Properties

Label 22.14.a.a.1.1
Level $22$
Weight $14$
Character 22.1
Self dual yes
Analytic conductor $23.591$
Analytic rank $1$
Dimension $2$
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] = [22,14,Mod(1,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 22.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: \(23.5908043694\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{100039}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 100039 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-316.289\) of defining polynomial
Character \(\chi\) \(=\) 22.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-64.0000 q^{2} -1596.16 q^{3} +4096.00 q^{4} -57177.1 q^{5} +102154. q^{6} +550172. q^{7} -262144. q^{8} +953396. q^{9} +O(q^{10})\) \(q-64.0000 q^{2} -1596.16 q^{3} +4096.00 q^{4} -57177.1 q^{5} +102154. q^{6} +550172. q^{7} -262144. q^{8} +953396. q^{9} +3.65933e6 q^{10} -1.77156e6 q^{11} -6.53786e6 q^{12} +2.35813e7 q^{13} -3.52110e7 q^{14} +9.12637e7 q^{15} +1.67772e7 q^{16} +1.01512e8 q^{17} -6.10174e7 q^{18} -1.12633e8 q^{19} -2.34197e8 q^{20} -8.78162e8 q^{21} +1.13380e8 q^{22} -6.98413e8 q^{23} +4.18423e8 q^{24} +2.04852e9 q^{25} -1.50921e9 q^{26} +1.02302e9 q^{27} +2.25351e9 q^{28} -5.69290e9 q^{29} -5.84087e9 q^{30} -2.48239e9 q^{31} -1.07374e9 q^{32} +2.82769e9 q^{33} -6.49679e9 q^{34} -3.14573e10 q^{35} +3.90511e9 q^{36} +1.34083e7 q^{37} +7.20848e9 q^{38} -3.76395e10 q^{39} +1.49886e10 q^{40} +3.85108e10 q^{41} +5.62024e10 q^{42} +9.49634e9 q^{43} -7.25631e9 q^{44} -5.45124e10 q^{45} +4.46984e10 q^{46} -1.90209e10 q^{47} -2.67791e10 q^{48} +2.05801e11 q^{49} -1.31105e11 q^{50} -1.62030e11 q^{51} +9.65892e10 q^{52} -2.12042e10 q^{53} -6.54733e10 q^{54} +1.01293e11 q^{55} -1.44224e11 q^{56} +1.79779e11 q^{57} +3.64346e11 q^{58} +1.43149e11 q^{59} +3.73816e11 q^{60} -4.46635e11 q^{61} +1.58873e11 q^{62} +5.24532e11 q^{63} +6.87195e10 q^{64} -1.34831e12 q^{65} -1.80972e11 q^{66} -2.32131e11 q^{67} +4.15794e11 q^{68} +1.11478e12 q^{69} +2.01326e12 q^{70} +1.59319e12 q^{71} -2.49927e11 q^{72} -1.31830e12 q^{73} -8.58129e8 q^{74} -3.26976e12 q^{75} -4.61343e11 q^{76} -9.74664e11 q^{77} +2.40893e12 q^{78} -6.52882e11 q^{79} -9.59273e11 q^{80} -3.15292e12 q^{81} -2.46469e12 q^{82} -4.15430e12 q^{83} -3.59695e12 q^{84} -5.80418e12 q^{85} -6.07766e11 q^{86} +9.08677e12 q^{87} +4.64404e11 q^{88} -3.61368e12 q^{89} +3.48880e12 q^{90} +1.29738e13 q^{91} -2.86070e12 q^{92} +3.96228e12 q^{93} +1.21734e12 q^{94} +6.44000e12 q^{95} +1.71386e12 q^{96} -1.33685e13 q^{97} -1.31712e13 q^{98} -1.68900e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 128 q^{2} - 662 q^{3} + 8192 q^{4} - 48566 q^{5} + 42368 q^{6} + 404508 q^{7} - 524288 q^{8} + 231724 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 128 q^{2} - 662 q^{3} + 8192 q^{4} - 48566 q^{5} + 42368 q^{6} + 404508 q^{7} - 524288 q^{8} + 231724 q^{9} + 3108224 q^{10} - 3543122 q^{11} - 2711552 q^{12} + 28445952 q^{13} - 25888512 q^{14} + 99307794 q^{15} + 33554432 q^{16} + 107032052 q^{17} - 14830336 q^{18} - 73524568 q^{19} - 198926336 q^{20} - 1014235348 q^{21} + 226759808 q^{22} - 987164862 q^{23} + 173539328 q^{24} + 901965576 q^{25} - 1820540928 q^{26} - 1140484994 q^{27} + 1656864768 q^{28} - 9516399376 q^{29} - 6355698816 q^{30} - 6865940430 q^{31} - 2147483648 q^{32} + 1172773382 q^{33} - 6850051328 q^{34} - 32711590964 q^{35} + 949141504 q^{36} - 4145233266 q^{37} + 4705572352 q^{38} - 33095241568 q^{39} + 12731285504 q^{40} + 39451523656 q^{41} + 64911062272 q^{42} + 5532549228 q^{43} - 14512627712 q^{44} - 60726834468 q^{45} + 63178551168 q^{46} - 28411609744 q^{47} - 11106516992 q^{48} + 130129720218 q^{49} - 57725796864 q^{50} - 156873354588 q^{51} + 116514619392 q^{52} - 49178542972 q^{53} + 72991039616 q^{54} + 86037631526 q^{55} - 106039345152 q^{56} + 216312273320 q^{57} + 609049560064 q^{58} + 110326136718 q^{59} + 406764724224 q^{60} - 161816895480 q^{61} + 439420187520 q^{62} + 629654304296 q^{63} + 137438953472 q^{64} - 1306423470272 q^{65} - 75057496448 q^{66} - 483661746106 q^{67} + 438403284992 q^{68} + 845036821770 q^{69} + 2093541821696 q^{70} + 318713704774 q^{71} - 60745056256 q^{72} - 1073843539168 q^{73} + 265294929024 q^{74} - 4340817675224 q^{75} - 301156630528 q^{76} - 716610596988 q^{77} + 2118095460352 q^{78} - 742108796220 q^{79} - 814802272256 q^{80} - 4023398824910 q^{81} - 2524897513984 q^{82} - 6905249437156 q^{83} - 4154307985408 q^{84} - 5756648698492 q^{85} - 354083150592 q^{86} + 5515016618352 q^{87} + 928808173568 q^{88} - 8233927751362 q^{89} + 3886517405952 q^{90} + 12265206226208 q^{91} - 4043427274752 q^{92} - 132647408710 q^{93} + 1818343023616 q^{94} + 6776763758856 q^{95} + 710817087488 q^{96} - 4680888780654 q^{97} - 8328302093952 q^{98} - 410513201164 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −64.0000 −0.707107
\(3\) −1596.16 −1.26412 −0.632059 0.774920i \(-0.717790\pi\)
−0.632059 + 0.774920i \(0.717790\pi\)
\(4\) 4096.00 0.500000
\(5\) −57177.1 −1.63650 −0.818252 0.574860i \(-0.805057\pi\)
−0.818252 + 0.574860i \(0.805057\pi\)
\(6\) 102154. 0.893866
\(7\) 550172. 1.76751 0.883754 0.467951i \(-0.155008\pi\)
0.883754 + 0.467951i \(0.155008\pi\)
\(8\) −262144. −0.353553
\(9\) 953396. 0.597995
\(10\) 3.65933e6 1.15718
\(11\) −1.77156e6 −0.301511
\(12\) −6.53786e6 −0.632059
\(13\) 2.35813e7 1.35499 0.677496 0.735526i \(-0.263065\pi\)
0.677496 + 0.735526i \(0.263065\pi\)
\(14\) −3.52110e7 −1.24982
\(15\) 9.12637e7 2.06873
\(16\) 1.67772e7 0.250000
\(17\) 1.01512e8 1.02000 0.510001 0.860174i \(-0.329645\pi\)
0.510001 + 0.860174i \(0.329645\pi\)
\(18\) −6.10174e7 −0.422846
\(19\) −1.12633e8 −0.549244 −0.274622 0.961552i \(-0.588553\pi\)
−0.274622 + 0.961552i \(0.588553\pi\)
\(20\) −2.34197e8 −0.818252
\(21\) −8.78162e8 −2.23434
