Properties

Label 1323.2.h.f.226.5
Level $1323$
Weight $2$
Character 1323.226
Analytic conductor $10.564$
Analytic rank $0$
Dimension $10$
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] = [1323,2,Mod(226,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.h (of order \(3\), 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: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.5
Root \(1.19343 - 2.06709i\) of defining polynomial
Character \(\chi\) \(=\) 1323.226
Dual form 1323.2.h.f.802.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.38687 q^{2} +3.69714 q^{4} +(1.46043 + 2.52954i) q^{5} +4.05086 q^{8} +O(q^{10})\) \(q+2.38687 q^{2} +3.69714 q^{4} +(1.46043 + 2.52954i) q^{5} +4.05086 q^{8} +(3.48586 + 6.03769i) q^{10} +(-0.676857 + 1.17235i) q^{11} +(0.733001 - 1.26960i) q^{13} +2.27458 q^{16} +(1.65514 + 2.86678i) q^{17} +(1.10329 - 1.91096i) q^{19} +(5.39943 + 9.35209i) q^{20} +(-1.61557 + 2.79825i) q^{22} +(1.31415 + 2.27617i) q^{23} +(-1.76573 + 3.05833i) q^{25} +(1.74958 - 3.03036i) q^{26} +(-0.521720 - 0.903646i) q^{29} -3.27458 q^{31} -2.67259 q^{32} +(3.95060 + 6.84263i) q^{34} +(5.43773 - 9.41842i) q^{37} +(2.63342 - 4.56121i) q^{38} +(5.91601 + 10.2468i) q^{40} +(-0.904289 + 1.56627i) q^{41} +(-2.17129 - 3.76078i) q^{43} +(-2.50244 + 4.33435i) q^{44} +(3.13670 + 5.43292i) q^{46} +3.97914 q^{47} +(-4.21456 + 7.29984i) q^{50} +(2.71001 - 4.69388i) q^{52} +(3.22743 + 5.59008i) q^{53} -3.95402 q^{55} +(-1.24528 - 2.15688i) q^{58} -12.2140 q^{59} -0.559734 q^{61} -7.81600 q^{62} -10.9283 q^{64} +4.28200 q^{65} +12.8118 q^{67} +(6.11928 + 10.5989i) q^{68} -12.9177 q^{71} +(-5.22772 - 9.05467i) q^{73} +(12.9791 - 22.4805i) q^{74} +(4.07903 - 7.06509i) q^{76} +0.767677 q^{79} +(3.32187 + 5.75365i) q^{80} +(-2.15842 + 3.73849i) q^{82} +(-0.983707 - 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} +(-5.18258 - 8.97649i) q^{86} +(-2.74185 + 4.74903i) q^{88} +(3.20356 - 5.54872i) q^{89} +(4.85859 + 8.41533i) q^{92} +9.49769 q^{94} +6.44514 q^{95} +(4.14143 + 7.17316i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 4 q^{2} + 8 q^{4} + 4 q^{5} + 6 q^{8} + 7 q^{10} - 4 q^{11} + 8 q^{13} - 4 q^{16} + 12 q^{17} - q^{19} + 5 q^{20} - q^{22} - 3 q^{23} - q^{25} + 11 q^{26} - 7 q^{29} - 6 q^{31} - 4 q^{32} - 3 q^{34} + 20 q^{38} + 3 q^{40} + 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} - 54 q^{47} - 19 q^{50} + 10 q^{52} + 21 q^{53} - 4 q^{55} - 10 q^{58} - 60 q^{59} - 28 q^{61} - 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} + 27 q^{68} + 6 q^{71} - 15 q^{73} + 36 q^{74} - 5 q^{76} + 8 q^{79} + 20 q^{80} + 5 q^{82} + 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} + 28 q^{89} - 27 q^{92} - 6 q^{94} - 28 q^{95} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.38687 1.68777 0.843886 0.536523i \(-0.180263\pi\)
0.843886 + 0.536523i \(0.180263\pi\)
\(3\) 0 0
\(4\) 3.69714 1.84857
\(5\) 1.46043 + 2.52954i 0.653125 + 1.13125i 0.982360 + 0.186998i \(0.0598759\pi\)
−0.329235 + 0.944248i \(0.606791\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 4.05086 1.43219
\(9\) 0 0
\(10\) 3.48586 + 6.03769i 1.10233 + 1.90929i
\(11\) −0.676857 + 1.17235i −0.204080 + 0.353477i −0.949839 0.312738i \(-0.898754\pi\)
0.745759 + 0.666216i \(0.232087\pi\)
\(12\) 0 0
\(13\) 0.733001 1.26960i 0.203298 0.352123i −0.746291 0.665620i \(-0.768167\pi\)
0.949589 + 0.313497i \(0.101501\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.27458 0.568645
\(17\) 1.65514 + 2.86678i 0.401430 + 0.695297i 0.993899 0.110297i \(-0.0351801\pi\)
−0.592469 + 0.805593i \(0.701847\pi\)
\(18\) 0 0
\(19\) 1.10329 1.91096i 0.253113 0.438404i −0.711268 0.702921i \(-0.751879\pi\)
0.964381 + 0.264516i \(0.0852123\pi\)
\(20\) 5.39943 + 9.35209i 1.20735 + 2.09119i
\(21\) 0 0
\(22\) −1.61557 + 2.79825i −0.344441 + 0.596589i
\(23\) 1.31415 + 2.27617i 0.274019 + 0.474614i 0.969887 0.243555i \(-0.0783136\pi\)
−0.695868 + 0.718169i \(0.744980\pi\)
\(24\) 0 0
\(25\) −1.76573 + 3.05833i −0.353146 + 0.611666i
\(26\) 1.74958 3.03036i 0.343121 0.594302i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.521720 0.903646i −0.0968810 0.167803i 0.813511 0.581549i \(-0.197553\pi\)
−0.910392 + 0.413747i \(0.864220\pi\)
\(30\) 0 0
\(31\) −3.27458 −0.588132 −0.294066 0.955785i \(-0.595009\pi\)
−0.294066 + 0.955785i \(0.595009\pi\)
\(32\) −2.67259 −0.472452
\(33\) 0 0
\(34\) 3.95060 + 6.84263i 0.677521 + 1.17350i
\(35\) 0 0
\(36\) 0 0
\(37\) 5.43773 9.41842i 0.893957 1.54838i 0.0588664 0.998266i \(-0.481251\pi\)
0.835090 0.550113i \(-0.185415\pi\)
\(38\) 2.63342 4.56121i 0.427197 0.739926i
\(39\) 0 0
\(40\) 5.91601 + 10.2468i 0.935403 + 1.62017i
\(41\) −0.904289 + 1.56627i −0.141226 + 0.244611i −0.927959 0.372683i \(-0.878438\pi\)
0.786732 + 0.617294i \(0.211771\pi\)
\(42\) 0 0
\(43\) −2.17129 3.76078i −0.331118 0.573514i 0.651613 0.758551i \(-0.274093\pi\)
−0.982731 + 0.185038i \(0.940759\pi\)
\(44\) −2.50244 + 4.33435i −0.377257 + 0.653428i
\(45\) 0 0
\(46\) 3.13670 + 5.43292i 0.462481 + 0.801041i
\(47\) 3.97914 0.580417 0.290209 0.956963i \(-0.406275\pi\)
0.290209 + 0.956963i \(0.406275\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −4.21456 + 7.29984i −0.596029 + 1.03235i
\(51\) 0 0
\(52\) 2.71001 4.69388i 0.375811 0.650924i
\(53\) 3.22743 + 5.59008i 0.443322 + 0.767856i 0.997934 0.0642533i \(-0.0204666\pi\)
−0.554612 + 0.832109i \(0.687133\pi\)
\(54\) 0 0
\(55\) −3.95402 −0.533160
\(56\) 0 0
\(57\) 0 0
\(58\) −1.24528 2.15688i −0.163513 0.283213i
\(59\) −12.2140 −1.59013 −0.795064 0.606526i \(-0.792563\pi\)
−0.795064 + 0.606526i \(0.792563\pi\)
\(60\) 0 0
\(61\) −0.559734 −0.0716666 −0.0358333 0.999358i \(-0.511409\pi\)
−0.0358333 + 0.999358i \(0.511409\pi\)
\(62\) −7.81600 −0.992632
\(63\) 0 0
\(64\) −10.9283 −1.36604
\(65\) 4.28200 0.531117
\(66\) 0 0
