Properties

Label 336.7.bh.e.241.4
Level $336$
Weight $7$
Character 336.241
Analytic conductor $77.298$
Analytic rank $0$
Dimension $8$
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] = [336,7,Mod(145,336)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(336, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("336.145");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 336.bh (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: \(77.2981720963\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 82x^{6} - 165x^{5} + 5606x^{4} - 7807x^{3} + 102447x^{2} + 132594x + 1162084 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{10}\cdot 3^{4}\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 241.4
Root \(3.42459 - 5.93157i\) of defining polynomial
Character \(\chi\) \(=\) 336.241
Dual form 336.7.bh.e.145.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(13.5000 + 7.79423i) q^{3} +(201.438 - 116.300i) q^{5} +(-184.358 + 289.242i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})\) \(q+(13.5000 + 7.79423i) q^{3} +(201.438 - 116.300i) q^{5} +(-184.358 + 289.242i) q^{7} +(121.500 + 210.444i) q^{9} +(460.090 - 796.899i) q^{11} +536.864i q^{13} +3625.88 q^{15} +(2610.93 + 1507.42i) q^{17} +(-7374.63 + 4257.75i) q^{19} +(-4743.25 + 2467.85i) q^{21} +(10535.7 + 18248.4i) q^{23} +(19239.0 - 33322.9i) q^{25} +3788.00i q^{27} -3910.02 q^{29} +(19930.8 + 11507.1i) q^{31} +(12422.4 - 7172.09i) q^{33} +(-3497.70 + 79705.3i) q^{35} +(22097.3 + 38273.6i) q^{37} +(-4184.44 + 7247.66i) q^{39} +56637.1i q^{41} +120736. q^{43} +(48949.4 + 28261.0i) q^{45} +(-131321. + 75818.3i) q^{47} +(-49673.4 - 106648. i) q^{49} +(23498.4 + 40700.4i) q^{51} +(115683. - 200370. i) q^{53} -214034. i q^{55} -132743. q^{57} +(7463.43 + 4309.02i) q^{59} +(68573.4 - 39590.9i) q^{61} +(-83268.9 - 3654.08i) q^{63} +(62437.4 + 108145. i) q^{65} +(156755. - 271508. i) q^{67} +328471. i q^{69} +212805. q^{71} +(-198776. - 114764. i) q^{73} +(519453. - 299906. i) q^{75} +(145676. + 279992. i) q^{77} +(-379148. - 656704. i) q^{79} +(-29524.5 + 51137.9i) q^{81} +161117. i q^{83} +701254. q^{85} +(-52785.2 - 30475.6i) q^{87} +(-486510. + 280886. i) q^{89} +(-155284. - 98975.1i) q^{91} +(179377. + 310691. i) q^{93} +(-990354. + 1.71534e6i) q^{95} +199575. i q^{97} +223604. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 108 q^{3} - 42 q^{5} + 92 q^{7} + 972 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 108 q^{3} - 42 q^{5} + 92 q^{7} + 972 q^{9} - 126 q^{11} - 756 q^{15} - 2532 q^{17} - 19998 q^{19} - 5886 q^{21} + 15648 q^{23} + 42698 q^{25} + 129468 q^{29} + 42096 q^{31} - 3402 q^{33} - 73524 q^{35} + 9866 q^{37} - 29106 q^{39} + 71764 q^{43} - 10206 q^{45} - 86988 q^{47} + 314588 q^{49} - 22788 q^{51} + 391710 q^{53} - 359964 q^{57} + 553434 q^{59} - 1009104 q^{61} - 181278 q^{63} + 589452 q^{65} - 229762 q^{67} - 208488 q^{71} - 1249290 q^{73} + 1152846 q^{75} + 1009566 q^{77} - 693808 q^{79} - 236196 q^{81} - 1302600 q^{85} + 1747818 q^{87} - 1414692 q^{89} + 766410 q^{91} + 378864 q^{93} - 3047568 q^{95} - 61236 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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
\(3\) 13.5000 + 7.79423i 0.500000 + 0.288675i
\(4\) 0 0
\(5\) 201.438 116.300i 1.61150 0.930402i 0.622482 0.782634i \(-0.286124\pi\)
0.989022 0.147768i \(-0.0472088\pi\)
\(6\) 0 0
\(7\) −184.358 + 289.242i −0.537486 + 0.843272i
\(8\) 0 0
\(9\) 121.500 + 210.444i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 460.090 796.899i 0.345672 0.598722i −0.639803 0.768539i \(-0.720984\pi\)
0.985476 + 0.169817i \(0.0543175\pi\)
\(12\) 0 0
\(13\) 536.864i 0.244362i 0.992508 + 0.122181i \(0.0389889\pi\)
−0.992508 + 0.122181i \(0.961011\pi\)
\(14\) 0 0
\(15\) 3625.88 1.07434
\(16\) 0 0
\(17\) 2610.93 + 1507.42i 0.531433 + 0.306823i 0.741600 0.670843i \(-0.234067\pi\)
−0.210167 + 0.977666i \(0.567401\pi\)
\(18\) 0 0
\(19\) −7374.63 + 4257.75i −1.07518 + 0.620753i −0.929591 0.368592i \(-0.879840\pi\)
−0.145585 + 0.989346i \(0.546506\pi\)
\(20\) 0 0
\(21\) −4743.25 + 2467.85i −0.512175 + 0.266477i
\(22\) 0 0
\(23\) 10535.7 + 18248.4i 0.865924 + 1.49982i 0.866127 + 0.499825i \(0.166602\pi\)
−0.000202610 1.00000i \(0.500064\pi\)
\(24\) 0 0
\(25\) 19239.0 33322.9i 1.23130 2.13267i
\(26\) 0 0
\(27\) 3788.00i 0.192450i
\(28\) 0 0
\(29\) −3910.02 −0.160319 −0.0801594 0.996782i \(-0.525543\pi\)
−0.0801594 + 0.996782i \(0.525543\pi\)
\(30\) 0 0
\(31\) 19930.8 + 11507.1i 0.669021 + 0.386260i 0.795706 0.605683i \(-0.207100\pi\)
−0.126684 + 0.991943i \(0.540434\pi\)
\(32\) 0 0
\(33\) 12422.4 7172.09i 0.345672 0.199574i
\(34\) 0 0
\(35\) −3497.70 + 79705.3i −0.0815790 + 1.85902i
\(36\) 0 0
\(37\) 22097.3 + 38273.6i 0.436249 + 0.755605i 0.997397 0.0721108i \(-0.0229735\pi\)
−0.561148 + 0.827715i \(0.689640\pi\)
\(38\) 0 0
\(39\) −4184.44 + 7247.66i −0.0705413 + 0.122181i
\(40\) 0 0
\(41\) 56637.1i 0.821768i 0.911688 + 0.410884i \(0.134780\pi\)
−0.911688 + 0.410884i \(0.865220\pi\)
\(42\) 0 0
\(43\) 120736. 1.51856 0.759280 0.650764i \(-0.225551\pi\)
0.759280 + 0.650764i \(0.225551\pi\)
\(44\) 0 0
\(45\) 48949.4 + 28261.0i 0.537168 + 0.310134i
\(46\) 0 0
\(47\) −131321. + 75818.3i −1.26486 + 0.730265i −0.974010 0.226505i \(-0.927270\pi\)
−0.290845 + 0.956770i \(0.593937\pi\)
\(48\) 0 0
\(49\) −49673.4 106648.i −0.422217 0.906495i
\(50\) 0 0
\(51\) 23498.4 + 40700.4i 0.177144 + 0.306823i
\(52\) 0 0
\(53\) 115683. 200370.i 0.777041 1.34587i −0.156600 0.987662i \(-0.550053\pi\)
0.933640 0.358212i \(-0.116613\pi\)
\(54\) 0 0
