Properties

Label 197.14.a.b.1.10
Level $197$
Weight $14$
Character 197.1
Self dual yes
Analytic conductor $211.245$
Analytic rank $0$
Dimension $109$
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] = [197,14,Mod(1,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, 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("197.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 197.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: \(211.244930035\)
Analytic rank: \(0\)
Dimension: \(109\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 197.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-155.970 q^{2} +2509.18 q^{3} +16134.6 q^{4} -12965.5 q^{5} -391357. q^{6} +428722. q^{7} -1.23881e6 q^{8} +4.70166e6 q^{9} +O(q^{10})\) \(q-155.970 q^{2} +2509.18 q^{3} +16134.6 q^{4} -12965.5 q^{5} -391357. q^{6} +428722. q^{7} -1.23881e6 q^{8} +4.70166e6 q^{9} +2.02223e6 q^{10} -1.10577e7 q^{11} +4.04847e7 q^{12} +1.87853e7 q^{13} -6.68678e7 q^{14} -3.25328e7 q^{15} +6.10426e7 q^{16} -1.84750e7 q^{17} -7.33318e8 q^{18} +2.47569e8 q^{19} -2.09194e8 q^{20} +1.07574e9 q^{21} +1.72467e9 q^{22} +5.09140e8 q^{23} -3.10840e9 q^{24} -1.05260e9 q^{25} -2.92995e9 q^{26} +7.79687e9 q^{27} +6.91728e9 q^{28} +9.32197e8 q^{29} +5.07414e9 q^{30} -1.35265e8 q^{31} +6.27540e8 q^{32} -2.77457e10 q^{33} +2.88155e9 q^{34} -5.55861e9 q^{35} +7.58596e10 q^{36} +7.65238e8 q^{37} -3.86133e10 q^{38} +4.71358e10 q^{39} +1.60618e10 q^{40} -4.53532e10 q^{41} -1.67783e11 q^{42} -6.13610e10 q^{43} -1.78412e11 q^{44} -6.09595e10 q^{45} -7.94105e10 q^{46} +9.71747e10 q^{47} +1.53167e11 q^{48} +8.69139e10 q^{49} +1.64174e11 q^{50} -4.63571e10 q^{51} +3.03094e11 q^{52} +1.05544e11 q^{53} -1.21608e12 q^{54} +1.43369e11 q^{55} -5.31106e11 q^{56} +6.21195e11 q^{57} -1.45395e11 q^{58} +4.85318e11 q^{59} -5.24905e11 q^{60} +1.08531e11 q^{61} +2.10973e10 q^{62} +2.01571e12 q^{63} -5.97938e11 q^{64} -2.43562e11 q^{65} +4.32750e12 q^{66} -3.62070e11 q^{67} -2.98088e11 q^{68} +1.27752e12 q^{69} +8.66976e11 q^{70} -9.45914e11 q^{71} -5.82447e12 q^{72} +2.20920e12 q^{73} -1.19354e11 q^{74} -2.64116e12 q^{75} +3.99443e12 q^{76} -4.74067e12 q^{77} -7.35177e12 q^{78} +1.65336e12 q^{79} -7.91449e11 q^{80} +1.20678e13 q^{81} +7.07373e12 q^{82} -1.35427e11 q^{83} +1.73567e13 q^{84} +2.39538e11 q^{85} +9.57047e12 q^{86} +2.33905e12 q^{87} +1.36984e13 q^{88} -2.58441e11 q^{89} +9.50785e12 q^{90} +8.05369e12 q^{91} +8.21478e12 q^{92} -3.39404e11 q^{93} -1.51563e13 q^{94} -3.20986e12 q^{95} +1.57461e12 q^{96} +1.26391e13 q^{97} -1.35560e13 q^{98} -5.19894e13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 109 q + 192 q^{2} + 8018 q^{3} + 471040 q^{4} + 88496 q^{5} + 383232 q^{6} + 1680731 q^{7} + 1820859 q^{8} + 59521391 q^{9} + 16373653 q^{10} + 21199298 q^{11} + 63225856 q^{12} + 59695238 q^{13} + 37888529 q^{14} + 87246239 q^{15} + 2130706432 q^{16} + 228353715 q^{17} + 400647337 q^{18} + 1139301305 q^{19} + 1109969259 q^{20} + 539982398 q^{21} + 1613315649 q^{22} + 920306804 q^{23} + 5542439613 q^{24} + 31241700999 q^{25} + 1864366110 q^{26} + 17825460755 q^{27} + 20413389070 q^{28} + 7185436621 q^{29} + 2050251883 q^{30} + 28475592572 q^{31} + 8334714660 q^{32} + 19623425846 q^{33} + 37845014194 q^{34} + 25255003636 q^{35} + 287968706746 q^{36} + 71523920490 q^{37} + 67778214914 q^{38} + 44951568463 q^{39} + 169184871486 q^{40} + 69139231052 q^{41} + 58715177635 q^{42} + 247544146139 q^{43} + 63861560722 q^{44} + 257443045479 q^{45} + 160530477869 q^{46} + 308496573061 q^{47} + 412228130018 q^{48} + 1736616239908 q^{49} + 1680360028531 q^{50} + 756579032995 q^{51} + 928015404666 q^{52} + 342783723680 q^{53} - 597894730601 q^{54} + 59276330527 q^{55} - 3822929869144 q^{56} - 562905761941 q^{57} + 62740419347 q^{58} + 827401964151 q^{59} - 2247133283907 q^{60} + 988213134514 q^{61} + 1937380192071 q^{62} + 1788190111357 q^{63} + 11682175668457 q^{64} + 2494670804291 q^{65} + 11819807890512 q^{66} + 8038740399790 q^{67} + 10126245189885 q^{68} + 5225665164579 q^{69} + 11464042631319 q^{70} + 4867145119603 q^{71} + 18133468947055 q^{72} + 9684156738615 q^{73} + 16996786880941 q^{74} + 16718732018262 q^{75} + 21454522032798 q^{76} + 6593100920650 q^{77} + 33749579076633 q^{78} + 7591753073823 q^{79} + 24349241260570 q^{80} + 38778649605417 q^{81} + 25555033184251 q^{82} + 16945724819556 q^{83} + 21855489402730 q^{84} + 15544906794766 q^{85} + 18664144286914 q^{86} + 19049540636401 q^{87} + 17318749473003 q^{88} + 11289674998576 q^{89} + 20983303956671 q^{90} + 47242561944227 q^{91} - 25046698097386 q^{92} - 5411884145985 q^{93} + 18338784709341 q^{94} + 6784117894603 q^{95} - 36827486682955 q^{96} + 45969533477736 q^{97} - 42983409526150 q^{98} + 12084396239183 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −155.970 −1.72324 −0.861620 0.507553i \(-0.830550\pi\)
−0.861620 + 0.507553i \(0.830550\pi\)
\(3\) 2509.18 1.98721 0.993605 0.112915i \(-0.0360187\pi\)
0.993605 + 0.112915i \(0.0360187\pi\)
\(4\) 16134.6 1.96956
\(5\) −12965.5 −0.371095 −0.185547 0.982635i \(-0.559406\pi\)
−0.185547 + 0.982635i \(0.559406\pi\)
\(6\) −391357. −3.42444
\(7\) 428722. 1.37733 0.688666 0.725078i \(-0.258196\pi\)
0.688666 + 0.725078i \(0.258196\pi\)
\(8\) −1.23881e6 −1.67078
\(9\) 4.70166e6 2.94900
\(10\) 2.02223e6 0.639486
\(11\) −1.10577e7 −1.88196 −0.940982 0.338456i \(-0.890095\pi\)
−0.940982 + 0.338456i \(0.890095\pi\)
\(12\) 4.04847e7 3.91393
\(13\) 1.87853e7 1.07941 0.539706 0.841854i \(-0.318535\pi\)
0.539706 + 0.841854i \(0.318535\pi\)
\(14\) −6.68678e7 −2.37348
\(15\) −3.25328e7 −0.737443
\(16\) 6.10426e7 0.909605
\(17\) −1.84750e7 −0.185638 −0.0928190 0.995683i \(-0.529588\pi\)
−0.0928190 + 0.995683i \(0.529588\pi\)
\(18\) −7.33318e8 −5.08184
