Properties

Label 336.7.bh.f.145.2
Level $336$
Weight $7$
Character 336.145
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: \( x^{8} - 2x^{7} + 193x^{6} + 306x^{5} + 29845x^{4} + 16988x^{3} + 1125468x^{2} + 214128x + 35378704 \) 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 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 145.2
Root \(-3.27778 + 5.67728i\) of defining polynomial
Character \(\chi\) \(=\) 336.145
Dual form 336.7.bh.f.241.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(13.5000 - 7.79423i) q^{3} +(63.2658 + 36.5265i) q^{5} +(271.352 - 209.802i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\) \(q+(13.5000 - 7.79423i) q^{3} +(63.2658 + 36.5265i) q^{5} +(271.352 - 209.802i) q^{7} +(121.500 - 210.444i) q^{9} +(-1073.02 - 1858.52i) q^{11} +2550.94i q^{13} +1138.79 q^{15} +(2870.93 - 1657.53i) q^{17} +(-3813.46 - 2201.70i) q^{19} +(2028.01 - 4947.31i) q^{21} +(8548.49 - 14806.4i) q^{23} +(-5144.12 - 8909.88i) q^{25} -3788.00i q^{27} -33248.2 q^{29} +(-10149.7 + 5859.92i) q^{31} +(-28971.4 - 16726.7i) q^{33} +(24830.7 - 3361.73i) q^{35} +(-24322.8 + 42128.4i) q^{37} +(19882.6 + 34437.7i) q^{39} -71461.4i q^{41} -86836.9 q^{43} +(15373.6 - 8875.95i) q^{45} +(143252. + 82706.7i) q^{47} +(29615.3 - 113861. i) q^{49} +(25838.4 - 44753.4i) q^{51} +(42419.4 + 73472.5i) q^{53} -156774. i q^{55} -68642.2 q^{57} +(18534.0 - 10700.6i) q^{59} +(235369. + 135891. i) q^{61} +(-11182.3 - 82595.5i) q^{63} +(-93177.0 + 161387. i) q^{65} +(-239484. - 414798. i) q^{67} -266516. i q^{69} -337334. q^{71} +(340100. - 196357. i) q^{73} +(-138891. - 80188.9i) q^{75} +(-681087. - 279193. i) q^{77} +(5038.26 - 8726.52i) q^{79} +(-29524.5 - 51137.9i) q^{81} -77744.9i q^{83} +242176. q^{85} +(-448851. + 259144. i) q^{87} +(478066. + 276012. i) q^{89} +(535192. + 692203. i) q^{91} +(-91347.1 + 158218. i) q^{93} +(-160841. - 278585. i) q^{95} -1.06023e6i q^{97} -521486. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 108 q^{3} + 462 q^{5} - 580 q^{7} + 972 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 108 q^{3} + 462 q^{5} - 580 q^{7} + 972 q^{9} - 1806 q^{11} + 8316 q^{15} + 9564 q^{17} - 23022 q^{19} - 1350 q^{21} - 2400 q^{23} + 32762 q^{25} - 2484 q^{29} - 148416 q^{31} - 48762 q^{33} - 11412 q^{35} - 84046 q^{37} + 75222 q^{39} - 92972 q^{43} + 112266 q^{45} + 323124 q^{47} - 8644 q^{49} + 86076 q^{51} + 358086 q^{53} - 414396 q^{57} - 719382 q^{59} + 421536 q^{61} + 104490 q^{63} - 322740 q^{65} - 267010 q^{67} + 464664 q^{71} + 1944486 q^{73} + 884574 q^{75} - 1713498 q^{77} + 685904 q^{79} - 236196 q^{81} - 3876168 q^{85} - 33534 q^{87} + 4130604 q^{89} + 484266 q^{91} - 1335744 q^{93} + 2105232 q^{95} - 877716 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(5\) 63.2658 + 36.5265i 0.506127 + 0.292212i 0.731240 0.682120i \(-0.238942\pi\)
−0.225113 + 0.974333i \(0.572275\pi\)
\(6\) 0 0
\(7\) 271.352 209.802i 0.791115 0.611667i
\(8\) 0 0
\(9\) 121.500 210.444i 0.166667 0.288675i
\(10\) 0 0
\(11\) −1073.02 1858.52i −0.806173 1.39633i −0.915496 0.402327i \(-0.868202\pi\)
0.109323 0.994006i \(-0.465132\pi\)
\(12\) 0 0
\(13\) 2550.94i 1.16110i 0.814224 + 0.580550i \(0.197163\pi\)
−0.814224 + 0.580550i \(0.802837\pi\)
\(14\) 0 0
\(15\) 1138.79 0.337418
\(16\) 0 0
\(17\) 2870.93 1657.53i 0.584355 0.337377i −0.178508 0.983939i \(-0.557127\pi\)
0.762862 + 0.646561i \(0.223794\pi\)
\(18\) 0 0
\(19\) −3813.46 2201.70i −0.555978 0.320994i 0.195551 0.980693i \(-0.437350\pi\)
−0.751530 + 0.659699i \(0.770684\pi\)
\(20\) 0 0
\(21\) 2028.01 4947.31i 0.218984 0.534209i
\(22\) 0 0
\(23\) 8548.49 14806.4i 0.702597 1.21693i −0.264955 0.964261i \(-0.585357\pi\)
0.967552 0.252673i \(-0.0813095\pi\)
\(24\) 0 0
\(25\) −5144.12 8909.88i −0.329224 0.570232i
\(26\) 0 0
\(27\) 3788.00i 0.192450i
\(28\) 0 0
\(29\) −33248.2 −1.36325 −0.681623 0.731703i \(-0.738726\pi\)
−0.681623 + 0.731703i \(0.738726\pi\)
\(30\) 0 0
\(31\) −10149.7 + 5859.92i −0.340696 + 0.196701i −0.660580 0.750756i \(-0.729689\pi\)
0.319884 + 0.947457i \(0.396356\pi\)
\(32\) 0 0
\(33\) −28971.4 16726.7i −0.806173 0.465444i
\(34\) 0 0
\(35\) 24830.7 3361.73i 0.579141 0.0784076i
\(36\) 0 0
\(37\) −24322.8 + 42128.4i −0.480185 + 0.831706i −0.999742 0.0227307i \(-0.992764\pi\)
0.519556 + 0.854436i \(0.326097\pi\)
\(38\) 0 0
\(39\) 19882.6 + 34437.7i 0.335181 + 0.580550i
\(40\) 0 0
\(41\) 71461.4i 1.03686i −0.855120 0.518430i \(-0.826517\pi\)
0.855120 0.518430i \(-0.173483\pi\)
\(42\) 0 0
\(43\) −86836.9 −1.09219 −0.546096 0.837723i \(-0.683887\pi\)
−0.546096 + 0.837723i \(0.683887\pi\)
\(44\) 0 0
\(45\) 15373.6 8875.95i 0.168709 0.0974041i
\(46\) 0 0
\(47\) 143252. + 82706.7i 1.37977 + 0.796612i 0.992132 0.125198i \(-0.0399566\pi\)
0.387641 + 0.921810i \(0.373290\pi\)
\(48\) 0 0
\(49\) 29615.3 113861.i 0.251726 0.967799i
\(50\) 0 0
\(51\) 25838.4 44753.4i 0.194785 0.337377i
\(52\) 0 0
\(53\) 42419.4 + 73472.5i 0.284929 + 0.493512i 0.972592 0.232519i \(-0.0746966\pi\)
−0.687663 + 0.726030i \(0.741363\pi\)
\(54\) 0 0
\(55\) 156774.i 0.942295i
\(56\) 0 0
\(57\) −68642.2 −0.370652
\(58\) 0 0
\(59\) 18534.0 10700.6i 0.0902428 0.0521017i −0.454199 0.890900i \(-0.650075\pi\)
0.544442 + 0.838798i \(0.316741\pi\)
\(60\) 0 0
\(61\) 235369. + 135891.i 1.03696 + 0.598687i 0.918970 0.394328i \(-0.129023\pi\)
0.117986 + 0.993015i \(0.462356\pi\)
\(62\) 0 0
\(63\) −11182.3 82595.5i −0.0447207 0.330320i
\(64\) 0 0
\(65\) −93177.0 + 161387.i −0.339288 + 0.587664i
\(66\) 0 0