\(55\) 214034.i 1.28646i
\(56\) 0 0
\(57\) −132743. −0.716784
\(58\) 0 0
\(59\) 7463.43 + 4309.02i 0.0363398 + 0.0209808i 0.518060 0.855344i \(-0.326654\pi\)
−0.481720 + 0.876325i \(0.659988\pi\)
\(60\) 0 0
\(61\) 68573.4 39590.9i 0.302111 0.174424i −0.341280 0.939962i \(-0.610860\pi\)
0.643391 + 0.765538i \(0.277527\pi\)
\(62\) 0 0
\(63\) −83268.9 3654.08i −0.333013 0.0146136i
\(64\) 0 0
\(65\) 62437.4 + 108145.i 0.227355 + 0.393791i
\(66\) 0 0
\(67\) 156755. 271508.i 0.521192 0.902730i −0.478505 0.878085i \(-0.658821\pi\)
0.999696 0.0246453i \(-0.00784565\pi\)
\(68\) 0 0
\(69\) 328471.i 0.999883i
\(70\) 0 0
\(71\) 212805. 0.594576 0.297288 0.954788i \(-0.403918\pi\)
0.297288 + 0.954788i \(0.403918\pi\)
\(72\) 0 0
\(73\) −198776. 114764.i −0.510971 0.295009i 0.222262 0.974987i \(-0.428656\pi\)
−0.733233 + 0.679978i \(0.761989\pi\)
\(74\) 0 0
\(75\) 519453. 299906.i 1.23130 0.710889i
\(76\) 0 0
\(77\) 145676. + 279992.i 0.319092 + 0.613301i
\(78\) 0 0
\(79\) −379148. 656704.i −0.769003 1.33195i −0.938104 0.346353i \(-0.887420\pi\)
0.169101 0.985599i \(-0.445914\pi\)
\(80\) 0 0
\(81\) −29524.5 + 51137.9i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 161117.i 0.281779i 0.990025 + 0.140889i \(0.0449962\pi\)
−0.990025 + 0.140889i \(0.955004\pi\)
\(84\) 0 0
\(85\) 701254. 1.14187
\(86\) 0 0
\(87\) −52785.2 30475.6i −0.0801594 0.0462801i
\(88\) 0 0
\(89\) −486510. + 280886.i −0.690115 + 0.398438i −0.803655 0.595095i \(-0.797114\pi\)
0.113540 + 0.993533i \(0.463781\pi\)
\(90\) 0 0
\(91\) −155284. 98975.1i −0.206064 0.131341i
\(92\) 0 0
\(93\) 179377. + 310691.i 0.223007 + 0.386260i
\(94\) 0 0
\(95\) −990354. + 1.71534e6i −1.15510 + 2.00069i
\(96\) 0 0
\(97\) 199575.i 0.218670i 0.994005 + 0.109335i \(0.0348722\pi\)
−0.994005 + 0.109335i \(0.965128\pi\)
\(98\) 0 0
\(99\) 223604. 0.230448
\(100\) 0 0
\(101\) 958861. + 553599.i 0.930661 + 0.537318i 0.887021 0.461730i \(-0.152771\pi\)
0.0436406 + 0.999047i \(0.486104\pi\)
\(102\) 0 0
\(103\) 1.19877e6 692111.i 1.09705 0.633380i 0.161602 0.986856i \(-0.448334\pi\)
0.935443 + 0.353476i \(0.115001\pi\)
\(104\) 0 0
\(105\) −668460. + 1.04876e6i −0.577441 + 0.905958i
\(106\) 0 0
\(107\) 786950. + 1.36304e6i 0.642386 + 1.11264i 0.984899 + 0.173131i \(0.0553885\pi\)
−0.342513 + 0.939513i \(0.611278\pi\)
\(108\) 0 0
\(109\) −1.05699e6 + 1.83076e6i −0.816191 + 1.41368i 0.0922779 + 0.995733i \(0.470585\pi\)
−0.908469 + 0.417952i \(0.862748\pi\)
\(110\) 0 0
\(111\) 688926.i 0.503736i
\(112\) 0 0
\(113\) 2.61150e6 1.80990 0.904951 0.425516i \(-0.139907\pi\)
0.904951 + 0.425516i \(0.139907\pi\)
\(114\) 0 0
\(115\) 4.24458e6 + 2.45061e6i 2.79088 + 1.61132i
\(116\) 0 0
\(117\) −112980. + 65229.0i −0.0705413 + 0.0407271i
\(118\) 0 0
\(119\) −917356. + 477287.i −0.544373 + 0.283230i
\(120\) 0 0
\(121\) 462415. + 800926.i 0.261021 + 0.452102i
\(122\) 0 0
\(123\) −441443. + 764601.i −0.237224 + 0.410884i
\(124\) 0 0
\(125\) 5.31562e6i 2.72160i
\(126\) 0 0
\(127\) −2.99941e6 −1.46428 −0.732141 0.681154i \(-0.761479\pi\)
−0.732141 + 0.681154i \(0.761479\pi\)
\(128\) 0 0
\(129\) 1.62994e6 + 941046.i 0.759280 + 0.438371i
\(130\) 0 0
\(131\) 36359.2 20992.0i 0.0161734 0.00933769i −0.491892 0.870656i \(-0.663694\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(132\) 0 0
\(133\) 128051. 2.91801e6i 0.0544286 1.24031i
\(134\) 0 0
\(135\) 440545. + 763046.i 0.179056 + 0.310134i
\(136\) 0 0
\(137\) 1.40463e6 2.43290e6i 0.546263 0.946155i −0.452264 0.891884i \(-0.649383\pi\)
0.998526 0.0542704i \(-0.0172833\pi\)
\(138\) 0 0
\(139\) 224325.i 0.0835281i 0.999128 + 0.0417640i \(0.0132978\pi\)
−0.999128 + 0.0417640i \(0.986702\pi\)
\(140\) 0 0
\(141\) −2.36378e6 −0.843237
\(142\) 0 0
\(143\) 427827. + 247006.i 0.146305 + 0.0844693i
\(144\) 0 0
\(145\) −787626. + 454736.i −0.258354 + 0.149161i
\(146\) 0 0
\(147\) 160650. 1.82692e6i 0.0505743 0.575131i
\(148\) 0 0
\(149\) 2.03342e6 + 3.52199e6i 0.614707 + 1.06470i 0.990436 + 0.137974i \(0.0440591\pi\)
−0.375729 + 0.926730i \(0.622608\pi\)
\(150\) 0 0
\(151\) −562185. + 973733.i −0.163286 + 0.282819i −0.936045 0.351880i \(-0.885543\pi\)
0.772759 + 0.634699i \(0.218876\pi\)
\(152\) 0 0
\(153\) 732607.i 0.204549i
\(154\) 0 0
\(155\) 5.35310e6 1.43751
\(156\) 0 0
\(157\) 5.12354e6 + 2.95807e6i 1.32395 + 0.764382i 0.984356 0.176191i \(-0.0563778\pi\)
0.339592 + 0.940573i \(0.389711\pi\)
\(158\) 0 0
\(159\) 3.12345e6 1.80333e6i 0.777041 0.448625i
\(160\) 0 0
\(161\) −7.22054e6 316858.i −1.73018 0.0759255i
\(162\) 0 0
\(163\) −2.01094e6 3.48305e6i −0.464340 0.804260i 0.534832 0.844959i \(-0.320375\pi\)
−0.999171 + 0.0406983i \(0.987042\pi\)
\(164\) 0 0
\(165\) 1.66823e6 2.88946e6i 0.371368 0.643229i
\(166\) 0 0
\(167\) 5.97767e6i 1.28346i −0.766930 0.641730i \(-0.778217\pi\)
0.766930 0.641730i \(-0.221783\pi\)
\(168\) 0 0
\(169\) 4.53859e6 0.940287
\(170\) 0 0
\(171\) −1.79204e6 1.03463e6i −0.358392 0.206918i
\(172\) 0 0
\(173\) 1.81172e6 1.04600e6i 0.349907 0.202019i −0.314737 0.949179i \(-0.601916\pi\)
0.664644 + 0.747160i \(0.268583\pi\)
\(174\) 0 0
\(175\) 6.09154e6 + 1.17081e7i 1.13661 + 2.18460i
\(176\) 0 0
\(177\) 67170.9 + 116343.i 0.0121133 + 0.0209808i
\(178\) 0 0
\(179\) −2.05976e6 + 3.56761e6i −0.359135 + 0.622040i −0.987817 0.155623i \(-0.950262\pi\)
0.628682 + 0.777663i \(0.283595\pi\)
\(180\) 0 0
\(181\) 651520.i 0.109873i 0.998490 + 0.0549366i \(0.0174957\pi\)
−0.998490 + 0.0549366i \(0.982504\pi\)
\(182\) 0 0
\(183\) 1.23432e6 0.201407
\(184\) 0 0
\(185\) 8.90247e6 + 5.13984e6i 1.40603 + 0.811773i
\(186\) 0 0
\(187\) 2.40253e6 1.38710e6i 0.367403 0.212120i
