Properties

Label 448.2.ba.c.81.9
Level $448$
Weight $2$
Character 448.81
Analytic conductor $3.577$
Analytic rank $0$
Dimension $48$
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] = [448,2,Mod(81,448)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(448, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 9, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("448.81");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 448.ba (of order \(12\), degree \(4\), 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: \(3.57729801055\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 81.9
Character \(\chi\) \(=\) 448.81
Dual form 448.2.ba.c.177.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.60845 - 0.430984i) q^{3} +(1.94900 + 0.522232i) q^{5} +(1.89075 - 1.85069i) q^{7} +(-0.196696 + 0.113563i) q^{9} +O(q^{10})\) \(q+(1.60845 - 0.430984i) q^{3} +(1.94900 + 0.522232i) q^{5} +(1.89075 - 1.85069i) q^{7} +(-0.196696 + 0.113563i) q^{9} +(-1.63411 - 6.09856i) q^{11} +(1.13388 + 1.13388i) q^{13} +3.35995 q^{15} +(-0.960789 + 1.66414i) q^{17} +(-1.63324 + 6.09532i) q^{19} +(2.24357 - 3.79164i) q^{21} +(0.924606 - 0.533821i) q^{23} +(-0.804265 - 0.464342i) q^{25} +(-3.79985 + 3.79985i) q^{27} +(5.08936 + 5.08936i) q^{29} +(0.198293 - 0.343454i) q^{31} +(-5.25677 - 9.10499i) q^{33} +(4.65156 - 2.61958i) q^{35} +(0.327303 + 0.0877006i) q^{37} +(2.31247 + 1.33510i) q^{39} -7.26189i q^{41} +(-1.75565 + 1.75565i) q^{43} +(-0.442666 + 0.118612i) q^{45} +(1.08118 + 1.87265i) q^{47} +(0.149895 - 6.99839i) q^{49} +(-0.828170 + 3.09077i) q^{51} +(0.111394 + 0.415727i) q^{53} -12.7395i q^{55} +10.5079i q^{57} +(2.32453 + 8.67527i) q^{59} +(-2.72673 + 10.1763i) q^{61} +(-0.161735 + 0.578743i) q^{63} +(1.61777 + 2.80206i) q^{65} +(-7.87441 + 2.10994i) q^{67} +(1.25712 - 1.25712i) q^{69} -2.78982i q^{71} +(2.05730 + 1.18779i) q^{73} +(-1.49375 - 0.400248i) q^{75} +(-14.3762 - 8.50666i) q^{77} +(-5.10829 - 8.84782i) q^{79} +(-4.13352 + 7.15947i) q^{81} +(-1.17951 - 1.17951i) q^{83} +(-2.74164 + 2.74164i) q^{85} +(10.3794 + 5.99257i) q^{87} +(11.0470 - 6.37800i) q^{89} +(4.24233 + 0.0454269i) q^{91} +(0.170922 - 0.637891i) q^{93} +(-6.36634 + 11.0268i) q^{95} -2.21148 q^{97} +(1.01399 + 1.01399i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 4 q^{5} + 4 q^{11} - 24 q^{13} + 40 q^{15} + 8 q^{17} + 4 q^{19} - 8 q^{21} + 24 q^{27} + 24 q^{29} - 28 q^{31} + 16 q^{33} - 28 q^{35} - 24 q^{37} + 40 q^{43} - 28 q^{45} + 20 q^{47} - 24 q^{51} - 16 q^{53} + 20 q^{59} + 8 q^{61} + 16 q^{63} + 8 q^{65} - 48 q^{67} - 40 q^{69} + 4 q^{75} - 20 q^{77} + 36 q^{79} + 8 q^{83} - 64 q^{91} + 8 q^{93} + 4 q^{95} - 48 q^{97} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.60845 0.430984i 0.928642 0.248829i 0.237366 0.971420i \(-0.423716\pi\)
0.691275 + 0.722591i \(0.257049\pi\)
\(4\) 0 0
\(5\) 1.94900 + 0.522232i 0.871618 + 0.233549i 0.666787 0.745248i \(-0.267669\pi\)
0.204831 + 0.978797i \(0.434336\pi\)
\(6\) 0 0
\(7\) 1.89075 1.85069i 0.714638 0.699495i
\(8\) 0 0
\(9\) −0.196696 + 0.113563i −0.0655654 + 0.0378542i
\(10\) 0 0
\(11\) −1.63411 6.09856i −0.492701 1.83879i −0.542542 0.840029i \(-0.682538\pi\)
0.0498403 0.998757i \(-0.484129\pi\)
\(12\) 0 0
\(13\) 1.13388 + 1.13388i 0.314480 + 0.314480i 0.846642 0.532162i \(-0.178620\pi\)
−0.532162 + 0.846642i \(0.678620\pi\)
\(14\) 0 0
\(15\) 3.35995 0.867535
\(16\) 0 0
\(17\) −0.960789 + 1.66414i −0.233026 + 0.403612i −0.958697 0.284429i \(-0.908196\pi\)
0.725671 + 0.688041i \(0.241529\pi\)
\(18\) 0 0
\(19\) −1.63324 + 6.09532i −0.374690 + 1.39836i 0.479107 + 0.877756i \(0.340960\pi\)
−0.853797 + 0.520605i \(0.825706\pi\)
\(20\) 0 0
\(21\) 2.24357 3.79164i 0.489588 0.827403i
\(22\) 0 0
\(23\) 0.924606 0.533821i 0.192794 0.111309i −0.400496 0.916298i \(-0.631162\pi\)
0.593290 + 0.804989i \(0.297829\pi\)
\(24\) 0 0
\(25\) −0.804265 0.464342i −0.160853 0.0928685i
\(26\) 0 0
\(27\) −3.79985 + 3.79985i −0.731281 + 0.731281i
\(28\) 0 0
\(29\) 5.08936 + 5.08936i 0.945070 + 0.945070i 0.998568 0.0534979i \(-0.0170370\pi\)
−0.0534979 + 0.998568i \(0.517037\pi\)
\(30\) 0 0
\(31\) 0.198293 0.343454i 0.0356145 0.0616861i −0.847669 0.530526i \(-0.821994\pi\)
0.883283 + 0.468840i \(0.155328\pi\)
\(32\) 0 0
\(33\) −5.25677 9.10499i −0.915086 1.58498i
\(34\) 0 0
\(35\) 4.65156 2.61958i 0.786257 0.442789i
\(36\) 0 0
\(37\) 0.327303 + 0.0877006i 0.0538083 + 0.0144179i 0.285623 0.958342i \(-0.407800\pi\)
−0.231814 + 0.972760i \(0.574466\pi\)
\(38\) 0 0
\(39\) 2.31247 + 1.33510i 0.370291 + 0.213788i
\(40\) 0 0
\(41\) 7.26189i 1.13412i −0.823678 0.567058i \(-0.808081\pi\)
0.823678 0.567058i \(-0.191919\pi\)
\(42\) 0 0
\(43\) −1.75565 + 1.75565i −0.267734 + 0.267734i −0.828187 0.560452i \(-0.810627\pi\)
0.560452 + 0.828187i \(0.310627\pi\)
\(44\) 0 0
\(45\) −0.442666 + 0.118612i −0.0659888 + 0.0176816i
\(46\) 0 0
\(47\) 1.08118 + 1.87265i 0.157706 + 0.273155i 0.934041 0.357166i \(-0.116257\pi\)
−0.776335 + 0.630320i \(0.782924\pi\)
\(48\) 0 0
\(49\) 0.149895 6.99839i 0.0214136 0.999771i
\(50\) 0 0
\(51\) −0.828170 + 3.09077i −0.115967 + 0.432795i
\(52\) 0 0
\(53\) 0.111394 + 0.415727i 0.0153011 + 0.0571045i 0.973154 0.230154i \(-0.0739229\pi\)
−0.957853 + 0.287258i \(0.907256\pi\)
\(54\) 0 0
\(55\) 12.7395i 1.71779i
\(56\) 0 0
\(57\) 10.5079i 1.39181i
\(58\) 0 0
\(59\) 2.32453 + 8.67527i 0.302628 + 1.12942i 0.934968 + 0.354732i \(0.115428\pi\)
−0.632340 + 0.774691i \(0.717905\pi\)
\(60\) 0 0
\(61\) −2.72673 + 10.1763i −0.349122 + 1.30294i 0.538601 + 0.842561i \(0.318953\pi\)
−0.887722 + 0.460379i \(0.847713\pi\)
\(62\) 0 0
\(63\) −0.161735 + 0.578743i −0.0203767 + 0.0729147i
\(64\) 0 0
