Properties

Label 1008.3.cg.q.145.1
Level $1008$
Weight $3$
Character 1008.145
Analytic conductor $27.466$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,3,Mod(145,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.145");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1008.cg (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: \(27.4660106475\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 2 x^{15} + 81 x^{14} - 118 x^{13} + 1960 x^{12} - 366 x^{11} + 37625 x^{10} - 83714 x^{9} + 623931 x^{8} + 289492 x^{7} + 241286 x^{6} - 4777608 x^{5} + \cdots + 1148023744 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{18} \)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 145.1
Root \(-0.338813 - 1.51822i\) of defining polynomial
Character \(\chi\) \(=\) 1008.145
Dual form 1008.3.cg.q.577.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.85541 - 4.53532i) q^{5} +(-1.17763 + 6.90023i) q^{7} +O(q^{10})\) \(q+(-7.85541 - 4.53532i) q^{5} +(-1.17763 + 6.90023i) q^{7} +(-8.81372 - 15.2658i) q^{11} -19.0631i q^{13} +(-14.7807 + 8.53366i) q^{17} +(7.74221 + 4.46997i) q^{19} +(4.72676 - 8.18700i) q^{23} +(28.6383 + 49.6030i) q^{25} -10.0174 q^{29} +(39.5511 - 22.8348i) q^{31} +(40.5455 - 48.8632i) q^{35} +(-26.9278 + 46.6403i) q^{37} +58.9153i q^{41} -69.3894 q^{43} +(41.7123 + 24.0826i) q^{47} +(-46.2264 - 16.2518i) q^{49} +(-21.6496 - 37.4982i) q^{53} +159.892i q^{55} +(0.930469 - 0.537207i) q^{59} +(45.3875 + 26.2045i) q^{61} +(-86.4572 + 149.748i) q^{65} +(24.0006 + 41.5702i) q^{67} +53.5026 q^{71} +(-2.16558 + 1.25030i) q^{73} +(115.717 - 42.8393i) q^{77} +(11.2927 - 19.5596i) q^{79} +51.2015i q^{83} +154.812 q^{85} +(43.9536 + 25.3766i) q^{89} +(131.540 + 22.4492i) q^{91} +(-40.5455 - 70.2269i) q^{95} +126.711i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{7} + 24 q^{19} + 36 q^{25} + 84 q^{31} - 68 q^{37} - 80 q^{43} - 184 q^{49} + 216 q^{61} - 56 q^{67} + 156 q^{73} - 28 q^{79} + 448 q^{85} - 48 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −7.85541 4.53532i −1.57108 0.907064i −0.996037 0.0889425i \(-0.971651\pi\)
−0.575045 0.818122i \(-0.695015\pi\)
\(6\) 0 0
\(7\) −1.17763 + 6.90023i −0.168232 + 0.985747i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −8.81372 15.2658i −0.801247 1.38780i −0.918796 0.394733i \(-0.870837\pi\)
0.117549 0.993067i \(-0.462496\pi\)
\(12\) 0 0
\(13\) 19.0631i 1.46639i −0.680018 0.733195i \(-0.738028\pi\)
0.680018 0.733195i \(-0.261972\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −14.7807 + 8.53366i −0.869454 + 0.501980i −0.867167 0.498018i \(-0.834061\pi\)
−0.00228757 + 0.999997i \(0.500728\pi\)
\(18\) 0 0
\(19\) 7.74221 + 4.46997i 0.407485 + 0.235262i 0.689709 0.724087i \(-0.257739\pi\)
−0.282224 + 0.959349i \(0.591072\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.72676 8.18700i 0.205512 0.355956i −0.744784 0.667306i \(-0.767448\pi\)
0.950296 + 0.311349i \(0.100781\pi\)
\(24\) 0 0
\(25\) 28.6383 + 49.6030i 1.14553 + 1.98412i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −10.0174 −0.345428 −0.172714 0.984972i \(-0.555254\pi\)
−0.172714 + 0.984972i \(0.555254\pi\)
\(30\) 0 0
\(31\) 39.5511 22.8348i 1.27584 0.736608i 0.299761 0.954014i \(-0.403093\pi\)
0.976081 + 0.217407i \(0.0697598\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 40.5455 48.8632i 1.15844 1.39609i
\(36\) 0 0
\(37\) −26.9278 + 46.6403i −0.727778 + 1.26055i 0.230042 + 0.973181i \(0.426114\pi\)
−0.957820 + 0.287368i \(0.907220\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 58.9153i 1.43696i 0.695549 + 0.718479i \(0.255161\pi\)
−0.695549 + 0.718479i \(0.744839\pi\)
\(42\) 0 0
\(43\) −69.3894 −1.61371 −0.806853 0.590752i \(-0.798831\pi\)
−0.806853 + 0.590752i \(0.798831\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 41.7123 + 24.0826i 0.887495 + 0.512395i 0.873122 0.487501i \(-0.162092\pi\)
0.0143726 + 0.999897i \(0.495425\pi\)
\(48\) 0 0
\(49\) −46.2264 16.2518i −0.943396 0.331669i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −21.6496 37.4982i −0.408483 0.707514i 0.586237 0.810140i \(-0.300609\pi\)
−0.994720 + 0.102626i \(0.967275\pi\)
\(54\) 0 0
\(55\) 159.892i 2.90713i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0.930469 0.537207i 0.0157707 0.00910520i −0.492094 0.870542i \(-0.663768\pi\)
0.507865 + 0.861437i \(0.330435\pi\)
\(60\) 0 0
\(61\) 45.3875 + 26.2045i 0.744058 + 0.429582i 0.823543 0.567254i \(-0.191994\pi\)
−0.0794850 + 0.996836i \(0.525328\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −86.4572 + 149.748i −1.33011 + 2.30382i
\(66\) 0 0
\(67\) 24.0006 + 41.5702i 0.358217 + 0.620451i 0.987663 0.156594i \(-0.0500513\pi\)
−0.629446 + 0.777045i \(0.716718\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 53.5026 0.753558 0.376779 0.926303i \(-0.377032\pi\)