\(188\) 0 0
\(189\) −1.09565e6 698347.i −0.162288 0.103439i
\(190\) 0 0
\(191\) −3.48252e6 6.03189e6i −0.499796 0.865673i 0.500204 0.865908i \(-0.333258\pi\)
−1.00000 0.000235235i \(0.999925\pi\)
\(192\) 0 0
\(193\) −6.65162e6 + 1.15209e7i −0.925242 + 1.60257i −0.134070 + 0.990972i \(0.542805\pi\)
−0.791172 + 0.611594i \(0.790529\pi\)
\(194\) 0 0
\(195\) 1.94661e6i 0.262527i
\(196\) 0 0
\(197\) −5.32260e6 −0.696186 −0.348093 0.937460i \(-0.613171\pi\)
−0.348093 + 0.937460i \(0.613171\pi\)
\(198\) 0 0
\(199\) 4.54482e6 + 2.62395e6i 0.576710 + 0.332963i 0.759825 0.650128i \(-0.225285\pi\)
−0.183115 + 0.983091i \(0.558618\pi\)
\(200\) 0 0
\(201\) 4.23239e6 2.44357e6i 0.521192 0.300910i
\(202\) 0 0
\(203\) 720842. 1.13094e6i 0.0861692 0.135192i
\(204\) 0 0
\(205\) 6.58691e6 + 1.14089e7i 0.764575 + 1.32428i
\(206\) 0 0
\(207\) −2.56017e6 + 4.43435e6i −0.288641 + 0.499942i
\(208\) 0 0
\(209\) 7.83579e6i 0.858309i
\(210\) 0 0
\(211\) −522144. −0.0555831 −0.0277916 0.999614i \(-0.508847\pi\)
−0.0277916 + 0.999614i \(0.508847\pi\)
\(212\) 0 0
\(213\) 2.87287e6 + 1.65865e6i 0.297288 + 0.171639i
\(214\) 0 0
\(215\) 2.43209e7 1.40417e7i 2.44717 1.41287i
\(216\) 0 0
\(217\) −7.00273e6 + 3.64342e6i −0.685312 + 0.356558i
\(218\) 0 0
\(219\) −1.78899e6 3.09862e6i −0.170324 0.295009i
\(220\) 0 0
\(221\) −809280. + 1.40171e6i −0.0749760 + 0.129862i
\(222\) 0 0
\(223\) 1.02146e6i 0.0921096i −0.998939 0.0460548i \(-0.985335\pi\)
0.998939 0.0460548i \(-0.0146649\pi\)
\(224\) 0 0
\(225\) 9.35016e6 0.820864
\(226\) 0 0
\(227\) −9.65010e6 5.57149e6i −0.825001 0.476314i 0.0271371 0.999632i \(-0.491361\pi\)
−0.852138 + 0.523317i \(0.824694\pi\)
\(228\) 0 0
\(229\) 4.09488e6 2.36418e6i 0.340984 0.196867i −0.319723 0.947511i \(-0.603590\pi\)
0.660707 + 0.750644i \(0.270256\pi\)
\(230\) 0 0
\(231\) −215699. + 4.91533e6i −0.0174989 + 0.398764i
\(232\) 0 0
\(233\) 480558. + 832352.i 0.0379908 + 0.0658020i 0.884396 0.466738i \(-0.154571\pi\)
−0.846405 + 0.532540i \(0.821238\pi\)
\(234\) 0 0
\(235\) −1.76354e7 + 3.05454e7i −1.35888 + 2.35365i
\(236\) 0 0
\(237\) 1.18207e7i 0.887968i
\(238\) 0 0
\(239\) −1.35988e7 −0.996108 −0.498054 0.867146i \(-0.665952\pi\)
−0.498054 + 0.867146i \(0.665952\pi\)
\(240\) 0 0
\(241\) −1.11183e7 6.41918e6i −0.794308 0.458594i 0.0471692 0.998887i \(-0.484980\pi\)
−0.841477 + 0.540293i \(0.818313\pi\)
\(242\) 0 0
\(243\) −797162. + 460241.i −0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) −2.24093e7 1.57060e7i −1.52381 1.06799i
\(246\) 0 0
\(247\) −2.28583e6 3.95918e6i −0.151689 0.262733i
\(248\) 0 0
\(249\) −1.25579e6 + 2.17509e6i −0.0813425 + 0.140889i
\(250\) 0 0
\(251\) 1.03894e7i 0.657007i 0.944503 + 0.328504i \(0.106544\pi\)
−0.944503 + 0.328504i \(0.893456\pi\)
\(252\) 0 0
\(253\) 1.93895e7 1.19730
\(254\) 0 0
\(255\) 9.46693e6 + 5.46573e6i 0.570937 + 0.329631i
\(256\) 0 0
\(257\) −1.65816e7 + 9.57337e6i −0.976846 + 0.563982i −0.901316 0.433162i \(-0.857398\pi\)
−0.0755293 + 0.997144i \(0.524065\pi\)
\(258\) 0 0
\(259\) −1.51442e7 664571.i −0.871658 0.0382509i
\(260\) 0 0
\(261\) −475067. 822840.i −0.0267198 0.0462801i
\(262\) 0 0
\(263\) 2.00250e6 3.46843e6i 0.110079 0.190663i −0.805723 0.592293i \(-0.798223\pi\)
0.915802 + 0.401630i \(0.131556\pi\)
\(264\) 0 0
\(265\) 5.38161e7i 2.89184i
\(266\) 0 0
\(267\) −8.75717e6 −0.460077
\(268\) 0 0
\(269\) −2.73993e7 1.58190e7i −1.40761 0.812685i −0.412455 0.910978i \(-0.635328\pi\)
−0.995158 + 0.0982929i \(0.968662\pi\)
\(270\) 0 0
\(271\) 3.16572e7 1.82773e7i 1.59061 0.918341i 0.597413 0.801934i \(-0.296196\pi\)
0.993202 0.116407i \(-0.0371378\pi\)
\(272\) 0 0
\(273\) −1.32490e6 2.54648e6i −0.0651170 0.125156i
\(274\) 0 0
\(275\) −1.77033e7 3.06631e7i −0.851250 1.47441i
\(276\) 0 0
\(277\) 1.95609e7 3.38804e7i 0.920341 1.59408i 0.121452 0.992597i \(-0.461245\pi\)
0.798888 0.601479i \(-0.205422\pi\)
\(278\) 0 0
\(279\) 5.59243e6i 0.257506i
\(280\) 0 0
\(281\) −480023. −0.0216343 −0.0108172 0.999941i \(-0.503443\pi\)
−0.0108172 + 0.999941i \(0.503443\pi\)
\(282\) 0 0
\(283\) −3.30947e7 1.91072e7i −1.46015 0.843020i −0.461136 0.887329i \(-0.652558\pi\)
−0.999018 + 0.0443090i \(0.985891\pi\)
\(284\) 0 0
\(285\) −2.67396e7 + 1.54381e7i −1.15510 + 0.666897i
\(286\) 0 0
\(287\) −1.63819e7 1.04415e7i −0.692975 0.441689i
\(288\) 0 0
\(289\) −7.52415e6 1.30322e7i −0.311719 0.539914i
\(290\) 0 0
\(291\) −1.55553e6 + 2.69426e6i −0.0631247 + 0.109335i
\(292\) 0 0
\(293\) 1.03603e7i 0.411878i −0.978565 0.205939i \(-0.933975\pi\)
0.978565 0.205939i \(-0.0660248\pi\)
\(294\) 0 0
\(295\) 2.00456e6 0.0780823
\(296\) 0 0
\(297\) 3.01865e6 + 1.74282e6i 0.115224 + 0.0665247i
\(298\) 0 0
\(299\) −9.79689e6 + 5.65624e6i −0.366501 + 0.211599i
\(300\) 0 0
\(301\) −2.22587e7 + 3.49220e7i −0.816206 + 1.28056i
\(302\) 0 0
\(303\) 8.62975e6 + 1.49472e7i 0.310220 + 0.537318i
\(304\) 0 0
\(305\) 9.20886e6 1.59502e7i 0.324569 0.562169i
\(306\) 0 0
\(307\) 8.06102e6i 0.278596i −0.990251 0.139298i \(-0.955515\pi\)
0.990251 0.139298i \(-0.0444846\pi\)
\(308\) 0 0
\(309\) 2.15779e7 0.731364
\(310\) 0 0
\(311\) 2.21674e7 + 1.27983e7i 0.736942 + 0.425474i 0.820956 0.570991i \(-0.193441\pi\)
−0.0840143 + 0.996465i \(0.526774\pi\)
\(312\) 0 0
\(313\) −3.03923e7 + 1.75470e7i −0.991129 + 0.572229i −0.905612 0.424108i \(-0.860588\pi\)
−0.0855178 + 0.996337i \(0.527254\pi\)
\(314\) 0 0
\(315\) −1.71985e7 + 8.94812e6i −0.550248 + 0.286286i
\(316\) 0 0
\(317\) 1.04219e7 + 1.80513e7i 0.327167 + 0.566669i 0.981948 0.189149i \(-0.0605728\pi\)
−0.654782 + 0.755818i \(0.727239\pi\)