\(65\) 1.61777 + 2.80206i 0.200660 + 0.347553i
\(66\) 0 0
\(67\) −7.87441 + 2.10994i −0.962012 + 0.257770i −0.705452 0.708758i \(-0.749256\pi\)
−0.256560 + 0.966528i \(0.582589\pi\)
\(68\) 0 0
\(69\) 1.25712 1.25712i 0.151339 0.151339i
\(70\) 0 0
\(71\) 2.78982i 0.331090i −0.986202 0.165545i \(-0.947062\pi\)
0.986202 0.165545i \(-0.0529384\pi\)
\(72\) 0 0
\(73\) 2.05730 + 1.18779i 0.240789 + 0.139020i 0.615539 0.788106i \(-0.288938\pi\)
−0.374750 + 0.927126i \(0.622272\pi\)
\(74\) 0 0
\(75\) −1.49375 0.400248i −0.172483 0.0462167i
\(76\) 0 0
\(77\) −14.3762 8.50666i −1.63832 0.969424i
\(78\) 0 0
\(79\) −5.10829 8.84782i −0.574727 0.995457i −0.996071 0.0885562i \(-0.971775\pi\)
0.421344 0.906901i \(-0.361559\pi\)
\(80\) 0 0
\(81\) −4.13352 + 7.15947i −0.459280 + 0.795496i
\(82\) 0 0
\(83\) −1.17951 1.17951i −0.129468 0.129468i 0.639404 0.768871i \(-0.279181\pi\)
−0.768871 + 0.639404i \(0.779181\pi\)
\(84\) 0 0
\(85\) −2.74164 + 2.74164i −0.297373 + 0.297373i
\(86\) 0 0
\(87\) 10.3794 + 5.99257i 1.11279 + 0.642471i
\(88\) 0 0
\(89\) 11.0470 6.37800i 1.17098 0.676066i 0.217070 0.976156i \(-0.430350\pi\)
0.953911 + 0.300089i \(0.0970165\pi\)
\(90\) 0 0
\(91\) 4.24233 + 0.0454269i 0.444717 + 0.00476204i
\(92\) 0 0
\(93\) 0.170922 0.637891i 0.0177238 0.0661462i
\(94\) 0 0
\(95\) −6.36634 + 11.0268i −0.653173 + 1.13133i
\(96\) 0 0
\(97\) −2.21148 −0.224542 −0.112271 0.993678i \(-0.535813\pi\)
−0.112271 + 0.993678i \(0.535813\pi\)
\(98\) 0 0
\(99\) 1.01399 + 1.01399i 0.101910 + 0.101910i
\(100\) 0 0
\(101\) 1.86231 + 6.95024i 0.185307 + 0.691575i 0.994565 + 0.104121i \(0.0332030\pi\)
−0.809258 + 0.587454i \(0.800130\pi\)
\(102\) 0 0
\(103\) −15.1457 + 8.74438i −1.49235 + 0.861609i −0.999962 0.00876536i \(-0.997210\pi\)
−0.492390 + 0.870375i \(0.663877\pi\)
\(104\) 0 0
\(105\) 6.35283 6.21822i 0.619973 0.606836i
\(106\) 0 0
\(107\) −2.90855 0.779344i −0.281180 0.0753420i 0.115473 0.993311i \(-0.463162\pi\)
−0.396653 + 0.917969i \(0.629828\pi\)
\(108\) 0 0
\(109\) 6.86536 1.83957i 0.657583 0.176199i 0.0854277 0.996344i \(-0.472774\pi\)
0.572155 + 0.820146i \(0.306108\pi\)
\(110\) 0 0
\(111\) 0.564250 0.0535562
\(112\) 0 0
\(113\) −5.96535 −0.561173 −0.280586 0.959829i \(-0.590529\pi\)
−0.280586 + 0.959829i \(0.590529\pi\)
\(114\) 0 0
\(115\) 2.08083 0.557557i 0.194039 0.0519925i
\(116\) 0 0
\(117\) −0.351795 0.0942631i −0.0325234 0.00871463i
\(118\) 0 0
\(119\) 1.26318 + 4.92459i 0.115796 + 0.451437i
\(120\) 0 0
\(121\) −24.9959 + 14.4314i −2.27235 + 1.31194i
\(122\) 0 0
\(123\) −3.12976 11.6804i −0.282201 1.05319i
\(124\) 0 0
\(125\) −8.45884 8.45884i −0.756582 0.756582i
\(126\) 0 0
\(127\) −6.41296 −0.569058 −0.284529 0.958667i \(-0.591837\pi\)
−0.284529 + 0.958667i \(0.591837\pi\)
\(128\) 0 0
\(129\) −2.06723 + 3.58055i −0.182009 + 0.315250i
\(130\) 0 0
\(131\) 3.87298 14.4542i 0.338384 1.26287i −0.561769 0.827294i \(-0.689879\pi\)
0.900154 0.435573i \(-0.143454\pi\)
\(132\) 0 0
\(133\) 8.19250 + 14.5474i 0.710380 + 1.26142i
\(134\) 0 0
\(135\) −9.39029 + 5.42149i −0.808187 + 0.466607i
\(136\) 0 0
\(137\) 1.50928 + 0.871382i 0.128946 + 0.0744472i 0.563086 0.826399i \(-0.309614\pi\)
−0.434139 + 0.900846i \(0.642947\pi\)
\(138\) 0 0
\(139\) −2.84436 + 2.84436i −0.241256 + 0.241256i −0.817370 0.576114i \(-0.804569\pi\)
0.576114 + 0.817370i \(0.304569\pi\)
\(140\) 0 0
\(141\) 2.54611 + 2.54611i 0.214421 + 0.214421i
\(142\) 0 0
\(143\) 5.06214 8.76788i 0.423317 0.733207i
\(144\) 0 0
\(145\) 7.26132 + 12.5770i 0.603020 + 1.04446i
\(146\) 0 0
\(147\) −2.77510 11.3212i −0.228886 0.933757i
\(148\) 0 0
\(149\) −17.7848 4.76543i −1.45699 0.390399i −0.558541 0.829477i \(-0.688639\pi\)
−0.898449 + 0.439077i \(0.855305\pi\)
\(150\) 0 0
\(151\) 5.52437 + 3.18949i 0.449567 + 0.259557i 0.707647 0.706566i \(-0.249757\pi\)
−0.258081 + 0.966123i \(0.583090\pi\)
\(152\) 0 0
\(153\) 0.436439i 0.0352840i
\(154\) 0 0
\(155\) 0.565835 0.565835i 0.0454490 0.0454490i
\(156\) 0 0
\(157\) 17.6177 4.72065i 1.40605 0.376749i 0.525534 0.850773i \(-0.323866\pi\)
0.880512 + 0.474024i \(0.157199\pi\)
\(158\) 0 0
\(159\) 0.358344 + 0.620669i 0.0284185 + 0.0492223i
\(160\) 0 0
\(161\) 0.760264 2.72048i 0.0599172 0.214404i
\(162\) 0 0
\(163\) −2.97338 + 11.0968i −0.232893 + 0.869170i 0.746194 + 0.665729i \(0.231879\pi\)
−0.979087 + 0.203441i \(0.934787\pi\)
\(164\) 0 0
\(165\) −5.49051 20.4909i −0.427435 1.59521i
\(166\) 0 0
\(167\) 21.6693i 1.67682i −0.545040 0.838410i \(-0.683486\pi\)
0.545040 0.838410i \(-0.316514\pi\)
\(168\) 0 0
\(169\) 10.4287i 0.802204i
\(170\) 0 0
\(171\) −0.370949 1.38440i −0.0283672 0.105868i
\(172\) 0 0
\(173\) 3.31175 12.3596i 0.251788 0.939684i −0.718062 0.695979i \(-0.754970\pi\)
0.969849 0.243705i \(-0.0783629\pi\)
\(174\) 0 0
\(175\) −2.38002 + 0.610487i −0.179913 + 0.0461485i
\(176\) 0 0
\(177\) 7.47780 + 12.9519i 0.562066 + 0.973527i
\(178\) 0 0
\(179\) −3.05939 + 0.819762i −0.228670 + 0.0612719i −0.371334 0.928499i \(-0.621100\pi\)
0.142665 + 0.989771i \(0.454433\pi\)
\(180\) 0 0
\(181\) −14.3765 + 14.3765i −1.06860 + 1.06860i −0.0711279 + 0.997467i \(0.522660\pi\)
−0.997467 + 0.0711279i \(0.977340\pi\)
\(182\) 0 0
\(183\) 17.5433i 1.29684i
\(184\) 0 0
\(185\) 0.592113 + 0.341857i 0.0435330 + 0.0251338i
\(186\) 0 0
\(187\) 11.7189 + 3.14006i 0.856969 + 0.229624i
\(188\) 0 0
\(189\) −0.152235 + 14.2169i −0.0110735 + 1.03413i
\(190\) 0 0
\(191\) 6.12089 + 10.6017i 0.442892 + 0.767111i 0.997903 0.0647319i \(-0.0206192\pi\)
−0.555011 + 0.831843i \(0.687286\pi\)
\(192\) 0 0
\(193\) 1.08900 1.88620i 0.0783877 0.135771i −0.824167 0.566347i \(-0.808356\pi\)
0.902554 + 0.430576i \(0.141689\pi\)
\(194\) 0 0
\(195\) 3.80976 + 3.80976i 0.272823 + 0.272823i
