Properties

Label 1008.3.cg.l.145.1
Level $1008$
Weight $3$
Character 1008.145
Analytic conductor $27.466$
Analytic rank $0$
Dimension $4$
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] = [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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 145.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1008.145
Dual form 1008.3.cg.l.577.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.74264 - 1.58346i) q^{5} +(2.24264 + 6.63103i) q^{7} +O(q^{10})\) \(q+(-2.74264 - 1.58346i) q^{5} +(2.24264 + 6.63103i) q^{7} +(6.62132 + 11.4685i) q^{11} -5.49333i q^{13} +(11.7426 - 6.77962i) q^{17} +(0.621320 + 0.358719i) q^{19} +(1.13604 - 1.96768i) q^{23} +(-7.48528 - 12.9649i) q^{25} -20.4853 q^{29} +(-21.3198 + 12.3090i) q^{31} +(4.34924 - 21.7377i) q^{35} +(-32.4706 + 56.2407i) q^{37} +21.0308i q^{41} -6.48528 q^{43} +(41.3787 + 23.8900i) q^{47} +(-38.9411 + 29.7420i) q^{49} +(11.0147 + 19.0781i) q^{53} -41.9385i q^{55} +(-72.5330 + 41.8770i) q^{59} +(57.3823 + 33.1297i) q^{61} +(-8.69848 + 15.0662i) q^{65} +(46.3198 + 80.2283i) q^{67} -48.4264 q^{71} +(113.441 - 65.4953i) q^{73} +(-61.1985 + 69.6258i) q^{77} +(-38.1066 + 66.0026i) q^{79} +107.981i q^{83} -42.9411 q^{85} +(145.412 + 83.9535i) q^{89} +(36.4264 - 12.3196i) q^{91} +(-1.13604 - 1.96768i) q^{95} +25.5816i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{5} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{5} - 8 q^{7} + 18 q^{11} + 30 q^{17} - 6 q^{19} + 30 q^{23} + 4 q^{25} - 48 q^{29} + 42 q^{31} - 42 q^{35} - 62 q^{37} + 8 q^{43} + 174 q^{47} - 20 q^{49} + 78 q^{53} - 78 q^{59} - 42 q^{61} + 84 q^{65} + 58 q^{67} - 24 q^{71} + 318 q^{73} - 126 q^{77} - 110 q^{79} - 36 q^{85} + 378 q^{89} - 24 q^{91} - 30 q^{95}+O(q^{100}) \) 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
\(5\) −2.74264 1.58346i −0.548528 0.316693i 0.200000 0.979796i \(-0.435906\pi\)
−0.748528 + 0.663103i \(0.769239\pi\)
\(6\) 0 0
\(7\) 2.24264 + 6.63103i 0.320377 + 0.947290i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 6.62132 + 11.4685i 0.601938 + 1.04259i 0.992527 + 0.122022i \(0.0389380\pi\)
−0.390589 + 0.920565i \(0.627729\pi\)
\(12\) 0 0
\(13\) 5.49333i 0.422563i −0.977425 0.211282i \(-0.932236\pi\)
0.977425 0.211282i \(-0.0677638\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 11.7426 6.77962i 0.690744 0.398801i −0.113147 0.993578i \(-0.536093\pi\)
0.803891 + 0.594777i \(0.202760\pi\)
\(18\) 0 0
\(19\) 0.621320 + 0.358719i 0.0327011 + 0.0188800i 0.516261 0.856431i \(-0.327323\pi\)
−0.483560 + 0.875311i \(0.660657\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.13604 1.96768i 0.0493930 0.0855512i −0.840272 0.542165i \(-0.817605\pi\)
0.889665 + 0.456614i \(0.150938\pi\)
\(24\) 0 0
\(25\) −7.48528 12.9649i −0.299411 0.518596i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −20.4853 −0.706389 −0.353195 0.935550i \(-0.614905\pi\)
−0.353195 + 0.935550i \(0.614905\pi\)
\(30\) 0 0
\(31\) −21.3198 + 12.3090i −0.687736 + 0.397064i −0.802763 0.596298i \(-0.796638\pi\)
0.115028 + 0.993362i \(0.463304\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.34924 21.7377i 0.124264 0.621076i
\(36\) 0 0
\(37\) −32.4706 + 56.2407i −0.877583 + 1.52002i −0.0235970 + 0.999722i \(0.507512\pi\)
−0.853986 + 0.520296i \(0.825821\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 21.0308i 0.512946i 0.966551 + 0.256473i \(0.0825605\pi\)
−0.966551 + 0.256473i \(0.917439\pi\)
\(42\) 0 0
\(43\) −6.48528 −0.150820 −0.0754102 0.997153i \(-0.524027\pi\)
−0.0754102 + 0.997153i \(0.524027\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 41.3787 + 23.8900i 0.880397 + 0.508298i 0.870789 0.491656i \(-0.163608\pi\)
0.00960801 + 0.999954i \(0.496942\pi\)
\(48\) 0 0
\(49\) −38.9411 + 29.7420i −0.794717 + 0.606980i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 11.0147 + 19.0781i 0.207825 + 0.359963i 0.951029 0.309101i \(-0.100028\pi\)
−0.743204 + 0.669065i \(0.766695\pi\)
\(54\) 0 0
\(55\) 41.9385i 0.762518i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −72.5330 + 41.8770i −1.22937 + 0.709779i −0.966899 0.255160i \(-0.917872\pi\)
−0.262474 + 0.964939i \(0.584538\pi\)
\(60\) 0 0
\(61\) 57.3823 + 33.1297i 0.940693 + 0.543109i 0.890177 0.455614i \(-0.150580\pi\)
0.0505153 + 0.998723i \(0.483914\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −8.69848 + 15.0662i −0.133823 + 0.231788i
\(66\) 0 0
\(67\) 46.3198 + 80.2283i 0.691340 + 1.19744i 0.971399 + 0.237454i \(0.0763128\pi\)
−0.280058 + 0.959983i \(0.590354\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −48.4264 −0.682062 −0.341031 0.940052i \(-0.610776\pi\)
−0.341031 + 0.940052i \(0.610776\pi\)
\(72\) 0 0
\(73\) 113.441 65.4953i 1.55399 0.897195i 0.556177 0.831064i \(-0.312268\pi\)
0.997811 0.0661316i \(-0.0210657\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −61.1985 + 69.6258i −0.794786 + 0.904231i