\(318\) 0 0
\(319\) −1.79896e6 + 3.11589e6i −0.0554178 + 0.0959864i
\(320\) 0 0
\(321\) 2.45347e7i 0.741763i
\(322\) 0 0
\(323\) −2.56729e7 −0.761845
\(324\) 0 0
\(325\) 1.78899e7 + 1.03287e7i 0.521144 + 0.300882i
\(326\) 0 0
\(327\) −2.85388e7 + 1.64769e7i −0.816191 + 0.471228i
\(328\) 0 0
\(329\) 2.28022e6 5.19613e7i 0.0640307 1.45912i
\(330\) 0 0
\(331\) −1.10153e7 1.90791e7i −0.303748 0.526107i 0.673234 0.739430i \(-0.264905\pi\)
−0.976982 + 0.213323i \(0.931571\pi\)
\(332\) 0 0
\(333\) −5.36964e6 + 9.30049e6i −0.145416 + 0.251868i
\(334\) 0 0
\(335\) 7.29227e7i 1.93967i
\(336\) 0 0
\(337\) −5.41316e7 −1.41436 −0.707181 0.707032i \(-0.750034\pi\)
−0.707181 + 0.707032i \(0.750034\pi\)
\(338\) 0 0
\(339\) 3.52553e7 + 2.03546e7i 0.904951 + 0.522474i
\(340\) 0 0
\(341\) 1.83399e7 1.05886e7i 0.462524 0.267039i
\(342\) 0 0
\(343\) 4.00049e7 + 5.29379e6i 0.991358 + 0.131185i
\(344\) 0 0
\(345\) 3.82012e7 + 6.61664e7i 0.930293 + 1.61132i
\(346\) 0 0
\(347\) 4.14201e6 7.17416e6i 0.0991339 0.171705i −0.812192 0.583390i \(-0.801726\pi\)
0.911326 + 0.411685i \(0.135059\pi\)
\(348\) 0 0
\(349\) 7.43895e7i 1.74999i 0.484133 + 0.874994i \(0.339135\pi\)
−0.484133 + 0.874994i \(0.660865\pi\)
\(350\) 0 0
\(351\) −2.03364e6 −0.0470276
\(352\) 0 0
\(353\) 3.81691e6 + 2.20369e6i 0.0867736 + 0.0500988i 0.542759 0.839889i \(-0.317380\pi\)
−0.455985 + 0.889987i \(0.650713\pi\)
\(354\) 0 0
\(355\) 4.28670e7 2.47493e7i 0.958161 0.553194i
\(356\) 0 0
\(357\) −1.61044e7 706707.i −0.353948 0.0155323i
\(358\) 0 0
\(359\) −1.12174e7 1.94292e7i −0.242443 0.419924i 0.718966 0.695045i \(-0.244616\pi\)
−0.961410 + 0.275121i \(0.911282\pi\)
\(360\) 0 0
\(361\) 1.27339e7 2.20557e7i 0.270669 0.468813i
\(362\) 0 0
\(363\) 1.44167e7i 0.301401i
\(364\) 0 0
\(365\) −5.33882e7 −1.09791
\(366\) 0 0
\(367\) −5.41637e7 3.12714e7i −1.09575 0.632630i −0.160646 0.987012i \(-0.551358\pi\)
−0.935101 + 0.354382i \(0.884691\pi\)
\(368\) 0 0
\(369\) −1.19189e7 + 6.88141e6i −0.237224 + 0.136961i
\(370\) 0 0
\(371\) 3.66282e7 + 7.04003e7i 0.717289 + 1.37865i
\(372\) 0 0
\(373\) 4.97129e6 + 8.61053e6i 0.0957950 + 0.165922i 0.909940 0.414740i \(-0.136127\pi\)
−0.814145 + 0.580661i \(0.802794\pi\)
\(374\) 0 0
\(375\) 4.14312e7 7.17609e7i 0.785658 1.36080i
\(376\) 0 0
\(377\) 2.09915e6i 0.0391759i
\(378\) 0 0
\(379\) 1.56872e7 0.288157 0.144078 0.989566i \(-0.453978\pi\)
0.144078 + 0.989566i \(0.453978\pi\)
\(380\) 0 0
\(381\) −4.04920e7 2.33781e7i −0.732141 0.422702i
\(382\) 0 0
\(383\) −5.32230e7 + 3.07283e7i −0.947333 + 0.546943i −0.892251 0.451539i \(-0.850875\pi\)
−0.0550816 + 0.998482i \(0.517542\pi\)
\(384\) 0 0
\(385\) 6.19078e7 + 3.94589e7i 1.08483 + 0.691453i
\(386\) 0 0
\(387\) 1.46695e7 + 2.54082e7i 0.253093 + 0.438371i
\(388\) 0 0
\(389\) 4.45518e7 7.71659e7i 0.756861 1.31092i −0.187583 0.982249i \(-0.560065\pi\)
0.944444 0.328673i \(-0.106601\pi\)
\(390\) 0 0
\(391\) 6.35269e7i 1.06274i
\(392\) 0 0
\(393\) 654465. 0.0107822
\(394\) 0 0
\(395\) −1.52750e8 8.81901e7i −2.47850 1.43096i
\(396\) 0 0
\(397\) 5.73411e7 3.31059e7i 0.916421 0.529096i 0.0339293 0.999424i \(-0.489198\pi\)
0.882491 + 0.470329i \(0.155865\pi\)
\(398\) 0 0
\(399\) 2.44723e7 3.83950e7i 0.385262 0.604444i
\(400\) 0 0
\(401\) −3.38142e7 5.85679e7i −0.524404 0.908294i −0.999596 0.0284121i \(-0.990955\pi\)
0.475193 0.879882i \(-0.342378\pi\)
\(402\) 0 0
\(403\) −6.17773e6 + 1.07001e7i −0.0943873 + 0.163484i
\(404\) 0 0
\(405\) 1.37348e7i 0.206756i
\(406\) 0 0
\(407\) 4.06670e7 0.603196
\(408\) 0 0
\(409\) −4.54171e7 2.62216e7i −0.663818 0.383256i 0.129912 0.991526i \(-0.458530\pi\)
−0.793730 + 0.608270i \(0.791864\pi\)
\(410\) 0 0
\(411\) 3.79251e7 2.18961e7i 0.546263 0.315385i
\(412\) 0 0
\(413\) −2.62229e6 + 1.36434e6i −0.0372247 + 0.0193675i
\(414\) 0 0
\(415\) 1.87380e7 + 3.24552e7i 0.262168 + 0.454088i
\(416\) 0 0
\(417\) −1.74844e6 + 3.02838e6i −0.0241125 + 0.0417640i
\(418\) 0 0
\(419\) 8.47286e6i 0.115183i 0.998340 + 0.0575915i \(0.0183421\pi\)
−0.998340 + 0.0575915i \(0.981658\pi\)
\(420\) 0 0
\(421\) 7.34469e6 0.0984299 0.0492149 0.998788i \(-0.484328\pi\)
0.0492149 + 0.998788i \(0.484328\pi\)
\(422\) 0 0
\(423\) −3.19110e7 1.84238e7i −0.421618 0.243422i
\(424\) 0 0
\(425\) 1.00463e8 5.80026e7i 1.30870 0.755580i
\(426\) 0 0
\(427\) −1.19069e6 + 2.71332e7i −0.0152937 + 0.348512i
\(428\) 0 0
\(429\) 3.85044e6 + 6.66916e6i 0.0487684 + 0.0844693i
\(430\) 0 0
\(431\) 2.67489e7 4.63304e7i 0.334098 0.578675i −0.649213 0.760607i \(-0.724902\pi\)
0.983311 + 0.181932i \(0.0582350\pi\)
\(432\) 0 0
\(433\) 8.43895e7i 1.03950i 0.854318 + 0.519751i \(0.173975\pi\)
−0.854318 + 0.519751i \(0.826025\pi\)
\(434\) 0 0
\(435\) −1.41773e7 −0.172236
\(436\) 0 0
\(437\) −1.55394e8 8.97167e7i −1.86204 1.07505i
\(438\) 0 0
\(439\) 6.39114e6 3.68993e6i 0.0755414 0.0436138i −0.461754 0.887008i \(-0.652780\pi\)
0.537295 + 0.843394i \(0.319446\pi\)
\(440\) 0 0
\(441\) 1.64082e7 2.34112e7i 0.191313 0.272966i
\(442\) 0 0
\(443\) 3.86184e7 + 6.68890e7i 0.444204 + 0.769384i 0.997996 0.0632707i \(-0.0201531\pi\)
−0.553792 + 0.832655i \(0.686820\pi\)
\(444\) 0 0
\(445\) −6.53343e7 + 1.13162e8i −0.741415 + 1.28417i
\(446\) 0 0
\(447\) 6.33958e7i 0.709803i
\(448\) 0 0
\(449\) 1.13928e7 0.125861 0.0629305 0.998018i \(-0.479955\pi\)
0.0629305 + 0.998018i \(0.479955\pi\)
\(450\) 0 0
\(451\) 4.51341e7 + 2.60582e7i 0.492011 + 0.284063i
\(452\) 0 0
\(453\) −1.51790e7 + 8.76360e6i −0.163286 + 0.0942731i
\(454\) 0 0
\(455\) −4.27909e7 1.87779e6i −0.454273 0.0199348i
\(456\) 0 0
\(457\) −7.68556e7 1.33118e8i −0.805243 1.39472i −0.916127 0.400888i \(-0.868702\pi\)
