Properties

Label 900.3.y.a.89.19
Level $900$
Weight $3$
Character 900.89
Analytic conductor $24.523$
Analytic rank $0$
Dimension $80$
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] = [900,3,Mod(89,900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(900, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("900.89");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 900.y (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(24.5232237924\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 89.19
Character \(\chi\) \(=\) 900.89
Dual form 900.3.y.a.809.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.98426 + 0.396382i) q^{5} +2.05133i q^{7} +O(q^{10})\) \(q+(4.98426 + 0.396382i) q^{5} +2.05133i q^{7} +(3.20226 + 4.40754i) q^{11} +(-8.49111 + 11.6870i) q^{13} +(3.07013 + 9.44890i) q^{17} +(-0.491549 - 1.51283i) q^{19} +(-24.6338 + 17.8975i) q^{23} +(24.6858 + 3.95134i) q^{25} +(-14.1695 - 4.60394i) q^{29} +(7.49004 + 23.0520i) q^{31} +(-0.813109 + 10.2244i) q^{35} +(-10.4512 + 14.3848i) q^{37} +(-0.622089 + 0.856233i) q^{41} -39.1512i q^{43} +(-5.02223 + 15.4568i) q^{47} +44.7921 q^{49} +(-10.5064 + 32.3353i) q^{53} +(14.2139 + 23.2377i) q^{55} +(-18.6182 + 25.6258i) q^{59} +(43.0338 - 31.2659i) q^{61} +(-46.9544 + 54.8854i) q^{65} +(42.1147 - 13.6839i) q^{67} +(-119.863 - 38.9457i) q^{71} +(39.3118 + 54.1080i) q^{73} +(-9.04131 + 6.56889i) q^{77} +(-4.27671 + 13.1624i) q^{79} +(21.0918 + 64.9140i) q^{83} +(11.5570 + 48.3128i) q^{85} +(20.5399 + 28.2707i) q^{89} +(-23.9739 - 17.4181i) q^{91} +(-1.85035 - 7.73520i) q^{95} +(76.8092 + 24.9568i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q+O(q^{10}) \) Copy content Toggle raw display \( 80 q + 60 q^{19} + 56 q^{25} - 120 q^{31} + 20 q^{37} - 680 q^{49} - 56 q^{55} - 80 q^{61} - 280 q^{67} - 360 q^{73} + 40 q^{79} + 192 q^{85} + 140 q^{91} - 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(451\) \(577\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\)

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 0
\(3\) 0 0
\(4\) 0 0
\(5\) 4.98426 + 0.396382i 0.996853 + 0.0792764i
\(6\) 0 0
\(7\) 2.05133i 0.293047i 0.989207 + 0.146523i \(0.0468084\pi\)
−0.989207 + 0.146523i \(0.953192\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.20226 + 4.40754i 0.291115 + 0.400685i 0.929376 0.369135i \(-0.120346\pi\)
−0.638261 + 0.769820i \(0.720346\pi\)
\(12\) 0 0
\(13\) −8.49111 + 11.6870i −0.653162 + 0.899001i −0.999231 0.0392084i \(-0.987516\pi\)
0.346069 + 0.938209i \(0.387516\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.07013 + 9.44890i 0.180596 + 0.555818i 0.999845 0.0176208i \(-0.00560915\pi\)
−0.819249 + 0.573439i \(0.805609\pi\)
\(18\) 0 0
\(19\) −0.491549 1.51283i −0.0258710 0.0796228i 0.937287 0.348558i \(-0.113328\pi\)
−0.963158 + 0.268935i \(0.913328\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −24.6338 + 17.8975i −1.07103 + 0.778152i −0.976098 0.217331i \(-0.930265\pi\)
−0.0949365 + 0.995483i \(0.530265\pi\)
\(24\) 0 0
\(25\) 24.6858 + 3.95134i 0.987431 + 0.158054i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −14.1695 4.60394i −0.488603 0.158757i 0.0543465 0.998522i \(-0.482692\pi\)
−0.542949 + 0.839765i \(0.682692\pi\)
\(30\) 0 0
\(31\) 7.49004 + 23.0520i 0.241614 + 0.743612i 0.996175 + 0.0873818i \(0.0278500\pi\)
−0.754561 + 0.656230i \(0.772150\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.813109 + 10.2244i −0.0232317 + 0.292125i
\(36\) 0 0
\(37\) −10.4512 + 14.3848i −0.282464 + 0.388778i −0.926548 0.376177i \(-0.877239\pi\)
0.644084 + 0.764955i \(0.277239\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.622089 + 0.856233i −0.0151729 + 0.0208837i −0.816536 0.577294i \(-0.804108\pi\)
0.801363 + 0.598178i \(0.204108\pi\)
\(42\) 0 0
\(43\) 39.1512i 0.910494i −0.890365 0.455247i \(-0.849551\pi\)
0.890365 0.455247i \(-0.150449\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.02223 + 15.4568i −0.106856 + 0.328869i −0.990162 0.139929i \(-0.955313\pi\)
0.883306 + 0.468798i \(0.155313\pi\)
\(48\) 0 0
\(49\) 44.7921 0.914124
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −10.5064 + 32.3353i −0.198233 + 0.610099i 0.801690 + 0.597740i \(0.203934\pi\)
−0.999924 + 0.0123597i \(0.996066\pi\)
\(54\) 0 0
\(55\) 14.2139 + 23.2377i 0.258434 + 0.422503i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −18.6182 + 25.6258i −0.315563 + 0.434336i −0.937106 0.349044i \(-0.886506\pi\)
0.621543 + 0.783380i \(0.286506\pi\)
\(60\) 0 0
\(61\) 43.0338 31.2659i 0.705473 0.512556i −0.176237 0.984348i \(-0.556393\pi\)
0.881710 + 0.471792i \(0.156393\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −46.9544 + 54.8854i −0.722376 + 0.844391i
\(66\) 0 0
\(67\) 42.1147 13.6839i 0.628578 0.204237i 0.0226328 0.999744i \(-0.492795\pi\)