\(19\) 2.47569e8 1.20725 0.603626 0.797268i \(-0.293722\pi\)
0.603626 + 0.797268i \(0.293722\pi\)
\(20\) −2.09194e8 −0.730893
\(21\) 1.07574e9 2.73705
\(22\) 1.72467e9 3.24308
\(23\) 5.09140e8 0.717144 0.358572 0.933502i \(-0.383264\pi\)
0.358572 + 0.933502i \(0.383264\pi\)
\(24\) −3.10840e9 −3.32020
\(25\) −1.05260e9 −0.862289
\(26\) −2.92995e9 −1.86009
\(27\) 7.79687e9 3.87307
\(28\) 6.91728e9 2.71274
\(29\) 9.32197e8 0.291019 0.145509 0.989357i \(-0.453518\pi\)
0.145509 + 0.989357i \(0.453518\pi\)
\(30\) 5.07414e9 1.27079
\(31\) −1.35265e8 −0.0273737 −0.0136869 0.999906i \(-0.504357\pi\)
−0.0136869 + 0.999906i \(0.504357\pi\)
\(32\) 6.27540e8 0.103316
\(33\) −2.77457e10 −3.73986
\(34\) 2.88155e9 0.319899
\(35\) −5.55861e9 −0.511121
\(36\) 7.58596e10 5.80823
\(37\) 7.65238e8 0.0490327 0.0245163 0.999699i \(-0.492195\pi\)
0.0245163 + 0.999699i \(0.492195\pi\)
\(38\) −3.86133e10 −2.08039
\(39\) 4.71358e10 2.14502
\(40\) 1.60618e10 0.620020
\(41\) −4.53532e10 −1.49112 −0.745560 0.666438i \(-0.767818\pi\)
−0.745560 + 0.666438i \(0.767818\pi\)
\(42\) −1.67783e11 −4.71659
\(43\) −6.13610e10 −1.48029 −0.740146 0.672447i \(-0.765243\pi\)
−0.740146 + 0.672447i \(0.765243\pi\)
\(44\) −1.78412e11 −3.70664
\(45\) −6.09595e10 −1.09436
\(46\) −7.94105e10 −1.23581
\(47\) 9.71747e10 1.31497 0.657487 0.753466i \(-0.271619\pi\)
0.657487 + 0.753466i \(0.271619\pi\)
\(48\) 1.53167e11 1.80758
\(49\) 8.69139e10 0.897046
\(50\) 1.64174e11 1.48593
\(51\) −4.63571e10 −0.368901
\(52\) 3.03094e11 2.12597
\(53\) 1.05544e11 0.654095 0.327047 0.945008i \(-0.393946\pi\)
0.327047 + 0.945008i \(0.393946\pi\)
\(54\) −1.21608e12 −6.67424
\(55\) 1.43369e11 0.698387
\(56\) −5.31106e11 −2.30123
\(57\) 6.21195e11 2.39906
\(58\) −1.45395e11 −0.501495
\(59\) 4.85318e11 1.49792 0.748959 0.662616i \(-0.230554\pi\)
0.748959 + 0.662616i \(0.230554\pi\)
\(60\) −5.24905e11 −1.45244
\(61\) 1.08531e11 0.269717 0.134859 0.990865i \(-0.456942\pi\)
0.134859 + 0.990865i \(0.456942\pi\)
\(62\) 2.10973e10 0.0471716
\(63\) 2.01571e12 4.06176
\(64\) −5.97938e11 −1.08764
\(65\) −2.43562e11 −0.400564
\(66\) 4.32750e12 6.44468
\(67\) −3.62070e11 −0.488997 −0.244498 0.969650i \(-0.578623\pi\)
−0.244498 + 0.969650i \(0.578623\pi\)
\(68\) −2.98088e11 −0.365625
\(69\) 1.27752e12 1.42511
\(70\) 8.66976e11 0.880785
\(71\) −9.45914e11 −0.876339 −0.438170 0.898892i \(-0.644373\pi\)
−0.438170 + 0.898892i \(0.644373\pi\)
\(72\) −5.82447e12 −4.92715
\(73\) 2.20920e12 1.70859 0.854294 0.519791i \(-0.173990\pi\)
0.854294 + 0.519791i \(0.173990\pi\)
\(74\) −1.19354e11 −0.0844951
\(75\) −2.64116e12 −1.71355
\(76\) 3.99443e12 2.37775
\(77\) −4.74067e12 −2.59209
\(78\) −7.35177e12 −3.69638
\(79\) 1.65336e12 0.765227 0.382614 0.923908i \(-0.375024\pi\)
0.382614 + 0.923908i \(0.375024\pi\)
\(80\) −7.91449e11 −0.337550
\(81\) 1.20678e13 4.74761
\(82\) 7.07373e12 2.56956
\(83\) −1.35427e11 −0.0454673 −0.0227336 0.999742i \(-0.507237\pi\)
−0.0227336 + 0.999742i \(0.507237\pi\)
\(84\) 1.73567e13 5.39078
\(85\) 2.39538e11 0.0688893
\(86\) 9.57047e12 2.55090
\(87\) 2.33905e12 0.578315
\(88\) 1.36984e13 3.14436
\(89\) −2.58441e11 −0.0551221 −0.0275610 0.999620i \(-0.508774\pi\)
−0.0275610 + 0.999620i \(0.508774\pi\)
\(90\) 9.50785e12 1.88584
\(91\) 8.05369e12 1.48671
\(92\) 8.21478e12 1.41246
\(93\) −3.39404e11 −0.0543974
\(94\) −1.51563e13 −2.26602
\(95\) −3.20986e12 −0.448005
\(96\) 1.57461e12 0.205310
\(97\) 1.26391e13 1.54064 0.770320 0.637657i \(-0.220096\pi\)
0.770320 + 0.637657i \(0.220096\pi\)
\(98\) −1.35560e13 −1.54583
\(99\) −5.19894e13 −5.54992
\(100\) −1.69833e13 −1.69833
\(101\) −1.20790e13 −1.13225 −0.566124 0.824320i \(-0.691557\pi\)
−0.566124 + 0.824320i \(0.691557\pi\)
\(102\) 7.23032e12 0.635706
\(103\) 1.93406e13 1.59598 0.797992 0.602668i \(-0.205896\pi\)
0.797992 + 0.602668i \(0.205896\pi\)
\(104\) −2.32715e13 −1.80346
\(105\) −1.39475e13 −1.01570
\(106\) −1.64617e13 −1.12716
\(107\) 6.57218e12 0.423365 0.211683 0.977338i \(-0.432106\pi\)
0.211683 + 0.977338i \(0.432106\pi\)
\(108\) 1.25800e14 7.62825
\(109\) 1.38956e13 0.793607 0.396803 0.917904i \(-0.370119\pi\)
0.396803 + 0.917904i \(0.370119\pi\)
\(110\) −2.23612e13 −1.20349
\(111\) 1.92012e12 0.0974382
\(112\) 2.61703e13 1.25283
\(113\) −2.01596e13 −0.910904 −0.455452 0.890260i \(-0.650522\pi\)
−0.455452 + 0.890260i \(0.650522\pi\)
\(114\) −9.68878e13 −4.13416
\(115\) −6.60126e12 −0.266128
\(116\) 1.50407e13 0.573178
\(117\) 8.83223e13 3.18319
\(118\) −7.56950e13 −2.58127
\(119\) −7.92065e12 −0.255685
\(120\) 4.03021e13 1.23211
\(121\) 8.77495e13 2.54179
\(122\) −1.69275e13 −0.464788
\(123\) −1.13799e14 −2.96317
\(124\) −2.18245e12 −0.0539142
\(125\) 2.94745e13 0.691086
\(126\) −3.14390e14 −6.99938
\(127\) 5.03593e13 1.06502 0.532508 0.846425i \(-0.321250\pi\)
0.532508 + 0.846425i \(0.321250\pi\)
\(128\) 8.81196e13 1.77096
\(129\) −1.53966e14 −2.94165
\(130\) 3.79883e13 0.690269
\(131\) −4.70768e13 −0.813848 −0.406924 0.913462i \(-0.633399\pi\)
−0.406924 + 0.913462i \(0.633399\pi\)
\(132\) −4.47667e14 −7.36587
\(133\) 1.06138e14 1.66279
\(134\) 5.64720e13 0.842659
\(135\) −1.01090e14 −1.43728
\(136\) 2.28871e13 0.310161
\(137\) −7.19811e13 −0.930111 −0.465055 0.885282i \(-0.653966\pi\)
−0.465055 + 0.885282i \(0.653966\pi\)
\(138\) −1.99255e14 −2.45582
\(139\) −1.21312e14 −1.42661 −0.713307 0.700852i \(-0.752803\pi\)
−0.713307 + 0.700852i \(0.752803\pi\)
\(140\) −8.96861e13 −1.00668
\(141\) 2.43829e14 2.61313
\(142\) 1.47534e14 1.51014
\(143\) −2.07722e14 −2.03141
\(144\) 2.87001e14 2.68243
\(145\) −1.20864e13 −0.107995
\(146\) −3.44569e14 −2.94431
\(147\) 2.18082e14 1.78262
\(148\) 1.23468e13 0.0965728
\(149\) 8.87453e13 0.664408 0.332204 0.943208i \(-0.392208\pi\)
0.332204 + 0.943208i \(0.392208\pi\)
