Properties

Label 197.10.a.b.1.8
Level $197$
Weight $10$
Character 197.1
Self dual yes
Analytic conductor $101.462$
Analytic rank $0$
Dimension $76$
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] = [197,10,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, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 10 \)
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: \(101.462059724\)
Analytic rank: \(0\)
Dimension: \(76\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
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)
 
\(f(q)\) \(=\) \(q-38.2269 q^{2} -153.641 q^{3} +949.295 q^{4} +2107.84 q^{5} +5873.22 q^{6} +5202.74 q^{7} -16716.4 q^{8} +3922.60 q^{9} +O(q^{10})\) \(q-38.2269 q^{2} -153.641 q^{3} +949.295 q^{4} +2107.84 q^{5} +5873.22 q^{6} +5202.74 q^{7} -16716.4 q^{8} +3922.60 q^{9} -80576.2 q^{10} +14459.1 q^{11} -145851. q^{12} -27160.2 q^{13} -198885. q^{14} -323851. q^{15} +152978. q^{16} +305985. q^{17} -149949. q^{18} +750970. q^{19} +2.00096e6 q^{20} -799355. q^{21} -552727. q^{22} +30312.0 q^{23} +2.56833e6 q^{24} +2.48987e6 q^{25} +1.03825e6 q^{26} +2.42145e6 q^{27} +4.93893e6 q^{28} +3.93647e6 q^{29} +1.23798e7 q^{30} +952075. q^{31} +2.71094e6 q^{32} -2.22152e6 q^{33} -1.16969e7 q^{34} +1.09665e7 q^{35} +3.72371e6 q^{36} -267723. q^{37} -2.87072e7 q^{38} +4.17293e6 q^{39} -3.52356e7 q^{40} +1.05316e7 q^{41} +3.05568e7 q^{42} +8.50472e6 q^{43} +1.37260e7 q^{44} +8.26822e6 q^{45} -1.15873e6 q^{46} +7.59559e6 q^{47} -2.35037e7 q^{48} -1.32851e7 q^{49} -9.51799e7 q^{50} -4.70120e7 q^{51} -2.57831e7 q^{52} +4.98917e7 q^{53} -9.25643e7 q^{54} +3.04775e7 q^{55} -8.69712e7 q^{56} -1.15380e8 q^{57} -1.50479e8 q^{58} +6.81953e6 q^{59} -3.07430e8 q^{60} +1.19460e8 q^{61} -3.63949e7 q^{62} +2.04083e7 q^{63} -1.81955e8 q^{64} -5.72495e7 q^{65} +8.49217e7 q^{66} -5.06638e7 q^{67} +2.90470e8 q^{68} -4.65716e6 q^{69} -4.19217e8 q^{70} -2.45300e8 q^{71} -6.55719e7 q^{72} +1.17975e8 q^{73} +1.02342e7 q^{74} -3.82546e8 q^{75} +7.12892e8 q^{76} +7.52270e7 q^{77} -1.59518e8 q^{78} +5.16564e8 q^{79} +3.22454e8 q^{80} -4.49242e8 q^{81} -4.02589e8 q^{82} +3.97742e7 q^{83} -7.58824e8 q^{84} +6.44969e8 q^{85} -3.25109e8 q^{86} -6.04804e8 q^{87} -2.41705e8 q^{88} +1.21044e8 q^{89} -3.16068e8 q^{90} -1.41308e8 q^{91} +2.87750e7 q^{92} -1.46278e8 q^{93} -2.90356e8 q^{94} +1.58293e9 q^{95} -4.16511e8 q^{96} -5.64314e7 q^{97} +5.07849e8 q^{98} +5.67174e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15} + 5963776 q^{16} + 942582 q^{17} + 1483945 q^{18} + 3097319 q^{19} + 3237739 q^{20} + 889076 q^{21} + 3791921 q^{22} + 5139200 q^{23} + 1999533 q^{24} + 34080519 q^{25} + 2791454 q^{26} + 24386486 q^{27} + 20891166 q^{28} + 6886818 q^{29} + 14171083 q^{30} + 28002851 q^{31} + 16857332 q^{32} + 30921422 q^{33} + 33506194 q^{34} + 16271736 q^{35} + 151430458 q^{36} + 55950976 q^{37} + 62370882 q^{38} - 11569592 q^{39} + 129854766 q^{40} + 14990859 q^{41} + 82216531 q^{42} + 169867467 q^{43} + 41872434 q^{44} + 205007649 q^{45} + 144032301 q^{46} + 78743342 q^{47} + 156250562 q^{48} + 533861890 q^{49} + 626841163 q^{50} + 477099244 q^{51} + 560784114 q^{52} + 188670216 q^{53} + 525901687 q^{54} + 298497914 q^{55} + 56575048 q^{56} + 213972590 q^{57} + 338315251 q^{58} + 208222151 q^{59} - 615921507 q^{60} - 233556134 q^{61} - 399368105 q^{62} + 329825056 q^{63} + 876517017 q^{64} - 840557006 q^{65} - 2482481592 q^{66} + 1210808414 q^{67} - 1266757099 q^{68} + 327801786 q^{69} - 546384313 q^{70} + 345300221 q^{71} - 1549481681 q^{72} + 1192286460 q^{73} - 1471133595 q^{74} + 761630676 q^{75} - 398699826 q^{76} - 101106252 q^{77} - 2609825943 q^{78} + 955627631 q^{79} + 1059617770 q^{80} + 3387041436 q^{81} + 1062705523 q^{82} + 1538917201 q^{83} + 1394513218 q^{84} + 225481100 q^{85} + 701644810 q^{86} + 1758812842 q^{87} + 3151474875 q^{88} + 855413630 q^{89} + 6070671455 q^{90} + 4652436248 q^{91} + 8082863606 q^{92} + 3462095982 q^{93} + 2660342117 q^{94} + 1036805508 q^{95} + 12370989029 q^{96} + 6393874545 q^{97} + 7510976010 q^{98} + 8731109606 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −38.2269 −1.68941 −0.844703 0.535235i \(-0.820223\pi\)
−0.844703 + 0.535235i \(0.820223\pi\)
\(3\) −153.641 −1.09512 −0.547560 0.836766i \(-0.684443\pi\)
−0.547560 + 0.836766i \(0.684443\pi\)
\(4\) 949.295 1.85409
\(5\) 2107.84 1.50825 0.754124 0.656732i \(-0.228062\pi\)
0.754124 + 0.656732i \(0.228062\pi\)
\(6\) 5873.22 1.85010
\(7\) 5202.74 0.819013 0.409507 0.912307i \(-0.365701\pi\)
0.409507 + 0.912307i \(0.365701\pi\)
\(8\) −16716.4 −1.44291
\(9\) 3922.60 0.199289
\(10\) −80576.2 −2.54804
\(11\) 14459.1 0.297766 0.148883 0.988855i \(-0.452432\pi\)
0.148883 + 0.988855i \(0.452432\pi\)
\(12\) −145851. −2.03045
\(13\) −27160.2 −0.263748 −0.131874 0.991267i \(-0.542099\pi\)
−0.131874 + 0.991267i \(0.542099\pi\)
\(14\) −198885. −1.38365
\(15\) −323851. −1.65171
\(16\) 152978. 0.583565
\(17\) 305985. 0.888547 0.444274 0.895891i \(-0.353462\pi\)
0.444274 + 0.895891i \(0.353462\pi\)
\(18\) −149949. −0.336680
\(19\) 750970. 1.32200 0.661000 0.750386i \(-0.270132\pi\)
0.661000 + 0.750386i \(0.270132\pi\)
\(20\) 2.00096e6 2.79643
\(21\) −799355. −0.896918
\(22\) −552727. −0.503047
\(23\) 30312.0 0.0225860 0.0112930 0.999936i \(-0.496405\pi\)
0.0112930 + 0.999936i \(0.496405\pi\)
\(24\) 2.56833e6 1.58016
\(25\) 2.48987e6 1.27481
\(26\) 1.03825e6 0.445577
\(27\) 2.42145e6 0.876875
\(28\) 4.93893e6 1.51853
\(29\) 3.93647e6 1.03351 0.516757 0.856132i \(-0.327139\pi\)
0.516757 + 0.856132i \(0.327139\pi\)
\(30\) 1.23798e7 2.79041
\(31\) 952075. 0.185158 0.0925792 0.995705i \(-0.470489\pi\)
0.0925792 + 0.995705i \(0.470489\pi\)