0.376779 + 0.926303i \(0.377032\pi\)
\(72\) 0 0
\(73\) −2.16558 + 1.25030i −0.0296655 + 0.0171274i −0.514759 0.857335i \(-0.672119\pi\)
0.485094 + 0.874462i \(0.338785\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 115.717 42.8393i 1.50282 0.556354i
\(78\) 0 0
\(79\) 11.2927 19.5596i 0.142946 0.247590i −0.785659 0.618660i \(-0.787676\pi\)
0.928605 + 0.371070i \(0.121009\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 51.2015i 0.616886i 0.951243 + 0.308443i \(0.0998078\pi\)
−0.951243 + 0.308443i \(0.900192\pi\)
\(84\) 0 0
\(85\) 154.812 1.82131
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 43.9536 + 25.3766i 0.493861 + 0.285131i 0.726175 0.687510i \(-0.241296\pi\)
−0.232314 + 0.972641i \(0.574630\pi\)
\(90\) 0 0
\(91\) 131.540 + 22.4492i 1.44549 + 0.246694i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −40.5455 70.2269i −0.426795 0.739230i
\(96\) 0 0
\(97\) 126.711i 1.30630i 0.757230 + 0.653149i \(0.226552\pi\)
−0.757230 + 0.653149i \(0.773448\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.57104 + 1.48439i −0.0254558 + 0.0146969i −0.512674 0.858583i \(-0.671345\pi\)
0.487218 + 0.873280i \(0.338012\pi\)
\(102\) 0 0
\(103\) 6.15906 + 3.55593i 0.0597967 + 0.0345236i 0.529600 0.848247i \(-0.322342\pi\)
−0.469804 + 0.882771i \(0.655675\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −27.3521 + 47.3753i −0.255627 + 0.442759i −0.965066 0.262008i \(-0.915615\pi\)
0.709438 + 0.704767i \(0.248949\pi\)
\(108\) 0 0
\(109\) −6.54259 11.3321i −0.0600237 0.103964i 0.834452 0.551081i \(-0.185784\pi\)
−0.894476 + 0.447116i \(0.852451\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 39.6743 0.351100 0.175550 0.984471i \(-0.443830\pi\)
0.175550 + 0.984471i \(0.443830\pi\)
\(114\) 0 0
\(115\) −74.2613 + 42.8748i −0.645751 + 0.372824i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −41.4780 112.040i −0.348555 0.941512i
\(120\) 0 0
\(121\) −94.8632 + 164.308i −0.783993 + 1.35792i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 292.769i 2.34215i
\(126\) 0 0
\(127\) 110.071 0.866701 0.433351 0.901225i \(-0.357331\pi\)
0.433351 + 0.901225i \(0.357331\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 200.578 + 115.804i 1.53113 + 0.883998i 0.999310 + 0.0371405i \(0.0118249\pi\)
0.531820 + 0.846858i \(0.321508\pi\)
\(132\) 0 0
\(133\) −39.9613 + 48.1591i −0.300461 + 0.362099i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −126.475 219.062i −0.923178 1.59899i −0.794465 0.607309i \(-0.792249\pi\)
−0.128713 0.991682i \(-0.541084\pi\)
\(138\) 0 0
\(139\) 40.9631i 0.294699i −0.989085 0.147349i \(-0.952926\pi\)
0.989085 0.147349i \(-0.0470742\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −291.013 + 168.017i −2.03506 + 1.17494i
\(144\) 0 0
\(145\) 78.6908 + 45.4322i 0.542695 + 0.313325i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −79.7034 + 138.050i −0.534922 + 0.926512i 0.464245 + 0.885707i \(0.346326\pi\)
−0.999167 + 0.0408055i \(0.987008\pi\)
\(150\) 0 0
\(151\) −27.4354 47.5195i −0.181691 0.314699i 0.760765 0.649027i \(-0.224824\pi\)
−0.942457 + 0.334328i \(0.891491\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −414.253 −2.67260
\(156\) 0 0
\(157\) 95.5760 55.1808i 0.608764 0.351470i −0.163717 0.986507i \(-0.552349\pi\)
0.772482 + 0.635037i \(0.219015\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 50.9258 + 42.2570i 0.316309 + 0.262466i
\(162\) 0 0
\(163\) −113.229 + 196.118i −0.694657 + 1.20318i 0.275640 + 0.961261i \(0.411110\pi\)
−0.970296 + 0.241920i \(0.922223\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 175.214i 1.04918i −0.851354 0.524592i \(-0.824218\pi\)
0.851354 0.524592i \(-0.175782\pi\)
\(168\) 0 0
\(169\) −194.401 −1.15030
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −12.3775 7.14614i −0.0715461 0.0413072i 0.463800 0.885940i \(-0.346486\pi\)
−0.535346 + 0.844633i \(0.679819\pi\)
\(174\) 0 0
\(175\) −375.997 + 139.197i −2.14856 + 0.795412i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −0.121347 0.210178i −0.000677914 0.00117418i 0.865686 0.500587i \(-0.166882\pi\)
−0.866364 + 0.499413i \(0.833549\pi\)
\(180\) 0 0
\(181\) 1.08434i 0.00599080i 0.999996 + 0.00299540i \(0.000953467\pi\)
−0.999996 + 0.00299540i \(0.999047\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 423.057 244.252i 2.28680 1.32028i
\(186\) 0 0
\(187\) 260.546 + 150.426i 1.39330 + 0.804419i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −101.580 + 175.942i −0.531833 + 0.921162i 0.467476 + 0.884006i \(0.345163\pi\)
−0.999309 + 0.0371565i \(0.988170\pi\)
\(192\) 0 0
\(193\) −118.113 204.578i −0.611985 1.05999i −0.990905 0.134560i \(-0.957038\pi\)
0.378920 0.925429i \(-0.376295\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −50.1145 −0.254388 −0.127194 0.991878i \(-0.540597\pi\)