\(150\) 4.11941e14 2.95286
\(151\) 1.15727e14 0.794481 0.397240 0.917715i \(-0.369968\pi\)
0.397240 + 0.917715i \(0.369968\pi\)
\(152\) −3.06691e14 −2.01706
\(153\) −8.68632e13 −0.547447
\(154\) 7.39403e14 4.46680
\(155\) 1.75378e12 0.0101583
\(156\) 7.60518e14 4.22474
\(157\) −2.99206e14 −1.59449 −0.797246 0.603655i \(-0.793711\pi\)
−0.797246 + 0.603655i \(0.793711\pi\)
\(158\) −2.57874e14 −1.31867
\(159\) 2.64829e14 1.29982
\(160\) −8.13638e12 −0.0383399
\(161\) 2.18280e14 0.987746
\(162\) −1.88221e15 −8.18127
\(163\) −7.83819e13 −0.327338 −0.163669 0.986515i \(-0.552333\pi\)
−0.163669 + 0.986515i \(0.552333\pi\)
\(164\) −7.31757e14 −2.93685
\(165\) 3.59737e14 1.38784
\(166\) 2.11226e13 0.0783511
\(167\) 7.91587e13 0.282385 0.141192 0.989982i \(-0.454906\pi\)
0.141192 + 0.989982i \(0.454906\pi\)
\(168\) −1.33264e15 −4.57302
\(169\) 5.00137e13 0.165130
\(170\) −3.73608e13 −0.118713
\(171\) 1.16399e15 3.56019
\(172\) −9.90036e14 −2.91552
\(173\) 5.35739e14 1.51933 0.759667 0.650312i \(-0.225362\pi\)
0.759667 + 0.650312i \(0.225362\pi\)
\(174\) −3.64822e14 −0.996576
\(175\) −4.51272e14 −1.18766
\(176\) −6.74989e14 −1.71184
\(177\) 1.21775e15 2.97668
\(178\) 4.03090e13 0.0949886
\(179\) −2.80170e14 −0.636615 −0.318307 0.947988i \(-0.603114\pi\)
−0.318307 + 0.947988i \(0.603114\pi\)
\(180\) −9.83559e14 −2.15541
\(181\) 5.14060e14 1.08668 0.543342 0.839511i \(-0.317159\pi\)
0.543342 + 0.839511i \(0.317159\pi\)
\(182\) −1.25613e15 −2.56196
\(183\) 2.72323e14 0.535984
\(184\) −6.30729e14 −1.19819
\(185\) −9.92172e12 −0.0181958
\(186\) 5.29368e13 0.0937398
\(187\) 2.04291e14 0.349364
\(188\) 1.56788e15 2.58992
\(189\) 3.34269e15 5.33451
\(190\) 5.00642e14 0.772020
\(191\) −1.00129e15 −1.49225 −0.746124 0.665807i \(-0.768087\pi\)
−0.746124 + 0.665807i \(0.768087\pi\)
\(192\) −1.50033e15 −2.16137
\(193\) −4.90266e14 −0.682825 −0.341412 0.939914i \(-0.610905\pi\)
−0.341412 + 0.939914i \(0.610905\pi\)
\(194\) −1.97133e15 −2.65490
\(195\) −6.11140e14 −0.796005
\(196\) 1.40232e15 1.76678
\(197\) 5.84517e13 0.0712470
\(198\) 8.10879e15 9.56384
\(199\) −5.81232e14 −0.663444 −0.331722 0.943377i \(-0.607630\pi\)
−0.331722 + 0.943377i \(0.607630\pi\)
\(200\) 1.30397e15 1.44070
\(201\) −9.08498e14 −0.971739
\(202\) 1.88396e15 1.95113
\(203\) 3.99654e14 0.400829
\(204\) −7.47955e14 −0.726573
\(205\) 5.88028e14 0.553347
\(206\) −3.01656e15 −2.75026
\(207\) 2.39380e15 2.11486
\(208\) 1.14671e15 0.981839
\(209\) −2.73754e15 −2.27200
\(210\) 2.17540e15 1.75030
\(211\) 4.92372e14 0.384111 0.192056 0.981384i \(-0.438485\pi\)
0.192056 + 0.981384i \(0.438485\pi\)
\(212\) 1.70292e15 1.28828
\(213\) −2.37347e15 −1.74147
\(214\) −1.02506e15 −0.729560
\(215\) 7.95577e14 0.549328
\(216\) −9.65885e15 −6.47107
\(217\) −5.79911e13 −0.0377028
\(218\) −2.16730e15 −1.36758
\(219\) 5.54329e15 3.39532
\(220\) 2.31320e15 1.37552
\(221\) −3.47059e14 −0.200380
\(222\) −2.99481e14 −0.167909
\(223\) −1.35774e15 −0.739322 −0.369661 0.929167i \(-0.620526\pi\)
−0.369661 + 0.929167i \(0.620526\pi\)
\(224\) 2.69040e14 0.142300
\(225\) −4.94896e15 −2.54289
\(226\) 3.14429e15 1.56971
\(227\) −1.74739e15 −0.847661 −0.423831 0.905741i \(-0.639315\pi\)
−0.423831 + 0.905741i \(0.639315\pi\)
\(228\) 1.00228e16 4.72510
\(229\) 7.26003e14 0.332666 0.166333 0.986070i \(-0.446807\pi\)
0.166333 + 0.986070i \(0.446807\pi\)
\(230\) 1.02960e15 0.458603
\(231\) −1.18952e16 −5.15103
\(232\) −1.15482e15 −0.486229
\(233\) −2.41004e15 −0.986756 −0.493378 0.869815i \(-0.664238\pi\)
−0.493378 + 0.869815i \(0.664238\pi\)
\(234\) −1.37756e16 −5.48540
\(235\) −1.25992e15 −0.487980
\(236\) 7.83042e15 2.95024
\(237\) 4.14857e15 1.52067
\(238\) 1.23538e15 0.440607
\(239\) 1.43672e15 0.498639 0.249320 0.968421i \(-0.419793\pi\)
0.249320 + 0.968421i \(0.419793\pi\)
\(240\) −1.98589e15 −0.670782
\(241\) −2.05994e15 −0.677242 −0.338621 0.940923i \(-0.609960\pi\)
−0.338621 + 0.940923i \(0.609960\pi\)
\(242\) −1.36863e16 −4.38012
\(243\) 1.78495e16 5.56142
\(244\) 1.75110e15 0.531224
\(245\) −1.12688e15 −0.332889
\(246\) 1.77493e16 5.10625
\(247\) 4.65067e15 1.30312
\(248\) 1.67568e14 0.0457356
\(249\) −3.39812e14 −0.0903530
\(250\) −4.59714e15 −1.19091
\(251\) 2.86312e15 0.722704 0.361352 0.932430i \(-0.382315\pi\)
0.361352 + 0.932430i \(0.382315\pi\)
\(252\) 3.25227e16 7.99987
\(253\) −5.62990e15 −1.34964
\(254\) −7.85454e15 −1.83528
\(255\) 6.01044e14 0.136897
\(256\) −8.84570e15 −1.96414
\(257\) 1.18597e15 0.256749 0.128375 0.991726i \(-0.459024\pi\)
0.128375 + 0.991726i \(0.459024\pi\)
\(258\) 2.40140e16 5.06917
\(259\) 3.28075e14 0.0675343
\(260\) −3.92978e15 −0.788935
\(261\) 4.38287e15 0.858214
\(262\) 7.34257e15 1.40246
\(263\) 2.56539e15 0.478015 0.239008 0.971018i \(-0.423178\pi\)
0.239008 + 0.971018i \(0.423178\pi\)
\(264\) 3.43717e16 6.24850
\(265\) −1.36843e15 −0.242731
\(266\) −1.65544e16 −2.86538
\(267\) −6.48474e14 −0.109539
\(268\) −5.84186e15 −0.963108
\(269\) 2.62105e14 0.0421780 0.0210890 0.999778i \(-0.493287\pi\)
0.0210890 + 0.999778i \(0.493287\pi\)
\(270\) 1.57671e16 2.47678
\(271\) 1.23467e16 1.89344 0.946722 0.322053i \(-0.104373\pi\)
0.946722 + 0.322053i \(0.104373\pi\)
\(272\) −1.12776e15 −0.168857
\(273\) 2.02082e16 2.95440
\(274\) 1.12269e16 1.60280
\(275\) 1.16393e16 1.62280
\(276\) 2.06124e16 2.80685
\(277\) 3.96634e15 0.527560 0.263780 0.964583i \(-0.415031\pi\)
0.263780 + 0.964583i \(0.415031\pi\)
\(278\) 1.89210e16 2.45840
\(279\) −6.35970e14 −0.0807252
\(280\) 6.88607e15 0.853973
\(281\) −8.18647e14 −0.0991986 −0.0495993 0.998769i \(-0.515794\pi\)
−0.0495993 + 0.998769i \(0.515794\pi\)
\(282\) −3.80300e16 −4.50305
\(283\) 8.53591e15 0.987729 0.493865 0.869539i \(-0.335584\pi\)
0.493865 + 0.869539i \(0.335584\pi\)
\(284\) −1.52620e16 −1.72600
\(285\) −8.05412e15 −0.890280
