Properties

Label 197.12.a.b.1.11
Level $197$
Weight $12$
Character 197.1
Self dual yes
Analytic conductor $151.364$
Analytic rank $0$
Dimension $92$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [197,12,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, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.1");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 12 \)
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: \(151.363606570\)
Analytic rank: \(0\)
Dimension: \(92\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
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)
 
\(f(q)\) \(=\) \(q-73.7285 q^{2} +331.029 q^{3} +3387.90 q^{4} +2290.71 q^{5} -24406.3 q^{6} -50357.4 q^{7} -98788.6 q^{8} -67567.1 q^{9} +O(q^{10})\) \(q-73.7285 q^{2} +331.029 q^{3} +3387.90 q^{4} +2290.71 q^{5} -24406.3 q^{6} -50357.4 q^{7} -98788.6 q^{8} -67567.1 q^{9} -168891. q^{10} +399282. q^{11} +1.12149e6 q^{12} +2.01831e6 q^{13} +3.71278e6 q^{14} +758291. q^{15} +345128. q^{16} +7.93307e6 q^{17} +4.98162e6 q^{18} -1.59268e6 q^{19} +7.76069e6 q^{20} -1.66698e7 q^{21} -2.94385e7 q^{22} +1.64035e7 q^{23} -3.27019e7 q^{24} -4.35808e7 q^{25} -1.48807e8 q^{26} -8.10074e7 q^{27} -1.70606e8 q^{28} +1.26271e8 q^{29} -5.59077e7 q^{30} +5.07699e7 q^{31} +1.76873e8 q^{32} +1.32174e8 q^{33} -5.84894e8 q^{34} -1.15354e8 q^{35} -2.28910e8 q^{36} -2.64162e8 q^{37} +1.17426e8 q^{38} +6.68117e8 q^{39} -2.26296e8 q^{40} +2.37687e8 q^{41} +1.22904e9 q^{42} +5.44415e8 q^{43} +1.35273e9 q^{44} -1.54777e8 q^{45} -1.20941e9 q^{46} -9.15873e8 q^{47} +1.14247e8 q^{48} +5.58546e8 q^{49} +3.21315e9 q^{50} +2.62607e9 q^{51} +6.83782e9 q^{52} +1.92825e9 q^{53} +5.97255e9 q^{54} +9.14639e8 q^{55} +4.97474e9 q^{56} -5.27223e8 q^{57} -9.30980e9 q^{58} -3.00106e9 q^{59} +2.56901e9 q^{60} +5.15404e8 q^{61} -3.74319e9 q^{62} +3.40251e9 q^{63} -1.37474e10 q^{64} +4.62336e9 q^{65} -9.74497e9 q^{66} -8.98974e9 q^{67} +2.68764e10 q^{68} +5.43003e9 q^{69} +8.50491e9 q^{70} +2.10232e10 q^{71} +6.67486e9 q^{72} +9.54887e9 q^{73} +1.94763e10 q^{74} -1.44265e10 q^{75} -5.39584e9 q^{76} -2.01068e10 q^{77} -4.92593e10 q^{78} -4.59180e9 q^{79} +7.90589e8 q^{80} -1.48464e10 q^{81} -1.75243e10 q^{82} +1.48825e10 q^{83} -5.64754e10 q^{84} +1.81724e10 q^{85} -4.01389e10 q^{86} +4.17994e10 q^{87} -3.94445e10 q^{88} -1.42235e10 q^{89} +1.14115e10 q^{90} -1.01637e11 q^{91} +5.55734e10 q^{92} +1.68063e10 q^{93} +6.75259e10 q^{94} -3.64837e9 q^{95} +5.85501e10 q^{96} -1.15451e11 q^{97} -4.11808e10 