\(22\) 1.13380e8 0.213201
\(23\) −6.98413e8 −0.983742 −0.491871 0.870668i \(-0.663687\pi\)
−0.491871 + 0.870668i \(0.663687\pi\)
\(24\) 4.18423e8 0.446933
\(25\) 2.04852e9 1.67815
\(26\) −1.50921e9 −0.958124
\(27\) 1.02302e9 0.508182
\(28\) 2.25351e9 0.883754
\(29\) −5.69290e9 −1.77724 −0.888621 0.458642i \(-0.848336\pi\)
−0.888621 + 0.458642i \(0.848336\pi\)
\(30\) −5.84087e9 −1.46282
\(31\) −2.48239e9 −0.502364 −0.251182 0.967940i \(-0.580819\pi\)
−0.251182 + 0.967940i \(0.580819\pi\)
\(32\) −1.07374e9 −0.176777
\(33\) 2.82769e9 0.381146
\(34\) −6.49679e9 −0.721250
\(35\) −3.14573e10 −2.89253
\(36\) 3.90511e9 0.298997
\(37\) 1.34083e7 0.000859135 0 0.000429568 1.00000i \(-0.499863\pi\)
0.000429568 1.00000i \(0.499863\pi\)
\(38\) 7.20848e9 0.388374
\(39\) −3.76395e10 −1.71287
\(40\) 1.49886e10 0.578592
\(41\) 3.85108e10 1.26616 0.633079 0.774087i \(-0.281791\pi\)
0.633079 + 0.774087i \(0.281791\pi\)
\(42\) 5.62024e10 1.57992
\(43\) 9.49634e9 0.229093 0.114546 0.993418i \(-0.463459\pi\)
0.114546 + 0.993418i \(0.463459\pi\)
\(44\) −7.25631e9 −0.150756
\(45\) −5.45124e10 −0.978620
\(46\) 4.46984e10 0.695611
\(47\) −1.90209e10 −0.257391 −0.128696 0.991684i \(-0.541079\pi\)
−0.128696 + 0.991684i \(0.541079\pi\)
\(48\) −2.67791e10 −0.316030
\(49\) 2.05801e11 2.12409
\(50\) −1.31105e11 −1.18663
\(51\) −1.62030e11 −1.28940
\(52\) 9.65892e10 0.677496
\(53\) −2.12042e10 −0.131410 −0.0657050 0.997839i \(-0.520930\pi\)
−0.0657050 + 0.997839i \(0.520930\pi\)
\(54\) −6.54733e10 −0.359339
\(55\) 1.01293e11 0.493425
\(56\) −1.44224e11 −0.624909
\(57\) 1.79779e11 0.694309
\(58\) 3.64346e11 1.25670
\(59\) 1.43149e11 0.441825 0.220913 0.975294i \(-0.429096\pi\)
0.220913 + 0.975294i \(0.429096\pi\)
\(60\) 3.73816e11 1.03437
\(61\) −4.46635e11 −1.10996 −0.554982 0.831863i \(-0.687275\pi\)
−0.554982 + 0.831863i \(0.687275\pi\)
\(62\) 1.58873e11 0.355225
\(63\) 5.24532e11 1.05696
\(64\) 6.87195e10 0.125000
\(65\) −1.34831e12 −2.21745
\(66\) −1.80972e11 −0.269511
\(67\) −2.32131e11 −0.313507 −0.156753 0.987638i \(-0.550103\pi\)
−0.156753 + 0.987638i \(0.550103\pi\)
\(68\) 4.15794e11 0.510001
\(69\) 1.11478e12 1.24357
\(70\) 2.01326e12 2.04533
\(71\) 1.59319e12 1.47601 0.738005 0.674795i \(-0.235768\pi\)
0.738005 + 0.674795i \(0.235768\pi\)
\(72\) −2.49927e11 −0.211423
\(73\) −1.31830e12 −1.01957 −0.509785 0.860302i \(-0.670275\pi\)
−0.509785 + 0.860302i \(0.670275\pi\)
\(74\) −8.58129e8 −0.000607501 0
\(75\) −3.26976e12 −2.12137
\(76\) −4.61343e11 −0.274622
\(77\) −9.74664e11 −0.532924
\(78\) 2.40893e12 1.21118
\(79\) −6.52882e11 −0.302175 −0.151088 0.988520i \(-0.548278\pi\)
−0.151088 + 0.988520i \(0.548278\pi\)
\(80\) −9.59273e11 −0.409126
\(81\) −3.15292e12 −1.24040
\(82\) −2.46469e12 −0.895308
\(83\) −4.15430e12 −1.39473 −0.697365 0.716716i \(-0.745644\pi\)
−0.697365 + 0.716716i \(0.745644\pi\)
\(84\) −3.59695e12 −1.11717
\(85\) −5.80418e12 −1.66924
\(86\) −6.07766e11 −0.161993
\(87\) 9.08677e12 2.24664
\(88\) 4.64404e11 0.106600
\(89\) −3.61368e12 −0.770752 −0.385376 0.922760i \(-0.625928\pi\)
−0.385376 + 0.922760i \(0.625928\pi\)
\(90\) 3.48880e12 0.691989
\(91\) 1.29738e13 2.39496
\(92\) −2.86070e12 −0.491871
\(93\) 3.96228e12 0.635048
\(94\) 1.21734e12 0.182003
\(95\) 6.44000e12 0.898840
\(96\) 1.71386e12 0.223467
\(97\) −1.33685e13 −1.62955 −0.814776 0.579776i \(-0.803140\pi\)
−0.814776 + 0.579776i \(0.803140\pi\)
\(98\) −1.31712e13 −1.50196
\(99\) −1.68900e12 −0.180302
\(100\) 8.39073e12 0.839073
\(101\) 1.23469e13 1.15736 0.578679 0.815555i \(-0.303568\pi\)
0.578679 + 0.815555i \(0.303568\pi\)
\(102\) 1.03699e13 0.911745
\(103\) −1.94307e13 −1.60342 −0.801708 0.597716i \(-0.796075\pi\)
−0.801708 + 0.597716i \(0.796075\pi\)
\(104\) −6.18171e12 −0.479062
\(105\) 5.02107e13 3.65651
\(106\) 1.35707e12 0.0929209
\(107\) 8.96933e12 0.577784 0.288892 0.957362i \(-0.406713\pi\)
0.288892 + 0.957362i \(0.406713\pi\)
\(108\) 4.19029e12 0.254091
\(109\) −3.01725e13 −1.72322 −0.861608 0.507575i \(-0.830542\pi\)
−0.861608 + 0.507575i \(0.830542\pi\)
\(110\) −6.48273e12 −0.348904
\(111\) −2.14017e10 −0.00108605
\(112\) 9.23036e12 0.441877
\(113\) −1.82775e13 −0.825860 −0.412930 0.910763i \(-0.635495\pi\)
−0.412930 + 0.910763i \(0.635495\pi\)
\(114\) −1.15059e13 −0.490951
\(115\) 3.99332e13 1.60990
\(116\) −2.33181e13 −0.888621
\(117\) 2.24824e13 0.810278
\(118\) −9.16155e12 −0.312418
\(119\) 5.58493e13 1.80286
\(120\) −2.39242e13 −0.731408
\(121\) 3.13843e12 0.0909091
\(122\) 2.85846e13 0.784862
\(123\) −6.14693e13 −1.60057
\(124\) −1.01679e13 −0.251182
\(125\) −4.73320e13 −1.10979
\(126\) −3.35701e13 −0.747384
\(127\) 6.08576e13 1.28704 0.643518 0.765431i \(-0.277474\pi\)
0.643518 + 0.765431i \(0.277474\pi\)
\(128\) −4.39805e12 −0.0883883
\(129\) −1.51577e13 −0.289600
\(130\) 8.62920e13 1.56797
\(131\) −4.11962e13 −0.712187 −0.356093 0.934450i \(-0.615891\pi\)
−0.356093 + 0.934450i \(0.615891\pi\)
\(132\) 1.15822e13 0.190573
\(133\) −6.19673e13 −0.970794
\(134\) 1.48564e13 0.221683
\(135\) −5.84933e13 −0.831643
\(136\) −2.66108e13 −0.360625
\(137\) 8.81865e13 1.13951 0.569755 0.821814i \(-0.307038\pi\)
0.569755 + 0.821814i \(0.307038\pi\)
\(138\) −7.13457e13 −0.879334
\(139\) −4.18391e13 −0.492023 −0.246012 0.969267i \(-0.579120\pi\)
−0.246012 + 0.969267i \(0.579120\pi\)
\(140\) −1.28849e14 −1.44627
\(141\) 3.03603e13 0.325373
\(142\) −1.01964e14 −1.04370
\(143\) −4.17758e13 −0.408546
\(144\) 1.59953e13 0.149499
\(145\) 3.25504e14 2.90846
\(146\) 8.43714e13 0.720944
\(147\) −3.28490e14 −2.68510
\(148\) 5.49203e10 0.000429568 0
\(149\) −1.09308e14 −0.818356 −0.409178 0.912455i \(-0.634185\pi\)
−0.409178 + 0.912455i \(0.634185\pi\)
\(150\) 2.09264e14 1.50004
\(151\) −6.17494e12 −0.0423919 −0.0211959 0.999775i \(-0.506747\pi\)
−0.0211959 + 0.999775i \(0.506747\pi\)
