i 0.222783 + 0.128624i
\(137\) 15.5885 + 9.00000i 1.33181 + 0.768922i 0.985577 0.169226i \(-0.0541268\pi\)
0.346235 + 0.938148i \(0.387460\pi\)
\(138\) 5.19615 3.00000i 0.442326 0.255377i
\(139\) −5.00000 −0.424094 −0.212047 0.977259i \(-0.568013\pi\)
−0.212047 + 0.977259i \(0.568013\pi\)
\(140\) 0 0
\(141\) 3.00000i 0.252646i
\(142\) 7.50000 + 12.9904i 0.629386 + 1.09013i
\(143\) 0 0
\(144\) 1.00000 1.73205i 0.0833333 0.144338i
\(145\) 0 0
\(146\) 6.00000 0.496564
\(147\) 0 0
\(148\) 3.00000i 0.246598i
\(149\) 5.19615 3.00000i 0.425685 0.245770i −0.271821 0.962348i \(-0.587626\pi\)
0.697507 + 0.716578i \(0.254293\pi\)
\(150\) −3.46410 2.00000i −0.282843 0.163299i
\(151\) −12.9904 7.50000i −1.05714 0.610341i −0.132502 0.991183i \(-0.542301\pi\)
−0.924640 + 0.380841i \(0.875634\pi\)
\(152\) −3.00000 5.19615i −0.243332 0.421464i
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) −3.59808 0.232051i −0.288077 0.0185789i
\(157\) −11.0000 + 19.0526i −0.877896 + 1.52056i −0.0242497 + 0.999706i \(0.507720\pi\)
−0.853646 + 0.520854i \(0.825614\pi\)
\(158\) 8.66025 + 5.00000i 0.688973 + 0.397779i
\(159\) 3.00000 + 5.19615i 0.237915 + 0.412082i
\(160\) −3.00000 −0.237171
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) −5.19615 + 3.00000i −0.406994 + 0.234978i −0.689497 0.724288i \(-0.742169\pi\)
0.282503 + 0.959266i \(0.408835\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 0 0
\(169\) −5.00000 12.0000i −0.384615 0.923077i
\(170\) −4.50000 7.79423i −0.345134 0.597790i
\(171\) −10.3923 6.00000i −0.794719 0.458831i
\(172\) −0.500000 + 0.866025i −0.0381246 + 0.0660338i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5.19615 + 3.00000i −0.390567 + 0.225494i
\(178\) 3.00000 5.19615i 0.224860 0.389468i
\(179\) −7.50000 + 12.9904i −0.560576 + 0.970947i 0.436870 + 0.899525i \(0.356087\pi\)
−0.997446 + 0.0714220i \(0.977246\pi\)
\(180\) −5.19615 + 3.00000i −0.387298 + 0.223607i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 8.00000 0.591377
\(184\) −5.19615 + 3.00000i −0.383065 + 0.221163i
\(185\) 4.50000 7.79423i 0.330847 0.573043i
\(186\) 0 0
\(187\) 0 0
\(188\) 3.00000i 0.218797i
\(189\) 0 0
\(190\) 18.0000i 1.30586i
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 5.19615 + 3.00000i 0.374027 + 0.215945i 0.675216 0.737620i \(-0.264050\pi\)
−0.301189 + 0.953564i \(0.597384\pi\)
\(194\) 6.00000 + 10.3923i 0.430775 + 0.746124i
\(195\) 9.00000 + 6.00000i 0.644503 + 0.429669i
\(196\) 0 0
\(197\) 3.00000i 0.213741i −0.994273 0.106871i \(-0.965917\pi\)
0.994273 0.106871i \(-0.0340831\pi\)
\(198\) 0 0
\(199\) −10.0000 + 17.3205i −0.708881 + 1.22782i 0.256391 + 0.966573i \(0.417466\pi\)
−0.965272 + 0.261245i \(0.915867\pi\)
\(200\) 3.46410 + 2.00000i 0.244949 + 0.141421i
\(201\) 10.3923 6.00000i 0.733017 0.423207i
\(202\) 12.0000i 0.844317i
\(203\) 0 0
\(204\) 3.00000 0.210042
\(205\) 0 0
\(206\) −12.1244 7.00000i −0.844744 0.487713i
\(207\) −6.00000 + 10.3923i −0.417029 + 0.722315i
\(208\) 3.59808 + 0.232051i 0.249482 + 0.0160898i
\(209\) 0 0
\(210\) 0 0
\(211\) −23.0000 −1.58339 −0.791693 0.610920i \(-0.790800\pi\)
−0.791693 + 0.610920i \(0.790800\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 12.9904 + 7.50000i 0.890086 + 0.513892i
\(214\) −10.3923 6.00000i −0.710403 0.410152i
\(215\) 2.59808 1.50000i 0.177187 0.102299i
\(216\) 5.00000i 0.340207i
\(217\) 0 0
\(218\) −9.00000 −0.609557
\(219\) 5.19615 3.00000i 0.351123 0.202721i
\(220\) 0 0
\(221\) 4.79423 + 9.69615i 0.322495 + 0.652234i
\(222\) 1.50000 + 2.59808i 0.100673 + 0.174371i
\(223\) 9.00000i 0.602685i −0.953516 0.301342i \(-0.902565\pi\)
0.953516 0.301342i \(-0.0974347\pi\)
\(224\) 0 0
\(225\) 8.00000 0.533333
\(226\) 5.19615 3.00000i 0.345643 0.199557i
\(227\) 10.3923 + 6.00000i 0.689761 + 0.398234i 0.803523 0.595274i \(-0.202957\pi\)
−0.113761 + 0.993508i \(0.536290\pi\)
\(228\) −5.19615 3.00000i −0.344124 0.198680i
\(229\) 7.79423 4.50000i 0.515057 0.297368i −0.219853 0.975533i \(-0.570558\pi\)
0.734910 + 0.678165i \(0.237224\pi\)
\(230\) 18.0000 1.18688
\(231\) 0 0
\(232\) 0 0
\(233\) 10.5000 + 18.1865i 0.687878 + 1.19144i 0.972523 + 0.232806i \(0.0747909\pi\)
−0.284645 + 0.958633i \(0.591876\pi\)
\(234\) 6.46410 3.19615i 0.422572 0.208939i
\(235\) −4.50000 + 7.79423i −0.293548 + 0.508439i
\(236\) 5.19615 3.00000i 0.338241 0.195283i
\(237\) 10.0000 0.649570
\(238\) 0 0
\(239\) 9.00000i 0.582162i −0.956698 0.291081i \(-0.905985\pi\)
0.956698 0.291081i \(-0.0940149\pi\)
\(240\) −2.59808 + 1.50000i −0.167705 + 0.0968246i
\(241\) 25.9808 + 15.0000i 1.67357 + 0.966235i 0.965615 + 0.259975i \(0.0837143\pi\)
0.707953 + 0.706260i \(0.249619\pi\)
\(242\) 9.52628 + 5.50000i 0.612372 + 0.353553i
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) 0 0
\(247\) 1.39230 21.5885i 0.0885902 1.37364i
\(248\) 0 0
\(249\) −5.19615 3.00000i −0.329293 0.190117i
\(250\) 1.50000 + 2.59808i 0.0948683 + 0.164317i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.73205 1.00000i 0.108679 0.0627456i