\(32\) 2.71094e6 0.457029
\(33\) −2.22152e6 −0.326089
\(34\) −1.16969e7 −1.50112
\(35\) 1.09665e7 1.23527
\(36\) 3.72371e6 0.369500
\(37\) −267723. −0.0234843 −0.0117422 0.999931i \(-0.503738\pi\)
−0.0117422 + 0.999931i \(0.503738\pi\)
\(38\) −2.87072e7 −2.23339
\(39\) 4.17293e6 0.288835
\(40\) −3.52356e7 −2.17626
\(41\) 1.05316e7 0.582056 0.291028 0.956714i \(-0.406003\pi\)
0.291028 + 0.956714i \(0.406003\pi\)
\(42\) 3.05568e7 1.51526
\(43\) 8.50472e6 0.379360 0.189680 0.981846i \(-0.439255\pi\)
0.189680 + 0.981846i \(0.439255\pi\)
\(44\) 1.37260e7 0.552085
\(45\) 8.26822e6 0.300577
\(46\) −1.15873e6 −0.0381569
\(47\) 7.59559e6 0.227050 0.113525 0.993535i \(-0.463786\pi\)
0.113525 + 0.993535i \(0.463786\pi\)
\(48\) −2.35037e7 −0.639074
\(49\) −1.32851e7 −0.329218
\(50\) −9.51799e7 −2.15367
\(51\) −4.70120e7 −0.973066
\(52\) −2.57831e7 −0.489012
\(53\) 4.98917e7 0.868534 0.434267 0.900784i \(-0.357007\pi\)
0.434267 + 0.900784i \(0.357007\pi\)
\(54\) −9.25643e7 −1.48140
\(55\) 3.04775e7 0.449105
\(56\) −8.69712e7 −1.18176
\(57\) −1.15380e8 −1.44775
\(58\) −1.50479e8 −1.74602
\(59\) 6.81953e6 0.0732690 0.0366345 0.999329i \(-0.488336\pi\)
0.0366345 + 0.999329i \(0.488336\pi\)
\(60\) −3.07430e8 −3.06243
\(61\) 1.19460e8 1.10469 0.552343 0.833617i \(-0.313734\pi\)
0.552343 + 0.833617i \(0.313734\pi\)
\(62\) −3.63949e7 −0.312808
\(63\) 2.04083e7 0.163220
\(64\) −1.81955e8 −1.35567
\(65\) −5.72495e7 −0.397797
\(66\) 8.49217e7 0.550897
\(67\) −5.06638e7 −0.307157 −0.153579 0.988136i \(-0.549080\pi\)
−0.153579 + 0.988136i \(0.549080\pi\)
\(68\) 2.90470e8 1.64745
\(69\) −4.65716e6 −0.0247344
\(70\) −4.19217e8 −2.08688
\(71\) −2.45300e8 −1.14560 −0.572802 0.819694i \(-0.694144\pi\)
−0.572802 + 0.819694i \(0.694144\pi\)
\(72\) −6.55719e7 −0.287555
\(73\) 1.17975e8 0.486225 0.243112 0.969998i \(-0.421832\pi\)
0.243112 + 0.969998i \(0.421832\pi\)
\(74\) 1.02342e7 0.0396745
\(75\) −3.82546e8 −1.39607
\(76\) 7.12892e8 2.45111
\(77\) 7.52270e7 0.243874
\(78\) −1.59518e8 −0.487960
\(79\) 5.16564e8 1.49212 0.746058 0.665882i \(-0.231944\pi\)
0.746058 + 0.665882i \(0.231944\pi\)
\(80\) 3.22454e8 0.880161
\(81\) −4.49242e8 −1.15957
\(82\) −4.02589e8 −0.983330
\(83\) 3.97742e7 0.0919919 0.0459960 0.998942i \(-0.485354\pi\)
0.0459960 + 0.998942i \(0.485354\pi\)
\(84\) −7.58824e8 −1.66297
\(85\) 6.44969e8 1.34015
\(86\) −3.25109e8 −0.640893
\(87\) −6.04804e8 −1.13182
\(88\) −2.41705e8 −0.429649
\(89\) 1.21044e8 0.204498 0.102249 0.994759i \(-0.467396\pi\)
0.102249 + 0.994759i \(0.467396\pi\)
\(90\) −3.16068e8 −0.507796
\(91\) −1.41308e8 −0.216013
\(92\) 2.87750e7 0.0418765
\(93\) −1.46278e8 −0.202771
\(94\) −2.90356e8 −0.383579
\(95\) 1.58293e9 1.99390
\(96\) −4.16511e8 −0.500502
\(97\) −5.64314e7 −0.0647214 −0.0323607 0.999476i \(-0.510303\pi\)
−0.0323607 + 0.999476i \(0.510303\pi\)
\(98\) 5.07849e8 0.556182
\(99\) 5.67174e7 0.0593414
\(100\) 2.36362e9 2.36362
\(101\) −4.08268e8 −0.390391 −0.195195 0.980764i \(-0.562534\pi\)
−0.195195 + 0.980764i \(0.562534\pi\)
\(102\) 1.79712e9 1.64390
\(103\) −6.99257e8 −0.612166 −0.306083 0.952005i \(-0.599018\pi\)
−0.306083 + 0.952005i \(0.599018\pi\)
\(104\) 4.54022e8 0.380564
\(105\) −1.68491e9 −1.35277
\(106\) −1.90720e9 −1.46731
\(107\) −9.08297e8 −0.669886 −0.334943 0.942238i \(-0.608717\pi\)
−0.334943 + 0.942238i \(0.608717\pi\)
\(108\) 2.29867e9 1.62581
\(109\) 1.34403e7 0.00911989 0.00455994 0.999990i \(-0.498549\pi\)
0.00455994 + 0.999990i \(0.498549\pi\)
\(110\) −1.16506e9 −0.758720
\(111\) 4.11333e7 0.0257181
\(112\) 7.95905e8 0.477948
\(113\) −2.36910e7 −0.0136688 −0.00683440 0.999977i \(-0.502175\pi\)
−0.00683440 + 0.999977i \(0.502175\pi\)
\(114\) 4.41061e9 2.44584
\(115\) 6.38928e7 0.0340652
\(116\) 3.73687e9 1.91623
\(117\) −1.06539e8 −0.0525619
\(118\) −2.60689e8 −0.123781
\(119\) 1.59196e9 0.727732
\(120\) 5.41363e9 2.38327
\(121\) −2.14888e9 −0.911335
\(122\) −4.56659e9 −1.86626
\(123\) −1.61808e9 −0.637422
\(124\) 9.03800e8 0.343301
\(125\) 1.13137e9 0.414484
\(126\) −7.80144e8 −0.275745
\(127\) 1.36484e8 0.0465547 0.0232774 0.999729i \(-0.492590\pi\)
0.0232774 + 0.999729i \(0.492590\pi\)
\(128\) 5.56759e9 1.83325
\(129\) −1.30667e9 −0.415445
\(130\) 2.18847e9 0.672040
\(131\) −1.63921e9 −0.486310 −0.243155 0.969987i \(-0.578182\pi\)
−0.243155 + 0.969987i \(0.578182\pi\)
\(132\) −2.10887e9 −0.604600
\(133\) 3.90710e9 1.08274
\(134\) 1.93672e9 0.518913
\(135\) 5.10402e9 1.32255
\(136\) −5.11499e9 −1.28209
\(137\) 2.43866e9 0.591438 0.295719 0.955275i \(-0.404441\pi\)
0.295719 + 0.955275i \(0.404441\pi\)
\(138\) 1.78029e8 0.0417864
\(139\) −4.13325e9 −0.939128 −0.469564 0.882899i \(-0.655589\pi\)
−0.469564 + 0.882899i \(0.655589\pi\)
\(140\) 1.04105e10 2.29031
\(141\) −1.16700e9 −0.248647
\(142\) 9.37704e9 1.93539
\(143\) −3.92713e8 −0.0785351
\(144\) 6.00072e8 0.116298
\(145\) 8.29745e9 1.55879
\(146\) −4.50982e9 −0.821431
\(147\) 2.04114e9 0.360533
\(148\) −2.54148e8 −0.0435421
\(149\) −6.01056e9 −0.999025 −0.499513 0.866307i \(-0.666488\pi\)
−0.499513 + 0.866307i \(0.666488\pi\)
\(150\) 1.46235e10 2.35853
\(151\) 1.06469e10 1.66658 0.833291 0.552834i \(-0.186454\pi\)
0.833291 + 0.552834i \(0.186454\pi\)
\(152\) −1.25535e10 −1.90752
\(153\) 1.20026e9 0.177077
\(154\) −2.87570e9 −0.412002
\(155\) 2.00682e9 0.279265
\(156\) 3.96134e9 0.535528
\(157\) −6.94726e9 −0.912567 −0.456284 0.889834i \(-0.650820\pi\)
−0.456284 + 0.889834i \(0.650820\pi\)
\(158\) −1.97466e10 −2.52079
\(159\) −7.66542e9 −0.951149
\(160\) 5.71422e9 0.689314
\(161\) 1.57705e8 0.0184982
\(162\) 1.71731e10 1.95899
\(163\) −9.81379e9 −1.08891 −0.544455 0.838790i \(-0.683264\pi\)
−0.544455 + 0.838790i \(0.683264\pi\)