\(152\) 2.95259e13 0.194187
\(153\) 9.67815e13 0.609955
\(154\) 6.23785e13 0.376834
\(155\) 1.41936e14 0.822121
\(156\) −1.54172e14 −0.856435
\(157\) 2.50232e13 0.133351 0.0666753 0.997775i \(-0.478761\pi\)
0.0666753 + 0.997775i \(0.478761\pi\)
\(158\) 4.17845e13 0.213670
\(159\) 3.38452e13 0.166118
\(160\) 6.13934e13 0.289296
\(161\) −3.84247e14 −1.73877
\(162\) 2.01787e14 0.877093
\(163\) −1.60361e14 −0.669697 −0.334849 0.942272i \(-0.608685\pi\)
−0.334849 + 0.942272i \(0.608685\pi\)
\(164\) 1.57740e14 0.633079
\(165\) −1.61679e14 −0.623747
\(166\) 2.65875e14 0.986223
\(167\) −7.33398e13 −0.261627 −0.130814 0.991407i \(-0.541759\pi\)
−0.130814 + 0.991407i \(0.541759\pi\)
\(168\) 2.30205e14 0.789958
\(169\) 2.53205e14 0.836004
\(170\) 3.71468e14 1.18033
\(171\) −1.07383e14 −0.328445
\(172\) 3.88970e13 0.114546
\(173\) −4.42176e14 −1.25399 −0.626997 0.779022i \(-0.715716\pi\)
−0.626997 + 0.779022i \(0.715716\pi\)
\(174\) −5.81553e14 −1.58862
\(175\) 1.12704e15 2.96614
\(176\) −2.97219e13 −0.0753778
\(177\) −2.28489e14 −0.558520
\(178\) 2.31275e14 0.545004
\(179\) −2.35232e14 −0.534504 −0.267252 0.963627i \(-0.586116\pi\)
−0.267252 + 0.963627i \(0.586116\pi\)
\(180\) −2.23283e14 −0.489310
\(181\) −1.49801e14 −0.316667 −0.158334 0.987386i \(-0.550612\pi\)
−0.158334 + 0.987386i \(0.550612\pi\)
\(182\) −8.30324e14 −1.69349
\(183\) 7.12899e14 1.40312
\(184\) 1.83085e14 0.347805
\(185\) −7.66646e11 −0.00140598
\(186\) −2.53586e14 −0.449046
\(187\) −1.79835e14 −0.307542
\(188\) −7.79094e13 −0.128696
\(189\) 5.62837e14 0.898217
\(190\) −4.12160e14 −0.635576
\(191\) 8.53215e14 1.27157 0.635787 0.771865i \(-0.280676\pi\)
0.635787 + 0.771865i \(0.280676\pi\)
\(192\) −1.09687e14 −0.158015
\(193\) −7.34539e14 −1.02304 −0.511520 0.859271i \(-0.670917\pi\)
−0.511520 + 0.859271i \(0.670917\pi\)
\(194\) 8.55587e14 1.15227
\(195\) 2.15212e15 2.80312
\(196\) 8.42959e14 1.06204
\(197\) −2.60261e14 −0.317233 −0.158617 0.987340i \(-0.550703\pi\)
−0.158617 + 0.987340i \(0.550703\pi\)
\(198\) 1.08096e14 0.127493
\(199\) −7.73756e14 −0.883200 −0.441600 0.897212i \(-0.645589\pi\)
−0.441600 + 0.897212i \(0.645589\pi\)
\(200\) −5.37007e14 −0.593314
\(201\) 3.70518e14 0.396309
\(202\) −7.90200e14 −0.818376
\(203\) −3.13208e15 −3.14129
\(204\) −6.63673e14 −0.644701
\(205\) −2.20194e15 −2.07207
\(206\) 1.24356e15 1.13379
\(207\) −6.65864e14 −0.588272
\(208\) 3.95629e14 0.338748
\(209\) 1.99535e14 0.165603
\(210\) −3.21349e15 −2.58554
\(211\) 1.07625e15 0.839608 0.419804 0.907615i \(-0.362099\pi\)
0.419804 + 0.907615i \(0.362099\pi\)
\(212\) −8.68523e13 −0.0657050
\(213\) −2.54299e15 −1.86585
\(214\) −5.74037e14 −0.408555
\(215\) −5.42973e14 −0.374911
\(216\) −2.68179e14 −0.179670
\(217\) −1.36574e15 −0.887933
\(218\) 1.93104e15 1.21850
\(219\) 2.10422e15 1.28886
\(220\) 4.14895e14 0.246712
\(221\) 2.39380e15 1.38209
\(222\) 1.36971e12 0.000767952 0
\(223\) 1.47017e15 0.800545 0.400272 0.916396i \(-0.368915\pi\)
0.400272 + 0.916396i \(0.368915\pi\)
\(224\) −5.90743e14 −0.312454
\(225\) 1.95305e15 1.00352
\(226\) 1.16976e15 0.583971
\(227\) 3.30482e15 1.60317 0.801586 0.597879i \(-0.203990\pi\)
0.801586 + 0.597879i \(0.203990\pi\)
\(228\) 7.36376e14 0.347155
\(229\) 1.73135e15 0.793329 0.396664 0.917964i \(-0.370168\pi\)
0.396664 + 0.917964i \(0.370168\pi\)
\(230\) −2.55573e15 −1.13837
\(231\) 1.55572e15 0.673679
\(232\) 1.49236e15 0.628350
\(233\) 4.23290e14 0.173310 0.0866551 0.996238i \(-0.472382\pi\)
0.0866551 + 0.996238i \(0.472382\pi\)
\(234\) −1.43887e15 −0.572953
\(235\) 1.08756e15 0.421222
\(236\) 5.86339e14 0.220913
\(237\) 1.04210e15 0.381985
\(238\) −3.57435e15 −1.27482
\(239\) −3.81996e14 −0.132578 −0.0662892 0.997800i \(-0.521116\pi\)
−0.0662892 + 0.997800i \(0.521116\pi\)
\(240\) 1.53115e15 0.517184
\(241\) 2.50661e15 0.824093 0.412047 0.911163i \(-0.364814\pi\)
0.412047 + 0.911163i \(0.364814\pi\)
\(242\) −2.00859e14 −0.0642824
\(243\) 3.40154e15 1.05983
\(244\) −1.82942e15 −0.554982
\(245\) −1.17671e16 −3.47608
\(246\) 3.93404e15 1.13178
\(247\) −2.65603e15 −0.744222
\(248\) 6.50743e14 0.177613
\(249\) 6.63092e15 1.76310
\(250\) 3.02925e15 0.784739
\(251\) −6.17245e15 −1.55804 −0.779020 0.626999i \(-0.784283\pi\)
−0.779020 + 0.626999i \(0.784283\pi\)
\(252\) 2.14848e15 0.528480
\(253\) 1.23728e15 0.296609
\(254\) −3.89489e15 −0.910072
\(255\) 9.26439e15 2.11011
\(256\) 2.81475e14 0.0625000
\(257\) −7.04282e15 −1.52469 −0.762344 0.647172i \(-0.775952\pi\)
−0.762344 + 0.647172i \(0.775952\pi\)
\(258\) 9.70090e14 0.204778
\(259\) 7.37686e12 0.00151853
\(260\) −5.52269e15 −1.10873
\(261\) −5.42759e15 −1.06278
\(262\) 2.63656e15 0.503592
\(263\) 2.19808e15 0.409572 0.204786 0.978807i \(-0.434350\pi\)
0.204786 + 0.978807i \(0.434350\pi\)
\(264\) −7.41262e14 −0.134755
\(265\) 1.21239e15 0.215053
\(266\) 3.96591e15 0.686455
\(267\) 5.76800e15 0.974321
\(268\) −9.50808e14 −0.156753
\(269\) −5.10332e15 −0.821227 −0.410614 0.911809i \(-0.634685\pi\)
−0.410614 + 0.911809i \(0.634685\pi\)
\(270\) 3.74357e15 0.588060
\(271\) −5.82993e15 −0.894053 −0.447026 0.894521i \(-0.647517\pi\)
−0.447026 + 0.894521i \(0.647517\pi\)
\(272\) 1.70309e15 0.255000
\(273\) −2.07082e16 −3.02751
\(274\) −5.64393e15 −0.805756
\(275\) −3.62907e15 −0.505980
\(276\) 4.56613e15 0.621783
\(277\) −2.72263e15 −0.362135 −0.181067 0.983471i \(-0.557955\pi\)
−0.181067 + 0.983471i \(0.557955\pi\)
\(278\) 2.67770e15 0.347913
\(279\) −2.36670e15 −0.300411
\(280\) 8.24633e15 1.02267
\(281\) 6.94126e15 0.841100 0.420550 0.907269i \(-0.361837\pi\)
0.420550 + 0.907269i \(0.361837\pi\)
\(282\) −1.94306e15 −0.230074
\(283\) −2.19270e15 −0.253728 −0.126864 0.991920i \(-0.540491\pi\)
−0.126864 + 0.991920i \(0.540491\pi\)
\(284\) 6.52572e15 0.738005
\(285\) −1.02793e16 −1.13624
\(286\) 2.67365e15 0.288885
\(287\) 2.11876e16 2.23794
