Properties

Label 7.10.a.b.1.2
Level $7$
Weight $10$
Character 7.1
Self dual yes
Analytic conductor $3.605$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7,10,Mod(1,7)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 7.a (trivial)

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: yes
Analytic conductor: \(3.60525085315\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 426x + 2016 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-22.2358\) of defining polynomial
Character \(\chi\) \(=\) 7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+13.3607 q^{2} +163.415 q^{3} -333.491 q^{4} +1922.19 q^{5} +2183.34 q^{6} +2401.00 q^{7} -11296.4 q^{8} +7021.32 q^{9} +O(q^{10})\) \(q+13.3607 q^{2} +163.415 q^{3} -333.491 q^{4} +1922.19 q^{5} +2183.34 q^{6} +2401.00 q^{7} -11296.4 q^{8} +7021.32 q^{9} +25681.8 q^{10} -90199.9 q^{11} -54497.3 q^{12} -3199.89 q^{13} +32079.1 q^{14} +314114. q^{15} +19819.7 q^{16} +116494. q^{17} +93809.9 q^{18} -142449. q^{19} -641033. q^{20} +392358. q^{21} -1.20514e6 q^{22} +1.27391e6 q^{23} -1.84599e6 q^{24} +1.74168e6 q^{25} -42752.8 q^{26} -2.06910e6 q^{27} -800712. q^{28} -1.42931e6 q^{29} +4.19679e6 q^{30} +9.67494e6 q^{31} +6.04855e6 q^{32} -1.47400e7 q^{33} +1.55645e6 q^{34} +4.61518e6 q^{35} -2.34155e6 q^{36} -8.67744e6 q^{37} -1.90323e6 q^{38} -522908. q^{39} -2.17138e7 q^{40} +1.32544e7 q^{41} +5.24219e6 q^{42} -2.97554e7 q^{43} +3.00809e7 q^{44} +1.34963e7 q^{45} +1.70204e7 q^{46} -1.07969e7 q^{47} +3.23882e6 q^{48} +5.76480e6 q^{49} +2.32702e7 q^{50} +1.90369e7 q^{51} +1.06713e6 q^{52} +7.07399e7 q^{53} -2.76447e7 q^{54} -1.73381e8 q^{55} -2.71226e7 q^{56} -2.32783e7 q^{57} -1.90966e7 q^{58} +6.40400e6 q^{59} -1.04754e8 q^{60} +1.69190e8 q^{61} +1.29264e8 q^{62} +1.68582e7 q^{63} +7.06653e7 q^{64} -6.15078e6 q^{65} -1.96937e8 q^{66} -1.16276e8 q^{67} -3.88498e7 q^{68} +2.08176e8 q^{69} +6.16621e7 q^{70} +1.44496e8 q^{71} -7.93154e7 q^{72} +1.60155e8 q^{73} -1.15937e8 q^{74} +2.84617e8 q^{75} +4.75056e7 q^{76} -2.16570e8 q^{77} -6.98643e6 q^{78} -4.89322e8 q^{79} +3.80972e7 q^{80} -4.76322e8 q^{81} +1.77088e8 q^{82} -8.31590e7 q^{83} -1.30848e8 q^{84} +2.23924e8 q^{85} -3.97553e8 q^{86} -2.33569e8 q^{87} +1.01893e9 q^{88} +2.08083e6 q^{89} +1.80320e8 q^{90} -7.68292e6 q^{91} -4.24838e8 q^{92} +1.58103e9 q^{93} -1.44255e8 q^{94} -2.73815e8 q^{95} +9.88421e8 q^{96} -3.15885e8 q^{97} +7.70219e7 q^{98} -6.33322e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 21 q^{2} + 84 q^{3} + 1557 q^{4} + 1554 q^{5} + 4914 q^{6} + 7203 q^{7} + 14055 q^{8} - 26001 q^{9} - 97860 q^{10} - 3444 q^{11} - 106386 q^{12} - 19782 q^{13} + 50421 q^{14} + 200304 q^{15} + 482961 q^{16} + 1016694 q^{17} - 273267 q^{18} + 222852 q^{19} - 1922088 q^{20} + 201684 q^{21} - 2847048 q^{22} + 1885632 q^{23} - 1449630 q^{24} + 3073221 q^{25} - 8785056 q^{26} + 551880 q^{27} + 3738357 q^{28} + 4081818 q^{29} + 8053200 q^{30} + 2869440 q^{31} + 25221951 q^{32} - 20259792 q^{33} - 3981642 q^{34} + 3731154 q^{35} - 35396379 q^{36} + 1395618 q^{37} + 43479870 q^{38} - 8990688 q^{39} - 82859280 q^{40} - 14420658 q^{41} + 11798514 q^{42} - 61631172 q^{43} + 97011984 q^{44} + 29774682 q^{45} + 89747664 q^{46} - 10368960 q^{47} + 16798782 q^{48} + 17294403 q^{49} + 73325055 q^{50} - 26146728 q^{51} - 80908044 q^{52} + 67502610 q^{53} - 117879300 q^{54} - 105823032 q^{55} + 33746055 q^{56} + 8471112 q^{57} - 159163830 q^{58} - 42590100 q^{59} - 179551008 q^{60} + 191746842 q^{61} - 46983468 q^{62} - 62428401 q^{63} + 7852161 q^{64} + 364283220 q^{65} - 8057952 q^{66} - 255175788 q^{67} + 743485806 q^{68} + 257903856 q^{69} - 234961860 q^{70} + 296514504 q^{71} - 609314265 q^{72} + 344213310 q^{73} - 690696462 q^{74} + 279031116 q^{75} + 728839986 q^{76} - 8269044 q^{77} + 280132776 q^{78} - 960412656 q^{79} - 1333333344 q^{80} - 35827677 q^{81} + 562675302 q^{82} - 1100517180 q^{83} - 255432786 q^{84} + 438179412 q^{85} - 880982256 q^{86} - 621821592 q^{87} + 1206124800 q^{88} + 506816478 q^{89} + 2303452620 q^{90} - 47496582 q^{91} + 691123488 q^{92} + 1693258512 q^{93} + 1388004828 q^{94} - 2203071072 q^{95} + 333385794 q^{96} - 647498250 q^{97} + 121060821 q^{98} - 1900979172 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.3607 0.590466 0.295233 0.955425i \(-0.404603\pi\)
0.295233 + 0.955425i \(0.404603\pi\)
\(3\) 163.415 1.16478 0.582392 0.812908i \(-0.302117\pi\)
0.582392 + 0.812908i \(0.302117\pi\)
\(4\) −333.491 −0.651350
\(5\) 1922.19 1.37541 0.687703 0.725992i \(-0.258619\pi\)
0.687703 + 0.725992i \(0.258619\pi\)
\(6\) 2183.34 0.687765
\(7\) 2401.00 0.377964
\(8\) −11296.4 −0.975066
\(9\) 7021.32 0.356720
\(10\) 25681.8 0.812131
\(11\) −90199.9 −1.85754 −0.928772 0.370652i \(-0.879134\pi\)
−0.928772 + 0.370652i \(0.879134\pi\)
\(12\) −54497.3 −0.758681
\(13\) −3199.89 −0.0310734 −0.0155367 0.999879i \(-0.504946\pi\)
−0.0155367 + 0.999879i \(0.504946\pi\)
\(14\) 32079.1 0.223175
\(15\) 314114. 1.60205
\(16\) 19819.7 0.0756061
\(17\) 116494. 0.338286 0.169143 0.985591i \(-0.445900\pi\)
0.169143 + 0.985591i \(0.445900\pi\)
\(18\) 93809.9 0.210631
\(19\) −142449. −0.250767 −0.125383 0.992108i \(-0.540016\pi\)
−0.125383 + 0.992108i \(0.540016\pi\)
\(20\) −641033. −0.895870
\(21\) 392358. 0.440247
\(22\) −1.20514e6 −1.09682
\(23\) 1.27391e6 0.949213 0.474606 0.880198i \(-0.342590\pi\)
0.474606 + 0.880198i \(0.342590\pi\)
\(24\) −1.84599e6 −1.13574
\(25\) 1.74168e6 0.891742
\(26\) −42752.8 −0.0183478
\(27\) −2.06910e6 −0.749282
\(28\) −800712. −0.246187
\(29\) −1.42931e6 −0.375262 −0.187631 0.982240i \(-0.560081\pi\)
−0.187631 + 0.982240i \(0.560081\pi\)
\(30\) 4.19679e6 0.945956
\(31\) 9.67494e6 1.88157 0.940786 0.339001i \(-0.110089\pi\)
0.940786 + 0.339001i \(0.110089\pi\)
\(32\) 6.04855e6 1.01971