\(255\) −7.79423 4.50000i −0.488094 0.281801i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.50000 + 2.59808i 0.0935674 + 0.162064i 0.909010 0.416775i \(-0.136840\pi\)
−0.815442 + 0.578838i \(0.803506\pi\)
\(258\) 1.00000i 0.0622573i
\(259\) 0 0
\(260\) −9.00000 6.00000i −0.558156 0.372104i
\(261\) 0 0
\(262\) 2.59808 + 1.50000i 0.160510 + 0.0926703i
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) 0 0
\(265\) 18.0000i 1.10573i
\(266\) 0 0
\(267\) 6.00000i 0.367194i
\(268\) −10.3923 + 6.00000i −0.634811 + 0.366508i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) −7.50000 + 12.9904i −0.456435 + 0.790569i
\(271\) 12.9904 7.50000i 0.789109 0.455593i −0.0505395 0.998722i \(-0.516094\pi\)
0.839649 + 0.543130i \(0.182761\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) −3.00000 + 5.19615i −0.180579 + 0.312772i
\(277\) −4.00000 + 6.92820i −0.240337 + 0.416275i −0.960810 0.277207i \(-0.910591\pi\)
0.720473 + 0.693482i \(0.243925\pi\)
\(278\) 4.33013 2.50000i 0.259704 0.149940i
\(279\) 0 0
\(280\) 0 0
\(281\) 30.0000i 1.78965i 0.446417 + 0.894825i \(0.352700\pi\)
−0.446417 + 0.894825i \(0.647300\pi\)
\(282\) −1.50000 2.59808i −0.0893237 0.154713i
\(283\) 2.00000 3.46410i 0.118888 0.205919i −0.800439 0.599414i \(-0.795400\pi\)
0.919327 + 0.393494i \(0.128734\pi\)
\(284\) −12.9904 7.50000i −0.770837 0.445043i
\(285\) 9.00000 + 15.5885i 0.533114 + 0.923381i
\(286\) 0 0
\(287\) 0 0
\(288\) 2.00000i 0.117851i
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 10.3923 + 6.00000i 0.609208 + 0.351726i
\(292\) −5.19615 + 3.00000i −0.304082 + 0.175562i
\(293\) 9.00000i 0.525786i −0.964825 0.262893i \(-0.915323\pi\)
0.964825 0.262893i \(-0.0846766\pi\)
\(294\) 0 0
\(295\) −18.0000 −1.04800
\(296\) −1.50000 2.59808i −0.0871857 0.151010i
\(297\) 0 0
\(298\) −3.00000 + 5.19615i −0.173785 + 0.301005i
\(299\) −21.5885 1.39230i −1.24849 0.0805191i
\(300\) 4.00000 0.230940
\(301\) 0 0
\(302\) 15.0000 0.863153
\(303\) 6.00000 + 10.3923i 0.344691 + 0.597022i
\(304\) 5.19615 + 3.00000i 0.298020 + 0.172062i
\(305\) 20.7846 + 12.0000i 1.19012 + 0.687118i
\(306\) −5.19615 + 3.00000i −0.297044 + 0.171499i
\(307\) 18.0000i 1.02731i 0.857996 + 0.513657i \(0.171710\pi\)
−0.857996 + 0.513657i \(0.828290\pi\)
\(308\) 0 0
\(309\) −14.0000 −0.796432
\(310\) 0 0
\(311\) −9.00000 + 15.5885i −0.510343 + 0.883940i 0.489585 + 0.871956i \(0.337148\pi\)
−0.999928 + 0.0119847i \(0.996185\pi\)
\(312\) 3.23205 1.59808i 0.182979 0.0904732i
\(313\) 9.50000 + 16.4545i 0.536972 + 0.930062i 0.999065 + 0.0432311i \(0.0137652\pi\)
−0.462093 + 0.886831i \(0.652902\pi\)
\(314\) 22.0000i 1.24153i
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −15.5885 + 9.00000i −0.875535 + 0.505490i −0.869184 0.494489i \(-0.835355\pi\)
−0.00635137 + 0.999980i \(0.502022\pi\)
\(318\) −5.19615 3.00000i −0.291386 0.168232i
\(319\) 0 0
\(320\) 2.59808 1.50000i 0.145237 0.0838525i
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 18.0000i 1.00155i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 6.39230 + 12.9282i 0.354581 + 0.717128i
\(326\) 3.00000 5.19615i 0.166155 0.287788i
\(327\) −7.79423 + 4.50000i −0.431022 + 0.248851i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −25.9808 + 15.0000i −1.42803 + 0.824475i −0.996965 0.0778456i \(-0.975196\pi\)
−0.431066 + 0.902320i \(0.641863\pi\)
\(332\) 5.19615 + 3.00000i 0.285176 + 0.164646i
\(333\) −5.19615 3.00000i −0.284747 0.164399i
\(334\) 6.00000 + 10.3923i 0.328305 + 0.568642i
\(335\) 36.0000 1.96689
\(336\) 0 0
\(337\) 13.0000 0.708155 0.354078 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) 10.3301 + 7.89230i 0.561885 + 0.429285i
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) 7.79423 + 4.50000i 0.422701 + 0.244047i
\(341\) 0 0
\(342\) 12.0000 0.648886
\(343\) 0 0
\(344\) 1.00000i 0.0539164i
\(345\) 15.5885 9.00000i 0.839254 0.484544i
\(346\) 5.19615 + 3.00000i 0.279347 + 0.161281i
\(347\) −16.5000 + 28.5788i −0.885766 + 1.53419i −0.0409337 + 0.999162i \(0.513033\pi\)
−0.844833 + 0.535031i \(0.820300\pi\)
\(348\) 0 0
\(349\) 21.0000i 1.12410i −0.827102 0.562052i \(-0.810012\pi\)
0.827102 0.562052i \(-0.189988\pi\)
\(350\) 0 0
\(351\) 10.0000 15.0000i 0.533761 0.800641i
\(352\) 0 0
\(353\) −5.19615 3.00000i −0.276563 0.159674i 0.355303 0.934751i \(-0.384378\pi\)
−0.631867 + 0.775077i \(0.717711\pi\)
\(354\) 3.00000 5.19615i 0.159448 0.276172i
\(355\) 22.5000 + 38.9711i 1.19418 + 2.06837i
\(356\) 6.00000i 0.317999i
\(357\) 0 0
\(358\) 15.0000i 0.792775i
\(359\) −20.7846 + 12.0000i −1.09697 + 0.633336i −0.935423 0.353529i \(-0.884981\pi\)
−0.161546 + 0.986865i \(0.551648\pi\)
\(360\) 3.00000 5.19615i 0.158114 0.273861i
\(361\) 8.50000 14.7224i 0.447368 0.774865i
\(362\) 1.73205 1.00000i 0.0910346 0.0525588i
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 18.0000 0.942163
\(366\) −6.92820 + 4.00000i −0.362143 + 0.209083i
\(367\) 4.00000 6.92820i 0.208798 0.361649i −0.742538 0.669804i \(-0.766378\pi\)
0.951336 + 0.308155i \(0.0997115\pi\)
\(368\) 3.00000 5.19615i 0.156386 0.270868i
\(369\) 0 0
\(370\) 9.00000i 0.467888i
\(371\) 0 0