\(288\) −1.02370e15 −0.105711
\(289\) 4.00172e14 0.0404027
\(290\) −2.08322e16 −2.05659
\(291\) 2.13383e16 2.05995
\(292\) −5.39977e15 −0.509785
\(293\) −1.73532e16 −1.60229 −0.801145 0.598470i \(-0.795775\pi\)
−0.801145 + 0.598470i \(0.795775\pi\)
\(294\) 2.10234e16 1.89865
\(295\) −8.18485e15 −0.723049
\(296\) −3.51490e12 −0.000303750 0
\(297\) −1.81234e15 −0.153223
\(298\) 6.99573e15 0.578665
\(299\) −1.64695e16 −1.33296
\(300\) −1.33929e16 −1.06069
\(301\) 5.22462e15 0.404923
\(302\) 3.95196e14 0.0299756
\(303\) −1.97076e16 −1.46304
\(304\) −1.88966e15 −0.137311
\(305\) 2.55373e16 1.81646
\(306\) −6.19401e15 −0.431303
\(307\) −9.28494e15 −0.632965 −0.316482 0.948598i \(-0.602502\pi\)
−0.316482 + 0.948598i \(0.602502\pi\)
\(308\) −3.99222e15 −0.266462
\(309\) 3.10144e16 2.02691
\(310\) −9.08389e15 −0.581327
\(311\) 8.22137e15 0.515231 0.257615 0.966248i \(-0.417063\pi\)
0.257615 + 0.966248i \(0.417063\pi\)
\(312\) 9.86698e15 0.605591
\(313\) 1.31274e16 0.789113 0.394557 0.918872i \(-0.370898\pi\)
0.394557 + 0.918872i \(0.370898\pi\)
\(314\) −1.60148e15 −0.0942931
\(315\) −2.99912e16 −1.72972
\(316\) −2.67421e15 −0.151088
\(317\) 3.62350e15 0.200559 0.100280 0.994959i \(-0.468026\pi\)
0.100280 + 0.994959i \(0.468026\pi\)
\(318\) −2.16609e15 −0.117463
\(319\) 1.00853e16 0.535859
\(320\) −3.92918e15 −0.204563
\(321\) −1.43165e16 −0.730387
\(322\) 2.45918e16 1.22950
\(323\) −1.14336e16 −0.560230
\(324\) −1.29144e16 −0.620199
\(325\) 4.83068e16 2.27387
\(326\) 1.02631e16 0.473548
\(327\) 4.81601e16 2.17835
\(328\) −1.00954e16 −0.447654
\(329\) −1.04648e16 −0.454942
\(330\) 1.03475e16 0.441056
\(331\) 1.32109e16 0.552140 0.276070 0.961138i \(-0.410968\pi\)
0.276070 + 0.961138i \(0.410968\pi\)
\(332\) −1.70160e16 −0.697365
\(333\) 1.27834e13 0.000513758 0
\(334\) 4.69375e15 0.184998
\(335\) 1.32726e16 0.513055
\(336\) −1.47331e16 −0.558585
\(337\) −1.36437e16 −0.507387 −0.253693 0.967285i \(-0.581645\pi\)
−0.253693 + 0.967285i \(0.581645\pi\)
\(338\) −1.62051e16 −0.591144
\(339\) 2.91737e16 1.04398
\(340\) −2.37739e16 −0.834618
\(341\) 4.39770e15 0.151468
\(342\) 6.87254e15 0.232246
\(343\) 5.99202e16 1.98683
\(344\) −2.48941e15 −0.0809965
\(345\) −6.37397e16 −2.03510
\(346\) 2.82993e16 0.886708
\(347\) −1.84147e16 −0.566268 −0.283134 0.959080i \(-0.591374\pi\)
−0.283134 + 0.959080i \(0.591374\pi\)
\(348\) 3.72194e16 1.12332
\(349\) 3.04103e16 0.900855 0.450428 0.892813i \(-0.351271\pi\)
0.450428 + 0.892813i \(0.351271\pi\)
\(350\) −7.21304e16 −2.09738
\(351\) 2.41242e16 0.688583
\(352\) 1.90220e15 0.0533002
\(353\) −4.38109e16 −1.20516 −0.602582 0.798057i \(-0.705861\pi\)
−0.602582 + 0.798057i \(0.705861\pi\)
\(354\) 1.46233e16 0.394933
\(355\) −9.10942e16 −2.41550
\(356\) −1.48016e16 −0.385376
\(357\) −8.91442e16 −2.27903
\(358\) 1.50548e16 0.377952
\(359\) −1.99730e16 −0.492412 −0.246206 0.969218i \(-0.579184\pi\)
−0.246206 + 0.969218i \(0.579184\pi\)
\(360\) 1.42901e16 0.345995
\(361\) −2.93669e16 −0.698331
\(362\) 9.58724e15 0.223917
\(363\) −5.00943e15 −0.114920
\(364\) 5.31407e16 1.19748
\(365\) 7.53768e16 1.66853
\(366\) −4.56256e16 −0.992159
\(367\) 2.51327e16 0.536920 0.268460 0.963291i \(-0.413485\pi\)
0.268460 + 0.963291i \(0.413485\pi\)
\(368\) −1.17174e16 −0.245935
\(369\) 3.67161e16 0.757155
\(370\) 4.90654e13 0.000994177 0
\(371\) −1.16660e16 −0.232268
\(372\) 1.62295e16 0.317524
\(373\) 4.48712e16 0.862701 0.431351 0.902184i \(-0.358037\pi\)
0.431351 + 0.902184i \(0.358037\pi\)
\(374\) 1.15095e16 0.217465
\(375\) 7.55494e16 1.40290
\(376\) 4.98620e15 0.0910016
\(377\) −1.34246e17 −2.40815
\(378\) −3.60216e16 −0.635135
\(379\) 8.14810e16 1.41222 0.706108 0.708104i \(-0.250449\pi\)
0.706108 + 0.708104i \(0.250449\pi\)
\(380\) 2.63782e16 0.449420
\(381\) −9.71384e16 −1.62697
\(382\) −5.46057e16 −0.899138
\(383\) −7.68561e16 −1.24419 −0.622095 0.782942i \(-0.713718\pi\)
−0.622095 + 0.782942i \(0.713718\pi\)
\(384\) 7.01998e15 0.111733
\(385\) 5.57285e16 0.872132
\(386\) 4.70105e16 0.723398
\(387\) 9.05378e15 0.136996
\(388\) −5.47576e16 −0.814776
\(389\) −1.01853e16 −0.149040 −0.0745200 0.997220i \(-0.523742\pi\)
−0.0745200 + 0.997220i \(0.523742\pi\)
\(390\) −1.37736e17 −1.98210
\(391\) −7.08975e16 −1.00342
\(392\) −5.39494e16 −0.750978
\(393\) 6.57556e16 0.900288
\(394\) 1.66567e16 0.224318
\(395\) 3.73299e16 0.494511
\(396\) −6.91814e15 −0.0901511
\(397\) −5.19589e16 −0.666072 −0.333036 0.942914i \(-0.608073\pi\)
−0.333036 + 0.942914i \(0.608073\pi\)
\(398\) 4.95204e16 0.624517
\(399\) 9.89096e16 1.22720
\(400\) 3.43684e16 0.419536
\(401\) −4.16402e16 −0.500120 −0.250060 0.968230i \(-0.580450\pi\)
−0.250060 + 0.968230i \(0.580450\pi\)
\(402\) −2.37131e16 −0.280233
\(403\) −5.85380e16 −0.680699
\(404\) 5.05728e16 0.578679
\(405\) 1.80275e17 2.02991
\(406\) 2.00453e17 2.22123
\(407\) −2.37536e13 −0.000259039 0
\(408\) 4.24751e16 0.455872
\(409\) −1.52221e17 −1.60795 −0.803977 0.594660i \(-0.797287\pi\)
−0.803977 + 0.594660i \(0.797287\pi\)
\(410\) 1.40924e17 1.46518
\(411\) −1.40760e17 −1.44048
\(412\) −7.95881e16 −0.801708
\(413\) 7.87567e16 0.780930
\(414\) 4.26153e16 0.415971
\(415\) 2.37531e17 2.28248
\(416\) −2.53203e16 −0.239531
\(417\) 6.67817e16 0.621976
\(418\) −1.27703e16 −0.117099
\(419\) −1.80246e17 −1.62732 −0.813661 0.581339i \(-0.802529\pi\)
−0.813661 + 0.581339i \(0.802529\pi\)
\(420\) 2.05663e17 1.82825
\(421\) −1.53615e17 −1.34462 −0.672310 0.740269i \(-0.734698\pi\)
−0.672310 + 0.740269i \(0.734698\pi\)
\(422\) −6.88799e16 −0.593693
\(423\) −1.81344e16 −0.153919
\(424\) 5.55855e15 0.0464604
\(425\) 2.07950e17 1.71171
\(426\) 1.62751e17 1.31936
\(427\) −2.45726e17 −1.96187
\(428\) 3.67384e16 0.288892
\(429\) 6.66808e16 0.516450
\(430\) 3.47503e16 0.265102
\(431\) 1.39142e17 1.04558 0.522788 0.852463i \(-0.324892\pi\)