0.605945 + 0.795507i \(0.292795\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −119.863 38.9457i −1.68821 0.548531i −0.701730 0.712443i \(-0.747589\pi\)
−0.986475 + 0.163912i \(0.947589\pi\)
\(72\) 0 0
\(73\) 39.3118 + 54.1080i 0.538518 + 0.741206i 0.988399 0.151883i \(-0.0485335\pi\)
−0.449881 + 0.893089i \(0.648534\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.04131 + 6.56889i −0.117420 + 0.0853103i
\(78\) 0 0
\(79\) −4.27671 + 13.1624i −0.0541356 + 0.166612i −0.974469 0.224523i \(-0.927918\pi\)
0.920333 + 0.391135i \(0.127918\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 21.0918 + 64.9140i 0.254119 + 0.782096i 0.994002 + 0.109361i \(0.0348806\pi\)
−0.739883 + 0.672735i \(0.765119\pi\)
\(84\) 0 0
\(85\) 11.5570 + 48.3128i 0.135965 + 0.568385i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 20.5399 + 28.2707i 0.230785 + 0.317649i 0.908666 0.417523i \(-0.137102\pi\)
−0.677881 + 0.735171i \(0.737102\pi\)
\(90\) 0 0
\(91\) −23.9739 17.4181i −0.263449 0.191407i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.85035 7.73520i −0.0194774 0.0814232i
\(96\) 0 0
\(97\) 76.8092 + 24.9568i 0.791847 + 0.257287i 0.676890 0.736084i \(-0.263327\pi\)
0.114957 + 0.993371i \(0.463327\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 179.542i 1.77765i 0.458249 + 0.888824i \(0.348477\pi\)
−0.458249 + 0.888824i \(0.651523\pi\)
\(102\) 0 0
\(103\) −65.6376 21.3269i −0.637258 0.207058i −0.0274704 0.999623i \(-0.508745\pi\)
−0.609787 + 0.792565i \(0.708745\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −47.0450 −0.439673 −0.219836 0.975537i \(-0.570552\pi\)
−0.219836 + 0.975537i \(0.570552\pi\)
\(108\) 0 0
\(109\) 95.5599 + 69.4283i 0.876696 + 0.636957i 0.932375 0.361492i \(-0.117732\pi\)
−0.0556793 + 0.998449i \(0.517732\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.47884 1.07444i −0.0130871 0.00950831i 0.581222 0.813745i \(-0.302575\pi\)
−0.594310 + 0.804236i \(0.702575\pi\)
\(114\) 0 0
\(115\) −129.876 + 79.4414i −1.12935 + 0.690795i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −19.3828 + 6.29785i −0.162881 + 0.0529231i
\(120\) 0 0
\(121\) 28.2192 86.8496i 0.233216 0.717766i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 121.474 + 29.4795i 0.971793 + 0.235836i
\(126\) 0 0
\(127\) 82.7252 + 113.861i 0.651379 + 0.896546i 0.999158 0.0410302i \(-0.0130640\pi\)
−0.347779 + 0.937577i \(0.613064\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −5.33914 + 1.73479i −0.0407568 + 0.0132427i −0.329324 0.944217i \(-0.606821\pi\)
0.288568 + 0.957460i \(0.406821\pi\)
\(132\) 0 0
\(133\) 3.10332 1.00833i 0.0233332 0.00758142i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 73.8739 + 53.6725i 0.539225 + 0.391770i 0.823797 0.566885i \(-0.191851\pi\)
−0.284572 + 0.958655i \(0.591851\pi\)
\(138\) 0 0
\(139\) 15.6006 11.3345i 0.112235 0.0815433i −0.530252 0.847840i \(-0.677903\pi\)
0.642487 + 0.766297i \(0.277903\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −78.7017 −0.550362
\(144\) 0 0
\(145\) −68.7995 28.5638i −0.474479 0.196992i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 113.967i 0.764882i −0.923980 0.382441i \(-0.875083\pi\)
0.923980 0.382441i \(-0.124917\pi\)
\(150\) 0 0
\(151\) 59.5217 0.394183 0.197092 0.980385i \(-0.436850\pi\)
0.197092 + 0.980385i \(0.436850\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 28.1949 + 117.866i 0.181903 + 0.760426i
\(156\) 0 0
\(157\) 108.076i 0.688379i 0.938900 + 0.344190i \(0.111846\pi\)
−0.938900 + 0.344190i \(0.888154\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −36.7136 50.5320i −0.228035 0.313863i
\(162\) 0 0
\(163\) −103.594 + 142.585i −0.635548 + 0.874757i −0.998368 0.0571021i \(-0.981814\pi\)
0.362820 + 0.931859i \(0.381814\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −35.9581 110.668i −0.215318 0.662680i −0.999131 0.0416831i \(-0.986728\pi\)
0.783813 0.620997i \(-0.213272\pi\)
\(168\) 0 0
\(169\) −12.2634 37.7428i −0.0725644 0.223330i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −28.3258 + 20.5799i −0.163733 + 0.118959i −0.666635 0.745385i \(-0.732266\pi\)
0.502902 + 0.864344i \(0.332266\pi\)
\(174\) 0 0
\(175\) −8.10550 + 50.6386i −0.0463172 + 0.289363i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −81.2722 26.4069i −0.454035 0.147525i 0.0730670 0.997327i \(-0.476721\pi\)
−0.527102 + 0.849802i \(0.676721\pi\)
\(180\) 0 0
\(181\) −68.8759 211.978i −0.380530 1.17115i −0.939671 0.342079i \(-0.888869\pi\)
0.559141 0.829072i \(-0.311131\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −57.7932 + 67.5549i −0.312396 + 0.365162i
\(186\) 0 0
\(187\) −31.8150 + 43.7896i −0.170134 + 0.234169i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 48.7407 67.0859i 0.255187 0.351235i −0.662132 0.749387i \(-0.730348\pi\)
0.917319 + 0.398152i \(0.130348\pi\)
\(192\) 0 0
\(193\) 212.949i 1.10336i −0.834056 0.551680i \(-0.813987\pi\)