q^{98} -2.69783e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 92 q + 64 q^{2} + 2420 q^{3} + 98304 q^{4} + 16604 q^{5} + 46656 q^{6} + 305891 q^{7} + 234027 q^{8} + 5900444 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 92 q + 64 q^{2} + 2420 q^{3} + 98304 q^{4} + 16604 q^{5} + 46656 q^{6} + 305891 q^{7} + 234027 q^{8} + 5900444 q^{9} + 1074277 q^{10} + 595928 q^{11} + 4956160 q^{12} + 7463810 q^{13} + 4915769 q^{14} + 6749159 q^{15} + 109051904 q^{16} + 9869683 q^{17} + 15324721 q^{18} + 71500013 q^{19} + 79804779 q^{20} + 55741034 q^{21} + 120367289 q^{22} + 38597564 q^{23} + 104015637 q^{24} + 1039976880 q^{25} + 51802726 q^{26} + 665312351 q^{27} + 713160630 q^{28} - 2827541 q^{29} - 43013765 q^{30} + 939775728 q^{31} + 723479980 q^{32} + 978717002 q^{33} + 1063528738 q^{34} + 843197112 q^{35} + 6613742458 q^{36} + 2009031770 q^{37} + 918086794 q^{38} + 2279970607 q^{39} + 3093842646 q^{40} - 30014736 q^{41} + 3159549307 q^{42} + 6320365127 q^{43} + 3019176802 q^{44} + 5538230697 q^{45} + 4344764621 q^{46} + 2853606373 q^{47} + 15616060178 q^{48} + 31617715853 q^{49} - 28784136763 q^{50} - 7216660253 q^{51} + 19141188860 q^{52} + 3389732468 q^{53} + 14059623295 q^{54} + 23123173075 q^{55} + 75592019872 q^{56} + 27508365203 q^{57} + 42079603023 q^{58} + 40032802875 q^{59} + 99482549469 q^{60} + 31816702886 q^{61} + 35401555571 q^{62} + 79170604993 q^{63} + 168463042533 q^{64} + 50313809737 q^{65} + 93218912814 q^{66} + 129966589578 q^{67} + 73640879491 q^{68} - 9850635033 q^{69} + 62387700391 q^{70} + 32189826123 q^{71} + 47439469795 q^{72} + 60612500511 q^{73} - 110473527245 q^{74} + 48823210110 q^{75} + 48170982110 q^{76} - 9381499362 q^{77} - 251751253299 q^{78} + 40812909551 q^{79} - 36932560002 q^{80} + 294126355776 q^{81} + 29914326881 q^{82} + 112077199076 q^{83} - 242466547988 q^{84} - 65194167314 q^{85} - 384596985360 q^{86} + 30701235703 q^{87} + 102229734783 q^{88} - 47595308310 q^{89} - 957657692329 q^{90} + 217575098757 q^{91} - 762245602306 q^{92} - 47762776839 q^{93} - 251435906373 q^{94} - 84935429021 q^{95} - 1089429573223 q^{96} + 432665748880 q^{97} - 404245603446 q^{98} + 9542377031 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −73.7285 −1.62919 −0.814593 0.580033i \(-0.803040\pi\)
−0.814593 + 0.580033i \(0.803040\pi\)
\(3\) 331.029 0.786500 0.393250 0.919432i \(-0.371351\pi\)
0.393250 + 0.919432i \(0.371351\pi\)
\(4\) 3387.90 1.65425
\(5\) 2290.71 0.327820 0.163910 0.986475i \(-0.447589\pi\)