\(78\) 0 0
\(79\) −38.1066 + 66.0026i −0.482362 + 0.835476i −0.999795 0.0202482i \(-0.993554\pi\)
0.517433 + 0.855724i \(0.326888\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 107.981i 1.30098i 0.759514 + 0.650491i \(0.225437\pi\)
−0.759514 + 0.650491i \(0.774563\pi\)
\(84\) 0 0
\(85\) −42.9411 −0.505190
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 145.412 + 83.9535i 1.63384 + 0.943297i 0.982894 + 0.184173i \(0.0589606\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(90\) 0 0
\(91\) 36.4264 12.3196i 0.400290 0.135380i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.13604 1.96768i −0.0119583 0.0207124i
\(96\) 0 0
\(97\) 25.5816i 0.263728i 0.991268 + 0.131864i \(0.0420962\pi\)
−0.991268 + 0.131864i \(0.957904\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −24.6838 + 14.2512i −0.244394 + 0.141101i −0.617194 0.786811i \(-0.711731\pi\)
0.372801 + 0.927911i \(0.378397\pi\)
\(102\) 0 0
\(103\) −48.9228 28.2456i −0.474979 0.274229i 0.243343 0.969940i \(-0.421756\pi\)
−0.718322 + 0.695711i \(0.755089\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −23.8051 + 41.2316i −0.222477 + 0.385342i −0.955560 0.294798i \(-0.904748\pi\)
0.733082 + 0.680140i \(0.238081\pi\)
\(108\) 0 0
\(109\) −37.6543 65.2192i −0.345453 0.598341i 0.639983 0.768389i \(-0.278941\pi\)
−0.985436 + 0.170047i \(0.945608\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −85.4558 −0.756246 −0.378123 0.925755i \(-0.623430\pi\)
−0.378123 + 0.925755i \(0.623430\pi\)
\(114\) 0 0
\(115\) −6.23149 + 3.59775i −0.0541869 + 0.0312848i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 71.2904 + 62.6616i 0.599079 + 0.526568i
\(120\) 0 0
\(121\) −27.1838 + 47.0837i −0.224659 + 0.389121i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 126.584i 1.01267i
\(126\) 0 0
\(127\) 60.6619 0.477653 0.238826 0.971062i \(-0.423237\pi\)
0.238826 + 0.971062i \(0.423237\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −115.136 66.4738i −0.878901 0.507434i −0.00860515 0.999963i \(-0.502739\pi\)
−0.870296 + 0.492529i \(0.836072\pi\)
\(132\) 0 0
\(133\) −0.985281 + 4.92447i −0.00740813 + 0.0370261i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −58.7132 101.694i −0.428564 0.742294i 0.568182 0.822903i \(-0.307647\pi\)
−0.996746 + 0.0806089i \(0.974314\pi\)
\(138\) 0 0
\(139\) 68.5857i 0.493422i −0.969089 0.246711i \(-0.920650\pi\)
0.969089 0.246711i \(-0.0793499\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 63.0000 36.3731i 0.440559 0.254357i
\(144\) 0 0
\(145\) 56.1838 + 32.4377i 0.387474 + 0.223708i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −13.1985 + 22.8604i −0.0885804 + 0.153426i −0.906911 0.421322i \(-0.861566\pi\)
0.818331 + 0.574747i \(0.194900\pi\)
\(150\) 0 0
\(151\) −67.1066 116.232i −0.444415 0.769749i 0.553597 0.832785i \(-0.313255\pi\)
−0.998011 + 0.0630363i \(0.979922\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 77.9634 0.502990
\(156\) 0 0
\(157\) −196.323 + 113.347i −1.25047 + 0.721958i −0.971202 0.238256i \(-0.923424\pi\)
−0.279265 + 0.960214i \(0.590091\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 15.5955 + 3.12032i 0.0968662 + 0.0193808i
\(162\) 0 0
\(163\) −45.9889 + 79.6550i −0.282140 + 0.488681i −0.971912 0.235346i \(-0.924378\pi\)
0.689771 + 0.724027i \(0.257711\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 203.482i 1.21845i 0.792996 + 0.609227i \(0.208520\pi\)
−0.792996 + 0.609227i \(0.791480\pi\)
\(168\) 0 0
\(169\) 138.823 0.821440
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −61.3234 35.4051i −0.354470 0.204654i 0.312182 0.950022i \(-0.398940\pi\)
−0.666652 + 0.745369i \(0.732273\pi\)
\(174\) 0 0
\(175\) 69.1838 78.7107i 0.395336 0.449775i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −54.4081 94.2376i −0.303956 0.526467i 0.673072 0.739577i \(-0.264974\pi\)
−0.977028 + 0.213109i \(0.931641\pi\)
\(180\) 0 0
\(181\) 99.6607i 0.550611i −0.961357 0.275306i \(-0.911221\pi\)
0.961357 0.275306i \(-0.0887791\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 178.110 102.832i 0.962758 0.555848i
\(186\) 0 0
\(187\) 155.504 + 89.7800i 0.831570 + 0.480107i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −34.9523 + 60.5391i −0.182996 + 0.316959i −0.942899 0.333077i \(-0.891913\pi\)
0.759903 + 0.650036i \(0.225246\pi\)
\(192\) 0 0
\(193\) 16.1690 + 28.0056i 0.0837774 + 0.145107i 0.904870 0.425689i \(-0.139968\pi\)
−0.821092 + 0.570796i \(0.806635\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −277.103 −1.40661 −0.703306 0.710887i \(-0.748294\pi\)
−0.703306 + 0.710887i \(0.748294\pi\)
\(198\) 0 0
\(199\) −145.011 + 83.7222i −0.728699 + 0.420715i −0.817946 0.575295i \(-0.804887\pi\)
0.0892469 + 0.996010i \(0.471554\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −45.9411 135.839i −0.226311 0.669155i
\(204\) 0 0