\(196\) 0 0
\(197\) 9.97878 9.97878i 0.710959 0.710959i −0.255777 0.966736i \(-0.582331\pi\)
0.966736 + 0.255777i \(0.0823313\pi\)
\(198\) 0 0
\(199\) 9.14271 + 5.27854i 0.648109 + 0.374186i 0.787731 0.616019i \(-0.211255\pi\)
−0.139622 + 0.990205i \(0.544589\pi\)
\(200\) 0 0
\(201\) −11.7563 + 6.78749i −0.829224 + 0.478753i
\(202\) 0 0
\(203\) 19.0415 + 0.203897i 1.33645 + 0.0143108i
\(204\) 0 0
\(205\) 3.79239 14.1534i 0.264872 0.988516i
\(206\) 0 0
\(207\) −0.121244 + 0.210001i −0.00842706 + 0.0145961i
\(208\) 0 0
\(209\) 39.8416 2.75590
\(210\) 0 0
\(211\) −5.20378 5.20378i −0.358243 0.358243i 0.504922 0.863165i \(-0.331521\pi\)
−0.863165 + 0.504922i \(0.831521\pi\)
\(212\) 0 0
\(213\) −1.20237 4.48730i −0.0823849 0.307464i
\(214\) 0 0
\(215\) −4.33862 + 2.50490i −0.295891 + 0.170833i
\(216\) 0 0
\(217\) −0.260703 1.01636i −0.0176977 0.0689953i
\(218\) 0 0
\(219\) 3.82100 + 1.02383i 0.258199 + 0.0691843i
\(220\) 0 0
\(221\) −2.97634 + 0.797507i −0.200210 + 0.0536461i
\(222\) 0 0
\(223\) 22.3888 1.49926 0.749632 0.661855i \(-0.230230\pi\)
0.749632 + 0.661855i \(0.230230\pi\)
\(224\) 0 0
\(225\) 0.210928 0.0140619
\(226\) 0 0
\(227\) 17.9753 4.81647i 1.19306 0.319680i 0.392967 0.919552i \(-0.371448\pi\)
0.800096 + 0.599872i \(0.204782\pi\)
\(228\) 0 0
\(229\) 8.12426 + 2.17689i 0.536866 + 0.143853i 0.517057 0.855951i \(-0.327027\pi\)
0.0198093 + 0.999804i \(0.493694\pi\)
\(230\) 0 0
\(231\) −26.7898 7.48664i −1.76264 0.492585i
\(232\) 0 0
\(233\) 14.9278 8.61859i 0.977955 0.564623i 0.0763032 0.997085i \(-0.475688\pi\)
0.901652 + 0.432462i \(0.142355\pi\)
\(234\) 0 0
\(235\) 1.12925 + 4.21442i 0.0736642 + 0.274919i
\(236\) 0 0
\(237\) −12.0297 12.0297i −0.781414 0.781414i
\(238\) 0 0
\(239\) 0.572679 0.0370435 0.0185218 0.999828i \(-0.494104\pi\)
0.0185218 + 0.999828i \(0.494104\pi\)
\(240\) 0 0
\(241\) 5.89318 10.2073i 0.379613 0.657510i −0.611393 0.791327i \(-0.709390\pi\)
0.991006 + 0.133818i \(0.0427237\pi\)
\(242\) 0 0
\(243\) 0.609557 2.27490i 0.0391031 0.145935i
\(244\) 0 0
\(245\) 3.94693 13.5616i 0.252160 0.866417i
\(246\) 0 0
\(247\) −8.76321 + 5.05944i −0.557590 + 0.321925i
\(248\) 0 0
\(249\) −2.40553 1.38883i −0.152444 0.0880137i
\(250\) 0 0
\(251\) 5.57539 5.57539i 0.351916 0.351916i −0.508906 0.860822i \(-0.669950\pi\)
0.860822 + 0.508906i \(0.169950\pi\)
\(252\) 0 0
\(253\) −4.76645 4.76645i −0.299664 0.299664i
\(254\) 0 0
\(255\) −3.22820 + 5.59141i −0.202158 + 0.350148i
\(256\) 0 0
\(257\) −14.5328 25.1715i −0.906528 1.57015i −0.818853 0.574004i \(-0.805390\pi\)
−0.0876753 0.996149i \(-0.527944\pi\)
\(258\) 0 0
\(259\) 0.781156 0.439916i 0.0485387 0.0273351i
\(260\) 0 0
\(261\) −1.57902 0.423097i −0.0977388 0.0261890i
\(262\) 0 0
\(263\) 15.3142 + 8.84163i 0.944311 + 0.545198i 0.891309 0.453396i \(-0.149788\pi\)
0.0530021 + 0.998594i \(0.483121\pi\)
\(264\) 0 0
\(265\) 0.868424i 0.0533469i
\(266\) 0 0
\(267\) 15.0198 15.0198i 0.919198 0.919198i
\(268\) 0 0
\(269\) 14.4268 3.86566i 0.879620 0.235693i 0.209377 0.977835i \(-0.432856\pi\)
0.670243 + 0.742142i \(0.266190\pi\)
\(270\) 0 0
\(271\) −6.93172 12.0061i −0.421072 0.729319i 0.574972 0.818173i \(-0.305013\pi\)
−0.996045 + 0.0888543i \(0.971679\pi\)
\(272\) 0 0
\(273\) 6.84317 1.75531i 0.414168 0.106236i
\(274\) 0 0
\(275\) −1.51757 + 5.66364i −0.0915128 + 0.341531i
\(276\) 0 0
\(277\) −0.597472 2.22980i −0.0358986 0.133975i 0.945651 0.325184i \(-0.105426\pi\)
−0.981550 + 0.191208i \(0.938759\pi\)
\(278\) 0 0
\(279\) 0.0900747i 0.00539263i
\(280\) 0 0
\(281\) 0.680351i 0.0405863i 0.999794 + 0.0202932i \(0.00645996\pi\)
−0.999794 + 0.0202932i \(0.993540\pi\)
\(282\) 0 0
\(283\) −0.0985120 0.367652i −0.00585593 0.0218546i 0.962936 0.269730i \(-0.0869344\pi\)
−0.968792 + 0.247875i \(0.920268\pi\)
\(284\) 0 0
\(285\) −5.48759 + 20.4799i −0.325056 + 1.21313i
\(286\) 0 0
\(287\) −13.4395 13.7304i −0.793309 0.810482i
\(288\) 0 0
\(289\) 6.65377 + 11.5247i 0.391398 + 0.677921i
\(290\) 0 0
\(291\) −3.55707 + 0.953115i −0.208519 + 0.0558726i
\(292\) 0 0
\(293\) 7.49220 7.49220i 0.437699 0.437699i −0.453538 0.891237i \(-0.649838\pi\)
0.891237 + 0.453538i \(0.149838\pi\)
\(294\) 0 0
\(295\) 18.1220i 1.05510i
\(296\) 0 0
\(297\) 29.3829 + 16.9643i 1.70497 + 0.984366i
\(298\) 0 0
\(299\) 1.65367 + 0.443101i 0.0956345 + 0.0256252i
\(300\) 0 0
\(301\) −0.0703375 + 6.56867i −0.00405418 + 0.378612i
\(302\) 0 0
\(303\) 5.99089 + 10.3765i 0.344168 + 0.596116i
\(304\) 0 0
\(305\) −10.6288 + 18.4096i −0.608602 + 1.05413i
\(306\) 0 0
\(307\) 6.27988 + 6.27988i 0.358412 + 0.358412i 0.863227 0.504816i \(-0.168439\pi\)
−0.504816 + 0.863227i \(0.668439\pi\)
\(308\) 0 0
\(309\) −20.5925 + 20.5925i −1.17147 + 1.17147i
\(310\) 0 0
\(311\) −8.55685 4.94030i −0.485215 0.280139i 0.237372 0.971419i \(-0.423714\pi\)
−0.722587 + 0.691280i \(0.757047\pi\)
\(312\) 0 0
\(313\) −14.8734 + 8.58714i −0.840692 + 0.485374i −0.857499 0.514485i \(-0.827983\pi\)
0.0168075 + 0.999859i \(0.494650\pi\)
\(314\) 0 0
\(315\) −0.617459 + 1.04350i −0.0347899 + 0.0587948i
\(316\) 0 0
\(317\) −5.49870 + 20.5214i −0.308838 + 1.15260i 0.620754 + 0.784006i \(0.286827\pi\)
−0.929591 + 0.368592i \(0.879840\pi\)
\(318\) 0 0
\(319\) 22.7212 39.3543i 1.27214 2.20342i
\(320\) 0 0
\(321\) −5.01416 −0.279863
\(322\) 0 0
\(323\) −8.57424 8.57424i −0.477084 0.477084i
\(324\) 0 0
\(325\) −0.385429 1.43844i −0.0213798 0.0797904i
\(326\) 0 0
\(327\) 10.2498 5.91773i 0.566815 0.327251i
\(328\) 0 0
\(329\) 5.50994 + 1.53980i 0.303773 + 0.0848921i
\(330\) 0 0
\(331\) −23.3748 6.26326i −1.28479 0.344260i −0.449113 0.893475i \(-0.648260\pi\)
−0.835681 + 0.549215i \(0.814927\pi\)
\(332\) 0 0