\(67\) −239484. 414798.i −0.796253 1.37915i −0.922040 0.387094i \(-0.873479\pi\)
0.125787 0.992057i \(-0.459854\pi\)
\(68\) 0 0
\(69\) 266516.i 0.811289i
\(70\) 0 0
\(71\) −337334. −0.942507 −0.471254 0.881998i \(-0.656198\pi\)
−0.471254 + 0.881998i \(0.656198\pi\)
\(72\) 0 0
\(73\) 340100. 196357.i 0.874254 0.504751i 0.00549449 0.999985i \(-0.498251\pi\)
0.868760 + 0.495234i \(0.164918\pi\)
\(74\) 0 0
\(75\) −138891. 80188.9i −0.329224 0.190077i
\(76\) 0 0
\(77\) −681087. 279193.i −1.49187 0.611550i
\(78\) 0 0
\(79\) 5038.26 8726.52i 0.0102188 0.0176994i −0.860871 0.508824i \(-0.830081\pi\)
0.871090 + 0.491124i \(0.163414\pi\)
\(80\) 0 0
\(81\) −29524.5 51137.9i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 77744.9i 0.135968i −0.997686 0.0679841i \(-0.978343\pi\)
0.997686 0.0679841i \(-0.0216567\pi\)
\(84\) 0 0
\(85\) 242176. 0.394343
\(86\) 0 0
\(87\) −448851. + 259144.i −0.681623 + 0.393535i
\(88\) 0 0
\(89\) 478066. + 276012.i 0.678138 + 0.391523i 0.799153 0.601128i \(-0.205282\pi\)
−0.121015 + 0.992651i \(0.538615\pi\)
\(90\) 0 0
\(91\) 535192. + 692203.i 0.710208 + 0.918564i
\(92\) 0 0
\(93\) −91347.1 + 158218.i −0.113565 + 0.196701i
\(94\) 0 0
\(95\) −160841. 278585.i −0.187597 0.324928i
\(96\) 0 0
\(97\) 1.06023e6i 1.16168i −0.814020 0.580838i \(-0.802725\pi\)
0.814020 0.580838i \(-0.197275\pi\)
\(98\) 0 0
\(99\) −521486. −0.537449
\(100\) 0 0
\(101\) −763243. + 440658.i −0.740796 + 0.427699i −0.822359 0.568970i \(-0.807342\pi\)
0.0815629 + 0.996668i \(0.474009\pi\)
\(102\) 0 0
\(103\) 82998.1 + 47918.9i 0.0759550 + 0.0438526i 0.537496 0.843266i \(-0.319370\pi\)
−0.461542 + 0.887119i \(0.652703\pi\)
\(104\) 0 0
\(105\) 309012. 238919.i 0.266936 0.206387i
\(106\) 0 0
\(107\) 463383. 802602.i 0.378258 0.655162i −0.612551 0.790431i \(-0.709856\pi\)
0.990809 + 0.135269i \(0.0431898\pi\)
\(108\) 0 0
\(109\) −1.17618e6 2.03720e6i −0.908224 1.57309i −0.816530 0.577303i \(-0.804105\pi\)
−0.0916936 0.995787i \(-0.529228\pi\)
\(110\) 0 0
\(111\) 758311.i 0.554470i
\(112\) 0 0
\(113\) −658872. −0.456631 −0.228316 0.973587i \(-0.573322\pi\)
−0.228316 + 0.973587i \(0.573322\pi\)
\(114\) 0 0
\(115\) 1.08166e6 624494.i 0.711206 0.410615i
\(116\) 0 0
\(117\) 536830. + 309939.i 0.335181 + 0.193517i
\(118\) 0 0
\(119\) 431281. 1.05210e6i 0.255929 0.624335i
\(120\) 0 0
\(121\) −1.41695e6 + 2.45423e6i −0.799831 + 1.38535i
\(122\) 0 0
\(123\) −556986. 964729.i −0.299316 0.518430i
\(124\) 0 0
\(125\) 1.89304e6i 0.969238i
\(126\) 0 0
\(127\) −3.10460e6 −1.51564 −0.757818 0.652465i \(-0.773735\pi\)
−0.757818 + 0.652465i \(0.773735\pi\)
\(128\) 0 0
\(129\) −1.17230e6 + 676826.i −0.546096 + 0.315288i
\(130\) 0 0
\(131\) −3.03561e6 1.75261e6i −1.35031 0.779600i −0.362015 0.932172i \(-0.617911\pi\)
−0.988292 + 0.152572i \(0.951244\pi\)
\(132\) 0 0
\(133\) −1.49671e6 + 202634.i −0.636185 + 0.0861305i
\(134\) 0 0
\(135\) 138362. 239651.i 0.0562363 0.0974041i
\(136\) 0 0
\(137\) −142894. 247500.i −0.0555717 0.0962530i 0.836901 0.547354i \(-0.184365\pi\)
−0.892473 + 0.451101i \(0.851031\pi\)
\(138\) 0 0
\(139\) 2.54890e6i 0.949093i 0.880230 + 0.474547i \(0.157388\pi\)
−0.880230 + 0.474547i \(0.842612\pi\)
\(140\) 0 0
\(141\) 2.57854e6 0.919849
\(142\) 0 0
\(143\) 4.74097e6 2.73720e6i 1.62128 0.936048i
\(144\) 0 0
\(145\) −2.10348e6 1.21444e6i −0.689975 0.398358i
\(146\) 0 0
\(147\) −487648. 1.76795e6i −0.153516 0.556566i
\(148\) 0 0
\(149\) 405472. 702298.i 0.122575 0.212306i −0.798207 0.602383i \(-0.794218\pi\)
0.920782 + 0.390077i \(0.127551\pi\)
\(150\) 0 0
\(151\) −1.10258e6 1.90972e6i −0.320241 0.554674i 0.660296 0.751005i \(-0.270431\pi\)
−0.980538 + 0.196331i \(0.937097\pi\)
\(152\) 0 0
\(153\) 805562.i 0.224918i
\(154\) 0 0
\(155\) −856171. −0.229914
\(156\) 0 0
\(157\) 3.89107e6 2.24651e6i 1.00547 0.580510i 0.0956099 0.995419i \(-0.469520\pi\)
0.909863 + 0.414909i \(0.136187\pi\)
\(158\) 0 0
\(159\) 1.14532e6 + 661253.i 0.284929 + 0.164504i
\(160\) 0 0
\(161\) −786762. 5.81125e6i −0.188524 1.39249i
\(162\) 0 0
\(163\) 3.67950e6 6.37308e6i 0.849622 1.47159i −0.0319242 0.999490i \(-0.510164\pi\)
0.881546 0.472098i \(-0.156503\pi\)
\(164\) 0 0
\(165\) −1.22194e6 2.11645e6i −0.272017 0.471148i
\(166\) 0 0
\(167\) 2.46735e6i 0.529763i 0.964281 + 0.264881i \(0.0853328\pi\)
−0.964281 + 0.264881i \(0.914667\pi\)
\(168\) 0 0
\(169\) −1.68048e6 −0.348155
\(170\) 0 0
\(171\) −926670. + 535013.i −0.185326 + 0.106998i
\(172\) 0 0
\(173\) 607596. + 350796.i 0.117348 + 0.0677511i 0.557525 0.830160i \(-0.311751\pi\)
−0.440177 + 0.897911i \(0.645084\pi\)
\(174\) 0 0
\(175\) −3.26518e6 1.33847e6i −0.609246 0.249744i
\(176\) 0 0
\(177\) 166806. 288916.i 0.0300809 0.0521017i
\(178\) 0 0
\(179\) 1.12866e6 + 1.95490e6i 0.196791 + 0.340852i 0.947486 0.319797i \(-0.103615\pi\)
−0.750695 + 0.660649i \(0.770281\pi\)
\(180\) 0 0
\(181\) 2.39583e6i 0.404036i −0.979382 0.202018i \(-0.935250\pi\)
0.979382 0.202018i \(-0.0647499\pi\)
\(182\) 0 0
\(183\) 4.23665e6 0.691304
\(184\) 0 0
\(185\) −3.07761e6 + 1.77686e6i −0.486069 + 0.280632i
\(186\) 0 0
\(187\) −6.16112e6 3.55712e6i −0.942182 0.543969i
\(188\) 0 0
\(189\) −794729. 1.02788e6i −0.117715 0.152250i
\(190\) 0 0
\(191\) 648809. 1.12377e6i 0.0931144 0.161279i −0.815706 0.578467i \(-0.803651\pi\)
0.908820 + 0.417188i \(0.136984\pi\)
\(192\) 0 0
\(193\) −1.49829e6 2.59511e6i −0.208412 0.360980i 0.742802 0.669511i \(-0.233496\pi\)
−0.951214 + 0.308530i \(0.900163\pi\)
\(194\) 0 0
\(195\) 2.90497e6i 0.391776i
\(196\) 0 0