0.834056 0.551680i \(-0.186013\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 22.7002 69.8641i 0.115230 0.354640i −0.876765 0.480919i \(-0.840303\pi\)
0.991995 + 0.126278i \(0.0403033\pi\)
\(198\) 0 0
\(199\) 288.811 1.45131 0.725655 0.688059i \(-0.241537\pi\)
0.725655 + 0.688059i \(0.241537\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 9.44420 29.0663i 0.0465231 0.143184i
\(204\) 0 0
\(205\) −3.44005 + 4.02110i −0.0167807 + 0.0196151i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.09380 7.01102i 0.0243723 0.0335455i
\(210\) 0 0
\(211\) 34.2306 24.8700i 0.162230 0.117867i −0.503708 0.863874i \(-0.668031\pi\)
0.665939 + 0.746007i \(0.268031\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 15.5188 195.140i 0.0721807 0.907628i
\(216\) 0 0
\(217\) −47.2872 + 15.3645i −0.217913 + 0.0708043i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −136.498 44.3510i −0.617639 0.200683i
\(222\) 0 0
\(223\) −225.021 309.714i −1.00906 1.38885i −0.919597 0.392864i \(-0.871484\pi\)
−0.0894651 0.995990i \(-0.528516\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 318.423 231.348i 1.40274 1.01915i 0.408414 0.912797i \(-0.366082\pi\)
0.994328 0.106355i \(-0.0339181\pi\)
\(228\) 0 0
\(229\) 123.150 379.017i 0.537773 1.65509i −0.199807 0.979835i \(-0.564032\pi\)
0.737580 0.675260i \(-0.235968\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 110.999 + 341.620i 0.476391 + 1.46618i 0.844072 + 0.536230i \(0.180152\pi\)
−0.367681 + 0.929952i \(0.619848\pi\)
\(234\) 0 0
\(235\) −31.1590 + 75.0503i −0.132591 + 0.319363i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −207.960 286.233i −0.870128 1.19763i −0.979059 0.203579i \(-0.934743\pi\)
0.108931 0.994049i \(-0.465257\pi\)
\(240\) 0 0
\(241\) −222.025 161.311i −0.921267 0.669340i 0.0225722 0.999745i \(-0.492814\pi\)
−0.943839 + 0.330406i \(0.892814\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 223.255 + 17.7548i 0.911246 + 0.0724684i
\(246\) 0 0
\(247\) 21.8543 + 7.10089i 0.0884789 + 0.0287486i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 219.804i 0.875712i −0.899045 0.437856i \(-0.855738\pi\)
0.899045 0.437856i \(-0.144262\pi\)
\(252\) 0 0
\(253\) −157.768 51.2619i −0.623588 0.202616i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 374.482 1.45713 0.728564 0.684978i \(-0.240188\pi\)
0.728564 + 0.684978i \(0.240188\pi\)
\(258\) 0 0
\(259\) −29.5079 21.4388i −0.113930 0.0827751i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −171.870 124.871i −0.653497 0.474793i 0.210964 0.977494i \(-0.432340\pi\)
−0.864461 + 0.502700i \(0.832340\pi\)
\(264\) 0 0
\(265\) −65.1836 + 157.003i −0.245976 + 0.592464i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 258.977 84.1467i 0.962740 0.312813i 0.214858 0.976645i \(-0.431071\pi\)
0.747882 + 0.663832i \(0.231071\pi\)
\(270\) 0 0
\(271\) −37.1986 + 114.485i −0.137264 + 0.422455i −0.995935 0.0900714i \(-0.971290\pi\)
0.858671 + 0.512527i \(0.171290\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 61.6346 + 121.457i 0.224126 + 0.441661i
\(276\) 0 0
\(277\) 88.5679 + 121.903i 0.319740 + 0.440084i 0.938388 0.345584i \(-0.112319\pi\)
−0.618648 + 0.785668i \(0.712319\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −150.839 + 49.0106i −0.536794 + 0.174415i −0.564853 0.825191i \(-0.691067\pi\)
0.0280595 + 0.999606i \(0.491067\pi\)
\(282\) 0 0
\(283\) −413.859 + 134.471i −1.46240 + 0.475162i −0.928802 0.370578i \(-0.879160\pi\)
−0.533596 + 0.845739i \(0.679160\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.75641 1.27611i −0.00611991 0.00444637i
\(288\) 0 0
\(289\) 153.950 111.851i 0.532699 0.387028i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 48.8663 0.166779 0.0833896 0.996517i \(-0.473425\pi\)
0.0833896 + 0.996517i \(0.473425\pi\)
\(294\) 0 0
\(295\) −102.956 + 120.346i −0.349003 + 0.407952i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 439.865i 1.47112i
\(300\) 0 0
\(301\) 80.3120 0.266817
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 226.885 138.780i 0.743886 0.455015i
\(306\) 0 0
\(307\) 362.825i 1.18184i 0.806731 + 0.590920i \(0.201235\pi\)
−0.806731 + 0.590920i \(0.798765\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −52.7404 72.5909i −0.169583 0.233411i 0.715763 0.698343i \(-0.246079\pi\)
−0.885347 + 0.464932i \(0.846079\pi\)
\(312\) 0 0
\(313\) 32.5543 44.8072i 0.104007 0.143154i −0.753841 0.657057i \(-0.771801\pi\)
0.857848 + 0.513903i \(0.171801\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 9.19358 + 28.2949i 0.0290018 + 0.0892585i 0.964510 0.264047i \(-0.0850575\pi\)
−0.935508 + 0.353306i \(0.885058\pi\)
\(318\) 0 0
\(319\) −25.0824 77.1956i −0.0786281 0.241992i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 12.7855 9.28920i 0.0395836 0.0287591i
\(324\) 0 0
\(325\) −255.789 + 254.951i −0.787043 + 0.784466i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −31.7071 10.3023i −0.0963741 0.0313138i