\(33\) −1.47400e7 −2.16364
\(34\) 1.55645e6 0.199747
\(35\) 4.61518e6 0.519855
\(36\) −2.34155e6 −0.232349
\(37\) −8.67744e6 −0.761174 −0.380587 0.924745i \(-0.624278\pi\)
−0.380587 + 0.924745i \(0.624278\pi\)
\(38\) −1.90323e6 −0.148069
\(39\) −522908. −0.0361938
\(40\) −2.17138e7 −1.34111
\(41\) 1.32544e7 0.732541 0.366271 0.930508i \(-0.380634\pi\)
0.366271 + 0.930508i \(0.380634\pi\)
\(42\) 5.24219e6 0.259951
\(43\) −2.97554e7 −1.32726 −0.663632 0.748060i \(-0.730986\pi\)
−0.663632 + 0.748060i \(0.730986\pi\)
\(44\) 3.00809e7 1.20991
\(45\) 1.34963e7 0.490635
\(46\) 1.70204e7 0.560478
\(47\) −1.07969e7 −0.322745 −0.161373 0.986894i \(-0.551592\pi\)
−0.161373 + 0.986894i \(0.551592\pi\)
\(48\) 3.23882e6 0.0880647
\(49\) 5.76480e6 0.142857
\(50\) 2.32702e7 0.526544
\(51\) 1.90369e7 0.394030
\(52\) 1.06713e6 0.0202397
\(53\) 7.07399e7 1.23147 0.615734 0.787954i \(-0.288860\pi\)
0.615734 + 0.787954i \(0.288860\pi\)
\(54\) −2.76447e7 −0.442426
\(55\) −1.73381e8 −2.55488
\(56\) −2.71226e7 −0.368540
\(57\) −2.32783e7 −0.292089
\(58\) −1.90966e7 −0.221579
\(59\) 6.40400e6 0.0688046 0.0344023 0.999408i \(-0.489047\pi\)
0.0344023 + 0.999408i \(0.489047\pi\)
\(60\) −1.04754e8 −1.04349
\(61\) 1.69190e8 1.56455 0.782275 0.622933i \(-0.214059\pi\)
0.782275 + 0.622933i \(0.214059\pi\)
\(62\) 1.29264e8 1.11100
\(63\) 1.68582e7 0.134827
\(64\) 7.06653e7 0.526498
\(65\) −6.15078e6 −0.0427386
\(66\) −1.96937e8 −1.27755
\(67\) −1.16276e8 −0.704943 −0.352471 0.935823i \(-0.614659\pi\)
−0.352471 + 0.935823i \(0.614659\pi\)
\(68\) −3.88498e7 −0.220343
\(69\) 2.08176e8 1.10563
\(70\) 6.16621e7 0.306957
\(71\) 1.44496e8 0.674826 0.337413 0.941357i \(-0.390448\pi\)
0.337413 + 0.941357i \(0.390448\pi\)
\(72\) −7.93154e7 −0.347825
\(73\) 1.60155e8 0.660066 0.330033 0.943969i \(-0.392940\pi\)
0.330033 + 0.943969i \(0.392940\pi\)
\(74\) −1.15937e8 −0.449447
\(75\) 2.84617e8 1.03869
\(76\) 4.75056e7 0.163337
\(77\) −2.16570e8 −0.702085
\(78\) −6.98643e6 −0.0213712
\(79\) −4.89322e8 −1.41343 −0.706713 0.707500i \(-0.749823\pi\)
−0.706713 + 0.707500i \(0.749823\pi\)
\(80\) 3.80972e7 0.103989
\(81\) −4.76322e8 −1.22947
\(82\) 1.77088e8 0.432541
\(83\) −8.31590e7 −0.192335 −0.0961674 0.995365i \(-0.530658\pi\)
−0.0961674 + 0.995365i \(0.530658\pi\)
\(84\) −1.30848e8 −0.286755
\(85\) 2.23924e8 0.465281
\(86\) −3.97553e8 −0.783704
\(87\) −2.33569e8 −0.437098
\(88\) 1.01893e9 1.81123
\(89\) 2.08083e6 0.00351546 0.00175773 0.999998i \(-0.499440\pi\)
0.00175773 + 0.999998i \(0.499440\pi\)
\(90\) 1.80320e8 0.289703
\(91\) −7.68292e6 −0.0117447
\(92\) −4.24838e8 −0.618270
\(93\) 1.58103e9 2.19162
\(94\) −1.44255e8 −0.190570
\(95\) −2.73815e8 −0.344906
\(96\) 9.88421e8 1.18774
\(97\) −3.15885e8 −0.362290 −0.181145 0.983456i \(-0.557980\pi\)
−0.181145 + 0.983456i \(0.557980\pi\)
\(98\) 7.70219e7 0.0843523
\(99\) −6.33322e8 −0.662623
\(100\) −5.80836e8 −0.580836
\(101\) −5.74841e8 −0.549669 −0.274835 0.961492i \(-0.588623\pi\)
−0.274835 + 0.961492i \(0.588623\pi\)
\(102\) 2.54346e8 0.232662
\(103\) −1.51870e9 −1.32955 −0.664775 0.747044i \(-0.731473\pi\)
−0.664775 + 0.747044i \(0.731473\pi\)
\(104\) 3.61471e7 0.0302987
\(105\) 7.54187e8 0.605518
\(106\) 9.45137e8 0.727140
\(107\) −2.01863e8 −0.148878 −0.0744390 0.997226i \(-0.523717\pi\)
−0.0744390 + 0.997226i \(0.523717\pi\)
\(108\) 6.90027e8 0.488044
\(109\) −8.73952e8 −0.593019 −0.296509 0.955030i \(-0.595823\pi\)
−0.296509 + 0.955030i \(0.595823\pi\)
\(110\) −2.31650e9 −1.50857
\(111\) −1.41802e9 −0.886603
\(112\) 4.75871e7 0.0285764
\(113\) 1.52955e9 0.882491 0.441245 0.897386i \(-0.354537\pi\)
0.441245 + 0.897386i \(0.354537\pi\)
\(114\) −3.11015e8 −0.172469
\(115\) 2.44870e9 1.30555
\(116\) 4.76661e8 0.244427
\(117\) −2.24674e7 −0.0110845
\(118\) 8.55621e7 0.0406268
\(119\) 2.79703e8 0.127860
\(120\) −3.54834e9 −1.56210
\(121\) 5.77807e9 2.45047
\(122\) 2.26050e9 0.923814
\(123\) 2.16596e9 0.853252
\(124\) −3.22651e9 −1.22556
\(125\) −4.06429e8 −0.148898
\(126\) 2.25238e8 0.0796110
\(127\) −8.71958e8 −0.297426 −0.148713 0.988880i \(-0.547513\pi\)
−0.148713 + 0.988880i \(0.547513\pi\)
\(128\) −2.15272e9 −0.708830
\(129\) −4.86246e9 −1.54597
\(130\) −8.21789e7 −0.0252357
\(131\) 2.24404e9 0.665747 0.332874 0.942971i \(-0.391982\pi\)
0.332874 + 0.942971i \(0.391982\pi\)
\(132\) 4.91565e9 1.40928
\(133\) −3.42021e8 −0.0947809
\(134\) −1.55353e9 −0.416245
\(135\) −3.97721e9 −1.03057
\(136\) −1.31596e9 −0.329852
\(137\) 4.16141e9 1.00925 0.504624 0.863339i \(-0.331631\pi\)
0.504624 + 0.863339i \(0.331631\pi\)
\(138\) 2.78138e9 0.652836
\(139\) −6.03383e9 −1.37097 −0.685483 0.728089i \(-0.740409\pi\)
−0.685483 + 0.728089i \(0.740409\pi\)
\(140\) −1.53912e9 −0.338607
\(141\) −1.76438e9 −0.375928
\(142\) 1.93057e9 0.398462
\(143\) 2.88629e8 0.0577203
\(144\) 1.39160e8 0.0269702
\(145\) −2.74740e9 −0.516137
\(146\) 2.13979e9 0.389747
\(147\) 9.42052e8 0.166398
\(148\) 2.89385e9 0.495790
\(149\) −4.37832e9 −0.727728 −0.363864 0.931452i \(-0.618543\pi\)
−0.363864 + 0.931452i \(0.618543\pi\)
\(150\) 3.80268e9 0.613309
\(151\) −2.69365e9 −0.421642 −0.210821 0.977525i \(-0.567614\pi\)
−0.210821 + 0.977525i \(0.567614\pi\)
\(152\) 1.60916e9 0.244514
\(153\) 8.17943e8 0.120673
\(154\) −2.89353e9 −0.414558
\(155\) 1.85971e10 2.58793
\(156\) 1.74385e8 0.0235748
\(157\) −1.33044e9 −0.174762 −0.0873810 0.996175i \(-0.527850\pi\)
−0.0873810 + 0.996175i \(0.527850\pi\)
\(158\) −6.53770e9 −0.834580
\(159\) 1.15599e10 1.43439
\(160\) 1.16265e10 1.40251
\(161\) 3.05866e9 0.358769
\(162\) −6.36401e9 −0.725961
\(163\) −3.56094e9 −0.395112 −0.197556 0.980292i \(-0.563301\pi\)
−0.197556 + 0.980292i \(0.563301\pi\)
\(164\) −4.42022e9 −0.477140
\(165\) −2.83330e10 −2.97588
\(166\) −1.11106e9 −0.113567
\(167\) −1.04285e10 −1.03752 −0.518762 0.854919i \(-0.673607\pi\)