\(197\) 6.72245e6 0.879283 0.439641 0.898173i \(-0.355106\pi\)
0.439641 + 0.898173i \(0.355106\pi\)
\(198\) 0 0
\(199\) −9.71212e6 + 5.60729e6i −1.23241 + 0.711531i −0.967531 0.252751i \(-0.918665\pi\)
−0.264877 + 0.964282i \(0.585331\pi\)
\(200\) 0 0
\(201\) −6.46606e6 3.73318e6i −0.796253 0.459717i
\(202\) 0 0
\(203\) −9.02199e6 + 6.97554e6i −1.07848 + 0.833853i
\(204\) 0 0
\(205\) 2.61024e6 4.52106e6i 0.302983 0.524782i
\(206\) 0 0
\(207\) −2.07728e6 3.59796e6i −0.234199 0.405644i
\(208\) 0 0
\(209\) 9.44984e6i 1.03511i
\(210\) 0 0
\(211\) 273141. 0.0290763 0.0145381 0.999894i \(-0.495372\pi\)
0.0145381 + 0.999894i \(0.495372\pi\)
\(212\) 0 0
\(213\) −4.55400e6 + 2.62926e6i −0.471254 + 0.272078i
\(214\) 0 0
\(215\) −5.49381e6 3.17185e6i −0.552787 0.319152i
\(216\) 0 0
\(217\) −1.52472e6 + 3.71953e6i −0.149214 + 0.364006i
\(218\) 0 0
\(219\) 3.06090e6 5.30163e6i 0.291418 0.504751i
\(220\) 0 0
\(221\) 4.22827e6 + 7.32358e6i 0.391729 + 0.678495i
\(222\) 0 0
\(223\) 2.12335e7i 1.91472i −0.288890 0.957362i \(-0.593286\pi\)
0.288890 0.957362i \(-0.406714\pi\)
\(224\) 0 0
\(225\) −2.50004e6 −0.219483
\(226\) 0 0
\(227\) 4.68100e6 2.70258e6i 0.400186 0.231047i −0.286378 0.958117i \(-0.592451\pi\)
0.686564 + 0.727069i \(0.259118\pi\)
\(228\) 0 0
\(229\) 2.00874e7 + 1.15975e7i 1.67270 + 0.965732i 0.966119 + 0.258097i \(0.0830953\pi\)
0.706578 + 0.707635i \(0.250238\pi\)
\(230\) 0 0
\(231\) −1.13708e7 + 1.53944e6i −0.922473 + 0.124890i
\(232\) 0 0
\(233\) 3.77717e6 6.54226e6i 0.298607 0.517202i −0.677211 0.735789i \(-0.736812\pi\)
0.975817 + 0.218587i \(0.0701448\pi\)
\(234\) 0 0
\(235\) 6.04198e6 + 1.04650e7i 0.465560 + 0.806374i
\(236\) 0 0
\(237\) 157077.i 0.0117996i
\(238\) 0 0
\(239\) 2.64637e7 1.93846 0.969230 0.246155i \(-0.0791673\pi\)
0.969230 + 0.246155i \(0.0791673\pi\)
\(240\) 0 0
\(241\) −5.18988e6 + 2.99638e6i −0.370771 + 0.214065i −0.673795 0.738918i \(-0.735337\pi\)
0.303024 + 0.952983i \(0.402004\pi\)
\(242\) 0 0
\(243\) −797162. 460241.i −0.0555556 0.0320750i
\(244\) 0 0
\(245\) 6.03257e6 6.12174e6i 0.410208 0.416271i
\(246\) 0 0
\(247\) 5.61640e6 9.72789e6i 0.372707 0.645547i
\(248\) 0 0
\(249\) −605961. 1.04956e6i −0.0392506 0.0679841i
\(250\) 0 0
\(251\) 2.47242e7i 1.56351i 0.623583 + 0.781757i \(0.285676\pi\)
−0.623583 + 0.781757i \(0.714324\pi\)
\(252\) 0 0
\(253\) −3.66907e7 −2.26566
\(254\) 0 0
\(255\) 3.26938e6 1.88758e6i 0.197172 0.113837i
\(256\) 0 0
\(257\) 1.30814e7 + 7.55255e6i 0.770646 + 0.444932i 0.833105 0.553115i \(-0.186561\pi\)
−0.0624592 + 0.998048i \(0.519894\pi\)
\(258\) 0 0
\(259\) 2.23856e6 + 1.65346e7i 0.128845 + 0.951689i
\(260\) 0 0
\(261\) −4.03966e6 + 6.99689e6i −0.227208 + 0.393535i
\(262\) 0 0
\(263\) 7.01596e6 + 1.21520e7i 0.385674 + 0.668007i 0.991862 0.127314i \(-0.0406357\pi\)
−0.606189 + 0.795321i \(0.707302\pi\)
\(264\) 0 0
\(265\) 6.19773e6i 0.333039i
\(266\) 0 0
\(267\) 8.60519e6 0.452092
\(268\) 0 0
\(269\) 2.14076e7 1.23597e7i 1.09979 0.634965i 0.163625 0.986523i \(-0.447681\pi\)
0.936166 + 0.351558i \(0.114348\pi\)
\(270\) 0 0
\(271\) 2.96220e7 + 1.71022e7i 1.48835 + 0.859301i 0.999912 0.0132962i \(-0.00423244\pi\)
0.488441 + 0.872597i \(0.337566\pi\)
\(272\) 0 0
\(273\) 1.26203e7 + 5.17334e6i 0.620270 + 0.254263i
\(274\) 0 0
\(275\) −1.10395e7 + 1.91209e7i −0.530823 + 0.919412i
\(276\) 0 0
\(277\) −1.91114e7 3.31020e7i −0.899196 1.55745i −0.828524 0.559953i \(-0.810819\pi\)
−0.0706716 0.997500i \(-0.522514\pi\)
\(278\) 0 0
\(279\) 2.84792e6i 0.131134i
\(280\) 0 0
\(281\) −4.38890e6 −0.197805 −0.0989025 0.995097i \(-0.531533\pi\)
−0.0989025 + 0.995097i \(0.531533\pi\)
\(282\) 0 0
\(283\) −1.92918e7 + 1.11381e7i −0.851166 + 0.491421i −0.861044 0.508531i \(-0.830189\pi\)
0.00987835 + 0.999951i \(0.496856\pi\)
\(284\) 0 0
\(285\) −4.34271e6 2.50726e6i −0.187597 0.108309i
\(286\) 0 0
\(287\) −1.49927e7 1.93912e7i −0.634213 0.820275i
\(288\) 0 0
\(289\) −6.57394e6 + 1.13864e7i −0.272353 + 0.471730i
\(290\) 0 0
\(291\) −8.26367e6 1.43131e7i −0.335347 0.580838i
\(292\) 0 0
\(293\) 4.03269e7i 1.60322i 0.597849 + 0.801608i \(0.296022\pi\)
−0.597849 + 0.801608i \(0.703978\pi\)
\(294\) 0 0
\(295\) 1.56342e6 0.0608991
\(296\) 0 0
\(297\) −7.04006e6 + 4.06458e6i −0.268724 + 0.155148i
\(298\) 0 0
\(299\) 3.77703e7 + 2.18067e7i 1.41298 + 0.815786i
\(300\) 0 0
\(301\) −2.35634e7 + 1.82185e7i −0.864049 + 0.668058i
\(302\) 0 0
\(303\) −6.86918e6 + 1.18978e7i −0.246932 + 0.427699i
\(304\) 0 0
\(305\) 9.92722e6 + 1.71945e7i 0.349887 + 0.606023i
\(306\) 0 0
\(307\) 1.99914e7i 0.690921i −0.938433 0.345461i \(-0.887723\pi\)
0.938433 0.345461i \(-0.112277\pi\)
\(308\) 0 0
\(309\) 1.49396e6 0.0506366
\(310\) 0 0
\(311\) 1.04940e7 6.05872e6i 0.348868 0.201419i −0.315319 0.948986i \(-0.602111\pi\)
0.664186 + 0.747567i \(0.268778\pi\)
\(312\) 0 0
\(313\) 4.91209e7 + 2.83600e7i 1.60189 + 0.924853i 0.991108 + 0.133057i \(0.0424792\pi\)
0.610785 + 0.791797i \(0.290854\pi\)
\(314\) 0 0
\(315\) 2.30947e6 5.63392e6i 0.0738892 0.180252i
\(316\) 0 0
\(317\) −1.24114e7 + 2.14971e7i −0.389621 + 0.674843i −0.992398 0.123066i \(-0.960727\pi\)
0.602778 + 0.797909i \(0.294061\pi\)
\(318\) 0 0
\(319\) 3.56759e7 + 6.17925e7i 1.09901 + 1.90355i
\(320\) 0 0
\(321\) 1.44468e7i 0.436775i
\(322\) 0 0
\(323\) −1.45976e7 −0.433185
\(324\) 0 0
\(325\) 2.27286e7 1.31223e7i 0.662097 0.382262i
\(326\) 0 0
\(327\) −3.17568e7 1.83348e7i −0.908224 0.524363i
\(328\) 0 0
\(329\) 5.62239e7 7.61192e6i 1.57882 0.213750i
\(330\) 0 0