\(67\) 12.8118 1.56521 0.782603 0.622521i \(-0.213891\pi\)
0.782603 + 0.622521i \(0.213891\pi\)
\(68\) 6.11928 + 10.5989i 0.742072 + 1.28531i
\(69\) 0 0
\(70\) 0 0
\(71\) −12.9177 −1.53305 −0.766525 0.642214i \(-0.778016\pi\)
−0.766525 + 0.642214i \(0.778016\pi\)
\(72\) 0 0
\(73\) −5.22772 9.05467i −0.611858 1.05977i −0.990927 0.134401i \(-0.957089\pi\)
0.379069 0.925368i \(-0.376244\pi\)
\(74\) 12.9791 22.4805i 1.50879 2.61331i
\(75\) 0 0
\(76\) 4.07903 7.06509i 0.467897 0.810422i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.767677 0.0863704 0.0431852 0.999067i \(-0.486249\pi\)
0.0431852 + 0.999067i \(0.486249\pi\)
\(80\) 3.32187 + 5.75365i 0.371397 + 0.643278i
\(81\) 0 0
\(82\) −2.15842 + 3.73849i −0.238358 + 0.412847i
\(83\) −0.983707 1.70383i −0.107976 0.187020i 0.806974 0.590587i \(-0.201104\pi\)
−0.914950 + 0.403567i \(0.867770\pi\)
\(84\) 0 0
\(85\) −4.83443 + 8.37348i −0.524368 + 0.908232i
\(86\) −5.18258 8.97649i −0.558852 0.967960i
\(87\) 0 0
\(88\) −2.74185 + 4.74903i −0.292283 + 0.506248i
\(89\) 3.20356 5.54872i 0.339576 0.588163i −0.644777 0.764371i \(-0.723050\pi\)
0.984353 + 0.176208i \(0.0563830\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.85859 + 8.41533i 0.506543 + 0.877359i
\(93\) 0 0
\(94\) 9.49769 0.979612
\(95\) 6.44514 0.661258
\(96\) 0 0
\(97\) 4.14143 + 7.17316i 0.420498 + 0.728324i 0.995988 0.0894847i \(-0.0285220\pi\)
−0.575490 + 0.817809i \(0.695189\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −6.52815 + 11.3071i −0.652815 + 1.13071i
\(101\) 8.11331 14.0527i 0.807305 1.39829i −0.107419 0.994214i \(-0.534259\pi\)
0.914724 0.404079i \(-0.132408\pi\)
\(102\) 0 0
\(103\) −1.11342 1.92849i −0.109708 0.190020i 0.805944 0.591992i \(-0.201658\pi\)
−0.915652 + 0.401972i \(0.868325\pi\)
\(104\) 2.96929 5.14295i 0.291162 0.504308i
\(105\) 0 0
\(106\) 7.70346 + 13.3428i 0.748226 + 1.29597i
\(107\) 8.75403 15.1624i 0.846284 1.46581i −0.0382175 0.999269i \(-0.512168\pi\)
0.884501 0.466537i \(-0.154499\pi\)
\(108\) 0 0
\(109\) −7.79917 13.5086i −0.747025 1.29388i −0.949243 0.314544i \(-0.898148\pi\)
0.202218 0.979341i \(-0.435185\pi\)
\(110\) −9.43773 −0.899852
\(111\) 0 0
\(112\) 0 0
\(113\) 0.844555 1.46281i 0.0794491 0.137610i −0.823563 0.567224i \(-0.808017\pi\)
0.903012 + 0.429615i \(0.141351\pi\)
\(114\) 0 0
\(115\) −3.83845 + 6.64839i −0.357937 + 0.619966i
\(116\) −1.92887 3.34091i −0.179092 0.310196i
\(117\) 0 0
\(118\) −29.1532 −2.68377
\(119\) 0 0
\(120\) 0 0
\(121\) 4.58373 + 7.93925i 0.416703 + 0.721750i
\(122\) −1.33601 −0.120957
\(123\) 0 0
\(124\) −12.1066 −1.08720
\(125\) 4.28942 0.383657
\(126\) 0 0
\(127\) −3.96918 −0.352208 −0.176104 0.984372i \(-0.556350\pi\)
−0.176104 + 0.984372i \(0.556350\pi\)
\(128\) −20.7392 −1.83310
\(129\) 0 0
\(130\) 10.2206 0.896403
\(131\) −2.66432 4.61473i −0.232782 0.403191i 0.725844 0.687860i \(-0.241450\pi\)
−0.958626 + 0.284669i \(0.908116\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 30.5800 2.64171
\(135\) 0 0
\(136\) 6.70473 + 11.6129i 0.574925 + 0.995800i
\(137\) −3.74772 + 6.49124i −0.320189 + 0.554584i −0.980527 0.196385i \(-0.937080\pi\)
0.660338 + 0.750969i \(0.270413\pi\)
\(138\) 0 0
\(139\) −7.03285 + 12.1812i −0.596518 + 1.03320i 0.396812 + 0.917900i \(0.370116\pi\)
−0.993331 + 0.115300i \(0.963217\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −30.8329 −2.58744
\(143\) 0.992275 + 1.71867i 0.0829782 + 0.143722i
\(144\) 0 0
\(145\) 1.52388 2.63943i 0.126551 0.219193i
\(146\) −12.4779 21.6123i −1.03268 1.78865i
\(147\) 0 0
\(148\) 20.1041 34.8212i 1.65254 2.86229i
\(149\) 1.08986 + 1.88769i 0.0892846 + 0.154645i 0.907209 0.420680i \(-0.138209\pi\)
−0.817924 + 0.575326i \(0.804875\pi\)
\(150\) 0 0
\(151\) −7.01387 + 12.1484i −0.570781 + 0.988621i 0.425705 + 0.904862i \(0.360026\pi\)
−0.996486 + 0.0837595i \(0.973307\pi\)
\(152\) 4.46929 7.74103i 0.362507 0.627880i
\(153\) 0 0
\(154\) 0 0
\(155\) −4.78231 8.28320i −0.384124 0.665322i
\(156\) 0 0
\(157\) −2.96623 −0.236731 −0.118365 0.992970i \(-0.537765\pi\)
−0.118365 + 0.992970i \(0.537765\pi\)
\(158\) 1.83234 0.145773
\(159\) 0 0
\(160\) −3.90314 6.76043i −0.308570 0.534459i
\(161\) 0 0
\(162\) 0 0
\(163\) −0.194278 + 0.336499i −0.0152170 + 0.0263566i −0.873534 0.486764i \(-0.838177\pi\)
0.858317 + 0.513120i \(0.171511\pi\)
\(164\) −3.34329 + 5.79074i −0.261067 + 0.452181i
\(165\) 0 0
\(166\) −2.34798 4.06682i −0.182239 0.315646i
\(167\) 3.64889 6.32006i 0.282360 0.489061i −0.689606 0.724185i \(-0.742216\pi\)
0.971965 + 0.235124i \(0.0755496\pi\)
\(168\) 0 0
\(169\) 5.42542 + 9.39710i 0.417340 + 0.722854i
\(170\) −11.5392 + 19.9864i −0.885013 + 1.53289i
\(171\) 0 0
\(172\) −8.02756 13.9041i −0.612096 1.06018i
\(173\) −4.05508 −0.308302 −0.154151 0.988047i \(-0.549264\pi\)
−0.154151 + 0.988047i \(0.549264\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.53957 + 2.66661i −0.116049 + 0.201003i
\(177\) 0 0
\(178\) 7.64647 13.2441i 0.573127 0.992685i
\(179\) −5.29243 9.16675i −0.395575 0.685155i 0.597600 0.801795i \(-0.296121\pi\)
−0.993174 + 0.116639i \(0.962788\pi\)
\(180\) 0 0
\(181\) 19.6312 1.45917 0.729586 0.683889i \(-0.239713\pi\)
0.729586 + 0.683889i \(0.239713\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 5.32343 + 9.22045i 0.392448 + 0.679740i
\(185\) 31.7657 2.33546
\(186\) 0 0
\(187\) −4.48117 −0.327695
\(188\) 14.7115 1.07294
\(189\) 0 0
\(190\) 15.3837 1.11605
\(191\) −8.28714 −0.599637 −0.299818 0.953996i \(-0.596926\pi\)
−0.299818 + 0.953996i \(0.596926\pi\)
\(192\) 0 0
\(193\) −18.7848 −1.35216 −0.676082 0.736827i \(-0.736323\pi\)
−0.676082 + 0.736827i \(0.736323\pi\)
\(194\) 9.88504 + 17.1214i 0.709705 + 1.22924i
\(195\) 0 0
\(196\) 0 0
\(197\) −5.99634 −0.427222 −0.213611 0.976919i \(-0.568522\pi\)
−0.213611 + 0.976919i \(0.568522\pi\)
\(198\) 0 0