−0.518762 + 0.854919i \(0.673607\pi\)
\(168\) −4.43223e9 −0.429270
\(169\) −1.05943e10 −0.999034
\(170\) 2.99179e9 0.274733
\(171\) −1.00018e9 −0.0894534
\(172\) 9.92314e9 0.864512
\(173\) 2.04717e10 1.73759 0.868793 0.495176i \(-0.164896\pi\)
0.868793 + 0.495176i \(0.164896\pi\)
\(174\) −3.12066e9 −0.258092
\(175\) 4.18178e9 0.337047
\(176\) −1.78773e9 −0.140442
\(177\) 1.04651e9 0.0801424
\(178\) 2.78014e7 0.00207576
\(179\) 5.46705e9 0.398029 0.199014 0.979997i \(-0.436226\pi\)
0.199014 + 0.979997i \(0.436226\pi\)
\(180\) −4.50089e9 −0.319575
\(181\) −2.11628e9 −0.146561 −0.0732807 0.997311i \(-0.523347\pi\)
−0.0732807 + 0.997311i \(0.523347\pi\)
\(182\) −1.02649e8 −0.00693482
\(183\) 2.76481e10 1.82236
\(184\) −1.43906e10 −0.925545
\(185\) −1.66797e10 −1.04692
\(186\) 2.11237e10 1.29408
\(187\) −1.05078e10 −0.628381
\(188\) 3.60068e9 0.210220
\(189\) −4.96792e9 −0.283202
\(190\) −3.65836e9 −0.203655
\(191\) 1.72421e10 0.937431 0.468715 0.883349i \(-0.344717\pi\)
0.468715 + 0.883349i \(0.344717\pi\)
\(192\) 1.15477e10 0.613256
\(193\) 2.02030e10 1.04811 0.524055 0.851684i \(-0.324418\pi\)
0.524055 + 0.851684i \(0.324418\pi\)
\(194\) −4.22045e9 −0.213920
\(195\) −1.00513e9 −0.0497812
\(196\) −1.92251e9 −0.0930500
\(197\) −2.22592e10 −1.05296 −0.526481 0.850187i \(-0.676489\pi\)
−0.526481 + 0.850187i \(0.676489\pi\)
\(198\) −8.46164e9 −0.391256
\(199\) 1.70588e10 0.771098 0.385549 0.922687i \(-0.374012\pi\)
0.385549 + 0.922687i \(0.374012\pi\)
\(200\) −1.96747e10 −0.869508
\(201\) −1.90012e10 −0.821105
\(202\) −7.68029e9 −0.324561
\(203\) −3.43176e9 −0.141836
\(204\) −6.34862e9 −0.256651
\(205\) 2.54774e10 1.00754
\(206\) −2.02909e10 −0.785054
\(207\) 8.94453e9 0.338603
\(208\) −6.34207e7 −0.00234934
\(209\) 1.28489e10 0.465810
\(210\) 1.00765e10 0.357538
\(211\) −3.19873e10 −1.11098 −0.555490 0.831523i \(-0.687469\pi\)
−0.555490 + 0.831523i \(0.687469\pi\)
\(212\) −2.35911e10 −0.802116
\(213\) 2.36127e10 0.786026
\(214\) −2.69704e9 −0.0879074
\(215\) −5.71954e10 −1.82553
\(216\) 2.33734e10 0.730599
\(217\) 2.32295e10 0.711167
\(218\) −1.16766e10 −0.350157
\(219\) 2.61717e10 0.768834
\(220\) 5.78211e10 1.66412
\(221\) −3.72768e8 −0.0105117
\(222\) −1.89458e10 −0.523509
\(223\) −2.30967e10 −0.625428 −0.312714 0.949847i \(-0.601238\pi\)
−0.312714 + 0.949847i \(0.601238\pi\)
\(224\) 1.45226e10 0.385414
\(225\) 1.22289e10 0.318102
\(226\) 2.04359e10 0.521081
\(227\) −2.30894e10 −0.577160 −0.288580 0.957456i \(-0.593183\pi\)
−0.288580 + 0.957456i \(0.593183\pi\)
\(228\) 7.76311e9 0.190252
\(229\) 4.25496e10 1.02244 0.511218 0.859451i \(-0.329195\pi\)
0.511218 + 0.859451i \(0.329195\pi\)
\(230\) 3.27164e10 0.770885
\(231\) −3.53907e10 −0.817777
\(232\) 1.61460e10 0.365905
\(233\) −1.26679e10 −0.281582 −0.140791 0.990039i \(-0.544964\pi\)
−0.140791 + 0.990039i \(0.544964\pi\)
\(234\) −3.00181e8 −0.00654503
\(235\) −2.07537e10 −0.443906
\(236\) −2.13568e9 −0.0448158
\(237\) −7.99624e10 −1.64633
\(238\) 3.73703e9 0.0754971
\(239\) 6.37875e10 1.26458 0.632289 0.774733i \(-0.282116\pi\)
0.632289 + 0.774733i \(0.282116\pi\)
\(240\) 6.22563e9 0.121125
\(241\) −2.91604e10 −0.556823 −0.278412 0.960462i \(-0.589808\pi\)
−0.278412 + 0.960462i \(0.589808\pi\)
\(242\) 7.71992e10 1.44692
\(243\) −3.71118e10 −0.682785
\(244\) −5.64232e10 −1.01907
\(245\) 1.10810e10 0.196487
\(246\) 2.89388e10 0.503816
\(247\) 4.55822e8 0.00779218
\(248\) −1.09292e11 −1.83466
\(249\) −1.35894e10 −0.224028
\(250\) −5.43018e9 −0.0879194
\(251\) 6.28939e10 1.00018 0.500088 0.865974i \(-0.333301\pi\)
0.500088 + 0.865974i \(0.333301\pi\)
\(252\) −5.62205e9 −0.0878198
\(253\) −1.14907e11 −1.76320
\(254\) −1.16500e10 −0.175620
\(255\) 3.65924e10 0.541952
\(256\) −6.49425e10 −0.945038
\(257\) 1.14480e11 1.63694 0.818469 0.574551i \(-0.194823\pi\)
0.818469 + 0.574551i \(0.194823\pi\)
\(258\) −6.49660e10 −0.912845
\(259\) −2.08345e10 −0.287697
\(260\) 2.05123e9 0.0278378
\(261\) −1.00356e10 −0.133863
\(262\) 2.99820e10 0.393101
\(263\) 1.40705e10 0.181346 0.0906728 0.995881i \(-0.471098\pi\)
0.0906728 + 0.995881i \(0.471098\pi\)
\(264\) 1.66508e11 2.10969
\(265\) 1.35975e11 1.69377
\(266\) −4.56965e9 −0.0559649
\(267\) 3.40038e8 0.00409475
\(268\) 3.87770e10 0.459164
\(269\) 8.39143e10 0.977127 0.488563 0.872528i \(-0.337521\pi\)
0.488563 + 0.872528i \(0.337521\pi\)
\(270\) −5.31384e10 −0.608515
\(271\) 1.98401e10 0.223451 0.111726 0.993739i \(-0.464362\pi\)
0.111726 + 0.993739i \(0.464362\pi\)
\(272\) 2.30888e9 0.0255765
\(273\) −1.25550e9 −0.0136800
\(274\) 5.55995e10 0.595927
\(275\) −1.57100e11 −1.65645
\(276\) −6.94247e10 −0.720150
\(277\) −7.17911e10 −0.732675 −0.366338 0.930482i \(-0.619389\pi\)
−0.366338 + 0.930482i \(0.619389\pi\)
\(278\) −8.06163e10 −0.809508
\(279\) 6.79308e10 0.671194
\(280\) −5.21347e10 −0.506893
\(281\) 1.02853e11 0.984101 0.492050 0.870567i \(-0.336248\pi\)
0.492050 + 0.870567i \(0.336248\pi\)
\(282\) −2.35733e10 −0.221973
\(283\) −5.52883e10 −0.512382 −0.256191 0.966626i \(-0.582468\pi\)
−0.256191 + 0.966626i \(0.582468\pi\)
\(284\) −4.81880e10 −0.439548
\(285\) −4.47453e10 −0.401741
\(286\) 3.85630e9 0.0340819
\(287\) 3.18238e10 0.276875
\(288\) 4.24688e10 0.363750
\(289\) −1.05017e11 −0.885562
\(290\) −3.67072e10 −0.304762
\(291\) −5.16202e10 −0.421989
\(292\) −5.34102e10 −0.429934
\(293\) 1.05721e11 0.838028 0.419014 0.907980i \(-0.362376\pi\)
0.419014 + 0.907980i \(0.362376\pi\)
\(294\) 1.25865e10 0.0982522
\(295\) 1.23097e10 0.0946343
\(296\) 9.80236e10 0.742195
\(297\) 1.86633e11 1.39182
\(298\) −5.84975e10 −0.429699
\(299\) −4.07637e9 −0.0294953
\(300\) −9.49171e10 −0.676548
\(301\) −7.14426e10 −0.501658
\(302\) −3.59891e10 −0.248966
\(303\) −9.39374e10 −0.640246
\(304\) −2.82330e9 −0.0189595
\(305\) 3.25214e11 2.15189