0.163910 + 0.986475i \(0.447589\pi\)
\(6\) −24406.3 −1.28135
\(7\) −50357.4 −1.13246 −0.566232 0.824246i \(-0.691599\pi\)
−0.566232 + 0.824246i \(0.691599\pi\)
\(8\) −98788.6 −1.06589
\(9\) −67567.1 −0.381418
\(10\) −168891. −0.534079
\(11\) 399282. 0.747514 0.373757 0.927527i \(-0.378069\pi\)
0.373757 + 0.927527i \(0.378069\pi\)
\(12\) 1.12149e6 1.30106
\(13\) 2.01831e6 1.50764 0.753822 0.657079i \(-0.228208\pi\)
0.753822 + 0.657079i \(0.228208\pi\)
\(14\) 3.71278e6 1.84499
\(15\) 758291. 0.257830
\(16\) 345128. 0.0822850
\(17\) 7.93307e6 1.35510 0.677551 0.735476i \(-0.263041\pi\)
0.677551 + 0.735476i \(0.263041\pi\)
\(18\) 4.98162e6 0.621401
\(19\) −1.59268e6 −0.147565 −0.0737826 0.997274i \(-0.523507\pi\)
−0.0737826 + 0.997274i \(0.523507\pi\)
\(20\) 7.76069e6 0.542295
\(21\) −1.66698e7 −0.890683
\(22\) −2.94385e7 −1.21784
\(23\) 1.64035e7 0.531415 0.265707 0.964054i \(-0.414395\pi\)
0.265707 + 0.964054i \(0.414395\pi\)
\(24\) −3.27019e7 −0.838322
\(25\) −4.35808e7 −0.892534
\(26\) −1.48807e8 −2.45623
\(27\) −8.10074e7 −1.08649
\(28\) −1.70606e8 −1.87337
\(29\) 1.26271e8 1.14318 0.571592 0.820538i \(-0.306326\pi\)
0.571592 + 0.820538i \(0.306326\pi\)
\(30\) −5.59077e7 −0.420053
\(31\) 5.07699e7 0.318505 0.159253 0.987238i \(-0.449092\pi\)
0.159253 + 0.987238i \(0.449092\pi\)
\(32\) 1.76873e8 0.931832
\(33\) 1.32174e8 0.587920
\(34\) −5.84894e8 −2.20771
\(35\) −1.15354e8 −0.371244
\(36\) −2.28910e8 −0.630960
\(37\) −2.64162e8 −0.626269 −0.313135 0.949709i \(-0.601379\pi\)
−0.313135 + 0.949709i \(0.601379\pi\)
\(38\) 1.17426e8 0.240411
\(39\) 6.68117e8 1.18576
\(40\) −2.26296e8 −0.349420
\(41\) 2.37687e8 0.320401 0.160201 0.987084i \(-0.448786\pi\)
0.160201 + 0.987084i \(0.448786\pi\)
\(42\) 1.22904e9 1.45109
\(43\) 5.44415e8 0.564747 0.282373 0.959305i \(-0.408878\pi\)
0.282373 + 0.959305i \(0.408878\pi\)
\(44\) 1.35273e9 1.23657
\(45\) −1.54777e8 −0.125036
\(46\) −1.20941e9 −0.865773
\(47\) −9.15873e8 −0.582501 −0.291251 0.956647i \(-0.594071\pi\)
−0.291251 + 0.956647i \(0.594071\pi\)
\(48\) 1.14247e8 0.0647171
\(49\) 5.58546e8 0.282475
\(50\) 3.21315e9 1.45410
\(51\) 2.62607e9 1.06579
\(52\) 6.83782e9 2.49401
\(53\) 1.92825e9 0.633352 0.316676 0.948534i \(-0.397433\pi\)
0.316676 + 0.948534i \(0.397433\pi\)
\(54\) 5.97255e9 1.77009
\(55\) 9.14639e8 0.245050
\(56\) 4.97474e9 1.20708
\(57\) −5.27223e8 −0.116060
\(58\) −9.30980e9 −1.86246
\(59\) −3.00106e9 −0.546498 −0.273249 0.961943i \(-0.588098\pi\)
−0.273249 + 0.961943i \(0.588098\pi\)