\(205\) 33.3015 57.6799i 0.162446 0.281365i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 9.50079i 0.0454583i
\(210\) 0 0
\(211\) 128.073 0.606982 0.303491 0.952834i \(-0.401848\pi\)
0.303491 + 0.952834i \(0.401848\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 17.7868 + 10.2692i 0.0827293 + 0.0477638i
\(216\) 0 0
\(217\) −129.434 113.768i −0.596470 0.524275i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −37.2426 64.5061i −0.168519 0.291883i
\(222\) 0 0
\(223\) 417.169i 1.87071i 0.353705 + 0.935357i \(0.384922\pi\)
−0.353705 + 0.935357i \(0.615078\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 201.143 116.130i 0.886093 0.511586i 0.0134307 0.999910i \(-0.495725\pi\)
0.872663 + 0.488324i \(0.162391\pi\)
\(228\) 0 0
\(229\) −72.4188 41.8110i −0.316239 0.182581i 0.333476 0.942759i \(-0.391778\pi\)
−0.649715 + 0.760178i \(0.725112\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 109.537 189.723i 0.470114 0.814261i −0.529302 0.848434i \(-0.677546\pi\)
0.999416 + 0.0341721i \(0.0108794\pi\)
\(234\) 0 0
\(235\) −75.6579 131.043i −0.321949 0.557631i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 193.103 0.807961 0.403980 0.914768i \(-0.367626\pi\)
0.403980 + 0.914768i \(0.367626\pi\)
\(240\) 0 0
\(241\) 42.8970 24.7666i 0.177996 0.102766i −0.408355 0.912823i \(-0.633897\pi\)
0.586351 + 0.810057i \(0.300564\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 153.897 19.9098i 0.628151 0.0812646i
\(246\) 0 0
\(247\) 1.97056 3.41311i 0.00797799 0.0138183i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 162.524i 0.647507i 0.946141 + 0.323754i \(0.104945\pi\)
−0.946141 + 0.323754i \(0.895055\pi\)
\(252\) 0 0
\(253\) 30.0883 0.118926
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 85.8747 + 49.5798i 0.334143 + 0.192917i 0.657679 0.753298i \(-0.271538\pi\)
−0.323536 + 0.946216i \(0.604872\pi\)
\(258\) 0 0
\(259\) −445.753 89.1857i −1.72106 0.344346i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −217.173 376.154i −0.825751 1.43024i −0.901344 0.433105i \(-0.857418\pi\)
0.0755923 0.997139i \(-0.475915\pi\)
\(264\) 0 0
\(265\) 69.7657i 0.263267i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 79.1619 45.7041i 0.294282 0.169904i −0.345589 0.938386i \(-0.612321\pi\)
0.639871 + 0.768482i \(0.278988\pi\)
\(270\) 0 0
\(271\) −14.8051 8.54772i −0.0546313 0.0315414i 0.472436 0.881365i \(-0.343375\pi\)
−0.527067 + 0.849824i \(0.676708\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 99.1249 171.689i 0.360454 0.624325i
\(276\) 0 0
\(277\) 200.206 + 346.766i 0.722764 + 1.25186i 0.959888 + 0.280385i \(0.0904620\pi\)
−0.237124 + 0.971479i \(0.576205\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 538.690 1.91705 0.958524 0.285012i \(-0.0919976\pi\)
0.958524 + 0.285012i \(0.0919976\pi\)
\(282\) 0 0
\(283\) 267.783 154.604i 0.946229 0.546306i 0.0543215 0.998523i \(-0.482700\pi\)
0.891907 + 0.452218i \(0.149367\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −139.456 + 47.1645i −0.485909 + 0.164336i
\(288\) 0 0
\(289\) −52.5736 + 91.0601i −0.181916 + 0.315087i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 327.391i 1.11738i −0.829378 0.558688i \(-0.811305\pi\)
0.829378 0.558688i \(-0.188695\pi\)
\(294\) 0 0
\(295\) 265.243 0.899128
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −10.8091 6.24063i −0.0361508 0.0208717i
\(300\) 0 0
\(301\) −14.5442 43.0041i −0.0483195 0.142871i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −104.919 181.725i −0.343998 0.595821i
\(306\) 0 0
\(307\) 256.140i 0.834331i −0.908831 0.417165i \(-0.863024\pi\)
0.908831 0.417165i \(-0.136976\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 187.349 108.166i 0.602409 0.347801i −0.167580 0.985859i \(-0.553595\pi\)
0.769989 + 0.638057i \(0.220262\pi\)
\(312\) 0 0
\(313\) 135.809 + 78.4092i 0.433893 + 0.250509i 0.701004 0.713157i \(-0.252736\pi\)
−0.267110 + 0.963666i \(0.586069\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −224.015 + 388.005i −0.706671 + 1.22399i 0.259414 + 0.965766i \(0.416471\pi\)
−0.966085 + 0.258224i \(0.916863\pi\)
\(318\) 0 0
\(319\) −135.640 234.935i −0.425203 0.736472i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 9.72792 0.0301174
\(324\) 0 0
\(325\) −71.2203 + 41.1191i −0.219140 + 0.126520i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −65.6177 + 327.960i −0.199446 + 0.996839i
\(330\) 0 0
\(331\) −27.5036 + 47.6376i −0.0830924 + 0.143920i −0.904577 0.426311i \(-0.859813\pi\)
0.821484 + 0.570231i \(0.193146\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 293.383i 0.875770i
\(336\) 0 0
\(337\) −111.632 −0.331254 −0.165627 0.986189i \(-0.552965\pi\)
−0.165627 + 0.986189i \(0.552965\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −282.331 163.004i −0.827949 0.478016i
\(342\) 0 0
\(343\) −284.551 191.519i −0.829596 0.558365i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −188.628 326.714i −0.543598 0.941539i −0.998694 0.0510967i \(-0.983728\pi\)