−0.127194 + 0.991878i \(0.540597\pi\)
\(198\) 0 0
\(199\) 106.338 61.3944i 0.534363 0.308514i −0.208429 0.978038i \(-0.566835\pi\)
0.742791 + 0.669523i \(0.233502\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 11.7968 69.1224i 0.0581121 0.340505i
\(204\) 0 0
\(205\) 267.200 462.803i 1.30341 2.25758i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 157.588i 0.754010i
\(210\) 0 0
\(211\) 247.973 1.17523 0.587614 0.809141i \(-0.300067\pi\)
0.587614 + 0.809141i \(0.300067\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 545.082 + 314.703i 2.53526 + 1.46374i
\(216\) 0 0
\(217\) 110.989 + 299.803i 0.511471 + 1.38158i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 162.678 + 281.766i 0.736099 + 1.27496i
\(222\) 0 0
\(223\) 205.854i 0.923114i −0.887111 0.461557i \(-0.847291\pi\)
0.887111 0.461557i \(-0.152709\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.36322 0.787054i 0.00600536 0.00346720i −0.496994 0.867754i \(-0.665563\pi\)
0.503000 + 0.864287i \(0.332230\pi\)
\(228\) 0 0
\(229\) 19.4017 + 11.2016i 0.0847238 + 0.0489153i 0.541763 0.840531i \(-0.317757\pi\)
−0.457040 + 0.889446i \(0.651090\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −39.2335 + 67.9543i −0.168384 + 0.291650i −0.937852 0.347036i \(-0.887188\pi\)
0.769468 + 0.638685i \(0.220521\pi\)
\(234\) 0 0
\(235\) −218.445 378.357i −0.929551 1.61003i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 47.4323 0.198462 0.0992308 0.995064i \(-0.468362\pi\)
0.0992308 + 0.995064i \(0.468362\pi\)
\(240\) 0 0
\(241\) −146.065 + 84.3309i −0.606080 + 0.349921i −0.771430 0.636314i \(-0.780458\pi\)
0.165349 + 0.986235i \(0.447125\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 289.420 + 337.316i 1.18131 + 1.37680i
\(246\) 0 0
\(247\) 85.2114 147.590i 0.344985 0.597532i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 482.804i 1.92352i 0.273893 + 0.961760i \(0.411689\pi\)
−0.273893 + 0.961760i \(0.588311\pi\)
\(252\) 0 0
\(253\) −166.641 −0.658662
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −81.5627 47.0903i −0.317365 0.183231i 0.332853 0.942979i \(-0.391989\pi\)
−0.650217 + 0.759748i \(0.725322\pi\)
\(258\) 0 0
\(259\) −290.118 240.733i −1.12015 0.929470i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 102.365 + 177.301i 0.389220 + 0.674149i 0.992345 0.123498i \(-0.0394112\pi\)
−0.603125 + 0.797647i \(0.706078\pi\)
\(264\) 0 0
\(265\) 392.752i 1.48208i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −155.173 + 89.5890i −0.576850 + 0.333045i −0.759881 0.650063i \(-0.774743\pi\)
0.183030 + 0.983107i \(0.441409\pi\)
\(270\) 0 0
\(271\) −172.307 99.4817i −0.635821 0.367091i 0.147182 0.989109i \(-0.452980\pi\)
−0.783003 + 0.622018i \(0.786313\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 504.819 874.373i 1.83571 3.17954i
\(276\) 0 0
\(277\) −212.444 367.963i −0.766945 1.32839i −0.939212 0.343338i \(-0.888442\pi\)
0.172267 0.985050i \(-0.444891\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −38.2443 −0.136101 −0.0680504 0.997682i \(-0.521678\pi\)
−0.0680504 + 0.997682i \(0.521678\pi\)
\(282\) 0 0
\(283\) 353.144 203.888i 1.24786 0.720452i 0.277178 0.960819i \(-0.410601\pi\)
0.970682 + 0.240366i \(0.0772675\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −406.529 69.3801i −1.41648 0.241743i
\(288\) 0 0
\(289\) 1.14658 1.98594i 0.00396741 0.00687175i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 94.4090i 0.322215i 0.986937 + 0.161107i \(0.0515066\pi\)
−0.986937 + 0.161107i \(0.948493\pi\)
\(294\) 0 0
\(295\) −9.74562 −0.0330360
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −156.069 90.1067i −0.521971 0.301360i
\(300\) 0 0
\(301\) 81.7147 478.803i 0.271477 1.59071i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −237.692 411.694i −0.779317 1.34982i
\(306\) 0 0
\(307\) 95.2741i 0.310339i 0.987888 + 0.155170i \(0.0495924\pi\)
−0.987888 + 0.155170i \(0.950408\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −6.40688 + 3.69902i −0.0206009 + 0.0118939i −0.510265 0.860017i \(-0.670453\pi\)
0.489664 + 0.871911i \(0.337119\pi\)
\(312\) 0 0
\(313\) −445.196 257.034i −1.42235 0.821196i −0.425853 0.904792i \(-0.640026\pi\)
−0.996500 + 0.0835965i \(0.973359\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −284.352 + 492.512i −0.897009 + 1.55367i −0.0657111 + 0.997839i \(0.520932\pi\)
−0.831298 + 0.555827i \(0.812402\pi\)
\(318\) 0 0
\(319\) 88.2906 + 152.924i 0.276773 + 0.479385i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −152.581 −0.472386
\(324\) 0 0
\(325\) 945.585 545.934i 2.90949 1.67980i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −215.297 + 259.464i −0.654398 + 0.788644i
\(330\) 0 0
\(331\) −188.061 + 325.731i −0.568159 + 0.984080i 0.428589 + 0.903499i \(0.359011\pi\)