0.522788 + 0.852463i \(0.324892\pi\)
\(432\) 1.71634e16 0.127046
\(433\) 2.08757e17 1.52220 0.761098 0.648637i \(-0.224661\pi\)
0.761098 + 0.648637i \(0.224661\pi\)
\(434\) 8.74074e16 0.627863
\(435\) −5.19555e17 −3.67664
\(436\) −1.23587e17 −0.861608
\(437\) 7.86640e16 0.540315
\(438\) −1.34670e17 −0.911359
\(439\) −2.48828e17 −1.65913 −0.829565 0.558410i \(-0.811411\pi\)
−0.829565 + 0.558410i \(0.811411\pi\)
\(440\) −2.65533e16 −0.174452
\(441\) 1.96210e17 1.27019
\(442\) −1.53203e17 −0.977288
\(443\) 2.88116e17 1.81110 0.905550 0.424238i \(-0.139458\pi\)
0.905550 + 0.424238i \(0.139458\pi\)
\(444\) −8.76614e13 −0.000543024 0
\(445\) 2.06620e17 1.26134
\(446\) −9.40908e16 −0.566071
\(447\) 1.74473e17 1.03450
\(448\) 3.78076e16 0.220939
\(449\) 2.89374e17 1.66670 0.833352 0.552742i \(-0.186418\pi\)
0.833352 + 0.552742i \(0.186418\pi\)
\(450\) −1.24995e17 −0.709597
\(451\) −6.82243e16 −0.381761
\(452\) −7.48645e16 −0.412930
\(453\) 9.85618e15 0.0535883
\(454\) −2.11509e17 −1.13361
\(455\) −7.41805e17 −3.91936
\(456\) −4.71281e16 −0.245475
\(457\) −1.46985e17 −0.754778 −0.377389 0.926055i \(-0.623178\pi\)
−0.377389 + 0.926055i \(0.623178\pi\)
\(458\) −1.10806e17 −0.560968
\(459\) 1.03849e17 0.518347
\(460\) 1.63566e17 0.804949
\(461\) −1.25707e17 −0.609962 −0.304981 0.952359i \(-0.598650\pi\)
−0.304981 + 0.952359i \(0.598650\pi\)
\(462\) −9.95659e16 −0.476363
\(463\) 8.57739e15 0.0404649 0.0202325 0.999795i \(-0.493559\pi\)
0.0202325 + 0.999795i \(0.493559\pi\)
\(464\) −9.55110e16 −0.444311
\(465\) −2.26552e17 −1.03926
\(466\) −2.70905e16 −0.122549
\(467\) 2.14149e17 0.955337 0.477669 0.878540i \(-0.341482\pi\)
0.477669 + 0.878540i \(0.341482\pi\)
\(468\) 9.20878e16 0.405139
\(469\) −1.27712e17 −0.554126
\(470\) −6.96037e16 −0.297849
\(471\) −3.99410e16 −0.168571
\(472\) −3.75257e16 −0.156209
\(473\) −1.68233e16 −0.0690741
\(474\) −6.66946e16 −0.270104
\(475\) −2.30730e17 −0.921712
\(476\) 2.28759e17 0.901431
\(477\) −2.02160e16 −0.0785824
\(478\) 2.44478e16 0.0937471
\(479\) −1.75601e17 −0.664272 −0.332136 0.943232i \(-0.607769\pi\)
−0.332136 + 0.943232i \(0.607769\pi\)
\(480\) −9.79936e16 −0.365704
\(481\) 3.16185e14 0.00116412
\(482\) −1.60423e17 −0.582722
\(483\) 6.13319e17 2.19801
\(484\) 1.28550e16 0.0454545
\(485\) 7.64375e17 2.66677
\(486\) −2.17698e17 −0.749410
\(487\) 1.40825e17 0.478345 0.239172 0.970977i \(-0.423124\pi\)
0.239172 + 0.970977i \(0.423124\pi\)
\(488\) 1.17083e17 0.392431
\(489\) 2.55961e17 0.846577
\(490\) 7.53093e17 2.45796
\(491\) −1.30979e17 −0.421864 −0.210932 0.977501i \(-0.567650\pi\)
−0.210932 + 0.977501i \(0.567650\pi\)
\(492\) −2.51778e17 −0.800286
\(493\) −5.77900e17 −1.81279
\(494\) 1.69986e17 0.526244
\(495\) 9.65721e16 0.295065
\(496\) −4.16476e16 −0.125591
\(497\) 8.76531e17 2.60886
\(498\) −4.24379e17 −1.24670
\(499\) 4.75923e17 1.38001 0.690007 0.723803i \(-0.257607\pi\)
0.690007 + 0.723803i \(0.257607\pi\)
\(500\) −1.93872e17 −0.554894
\(501\) 1.17062e17 0.330728
\(502\) 3.95037e17 1.10170
\(503\) −4.15310e17 −1.14335 −0.571676 0.820479i \(-0.693707\pi\)
−0.571676 + 0.820479i \(0.693707\pi\)
\(504\) −1.37503e17 −0.373692
\(505\) −7.05958e17 −1.89402
\(506\) −7.91860e16 −0.209734
\(507\) −4.04155e17 −1.05681
\(508\) 2.49273e17 0.643518
\(509\) 4.04654e16 0.103138 0.0515690 0.998669i \(-0.483578\pi\)
0.0515690 + 0.998669i \(0.483578\pi\)
\(510\) −5.92921e17 −1.49207
\(511\) −7.25294e17 −1.80210
\(512\) −1.80144e16 −0.0441942
\(513\) −1.15225e17 −0.279116
\(514\) 4.50740e17 1.07812
\(515\) 1.11099e18 2.62400
\(516\) −6.20858e16 −0.144800
\(517\) 3.36966e16 0.0776064
\(518\) −4.72119e14 −0.00107376
\(519\) 7.05783e17 1.58520
\(520\) 3.53452e17 0.783987
\(521\) −8.30318e16 −0.181886 −0.0909430 0.995856i \(-0.528988\pi\)
−0.0909430 + 0.995856i \(0.528988\pi\)
\(522\) 3.47366e17 0.751500
\(523\) 5.86014e17 1.25212 0.626062 0.779773i \(-0.284666\pi\)
0.626062 + 0.779773i \(0.284666\pi\)
\(524\) −1.68740e17 −0.356093
\(525\) −1.79893e18 −3.74955
\(526\) −1.40677e17 −0.289611
\(527\) −2.51993e17 −0.512412
\(528\) 4.74408e16 0.0952865
\(529\) −1.62560e16 −0.0322517
\(530\) −7.75932e16 −0.152065
\(531\) 1.36478e17 0.264209
\(532\) −2.53818e17 −0.485397
\(533\) 9.08137e17 1.71563
\(534\) −3.69152e17 −0.688949
\(535\) −5.12840e17 −0.945545
\(536\) 6.08517e16 0.110841
\(537\) 3.75467e17 0.675677
\(538\) 3.26613e17 0.580695
\(539\) −3.64588e17 −0.640436
\(540\) −2.39589e17 −0.415821
\(541\) −8.76345e17 −1.50277 −0.751385 0.659864i \(-0.770614\pi\)
−0.751385 + 0.659864i \(0.770614\pi\)
\(542\) 3.73116e17 0.632191
\(543\) 2.39105e17 0.400304
\(544\) −1.08998e17 −0.180312
\(545\) 1.72518e18 2.82005
\(546\) 1.32533e18 2.14077
\(547\) −6.52221e17 −1.04106 −0.520532 0.853842i \(-0.674266\pi\)
−0.520532 + 0.853842i \(0.674266\pi\)
\(548\) 3.61212e17 0.569755
\(549\) −4.25820e17 −0.663752
\(550\) 2.32261e17 0.357782
\(551\) 6.41206e17 0.976140
\(552\) −2.92232e17 −0.439667
\(553\) −3.59198e17 −0.534097
\(554\) 1.74248e17 0.256068
\(555\) 1.22369e15 0.00177732
\(556\) −1.71373e17 −0.246012
\(557\) 4.61565e16 0.0654898 0.0327449 0.999464i \(-0.489575\pi\)
0.0327449 + 0.999464i \(0.489575\pi\)
\(558\) 1.51469e17 0.212423
\(559\) 2.23937e17 0.310419
\(560\) −5.27765e17 −0.723134
\(561\) 2.87045e17 0.388769
\(562\) −4.44241e17 −0.594747
\(563\) 1.35065e16 0.0178747 0.00893733 0.999960i \(-0.497155\pi\)
0.00893733 + 0.999960i \(0.497155\pi\)
\(564\) 1.24356e17 0.162687
\(565\) 1.04505e18 1.35152
\(566\) 1.40333e17 0.179413
\(567\) −1.73465e18 −2.19241
\(568\) −4.17646e17 −0.521849
\(569\) 7.00697e17 0.865567 0.432783 0.901498i \(-0.357531\pi\)
0.432783 + 0.901498i \(0.357531\pi\)
\(570\) 6.57872e17 0.803443
\(571\) 6.01608e17 0.726405 0.363202 0.931710i \(-0.381683\pi\)
0.363202 + 0.931710i \(0.381683\pi\)
\(572\) −1.71114e17 −0.204273