0.455096 0.890442i \(-0.349605\pi\)
\(348\) 0 0
\(349\) 204.034i 0.584624i −0.956323 0.292312i \(-0.905575\pi\)
0.956323 0.292312i \(-0.0944246\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 361.198 208.538i 1.02323 0.590759i 0.108189 0.994130i \(-0.465495\pi\)
0.915036 + 0.403371i \(0.132162\pi\)
\(354\) 0 0
\(355\) 132.816 + 76.6815i 0.374130 + 0.216004i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 89.4153 154.872i 0.249068 0.431398i −0.714200 0.699942i \(-0.753209\pi\)
0.963267 + 0.268544i \(0.0865425\pi\)
\(360\) 0 0
\(361\) −180.243 312.189i −0.499287 0.864791i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −414.838 −1.13654
\(366\) 0 0
\(367\) 544.724 314.497i 1.48426 0.856939i 0.484422 0.874835i \(-0.339030\pi\)
0.999840 + 0.0178960i \(0.00569679\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −101.805 + 115.824i −0.274407 + 0.312194i
\(372\) 0 0
\(373\) 127.779 221.320i 0.342572 0.593351i −0.642338 0.766422i \(-0.722035\pi\)
0.984910 + 0.173070i \(0.0553687\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 112.532i 0.298494i
\(378\) 0 0
\(379\) −219.750 −0.579816 −0.289908 0.957055i \(-0.593625\pi\)
−0.289908 + 0.957055i \(0.593625\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14.7534 8.51785i −0.0385205 0.0222398i 0.480616 0.876931i \(-0.340413\pi\)
−0.519137 + 0.854691i \(0.673746\pi\)
\(384\) 0 0
\(385\) 278.095 94.0530i 0.722326 0.244293i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −76.1102 131.827i −0.195656 0.338886i 0.751459 0.659779i \(-0.229350\pi\)
−0.947115 + 0.320893i \(0.896017\pi\)
\(390\) 0 0
\(391\) 30.8076i 0.0787919i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 209.025 120.681i 0.529178 0.305521i
\(396\) 0 0
\(397\) −322.786 186.361i −0.813064 0.469423i 0.0349549 0.999389i \(-0.488871\pi\)
−0.848019 + 0.529966i \(0.822205\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 325.786 564.279i 0.812435 1.40718i −0.0987205 0.995115i \(-0.531475\pi\)
0.911155 0.412063i \(-0.135192\pi\)
\(402\) 0 0
\(403\) 67.6173 + 117.117i 0.167785 + 0.290612i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −859.992 −2.11300
\(408\) 0 0
\(409\) 462.081 266.782i 1.12978 0.652280i 0.185902 0.982568i \(-0.440479\pi\)
0.943880 + 0.330289i \(0.107146\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −440.353 387.054i −1.06623 0.937176i
\(414\) 0 0
\(415\) 170.985 296.154i 0.412012 0.713625i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 534.252i 1.27507i 0.770423 + 0.637533i \(0.220045\pi\)
−0.770423 + 0.637533i \(0.779955\pi\)
\(420\) 0 0
\(421\) 157.220 0.373445 0.186723 0.982413i \(-0.440213\pi\)
0.186723 + 0.982413i \(0.440213\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −175.794 101.495i −0.413633 0.238811i
\(426\) 0 0
\(427\) −90.9960 + 454.801i −0.213105 + 1.06511i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 114.268 + 197.918i 0.265123 + 0.459207i 0.967596 0.252504i \(-0.0812541\pi\)
−0.702473 + 0.711711i \(0.747921\pi\)
\(432\) 0 0
\(433\) 47.5549i 0.109827i −0.998491 0.0549133i \(-0.982512\pi\)
0.998491 0.0549133i \(-0.0174882\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.41169 0.815039i 0.00323041 0.00186508i
\(438\) 0 0
\(439\) 63.9594 + 36.9270i 0.145693 + 0.0841161i 0.571075 0.820898i \(-0.306527\pi\)
−0.425381 + 0.905014i \(0.639860\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −117.320 + 203.204i −0.264830 + 0.458699i −0.967519 0.252798i \(-0.918649\pi\)
0.702689 + 0.711497i \(0.251983\pi\)
\(444\) 0 0
\(445\) −265.875 460.508i −0.597471 1.03485i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 255.161 0.568288 0.284144 0.958782i \(-0.408291\pi\)
0.284144 + 0.958782i \(0.408291\pi\)
\(450\) 0 0
\(451\) −241.191 + 139.252i −0.534791 + 0.308762i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −119.412 23.8918i −0.262444 0.0525095i
\(456\) 0 0
\(457\) 72.8675 126.210i 0.159448 0.276171i −0.775222 0.631689i \(-0.782362\pi\)
0.934670 + 0.355518i \(0.115695\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 888.329i 1.92696i 0.267777 + 0.963481i \(0.413711\pi\)
−0.267777 + 0.963481i \(0.586289\pi\)
\(462\) 0 0
\(463\) −234.014 −0.505430 −0.252715 0.967541i \(-0.581324\pi\)
−0.252715 + 0.967541i \(0.581324\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 681.231 + 393.309i 1.45874 + 0.842204i 0.998950 0.0458237i \(-0.0145912\pi\)
0.459790 + 0.888028i \(0.347925\pi\)
\(468\) 0 0
\(469\) −428.117 + 487.071i −0.912830 + 1.03853i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −42.9411 74.3762i −0.0907846 0.157244i
\(474\) 0 0
\(475\) 10.7405i 0.0226115i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 638.202 368.466i 1.33236 0.769240i 0.346702 0.937975i \(-0.387302\pi\)
0.985661 + 0.168735i \(0.0539682\pi\)
\(480\) 0 0