\(372\) 0 0
\(373\) −2.00000 3.46410i −0.103556 0.179364i 0.809591 0.586994i \(-0.199689\pi\)
−0.913147 + 0.407630i \(0.866355\pi\)
\(374\) 0 0
\(375\) 2.59808 + 1.50000i 0.134164 + 0.0774597i
\(376\) 1.50000 + 2.59808i 0.0773566 + 0.133986i
\(377\) 0 0
\(378\) 0 0
\(379\) 6.00000i 0.308199i 0.988055 + 0.154100i \(0.0492477\pi\)
−0.988055 + 0.154100i \(0.950752\pi\)
\(380\) −9.00000 15.5885i −0.461690 0.799671i
\(381\) 1.00000 1.73205i 0.0512316 0.0887357i
\(382\) 10.3923 + 6.00000i 0.531717 + 0.306987i
\(383\) −7.79423 + 4.50000i −0.398266 + 0.229939i −0.685736 0.727851i \(-0.740519\pi\)
0.287469 + 0.957790i \(0.407186\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) 0 0
\(386\) −6.00000 −0.305392
\(387\) −1.00000 1.73205i −0.0508329 0.0880451i
\(388\) −10.3923 6.00000i −0.527589 0.304604i
\(389\) 15.0000 25.9808i 0.760530 1.31728i −0.182047 0.983290i \(-0.558272\pi\)
0.942578 0.333987i \(-0.108394\pi\)
\(390\) −10.7942 0.696152i −0.546587 0.0352510i
\(391\) 18.0000 0.910299
\(392\) 0 0
\(393\) 3.00000 0.151330
\(394\) 1.50000 + 2.59808i 0.0755689 + 0.130889i
\(395\) 25.9808 + 15.0000i 1.30723 + 0.754732i
\(396\) 0 0
\(397\) 15.5885 9.00000i 0.782362 0.451697i −0.0549046 0.998492i \(-0.517485\pi\)
0.837267 + 0.546795i \(0.184152\pi\)
\(398\) 20.0000i 1.00251i
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −25.9808 + 15.0000i −1.29742 + 0.749064i −0.979957 0.199207i \(-0.936163\pi\)
−0.317460 + 0.948272i \(0.602830\pi\)
\(402\) −6.00000 + 10.3923i −0.299253 + 0.518321i
\(403\) 0 0
\(404\) −6.00000 10.3923i −0.298511 0.517036i
\(405\) 3.00000i 0.149071i
\(406\) 0 0
\(407\) 0 0
\(408\) −2.59808 + 1.50000i −0.128624 + 0.0742611i
\(409\) 5.19615 + 3.00000i 0.256933 + 0.148340i 0.622935 0.782274i \(-0.285940\pi\)
−0.366002 + 0.930614i \(0.619274\pi\)
\(410\) 0 0
\(411\) −15.5885 + 9.00000i −0.768922 + 0.443937i
\(412\) 14.0000 0.689730
\(413\) 0 0
\(414\) 12.0000i 0.589768i
\(415\) −9.00000 15.5885i −0.441793 0.765207i
\(416\) −3.23205 + 1.59808i −0.158464 + 0.0783521i
\(417\) 2.50000 4.33013i 0.122426 0.212047i
\(418\) 0 0
\(419\) −15.0000 −0.732798 −0.366399 0.930458i \(-0.619409\pi\)
−0.366399 + 0.930458i \(0.619409\pi\)
\(420\) 0 0
\(421\) 15.0000i 0.731055i 0.930800 + 0.365528i \(0.119111\pi\)
−0.930800 + 0.365528i \(0.880889\pi\)
\(422\) 19.9186 11.5000i 0.969622 0.559811i
\(423\) 5.19615 + 3.00000i 0.252646 + 0.145865i
\(424\) 5.19615 + 3.00000i 0.252347 + 0.145693i
\(425\) −6.00000 10.3923i −0.291043 0.504101i
\(426\) −15.0000 −0.726752
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) −1.50000 + 2.59808i −0.0723364 + 0.125290i
\(431\) −12.9904 7.50000i −0.625725 0.361262i 0.153370 0.988169i \(-0.450987\pi\)
−0.779094 + 0.626907i \(0.784321\pi\)
\(432\) 2.50000 + 4.33013i 0.120281 + 0.208333i
\(433\) 11.0000 0.528626 0.264313 0.964437i \(-0.414855\pi\)
0.264313 + 0.964437i \(0.414855\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 7.79423 4.50000i 0.373276 0.215511i
\(437\) −31.1769 18.0000i −1.49139 0.861057i
\(438\) −3.00000 + 5.19615i −0.143346 + 0.248282i
\(439\) −5.00000 8.66025i −0.238637 0.413331i 0.721686 0.692220i \(-0.243367\pi\)
−0.960323 + 0.278889i \(0.910034\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −9.00000 6.00000i −0.428086 0.285391i
\(443\) 10.5000 + 18.1865i 0.498870 + 0.864068i 0.999999 0.00130426i \(-0.000415158\pi\)
−0.501129 + 0.865373i \(0.667082\pi\)
\(444\) −2.59808 1.50000i −0.123299 0.0711868i
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) 4.50000 + 7.79423i 0.213081 + 0.369067i
\(447\) 6.00000i 0.283790i
\(448\) 0 0
\(449\) 24.0000i 1.13263i −0.824189 0.566315i \(-0.808369\pi\)
0.824189 0.566315i \(-0.191631\pi\)
\(450\) −6.92820 + 4.00000i −0.326599 + 0.188562i
\(451\) 0 0
\(452\) −3.00000 + 5.19615i −0.141108 + 0.244406i
\(453\) 12.9904 7.50000i 0.610341 0.352381i
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) −15.5885 + 9.00000i −0.729197 + 0.421002i −0.818128 0.575036i \(-0.804988\pi\)
0.0889312 + 0.996038i \(0.471655\pi\)
\(458\) −4.50000 + 7.79423i −0.210271 + 0.364200i
\(459\) −7.50000 + 12.9904i −0.350070 + 0.606339i
\(460\) −15.5885 + 9.00000i −0.726816 + 0.419627i
\(461\) 15.0000i 0.698620i −0.937007 0.349310i \(-0.886416\pi\)
0.937007 0.349310i \(-0.113584\pi\)
\(462\) 0 0
\(463\) 24.0000i 1.11537i 0.830051 + 0.557687i \(0.188311\pi\)
−0.830051 + 0.557687i \(0.811689\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −18.1865 10.5000i −0.842475 0.486403i
\(467\) −6.00000 10.3923i −0.277647 0.480899i 0.693153 0.720791i \(-0.256221\pi\)
−0.970799 + 0.239892i \(0.922888\pi\)
\(468\) −4.00000 + 6.00000i −0.184900 + 0.277350i
\(469\) 0 0
\(470\) 9.00000i 0.415139i
\(471\) −11.0000 19.0526i −0.506853 0.877896i
\(472\) −3.00000 + 5.19615i −0.138086 + 0.239172i
\(473\) 0 0
\(474\) −8.66025 + 5.00000i −0.397779 + 0.229658i
\(475\) 24.0000i 1.10120i
\(476\) 0 0
\(477\) 12.0000 0.549442
\(478\) 4.50000 + 7.79423i 0.205825 + 0.356500i
\(479\) −33.7750 19.5000i −1.54322 0.890978i −0.998633 0.0522726i \(-0.983354\pi\)