0.110884 0.993833i \(-0.464632\pi\)
\(458\) 0 0
\(459\) −5.71010e6 + 9.89019e6i −0.0590481 + 0.102274i
\(460\) 0 0
\(461\) 8.01923e7i 0.818521i −0.912418 0.409261i \(-0.865787\pi\)
0.912418 0.409261i \(-0.134213\pi\)
\(462\) 0 0
\(463\) −3.37769e7 −0.340312 −0.170156 0.985417i \(-0.554427\pi\)
−0.170156 + 0.985417i \(0.554427\pi\)
\(464\) 0 0
\(465\) 7.22668e7 + 4.17233e7i 0.718754 + 0.414973i
\(466\) 0 0
\(467\) −1.47999e8 + 8.54475e7i −1.45315 + 0.838975i −0.998659 0.0517781i \(-0.983511\pi\)
−0.454488 + 0.890753i \(0.650178\pi\)
\(468\) 0 0
\(469\) 4.96326e7 + 9.53949e7i 0.481114 + 0.924712i
\(470\) 0 0
\(471\) 4.61118e7 + 7.98680e7i 0.441316 + 0.764382i
\(472\) 0 0
\(473\) 5.55495e7 9.62146e7i 0.524925 0.909196i
\(474\) 0 0
\(475\) 3.27659e8i 3.05732i
\(476\) 0 0
\(477\) 5.62222e7 0.518027
\(478\) 0 0
\(479\) −2.19520e7 1.26740e7i −0.199741 0.115321i 0.396794 0.917908i \(-0.370123\pi\)
−0.596535 + 0.802587i \(0.703456\pi\)
\(480\) 0 0
\(481\) −2.05477e7 + 1.18632e7i −0.184641 + 0.106603i
\(482\) 0 0
\(483\) −9.50076e7 6.05561e7i −0.843174 0.537424i
\(484\) 0 0
\(485\) 2.32106e7 + 4.02019e7i 0.203451 + 0.352388i
\(486\) 0 0
\(487\) 8.99675e7 1.55828e8i 0.778930 1.34915i −0.153628 0.988129i \(-0.549096\pi\)
0.932559 0.361018i \(-0.117571\pi\)
\(488\) 0 0
\(489\) 6.26949e7i 0.536174i
\(490\) 0 0
\(491\) 1.07343e8 0.906838 0.453419 0.891298i \(-0.350204\pi\)
0.453419 + 0.891298i \(0.350204\pi\)
\(492\) 0 0
\(493\) −1.02088e7 5.89404e6i −0.0851987 0.0491895i
\(494\) 0 0
\(495\) 4.50423e7 2.60052e7i 0.371368 0.214410i
\(496\) 0 0
\(497\) −3.92323e7 + 6.15523e7i −0.319576 + 0.501389i
\(498\) 0 0
\(499\) −1.37396e7 2.37977e7i −0.110579 0.191529i 0.805425 0.592698i \(-0.201937\pi\)
−0.916004 + 0.401169i \(0.868604\pi\)
\(500\) 0 0
\(501\) 4.65913e7 8.06985e7i 0.370503 0.641730i
\(502\) 0 0
\(503\) 1.17139e8i 0.920442i −0.887805 0.460221i \(-0.847770\pi\)
0.887805 0.460221i \(-0.152230\pi\)
\(504\) 0 0
\(505\) 2.57535e8 1.99969
\(506\) 0 0
\(507\) 6.12709e7 + 3.53748e7i 0.470144 + 0.271437i
\(508\) 0 0
\(509\) −8.18289e7 + 4.72439e7i −0.620517 + 0.358255i −0.777070 0.629414i \(-0.783295\pi\)
0.156554 + 0.987669i \(0.449962\pi\)
\(510\) 0 0
\(511\) 6.98405e7 3.63370e7i 0.523413 0.272324i
\(512\) 0 0
\(513\) −1.61283e7 2.79351e7i −0.119464 0.206918i
\(514\) 0 0
\(515\) 1.60985e8 2.78835e8i 1.17860 2.04139i
\(516\) 0 0
\(517\) 1.39533e8i 1.00973i
\(518\) 0 0
\(519\) 3.26110e7 0.233272
\(520\) 0 0
\(521\) 1.43465e8 + 8.28297e7i 1.01446 + 0.585697i 0.912494 0.409091i \(-0.134154\pi\)
0.101964 + 0.994788i \(0.467488\pi\)
\(522\) 0 0
\(523\) −3.74398e7 + 2.16159e7i −0.261715 + 0.151101i −0.625117 0.780531i \(-0.714949\pi\)
0.363402 + 0.931633i \(0.381615\pi\)
\(524\) 0 0
\(525\) −9.01961e6 + 2.05538e8i −0.0623318 + 1.42041i
\(526\) 0 0
\(527\) 3.46920e7 + 6.00883e7i 0.237027 + 0.410542i
\(528\) 0 0
\(529\) −1.47984e8 + 2.56316e8i −0.999649 + 1.73144i
\(530\) 0 0
\(531\) 2.09418e6i 0.0139872i
\(532\) 0 0
\(533\) −3.04064e7 −0.200809
\(534\) 0 0
\(535\) 3.17043e8 + 1.83045e8i 2.07041 + 1.19535i
\(536\) 0 0
\(537\) −5.56135e7 + 3.21085e7i −0.359135 + 0.207347i
\(538\) 0 0
\(539\) −1.07842e8 9.48312e6i −0.688687 0.0605599i
\(540\) 0 0
\(541\) 2.35853e7 + 4.08510e7i 0.148953 + 0.257995i 0.930841 0.365425i \(-0.119076\pi\)
−0.781887 + 0.623420i \(0.785743\pi\)
\(542\) 0 0
\(543\) −5.07809e6 + 8.79552e6i −0.0317177 + 0.0549366i
\(544\) 0 0
\(545\) 4.91714e8i 3.03754i
\(546\) 0 0
\(547\) −2.08291e8 −1.27265 −0.636323 0.771423i \(-0.719546\pi\)
−0.636323 + 0.771423i \(0.719546\pi\)
\(548\) 0 0
\(549\) 1.66633e7 + 9.62059e6i 0.100704 + 0.0581413i
\(550\) 0 0
\(551\) 2.88349e7 1.66479e7i 0.172371 0.0995184i
\(552\) 0 0
\(553\) 2.59846e8 + 1.14028e7i 1.53653 + 0.0674273i
\(554\) 0 0
\(555\) 8.01222e7 + 1.38776e8i 0.468677 + 0.811773i
\(556\) 0 0
\(557\) 3.52394e6 6.10364e6i 0.0203921 0.0353202i −0.855649 0.517556i \(-0.826842\pi\)
0.876041 + 0.482236i \(0.160175\pi\)
\(558\) 0 0
\(559\) 6.48189e7i 0.371079i
\(560\) 0 0
\(561\) 4.32455e7 0.244936
\(562\) 0 0
\(563\) −1.60089e8 9.24276e7i −0.897092 0.517936i −0.0208364 0.999783i \(-0.506633\pi\)
−0.876256 + 0.481847i \(0.839966\pi\)
\(564\) 0 0
\(565\) 5.26056e8 3.03718e8i 2.91666 1.68394i
\(566\) 0 0
\(567\) −9.34819e6 1.79674e7i −0.0512836 0.0985681i
\(568\) 0 0
\(569\) −1.29070e8 2.23556e8i −0.700629 1.21353i −0.968246 0.250000i \(-0.919569\pi\)
0.267616 0.963526i \(-0.413764\pi\)
\(570\) 0 0
\(571\) −8.79110e7 + 1.52266e8i −0.472209 + 0.817891i −0.999494 0.0317978i \(-0.989877\pi\)
0.527285 + 0.849689i \(0.323210\pi\)
\(572\) 0 0
\(573\) 1.08574e8i 0.577115i
\(574\) 0 0
\(575\) 8.10785e8 4.26484
\(576\) 0 0
\(577\) −1.14796e8 6.62773e7i −0.597582 0.345014i 0.170508 0.985356i \(-0.445459\pi\)
−0.768090 + 0.640342i \(0.778793\pi\)
\(578\) 0 0
\(579\) −1.79594e8 + 1.03688e8i −0.925242 + 0.534189i
\(580\) 0 0
\(581\) −4.66020e7 2.97033e7i −0.237616 0.151452i
\(582\) 0 0
\(583\) −1.06450e8 1.84376e8i −0.537203 0.930463i
\(584\) 0 0
\(585\) −1.51723e7 + 2.62792e7i −0.0757851 + 0.131264i
\(586\) 0 0
\(587\) 2.64040e8i 1.30543i −0.757602 0.652717i \(-0.773629\pi\)
0.757602 0.652717i \(-0.226371\pi\)
\(588\) 0 0
\(589\) −1.95977e8 −0.959088
\(590\) 0 0
\(591\) −7.18551e7 4.14855e7i −0.348093 0.200971i
\(592\) 0 0
\(593\) 5.83488e7 3.36877e7i 0.279813 0.161550i −0.353526 0.935425i \(-0.615017\pi\)
0.633339 + 0.773875i \(0.281684\pi\)
\(594\) 0 0
\(595\) −1.29282e8 + 2.02832e8i −0.613742 + 0.962912i
\(596\) 0 0
\(597\) 4.09034e7 + 7.08467e7i 0.192237 + 0.332963i
