Properties

Label 26.3.d.a.21.1
Level $26$
Weight $3$
Character 26.21
Analytic conductor $0.708$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [26,3,Mod(5,26)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(26, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("26.5");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 26 = 2 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 26.d (of order \(4\), degree \(2\), 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: \(0.708448687337\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 21.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 26.21
Dual form 26.3.d.a.5.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(-3.00000 - 3.00000i) q^{5} +(2.00000 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} -9.00000 q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +2.00000i q^{4} +(-3.00000 - 3.00000i) q^{5} +(2.00000 - 2.00000i) q^{7} +(-2.00000 + 2.00000i) q^{8} -9.00000 q^{9} -6.00000i q^{10} +(6.00000 - 6.00000i) q^{11} +13.0000i q^{13} +4.00000 q^{14} -4.00000 q^{16} +6.00000i q^{17} +(-9.00000 - 9.00000i) q^{18} +(26.0000 + 26.0000i) q^{19} +(6.00000 - 6.00000i) q^{20} +12.0000 q^{22} -24.0000i q^{23} -7.00000i q^{25} +(-13.0000 + 13.0000i) q^{26} +(4.00000 + 4.00000i) q^{28} -48.0000 q^{29} +(-14.0000 - 14.0000i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(-6.00000 + 6.00000i) q^{34} -12.0000 q^{35} -18.0000i q^{36} +(37.0000 - 37.0000i) q^{37} +52.0000i q^{38} +12.0000 q^{40} +(-9.00000 - 9.00000i) q^{41} +36.0000i q^{43} +(12.0000 + 12.0000i) q^{44} +(27.0000 + 27.0000i) q^{45} +(24.0000 - 24.0000i) q^{46} +(42.0000 - 42.0000i) q^{47} +41.0000i q^{49} +(7.00000 - 7.00000i) q^{50} -26.0000 q^{52} +30.0000 q^{53} -36.0000 q^{55} +8.00000i q^{56} +(-48.0000 - 48.0000i) q^{58} +(-54.0000 + 54.0000i) q^{59} -18.0000 q^{61} -28.0000i q^{62} +(-18.0000 + 18.0000i) q^{63} -8.00000i q^{64} +(39.0000 - 39.0000i) q^{65} +(-22.0000 - 22.0000i) q^{67} -12.0000 q^{68} +(-12.0000 - 12.0000i) q^{70} +(6.00000 + 6.00000i) q^{71} +(18.0000 - 18.0000i) q^{72} +(17.0000 - 17.0000i) q^{73} +74.0000 q^{74} +(-52.0000 + 52.0000i) q^{76} -24.0000i q^{77} -108.000 q^{79} +(12.0000 + 12.0000i) q^{80} +81.0000 q^{81} -18.0000i q^{82} +(78.0000 + 78.0000i) q^{83} +(18.0000 - 18.0000i) q^{85} +(-36.0000 + 36.0000i) q^{86} +24.0000i q^{88} +(-9.00000 + 9.00000i) q^{89} +54.0000i q^{90} +(26.0000 + 26.0000i) q^{91} +48.0000 q^{92} +84.0000 q^{94} -156.000i q^{95} +(-47.0000 - 47.0000i) q^{97} +(-41.0000 + 41.0000i) q^{98} +(-54.0000 + 54.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 6 q^{5} + 4 q^{7} - 4 q^{8} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 6 q^{5} + 4 q^{7} - 4 q^{8} - 18 q^{9} + 12 q^{11} + 8 q^{14} - 8 q^{16} - 18 q^{18} + 52 q^{19} + 12 q^{20} + 24 q^{22} - 26 q^{26} + 8 q^{28} - 96 q^{29} - 28 q^{31} - 8 q^{32} - 12 q^{34} - 24 q^{35} + 74 q^{37} + 24 q^{40} - 18 q^{41} + 24 q^{44} + 54 q^{45} + 48 q^{46} + 84 q^{47} + 14 q^{50} - 52 q^{52} + 60 q^{53} - 72 q^{55} - 96 q^{58} - 108 q^{59} - 36 q^{61} - 36 q^{63} + 78 q^{65} - 44 q^{67} - 24 q^{68} - 24 q^{70} + 12 q^{71} + 36 q^{72} + 34 q^{73} + 148 q^{74} - 104 q^{76} - 216 q^{79} + 24 q^{80} + 162 q^{81} + 156 q^{83} + 36 q^{85} - 72 q^{86} - 18 q^{89} + 52 q^{91} + 96 q^{92} + 168 q^{94} - 94 q^{97} - 82 q^{98} - 108 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/26\mathbb{Z}\right)^\times\).

\(n\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 2.00000i 0.500000i
\(5\) −3.00000 3.00000i −0.600000 0.600000i 0.340312 0.940312i \(-0.389467\pi\)
−0.940312 + 0.340312i \(0.889467\pi\)
\(6\) 0 0
\(7\) 2.00000 2.00000i 0.285714 0.285714i −0.549669 0.835383i \(-0.685246\pi\)
0.835383 + 0.549669i \(0.185246\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) −9.00000 −1.00000
\(10\) 6.00000i 0.600000i
\(11\) 6.00000 6.00000i 0.545455 0.545455i −0.379668 0.925123i \(-0.623962\pi\)
0.925123 + 0.379668i \(0.123962\pi\)
\(12\) 0 0
\(13\) 13.0000i 1.00000i
\(14\) 4.00000 0.285714
\(15\) 0 0
\(16\) −4.00000 −0.250000
\(17\) 6.00000i 0.352941i 0.984306 + 0.176471i \(0.0564680\pi\)
−0.984306 + 0.176471i \(0.943532\pi\)
\(18\) −9.00000 9.00000i −0.500000 0.500000i
\(19\) 26.0000 + 26.0000i 1.36842 + 1.36842i 0.862693 + 0.505728i \(0.168776\pi\)
0.505728 + 0.862693i \(0.331224\pi\)
\(20\) 6.00000 6.00000i 0.300000 0.300000i
\(21\) 0 0
\(22\) 12.0000 0.545455
\(23\) 24.0000i 1.04348i −0.853105 0.521739i \(-0.825283\pi\)
0.853105 0.521739i \(-0.174717\pi\)
\(24\) 0 0
\(25\) 7.00000i 0.280000i
\(26\) −13.0000 + 13.0000i −0.500000 + 0.500000i
\(27\) 0 0
\(28\) 4.00000 + 4.00000i 0.142857 + 0.142857i
\(29\) −48.0000 −1.65517 −0.827586 0.561339i \(-0.810287\pi\)
−0.827586 + 0.561339i \(0.810287\pi\)
\(30\) 0 0
\(31\) −14.0000 14.0000i −0.451613 0.451613i 0.444277 0.895890i \(-0.353461\pi\)
−0.895890 + 0.444277i \(0.853461\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 0 0
\(34\) −6.00000 + 6.00000i −0.176471 + 0.176471i
\(35\) −12.0000 −0.342857
\(36\) 18.0000i 0.500000i
\(37\) 37.0000 37.0000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(38\) 52.0000i 1.36842i
\(39\) 0 0
\(40\) 12.0000 0.300000
\(41\) −9.00000 9.00000i −0.219512 0.219512i 0.588781 0.808293i \(-0.299608\pi\)
−0.808293 + 0.588781i \(0.799608\pi\)
\(42\) 0 0
\(43\) 36.0000i 0.837209i 0.908169 + 0.418605i \(0.137481\pi\)
−0.908169 + 0.418605i \(0.862519\pi\)
\(44\) 12.0000 + 12.0000i 0.272727 + 0.272727i
\(45\) 27.0000 + 27.0000i 0.600000 + 0.600000i
\(46\) 24.0000 24.0000i 0.521739 0.521739i
\(47\) 42.0000 42.0000i 0.893617 0.893617i −0.101245 0.994862i \(-0.532282\pi\)
0.994862 + 0.101245i \(0.0322825\pi\)
\(48\) 0 0
\(49\) 41.0000i 0.836735i
\(50\) 7.00000 7.00000i 0.140000 0.140000i
\(51\) 0 0
\(52\) −26.0000 −0.500000
\(53\) 30.0000 0.566038 0.283019 0.959114i \(-0.408664\pi\)
0.283019 + 0.959114i \(0.408664\pi\)
\(54\) 0 0
\(55\) −36.0000 −0.654545
\(56\) 8.00000i 0.142857i
\(57\) 0 0