\(199\) −7.20434 12.4783i −0.510702 0.884562i −0.999923 0.0124022i \(-0.996052\pi\)
0.489221 0.872160i \(-0.337281\pi\)
\(200\) −7.15272 + 12.3889i −0.505773 + 0.876025i
\(201\) 0 0
\(202\) 19.3654 33.5419i 1.36255 2.36000i
\(203\) 0 0
\(204\) 0 0
\(205\) −5.28261 −0.368954
\(206\) −2.65758 4.60306i −0.185162 0.320710i
\(207\) 0 0
\(208\) 1.66727 2.88780i 0.115604 0.200233i
\(209\) 1.49354 + 2.58690i 0.103311 + 0.178939i
\(210\) 0 0
\(211\) −6.92418 + 11.9930i −0.476680 + 0.825634i −0.999643 0.0267212i \(-0.991493\pi\)
0.522963 + 0.852356i \(0.324827\pi\)
\(212\) 11.9323 + 20.6673i 0.819512 + 1.41944i
\(213\) 0 0
\(214\) 20.8947 36.1907i 1.42833 2.47395i
\(215\) 6.34204 10.9847i 0.432523 0.749153i
\(216\) 0 0
\(217\) 0 0
\(218\) −18.6156 32.2431i −1.26081 2.18378i
\(219\) 0 0
\(220\) −14.6186 −0.985584
\(221\) 4.85287 0.326439
\(222\) 0 0
\(223\) −2.33756 4.04878i −0.156535 0.271126i 0.777082 0.629399i \(-0.216699\pi\)
−0.933617 + 0.358273i \(0.883366\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 2.01584 3.49154i 0.134092 0.232254i
\(227\) −9.85631 + 17.0716i −0.654187 + 1.13308i 0.327910 + 0.944709i \(0.393656\pi\)
−0.982097 + 0.188376i \(0.939678\pi\)
\(228\) 0 0
\(229\) 14.0364 + 24.3118i 0.927552 + 1.60657i 0.787404 + 0.616437i \(0.211425\pi\)
0.140148 + 0.990131i \(0.455242\pi\)
\(230\) −9.16188 + 15.8688i −0.604116 + 1.04636i
\(231\) 0 0
\(232\) −2.11342 3.66054i −0.138753 0.240326i
\(233\) 6.90113 11.9531i 0.452108 0.783074i −0.546409 0.837518i \(-0.684006\pi\)
0.998517 + 0.0544448i \(0.0173389\pi\)
\(234\) 0 0
\(235\) 5.81127 + 10.0654i 0.379085 + 0.656595i
\(236\) −45.1569 −2.93947
\(237\) 0 0
\(238\) 0 0
\(239\) −5.53069 + 9.57944i −0.357751 + 0.619642i −0.987585 0.157087i \(-0.949790\pi\)
0.629834 + 0.776730i \(0.283123\pi\)
\(240\) 0 0
\(241\) −11.5849 + 20.0656i −0.746247 + 1.29254i 0.203362 + 0.979104i \(0.434813\pi\)
−0.949610 + 0.313435i \(0.898520\pi\)
\(242\) 10.9408 + 18.9499i 0.703299 + 1.21815i
\(243\) 0 0
\(244\) −2.06942 −0.132481
\(245\) 0 0
\(246\) 0 0
\(247\) −1.61743 2.80147i −0.102915 0.178253i
\(248\) −13.2649 −0.842320
\(249\) 0 0
\(250\) 10.2383 0.647525
\(251\) −7.78402 −0.491323 −0.245662 0.969356i \(-0.579005\pi\)
−0.245662 + 0.969356i \(0.579005\pi\)
\(252\) 0 0
\(253\) −3.55796 −0.223687
\(254\) −9.47392 −0.594447
\(255\) 0 0
\(256\) −27.6452 −1.72782
\(257\) −5.18798 8.98585i −0.323618 0.560522i 0.657614 0.753355i \(-0.271566\pi\)
−0.981232 + 0.192833i \(0.938232\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 15.8312 0.981807
\(261\) 0 0
\(262\) −6.35937 11.0148i −0.392883 0.680494i
\(263\) −9.56654 + 16.5697i −0.589898 + 1.02173i 0.404347 + 0.914605i \(0.367499\pi\)
−0.994245 + 0.107128i \(0.965835\pi\)
\(264\) 0 0
\(265\) −9.42689 + 16.3279i −0.579090 + 1.00301i
\(266\) 0 0
\(267\) 0 0
\(268\) 47.3669 2.89340
\(269\) −4.41840 7.65290i −0.269395 0.466605i 0.699311 0.714818i \(-0.253490\pi\)
−0.968706 + 0.248212i \(0.920157\pi\)
\(270\) 0 0
\(271\) 9.16955 15.8821i 0.557010 0.964770i −0.440734 0.897638i \(-0.645282\pi\)
0.997744 0.0671321i \(-0.0213849\pi\)
\(272\) 3.76474 + 6.52073i 0.228271 + 0.395377i
\(273\) 0 0
\(274\) −8.94531 + 15.4937i −0.540406 + 0.936010i
\(275\) −2.39029 4.14011i −0.144140 0.249658i
\(276\) 0 0
\(277\) −2.55241 + 4.42091i −0.153360 + 0.265627i −0.932460 0.361272i \(-0.882343\pi\)
0.779101 + 0.626899i \(0.215676\pi\)
\(278\) −16.7865 + 29.0750i −1.00679 + 1.74381i
\(279\) 0 0
\(280\) 0 0
\(281\) 0.853180 + 1.47775i 0.0508964 + 0.0881552i 0.890351 0.455274i \(-0.150459\pi\)
−0.839455 + 0.543430i \(0.817125\pi\)
\(282\) 0 0
\(283\) 12.4883 0.742352 0.371176 0.928562i \(-0.378955\pi\)
0.371176 + 0.928562i \(0.378955\pi\)
\(284\) −47.7586 −2.83395
\(285\) 0 0
\(286\) 2.36843 + 4.10224i 0.140048 + 0.242571i
\(287\) 0 0
\(288\) 0 0
\(289\) 3.02104 5.23260i 0.177708 0.307800i
\(290\) 3.63729 6.29997i 0.213589 0.369947i
\(291\) 0 0
\(292\) −19.3276 33.4764i −1.13106 1.95906i
\(293\) −2.60202 + 4.50684i −0.152012 + 0.263292i −0.931967 0.362543i \(-0.881909\pi\)
0.779955 + 0.625835i \(0.215242\pi\)
\(294\) 0 0
\(295\) −17.8377 30.8959i −1.03855 1.79883i
\(296\) 22.0275 38.1527i 1.28032 2.21758i
\(297\) 0 0
\(298\) 2.60135 + 4.50566i 0.150692 + 0.261006i
\(299\) 3.85309 0.222830
\(300\) 0 0
\(301\) 0 0
\(302\) −16.7412 + 28.9966i −0.963347 + 1.66857i
\(303\) 0 0
\(304\) 2.50953 4.34663i 0.143931 0.249297i
\(305\) −0.817453 1.41587i −0.0468072 0.0810725i
\(306\) 0 0
\(307\) −5.00136 −0.285442 −0.142721 0.989763i \(-0.545585\pi\)
−0.142721 + 0.989763i \(0.545585\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −11.4147 19.7709i −0.648313 1.12291i
\(311\) −32.3968 −1.83706 −0.918528 0.395355i \(-0.870621\pi\)
−0.918528 + 0.395355i \(0.870621\pi\)
\(312\) 0 0
\(313\) −1.51907 −0.0858629 −0.0429315 0.999078i \(-0.513670\pi\)
−0.0429315 + 0.999078i \(0.513670\pi\)
\(314\) −7.08000 −0.399548
\(315\) 0 0
\(316\) 2.83821 0.159662
\(317\) 21.5089 1.20806 0.604029 0.796962i \(-0.293561\pi\)
0.604029 + 0.796962i \(0.293561\pi\)
\(318\) 0 0
\(319\) 1.41252 0.0790860
\(320\) −15.9600 27.6436i −0.892193 1.54532i
\(321\) 0 0
\(322\) 0 0
\(323\) 7.30441 0.406428
\(324\) 0 0
\(325\) 2.58856 + 4.48352i 0.143588 + 0.248701i
\(326\) −0.463715 + 0.803178i −0.0256828 + 0.0444839i
\(327\) 0 0
\(328\) −3.66315 + 6.34476i −0.202263 + 0.350330i
\(329\) 0 0
\(330\) 0 0
\(331\) 19.4780 1.07061 0.535305 0.844659i \(-0.320197\pi\)
0.535305 + 0.844659i \(0.320197\pi\)
\(332\) −3.63691 6.29931i −0.199601 0.345719i
\(333\) 0 0
\(334\) 8.70942 15.0852i 0.476558 0.825423i
\(335\) 18.7107 + 32.4079i 1.02228 + 1.77063i
\(336\) 0 0
\(337\) 4.84742 8.39598i 0.264056 0.457358i −0.703260 0.710933i \(-0.748273\pi\)
0.967316 + 0.253575i \(0.0816063\pi\)
\(338\) 12.9498 + 22.4296i 0.704374 + 1.22001i
\(339\) 0 0
\(340\) −17.8736 + 30.9580i −0.969332 + 1.67893i