\(164\) 9.99755e9 1.07919
\(165\) −4.68260e9 −0.491824
\(166\) −1.52044e9 −0.155412
\(167\) 1.52995e10 1.52213 0.761067 0.648673i \(-0.224676\pi\)
0.761067 + 0.648673i \(0.224676\pi\)
\(168\) 1.33624e10 1.29417
\(169\) −9.86682e9 −0.930437
\(170\) −2.46551e10 −2.26406
\(171\) 2.94576e9 0.263460
\(172\) 8.07349e9 0.703369
\(173\) 1.50390e10 1.27647 0.638235 0.769842i \(-0.279665\pi\)
0.638235 + 0.769842i \(0.279665\pi\)
\(174\) 2.31198e10 1.91211
\(175\) 1.29541e10 1.04409
\(176\) 2.21193e9 0.173766
\(177\) −1.04776e9 −0.0802384
\(178\) −4.62715e9 −0.345480
\(179\) 2.77580e8 0.0202092 0.0101046 0.999949i \(-0.496784\pi\)
0.0101046 + 0.999949i \(0.496784\pi\)
\(180\) 7.84898e9 0.557297
\(181\) −1.00484e10 −0.695897 −0.347948 0.937514i \(-0.613122\pi\)
−0.347948 + 0.937514i \(0.613122\pi\)
\(182\) 5.40175e9 0.364933
\(183\) −1.83540e10 −1.20976
\(184\) −5.06708e8 −0.0325895
\(185\) −5.64317e8 −0.0354202
\(186\) 5.59175e9 0.342562
\(187\) 4.42428e9 0.264579
\(188\) 7.21046e9 0.420971
\(189\) 1.25981e10 0.718172
\(190\) −6.05103e10 −3.36851
\(191\) −1.52351e10 −0.828315 −0.414158 0.910205i \(-0.635924\pi\)
−0.414158 + 0.910205i \(0.635924\pi\)
\(192\) 2.79558e10 1.48463
\(193\) −3.17609e9 −0.164772 −0.0823862 0.996600i \(-0.526254\pi\)
−0.0823862 + 0.996600i \(0.526254\pi\)
\(194\) 2.15720e9 0.109341
\(195\) 8.79587e9 0.435636
\(196\) −1.26115e10 −0.610400
\(197\) 1.50614e9 0.0712470
\(198\) −2.16813e9 −0.100252
\(199\) 1.28543e10 0.581044 0.290522 0.956868i \(-0.406171\pi\)
0.290522 + 0.956868i \(0.406171\pi\)
\(200\) −4.16217e10 −1.83944
\(201\) 7.78404e9 0.336374
\(202\) 1.56068e10 0.659529
\(203\) 2.04804e10 0.846461
\(204\) −4.46282e10 −1.80415
\(205\) 2.21988e10 0.877885
\(206\) 2.67304e10 1.03420
\(207\) 1.18902e8 0.00450113
\(208\) −4.15492e9 −0.153914
\(209\) 1.08584e10 0.393646
\(210\) 6.44090e10 2.28539
\(211\) 3.19945e10 1.11123 0.555616 0.831439i \(-0.312482\pi\)
0.555616 + 0.831439i \(0.312482\pi\)
\(212\) 4.73619e10 1.61034
\(213\) 3.76881e10 1.25457
\(214\) 3.47214e10 1.13171
\(215\) 1.79266e10 0.572169
\(216\) −4.04779e10 −1.26525
\(217\) 4.95340e9 0.151647
\(218\) −5.13781e8 −0.0154072
\(219\) −1.81258e10 −0.532475
\(220\) 2.89322e10 0.832682
\(221\) −8.31064e9 −0.234352
\(222\) −1.57240e9 −0.0434484
\(223\) 6.58160e10 1.78221 0.891107 0.453793i \(-0.149929\pi\)
0.891107 + 0.453793i \(0.149929\pi\)
\(224\) 1.41043e10 0.374313
\(225\) 9.76675e9 0.254056
\(226\) 9.05634e8 0.0230922
\(227\) −5.91660e10 −1.47896 −0.739479 0.673179i \(-0.764928\pi\)
−0.739479 + 0.673179i \(0.764928\pi\)
\(228\) −1.09530e11 −2.68426
\(229\) −3.32122e10 −0.798065 −0.399033 0.916937i \(-0.630654\pi\)
−0.399033 + 0.916937i \(0.630654\pi\)
\(230\) −2.44242e9 −0.0575500
\(231\) −1.15580e10 −0.267072
\(232\) −6.58038e10 −1.49126
\(233\) −1.36784e9 −0.0304041 −0.0152021 0.999884i \(-0.504839\pi\)
−0.0152021 + 0.999884i \(0.504839\pi\)
\(234\) 4.07265e9 0.0887985
\(235\) 1.60103e10 0.342447
\(236\) 6.47375e9 0.135847
\(237\) −7.93655e10 −1.63405
\(238\) −6.08558e10 −1.22943
\(239\) −8.40292e10 −1.66586 −0.832932 0.553375i \(-0.813339\pi\)
−0.832932 + 0.553375i \(0.813339\pi\)
\(240\) −4.95421e10 −0.963882
\(241\) 5.38143e9 0.102759 0.0513796 0.998679i \(-0.483638\pi\)
0.0513796 + 0.998679i \(0.483638\pi\)
\(242\) 8.21451e10 1.53962
\(243\) 2.13608e10 0.392997
\(244\) 1.13403e11 2.04819
\(245\) −2.80029e10 −0.496542
\(246\) 6.18542e10 1.07686
\(247\) −2.03965e10 −0.348674
\(248\) −1.59153e10 −0.267167
\(249\) −6.11095e9 −0.100742
\(250\) −4.32486e10 −0.700232
\(251\) −5.96891e10 −0.949212 −0.474606 0.880198i \(-0.657409\pi\)
−0.474606 + 0.880198i \(0.657409\pi\)
\(252\) 1.93735e10 0.302625
\(253\) 4.38284e8 0.00672533
\(254\) −5.21734e9 −0.0786498
\(255\) −9.90937e10 −1.46763
\(256\) −1.19671e11 −1.74144
\(257\) −1.06712e11 −1.52585 −0.762926 0.646486i \(-0.776238\pi\)
−0.762926 + 0.646486i \(0.776238\pi\)
\(258\) 4.99501e10 0.701855
\(259\) −1.39289e9 −0.0192340
\(260\) −5.43466e10 −0.737552
\(261\) 1.54412e10 0.205968
\(262\) 6.26619e10 0.821576
\(263\) 1.62217e10 0.209072 0.104536 0.994521i \(-0.466664\pi\)
0.104536 + 0.994521i \(0.466664\pi\)
\(264\) 3.71358e10 0.470517
\(265\) 1.05164e11 1.30996
\(266\) −1.49356e11 −1.82918
\(267\) −1.85974e10 −0.223950
\(268\) −4.80949e10 −0.569498
\(269\) −1.05738e11 −1.23125 −0.615624 0.788040i \(-0.711096\pi\)
−0.615624 + 0.788040i \(0.711096\pi\)
\(270\) −1.95111e11 −2.23432
\(271\) 1.03622e11 1.16705 0.583527 0.812094i \(-0.301672\pi\)
0.583527 + 0.812094i \(0.301672\pi\)
\(272\) 4.68091e10 0.518525
\(273\) 2.17107e10 0.236560
\(274\) −9.32225e10 −0.999179
\(275\) 3.60013e10 0.379595
\(276\) −4.42102e9 −0.0458598
\(277\) 1.03616e11 1.05747 0.528734 0.848788i \(-0.322667\pi\)
0.528734 + 0.848788i \(0.322667\pi\)
\(278\) 1.58001e11 1.58657
\(279\) 3.73461e9 0.0369000
\(280\) −1.83321e11 −1.78239
\(281\) −4.10264e10 −0.392541 −0.196271 0.980550i \(-0.562883\pi\)
−0.196271 + 0.980550i \(0.562883\pi\)
\(282\) 4.46106e10 0.420066
\(283\) 8.45522e9 0.0783584 0.0391792 0.999232i \(-0.487526\pi\)
0.0391792 + 0.999232i \(0.487526\pi\)
\(284\) −2.32862e11 −2.12405
\(285\) −2.43202e11 −2.18356
\(286\) 1.50122e10 0.132678
\(287\) 5.47929e10 0.476712
\(288\) 1.06339e10 0.0910808
\(289\) −2.49608e10 −0.210483
\(290\) −3.17186e11 −2.63344
\(291\) 8.67018e9 0.0708777
\(292\) 1.11993e11 0.901505
\(293\) 7.16759e10 0.568158 0.284079 0.958801i \(-0.408312\pi\)
0.284079 + 0.958801i \(0.408312\pi\)
\(294\) −7.80265e10 −0.609086
\(295\) 1.43745e10 0.110508
\(296\) 4.47537e9 0.0338857
\(297\) 3.50120e10 0.261104
\(298\) 2.29765e11 1.68776
\(299\) −8.23280e8 −0.00595700
\(300\) −3.63149e11 −2.58845
\(301\) 4.42478e10 0.310701