−0.996748 + 0.0805806i \(0.974323\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 435.401i 1.29971i
\(336\) 0 0
\(337\) −48.6640 −0.144403 −0.0722017 0.997390i \(-0.523003\pi\)
−0.0722017 + 0.997390i \(0.523003\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −697.184 402.520i −2.04453 1.18041i
\(342\) 0 0
\(343\) 166.578 299.834i 0.485652 0.874153i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −61.0477 105.738i −0.175930 0.304720i 0.764553 0.644561i \(-0.222960\pi\)
−0.940483 + 0.339841i \(0.889627\pi\)
\(348\) 0 0
\(349\) 42.6904i 0.122322i −0.998128 0.0611611i \(-0.980520\pi\)
0.998128 0.0611611i \(-0.0194803\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 259.656 149.913i 0.735571 0.424682i −0.0848860 0.996391i \(-0.527053\pi\)
0.820457 + 0.571709i \(0.193719\pi\)
\(354\) 0 0
\(355\) −420.285 242.652i −1.18390 0.683525i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 288.227 499.224i 0.802861 1.39060i −0.114864 0.993381i \(-0.536643\pi\)
0.917725 0.397215i \(-0.130023\pi\)
\(360\) 0 0
\(361\) −140.539 243.420i −0.389304 0.674294i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 22.6821 0.0621426
\(366\) 0 0
\(367\) −129.450 + 74.7379i −0.352724 + 0.203646i −0.665885 0.746055i \(-0.731946\pi\)
0.313160 + 0.949700i \(0.398612\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 284.242 105.228i 0.766150 0.283635i
\(372\) 0 0
\(373\) −237.012 + 410.517i −0.635421 + 1.10058i 0.351005 + 0.936374i \(0.385840\pi\)
−0.986426 + 0.164208i \(0.947493\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 190.963i 0.506532i
\(378\) 0 0
\(379\) −128.926 −0.340174 −0.170087 0.985429i \(-0.554405\pi\)
−0.170087 + 0.985429i \(0.554405\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −442.382 255.410i −1.15505 0.666866i −0.204933 0.978776i \(-0.565698\pi\)
−0.950112 + 0.311910i \(0.899031\pi\)
\(384\) 0 0
\(385\) −1103.29 188.293i −2.86570 0.489073i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 99.7955 + 172.851i 0.256544 + 0.444347i 0.965314 0.261093i \(-0.0840829\pi\)
−0.708770 + 0.705440i \(0.750750\pi\)
\(390\) 0 0
\(391\) 161.346i 0.412650i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −177.418 + 102.432i −0.449160 + 0.259323i
\(396\) 0 0
\(397\) 272.159 + 157.131i 0.685538 + 0.395795i 0.801938 0.597407i \(-0.203802\pi\)
−0.116400 + 0.993202i \(0.537136\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −165.788 + 287.154i −0.413437 + 0.716094i −0.995263 0.0972191i \(-0.969005\pi\)
0.581826 + 0.813314i \(0.302339\pi\)
\(402\) 0 0
\(403\) −435.302 753.966i −1.08015 1.87088i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 949.335 2.33252
\(408\) 0 0
\(409\) 44.7996 25.8650i 0.109534 0.0632397i −0.444232 0.895912i \(-0.646523\pi\)
0.553766 + 0.832672i \(0.313190\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.61111 + 7.05308i 0.00632229 + 0.0170777i
\(414\) 0 0
\(415\) 232.215 402.209i 0.559555 0.969178i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 779.507i 1.86040i 0.367055 + 0.930199i \(0.380366\pi\)
−0.367055 + 0.930199i \(0.619634\pi\)
\(420\) 0 0
\(421\) 610.247 1.44952 0.724759 0.689003i \(-0.241951\pi\)
0.724759 + 0.689003i \(0.241951\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −846.589 488.779i −1.99198 1.15007i
\(426\) 0 0
\(427\) −234.267 + 282.325i −0.548634 + 0.661184i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 309.626 + 536.287i 0.718389 + 1.24429i 0.961638 + 0.274322i \(0.0884534\pi\)
−0.243249 + 0.969964i \(0.578213\pi\)
\(432\) 0 0
\(433\) 6.27297i 0.0144872i 0.999974 + 0.00724361i \(0.00230573\pi\)
−0.999974 + 0.00724361i \(0.997694\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 73.1913 42.2570i 0.167486 0.0966979i
\(438\) 0 0
\(439\) 438.913 + 253.406i 0.999802 + 0.577236i 0.908190 0.418559i \(-0.137465\pi\)
0.0916121 + 0.995795i \(0.470798\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 231.039 400.171i 0.521533 0.903321i −0.478154 0.878276i \(-0.658694\pi\)
0.999686 0.0250447i \(-0.00797281\pi\)
\(444\) 0 0
\(445\) −230.183 398.688i −0.517264 0.895928i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 773.455 1.72262 0.861308 0.508083i \(-0.169646\pi\)
0.861308 + 0.508083i \(0.169646\pi\)
\(450\) 0 0
\(451\) 899.389 519.262i 1.99421 1.15136i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −931.484 772.922i −2.04722 1.69873i
\(456\) 0 0
\(457\) −340.636 + 589.999i −0.745374 + 1.29103i 0.204645 + 0.978836i \(0.434396\pi\)
−0.950020 + 0.312190i \(0.898937\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 141.028i 0.305918i 0.988233 + 0.152959i \(0.0488802\pi\)
−0.988233 + 0.152959i \(0.951120\pi\)
\(462\) 0 0
\(463\) −488.209 −1.05445 −0.527224 0.849727i \(-0.676767\pi\)