\(341\) 2.21642 3.83896i 0.120026 0.207891i
\(342\) 0 0
\(343\) 0 0
\(344\) −8.79558 15.2344i −0.474226 0.821383i
\(345\) 0 0
\(346\) −9.67895 −0.520344
\(347\) −2.02604 −0.108763 −0.0543817 0.998520i \(-0.517319\pi\)
−0.0543817 + 0.998520i \(0.517319\pi\)
\(348\) 0 0
\(349\) −8.14577 14.1089i −0.436033 0.755231i 0.561346 0.827581i \(-0.310284\pi\)
−0.997379 + 0.0723497i \(0.976950\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.80896 3.13321i 0.0964180 0.167001i
\(353\) −8.53072 + 14.7756i −0.454045 + 0.786428i −0.998633 0.0522753i \(-0.983353\pi\)
0.544588 + 0.838704i \(0.316686\pi\)
\(354\) 0 0
\(355\) −18.8655 32.6759i −1.00127 1.73426i
\(356\) 11.8440 20.5144i 0.627731 1.08726i
\(357\) 0 0
\(358\) −12.6323 21.8798i −0.667639 1.15639i
\(359\) −1.48363 + 2.56972i −0.0783030 + 0.135625i −0.902518 0.430652i \(-0.858283\pi\)
0.824215 + 0.566277i \(0.191617\pi\)
\(360\) 0 0
\(361\) 7.06549 + 12.2378i 0.371868 + 0.644094i
\(362\) 46.8570 2.46275
\(363\) 0 0
\(364\) 0 0
\(365\) 15.2695 26.4475i 0.799240 1.38432i
\(366\) 0 0
\(367\) −5.07874 + 8.79664i −0.265108 + 0.459181i −0.967592 0.252519i \(-0.918741\pi\)
0.702484 + 0.711700i \(0.252074\pi\)
\(368\) 2.98914 + 5.17733i 0.155819 + 0.269887i
\(369\) 0 0
\(370\) 75.8207 3.94173
\(371\) 0 0
\(372\) 0 0
\(373\) 12.7423 + 22.0703i 0.659771 + 1.14276i 0.980675 + 0.195645i \(0.0626799\pi\)
−0.320904 + 0.947112i \(0.603987\pi\)
\(374\) −10.6960 −0.553075
\(375\) 0 0
\(376\) 16.1189 0.831271
\(377\) −1.52969 −0.0787829
\(378\) 0 0
\(379\) 9.85497 0.506216 0.253108 0.967438i \(-0.418547\pi\)
0.253108 + 0.967438i \(0.418547\pi\)
\(380\) 23.8286 1.22238
\(381\) 0 0
\(382\) −19.7803 −1.01205
\(383\) 13.6563 + 23.6535i 0.697806 + 1.20864i 0.969225 + 0.246175i \(0.0791737\pi\)
−0.271419 + 0.962461i \(0.587493\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −44.8370 −2.28214
\(387\) 0 0
\(388\) 15.3114 + 26.5202i 0.777321 + 1.34636i
\(389\) 2.09223 3.62385i 0.106080 0.183736i −0.808099 0.589047i \(-0.799503\pi\)
0.914179 + 0.405311i \(0.132837\pi\)
\(390\) 0 0
\(391\) −4.35019 + 7.53475i −0.219999 + 0.381049i
\(392\) 0 0
\(393\) 0 0
\(394\) −14.3125 −0.721053
\(395\) 1.12114 + 1.94187i 0.0564107 + 0.0977062i
\(396\) 0 0
\(397\) −15.3354 + 26.5618i −0.769664 + 1.33310i 0.168082 + 0.985773i \(0.446243\pi\)
−0.937745 + 0.347323i \(0.887091\pi\)
\(398\) −17.1958 29.7840i −0.861948 1.49294i
\(399\) 0 0
\(400\) −4.01629 + 6.95642i −0.200815 + 0.347821i
\(401\) −3.42402 5.93057i −0.170987 0.296158i 0.767778 0.640716i \(-0.221362\pi\)
−0.938765 + 0.344557i \(0.888029\pi\)
\(402\) 0 0
\(403\) −2.40027 + 4.15739i −0.119566 + 0.207095i
\(404\) 29.9961 51.9547i 1.49236 2.58485i
\(405\) 0 0
\(406\) 0 0
\(407\) 7.36113 + 12.7499i 0.364878 + 0.631987i
\(408\) 0 0
\(409\) 18.2698 0.903384 0.451692 0.892174i \(-0.350821\pi\)
0.451692 + 0.892174i \(0.350821\pi\)
\(410\) −12.6089 −0.622709
\(411\) 0 0
\(412\) −4.11646 7.12991i −0.202803 0.351265i
\(413\) 0 0
\(414\) 0 0
\(415\) 2.87328 4.97666i 0.141044 0.244295i
\(416\) −1.95901 + 3.39311i −0.0960485 + 0.166361i
\(417\) 0 0
\(418\) 3.56490 + 6.17458i 0.174365 + 0.302009i
\(419\) 11.2310 19.4526i 0.548669 0.950322i −0.449698 0.893181i \(-0.648468\pi\)
0.998366 0.0571410i \(-0.0181984\pi\)
\(420\) 0 0
\(421\) 10.4177 + 18.0440i 0.507728 + 0.879411i 0.999960 + 0.00894684i \(0.00284791\pi\)
−0.492232 + 0.870464i \(0.663819\pi\)
\(422\) −16.5271 + 28.6258i −0.804527 + 1.39348i
\(423\) 0 0
\(424\) 13.0739 + 22.6446i 0.634923 + 1.09972i
\(425\) −11.6901 −0.567053
\(426\) 0 0
\(427\) 0 0
\(428\) 32.3649 56.0577i 1.56442 2.70965i
\(429\) 0 0
\(430\) 15.1376 26.2191i 0.730001 1.26440i
\(431\) 10.1213 + 17.5307i 0.487527 + 0.844422i 0.999897 0.0143427i \(-0.00456557\pi\)
−0.512370 + 0.858765i \(0.671232\pi\)
\(432\) 0 0
\(433\) 21.6764 1.04170 0.520851 0.853648i \(-0.325615\pi\)
0.520851 + 0.853648i \(0.325615\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −28.8346 49.9431i −1.38093 2.39184i
\(437\) 5.79956 0.277431
\(438\) 0 0
\(439\) 35.4781 1.69328 0.846639 0.532168i \(-0.178623\pi\)
0.846639 + 0.532168i \(0.178623\pi\)
\(440\) −16.0172 −0.763589
\(441\) 0 0
\(442\) 11.5832 0.550955
\(443\) 19.2063 0.912517 0.456258 0.889847i \(-0.349189\pi\)
0.456258 + 0.889847i \(0.349189\pi\)
\(444\) 0 0
\(445\) 18.7143 0.887144
\(446\) −5.57946 9.66391i −0.264195 0.457599i
\(447\) 0 0
\(448\) 0 0
\(449\) 29.6082 1.39730 0.698648 0.715465i \(-0.253785\pi\)
0.698648 + 0.715465i \(0.253785\pi\)
\(450\) 0 0
\(451\) −1.22415 2.12029i −0.0576429 0.0998405i
\(452\) 3.12244 5.40823i 0.146867 0.254382i
\(453\) 0 0
\(454\) −23.5257 + 40.7478i −1.10412 + 1.91239i
\(455\) 0 0
\(456\) 0 0
\(457\) −9.56196 −0.447290 −0.223645 0.974671i \(-0.571796\pi\)
−0.223645 + 0.974671i \(0.571796\pi\)
\(458\) 33.5031 + 58.0290i 1.56550 + 2.71152i
\(459\) 0 0
\(460\) −14.1913 + 24.5800i −0.661673 + 1.14605i
\(461\) 10.9187 + 18.9118i 0.508536 + 0.880809i 0.999951 + 0.00988416i \(0.00314628\pi\)
−0.491416 + 0.870925i \(0.663520\pi\)
\(462\) 0 0
\(463\) 13.0744 22.6456i 0.607621 1.05243i −0.384010 0.923329i \(-0.625457\pi\)
0.991631 0.129102i \(-0.0412094\pi\)
\(464\) −1.18670 2.05542i −0.0550909 0.0954203i
\(465\) 0 0
\(466\) 16.4721 28.5305i 0.763054 1.32165i
\(467\) −17.4764 + 30.2699i −0.808709 + 1.40073i 0.105049 + 0.994467i \(0.466500\pi\)
−0.913758 + 0.406258i \(0.866833\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 13.8707 + 24.0248i 0.639809 + 1.10818i
\(471\) 0 0
\(472\) −49.4772 −2.27737
\(473\) 5.87861 0.270299
\(474\) 0 0
\(475\) 3.89623 + 6.74848i 0.178771 + 0.309641i
\(476\) 0 0
\(477\) 0 0
\(478\) −13.2010 + 22.8649i −0.603801 + 1.04581i
\(479\) 14.9054 25.8170i 0.681047 1.17961i −0.293615 0.955924i \(-0.594858\pi\)
0.974662 0.223684i \(-0.0718083\pi\)
\(480\) 0 0
\(481\) −7.97172 13.8074i −0.363479 0.629565i