\(302\) −4.06998e11 −2.81553
\(303\) 6.27268e10 0.427525
\(304\) 1.14882e11 0.771473
\(305\) 2.51803e11 1.66614
\(306\) −4.58822e10 −0.299156
\(307\) 1.84404e11 1.18481 0.592404 0.805641i \(-0.298179\pi\)
0.592404 + 0.805641i \(0.298179\pi\)
\(308\) 7.14127e10 0.452165
\(309\) 1.07435e11 0.670395
\(310\) −7.67146e10 −0.471792
\(311\) −6.53057e9 −0.0395849 −0.0197924 0.999804i \(-0.506301\pi\)
−0.0197924 + 0.999804i \(0.506301\pi\)
\(312\) −6.97565e10 −0.416763
\(313\) 2.62007e11 1.54299 0.771495 0.636235i \(-0.219509\pi\)
0.771495 + 0.636235i \(0.219509\pi\)
\(314\) 2.65572e11 1.54170
\(315\) 4.30174e10 0.246176
\(316\) 4.90372e11 2.76652
\(317\) −1.33176e11 −0.740727 −0.370363 0.928887i \(-0.620767\pi\)
−0.370363 + 0.928887i \(0.620767\pi\)
\(318\) 2.93025e11 1.60688
\(319\) 5.69179e10 0.307745
\(320\) −3.83533e11 −2.04469
\(321\) 1.39552e11 0.733606
\(322\) −6.02858e9 −0.0312510
\(323\) 2.29786e11 1.17466
\(324\) −4.26463e11 −2.14995
\(325\) −6.76254e10 −0.336229
\(326\) 3.75151e11 1.83961
\(327\) −2.06498e9 −0.00998738
\(328\) −1.76050e11 −0.839854
\(329\) 3.95179e10 0.185957
\(330\) 1.79001e11 0.830890
\(331\) 2.27005e11 1.03946 0.519732 0.854329i \(-0.326032\pi\)
0.519732 + 0.854329i \(0.326032\pi\)
\(332\) 3.77574e10 0.170561
\(333\) −1.05017e9 −0.00468016
\(334\) −5.84852e11 −2.57150
\(335\) −1.06791e11 −0.463269
\(336\) −1.22284e11 −0.523410
\(337\) −7.17572e9 −0.0303062 −0.0151531 0.999885i \(-0.504824\pi\)
−0.0151531 + 0.999885i \(0.504824\pi\)
\(338\) 3.77178e11 1.57189
\(339\) 3.63991e9 0.0149690
\(340\) 6.12265e11 2.48476
\(341\) 1.37662e10 0.0551339
\(342\) −1.12607e11 −0.445090
\(343\) −2.79068e11 −1.08865
\(344\) −1.42169e11 −0.547382
\(345\) −9.81656e9 −0.0373055
\(346\) −5.74893e11 −2.15648
\(347\) 8.58364e10 0.317826 0.158913 0.987293i \(-0.449201\pi\)
0.158913 + 0.987293i \(0.449201\pi\)
\(348\) −5.74137e11 −2.09850
\(349\) 1.96745e11 0.709888 0.354944 0.934888i \(-0.384500\pi\)
0.354944 + 0.934888i \(0.384500\pi\)
\(350\) −4.95196e11 −1.76389
\(351\) −6.57671e10 −0.231274
\(352\) 3.91977e10 0.136088
\(353\) 5.13579e11 1.76044 0.880219 0.474567i \(-0.157395\pi\)
0.880219 + 0.474567i \(0.157395\pi\)
\(354\) 4.00526e10 0.135555
\(355\) −5.17053e11 −1.72785
\(356\) 1.14907e11 0.379159
\(357\) −2.44591e11 −0.796954
\(358\) −1.06110e10 −0.0341416
\(359\) 1.92052e11 0.610229 0.305115 0.952316i \(-0.401305\pi\)
0.305115 + 0.952316i \(0.401305\pi\)
\(360\) −1.38215e11 −0.433705
\(361\) 2.41268e11 0.747684
\(362\) 3.84120e11 1.17565
\(363\) 3.30157e11 0.998022
\(364\) −1.34143e11 −0.400508
\(365\) 2.48672e11 0.733347
\(366\) 7.01616e11 2.04378
\(367\) −7.10357e10 −0.204399 −0.102200 0.994764i \(-0.532588\pi\)
−0.102200 + 0.994764i \(0.532588\pi\)
\(368\) 4.63707e9 0.0131804
\(369\) 4.13111e10 0.115997
\(370\) 2.15721e10 0.0598390
\(371\) 2.59573e11 0.711341
\(372\) −1.38861e11 −0.375956
\(373\) 5.97727e11 1.59887 0.799435 0.600753i \(-0.205132\pi\)
0.799435 + 0.600753i \(0.205132\pi\)
\(374\) −1.69127e11 −0.446981
\(375\) −1.73824e11 −0.453910
\(376\) −1.26971e11 −0.327612
\(377\) −1.06916e11 −0.272587
\(378\) −4.81588e11 −1.21328
\(379\) 6.94367e11 1.72867 0.864336 0.502914i \(-0.167739\pi\)
0.864336 + 0.502914i \(0.167739\pi\)
\(380\) 1.50266e12 3.69688
\(381\) −2.09695e10 −0.0509830
\(382\) 5.82391e11 1.39936
\(383\) −2.01772e11 −0.479145 −0.239572 0.970879i \(-0.577007\pi\)
−0.239572 + 0.970879i \(0.577007\pi\)
\(384\) −8.55411e11 −2.00763
\(385\) 1.58567e11 0.367823
\(386\) 1.21412e11 0.278367
\(387\) 3.33606e10 0.0756022
\(388\) −5.35701e10 −0.119999
\(389\) 3.61861e9 0.00801250 0.00400625 0.999992i \(-0.498725\pi\)
0.00400625 + 0.999992i \(0.498725\pi\)
\(390\) −3.36239e11 −0.735965
\(391\) 9.27502e9 0.0200687
\(392\) 2.22080e11 0.475031
\(393\) 2.51850e11 0.532569
\(394\) −5.75750e10 −0.120365
\(395\) 1.08883e12 2.25048
\(396\) 5.38415e10 0.110024
\(397\) 5.85838e11 1.18364 0.591821 0.806069i \(-0.298409\pi\)
0.591821 + 0.806069i \(0.298409\pi\)
\(398\) −4.91379e11 −0.981619
\(399\) −6.00291e11 −1.18573
\(400\) 3.80895e11 0.743936
\(401\) 5.63448e11 1.08819 0.544094 0.839024i \(-0.316873\pi\)
0.544094 + 0.839024i \(0.316873\pi\)
\(402\) −2.97560e11 −0.568272
\(403\) −2.58586e10 −0.0488351
\(404\) −3.87567e11 −0.723821
\(405\) −9.46931e11 −1.74892
\(406\) −7.82903e11 −1.43002
\(407\) −3.87104e9 −0.00699283
\(408\) 7.85872e11 1.40405
\(409\) −1.05392e12 −1.86232 −0.931161 0.364608i \(-0.881203\pi\)
−0.931161 + 0.364608i \(0.881203\pi\)
\(410\) −8.48592e11 −1.48310
\(411\) −3.74679e11 −0.647696
\(412\) −6.63801e11 −1.13501
\(413\) 3.54802e10 0.0600083
\(414\) −4.54524e9 −0.00760423
\(415\) 8.38376e10 0.138747
\(416\) −7.36297e10 −0.120540
\(417\) 6.35037e11 1.02846
\(418\) −4.15082e11 −0.665029
\(419\) 3.21361e11 0.509367 0.254683 0.967025i \(-0.418029\pi\)
0.254683 + 0.967025i \(0.418029\pi\)
\(420\) −1.59948e12 −2.50817
\(421\) −9.38143e11 −1.45546 −0.727729 0.685865i \(-0.759424\pi\)
−0.727729 + 0.685865i \(0.759424\pi\)
\(422\) −1.22305e12 −1.87732
\(423\) 2.97945e10 0.0452485
\(424\) −8.34011e11 −1.25321
\(425\) 7.61863e11 1.13273
\(426\) −1.44070e12 −2.11948
\(427\) 6.21520e11 0.904752
\(428\) −8.62242e11 −1.24203
\(429\) 6.03369e10 0.0860054
\(430\) −6.85278e11 −0.966626
\(431\) 9.37611e11 1.30881 0.654403 0.756146i \(-0.272920\pi\)
0.654403 + 0.756146i \(0.272920\pi\)
\(432\) 3.70428e11 0.511714
\(433\) 7.64066e11 1.04456 0.522282 0.852773i \(-0.325081\pi\)
0.522282 + 0.852773i \(0.325081\pi\)
\(434\) −1.89353e11 −0.256194
\(435\) −1.27483e12 −1.70707
\(436\) 1.27588e10 0.0169091
\(437\) 2.27634e10 0.0298586
\(438\) 6.92893e11 0.899566
\(439\) −2.67401e10 −0.0343616 −0.0171808 0.999852i \(-0.505469\pi\)