\(286\) 3.23984e16 3.50062
\(287\) −1.94439e16 −2.05377
\(288\) 2.95048e15 0.304678
\(289\) −9.56325e15 −0.965539
\(290\) 1.88512e15 0.186102
\(291\) 3.17139e16 3.06158
\(292\) 3.56447e16 3.36516
\(293\) −2.13064e15 −0.196730 −0.0983650 0.995150i \(-0.531361\pi\)
−0.0983650 + 0.995150i \(0.531361\pi\)
\(294\) −3.40143e16 −3.07188
\(295\) −6.29240e15 −0.555870
\(296\) −9.47987e14 −0.0819230
\(297\) −8.62152e16 −7.28899
\(298\) −1.38416e16 −1.14493
\(299\) 9.56436e15 0.774093
\(300\) −4.26141e16 −3.37493
\(301\) −2.63068e16 −2.03885
\(302\) −1.80499e16 −1.36908
\(303\) −3.03083e16 −2.25001
\(304\) 1.51122e16 1.09812
\(305\) −1.40716e15 −0.100091
\(306\) 1.35481e16 0.943382
\(307\) −1.20030e16 −0.818261 −0.409131 0.912476i \(-0.634168\pi\)
−0.409131 + 0.912476i \(0.634168\pi\)
\(308\) −7.64890e16 −5.10528
\(309\) 4.85291e16 3.17155
\(310\) −2.73537e14 −0.0175051
\(311\) 6.73209e15 0.421898 0.210949 0.977497i \(-0.432345\pi\)
0.210949 + 0.977497i \(0.432345\pi\)
\(312\) −5.83924e16 −3.58386
\(313\) 2.20435e16 1.32508 0.662541 0.749025i \(-0.269478\pi\)
0.662541 + 0.749025i \(0.269478\pi\)
\(314\) 4.66671e16 2.74769
\(315\) −2.61347e16 −1.50730
\(316\) 2.66763e16 1.50716
\(317\) −2.09394e16 −1.15899 −0.579495 0.814976i \(-0.696750\pi\)
−0.579495 + 0.814976i \(0.696750\pi\)
\(318\) −4.13054e16 −2.23991
\(319\) −1.03079e16 −0.547687
\(320\) 7.75258e15 0.403619
\(321\) 1.64908e16 0.841315
\(322\) −3.40451e16 −1.70212
\(323\) −4.57384e15 −0.224112
\(324\) 1.94709e17 9.35069
\(325\) −1.97734e16 −0.930764
\(326\) 1.22252e16 0.564082
\(327\) 3.48666e16 1.57706
\(328\) 5.61841e16 2.49134
\(329\) 4.16610e16 1.81116
\(330\) −5.61082e16 −2.39159
\(331\) 8.50904e15 0.355630 0.177815 0.984064i \(-0.443097\pi\)
0.177815 + 0.984064i \(0.443097\pi\)
\(332\) −2.18507e15 −0.0895505
\(333\) 3.59789e15 0.144597
\(334\) −1.23464e16 −0.486617
\(335\) 4.69442e15 0.181464
\(336\) 6.56660e16 2.48963
\(337\) −2.12037e16 −0.788528 −0.394264 0.918997i \(-0.629001\pi\)
−0.394264 + 0.918997i \(0.629001\pi\)
\(338\) −7.80063e15 −0.284558
\(339\) −5.05841e16 −1.81016
\(340\) 3.86486e15 0.135682
\(341\) 1.49572e15 0.0515164
\(342\) −1.81547e17 −6.13506
\(343\) −4.27657e15 −0.141803
\(344\) 7.60147e16 2.47325
\(345\) −1.65638e16 −0.528853
\(346\) −8.35592e16 −2.61818
\(347\) −5.39081e16 −1.65773 −0.828863 0.559452i \(-0.811012\pi\)
−0.828863 + 0.559452i \(0.811012\pi\)
\(348\) 3.77397e16 1.13903
\(349\) 2.21791e16 0.657020 0.328510 0.944500i \(-0.393454\pi\)
0.328510 + 0.944500i \(0.393454\pi\)
\(350\) 7.03850e16 2.04662
\(351\) 1.46467e17 4.18064
\(352\) −6.93913e15 −0.194436
\(353\) 1.65766e16 0.455995 0.227998 0.973662i \(-0.426782\pi\)
0.227998 + 0.973662i \(0.426782\pi\)
\(354\) −1.89932e17 −5.12953
\(355\) 1.22643e16 0.325205
\(356\) −4.16984e15 −0.108566
\(357\) −1.98743e16 −0.508100
\(358\) 4.36981e16 1.09704
\(359\) 6.16736e16 1.52050 0.760248 0.649633i \(-0.225077\pi\)
0.760248 + 0.649633i \(0.225077\pi\)
\(360\) 7.55173e16 1.82844
\(361\) 1.92374e16 0.457457
\(362\) −8.01780e16 −1.87262
\(363\) 2.20179e17 5.05107
\(364\) 1.29943e17 2.92816
\(365\) −2.86435e16 −0.634048
\(366\) −4.24742e16 −0.923630
\(367\) 3.90178e16 0.833554 0.416777 0.909009i \(-0.363160\pi\)
0.416777 + 0.909009i \(0.363160\pi\)
\(368\) 3.10792e16 0.652318
\(369\) −2.13235e17 −4.39732
\(370\) 1.54749e15 0.0313557
\(371\) 4.52491e16 0.900906
\(372\) −5.47616e15 −0.107139
\(373\) 5.39763e16 1.03776 0.518879 0.854848i \(-0.326350\pi\)
0.518879 + 0.854848i \(0.326350\pi\)
\(374\) −3.18632e16 −0.602038
\(375\) 7.39569e16 1.37333
\(376\) −1.20381e17 −2.19704
\(377\) 1.75116e16 0.314129
\(378\) −5.21360e17 −9.19265
\(379\) −1.78707e16 −0.309732 −0.154866 0.987935i \(-0.549495\pi\)
−0.154866 + 0.987935i \(0.549495\pi\)
\(380\) −5.17899e16 −0.882372
\(381\) 1.26361e17 2.11641
\(382\) 1.56170e17 2.57150
\(383\) 5.22730e16 0.846224 0.423112 0.906077i \(-0.360938\pi\)
0.423112 + 0.906077i \(0.360938\pi\)
\(384\) 2.21108e17 3.51926
\(385\) 6.14653e16 0.961912
\(386\) 7.64668e16 1.17667
\(387\) −2.88498e17 −4.36538
\(388\) 2.03928e17 3.03438
\(389\) 8.13700e16 1.19067 0.595336 0.803477i \(-0.297019\pi\)
0.595336 + 0.803477i \(0.297019\pi\)
\(390\) 9.53195e16 1.37171
\(391\) −9.40637e15 −0.133129
\(392\) −1.07670e17 −1.49877
\(393\) −1.18124e17 −1.61729
\(394\) −9.11671e15 −0.122776
\(395\) −2.14366e16 −0.283972
\(396\) −8.38830e17 −10.9309
\(397\) −2.21999e16 −0.284586 −0.142293 0.989825i \(-0.545447\pi\)
−0.142293 + 0.989825i \(0.545447\pi\)
\(398\) 9.06547e16 1.14327
\(399\) 2.66320e17 3.30431
\(400\) −6.42533e16 −0.784342
\(401\) 3.18496e15 0.0382530 0.0191265 0.999817i \(-0.493911\pi\)
0.0191265 + 0.999817i \(0.493911\pi\)
\(402\) 1.41698e17 1.67454
\(403\) −2.54100e15 −0.0295475
\(404\) −1.94890e17 −2.23003
\(405\) −1.56465e17 −1.76181
\(406\) −6.23340e16 −0.690726
\(407\) −8.46176e15 −0.0922778
\(408\) 5.74278e16 0.616355
\(409\) 4.57706e16 0.483487 0.241744 0.970340i \(-0.422281\pi\)
0.241744 + 0.970340i \(0.422281\pi\)
\(410\) −9.17146e16 −0.953550
\(411\) −1.80613e17 −1.84832
\(412\) 3.12054e17 3.14338
\(413\) 2.08067e17 2.06313
\(414\) −3.73361e17 −3.64441
\(415\) 1.75589e15 0.0168727
\(416\) 1.17885e16 0.111520
\(417\) −3.04393e17 −2.83498
\(418\) 4.26974e17 3.91521
\(419\) 5.97703e15 0.0539628 0.0269814 0.999636i \(-0.491411\pi\)
0.0269814 + 0.999636i \(0.491411\pi\)
\(420\) −2.25039e17 −2.00049
\(421\) 1.74495e17 1.52739 0.763695 0.645577i \(-0.223383\pi\)
0.763695 + 0.645577i \(0.223383\pi\)
\(422\) −7.67952e16 −0.661917
\(423\) 4.56883e17 3.87786
\(424\) −1.30749e17 −1.09285
\(425\) 1.94468e16 0.160073
\(426\) 3.70190e17 3.00097
\(427\) 4.65295e16 0.371490
\(428\) 1.06040e17 0.833843
\(429\) −5.21212e17 −4.03685
\(430\) −1.24086e17 −0.946625