\(481\) 308.948 + 178.371i 0.642304 + 0.370834i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 40.5076 70.1612i 0.0835208 0.144662i
\(486\) 0 0
\(487\) 135.349 + 234.432i 0.277925 + 0.481379i 0.970869 0.239612i \(-0.0770202\pi\)
−0.692944 + 0.720991i \(0.743687\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 760.161 1.54819 0.774094 0.633070i \(-0.218206\pi\)
0.774094 + 0.633070i \(0.218206\pi\)
\(492\) 0 0
\(493\) −240.551 + 138.882i −0.487934 + 0.281709i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −108.603 321.117i −0.218517 0.646111i
\(498\) 0 0
\(499\) 62.7462 108.680i 0.125744 0.217795i −0.796280 0.604929i \(-0.793202\pi\)
0.922023 + 0.387134i \(0.126535\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 117.083i 0.232770i −0.993204 0.116385i \(-0.962869\pi\)
0.993204 0.116385i \(-0.0371306\pi\)
\(504\) 0 0
\(505\) 90.2649 0.178742
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 574.110 + 331.463i 1.12792 + 0.651204i 0.943410 0.331627i \(-0.107598\pi\)
0.184507 + 0.982831i \(0.440931\pi\)
\(510\) 0 0
\(511\) 688.709 + 605.349i 1.34777 + 1.18464i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 89.4518 + 154.935i 0.173693 + 0.300845i
\(516\) 0 0
\(517\) 632.733i 1.22386i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 40.8229 23.5691i 0.0783550 0.0452383i −0.460311 0.887758i \(-0.652262\pi\)
0.538666 + 0.842520i \(0.318929\pi\)
\(522\) 0 0
\(523\) −432.554 249.735i −0.827064 0.477506i 0.0257824 0.999668i \(-0.491792\pi\)
−0.852846 + 0.522162i \(0.825126\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −166.901 + 289.080i −0.316699 + 0.548539i
\(528\) 0 0
\(529\) 261.919 + 453.657i 0.495121 + 0.857574i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 115.529 0.216752
\(534\) 0 0
\(535\) 130.578 75.3890i 0.244070 0.140914i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −598.937 249.663i −1.11120 0.463197i
\(540\) 0 0
\(541\) −249.405 + 431.981i −0.461007 + 0.798487i −0.999011 0.0444550i \(-0.985845\pi\)
0.538005 + 0.842942i \(0.319178\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 238.497i 0.437609i
\(546\) 0 0
\(547\) 279.897 0.511694 0.255847 0.966717i \(-0.417646\pi\)
0.255847 + 0.966717i \(0.417646\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −12.7279 7.34847i −0.0230997 0.0133366i
\(552\) 0 0
\(553\) −523.124 104.666i −0.945976 0.189269i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −130.890 226.708i −0.234991 0.407016i 0.724279 0.689507i \(-0.242173\pi\)
−0.959270 + 0.282491i \(0.908839\pi\)
\(558\) 0 0
\(559\) 35.6258i 0.0637312i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −420.076 + 242.531i −0.746139 + 0.430784i −0.824297 0.566157i \(-0.808429\pi\)
0.0781581 + 0.996941i \(0.475096\pi\)
\(564\) 0 0
\(565\) 234.375 + 135.316i 0.414822 + 0.239498i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −227.000 + 393.175i −0.398945 + 0.690993i −0.993596 0.112991i \(-0.963957\pi\)
0.594651 + 0.803984i \(0.297290\pi\)
\(570\) 0 0
\(571\) −115.769 200.517i −0.202747 0.351168i 0.746666 0.665200i \(-0.231654\pi\)
−0.949413 + 0.314032i \(0.898320\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −34.0143 −0.0591553
\(576\) 0 0
\(577\) 564.014 325.634i 0.977494 0.564356i 0.0759812 0.997109i \(-0.475791\pi\)
0.901513 + 0.432753i \(0.142458\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −716.029 + 242.164i −1.23241 + 0.416805i
\(582\) 0 0
\(583\) −145.864 + 252.644i −0.250195 + 0.433351i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 823.029i 1.40209i −0.713116 0.701046i \(-0.752717\pi\)
0.713116 0.701046i \(-0.247283\pi\)
\(588\) 0 0
\(589\) −17.6619 −0.0299863
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 700.110 + 404.209i 1.18062 + 0.681634i 0.956159 0.292848i \(-0.0946031\pi\)
0.224465 + 0.974482i \(0.427936\pi\)
\(594\) 0 0
\(595\) −96.3015 284.744i −0.161851 0.478561i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −265.422 459.725i −0.443109 0.767488i 0.554809 0.831978i \(-0.312791\pi\)
−0.997918 + 0.0644900i \(0.979458\pi\)
\(600\) 0 0
\(601\) 936.503i 1.55824i 0.626874 + 0.779121i \(0.284334\pi\)
−0.626874 + 0.779121i \(0.715666\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 149.111 86.0890i 0.246464 0.142296i
\(606\) 0 0
\(607\) −521.452 301.060i −0.859064 0.495981i 0.00463474 0.999989i \(-0.498525\pi\)
−0.863699 + 0.504008i \(0.831858\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 131.235 227.307i 0.214788 0.372024i
\(612\) 0 0
\(613\) −548.448 949.940i −0.894695 1.54966i −0.834181 0.551491i \(-0.814059\pi\)
−0.0605142 0.998167i \(-0.519274\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 432.956 0.701712 0.350856 0.936429i \(-0.385891\pi\)
0.350856 + 0.936429i \(0.385891\pi\)
\(618\) 0 0
\(619\) −194.951 + 112.555i −0.314946 + 0.181834i −0.649137 0.760671i \(-0.724870\pi\)
0.334192 + 0.942505i \(0.391537\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −230.592 + 1152.51i −0.370131 + 1.84993i