−0.0171808 + 0.999852i \(0.505469\pi\)
\(440\) −5.09476e11 −0.648017
\(441\) −5.21122e10 −0.0656094
\(442\) 3.17690e11 0.395916
\(443\) −2.85059e10 −0.0351656 −0.0175828 0.999845i \(-0.505597\pi\)
−0.0175828 + 0.999845i \(0.505597\pi\)
\(444\) 3.90476e10 0.0476838
\(445\) 2.55142e11 0.308434
\(446\) −2.51594e12 −3.01088
\(447\) 9.23469e11 1.09405
\(448\) −9.46666e11 −1.11031
\(449\) −1.51978e12 −1.76471 −0.882353 0.470589i \(-0.844042\pi\)
−0.882353 + 0.470589i \(0.844042\pi\)
\(450\) −3.73353e11 −0.429203
\(451\) 1.52277e11 0.173317
\(452\) −2.24898e10 −0.0253432
\(453\) −1.63580e12 −1.82511
\(454\) 2.26173e12 2.49856
\(455\) −2.97854e11 −0.325801
\(456\) 1.92874e12 2.08897
\(457\) 5.95490e11 0.638633 0.319317 0.947648i \(-0.396547\pi\)
0.319317 + 0.947648i \(0.396547\pi\)
\(458\) 1.26960e12 1.34826
\(459\) 7.40927e11 0.779145
\(460\) 6.06531e10 0.0631601
\(461\) −1.24624e12 −1.28513 −0.642565 0.766231i \(-0.722130\pi\)
−0.642565 + 0.766231i \(0.722130\pi\)
\(462\) 4.41825e11 0.451192
\(463\) 1.26834e12 1.28269 0.641346 0.767252i \(-0.278376\pi\)
0.641346 + 0.767252i \(0.278376\pi\)
\(464\) 6.02194e11 0.603122
\(465\) −3.08330e11 −0.305829
\(466\) 5.22881e10 0.0513649
\(467\) −7.05768e11 −0.686651 −0.343325 0.939217i \(-0.611553\pi\)
−0.343325 + 0.939217i \(0.611553\pi\)
\(468\) −1.01137e11 −0.0974547
\(469\) −2.63590e11 −0.251566
\(470\) −6.12024e11 −0.578533
\(471\) 1.06738e12 0.999371
\(472\) −1.13998e11 −0.105720
\(473\) 1.22971e11 0.112961
\(474\) 3.03390e12 2.76057
\(475\) 1.86982e12 1.68530
\(476\) 1.51124e12 1.34928
\(477\) 1.95705e11 0.173089
\(478\) 3.21217e12 2.81432
\(479\) 1.12193e12 0.973768 0.486884 0.873467i \(-0.338133\pi\)
0.486884 + 0.873467i \(0.338133\pi\)
\(480\) −8.77939e11 −0.754882
\(481\) 7.27142e9 0.00619393
\(482\) −2.05715e11 −0.173602
\(483\) −2.42300e10 −0.0202578
\(484\) −2.03992e12 −1.68970
\(485\) −1.18948e11 −0.0976159
\(486\) −8.16556e11 −0.663931
\(487\) 8.32354e11 0.670545 0.335272 0.942121i \(-0.391172\pi\)
0.335272 + 0.942121i \(0.391172\pi\)
\(488\) −1.99695e12 −1.59396
\(489\) 1.50780e12 1.19249
\(490\) 1.07046e12 0.838861
\(491\) 1.54507e12 1.19973 0.599863 0.800103i \(-0.295222\pi\)
0.599863 + 0.800103i \(0.295222\pi\)
\(492\) −1.53604e12 −1.18184
\(493\) 1.20450e12 0.918326
\(494\) 7.79696e11 0.589053
\(495\) 1.19551e11 0.0895015
\(496\) 1.45647e11 0.108052
\(497\) −1.27623e12 −0.938264
\(498\) 2.33603e11 0.170194
\(499\) 1.13614e12 0.820310 0.410155 0.912016i \(-0.365475\pi\)
0.410155 + 0.912016i \(0.365475\pi\)
\(500\) 1.07400e12 0.768492
\(501\) −2.35063e12 −1.66692
\(502\) 2.28173e12 1.60360
\(503\) −1.29522e12 −0.902170 −0.451085 0.892481i \(-0.648963\pi\)
−0.451085 + 0.892481i \(0.648963\pi\)
\(504\) −3.41153e11 −0.235512
\(505\) −8.60565e11 −0.588806
\(506\) −1.67542e10 −0.0113618
\(507\) 1.51595e12 1.01894
\(508\) 1.29563e11 0.0863167
\(509\) −9.48803e11 −0.626536 −0.313268 0.949665i \(-0.601424\pi\)
−0.313268 + 0.949665i \(0.601424\pi\)
\(510\) 3.78804e12 2.47942
\(511\) 6.13793e11 0.398224
\(512\) 1.72403e12 1.10874
\(513\) 1.81843e12 1.15923
\(514\) 4.07925e12 2.57778
\(515\) −1.47392e12 −0.923298
\(516\) −1.24042e12 −0.770274
\(517\) 1.09826e11 0.0676077
\(518\) 5.32459e10 0.0324940
\(519\) −2.31060e12 −1.39789
\(520\) 9.57007e11 0.573984
\(521\) −2.46207e12 −1.46396 −0.731981 0.681325i \(-0.761404\pi\)
−0.731981 + 0.681325i \(0.761404\pi\)
\(522\) −5.90269e11 −0.347963
\(523\) 2.42753e12 1.41875 0.709377 0.704829i \(-0.248976\pi\)
0.709377 + 0.704829i \(0.248976\pi\)
\(524\) −1.55609e12 −0.901664
\(525\) −1.99029e12 −1.14340
\(526\) −6.20106e11 −0.353208
\(527\) 2.91321e11 0.164522
\(528\) −3.39843e11 −0.190295
\(529\) −1.80023e12 −0.999490
\(530\) −4.02008e12 −2.21306
\(531\) 2.67503e10 0.0146017
\(532\) 3.70899e12 2.00749
\(533\) −2.86040e11 −0.153516
\(534\) 7.10921e11 0.378343
\(535\) −1.91455e12 −1.01035
\(536\) 8.46917e11 0.443200
\(537\) −4.26477e10 −0.0221315
\(538\) 4.04203e12 2.08008
\(539\) −1.92091e11 −0.0980298
\(540\) 4.84522e12 2.45212
\(541\) −3.08748e12 −1.54959 −0.774795 0.632213i \(-0.782147\pi\)
−0.774795 + 0.632213i \(0.782147\pi\)
\(542\) −3.96115e12 −1.97163
\(543\) 1.54385e12 0.762091
\(544\) 8.29507e11 0.406092
\(545\) 2.83300e10 0.0137551
\(546\) −8.29931e11 −0.399646
\(547\) 7.65281e11 0.365492 0.182746 0.983160i \(-0.441501\pi\)
0.182746 + 0.983160i \(0.441501\pi\)
\(548\) 2.31501e12 1.09658
\(549\) 4.68594e11 0.220151
\(550\) −1.37622e12 −0.641291
\(551\) 2.95617e12 1.36630
\(552\) 7.78512e10 0.0356894
\(553\) 2.68755e12 1.22206
\(554\) −3.96091e12 −1.78649
\(555\) 8.67023e10 0.0387893
\(556\) −3.92367e12 −1.74123
\(557\) −1.37829e12 −0.606727 −0.303364 0.952875i \(-0.598110\pi\)
−0.303364 + 0.952875i \(0.598110\pi\)
\(558\) −1.42762e11 −0.0623390
\(559\) −2.30990e11 −0.100055
\(560\) 1.67764e12 0.720863
\(561\) −6.79752e11 −0.289746
\(562\) 1.56831e12 0.663161
\(563\) 2.62254e12 1.10011 0.550054 0.835129i \(-0.314607\pi\)
0.550054 + 0.835129i \(0.314607\pi\)
\(564\) −1.10782e12 −0.461014
\(565\) −4.99369e10 −0.0206160
\(566\) −3.23217e11 −0.132379
\(567\) −2.33729e12 −0.949705
\(568\) 4.10054e12 1.65300
\(569\) 9.63896e11 0.385501 0.192750 0.981248i \(-0.438259\pi\)
0.192750 + 0.981248i \(0.438259\pi\)
\(570\) 9.29687e12 3.68893
\(571\) −2.36629e12 −0.931550 −0.465775 0.884903i \(-0.654224\pi\)
−0.465775 + 0.884903i \(0.654224\pi\)
\(572\) −3.72801e11 −0.145611
\(573\) 2.34074e12 0.907105
\(574\) −2.09456e12 −0.805360
\(575\) 7.54727e10 0.0287929
\(576\) −7.13738e11 −0.270170
\(577\) −3.34486e11 −0.125628 −0.0628140 0.998025i \(-0.520008\pi\)
−0.0628140 + 0.998025i \(0.520008\pi\)
\(578\) 9.54173e11 0.355592
\(579\) 4.87977e11 0.180446