−0.544586 0.838705i \(-0.683313\pi\)
\(480\) 1.50000 2.59808i 0.0684653 0.118585i
\(481\) 0.696152 10.7942i 0.0317418 0.492174i
\(482\) −30.0000 −1.36646
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 18.0000 + 31.1769i 0.817338 + 1.41567i
\(486\) 13.8564 + 8.00000i 0.628539 + 0.362887i
\(487\) −10.3923 6.00000i −0.470920 0.271886i 0.245705 0.969345i \(-0.420981\pi\)
−0.716625 + 0.697459i \(0.754314\pi\)
\(488\) 6.92820 4.00000i 0.313625 0.181071i
\(489\) 6.00000i 0.271329i
\(490\) 0 0
\(491\) 27.0000 1.21849 0.609246 0.792981i \(-0.291472\pi\)
0.609246 + 0.792981i \(0.291472\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 9.58846 + 19.3923i 0.431405 + 0.872501i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 6.00000 0.268866
\(499\) 31.1769 18.0000i 1.39567 0.805791i 0.401735 0.915756i \(-0.368407\pi\)
0.993935 + 0.109965i \(0.0350740\pi\)
\(500\) −2.59808 1.50000i −0.116190 0.0670820i
\(501\) 10.3923 + 6.00000i 0.464294 + 0.268060i
\(502\) 10.3923 6.00000i 0.463831 0.267793i
\(503\) 6.00000 0.267527 0.133763 0.991013i \(-0.457294\pi\)
0.133763 + 0.991013i \(0.457294\pi\)
\(504\) 0 0
\(505\) 36.0000i 1.60198i
\(506\) 0 0
\(507\) 12.8923 + 1.66987i 0.572567 + 0.0741617i
\(508\) −1.00000 + 1.73205i −0.0443678 + 0.0768473i
\(509\) −5.19615 + 3.00000i −0.230315 + 0.132973i −0.610718 0.791849i \(-0.709119\pi\)
0.380402 + 0.924821i \(0.375786\pi\)
\(510\) 9.00000 0.398527
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 25.9808 15.0000i 1.14708 0.662266i
\(514\) −2.59808 1.50000i −0.114596 0.0661622i
\(515\) −36.3731 21.0000i −1.60279 0.925371i
\(516\) −0.500000 0.866025i −0.0220113 0.0381246i
\(517\) 0 0
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 10.7942 + 0.696152i 0.473358 + 0.0305283i
\(521\) 13.5000 23.3827i 0.591446 1.02441i −0.402592 0.915379i \(-0.631891\pi\)
0.994038 0.109035i \(-0.0347759\pi\)
\(522\) 0 0
\(523\) −8.00000 13.8564i −0.349816 0.605898i 0.636401 0.771358i \(-0.280422\pi\)
−0.986216 + 0.165460i \(0.947089\pi\)
\(524\) −3.00000 −0.131056
\(525\) 0 0
\(526\) 24.0000i 1.04645i
\(527\) 0 0
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) −9.00000 15.5885i −0.390935 0.677119i
\(531\) 12.0000i 0.520756i
\(532\) 0 0
\(533\) 0 0
\(534\) 3.00000 + 5.19615i 0.129823 + 0.224860i
\(535\) −31.1769 18.0000i −1.34790 0.778208i
\(536\) 6.00000 10.3923i 0.259161 0.448879i
\(537\) −7.50000 12.9904i −0.323649 0.560576i
\(538\) 0 0
\(539\) 0 0
\(540\) 15.0000i 0.645497i
\(541\) 12.9904 7.50000i 0.558500 0.322450i −0.194043 0.980993i \(-0.562160\pi\)
0.752543 + 0.658543i \(0.228827\pi\)
\(542\) −7.50000 + 12.9904i −0.322153 + 0.557985i
\(543\) 1.00000 1.73205i 0.0429141 0.0743294i
\(544\) 2.59808 1.50000i 0.111392 0.0643120i
\(545\) −27.0000 −1.15655
\(546\) 0 0
\(547\) −37.0000 −1.58201 −0.791003 0.611812i \(-0.790441\pi\)
−0.791003 + 0.611812i \(0.790441\pi\)
\(548\) 15.5885 9.00000i 0.665906 0.384461i
\(549\) 8.00000 13.8564i 0.341432 0.591377i
\(550\) 0 0
\(551\) 0 0
\(552\) 6.00000i 0.255377i
\(553\) 0 0
\(554\) 8.00000i 0.339887i
\(555\) 4.50000 + 7.79423i 0.191014 + 0.330847i
\(556\) −2.50000 + 4.33013i −0.106024 + 0.183638i
\(557\) −23.3827 13.5000i −0.990756 0.572013i −0.0852559 0.996359i \(-0.527171\pi\)
−0.905500 + 0.424346i \(0.860504\pi\)
\(558\) 0 0
\(559\) 2.00000 3.00000i 0.0845910 0.126886i
\(560\) 0 0
\(561\) 0 0
\(562\) −15.0000 25.9808i −0.632737 1.09593i
\(563\) 19.5000 33.7750i 0.821827 1.42345i −0.0824933 0.996592i \(-0.526288\pi\)
0.904320 0.426855i \(-0.140378\pi\)
\(564\) 2.59808 + 1.50000i 0.109399 + 0.0631614i
\(565\) 15.5885 9.00000i 0.655811 0.378633i
\(566\) 4.00000i 0.168133i
\(567\) 0 0
\(568\) 15.0000 0.629386
\(569\) −22.5000 38.9711i −0.943249 1.63376i −0.759220 0.650835i \(-0.774419\pi\)
−0.184030 0.982921i \(-0.558914\pi\)
\(570\) −15.5885 9.00000i −0.652929 0.376969i
\(571\) 11.5000 19.9186i 0.481260 0.833567i −0.518509 0.855072i \(-0.673513\pi\)
0.999769 + 0.0215055i \(0.00684595\pi\)
\(572\) 0 0
\(573\) 12.0000 0.501307
\(574\) 0 0
\(575\) 24.0000 1.00087
\(576\) −1.00000 1.73205i −0.0416667 0.0721688i
\(577\) 36.3731 + 21.0000i 1.51423 + 0.874241i 0.999861 + 0.0166728i \(0.00530737\pi\)
0.514370 + 0.857569i \(0.328026\pi\)
\(578\) −6.92820 4.00000i −0.288175 0.166378i
\(579\) −5.19615 + 3.00000i −0.215945 + 0.124676i
\(580\) 0 0
\(581\) 0 0
\(582\) −12.0000 −0.497416
\(583\) 0 0
\(584\) 3.00000 5.19615i 0.124141 0.215018i
\(585\) 19.3923 9.58846i 0.801773 0.396434i
\(586\) 4.50000 + 7.79423i 0.185893 + 0.321977i
\(587\) 18.0000i 0.742940i 0.928445 + 0.371470i \(0.121146\pi\)
−0.928445 + 0.371470i \(0.878854\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 15.5885 9.00000i 0.641767 0.370524i
\(591\) 2.59808 + 1.50000i 0.106871 + 0.0617018i
\(592\) 2.59808 + 1.50000i 0.106780 + 0.0616496i
\(593\) 31.1769 18.0000i 1.28028 0.739171i 0.303383 0.952869i \(-0.401884\pi\)
0.976900 + 0.213697i \(0.0685507\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.00000i 0.245770i
\(597\) −10.0000 17.3205i −0.409273 0.708881i