\(482\) −27.6516 + 47.8939i −1.25949 + 2.18151i
\(483\) 0 0
\(484\) 16.9467 + 29.3525i 0.770304 + 1.33421i
\(485\) −12.0965 + 20.9518i −0.549276 + 0.951374i
\(486\) 0 0
\(487\) −11.2253 19.4428i −0.508667 0.881037i −0.999950 0.0100365i \(-0.996805\pi\)
0.491283 0.871000i \(-0.336528\pi\)
\(488\) −2.26740 −0.102640
\(489\) 0 0
\(490\) 0 0
\(491\) −17.5222 + 30.3494i −0.790767 + 1.36965i 0.134726 + 0.990883i \(0.456984\pi\)
−0.925493 + 0.378765i \(0.876349\pi\)
\(492\) 0 0
\(493\) 1.72704 2.99132i 0.0777819 0.134722i
\(494\) −3.86060 6.68675i −0.173696 0.300851i
\(495\) 0 0
\(496\) −7.44830 −0.334438
\(497\) 0 0
\(498\) 0 0
\(499\) 4.46760 + 7.73811i 0.199997 + 0.346405i 0.948527 0.316696i \(-0.102573\pi\)
−0.748530 + 0.663101i \(0.769240\pi\)
\(500\) 15.8586 0.709217
\(501\) 0 0
\(502\) −18.5794 −0.829241
\(503\) −12.6403 −0.563603 −0.281802 0.959473i \(-0.590932\pi\)
−0.281802 + 0.959473i \(0.590932\pi\)
\(504\) 0 0
\(505\) 47.3958 2.10909
\(506\) −8.49239 −0.377533
\(507\) 0 0
\(508\) −14.6746 −0.651082
\(509\) 14.0555 + 24.3449i 0.623000 + 1.07907i 0.988924 + 0.148423i \(0.0474196\pi\)
−0.365924 + 0.930645i \(0.619247\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −24.5070 −1.08307
\(513\) 0 0
\(514\) −12.3830 21.4480i −0.546192 0.946033i
\(515\) 3.25214 5.63287i 0.143306 0.248214i
\(516\) 0 0
\(517\) −2.69331 + 4.66495i −0.118452 + 0.205164i
\(518\) 0 0
\(519\) 0 0
\(520\) 17.3458 0.760662
\(521\) 4.23768 + 7.33988i 0.185656 + 0.321566i 0.943797 0.330524i \(-0.107226\pi\)
−0.758141 + 0.652090i \(0.773892\pi\)
\(522\) 0 0
\(523\) −16.7236 + 28.9662i −0.731273 + 1.26660i 0.225066 + 0.974344i \(0.427740\pi\)
−0.956339 + 0.292259i \(0.905593\pi\)
\(524\) −9.85035 17.0613i −0.430315 0.745327i
\(525\) 0 0
\(526\) −22.8341 + 39.5498i −0.995613 + 1.72445i
\(527\) −5.41988 9.38751i −0.236094 0.408926i
\(528\) 0 0
\(529\) 8.04603 13.9361i 0.349827 0.605919i
\(530\) −22.5008 + 38.9725i −0.977371 + 1.69286i
\(531\) 0 0
\(532\) 0 0
\(533\) 1.32569 + 2.29616i 0.0574220 + 0.0994579i
\(534\) 0 0
\(535\) 51.1387 2.21092
\(536\) 51.8987 2.24168
\(537\) 0 0
\(538\) −10.5461 18.2665i −0.454677 0.787523i
\(539\) 0 0
\(540\) 0 0
\(541\) −9.12929 + 15.8124i −0.392499 + 0.679828i −0.992778 0.119962i \(-0.961723\pi\)
0.600280 + 0.799790i \(0.295056\pi\)
\(542\) 21.8865 37.9085i 0.940106 1.62831i
\(543\) 0 0
\(544\) −4.42350 7.66173i −0.189656 0.328494i
\(545\) 22.7803 39.4567i 0.975802 1.69014i
\(546\) 0 0
\(547\) −2.88599 4.99869i −0.123396 0.213728i 0.797709 0.603043i \(-0.206045\pi\)
−0.921105 + 0.389315i \(0.872712\pi\)
\(548\) −13.8558 + 23.9990i −0.591892 + 1.02519i
\(549\) 0 0
\(550\) −5.70532 9.88190i −0.243276 0.421366i
\(551\) −2.30244 −0.0980874
\(552\) 0 0
\(553\) 0 0
\(554\) −6.09227 + 10.5521i −0.258836 + 0.448317i
\(555\) 0 0
\(556\) −26.0014 + 45.0358i −1.10271 + 1.90994i
\(557\) −16.6911 28.9098i −0.707223 1.22495i −0.965883 0.258977i \(-0.916614\pi\)
0.258661 0.965968i \(-0.416719\pi\)
\(558\) 0 0
\(559\) −6.36623 −0.269263
\(560\) 0 0
\(561\) 0 0
\(562\) 2.03643 + 3.52720i 0.0859015 + 0.148786i
\(563\) 2.19131 0.0923528 0.0461764 0.998933i \(-0.485296\pi\)
0.0461764 + 0.998933i \(0.485296\pi\)
\(564\) 0 0
\(565\) 4.93367 0.207561
\(566\) 29.8079 1.25292
\(567\) 0 0
\(568\) −52.3278 −2.19563
\(569\) −18.9860 −0.795936 −0.397968 0.917399i \(-0.630284\pi\)
−0.397968 + 0.917399i \(0.630284\pi\)
\(570\) 0 0
\(571\) −21.7380 −0.909709 −0.454854 0.890566i \(-0.650309\pi\)
−0.454854 + 0.890566i \(0.650309\pi\)
\(572\) 3.66858 + 6.35417i 0.153391 + 0.265681i
\(573\) 0 0
\(574\) 0 0
\(575\) −9.28172 −0.387074
\(576\) 0 0
\(577\) 15.4516 + 26.7629i 0.643258 + 1.11416i 0.984701 + 0.174253i \(0.0557511\pi\)
−0.341443 + 0.939903i \(0.610916\pi\)
\(578\) 7.21083 12.4895i 0.299931 0.519496i
\(579\) 0 0
\(580\) 5.63398 9.75835i 0.233938 0.405193i
\(581\) 0 0
\(582\) 0 0
\(583\) −8.73804 −0.361893
\(584\) −21.1767 36.6792i −0.876299 1.51780i
\(585\) 0 0
\(586\) −6.21069 + 10.7572i −0.256561 + 0.444377i
\(587\) −9.18332 15.9060i −0.379036 0.656510i 0.611886 0.790946i \(-0.290411\pi\)
−0.990922 + 0.134436i \(0.957078\pi\)
\(588\) 0 0
\(589\) −3.61282 + 6.25759i −0.148864 + 0.257840i
\(590\) −42.5763 73.7444i −1.75284 3.03601i
\(591\) 0 0
\(592\) 12.3685 21.4230i 0.508344 0.880478i
\(593\) 13.8775 24.0365i 0.569880 0.987061i −0.426698 0.904394i \(-0.640323\pi\)
0.996577 0.0826662i \(-0.0263435\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.02936 + 6.97905i 0.165049 + 0.285873i
\(597\) 0 0
\(598\) 9.19682 0.376086
\(599\) −0.402823 −0.0164589 −0.00822945 0.999966i \(-0.502620\pi\)
−0.00822945 + 0.999966i \(0.502620\pi\)
\(600\) 0 0
\(601\) −12.3733 21.4312i −0.504717 0.874196i −0.999985 0.00545577i \(-0.998263\pi\)
0.495268 0.868740i \(-0.335070\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −25.9313 + 44.9143i −1.05513 + 1.82754i
\(605\) −13.3885 + 23.1895i −0.544318 + 0.942787i
\(606\) 0 0
\(607\) 12.0348 + 20.8449i 0.488479 + 0.846070i 0.999912 0.0132531i \(-0.00421872\pi\)
−0.511434 + 0.859323i \(0.670885\pi\)
\(608\) −2.94865 + 5.10721i −0.119584 + 0.207125i
\(609\) 0 0
\(610\) −1.95115 3.37950i −0.0789999 0.136832i
\(611\) 2.91672 5.05190i 0.117998 0.204378i
\(612\) 0 0
\(613\) 10.1907 + 17.6509i 0.411600 + 0.712912i 0.995065 0.0992261i \(-0.0316367\pi\)
−0.583465 + 0.812138i \(0.698303\pi\)
\(614\) −11.9376 −0.481762
\(615\) 0 0
\(616\) 0 0
\(617\) 20.9315 36.2544i 0.842669 1.45955i −0.0449604 0.998989i \(-0.514316\pi\)
0.887630 0.460558i \(-0.152350\pi\)
\(618\) 0 0
\(619\) 7.41095 12.8361i 0.297871 0.515928i −0.677777 0.735267i \(-0.737057\pi\)
0.975649 + 0.219339i \(0.0703900\pi\)
\(620\) −17.6809 30.6242i −0.710081 1.22990i
\(621\) 0 0
\(622\) −77.3270 −3.10053
\(623\) 0 0
\(624\) 0 0
\(625\) 15.0930 + 26.1419i 0.603722 + 1.04568i