\(330\) 0 0
\(331\) −170.982 526.227i −0.516561 1.58981i −0.780424 0.625251i \(-0.784997\pi\)
0.263863 0.964560i \(-0.415003\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 215.335 51.5107i 0.642791 0.153763i
\(336\) 0 0
\(337\) 21.4423 29.5128i 0.0636269 0.0875750i −0.776018 0.630711i \(-0.782763\pi\)
0.839645 + 0.543136i \(0.182763\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −77.6174 + 106.831i −0.227617 + 0.313288i
\(342\) 0 0
\(343\) 192.398i 0.560928i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 94.5031 290.851i 0.272343 0.838186i −0.717567 0.696490i \(-0.754744\pi\)
0.989910 0.141697i \(-0.0452558\pi\)
\(348\) 0 0
\(349\) −112.309 −0.321803 −0.160901 0.986970i \(-0.551440\pi\)
−0.160901 + 0.986970i \(0.551440\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −35.4236 + 109.023i −0.100350 + 0.308846i −0.988611 0.150493i \(-0.951914\pi\)
0.888261 + 0.459339i \(0.151914\pi\)
\(354\) 0 0
\(355\) −581.989 241.627i −1.63941 0.680639i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 202.980 279.378i 0.565403 0.778211i −0.426597 0.904442i \(-0.640288\pi\)
0.992001 + 0.126231i \(0.0402879\pi\)
\(360\) 0 0
\(361\) 290.008 210.703i 0.803347 0.583665i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 174.493 + 285.271i 0.478063 + 0.781565i
\(366\) 0 0
\(367\) 81.5574 26.4996i 0.222227 0.0722060i −0.195787 0.980646i \(-0.562726\pi\)
0.418014 + 0.908440i \(0.362726\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −66.3302 21.5520i −0.178788 0.0580916i
\(372\) 0 0
\(373\) −285.062 392.355i −0.764242 1.05189i −0.996849 0.0793182i \(-0.974726\pi\)
0.232607 0.972571i \(-0.425274\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 174.121 126.506i 0.461859 0.335560i
\(378\) 0 0
\(379\) −115.620 + 355.843i −0.305067 + 0.938899i 0.674586 + 0.738197i \(0.264322\pi\)
−0.979652 + 0.200702i \(0.935678\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 71.4740 + 219.974i 0.186616 + 0.574346i 0.999972 0.00742012i \(-0.00236192\pi\)
−0.813356 + 0.581766i \(0.802362\pi\)
\(384\) 0 0
\(385\) −47.6680 + 29.1573i −0.123813 + 0.0757332i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −61.9335 85.2441i −0.159212 0.219137i 0.721957 0.691938i \(-0.243243\pi\)
−0.881169 + 0.472801i \(0.843243\pi\)
\(390\) 0 0
\(391\) −244.741 177.815i −0.625935 0.454769i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −26.5336 + 63.9095i −0.0671736 + 0.161796i
\(396\) 0 0
\(397\) 534.778 + 173.760i 1.34705 + 0.437683i 0.891698 0.452630i \(-0.149514\pi\)
0.455350 + 0.890313i \(0.349514\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 286.946i 0.715575i −0.933803 0.357788i \(-0.883531\pi\)
0.933803 0.357788i \(-0.116469\pi\)
\(402\) 0 0
\(403\) −333.007 108.201i −0.826321 0.268488i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −96.8689 −0.238007
\(408\) 0 0
\(409\) 404.745 + 294.065i 0.989597 + 0.718984i 0.959833 0.280573i \(-0.0905244\pi\)
0.0297640 + 0.999557i \(0.490524\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −52.5669 38.1921i −0.127281 0.0924749i
\(414\) 0 0
\(415\) 79.3965 + 331.909i 0.191317 + 0.799781i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 287.204 93.3183i 0.685451 0.222717i 0.0544709 0.998515i \(-0.482653\pi\)
0.630980 + 0.775799i \(0.282653\pi\)
\(420\) 0 0
\(421\) 244.958 753.903i 0.581848 1.79074i −0.0297280 0.999558i \(-0.509464\pi\)
0.611576 0.791186i \(-0.290536\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 38.4527 + 245.385i 0.0904770 + 0.577375i
\(426\) 0 0
\(427\) 64.1366 + 88.2765i 0.150203 + 0.206737i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −509.183 + 165.444i −1.18140 + 0.383860i −0.832887 0.553444i \(-0.813313\pi\)
−0.348513 + 0.937304i \(0.613313\pi\)
\(432\) 0 0
\(433\) 36.2033 11.7632i 0.0836104 0.0271667i −0.266913 0.963721i \(-0.586004\pi\)
0.350523 + 0.936554i \(0.386004\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 39.1847 + 28.4693i 0.0896674 + 0.0651472i
\(438\) 0 0
\(439\) 678.560 493.002i 1.54569 1.12301i 0.599059 0.800705i \(-0.295542\pi\)
0.946635 0.322307i \(-0.104458\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −124.912 −0.281968 −0.140984 0.990012i \(-0.545027\pi\)
−0.140984 + 0.990012i \(0.545027\pi\)
\(444\) 0 0
\(445\) 91.1702 + 149.050i 0.204877 + 0.334945i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 90.2818i 0.201073i 0.994933 + 0.100537i \(0.0320559\pi\)
−0.994933 + 0.100537i \(0.967944\pi\)
\(450\) 0 0
\(451\) −5.76597 −0.0127849
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −112.588 96.3190i −0.247446 0.211690i
\(456\) 0 0
\(457\) 46.8085i 0.102426i 0.998688 + 0.0512128i \(0.0163087\pi\)
−0.998688 + 0.0512128i \(0.983691\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −90.1004 124.013i −0.195446 0.269008i 0.700035 0.714109i \(-0.253168\pi\)