\(598\) 19.3923 9.58846i 0.793010 0.392101i
\(599\) 15.0000 25.9808i 0.612883 1.06155i −0.377869 0.925859i \(-0.623343\pi\)
0.990752 0.135686i \(-0.0433238\pi\)
\(600\) −3.46410 + 2.00000i −0.141421 + 0.0816497i
\(601\) −37.0000 −1.50926 −0.754631 0.656150i \(-0.772184\pi\)
−0.754631 + 0.656150i \(0.772184\pi\)
\(602\) 0 0
\(603\) 24.0000i 0.977356i
\(604\) −12.9904 + 7.50000i −0.528571 + 0.305171i
\(605\) 28.5788 + 16.5000i 1.16190 + 0.670820i
\(606\) −10.3923 6.00000i −0.422159 0.243733i
\(607\) −11.0000 19.0526i −0.446476 0.773320i 0.551678 0.834058i \(-0.313988\pi\)
−0.998154 + 0.0607380i \(0.980655\pi\)
\(608\) −6.00000 −0.243332
\(609\) 0 0
\(610\) −24.0000 −0.971732
\(611\) −0.696152 + 10.7942i −0.0281633 + 0.436688i
\(612\) 3.00000 5.19615i 0.121268 0.210042i
\(613\) 5.19615 + 3.00000i 0.209871 + 0.121169i 0.601251 0.799060i \(-0.294669\pi\)
−0.391381 + 0.920229i \(0.628002\pi\)
\(614\) −9.00000 15.5885i −0.363210 0.629099i
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000i 0.483102i 0.970388 + 0.241551i \(0.0776561\pi\)
−0.970388 + 0.241551i \(0.922344\pi\)
\(618\) 12.1244 7.00000i 0.487713 0.281581i
\(619\) −20.7846 12.0000i −0.835404 0.482321i 0.0202954 0.999794i \(-0.493539\pi\)
−0.855699 + 0.517473i \(0.826873\pi\)
\(620\) 0 0
\(621\) −15.0000 25.9808i −0.601929 1.04257i
\(622\) 18.0000i 0.721734i
\(623\) 0 0
\(624\) −2.00000 + 3.00000i −0.0800641 + 0.120096i
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) −16.4545 9.50000i −0.657653 0.379696i
\(627\) 0 0
\(628\) 11.0000 + 19.0526i 0.438948 + 0.760280i
\(629\) 9.00000i 0.358854i
\(630\) 0 0
\(631\) 15.0000i 0.597141i 0.954388 + 0.298570i \(0.0965097\pi\)
−0.954388 + 0.298570i \(0.903490\pi\)
\(632\) 8.66025 5.00000i 0.344486 0.198889i
\(633\) 11.5000 19.9186i 0.457084 0.791693i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 5.19615 3.00000i 0.206203 0.119051i
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 25.9808 15.0000i 1.02778 0.593391i
\(640\) −1.50000 + 2.59808i −0.0592927 + 0.102698i
\(641\) 9.00000 15.5885i 0.355479 0.615707i −0.631721 0.775196i \(-0.717651\pi\)
0.987200 + 0.159489i \(0.0509845\pi\)
\(642\) 10.3923 6.00000i 0.410152 0.236801i
\(643\) 36.0000i 1.41970i 0.704352 + 0.709851i \(0.251238\pi\)
−0.704352 + 0.709851i \(0.748762\pi\)
\(644\) 0 0
\(645\) 3.00000i 0.118125i
\(646\) −9.00000 15.5885i −0.354100 0.613320i
\(647\) −21.0000 + 36.3731i −0.825595 + 1.42997i 0.0758684 + 0.997118i \(0.475827\pi\)
−0.901464 + 0.432855i \(0.857506\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 0 0
\(650\) −12.0000 8.00000i −0.470679 0.313786i
\(651\) 0 0
\(652\) 6.00000i 0.234978i
\(653\) 18.0000 + 31.1769i 0.704394 + 1.22005i 0.966910 + 0.255119i \(0.0821147\pi\)
−0.262515 + 0.964928i \(0.584552\pi\)
\(654\) 4.50000 7.79423i 0.175964 0.304778i
\(655\) 7.79423 + 4.50000i 0.304546 + 0.175830i
\(656\) 0 0
\(657\) 12.0000i 0.468165i
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) −25.9808 15.0000i −1.01053 0.583432i −0.0991864 0.995069i \(-0.531624\pi\)
−0.911348 + 0.411636i \(0.864957\pi\)
\(662\) 15.0000 25.9808i 0.582992 1.00977i
\(663\) −10.7942 0.696152i −0.419213 0.0270363i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 0 0
\(668\) −10.3923 6.00000i −0.402090 0.232147i
\(669\) 7.79423 + 4.50000i 0.301342 + 0.173980i
\(670\) −31.1769 + 18.0000i −1.20447 + 0.695401i
\(671\) 0 0
\(672\) 0 0
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) −11.2583 + 6.50000i −0.433655 + 0.250371i
\(675\) −10.0000 + 17.3205i −0.384900 + 0.666667i
\(676\) −12.8923 1.66987i −0.495858 0.0642259i
\(677\) 9.00000 + 15.5885i 0.345898 + 0.599113i 0.985517 0.169580i \(-0.0542410\pi\)
−0.639618 + 0.768693i \(0.720908\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 0 0
\(680\) −9.00000 −0.345134
\(681\) −10.3923 + 6.00000i −0.398234 + 0.229920i
\(682\) 0 0
\(683\) 5.19615 + 3.00000i 0.198825 + 0.114792i 0.596107 0.802905i \(-0.296713\pi\)
−0.397282 + 0.917697i \(0.630047\pi\)
\(684\) −10.3923 + 6.00000i −0.397360 + 0.229416i
\(685\) −54.0000 −2.06323
\(686\) 0 0
\(687\) 9.00000i 0.343371i
\(688\) 0.500000 + 0.866025i 0.0190623 + 0.0330169i
\(689\) 9.58846 + 19.3923i 0.365291 + 0.738788i
\(690\) −9.00000 + 15.5885i −0.342624 + 0.593442i
\(691\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 33.0000i 1.25266i
\(695\) 12.9904 7.50000i 0.492753 0.284491i
\(696\) 0 0
\(697\) 0 0
\(698\) 10.5000 + 18.1865i 0.397431 + 0.688370i
\(699\) −21.0000 −0.794293
\(700\) 0 0
\(701\) 42.0000 1.58632 0.793159 0.609015i \(-0.208435\pi\)
0.793159 + 0.609015i \(0.208435\pi\)
\(702\) −1.16025 + 17.9904i −0.0437910 + 0.679003i
\(703\) 9.00000 15.5885i 0.339441 0.587930i
\(704\) 0 0
\(705\) −4.50000 7.79423i −0.169480 0.293548i
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 6.00000i 0.225494i
\(709\) 5.19615 3.00000i 0.195146 0.112667i −0.399244 0.916845i \(-0.630727\pi\)
0.594389 + 0.804178i \(0.297394\pi\)
\(710\) −38.9711 22.5000i −1.46256 0.844410i
\(711\) 10.0000 17.3205i 0.375029 0.649570i