\(58\) −48.0000 48.0000i −0.827586 0.827586i
\(59\) −54.0000 + 54.0000i −0.915254 + 0.915254i −0.996679 0.0814252i \(-0.974053\pi\)
0.0814252 + 0.996679i \(0.474053\pi\)
\(60\) 0 0
\(61\) −18.0000 −0.295082 −0.147541 0.989056i \(-0.547136\pi\)
−0.147541 + 0.989056i \(0.547136\pi\)
\(62\) 28.0000i 0.451613i
\(63\) −18.0000 + 18.0000i −0.285714 + 0.285714i
\(64\) 8.00000i 0.125000i
\(65\) 39.0000 39.0000i 0.600000 0.600000i
\(66\) 0 0
\(67\) −22.0000 22.0000i −0.328358 0.328358i 0.523604 0.851962i \(-0.324587\pi\)
−0.851962 + 0.523604i \(0.824587\pi\)
\(68\) −12.0000 −0.176471
\(69\) 0 0
\(70\) −12.0000 12.0000i −0.171429 0.171429i
\(71\) 6.00000 + 6.00000i 0.0845070 + 0.0845070i 0.748097 0.663590i \(-0.230968\pi\)
−0.663590 + 0.748097i \(0.730968\pi\)
\(72\) 18.0000 18.0000i 0.250000 0.250000i
\(73\) 17.0000 17.0000i 0.232877 0.232877i −0.581016 0.813892i \(-0.697345\pi\)
0.813892 + 0.581016i \(0.197345\pi\)
\(74\) 74.0000 1.00000
\(75\) 0 0
\(76\) −52.0000 + 52.0000i −0.684211 + 0.684211i
\(77\) 24.0000i 0.311688i
\(78\) 0 0
\(79\) −108.000 −1.36709 −0.683544 0.729909i \(-0.739562\pi\)
−0.683544 + 0.729909i \(0.739562\pi\)
\(80\) 12.0000 + 12.0000i 0.150000 + 0.150000i
\(81\) 81.0000 1.00000
\(82\) 18.0000i 0.219512i
\(83\) 78.0000 + 78.0000i 0.939759 + 0.939759i 0.998286 0.0585268i \(-0.0186403\pi\)
−0.0585268 + 0.998286i \(0.518640\pi\)
\(84\) 0 0
\(85\) 18.0000 18.0000i 0.211765 0.211765i
\(86\) −36.0000 + 36.0000i −0.418605 + 0.418605i
\(87\) 0 0
\(88\) 24.0000i 0.272727i
\(89\) −9.00000 + 9.00000i −0.101124 + 0.101124i −0.755859 0.654735i \(-0.772780\pi\)
0.654735 + 0.755859i \(0.272780\pi\)
\(90\) 54.0000i 0.600000i
\(91\) 26.0000 + 26.0000i 0.285714 + 0.285714i
\(92\) 48.0000 0.521739
\(93\) 0 0
\(94\) 84.0000 0.893617
\(95\) 156.000i 1.64211i
\(96\) 0 0
\(97\) −47.0000 47.0000i −0.484536 0.484536i 0.422041 0.906577i \(-0.361314\pi\)
−0.906577 + 0.422041i \(0.861314\pi\)
\(98\) −41.0000 + 41.0000i −0.418367 + 0.418367i
\(99\) −54.0000 + 54.0000i −0.545455 + 0.545455i
\(100\) 14.0000 0.140000
\(101\) 120.000i 1.18812i 0.804421 + 0.594059i \(0.202476\pi\)
−0.804421 + 0.594059i \(0.797524\pi\)
\(102\) 0 0
\(103\) 144.000i 1.39806i −0.715093 0.699029i \(-0.753616\pi\)
0.715093 0.699029i \(-0.246384\pi\)
\(104\) −26.0000 26.0000i −0.250000 0.250000i
\(105\) 0 0
\(106\) 30.0000 + 30.0000i 0.283019 + 0.283019i
\(107\) 120.000 1.12150 0.560748 0.827987i \(-0.310514\pi\)
0.560748 + 0.827987i \(0.310514\pi\)
\(108\) 0 0
\(109\) −19.0000 19.0000i −0.174312 0.174312i 0.614559 0.788871i \(-0.289334\pi\)
−0.788871 + 0.614559i \(0.789334\pi\)
\(110\) −36.0000 36.0000i −0.327273 0.327273i
\(111\) 0 0
\(112\) −8.00000 + 8.00000i −0.0714286 + 0.0714286i
\(113\) −120.000 −1.06195 −0.530973 0.847388i \(-0.678174\pi\)
−0.530973 + 0.847388i \(0.678174\pi\)
\(114\) 0 0
\(115\) −72.0000 + 72.0000i −0.626087 + 0.626087i
\(116\) 96.0000i 0.827586i
\(117\) 117.000i 1.00000i
\(118\) −108.000 −0.915254
\(119\) 12.0000 + 12.0000i 0.100840 + 0.100840i
\(120\) 0 0
\(121\) 49.0000i 0.404959i
\(122\) −18.0000 18.0000i −0.147541 0.147541i
\(123\) 0 0
\(124\) 28.0000 28.0000i 0.225806 0.225806i
\(125\) −96.0000 + 96.0000i −0.768000 + 0.768000i
\(126\) −36.0000 −0.285714
\(127\) 56.0000i 0.440945i 0.975393 + 0.220472i \(0.0707599\pi\)
−0.975393 + 0.220472i \(0.929240\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 0 0
\(130\) 78.0000 0.600000
\(131\) 72.0000 0.549618 0.274809 0.961499i \(-0.411385\pi\)
0.274809 + 0.961499i \(0.411385\pi\)
\(132\) 0 0
\(133\) 104.000 0.781955
\(134\) 44.0000i 0.328358i
\(135\) 0 0
\(136\) −12.0000 12.0000i −0.0882353 0.0882353i
\(137\) −63.0000 + 63.0000i −0.459854 + 0.459854i −0.898607 0.438753i \(-0.855420\pi\)
0.438753 + 0.898607i \(0.355420\pi\)
\(138\) 0 0
\(139\) 152.000 1.09353 0.546763 0.837288i \(-0.315860\pi\)
0.546763 + 0.837288i \(0.315860\pi\)
\(140\) 24.0000i 0.171429i
\(141\) 0 0
\(142\) 12.0000i 0.0845070i
\(143\) 78.0000 + 78.0000i 0.545455 + 0.545455i
\(144\) 36.0000 0.250000
\(145\) 144.000 + 144.000i 0.993103 + 0.993103i
\(146\) 34.0000 0.232877
\(147\) 0 0
\(148\) 74.0000 + 74.0000i 0.500000 + 0.500000i
\(149\) −99.0000 99.0000i −0.664430 0.664430i 0.291991 0.956421i \(-0.405682\pi\)
−0.956421 + 0.291991i \(0.905682\pi\)
\(150\) 0 0
\(151\) 106.000 106.000i 0.701987 0.701987i −0.262850 0.964837i \(-0.584662\pi\)
0.964837 + 0.262850i \(0.0846624\pi\)
\(152\) −104.000 −0.684211
\(153\) 54.0000i 0.352941i
\(154\) 24.0000 24.0000i 0.155844 0.155844i
\(155\) 84.0000i 0.541935i
\(156\) 0 0
\(157\) −80.0000 −0.509554 −0.254777 0.967000i \(-0.582002\pi\)
−0.254777 + 0.967000i \(0.582002\pi\)
\(158\) −108.000 108.000i −0.683544 0.683544i
\(159\) 0 0
\(160\) 24.0000i 0.150000i
\(161\) −48.0000 48.0000i −0.298137 0.298137i
\(162\) 81.0000 + 81.0000i 0.500000 + 0.500000i
\(163\) 82.0000 82.0000i 0.503067 0.503067i −0.409322 0.912390i \(-0.634235\pi\)
0.912390 + 0.409322i \(0.134235\pi\)
\(164\) 18.0000 18.0000i 0.109756 0.109756i
\(165\) 0 0
\(166\) 156.000i 0.939759i
\(167\) −138.000 + 138.000i −0.826347 + 0.826347i −0.987009 0.160662i \(-0.948637\pi\)
0.160662 + 0.987009i \(0.448637\pi\)
\(168\) 0 0
\(169\) −169.000 −1.00000
\(170\) 36.0000 0.211765
\(171\) −234.000 234.000i −1.36842 1.36842i
\(172\) −72.0000 −0.418605
\(173\) 24.0000i 0.138728i −0.997591 0.0693642i \(-0.977903\pi\)
0.997591 0.0693642i \(-0.0220970\pi\)
\(174\) 0 0
\(175\) −14.0000 14.0000i −0.0800000 0.0800000i
\(176\) −24.0000 + 24.0000i −0.136364 + 0.136364i
\(177\) 0 0
\(178\) −18.0000 −0.101124
\(179\) 300.000i 1.67598i −0.545687 0.837989i \(-0.683731\pi\)
0.545687 0.837989i \(-0.316269\pi\)
\(180\) −54.0000 + 54.0000i −0.300000 + 0.300000i
\(181\) 90.0000i 0.497238i 0.968601 + 0.248619i \(0.0799766\pi\)
−0.968601 + 0.248619i \(0.920023\pi\)
\(182\) 52.0000i 0.285714i
\(183\) 0 0
\(184\) 48.0000 + 48.0000i 0.260870 + 0.260870i
\(185\) −222.000 −1.20000
\(186\) 0 0
\(187\) 36.0000 + 36.0000i 0.192513 + 0.192513i