\(431\) −6.38154e16 −0.479538 −0.239769 0.970830i \(-0.577072\pi\)
−0.239769 + 0.970830i \(0.577072\pi\)
\(432\) 4.75941e17 3.52297
\(433\) −2.60358e17 −1.89845 −0.949226 0.314595i \(-0.898131\pi\)
−0.949226 + 0.314595i \(0.898131\pi\)
\(434\) 9.04487e15 0.0649709
\(435\) −3.03270e16 −0.214610
\(436\) 2.24201e17 1.56306
\(437\) 1.26047e17 0.865773
\(438\) −8.64587e17 −5.85096
\(439\) −5.47246e16 −0.364891 −0.182446 0.983216i \(-0.558401\pi\)
−0.182446 + 0.983216i \(0.558401\pi\)
\(440\) −1.77607e17 −1.16685
\(441\) 4.08639e17 2.64539
\(442\) 5.41308e16 0.345303
\(443\) −9.11386e15 −0.0572899 −0.0286450 0.999590i \(-0.509119\pi\)
−0.0286450 + 0.999590i \(0.509119\pi\)
\(444\) 3.09804e16 0.191910
\(445\) 3.35082e15 0.0204555
\(446\) 2.11766e17 1.27403
\(447\) 2.22678e17 1.32032
\(448\) −2.56349e17 −1.49805
\(449\) −3.97393e16 −0.228886 −0.114443 0.993430i \(-0.536508\pi\)
−0.114443 + 0.993430i \(0.536508\pi\)
\(450\) 7.71889e17 4.38201
\(451\) 5.01501e17 2.80624
\(452\) −3.25268e17 −1.79408
\(453\) 2.90379e17 1.57880
\(454\) 2.72541e17 1.46072
\(455\) −1.04420e17 −0.551710
\(456\) −7.69544e17 −4.00832
\(457\) −2.70719e17 −1.39016 −0.695078 0.718935i \(-0.744630\pi\)
−0.695078 + 0.718935i \(0.744630\pi\)
\(458\) −1.13235e17 −0.573263
\(459\) −1.44047e17 −0.718989
\(460\) −1.06509e17 −0.524156
\(461\) 3.70630e17 1.79839 0.899197 0.437545i \(-0.144152\pi\)
0.899197 + 0.437545i \(0.144152\pi\)
\(462\) 1.85529e18 8.87646
\(463\) 2.17407e17 1.02565 0.512823 0.858494i \(-0.328600\pi\)
0.512823 + 0.858494i \(0.328600\pi\)
\(464\) 5.69037e16 0.264712
\(465\) 4.40055e15 0.0201866
\(466\) 3.75893e17 1.70042
\(467\) 1.82256e17 0.813058 0.406529 0.913638i \(-0.366739\pi\)
0.406529 + 0.913638i \(0.366739\pi\)
\(468\) 1.42505e18 6.26948
\(469\) −1.55227e17 −0.673511
\(470\) 1.96510e17 0.840908
\(471\) −7.50761e17 −3.16859
\(472\) −6.01217e17 −2.50270
\(473\) 6.78510e17 2.78586
\(474\) −6.47052e17 −2.62047
\(475\) −2.60591e17 −1.04100
\(476\) −1.27797e17 −0.503587
\(477\) 4.96232e17 1.92893
\(478\) −2.24085e17 −0.859275
\(479\) 1.08405e17 0.410080 0.205040 0.978754i \(-0.434268\pi\)
0.205040 + 0.978754i \(0.434268\pi\)
\(480\) −2.04156e16 −0.0761895
\(481\) 1.43753e16 0.0529264
\(482\) 3.21289e17 1.16705
\(483\) 5.47703e17 1.96286
\(484\) 1.41581e18 5.00621
\(485\) −1.63873e17 −0.571724
\(486\) −2.78399e18 −9.58366
\(487\) −1.41298e17 −0.479951 −0.239976 0.970779i \(-0.577139\pi\)
−0.239976 + 0.970779i \(0.577139\pi\)
\(488\) −1.34449e17 −0.450639
\(489\) −1.96674e17 −0.650489
\(490\) 1.75760e17 0.573648
\(491\) −2.70485e17 −0.871191 −0.435595 0.900143i \(-0.643462\pi\)
−0.435595 + 0.900143i \(0.643462\pi\)
\(492\) −1.83611e18 −5.83614
\(493\) −1.72224e16 −0.0540241
\(494\) −7.25364e17 −2.24559
\(495\) 6.74070e17 2.05955
\(496\) −8.25692e15 −0.0248993
\(497\) −4.05534e17 −1.20701
\(498\) 5.30004e16 0.155700
\(499\) 3.23433e17 0.937844 0.468922 0.883240i \(-0.344643\pi\)
0.468922 + 0.883240i \(0.344643\pi\)
\(500\) 4.75561e17 1.36113
\(501\) 1.98623e17 0.561158
\(502\) −4.46561e17 −1.24539
\(503\) −9.51693e16 −0.262002 −0.131001 0.991382i \(-0.541819\pi\)
−0.131001 + 0.991382i \(0.541819\pi\)
\(504\) −2.49708e18 −6.78632
\(505\) 1.56610e17 0.420171
\(506\) 8.78096e17 2.32575
\(507\) 1.25493e17 0.328147
\(508\) 8.12529e17 2.09761
\(509\) 6.94544e17 1.77025 0.885124 0.465355i \(-0.154073\pi\)
0.885124 + 0.465355i \(0.154073\pi\)
\(510\) −9.37449e16 −0.235907
\(511\) 9.47135e17 2.35329
\(512\) 6.57788e17 1.61373
\(513\) 1.93026e18 4.67577
\(514\) −1.84976e17 −0.442441
\(515\) −2.50761e17 −0.592261
\(516\) −2.48418e18 −5.79375
\(517\) −1.07453e18 −2.47473
\(518\) −5.11698e16 −0.116378
\(519\) 1.34426e18 3.01924
\(520\) 3.01727e17 0.669256
\(521\) −7.54275e17 −1.65228 −0.826142 0.563463i \(-0.809469\pi\)
−0.826142 + 0.563463i \(0.809469\pi\)
\(522\) −6.83597e17 −1.47891
\(523\) 5.73990e17 1.22643 0.613216 0.789915i \(-0.289875\pi\)
0.613216 + 0.789915i \(0.289875\pi\)
\(524\) −7.59567e17 −1.60292
\(525\) −1.13232e18 −2.36013
\(526\) −4.00125e17 −0.823736
\(527\) 2.49902e15 0.00508161
\(528\) −1.69367e18 −3.40179
\(529\) −2.44813e17 −0.485705
\(530\) 2.13435e17 0.418284
\(531\) 2.28180e18 4.41736
\(532\) 1.71250e18 3.27496
\(533\) −8.51975e17 −1.60953
\(534\) 1.01142e17 0.188762
\(535\) −8.52117e16 −0.157109
\(536\) 4.48536e17 0.817008
\(537\) −7.02996e17 −1.26509
\(538\) −4.08805e16 −0.0726828
\(539\) −9.61065e17 −1.68821
\(540\) −1.63106e18 −2.83080
\(541\) 1.64531e17 0.282141 0.141071 0.990000i \(-0.454946\pi\)
0.141071 + 0.990000i \(0.454946\pi\)
\(542\) −1.92572e18 −3.26286
\(543\) 1.28987e18 2.15947
\(544\) −1.15938e16 −0.0191793
\(545\) −1.80164e17 −0.294503
\(546\) −3.15187e18 −5.09115
\(547\) −1.13121e18 −1.80562 −0.902810 0.430040i \(-0.858500\pi\)
−0.902810 + 0.430040i \(0.858500\pi\)
\(548\) −1.16139e18 −1.83191
\(549\) 5.10274e17 0.795396
\(550\) −1.81538e18 −2.79647
\(551\) 2.30783e17 0.351333
\(552\) −1.58261e18 −2.38106
\(553\) 7.08831e17 1.05397
\(554\) −6.18630e17 −0.909112
\(555\) −2.48954e16 −0.0361588
\(556\) −1.95732e18 −2.80980
\(557\) 5.20463e17 0.738467 0.369233 0.929337i \(-0.379620\pi\)
0.369233 + 0.929337i \(0.379620\pi\)
\(558\) 9.91922e16 0.139109
\(559\) −1.15269e18 −1.59784
\(560\) −3.39312e17 −0.464918
\(561\) 5.12602e17 0.694260
\(562\) 1.27684e17 0.170943
\(563\) 4.15047e17 0.549278 0.274639 0.961547i \(-0.411442\pi\)
0.274639 + 0.961547i \(0.411442\pi\)
\(564\) 3.93409e18 5.14671
\(565\) 2.61380e17 0.338032
\(566\) −1.33135e18 −1.70210
\(567\) 5.17373e18 6.53903
\(568\) 1.17181e18 1.46417
\(569\) 7.54991e17 0.932636 0.466318 0.884617i \(-0.345580\pi\)
0.466318 + 0.884617i \(0.345580\pi\)
\(570\) 1.25620e18 1.53417
\(571\) −4.09580e17 −0.494544 −0.247272 0.968946i \(-0.579534\pi\)