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 7.50000 + 12.9904i 0.280288 + 0.485473i
\(717\) 7.79423 + 4.50000i 0.291081 + 0.168056i
\(718\) 12.0000 20.7846i 0.447836 0.775675i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 6.00000i 0.223607i
\(721\) 0 0
\(722\) 17.0000i 0.632674i
\(723\) −25.9808 + 15.0000i −0.966235 + 0.557856i
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) 0 0
\(726\) −9.52628 + 5.50000i −0.353553 + 0.204124i
\(727\) −28.0000 −1.03846 −0.519231 0.854634i \(-0.673782\pi\)
−0.519231 + 0.854634i \(0.673782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −15.5885 + 9.00000i −0.576955 + 0.333105i
\(731\) −1.50000 + 2.59808i −0.0554795 + 0.0960933i
\(732\) 4.00000 6.92820i 0.147844 0.256074i
\(733\) −7.79423 + 4.50000i −0.287886 + 0.166211i −0.636988 0.770873i \(-0.719820\pi\)
0.349102 + 0.937085i \(0.386487\pi\)
\(734\) 8.00000i 0.295285i
\(735\) 0 0
\(736\) 6.00000i 0.221163i
\(737\) 0 0
\(738\) 0 0
\(739\) −31.1769 18.0000i −1.14686 0.662141i −0.198741 0.980052i \(-0.563685\pi\)
−0.948120 + 0.317911i \(0.897019\pi\)
\(740\) −4.50000 7.79423i −0.165423 0.286522i
\(741\) 18.0000 + 12.0000i 0.661247 + 0.440831i
\(742\) 0 0
\(743\) 39.0000i 1.43077i 0.698730 + 0.715386i \(0.253749\pi\)
−0.698730 + 0.715386i \(0.746251\pi\)
\(744\) 0 0
\(745\) −9.00000 + 15.5885i −0.329734 + 0.571117i
\(746\) 3.46410 + 2.00000i 0.126830 + 0.0732252i
\(747\) −10.3923 + 6.00000i −0.380235 + 0.219529i
\(748\) 0 0
\(749\) 0 0
\(750\) −3.00000 −0.109545
\(751\) −16.0000 27.7128i −0.583848 1.01125i −0.995018 0.0996961i \(-0.968213\pi\)
0.411170 0.911559i \(-0.365120\pi\)
\(752\) −2.59808 1.50000i −0.0947421 0.0546994i
\(753\) 6.00000 10.3923i 0.218652 0.378717i
\(754\) 0 0
\(755\) 45.0000 1.63772
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −3.00000 5.19615i −0.108965 0.188733i
\(759\) 0 0
\(760\) 15.5885 + 9.00000i 0.565453 + 0.326464i
\(761\) −25.9808 + 15.0000i −0.941802 + 0.543750i −0.890525 0.454935i \(-0.849663\pi\)
−0.0512772 + 0.998684i \(0.516329\pi\)
\(762\) 2.00000i 0.0724524i
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) −15.5885 + 9.00000i −0.563602 + 0.325396i
\(766\) 4.50000 7.79423i 0.162592 0.281617i
\(767\) −19.3923 + 9.58846i −0.700216 + 0.346219i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 24.0000i 0.865462i 0.901523 + 0.432731i \(0.142450\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 0 0
\(771\) −3.00000 −0.108042
\(772\) 5.19615 3.00000i 0.187014 0.107972i
\(773\) −18.1865 10.5000i −0.654124 0.377659i 0.135910 0.990721i \(-0.456604\pi\)
−0.790034 + 0.613062i \(0.789937\pi\)
\(774\) 1.73205 + 1.00000i 0.0622573 + 0.0359443i
\(775\) 0 0
\(776\) 12.0000 0.430775
\(777\) 0 0
\(778\) 30.0000i 1.07555i
\(779\) 0 0
\(780\) 9.69615 4.79423i 0.347178 0.171661i
\(781\) 0 0
\(782\) −15.5885 + 9.00000i −0.557442 + 0.321839i
\(783\) 0 0
\(784\) 0 0
\(785\) 66.0000i 2.35564i
\(786\) −2.59808 + 1.50000i −0.0926703 + 0.0535032i
\(787\) 10.3923 + 6.00000i 0.370446 + 0.213877i 0.673653 0.739048i \(-0.264724\pi\)
−0.303207 + 0.952925i \(0.598058\pi\)
\(788\) −2.59808 1.50000i −0.0925526 0.0534353i
\(789\) −12.0000 20.7846i −0.427211 0.739952i
\(790\) −30.0000 −1.06735
\(791\) 0 0
\(792\) 0 0
\(793\) 28.7846 + 1.85641i 1.02217 + 0.0659229i
\(794\) −9.00000 + 15.5885i −0.319398 + 0.553214i
\(795\) −15.5885 9.00000i −0.552866 0.319197i
\(796\) 10.0000 + 17.3205i 0.354441 + 0.613909i
\(797\) −18.0000 −0.637593 −0.318796 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 0 0
\(799\) 9.00000i 0.318397i
\(800\) 3.46410 2.00000i 0.122474 0.0707107i
\(801\) −10.3923 6.00000i −0.367194 0.212000i
\(802\) 15.0000 25.9808i 0.529668 0.917413i
\(803\) 0 0
\(804\) 12.0000i 0.423207i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 10.3923 + 6.00000i 0.365600 + 0.211079i
\(809\) −7.50000 + 12.9904i −0.263686 + 0.456717i −0.967219 0.253946i \(-0.918272\pi\)
0.703533 + 0.710663i \(0.251605\pi\)
\(810\) 1.50000 + 2.59808i 0.0527046 + 0.0912871i
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 15.0000i 0.526073i
\(814\) 0 0
\(815\) 9.00000 15.5885i 0.315256 0.546040i
\(816\) 1.50000 2.59808i 0.0525105 0.0909509i
\(817\) 5.19615 3.00000i 0.181790 0.104957i
\(818\) −6.00000 −0.209785
\(819\) 0 0
\(820\) 0 0
\(821\) −38.9711 + 22.5000i −1.36010 + 0.785255i −0.989637 0.143591i \(-0.954135\pi\)
−0.370465 + 0.928846i \(0.620802\pi\)
\(822\) 9.00000 15.5885i 0.313911 0.543710i
\(823\) −7.00000 + 12.1244i −0.244005 + 0.422628i −0.961851 0.273573i \(-0.911795\pi\)
0.717847 + 0.696201i \(0.245128\pi\)
\(824\) −12.1244 + 7.00000i −0.422372 + 0.243857i
\(825\) 0 0
\(826\) 0 0
\(827\) 18.0000i 0.625921i −0.949766 0.312961i \(-0.898679\pi\)
0.949766 0.312961i \(-0.101321\pi\)
\(828\) 6.00000 + 10.3923i 0.208514 + 0.361158i
\(829\) −10.0000 + 17.3205i −0.347314 + 0.601566i −0.985771 0.168091i \(-0.946240\pi\)
0.638457 + 0.769657i \(0.279573\pi\)
\(830\) 15.5885 + 9.00000i 0.541083 + 0.312395i
\(831\) −4.00000 6.92820i −0.138758 0.240337i
\(832\) 2.00000 3.00000i 0.0693375 0.104006i
\(833\) 0 0
\(834\) 5.00000i 0.173136i