\(624\) 0 0
\(625\) 13.3091 23.0520i 0.0212945 0.0368832i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 880.552i 1.39992i
\(630\) 0 0
\(631\) −750.514 −1.18940 −0.594702 0.803946i \(-0.702730\pi\)
−0.594702 + 0.803946i \(0.702730\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −166.374 96.0560i −0.262006 0.151269i
\(636\) 0 0
\(637\) 163.383 + 213.916i 0.256488 + 0.335818i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −580.926 1006.19i −0.906281 1.56973i −0.819188 0.573525i \(-0.805575\pi\)
−0.0870937 0.996200i \(-0.527758\pi\)
\(642\) 0 0
\(643\) 121.957i 0.189669i 0.995493 + 0.0948347i \(0.0302322\pi\)
−0.995493 + 0.0948347i \(0.969768\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −137.504 + 79.3877i −0.212525 + 0.122701i −0.602484 0.798131i \(-0.705822\pi\)
0.389959 + 0.920832i \(0.372489\pi\)
\(648\) 0 0
\(649\) −960.529 554.561i −1.48001 0.854486i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −195.471 + 338.565i −0.299342 + 0.518476i −0.975986 0.217835i \(-0.930101\pi\)
0.676643 + 0.736311i \(0.263434\pi\)
\(654\) 0 0
\(655\) 210.518 + 364.628i 0.321401 + 0.556683i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −331.955 −0.503726 −0.251863 0.967763i \(-0.581043\pi\)
−0.251863 + 0.967763i \(0.581043\pi\)
\(660\) 0 0
\(661\) 561.029 323.910i 0.848758 0.490031i −0.0114736 0.999934i \(-0.503652\pi\)
0.860232 + 0.509904i \(0.170319\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 10.5000 11.9459i 0.0157895 0.0179638i
\(666\) 0 0
\(667\) −23.2721 + 40.3084i −0.0348907 + 0.0604324i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 877.448i 1.30767i
\(672\) 0 0
\(673\) 100.956 0.150009 0.0750047 0.997183i \(-0.476103\pi\)
0.0750047 + 0.997183i \(0.476103\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −643.610 371.588i −0.950679 0.548875i −0.0573873 0.998352i \(-0.518277\pi\)
−0.893292 + 0.449477i \(0.851610\pi\)
\(678\) 0 0
\(679\) −169.632 + 57.3704i −0.249827 + 0.0844924i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −2.21721 3.84032i −0.00324628 0.00562272i 0.864398 0.502809i \(-0.167700\pi\)
−0.867644 + 0.497186i \(0.834367\pi\)
\(684\) 0 0
\(685\) 371.881i 0.542892i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 104.802 60.5074i 0.152107 0.0878192i
\(690\) 0 0
\(691\) 846.253 + 488.584i 1.22468 + 0.707069i 0.965912 0.258871i \(-0.0833506\pi\)
0.258767 + 0.965940i \(0.416684\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −108.603 + 188.106i −0.156263 + 0.270656i
\(696\) 0 0
\(697\) 142.581 + 246.957i 0.204563 + 0.354314i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 840.177 1.19854 0.599270 0.800547i \(-0.295458\pi\)
0.599270 + 0.800547i \(0.295458\pi\)
\(702\) 0 0
\(703\) −40.3492 + 23.2956i −0.0573958 + 0.0331375i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −149.857 131.719i −0.211962 0.186306i
\(708\) 0 0
\(709\) −341.279 + 591.112i −0.481352 + 0.833727i −0.999771 0.0214003i \(-0.993188\pi\)
0.518419 + 0.855127i \(0.326521\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 55.9340i 0.0784488i
\(714\) 0 0
\(715\) −230.382 −0.322212
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 119.187 + 68.8126i 0.165768 + 0.0957060i 0.580589 0.814197i \(-0.302822\pi\)
−0.414821 + 0.909903i \(0.636156\pi\)
\(720\) 0 0
\(721\) 77.5812 387.754i 0.107602 0.537800i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 153.338 + 265.589i 0.211501 + 0.366330i
\(726\) 0 0
\(727\) 264.137i 0.363325i 0.983361 + 0.181662i \(0.0581478\pi\)
−0.983361 + 0.181662i \(0.941852\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −76.1543 + 43.9677i −0.104178 + 0.0601474i
\(732\) 0 0
\(733\) 501.705 + 289.660i 0.684455 + 0.395170i 0.801531 0.597953i \(-0.204019\pi\)
−0.117077 + 0.993123i \(0.537352\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −613.397 + 1062.43i −0.832288 + 1.44157i
\(738\) 0 0
\(739\) −99.0477 171.556i −0.134029 0.232146i 0.791197 0.611562i \(-0.209458\pi\)
−0.925226 + 0.379416i \(0.876125\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 976.690 1.31452 0.657261 0.753663i \(-0.271715\pi\)
0.657261 + 0.753663i \(0.271715\pi\)
\(744\) 0 0
\(745\) 72.3974 41.7987i 0.0971777 0.0561056i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −326.794 65.3845i −0.436308 0.0872958i
\(750\) 0 0
\(751\) −417.665 + 723.417i −0.556145 + 0.963272i 0.441668 + 0.897178i \(0.354387\pi\)
−0.997813 + 0.0660933i \(0.978947\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 425.044i 0.562972i
\(756\) 0 0
\(757\) 104.221 0.137677 0.0688383 0.997628i \(-0.478071\pi\)
0.0688383 + 0.997628i \(0.478071\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 473.785 + 273.540i 0.622583 + 0.359448i 0.777874 0.628420i \(-0.216298\pi\)
−0.155291 + 0.987869i \(0.549632\pi\)
\(762\) 0 0
\(763\) 348.025 395.950i 0.456128 0.518939i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 230.044 + 398.447i 0.299927 + 0.519488i