\(331\) −4.53145e6 + 7.84871e6i −0.124955 + 0.216428i −0.921715 0.387867i \(-0.873212\pi\)
0.796760 + 0.604295i \(0.206545\pi\)
\(332\) 0 0
\(333\) 5.91045e6 + 1.02372e7i 0.160062 + 0.277235i
\(334\) 0 0
\(335\) 3.49900e7i 0.930700i
\(336\) 0 0
\(337\) 3.31353e7 0.865767 0.432884 0.901450i \(-0.357496\pi\)
0.432884 + 0.901450i \(0.357496\pi\)
\(338\) 0 0
\(339\) −8.89477e6 + 5.13540e6i −0.228316 + 0.131818i
\(340\) 0 0
\(341\) 2.17815e7 + 1.25756e7i 0.549320 + 0.317150i
\(342\) 0 0
\(343\) −1.58520e7 3.71097e7i −0.392827 0.919613i
\(344\) 0 0
\(345\) 9.73490e6 1.68613e7i 0.237069 0.410615i
\(346\) 0 0
\(347\) 1.35157e7 + 2.34098e7i 0.323481 + 0.560286i 0.981204 0.192974i \(-0.0618133\pi\)
−0.657722 + 0.753260i \(0.728480\pi\)
\(348\) 0 0
\(349\) 1.26526e7i 0.297649i 0.988864 + 0.148824i \(0.0475489\pi\)
−0.988864 + 0.148824i \(0.952451\pi\)
\(350\) 0 0
\(351\) 9.66294e6 0.223454
\(352\) 0 0
\(353\) −6.20503e7 + 3.58248e7i −1.41065 + 0.814441i −0.995450 0.0952883i \(-0.969623\pi\)
−0.415203 + 0.909729i \(0.636289\pi\)
\(354\) 0 0
\(355\) −2.13417e7 1.23216e7i −0.477028 0.275412i
\(356\) 0 0
\(357\) −2.37804e6 1.75649e7i −0.0522654 0.386048i
\(358\) 0 0
\(359\) 5.75025e6 9.95972e6i 0.124281 0.215260i −0.797171 0.603754i \(-0.793671\pi\)
0.921451 + 0.388493i \(0.127004\pi\)
\(360\) 0 0
\(361\) −1.38280e7 2.39508e7i −0.293925 0.509094i
\(362\) 0 0
\(363\) 4.41761e7i 0.923565i
\(364\) 0 0
\(365\) 2.86889e7 0.589978
\(366\) 0 0
\(367\) −9.40666e6 + 5.43094e6i −0.190299 + 0.109869i −0.592123 0.805848i \(-0.701710\pi\)
0.401823 + 0.915717i \(0.368377\pi\)
\(368\) 0 0
\(369\) −1.50386e7 8.68256e6i −0.299316 0.172810i
\(370\) 0 0
\(371\) 2.69253e7 + 1.10373e7i 0.527277 + 0.216143i
\(372\) 0 0
\(373\) 2.63819e6 4.56949e6i 0.0508370 0.0880523i −0.839487 0.543380i \(-0.817144\pi\)
0.890324 + 0.455327i \(0.150478\pi\)
\(374\) 0 0
\(375\) −1.47548e7 2.55561e7i −0.279795 0.484619i
\(376\) 0 0
\(377\) 8.48142e7i 1.58287i
\(378\) 0 0
\(379\) −7.77449e7 −1.42809 −0.714043 0.700102i \(-0.753138\pi\)
−0.714043 + 0.700102i \(0.753138\pi\)
\(380\) 0 0
\(381\) −4.19122e7 + 2.41980e7i −0.757818 + 0.437527i
\(382\) 0 0
\(383\) 5.70488e7 + 3.29371e7i 1.01543 + 0.586259i 0.912777 0.408459i \(-0.133934\pi\)
0.102653 + 0.994717i \(0.467267\pi\)
\(384\) 0 0
\(385\) −3.28916e7 4.25411e7i −0.576371 0.745464i
\(386\) 0 0
\(387\) −1.05507e7 + 1.82743e7i −0.182032 + 0.315288i
\(388\) 0 0
\(389\) 1.99115e7 + 3.44878e7i 0.338264 + 0.585890i 0.984106 0.177581i \(-0.0568271\pi\)
−0.645842 + 0.763471i \(0.723494\pi\)
\(390\) 0 0
\(391\) 5.66777e7i 0.948161i
\(392\) 0 0
\(393\) −5.46410e7 −0.900205
\(394\) 0 0
\(395\) 637499. 368060.i 0.0103440 0.00597211i
\(396\) 0 0
\(397\) 1.44625e7 + 8.34992e6i 0.231138 + 0.133448i 0.611097 0.791556i \(-0.290729\pi\)
−0.379959 + 0.925003i \(0.624062\pi\)
\(398\) 0 0
\(399\) −1.86262e7 + 1.44013e7i −0.293229 + 0.226716i
\(400\) 0 0
\(401\) −1.77044e7 + 3.06649e7i −0.274567 + 0.475564i −0.970026 0.243002i \(-0.921868\pi\)
0.695459 + 0.718566i \(0.255201\pi\)
\(402\) 0 0
\(403\) −1.49483e7 2.58912e7i −0.228390 0.395583i
\(404\) 0 0
\(405\) 4.31371e6i 0.0649361i
\(406\) 0 0
\(407\) 1.04395e8 1.54845
\(408\) 0 0
\(409\) 3.81349e7 2.20172e7i 0.557381 0.321804i −0.194713 0.980860i \(-0.562377\pi\)
0.752094 + 0.659056i \(0.229044\pi\)
\(410\) 0 0
\(411\) −3.85815e6 2.22750e6i −0.0555717 0.0320843i
\(412\) 0 0
\(413\) 2.78424e6 6.79210e6i 0.0395235 0.0964171i
\(414\) 0 0
\(415\) 2.83975e6 4.91859e6i 0.0397316 0.0688172i
\(416\) 0 0
\(417\) 1.98667e7 + 3.44102e7i 0.273980 + 0.474547i
\(418\) 0 0
\(419\) 1.45445e8i 1.97723i 0.150456 + 0.988617i \(0.451926\pi\)
−0.150456 + 0.988617i \(0.548074\pi\)
\(420\) 0 0
\(421\) 1.72505e7 0.231182 0.115591 0.993297i \(-0.463124\pi\)
0.115591 + 0.993297i \(0.463124\pi\)
\(422\) 0 0
\(423\) 3.48103e7 2.00977e7i 0.459924 0.265537i
\(424\) 0 0
\(425\) −2.95369e7 1.70531e7i −0.384767 0.222145i
\(426\) 0 0
\(427\) 9.23781e7 1.25067e7i 1.18655 0.160642i
\(428\) 0 0
\(429\) 4.26687e7 7.39044e7i 0.540428 0.936048i
\(430\) 0 0
\(431\) 4.44477e6 + 7.69857e6i 0.0555159 + 0.0961564i 0.892448 0.451151i \(-0.148986\pi\)
−0.836932 + 0.547307i \(0.815653\pi\)
\(432\) 0 0
\(433\) 1.64906e7i 0.203130i 0.994829 + 0.101565i \(0.0323850\pi\)
−0.994829 + 0.101565i \(0.967615\pi\)
\(434\) 0 0
\(435\) −3.78626e7 −0.459984
\(436\) 0 0
\(437\) −6.51986e7 + 3.76424e7i −0.781257 + 0.451059i
\(438\) 0 0
\(439\) −7.87931e7 4.54912e7i −0.931310 0.537692i −0.0440846 0.999028i \(-0.514037\pi\)
−0.887226 + 0.461336i \(0.847370\pi\)
\(440\) 0 0
\(441\) −2.03630e7 2.00664e7i −0.237425 0.233967i
\(442\) 0 0
\(443\) 8.56112e7 1.48283e8i 0.984735 1.70561i 0.341627 0.939835i \(-0.389022\pi\)
0.643108 0.765776i \(-0.277645\pi\)
\(444\) 0 0
\(445\) 2.01635e7 + 3.49242e7i 0.228816 + 0.396320i
\(446\) 0 0
\(447\) 1.26414e7i 0.141537i
\(448\) 0 0
\(449\) 1.66699e8 1.84159 0.920796 0.390045i \(-0.127540\pi\)
0.920796 + 0.390045i \(0.127540\pi\)
\(450\) 0 0
\(451\) −1.32812e8 + 7.66793e7i −1.44780 + 0.835888i
\(452\) 0 0
\(453\) −2.97695e7 1.71874e7i −0.320241 0.184891i
\(454\) 0 0
\(455\) 8.57556e6 + 6.33415e7i 0.0910391 + 0.672441i
\(456\) 0 0
\(457\) −5.01139e7 + 8.67997e7i −0.525060 + 0.909431i 0.474514 + 0.880248i \(0.342624\pi\)
−0.999574 + 0.0291831i \(0.990709\pi\)
\(458\) 0 0
\(459\) −6.27873e6 1.08751e7i −0.0649283 0.112459i
\(460\) 0 0
\(461\) 7.26582e7i 0.741621i 0.928709 + 0.370810i \(0.120920\pi\)
−0.928709 + 0.370810i \(0.879080\pi\)
\(462\) 0 0
\(463\) 4.61814e7 0.465291 0.232645 0.972562i \(-0.425262\pi\)