\(188\) 84.0000 + 84.0000i 0.446809 + 0.446809i
\(189\) 0 0
\(190\) 156.000 156.000i 0.821053 0.821053i
\(191\) 252.000 1.31937 0.659686 0.751541i \(-0.270689\pi\)
0.659686 + 0.751541i \(0.270689\pi\)
\(192\) 0 0
\(193\) 257.000 257.000i 1.33161 1.33161i 0.427672 0.903934i \(-0.359334\pi\)
0.903934 0.427672i \(-0.140666\pi\)
\(194\) 94.0000i 0.484536i
\(195\) 0 0
\(196\) −82.0000 −0.418367
\(197\) 123.000 + 123.000i 0.624365 + 0.624365i 0.946645 0.322279i \(-0.104449\pi\)
−0.322279 + 0.946645i \(0.604449\pi\)
\(198\) −108.000 −0.545455
\(199\) 200.000i 1.00503i 0.864570 + 0.502513i \(0.167591\pi\)
−0.864570 + 0.502513i \(0.832409\pi\)
\(200\) 14.0000 + 14.0000i 0.0700000 + 0.0700000i
\(201\) 0 0
\(202\) −120.000 + 120.000i −0.594059 + 0.594059i
\(203\) −96.0000 + 96.0000i −0.472906 + 0.472906i
\(204\) 0 0
\(205\) 54.0000i 0.263415i
\(206\) 144.000 144.000i 0.699029 0.699029i
\(207\) 216.000i 1.04348i
\(208\) 52.0000i 0.250000i
\(209\) 312.000 1.49282
\(210\) 0 0
\(211\) −288.000 −1.36493 −0.682464 0.730919i \(-0.739092\pi\)
−0.682464 + 0.730919i \(0.739092\pi\)
\(212\) 60.0000i 0.283019i
\(213\) 0 0
\(214\) 120.000 + 120.000i 0.560748 + 0.560748i
\(215\) 108.000 108.000i 0.502326 0.502326i
\(216\) 0 0
\(217\) −56.0000 −0.258065
\(218\) 38.0000i 0.174312i
\(219\) 0 0
\(220\) 72.0000i 0.327273i
\(221\) −78.0000 −0.352941
\(222\) 0 0
\(223\) 38.0000 + 38.0000i 0.170404 + 0.170404i 0.787157 0.616753i \(-0.211552\pi\)
−0.616753 + 0.787157i \(0.711552\pi\)
\(224\) −16.0000 −0.0714286
\(225\) 63.0000i 0.280000i
\(226\) −120.000 120.000i −0.530973 0.530973i
\(227\) 138.000 + 138.000i 0.607930 + 0.607930i 0.942405 0.334475i \(-0.108559\pi\)
−0.334475 + 0.942405i \(0.608559\pi\)
\(228\) 0 0
\(229\) 131.000 131.000i 0.572052 0.572052i −0.360649 0.932702i \(-0.617445\pi\)
0.932702 + 0.360649i \(0.117445\pi\)
\(230\) −144.000 −0.626087
\(231\) 0 0
\(232\) 96.0000 96.0000i 0.413793 0.413793i
\(233\) 336.000i 1.44206i 0.692904 + 0.721030i \(0.256331\pi\)
−0.692904 + 0.721030i \(0.743669\pi\)
\(234\) 117.000 117.000i 0.500000 0.500000i
\(235\) −252.000 −1.07234
\(236\) −108.000 108.000i −0.457627 0.457627i
\(237\) 0 0
\(238\) 24.0000i 0.100840i
\(239\) −114.000 114.000i −0.476987 0.476987i 0.427179 0.904167i \(-0.359507\pi\)
−0.904167 + 0.427179i \(0.859507\pi\)
\(240\) 0 0
\(241\) 151.000 151.000i 0.626556 0.626556i −0.320644 0.947200i \(-0.603899\pi\)
0.947200 + 0.320644i \(0.103899\pi\)
\(242\) −49.0000 + 49.0000i −0.202479 + 0.202479i
\(243\) 0 0
\(244\) 36.0000i 0.147541i
\(245\) 123.000 123.000i 0.502041 0.502041i
\(246\) 0 0
\(247\) −338.000 + 338.000i −1.36842 + 1.36842i
\(248\) 56.0000 0.225806
\(249\) 0 0
\(250\) −192.000 −0.768000
\(251\) 180.000i 0.717131i −0.933504 0.358566i \(-0.883266\pi\)
0.933504 0.358566i \(-0.116734\pi\)
\(252\) −36.0000 36.0000i −0.142857 0.142857i
\(253\) −144.000 144.000i −0.569170 0.569170i
\(254\) −56.0000 + 56.0000i −0.220472 + 0.220472i
\(255\) 0 0
\(256\) 16.0000 0.0625000
\(257\) 144.000i 0.560311i −0.959955 0.280156i \(-0.909614\pi\)
0.959955 0.280156i \(-0.0903861\pi\)
\(258\) 0 0
\(259\) 148.000i 0.571429i
\(260\) 78.0000 + 78.0000i 0.300000 + 0.300000i
\(261\) 432.000 1.65517
\(262\) 72.0000 + 72.0000i 0.274809 + 0.274809i
\(263\) −60.0000 −0.228137 −0.114068 0.993473i \(-0.536388\pi\)
−0.114068 + 0.993473i \(0.536388\pi\)
\(264\) 0 0
\(265\) −90.0000 90.0000i −0.339623 0.339623i
\(266\) 104.000 + 104.000i 0.390977 + 0.390977i
\(267\) 0 0
\(268\) 44.0000 44.0000i 0.164179 0.164179i
\(269\) −288.000 −1.07063 −0.535316 0.844652i \(-0.679807\pi\)
−0.535316 + 0.844652i \(0.679807\pi\)
\(270\) 0 0
\(271\) −134.000 + 134.000i −0.494465 + 0.494465i −0.909710 0.415245i \(-0.863696\pi\)
0.415245 + 0.909710i \(0.363696\pi\)
\(272\) 24.0000i 0.0882353i
\(273\) 0 0
\(274\) −126.000 −0.459854
\(275\) −42.0000 42.0000i −0.152727 0.152727i
\(276\) 0 0
\(277\) 216.000i 0.779783i 0.920861 + 0.389892i \(0.127488\pi\)
−0.920861 + 0.389892i \(0.872512\pi\)
\(278\) 152.000 + 152.000i 0.546763 + 0.546763i
\(279\) 126.000 + 126.000i 0.451613 + 0.451613i
\(280\) 24.0000 24.0000i 0.0857143 0.0857143i
\(281\) −159.000 + 159.000i −0.565836 + 0.565836i −0.930959 0.365123i \(-0.881027\pi\)
0.365123 + 0.930959i \(0.381027\pi\)
\(282\) 0 0
\(283\) 404.000i 1.42756i −0.700369 0.713781i \(-0.746981\pi\)
0.700369 0.713781i \(-0.253019\pi\)
\(284\) −12.0000 + 12.0000i −0.0422535 + 0.0422535i
\(285\) 0 0
\(286\) 156.000i 0.545455i
\(287\) −36.0000 −0.125436
\(288\) 36.0000 + 36.0000i 0.125000 + 0.125000i
\(289\) 253.000 0.875433
\(290\) 288.000i 0.993103i
\(291\) 0 0
\(292\) 34.0000 + 34.0000i 0.116438 + 0.116438i
\(293\) 147.000 147.000i 0.501706 0.501706i −0.410261 0.911968i \(-0.634563\pi\)
0.911968 + 0.410261i \(0.134563\pi\)
\(294\) 0 0
\(295\) 324.000 1.09831
\(296\) 148.000i 0.500000i
\(297\) 0 0
\(298\) 198.000i 0.664430i
\(299\) 312.000 1.04348
\(300\) 0 0
\(301\) 72.0000 + 72.0000i 0.239203 + 0.239203i
\(302\) 212.000 0.701987
\(303\) 0 0
\(304\) −104.000 104.000i −0.342105 0.342105i
\(305\) 54.0000 + 54.0000i 0.177049 + 0.177049i
\(306\) 54.0000 54.0000i 0.176471 0.176471i
\(307\) 82.0000 82.0000i 0.267101 0.267101i −0.560830 0.827931i \(-0.689518\pi\)
0.827931 + 0.560830i \(0.189518\pi\)
\(308\) 48.0000 0.155844
\(309\) 0 0
\(310\) −84.0000 + 84.0000i −0.270968 + 0.270968i
\(311\) 120.000i 0.385852i −0.981213 0.192926i \(-0.938202\pi\)
0.981213 0.192926i \(-0.0617977\pi\)
\(312\) 0 0
\(313\) −360.000 −1.15016 −0.575080 0.818097i \(-0.695029\pi\)
−0.575080 + 0.818097i \(0.695029\pi\)
\(314\) −80.0000 80.0000i −0.254777 0.254777i
\(315\) 108.000 0.342857
\(316\) 216.000i 0.683544i
\(317\) −147.000 147.000i −0.463722 0.463722i 0.436151 0.899873i \(-0.356341\pi\)
−0.899873 + 0.436151i \(0.856341\pi\)
\(318\) 0 0
\(319\) −288.000 + 288.000i −0.902821 + 0.902821i
\(320\) −24.0000 + 24.0000i −0.0750000 + 0.0750000i
\(321\) 0 0
\(322\) 96.0000i 0.298137i
\(323\) −156.000 + 156.000i −0.482972 + 0.482972i