\(306\) 1.09283e10 0.0712536
\(307\) −8.10064e10 −0.520471 −0.260236 0.965545i \(-0.583800\pi\)
−0.260236 + 0.965545i \(0.583800\pi\)
\(308\) 7.22241e10 0.457303
\(309\) −2.48178e11 −1.54864
\(310\) 2.48470e11 1.52808
\(311\) −3.18435e11 −1.93018 −0.965091 0.261913i \(-0.915647\pi\)
−0.965091 + 0.261913i \(0.915647\pi\)
\(312\) 5.90696e9 0.0352914
\(313\) 1.28876e11 0.758965 0.379483 0.925199i \(-0.376102\pi\)
0.379483 + 0.925199i \(0.376102\pi\)
\(314\) −1.77757e10 −0.103191
\(315\) 3.24046e10 0.185443
\(316\) 1.63185e11 0.920635
\(317\) −7.44722e10 −0.414217 −0.207108 0.978318i \(-0.566405\pi\)
−0.207108 + 0.978318i \(0.566405\pi\)
\(318\) 1.54449e11 0.846961
\(319\) 1.28923e11 0.697065
\(320\) 1.35832e11 0.724148
\(321\) −3.29874e10 −0.173411
\(322\) 4.08659e10 0.211841
\(323\) −1.65945e10 −0.0848309
\(324\) 1.58849e11 0.800815
\(325\) −5.57319e9 −0.0277095
\(326\) −4.75768e10 −0.233301
\(327\) −1.42816e11 −0.690738
\(328\) −1.49726e11 −0.714276
\(329\) −2.59234e10 −0.121986
\(330\) −3.78550e11 −1.75715
\(331\) 2.83840e11 1.29971 0.649857 0.760057i \(-0.274829\pi\)
0.649857 + 0.760057i \(0.274829\pi\)
\(332\) 2.77328e10 0.125277
\(333\) −6.09271e10 −0.271526
\(334\) −1.39332e11 −0.612623
\(335\) −2.23505e11 −0.969583
\(336\) 7.77642e9 0.0332853
\(337\) −5.61414e9 −0.0237109 −0.0118555 0.999930i \(-0.503774\pi\)
−0.0118555 + 0.999930i \(0.503774\pi\)
\(338\) −1.41547e11 −0.589896
\(339\) 2.49950e11 1.02791
\(340\) −7.46766e10 −0.303061
\(341\) −8.72679e11 −3.49510
\(342\) −1.33632e10 −0.0528192
\(343\) 1.38413e10 0.0539949
\(344\) 3.36128e11 1.29417
\(345\) 4.00153e11 1.52069
\(346\) 2.73517e11 1.02599
\(347\) 3.39846e11 1.25834 0.629171 0.777267i \(-0.283394\pi\)
0.629171 + 0.777267i \(0.283394\pi\)
\(348\) 7.78933e10 0.284704
\(349\) 3.46718e10 0.125101 0.0625506 0.998042i \(-0.480077\pi\)
0.0625506 + 0.998042i \(0.480077\pi\)
\(350\) 5.58717e10 0.199015
\(351\) 6.62089e9 0.0232828
\(352\) −5.45578e11 −1.89415
\(353\) −3.46900e11 −1.18910 −0.594550 0.804059i \(-0.702670\pi\)
−0.594550 + 0.804059i \(0.702670\pi\)
\(354\) 1.39821e10 0.0473214
\(355\) 2.77748e11 0.928160
\(356\) −6.93939e8 −0.00228979
\(357\) 4.57075e10 0.148929
\(358\) 7.30438e10 0.235023
\(359\) −2.51011e11 −0.797569 −0.398785 0.917045i \(-0.630568\pi\)
−0.398785 + 0.917045i \(0.630568\pi\)
\(360\) −1.52459e11 −0.478401
\(361\) −3.02396e11 −0.937116
\(362\) −2.82750e10 −0.0865396
\(363\) 9.44221e11 2.85426
\(364\) 2.56219e9 0.00764988
\(365\) 3.07848e11 0.907859
\(366\) 3.69398e11 1.07604
\(367\) 4.79871e11 1.38079 0.690394 0.723433i \(-0.257437\pi\)
0.690394 + 0.723433i \(0.257437\pi\)
\(368\) 2.52485e10 0.0717663
\(369\) 9.30632e10 0.261312
\(370\) −2.22853e11 −0.618173
\(371\) 1.69847e11 0.465451
\(372\) −5.27258e11 −1.42751
\(373\) −1.84794e11 −0.494308 −0.247154 0.968976i \(-0.579495\pi\)
−0.247154 + 0.968976i \(0.579495\pi\)
\(374\) −1.40391e11 −0.371038
\(375\) −6.64164e10 −0.173434
\(376\) 1.21966e11 0.314698
\(377\) 4.57361e9 0.0116607
\(378\) −6.63750e10 −0.167221
\(379\) −7.08908e11 −1.76487 −0.882437 0.470431i \(-0.844098\pi\)
−0.882437 + 0.470431i \(0.844098\pi\)
\(380\) 9.13148e10 0.224654
\(381\) −1.42491e11 −0.346437
\(382\) 2.30367e11 0.553521
\(383\) 1.23789e11 0.293959 0.146980 0.989140i \(-0.453045\pi\)
0.146980 + 0.989140i \(0.453045\pi\)
\(384\) −3.51785e11 −0.825633
\(385\) −4.16288e11 −0.965653
\(386\) 2.69926e11 0.618874
\(387\) −2.08922e11 −0.473461
\(388\) 1.05345e11 0.235977
\(389\) −2.97971e11 −0.659782 −0.329891 0.944019i \(-0.607012\pi\)
−0.329891 + 0.944019i \(0.607012\pi\)
\(390\) −1.34292e10 −0.0293941
\(391\) 1.48403e11 0.321106
\(392\) −6.51213e10 −0.139295
\(393\) 3.66708e11 0.775451
\(394\) −2.97400e11 −0.621738
\(395\) −9.40570e11 −1.94404
\(396\) 2.11207e11 0.431599
\(397\) 5.33426e11 1.07775 0.538873 0.842387i \(-0.318850\pi\)
0.538873 + 0.842387i \(0.318850\pi\)
\(398\) 2.27918e11 0.455307
\(399\) −5.58912e10 −0.110399
\(400\) 3.45196e10 0.0674212
\(401\) 4.15640e11 0.802726 0.401363 0.915919i \(-0.368537\pi\)
0.401363 + 0.915919i \(0.368537\pi\)
\(402\) −2.53870e11 −0.484835
\(403\) −3.09587e10 −0.0584669
\(404\) 1.91704e11 0.358027
\(405\) −9.15581e11 −1.69102
\(406\) −4.58508e10 −0.0837491
\(407\) 7.82704e11 1.41391
\(408\) −2.15047e11 −0.384206
\(409\) 1.07978e12 1.90801 0.954006 0.299788i \(-0.0969159\pi\)
0.954006 + 0.299788i \(0.0969159\pi\)
\(410\) 3.40397e11 0.594919
\(411\) 6.80035e11 1.17556
\(412\) 5.06473e11 0.866002
\(413\) 1.53760e10 0.0260057
\(414\) 1.19505e11 0.199934
\(415\) −1.59847e11 −0.264539
\(416\) −1.93547e10 −0.0316859
\(417\) −9.86015e11 −1.59688
\(418\) 1.71671e11 0.275045
\(419\) −2.20998e11 −0.350289 −0.175144 0.984543i \(-0.556039\pi\)
−0.175144 + 0.984543i \(0.556039\pi\)
\(420\) −2.51515e11 −0.394404
\(421\) 3.47478e11 0.539086 0.269543 0.962988i \(-0.413127\pi\)
0.269543 + 0.962988i \(0.413127\pi\)
\(422\) −4.27373e11 −0.655996
\(423\) −7.58087e10 −0.115130
\(424\) −7.99105e11 −1.20076
\(425\) 2.02896e11 0.301664
\(426\) 3.15483e11 0.464122
\(427\) 4.06224e11 0.591344
\(428\) 6.73196e10 0.0969716
\(429\) 4.71662e10 0.0672316
\(430\) −7.64172e11 −1.07791
\(431\) 1.23574e11 0.172496 0.0862479 0.996274i \(-0.472512\pi\)
0.0862479 + 0.996274i \(0.472512\pi\)
\(432\) −4.10090e10 −0.0566503
\(433\) −7.27679e11 −0.994820 −0.497410 0.867516i \(-0.665716\pi\)
−0.497410 + 0.867516i \(0.665716\pi\)
\(434\) 3.10363e11 0.419920
\(435\) −4.48964e11 −0.601188
\(436\) 2.91455e11 0.386262
\(437\) −1.81468e11 −0.238031
\(438\) 3.49672e11 0.453970
\(439\) −5.85966e11 −0.752977 −0.376489 0.926421i \(-0.622869\pi\)
−0.376489 + 0.926421i \(0.622869\pi\)
\(440\) 1.95858e12 2.49117
\(441\) 4.04765e10 0.0509600
\(442\) −4.98045e9 −0.00620681
\(443\) −2.11546e11 −0.260969 −0.130484 0.991450i \(-0.541653\pi\)