−0.527224 + 0.849727i \(0.676767\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 403.532 + 232.979i 0.864095 + 0.498885i 0.865381 0.501114i \(-0.167076\pi\)
−0.00128656 + 0.999999i \(0.500410\pi\)
\(468\) 0 0
\(469\) −315.108 + 116.655i −0.671872 + 0.248732i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 611.578 + 1059.28i 1.29298 + 2.23950i
\(474\) 0 0
\(475\) 512.049i 1.07800i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −186.185 + 107.494i −0.388696 + 0.224414i −0.681595 0.731730i \(-0.738713\pi\)
0.292899 + 0.956143i \(0.405380\pi\)
\(480\) 0 0
\(481\) 889.108 + 513.327i 1.84846 + 1.06721i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 574.674 995.365i 1.18490 2.05230i
\(486\) 0 0
\(487\) −177.999 308.303i −0.365500 0.633065i 0.623356 0.781938i \(-0.285769\pi\)
−0.988856 + 0.148873i \(0.952435\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −386.760 −0.787698 −0.393849 0.919175i \(-0.628857\pi\)
−0.393849 + 0.919175i \(0.628857\pi\)
\(492\) 0 0
\(493\) 148.065 85.4851i 0.300334 0.173398i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −63.0061 + 369.180i −0.126773 + 0.742818i
\(498\) 0 0
\(499\) 200.322 346.968i 0.401447 0.695327i −0.592454 0.805604i \(-0.701841\pi\)
0.993901 + 0.110278i \(0.0351741\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 240.052i 0.477241i 0.971113 + 0.238621i \(0.0766952\pi\)
−0.971113 + 0.238621i \(0.923305\pi\)
\(504\) 0 0
\(505\) 26.9287 0.0533242
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −441.516 254.909i −0.867419 0.500804i −0.000929124 1.00000i \(-0.500296\pi\)
−0.866490 + 0.499195i \(0.833629\pi\)
\(510\) 0 0
\(511\) −6.07712 16.4154i −0.0118926 0.0321241i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −32.2546 55.8666i −0.0626303 0.108479i
\(516\) 0 0
\(517\) 849.028i 1.64222i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −183.183 + 105.761i −0.351600 + 0.202996i −0.665390 0.746496i \(-0.731735\pi\)
0.313790 + 0.949492i \(0.398401\pi\)
\(522\) 0 0
\(523\) 500.693 + 289.075i 0.957347 + 0.552725i 0.895356 0.445352i \(-0.146921\pi\)
0.0619917 + 0.998077i \(0.480255\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −389.729 + 675.031i −0.739524 + 1.28089i
\(528\) 0 0
\(529\) 219.815 + 380.731i 0.415530 + 0.719719i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1123.11 2.10714
\(534\) 0 0
\(535\) 429.724 248.101i 0.803223 0.463741i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 159.330 + 848.922i 0.295603 + 1.57499i
\(540\) 0 0
\(541\) 403.423 698.750i 0.745699 1.29159i −0.204168 0.978936i \(-0.565449\pi\)
0.949867 0.312653i \(-0.101218\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 118.691i 0.217782i
\(546\) 0 0
\(547\) −841.193 −1.53783 −0.768915 0.639351i \(-0.779203\pi\)
−0.768915 + 0.639351i \(0.779203\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −77.5569 44.7775i −0.140757 0.0812659i
\(552\) 0 0
\(553\) 121.667 + 100.956i 0.220013 + 0.182561i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −311.159 538.943i −0.558633 0.967582i −0.997611 0.0690834i \(-0.977993\pi\)
0.438977 0.898498i \(-0.355341\pi\)
\(558\) 0 0
\(559\) 1322.78i 2.36632i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −272.546 + 157.355i −0.484096 + 0.279493i −0.722122 0.691766i \(-0.756833\pi\)
0.238026 + 0.971259i \(0.423500\pi\)
\(564\) 0 0
\(565\) −311.658 179.936i −0.551607 0.318470i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 12.6505 21.9114i 0.0222329 0.0385085i −0.854695 0.519131i \(-0.826256\pi\)
0.876928 + 0.480622i \(0.159589\pi\)
\(570\) 0 0
\(571\) 96.6400 + 167.385i 0.169247 + 0.293144i 0.938155 0.346215i \(-0.112533\pi\)
−0.768908 + 0.639359i \(0.779200\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 541.466 0.941680
\(576\) 0 0
\(577\) −245.268 + 141.605i −0.425074 + 0.245417i −0.697246 0.716832i \(-0.745591\pi\)
0.272172 + 0.962249i \(0.412258\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −353.302 60.2962i −0.608093 0.103780i
\(582\) 0 0
\(583\) −381.627 + 660.997i −0.654592 + 1.13379i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 450.692i 0.767789i 0.923377 + 0.383895i \(0.125417\pi\)
−0.923377 + 0.383895i \(0.874583\pi\)
\(588\) 0 0
\(589\) 408.284 0.693182
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 428.895 + 247.623i 0.723264 + 0.417577i 0.815953 0.578119i \(-0.196213\pi\)
−0.0926890 + 0.995695i \(0.529546\pi\)
\(594\) 0 0
\(595\) −182.310 + 1068.24i −0.306403 + 1.79535i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 488.101 + 845.415i 0.814859 + 1.41138i 0.909429 + 0.415859i \(0.136519\pi\)
−0.0945697 + 0.995518i \(0.530148\pi\)
\(600\) 0 0
\(601\) 609.471i 1.01410i 0.861918 + 0.507048i \(0.169263\pi\)
−0.861918 + 0.507048i \(0.830737\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1490.38 860.470i 2.46343 1.42226i
\(606\) 0 0