\(324\) 162.000i 0.500000i
\(325\) 91.0000 0.280000
\(326\) 164.000 0.503067
\(327\) 0 0
\(328\) 36.0000 0.109756
\(329\) 168.000i 0.510638i
\(330\) 0 0
\(331\) −214.000 214.000i −0.646526 0.646526i 0.305626 0.952152i \(-0.401134\pi\)
−0.952152 + 0.305626i \(0.901134\pi\)
\(332\) −156.000 + 156.000i −0.469880 + 0.469880i
\(333\) −333.000 + 333.000i −1.00000 + 1.00000i
\(334\) −276.000 −0.826347
\(335\) 132.000i 0.394030i
\(336\) 0 0
\(337\) 314.000i 0.931751i −0.884850 0.465875i \(-0.845740\pi\)
0.884850 0.465875i \(-0.154260\pi\)
\(338\) −169.000 169.000i −0.500000 0.500000i
\(339\) 0 0
\(340\) 36.0000 + 36.0000i 0.105882 + 0.105882i
\(341\) −168.000 −0.492669
\(342\) 468.000i 1.36842i
\(343\) 180.000 + 180.000i 0.524781 + 0.524781i
\(344\) −72.0000 72.0000i −0.209302 0.209302i
\(345\) 0 0
\(346\) 24.0000 24.0000i 0.0693642 0.0693642i
\(347\) −120.000 −0.345821 −0.172911 0.984938i \(-0.555317\pi\)
−0.172911 + 0.984938i \(0.555317\pi\)
\(348\) 0 0
\(349\) 101.000 101.000i 0.289398 0.289398i −0.547444 0.836842i \(-0.684399\pi\)
0.836842 + 0.547444i \(0.184399\pi\)
\(350\) 28.0000i 0.0800000i
\(351\) 0 0
\(352\) −48.0000 −0.136364
\(353\) 33.0000 + 33.0000i 0.0934844 + 0.0934844i 0.752302 0.658818i \(-0.228943\pi\)
−0.658818 + 0.752302i \(0.728943\pi\)
\(354\) 0 0
\(355\) 36.0000i 0.101408i
\(356\) −18.0000 18.0000i −0.0505618 0.0505618i
\(357\) 0 0
\(358\) 300.000 300.000i 0.837989 0.837989i
\(359\) 186.000 186.000i 0.518106 0.518106i −0.398892 0.916998i \(-0.630605\pi\)
0.916998 + 0.398892i \(0.130605\pi\)
\(360\) −108.000 −0.300000
\(361\) 991.000i 2.74515i
\(362\) −90.0000 + 90.0000i −0.248619 + 0.248619i
\(363\) 0 0
\(364\) −52.0000 + 52.0000i −0.142857 + 0.142857i
\(365\) −102.000 −0.279452
\(366\) 0 0
\(367\) 580.000 1.58038 0.790191 0.612861i \(-0.209981\pi\)
0.790191 + 0.612861i \(0.209981\pi\)
\(368\) 96.0000i 0.260870i
\(369\) 81.0000 + 81.0000i 0.219512 + 0.219512i
\(370\) −222.000 222.000i −0.600000 0.600000i
\(371\) 60.0000 60.0000i 0.161725 0.161725i
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 72.0000i 0.192513i
\(375\) 0 0
\(376\) 168.000i 0.446809i
\(377\) 624.000i 1.65517i
\(378\) 0 0
\(379\) 226.000 + 226.000i 0.596306 + 0.596306i 0.939328 0.343021i \(-0.111450\pi\)
−0.343021 + 0.939328i \(0.611450\pi\)
\(380\) 312.000 0.821053
\(381\) 0 0
\(382\) 252.000 + 252.000i 0.659686 + 0.659686i
\(383\) 78.0000 + 78.0000i 0.203655 + 0.203655i 0.801564 0.597909i \(-0.204002\pi\)
−0.597909 + 0.801564i \(0.704002\pi\)
\(384\) 0 0
\(385\) −72.0000 + 72.0000i −0.187013 + 0.187013i
\(386\) 514.000 1.33161
\(387\) 324.000i 0.837209i
\(388\) 94.0000 94.0000i 0.242268 0.242268i
\(389\) 150.000i 0.385604i 0.981238 + 0.192802i \(0.0617575\pi\)
−0.981238 + 0.192802i \(0.938242\pi\)
\(390\) 0 0
\(391\) 144.000 0.368286
\(392\) −82.0000 82.0000i −0.209184 0.209184i
\(393\) 0 0
\(394\) 246.000i 0.624365i
\(395\) 324.000 + 324.000i 0.820253 + 0.820253i
\(396\) −108.000 108.000i −0.272727 0.272727i
\(397\) −253.000 + 253.000i −0.637280 + 0.637280i −0.949884 0.312604i \(-0.898799\pi\)
0.312604 + 0.949884i \(0.398799\pi\)
\(398\) −200.000 + 200.000i −0.502513 + 0.502513i
\(399\) 0 0
\(400\) 28.0000i 0.0700000i
\(401\) −249.000 + 249.000i −0.620948 + 0.620948i −0.945774 0.324826i \(-0.894694\pi\)
0.324826 + 0.945774i \(0.394694\pi\)
\(402\) 0 0
\(403\) 182.000 182.000i 0.451613 0.451613i
\(404\) −240.000 −0.594059
\(405\) −243.000 243.000i −0.600000 0.600000i
\(406\) −192.000 −0.472906
\(407\) 444.000i 1.09091i
\(408\) 0 0
\(409\) −319.000 319.000i −0.779951 0.779951i 0.199871 0.979822i \(-0.435948\pi\)
−0.979822 + 0.199871i \(0.935948\pi\)
\(410\) −54.0000 + 54.0000i −0.131707 + 0.131707i
\(411\) 0 0
\(412\) 288.000 0.699029
\(413\) 216.000i 0.523002i
\(414\) −216.000 + 216.000i −0.521739 + 0.521739i
\(415\) 468.000i 1.12771i
\(416\) 52.0000 52.0000i 0.125000 0.125000i
\(417\) 0 0
\(418\) 312.000 + 312.000i 0.746411 + 0.746411i
\(419\) −48.0000 −0.114558 −0.0572792 0.998358i \(-0.518243\pi\)
−0.0572792 + 0.998358i \(0.518243\pi\)
\(420\) 0 0
\(421\) 11.0000 + 11.0000i 0.0261283 + 0.0261283i 0.720050 0.693922i \(-0.244119\pi\)
−0.693922 + 0.720050i \(0.744119\pi\)
\(422\) −288.000 288.000i −0.682464 0.682464i
\(423\) −378.000 + 378.000i −0.893617 + 0.893617i
\(424\) −60.0000 + 60.0000i −0.141509 + 0.141509i
\(425\) 42.0000 0.0988235
\(426\) 0 0
\(427\) −36.0000 + 36.0000i −0.0843091 + 0.0843091i
\(428\) 240.000i 0.560748i
\(429\) 0 0
\(430\) 216.000 0.502326
\(431\) −414.000 414.000i −0.960557 0.960557i 0.0386943 0.999251i \(-0.487680\pi\)
−0.999251 + 0.0386943i \(0.987680\pi\)
\(432\) 0 0
\(433\) 16.0000i 0.0369515i 0.999829 + 0.0184758i \(0.00588135\pi\)
−0.999829 + 0.0184758i \(0.994119\pi\)
\(434\) −56.0000 56.0000i −0.129032 0.129032i
\(435\) 0 0
\(436\) 38.0000 38.0000i 0.0871560 0.0871560i
\(437\) 624.000 624.000i 1.42792 1.42792i
\(438\) 0 0
\(439\) 360.000i 0.820046i 0.912075 + 0.410023i \(0.134479\pi\)
−0.912075 + 0.410023i \(0.865521\pi\)
\(440\) 72.0000 72.0000i 0.163636 0.163636i
\(441\) 369.000i 0.836735i
\(442\) −78.0000 78.0000i −0.176471 0.176471i
\(443\) −600.000 −1.35440 −0.677201 0.735798i \(-0.736807\pi\)
−0.677201 + 0.735798i \(0.736807\pi\)
\(444\) 0 0
\(445\) 54.0000 0.121348
\(446\) 76.0000i 0.170404i
\(447\) 0 0
\(448\) −16.0000 16.0000i −0.0357143 0.0357143i
\(449\) −9.00000 + 9.00000i −0.0200445 + 0.0200445i −0.717058 0.697013i \(-0.754512\pi\)
0.697013 + 0.717058i \(0.254512\pi\)
\(450\) −63.0000 + 63.0000i −0.140000 + 0.140000i
\(451\) −108.000 −0.239468
\(452\) 240.000i 0.530973i
\(453\) 0 0
\(454\) 276.000i 0.607930i
\(455\) 156.000i 0.342857i
\(456\) 0 0
\(457\) −47.0000 47.0000i −0.102845 0.102845i 0.653812 0.756657i \(-0.273169\pi\)
−0.756657 + 0.653812i \(0.773169\pi\)
\(458\) 262.000 0.572052
\(459\) 0 0
\(460\) −144.000 144.000i −0.313043 0.313043i
\(461\) 171.000 + 171.000i 0.370933 + 0.370933i 0.867817 0.496884i \(-0.165523\pi\)
−0.496884 + 0.867817i \(0.665523\pi\)
\(462\) 0 0