−0.130484 + 0.991450i \(0.541653\pi\)
\(444\) 4.72897e11 0.577488
\(445\) 3.99975e9 0.00483519
\(446\) −3.08588e11 −0.369294
\(447\) −7.15480e11 −0.847645
\(448\) 1.69667e11 0.198997
\(449\) −9.21048e11 −1.06948 −0.534741 0.845016i \(-0.679591\pi\)
−0.534741 + 0.845016i \(0.679591\pi\)
\(450\) 1.63387e11 0.187829
\(451\) −1.19554e12 −1.36073
\(452\) −5.10091e11 −0.574810
\(453\) −4.40181e11 −0.491122
\(454\) −3.08491e11 −0.340794
\(455\) −1.47680e10 −0.0161537
\(456\) 2.62961e11 0.284806
\(457\) 8.11185e11 0.869955 0.434977 0.900441i \(-0.356756\pi\)
0.434977 + 0.900441i \(0.356756\pi\)
\(458\) 5.68493e11 0.603713
\(459\) −2.41039e11 −0.253472
\(460\) −8.16618e11 −0.850372
\(461\) −1.90069e11 −0.196001 −0.0980004 0.995186i \(-0.531245\pi\)
−0.0980004 + 0.995186i \(0.531245\pi\)
\(462\) −4.72845e11 −0.482870
\(463\) 4.76945e11 0.482341 0.241170 0.970483i \(-0.422469\pi\)
0.241170 + 0.970483i \(0.422469\pi\)
\(464\) −2.83284e10 −0.0283721
\(465\) 3.03903e12 3.01437
\(466\) −1.69253e11 −0.166264
\(467\) 1.06392e12 1.03510 0.517549 0.855653i \(-0.326844\pi\)
0.517549 + 0.855653i \(0.326844\pi\)
\(468\) 7.49268e9 0.00721990
\(469\) −2.79179e11 −0.266443
\(470\) −2.77285e11 −0.262111
\(471\) −2.17413e11 −0.203560
\(472\) −7.23420e10 −0.0670890
\(473\) 2.68393e12 2.46545
\(474\) −1.06836e12 −0.972105
\(475\) −2.48102e11 −0.223619
\(476\) −9.32784e10 −0.0832817
\(477\) 4.96687e11 0.439289
\(478\) 8.52248e11 0.746690
\(479\) −8.43415e11 −0.732034 −0.366017 0.930608i \(-0.619279\pi\)
−0.366017 + 0.930608i \(0.619279\pi\)
\(480\) 1.89993e12 1.63362
\(481\) 2.77668e10 0.0236523
\(482\) −3.89605e11 −0.328785
\(483\) 4.99829e11 0.417888
\(484\) −1.92694e12 −1.59611
\(485\) −6.07191e11 −0.498296
\(486\) −4.95841e11 −0.403162
\(487\) 1.15202e12 0.928065 0.464032 0.885818i \(-0.346402\pi\)
0.464032 + 0.885818i \(0.346402\pi\)
\(488\) −1.91123e12 −1.52554
\(489\) −5.81910e11 −0.460220
\(490\) 1.48051e11 0.116019
\(491\) −9.68703e11 −0.752184 −0.376092 0.926582i \(-0.622732\pi\)
−0.376092 + 0.926582i \(0.622732\pi\)
\(492\) −7.22328e11 −0.555765
\(493\) −1.66506e11 −0.126946
\(494\) 6.09011e9 0.00460102
\(495\) −1.21736e12 −0.911375
\(496\) 1.91754e11 0.142258
\(497\) 3.46934e11 0.255060
\(498\) −1.81564e11 −0.132281
\(499\) 2.62821e12 1.89761 0.948805 0.315863i \(-0.102294\pi\)
0.948805 + 0.315863i \(0.102294\pi\)
\(500\) 1.35540e11 0.0969848
\(501\) −1.70417e12 −1.20849
\(502\) 8.40308e11 0.590570
\(503\) 3.95070e11 0.275181 0.137590 0.990489i \(-0.456064\pi\)
0.137590 + 0.990489i \(0.456064\pi\)
\(504\) −1.90436e11 −0.131466
\(505\) −1.10495e12 −0.756019
\(506\) −1.53524e12 −1.04111
\(507\) −1.73126e12 −1.16366
\(508\) 2.90790e11 0.193728
\(509\) 6.64157e11 0.438572 0.219286 0.975661i \(-0.429627\pi\)
0.219286 + 0.975661i \(0.429627\pi\)
\(510\) 4.88901e11 0.320004
\(511\) 3.84532e11 0.249482
\(512\) 2.34512e11 0.150817
\(513\) 2.94743e11 0.187895
\(514\) 1.52954e12 0.966556
\(515\) −2.91923e12 −1.82867
\(516\) 1.62159e12 1.00697
\(517\) 9.73882e11 0.599513
\(518\) −2.78364e11 −0.169875
\(519\) 3.34537e12 2.02391
\(520\) 6.94815e10 0.0416730
\(521\) 5.22766e11 0.310841 0.155420 0.987848i \(-0.450327\pi\)
0.155420 + 0.987848i \(0.450327\pi\)
\(522\) −1.34083e11 −0.0790417
\(523\) −3.09135e12 −1.80672 −0.903360 0.428882i \(-0.858907\pi\)
−0.903360 + 0.428882i \(0.858907\pi\)
\(524\) −7.48366e11 −0.433634
\(525\) 6.83364e11 0.392587
\(526\) 1.87991e11 0.107078
\(527\) 1.12708e12 0.636510
\(528\) −2.92142e11 −0.163584
\(529\) −1.78305e11 −0.0989947
\(530\) 1.81673e12 1.00011
\(531\) 4.49645e10 0.0245440
\(532\) 1.14061e11 0.0617355
\(533\) −4.24125e10 −0.0227626
\(534\) 4.54316e9 0.00241781
\(535\) −3.88019e11 −0.204768
\(536\) 1.31350e12 0.687366
\(537\) 8.93396e11 0.463617
\(538\) 1.12116e12 0.576960
\(539\) −5.19984e11 −0.265363
\(540\) 1.32636e12 0.671259
\(541\) −1.47490e12 −0.740243 −0.370121 0.928983i \(-0.620684\pi\)
−0.370121 + 0.928983i \(0.620684\pi\)
\(542\) 2.65079e11 0.131940
\(543\) −3.45831e11 −0.170712
\(544\) 7.04621e11 0.344954
\(545\) −1.67990e12 −0.815642
\(546\) −1.67744e10 −0.00807756
\(547\) 2.12294e12 1.01390 0.506949 0.861976i \(-0.330773\pi\)
0.506949 + 0.861976i \(0.330773\pi\)
\(548\) −1.38779e12 −0.657374
\(549\) 1.18793e12 0.558106
\(550\) −2.09897e12 −0.978078
\(551\) 2.03604e11 0.0941031
\(552\) −2.35163e12 −1.07806
\(553\) −1.17486e12 −0.534225
\(554\) −9.59181e11 −0.432620
\(555\) −2.72570e12 −1.21944
\(556\) 2.01223e12 0.892978
\(557\) −3.52857e12 −1.55328 −0.776641 0.629943i \(-0.783078\pi\)
−0.776641 + 0.629943i \(0.783078\pi\)
\(558\) 9.07605e11 0.396317
\(559\) 9.52137e10 0.0412426
\(560\) 9.14713e10 0.0393042
\(561\) −1.71712e12 −0.731928
\(562\) 1.37419e12 0.581078
\(563\) −3.35280e12 −1.40644 −0.703218 0.710974i \(-0.748254\pi\)
−0.703218 + 0.710974i \(0.748254\pi\)
\(564\) 5.88403e11 0.244861
\(565\) 2.94008e12 1.21378
\(566\) −7.38691e11 −0.302544
\(567\) −1.14365e12 −0.464696
\(568\) −1.63228e12 −0.658000
\(569\) 2.99364e12 1.19727 0.598637 0.801020i \(-0.295709\pi\)
0.598637 + 0.801020i \(0.295709\pi\)
\(570\) −5.97830e11 −0.237214
\(571\) 4.67267e12 1.83951 0.919756 0.392490i \(-0.128386\pi\)
0.919756 + 0.392490i \(0.128386\pi\)
\(572\) −9.62553e10 −0.0375961
\(573\) 2.81761e12 1.09190
\(574\) 4.25189e11 0.163485
\(575\) 2.21875e12 0.846453
\(576\) 4.96164e11 0.187812
\(577\) −3.62799e12 −1.36262 −0.681310 0.731995i \(-0.738589\pi\)
−0.681310 + 0.731995i \(0.738589\pi\)
\(578\) −1.40310e12 −0.522895
\(579\) 3.30146e12 1.22082
\(580\) 9.16232e11 0.336186
\(581\) −1.99665e11 −0.0726957
\(582\) −6.89683e11 −0.249170
\(583\) −6.38073e12 −2.28751
\(584\) −1.80917e12 −0.643608
\(585\) −4.31866e10 −0.0152457
\(586\) 1.41252e12 0.494827
\(587\) 3.97200e12 1.38082 0.690411 0.723417i \(-0.257430\pi\)