\(333\) −0.0743388 + 0.0199190i −0.00407374 + 0.00109156i
\(334\) 0 0
\(335\) −16.4491 −0.898709
\(336\) 0 0
\(337\) −4.26739 −0.232460 −0.116230 0.993222i \(-0.537081\pi\)
−0.116230 + 0.993222i \(0.537081\pi\)
\(338\) 0 0
\(339\) −9.59499 + 2.57097i −0.521128 + 0.139636i
\(340\) 0 0
\(341\) −2.41861 0.648063i −0.130975 0.0350946i
\(342\) 0 0
\(343\) −12.6684 13.5096i −0.684032 0.729452i
\(344\) 0 0
\(345\) 3.10663 1.79361i 0.167255 0.0965648i
\(346\) 0 0
\(347\) 0.0139833 + 0.0521865i 0.000750664 + 0.00280152i 0.966300 0.257418i \(-0.0828717\pi\)
−0.965549 + 0.260220i \(0.916205\pi\)
\(348\) 0 0
\(349\) −15.4928 15.4928i −0.829309 0.829309i 0.158112 0.987421i \(-0.449459\pi\)
−0.987421 + 0.158112i \(0.949459\pi\)
\(350\) 0 0
\(351\) −8.61710 −0.459947
\(352\) 0 0
\(353\) −8.38161 + 14.5174i −0.446108 + 0.772682i −0.998129 0.0611484i \(-0.980524\pi\)
0.552020 + 0.833831i \(0.313857\pi\)
\(354\) 0 0
\(355\) 1.45693 5.43735i 0.0773259 0.288584i
\(356\) 0 0
\(357\) 4.15420 + 7.37657i 0.219863 + 0.390410i
\(358\) 0 0
\(359\) 29.8777 17.2499i 1.57689 0.910415i 0.581595 0.813479i \(-0.302429\pi\)
0.995291 0.0969365i \(-0.0309044\pi\)
\(360\) 0 0
\(361\) −18.0310 10.4102i −0.948998 0.547904i
\(362\) 0 0
\(363\) −33.9851 + 33.9851i −1.78375 + 1.78375i
\(364\) 0 0
\(365\) 3.38938 + 3.38938i 0.177408 + 0.177408i
\(366\) 0 0
\(367\) −10.2644 + 17.7785i −0.535799 + 0.928032i 0.463325 + 0.886189i \(0.346656\pi\)
−0.999124 + 0.0418433i \(0.986677\pi\)
\(368\) 0 0
\(369\) 0.824679 + 1.42839i 0.0429311 + 0.0743588i
\(370\) 0 0
\(371\) 0.980000 + 0.579882i 0.0508791 + 0.0301060i
\(372\) 0 0
\(373\) 15.2773 + 4.09353i 0.791027 + 0.211955i 0.631641 0.775261i \(-0.282382\pi\)
0.159386 + 0.987216i \(0.449049\pi\)
\(374\) 0 0
\(375\) −17.2513 9.96003i −0.890853 0.514334i
\(376\) 0 0
\(377\) 11.5414i 0.594412i
\(378\) 0 0
\(379\) −11.2717 + 11.2717i −0.578987 + 0.578987i −0.934624 0.355637i \(-0.884264\pi\)
0.355637 + 0.934624i \(0.384264\pi\)
\(380\) 0 0
\(381\) −10.3150 + 2.76388i −0.528451 + 0.141598i
\(382\) 0 0
\(383\) 5.14594 + 8.91303i 0.262945 + 0.455434i 0.967023 0.254688i \(-0.0819728\pi\)
−0.704078 + 0.710123i \(0.748640\pi\)
\(384\) 0 0
\(385\) −23.5768 24.0872i −1.20158 1.22760i
\(386\) 0 0
\(387\) 0.145954 0.544707i 0.00741925 0.0276890i
\(388\) 0 0
\(389\) 5.30513 + 19.7990i 0.268981 + 1.00385i 0.959769 + 0.280792i \(0.0905972\pi\)
−0.690788 + 0.723058i \(0.742736\pi\)
\(390\) 0 0
\(391\) 2.05156i 0.103752i
\(392\) 0 0
\(393\) 24.9181i 1.25695i
\(394\) 0 0
\(395\) −5.33543 19.9121i −0.268454 1.00189i
\(396\) 0 0
\(397\) −2.02632 + 7.56231i −0.101698 + 0.379542i −0.997950 0.0640041i \(-0.979613\pi\)
0.896252 + 0.443546i \(0.146280\pi\)
\(398\) 0 0
\(399\) 19.4469 + 19.8679i 0.973565 + 0.994640i
\(400\) 0 0
\(401\) −7.09985 12.2973i −0.354549 0.614098i 0.632491 0.774567i \(-0.282032\pi\)
−0.987041 + 0.160470i \(0.948699\pi\)
\(402\) 0 0
\(403\) 0.614273 0.164594i 0.0305991 0.00819901i
\(404\) 0 0
\(405\) −11.7951 + 11.7951i −0.586104 + 0.586104i
\(406\) 0 0
\(407\) 2.13939i 0.106046i
\(408\) 0 0
\(409\) −22.8759 13.2074i −1.13114 0.653065i −0.186920 0.982375i \(-0.559851\pi\)
−0.944222 + 0.329310i \(0.893184\pi\)
\(410\) 0 0
\(411\) 2.80316 + 0.751104i 0.138270 + 0.0370492i
\(412\) 0 0
\(413\) 20.4503 + 12.1008i 1.00630 + 0.595442i
\(414\) 0 0
\(415\) −1.68288 2.91483i −0.0826092 0.143083i
\(416\) 0 0
\(417\) −3.34915 + 5.80091i −0.164009 + 0.284072i
\(418\) 0 0
\(419\) 15.6893 + 15.6893i 0.766471 + 0.766471i 0.977483 0.211012i \(-0.0676759\pi\)
−0.211012 + 0.977483i \(0.567676\pi\)
\(420\) 0 0
\(421\) 25.7068 25.7068i 1.25287 1.25287i 0.298444 0.954427i \(-0.403532\pi\)
0.954427 0.298444i \(-0.0964675\pi\)
\(422\) 0 0
\(423\) −0.425327 0.245563i −0.0206801 0.0119397i
\(424\) 0 0
\(425\) 1.54546 0.892270i 0.0749657 0.0432815i
\(426\) 0 0
\(427\) 13.6776 + 24.2872i 0.661905 + 1.17534i
\(428\) 0 0
\(429\) 4.36340 16.2844i 0.210667 0.786220i
\(430\) 0 0
\(431\) −12.3981 + 21.4741i −0.597194 + 1.03437i 0.396039 + 0.918234i \(0.370384\pi\)
−0.993233 + 0.116137i \(0.962949\pi\)
\(432\) 0 0
\(433\) 5.22863 0.251272 0.125636 0.992076i \(-0.459903\pi\)
0.125636 + 0.992076i \(0.459903\pi\)
\(434\) 0 0
\(435\) 17.1000 + 17.1000i 0.819881 + 0.819881i
\(436\) 0 0
\(437\) 1.74371 + 6.50762i 0.0834131 + 0.311302i
\(438\) 0 0
\(439\) 19.1771 11.0719i 0.915273 0.528433i 0.0331491 0.999450i \(-0.489446\pi\)
0.882124 + 0.471017i \(0.156113\pi\)
\(440\) 0 0
\(441\) 0.765272 + 1.39358i 0.0364415 + 0.0663610i
\(442\) 0 0
\(443\) −21.8067 5.84309i −1.03607 0.277614i −0.299585 0.954070i \(-0.596848\pi\)
−0.736483 + 0.676456i \(0.763515\pi\)
\(444\) 0 0
\(445\) 24.8614 6.66159i 1.17854 0.315790i
\(446\) 0 0
\(447\) −30.6599 −1.45017
\(448\) 0 0
\(449\) −36.3678 −1.71630 −0.858152 0.513396i \(-0.828387\pi\)
−0.858152 + 0.513396i \(0.828387\pi\)
\(450\) 0 0
\(451\) −44.2871 + 11.8667i −2.08540 + 0.558781i
\(452\) 0 0
\(453\) 10.2603 + 2.74924i 0.482072 + 0.129171i
\(454\) 0 0
\(455\) 8.24456 + 2.30402i 0.386511 + 0.108014i
\(456\) 0 0
\(457\) 21.5807 12.4596i 1.00950 0.582837i 0.0984570 0.995141i \(-0.468609\pi\)
0.911046 + 0.412304i \(0.135276\pi\)
\(458\) 0 0
\(459\) −2.67261 9.97431i −0.124747 0.465561i
\(460\) 0 0
\(461\) −1.60588 1.60588i −0.0747933 0.0747933i 0.668721 0.743514i \(-0.266842\pi\)
−0.743514 + 0.668721i \(0.766842\pi\)
\(462\) 0 0
\(463\) 14.8176 0.688634 0.344317 0.938853i \(-0.388110\pi\)
0.344317 + 0.938853i \(0.388110\pi\)
\(464\) 0 0
\(465\) 0.666254 1.15399i 0.0308968 0.0535148i
\(466\) 0 0
\(467\) 3.21315 11.9916i 0.148687 0.554907i −0.850877 0.525365i \(-0.823929\pi\)
0.999564 0.0295414i \(-0.00940469\pi\)
\(468\) 0 0
\(469\) −10.9837 + 18.5625i −0.507181 + 0.857135i