\(463\) 202.000 202.000i 0.436285 0.436285i −0.454475 0.890760i \(-0.650173\pi\)
0.890760 + 0.454475i \(0.150173\pi\)
\(464\) 192.000 0.413793
\(465\) 0 0
\(466\) −336.000 + 336.000i −0.721030 + 0.721030i
\(467\) 516.000i 1.10493i 0.833538 + 0.552463i \(0.186312\pi\)
−0.833538 + 0.552463i \(0.813688\pi\)
\(468\) 234.000 0.500000
\(469\) −88.0000 −0.187633
\(470\) −252.000 252.000i −0.536170 0.536170i
\(471\) 0 0
\(472\) 216.000i 0.457627i
\(473\) 216.000 + 216.000i 0.456660 + 0.456660i
\(474\) 0 0
\(475\) 182.000 182.000i 0.383158 0.383158i
\(476\) −24.0000 + 24.0000i −0.0504202 + 0.0504202i
\(477\) −270.000 −0.566038
\(478\) 228.000i 0.476987i
\(479\) −234.000 + 234.000i −0.488518 + 0.488518i −0.907838 0.419321i \(-0.862268\pi\)
0.419321 + 0.907838i \(0.362268\pi\)
\(480\) 0 0
\(481\) 481.000 + 481.000i 1.00000 + 1.00000i
\(482\) 302.000 0.626556
\(483\) 0 0
\(484\) −98.0000 −0.202479
\(485\) 282.000i 0.581443i
\(486\) 0 0
\(487\) 298.000 + 298.000i 0.611910 + 0.611910i 0.943443 0.331534i \(-0.107566\pi\)
−0.331534 + 0.943443i \(0.607566\pi\)
\(488\) 36.0000 36.0000i 0.0737705 0.0737705i
\(489\) 0 0
\(490\) 246.000 0.502041
\(491\) 420.000i 0.855397i 0.903921 + 0.427699i \(0.140676\pi\)
−0.903921 + 0.427699i \(0.859324\pi\)
\(492\) 0 0
\(493\) 288.000i 0.584178i
\(494\) −676.000 −1.36842
\(495\) 324.000 0.654545
\(496\) 56.0000 + 56.0000i 0.112903 + 0.112903i
\(497\) 24.0000 0.0482897
\(498\) 0 0
\(499\) 346.000 + 346.000i 0.693387 + 0.693387i 0.962976 0.269589i \(-0.0868878\pi\)
−0.269589 + 0.962976i \(0.586888\pi\)
\(500\) −192.000 192.000i −0.384000 0.384000i
\(501\) 0 0
\(502\) 180.000 180.000i 0.358566 0.358566i
\(503\) −420.000 −0.834990 −0.417495 0.908679i \(-0.637092\pi\)
−0.417495 + 0.908679i \(0.637092\pi\)
\(504\) 72.0000i 0.142857i
\(505\) 360.000 360.000i 0.712871 0.712871i
\(506\) 288.000i 0.569170i
\(507\) 0 0
\(508\) −112.000 −0.220472
\(509\) 381.000 + 381.000i 0.748527 + 0.748527i 0.974202 0.225676i \(-0.0724590\pi\)
−0.225676 + 0.974202i \(0.572459\pi\)
\(510\) 0 0
\(511\) 68.0000i 0.133072i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) 0 0
\(514\) 144.000 144.000i 0.280156 0.280156i
\(515\) −432.000 + 432.000i −0.838835 + 0.838835i
\(516\) 0 0
\(517\) 504.000i 0.974855i
\(518\) 148.000 148.000i 0.285714 0.285714i
\(519\) 0 0
\(520\) 156.000i 0.300000i
\(521\) 312.000 0.598848 0.299424 0.954120i \(-0.403205\pi\)
0.299424 + 0.954120i \(0.403205\pi\)
\(522\) 432.000 + 432.000i 0.827586 + 0.827586i
\(523\) −560.000 −1.07075 −0.535373 0.844616i \(-0.679829\pi\)
−0.535373 + 0.844616i \(0.679829\pi\)
\(524\) 144.000i 0.274809i
\(525\) 0 0
\(526\) −60.0000 60.0000i −0.114068 0.114068i
\(527\) 84.0000 84.0000i 0.159393 0.159393i
\(528\) 0 0
\(529\) −47.0000 −0.0888469
\(530\) 180.000i 0.339623i
\(531\) 486.000 486.000i 0.915254 0.915254i
\(532\) 208.000i 0.390977i
\(533\) 117.000 117.000i 0.219512 0.219512i
\(534\) 0 0
\(535\) −360.000 360.000i −0.672897 0.672897i
\(536\) 88.0000 0.164179
\(537\) 0 0
\(538\) −288.000 288.000i −0.535316 0.535316i
\(539\) 246.000 + 246.000i 0.456401 + 0.456401i
\(540\) 0 0
\(541\) −379.000 + 379.000i −0.700555 + 0.700555i −0.964530 0.263975i \(-0.914966\pi\)
0.263975 + 0.964530i \(0.414966\pi\)
\(542\) −268.000 −0.494465
\(543\) 0 0
\(544\) 24.0000 24.0000i 0.0441176 0.0441176i
\(545\) 114.000i 0.209174i
\(546\) 0 0
\(547\) −400.000 −0.731261 −0.365631 0.930760i \(-0.619147\pi\)
−0.365631 + 0.930760i \(0.619147\pi\)
\(548\) −126.000 126.000i −0.229927 0.229927i
\(549\) 162.000 0.295082
\(550\) 84.0000i 0.152727i
\(551\) −1248.00 1248.00i −2.26497 2.26497i
\(552\) 0 0
\(553\) −216.000 + 216.000i −0.390597 + 0.390597i
\(554\) −216.000 + 216.000i −0.389892 + 0.389892i
\(555\) 0 0
\(556\) 304.000i 0.546763i
\(557\) 117.000 117.000i 0.210054 0.210054i −0.594236 0.804290i \(-0.702546\pi\)
0.804290 + 0.594236i \(0.202546\pi\)
\(558\) 252.000i 0.451613i
\(559\) −468.000 −0.837209
\(560\) 48.0000 0.0857143
\(561\) 0 0
\(562\) −318.000 −0.565836
\(563\) 876.000i 1.55595i 0.628295 + 0.777975i \(0.283753\pi\)
−0.628295 + 0.777975i \(0.716247\pi\)
\(564\) 0 0
\(565\) 360.000 + 360.000i 0.637168 + 0.637168i
\(566\) 404.000 404.000i 0.713781 0.713781i
\(567\) 162.000 162.000i 0.285714 0.285714i
\(568\) −24.0000 −0.0422535
\(569\) 720.000i 1.26538i −0.774406 0.632689i \(-0.781951\pi\)
0.774406 0.632689i \(-0.218049\pi\)
\(570\) 0 0
\(571\) 460.000i 0.805604i −0.915287 0.402802i \(-0.868036\pi\)
0.915287 0.402802i \(-0.131964\pi\)
\(572\) −156.000 + 156.000i −0.272727 + 0.272727i
\(573\) 0 0
\(574\) −36.0000 36.0000i −0.0627178 0.0627178i
\(575\) −168.000 −0.292174
\(576\) 72.0000i 0.125000i
\(577\) −377.000 377.000i −0.653380 0.653380i 0.300426 0.953805i \(-0.402871\pi\)
−0.953805 + 0.300426i \(0.902871\pi\)
\(578\) 253.000 + 253.000i 0.437716 + 0.437716i
\(579\) 0 0
\(580\) −288.000 + 288.000i −0.496552 + 0.496552i
\(581\) 312.000 0.537005
\(582\) 0 0
\(583\) 180.000 180.000i 0.308748 0.308748i
\(584\) 68.0000i 0.116438i
\(585\) −351.000 + 351.000i −0.600000 + 0.600000i
\(586\) 294.000 0.501706
\(587\) 738.000 + 738.000i 1.25724 + 1.25724i 0.952405 + 0.304835i \(0.0986013\pi\)
0.304835 + 0.952405i \(0.401399\pi\)
\(588\) 0 0
\(589\) 728.000i 1.23599i
\(590\) 324.000 + 324.000i 0.549153 + 0.549153i
\(591\) 0 0
\(592\) −148.000 + 148.000i −0.250000 + 0.250000i
\(593\) 327.000 327.000i 0.551433 0.551433i −0.375421 0.926854i \(-0.622502\pi\)
0.926854 + 0.375421i \(0.122502\pi\)
\(594\) 0 0
\(595\) 72.0000i 0.121008i
\(596\) 198.000 198.000i 0.332215 0.332215i
\(597\) 0 0
\(598\) 312.000 + 312.000i 0.521739 + 0.521739i
\(599\) 372.000 0.621035 0.310518 0.950568i \(-0.399498\pi\)
0.310518 + 0.950568i \(0.399498\pi\)
\(600\) 0 0
\(601\) −648.000 −1.07820 −0.539101 0.842241i \(-0.681236\pi\)
−0.539101 + 0.842241i \(0.681236\pi\)
\(602\) 144.000i 0.239203i
\(603\) 198.000 + 198.000i 0.328358 + 0.328358i
\(604\) 212.000 + 212.000i 0.350993 + 0.350993i
\(605\) 147.000 147.000i 0.242975 0.242975i