0.690411 + 0.723417i \(0.257430\pi\)
\(588\) −3.14166e11 −0.108383
\(589\) −1.37819e12 −0.471835
\(590\) 1.64466e11 0.0558783
\(591\) −3.63748e12 −1.22647
\(592\) −1.71984e11 −0.0575494
\(593\) 2.67436e12 0.888123 0.444061 0.895996i \(-0.353537\pi\)
0.444061 + 0.895996i \(0.353537\pi\)
\(594\) 2.49355e12 0.821825
\(595\) 5.37641e11 0.175860
\(596\) 1.46013e12 0.474005
\(597\) 2.78765e12 0.898162
\(598\) −5.44632e10 −0.0174160
\(599\) 4.84522e12 1.53777 0.768887 0.639384i \(-0.220811\pi\)
0.768887 + 0.639384i \(0.220811\pi\)
\(600\) −3.21513e12 −1.01279
\(601\) −4.64764e12 −1.45311 −0.726553 0.687110i \(-0.758879\pi\)
−0.726553 + 0.687110i \(0.758879\pi\)
\(602\) −9.54525e11 −0.296212
\(603\) −8.16411e11 −0.251467
\(604\) 8.98307e11 0.274637
\(605\) 1.11065e13 3.37039
\(606\) −1.25507e12 −0.378043
\(607\) −6.52447e12 −1.95073 −0.975363 0.220604i \(-0.929197\pi\)
−0.975363 + 0.220604i \(0.929197\pi\)
\(608\) −8.61613e11 −0.255709
\(609\) −5.60800e11 −0.165208
\(610\) 4.34510e12 1.27062
\(611\) 3.45489e10 0.0100288
\(612\) −2.72777e11 −0.0786006
\(613\) −9.54536e11 −0.273036 −0.136518 0.990638i \(-0.543591\pi\)
−0.136518 + 0.990638i \(0.543591\pi\)
\(614\) −1.08230e12 −0.307321
\(615\) 4.16338e12 1.17357
\(616\) 2.44645e12 0.684580
\(617\) −4.50764e12 −1.25218 −0.626088 0.779752i \(-0.715345\pi\)
−0.626088 + 0.779752i \(0.715345\pi\)
\(618\) −3.31583e12 −0.914418
\(619\) 3.64346e12 0.997484 0.498742 0.866750i \(-0.333796\pi\)
0.498742 + 0.866750i \(0.333796\pi\)
\(620\) −6.20195e12 −1.68564
\(621\) −2.63585e12 −0.711228
\(622\) −4.25452e12 −1.13971
\(623\) 4.99608e9 0.00132872
\(624\) −1.03639e10 −0.00273647
\(625\) −4.18296e12 −1.09654
\(626\) 1.72187e12 0.448143
\(627\) 2.09970e12 0.542567
\(628\) 4.43690e11 0.113831
\(629\) −1.01087e12 −0.257495
\(630\) 4.32949e11 0.109498
\(631\) 3.61498e12 0.907766 0.453883 0.891061i \(-0.350038\pi\)
0.453883 + 0.891061i \(0.350038\pi\)
\(632\) 5.52757e12 1.37818
\(633\) −5.22718e12 −1.29405
\(634\) −9.95003e11 −0.244581
\(635\) −1.67607e12 −0.409081
\(636\) −3.85513e12 −0.934292
\(637\) −1.84467e10 −0.00443906
\(638\) 1.72251e12 0.411593
\(639\) 1.01455e12 0.240724
\(640\) −4.13793e12 −0.974929
\(641\) −2.66304e12 −0.623041 −0.311521 0.950239i \(-0.600838\pi\)
−0.311521 + 0.950239i \(0.600838\pi\)
\(642\) −4.40736e11 −0.102393
\(643\) 4.09899e12 0.945644 0.472822 0.881158i \(-0.343235\pi\)
0.472822 + 0.881158i \(0.343235\pi\)
\(644\) −1.02004e12 −0.233684
\(645\) −9.34656e12 −2.12634
\(646\) −2.21715e11 −0.0500898
\(647\) 6.11325e12 1.37152 0.685761 0.727827i \(-0.259469\pi\)
0.685761 + 0.727827i \(0.259469\pi\)
\(648\) 5.38071e12 1.19882
\(649\) −5.77640e11 −0.127807
\(650\) −7.44619e10 −0.0163615
\(651\) 3.79604e12 0.828356
\(652\) 1.18754e12 0.257356
\(653\) 7.66270e12 1.64920 0.824598 0.565719i \(-0.191401\pi\)
0.824598 + 0.565719i \(0.191401\pi\)
\(654\) −1.90813e12 −0.407858
\(655\) 4.31346e12 0.915673
\(656\) 2.62698e11 0.0553846
\(657\) 1.12450e12 0.235459
\(658\) −3.46356e11 −0.0720287
\(659\) −8.20110e9 −0.00169390 −0.000846950 1.00000i \(-0.500270\pi\)
−0.000846950 1.00000i \(0.500270\pi\)
\(660\) 9.44881e12 1.93834
\(661\) 3.20922e12 0.653872 0.326936 0.945046i \(-0.393984\pi\)
0.326936 + 0.945046i \(0.393984\pi\)
\(662\) 3.79231e12 0.767437
\(663\) −6.09158e10 −0.0122439
\(664\) 9.39395e11 0.187539
\(665\) −6.57429e11 −0.130362
\(666\) −8.14030e11 −0.160327
\(667\) −1.82081e12 −0.356203
\(668\) 3.47781e12 0.675791
\(669\) −3.77433e12 −0.728488
\(670\) −2.98618e12 −0.572506
\(671\) −1.52609e13 −2.90622
\(672\) 2.37320e12 0.448923
\(673\) −4.91229e12 −0.923031 −0.461515 0.887132i \(-0.652694\pi\)
−0.461515 + 0.887132i \(0.652694\pi\)
\(674\) −7.50089e10 −0.0140005
\(675\) −3.60372e12 −0.668166
\(676\) 3.53309e12 0.650721
\(677\) −3.11910e12 −0.570664 −0.285332 0.958429i \(-0.592104\pi\)
−0.285332 + 0.958429i \(0.592104\pi\)
\(678\) 3.33952e12 0.606946
\(679\) −7.58440e11 −0.136933
\(680\) −2.52953e12 −0.453680
\(681\) −3.77315e12 −0.672267
\(682\) −1.16596e13 −2.06374
\(683\) 2.91806e12 0.513099 0.256550 0.966531i \(-0.417414\pi\)
0.256550 + 0.966531i \(0.417414\pi\)
\(684\) 3.33552e11 0.0582655
\(685\) 7.99902e12 1.38813
\(686\) 1.84930e11 0.0318822
\(687\) 6.95322e12 1.19092
\(688\) −5.89742e11 −0.100349
\(689\) −2.26360e11 −0.0382660
\(690\) 5.34633e12 0.897914
\(691\) 4.74697e12 0.792073 0.396037 0.918235i \(-0.370385\pi\)
0.396037 + 0.918235i \(0.370385\pi\)
\(692\) −6.82712e12 −1.13178
\(693\) −1.52061e12 −0.250448
\(694\) 4.54058e12 0.743009
\(695\) −1.15982e13 −1.88563
\(696\) 2.63849e12 0.426200
\(697\) 1.54406e12 0.247809
\(698\) 4.63240e11 0.0738680
\(699\) −2.07013e12 −0.327981
\(700\) −1.39459e12 −0.219535
\(701\) −2.24423e11 −0.0351023 −0.0175512 0.999846i \(-0.505587\pi\)
−0.0175512 + 0.999846i \(0.505587\pi\)
\(702\) 8.84599e10 0.0137477
\(703\) 1.23610e12 0.190877
\(704\) −6.37400e12 −0.977992
\(705\) −3.39146e12 −0.517054
\(706\) −4.63484e12 −0.702123
\(707\) −1.38019e12 −0.207755
\(708\) −3.49001e11 −0.0522007
\(709\) 4.25463e12 0.632344 0.316172 0.948702i \(-0.397602\pi\)
0.316172 + 0.948702i \(0.397602\pi\)
\(710\) 3.71091e12 0.548047
\(711\) −3.43569e12 −0.504197
\(712\) −2.35059e10 −0.00342781
\(713\) 1.23250e13 1.78601
\(714\) 6.10685e11 0.0879378
\(715\) 5.54800e11 0.0793888
\(716\) −1.82321e12 −0.259256
\(717\) 1.04238e13 1.47296
\(718\) −3.35369e12 −0.470938
\(719\) −4.28931e12 −0.598559 −0.299280 0.954165i \(-0.596746\pi\)
−0.299280 + 0.954165i \(0.596746\pi\)
\(720\) 2.67492e11 0.0370950
\(721\) −3.64640e12 −0.502523
\(722\) −4.04023e12 −0.553335
\(723\) −4.76524e12 −0.648578
\(724\) 7.05761e11 0.0954627
\(725\) −2.48940e12 −0.334637
\(726\) 1.26155e13 1.68535
\(727\) 1.28935e13 1.71185 0.855926 0.517098i \(-0.172988\pi\)
0.855926 + 0.517098i \(0.172988\pi\)