\(573\) −1.36187e18 −1.60742
\(574\) −1.35601e18 −1.58247
\(575\) −1.43071e18 −1.65086
\(576\) 6.55169e16 0.0747493
\(577\) −1.20723e18 −1.36191 −0.680954 0.732326i \(-0.738435\pi\)
−0.680954 + 0.732326i \(0.738435\pi\)
\(578\) −2.56110e16 −0.0285690
\(579\) 1.17244e18 1.29324
\(580\) 1.33326e18 1.45423
\(581\) −2.28558e18 −2.46520
\(582\) −1.36565e18 −1.45660
\(583\) 3.75645e16 0.0396216
\(584\) 3.45585e17 0.360472
\(585\) −1.28548e18 −1.32602
\(586\) 1.11061e18 1.13299
\(587\) 6.11321e17 0.616768 0.308384 0.951262i \(-0.400212\pi\)
0.308384 + 0.951262i \(0.400212\pi\)
\(588\) −1.34550e18 −1.34255
\(589\) 2.79598e17 0.275921
\(590\) 5.23831e17 0.511273
\(591\) 4.15417e17 0.401020
\(592\) 2.24953e14 0.000214784 0
\(593\) −1.45118e18 −1.37046 −0.685231 0.728325i \(-0.740299\pi\)
−0.685231 + 0.728325i \(0.740299\pi\)
\(594\) 1.15990e17 0.108345
\(595\) −3.19330e18 −2.95039
\(596\) −4.47727e17 −0.409178
\(597\) 1.23504e18 1.11647
\(598\) 1.05405e18 0.942547
\(599\) 1.87155e18 1.65549 0.827744 0.561106i \(-0.189624\pi\)
0.827744 + 0.561106i \(0.189624\pi\)
\(600\) 8.57147e17 0.750019
\(601\) −8.49533e17 −0.735353 −0.367677 0.929954i \(-0.619847\pi\)
−0.367677 + 0.929954i \(0.619847\pi\)
\(602\) −3.34376e17 −0.286324
\(603\) −2.21313e17 −0.187475
\(604\) −2.52926e16 −0.0211959
\(605\) −1.79446e17 −0.148773
\(606\) 1.26128e18 1.03452
\(607\) 8.39863e17 0.681526 0.340763 0.940149i \(-0.389315\pi\)
0.340763 + 0.940149i \(0.389315\pi\)
\(608\) 1.20938e17 0.0970936
\(609\) 4.99929e18 3.97096
\(610\) −1.63439e18 −1.28443
\(611\) −4.48538e17 −0.348763
\(612\) 3.96417e17 0.304978
\(613\) −5.83068e17 −0.443840 −0.221920 0.975065i \(-0.571232\pi\)
−0.221920 + 0.975065i \(0.571232\pi\)
\(614\) 5.94236e17 0.447574
\(615\) 3.51464e18 2.61934
\(616\) 2.55502e17 0.188417
\(617\) −1.08213e18 −0.789637 −0.394818 0.918759i \(-0.629192\pi\)
−0.394818 + 0.918759i \(0.629192\pi\)
\(618\) −1.98492e18 −1.43324
\(619\) 1.81567e18 1.29732 0.648660 0.761078i \(-0.275330\pi\)
0.648660 + 0.761078i \(0.275330\pi\)
\(620\) 5.81369e17 0.411060
\(621\) −7.14490e17 −0.499920
\(622\) −5.26168e17 −0.364323
\(623\) −1.98815e18 −1.36231
\(624\) −6.31487e17 −0.428218
\(625\) 2.05677e17 0.138027
\(626\) −8.40151e17 −0.557987
\(627\) −3.18490e17 −0.209342
\(628\) 1.02495e17 0.0666753
\(629\) 1.36110e15 0.000876319 0
\(630\) 1.91944e18 1.22310
\(631\) −5.64428e17 −0.355973 −0.177987 0.984033i \(-0.556958\pi\)
−0.177987 + 0.984033i \(0.556958\pi\)
\(632\) 1.71149e17 0.106835
\(633\) −1.71786e18 −1.06136
\(634\) −2.31904e17 −0.141817
\(635\) −3.47966e18 −2.10624
\(636\) 1.38630e17 0.0830589
\(637\) 4.85306e18 2.87812
\(638\) −6.45461e17 −0.378909
\(639\) 1.51895e18 0.882646
\(640\) 2.51468e17 0.144648
\(641\) 4.65459e17 0.265036 0.132518 0.991181i \(-0.457694\pi\)
0.132518 + 0.991181i \(0.457694\pi\)
\(642\) 9.16253e17 0.516461
\(643\) 2.52025e18 1.40628 0.703141 0.711050i \(-0.251780\pi\)
0.703141 + 0.711050i \(0.251780\pi\)
\(644\) −1.57388e18 −0.869386
\(645\) 8.66671e17 0.473932
\(646\) 7.31750e17 0.396142
\(647\) 1.73833e18 0.931651 0.465826 0.884877i \(-0.345757\pi\)
0.465826 + 0.884877i \(0.345757\pi\)
\(648\) 8.26520e17 0.438547
\(649\) −2.53597e17 −0.133215
\(650\) −3.09164e18 −1.60787
\(651\) 2.17994e18 1.12245
\(652\) −6.56838e17 −0.334849
\(653\) 2.64589e17 0.133548 0.0667738 0.997768i \(-0.478729\pi\)
0.0667738 + 0.997768i \(0.478729\pi\)
\(654\) −3.08225e18 −1.54032
\(655\) 2.35548e18 1.16550
\(656\) 6.46104e17 0.316539
\(657\) −1.25687e18 −0.609697
\(658\) 6.69744e17 0.321692
\(659\) 8.71362e17 0.414423 0.207211 0.978296i \(-0.433561\pi\)
0.207211 + 0.978296i \(0.433561\pi\)
\(660\) −6.62238e17 −0.311873
\(661\) 1.51786e18 0.707817 0.353908 0.935280i \(-0.384852\pi\)
0.353908 + 0.935280i \(0.384852\pi\)
\(662\) −8.45495e17 −0.390422
\(663\) −3.82088e18 −1.74713
\(664\) 1.08902e18 0.493111
\(665\) 3.54311e18 1.58871
\(666\) −8.18138e14 −0.000363282 0
\(667\) 3.97599e18 1.74835
\(668\) −3.00400e17 −0.130814
\(669\) −2.34662e18 −1.01198
\(670\) −8.49445e17 −0.362785
\(671\) 7.91241e17 0.334666
\(672\) 9.42919e17 0.394979
\(673\) −4.01721e18 −1.66658 −0.833291 0.552834i \(-0.813546\pi\)
−0.833291 + 0.552834i \(0.813546\pi\)
\(674\) 8.73199e17 0.358776
\(675\) 2.09567e18 0.852804
\(676\) 1.03713e18 0.418002
\(677\) 2.88503e18 1.15166 0.575830 0.817569i \(-0.304679\pi\)
0.575830 + 0.817569i \(0.304679\pi\)
\(678\) −1.86712e18 −0.738208
\(679\) −7.35501e18 −2.88025
\(680\) 1.52153e18 0.590164
\(681\) −5.27502e18 −2.02660
\(682\) −2.81453e17 −0.107104
\(683\) −2.23743e18 −0.843362 −0.421681 0.906744i \(-0.638560\pi\)
−0.421681 + 0.906744i \(0.638560\pi\)
\(684\) −4.39843e17 −0.164222
\(685\) −5.04225e18 −1.86481
\(686\) −3.83489e18 −1.40490
\(687\) −2.76350e18 −1.00286
\(688\) 1.59322e17 0.0572732
\(689\) −5.00023e17 −0.178059
\(690\) 4.07934e18 1.43903
\(691\) 5.27201e17 0.184234 0.0921168 0.995748i \(-0.470637\pi\)
0.0921168 + 0.995748i \(0.470637\pi\)
\(692\) −1.81115e18 −0.626997
\(693\) −9.29241e17 −0.318686
\(694\) 1.17854e18 0.400412
\(695\) 2.39224e18 0.805198
\(696\) −2.38204e18 −0.794309
\(697\) 3.90932e18 1.29148
\(698\) −1.94626e18 −0.637001
\(699\) −6.75637e17 −0.219085
\(700\) 4.61635e18 1.48307
\(701\) −2.64738e18 −0.842653 −0.421326 0.906909i \(-0.638435\pi\)
−0.421326 + 0.906909i \(0.638435\pi\)
\(702\) −1.54395e18 −0.486902
\(703\) −1.51021e15 −0.000471875 0
\(704\) −1.21741e17 −0.0376889
\(705\) −1.73591e18 −0.532475
\(706\) 2.80390e18 0.852180
\(707\) 6.79291e18 2.04564
\(708\) −9.35889e17 −0.279260
\(709\) 7.30026e17 0.215843 0.107922 0.994159i \(-0.465580\pi\)
0.107922 + 0.994159i \(0.465580\pi\)
\(710\) 5.83003e18 1.70801
\(711\) −6.22456e17 −0.180699
\(712\) 9.47304e17 0.272502
\(713\) 1.73373e18 0.494197
\(714\) 5.70523e18 1.61152
\(715\) 2.38862e18 0.668586