\(606\) 0 0
\(607\) −260.000 −0.428336 −0.214168 0.976797i \(-0.568704\pi\)
−0.214168 + 0.976797i \(0.568704\pi\)
\(608\) 208.000i 0.342105i
\(609\) 0 0
\(610\) 108.000i 0.177049i
\(611\) 546.000 + 546.000i 0.893617 + 0.893617i
\(612\) 108.000 0.176471
\(613\) −197.000 197.000i −0.321370 0.321370i 0.527922 0.849293i \(-0.322971\pi\)
−0.849293 + 0.527922i \(0.822971\pi\)
\(614\) 164.000 0.267101
\(615\) 0 0
\(616\) 48.0000 + 48.0000i 0.0779221 + 0.0779221i
\(617\) 753.000 + 753.000i 1.22042 + 1.22042i 0.967482 + 0.252939i \(0.0813973\pi\)
0.252939 + 0.967482i \(0.418603\pi\)
\(618\) 0 0
\(619\) −34.0000 + 34.0000i −0.0549273 + 0.0549273i −0.734037 0.679110i \(-0.762366\pi\)
0.679110 + 0.734037i \(0.262366\pi\)
\(620\) −168.000 −0.270968
\(621\) 0 0
\(622\) 120.000 120.000i 0.192926 0.192926i
\(623\) 36.0000i 0.0577849i
\(624\) 0 0
\(625\) 401.000 0.641600
\(626\) −360.000 360.000i −0.575080 0.575080i
\(627\) 0 0
\(628\) 160.000i 0.254777i
\(629\) 222.000 + 222.000i 0.352941 + 0.352941i
\(630\) 108.000 + 108.000i 0.171429 + 0.171429i
\(631\) 386.000 386.000i 0.611727 0.611727i −0.331669 0.943396i \(-0.607612\pi\)
0.943396 + 0.331669i \(0.107612\pi\)
\(632\) 216.000 216.000i 0.341772 0.341772i
\(633\) 0 0
\(634\) 294.000i 0.463722i
\(635\) 168.000 168.000i 0.264567 0.264567i
\(636\) 0 0
\(637\) −533.000 −0.836735
\(638\) −576.000 −0.902821
\(639\) −54.0000 54.0000i −0.0845070 0.0845070i
\(640\) −48.0000 −0.0750000
\(641\) 90.0000i 0.140406i 0.997533 + 0.0702028i \(0.0223646\pi\)
−0.997533 + 0.0702028i \(0.977635\pi\)
\(642\) 0 0
\(643\) −202.000 202.000i −0.314152 0.314152i 0.532363 0.846516i \(-0.321304\pi\)
−0.846516 + 0.532363i \(0.821304\pi\)
\(644\) 96.0000 96.0000i 0.149068 0.149068i
\(645\) 0 0
\(646\) −312.000 −0.482972
\(647\) 144.000i 0.222566i −0.993789 0.111283i \(-0.964504\pi\)
0.993789 0.111283i \(-0.0354960\pi\)
\(648\) −162.000 + 162.000i −0.250000 + 0.250000i
\(649\) 648.000i 0.998459i
\(650\) 91.0000 + 91.0000i 0.140000 + 0.140000i
\(651\) 0 0
\(652\) 164.000 + 164.000i 0.251534 + 0.251534i
\(653\) −240.000 −0.367534 −0.183767 0.982970i \(-0.558829\pi\)
−0.183767 + 0.982970i \(0.558829\pi\)
\(654\) 0 0
\(655\) −216.000 216.000i −0.329771 0.329771i
\(656\) 36.0000 + 36.0000i 0.0548780 + 0.0548780i
\(657\) −153.000 + 153.000i −0.232877 + 0.232877i
\(658\) 168.000 168.000i 0.255319 0.255319i
\(659\) −168.000 −0.254932 −0.127466 0.991843i \(-0.540684\pi\)
−0.127466 + 0.991843i \(0.540684\pi\)
\(660\) 0 0
\(661\) −509.000 + 509.000i −0.770045 + 0.770045i −0.978114 0.208069i \(-0.933282\pi\)
0.208069 + 0.978114i \(0.433282\pi\)
\(662\) 428.000i 0.646526i
\(663\) 0 0
\(664\) −312.000 −0.469880
\(665\) −312.000 312.000i −0.469173 0.469173i
\(666\) −666.000 −1.00000
\(667\) 1152.00i 1.72714i
\(668\) −276.000 276.000i −0.413174 0.413174i
\(669\) 0 0
\(670\) −132.000 + 132.000i −0.197015 + 0.197015i
\(671\) −108.000 + 108.000i −0.160954 + 0.160954i
\(672\) 0 0
\(673\) 954.000i 1.41753i −0.705443 0.708767i \(-0.749252\pi\)
0.705443 0.708767i \(-0.250748\pi\)
\(674\) 314.000 314.000i 0.465875 0.465875i
\(675\) 0 0
\(676\) 338.000i 0.500000i
\(677\) −930.000 −1.37371 −0.686854 0.726796i \(-0.741009\pi\)
−0.686854 + 0.726796i \(0.741009\pi\)
\(678\) 0 0
\(679\) −188.000 −0.276878
\(680\) 72.0000i 0.105882i
\(681\) 0 0
\(682\) −168.000 168.000i −0.246334 0.246334i
\(683\) 342.000 342.000i 0.500732 0.500732i −0.410933 0.911665i \(-0.634797\pi\)
0.911665 + 0.410933i \(0.134797\pi\)
\(684\) 468.000 468.000i 0.684211 0.684211i
\(685\) 378.000 0.551825
\(686\) 360.000i 0.524781i
\(687\) 0 0
\(688\) 144.000i 0.209302i
\(689\) 390.000i 0.566038i
\(690\) 0 0
\(691\) −254.000 254.000i −0.367583 0.367583i 0.499012 0.866595i \(-0.333696\pi\)
−0.866595 + 0.499012i \(0.833696\pi\)
\(692\) 48.0000 0.0693642
\(693\) 216.000i 0.311688i
\(694\) −120.000 120.000i −0.172911 0.172911i
\(695\) −456.000 456.000i −0.656115 0.656115i
\(696\) 0 0
\(697\) 54.0000 54.0000i 0.0774749 0.0774749i
\(698\) 202.000 0.289398
\(699\) 0 0
\(700\) 28.0000 28.0000i 0.0400000 0.0400000i
\(701\) 150.000i 0.213980i 0.994260 + 0.106990i \(0.0341213\pi\)
−0.994260 + 0.106990i \(0.965879\pi\)
\(702\) 0 0
\(703\) 1924.00 2.73684
\(704\) −48.0000 48.0000i −0.0681818 0.0681818i
\(705\) 0 0
\(706\) 66.0000i 0.0934844i
\(707\) 240.000 + 240.000i 0.339463 + 0.339463i
\(708\) 0 0
\(709\) −299.000 + 299.000i −0.421721 + 0.421721i −0.885796 0.464075i \(-0.846387\pi\)
0.464075 + 0.885796i \(0.346387\pi\)
\(710\) 36.0000 36.0000i 0.0507042 0.0507042i
\(711\) 972.000 1.36709
\(712\) 36.0000i 0.0505618i
\(713\) −336.000 + 336.000i −0.471248 + 0.471248i
\(714\) 0 0
\(715\) 468.000i 0.654545i
\(716\) 600.000 0.837989
\(717\) 0 0
\(718\) 372.000 0.518106
\(719\) 1200.00i 1.66898i −0.551020 0.834492i \(-0.685761\pi\)
0.551020 0.834492i \(-0.314239\pi\)
\(720\) −108.000 108.000i −0.150000 0.150000i
\(721\) −288.000 288.000i −0.399445 0.399445i
\(722\) −991.000 + 991.000i −1.37258 + 1.37258i
\(723\) 0 0
\(724\) −180.000 −0.248619
\(725\) 336.000i 0.463448i
\(726\) 0 0
\(727\) 1336.00i 1.83769i 0.394620 + 0.918845i \(0.370876\pi\)
−0.394620 + 0.918845i \(0.629124\pi\)
\(728\) −104.000 −0.142857
\(729\) −729.000 −1.00000
\(730\) −102.000 102.000i −0.139726 0.139726i
\(731\) −216.000 −0.295486
\(732\) 0 0
\(733\) 283.000 + 283.000i 0.386085 + 0.386085i 0.873288 0.487204i \(-0.161983\pi\)
−0.487204 + 0.873288i \(0.661983\pi\)
\(734\) 580.000 + 580.000i 0.790191 + 0.790191i
\(735\) 0 0
\(736\) −96.0000 + 96.0000i −0.130435 + 0.130435i
\(737\) −264.000 −0.358209
\(738\) 162.000i 0.219512i
\(739\) 926.000 926.000i 1.25304 1.25304i 0.298696 0.954348i \(-0.403448\pi\)
0.954348 0.298696i \(-0.0965518\pi\)
\(740\) 444.000i 0.600000i
\(741\) 0 0
\(742\) 120.000 0.161725
\(743\) 798.000 + 798.000i 1.07402 + 1.07402i 0.997032 + 0.0769926i \(0.0245318\pi\)
0.0769926 + 0.997032i \(0.475468\pi\)
\(744\) 0 0
\(745\) 594.000i 0.797315i
\(746\) 0 0
\(747\) −702.000 702.000i −0.939759 0.939759i