−0.247272 + 0.968946i \(0.579534\pi\)
\(572\) −3.35152e18 −4.00099
\(573\) −2.51241e18 −2.96541
\(574\) 3.03267e18 3.53914
\(575\) −5.35920e17 −0.618385
\(576\) −2.81130e18 −3.20746
\(577\) −2.64267e17 −0.298126 −0.149063 0.988828i \(-0.547626\pi\)
−0.149063 + 0.988828i \(0.547626\pi\)
\(578\) 1.49158e18 1.66386
\(579\) −1.23017e18 −1.35692
\(580\) −1.95010e17 −0.212704
\(581\) −5.80608e16 −0.0626236
\(582\) −4.94641e18 −5.27583
\(583\) −1.16707e18 −1.23098
\(584\) −2.73679e18 −2.85468
\(585\) −1.14514e18 −1.18126
\(586\) 3.32316e17 0.339013
\(587\) 3.22129e17 0.324999 0.162500 0.986709i \(-0.448044\pi\)
0.162500 + 0.986709i \(0.448044\pi\)
\(588\) 3.51868e18 3.51097
\(589\) −3.34874e16 −0.0330470
\(590\) 9.81425e17 0.957898
\(591\) 1.46666e17 0.141583
\(592\) 4.67121e16 0.0446004
\(593\) −2.59941e15 −0.00245482 −0.00122741 0.999999i \(-0.500391\pi\)
−0.00122741 + 0.999999i \(0.500391\pi\)
\(594\) 1.34470e19 12.5607
\(595\) 1.02695e17 0.0948835
\(596\) 1.43187e18 1.30859
\(597\) −1.45842e18 −1.31840
\(598\) −1.49175e18 −1.33395
\(599\) −7.33415e17 −0.648747 −0.324373 0.945929i \(-0.605153\pi\)
−0.324373 + 0.945929i \(0.605153\pi\)
\(600\) 3.27190e18 2.86297
\(601\) −1.30126e18 −1.12637 −0.563184 0.826331i \(-0.690424\pi\)
−0.563184 + 0.826331i \(0.690424\pi\)
\(602\) 4.10307e18 3.51344
\(603\) −1.70233e18 −1.44205
\(604\) 1.86721e18 1.56478
\(605\) −1.13772e18 −0.943245
\(606\) 4.72719e18 3.87731
\(607\) 1.97868e18 1.60564 0.802820 0.596222i \(-0.203332\pi\)
0.802820 + 0.596222i \(0.203332\pi\)
\(608\) 1.55359e17 0.124728
\(609\) 1.00280e18 0.796532
\(610\) 2.19474e17 0.172480
\(611\) 1.82546e18 1.41940
\(612\) −1.40151e18 −1.07823
\(613\) −2.65013e17 −0.201732 −0.100866 0.994900i \(-0.532161\pi\)
−0.100866 + 0.994900i \(0.532161\pi\)
\(614\) 1.87211e18 1.41006
\(615\) 1.47547e18 1.09962
\(616\) 5.87280e18 4.33083
\(617\) 7.81798e17 0.570481 0.285241 0.958456i \(-0.407927\pi\)
0.285241 + 0.958456i \(0.407927\pi\)
\(618\) −7.56908e18 −5.46535
\(619\) −1.63363e18 −1.16725 −0.583625 0.812023i \(-0.698366\pi\)
−0.583625 + 0.812023i \(0.698366\pi\)
\(620\) 2.82966e16 0.0200073
\(621\) 3.96970e18 2.77755
\(622\) −1.05000e18 −0.727032
\(623\) −1.10799e17 −0.0759215
\(624\) 2.87729e18 1.95112
\(625\) 9.02757e17 0.605830
\(626\) −3.43813e18 −2.28344
\(627\) −6.86897e18 −4.51495
\(628\) −4.82758e18 −3.14045
\(629\) −1.41378e16 −0.00910233
\(630\) 4.07623e18 2.59744
\(631\) −1.12255e18 −0.707970 −0.353985 0.935251i \(-0.615174\pi\)
−0.353985 + 0.935251i \(0.615174\pi\)
\(632\) −2.04820e18 −1.27853
\(633\) 1.23545e18 0.763310
\(634\) 3.26592e18 1.99722
\(635\) −6.52935e17 −0.395222
\(636\) 4.27292e18 2.56008
\(637\) 1.63271e18 0.968281
\(638\) 1.60773e18 0.943796
\(639\) −4.44736e18 −2.58433
\(640\) −1.14252e18 −0.657192
\(641\) 6.57260e17 0.374248 0.187124 0.982336i \(-0.440083\pi\)
0.187124 + 0.982336i \(0.440083\pi\)
\(642\) −2.57207e18 −1.44979
\(643\) −1.71692e17 −0.0958029 −0.0479014 0.998852i \(-0.515253\pi\)
−0.0479014 + 0.998852i \(0.515253\pi\)
\(644\) 3.52186e18 1.94542
\(645\) 1.99625e18 1.09163
\(646\) 7.13382e17 0.386199
\(647\) −3.32550e18 −1.78229 −0.891146 0.453717i \(-0.850098\pi\)
−0.891146 + 0.453717i \(0.850098\pi\)
\(648\) −1.49497e19 −7.93223
\(649\) −5.36649e18 −2.81903
\(650\) 3.08406e18 1.60393
\(651\) −1.45510e17 −0.0749233
\(652\) −1.26466e18 −0.644712
\(653\) −1.08906e18 −0.549687 −0.274844 0.961489i \(-0.588626\pi\)
−0.274844 + 0.961489i \(0.588626\pi\)
\(654\) −5.43814e18 −2.71766
\(655\) 6.10375e17 0.302015
\(656\) −2.76847e18 −1.35633
\(657\) 1.03869e19 5.03863
\(658\) −6.49786e18 −3.12106
\(659\) −1.12429e18 −0.534717 −0.267359 0.963597i \(-0.586151\pi\)
−0.267359 + 0.963597i \(0.586151\pi\)
\(660\) 5.80423e18 2.73344
\(661\) 2.44785e18 1.14150 0.570748 0.821125i \(-0.306653\pi\)
0.570748 + 0.821125i \(0.306653\pi\)
\(662\) −1.32715e18 −0.612836
\(663\) −8.70834e17 −0.398197
\(664\) 1.67769e17 0.0759660
\(665\) −1.37614e18 −0.617052
\(666\) −5.61163e17 −0.249176
\(667\) 4.74619e17 0.208702
\(668\) 1.27720e18 0.556174
\(669\) −3.40680e18 −1.46919
\(670\) −7.32189e17 −0.312707
\(671\) −1.20010e18 −0.507598
\(672\) 6.75070e17 0.282780
\(673\) −2.91529e17 −0.120944 −0.0604719 0.998170i \(-0.519261\pi\)
−0.0604719 + 0.998170i \(0.519261\pi\)
\(674\) 3.30714e18 1.35882
\(675\) −8.20697e18 −3.33971
\(676\) 8.06952e17 0.325233
\(677\) −2.22878e18 −0.889696 −0.444848 0.895606i \(-0.646742\pi\)
−0.444848 + 0.895606i \(0.646742\pi\)
\(678\) 7.88960e18 3.11934
\(679\) 5.41868e18 2.12197
\(680\) −2.96743e17 −0.115099
\(681\) −4.38452e18 −1.68448
\(682\) −2.33287e17 −0.0887752
\(683\) −2.24637e18 −0.846732 −0.423366 0.905959i \(-0.639152\pi\)
−0.423366 + 0.905959i \(0.639152\pi\)
\(684\) 1.87805e19 7.01200
\(685\) 9.33272e17 0.345159
\(686\) 6.67017e17 0.244360
\(687\) 1.82167e18 0.661076
\(688\) −3.74563e18 −1.34648
\(689\) 1.98268e18 0.706038
\(690\) 2.58345e18 0.911341
\(691\) 5.41506e17 0.189233 0.0946163 0.995514i \(-0.469838\pi\)
0.0946163 + 0.995514i \(0.469838\pi\)
\(692\) 8.64395e18 2.99242
\(693\) −2.22890e19 −7.64408
\(694\) 8.40805e18 2.85666
\(695\) 1.57287e18 0.529409
\(696\) −2.89764e18 −0.966240
\(697\) 8.37901e17 0.276809
\(698\) −3.45927e18 −1.13220
\(699\) −6.04721e18 −1.96089
\(700\) −7.28112e18 −2.33916
\(701\) 5.35148e17 0.170336 0.0851681 0.996367i \(-0.472857\pi\)
0.0851681 + 0.996367i \(0.472857\pi\)
\(702\) −2.28444e19 −7.20425
\(703\) 1.89449e17 0.0591948
\(704\) 6.61181e18 2.04691
\(705\) −3.16137e18 −0.969719
\(706\) −2.58545e18 −0.785789
\(707\) −5.17853e18 −1.55948
\(708\) 1.96479e19 5.86274
\(709\) 6.13908e18 1.81511 0.907555 0.419933i \(-0.137946\pi\)
0.907555 + 0.419933i \(0.137946\pi\)
\(710\) −1.91286e18 −0.560407
\(711\) 7.77352e18 2.25666
\(712\) 3.20159e17 0.0920971