\(716\) −9.63509e17 −0.267252
\(717\) 6.09726e17 0.167595
\(718\) 1.27827e18 0.348188
\(719\) −7.24722e18 −1.95629 −0.978146 0.207920i \(-0.933331\pi\)
−0.978146 + 0.207920i \(0.933331\pi\)
\(720\) −9.14567e17 −0.244655
\(721\) −1.06902e19 −2.83405
\(722\) 1.87948e18 0.493795
\(723\) −4.00095e18 −1.04175
\(724\) −6.13583e17 −0.158334
\(725\) −1.16620e19 −2.98247
\(726\) 3.20603e17 0.0812606
\(727\) −4.93763e18 −1.24035 −0.620176 0.784463i \(-0.712939\pi\)
−0.620176 + 0.784463i \(0.712939\pi\)
\(728\) −3.40101e18 −0.846746
\(729\) −4.02614e17 −0.0993481
\(730\) −4.82411e18 −1.17983
\(731\) 9.63996e17 0.233675
\(732\) 2.92004e18 0.701562
\(733\) −3.23406e17 −0.0770144 −0.0385072 0.999258i \(-0.512260\pi\)
−0.0385072 + 0.999258i \(0.512260\pi\)
\(734\) −1.60849e18 −0.379660
\(735\) 1.87821e19 4.39417
\(736\) 7.49915e17 0.173903
\(737\) 4.11234e17 0.0945258
\(738\) −2.34983e18 −0.535390
\(739\) 5.87474e18 1.32678 0.663392 0.748272i \(-0.269116\pi\)
0.663392 + 0.748272i \(0.269116\pi\)
\(740\) −3.14018e15 −0.000702989 0
\(741\) 4.23944e18 0.940784
\(742\) 7.46621e17 0.164238
\(743\) 2.43053e18 0.529998 0.264999 0.964249i \(-0.414628\pi\)
0.264999 + 0.964249i \(0.414628\pi\)
\(744\) −1.03869e18 −0.224523
\(745\) 6.24993e18 1.33924
\(746\) −2.87176e18 −0.610022
\(747\) −3.96069e18 −0.834041
\(748\) −7.36605e17 −0.153771
\(749\) 4.93468e18 1.02124
\(750\) −4.83516e18 −0.992002
\(751\) 4.44249e18 0.903581 0.451791 0.892124i \(-0.350785\pi\)
0.451791 + 0.892124i \(0.350785\pi\)
\(752\) −3.19117e17 −0.0643479
\(753\) 9.85221e18 1.96955
\(754\) 8.59176e18 1.70282
\(755\) 3.53065e17 0.0693745
\(756\) 2.30538e18 0.449108
\(757\) −1.55345e18 −0.300037 −0.150019 0.988683i \(-0.547933\pi\)
−0.150019 + 0.988683i \(0.547933\pi\)
\(758\) −5.21478e18 −0.998588
\(759\) −1.97490e18 −0.374949
\(760\) −1.68821e18 −0.317788
\(761\) 6.74934e18 1.25968 0.629841 0.776724i \(-0.283120\pi\)
0.629841 + 0.776724i \(0.283120\pi\)
\(762\) 6.21686e18 1.15044
\(763\) −1.66001e19 −3.04580
\(764\) 3.49477e18 0.635787
\(765\) −5.53368e18 −0.998194
\(766\) 4.91879e18 0.879775
\(767\) 3.37565e18 0.598670
\(768\) −4.49278e17 −0.0790074
\(769\) 8.13936e18 1.41928 0.709642 0.704563i \(-0.248857\pi\)
0.709642 + 0.704563i \(0.248857\pi\)
\(770\) −3.56662e18 −0.616691
\(771\) 1.12414e19 1.92739
\(772\) −3.00867e18 −0.511520
\(773\) 3.06638e17 0.0516963 0.0258481 0.999666i \(-0.491771\pi\)
0.0258481 + 0.999666i \(0.491771\pi\)
\(774\) −5.79442e17 −0.0968710
\(775\) −5.08521e18 −0.843040
\(776\) 3.50448e18 0.576133
\(777\) −1.17746e16 −0.00191960
\(778\) 6.51861e17 0.105387
\(779\) −4.33757e18 −0.695430
\(780\) 8.81508e18 1.40156
\(781\) −2.82244e18 −0.445034
\(782\) 4.53744e18 0.709524
\(783\) −5.82395e18 −0.903163
\(784\) 3.45276e18 0.531022
\(785\) −1.43075e18 −0.218229
\(786\) −4.20836e18 −0.636600
\(787\) −5.81951e18 −0.873073 −0.436536 0.899687i \(-0.643795\pi\)
−0.436536 + 0.899687i \(0.643795\pi\)
\(788\) −1.06603e18 −0.158617
\(789\) −3.50847e18 −0.517747
\(790\) −2.38912e18 −0.349672
\(791\) −1.00558e19 −1.45971
\(792\) 4.42761e17 0.0637464
\(793\) −1.05322e19 −1.50399
\(794\) 3.32537e18 0.470984
\(795\) −1.93517e18 −0.271852
\(796\) −3.16930e18 −0.441600
\(797\) −6.36403e18 −0.879535 −0.439768 0.898112i \(-0.644939\pi\)
−0.439768 + 0.898112i \(0.644939\pi\)
\(798\) −6.33021e18 −0.867760
\(799\) −1.93085e18 −0.262540
\(800\) −2.19958e18 −0.296657
\(801\) −3.44527e18 −0.460905
\(802\) 2.66497e18 0.353638
\(803\) 2.33545e18 0.307412
\(804\) 1.51764e18 0.198155
\(805\) 2.19702e19 2.84551
\(806\) 3.74643e18 0.481327
\(807\) 8.14571e18 1.03813
\(808\) −3.23666e18 −0.409188
\(809\) −4.31747e18 −0.541457 −0.270728 0.962656i \(-0.587265\pi\)
−0.270728 + 0.962656i \(0.587265\pi\)
\(810\) −1.15376e19 −1.43537
\(811\) −2.75385e18 −0.339864 −0.169932 0.985456i \(-0.554355\pi\)
−0.169932 + 0.985456i \(0.554355\pi\)
\(812\) −1.28290e19 −1.57065
\(813\) 9.30549e18 1.13019
\(814\) 1.52023e15 0.000183168 0
\(815\) 9.16896e18 1.09596
\(816\) −2.71841e18 −0.322351
\(817\) −1.06960e18 −0.125828
\(818\) 9.74216e18 1.13700
\(819\) 1.23692e19 1.43217
\(820\) −9.01913e18 −1.03604
\(821\) −1.61263e19 −1.83782 −0.918911 0.394466i \(-0.870930\pi\)
−0.918911 + 0.394466i \(0.870930\pi\)
\(822\) 9.00861e18 1.01857
\(823\) −1.08258e19 −1.21440 −0.607199 0.794550i \(-0.707707\pi\)
−0.607199 + 0.794550i \(0.707707\pi\)
\(824\) 5.09364e18 0.566893
\(825\) 5.79257e18 0.639618
\(826\) −5.04043e18 −0.552201
\(827\) −8.99840e18 −0.978091 −0.489046 0.872258i \(-0.662655\pi\)
−0.489046 + 0.872258i \(0.662655\pi\)
\(828\) −2.72738e18 −0.294136
\(829\) 1.13173e19 1.21098 0.605492 0.795852i \(-0.292977\pi\)
0.605492 + 0.795852i \(0.292977\pi\)
\(830\) −1.52020e19 −1.61396
\(831\) 4.34574e18 0.457781
\(832\) 1.62050e18 0.169374
\(833\) 2.08913e19 2.16657
\(834\) −4.27403e18 −0.439803
\(835\) 4.19336e18 0.428154
\(836\) 8.17297e17 0.0828017
\(837\) −2.53953e18 −0.255293
\(838\) 1.15357e19 1.15069
\(839\) −5.11110e18 −0.505896 −0.252948 0.967480i \(-0.581400\pi\)
−0.252948 + 0.967480i \(0.581400\pi\)
\(840\) −1.31624e19 −1.29277
\(841\) 2.21485e19 2.15859
\(842\) 9.83136e18 0.950791
\(843\) −1.10793e19 −1.06325
\(844\) 4.40831e18 0.419804
\(845\) −1.44775e19 −1.36812
\(846\) 1.16060e18 0.108837
\(847\) 1.72668e18 0.160683
\(848\) −3.55747e17 −0.0328525
\(849\) 3.49990e18 0.320742
\(850\) −1.33088e19 −1.21036
\(851\) −9.36451e15 −0.000845168 0
\(852\) −1.04161e19 −0.932926
\(853\) −4.20223e18 −0.373518 −0.186759 0.982406i \(-0.559798\pi\)
−0.186759 + 0.982406i \(0.559798\pi\)
\(854\) 1.57265e19 1.38725
\(855\) 6.13987e18 0.537502
\(856\) −2.35125e18 −0.204277
\(857\) −5.24084e18 −0.451883 −0.225941 0.974141i \(-0.572546\pi\)
−0.225941 + 0.974141i \(0.572546\pi\)
\(858\) −4.26757e18 −0.365185
\(859\) −6.62592e18 −0.562718 −0.281359 0.959603i \(-0.590785\pi\)