\(607\) 347.737 + 200.766i 0.572877 + 0.330751i 0.758298 0.651908i \(-0.226031\pi\)
−0.185420 + 0.982659i \(0.559365\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 459.088 795.164i 0.751372 1.30141i
\(612\) 0 0
\(613\) −21.8505 37.8461i −0.0356451 0.0617391i 0.847652 0.530552i \(-0.178015\pi\)
−0.883298 + 0.468813i \(0.844682\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −632.523 −1.02516 −0.512580 0.858640i \(-0.671310\pi\)
−0.512580 + 0.858640i \(0.671310\pi\)
\(618\) 0 0
\(619\) 206.161 119.027i 0.333055 0.192289i −0.324142 0.946009i \(-0.605075\pi\)
0.657196 + 0.753719i \(0.271742\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −226.866 + 273.406i −0.364150 + 0.438854i
\(624\) 0 0
\(625\) −611.846 + 1059.75i −0.978954 + 1.69560i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 919.170i 1.46132i
\(630\) 0 0
\(631\) 861.236 1.36487 0.682437 0.730944i \(-0.260920\pi\)
0.682437 + 0.730944i \(0.260920\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −864.653 499.208i −1.36166 0.786154i
\(636\) 0 0
\(637\) −309.809 + 881.217i −0.486356 + 1.38339i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −206.326 357.367i −0.321881 0.557514i 0.658995 0.752147i \(-0.270982\pi\)
−0.980876 + 0.194633i \(0.937648\pi\)
\(642\) 0 0
\(643\) 643.619i 1.00096i 0.865747 + 0.500482i \(0.166844\pi\)
−0.865747 + 0.500482i \(0.833156\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −673.471 + 388.829i −1.04091 + 0.600972i −0.920092 0.391703i \(-0.871886\pi\)
−0.120821 + 0.992674i \(0.538553\pi\)
\(648\) 0 0
\(649\) −16.4018 9.46957i −0.0252724 0.0145910i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −117.781 + 204.003i −0.180370 + 0.312410i −0.942007 0.335595i \(-0.891063\pi\)
0.761637 + 0.648004i \(0.224396\pi\)
\(654\) 0 0
\(655\) −1050.41 1819.37i −1.60369 2.77767i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1119.92 −1.69943 −0.849713 0.527246i \(-0.823225\pi\)
−0.849713 + 0.527246i \(0.823225\pi\)
\(660\) 0 0
\(661\) −174.861 + 100.956i −0.264541 + 0.152733i −0.626404 0.779499i \(-0.715474\pi\)
0.361863 + 0.932231i \(0.382141\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 532.329 197.072i 0.800495 0.296349i
\(666\) 0 0
\(667\) −47.3499 + 82.0125i −0.0709894 + 0.122957i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 923.836i 1.37681i
\(672\) 0 0
\(673\) 167.885 0.249457 0.124729 0.992191i \(-0.460194\pi\)
0.124729 + 0.992191i \(0.460194\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 630.551 + 364.049i 0.931391 + 0.537739i 0.887251 0.461287i \(-0.152612\pi\)
0.0441395 + 0.999025i \(0.485945\pi\)
\(678\) 0 0
\(679\) −874.334 149.218i −1.28768 0.219761i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −552.381 956.752i −0.808757 1.40081i −0.913725 0.406332i \(-0.866808\pi\)
0.104969 0.994476i \(-0.466526\pi\)
\(684\) 0 0
\(685\) 2294.43i 3.34953i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −714.832 + 412.708i −1.03749 + 0.598996i
\(690\) 0 0
\(691\) −846.017 488.448i −1.22434 0.706872i −0.258498 0.966012i \(-0.583228\pi\)
−0.965840 + 0.259140i \(0.916561\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −185.781 + 321.782i −0.267311 + 0.462996i
\(696\) 0 0
\(697\) −502.763 870.810i −0.721324 1.24937i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1099.72 −1.56878 −0.784392 0.620266i \(-0.787025\pi\)
−0.784392 + 0.620266i \(0.787025\pi\)
\(702\) 0 0
\(703\) −416.961 + 240.733i −0.593117 + 0.342436i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.21491 19.4888i −0.0102050 0.0275655i
\(708\) 0 0
\(709\) −44.5147 + 77.1017i −0.0627852 + 0.108747i −0.895709 0.444640i \(-0.853332\pi\)
0.832924 + 0.553387i \(0.186665\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 431.740i 0.605525i
\(714\) 0 0
\(715\) 3048.04 4.26299
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 412.423 + 238.113i 0.573607 + 0.331172i 0.758589 0.651570i \(-0.225889\pi\)
−0.184982 + 0.982742i \(0.559223\pi\)
\(720\) 0 0
\(721\) −31.7898 + 38.3114i −0.0440913 + 0.0531364i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −286.881 496.893i −0.395698 0.685370i
\(726\) 0 0
\(727\) 14.5314i 0.0199881i 0.999950 + 0.00999406i \(0.00318126\pi\)
−0.999950 + 0.00999406i \(0.996819\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1025.63 592.145i 1.40304 0.810048i
\(732\) 0 0
\(733\) 1103.82 + 637.293i 1.50590 + 0.869431i 0.999977 + 0.00685249i \(0.00218123\pi\)
0.505923 + 0.862579i \(0.331152\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 423.068 732.776i 0.574041 0.994269i
\(738\) 0 0
\(739\) 631.506 + 1093.80i 0.854541 + 1.48011i 0.877070 + 0.480362i \(0.159495\pi\)
−0.0225294 + 0.999746i \(0.507172\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1143.15 −1.53856 −0.769282 0.638909i \(-0.779386\pi\)