−0.895480 + 0.445101i \(0.853168\pi\)
\(462\) 0 0
\(463\) −172.110 + 236.890i −0.371729 + 0.511641i −0.953370 0.301805i \(-0.902411\pi\)
0.581641 + 0.813446i \(0.302411\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −125.913 387.520i −0.269621 0.829807i −0.990593 0.136843i \(-0.956304\pi\)
0.720972 0.692964i \(-0.243696\pi\)
\(468\) 0 0
\(469\) 28.0702 + 86.3911i 0.0598511 + 0.184203i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 172.561 125.373i 0.364821 0.265058i
\(474\) 0 0
\(475\) −6.15655 39.2877i −0.0129611 0.0827110i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −605.960 196.888i −1.26505 0.411040i −0.401760 0.915745i \(-0.631601\pi\)
−0.863292 + 0.504704i \(0.831601\pi\)
\(480\) 0 0
\(481\) −79.3732 244.286i −0.165017 0.507870i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 372.945 + 154.837i 0.768958 + 0.319252i
\(486\) 0 0
\(487\) −58.3510 + 80.3132i −0.119817 + 0.164914i −0.864712 0.502267i \(-0.832499\pi\)
0.744895 + 0.667181i \(0.232499\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −242.967 + 334.415i −0.494840 + 0.681089i −0.981272 0.192630i \(-0.938298\pi\)
0.486431 + 0.873719i \(0.338298\pi\)
\(492\) 0 0
\(493\) 148.021i 0.300245i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 79.8904 245.877i 0.160745 0.494723i
\(498\) 0 0
\(499\) 438.011 0.877778 0.438889 0.898541i \(-0.355372\pi\)
0.438889 + 0.898541i \(0.355372\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −298.017 + 917.202i −0.592479 + 1.82346i −0.0255832 + 0.999673i \(0.508144\pi\)
−0.566896 + 0.823790i \(0.691856\pi\)
\(504\) 0 0
\(505\) −71.1674 + 894.887i −0.140926 + 1.77205i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −511.890 + 704.557i −1.00568 + 1.38420i −0.0839033 + 0.996474i \(0.526739\pi\)
−0.921775 + 0.387724i \(0.873261\pi\)
\(510\) 0 0
\(511\) −110.993 + 80.6414i −0.217208 + 0.157811i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −318.701 132.317i −0.618837 0.256925i
\(516\) 0 0
\(517\) −84.2092 + 27.3612i −0.162880 + 0.0529231i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 20.2982 + 6.59529i 0.0389601 + 0.0126589i 0.328432 0.944528i \(-0.393480\pi\)
−0.289472 + 0.957186i \(0.593480\pi\)
\(522\) 0 0
\(523\) −260.381 358.384i −0.497860 0.685246i 0.483953 0.875094i \(-0.339200\pi\)
−0.981813 + 0.189848i \(0.939200\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −194.820 + 141.545i −0.369678 + 0.268587i
\(528\) 0 0
\(529\) 123.033 378.657i 0.232577 0.715799i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.72457 14.5407i −0.00886411 0.0272809i
\(534\) 0 0
\(535\) −234.485 18.6478i −0.438289 0.0348557i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 143.436 + 197.423i 0.266115 + 0.366276i
\(540\) 0 0
\(541\) 473.315 + 343.884i 0.874890 + 0.635645i 0.931895 0.362729i \(-0.118155\pi\)
−0.0570047 + 0.998374i \(0.518155\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 448.775 + 383.927i 0.823441 + 0.704454i
\(546\) 0 0
\(547\) 261.467 + 84.9558i 0.478002 + 0.155312i 0.538101 0.842880i \(-0.319142\pi\)
−0.0600995 + 0.998192i \(0.519142\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 23.6991i 0.0430111i
\(552\) 0 0
\(553\) −27.0003 8.77293i −0.0488252 0.0158643i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 429.452 0.771009 0.385504 0.922706i \(-0.374028\pi\)
0.385504 + 0.922706i \(0.374028\pi\)
\(558\) 0 0
\(559\) 457.561 + 332.437i 0.818534 + 0.594700i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 316.374 + 229.859i 0.561943 + 0.408276i 0.832170 0.554521i \(-0.187099\pi\)
−0.270226 + 0.962797i \(0.587099\pi\)
\(564\) 0 0
\(565\) −6.94503 5.94147i −0.0122921 0.0105159i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 96.4412 31.3357i 0.169493 0.0550715i −0.223041 0.974809i \(-0.571599\pi\)
0.392534 + 0.919738i \(0.371599\pi\)
\(570\) 0 0
\(571\) 222.246 684.003i 0.389223 1.19790i −0.544148 0.838990i \(-0.683147\pi\)
0.933370 0.358915i \(-0.116853\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −678.823 + 344.477i −1.18056 + 0.599090i
\(576\) 0 0
\(577\) 457.281 + 629.394i 0.792515 + 1.09080i 0.993790 + 0.111269i \(0.0354914\pi\)
−0.201275 + 0.979535i \(0.564509\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −133.160 + 43.2663i −0.229191 + 0.0744686i
\(582\) 0 0
\(583\) −176.163 + 57.2388i −0.302166 + 0.0981798i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 232.300 + 168.776i 0.395741 + 0.287523i 0.767804 0.640685i \(-0.221349\pi\)
−0.372063 + 0.928207i \(0.621349\pi\)
\(588\) 0 0
\(589\) 31.1921 22.6624i 0.0529577 0.0384760i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −742.051 −1.25135 −0.625675 0.780084i \(-0.715177\pi\)
−0.625675 + 0.780084i \(0.715177\pi\)
\(594\) 0 0
\(595\) −99.1053 + 23.7072i −0.166564 + 0.0398440i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 540.081i 0.901638i −0.892616 0.450819i \(-0.851132\pi\)