\(470\) 0 0
\(471\) 26.3028 15.1859i 1.21197 0.699730i
\(472\) 0 0
\(473\) 13.5759 + 7.83804i 0.624220 + 0.360393i
\(474\) 0 0
\(475\) 4.14387 4.14387i 0.190134 0.190134i
\(476\) 0 0
\(477\) −0.0691218 0.0691218i −0.00316487 0.00316487i
\(478\) 0 0
\(479\) −1.02709 + 1.77897i −0.0469288 + 0.0812831i −0.888536 0.458808i \(-0.848277\pi\)
0.841607 + 0.540091i \(0.181610\pi\)
\(480\) 0 0
\(481\) 0.271679 + 0.470563i 0.0123875 + 0.0214558i
\(482\) 0 0
\(483\) 0.0503645 4.70344i 0.00229166 0.214014i
\(484\) 0 0
\(485\) −4.31018 1.15491i −0.195715 0.0524417i
\(486\) 0 0
\(487\) 35.4045 + 20.4408i 1.60433 + 0.926261i 0.990607 + 0.136740i \(0.0436625\pi\)
0.613724 + 0.789521i \(0.289671\pi\)
\(488\) 0 0
\(489\) 19.1302i 0.865098i
\(490\) 0 0
\(491\) 0.278015 0.278015i 0.0125466 0.0125466i −0.700806 0.713352i \(-0.747176\pi\)
0.713352 + 0.700806i \(0.247176\pi\)
\(492\) 0 0
\(493\) −13.3592 + 3.57958i −0.601667 + 0.161216i
\(494\) 0 0
\(495\) 1.44673 + 2.50580i 0.0650255 + 0.112628i
\(496\) 0 0
\(497\) −5.16309 5.27486i −0.231596 0.236610i
\(498\) 0 0
\(499\) 3.19039 11.9067i 0.142822 0.533018i −0.857021 0.515281i \(-0.827687\pi\)
0.999843 0.0177363i \(-0.00564595\pi\)
\(500\) 0 0
\(501\) −9.33912 34.8541i −0.417241 1.55717i
\(502\) 0 0
\(503\) 0.367839i 0.0164011i −0.999966 0.00820057i \(-0.997390\pi\)
0.999966 0.00820057i \(-0.00261035\pi\)
\(504\) 0 0
\(505\) 14.5186i 0.646068i
\(506\) 0 0
\(507\) −4.49459 16.7740i −0.199612 0.744960i
\(508\) 0 0
\(509\) −2.09820 + 7.83060i −0.0930012 + 0.347085i −0.996709 0.0810649i \(-0.974168\pi\)
0.903708 + 0.428150i \(0.140835\pi\)
\(510\) 0 0
\(511\) 6.08808 1.56162i 0.269321 0.0690822i
\(512\) 0 0
\(513\) −16.9552 29.3673i −0.748591 1.29660i
\(514\) 0 0
\(515\) −34.0855 + 9.13319i −1.50199 + 0.402457i
\(516\) 0 0
\(517\) 9.65374 9.65374i 0.424571 0.424571i
\(518\) 0 0
\(519\) 21.3072i 0.935282i
\(520\) 0 0
\(521\) −11.5215 6.65193i −0.504766 0.291427i 0.225914 0.974147i \(-0.427463\pi\)
−0.730679 + 0.682721i \(0.760797\pi\)
\(522\) 0 0
\(523\) 27.4536 + 7.35616i 1.20046 + 0.321663i 0.803013 0.595962i \(-0.203229\pi\)
0.397448 + 0.917625i \(0.369896\pi\)
\(524\) 0 0
\(525\) −3.56504 + 2.00769i −0.155591 + 0.0876229i
\(526\) 0 0
\(527\) 0.381036 + 0.659973i 0.0165982 + 0.0287489i
\(528\) 0 0
\(529\) −10.9301 + 18.9314i −0.475220 + 0.823106i
\(530\) 0 0
\(531\) −1.44241 1.44241i −0.0625954 0.0625954i
\(532\) 0 0
\(533\) 8.23408 8.23408i 0.356657 0.356657i
\(534\) 0 0
\(535\) −5.26176 3.03788i −0.227486 0.131339i
\(536\) 0 0
\(537\) −4.56759 + 2.63710i −0.197106 + 0.113799i
\(538\) 0 0
\(539\) −42.9251 + 10.5220i −1.84892 + 0.453213i
\(540\) 0 0
\(541\) −4.75802 + 17.7572i −0.204563 + 0.763441i 0.785019 + 0.619472i \(0.212653\pi\)
−0.989582 + 0.143969i \(0.954013\pi\)
\(542\) 0 0
\(543\) −16.9279 + 29.3199i −0.726445 + 1.25824i
\(544\) 0 0
\(545\) 14.3413 0.614312
\(546\) 0 0
\(547\) 22.9801 + 22.9801i 0.982558 + 0.982558i 0.999850 0.0172930i \(-0.00550479\pi\)
−0.0172930 + 0.999850i \(0.505505\pi\)
\(548\) 0 0
\(549\) −0.619309 2.31129i −0.0264315 0.0986436i
\(550\) 0 0
\(551\) −39.3334 + 22.7091i −1.67566 + 0.967442i
\(552\) 0 0
\(553\) −26.0331 7.27518i −1.10704 0.309372i
\(554\) 0 0
\(555\) 1.09972 + 0.294670i 0.0466806 + 0.0125080i
\(556\) 0 0
\(557\) 4.50327 1.20665i 0.190810 0.0511273i −0.162149 0.986766i \(-0.551842\pi\)
0.352958 + 0.935639i \(0.385176\pi\)
\(558\) 0 0
\(559\) −3.98138 −0.168394
\(560\) 0 0
\(561\) 20.2026 0.852954
\(562\) 0 0
\(563\) 4.04301 1.08332i 0.170393 0.0456566i −0.172614 0.984990i \(-0.555221\pi\)
0.343007 + 0.939333i \(0.388555\pi\)
\(564\) 0 0
\(565\) −11.6264 3.11530i −0.489128 0.131061i
\(566\) 0 0
\(567\) 5.43448 + 21.1866i 0.228227 + 0.889755i
\(568\) 0 0
\(569\) 3.88173 2.24111i 0.162730 0.0939524i −0.416423 0.909171i \(-0.636717\pi\)
0.579154 + 0.815218i \(0.303383\pi\)
\(570\) 0 0
\(571\) 0.126176 + 0.470896i 0.00528031 + 0.0197064i 0.968516 0.248952i \(-0.0800863\pi\)
−0.963235 + 0.268659i \(0.913420\pi\)
\(572\) 0 0
\(573\) 14.4143 + 14.4143i 0.602167 + 0.602167i
\(574\) 0 0
\(575\) −0.991504 −0.0413486
\(576\) 0 0
\(577\) 5.31982 9.21420i 0.221467 0.383592i −0.733787 0.679380i \(-0.762249\pi\)
0.955254 + 0.295788i \(0.0955821\pi\)
\(578\) 0 0
\(579\) 0.938680 3.50320i 0.0390102 0.145588i
\(580\) 0 0
\(581\) −4.41305 0.0472550i −0.183084 0.00196047i
\(582\) 0 0
\(583\) 2.35331 1.35868i 0.0974641 0.0562709i
\(584\) 0 0
\(585\) −0.636420 0.367437i −0.0263127 0.0151917i
\(586\) 0 0
\(587\) 13.2861 13.2861i 0.548376 0.548376i −0.377595 0.925971i \(-0.623249\pi\)
0.925971 + 0.377595i \(0.123249\pi\)
\(588\) 0 0
\(589\) 1.76960 + 1.76960i 0.0729151 + 0.0729151i
\(590\) 0 0
\(591\) 11.7497 20.3511i 0.483319 0.837133i
\(592\) 0 0
\(593\) 0.198497 + 0.343806i 0.00815128 + 0.0141184i 0.870072 0.492924i \(-0.164072\pi\)
−0.861921 + 0.507043i \(0.830739\pi\)
\(594\) 0 0
\(595\) −0.109840 + 10.2577i −0.00450298 + 0.420524i
\(596\) 0 0
\(597\) 16.9806 + 4.54994i 0.694970 + 0.186217i
\(598\) 0 0
\(599\) −11.9718 6.91190i −0.489153 0.282412i 0.235070 0.971978i \(-0.424468\pi\)
−0.724223 + 0.689566i \(0.757801\pi\)
\(600\) 0 0
\(601\) 8.73396i 0.356266i −0.984006 0.178133i \(-0.942994\pi\)
0.984006 0.178133i \(-0.0570057\pi\)
\(602\) 0 0
\(603\) 1.30926 1.30926i 0.0533170 0.0533170i
\(604\) 0 0
\(605\) −56.2535 + 15.0731i −2.28703 + 0.612807i
\(606\) 0 0
\(607\) −14.3937 24.9305i −0.584220 1.01190i −0.994972 0.100152i \(-0.968067\pi\)
0.410752 0.911747i \(-0.365266\pi\)
\(608\) 0 0
\(609\) 30.7153 7.87864i 1.24465 0.319259i
\(610\) 0 0
\(611\) −0.897436 + 3.34928i −0.0363064 + 0.135497i
\(612\) 0 0