−0.769282 + 0.638909i \(0.779386\pi\)
\(744\) 0 0
\(745\) 1252.21 722.961i 1.68081 0.970418i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −294.690 244.526i −0.393444 0.326470i
\(750\) 0 0
\(751\) −315.689 + 546.790i −0.420359 + 0.728082i −0.995974 0.0896378i \(-0.971429\pi\)
0.575616 + 0.817720i \(0.304762\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 497.714i 0.659223i
\(756\) 0 0
\(757\) 705.180 0.931546 0.465773 0.884904i \(-0.345776\pi\)
0.465773 + 0.884904i \(0.345776\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 43.2391 + 24.9641i 0.0568188 + 0.0328043i 0.528140 0.849157i \(-0.322890\pi\)
−0.471322 + 0.881961i \(0.656223\pi\)
\(762\) 0 0
\(763\) 85.8988 31.8004i 0.112580 0.0416781i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −10.2408 17.7376i −0.0133518 0.0231260i
\(768\) 0 0
\(769\) 909.426i 1.18261i 0.806448 + 0.591304i \(0.201387\pi\)
−0.806448 + 0.591304i \(0.798613\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1079.76 + 623.402i −1.39685 + 0.806471i −0.994061 0.108823i \(-0.965292\pi\)
−0.402787 + 0.915294i \(0.631959\pi\)
\(774\) 0 0
\(775\) 2265.35 + 1307.90i 2.92303 + 1.68761i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −263.349 + 456.135i −0.338061 + 0.585539i
\(780\) 0 0
\(781\) −471.557 816.760i −0.603786 1.04579i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −1001.05 −1.27522
\(786\) 0 0
\(787\) −686.254 + 396.209i −0.871988 + 0.503442i −0.868008 0.496550i \(-0.834600\pi\)
−0.00397939 + 0.999992i \(0.501267\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −46.7215 + 273.762i −0.0590663 + 0.346096i
\(792\) 0 0
\(793\) 499.539 865.226i 0.629935 1.09108i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1067.43i 1.33932i 0.742670 + 0.669658i \(0.233559\pi\)
−0.742670 + 0.669658i \(0.766441\pi\)
\(798\) 0 0
\(799\) −822.050 −1.02885
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 38.1737 + 22.0396i 0.0475388 + 0.0274466i
\(804\) 0 0
\(805\) −208.394 562.911i −0.258875 0.699268i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 492.247 + 852.596i 0.608463 + 1.05389i 0.991494 + 0.130154i \(0.0415471\pi\)
−0.383031 + 0.923736i \(0.625120\pi\)
\(810\) 0 0
\(811\) 1036.21i 1.27769i −0.769336 0.638845i \(-0.779413\pi\)
0.769336 0.638845i \(-0.220587\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1778.92 1027.06i 2.18272 1.26020i
\(816\) 0 0
\(817\) −537.227 310.168i −0.657561 0.379643i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −495.184 + 857.685i −0.603148 + 1.04468i 0.389193 + 0.921156i \(0.372754\pi\)
−0.992341 + 0.123527i \(0.960580\pi\)
\(822\) 0 0
\(823\) 535.120 + 926.855i 0.650206 + 1.12619i 0.983073 + 0.183217i \(0.0586509\pi\)
−0.332866 + 0.942974i \(0.608016\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1035.41 1.25201 0.626005 0.779819i \(-0.284689\pi\)
0.626005 + 0.779819i \(0.284689\pi\)
\(828\) 0 0
\(829\) 672.235 388.115i 0.810899 0.468173i −0.0363691 0.999338i \(-0.511579\pi\)
0.847268 + 0.531166i \(0.178246\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 821.947 154.267i 0.986731 0.185194i
\(834\) 0 0
\(835\) −794.651 + 1376.38i −0.951677 + 1.64835i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1582.78i 1.88651i −0.332076 0.943253i \(-0.607749\pi\)
0.332076 0.943253i \(-0.392251\pi\)
\(840\) 0 0
\(841\) −740.652 −0.880680
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1527.10 + 881.671i 1.80722 + 1.04340i
\(846\) 0 0
\(847\) −1022.05 848.071i −1.20667 1.00126i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 254.563 + 440.915i 0.299134 + 0.518114i
\(852\) 0 0
\(853\) 499.247i 0.585283i 0.956222 + 0.292642i \(0.0945343\pi\)
−0.956222 + 0.292642i \(0.905466\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 200.112 115.535i 0.233503 0.134813i −0.378684 0.925526i \(-0.623623\pi\)
0.612187 + 0.790713i \(0.290290\pi\)
\(858\) 0 0
\(859\) −1104.81 637.860i −1.28615 0.742562i −0.308188 0.951325i \(-0.599723\pi\)
−0.977966 + 0.208764i \(0.933056\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −554.074 + 959.684i −0.642032 + 1.11203i 0.342946 + 0.939355i \(0.388575\pi\)
−0.984978 + 0.172677i \(0.944758\pi\)
\(864\) 0 0
\(865\) 64.8201 + 112.272i 0.0749365 + 0.129794i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −398.124 −0.458141
\(870\) 0 0
\(871\) 792.456 457.525i 0.909823 0.525287i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2020.18 + 344.773i 2.30877 + 0.394026i
\(876\) 0 0
\(877\) −371.376 + 643.242i −0.423462 + 0.733458i −0.996275 0.0862280i \(-0.972519\pi\)
0.572813 + 0.819686i \(0.305852\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 544.827i 0.618419i −0.950994 0.309209i \(-0.899936\pi\)
0.950994 0.309209i \(-0.100064\pi\)
\(882\) 0 0
\(883\) −915.864 −1.03722 −0.518609 0.855011i \(-0.673550\pi\)