0.232645 + 0.972562i \(0.425262\pi\)
\(464\) 0 0
\(465\) −1.15583e7 + 6.67319e6i −0.114957 + 0.0663704i
\(466\) 0 0
\(467\) 8.53270e7 + 4.92635e7i 0.837791 + 0.483699i 0.856513 0.516126i \(-0.172626\pi\)
−0.0187219 + 0.999825i \(0.505960\pi\)
\(468\) 0 0
\(469\) −1.52010e8 6.23123e7i −1.47351 0.604025i
\(470\) 0 0
\(471\) 3.50197e7 6.06558e7i 0.335158 0.580510i
\(472\) 0 0
\(473\) 9.31774e7 + 1.61388e8i 0.880495 + 1.52506i
\(474\) 0 0
\(475\) 4.53033e7i 0.422716i
\(476\) 0 0
\(477\) 2.06158e7 0.189953
\(478\) 0 0
\(479\) 1.06047e7 6.12260e6i 0.0964917 0.0557095i −0.450978 0.892535i \(-0.648925\pi\)
0.547469 + 0.836826i \(0.315591\pi\)
\(480\) 0 0
\(481\) −1.07467e8 6.20460e7i −0.965694 0.557544i
\(482\) 0 0
\(483\) −5.59155e7 7.23197e7i −0.496239 0.641823i
\(484\) 0 0
\(485\) 3.87265e7 6.70763e7i 0.339456 0.587955i
\(486\) 0 0
\(487\) −6.09340e7 1.05541e8i −0.527561 0.913763i −0.999484 0.0321229i \(-0.989773\pi\)
0.471923 0.881640i \(-0.343560\pi\)
\(488\) 0 0
\(489\) 1.14715e8i 0.981059i
\(490\) 0 0
\(491\) −1.25121e8 −1.05703 −0.528513 0.848925i \(-0.677250\pi\)
−0.528513 + 0.848925i \(0.677250\pi\)
\(492\) 0 0
\(493\) −9.54534e7 + 5.51101e7i −0.796619 + 0.459928i
\(494\) 0 0
\(495\) −3.29923e7 1.90481e7i −0.272017 0.157049i
\(496\) 0 0
\(497\) −9.15363e7 + 7.07732e7i −0.745632 + 0.576501i
\(498\) 0 0
\(499\) −1.01359e8 + 1.75559e8i −0.815758 + 1.41293i 0.0930245 + 0.995664i \(0.470347\pi\)
−0.908782 + 0.417270i \(0.862987\pi\)
\(500\) 0 0
\(501\) 1.92311e7 + 3.33092e7i 0.152929 + 0.264881i
\(502\) 0 0
\(503\) 1.91474e8i 1.50455i −0.658851 0.752274i \(-0.728957\pi\)
0.658851 0.752274i \(-0.271043\pi\)
\(504\) 0 0
\(505\) −6.43829e7 −0.499915
\(506\) 0 0
\(507\) −2.26865e7 + 1.30980e7i −0.174078 + 0.100504i
\(508\) 0 0
\(509\) −8.96152e7 5.17394e7i −0.679561 0.392345i 0.120129 0.992758i \(-0.461669\pi\)
−0.799690 + 0.600414i \(0.795003\pi\)
\(510\) 0 0
\(511\) 5.10909e7 1.24635e8i 0.382896 0.934069i
\(512\) 0 0
\(513\) −8.34003e6 + 1.44454e7i −0.0617754 + 0.106998i
\(514\) 0 0
\(515\) 3.50063e6 + 6.06326e6i 0.0256286 + 0.0443900i
\(516\) 0 0
\(517\) 3.54983e8i 2.56883i
\(518\) 0 0
\(519\) 1.09367e7 0.0782322
\(520\) 0 0
\(521\) 1.72264e8 9.94565e7i 1.21809 0.703267i 0.253584 0.967313i \(-0.418391\pi\)
0.964510 + 0.264047i \(0.0850573\pi\)
\(522\) 0 0
\(523\) −1.02914e8 5.94177e7i −0.719401 0.415346i 0.0951311 0.995465i \(-0.469673\pi\)
−0.814532 + 0.580118i \(0.803006\pi\)
\(524\) 0 0
\(525\) −5.45123e7 + 7.38020e6i −0.376718 + 0.0510023i
\(526\) 0 0
\(527\) −1.94260e7 + 3.36469e7i −0.132725 + 0.229886i
\(528\) 0 0
\(529\) −7.21356e7 1.24942e8i −0.487284 0.844001i
\(530\) 0 0
\(531\) 5.20049e6i 0.0347345i
\(532\) 0 0
\(533\) 1.82294e8 1.20390
\(534\) 0 0
\(535\) 5.86326e7 3.38515e7i 0.382893 0.221063i
\(536\) 0 0
\(537\) 3.04739e7 + 1.75941e7i 0.196791 + 0.113617i
\(538\) 0 0
\(539\) −2.43390e8 + 6.71336e7i −1.55430 + 0.428720i
\(540\) 0 0
\(541\) −1.70729e6 + 2.95711e6i −0.0107824 + 0.0186757i −0.871366 0.490633i \(-0.836766\pi\)
0.860584 + 0.509309i \(0.170099\pi\)
\(542\) 0 0
\(543\) −1.86736e7 3.23437e7i −0.116635 0.202018i
\(544\) 0 0
\(545\) 1.71847e8i 1.06158i
\(546\) 0 0
\(547\) 1.24520e8 0.760813 0.380406 0.924819i \(-0.375784\pi\)
0.380406 + 0.924819i \(0.375784\pi\)
\(548\) 0 0
\(549\) 5.71947e7 3.30214e7i 0.345652 0.199562i
\(550\) 0 0
\(551\) 1.26791e8 + 7.32026e7i 0.757936 + 0.437594i
\(552\) 0 0
\(553\) −463697. 3.42500e6i −0.00274194 0.0202528i
\(554\) 0 0
\(555\) −2.76985e7 + 4.79752e7i −0.162023 + 0.280632i
\(556\) 0 0
\(557\) −1.83383e7 3.17629e7i −0.106119 0.183804i 0.808076 0.589078i \(-0.200509\pi\)
−0.914195 + 0.405275i \(0.867176\pi\)
\(558\) 0 0
\(559\) 2.21515e8i 1.26814i
\(560\) 0 0
\(561\) −1.10900e8 −0.628121
\(562\) 0 0
\(563\) 4.08896e7 2.36076e7i 0.229133 0.132290i −0.381039 0.924559i \(-0.624434\pi\)
0.610172 + 0.792269i \(0.291100\pi\)
\(564\) 0 0
\(565\) −4.16841e7 2.40663e7i −0.231113 0.133433i
\(566\) 0 0
\(567\) −1.87404e7 7.68211e6i −0.102809 0.0421436i
\(568\) 0 0
\(569\) 7.48737e7 1.29685e8i 0.406437 0.703969i −0.588051 0.808824i \(-0.700105\pi\)
0.994488 + 0.104855i \(0.0334379\pi\)
\(570\) 0 0
\(571\) 4.86751e7 + 8.43077e7i 0.261456 + 0.452855i 0.966629 0.256180i \(-0.0824641\pi\)
−0.705173 + 0.709035i \(0.749131\pi\)
\(572\) 0 0
\(573\) 2.02279e7i 0.107519i
\(574\) 0 0
\(575\) −1.75898e8 −0.925246
\(576\) 0 0
\(577\) 1.19272e8 6.88620e7i 0.620887 0.358469i −0.156327 0.987705i \(-0.549965\pi\)
0.777214 + 0.629236i \(0.216632\pi\)
\(578\) 0 0
\(579\) −4.04537e7 2.33560e7i −0.208412 0.120327i
\(580\) 0 0
\(581\) −1.63110e7 2.10963e7i −0.0831673 0.107567i
\(582\) 0 0
\(583\) 9.10334e7 1.57674e8i 0.459404 0.795712i
\(584\) 0 0
\(585\) 2.26420e7 + 3.92171e7i 0.113096 + 0.195888i
\(586\) 0 0
\(587\) 2.35474e8i 1.16420i −0.813116 0.582101i \(-0.802231\pi\)
0.813116 0.582101i \(-0.197769\pi\)
\(588\) 0 0
\(589\) 5.16071e7 0.252560
\(590\) 0 0
\(591\) 9.07530e7 5.23963e7i 0.439641 0.253827i
\(592\) 0 0
\(593\) −1.56277e7 9.02267e6i −0.0749431 0.0432684i 0.462060 0.886849i \(-0.347110\pi\)
−0.537003 + 0.843580i \(0.680444\pi\)
\(594\) 0 0
\(595\) 6.57151e7 5.08090e7i 0.311971 0.241207i
\(596\) 0 0
\(597\) −8.74090e7 + 1.51397e8i −0.410803 + 0.711531i
\(598\) 0 0
\(599\) −4.75156e7 8.22994e7i −0.221083 0.382927i 0.734054 0.679091i \(-0.237626\pi\)
−0.955137 + 0.296164i \(0.904293\pi\)
\(600\) 0 0
\(601\) 3.02566e8i 1.39379i 0.717175 + 0.696894i \(0.245435\pi\)