\(713\) −6.88688e16 −0.0196309
\(714\) 3.09980e18 0.875579
\(715\) 2.69323e18 0.753847
\(716\) −4.52044e18 −1.25385
\(717\) 3.60499e18 0.990900
\(718\) −9.61923e18 −2.62018
\(719\) 5.94931e18 1.60594 0.802969 0.596021i \(-0.203253\pi\)
0.802969 + 0.596021i \(0.203253\pi\)
\(720\) −3.72112e18 −0.995435
\(721\) 8.29176e18 2.19820
\(722\) −3.00046e18 −0.788308
\(723\) −5.16876e18 −1.34582
\(724\) 8.29417e18 2.14029
\(725\) −9.81229e17 −0.250942
\(726\) −3.43414e19 −8.70421
\(727\) 1.70242e18 0.427654 0.213827 0.976871i \(-0.431407\pi\)
0.213827 + 0.976871i \(0.431407\pi\)
\(728\) −9.97701e18 −2.48397
\(729\) 2.55477e19 6.30409
\(730\) 4.46752e18 1.09262
\(731\) 1.13364e18 0.274798
\(732\) 4.39383e18 1.05565
\(733\) −2.77760e18 −0.661445 −0.330722 0.943728i \(-0.607292\pi\)
−0.330722 + 0.943728i \(0.607292\pi\)
\(734\) −6.08561e18 −1.43641
\(735\) −2.82755e18 −0.661520
\(736\) 3.19505e17 0.0740922
\(737\) 4.00365e18 0.920275
\(738\) 3.32583e19 7.57763
\(739\) −1.72660e17 −0.0389945 −0.0194972 0.999810i \(-0.506207\pi\)
−0.0194972 + 0.999810i \(0.506207\pi\)
\(740\) −1.60083e17 −0.0358377
\(741\) 1.16694e19 2.58958
\(742\) −7.05750e18 −1.55248
\(743\) −2.60998e18 −0.569127 −0.284564 0.958657i \(-0.591849\pi\)
−0.284564 + 0.958657i \(0.591849\pi\)
\(744\) 4.20458e17 0.0908863
\(745\) −1.15063e18 −0.246558
\(746\) −8.41869e18 −1.78831
\(747\) −6.36734e17 −0.134083
\(748\) 3.29616e18 0.688093
\(749\) 2.81764e18 0.583114
\(750\) −1.15351e19 −2.36658
\(751\) 6.40691e17 0.130313 0.0651567 0.997875i \(-0.479245\pi\)
0.0651567 + 0.997875i \(0.479245\pi\)
\(752\) 5.93180e18 1.19611
\(753\) 7.18408e18 1.43616
\(754\) −2.73129e18 −0.541320
\(755\) −1.50046e18 −0.294828
\(756\) 5.39331e19 10.5066
\(757\) −1.11215e18 −0.214804 −0.107402 0.994216i \(-0.534253\pi\)
−0.107402 + 0.994216i \(0.534253\pi\)
\(758\) 2.78729e18 0.533743
\(759\) −1.41264e19 −2.68202
\(760\) 3.97641e18 0.748520
\(761\) 2.07797e18 0.387829 0.193914 0.981018i \(-0.437882\pi\)
0.193914 + 0.981018i \(0.437882\pi\)
\(762\) −1.97085e19 −3.64708
\(763\) 5.95736e18 1.09306
\(764\) −1.61554e19 −2.93907
\(765\) 1.12623e18 0.203155
\(766\) −8.15302e18 −1.45825
\(767\) 9.11686e18 1.61687
\(768\) −2.21955e19 −3.90316
\(769\) 5.93573e18 1.03503 0.517515 0.855674i \(-0.326857\pi\)
0.517515 + 0.855674i \(0.326857\pi\)
\(770\) −9.58674e18 −1.65761
\(771\) 2.97582e18 0.510214
\(772\) −7.91026e18 −1.34486
\(773\) 1.57618e18 0.265729 0.132865 0.991134i \(-0.457582\pi\)
0.132865 + 0.991134i \(0.457582\pi\)
\(774\) 4.49971e19 7.52260
\(775\) 1.42380e17 0.0236041
\(776\) −1.56575e19 −2.57408
\(777\) 8.23199e17 0.134205
\(778\) −1.26913e19 −2.05181
\(779\) −1.12280e19 −1.80016
\(780\) −9.86052e18 −1.56778
\(781\) 1.04596e19 1.64924
\(782\) 1.46711e18 0.229414
\(783\) 7.26822e18 1.12714
\(784\) 5.30545e18 0.815957
\(785\) 3.87936e18 0.591708
\(786\) 1.84238e19 2.78697
\(787\) −1.59516e18 −0.239314 −0.119657 0.992815i \(-0.538179\pi\)
−0.119657 + 0.992815i \(0.538179\pi\)
\(788\) 9.43097e17 0.140325
\(789\) 6.43704e18 0.949916
\(790\) 3.34347e18 0.489352
\(791\) −8.64288e18 −1.25462
\(792\) 6.44051e19 9.27271
\(793\) 2.03878e18 0.291136
\(794\) 3.46252e18 0.490410
\(795\) −3.43365e18 −0.482358
\(796\) −9.37796e18 −1.30669
\(797\) 7.08181e18 0.978735 0.489368 0.872078i \(-0.337228\pi\)
0.489368 + 0.872078i \(0.337228\pi\)
\(798\) −4.15380e19 −5.69412
\(799\) −1.79530e18 −0.244109
\(800\) −6.60547e17 −0.0890880
\(801\) −1.21510e18 −0.162555
\(802\) −4.96758e17 −0.0659191
\(803\) −2.44287e19 −3.21550
\(804\) −1.46583e19 −1.91390
\(805\) −2.83011e18 −0.366547
\(806\) 3.96319e17 0.0509175
\(807\) 6.57669e17 0.0838164
\(808\) 1.49636e19 1.89174
\(809\) −9.56351e18 −1.19937 −0.599684 0.800237i \(-0.704707\pi\)
−0.599684 + 0.800237i \(0.704707\pi\)
\(810\) 2.44038e19 3.03603
\(811\) −6.66298e17 −0.0822304 −0.0411152 0.999154i \(-0.513091\pi\)
−0.0411152 + 0.999154i \(0.513091\pi\)
\(812\) 6.44826e18 0.789457
\(813\) 3.09802e19 3.76267
\(814\) 1.31978e18 0.159017
\(815\) 1.01626e18 0.121473
\(816\) −2.82976e18 −0.335555
\(817\) −1.51911e19 −1.78708
\(818\) −7.13884e18 −0.833165
\(819\) 3.78657e19 4.38431
\(820\) 9.48761e18 1.08985
\(821\) −8.62414e18 −0.982845 −0.491423 0.870921i \(-0.663523\pi\)
−0.491423 + 0.870921i \(0.663523\pi\)
\(822\) 2.81703e19 3.18511
\(823\) 5.17351e18 0.580345 0.290173 0.956974i \(-0.406287\pi\)
0.290173 + 0.956974i \(0.406287\pi\)
\(824\) −2.39594e19 −2.66655
\(825\) 2.92051e19 3.22484
\(826\) −3.24521e19 −3.55527
\(827\) −1.51864e19 −1.65070 −0.825351 0.564620i \(-0.809023\pi\)
−0.825351 + 0.564620i \(0.809023\pi\)
\(828\) 3.86231e19 4.16534
\(829\) −6.55630e18 −0.701543 −0.350772 0.936461i \(-0.614081\pi\)
−0.350772 + 0.936461i \(0.614081\pi\)
\(830\) −2.73866e17 −0.0290757
\(831\) 9.95226e18 1.04837
\(832\) −1.12325e19 −1.17401
\(833\) −1.60573e18 −0.166526
\(834\) 4.74761e19 4.88535
\(835\) −1.02633e18 −0.104792
\(836\) −4.41692e19 −4.47485
\(837\) −1.05464e18 −0.106021
\(838\) −9.32237e17 −0.0929909
\(839\) −9.08342e17 −0.0899076 −0.0449538 0.998989i \(-0.514314\pi\)
−0.0449538 + 0.998989i \(0.514314\pi\)
\(840\) 1.72784e19 1.69702
\(841\) −9.39164e18 −0.915308
\(842\) −2.72160e19 −2.63206
\(843\) −2.05413e18 −0.197128
\(844\) 7.94424e18 0.756530
\(845\) −6.48453e17 −0.0612788
\(846\) −7.12600e19 −6.68249
\(847\) 3.76202e19 3.50089
\(848\) 6.44268e18 0.594968
\(849\) 2.14181e19 1.96283
\(850\) −3.03311e18 −0.275845
\(851\) 3.89613e17 0.0351635
\(852\) −3.82950e19 −3.42993
\(853\) 8.27209e18 0.735270 0.367635 0.929970i \(-0.380168\pi\)
0.367635 + 0.929970i \(0.380168\pi\)
\(854\) −7.25721e18 −0.640167
\(855\) −1.50917e19 −1.32117
\(856\) −8.14170e18 −0.707352
\(857\) −3.68435e18 −0.317677 −0.158838 0.987305i \(-0.550775\pi\)
−0.158838 + 0.987305i \(0.550775\pi\)