\(580\) 7.87673e12 2.89015
\(581\) 2.06935e11 0.0753426
\(582\) −3.31434e11 −0.119741
\(583\) 7.21390e11 0.258620
\(584\) −1.97212e12 −0.701578
\(585\) −2.24567e11 −0.0792764
\(586\) −2.73995e12 −0.959849
\(587\) 2.97724e12 1.03501 0.517503 0.855682i \(-0.326862\pi\)
0.517503 + 0.855682i \(0.326862\pi\)
\(588\) 1.93765e12 0.668461
\(589\) 7.14980e11 0.244779
\(590\) −5.49492e11 −0.186693
\(591\) −2.31405e11 −0.0780241
\(592\) −4.09558e10 −0.0137046
\(593\) −2.95484e12 −0.981269 −0.490634 0.871366i \(-0.663235\pi\)
−0.490634 + 0.871366i \(0.663235\pi\)
\(594\) −1.33840e12 −0.441110
\(595\) 3.35560e12 1.09760
\(596\) −5.70579e12 −1.85228
\(597\) −1.97495e12 −0.636313
\(598\) 3.14714e10 0.0100638
\(599\) −2.19881e12 −0.697857 −0.348929 0.937149i \(-0.613454\pi\)
−0.348929 + 0.937149i \(0.613454\pi\)
\(600\) 6.39480e12 2.01440
\(601\) 1.04958e12 0.328156 0.164078 0.986447i \(-0.447535\pi\)
0.164078 + 0.986447i \(0.447535\pi\)
\(602\) −1.69146e12 −0.524900
\(603\) −1.98734e11 −0.0612130
\(604\) 1.01070e13 3.09000
\(605\) −4.52950e12 −1.37452
\(606\) −2.39785e12 −0.722263
\(607\) 4.96644e11 0.148490 0.0742449 0.997240i \(-0.476345\pi\)
0.0742449 + 0.997240i \(0.476345\pi\)
\(608\) 2.03583e12 0.604193
\(609\) −3.14664e12 −0.926977
\(610\) −9.62564e12 −2.81479
\(611\) −2.06298e11 −0.0598839
\(612\) 1.13940e12 0.328318
\(613\) −2.11053e11 −0.0603699 −0.0301849 0.999544i \(-0.509610\pi\)
−0.0301849 + 0.999544i \(0.509610\pi\)
\(614\) −7.04919e12 −2.00162
\(615\) −3.41065e12 −0.961390
\(616\) −1.25753e12 −0.351888
\(617\) −3.15337e12 −0.875974 −0.437987 0.898981i \(-0.644308\pi\)
−0.437987 + 0.898981i \(0.644308\pi\)
\(618\) −4.10689e12 −1.13257
\(619\) 1.40671e12 0.385121 0.192561 0.981285i \(-0.438321\pi\)
0.192561 + 0.981285i \(0.438321\pi\)
\(620\) 1.90507e12 0.517783
\(621\) 7.33988e10 0.0198051
\(622\) 2.49643e11 0.0668749
\(623\) 6.29762e11 0.167487
\(624\) 6.38367e11 0.168554
\(625\) −2.47828e12 −0.649667
\(626\) −1.00157e13 −2.60674
\(627\) −1.66829e12 −0.431090
\(628\) −6.59500e12 −1.69198
\(629\) −8.19193e10 −0.0208669
\(630\) −1.64442e12 −0.415892
\(631\) 4.63510e12 1.16393 0.581966 0.813213i \(-0.302284\pi\)
0.581966 + 0.813213i \(0.302284\pi\)
\(632\) −8.63511e12 −2.15298
\(633\) −4.91568e12 −1.21693
\(634\) 5.09089e12 1.25139
\(635\) 2.87686e11 0.0702160
\(636\) −7.27674e12 −1.76352
\(637\) 3.60827e11 0.0868304
\(638\) −2.17580e12 −0.519906
\(639\) −9.62213e11 −0.228306
\(640\) 1.17356e13 2.76500
\(641\) 2.74470e12 0.642145 0.321073 0.947055i \(-0.395957\pi\)
0.321073 + 0.947055i \(0.395957\pi\)
\(642\) −5.33463e12 −1.23936
\(643\) −4.81477e12 −1.11078 −0.555388 0.831591i \(-0.687430\pi\)
−0.555388 + 0.831591i \(0.687430\pi\)
\(644\) 1.49709e11 0.0342974
\(645\) −2.75426e12 −0.626594
\(646\) −8.78400e12 −1.98448
\(647\) −7.31467e12 −1.64106 −0.820531 0.571602i \(-0.806322\pi\)
−0.820531 + 0.571602i \(0.806322\pi\)
\(648\) 7.50973e12 1.67316
\(649\) 9.86044e10 0.0218170
\(650\) 2.58511e12 0.568027
\(651\) −7.61045e11 −0.166072
\(652\) −9.31618e12 −2.01894
\(653\) −4.80438e12 −1.03402 −0.517009 0.855980i \(-0.672955\pi\)
−0.517009 + 0.855980i \(0.672955\pi\)
\(654\) 7.89379e10 0.0168727
\(655\) −3.45519e12 −0.733477
\(656\) 1.61110e12 0.339668
\(657\) 4.62769e11 0.0968991
\(658\) −1.51065e12 −0.314156
\(659\) −3.89676e12 −0.804858 −0.402429 0.915451i \(-0.631834\pi\)
−0.402429 + 0.915451i \(0.631834\pi\)
\(660\) −4.44517e12 −0.911887
\(661\) 3.64506e12 0.742673 0.371336 0.928498i \(-0.378900\pi\)
0.371336 + 0.928498i \(0.378900\pi\)
\(662\) −8.67769e12 −1.75608
\(663\) 1.27686e12 0.256644
\(664\) −6.64882e11 −0.132736
\(665\) 8.23555e12 1.63303
\(666\) 4.01447e10 0.00790669
\(667\) 1.19322e11 0.0233429
\(668\) 1.45237e13 2.82218
\(669\) −1.01121e13 −1.95174
\(670\) 4.08229e12 0.782650
\(671\) 1.72729e12 0.328938
\(672\) −2.16700e12 −0.409918
\(673\) 5.49056e12 1.03169 0.515844 0.856682i \(-0.327478\pi\)
0.515844 + 0.856682i \(0.327478\pi\)
\(674\) 2.74306e11 0.0511994
\(675\) 6.02908e12 1.11785
\(676\) −9.36652e12 −1.72512
\(677\) −1.69761e12 −0.310591 −0.155296 0.987868i \(-0.549633\pi\)
−0.155296 + 0.987868i \(0.549633\pi\)
\(678\) −1.39143e11 −0.0252887
\(679\) −2.93598e11 −0.0530077
\(680\) −1.07816e13 −1.93371
\(681\) 9.09033e12 1.61964
\(682\) −5.26238e11 −0.0931435
\(683\) −7.52172e9 −0.00132259 −0.000661293 1.00000i \(-0.500210\pi\)
−0.000661293 1.00000i \(0.500210\pi\)
\(684\) 2.79639e12 0.488478
\(685\) 5.14031e12 0.892036
\(686\) 1.06679e13 1.83917
\(687\) 5.10277e12 0.873978
\(688\) 1.30104e12 0.221381
\(689\) −1.35507e12 −0.229074
\(690\) 3.75256e11 0.0630242
\(691\) −3.24633e12 −0.541679 −0.270840 0.962625i \(-0.587301\pi\)
−0.270840 + 0.962625i \(0.587301\pi\)
\(692\) 1.42764e13 2.36669
\(693\) 2.95086e11 0.0486014
\(694\) −3.28126e12 −0.536937
\(695\) −8.71222e12 −1.41644
\(696\) 1.01102e13 1.63311
\(697\) 3.22250e12 0.517185
\(698\) −7.52096e12 −1.19929
\(699\) 2.10156e11 0.0332962
\(700\) 1.22973e13 1.93583
\(701\) 1.14756e12 0.179492 0.0897462 0.995965i \(-0.471394\pi\)
0.0897462 + 0.995965i \(0.471394\pi\)
\(702\) 2.51407e12 0.390715
\(703\) −2.01052e11 −0.0310463
\(704\) −2.63092e12 −0.403673
\(705\) −2.45984e12 −0.375021
\(706\) −1.96325e13 −2.97410
\(707\) −2.12411e12 −0.319735
\(708\) −9.94634e11 −0.148769
\(709\) −1.08250e13 −1.60886 −0.804432 0.594044i \(-0.797530\pi\)
−0.804432 + 0.594044i \(0.797530\pi\)
\(710\) 1.97653e13 2.91905
\(711\) 2.02627e12 0.297362
\(712\) −2.02343e12 −0.295072
\(713\) 2.88592e10 0.00418198
\(714\) 9.34995e12 1.34638
\(715\) −8.27777e11 −0.118450
\(716\) 2.63505e11 0.0374698
\(717\) 1.29103e13 1.82432
\(718\) −7.34154e12 −1.03093
\(719\) −7.26303e12 −1.01353 −0.506766 0.862083i \(-0.669159\pi\)