\(598\) 0 0
\(599\) −3.28119e7 + 5.68319e7i −0.152669 + 0.264430i −0.932208 0.361923i \(-0.882120\pi\)
0.779539 + 0.626354i \(0.215454\pi\)
\(600\) 0 0
\(601\) 2.08034e8i 0.958320i 0.877728 + 0.479160i \(0.159059\pi\)
−0.877728 + 0.479160i \(0.840941\pi\)
\(602\) 0 0
\(603\) 7.61830e7 0.347461
\(604\) 0 0
\(605\) 1.86296e8 + 1.07558e8i 0.841273 + 0.485709i
\(606\) 0 0
\(607\) 3.48090e8 2.00970e8i 1.55642 0.898598i 0.558822 0.829288i \(-0.311253\pi\)
0.997595 0.0693104i \(-0.0220799\pi\)
\(608\) 0 0
\(609\) 1.85462e7 9.64932e6i 0.0821113 0.0427213i
\(610\) 0 0
\(611\) −4.07041e7 7.05016e7i −0.178449 0.309083i
\(612\) 0 0
\(613\) −5.14774e7 + 8.91614e7i −0.223478 + 0.387075i −0.955862 0.293817i \(-0.905074\pi\)
0.732384 + 0.680892i \(0.238408\pi\)
\(614\) 0 0
\(615\) 2.05360e8i 0.882855i
\(616\) 0 0
\(617\) −3.54994e8 −1.51135 −0.755676 0.654945i \(-0.772692\pi\)
−0.755676 + 0.654945i \(0.772692\pi\)
\(618\) 0 0
\(619\) −8.87611e7 5.12462e7i −0.374240 0.216068i 0.301069 0.953602i \(-0.402657\pi\)
−0.675309 + 0.737535i \(0.735990\pi\)
\(620\) 0 0
\(621\) −6.91247e7 + 3.99092e7i −0.288641 + 0.166647i
\(622\) 0 0
\(623\) 8.44759e6 1.92503e8i 0.0349356 0.796110i
\(624\) 0 0
\(625\) −3.17599e8 5.50097e8i −1.30089 2.25320i
\(626\) 0 0
\(627\) −6.10739e7 + 1.05783e8i −0.247772 + 0.429155i
\(628\) 0 0
\(629\) 1.33240e8i 0.535404i
\(630\) 0 0
\(631\) 5.10491e7 0.203189 0.101595 0.994826i \(-0.467606\pi\)
0.101595 + 0.994826i \(0.467606\pi\)
\(632\) 0 0
\(633\) −7.04894e6 4.06971e6i −0.0277916 0.0160455i
\(634\) 0 0
\(635\) −6.04195e8 + 3.48832e8i −2.35969 + 1.36237i
\(636\) 0 0
\(637\) 5.72556e7 2.66678e7i 0.221513 0.103174i
\(638\) 0 0
\(639\) 2.58558e7 + 4.47836e7i 0.0990959 + 0.171639i
\(640\) 0 0
\(641\) 1.19118e8 2.06319e8i 0.452276 0.783365i −0.546251 0.837622i \(-0.683945\pi\)
0.998527 + 0.0542563i \(0.0172788\pi\)
\(642\) 0 0
\(643\) 2.38667e8i 0.897758i −0.893593 0.448879i \(-0.851823\pi\)
0.893593 0.448879i \(-0.148177\pi\)
\(644\) 0 0
\(645\) 4.37775e8 1.63144
\(646\) 0 0
\(647\) 2.59300e8 + 1.49707e8i 0.957391 + 0.552750i 0.895369 0.445325i \(-0.146912\pi\)
0.0620217 + 0.998075i \(0.480245\pi\)
\(648\) 0 0
\(649\) 6.86770e6 3.96507e6i 0.0251233 0.0145050i
\(650\) 0 0
\(651\) −1.22935e8 5.39473e6i −0.445585 0.0195536i
\(652\) 0 0
\(653\) 1.90019e8 + 3.29122e8i 0.682429 + 1.18200i 0.974237 + 0.225525i \(0.0724096\pi\)
−0.291809 + 0.956477i \(0.594257\pi\)
\(654\) 0 0
\(655\) 4.88275e6 8.45716e6i 0.0173756 0.0300954i
\(656\) 0 0
\(657\) 5.57751e7i 0.196673i
\(658\) 0 0
\(659\) −6.92456e7 −0.241956 −0.120978 0.992655i \(-0.538603\pi\)
−0.120978 + 0.992655i \(0.538603\pi\)
\(660\) 0 0
\(661\) −4.39149e8 2.53543e8i −1.52057 0.877904i −0.999706 0.0242670i \(-0.992275\pi\)
−0.520869 0.853637i \(-0.674392\pi\)
\(662\) 0 0
\(663\) −2.18506e7 + 1.26154e7i −0.0749760 + 0.0432874i
\(664\) 0 0
\(665\) −3.13571e8 6.02690e8i −1.06628 2.04941i
\(666\) 0 0
\(667\) −4.11948e7 7.13514e7i −0.138824 0.240450i
\(668\) 0 0
\(669\) 7.96146e6 1.37896e7i 0.0265897 0.0460548i
\(670\) 0 0
\(671\) 7.28615e7i 0.241174i
\(672\) 0 0
\(673\) 3.94455e8 1.29405 0.647027 0.762467i \(-0.276012\pi\)
0.647027 + 0.762467i \(0.276012\pi\)
\(674\) 0 0
\(675\) 1.26227e8 + 7.28773e7i 0.410432 + 0.236963i
\(676\) 0 0
\(677\) 3.66631e8 2.11675e8i 1.18158 0.682186i 0.225201 0.974312i \(-0.427696\pi\)
0.956380 + 0.292126i \(0.0943627\pi\)
\(678\) 0 0
\(679\) −5.77254e7 3.67931e7i −0.184399 0.117532i
\(680\) 0 0
\(681\) −8.68509e7 1.50430e8i −0.275000 0.476314i
\(682\) 0 0
\(683\) −9.89199e7 + 1.71334e8i −0.310471 + 0.537752i −0.978464 0.206415i \(-0.933820\pi\)
0.667993 + 0.744168i \(0.267154\pi\)
\(684\) 0 0
\(685\) 6.53437e8i 2.03298i
\(686\) 0 0
\(687\) 7.37078e7 0.227323
\(688\) 0 0
\(689\) 1.07571e8 + 6.21063e7i 0.328881 + 0.189879i
\(690\) 0 0
\(691\) −9.88719e6 + 5.70837e6i −0.0299667 + 0.0173013i −0.514909 0.857245i \(-0.672174\pi\)
0.484942 + 0.874546i \(0.338841\pi\)
\(692\) 0 0
\(693\) −4.12231e7 + 6.46757e7i −0.123863 + 0.194331i
\(694\) 0 0
\(695\) 2.60890e7 + 4.51875e7i 0.0777147 + 0.134606i
\(696\) 0 0
\(697\) −8.53760e7 + 1.47875e8i −0.252137 + 0.436715i
\(698\) 0 0
\(699\) 1.49823e7i 0.0438680i
\(700\) 0 0
\(701\) −2.88915e8 −0.838717 −0.419359 0.907821i \(-0.637745\pi\)
−0.419359 + 0.907821i \(0.637745\pi\)
\(702\) 0 0
\(703\) −3.25919e8 1.88169e8i −0.938088 0.541605i
\(704\) 0 0
\(705\) −4.76155e8 + 2.74908e8i −1.35888 + 0.784549i
\(706\) 0 0
\(707\) −3.36898e8 + 1.75283e8i −0.953323 + 0.496000i
\(708\) 0 0
\(709\) −1.87067e8 3.24009e8i −0.524877 0.909113i −0.999580 0.0289676i \(-0.990778\pi\)
0.474703 0.880146i \(-0.342555\pi\)
\(710\) 0 0
\(711\) 9.21331e7 1.59579e8i 0.256334 0.443984i
\(712\) 0 0
\(713\) 4.84940e8i 1.33789i
\(714\) 0 0
\(715\) 1.14907e8 0.314362
\(716\) 0 0
\(717\) −1.83584e8 1.05992e8i −0.498054 0.287552i
\(718\) 0 0
\(719\) 3.32566e7 1.92007e7i 0.0894728 0.0516572i −0.454596 0.890698i \(-0.650216\pi\)
0.544069 + 0.839041i \(0.316883\pi\)
\(720\) 0 0
\(721\) −2.08151e7 + 4.74332e8i −0.0555357 + 1.26554i
\(722\) 0 0
\(723\) −1.00065e8 1.73318e8i −0.264769 0.458594i
\(724\) 0 0
\(725\) −7.52248e7 + 1.30293e8i −0.197400 + 0.341907i
\(726\) 0 0
\(727\) 3.25563e8i 0.847290i 0.905828 + 0.423645i \(0.139250\pi\)
−0.905828 + 0.423645i \(0.860750\pi\)
\(728\) 0 0
\(729\) −1.43489e7 −0.0370370
\(730\) 0 0
\(731\) 3.15234e8 + 1.82000e8i 0.807013 + 0.465929i
\(732\) 0 0
\(733\) −1.37433e8 + 7.93472e7i −0.348964 + 0.201474i −0.664229 0.747529i \(-0.731240\pi\)
0.315265 + 0.949004i \(0.397907\pi\)
\(734\) 0 0