\(626\) −3.62582 −0.144917
\(627\) 0 0
\(628\) −10.9666 −0.437614
\(629\) 36.0007 1.43544
\(630\) 0 0
\(631\) −21.0294 −0.837169 −0.418585 0.908178i \(-0.637474\pi\)
−0.418585 + 0.908178i \(0.637474\pi\)
\(632\) 3.10975 0.123699
\(633\) 0 0
\(634\) 51.3388 2.03893
\(635\) −5.79673 10.0402i −0.230036 0.398434i
\(636\) 0 0
\(637\) 0 0
\(638\) 3.37150 0.133479
\(639\) 0 0
\(640\) −30.2882 52.4607i −1.19725 2.07369i
\(641\) 5.96592 10.3333i 0.235640 0.408140i −0.723819 0.689990i \(-0.757615\pi\)
0.959458 + 0.281850i \(0.0909481\pi\)
\(642\) 0 0
\(643\) 19.9678 34.5852i 0.787452 1.36391i −0.140072 0.990141i \(-0.544733\pi\)
0.927524 0.373765i \(-0.121933\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 17.4347 0.685958
\(647\) 0.494477 + 0.856459i 0.0194399 + 0.0336709i 0.875582 0.483070i \(-0.160478\pi\)
−0.856142 + 0.516741i \(0.827145\pi\)
\(648\) 0 0
\(649\) 8.26714 14.3191i 0.324514 0.562074i
\(650\) 6.17856 + 10.7016i 0.242343 + 0.419751i
\(651\) 0 0
\(652\) −0.718272 + 1.24408i −0.0281297 + 0.0487221i
\(653\) 11.3573 + 19.6715i 0.444447 + 0.769804i 0.998014 0.0630004i \(-0.0200669\pi\)
−0.553567 + 0.832805i \(0.686734\pi\)
\(654\) 0 0
\(655\) 7.78211 13.4790i 0.304072 0.526668i
\(656\) −2.05688 + 3.56262i −0.0803076 + 0.139097i
\(657\) 0 0
\(658\) 0 0
\(659\) 19.1943 + 33.2454i 0.747702 + 1.29506i 0.948922 + 0.315512i \(0.102176\pi\)
−0.201220 + 0.979546i \(0.564491\pi\)
\(660\) 0 0
\(661\) −33.9258 −1.31956 −0.659780 0.751459i \(-0.729351\pi\)
−0.659780 + 0.751459i \(0.729351\pi\)
\(662\) 46.4915 1.80694
\(663\) 0 0
\(664\) −3.98486 6.90198i −0.154642 0.267849i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.37124 2.37505i 0.0530944 0.0919623i
\(668\) 13.4905 23.3662i 0.521962 0.904064i
\(669\) 0 0
\(670\) 44.6601 + 77.3535i 1.72537 + 2.98843i
\(671\) 0.378860 0.656205i 0.0146257 0.0253325i
\(672\) 0 0
\(673\) −16.1030 27.8912i −0.620725 1.07513i −0.989351 0.145549i \(-0.953505\pi\)
0.368626 0.929578i \(-0.379828\pi\)
\(674\) 11.5702 20.0401i 0.445666 0.771916i
\(675\) 0 0
\(676\) 20.0585 + 34.7424i 0.771483 + 1.33625i
\(677\) −37.9684 −1.45924 −0.729622 0.683850i \(-0.760304\pi\)
−0.729622 + 0.683850i \(0.760304\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −19.5836 + 33.9198i −0.750997 + 1.30076i
\(681\) 0 0
\(682\) 5.29031 9.16309i 0.202577 0.350873i
\(683\) −7.59357 13.1525i −0.290560 0.503265i 0.683382 0.730061i \(-0.260508\pi\)
−0.973942 + 0.226796i \(0.927175\pi\)
\(684\) 0 0
\(685\) −21.8932 −0.836495
\(686\) 0 0
\(687\) 0 0
\(688\) −4.93877 8.55420i −0.188289 0.326126i
\(689\) 9.46285 0.360506
\(690\) 0 0
\(691\) −2.69148 −0.102389 −0.0511943 0.998689i \(-0.516303\pi\)
−0.0511943 + 0.998689i \(0.516303\pi\)
\(692\) −14.9922 −0.569919
\(693\) 0 0
\(694\) −4.83589 −0.183568
\(695\) −41.0840 −1.55841
\(696\) 0 0
\(697\) −5.98689 −0.226770
\(698\) −19.4429 33.6761i −0.735924 1.27466i
\(699\) 0 0
\(700\) 0 0
\(701\) 11.8515 0.447625 0.223813 0.974632i \(-0.428150\pi\)
0.223813 + 0.974632i \(0.428150\pi\)
\(702\) 0 0
\(703\) −11.9988 20.7826i −0.452544 0.783829i
\(704\) 7.39689 12.8118i 0.278781 0.482862i
\(705\) 0 0
\(706\) −20.3617 + 35.2675i −0.766323 + 1.32731i
\(707\) 0 0
\(708\) 0 0
\(709\) −41.0333 −1.54104 −0.770520 0.637416i \(-0.780003\pi\)
−0.770520 + 0.637416i \(0.780003\pi\)
\(710\) −45.0294 77.9931i −1.68992 2.92703i
\(711\) 0 0
\(712\) 12.9772 22.4771i 0.486339 0.842364i
\(713\) −4.30328 7.45351i −0.161159 0.279136i
\(714\) 0 0
\(715\) −2.89830 + 5.02001i −0.108390 + 0.187738i
\(716\) −19.5669 33.8908i −0.731248 1.26656i
\(717\) 0 0
\(718\) −3.54123 + 6.13359i −0.132158 + 0.228904i
\(719\) 10.4555 18.1094i 0.389923 0.675366i −0.602516 0.798107i \(-0.705835\pi\)
0.992439 + 0.122741i \(0.0391685\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 16.8644 + 29.2100i 0.627628 + 1.08708i
\(723\) 0 0
\(724\) 72.5792 2.69738
\(725\) 3.68487 0.136853
\(726\) 0 0
\(727\) −1.32165 2.28917i −0.0490173 0.0849005i 0.840476 0.541849i \(-0.182276\pi\)
−0.889493 + 0.456949i \(0.848942\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 36.4462 63.1267i 1.34893 2.33642i
\(731\) 7.18756 12.4492i 0.265841 0.460451i
\(732\) 0 0
\(733\) 7.07446 + 12.2533i 0.261301 + 0.452587i 0.966588 0.256335i \(-0.0825151\pi\)
−0.705287 + 0.708922i \(0.749182\pi\)
\(734\) −12.1223 + 20.9964i −0.447442 + 0.774992i
\(735\) 0 0
\(736\) −3.51218 6.08327i −0.129461 0.224232i
\(737\) −8.67174 + 15.0199i −0.319428 + 0.553265i
\(738\) 0 0
\(739\) −7.85905 13.6123i −0.289100 0.500736i 0.684495 0.729017i \(-0.260023\pi\)
−0.973595 + 0.228282i \(0.926689\pi\)
\(740\) 117.442 4.31727
\(741\) 0 0
\(742\) 0 0
\(743\) −10.5496 + 18.2724i −0.387026 + 0.670348i −0.992048 0.125861i \(-0.959831\pi\)
0.605022 + 0.796208i \(0.293164\pi\)
\(744\) 0 0
\(745\) −3.18333 + 5.51368i −0.116628 + 0.202006i
\(746\) 30.4142 + 52.6789i 1.11354 + 1.92871i
\(747\) 0 0
\(748\) −16.5675 −0.605768
\(749\) 0 0
\(750\) 0 0
\(751\) −6.51848 11.2903i −0.237863 0.411990i 0.722238 0.691644i \(-0.243113\pi\)
−0.960101 + 0.279654i \(0.909780\pi\)
\(752\) 9.05088 0.330052
\(753\) 0 0
\(754\) −3.65116 −0.132968
\(755\) −40.9732 −1.49117
\(756\) 0 0
\(757\) −12.6856 −0.461065 −0.230532 0.973065i \(-0.574047\pi\)
−0.230532 + 0.973065i \(0.574047\pi\)
\(758\) 23.5225 0.854377
\(759\) 0 0
\(760\) 26.1084 0.947050
\(761\) 3.02038 + 5.23146i 0.109489 + 0.189640i 0.915563 0.402174i \(-0.131745\pi\)
−0.806074 + 0.591814i \(0.798412\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −30.6388 −1.10847
\(765\) 0 0
\(766\) 32.5959 + 56.4577i 1.17774 + 2.03990i
\(767\) −8.95288 + 15.5068i −0.323270 + 0.559920i
\(768\) 0 0
\(769\) −0.108129 + 0.187285i −0.00389924 + 0.00675368i −0.867968 0.496619i \(-0.834575\pi\)
0.864069 + 0.503373i \(0.167908\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −69.4503 −2.49957