\(728\) 8.67892e10 0.0114518
\(729\) 3.31084e12 0.434174
\(730\) 4.11307e12 0.536060
\(731\) −3.46633e12 −0.448995
\(732\) −9.22038e12 −1.18699
\(733\) 2.71447e12 0.347310 0.173655 0.984807i \(-0.444442\pi\)
0.173655 + 0.984807i \(0.444442\pi\)
\(734\) 6.41143e12 0.815309
\(735\) 1.81080e12 0.228864
\(736\) 7.70531e12 0.967921
\(737\) 1.04881e13 1.30946
\(738\) 1.24339e12 0.154296
\(739\) −9.62579e12 −1.18723 −0.593617 0.804747i \(-0.702301\pi\)
−0.593617 + 0.804747i \(0.702301\pi\)
\(740\) 5.56252e12 0.681913
\(741\) 7.44880e10 0.00907620
\(742\) 2.26927e12 0.274833
\(743\) −1.24362e13 −1.49706 −0.748529 0.663103i \(-0.769239\pi\)
−0.748529 + 0.663103i \(0.769239\pi\)
\(744\) −1.78599e13 −2.13698
\(745\) −8.41595e12 −1.00092
\(746\) −2.46898e12 −0.291872
\(747\) −5.83886e11 −0.0686097
\(748\) 3.50425e12 0.409296
\(749\) −4.84674e11 −0.0562706
\(750\) −8.87371e11 −0.102407
\(751\) 4.26959e12 0.489786 0.244893 0.969550i \(-0.421247\pi\)
0.244893 + 0.969550i \(0.421247\pi\)
\(752\) −2.13992e11 −0.0244015
\(753\) 1.02778e13 1.16499
\(754\) 6.11068e10 0.00688523
\(755\) −5.17770e12 −0.579930
\(756\) 1.65676e12 0.184463
\(757\) 9.76840e12 1.08116 0.540582 0.841291i \(-0.318204\pi\)
0.540582 + 0.841291i \(0.318204\pi\)
\(758\) −9.47153e12 −1.04210
\(759\) −1.87774e13 −2.05375
\(760\) 3.09311e12 0.336306
\(761\) 1.23336e13 1.33309 0.666543 0.745466i \(-0.267773\pi\)
0.666543 + 0.745466i \(0.267773\pi\)
\(762\) −1.90378e12 −0.204559
\(763\) −2.09836e12 −0.224140
\(764\) −5.75008e12 −0.610595
\(765\) 1.57224e12 0.165975
\(766\) 1.65391e12 0.173573
\(767\) −2.04921e10 −0.00213800
\(768\) −1.06125e13 −1.10076
\(769\) −1.68919e13 −1.74185 −0.870926 0.491415i \(-0.836480\pi\)
−0.870926 + 0.491415i \(0.836480\pi\)
\(770\) −5.56191e12 −0.570185
\(771\) 1.87078e13 1.90668
\(772\) −6.73751e12 −0.682687
\(773\) 1.47186e13 1.48272 0.741359 0.671109i \(-0.234182\pi\)
0.741359 + 0.671109i \(0.234182\pi\)
\(774\) −2.79135e12 −0.279563
\(775\) 1.68507e13 1.67788
\(776\) 3.56835e12 0.353257
\(777\) −3.40467e12 −0.335104
\(778\) −3.98111e12 −0.389579
\(779\) −1.88808e12 −0.183697
\(780\) 3.35201e11 0.0324250
\(781\) −1.30335e13 −1.25352
\(782\) 1.98278e12 0.189602
\(783\) 2.95738e12 0.281177
\(784\) 1.14257e11 0.0108009
\(785\) −2.55736e12 −0.240369
\(786\) 4.89949e12 0.457878
\(787\) −1.82466e13 −1.69549 −0.847744 0.530406i \(-0.822040\pi\)
−0.847744 + 0.530406i \(0.822040\pi\)
\(788\) 7.42326e12 0.685846
\(789\) 2.29932e12 0.211228
\(790\) −1.25667e13 −1.14789
\(791\) 3.67245e12 0.333550
\(792\) 7.15424e12 0.646101
\(793\) −5.41388e11 −0.0486160
\(794\) 7.12695e12 0.636373
\(795\) 2.22204e13 1.97287
\(796\) −5.68895e12 −0.502254
\(797\) −1.21558e13 −1.06714 −0.533568 0.845757i \(-0.679149\pi\)
−0.533568 + 0.845757i \(0.679149\pi\)
\(798\) −7.46748e11 −0.0651870
\(799\) −1.25778e12 −0.109180
\(800\) 1.05347e13 0.909318
\(801\) 1.46102e10 0.00125403
\(802\) 5.55325e12 0.473982
\(803\) −1.44460e13 −1.22610
\(804\) 6.33673e12 0.534827
\(805\) 5.87932e12 0.493453
\(806\) −4.13631e11 −0.0345227
\(807\) 1.37128e13 1.13814
\(808\) 6.49362e12 0.535964
\(809\) −2.61893e12 −0.214959 −0.107479 0.994207i \(-0.534278\pi\)
−0.107479 + 0.994207i \(0.534278\pi\)
\(810\) −1.22328e13 −0.998491
\(811\) 1.16994e13 0.949662 0.474831 0.880077i \(-0.342509\pi\)
0.474831 + 0.880077i \(0.342509\pi\)
\(812\) 1.14446e12 0.0923845
\(813\) 3.24217e12 0.260272
\(814\) 1.04575e13 0.834868
\(815\) −6.84480e12 −0.543440
\(816\) 3.77305e11 0.0297911
\(817\) 4.23863e12 0.332833
\(818\) 1.44267e13 1.12662
\(819\) −5.39443e10 −0.00418955
\(820\) −8.49649e12 −0.656262
\(821\) 5.17673e12 0.397659 0.198830 0.980034i \(-0.436286\pi\)
0.198830 + 0.980034i \(0.436286\pi\)
\(822\) 9.08577e12 0.694126
\(823\) −7.84017e12 −0.595698 −0.297849 0.954613i \(-0.596269\pi\)
−0.297849 + 0.954613i \(0.596269\pi\)
\(824\) 1.71558e13 1.29640
\(825\) −2.56724e13 −1.92941
\(826\) 2.05435e11 0.0153555
\(827\) −1.43263e13 −1.06502 −0.532512 0.846422i \(-0.678752\pi\)
−0.532512 + 0.846422i \(0.678752\pi\)
\(828\) −2.98292e12 −0.220549
\(829\) 4.95546e12 0.364408 0.182204 0.983261i \(-0.441677\pi\)
0.182204 + 0.983261i \(0.441677\pi\)
\(830\) −2.13568e12 −0.156201
\(831\) −1.17317e13 −0.853408
\(832\) −2.26121e11 −0.0163601
\(833\) 6.71566e11 0.0483266
\(834\) −1.31739e13 −0.942902
\(835\) −2.00456e13 −1.42702
\(836\) −4.28500e12 −0.303405
\(837\) −2.00185e13 −1.40983
\(838\) −2.95270e12 −0.206834
\(839\) 7.38235e12 0.514358 0.257179 0.966364i \(-0.417207\pi\)
0.257179 + 0.966364i \(0.417207\pi\)
\(840\) −8.51958e12 −0.590420
\(841\) −1.24642e13 −0.859179
\(842\) 4.64256e12 0.318312
\(843\) 1.68077e13 1.14626
\(844\) 1.06675e13 0.723636
\(845\) −2.03642e13 −1.37408
\(846\) −1.01286e12 −0.0679802
\(847\) 1.38732e13 0.926189
\(848\) 1.40204e12 0.0931065
\(849\) −9.03491e12 −0.596814
\(850\) 2.71084e12 0.178123
\(851\) −1.10543e13 −0.722516
\(852\) −7.87462e12 −0.511978
\(853\) 2.13356e13 1.37985 0.689927 0.723879i \(-0.257643\pi\)
0.689927 + 0.723879i \(0.257643\pi\)
\(854\) 5.42745e12 0.349169
\(855\) −1.92254e12 −0.123035
\(856\) 2.28032e12 0.145166
\(857\) 1.65008e13 1.04494 0.522468 0.852659i \(-0.325011\pi\)
0.522468 + 0.852659i \(0.325011\pi\)
\(858\) 6.30175e11 0.0396980
\(859\) −1.94817e13 −1.22083 −0.610417 0.792080i \(-0.708998\pi\)
−0.610417 + 0.792080i \(0.708998\pi\)
\(860\) 1.90742e13 1.18906
\(861\) 5.20047e12 0.322499
\(862\) 1.65103e12 0.101853
\(863\) 1.61059e13 0.988411 0.494205 0.869345i \(-0.335459\pi\)
0.494205 + 0.869345i \(0.335459\pi\)
\(864\) −1.25151e13 −0.764049
\(865\) 3.93504e13 2.38989
\(866\) −9.72232e12 −0.587408
\(867\) −1.71613e13 −1.03149
\(868\) −7.74684e12 −0.463219
\(869\) 4.41368e13 2.62550
\(870\) −5.99849e12 −0.354981
\(871\) 3.72070e11 0.0219050
\(872\) 9.87249e12 0.578232