\(768\) 0 0
\(769\) 341.205i 0.443700i 0.975081 + 0.221850i \(0.0712095\pi\)
−0.975081 + 0.221850i \(0.928790\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 425.213 245.497i 0.550081 0.317590i −0.199074 0.979985i \(-0.563793\pi\)
0.749155 + 0.662395i \(0.230460\pi\)
\(774\) 0 0
\(775\) 319.169 + 184.273i 0.411832 + 0.237771i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.54416 + 13.0669i −0.00968441 + 0.0167739i
\(780\) 0 0
\(781\) −320.647 555.376i −0.410559 0.711109i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 717.926 0.914555
\(786\) 0 0
\(787\) −260.202 + 150.228i −0.330625 + 0.190887i −0.656119 0.754658i \(-0.727803\pi\)
0.325493 + 0.945544i \(0.394470\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −191.647 566.660i −0.242284 0.716385i
\(792\) 0 0
\(793\) 181.992 315.219i 0.229498 0.397502i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 370.072i 0.464331i −0.972676 0.232165i \(-0.925419\pi\)
0.972676 0.232165i \(-0.0745811\pi\)
\(798\) 0 0
\(799\) 647.860 0.810838
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1502.26 + 867.330i 1.87081 + 1.08011i
\(804\) 0 0
\(805\) −37.8318 33.2528i −0.0469960 0.0413078i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 245.618 + 425.422i 0.303607 + 0.525862i 0.976950 0.213468i \(-0.0684758\pi\)
−0.673344 + 0.739330i \(0.735142\pi\)
\(810\) 0 0
\(811\) 156.802i 0.193344i 0.995316 + 0.0966722i \(0.0308199\pi\)
−0.995316 + 0.0966722i \(0.969180\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 252.262 145.643i 0.309524 0.178704i
\(816\) 0 0
\(817\) −4.02944 2.32640i −0.00493199 0.00284749i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −215.316 + 372.939i −0.262261 + 0.454249i −0.966842 0.255374i \(-0.917801\pi\)
0.704581 + 0.709623i \(0.251135\pi\)
\(822\) 0 0
\(823\) −354.371 613.788i −0.430584 0.745793i 0.566340 0.824172i \(-0.308359\pi\)
−0.996924 + 0.0783785i \(0.975026\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1460.10 −1.76554 −0.882770 0.469805i \(-0.844324\pi\)
−0.882770 + 0.469805i \(0.844324\pi\)
\(828\) 0 0
\(829\) −223.095 + 128.804i −0.269113 + 0.155373i −0.628485 0.777822i \(-0.716325\pi\)
0.359371 + 0.933195i \(0.382991\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −255.632 + 613.256i −0.306881 + 0.736202i
\(834\) 0 0
\(835\) 322.206 558.077i 0.385876 0.668356i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 213.621i 0.254613i 0.991863 + 0.127307i \(0.0406332\pi\)
−0.991863 + 0.127307i \(0.959367\pi\)
\(840\) 0 0
\(841\) −421.353 −0.501015
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −380.743 219.822i −0.450583 0.260144i
\(846\) 0 0
\(847\) −373.177 74.6646i −0.440586 0.0881519i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 73.7756 + 127.783i 0.0866929 + 0.150156i
\(852\) 0 0
\(853\) 1127.37i 1.32165i 0.750539 + 0.660826i \(0.229794\pi\)
−0.750539 + 0.660826i \(0.770206\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1100.22 + 635.212i −1.28380 + 0.741204i −0.977541 0.210744i \(-0.932412\pi\)
−0.306261 + 0.951947i \(0.599078\pi\)
\(858\) 0 0
\(859\) 221.488 + 127.876i 0.257844 + 0.148867i 0.623351 0.781942i \(-0.285771\pi\)
−0.365506 + 0.930809i \(0.619104\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −557.364 + 965.382i −0.645844 + 1.11863i 0.338262 + 0.941052i \(0.390161\pi\)
−0.984106 + 0.177583i \(0.943172\pi\)
\(864\) 0 0
\(865\) 112.125 + 194.207i 0.129625 + 0.224516i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1009.26 −1.16141
\(870\) 0 0
\(871\) 440.720 254.450i 0.505993 0.292135i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −839.382 + 283.882i −0.959294 + 0.324437i
\(876\) 0 0
\(877\) 550.904 954.194i 0.628169 1.08802i −0.359750 0.933049i \(-0.617138\pi\)
0.987919 0.154972i \(-0.0495286\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 217.067i 0.246387i 0.992383 + 0.123194i \(0.0393136\pi\)
−0.992383 + 0.123194i \(0.960686\pi\)
\(882\) 0 0
\(883\) 516.544 0.584988 0.292494 0.956267i \(-0.405515\pi\)
0.292494 + 0.956267i \(0.405515\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −978.445 564.905i −1.10309 0.636872i −0.166062 0.986115i \(-0.553105\pi\)
−0.937032 + 0.349243i \(0.886439\pi\)
\(888\) 0 0
\(889\) 136.043 + 402.251i 0.153029 + 0.452476i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 17.1396 + 29.6867i 0.0191933 + 0.0332438i
\(894\) 0 0
\(895\) 344.613i 0.385043i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 436.742 252.153i 0.485809 0.280482i
\(900\) 0 0
\(901\) 258.684 + 149.351i 0.287107 + 0.165762i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −157.809 + 273.333i −0.174375 + 0.302026i
\(906\) 0 0
\(907\) 30.0111 + 51.9808i 0.0330884 + 0.0573107i 0.882095 0.471071i \(-0.156132\pi\)
−0.849007 + 0.528382i \(0.822799\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1422.25 1.56120 0.780598 0.625033i \(-0.214915\pi\)