0.892616 0.450819i \(-0.148868\pi\)
\(600\) 0 0
\(601\) −441.008 −0.733790 −0.366895 0.930262i \(-0.619579\pi\)
−0.366895 + 0.930262i \(0.619579\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 175.077 421.696i 0.289384 0.697018i
\(606\) 0 0
\(607\) 566.768i 0.933720i 0.884331 + 0.466860i \(0.154615\pi\)
−0.884331 + 0.466860i \(0.845385\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −138.000 189.941i −0.225859 0.310869i
\(612\) 0 0
\(613\) −192.132 + 264.447i −0.313429 + 0.431398i −0.936447 0.350809i \(-0.885906\pi\)
0.623018 + 0.782208i \(0.285906\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 229.928 + 707.647i 0.372655 + 1.14692i 0.945047 + 0.326935i \(0.106016\pi\)
−0.572391 + 0.819980i \(0.693984\pi\)
\(618\) 0 0
\(619\) −11.3534 34.9420i −0.0183414 0.0564492i 0.941467 0.337105i \(-0.109448\pi\)
−0.959808 + 0.280656i \(0.909448\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −57.9925 + 42.1340i −0.0930859 + 0.0676309i
\(624\) 0 0
\(625\) 593.774 + 195.084i 0.950038 + 0.312134i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −168.007 54.5887i −0.267102 0.0867866i
\(630\) 0 0
\(631\) 363.832 + 1119.76i 0.576596 + 1.77458i 0.630679 + 0.776044i \(0.282776\pi\)
−0.0540832 + 0.998536i \(0.517224\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 367.191 + 600.306i 0.578254 + 0.945364i
\(636\) 0 0
\(637\) −380.334 + 523.485i −0.597071 + 0.821798i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −461.804 + 635.619i −0.720443 + 0.991605i 0.279066 + 0.960272i \(0.409975\pi\)
−0.999509 + 0.0313333i \(0.990025\pi\)
\(642\) 0 0
\(643\) 235.295i 0.365933i 0.983119 + 0.182967i \(0.0585700\pi\)
−0.983119 + 0.182967i \(0.941430\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −172.197 + 529.967i −0.266147 + 0.819115i 0.725280 + 0.688453i \(0.241710\pi\)
−0.991427 + 0.130661i \(0.958290\pi\)
\(648\) 0 0
\(649\) −172.567 −0.265897
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −317.263 + 976.435i −0.485855 + 1.49531i 0.344885 + 0.938645i \(0.387918\pi\)
−0.830739 + 0.556662i \(0.812082\pi\)
\(654\) 0 0
\(655\) −27.2993 + 6.53032i −0.0416783 + 0.00996995i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 208.299 286.699i 0.316084 0.435052i −0.621183 0.783666i \(-0.713348\pi\)
0.937266 + 0.348614i \(0.113348\pi\)
\(660\) 0 0
\(661\) 285.049 207.100i 0.431239 0.313314i −0.350905 0.936411i \(-0.614126\pi\)
0.782144 + 0.623097i \(0.214126\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 15.8674 3.79568i 0.0238608 0.00570779i
\(666\) 0 0
\(667\) 431.447 140.186i 0.646847 0.210173i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 275.611 + 89.5515i 0.410747 + 0.133460i
\(672\) 0 0
\(673\) −287.332 395.479i −0.426943 0.587636i 0.540305 0.841469i \(-0.318309\pi\)
−0.967248 + 0.253833i \(0.918309\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −234.956 + 170.705i −0.347054 + 0.252150i −0.747632 0.664113i \(-0.768809\pi\)
0.400578 + 0.916263i \(0.368809\pi\)
\(678\) 0 0
\(679\) −51.1946 + 157.561i −0.0753971 + 0.232048i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 110.905 + 341.332i 0.162380 + 0.499753i 0.998834 0.0482838i \(-0.0153752\pi\)
−0.836454 + 0.548037i \(0.815375\pi\)
\(684\) 0 0
\(685\) 346.932 + 296.800i 0.506470 + 0.433285i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −288.692 397.350i −0.419001 0.576706i
\(690\) 0 0
\(691\) 167.737 + 121.868i 0.242746 + 0.176365i 0.702506 0.711678i \(-0.252065\pi\)
−0.459760 + 0.888043i \(0.652065\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 82.2505 50.3104i 0.118346 0.0723891i
\(696\) 0 0
\(697\) −10.0004 3.24931i −0.0143477 0.00466185i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 634.998i 0.905846i 0.891550 + 0.452923i \(0.149619\pi\)
−0.891550 + 0.452923i \(0.850381\pi\)
\(702\) 0 0
\(703\) 26.8990 + 8.74003i 0.0382632 + 0.0124325i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −368.300 −0.520934
\(708\) 0 0
\(709\) 139.720 + 101.513i 0.197067 + 0.143178i 0.681943 0.731405i \(-0.261135\pi\)
−0.484876 + 0.874583i \(0.661135\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −597.081 433.805i −0.837420 0.608422i
\(714\) 0 0
\(715\) −392.270 31.1959i −0.548629 0.0436307i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −395.152 + 128.393i −0.549586 + 0.178571i −0.570630 0.821207i \(-0.693301\pi\)
0.0210442 + 0.999779i \(0.493301\pi\)
\(720\) 0 0
\(721\) 43.7485 134.644i 0.0606776 0.186746i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −331.593 169.640i −0.457369 0.233987i
\(726\) 0 0
\(727\) −60.8119 83.7004i −0.0836477 0.115131i 0.765143 0.643861i \(-0.222668\pi\)
−0.848790 + 0.528730i \(0.822668\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 369.936 120.200i 0.506069 0.164432i
\(732\) 0 0
\(733\) 1137.30 369.530i 1.55157 0.504134i 0.597027 0.802221i \(-0.296349\pi\)