\(858\) 8.12935e19 6.95646
\(859\) 2.27542e19 1.93244 0.966219 0.257724i \(-0.0829725\pi\)
0.966219 + 0.257724i \(0.0829725\pi\)
\(860\) 1.28363e19 1.08194
\(861\) −4.87883e19 −4.08127
\(862\) 9.95328e18 0.826360
\(863\) 4.98035e18 0.410384 0.205192 0.978722i \(-0.434218\pi\)
0.205192 + 0.978722i \(0.434218\pi\)
\(864\) 4.89284e18 0.400149
\(865\) −6.94613e18 −0.563817
\(866\) 4.06080e19 3.27149
\(867\) −2.39959e19 −1.91873
\(868\) −9.35665e17 −0.0742578
\(869\) −1.82823e19 −1.44013
\(870\) 4.73010e18 0.369824
\(871\) −6.80160e18 −0.527829
\(872\) −1.72141e19 −1.32595
\(873\) 5.94250e19 4.54335
\(874\) −1.96596e19 −1.49194
\(875\) 1.26364e19 0.951855
\(876\) 8.94389e19 6.68729
\(877\) −1.48476e19 −1.10194 −0.550970 0.834525i \(-0.685742\pi\)
−0.550970 + 0.834525i \(0.685742\pi\)
\(878\) 8.53539e18 0.628795
\(879\) −5.34616e18 −0.390944
\(880\) 8.75158e18 0.635257
\(881\) 7.50276e18 0.540602 0.270301 0.962776i \(-0.412877\pi\)
0.270301 + 0.962776i \(0.412877\pi\)
\(882\) −6.37355e19 −4.55864
\(883\) 5.81660e18 0.412976 0.206488 0.978449i \(-0.433797\pi\)
0.206488 + 0.978449i \(0.433797\pi\)
\(884\) −5.59967e18 −0.394660
\(885\) −1.57888e19 −1.10463
\(886\) 1.42149e18 0.0987243
\(887\) 2.13508e18 0.147201 0.0736006 0.997288i \(-0.476551\pi\)
0.0736006 + 0.997288i \(0.476551\pi\)
\(888\) −2.37867e18 −0.162798
\(889\) 2.15902e19 1.46688
\(890\) −5.22627e17 −0.0352498
\(891\) −1.33442e20 −8.93483
\(892\) −2.19066e19 −1.45614
\(893\) 2.40574e19 1.58750
\(894\) −3.47311e19 −2.27523
\(895\) 3.63255e18 0.236244
\(896\) 3.77788e19 2.43919
\(897\) 2.39987e19 1.53829
\(898\) 6.19814e18 0.394425
\(899\) −1.26094e17 −0.00796627
\(900\) −7.98496e19 −5.00837
\(901\) −1.94993e18 −0.121425
\(902\) −7.82191e19 −4.83582
\(903\) −6.60085e19 −4.05163
\(904\) 2.49740e19 1.52192
\(905\) −6.66506e18 −0.403263
\(906\) −4.52904e19 −2.72065
\(907\) 2.34252e19 1.39713 0.698564 0.715548i \(-0.253823\pi\)
0.698564 + 0.715548i \(0.253823\pi\)
\(908\) −2.81935e19 −1.66952
\(909\) −5.67912e19 −3.33900
\(910\) 1.62864e19 0.950729
\(911\) −1.13703e18 −0.0659028 −0.0329514 0.999457i \(-0.510491\pi\)
−0.0329514 + 0.999457i \(0.510491\pi\)
\(912\) 3.79193e19 2.18220
\(913\) 1.49751e18 0.0855678
\(914\) 4.22240e19 2.39557
\(915\) −3.53081e18 −0.198901
\(916\) 1.17138e19 0.655205
\(917\) −2.01829e19 −1.12094
\(918\) 2.24670e19 1.23899
\(919\) −2.69929e18 −0.147808 −0.0739041 0.997265i \(-0.523546\pi\)
−0.0739041 + 0.997265i \(0.523546\pi\)
\(920\) 8.17773e18 0.444643
\(921\) −3.01178e19 −1.62606
\(922\) −5.78072e19 −3.09906
\(923\) −1.77693e19 −0.945931
\(924\) −1.91925e20 −10.1453
\(925\) −8.05489e17 −0.0422803
\(926\) −3.39090e19 −1.76744
\(927\) 9.09330e19 4.70656
\(928\) 5.84991e17 0.0300668
\(929\) 3.67718e19 1.87678 0.938390 0.345579i \(-0.112317\pi\)
0.938390 + 0.345579i \(0.112317\pi\)
\(930\) −6.86354e17 −0.0347863
\(931\) 2.15172e19 1.08296
\(932\) −3.88850e19 −1.94348
\(933\) 1.68920e19 0.838399
\(934\) −2.84264e19 −1.40110
\(935\) −2.64874e18 −0.129647
\(936\) −1.09415e20 −5.31842
\(937\) 1.61659e19 0.780356 0.390178 0.920739i \(-0.372413\pi\)
0.390178 + 0.920739i \(0.372413\pi\)
\(938\) 2.42108e19 1.16062
\(939\) 5.53112e19 2.63322
\(940\) −2.03284e19 −0.961106
\(941\) 2.89880e19 1.36109 0.680544 0.732707i \(-0.261744\pi\)
0.680544 + 0.732707i \(0.261744\pi\)
\(942\) 1.17096e20 5.46024
\(943\) −2.30911e19 −1.06935
\(944\) 2.96250e19 1.36251
\(945\) −4.33397e19 −1.97961
\(946\) −1.05827e20 −4.80070
\(947\) 4.32869e19 1.95021 0.975106 0.221741i \(-0.0711741\pi\)
0.975106 + 0.221741i \(0.0711741\pi\)
\(948\) 6.69356e19 2.99504
\(949\) 4.15006e19 1.84427
\(950\) 4.06443e19 1.79389
\(951\) −5.25408e19 −2.30316
\(952\) 9.81220e18 0.427195
\(953\) 1.12843e19 0.487944 0.243972 0.969782i \(-0.421549\pi\)
0.243972 + 0.969782i \(0.421549\pi\)
\(954\) −7.73974e19 −3.32401
\(955\) 1.29822e19 0.553766
\(956\) 2.31810e19 0.982099
\(957\) −2.58645e19 −1.08837
\(958\) −1.69079e19 −0.706667
\(959\) −3.08599e19 −1.28107
\(960\) 1.94526e19 0.802075
\(961\) −2.43992e19 −0.999251
\(962\) −2.24211e18 −0.0912050
\(963\) 3.09002e19 1.24850
\(964\) −3.32364e19 −1.33387
\(965\) 6.35656e18 0.253393
\(966\) −8.54252e19 −3.38248
\(967\) −2.87228e19 −1.12968 −0.564840 0.825201i \(-0.691062\pi\)
−0.564840 + 0.825201i \(0.691062\pi\)
\(968\) −1.08705e20 −4.24678
\(969\) −1.14766e19 −0.445357
\(970\) 2.55593e19 0.985218
\(971\) 2.53595e19 0.970991 0.485495 0.874239i \(-0.338639\pi\)
0.485495 + 0.874239i \(0.338639\pi\)
\(972\) 2.87995e20 10.9535
\(973\) −5.20090e19 −1.96492
\(974\) 2.20382e19 0.827072
\(975\) −4.96150e19 −1.84962
\(976\) 6.62499e18 0.245336
\(977\) 1.75793e19 0.646678 0.323339 0.946283i \(-0.395195\pi\)
0.323339 + 0.946283i \(0.395195\pi\)
\(978\) 3.06753e19 1.12095
\(979\) 2.85775e18 0.103738
\(980\) −1.81818e19 −0.655645
\(981\) 6.53324e19 2.34035
\(982\) 4.21875e19 1.50127
\(983\) −5.51691e18 −0.195029 −0.0975143 0.995234i \(-0.531089\pi\)
−0.0975143 + 0.995234i \(0.531089\pi\)
\(984\) 1.40976e20 4.95082
\(985\) −7.57857e17 −0.0264394
\(986\) 2.68617e18 0.0930965
\(987\) 1.04535e20 3.59915
\(988\) 7.50368e19 2.56658
\(989\) −3.12413e19 −1.06158
\(990\) −1.05135e20 −3.54909
\(991\) 3.31548e19 1.11190 0.555952 0.831214i \(-0.312354\pi\)
0.555952 + 0.831214i \(0.312354\pi\)
\(992\) −8.48841e16 −0.00282814
\(993\) 2.13507e19 0.706711
\(994\) 6.32512e19 2.07997
\(995\) 7.53597e18 0.246201
\(996\) −5.48274e18 −0.177956
\(997\) −4.04706e19 −1.30503 −0.652517 0.757775i \(-0.726287\pi\)
−0.652517 + 0.757775i \(0.726287\pi\)
\(998\) −5.04458e19 −1.61613
\(999\) 5.96646e18 0.189907
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 197.14.a.b.1.10 109
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.14.a.b.1.10 109 1.1 even 1 trivial