\(835\) 18.0000 + 31.1769i 0.622916 + 1.07892i
\(836\) 0 0
\(837\) 0 0
\(838\) 12.9904 7.50000i 0.448745 0.259083i
\(839\) 24.0000i 0.828572i 0.910147 + 0.414286i \(0.135969\pi\)
−0.910147 + 0.414286i \(0.864031\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) −7.50000 12.9904i −0.258467 0.447678i
\(843\) −25.9808 15.0000i −0.894825 0.516627i
\(844\) −11.5000 + 19.9186i −0.395846 + 0.685626i
\(845\) 30.9904 + 23.6769i 1.06610 + 0.814511i
\(846\) −6.00000 −0.206284
\(847\) 0 0
\(848\) −6.00000 −0.206041
\(849\) 2.00000 + 3.46410i 0.0686398 + 0.118888i
\(850\) 10.3923 + 6.00000i 0.356453 + 0.205798i
\(851\) −15.5885 9.00000i −0.534365 0.308516i
\(852\) 12.9904 7.50000i 0.445043 0.256946i
\(853\) 39.0000i 1.33533i −0.744460 0.667667i \(-0.767293\pi\)
0.744460 0.667667i \(-0.232707\pi\)
\(854\) 0 0
\(855\) 36.0000 1.23117
\(856\) −10.3923 + 6.00000i −0.355202 + 0.205076i
\(857\) 9.00000 15.5885i 0.307434 0.532492i −0.670366 0.742030i \(-0.733863\pi\)
0.977800 + 0.209539i \(0.0671963\pi\)
\(858\) 0 0
\(859\) 20.0000 + 34.6410i 0.682391 + 1.18194i 0.974249 + 0.225475i \(0.0723932\pi\)
−0.291858 + 0.956462i \(0.594273\pi\)
\(860\) 3.00000i 0.102299i
\(861\) 0 0
\(862\) 15.0000 0.510902
\(863\) 33.7750 19.5000i 1.14971 0.663788i 0.200897 0.979612i \(-0.435615\pi\)
0.948818 + 0.315825i \(0.102281\pi\)
\(864\) −4.33013 2.50000i −0.147314 0.0850517i
\(865\) 15.5885 + 9.00000i 0.530023 + 0.306009i
\(866\) −9.52628 + 5.50000i −0.323716 + 0.186898i
\(867\) −8.00000 −0.271694
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 38.7846 19.1769i 1.31417 0.649785i
\(872\) −4.50000 + 7.79423i −0.152389 + 0.263946i
\(873\) 20.7846 12.0000i 0.703452 0.406138i
\(874\) 36.0000 1.21772
\(875\) 0 0
\(876\) 6.00000i 0.202721i
\(877\) −2.59808 + 1.50000i −0.0877308 + 0.0506514i −0.543224 0.839588i \(-0.682796\pi\)
0.455493 + 0.890239i \(0.349463\pi\)
\(878\) 8.66025 + 5.00000i 0.292269 + 0.168742i
\(879\) 7.79423 + 4.50000i 0.262893 + 0.151781i
\(880\) 0 0
\(881\) 33.0000 1.11180 0.555899 0.831250i \(-0.312374\pi\)
0.555899 + 0.831250i \(0.312374\pi\)
\(882\) 0 0
\(883\) −11.0000 −0.370179 −0.185090 0.982722i \(-0.559258\pi\)
−0.185090 + 0.982722i \(0.559258\pi\)
\(884\) 10.7942 + 0.696152i 0.363049 + 0.0234141i
\(885\) 9.00000 15.5885i 0.302532 0.524000i
\(886\) −18.1865 10.5000i −0.610989 0.352754i
\(887\) −6.00000 10.3923i −0.201460 0.348939i 0.747539 0.664218i \(-0.231235\pi\)
−0.948999 + 0.315279i \(0.897902\pi\)
\(888\) 3.00000 0.100673
\(889\) 0 0
\(890\) 18.0000i 0.603361i
\(891\) 0 0
\(892\) −7.79423 4.50000i −0.260970 0.150671i
\(893\) −9.00000 + 15.5885i −0.301174 + 0.521648i
\(894\) −3.00000 5.19615i −0.100335 0.173785i
\(895\) 45.0000i 1.50418i
\(896\) 0 0
\(897\) 12.0000 18.0000i 0.400668 0.601003i
\(898\) 12.0000 + 20.7846i 0.400445 + 0.693591i
\(899\) 0 0
\(900\) 4.00000 6.92820i 0.133333 0.230940i
\(901\) −9.00000 15.5885i −0.299833 0.519327i
\(902\) 0 0
\(903\) 0 0
\(904\) 6.00000i 0.199557i
\(905\) 5.19615 3.00000i 0.172726 0.0997234i
\(906\) −7.50000 + 12.9904i −0.249171 + 0.431577i
\(907\) 8.50000 14.7224i 0.282238 0.488850i −0.689698 0.724097i \(-0.742257\pi\)
0.971936 + 0.235247i \(0.0755899\pi\)
\(908\) 10.3923 6.00000i 0.344881 0.199117i
\(909\) 24.0000 0.796030
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) −5.19615 + 3.00000i −0.172062 + 0.0993399i
\(913\) 0 0
\(914\) 9.00000 15.5885i 0.297694 0.515620i
\(915\) −20.7846 + 12.0000i −0.687118 + 0.396708i
\(916\) 9.00000i 0.297368i
\(917\) 0 0
\(918\) 15.0000i 0.495074i
\(919\) 10.0000 + 17.3205i 0.329870 + 0.571351i 0.982486 0.186338i \(-0.0596619\pi\)
−0.652616 + 0.757689i \(0.726329\pi\)
\(920\) 9.00000 15.5885i 0.296721 0.513936i
\(921\) −15.5885 9.00000i −0.513657 0.296560i
\(922\) 7.50000 + 12.9904i 0.246999 + 0.427815i
\(923\) 45.0000 + 30.0000i 1.48119 + 0.987462i
\(924\) 0 0
\(925\) 12.0000i 0.394558i
\(926\) −12.0000 20.7846i −0.394344 0.683025i
\(927\) −14.0000 + 24.2487i −0.459820 + 0.796432i
\(928\) 0 0
\(929\) −31.1769 + 18.0000i −1.02288 + 0.590561i −0.914937 0.403596i \(-0.867760\pi\)
−0.107944 + 0.994157i \(0.534427\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 21.0000 0.687878
\(933\) −9.00000 15.5885i −0.294647 0.510343i
\(934\) 10.3923 + 6.00000i 0.340047 + 0.196326i
\(935\) 0 0
\(936\) 0.464102 7.19615i 0.0151696 0.235214i
\(937\) 2.00000 0.0653372 0.0326686 0.999466i \(-0.489599\pi\)
0.0326686 + 0.999466i \(0.489599\pi\)
\(938\) 0 0
\(939\) −19.0000 −0.620042
\(940\) 4.50000 + 7.79423i 0.146774 + 0.254220i
\(941\) 38.9711 + 22.5000i 1.27042 + 0.733479i 0.975068 0.221908i \(-0.0712286\pi\)
0.295355 + 0.955387i \(0.404562\pi\)
\(942\) 19.0526 + 11.0000i 0.620766 + 0.358399i
\(943\) 0 0
\(944\) 6.00000i 0.195283i
\(945\) 0 0
\(946\) 0 0
\(947\) −41.5692 + 24.0000i −1.35082 + 0.779895i −0.988364 0.152106i \(-0.951394\pi\)
−0.362454 + 0.932002i \(0.618061\pi\)
\(948\) 5.00000 8.66025i 0.162392 0.281272i
\(949\) 19.3923 9.58846i 0.629501 0.311254i
\(950\) −12.0000 20.7846i −0.389331 0.674342i
\(951\) 18.0000i 0.583690i