−0.717175 + 0.696894i \(0.754565\pi\)
\(602\) 0 0
\(603\) −1.16389e8 −0.530836
\(604\) 0 0
\(605\) −1.79289e8 + 1.03512e8i −0.809631 + 0.467441i
\(606\) 0 0
\(607\) 5.14464e7 + 2.97026e7i 0.230032 + 0.132809i 0.610587 0.791949i \(-0.290934\pi\)
−0.380555 + 0.924758i \(0.624267\pi\)
\(608\) 0 0
\(609\) −6.74279e7 + 1.64489e8i −0.298530 + 0.728258i
\(610\) 0 0
\(611\) −2.10980e8 + 3.65427e8i −0.924947 + 1.60206i
\(612\) 0 0
\(613\) 9.34358e7 + 1.61836e8i 0.405632 + 0.702575i 0.994395 0.105731i \(-0.0337182\pi\)
−0.588763 + 0.808306i \(0.700385\pi\)
\(614\) 0 0
\(615\) 8.13792e7i 0.349855i
\(616\) 0 0
\(617\) 7.25028e7 0.308674 0.154337 0.988018i \(-0.450676\pi\)
0.154337 + 0.988018i \(0.450676\pi\)
\(618\) 0 0
\(619\) −1.69087e8 + 9.76227e7i −0.712918 + 0.411603i −0.812140 0.583462i \(-0.801698\pi\)
0.0992227 + 0.995065i \(0.468364\pi\)
\(620\) 0 0
\(621\) −5.60867e7 3.23817e7i −0.234199 0.135215i
\(622\) 0 0
\(623\) 1.87632e8 2.54028e7i 0.775967 0.105055i
\(624\) 0 0
\(625\) −1.12306e7 + 1.94520e7i −0.0460005 + 0.0796752i
\(626\) 0 0
\(627\) 7.36542e7 + 1.27573e8i 0.298810 + 0.517554i
\(628\) 0 0
\(629\) 1.61264e8i 0.648015i
\(630\) 0 0
\(631\) 7.65603e7 0.304730 0.152365 0.988324i \(-0.451311\pi\)
0.152365 + 0.988324i \(0.451311\pi\)
\(632\) 0 0
\(633\) 3.68740e6 2.12892e6i 0.0145381 0.00839360i
\(634\) 0 0
\(635\) −1.96415e8 1.13401e8i −0.767104 0.442888i
\(636\) 0 0
\(637\) 2.90451e8 + 7.55468e7i 1.12371 + 0.292279i
\(638\) 0 0
\(639\) −4.09860e7 + 7.09899e7i −0.157085 + 0.272078i
\(640\) 0 0
\(641\) −1.89649e8 3.28481e8i −0.720071 1.24720i −0.960971 0.276650i \(-0.910776\pi\)
0.240899 0.970550i \(-0.422558\pi\)
\(642\) 0 0
\(643\) 2.99610e7i 0.112700i 0.998411 + 0.0563500i \(0.0179463\pi\)
−0.998411 + 0.0563500i \(0.982054\pi\)
\(644\) 0 0
\(645\) −9.88885e7 −0.368525
\(646\) 0 0
\(647\) 3.22339e7 1.86103e7i 0.119015 0.0687132i −0.439311 0.898335i \(-0.644777\pi\)
0.558326 + 0.829622i \(0.311444\pi\)
\(648\) 0 0
\(649\) −3.97745e7 2.29638e7i −0.145503 0.0840060i
\(650\) 0 0
\(651\) 8.40714e6 + 6.20976e7i 0.0304723 + 0.225077i
\(652\) 0 0
\(653\) 9.92694e7 1.71940e8i 0.356513 0.617499i −0.630862 0.775895i \(-0.717299\pi\)
0.987376 + 0.158396i \(0.0506321\pi\)
\(654\) 0 0
\(655\) −1.28034e8 2.21761e8i −0.455618 0.789153i
\(656\) 0 0
\(657\) 9.54293e7i 0.336501i
\(658\) 0 0
\(659\) 5.59686e8 1.95564 0.977818 0.209454i \(-0.0671687\pi\)
0.977818 + 0.209454i \(0.0671687\pi\)
\(660\) 0 0
\(661\) −1.31767e8 + 7.60755e7i −0.456248 + 0.263415i −0.710465 0.703732i \(-0.751516\pi\)
0.254217 + 0.967147i \(0.418182\pi\)
\(662\) 0 0
\(663\) 1.14163e8 + 6.59122e7i 0.391729 + 0.226165i
\(664\) 0 0
\(665\) −1.02092e8 4.18499e7i −0.347158 0.142308i
\(666\) 0 0
\(667\) −2.84222e8 + 4.92287e8i −0.957813 + 1.65898i
\(668\) 0 0
\(669\) −1.65499e8 2.86652e8i −0.552733 0.957362i
\(670\) 0 0
\(671\) 5.83251e8i 1.93058i
\(672\) 0 0
\(673\) 2.07554e8 0.680903 0.340451 0.940262i \(-0.389420\pi\)
0.340451 + 0.940262i \(0.389420\pi\)
\(674\) 0 0
\(675\) −3.37506e7 + 1.94859e7i −0.109741 + 0.0633592i
\(676\) 0 0
\(677\) 1.72463e8 + 9.95717e7i 0.555815 + 0.320900i 0.751464 0.659774i \(-0.229348\pi\)
−0.195649 + 0.980674i \(0.562681\pi\)
\(678\) 0 0
\(679\) −2.22438e8 2.87696e8i −0.710559 0.919019i
\(680\) 0 0
\(681\) 4.21290e7 7.29696e7i 0.133395 0.231047i
\(682\) 0 0
\(683\) 2.58231e8 + 4.47269e8i 0.810486 + 1.40380i 0.912524 + 0.409023i \(0.134130\pi\)
−0.102037 + 0.994781i \(0.532536\pi\)
\(684\) 0 0
\(685\) 2.08778e7i 0.0649550i
\(686\) 0 0
\(687\) 3.61573e8 1.11513
\(688\) 0 0
\(689\) −1.87424e8 + 1.08209e8i −0.573017 + 0.330831i
\(690\) 0 0
\(691\) 5.07493e8 + 2.93001e8i 1.53814 + 0.888046i 0.998948 + 0.0458631i \(0.0146038\pi\)
0.539192 + 0.842183i \(0.318730\pi\)
\(692\) 0 0
\(693\) −1.41507e8 + 1.09409e8i −0.425184 + 0.328740i
\(694\) 0 0
\(695\) −9.31026e7 + 1.61259e8i −0.277337 + 0.480362i
\(696\) 0 0
\(697\) −1.18450e8 2.05161e8i −0.349813 0.605894i
\(698\) 0 0
\(699\) 1.17761e8i 0.344801i
\(700\) 0 0
\(701\) 8.34906e7 0.242373 0.121186 0.992630i \(-0.461330\pi\)
0.121186 + 0.992630i \(0.461330\pi\)
\(702\) 0 0
\(703\) 1.85508e8 1.07103e8i 0.533945 0.308274i
\(704\) 0 0
\(705\) 1.63133e8 + 9.41851e7i 0.465560 + 0.268791i
\(706\) 0 0
\(707\) −1.14657e8 + 2.79703e8i −0.324445 + 0.791479i
\(708\) 0 0
\(709\) −7.43808e7 + 1.28831e8i −0.208700 + 0.361479i −0.951305 0.308251i \(-0.900256\pi\)
0.742605 + 0.669729i \(0.233590\pi\)
\(710\) 0 0
\(711\) −1.22430e6 2.12054e6i −0.00340626 0.00589981i
\(712\) 0 0
\(713\) 2.00374e8i 0.552806i
\(714\) 0 0
\(715\) 3.99922e8 1.09410
\(716\) 0 0
\(717\) 3.57260e8 2.06264e8i 0.969230 0.559585i
\(718\) 0 0
\(719\) 3.24690e8 + 1.87460e8i 0.873540 + 0.504338i 0.868523 0.495649i \(-0.165070\pi\)
0.00501672 + 0.999987i \(0.498403\pi\)
\(720\) 0 0
\(721\) 3.25752e7 4.41023e6i 0.0869123 0.0117667i
\(722\) 0 0
\(723\) −4.67089e7 + 8.09022e7i −0.123590 + 0.214065i
\(724\) 0 0
\(725\) 1.71033e8 + 2.96238e8i 0.448813 + 0.777367i
\(726\) 0 0
\(727\) 5.14759e8i 1.33968i 0.742506 + 0.669840i \(0.233637\pi\)
−0.742506 + 0.669840i \(0.766363\pi\)
\(728\) 0 0
\(729\) −1.43489e7 −0.0370370
\(730\) 0 0
\(731\) −2.49303e8 + 1.43935e8i −0.638227 + 0.368481i
\(732\) 0 0
\(733\) 2.31672e8 + 1.33756e8i 0.588249 + 0.339626i 0.764405 0.644737i \(-0.223033\pi\)
−0.176156 + 0.984362i \(0.556366\pi\)
\(734\) 0 0
\(735\) 3.37255e7 1.29663e8i 0.0849368 0.326552i
\(736\) 0 0
\(737\) −5.13940e8 + 8.90170e8i −1.28384 + 2.22367i
\(738\) 0 0