\(748\) −72.0000 + 72.0000i −0.0962567 + 0.0962567i
\(749\) 240.000 240.000i 0.320427 0.320427i
\(750\) 0 0
\(751\) 1080.00i 1.43808i 0.694967 + 0.719041i \(0.255419\pi\)
−0.694967 + 0.719041i \(0.744581\pi\)
\(752\) −168.000 + 168.000i −0.223404 + 0.223404i
\(753\) 0 0
\(754\) 624.000 624.000i 0.827586 0.827586i
\(755\) −636.000 −0.842384
\(756\) 0 0
\(757\) 990.000 1.30779 0.653897 0.756584i \(-0.273133\pi\)
0.653897 + 0.756584i \(0.273133\pi\)
\(758\) 452.000i 0.596306i
\(759\) 0 0
\(760\) 312.000 + 312.000i 0.410526 + 0.410526i
\(761\) 801.000 801.000i 1.05256 1.05256i 0.0540227 0.998540i \(-0.482796\pi\)
0.998540 0.0540227i \(-0.0172043\pi\)
\(762\) 0 0
\(763\) −76.0000 −0.0996068
\(764\) 504.000i 0.659686i
\(765\) −162.000 + 162.000i −0.211765 + 0.211765i
\(766\) 156.000i 0.203655i
\(767\) −702.000 702.000i −0.915254 0.915254i
\(768\) 0 0
\(769\) −329.000 329.000i −0.427828 0.427828i 0.460060 0.887888i \(-0.347828\pi\)
−0.887888 + 0.460060i \(0.847828\pi\)
\(770\) −144.000 −0.187013
\(771\) 0 0
\(772\) 514.000 + 514.000i 0.665803 + 0.665803i
\(773\) −867.000 867.000i −1.12160 1.12160i −0.991500 0.130104i \(-0.958469\pi\)
−0.130104 0.991500i \(-0.541531\pi\)
\(774\) 324.000 324.000i 0.418605 0.418605i
\(775\) −98.0000 + 98.0000i −0.126452 + 0.126452i
\(776\) 188.000 0.242268
\(777\) 0 0
\(778\) −150.000 + 150.000i −0.192802 + 0.192802i
\(779\) 468.000i 0.600770i
\(780\) 0 0
\(781\) 72.0000 0.0921895
\(782\) 144.000 + 144.000i 0.184143 + 0.184143i
\(783\) 0 0
\(784\) 164.000i 0.209184i
\(785\) 240.000 + 240.000i 0.305732 + 0.305732i
\(786\) 0 0
\(787\) −158.000 + 158.000i −0.200762 + 0.200762i −0.800327 0.599564i \(-0.795341\pi\)
0.599564 + 0.800327i \(0.295341\pi\)
\(788\) −246.000 + 246.000i −0.312183 + 0.312183i
\(789\) 0 0
\(790\) 648.000i 0.820253i
\(791\) −240.000 + 240.000i −0.303413 + 0.303413i
\(792\) 216.000i 0.272727i
\(793\) 234.000i 0.295082i
\(794\) −506.000 −0.637280
\(795\) 0 0
\(796\) −400.000 −0.502513
\(797\) 954.000i 1.19699i −0.801127 0.598494i \(-0.795766\pi\)
0.801127 0.598494i \(-0.204234\pi\)
\(798\) 0 0
\(799\) 252.000 + 252.000i 0.315394 + 0.315394i
\(800\) −28.0000 + 28.0000i −0.0350000 + 0.0350000i
\(801\) 81.0000 81.0000i 0.101124 0.101124i
\(802\) −498.000 −0.620948
\(803\) 204.000i 0.254047i
\(804\) 0 0
\(805\) 288.000i 0.357764i
\(806\) 364.000 0.451613
\(807\) 0 0
\(808\) −240.000 240.000i −0.297030 0.297030i
\(809\) 312.000 0.385661 0.192831 0.981232i \(-0.438233\pi\)
0.192831 + 0.981232i \(0.438233\pi\)
\(810\) 486.000i 0.600000i
\(811\) 566.000 + 566.000i 0.697904 + 0.697904i 0.963958 0.266054i \(-0.0857200\pi\)
−0.266054 + 0.963958i \(0.585720\pi\)
\(812\) −192.000 192.000i −0.236453 0.236453i
\(813\) 0 0
\(814\) 444.000 444.000i 0.545455 0.545455i
\(815\) −492.000 −0.603681
\(816\) 0 0
\(817\) −936.000 + 936.000i −1.14565 + 1.14565i
\(818\) 638.000i 0.779951i
\(819\) −234.000 234.000i −0.285714 0.285714i
\(820\) −108.000 −0.131707
\(821\) −339.000 339.000i −0.412911 0.412911i 0.469840 0.882751i \(-0.344311\pi\)
−0.882751 + 0.469840i \(0.844311\pi\)
\(822\) 0 0
\(823\) 1224.00i 1.48724i −0.668601 0.743621i \(-0.733107\pi\)
0.668601 0.743621i \(-0.266893\pi\)
\(824\) 288.000 + 288.000i 0.349515 + 0.349515i
\(825\) 0 0
\(826\) −216.000 + 216.000i −0.261501 + 0.261501i
\(827\) −678.000 + 678.000i −0.819831 + 0.819831i −0.986083 0.166253i \(-0.946833\pi\)
0.166253 + 0.986083i \(0.446833\pi\)
\(828\) −432.000 −0.521739
\(829\) 920.000i 1.10977i −0.831927 0.554885i \(-0.812762\pi\)
0.831927 0.554885i \(-0.187238\pi\)
\(830\) 468.000 468.000i 0.563855 0.563855i
\(831\) 0 0
\(832\) 104.000 0.125000
\(833\) −246.000 −0.295318
\(834\) 0 0
\(835\) 828.000 0.991617
\(836\) 624.000i 0.746411i
\(837\) 0 0
\(838\) −48.0000 48.0000i −0.0572792 0.0572792i
\(839\) −774.000 + 774.000i −0.922527 + 0.922527i −0.997207 0.0746807i \(-0.976206\pi\)
0.0746807 + 0.997207i \(0.476206\pi\)
\(840\) 0 0
\(841\) 1463.00 1.73960
\(842\) 22.0000i 0.0261283i
\(843\) 0 0
\(844\) 576.000i 0.682464i
\(845\) 507.000 + 507.000i 0.600000 + 0.600000i
\(846\) −756.000 −0.893617
\(847\) 98.0000 + 98.0000i 0.115702 + 0.115702i
\(848\) −120.000 −0.141509
\(849\) 0 0
\(850\) 42.0000 + 42.0000i 0.0494118 + 0.0494118i
\(851\) −888.000 888.000i −1.04348 1.04348i
\(852\) 0 0
\(853\) −443.000 + 443.000i −0.519343 + 0.519343i −0.917373 0.398029i \(-0.869694\pi\)
0.398029 + 0.917373i \(0.369694\pi\)
\(854\) −72.0000 −0.0843091
\(855\) 1404.00i 1.64211i
\(856\) −240.000 + 240.000i −0.280374 + 0.280374i
\(857\) 384.000i 0.448075i −0.974581 0.224037i \(-0.928076\pi\)
0.974581 0.224037i \(-0.0719238\pi\)
\(858\) 0 0
\(859\) 72.0000 0.0838184 0.0419092 0.999121i \(-0.486656\pi\)
0.0419092 + 0.999121i \(0.486656\pi\)
\(860\) 216.000 + 216.000i 0.251163 + 0.251163i
\(861\) 0 0
\(862\) 828.000i 0.960557i
\(863\) −702.000 702.000i −0.813441 0.813441i 0.171707 0.985148i \(-0.445072\pi\)
−0.985148 + 0.171707i \(0.945072\pi\)
\(864\) 0 0
\(865\) −72.0000 + 72.0000i −0.0832370 + 0.0832370i
\(866\) −16.0000 + 16.0000i −0.0184758 + 0.0184758i
\(867\) 0 0
\(868\) 112.000i 0.129032i
\(869\) −648.000 + 648.000i −0.745685 + 0.745685i
\(870\) 0 0
\(871\) 286.000 286.000i 0.328358 0.328358i
\(872\) 76.0000 0.0871560
\(873\) 423.000 + 423.000i 0.484536 + 0.484536i
\(874\) 1248.00 1.42792
\(875\) 384.000i 0.438857i
\(876\) 0 0
\(877\) 733.000 + 733.000i 0.835804 + 0.835804i 0.988304 0.152500i \(-0.0487323\pi\)
−0.152500 + 0.988304i \(0.548732\pi\)
\(878\) −360.000 + 360.000i −0.410023 + 0.410023i
\(879\) 0 0
\(880\) 144.000 0.163636
\(881\) 960.000i 1.08967i 0.838543 + 0.544835i \(0.183408\pi\)
−0.838543 + 0.544835i \(0.816592\pi\)
\(882\) 369.000 369.000i 0.418367 0.418367i
\(883\) 236.000i 0.267271i 0.991031 + 0.133635i \(0.0426651\pi\)
−0.991031 + 0.133635i \(0.957335\pi\)
\(884\) 156.000i 0.176471i
\(885\) 0 0
\(886\) −600.000 600.000i −0.677201 0.677201i
\(887\) 1380.00 1.55581 0.777903 0.628384i \(-0.216283\pi\)