−0.506766 + 0.862083i \(0.669159\pi\)
\(720\) 1.26486e12 0.175406
\(721\) −3.63805e12 −0.501372
\(722\) −9.22294e12 −1.26314
\(723\) −8.26809e11 −0.112534
\(724\) −9.53893e12 −1.29026
\(725\) 9.80129e12 1.31753
\(726\) −1.26209e13 −1.68606
\(727\) −7.97647e11 −0.105902 −0.0529512 0.998597i \(-0.516863\pi\)
−0.0529512 + 0.998597i \(0.516863\pi\)
\(728\) 2.36216e12 0.311687
\(729\) 5.56054e12 0.729194
\(730\) −9.50597e12 −1.23892
\(731\) 2.60232e12 0.337080
\(732\) −1.74234e13 −2.24301
\(733\) −3.30785e12 −0.423232 −0.211616 0.977353i \(-0.567873\pi\)
−0.211616 + 0.977353i \(0.567873\pi\)
\(734\) 2.71547e12 0.345313
\(735\) 4.30240e12 0.543773
\(736\) 8.21737e10 0.0103225
\(737\) −7.32554e11 −0.0914609
\(738\) −1.57919e12 −0.195966
\(739\) 9.17440e12 1.13156 0.565780 0.824556i \(-0.308575\pi\)
0.565780 + 0.824556i \(0.308575\pi\)
\(740\) −5.35704e11 −0.0656722
\(741\) 3.13375e12 0.381840
\(742\) −9.92269e12 −1.20174
\(743\) 1.29134e13 1.55451 0.777253 0.629189i \(-0.216613\pi\)
0.777253 + 0.629189i \(0.216613\pi\)
\(744\) 2.44524e12 0.292580
\(745\) −1.26693e13 −1.50678
\(746\) −2.28492e13 −2.70114
\(747\) 1.56018e11 0.0183329
\(748\) 4.19995e12 0.490554
\(749\) −4.72563e12 −0.548645
\(750\) 6.64477e12 0.766839
\(751\) 1.13700e13 1.30431 0.652153 0.758087i \(-0.273866\pi\)
0.652153 + 0.758087i \(0.273866\pi\)
\(752\) 1.16196e12 0.132498
\(753\) 9.17070e12 1.03950
\(754\) 4.08705e12 0.460510
\(755\) 2.24420e13 2.51362
\(756\) 1.19594e13 1.33156
\(757\) 6.02655e12 0.667017 0.333509 0.942747i \(-0.391767\pi\)
0.333509 + 0.942747i \(0.391767\pi\)
\(758\) −2.65435e13 −2.92043
\(759\) −6.73385e10 −0.00736505
\(760\) −2.64609e13 −2.87702
\(761\) −9.14307e11 −0.0988237 −0.0494119 0.998778i \(-0.515735\pi\)
−0.0494119 + 0.998778i \(0.515735\pi\)
\(762\) 8.01598e11 0.0861310
\(763\) 6.99263e10 0.00746931
\(764\) −1.44626e13 −1.53577
\(765\) 2.52995e12 0.267077
\(766\) 7.71312e12 0.809470
\(767\) −1.85220e11 −0.0193245
\(768\) 1.83863e13 1.90708
\(769\) 3.48454e12 0.359316 0.179658 0.983729i \(-0.442501\pi\)
0.179658 + 0.983729i \(0.442501\pi\)
\(770\) −6.06151e12 −0.621402
\(771\) 1.63953e13 1.67099
\(772\) −3.01504e12 −0.305503
\(773\) −9.06972e12 −0.913663 −0.456832 0.889553i \(-0.651016\pi\)
−0.456832 + 0.889553i \(0.651016\pi\)
\(774\) −1.27527e12 −0.127723
\(775\) 2.37054e12 0.236042
\(776\) 9.43332e11 0.0933871
\(777\) 2.14006e11 0.0210635
\(778\) −1.38328e11 −0.0135364
\(779\) 7.90888e12 0.769479
\(780\) 8.34988e12 0.807708
\(781\) −3.54682e12 −0.341122
\(782\) −3.54555e11 −0.0339042
\(783\) 9.53195e12 0.906262
\(784\) −2.03233e12 −0.192120
\(785\) −1.46437e13 −1.37638
\(786\) −9.62744e12 −0.899724
\(787\) −2.91276e12 −0.270657 −0.135328 0.990801i \(-0.543209\pi\)
−0.135328 + 0.990801i \(0.543209\pi\)
\(788\) 1.42977e12 0.132099
\(789\) −2.49232e12 −0.228959
\(790\) −4.16228e13 −3.80197
\(791\) −1.23258e11 −0.0111949
\(792\) −9.48112e11 −0.0856242
\(793\) −3.24457e12 −0.291358
\(794\) −2.23948e13 −1.99965
\(795\) −1.61575e13 −1.43457
\(796\) 1.22025e13 1.07731
\(797\) 1.37467e13 1.20680 0.603400 0.797439i \(-0.293812\pi\)
0.603400 + 0.797439i \(0.293812\pi\)
\(798\) 2.29473e13 2.00317
\(799\) 2.32414e12 0.201745
\(800\) 6.74987e12 0.582627
\(801\) 4.74809e11 0.0407542
\(802\) −2.15389e13 −1.83839
\(803\) 1.70582e12 0.144781
\(804\) 7.38935e12 0.623669
\(805\) 3.32417e11 0.0278999
\(806\) 9.88493e11 0.0825023
\(807\) 1.62457e13 1.34837
\(808\) 6.82479e12 0.563298
\(809\) 2.09640e13 1.72070 0.860352 0.509700i \(-0.170244\pi\)
0.860352 + 0.509700i \(0.170244\pi\)
\(810\) 3.61982e13 2.95464
\(811\) 1.80143e13 1.46226 0.731130 0.682238i \(-0.238993\pi\)
0.731130 + 0.682238i \(0.238993\pi\)
\(812\) 1.94420e13 1.56942
\(813\) −1.59206e13 −1.27806
\(814\) 1.47978e11 0.0118137
\(815\) −2.06859e13 −1.64235
\(816\) −7.19180e12 −0.567848
\(817\) 6.38679e12 0.501514
\(818\) 4.02883e13 3.14622
\(819\) −5.54294e11 −0.0430489
\(820\) 2.10732e13 1.62768
\(821\) −1.41619e13 −1.08787 −0.543934 0.839128i \(-0.683066\pi\)
−0.543934 + 0.839128i \(0.683066\pi\)
\(822\) 1.43228e13 1.09422
\(823\) 1.99084e13 1.51264 0.756321 0.654201i \(-0.226995\pi\)
0.756321 + 0.654201i \(0.226995\pi\)
\(824\) 1.16891e13 0.883299
\(825\) −5.53128e12 −0.415703
\(826\) −1.35630e12 −0.101378
\(827\) −1.21535e12 −0.0903497 −0.0451749 0.998979i \(-0.514385\pi\)
−0.0451749 + 0.998979i \(0.514385\pi\)
\(828\) 1.12873e11 0.00834551
\(829\) 1.43806e13 1.05750 0.528752 0.848777i \(-0.322660\pi\)
0.528752 + 0.848777i \(0.322660\pi\)
\(830\) −3.20485e12 −0.234399
\(831\) −1.59196e13 −1.15805
\(832\) 4.94195e12 0.357556
\(833\) −4.06505e12 −0.292525
\(834\) −2.42755e13 −1.73748
\(835\) 3.22489e13 2.29576
\(836\) 1.03078e13 0.729857
\(837\) 2.30540e12 0.162361
\(838\) −1.22846e13 −0.860527
\(839\) 1.95134e11 0.0135958 0.00679790 0.999977i \(-0.497836\pi\)
0.00679790 + 0.999977i \(0.497836\pi\)
\(840\) 2.81657e13 1.95193
\(841\) 9.88657e11 0.0681497
\(842\) 3.58623e13 2.45886
\(843\) 6.30335e12 0.429880
\(844\) 3.03723e13 2.06033
\(845\) −2.07977e13 −1.40333
\(846\) −1.13895e12 −0.0764430
\(847\) −1.11801e13 −0.746396
\(848\) 7.63234e12 0.506846
\(849\) −1.29907e12 −0.0858119
\(850\) −2.91237e13 −1.91364
\(851\) −8.11520e9 −0.000530416 0
\(852\) 3.57772e13 2.32610
\(853\) −1.61260e13 −1.04293 −0.521467 0.853271i \(-0.674615\pi\)
−0.521467 + 0.853271i \(0.674615\pi\)
\(854\) −2.37588e13 −1.52849
\(855\) 6.20918e12 0.397363
\(856\) 1.51835e13 0.966584
\(857\) 2.32841e13 1.47450 0.737252 0.675618i \(-0.236123\pi\)
0.737252 + 0.675618i \(0.236123\pi\)
\(858\) −2.30649e12 −0.145298
\(859\) −2.80294e13 −1.75649 −0.878244 0.478212i \(-0.841285\pi\)