\(613\) 9.13486 + 34.0918i 0.368954 + 1.37695i 0.861981 + 0.506940i \(0.169223\pi\)
−0.493028 + 0.870014i \(0.664110\pi\)
\(614\) 0 0
\(615\) 24.3996i 0.983886i
\(616\) 0 0
\(617\) 33.4612i 1.34710i 0.739143 + 0.673548i \(0.235231\pi\)
−0.739143 + 0.673548i \(0.764769\pi\)
\(618\) 0 0
\(619\) 2.41362 + 9.00777i 0.0970118 + 0.362053i 0.997317 0.0732067i \(-0.0233233\pi\)
−0.900305 + 0.435260i \(0.856657\pi\)
\(620\) 0 0
\(621\) −1.48492 + 5.54180i −0.0595878 + 0.222385i
\(622\) 0 0
\(623\) 9.08349 32.5038i 0.363922 1.30224i
\(624\) 0 0
\(625\) −9.74706 16.8824i −0.389882 0.675296i
\(626\) 0 0
\(627\) 64.0834 17.1711i 2.55924 0.685747i
\(628\) 0 0
\(629\) −0.460415 + 0.460415i −0.0183580 + 0.0183580i
\(630\) 0 0
\(631\) 22.2587i 0.886105i −0.896496 0.443053i \(-0.853896\pi\)
0.896496 0.443053i \(-0.146104\pi\)
\(632\) 0 0
\(633\) −10.6128 6.12730i −0.421821 0.243538i
\(634\) 0 0
\(635\) −12.4988 3.34905i −0.496001 0.132903i
\(636\) 0 0
\(637\) 8.10527 7.76534i 0.321142 0.307674i
\(638\) 0 0
\(639\) 0.316819 + 0.548747i 0.0125332 + 0.0217081i
\(640\) 0 0
\(641\) 4.13758 7.16649i 0.163424 0.283059i −0.772670 0.634808i \(-0.781079\pi\)
0.936095 + 0.351748i \(0.114413\pi\)
\(642\) 0 0
\(643\) −4.19175 4.19175i −0.165307 0.165307i 0.619606 0.784913i \(-0.287292\pi\)
−0.784913 + 0.619606i \(0.787292\pi\)
\(644\) 0 0
\(645\) −5.89890 + 5.89890i −0.232269 + 0.232269i
\(646\) 0 0
\(647\) −18.2428 10.5325i −0.717199 0.414075i 0.0965221 0.995331i \(-0.469228\pi\)
−0.813721 + 0.581256i \(0.802561\pi\)
\(648\) 0 0
\(649\) 49.1081 28.3526i 1.92766 1.11294i
\(650\) 0 0
\(651\) −0.857366 1.52242i −0.0336028 0.0596683i
\(652\) 0 0
\(653\) 4.43173 16.5394i 0.173427 0.647239i −0.823387 0.567480i \(-0.807918\pi\)
0.996814 0.0797585i \(-0.0254149\pi\)
\(654\) 0 0
\(655\) 15.0969 26.1485i 0.589883 1.02171i
\(656\) 0 0
\(657\) −0.539552 −0.0210499
\(658\) 0 0
\(659\) −19.9513 19.9513i −0.777192 0.777192i 0.202161 0.979352i \(-0.435204\pi\)
−0.979352 + 0.202161i \(0.935204\pi\)
\(660\) 0 0
\(661\) −5.55822 20.7436i −0.216190 0.806831i −0.985744 0.168250i \(-0.946188\pi\)
0.769555 0.638581i \(-0.220478\pi\)
\(662\) 0 0
\(663\) −4.44359 + 2.56551i −0.172575 + 0.0996361i
\(664\) 0 0
\(665\) 8.37005 + 32.6311i 0.324577 + 1.26538i
\(666\) 0 0
\(667\) 7.42246 + 1.98884i 0.287399 + 0.0770083i
\(668\) 0 0
\(669\) 36.0114 9.64922i 1.39228 0.373060i
\(670\) 0 0
\(671\) 66.5165 2.56784
\(672\) 0 0
\(673\) 21.0339 0.810796 0.405398 0.914140i \(-0.367133\pi\)
0.405398 + 0.914140i \(0.367133\pi\)
\(674\) 0 0
\(675\) 4.82051 1.29165i 0.185542 0.0497157i
\(676\) 0 0
\(677\) 6.02033 + 1.61314i 0.231380 + 0.0619982i 0.372646 0.927974i \(-0.378451\pi\)
−0.141266 + 0.989972i \(0.545117\pi\)
\(678\) 0 0
\(679\) −4.18137 + 4.09277i −0.160466 + 0.157066i
\(680\) 0 0
\(681\) 26.8367 15.4942i 1.02838 0.593737i
\(682\) 0 0
\(683\) 5.78001 + 21.5713i 0.221166 + 0.825402i 0.983904 + 0.178695i \(0.0571876\pi\)
−0.762739 + 0.646707i \(0.776146\pi\)
\(684\) 0 0
\(685\) 2.48651 + 2.48651i 0.0950048 + 0.0950048i
\(686\) 0 0
\(687\) 14.0057 0.534351
\(688\) 0 0
\(689\) −0.345076 + 0.597689i −0.0131463 + 0.0227701i
\(690\) 0 0
\(691\) −9.94413 + 37.1120i −0.378292 + 1.41181i 0.470182 + 0.882570i \(0.344188\pi\)
−0.848474 + 0.529237i \(0.822478\pi\)
\(692\) 0 0
\(693\) 3.79379 + 0.0406240i 0.144114 + 0.00154318i
\(694\) 0 0
\(695\) −7.02907 + 4.05824i −0.266628 + 0.153938i
\(696\) 0 0
\(697\) 12.0848 + 6.97715i 0.457743 + 0.264278i
\(698\) 0 0
\(699\) 20.2963 20.2963i 0.767676 0.767676i
\(700\) 0 0
\(701\) 1.40129 + 1.40129i 0.0529259 + 0.0529259i 0.733074 0.680148i \(-0.238085\pi\)
−0.680148 + 0.733074i \(0.738085\pi\)
\(702\) 0 0
\(703\) −1.06913 + 1.85178i −0.0403229 + 0.0698413i
\(704\) 0 0
\(705\) 3.63270 + 6.29202i 0.136815 + 0.236971i
\(706\) 0 0
\(707\) 16.3839 + 9.69463i 0.616181 + 0.364604i
\(708\) 0 0
\(709\) −8.42034 2.25622i −0.316232 0.0847342i 0.0972117 0.995264i \(-0.469008\pi\)
−0.413444 + 0.910530i \(0.635674\pi\)
\(710\) 0 0
\(711\) 2.00956 + 1.16022i 0.0753645 + 0.0435117i
\(712\) 0 0
\(713\) 0.423412i 0.0158569i
\(714\) 0 0
\(715\) 14.4450 14.4450i 0.540211 0.540211i
\(716\) 0 0
\(717\) 0.921129 0.246816i 0.0344002 0.00921750i
\(718\) 0 0
\(719\) 13.3330 + 23.0934i 0.497236 + 0.861239i 0.999995 0.00318810i \(-0.00101481\pi\)
−0.502758 + 0.864427i \(0.667681\pi\)
\(720\) 0 0
\(721\) −12.4537 + 44.5635i −0.463799 + 1.65963i
\(722\) 0 0
\(723\) 5.07974 18.9578i 0.188917 0.705050i
\(724\) 0 0
\(725\) −1.72999 6.45640i −0.0642501 0.239785i
\(726\) 0 0
\(727\) 37.7224i 1.39905i 0.714610 + 0.699523i \(0.246604\pi\)
−0.714610 + 0.699523i \(0.753396\pi\)
\(728\) 0 0
\(729\) 28.7229i 1.06381i
\(730\) 0 0
\(731\) −1.23483 4.60846i −0.0456719 0.170450i
\(732\) 0 0
\(733\) 5.88050 21.9463i 0.217201 0.810606i −0.768179 0.640235i \(-0.778837\pi\)
0.985380 0.170371i \(-0.0544965\pi\)
\(734\) 0 0
\(735\) 0.503639 23.5142i 0.0185770 0.867336i
\(736\) 0 0
\(737\) 25.7352 + 44.5747i 0.947969 + 1.64193i
\(738\) 0 0
\(739\) −25.3304 + 6.78727i −0.931795 + 0.249674i −0.692620 0.721303i \(-0.743544\pi\)
−0.239175 + 0.970977i \(0.576877\pi\)
\(740\) 0 0
\(741\) −11.9147 + 11.9147i −0.437697 + 0.437697i
\(742\) 0 0
\(743\) 20.7110i 0.759812i 0.925025 + 0.379906i \(0.124044\pi\)
−0.925025 + 0.379906i \(0.875956\pi\)
\(744\) 0 0
\(745\) −32.1739 18.5756i −1.17876 0.680558i
\(746\) 0 0
\(747\) 0.365952 + 0.0980566i 0.0133895 + 0.00358770i
\(748\) 0 0
\(749\) −6.94168 + 3.90928i −0.253643 + 0.142842i
\(750\) 0 0
\(751\) −7.73865 13.4037i −0.282387 0.489109i 0.689585 0.724205i \(-0.257793\pi\)
−0.971972 + 0.235096i \(0.924460\pi\)
\(752\) 0 0
\(753\) 6.56486 11.3707i 0.239237 0.414370i
\(754\) 0 0
\(755\) 9.10132 + 9.10132i 0.331231 + 0.331231i