0.954539 + 0.298087i \(0.0963487\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 195.175 + 141.803i 0.264823 + 0.192405i
\(738\) 0 0
\(739\) 727.911 528.858i 0.984995 0.715641i 0.0261754 0.999657i \(-0.491667\pi\)
0.958819 + 0.284017i \(0.0916672\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −39.4286 −0.0530667 −0.0265334 0.999648i \(-0.508447\pi\)
−0.0265334 + 0.999648i \(0.508447\pi\)
\(744\) 0 0
\(745\) 45.1747 568.044i 0.0606371 0.762475i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 96.5047i 0.128845i
\(750\) 0 0
\(751\) −197.135 −0.262497 −0.131248 0.991350i \(-0.541899\pi\)
−0.131248 + 0.991350i \(0.541899\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 296.672 + 23.5933i 0.392943 + 0.0312494i
\(756\) 0 0
\(757\) 232.670i 0.307358i 0.988121 + 0.153679i \(0.0491121\pi\)
−0.988121 + 0.153679i \(0.950888\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −344.143 473.672i −0.452224 0.622433i 0.520649 0.853771i \(-0.325690\pi\)
−0.972874 + 0.231337i \(0.925690\pi\)
\(762\) 0 0
\(763\) −142.420 + 196.025i −0.186658 + 0.256913i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −141.400 435.183i −0.184354 0.567383i
\(768\) 0 0
\(769\) −358.777 1104.20i −0.466550 1.43589i −0.857023 0.515279i \(-0.827688\pi\)
0.390473 0.920615i \(-0.372312\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 947.468 688.376i 1.22570 0.890525i 0.229142 0.973393i \(-0.426408\pi\)
0.996561 + 0.0828679i \(0.0264079\pi\)
\(774\) 0 0
\(775\) 93.8111 + 598.651i 0.121047 + 0.772453i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.60112 + 0.520237i 0.00205536 + 0.000667827i
\(780\) 0 0
\(781\) −212.177 653.013i −0.271673 0.836124i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −42.8392 + 538.677i −0.0545722 + 0.686213i
\(786\) 0 0
\(787\) 743.066 1022.74i 0.944176 1.29955i −0.00989081 0.999951i \(-0.503148\pi\)
0.954066 0.299595i \(-0.0968516\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.20403 3.03358i 0.00278638 0.00383512i
\(792\) 0 0
\(793\) 768.419i 0.969002i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 89.8487 276.526i 0.112734 0.346958i −0.878734 0.477312i \(-0.841611\pi\)
0.991468 + 0.130354i \(0.0416112\pi\)
\(798\) 0 0
\(799\) −161.469 −0.202089
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −112.597 + 346.536i −0.140220 + 0.431552i
\(804\) 0 0
\(805\) −162.960 266.417i −0.202435 0.330953i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −138.231 + 190.258i −0.170866 + 0.235177i −0.885859 0.463955i \(-0.846430\pi\)
0.714993 + 0.699132i \(0.246430\pi\)
\(810\) 0 0
\(811\) −118.793 + 86.3083i −0.146477 + 0.106422i −0.658610 0.752484i \(-0.728855\pi\)
0.512133 + 0.858906i \(0.328855\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −572.860 + 669.620i −0.702896 + 0.821620i
\(816\) 0 0
\(817\) −59.2293 + 19.2448i −0.0724961 + 0.0235554i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1089.13 353.880i −1.32659 0.431035i −0.441837 0.897095i \(-0.645673\pi\)
−0.884753 + 0.466060i \(0.845673\pi\)
\(822\) 0 0
\(823\) −207.402 285.464i −0.252007 0.346858i 0.664206 0.747550i \(-0.268770\pi\)
−0.916213 + 0.400692i \(0.868770\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1187.70 862.913i 1.43615 1.04343i 0.447323 0.894373i \(-0.352378\pi\)
0.988829 0.149053i \(-0.0476225\pi\)
\(828\) 0 0
\(829\) −305.680 + 940.787i −0.368733 + 1.13484i 0.578876 + 0.815415i \(0.303491\pi\)
−0.947610 + 0.319430i \(0.896509\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 137.518 + 423.236i 0.165087 + 0.508086i
\(834\) 0 0
\(835\) −135.358 565.849i −0.162105 0.677664i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 754.096 + 1037.92i 0.898803 + 1.23710i 0.970848 + 0.239695i \(0.0770475\pi\)
−0.0720449 + 0.997401i \(0.522953\pi\)
\(840\) 0 0
\(841\) −500.805 363.856i −0.595488 0.432647i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −46.1634 192.981i −0.0546312 0.228380i
\(846\) 0 0
\(847\) 178.157 + 57.8867i 0.210339 + 0.0683433i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 541.401i 0.636194i
\(852\) 0 0
\(853\) 248.068 + 80.6021i 0.290818 + 0.0944925i 0.450793 0.892629i \(-0.351141\pi\)
−0.159975 + 0.987121i \(0.551141\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 109.541 0.127819 0.0639093 0.997956i \(-0.479643\pi\)
0.0639093 + 0.997956i \(0.479643\pi\)
\(858\) 0 0
\(859\) 453.169 + 329.247i 0.527554 + 0.383291i 0.819442 0.573162i \(-0.194283\pi\)
−0.291888 + 0.956453i \(0.594283\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −900.930 654.564i −1.04395 0.758475i −0.0728985 0.997339i \(-0.523225\pi\)
−0.971053 + 0.238864i \(0.923225\pi\)
\(864\) 0 0
\(865\) −149.341 + 91.3478i −0.172648 + 0.105604i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −71.7088 + 23.2996i −0.0825187 + 0.0268120i
\(870\) 0 0