\(735\) −1.80110e8 3.86694e8i −0.453602 0.973880i
\(736\) 0 0
\(737\) −1.44243e8 2.49836e8i −0.360323 0.624098i
\(738\) 0 0
\(739\) −1.17829e8 + 2.04087e8i −0.291958 + 0.505686i −0.974273 0.225373i \(-0.927640\pi\)
0.682315 + 0.731059i \(0.260973\pi\)
\(740\) 0 0
\(741\) 7.12652e7i 0.175155i
\(742\) 0 0
\(743\) −1.12156e8 −0.273436 −0.136718 0.990610i \(-0.543655\pi\)
−0.136718 + 0.990610i \(0.543655\pi\)
\(744\) 0 0
\(745\) 8.19216e8 + 4.72975e8i 1.98121 + 1.14385i
\(746\) 0 0
\(747\) −3.39062e7 + 1.95758e7i −0.0813425 + 0.0469631i
\(748\) 0 0
\(749\) −5.39329e8 2.36673e7i −1.28354 0.0563253i
\(750\) 0 0
\(751\) −1.19826e8 2.07544e8i −0.282898 0.489994i 0.689199 0.724572i \(-0.257962\pi\)
−0.972097 + 0.234578i \(0.924629\pi\)
\(752\) 0 0
\(753\) −8.09775e7 + 1.40257e8i −0.189662 + 0.328504i
\(754\) 0 0
\(755\) 2.61529e8i 0.607686i
\(756\) 0 0
\(757\) 2.05564e7 0.0473871 0.0236936 0.999719i \(-0.492457\pi\)
0.0236936 + 0.999719i \(0.492457\pi\)
\(758\) 0 0
\(759\) 2.61758e8 + 1.51126e8i 0.598652 + 0.345632i
\(760\) 0 0
\(761\) −4.34822e8 + 2.51044e8i −0.986637 + 0.569635i −0.904267 0.426967i \(-0.859582\pi\)
−0.0823696 + 0.996602i \(0.526249\pi\)
\(762\) 0 0
\(763\) −3.34670e8 6.43242e8i −0.753430 1.44811i
\(764\) 0 0
\(765\) 8.52023e7 + 1.47575e8i 0.190312 + 0.329631i
\(766\) 0 0
\(767\) −2.31336e6 + 4.00685e6i −0.00512692 + 0.00888008i
\(768\) 0 0
\(769\) 1.32826e8i 0.292081i −0.989279 0.146041i \(-0.953347\pi\)
0.989279 0.146041i \(-0.0466530\pi\)
\(770\) 0 0
\(771\) −2.98468e8 −0.651230
\(772\) 0 0
\(773\) 6.75312e7 + 3.89892e7i 0.146206 + 0.0844122i 0.571319 0.820728i \(-0.306432\pi\)
−0.425112 + 0.905141i \(0.639765\pi\)
\(774\) 0 0
\(775\) 7.66898e8 4.42769e8i 1.64753 0.951200i
\(776\) 0 0
\(777\) −1.99266e8 1.27009e8i −0.424787 0.270751i
\(778\) 0 0
\(779\) −2.41146e8 4.17678e8i −0.510115 0.883546i
\(780\) 0 0
\(781\) 9.79095e7 1.69584e8i 0.205528 0.355986i
\(782\) 0 0
\(783\) 1.48111e7i 0.0308534i
\(784\) 0 0
\(785\) 1.37610e9 2.84473
\(786\) 0 0
\(787\) 1.28535e8 + 7.42095e7i 0.263691 + 0.152242i 0.626017 0.779809i \(-0.284684\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(788\) 0 0
\(789\) 5.40675e7 3.12159e7i 0.110079 0.0635542i
\(790\) 0 0
\(791\) −4.81451e8 + 7.55357e8i −0.972798 + 1.52624i
\(792\) 0 0
\(793\) 2.12549e7 + 3.68146e7i 0.0426226 + 0.0738245i
\(794\) 0 0
\(795\) 4.19455e8 7.26517e8i 0.834802 1.44592i
\(796\) 0 0
\(797\) 3.50628e7i 0.0692583i −0.999400 0.0346292i \(-0.988975\pi\)
0.999400 0.0346292i \(-0.0110250\pi\)
\(798\) 0 0
\(799\) −4.57160e8 −0.896248
\(800\) 0 0
\(801\) −1.18222e8 6.82554e7i −0.230038 0.132813i
\(802\) 0 0
\(803\) −1.82910e8 + 1.05603e8i −0.353257 + 0.203953i
\(804\) 0 0
\(805\) −1.49134e9 + 7.75923e8i −2.85884 + 1.48741i
\(806\) 0 0
\(807\) −2.46594e8 4.27113e8i −0.469204 0.812685i
\(808\) 0 0
\(809\) −1.88273e8 + 3.26099e8i −0.355585 + 0.615892i −0.987218 0.159376i \(-0.949052\pi\)
0.631633 + 0.775268i \(0.282385\pi\)
\(810\) 0 0
\(811\) 5.58329e8i 1.04671i 0.852114 + 0.523356i \(0.175320\pi\)
−0.852114 + 0.523356i \(0.824680\pi\)
\(812\) 0 0
\(813\) 5.69830e8 1.06041
\(814\) 0 0
\(815\) −8.10159e8 4.67745e8i −1.49657 0.864046i
\(816\) 0 0
\(817\) −8.90385e8 + 5.14064e8i −1.63272 + 0.942652i
\(818\) 0 0
\(819\) 1.96175e6 4.47041e7i 0.00357101 0.0813758i
\(820\) 0 0
\(821\) −1.85684e8 3.21615e8i −0.335541 0.581174i 0.648047 0.761600i \(-0.275586\pi\)
−0.983589 + 0.180426i \(0.942253\pi\)
\(822\) 0 0
\(823\) −4.07943e7 + 7.06579e7i −0.0731813 + 0.126754i −0.900294 0.435282i \(-0.856649\pi\)
0.827113 + 0.562036i \(0.189982\pi\)
\(824\) 0 0
\(825\) 5.51936e8i 0.982939i
\(826\) 0 0
\(827\) 9.21411e8 1.62906 0.814529 0.580123i \(-0.196995\pi\)
0.814529 + 0.580123i \(0.196995\pi\)
\(828\) 0 0
\(829\) −4.35666e7 2.51532e7i −0.0764698 0.0441499i 0.461278 0.887256i \(-0.347391\pi\)
−0.537747 + 0.843106i \(0.680725\pi\)
\(830\) 0 0
\(831\) 5.28143e8 3.04924e8i 0.920341 0.531359i
\(832\) 0 0
\(833\) 3.10701e7 3.53330e8i 0.0537536 0.611287i
\(834\) 0 0
\(835\) −6.95205e8 1.20413e9i −1.19413 2.06830i
\(836\) 0 0
\(837\) −4.35887e7 + 7.54978e7i −0.0743357 + 0.128753i
\(838\) 0 0
\(839\) 1.18275e8i 0.200266i −0.994974 0.100133i \(-0.968073\pi\)
0.994974 0.100133i \(-0.0319269\pi\)
\(840\) 0 0
\(841\) −5.79535e8 −0.974298
\(842\) 0 0
\(843\) −6.48031e6 3.74141e6i −0.0108172 0.00624529i
\(844\) 0 0
\(845\) 9.14244e8 5.27839e8i 1.51528 0.874845i
\(846\) 0 0
\(847\) −3.16912e8 1.39070e7i −0.521540 0.0228867i
\(848\) 0 0
\(849\) −2.97852e8 5.15895e8i −0.486718 0.843020i
\(850\) 0 0
\(851\) −4.65621e8 + 8.06479e8i −0.755516 + 1.30859i
\(852\) 0 0
\(853\) 5.72140e8i 0.921840i 0.887442 + 0.460920i \(0.152480\pi\)
−0.887442 + 0.460920i \(0.847520\pi\)
\(854\) 0 0
\(855\) −4.81312e8 −0.770067
\(856\) 0 0
\(857\) 3.38731e8 + 1.95567e8i 0.538162 + 0.310708i 0.744334 0.667808i \(-0.232767\pi\)
−0.206172 + 0.978516i \(0.566101\pi\)
\(858\) 0 0
\(859\) 6.62106e8 3.82267e8i 1.04460 0.603097i 0.123464 0.992349i \(-0.460600\pi\)
0.921131 + 0.389252i \(0.127266\pi\)
\(860\) 0 0
\(861\) −1.39772e8 2.68644e8i −0.218983 0.420889i
\(862\) 0 0
\(863\) −6.28637e8 1.08883e9i −0.978065 1.69406i −0.669426 0.742879i \(-0.733460\pi\)
−0.308639 0.951179i \(-0.599874\pi\)
\(864\) 0 0
\(865\) 2.43300e8 4.21407e8i 0.375918 0.651109i
\(866\) 0 0
\(867\) 2.34580e8i 0.359943i
\(868\) 0 0
\(869\) −6.97770e8 −1.06329
\(870\) 0 0
\(871\) 1.45763e8 + 8.41562e7i 0.220593 + 0.127360i
\(872\) 0 0
\(873\) −4.19993e7 + 2.42483e7i −0.0631247 + 0.0364451i
\(874\) 0 0
\(875\) 1.53750e9 + 9.79977e8i 2.29505 + 1.46282i
\(876\) 0 0