\(756\) 0 0
\(757\) 18.4631 18.4631i 0.671051 0.671051i −0.286907 0.957958i \(-0.592627\pi\)
0.957958 + 0.286907i \(0.0926272\pi\)
\(758\) 0 0
\(759\) −9.72088 5.61235i −0.352846 0.203715i
\(760\) 0 0
\(761\) −11.1420 + 6.43283i −0.403897 + 0.233190i −0.688164 0.725555i \(-0.741583\pi\)
0.284267 + 0.958745i \(0.408250\pi\)
\(762\) 0 0
\(763\) 9.57624 16.1838i 0.346683 0.585894i
\(764\) 0 0
\(765\) 0.227923 0.850618i 0.00824056 0.0307542i
\(766\) 0 0
\(767\) −7.20094 + 12.4724i −0.260011 + 0.450352i
\(768\) 0 0
\(769\) −16.5676 −0.597443 −0.298722 0.954340i \(-0.596560\pi\)
−0.298722 + 0.954340i \(0.596560\pi\)
\(770\) 0 0
\(771\) −34.2238 34.2238i −1.23254 1.23254i
\(772\) 0 0
\(773\) −12.6807 47.3250i −0.456093 1.70216i −0.684856 0.728679i \(-0.740135\pi\)
0.228763 0.973482i \(-0.426532\pi\)
\(774\) 0 0
\(775\) −0.318960 + 0.184152i −0.0114574 + 0.00661492i
\(776\) 0 0
\(777\) 1.06686 1.04425i 0.0382733 0.0374623i
\(778\) 0 0
\(779\) 44.2635 + 11.8604i 1.58591 + 0.424942i
\(780\) 0 0
\(781\) −17.0139 + 4.55886i −0.608805 + 0.163129i
\(782\) 0 0
\(783\) −38.6776 −1.38222
\(784\) 0 0
\(785\) 36.8021 1.31352
\(786\) 0 0
\(787\) 5.05999 1.35582i 0.180369 0.0483298i −0.167504 0.985871i \(-0.553571\pi\)
0.347873 + 0.937542i \(0.386904\pi\)
\(788\) 0 0
\(789\) 28.4427 + 7.62121i 1.01259 + 0.271322i
\(790\) 0 0
\(791\) −11.2790 + 11.0400i −0.401035 + 0.392537i
\(792\) 0 0
\(793\) −14.6304 + 8.44687i −0.519541 + 0.299957i
\(794\) 0 0
\(795\) 0.374277 + 1.39682i 0.0132742 + 0.0495401i
\(796\) 0 0
\(797\) 20.4204 + 20.4204i 0.723329 + 0.723329i 0.969282 0.245953i \(-0.0791009\pi\)
−0.245953 + 0.969282i \(0.579101\pi\)
\(798\) 0 0
\(799\) −4.15514 −0.146998
\(800\) 0 0
\(801\) −1.44860 + 2.50906i −0.0511839 + 0.0886532i
\(802\) 0 0
\(803\) 3.88193 14.4876i 0.136990 0.511255i
\(804\) 0 0
\(805\) 2.90248 4.90518i 0.102299 0.172885i
\(806\) 0 0
\(807\) 21.5389 12.4355i 0.758205 0.437750i
\(808\) 0 0
\(809\) −33.6734 19.4413i −1.18389 0.683521i −0.226981 0.973899i \(-0.572886\pi\)
−0.956912 + 0.290378i \(0.906219\pi\)
\(810\) 0 0
\(811\) −12.4718 + 12.4718i −0.437945 + 0.437945i −0.891320 0.453375i \(-0.850220\pi\)
0.453375 + 0.891320i \(0.350220\pi\)
\(812\) 0 0
\(813\) −16.3238 16.3238i −0.572501 0.572501i
\(814\) 0 0
\(815\) −11.5902 + 20.0749i −0.405988 + 0.703192i
\(816\) 0 0
\(817\) −7.83387 13.5687i −0.274072 0.474707i
\(818\) 0 0
\(819\) −0.839609 + 0.472835i −0.0293383 + 0.0165222i
\(820\) 0 0
\(821\) −18.4979 4.95650i −0.645581 0.172983i −0.0788511 0.996886i \(-0.525125\pi\)
−0.566730 + 0.823903i \(0.691792\pi\)
\(822\) 0 0
\(823\) −8.96748 5.17738i −0.312587 0.180472i 0.335497 0.942041i \(-0.391096\pi\)
−0.648083 + 0.761569i \(0.724429\pi\)
\(824\) 0 0
\(825\) 9.76376i 0.339931i
\(826\) 0 0
\(827\) 9.65786 9.65786i 0.335837 0.335837i −0.518961 0.854798i \(-0.673681\pi\)
0.854798 + 0.518961i \(0.173681\pi\)
\(828\) 0 0
\(829\) 25.6983 6.88583i 0.892538 0.239155i 0.216729 0.976232i \(-0.430461\pi\)
0.675809 + 0.737077i \(0.263795\pi\)
\(830\) 0 0
\(831\) −1.92201 3.32902i −0.0666739 0.115483i
\(832\) 0 0
\(833\) 11.5023 + 6.97343i 0.398530 + 0.241615i
\(834\) 0 0
\(835\) 11.3164 42.2334i 0.391620 1.46155i
\(836\) 0 0
\(837\) 0.551588 + 2.05855i 0.0190657 + 0.0711540i
\(838\) 0 0
\(839\) 46.4429i 1.60339i 0.597736 + 0.801693i \(0.296067\pi\)
−0.597736 + 0.801693i \(0.703933\pi\)
\(840\) 0 0
\(841\) 22.8031i 0.786315i
\(842\) 0 0
\(843\) 0.293220 + 1.09431i 0.0100990 + 0.0376902i
\(844\) 0 0
\(845\) 5.44618 20.3254i 0.187354 0.699216i
\(846\) 0 0
\(847\) −20.5531 + 73.5459i −0.706211 + 2.52707i
\(848\) 0 0
\(849\) −0.316904 0.548894i −0.0108761 0.0188380i
\(850\) 0 0
\(851\) 0.349443 0.0936330i 0.0119788 0.00320970i
\(852\) 0 0
\(853\) −31.3013 + 31.3013i −1.07174 + 1.07174i −0.0745177 + 0.997220i \(0.523742\pi\)
−0.997220 + 0.0745177i \(0.976258\pi\)
\(854\) 0 0
\(855\) 2.89191i 0.0989014i
\(856\) 0 0
\(857\) 22.8393 + 13.1863i 0.780175 + 0.450434i 0.836492 0.547979i \(-0.184602\pi\)
−0.0563171 + 0.998413i \(0.517936\pi\)
\(858\) 0 0
\(859\) 2.91867 + 0.782055i 0.0995837 + 0.0266834i 0.308267 0.951300i \(-0.400251\pi\)
−0.208683 + 0.977983i \(0.566918\pi\)
\(860\) 0 0
\(861\) −27.5344 16.2926i −0.938371 0.555250i
\(862\) 0 0
\(863\) 3.50456 + 6.07008i 0.119297 + 0.206628i 0.919489 0.393115i \(-0.128603\pi\)
−0.800192 + 0.599743i \(0.795269\pi\)
\(864\) 0 0
\(865\) 12.9092 22.3594i 0.438925 0.760241i
\(866\) 0 0
\(867\) 15.6692 + 15.6692i 0.532155 + 0.532155i
\(868\) 0 0
\(869\) −45.6115 + 45.6115i −1.54726 + 1.54726i
\(870\) 0 0
\(871\) −11.3210 6.53619i −0.383598 0.221470i
\(872\) 0 0
\(873\) 0.434991 0.251142i 0.0147222 0.00849987i
\(874\) 0 0
\(875\) −31.6483 0.338890i −1.06991 0.0114566i
\(876\) 0 0
\(877\) 10.6267 39.6594i 0.358838 1.33920i −0.516748 0.856138i \(-0.672857\pi\)
0.875585 0.483063i \(-0.160476\pi\)
\(878\) 0 0
\(879\) 8.82185 15.2799i 0.297554 0.515378i
\(880\) 0 0
\(881\) −13.6166 −0.458755 −0.229377 0.973338i \(-0.573669\pi\)
−0.229377 + 0.973338i \(0.573669\pi\)
\(882\) 0 0
\(883\) −35.2238 35.2238i −1.18537 1.18537i −0.978332 0.207042i \(-0.933616\pi\)
−0.207042 0.978332i \(-0.566384\pi\)
\(884\) 0 0
\(885\) 7.81030 + 29.1484i 0.262540 + 0.979814i
\(886\) 0 0
\(887\) 5.44911 3.14604i 0.182963 0.105634i −0.405721 0.913997i \(-0.632980\pi\)
0.588684 + 0.808363i \(0.299646\pi\)
\(888\) 0 0
\(889\) −12.1253 + 11.8684i −0.406670 + 0.398053i
\(890\) 0 0
\(891\) 50.4171 + 13.5092i 1.68904 + 0.452576i
\(892\) 0 0
\(893\) −13.1802 + 3.53163i −0.441060 + 0.118182i
\(894\) 0 0
\(895\) −6.39085 −0.213623
\(896\) 0 0
\(897\) 2.85083 0.0951864
\(898\) 0 0
\(899\) 2.75714 0.738774i 0.0919559 0.0246395i