0.777903 + 0.628384i \(0.216283\pi\)
\(888\) 0 0
\(889\) 112.000 + 112.000i 0.125984 + 0.125984i
\(890\) 54.0000 + 54.0000i 0.0606742 + 0.0606742i
\(891\) 486.000 486.000i 0.545455 0.545455i
\(892\) −76.0000 + 76.0000i −0.0852018 + 0.0852018i
\(893\) 2184.00 2.44569
\(894\) 0 0
\(895\) −900.000 + 900.000i −1.00559 + 1.00559i
\(896\) 32.0000i 0.0357143i
\(897\) 0 0
\(898\) −18.0000 −0.0200445
\(899\) 672.000 + 672.000i 0.747497 + 0.747497i
\(900\) −126.000 −0.140000
\(901\) 180.000i 0.199778i
\(902\) −108.000 108.000i −0.119734 0.119734i
\(903\) 0 0
\(904\) 240.000 240.000i 0.265487 0.265487i
\(905\) 270.000 270.000i 0.298343 0.298343i
\(906\) 0 0
\(907\) 1444.00i 1.59206i −0.605256 0.796031i \(-0.706929\pi\)
0.605256 0.796031i \(-0.293071\pi\)
\(908\) −276.000 + 276.000i −0.303965 + 0.303965i
\(909\) 1080.00i 1.18812i
\(910\) 156.000 156.000i 0.171429 0.171429i
\(911\) 612.000 0.671789 0.335895 0.941900i \(-0.390961\pi\)
0.335895 + 0.941900i \(0.390961\pi\)
\(912\) 0 0
\(913\) 936.000 1.02519
\(914\) 94.0000i 0.102845i
\(915\) 0 0
\(916\) 262.000 + 262.000i 0.286026 + 0.286026i
\(917\) 144.000 144.000i 0.157034 0.157034i
\(918\) 0 0
\(919\) −1548.00 −1.68444 −0.842220 0.539134i \(-0.818752\pi\)
−0.842220 + 0.539134i \(0.818752\pi\)
\(920\) 288.000i 0.313043i
\(921\) 0 0
\(922\) 342.000i 0.370933i
\(923\) −78.0000 + 78.0000i −0.0845070 + 0.0845070i
\(924\) 0 0
\(925\) −259.000 259.000i −0.280000 0.280000i
\(926\) 404.000 0.436285
\(927\) 1296.00i 1.39806i
\(928\) 192.000 + 192.000i 0.206897 + 0.206897i
\(929\) −969.000 969.000i −1.04306 1.04306i −0.999030 0.0440267i \(-0.985981\pi\)
−0.0440267 0.999030i \(-0.514019\pi\)
\(930\) 0 0
\(931\) −1066.00 + 1066.00i −1.14501 + 1.14501i
\(932\) −672.000 −0.721030
\(933\) 0 0
\(934\) −516.000 + 516.000i −0.552463 + 0.552463i
\(935\) 216.000i 0.231016i
\(936\) 234.000 + 234.000i 0.250000 + 0.250000i
\(937\) −450.000 −0.480256 −0.240128 0.970741i \(-0.577189\pi\)
−0.240128 + 0.970741i \(0.577189\pi\)
\(938\) −88.0000 88.0000i −0.0938166 0.0938166i
\(939\) 0 0
\(940\) 504.000i 0.536170i
\(941\) 411.000 + 411.000i 0.436769 + 0.436769i 0.890923 0.454154i \(-0.150058\pi\)
−0.454154 + 0.890923i \(0.650058\pi\)
\(942\) 0 0
\(943\) −216.000 + 216.000i −0.229056 + 0.229056i
\(944\) 216.000 216.000i 0.228814 0.228814i
\(945\) 0 0
\(946\) 432.000i 0.456660i
\(947\) 582.000 582.000i 0.614572 0.614572i −0.329562 0.944134i \(-0.606901\pi\)
0.944134 + 0.329562i \(0.106901\pi\)
\(948\) 0 0
\(949\) 221.000 + 221.000i 0.232877 + 0.232877i
\(950\) 364.000 0.383158
\(951\) 0 0
\(952\) −48.0000 −0.0504202
\(953\) 1344.00i 1.41028i −0.709066 0.705142i \(-0.750883\pi\)
0.709066 0.705142i \(-0.249117\pi\)
\(954\) −270.000 270.000i −0.283019 0.283019i
\(955\) −756.000 756.000i −0.791623 0.791623i
\(956\) 228.000 228.000i 0.238494 0.238494i
\(957\) 0 0
\(958\) −468.000 −0.488518
\(959\) 252.000i 0.262774i
\(960\) 0 0
\(961\) 569.000i 0.592092i
\(962\) 962.000i 1.00000i
\(963\) −1080.00 −1.12150
\(964\) 302.000 + 302.000i 0.313278 + 0.313278i
\(965\) −1542.00 −1.59793
\(966\) 0 0
\(967\) −562.000 562.000i −0.581179 0.581179i 0.354048 0.935227i \(-0.384805\pi\)
−0.935227 + 0.354048i \(0.884805\pi\)
\(968\) −98.0000 98.0000i −0.101240 0.101240i
\(969\) 0 0
\(970\) −282.000 + 282.000i −0.290722 + 0.290722i
\(971\) −1248.00 −1.28527 −0.642636 0.766171i \(-0.722159\pi\)
−0.642636 + 0.766171i \(0.722159\pi\)
\(972\) 0 0
\(973\) 304.000 304.000i 0.312436 0.312436i
\(974\) 596.000i 0.611910i
\(975\) 0 0
\(976\) 72.0000 0.0737705
\(977\) 33.0000 + 33.0000i 0.0337769 + 0.0337769i 0.723794 0.690017i \(-0.242397\pi\)
−0.690017 + 0.723794i \(0.742397\pi\)
\(978\) 0 0
\(979\) 108.000i 0.110317i
\(980\) 246.000 + 246.000i 0.251020 + 0.251020i
\(981\) 171.000 + 171.000i 0.174312 + 0.174312i
\(982\) −420.000 + 420.000i −0.427699 + 0.427699i
\(983\) 702.000 702.000i 0.714140 0.714140i −0.253258 0.967399i \(-0.581502\pi\)
0.967399 + 0.253258i \(0.0815023\pi\)
\(984\) 0 0
\(985\) 738.000i 0.749239i
\(986\) 288.000 288.000i 0.292089 0.292089i
\(987\) 0 0
\(988\) −676.000 676.000i −0.684211 0.684211i
\(989\) 864.000 0.873610
\(990\) 324.000 + 324.000i 0.327273 + 0.327273i
\(991\) −268.000 −0.270434 −0.135217 0.990816i \(-0.543173\pi\)
−0.135217 + 0.990816i \(0.543173\pi\)
\(992\) 112.000i 0.112903i
\(993\) 0 0
\(994\) 24.0000 + 24.0000i 0.0241449 + 0.0241449i
\(995\) 600.000 600.000i 0.603015 0.603015i
\(996\) 0 0
\(997\) −1310.00 −1.31394 −0.656971 0.753916i \(-0.728163\pi\)
−0.656971 + 0.753916i \(0.728163\pi\)
\(998\) 692.000i 0.693387i
\(999\) 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 26.3.d.a.21.1 yes 2
3.2 odd 2 234.3.i.a.73.1 2
4.3 odd 2 208.3.t.b.177.1 2
5.2 odd 4 650.3.f.b.99.1 2
5.3 odd 4 650.3.f.e.99.1 2
5.4 even 2 650.3.k.b.151.1 2
13.2 odd 12 338.3.f.b.19.1 4
13.3 even 3 338.3.f.b.319.1 4
13.4 even 6 338.3.f.g.89.1 4
13.5 odd 4 inner 26.3.d.a.5.1 2
13.6 odd 12 338.3.f.b.249.1 4
13.7 odd 12 338.3.f.g.249.1 4
13.8 odd 4 338.3.d.a.239.1 2
13.9 even 3 338.3.f.b.89.1 4
13.10 even 6 338.3.f.g.319.1 4
13.11 odd 12 338.3.f.g.19.1 4
13.12 even 2 338.3.d.a.99.1 2
39.5 even 4 234.3.i.a.109.1 2
52.31 even 4 208.3.t.b.161.1 2
65.18 even 4 650.3.f.b.499.1 2
65.44 odd 4 650.3.k.b.551.1 2
65.57 even 4 650.3.f.e.499.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
26.3.d.a.5.1 2 13.5 odd 4 inner
26.3.d.a.21.1 yes 2 1.1 even 1 trivial
208.3.t.b.161.1 2 52.31 even 4
208.3.t.b.177.1 2 4.3 odd 2
234.3.i.a.73.1 2 3.2 odd 2
234.3.i.a.109.1 2 39.5 even 4
338.3.d.a.99.1 2 13.12 even 2
338.3.d.a.239.1 2 13.8 odd 4
338.3.f.b.19.1 4 13.2 odd 12
338.3.f.b.89.1 4 13.9 even 3
338.3.f.b.249.1 4 13.6 odd 12
338.3.f.b.319.1 4 13.3 even 3
338.3.f.g.19.1 4 13.11 odd 12
338.3.f.g.89.1 4 13.4 even 6
338.3.f.g.249.1 4 13.7 odd 12
338.3.f.g.319.1 4 13.10 even 6
650.3.f.b.99.1 2 5.2 odd 4
650.3.f.b.499.1 2 65.18 even 4
650.3.f.e.99.1 2 5.3 odd 4
650.3.f.e.499.1 2 65.57 even 4
650.3.k.b.151.1 2 5.4 even 2
650.3.k.b.551.1 2 65.44 odd 4