\(739\) −2.45455e8 4.25141e8i −0.608189 1.05341i −0.991539 0.129811i \(-0.958563\pi\)
0.383349 0.923603i \(-0.374770\pi\)
\(740\) 0 0
\(741\) 1.75102e8i 0.430365i
\(742\) 0 0
\(743\) −8.00568e7 −0.195178 −0.0975892 0.995227i \(-0.531113\pi\)
−0.0975892 + 0.995227i \(0.531113\pi\)
\(744\) 0 0
\(745\) 5.13050e7 2.96210e7i 0.124077 0.0716358i
\(746\) 0 0
\(747\) −1.63610e7 9.44600e6i −0.0392506 0.0226614i
\(748\) 0 0
\(749\) −4.26475e7 3.15007e8i −0.101496 0.749677i
\(750\) 0 0
\(751\) −2.18469e8 + 3.78400e8i −0.515788 + 0.893370i 0.484044 + 0.875043i \(0.339167\pi\)
−0.999832 + 0.0183270i \(0.994166\pi\)
\(752\) 0 0
\(753\) 1.92706e8 + 3.33777e8i 0.451348 + 0.781757i
\(754\) 0 0
\(755\) 1.61093e8i 0.374314i
\(756\) 0 0
\(757\) −1.56135e8 −0.359925 −0.179962 0.983673i \(-0.557598\pi\)
−0.179962 + 0.983673i \(0.557598\pi\)
\(758\) 0 0
\(759\) −4.95325e8 + 2.85976e8i −1.13283 + 0.654039i
\(760\) 0 0
\(761\) −3.13313e8 1.80891e8i −0.710926 0.410453i 0.100478 0.994939i \(-0.467963\pi\)
−0.811404 + 0.584486i \(0.801296\pi\)
\(762\) 0 0
\(763\) −7.46566e8 3.06034e8i −1.68072 0.688964i
\(764\) 0 0
\(765\) 2.94244e7 5.09645e7i 0.0657239 0.113837i
\(766\) 0 0
\(767\) 2.72966e7 + 4.72791e7i 0.0604954 + 0.104781i
\(768\) 0 0
\(769\) 1.92526e8i 0.423361i −0.977339 0.211680i \(-0.932106\pi\)
0.977339 0.211680i \(-0.0678936\pi\)
\(770\) 0 0
\(771\) 2.35465e8 0.513764
\(772\) 0 0
\(773\) 3.54462e8 2.04648e8i 0.767416 0.443068i −0.0645363 0.997915i \(-0.520557\pi\)
0.831952 + 0.554848i \(0.187223\pi\)
\(774\) 0 0
\(775\) 1.04422e8 + 6.02883e7i 0.224331 + 0.129517i
\(776\) 0 0
\(777\) 1.59095e8 + 2.05770e8i 0.339151 + 0.438650i
\(778\) 0 0
\(779\) −1.57337e8 + 2.72515e8i −0.332826 + 0.576471i
\(780\) 0 0
\(781\) 3.61965e8 + 6.26941e8i 0.759824 + 1.31605i
\(782\) 0 0
\(783\) 1.25944e8i 0.262357i
\(784\) 0 0
\(785\) 3.28229e8 0.678529
\(786\) 0 0
\(787\) −2.32826e7 + 1.34422e7i −0.0477648 + 0.0275770i −0.523692 0.851908i \(-0.675446\pi\)
0.475927 + 0.879485i \(0.342112\pi\)
\(788\) 0 0
\(789\) 1.89431e8 + 1.09368e8i 0.385674 + 0.222669i
\(790\) 0 0
\(791\) −1.78787e8 + 1.38233e8i −0.361248 + 0.279306i
\(792\) 0 0
\(793\) −3.46648e8 + 6.00413e8i −0.695136 + 1.20401i
\(794\) 0 0
\(795\) 4.83066e7 + 8.36694e7i 0.0961401 + 0.166520i
\(796\) 0 0
\(797\) 3.01544e8i 0.595630i 0.954624 + 0.297815i \(0.0962578\pi\)
−0.954624 + 0.297815i \(0.903742\pi\)
\(798\) 0 0
\(799\) 5.48357e8 1.07504
\(800\) 0 0
\(801\) 1.16170e8 6.70708e7i 0.226046 0.130508i
\(802\) 0 0
\(803\) −7.29865e8 4.21388e8i −1.40960 0.813833i
\(804\) 0 0
\(805\) 1.62490e8 3.96391e8i 0.311486 0.759865i
\(806\) 0 0
\(807\) 1.92668e8 3.33711e8i 0.366597 0.634965i
\(808\) 0 0
\(809\) 1.91561e8 + 3.31793e8i 0.361794 + 0.626646i 0.988256 0.152806i \(-0.0488310\pi\)
−0.626462 + 0.779452i \(0.715498\pi\)
\(810\) 0 0
\(811\) 2.36880e8i 0.444085i 0.975037 + 0.222042i \(0.0712723\pi\)
−0.975037 + 0.222042i \(0.928728\pi\)
\(812\) 0 0
\(813\) 5.33195e8 0.992235
\(814\) 0 0
\(815\) 4.65573e8 2.68799e8i 0.860033 0.496540i
\(816\) 0 0
\(817\) 3.31149e8 + 1.91189e8i 0.607235 + 0.350587i
\(818\) 0 0
\(819\) 2.10696e8 2.85253e7i 0.383535 0.0519252i
\(820\) 0 0
\(821\) −3.06951e8 + 5.31655e8i −0.554676 + 0.960727i 0.443252 + 0.896397i \(0.353825\pi\)
−0.997929 + 0.0643305i \(0.979509\pi\)
\(822\) 0 0
\(823\) 3.29240e8 + 5.70261e8i 0.590628 + 1.02300i 0.994148 + 0.108026i \(0.0344531\pi\)
−0.403520 + 0.914971i \(0.632214\pi\)
\(824\) 0 0
\(825\) 3.44176e8i 0.612941i
\(826\) 0 0
\(827\) 6.88166e7 0.121668 0.0608341 0.998148i \(-0.480624\pi\)
0.0608341 + 0.998148i \(0.480624\pi\)
\(828\) 0 0
\(829\) −4.17661e8 + 2.41137e8i −0.733096 + 0.423253i −0.819554 0.573003i \(-0.805779\pi\)
0.0864579 + 0.996256i \(0.472445\pi\)
\(830\) 0 0
\(831\) −5.16009e8 2.97918e8i −0.899196 0.519151i
\(832\) 0 0
\(833\) −1.03704e8 3.75974e8i −0.179416 0.650464i
\(834\) 0 0
\(835\) −9.01238e7 + 1.56099e8i −0.154803 + 0.268127i
\(836\) 0 0
\(837\) 2.21973e7 + 3.84469e7i 0.0378551 + 0.0655670i
\(838\) 0 0
\(839\) 2.98764e8i 0.505874i −0.967483 0.252937i \(-0.918603\pi\)
0.967483 0.252937i \(-0.0813965\pi\)
\(840\) 0 0
\(841\) 5.10621e8 0.858441
\(842\) 0 0
\(843\) −5.92502e7 + 3.42081e7i −0.0989025 + 0.0571014i
\(844\) 0 0
\(845\) −1.06317e8 6.13821e7i −0.176211 0.101735i
\(846\) 0 0
\(847\) 1.30409e8 + 9.63239e8i 0.214614 + 1.58520i
\(848\) 0 0
\(849\) −1.73626e8 + 3.00730e8i −0.283722 + 0.491421i
\(850\) 0 0
\(851\) 4.15847e8 + 7.20268e8i 0.674753 + 1.16871i
\(852\) 0 0
\(853\) 1.21454e9i 1.95688i −0.206537 0.978439i \(-0.566219\pi\)
0.206537 0.978439i \(-0.433781\pi\)
\(854\) 0 0
\(855\) −7.81687e7 −0.125065
\(856\) 0 0
\(857\) 2.95805e8 1.70783e8i 0.469962 0.271333i −0.246262 0.969203i \(-0.579202\pi\)
0.716224 + 0.697871i \(0.245869\pi\)
\(858\) 0 0
\(859\) 4.92186e7 + 2.84164e7i 0.0776515 + 0.0448321i 0.538323 0.842739i \(-0.319058\pi\)
−0.460672 + 0.887571i \(0.652391\pi\)
\(860\) 0 0
\(861\) −3.53542e8 1.44925e8i −0.553900 0.227056i
\(862\) 0 0
\(863\) 2.73857e8 4.74335e8i 0.426081 0.737993i −0.570440 0.821339i \(-0.693227\pi\)
0.996521 + 0.0833459i \(0.0265606\pi\)
\(864\) 0 0
\(865\) 2.56267e7 + 4.43868e7i 0.0395954 + 0.0685812i
\(866\) 0 0
\(867\) 2.04955e8i 0.314486i
\(868\) 0 0
\(869\) −2.16245e7 −0.0329524
\(870\) 0 0
\(871\) 1.05812e9 6.10908e8i 1.60133 0.924530i
\(872\) 0 0
\(873\) −2.23119e8 1.28818e8i −0.335347 0.193613i
\(874\) 0 0
\(875\) −3.97164e8 5.13682e8i −0.592851 0.766779i
\(876\) 0 0
\(877\) 2.77263e8 4.80234e8i 0.411049 0.711958i −0.583956 0.811785i \(-0.698496\pi\)