\(773\) 18.8132 + 32.5854i 0.676663 + 1.17202i 0.975980 + 0.217861i \(0.0699081\pi\)
−0.299316 + 0.954154i \(0.596759\pi\)
\(774\) 0 0
\(775\) 5.78202 10.0148i 0.207696 0.359741i
\(776\) 16.7763 + 29.0575i 0.602235 + 1.04310i
\(777\) 0 0
\(778\) 4.99388 8.64965i 0.179039 0.310105i
\(779\) 1.99539 + 3.45612i 0.0714923 + 0.123828i
\(780\) 0 0
\(781\) 8.74345 15.1441i 0.312865 0.541898i
\(782\) −10.3833 + 17.9845i −0.371307 + 0.643123i
\(783\) 0 0
\(784\) 0 0
\(785\) −4.33198 7.50321i −0.154615 0.267801i
\(786\) 0 0
\(787\) −30.8135 −1.09838 −0.549191 0.835697i \(-0.685064\pi\)
−0.549191 + 0.835697i \(0.685064\pi\)
\(788\) −22.1693 −0.789750
\(789\) 0 0
\(790\) 2.67601 + 4.63499i 0.0952083 + 0.164906i
\(791\) 0 0
\(792\) 0 0
\(793\) −0.410286 + 0.710636i −0.0145697 + 0.0252354i
\(794\) −36.6037 + 63.3994i −1.29902 + 2.24996i
\(795\) 0 0
\(796\) −26.6355 46.1340i −0.944070 1.63518i
\(797\) −17.9792 + 31.1408i −0.636855 + 1.10306i 0.349264 + 0.937024i \(0.386431\pi\)
−0.986119 + 0.166040i \(0.946902\pi\)
\(798\) 0 0
\(799\) 6.58602 + 11.4073i 0.232997 + 0.403562i
\(800\) 4.71907 8.17367i 0.166844 0.288983i
\(801\) 0 0
\(802\) −8.17268 14.1555i −0.288587 0.499848i
\(803\) 14.1537 0.499472
\(804\) 0 0
\(805\) 0 0
\(806\) −5.72914 + 9.92315i −0.201800 + 0.349528i
\(807\) 0 0
\(808\) 32.8659 56.9254i 1.15622 2.00263i
\(809\) 19.4818 + 33.7435i 0.684943 + 1.18636i 0.973455 + 0.228880i \(0.0735065\pi\)
−0.288511 + 0.957477i \(0.593160\pi\)
\(810\) 0 0
\(811\) 28.2811 0.993082 0.496541 0.868013i \(-0.334603\pi\)
0.496541 + 0.868013i \(0.334603\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 17.5701 + 30.4322i 0.615830 + 1.06665i
\(815\) −1.13492 −0.0397544
\(816\) 0 0
\(817\) −9.58227 −0.335241
\(818\) 43.6076 1.52471
\(819\) 0 0
\(820\) −19.5306 −0.682037
\(821\) −41.5834 −1.45127 −0.725635 0.688080i \(-0.758454\pi\)
−0.725635 + 0.688080i \(0.758454\pi\)
\(822\) 0 0
\(823\) 8.45998 0.294896 0.147448 0.989070i \(-0.452894\pi\)
0.147448 + 0.989070i \(0.452894\pi\)
\(824\) −4.51029 7.81205i −0.157123 0.272146i
\(825\) 0 0
\(826\) 0 0
\(827\) −44.2823 −1.53985 −0.769923 0.638137i \(-0.779706\pi\)
−0.769923 + 0.638137i \(0.779706\pi\)
\(828\) 0 0
\(829\) 8.31637 + 14.4044i 0.288839 + 0.500284i 0.973533 0.228547i \(-0.0733973\pi\)
−0.684694 + 0.728831i \(0.740064\pi\)
\(830\) 6.85813 11.8786i 0.238049 0.412314i
\(831\) 0 0
\(832\) −8.01045 + 13.8745i −0.277712 + 0.481012i
\(833\) 0 0
\(834\) 0 0
\(835\) 21.3158 0.737665
\(836\) 5.52185 + 9.56412i 0.190977 + 0.330782i
\(837\) 0 0
\(838\) 26.8068 46.4308i 0.926027 1.60393i
\(839\) 14.8006 + 25.6354i 0.510974 + 0.885033i 0.999919 + 0.0127182i \(0.00404843\pi\)
−0.488945 + 0.872314i \(0.662618\pi\)
\(840\) 0 0
\(841\) 13.9556 24.1718i 0.481228 0.833512i
\(842\) 24.8657 + 43.0687i 0.856929 + 1.48424i
\(843\) 0 0
\(844\) −25.5997 + 44.3400i −0.881178 + 1.52624i
\(845\) −15.8469 + 27.4477i −0.545151 + 0.944228i
\(846\) 0 0
\(847\) 0 0
\(848\) 7.34105 + 12.7151i 0.252093 + 0.436638i
\(849\) 0 0
\(850\) −27.9027 −0.957055
\(851\) 28.5839 0.979844
\(852\) 0 0
\(853\) 15.0619 + 26.0880i 0.515710 + 0.893236i 0.999834 + 0.0182366i \(0.00580520\pi\)
−0.484124 + 0.875000i \(0.660861\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 35.4613 61.4208i 1.21204 2.09932i
\(857\) −18.5447 + 32.1204i −0.633475 + 1.09721i 0.353361 + 0.935487i \(0.385039\pi\)
−0.986836 + 0.161724i \(0.948295\pi\)
\(858\) 0 0
\(859\) −1.89166 3.27646i −0.0645427 0.111791i 0.831948 0.554853i \(-0.187226\pi\)
−0.896491 + 0.443062i \(0.853892\pi\)
\(860\) 23.4474 40.6121i 0.799551 1.38486i
\(861\) 0 0
\(862\) 24.1583 + 41.8434i 0.822835 + 1.42519i
\(863\) −0.213559 + 0.369895i −0.00726963 + 0.0125914i −0.869637 0.493691i \(-0.835647\pi\)
0.862368 + 0.506282i \(0.168981\pi\)
\(864\) 0 0
\(865\) −5.92218 10.2575i −0.201360 0.348766i
\(866\) 51.7388 1.75815
\(867\) 0 0
\(868\) 0 0
\(869\) −0.519608 + 0.899987i −0.0176265 + 0.0305300i
\(870\) 0 0
\(871\) 9.39105 16.2658i 0.318203 0.551145i
\(872\) −31.5933 54.7212i −1.06988 1.85309i
\(873\) 0 0
\(874\) 13.8428 0.468240
\(875\) 0 0
\(876\) 0 0
\(877\) −5.63038 9.75210i −0.190124 0.329305i 0.755167 0.655532i \(-0.227556\pi\)
−0.945291 + 0.326228i \(0.894222\pi\)
\(878\) 84.6816 2.85786
\(879\) 0 0
\(880\) −8.99374 −0.303179
\(881\) −35.4810 −1.19538 −0.597692 0.801726i \(-0.703916\pi\)
−0.597692 + 0.801726i \(0.703916\pi\)
\(882\) 0 0
\(883\) −5.30092 −0.178390 −0.0891952 0.996014i \(-0.528429\pi\)
−0.0891952 + 0.996014i \(0.528429\pi\)
\(884\) 17.9418 0.603447
\(885\) 0 0
\(886\) 45.8428 1.54012
\(887\) −28.7832 49.8540i −0.966446 1.67393i −0.705679 0.708532i \(-0.749358\pi\)
−0.260767 0.965402i \(-0.583975\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 44.6686 1.49730
\(891\) 0 0
\(892\) −8.64231 14.9689i −0.289366 0.501197i
\(893\) 4.39016 7.60398i 0.146911 0.254458i
\(894\) 0 0
\(895\) 15.4585 26.7749i 0.516720 0.894985i
\(896\) 0 0
\(897\) 0 0
\(898\) 70.6708 2.35832
\(899\) 1.70842 + 2.95906i 0.0569788 + 0.0986903i
\(900\) 0 0
\(901\) −10.6837 + 18.5047i −0.355925 + 0.616480i
\(902\) −2.92188 5.06085i −0.0972881 0.168508i
\(903\) 0 0
\(904\) 3.42117 5.92565i 0.113787 0.197084i
\(905\) 28.6700 + 49.6579i 0.953023 + 1.65068i
\(906\) 0 0
\(907\) −10.4486 + 18.0975i −0.346939 + 0.600917i −0.985704 0.168485i \(-0.946112\pi\)
0.638765 + 0.769402i \(0.279446\pi\)
\(908\) −36.4402 + 63.1163i −1.20931 + 2.09459i
\(909\) 0 0
\(910\) 0 0
\(911\) −11.3819 19.7141i −0.377101 0.653157i 0.613539 0.789665i \(-0.289746\pi\)
−0.990639 + 0.136508i \(0.956412\pi\)
\(912\) 0 0
\(913\) 2.66332 0.0881430
\(914\) −22.8231 −0.754923
\(915\) 0 0
\(916\) 51.8946 + 89.8841i 1.71465 + 2.96986i
\(917\) 0 0
\(918\) 0 0
\(919\) 18.6515 32.3054i 0.615257 1.06566i −0.375083 0.926991i \(-0.622386\pi\)
0.990339 0.138664i \(-0.0442809\pi\)