0.780598 + 0.625033i \(0.214915\pi\)
\(912\) 0 0
\(913\) −1238.38 + 714.980i −1.35639 + 0.783111i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 182.581 912.547i 0.199107 0.995144i
\(918\) 0 0
\(919\) 834.849 1446.00i 0.908432 1.57345i 0.0921886 0.995742i \(-0.470614\pi\)
0.816243 0.577708i \(-0.196053\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 266.022i 0.288215i
\(924\) 0 0
\(925\) 972.205 1.05103
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −839.058 484.430i −0.903184 0.521453i −0.0249519 0.999689i \(-0.507943\pi\)
−0.878232 + 0.478235i \(0.841277\pi\)
\(930\) 0 0
\(931\) −34.8640 + 4.51039i −0.0374479 + 0.00484468i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −284.327 492.469i −0.304093 0.526705i
\(936\) 0 0
\(937\) 1212.57i 1.29410i −0.762449 0.647049i \(-0.776003\pi\)
0.762449 0.647049i \(-0.223997\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1293.90 747.032i 1.37502 0.793870i 0.383468 0.923554i \(-0.374730\pi\)
0.991555 + 0.129684i \(0.0413963\pi\)
\(942\) 0 0
\(943\) 41.3818 + 23.8918i 0.0438832 + 0.0253360i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −387.731 + 671.570i −0.409431 + 0.709155i −0.994826 0.101593i \(-0.967606\pi\)
0.585395 + 0.810748i \(0.300939\pi\)
\(948\) 0 0
\(949\) −359.787 623.169i −0.379122 0.656659i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −1055.40 −1.10745 −0.553723 0.832701i \(-0.686794\pi\)
−0.553723 + 0.832701i \(0.686794\pi\)
\(954\) 0 0
\(955\) 191.723 110.691i 0.200757 0.115907i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 542.665 617.393i 0.565866 0.643788i
\(960\) 0 0
\(961\) −177.477 + 307.400i −0.184680 + 0.319875i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 102.412i 0.106127i
\(966\) 0 0
\(967\) −1221.63 −1.26332 −0.631661 0.775245i \(-0.717627\pi\)
−0.631661 + 0.775245i \(0.717627\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −455.753 263.129i −0.469365 0.270988i 0.246609 0.969115i \(-0.420684\pi\)
−0.715974 + 0.698127i \(0.754017\pi\)
\(972\) 0 0
\(973\) 454.794 153.813i 0.467414 0.158081i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −500.051 866.114i −0.511823 0.886504i −0.999906 0.0137065i \(-0.995637\pi\)
0.488083 0.872797i \(-0.337696\pi\)
\(978\) 0 0
\(979\) 2223.53i 2.27123i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 931.584 537.850i 0.947695 0.547152i 0.0553306 0.998468i \(-0.482379\pi\)
0.892364 + 0.451316i \(0.149045\pi\)
\(984\) 0 0
\(985\) 759.993 + 438.782i 0.771566 + 0.445464i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.36753 + 12.7609i −0.00744948 + 0.0129029i
\(990\) 0 0
\(991\) −938.017 1624.69i −0.946536 1.63945i −0.752646 0.658426i \(-0.771223\pi\)
−0.193891 0.981023i \(-0.562111\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 530.285 0.532949
\(996\) 0 0
\(997\) 504.221 291.112i 0.505738 0.291988i −0.225342 0.974280i \(-0.572350\pi\)
0.731080 + 0.682292i \(0.239017\pi\)
\(998\) 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.l.145.1 4
3.2 odd 2 112.3.s.b.33.2 4
4.3 odd 2 126.3.n.c.19.1 4
7.3 odd 6 inner 1008.3.cg.l.577.1 4
12.11 even 2 14.3.d.a.5.2 yes 4
21.2 odd 6 784.3.c.e.97.4 4
21.5 even 6 784.3.c.e.97.1 4
21.11 odd 6 784.3.s.c.129.1 4
21.17 even 6 112.3.s.b.17.2 4
21.20 even 2 784.3.s.c.705.1 4
24.5 odd 2 448.3.s.c.257.1 4
24.11 even 2 448.3.s.d.257.2 4
28.3 even 6 126.3.n.c.73.1 4
28.11 odd 6 882.3.n.b.325.1 4
28.19 even 6 882.3.c.f.685.3 4
28.23 odd 6 882.3.c.f.685.4 4
28.27 even 2 882.3.n.b.19.1 4
60.23 odd 4 350.3.i.a.299.1 8
60.47 odd 4 350.3.i.a.299.4 8
60.59 even 2 350.3.k.a.201.1 4
84.11 even 6 98.3.d.a.31.2 4
84.23 even 6 98.3.b.b.97.1 4
84.47 odd 6 98.3.b.b.97.2 4
84.59 odd 6 14.3.d.a.3.2 4
84.83 odd 2 98.3.d.a.19.2 4
168.59 odd 6 448.3.s.d.129.2 4
168.101 even 6 448.3.s.c.129.1 4
420.59 odd 6 350.3.k.a.101.1 4
420.143 even 12 350.3.i.a.199.4 8
420.227 even 12 350.3.i.a.199.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.3.d.a.3.2 4 84.59 odd 6
14.3.d.a.5.2 yes 4 12.11 even 2
98.3.b.b.97.1 4 84.23 even 6
98.3.b.b.97.2 4 84.47 odd 6
98.3.d.a.19.2 4 84.83 odd 2
98.3.d.a.31.2 4 84.11 even 6
112.3.s.b.17.2 4 21.17 even 6
112.3.s.b.33.2 4 3.2 odd 2
126.3.n.c.19.1 4 4.3 odd 2
126.3.n.c.73.1 4 28.3 even 6
350.3.i.a.199.1 8 420.227 even 12
350.3.i.a.199.4 8 420.143 even 12
350.3.i.a.299.1 8 60.23 odd 4
350.3.i.a.299.4 8 60.47 odd 4
350.3.k.a.101.1 4 420.59 odd 6
350.3.k.a.201.1 4 60.59 even 2
448.3.s.c.129.1 4 168.101 even 6
448.3.s.c.257.1 4 24.5 odd 2
448.3.s.d.129.2 4 168.59 odd 6
448.3.s.d.257.2 4 24.11 even 2
784.3.c.e.97.1 4 21.5 even 6
784.3.c.e.97.4 4 21.2 odd 6
784.3.s.c.129.1 4 21.11 odd 6
784.3.s.c.705.1 4 21.20 even 2
882.3.c.f.685.3 4 28.19 even 6
882.3.c.f.685.4 4 28.23 odd 6
882.3.n.b.19.1 4 28.27 even 2
882.3.n.b.325.1 4 28.11 odd 6
1008.3.cg.l.145.1 4 1.1 even 1 trivial
1008.3.cg.l.577.1 4 7.3 odd 6 inner