−0.281359 + 0.959603i \(0.590785\pi\)
\(860\) −2.22402e18 −0.187456
\(861\) −3.38187e19 −2.82903
\(862\) −8.90508e18 −0.739334
\(863\) 4.51292e18 0.371867 0.185933 0.982562i \(-0.440469\pi\)
0.185933 + 0.982562i \(0.440469\pi\)
\(864\) −1.09846e18 −0.0898348
\(865\) 2.52823e19 2.05217
\(866\) −1.33605e19 −1.07635
\(867\) −6.38737e17 −0.0510738
\(868\) −5.59408e18 −0.443966
\(869\) 1.15662e18 0.0911093
\(870\) 3.32515e19 2.59978
\(871\) −5.47396e18 −0.424799
\(872\) 7.90955e18 0.609249
\(873\) −1.27455e19 −0.974463
\(874\) −5.03450e18 −0.382060
\(875\) −2.60408e19 −1.96156
\(876\) 8.61888e18 0.644428
\(877\) −8.14871e18 −0.604772 −0.302386 0.953186i \(-0.597783\pi\)
−0.302386 + 0.953186i \(0.597783\pi\)
\(878\) 1.59250e19 1.17318
\(879\) 2.76985e19 2.02548
\(880\) 1.69941e18 0.123356
\(881\) 3.53169e18 0.254472 0.127236 0.991872i \(-0.459389\pi\)
0.127236 + 0.991872i \(0.459389\pi\)
\(882\) −1.25574e19 −0.898161
\(883\) −4.22219e18 −0.299773 −0.149887 0.988703i \(-0.547891\pi\)
−0.149887 + 0.988703i \(0.547891\pi\)
\(884\) 9.80499e18 0.691047
\(885\) 1.30643e19 0.914020
\(886\) −1.84394e19 −1.28064
\(887\) −2.82399e19 −1.94697 −0.973487 0.228741i \(-0.926539\pi\)
−0.973487 + 0.228741i \(0.926539\pi\)
\(888\) 5.61033e15 0.000383976 0
\(889\) 3.34822e19 2.27485
\(890\) −1.32237e19 −0.891901
\(891\) 5.58560e18 0.373994
\(892\) 6.02181e18 0.400272
\(893\) 2.14237e18 0.141371
\(894\) −1.11663e19 −0.731501
\(895\) 1.34499e19 0.874719
\(896\) −2.41968e18 −0.156227
\(897\) 2.62879e19 1.68502
\(898\) −1.85200e19 −1.17854
\(899\) 1.41320e19 0.892823
\(900\) 7.99969e18 0.501761
\(901\) −2.15249e18 −0.134038
\(902\) 4.36635e18 0.269946
\(903\) −8.33933e18 −0.511871
\(904\) 4.79133e18 0.291985
\(905\) 8.56516e18 0.518227
\(906\) −6.30795e17 −0.0378927
\(907\) −3.06265e19 −1.82662 −0.913312 0.407259i \(-0.866484\pi\)
−0.913312 + 0.407259i \(0.866484\pi\)
\(908\) 1.35366e19 0.801586
\(909\) 1.17715e19 0.692094
\(910\) 4.74755e19 2.77141
\(911\) 1.12833e19 0.653985 0.326993 0.945027i \(-0.393965\pi\)
0.326993 + 0.945027i \(0.393965\pi\)
\(912\) 3.01620e18 0.173577
\(913\) 7.35959e18 0.420527
\(914\) 9.40707e18 0.533708
\(915\) −4.07615e19 −2.29622
\(916\) 7.09159e18 0.396664
\(917\) −2.26650e19 −1.25880
\(918\) −6.64634e18 −0.366526
\(919\) 1.90702e19 1.04425 0.522125 0.852869i \(-0.325139\pi\)
0.522125 + 0.852869i \(0.325139\pi\)
\(920\) −1.04683e19 −0.569185
\(921\) 1.48202e19 0.800142
\(922\) 8.04523e18 0.431308
\(923\) 3.75697e19 1.99998
\(924\) 6.37222e18 0.336839
\(925\) 2.74671e16 0.00144175
\(926\) −5.48953e17 −0.0286130
\(927\) −1.85251e19 −0.958834
\(928\) 6.11271e18 0.314175
\(929\) −6.07406e18 −0.310011 −0.155005 0.987914i \(-0.549539\pi\)
−0.155005 + 0.987914i \(0.549539\pi\)
\(930\) 1.44993e19 0.734866
\(931\) −2.31798e19 −1.16664
\(932\) 1.73379e18 0.0866551
\(933\) −1.31226e19 −0.651313
\(934\) −1.37055e19 −0.675525
\(935\) 1.02825e19 0.503294
\(936\) −5.89362e18 −0.286477
\(937\) 2.58159e19 1.24618 0.623089 0.782151i \(-0.285877\pi\)
0.623089 + 0.782151i \(0.285877\pi\)
\(938\) 8.17357e18 0.391826
\(939\) −2.09533e19 −0.997533
\(940\) 4.45464e18 0.210611
\(941\) 1.18315e19 0.555532 0.277766 0.960649i \(-0.410406\pi\)
0.277766 + 0.960649i \(0.410406\pi\)
\(942\) 2.55622e18 0.119198
\(943\) −2.68964e19 −1.24557
\(944\) 2.40164e18 0.110456
\(945\) −3.21814e19 −1.46994
\(946\) 1.07669e18 0.0488427
\(947\) 1.59848e19 0.720166 0.360083 0.932920i \(-0.382748\pi\)
0.360083 + 0.932920i \(0.382748\pi\)
\(948\) 4.26846e18 0.190993
\(949\) −3.10874e19 −1.38151
\(950\) 1.47667e19 0.651749
\(951\) −5.78368e18 −0.253531
\(952\) −1.46406e19 −0.637408
\(953\) 4.13637e18 0.178861 0.0894304 0.995993i \(-0.471495\pi\)
0.0894304 + 0.995993i \(0.471495\pi\)
\(954\) 1.29382e18 0.0555662
\(955\) −4.87843e19 −2.08094
\(956\) −1.56466e18 −0.0662892
\(957\) −1.60978e19 −0.677389
\(958\) 1.12385e19 0.469711
\(959\) 4.85178e19 2.01409
\(960\) 6.27159e18 0.258592
\(961\) −1.82553e19 −0.747630
\(962\) −2.02358e16 −0.000823159 0
\(963\) 8.55132e18 0.345511
\(964\) 1.02671e19 0.412047
\(965\) 4.19988e19 1.67421
\(966\) −3.92524e19 −1.55423
\(967\) −2.38637e19 −0.938566 −0.469283 0.883048i \(-0.655488\pi\)
−0.469283 + 0.883048i \(0.655488\pi\)
\(968\) −8.22720e17 −0.0321412
\(969\) 1.82498e19 0.708197
\(970\) −4.89200e19 −1.88569
\(971\) −2.32623e19 −0.890692 −0.445346 0.895359i \(-0.646919\pi\)
−0.445346 + 0.895359i \(0.646919\pi\)
\(972\) 1.39327e19 0.529913
\(973\) −2.30187e19 −0.869655
\(974\) −9.01279e18 −0.338241
\(975\) −7.71053e19 −2.87445
\(976\) −7.49329e18 −0.277491
\(977\) −3.26857e19 −1.20238 −0.601192 0.799105i \(-0.705307\pi\)
−0.601192 + 0.799105i \(0.705307\pi\)
\(978\) −1.63815e19 −0.598620
\(979\) 6.40185e18 0.232390
\(980\) −4.81980e19 −1.73804
\(981\) −2.87664e19 −1.03047
\(982\) 8.38266e18 0.298303
\(983\) 5.16168e19 1.82471 0.912353 0.409404i \(-0.134263\pi\)
0.912353 + 0.409404i \(0.134263\pi\)
\(984\) 1.61138e19 0.565888
\(985\) 1.48810e19 0.519153
\(986\) 3.69856e19 1.28184
\(987\) 1.67034e19 0.575100
\(988\) −1.08791e19 −0.372111
\(989\) −6.63237e18 −0.225368
\(990\) −6.18062e18 −0.208643
\(991\) 4.73013e19 1.58633 0.793167 0.609005i \(-0.208431\pi\)
0.793167 + 0.609005i \(0.208431\pi\)
\(992\) 2.66544e18 0.0888063
\(993\) −2.10866e19 −0.697970
\(994\) −5.60980e19 −1.84474
\(995\) 4.42411e19 1.44536
\(996\) 2.71602e19 0.881552
\(997\) 3.86881e19 1.24755 0.623776 0.781603i \(-0.285598\pi\)
0.623776 + 0.781603i \(0.285598\pi\)
\(998\) −3.04591e19 −0.975817
\(999\) 1.37169e16 0.000436598 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 22.14.a.a.1.1 2
3.2 odd 2 198.14.a.e.1.2 2
4.3 odd 2 176.14.a.b.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.14.a.a.1.1 2 1.1 even 1 trivial
176.14.a.b.1.2 2 4.3 odd 2
198.14.a.e.1.2 2 3.2 odd 2