−0.518609 + 0.855011i \(0.673550\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1344.46 + 776.222i 1.51573 + 0.875109i 0.999830 + 0.0184631i \(0.00587731\pi\)
0.515904 + 0.856646i \(0.327456\pi\)
\(888\) 0 0
\(889\) −129.623 + 759.516i −0.145807 + 0.854349i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 215.297 + 372.905i 0.241094 + 0.417587i
\(894\) 0 0
\(895\) 2.20138i 0.00245964i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −396.199 + 228.746i −0.440711 + 0.254445i
\(900\) 0 0
\(901\) 639.994 + 369.501i 0.710315 + 0.410101i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 4.91781 8.51790i 0.00543404 0.00941204i
\(906\) 0 0
\(907\) 354.727 + 614.406i 0.391099 + 0.677404i 0.992595 0.121472i \(-0.0387615\pi\)
−0.601495 + 0.798876i \(0.705428\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1178.08 1.29317 0.646584 0.762842i \(-0.276197\pi\)
0.646584 + 0.762842i \(0.276197\pi\)
\(912\) 0 0
\(913\) 781.632 451.275i 0.856114 0.494278i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1035.28 + 1247.66i −1.12898 + 1.36059i
\(918\) 0 0
\(919\) 298.271 516.621i 0.324560 0.562155i −0.656863 0.754010i \(-0.728117\pi\)
0.981423 + 0.191855i \(0.0614503\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1019.92i 1.10501i
\(924\) 0 0
\(925\) −3084.66 −3.33477
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 612.089 + 353.390i 0.658868 + 0.380398i 0.791846 0.610721i \(-0.209120\pi\)
−0.132977 + 0.991119i \(0.542454\pi\)
\(930\) 0 0
\(931\) −285.250 332.455i −0.306391 0.357095i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1364.46 2363.32i −1.45932 2.52762i
\(936\) 0 0
\(937\) 732.454i 0.781701i 0.920454 + 0.390851i \(0.127819\pi\)
−0.920454 + 0.390851i \(0.872181\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −37.5804 + 21.6970i −0.0399366 + 0.0230574i −0.519835 0.854266i \(-0.674007\pi\)
0.479899 + 0.877324i \(0.340673\pi\)
\(942\) 0 0
\(943\) 482.339 + 278.479i 0.511494 + 0.295311i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −463.757 + 803.251i −0.489712 + 0.848206i −0.999930 0.0118393i \(-0.996231\pi\)
0.510218 + 0.860045i \(0.329565\pi\)
\(948\) 0 0
\(949\) 23.8346 + 41.2827i 0.0251155 + 0.0435013i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 692.901 0.727073 0.363537 0.931580i \(-0.381569\pi\)
0.363537 + 0.931580i \(0.381569\pi\)
\(954\) 0 0
\(955\) 1595.91 921.397i 1.67111 0.964814i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1660.52 614.737i 1.73151 0.641018i
\(960\) 0 0
\(961\) 562.360 974.036i 0.585182 1.01356i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2142.72i 2.22044i
\(966\) 0 0
\(967\) −202.072 −0.208968 −0.104484 0.994527i \(-0.533319\pi\)
−0.104484 + 0.994527i \(0.533319\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 530.638 + 306.364i 0.546486 + 0.315514i 0.747704 0.664033i \(-0.231156\pi\)
−0.201217 + 0.979547i \(0.564490\pi\)
\(972\) 0 0
\(973\) 282.655 + 48.2392i 0.290499 + 0.0495778i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −405.699 702.692i −0.415250 0.719234i 0.580205 0.814471i \(-0.302973\pi\)
−0.995455 + 0.0952366i \(0.969639\pi\)
\(978\) 0 0
\(979\) 894.650i 0.913841i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1250.68 + 722.082i −1.27231 + 0.734570i −0.975423 0.220342i \(-0.929283\pi\)
−0.296889 + 0.954912i \(0.595949\pi\)
\(984\) 0 0
\(985\) 393.670 + 227.285i 0.399664 + 0.230746i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −327.987 + 568.091i −0.331635 + 0.574409i
\(990\) 0 0
\(991\) −413.395 716.021i −0.417149 0.722523i 0.578502 0.815681i \(-0.303637\pi\)
−0.995651 + 0.0931574i \(0.970304\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1113.77 −1.11937
\(996\) 0 0
\(997\) −437.754 + 252.737i −0.439071 + 0.253498i −0.703204 0.710989i \(-0.748248\pi\)
0.264132 + 0.964486i \(0.414914\pi\)
\(998\) 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 1008.3.cg.q.145.1 16
3.2 odd 2 inner 1008.3.cg.q.145.8 16
4.3 odd 2 504.3.by.d.145.1 yes 16
7.3 odd 6 inner 1008.3.cg.q.577.1 16
12.11 even 2 504.3.by.d.145.8 yes 16
21.17 even 6 inner 1008.3.cg.q.577.8 16
28.3 even 6 504.3.by.d.73.1 16
28.19 even 6 3528.3.f.i.2449.1 16
28.23 odd 6 3528.3.f.i.2449.15 16
84.23 even 6 3528.3.f.i.2449.2 16
84.47 odd 6 3528.3.f.i.2449.16 16
84.59 odd 6 504.3.by.d.73.8 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.3.by.d.73.1 16 28.3 even 6
504.3.by.d.73.8 yes 16 84.59 odd 6
504.3.by.d.145.1 yes 16 4.3 odd 2
504.3.by.d.145.8 yes 16 12.11 even 2
1008.3.cg.q.145.1 16 1.1 even 1 trivial
1008.3.cg.q.145.8 16 3.2 odd 2 inner
1008.3.cg.q.577.1 16 7.3 odd 6 inner
1008.3.cg.q.577.8 16 21.17 even 6 inner
3528.3.f.i.2449.1 16 28.19 even 6
3528.3.f.i.2449.2 16 84.23 even 6
3528.3.f.i.2449.15 16 28.23 odd 6
3528.3.f.i.2449.16 16 84.47 odd 6