\(952\) 0 0
\(953\) 9.00000 0.291539 0.145769 0.989319i \(-0.453434\pi\)
0.145769 + 0.989319i \(0.453434\pi\)
\(954\) −10.3923 + 6.00000i −0.336463 + 0.194257i
\(955\) 31.1769 + 18.0000i 1.00886 + 0.582466i
\(956\) −7.79423 4.50000i −0.252083 0.145540i
\(957\) 0 0
\(958\) 39.0000 1.26003
\(959\) 0 0
\(960\) 3.00000i 0.0968246i
\(961\) −15.5000 26.8468i −0.500000 0.866025i
\(962\) 4.79423 + 9.69615i 0.154572 + 0.312617i
\(963\) −12.0000 + 20.7846i −0.386695 + 0.669775i
\(964\) 25.9808 15.0000i 0.836784 0.483117i
\(965\) −18.0000 −0.579441
\(966\) 0 0
\(967\) 3.00000i 0.0964735i −0.998836 0.0482367i \(-0.984640\pi\)
0.998836 0.0482367i \(-0.0153602\pi\)
\(968\) 9.52628 5.50000i 0.306186 0.176777i
\(969\) −15.5885 9.00000i −0.500773 0.289122i
\(970\) −31.1769 18.0000i −1.00103 0.577945i
\(971\) 13.5000 + 23.3827i 0.433236 + 0.750386i 0.997150 0.0754473i \(-0.0240385\pi\)
−0.563914 + 0.825833i \(0.690705\pi\)
\(972\) −16.0000 −0.513200
\(973\) 0 0
\(974\) 12.0000 0.384505
\(975\) −14.3923 0.928203i −0.460923 0.0297263i
\(976\) −4.00000 + 6.92820i −0.128037 + 0.221766i
\(977\) −10.3923 6.00000i −0.332479 0.191957i 0.324462 0.945899i \(-0.394817\pi\)
−0.656941 + 0.753942i \(0.728150\pi\)
\(978\) 3.00000 + 5.19615i 0.0959294 + 0.166155i
\(979\) 0 0
\(980\) 0 0
\(981\) 18.0000i 0.574696i
\(982\) −23.3827 + 13.5000i −0.746171 + 0.430802i
\(983\) 7.79423 + 4.50000i 0.248597 + 0.143528i 0.619122 0.785295i \(-0.287489\pi\)
−0.370525 + 0.928823i \(0.620822\pi\)
\(984\) 0 0
\(985\) 4.50000 + 7.79423i 0.143382 + 0.248345i
\(986\) 0 0
\(987\) 0 0
\(988\) −18.0000 12.0000i −0.572656 0.381771i
\(989\) −3.00000 5.19615i −0.0953945 0.165228i
\(990\) 0 0
\(991\) −1.00000 + 1.73205i −0.0317660 + 0.0550204i −0.881471 0.472237i \(-0.843446\pi\)
0.849705 + 0.527258i \(0.176780\pi\)
\(992\) 0 0
\(993\) 30.0000i 0.952021i
\(994\) 0 0
\(995\) 60.0000i 1.90213i
\(996\) −5.19615 + 3.00000i −0.164646 + 0.0950586i
\(997\) 4.00000 6.92820i 0.126681 0.219418i −0.795708 0.605681i \(-0.792901\pi\)
0.922389 + 0.386263i \(0.126234\pi\)
\(998\) −18.0000 + 31.1769i −0.569780 + 0.986888i
\(999\) 12.9904 7.50000i 0.410997 0.237289i
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 1274.2.n.c.753.1 4
7.2 even 3 inner 1274.2.n.c.961.2 4
7.3 odd 6 26.2.b.a.25.1 2
7.4 even 3 1274.2.d.c.883.1 2
7.5 odd 6 1274.2.n.d.961.2 4
7.6 odd 2 1274.2.n.d.753.1 4
13.12 even 2 inner 1274.2.n.c.753.2 4
21.17 even 6 234.2.b.b.181.2 2
28.3 even 6 208.2.f.a.129.2 2
35.3 even 12 650.2.c.a.649.1 2
35.17 even 12 650.2.c.d.649.2 2
35.24 odd 6 650.2.d.b.51.2 2
56.3 even 6 832.2.f.b.129.1 2
56.45 odd 6 832.2.f.d.129.1 2
84.59 odd 6 1872.2.c.f.1585.1 2
91.3 odd 6 338.2.e.c.147.2 4
91.10 odd 6 338.2.e.c.147.1 4
91.12 odd 6 1274.2.n.d.961.1 4
91.17 odd 6 338.2.e.c.23.2 4
91.24 even 12 338.2.c.b.191.1 2
91.25 even 6 1274.2.d.c.883.2 2
91.31 even 12 338.2.a.b.1.1 1
91.38 odd 6 26.2.b.a.25.2 yes 2
91.45 even 12 338.2.c.f.315.1 2
91.51 even 6 inner 1274.2.n.c.961.1 4
91.59 even 12 338.2.c.b.315.1 2
91.73 even 12 338.2.a.d.1.1 1
91.80 even 12 338.2.c.f.191.1 2
91.87 odd 6 338.2.e.c.23.1 4
91.90 odd 2 1274.2.n.d.753.2 4
273.38 even 6 234.2.b.b.181.1 2
273.122 odd 12 3042.2.a.j.1.1 1
273.164 odd 12 3042.2.a.g.1.1 1
364.31 odd 12 2704.2.a.k.1.1 1
364.255 odd 12 2704.2.a.j.1.1 1
364.311 even 6 208.2.f.a.129.1 2
455.38 even 12 650.2.c.d.649.1 2
455.129 odd 6 650.2.d.b.51.1 2
455.164 even 12 8450.2.a.h.1.1 1
455.304 even 12 8450.2.a.u.1.1 1
455.402 even 12 650.2.c.a.649.2 2
728.493 odd 6 832.2.f.d.129.2 2
728.675 even 6 832.2.f.b.129.2 2
1092.311 odd 6 1872.2.c.f.1585.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
26.2.b.a.25.1 2 7.3 odd 6
26.2.b.a.25.2 yes 2 91.38 odd 6
208.2.f.a.129.1 2 364.311 even 6
208.2.f.a.129.2 2 28.3 even 6
234.2.b.b.181.1 2 273.38 even 6
234.2.b.b.181.2 2 21.17 even 6
338.2.a.b.1.1 1 91.31 even 12
338.2.a.d.1.1 1 91.73 even 12
338.2.c.b.191.1 2 91.24 even 12
338.2.c.b.315.1 2 91.59 even 12
338.2.c.f.191.1 2 91.80 even 12
338.2.c.f.315.1 2 91.45 even 12
338.2.e.c.23.1 4 91.87 odd 6
338.2.e.c.23.2 4 91.17 odd 6
338.2.e.c.147.1 4 91.10 odd 6
338.2.e.c.147.2 4 91.3 odd 6
650.2.c.a.649.1 2 35.3 even 12
650.2.c.a.649.2 2 455.402 even 12
650.2.c.d.649.1 2 455.38 even 12
650.2.c.d.649.2 2 35.17 even 12
650.2.d.b.51.1 2 455.129 odd 6
650.2.d.b.51.2 2 35.24 odd 6
832.2.f.b.129.1 2 56.3 even 6
832.2.f.b.129.2 2 728.675 even 6
832.2.f.d.129.1 2 56.45 odd 6
832.2.f.d.129.2 2 728.493 odd 6
1274.2.d.c.883.1 2 7.4 even 3
1274.2.d.c.883.2 2 91.25 even 6
1274.2.n.c.753.1 4 1.1 even 1 trivial
1274.2.n.c.753.2 4 13.12 even 2 inner
1274.2.n.c.961.1 4 91.51 even 6 inner
1274.2.n.c.961.2 4 7.2 even 3 inner
1274.2.n.d.753.1 4 7.6 odd 2
1274.2.n.d.753.2 4 91.90 odd 2
1274.2.n.d.961.1 4 91.12 odd 6
1274.2.n.d.961.2 4 7.5 odd 6
1872.2.c.f.1585.1 2 84.59 odd 6
1872.2.c.f.1585.2 2 1092.311 odd 6
2704.2.a.j.1.1 1 364.255 odd 12
2704.2.a.k.1.1 1 364.31 odd 12
3042.2.a.g.1.1 1 273.164 odd 12
3042.2.a.j.1.1 1 273.122 odd 12
8450.2.a.h.1.1 1 455.164 even 12
8450.2.a.u.1.1 1 455.304 even 12