\(871\) −197.677 + 608.387i −0.226954 + 0.698492i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −60.4722 + 249.183i −0.0691111 + 0.284781i
\(876\) 0 0
\(877\) −188.027 258.797i −0.214398 0.295094i 0.688249 0.725474i \(-0.258379\pi\)
−0.902648 + 0.430380i \(0.858379\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −309.821 + 100.667i −0.351670 + 0.114264i −0.479525 0.877528i \(-0.659191\pi\)
0.127855 + 0.991793i \(0.459191\pi\)
\(882\) 0 0
\(883\) 610.017 198.206i 0.690846 0.224469i 0.0575081 0.998345i \(-0.481685\pi\)
0.633338 + 0.773876i \(0.281685\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −980.399 712.302i −1.10530 0.803046i −0.123381 0.992359i \(-0.539374\pi\)
−0.981917 + 0.189314i \(0.939374\pi\)
\(888\) 0 0
\(889\) −233.567 + 169.696i −0.262730 + 0.190885i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 25.8523 0.0289500
\(894\) 0 0
\(895\) −394.615 163.834i −0.440910 0.183055i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 361.118i 0.401689i
\(900\) 0 0
\(901\) −337.789 −0.374904
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −259.271 1083.86i −0.286488 1.19763i
\(906\) 0 0
\(907\) 1376.74i 1.51790i −0.651148 0.758951i \(-0.725712\pi\)
0.651148 0.758951i \(-0.274288\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 731.341 + 1006.60i 0.802789 + 1.10494i 0.992396 + 0.123084i \(0.0392784\pi\)
−0.189608 + 0.981860i \(0.560722\pi\)
\(912\) 0 0
\(913\) −218.569 + 300.835i −0.239397 + 0.329502i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3.55863 10.9523i −0.00388073 0.0119436i
\(918\) 0 0
\(919\) 268.155 + 825.295i 0.291789 + 0.898036i 0.984281 + 0.176610i \(0.0565130\pi\)
−0.692491 + 0.721426i \(0.743487\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1472.92 1070.14i 1.59580 1.15942i
\(924\) 0 0
\(925\) −314.834 + 313.803i −0.340361 + 0.339247i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −27.2022 8.83852i −0.0292811 0.00951402i 0.294340 0.955701i \(-0.404900\pi\)
−0.323621 + 0.946187i \(0.604900\pi\)
\(930\) 0 0
\(931\) −22.0175 67.7629i −0.0236493 0.0727851i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −175.932 + 205.648i −0.188162 + 0.219944i
\(936\) 0 0
\(937\) −970.825 + 1336.23i −1.03610 + 1.42607i −0.135832 + 0.990732i \(0.543371\pi\)
−0.900268 + 0.435337i \(0.856629\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 783.812 1078.82i 0.832956 1.14647i −0.154409 0.988007i \(-0.549347\pi\)
0.987366 0.158459i \(-0.0506525\pi\)
\(942\) 0 0
\(943\) 32.2261i 0.0341740i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −9.64433 + 29.6822i −0.0101841 + 0.0313434i −0.956019 0.293303i \(-0.905245\pi\)
0.945835 + 0.324647i \(0.105245\pi\)
\(948\) 0 0
\(949\) −966.162 −1.01808
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 537.860 1655.36i 0.564387 1.73700i −0.105381 0.994432i \(-0.533606\pi\)
0.669767 0.742571i \(-0.266394\pi\)
\(954\) 0 0
\(955\) 269.528 315.054i 0.282229 0.329899i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −110.100 + 151.540i −0.114807 + 0.158018i
\(960\) 0 0
\(961\) 302.173 219.541i 0.314436 0.228451i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 84.4090 1061.39i 0.0874704 1.09989i
\(966\) 0 0
\(967\) 129.567 42.0987i 0.133988 0.0435354i −0.241255 0.970462i \(-0.577559\pi\)
0.375243 + 0.926926i \(0.377559\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1285.89 + 417.810i 1.32429 + 0.430288i 0.883966 0.467550i \(-0.154863\pi\)
0.440325 + 0.897839i \(0.354863\pi\)
\(972\) 0 0
\(973\) 23.2508 + 32.0020i 0.0238960 + 0.0328900i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −740.590 + 538.070i −0.758024 + 0.550737i −0.898304 0.439375i \(-0.855200\pi\)
0.140279 + 0.990112i \(0.455200\pi\)
\(978\) 0 0
\(979\) −58.8302 + 181.061i −0.0600921 + 0.184945i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 519.879 + 1600.02i 0.528870 + 1.62770i 0.756533 + 0.653955i \(0.226892\pi\)
−0.227663 + 0.973740i \(0.573108\pi\)
\(984\) 0 0
\(985\) 140.837 339.223i 0.142982 0.344389i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 700.709 + 964.443i 0.708502 + 0.975170i
\(990\) 0 0
\(991\) 102.185 + 74.2417i 0.103113 + 0.0749159i 0.638147 0.769915i \(-0.279701\pi\)
−0.535034 + 0.844831i \(0.679701\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1439.51 + 114.479i 1.44674 + 0.115055i
\(996\) 0 0
\(997\) −1630.20 529.685i −1.63511 0.531279i −0.659671 0.751554i \(-0.729304\pi\)
−0.975438 + 0.220275i \(0.929304\pi\)
\(998\) 0 0
\(999\) 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 900.3.y.a.89.19 yes 80
3.2 odd 2 inner 900.3.y.a.89.2 80
25.9 even 10 inner 900.3.y.a.809.2 yes 80
75.59 odd 10 inner 900.3.y.a.809.19 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
900.3.y.a.89.2 80 3.2 odd 2 inner
900.3.y.a.89.19 yes 80 1.1 even 1 trivial
900.3.y.a.809.2 yes 80 25.9 even 10 inner
900.3.y.a.809.19 yes 80 75.59 odd 10 inner