−0.878244 + 0.478212i \(0.841285\pi\)
\(860\) 1.70176e13 1.06085
\(861\) −8.41845e12 −0.522057
\(862\) −3.58420e13 −2.21110
\(863\) 1.95516e13 1.19987 0.599933 0.800050i \(-0.295194\pi\)
0.599933 + 0.800050i \(0.295194\pi\)
\(864\) 6.56438e12 0.400758
\(865\) 3.16997e13 1.92523
\(866\) −2.92079e13 −1.76469
\(867\) 3.83500e12 0.230505
\(868\) 4.70223e12 0.281168
\(869\) 7.46906e12 0.444301
\(870\) 4.87328e13 2.88393
\(871\) 1.37604e12 0.0810120
\(872\) −2.24674e11 −0.0131592
\(873\) −2.21358e11 −0.0128982
\(874\) −8.70173e11 −0.0504434
\(875\) 5.88620e12 0.339468
\(876\) −1.72067e13 −0.987257
\(877\) −2.28721e13 −1.30560 −0.652798 0.757532i \(-0.726405\pi\)
−0.652798 + 0.757532i \(0.726405\pi\)
\(878\) 1.02219e12 0.0580506
\(879\) −1.10124e13 −0.622201
\(880\) 4.66240e12 0.262082
\(881\) −1.32499e13 −0.741007 −0.370504 0.928831i \(-0.620815\pi\)
−0.370504 + 0.928831i \(0.620815\pi\)
\(882\) 1.99209e12 0.110841
\(883\) 4.12981e12 0.228616 0.114308 0.993445i \(-0.463535\pi\)
0.114308 + 0.993445i \(0.463535\pi\)
\(884\) −7.88925e12 −0.434511
\(885\) −2.20851e12 −0.121019
\(886\) 1.08969e12 0.0594089
\(887\) 2.42722e13 1.31660 0.658298 0.752757i \(-0.271277\pi\)
0.658298 + 0.752757i \(0.271277\pi\)
\(888\) −6.87601e11 −0.0371089
\(889\) 7.10088e11 0.0381289
\(890\) −9.75329e12 −0.521070
\(891\) −6.49565e12 −0.345281
\(892\) 6.24788e13 3.30439
\(893\) 5.70406e12 0.300160
\(894\) −3.53013e13 −1.84830
\(895\) 5.85094e11 0.0304805
\(896\) 2.89667e13 1.50146
\(897\) 1.26490e11 0.00652363
\(898\) 5.80965e13 2.98130
\(899\) 3.74781e12 0.191364
\(900\) 9.27153e12 0.471043
\(901\) 1.52661e13 0.771734
\(902\) −5.82108e12 −0.292802
\(903\) −6.79829e12 −0.340255
\(904\) 3.96029e11 0.0197228
\(905\) −2.11805e13 −1.04958
\(906\) 6.25316e13 3.08335
\(907\) 3.60325e12 0.176792 0.0883958 0.996085i \(-0.471826\pi\)
0.0883958 + 0.996085i \(0.471826\pi\)
\(908\) −5.61660e13 −2.74212
\(909\) −1.60147e12 −0.0778005
\(910\) 1.13860e13 0.550410
\(911\) 1.38844e12 0.0667872 0.0333936 0.999442i \(-0.489369\pi\)
0.0333936 + 0.999442i \(0.489369\pi\)
\(912\) −1.76506e13 −0.844856
\(913\) 5.75100e11 0.0273920
\(914\) −2.27637e13 −1.07891
\(915\) −3.86873e13 −1.82462
\(916\) −3.15282e13 −1.47969
\(917\) −8.52838e12 −0.398295
\(918\) −2.83233e13 −1.31629
\(919\) 1.30682e13 0.604361 0.302180 0.953251i \(-0.402285\pi\)
0.302180 + 0.953251i \(0.402285\pi\)
\(920\) −1.06806e12 −0.0491530
\(921\) −2.83320e13 −1.29751
\(922\) 4.76398e13 2.17111
\(923\) 6.66240e12 0.302150
\(924\) −1.09719e13 −0.495175
\(925\) −6.66594e11 −0.0299381
\(926\) −4.84848e13 −2.16699
\(927\) −2.74290e12 −0.121998
\(928\) 1.06715e13 0.472346
\(929\) −2.19012e13 −0.964709 −0.482354 0.875976i \(-0.660218\pi\)
−0.482354 + 0.875976i \(0.660218\pi\)
\(930\) 1.17865e13 0.516669
\(931\) −9.97673e12 −0.435226
\(932\) −1.29848e12 −0.0563720
\(933\) 1.00336e12 0.0433502
\(934\) 2.69793e13 1.16003
\(935\) 9.32568e12 0.399051
\(936\) 1.78095e12 0.0758421
\(937\) 1.20196e13 0.509403 0.254701 0.967020i \(-0.418023\pi\)
0.254701 + 0.967020i \(0.418023\pi\)
\(938\) 1.00762e13 0.424997
\(939\) −4.02550e13 −1.68976
\(940\) 1.51985e13 0.634929
\(941\) 2.50039e13 1.03957 0.519786 0.854297i \(-0.326012\pi\)
0.519786 + 0.854297i \(0.326012\pi\)
\(942\) −4.08028e13 −1.68834
\(943\) 3.19232e11 0.0131463
\(944\) 1.04324e12 0.0427573
\(945\) 2.65549e13 1.08318
\(946\) −4.70079e12 −0.190836
\(947\) 3.96314e13 1.60127 0.800636 0.599151i \(-0.204495\pi\)
0.800636 + 0.599151i \(0.204495\pi\)
\(948\) −7.53413e13 −3.02967
\(949\) −3.20423e12 −0.128241
\(950\) −7.14772e13 −2.84716
\(951\) 2.04613e13 0.811185
\(952\) −2.66119e13 −1.05005
\(953\) −6.42157e12 −0.252187 −0.126094 0.992018i \(-0.540244\pi\)
−0.126094 + 0.992018i \(0.540244\pi\)
\(954\) −7.48120e12 −0.292418
\(955\) −3.21132e13 −1.24930
\(956\) −7.97685e13 −3.08866
\(957\) −8.74494e12 −0.337018
\(958\) −4.28878e13 −1.64509
\(959\) 1.26877e13 0.484396
\(960\) 5.89265e13 2.23918
\(961\) −2.55332e13 −0.965716
\(962\) −2.77964e11 −0.0104641
\(963\) −3.56289e12 −0.133501
\(964\) 5.10857e12 0.190525
\(965\) −6.69468e12 −0.248518
\(966\) 9.26238e11 0.0342236
\(967\) 3.50542e13 1.28920 0.644600 0.764520i \(-0.277024\pi\)
0.644600 + 0.764520i \(0.277024\pi\)
\(968\) 3.59216e13 1.31497
\(969\) −3.53046e13 −1.28639
\(970\) 4.54703e12 0.164913
\(971\) −5.00924e13 −1.80836 −0.904181 0.427150i \(-0.859517\pi\)
−0.904181 + 0.427150i \(0.859517\pi\)
\(972\) 2.02777e13 0.728652
\(973\) −2.15042e13 −0.769158
\(974\) −3.18183e13 −1.13282
\(975\) 1.03900e13 0.368211
\(976\) 1.82748e13 0.644656
\(977\) −3.04571e13 −1.06946 −0.534728 0.845024i \(-0.679586\pi\)
−0.534728 + 0.845024i \(0.679586\pi\)
\(978\) −5.76386e13 −2.01460
\(979\) 1.75020e12 0.0608926
\(980\) −2.65830e13 −0.920634
\(981\) 5.27209e10 0.00181749
\(982\) −5.90633e13 −2.02682
\(983\) −4.68733e13 −1.60116 −0.800579 0.599227i \(-0.795475\pi\)
−0.800579 + 0.599227i \(0.795475\pi\)
\(984\) 2.70485e13 0.919741
\(985\) 3.17470e12 0.107458
\(986\) −4.60444e13 −1.55142
\(987\) −6.07157e12 −0.203645
\(988\) −1.93623e13 −0.646474
\(989\) 2.57795e11 0.00856822
\(990\) −4.57007e12 −0.151204
\(991\) −1.75561e13 −0.578224 −0.289112 0.957295i \(-0.593360\pi\)
−0.289112 + 0.957295i \(0.593360\pi\)
\(992\) 2.58101e12 0.0846228
\(993\) −3.48773e13 −1.13834
\(994\) 4.87863e13 1.58511
\(995\) 2.70948e13 0.876358
\(996\) −5.80109e12 −0.186785
\(997\) 2.86332e13 0.917787 0.458893 0.888491i \(-0.348246\pi\)
0.458893 + 0.888491i \(0.348246\pi\)
\(998\) −4.34310e13 −1.38584
\(999\) −6.48277e11 −0.0205928
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 197.10.a.b.1.8 76
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.10.a.b.1.8 76 1.1 even 1 trivial