\(873\) −2.21793e12 −0.129236
\(874\) −2.42454e12 −0.140549
\(875\) −9.75836e11 −0.0562782
\(876\) −8.72801e12 −0.500780
\(877\) −1.84919e13 −1.05556 −0.527780 0.849381i \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(878\) −7.82892e12 −0.444607
\(879\) 1.72764e13 0.976121
\(880\) −3.43636e12 −0.193164
\(881\) −2.83078e13 −1.58312 −0.791562 0.611089i \(-0.790732\pi\)
−0.791562 + 0.611089i \(0.790732\pi\)
\(882\) 5.40795e11 0.0300901
\(883\) −7.32328e12 −0.405399 −0.202700 0.979241i \(-0.564971\pi\)
−0.202700 + 0.979241i \(0.564971\pi\)
\(884\) 1.24315e11 0.00684681
\(885\) 2.01158e12 0.110228
\(886\) −2.82641e12 −0.154093
\(887\) 1.51372e13 0.821087 0.410544 0.911841i \(-0.365339\pi\)
0.410544 + 0.911841i \(0.365339\pi\)
\(888\) 1.60185e13 0.864496
\(889\) −2.09357e12 −0.112416
\(890\) 5.34396e10 0.00285501
\(891\) 4.29642e13 2.28380
\(892\) 7.70253e12 0.407372
\(893\) 1.53802e12 0.0809337
\(894\) −9.55934e12 −0.500506
\(895\) 1.05087e13 0.547451
\(896\) −5.16867e12 −0.267913
\(897\) −6.66138e11 −0.0343556
\(898\) −1.23059e13 −0.631493
\(899\) −1.38285e13 −0.706082
\(900\) −4.07823e12 −0.207196
\(901\) 8.24080e12 0.416589
\(902\) −1.59733e13 −0.803463
\(903\) −1.16748e13 −0.584323
\(904\) −1.72783e13 −0.860487
\(905\) −4.06789e12 −0.201582
\(906\) −5.88114e12 −0.289991
\(907\) −2.24337e13 −1.10070 −0.550349 0.834935i \(-0.685505\pi\)
−0.550349 + 0.834935i \(0.685505\pi\)
\(908\) 7.70011e12 0.375933
\(909\) −4.03614e12 −0.196078
\(910\) −1.97312e11 −0.00953820
\(911\) −6.34178e12 −0.305055 −0.152528 0.988299i \(-0.548741\pi\)
−0.152528 + 0.988299i \(0.548741\pi\)
\(912\) −4.61369e11 −0.0220837
\(913\) 7.50094e12 0.357270
\(914\) 1.08380e13 0.513679
\(915\) 5.31448e13 2.50649
\(916\) −1.41899e13 −0.665963
\(917\) 5.38793e12 0.251629
\(918\) −3.22045e12 −0.149667
\(919\) 9.04471e12 0.418288 0.209144 0.977885i \(-0.432932\pi\)
0.209144 + 0.977885i \(0.432932\pi\)
\(920\) −2.76614e13 −1.27300
\(921\) −1.32376e13 −0.606236
\(922\) −2.53946e12 −0.115732
\(923\) −4.62369e11 −0.0209692
\(924\) 1.18025e13 0.532659
\(925\) −1.51134e13 −0.678771
\(926\) 6.37233e12 0.284806
\(927\) −1.06633e13 −0.474277
\(928\) −8.64522e12 −0.382658
\(929\) 8.50641e12 0.374693 0.187346 0.982294i \(-0.440011\pi\)
0.187346 + 0.982294i \(0.440011\pi\)
\(930\) 4.06037e13 1.77988
\(931\) −8.21193e11 −0.0358238
\(932\) 4.22464e12 0.183408
\(933\) −5.20368e13 −2.24824
\(934\) 1.42147e13 0.611191
\(935\) −2.01979e13 −0.864280
\(936\) 2.53800e11 0.0108081
\(937\) −3.00276e13 −1.27260 −0.636300 0.771442i \(-0.719536\pi\)
−0.636300 + 0.771442i \(0.719536\pi\)
\(938\) −3.73003e12 −0.157326
\(939\) 2.10602e13 0.884030
\(940\) 6.92118e12 0.289138
\(941\) −3.15982e13 −1.31374 −0.656870 0.754004i \(-0.728120\pi\)
−0.656870 + 0.754004i \(0.728120\pi\)
\(942\) −2.90480e12 −0.120195
\(943\) 1.68849e13 0.695338
\(944\) 1.26925e11 0.00520205
\(945\) −9.54927e12 −0.389518
\(946\) 3.58592e13 1.45576
\(947\) −8.84885e12 −0.357529 −0.178765 0.983892i \(-0.557210\pi\)
−0.178765 + 0.983892i \(0.557210\pi\)
\(948\) 2.66667e13 1.07234
\(949\) −5.12477e11 −0.0205105
\(950\) −3.31482e12 −0.132040
\(951\) −1.21698e13 −0.482473
\(952\) −3.15963e12 −0.124672
\(953\) −4.90260e12 −0.192534 −0.0962672 0.995356i \(-0.530690\pi\)
−0.0962672 + 0.995356i \(0.530690\pi\)
\(954\) 6.63610e12 0.259385
\(955\) 3.31425e13 1.28935
\(956\) −2.12726e13 −0.823682
\(957\) 2.10679e13 0.811929
\(958\) −1.12686e13 −0.432241
\(959\) 9.99155e12 0.381460
\(960\) 2.21969e13 0.843476
\(961\) 6.71649e13 2.54031
\(962\) 3.70985e11 0.0139659
\(963\) −1.41735e12 −0.0531077
\(964\) 9.72475e12 0.362687
\(965\) 3.88339e13 1.44158
\(966\) 6.67808e12 0.246749
\(967\) 1.55633e13 0.572378 0.286189 0.958173i \(-0.407612\pi\)
0.286189 + 0.958173i \(0.407612\pi\)
\(968\) −6.52713e13 −2.38937
\(969\) −2.71179e12 −0.0988096
\(970\) −8.11251e12 −0.294227
\(971\) −2.49197e13 −0.899613 −0.449806 0.893126i \(-0.648507\pi\)
−0.449806 + 0.893126i \(0.648507\pi\)
\(972\) 1.23765e13 0.444732
\(973\) −1.44872e13 −0.518176
\(974\) 1.53918e13 0.547991
\(975\) −9.10740e11 −0.0322756
\(976\) 3.35329e12 0.118290
\(977\) 4.47898e12 0.157273 0.0786364 0.996903i \(-0.474943\pi\)
0.0786364 + 0.996903i \(0.474943\pi\)
\(978\) −7.77474e12 −0.271745
\(979\) −1.87691e11 −0.00653012
\(980\) −3.69543e12 −0.127981
\(981\) −6.13629e12 −0.211542
\(982\) −1.29426e13 −0.444139
\(983\) −1.43233e13 −0.489275 −0.244637 0.969615i \(-0.578669\pi\)
−0.244637 + 0.969615i \(0.578669\pi\)
\(984\) −2.44675e13 −0.831977
\(985\) −4.27865e13 −1.44825
\(986\) −2.22464e12 −0.0749572
\(987\) −4.23626e12 −0.142088
\(988\) −1.52013e11 −0.00507543
\(989\) −3.79057e13 −1.25986
\(990\) −1.62649e13 −0.538136
\(991\) −2.28575e13 −0.752829 −0.376415 0.926451i \(-0.622843\pi\)
−0.376415 + 0.926451i \(0.622843\pi\)
\(992\) 5.85194e13 1.91866
\(993\) 4.63836e13 1.51388
\(994\) 4.63529e12 0.150605
\(995\) 3.27902e13 1.06057
\(996\) 4.53194e12 0.145921
\(997\) −2.67132e13 −0.856243 −0.428121 0.903721i \(-0.640824\pi\)
−0.428121 + 0.903721i \(0.640824\pi\)
\(998\) 3.51147e13 1.12047
\(999\) 1.79545e13 0.570334
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 7.10.a.b.1.2 3
3.2 odd 2 63.10.a.e.1.2 3
4.3 odd 2 112.10.a.h.1.1 3
5.2 odd 4 175.10.b.d.99.4 6
5.3 odd 4 175.10.b.d.99.3 6
5.4 even 2 175.10.a.d.1.2 3
7.2 even 3 49.10.c.d.18.2 6
7.3 odd 6 49.10.c.e.30.2 6
7.4 even 3 49.10.c.d.30.2 6
7.5 odd 6 49.10.c.e.18.2 6
7.6 odd 2 49.10.a.c.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7.10.a.b.1.2 3 1.1 even 1 trivial
49.10.a.c.1.2 3 7.6 odd 2
49.10.c.d.18.2 6 7.2 even 3
49.10.c.d.30.2 6 7.4 even 3
49.10.c.e.18.2 6 7.5 odd 6
49.10.c.e.30.2 6 7.3 odd 6
63.10.a.e.1.2 3 3.2 odd 2
112.10.a.h.1.1 3 4.3 odd 2
175.10.a.d.1.2 3 5.4 even 2
175.10.b.d.99.3 6 5.3 odd 4
175.10.b.d.99.4 6 5.2 odd 4