\(900\) 0 0
\(901\) −0.798852 0.214052i −0.0266136 0.00713110i
\(902\) 0 0
\(903\) 2.71786 + 10.5957i 0.0904447 + 0.352604i
\(904\) 0 0
\(905\) −35.5276 + 20.5118i −1.18098 + 0.681837i
\(906\) 0 0
\(907\) −11.6035 43.3049i −0.385289 1.43792i −0.837711 0.546113i \(-0.816107\pi\)
0.452423 0.891804i \(-0.350560\pi\)
\(908\) 0 0
\(909\) −1.15560 1.15560i −0.0383288 0.0383288i
\(910\) 0 0
\(911\) −42.8973 −1.42125 −0.710625 0.703571i \(-0.751588\pi\)
−0.710625 + 0.703571i \(0.751588\pi\)
\(912\) 0 0
\(913\) −5.26585 + 9.12073i −0.174274 + 0.301852i
\(914\) 0 0
\(915\) −9.16166 + 34.1918i −0.302875 + 1.13035i
\(916\) 0 0
\(917\) −19.4273 34.4970i −0.641547 1.13919i
\(918\) 0 0
\(919\) −26.2242 + 15.1405i −0.865056 + 0.499440i −0.865702 0.500560i \(-0.833128\pi\)
0.000646343 1.00000i \(0.499794\pi\)
\(920\) 0 0
\(921\) 12.8074 + 7.39438i 0.422019 + 0.243653i
\(922\) 0 0
\(923\) 3.16330 3.16330i 0.104121 0.104121i
\(924\) 0 0
\(925\) −0.222515 0.222515i −0.00731626 0.00731626i
\(926\) 0 0
\(927\) 1.98607 3.43997i 0.0652311 0.112984i
\(928\) 0 0
\(929\) 6.93334 + 12.0089i 0.227475 + 0.393999i 0.957059 0.289892i \(-0.0936195\pi\)
−0.729584 + 0.683891i \(0.760286\pi\)
\(930\) 0 0
\(931\) 42.4126 + 12.3437i 1.39002 + 0.404548i
\(932\) 0 0
\(933\) −15.8925 4.25838i −0.520297 0.139413i
\(934\) 0 0
\(935\) 21.2002 + 12.2399i 0.693321 + 0.400289i
\(936\) 0 0
\(937\) 46.7544i 1.52740i 0.645572 + 0.763699i \(0.276619\pi\)
−0.645572 + 0.763699i \(0.723381\pi\)
\(938\) 0 0
\(939\) −20.2222 + 20.2222i −0.659927 + 0.659927i
\(940\) 0 0
\(941\) 8.04407 2.15540i 0.262229 0.0702641i −0.125309 0.992118i \(-0.539992\pi\)
0.387538 + 0.921854i \(0.373326\pi\)
\(942\) 0 0
\(943\) −3.87655 6.71439i −0.126238 0.218651i
\(944\) 0 0
\(945\) −7.72123 + 27.6292i −0.251172 + 0.898778i
\(946\) 0 0
\(947\) −1.89988 + 7.09044i −0.0617378 + 0.230408i −0.989900 0.141767i \(-0.954722\pi\)
0.928162 + 0.372176i \(0.121388\pi\)
\(948\) 0 0
\(949\) 0.985926 + 3.67953i 0.0320045 + 0.119442i
\(950\) 0 0
\(951\) 35.3776i 1.14720i
\(952\) 0 0
\(953\) 41.3553i 1.33963i −0.742528 0.669815i \(-0.766373\pi\)
0.742528 0.669815i \(-0.233627\pi\)
\(954\) 0 0
\(955\) 6.39305 + 23.8592i 0.206874 + 0.772065i
\(956\) 0 0
\(957\) 19.5850 73.0921i 0.633093 2.36273i
\(958\) 0 0
\(959\) 4.46633 1.14564i 0.144225 0.0369945i
\(960\) 0 0
\(961\) 15.4214 + 26.7106i 0.497463 + 0.861632i
\(962\) 0 0
\(963\) 0.660606 0.177009i 0.0212877 0.00570403i
\(964\) 0 0
\(965\) 3.10748 3.10748i 0.100033 0.100033i
\(966\) 0 0
\(967\) 40.5984i 1.30556i −0.757549 0.652778i \(-0.773603\pi\)
0.757549 0.652778i \(-0.226397\pi\)
\(968\) 0 0
\(969\) −17.4866 10.0959i −0.561752 0.324328i
\(970\) 0 0
\(971\) −31.4132 8.41714i −1.00810 0.270119i −0.283263 0.959042i \(-0.591417\pi\)
−0.724834 + 0.688924i \(0.758084\pi\)
\(972\) 0 0
\(973\) −0.113955 + 10.6420i −0.00365323 + 0.341168i
\(974\) 0 0
\(975\) −1.23989 2.14755i −0.0397083 0.0687768i
\(976\) 0 0
\(977\) 8.34286 14.4503i 0.266912 0.462305i −0.701151 0.713013i \(-0.747330\pi\)
0.968063 + 0.250708i \(0.0806635\pi\)
\(978\) 0 0
\(979\) −56.9486 56.9486i −1.82009 1.82009i
\(980\) 0 0
\(981\) −1.14148 + 1.14148i −0.0364448 + 0.0364448i
\(982\) 0 0
\(983\) 10.1999 + 5.88892i 0.325326 + 0.187827i 0.653764 0.756698i \(-0.273189\pi\)
−0.328438 + 0.944526i \(0.606522\pi\)
\(984\) 0 0
\(985\) 24.6599 14.2374i 0.785728 0.453640i
\(986\) 0 0
\(987\) 9.52612 + 0.102006i 0.303220 + 0.00324688i
\(988\) 0 0
\(989\) −0.686082 + 2.56049i −0.0218161 + 0.0814189i
\(990\) 0 0
\(991\) −15.8872 + 27.5175i −0.504675 + 0.874122i 0.495311 + 0.868716i \(0.335054\pi\)
−0.999985 + 0.00540613i \(0.998279\pi\)
\(992\) 0 0
\(993\) −40.2967 −1.27878
\(994\) 0 0
\(995\) 15.0625 + 15.0625i 0.477513 + 0.477513i
\(996\) 0 0
\(997\) −0.309461 1.15492i −0.00980073 0.0365768i 0.960852 0.277061i \(-0.0893604\pi\)
−0.970653 + 0.240484i \(0.922694\pi\)
\(998\) 0 0
\(999\) −1.57695 + 0.910453i −0.0498925 + 0.0288055i
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 448.2.ba.c.81.9 48
4.3 odd 2 112.2.w.c.109.2 yes 48
7.2 even 3 inner 448.2.ba.c.401.4 48
8.3 odd 2 896.2.ba.f.417.9 48
8.5 even 2 896.2.ba.e.417.4 48
16.3 odd 4 896.2.ba.f.865.4 48
16.5 even 4 inner 448.2.ba.c.305.4 48
16.11 odd 4 112.2.w.c.53.10 yes 48
16.13 even 4 896.2.ba.e.865.9 48
28.3 even 6 784.2.m.k.589.6 24
28.11 odd 6 784.2.m.j.589.6 24
28.19 even 6 784.2.x.o.765.10 48
28.23 odd 6 112.2.w.c.93.10 yes 48
28.27 even 2 784.2.x.o.557.2 48
56.37 even 6 896.2.ba.e.289.9 48
56.51 odd 6 896.2.ba.f.289.4 48
112.11 odd 12 784.2.m.j.197.6 24
112.27 even 4 784.2.x.o.165.10 48
112.37 even 12 inner 448.2.ba.c.177.9 48
112.51 odd 12 896.2.ba.f.737.9 48
112.59 even 12 784.2.m.k.197.6 24
112.75 even 12 784.2.x.o.373.2 48
112.93 even 12 896.2.ba.e.737.4 48
112.107 odd 12 112.2.w.c.37.2 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.w.c.37.2 48 112.107 odd 12
112.2.w.c.53.10 yes 48 16.11 odd 4
112.2.w.c.93.10 yes 48 28.23 odd 6
112.2.w.c.109.2 yes 48 4.3 odd 2
448.2.ba.c.81.9 48 1.1 even 1 trivial
448.2.ba.c.177.9 48 112.37 even 12 inner
448.2.ba.c.305.4 48 16.5 even 4 inner
448.2.ba.c.401.4 48 7.2 even 3 inner
784.2.m.j.197.6 24 112.11 odd 12
784.2.m.j.589.6 24 28.11 odd 6
784.2.m.k.197.6 24 112.59 even 12
784.2.m.k.589.6 24 28.3 even 6
784.2.x.o.165.10 48 112.27 even 4
784.2.x.o.373.2 48 112.75 even 12
784.2.x.o.557.2 48 28.27 even 2
784.2.x.o.765.10 48 28.19 even 6
896.2.ba.e.289.9 48 56.37 even 6
896.2.ba.e.417.4 48 8.5 even 2
896.2.ba.e.737.4 48 112.93 even 12
896.2.ba.e.865.9 48 16.13 even 4
896.2.ba.f.289.4 48 56.51 odd 6
896.2.ba.f.417.9 48 8.3 odd 2
896.2.ba.f.737.9 48 112.51 odd 12
896.2.ba.f.865.4 48 16.3 odd 4