\(877\) −3.91957e8 6.78889e8i −0.581084 1.00647i −0.995351 0.0963122i \(-0.969295\pi\)
0.414267 0.910155i \(-0.364038\pi\)
\(878\) 0 0
\(879\) 8.07504e7 1.39864e8i 0.118899 0.205939i
\(880\) 0 0
\(881\) 3.67078e7i 0.0536823i −0.999640 0.0268412i \(-0.991455\pi\)
0.999640 0.0268412i \(-0.00854483\pi\)
\(882\) 0 0
\(883\) 7.33429e8 1.06531 0.532655 0.846332i \(-0.321194\pi\)
0.532655 + 0.846332i \(0.321194\pi\)
\(884\) 0 0
\(885\) 2.70615e7 + 1.56240e7i 0.0390412 + 0.0225404i
\(886\) 0 0
\(887\) −4.97098e8 + 2.87000e8i −0.712313 + 0.411254i −0.811917 0.583773i \(-0.801576\pi\)
0.0996037 + 0.995027i \(0.468242\pi\)
\(888\) 0 0
\(889\) 5.52965e8 8.67556e8i 0.787031 1.23479i
\(890\) 0 0
\(891\) 2.71679e7 + 4.70561e7i 0.0384080 + 0.0665247i
\(892\) 0 0
\(893\) 6.45630e8 1.11826e9i 0.906628 1.57033i
\(894\) 0 0
\(895\) 9.58203e8i 1.33656i
\(896\) 0 0
\(897\) −1.76344e8 −0.244334
\(898\) 0 0
\(899\) −7.79298e7 4.49928e7i −0.107257 0.0619247i
\(900\) 0 0
\(901\) 6.04083e8 3.48767e8i 0.825890 0.476828i
\(902\) 0 0
\(903\) −5.72682e8 + 2.97958e8i −0.777769 + 0.404662i
\(904\) 0 0
\(905\) 7.57719e7 + 1.31241e8i 0.102226 + 0.177061i
\(906\) 0 0
\(907\) −5.53301e8 + 9.58345e8i −0.741548 + 1.28440i 0.210242 + 0.977649i \(0.432575\pi\)
−0.951790 + 0.306750i \(0.900759\pi\)
\(908\) 0 0
\(909\) 2.69049e8i 0.358212i
\(910\) 0 0
\(911\) 7.63025e8 1.00921 0.504607 0.863349i \(-0.331637\pi\)
0.504607 + 0.863349i \(0.331637\pi\)
\(912\) 0 0
\(913\) 1.28394e8 + 7.41285e7i 0.168707 + 0.0974031i
\(914\) 0 0
\(915\) 2.48639e8 1.43552e8i 0.324569 0.187390i
\(916\) 0 0
\(917\) −631328. + 1.43867e7i −0.000818743 + 0.0186574i
\(918\) 0 0
\(919\) −9.28030e7 1.60740e8i −0.119568 0.207098i 0.800028 0.599962i \(-0.204818\pi\)
−0.919597 + 0.392864i \(0.871484\pi\)
\(920\) 0 0
\(921\) 6.28294e7 1.08824e8i 0.0804237 0.139298i
\(922\) 0 0
\(923\) 1.14247e8i 0.145292i
\(924\) 0 0
\(925\) 1.70052e9 2.14860
\(926\) 0 0
\(927\) 2.91301e8 + 1.68183e8i 0.365682 + 0.211127i
\(928\) 0 0
\(929\) 1.21183e7 6.99652e6i 0.0151146 0.00872639i −0.492424 0.870356i \(-0.663889\pi\)
0.507538 + 0.861629i \(0.330556\pi\)
\(930\) 0 0
\(931\) 8.20404e8 + 5.74995e8i 1.01667 + 0.712549i
\(932\) 0 0
\(933\) 1.99507e8 + 3.45555e8i 0.245647 + 0.425474i
\(934\) 0 0
\(935\) 3.22640e8 5.58829e8i 0.394715 0.683666i
\(936\) 0 0
\(937\) 5.41893e8i 0.658711i 0.944206 + 0.329355i \(0.106831\pi\)
−0.944206 + 0.329355i \(0.893169\pi\)
\(938\) 0 0
\(939\) −5.47061e8 −0.660753
\(940\) 0 0
\(941\) −1.09435e9 6.31821e8i −1.31337 0.758273i −0.330715 0.943731i \(-0.607290\pi\)
−0.982652 + 0.185458i \(0.940623\pi\)
\(942\) 0 0
\(943\) −1.03353e9 + 5.96711e8i −1.23251 + 0.711589i
\(944\) 0 0
\(945\) −3.01923e8 1.32493e7i −0.357768 0.0156999i
\(946\) 0 0
\(947\) 1.41001e8 + 2.44221e8i 0.166024 + 0.287562i 0.937019 0.349280i \(-0.113574\pi\)
−0.770994 + 0.636842i \(0.780240\pi\)
\(948\) 0 0
\(949\) 6.16125e7 1.06716e8i 0.0720892 0.124862i
\(950\) 0 0
\(951\) 3.24923e8i 0.377780i
\(952\) 0 0
\(953\) 4.16665e8 0.481403 0.240701 0.970599i \(-0.422623\pi\)
0.240701 + 0.970599i \(0.422623\pi\)
\(954\) 0 0
\(955\) −1.40302e9 8.10035e8i −1.61085 0.930023i
\(956\) 0 0
\(957\) −4.85719e7 + 2.80430e7i −0.0554178 + 0.0319955i
\(958\) 0 0
\(959\) 4.44742e8 + 8.54804e8i 0.504257 + 0.969194i
\(960\) 0 0
\(961\) −1.78927e8 3.09911e8i −0.201607 0.349194i
\(962\) 0 0
\(963\) −1.91229e8 + 3.31218e8i −0.214129 + 0.370881i
\(964\) 0 0
\(965\) 3.09434e9i 3.44339i
\(966\) 0 0
\(967\) 3.24846e8 0.359251 0.179626 0.983735i \(-0.442511\pi\)
0.179626 + 0.983735i \(0.442511\pi\)
\(968\) 0 0
\(969\) −3.46584e8 2.00100e8i −0.380923 0.219926i
\(970\) 0 0
\(971\) 1.37705e9 7.95041e8i 1.50416 0.868425i 0.504167 0.863606i \(-0.331800\pi\)
0.999988 0.00481836i \(-0.00153374\pi\)
\(972\) 0 0
\(973\) −6.48842e7 4.13560e7i −0.0704369 0.0448952i
\(974\) 0 0
\(975\) 1.61009e8 + 2.78876e8i 0.173715 + 0.300882i
\(976\) 0 0
\(977\) 3.51811e8 6.09355e8i 0.377247 0.653411i −0.613413 0.789762i \(-0.710204\pi\)
0.990661 + 0.136351i \(0.0435374\pi\)
\(978\) 0 0
\(979\) 5.16932e8i 0.550916i
\(980\) 0 0
\(981\) −5.13698e8 −0.544128
\(982\) 0 0
\(983\) −1.23385e8 7.12362e7i −0.129897 0.0749963i 0.433643 0.901085i \(-0.357228\pi\)
−0.563541 + 0.826088i \(0.690561\pi\)
\(984\) 0 0
\(985\) −1.07217e9 + 6.19020e8i −1.12191 + 0.647733i
\(986\) 0 0
\(987\) 4.35781e8 6.83705e8i 0.453228 0.711078i
\(988\) 0 0
\(989\) 1.27204e9 + 2.20324e9i 1.31496 + 2.27757i
\(990\) 0 0
\(991\) 2.14982e8 3.72360e8i 0.220893 0.382598i −0.734186 0.678948i \(-0.762436\pi\)
0.955079 + 0.296350i \(0.0957695\pi\)
\(992\) 0 0
\(993\) 3.43424e8i 0.350738i
\(994\) 0 0
\(995\) 1.22067e9 1.23916
\(996\) 0 0
\(997\) −5.64708e8 3.26034e8i −0.569821 0.328986i 0.187257 0.982311i \(-0.440040\pi\)
−0.757078 + 0.653325i \(0.773374\pi\)
\(998\) 0 0
\(999\) −1.44980e8 + 8.37044e7i −0.145416 + 0.0839561i
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 336.7.bh.e.241.4 8
4.3 odd 2 84.7.m.a.73.4 yes 8
7.5 odd 6 inner 336.7.bh.e.145.4 8
12.11 even 2 252.7.z.d.73.1 8
28.3 even 6 588.7.d.b.97.1 8
28.11 odd 6 588.7.d.b.97.8 8
28.19 even 6 84.7.m.a.61.4 8
28.23 odd 6 588.7.m.c.313.1 8
28.27 even 2 588.7.m.c.325.1 8
84.47 odd 6 252.7.z.d.145.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.7.m.a.61.4 8 28.19 even 6
84.7.m.a.73.4 yes 8 4.3 odd 2
252.7.z.d.73.1 8 12.11 even 2
252.7.z.d.145.1 8 84.47 odd 6
336.7.bh.e.145.4 8 7.5 odd 6 inner
336.7.bh.e.241.4 8 1.1 even 1 trivial
588.7.d.b.97.1 8 28.3 even 6
588.7.d.b.97.8 8 28.11 odd 6
588.7.m.c.313.1 8 28.23 odd 6
588.7.m.c.325.1 8 28.27 even 2