\(920\) −15.5490 + 26.9317i −0.512636 + 0.887911i
\(921\) 0 0
\(922\) 26.0616 + 45.1399i 0.858292 + 1.48660i
\(923\) −9.46870 + 16.4003i −0.311666 + 0.539822i
\(924\) 0 0
\(925\) 19.2031 + 33.2607i 0.631394 + 1.09361i
\(926\) 31.2070 54.0521i 1.02553 1.77626i
\(927\) 0 0
\(928\) 1.39434 + 2.41508i 0.0457716 + 0.0792787i
\(929\) 5.66725 0.185937 0.0929683 0.995669i \(-0.470364\pi\)
0.0929683 + 0.995669i \(0.470364\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 25.5145 44.1923i 0.835754 1.44757i
\(933\) 0 0
\(934\) −41.7138 + 72.2503i −1.36492 + 2.36410i
\(935\) −6.54444 11.3353i −0.214026 0.370704i
\(936\) 0 0
\(937\) 7.64754 0.249834 0.124917 0.992167i \(-0.460134\pi\)
0.124917 + 0.992167i \(0.460134\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 21.4851 + 37.2133i 0.700766 + 1.21376i
\(941\) 20.4552 0.666819 0.333410 0.942782i \(-0.391801\pi\)
0.333410 + 0.942782i \(0.391801\pi\)
\(942\) 0 0
\(943\) −4.75348 −0.154795
\(944\) −27.7817 −0.904219
\(945\) 0 0
\(946\) 14.0315 0.456202
\(947\) 4.76687 0.154902 0.0774512 0.996996i \(-0.475322\pi\)
0.0774512 + 0.996996i \(0.475322\pi\)
\(948\) 0 0
\(949\) −15.3277 −0.497558
\(950\) 9.29980 + 16.1077i 0.301725 + 0.522604i
\(951\) 0 0
\(952\) 0 0
\(953\) 48.9412 1.58536 0.792680 0.609638i \(-0.208685\pi\)
0.792680 + 0.609638i \(0.208685\pi\)
\(954\) 0 0
\(955\) −12.1028 20.9627i −0.391638 0.678337i
\(956\) −20.4478 + 35.4166i −0.661328 + 1.14545i
\(957\) 0 0
\(958\) 35.5773 61.6217i 1.14945 1.99091i
\(959\) 0 0
\(960\) 0 0
\(961\) −20.2771 −0.654101
\(962\) −19.0275 32.9565i −0.613470 1.06256i
\(963\) 0 0
\(964\) −42.8309 + 74.1854i −1.37949 + 2.38935i
\(965\) −27.4340 47.5171i −0.883132 1.52963i
\(966\) 0 0
\(967\) −2.95856 + 5.12438i −0.0951409 + 0.164789i −0.909667 0.415337i \(-0.863664\pi\)
0.814526 + 0.580126i \(0.196997\pi\)
\(968\) 18.5680 + 32.1608i 0.596799 + 1.03369i
\(969\) 0 0
\(970\) −28.8729 + 50.0093i −0.927052 + 1.60570i
\(971\) 14.4888 25.0953i 0.464966 0.805345i −0.534234 0.845337i \(-0.679400\pi\)
0.999200 + 0.0399914i \(0.0127331\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −26.7933 46.4074i −0.858513 1.48699i
\(975\) 0 0
\(976\) −1.27316 −0.0407528
\(977\) −22.8455 −0.730893 −0.365447 0.930832i \(-0.619084\pi\)
−0.365447 + 0.930832i \(0.619084\pi\)
\(978\) 0 0
\(979\) 4.33670 + 7.51139i 0.138602 + 0.240065i
\(980\) 0 0
\(981\) 0 0
\(982\) −41.8232 + 72.4400i −1.33463 + 2.31165i
\(983\) 15.6351 27.0809i 0.498684 0.863745i −0.501315 0.865265i \(-0.667150\pi\)
0.999999 + 0.00151933i \(0.000483619\pi\)
\(984\) 0 0
\(985\) −8.75726 15.1680i −0.279029 0.483293i
\(986\) 4.12221 7.13988i 0.131278 0.227380i
\(987\) 0 0
\(988\) −5.97988 10.3574i −0.190245 0.329514i
\(989\) 5.70679 9.88444i 0.181465 0.314307i
\(990\) 0 0
\(991\) 3.50732 + 6.07485i 0.111414 + 0.192974i 0.916340 0.400400i \(-0.131129\pi\)
−0.804927 + 0.593374i \(0.797796\pi\)
\(992\) 8.75161 0.277864
\(993\) 0 0
\(994\) 0 0
\(995\) 21.0429 36.4474i 0.667105 1.15546i
\(996\) 0 0
\(997\) −10.6439 + 18.4358i −0.337095 + 0.583866i −0.983885 0.178802i \(-0.942778\pi\)
0.646790 + 0.762668i \(0.276111\pi\)
\(998\) 10.6636 + 18.4698i 0.337549 + 0.584653i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1323.2.h.f.226.5 10
3.2 odd 2 441.2.h.f.373.1 10
7.2 even 3 1323.2.f.f.442.1 10
7.3 odd 6 189.2.g.b.172.1 10
7.4 even 3 1323.2.g.f.361.1 10
7.5 odd 6 1323.2.f.e.442.1 10
7.6 odd 2 189.2.h.b.37.5 10
9.2 odd 6 441.2.g.f.79.5 10
9.7 even 3 1323.2.g.f.667.1 10
21.2 odd 6 441.2.f.f.148.5 10
21.5 even 6 441.2.f.e.148.5 10
21.11 odd 6 441.2.g.f.67.5 10
21.17 even 6 63.2.g.b.4.5 10
21.20 even 2 63.2.h.b.58.1 yes 10
28.3 even 6 3024.2.t.i.1873.4 10
28.27 even 2 3024.2.q.i.2305.2 10
63.2 odd 6 441.2.f.f.295.5 10
63.5 even 6 3969.2.a.z.1.1 5
63.11 odd 6 441.2.h.f.214.1 10
63.13 odd 6 567.2.e.e.163.1 10
63.16 even 3 1323.2.f.f.883.1 10
63.20 even 6 63.2.g.b.16.5 yes 10
63.23 odd 6 3969.2.a.ba.1.1 5
63.25 even 3 inner 1323.2.h.f.802.5 10
63.31 odd 6 567.2.e.e.487.1 10
63.34 odd 6 189.2.g.b.100.1 10
63.38 even 6 63.2.h.b.25.1 yes 10
63.40 odd 6 3969.2.a.bc.1.5 5
63.41 even 6 567.2.e.f.163.5 10
63.47 even 6 441.2.f.e.295.5 10
63.52 odd 6 189.2.h.b.46.5 10
63.58 even 3 3969.2.a.bb.1.5 5
63.59 even 6 567.2.e.f.487.5 10
63.61 odd 6 1323.2.f.e.883.1 10
84.59 odd 6 1008.2.t.i.193.3 10
84.83 odd 2 1008.2.q.i.625.4 10
252.83 odd 6 1008.2.t.i.961.3 10
252.115 even 6 3024.2.q.i.2881.2 10
252.223 even 6 3024.2.t.i.289.4 10
252.227 odd 6 1008.2.q.i.529.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.g.b.4.5 10 21.17 even 6
63.2.g.b.16.5 yes 10 63.20 even 6
63.2.h.b.25.1 yes 10 63.38 even 6
63.2.h.b.58.1 yes 10 21.20 even 2
189.2.g.b.100.1 10 63.34 odd 6
189.2.g.b.172.1 10 7.3 odd 6
189.2.h.b.37.5 10 7.6 odd 2
189.2.h.b.46.5 10 63.52 odd 6
441.2.f.e.148.5 10 21.5 even 6
441.2.f.e.295.5 10 63.47 even 6
441.2.f.f.148.5 10 21.2 odd 6
441.2.f.f.295.5 10 63.2 odd 6
441.2.g.f.67.5 10 21.11 odd 6
441.2.g.f.79.5 10 9.2 odd 6
441.2.h.f.214.1 10 63.11 odd 6
441.2.h.f.373.1 10 3.2 odd 2
567.2.e.e.163.1 10 63.13 odd 6
567.2.e.e.487.1 10 63.31 odd 6
567.2.e.f.163.5 10 63.41 even 6
567.2.e.f.487.5 10 63.59 even 6
1008.2.q.i.529.4 10 252.227 odd 6
1008.2.q.i.625.4 10 84.83 odd 2
1008.2.t.i.193.3 10 84.59 odd 6
1008.2.t.i.961.3 10 252.83 odd 6
1323.2.f.e.442.1 10 7.5 odd 6
1323.2.f.e.883.1 10 63.61 odd 6
1323.2.f.f.442.1 10 7.2 even 3
1323.2.f.f.883.1 10 63.16 even 3
1323.2.g.f.361.1 10 7.4 even 3
1323.2.g.f.667.1 10 9.7 even 3
1323.2.h.f.226.5 10 1.1 even 1 trivial
1323.2.h.f.802.5 10 63.25 even 3 inner
3024.2.q.i.2305.2 10 28.27 even 2
3024.2.q.i.2881.2 10 252.115 even 6
3024.2.t.i.289.4 10 252.223 even 6
3024.2.t.i.1873.4 10 28.3 even 6
3969.2.a.z.1.1 5 63.5 even 6
3969.2.a.ba.1.1 5 63.23 odd 6
3969.2.a.bb.1.5 5 63.58 even 3
3969.2.a.bc.1.5 5 63.40 odd 6