0.995005 + 0.0998278i \(0.0318292\pi\)
\(878\) 0 0
\(879\) 3.14317e8 + 5.44414e8i 0.462809 + 0.801608i
\(880\) 0 0
\(881\) 1.02196e9i 1.49454i −0.664521 0.747270i \(-0.731364\pi\)
0.664521 0.747270i \(-0.268636\pi\)
\(882\) 0 0
\(883\) 9.10455e8 1.32244 0.661220 0.750192i \(-0.270039\pi\)
0.661220 + 0.750192i \(0.270039\pi\)
\(884\) 0 0
\(885\) 2.11062e7 1.21857e7i 0.0304495 0.0175801i
\(886\) 0 0
\(887\) 5.43780e7 + 3.13951e7i 0.0779206 + 0.0449875i 0.538454 0.842655i \(-0.319009\pi\)
−0.460533 + 0.887642i \(0.652342\pi\)
\(888\) 0 0
\(889\) −8.42442e8 + 6.51352e8i −1.19904 + 0.927066i
\(890\) 0 0
\(891\) −6.33606e7 + 1.09744e8i −0.0895748 + 0.155148i
\(892\) 0 0
\(893\) −3.64191e8 6.30797e8i −0.511416 0.885798i
\(894\) 0 0
\(895\) 1.64905e8i 0.230019i
\(896\) 0 0
\(897\) 6.79865e8 0.941988
\(898\) 0 0
\(899\) 3.37459e8 1.94832e8i 0.464453 0.268152i
\(900\) 0 0
\(901\) 2.43566e8 + 1.40623e8i 0.332999 + 0.192257i
\(902\) 0 0
\(903\) −1.76106e8 + 4.29609e8i −0.239173 + 0.583458i
\(904\) 0 0
\(905\) 8.75114e7 1.51574e8i 0.118064 0.204493i
\(906\) 0 0
\(907\) −2.52448e8 4.37253e8i −0.338338 0.586018i 0.645782 0.763521i \(-0.276531\pi\)
−0.984120 + 0.177503i \(0.943198\pi\)
\(908\) 0 0
\(909\) 2.14160e8i 0.285132i
\(910\) 0 0
\(911\) −1.07163e9 −1.41739 −0.708694 0.705516i \(-0.750715\pi\)
−0.708694 + 0.705516i \(0.750715\pi\)
\(912\) 0 0
\(913\) −1.44490e8 + 8.34215e7i −0.189857 + 0.109614i
\(914\) 0 0
\(915\) 2.68035e8 + 1.54750e8i 0.349887 + 0.202008i
\(916\) 0 0
\(917\) −1.19142e9 + 1.61302e8i −1.54510 + 0.209185i
\(918\) 0 0
\(919\) 2.08740e8 3.61547e8i 0.268942 0.465821i −0.699647 0.714489i \(-0.746659\pi\)
0.968589 + 0.248668i \(0.0799928\pi\)
\(920\) 0 0
\(921\) −1.55818e8 2.69884e8i −0.199452 0.345461i
\(922\) 0 0
\(923\) 8.60517e8i 1.09435i
\(924\) 0 0
\(925\) 5.00479e8 0.632354
\(926\) 0 0
\(927\) 2.01685e7 1.16443e7i 0.0253183 0.0146175i
\(928\) 0 0
\(929\) −8.29914e8 4.79151e8i −1.03511 0.597620i −0.116664 0.993171i \(-0.537220\pi\)
−0.918444 + 0.395551i \(0.870554\pi\)
\(930\) 0 0
\(931\) −3.63623e8 + 3.68998e8i −0.450612 + 0.457272i
\(932\) 0 0
\(933\) 9.44462e7 1.63586e8i 0.116289 0.201419i
\(934\) 0 0
\(935\) −2.59859e8 4.50089e8i −0.317909 0.550634i
\(936\) 0 0
\(937\) 1.53993e9i 1.87190i −0.352130 0.935951i \(-0.614543\pi\)
0.352130 0.935951i \(-0.385457\pi\)
\(938\) 0 0
\(939\) 8.84177e8 1.06793
\(940\) 0 0
\(941\) −8.92799e8 + 5.15458e8i −1.07148 + 0.618620i −0.928586 0.371117i \(-0.878975\pi\)
−0.142896 + 0.989738i \(0.545641\pi\)
\(942\) 0 0
\(943\) −1.05809e9 6.10887e8i −1.26179 0.728494i
\(944\) 0 0
\(945\) −1.27342e7 9.40585e7i −0.0150895 0.111456i
\(946\) 0 0
\(947\) 1.43760e8 2.48999e8i 0.169273 0.293189i −0.768892 0.639379i \(-0.779191\pi\)
0.938164 + 0.346190i \(0.112525\pi\)
\(948\) 0 0
\(949\) 5.00894e8 + 8.67573e8i 0.586067 + 1.01510i
\(950\) 0 0
\(951\) 3.86948e8i 0.449895i
\(952\) 0 0
\(953\) 4.50715e8 0.520743 0.260371 0.965509i \(-0.416155\pi\)
0.260371 + 0.965509i \(0.416155\pi\)
\(954\) 0 0
\(955\) 8.20949e7 4.73975e7i 0.0942554 0.0544184i
\(956\) 0 0
\(957\) 9.63249e8 + 5.56132e8i 1.09901 + 0.634515i
\(958\) 0 0
\(959\) −9.07008e7 3.71803e7i −0.102838 0.0421558i
\(960\) 0 0
\(961\) −3.75075e8 + 6.49648e8i −0.422617 + 0.731995i
\(962\) 0 0
\(963\) −1.12602e8 1.95032e8i −0.126086 0.218387i
\(964\) 0 0
\(965\) 2.18909e8i 0.243602i
\(966\) 0 0
\(967\) −8.35037e8 −0.923478 −0.461739 0.887016i \(-0.652774\pi\)
−0.461739 + 0.887016i \(0.652774\pi\)
\(968\) 0 0
\(969\) −1.97067e8 + 1.13777e8i −0.216592 + 0.125050i
\(970\) 0 0
\(971\) −6.46725e7 3.73387e7i −0.0706419 0.0407851i 0.464263 0.885697i \(-0.346319\pi\)
−0.534905 + 0.844912i \(0.679653\pi\)
\(972\) 0 0
\(973\) 5.34765e8 + 6.91651e8i 0.580530 + 0.750842i
\(974\) 0 0
\(975\) 2.04557e8 3.54303e8i 0.220699 0.382262i
\(976\) 0 0
\(977\) −2.79211e8 4.83607e8i −0.299398 0.518572i 0.676601 0.736350i \(-0.263452\pi\)
−0.975998 + 0.217778i \(0.930119\pi\)
\(978\) 0 0
\(979\) 1.18466e9i 1.26254i
\(980\) 0 0
\(981\) −5.71622e8 −0.605483
\(982\) 0 0
\(983\) −1.49108e9 + 8.60876e8i −1.56979 + 0.906317i −0.573594 + 0.819140i \(0.694451\pi\)
−0.996193 + 0.0871772i \(0.972215\pi\)
\(984\) 0 0
\(985\) 4.25301e8 + 2.45548e8i 0.445029 + 0.256937i
\(986\) 0 0
\(987\) 6.99693e8 5.40982e8i 0.727706 0.562641i
\(988\) 0 0
\(989\) −7.42324e8 + 1.28574e9i −0.767370 + 1.32912i
\(990\) 0 0
\(991\) 3.95954e8 + 6.85813e8i 0.406841 + 0.704668i 0.994534 0.104415i \(-0.0332971\pi\)
−0.587693 + 0.809084i \(0.699964\pi\)
\(992\) 0 0
\(993\) 1.41277e8i 0.144286i
\(994\) 0 0
\(995\) −8.19260e8 −0.831673
\(996\) 0 0
\(997\) −1.41568e9 + 8.17343e8i −1.42850 + 0.824743i −0.997002 0.0773726i \(-0.975347\pi\)
−0.431494 + 0.902116i \(0.642014\pi\)
\(998\) 0 0
\(999\) 1.59582e8 + 9.21348e7i 0.160062 + 0.0924117i
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.f.145.2 8
4.3 odd 2 42.7.g.a.19.3 8
7.3 odd 6 inner 336.7.bh.f.241.2 8
12.11 even 2 126.7.n.a.19.2 8
28.3 even 6 42.7.g.a.31.3 yes 8
28.11 odd 6 294.7.g.d.31.4 8
28.19 even 6 294.7.c.b.97.3 8
28.23 odd 6 294.7.c.b.97.2 8
28.27 even 2 294.7.g.d.19.4 8
84.59 odd 6 126.7.n.a.73.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.7.g.a.19.3 8 4.3 odd 2
42.7.g.a.31.3 yes 8 28.3 even 6
126.7.n.a.19.2 8 12.11 even 2
126.7.n.a.73.2 8 84.59 odd 6
294.7.c.b.97.2 8 28.23 odd 6
294.7.c.b.97.3 8 28.19 even 6
294.7.g.d.19.4 8 28.27 even 2
294.7.g.d.31.4 8 28.11 odd 6
336.7.bh.f.145.2 8 1.1 even 1 trivial
336.7.bh.f.241.2 8 7.3 odd 6 inner