\(60\) 2.56901e9 0.426515
\(61\) 5.15404e8 0.0781329 0.0390664 0.999237i \(-0.487562\pi\)
0.0390664 + 0.999237i \(0.487562\pi\)
\(62\) −3.74319e9 −0.518904
\(63\) 3.40251e9 0.431942
\(64\) −1.37474e10 −1.60041
\(65\) 4.62336e9 0.494235
\(66\) −9.74497e9 −0.957831
\(67\) −8.98974e9 −0.813459 −0.406729 0.913549i \(-0.633331\pi\)
−0.406729 + 0.913549i \(0.633331\pi\)
\(68\) 2.68764e10 2.24167
\(69\) 5.43003e9 0.417958
\(70\) 8.50491e9 0.604826
\(71\) 2.10232e10 1.38286 0.691429 0.722445i \(-0.256982\pi\)
0.691429 + 0.722445i \(0.256982\pi\)
\(72\) 6.67486e9 0.406549
\(73\) 9.54887e9 0.539108 0.269554 0.962985i \(-0.413124\pi\)
0.269554 + 0.962985i \(0.413124\pi\)
\(74\) 1.94763e10 1.02031
\(75\) −1.44265e10 −0.701978
\(76\) −5.39584e9 −0.244109
\(77\) −2.01068e10 −0.846533
\(78\) −4.92593e10 −1.93183
\(79\) −4.59180e9 −0.167894 −0.0839468 0.996470i \(-0.526753\pi\)
−0.0839468 + 0.996470i \(0.526753\pi\)
\(80\) 7.90589e8 0.0269747
\(81\) −1.48464e10 −0.473102
\(82\) −1.75243e10 −0.521994
\(83\) 1.48825e10 0.414713 0.207356 0.978265i \(-0.433514\pi\)
0.207356 + 0.978265i \(0.433514\pi\)
\(84\) −5.64754e10 −1.47341
\(85\) 1.81724e10 0.444229
\(86\) −4.01389e10 −0.920077
\(87\) 4.17994e10 0.899113
\(88\) −3.94445e10 −0.796768
\(89\) −1.42235e10 −0.269999 −0.135000 0.990846i \(-0.543103\pi\)
−0.135000 + 0.990846i \(0.543103\pi\)
\(90\) 1.14115e10 0.203708
\(91\) −1.01637e11 −1.70735
\(92\) 5.55734e10 0.879091
\(93\) 1.68063e10 0.250504
\(94\) 6.75259e10 0.949003
\(95\) −3.64837e9 −0.0483748
\(96\) 5.85501e10 0.732885
\(97\) −1.15451e11 −1.36506 −0.682532 0.730855i \(-0.739121\pi\)
−0.682532 + 0.730855i \(0.739121\pi\)
\(98\) −4.11808e10 −0.460204
\(99\) −2.69783e10 −0.285116
\(100\) −1.47647e11 −1.47647
\(101\) −9.99493e9 −0.0946264 −0.0473132 0.998880i \(-0.515066\pi\)
−0.0473132 + 0.998880i \(0.515066\pi\)
\(102\) −1.93616e11 −1.73637
\(103\) −8.26476e10 −0.702466 −0.351233 0.936288i \(-0.614238\pi\)
−0.351233 + 0.936288i \(0.614238\pi\)
\(104\) −1.99386e11 −1.60698
\(105\) −3.81856e10 −0.291983
\(106\) −1.42167e11 −1.03185
\(107\) 6.11104e10 0.421215 0.210608 0.977571i \(-0.432456\pi\)
0.210608 + 0.977571i \(0.432456\pi\)
\(108\) −2.74445e11 −1.79731
\(109\) 2.25343e11 1.40281 0.701404 0.712764i \(-0.252557\pi\)
0.701404 + 0.712764i \(0.252557\pi\)
\(110\) −6.74350e10 −0.399232
\(111\) −8.74452e10 −0.492561
\(112\) −1.73798e10 −0.0931848
\(113\) −1.62232e11 −0.828332 −0.414166 0.910201i \(-0.635927\pi\)
−0.414166 + 0.910201i \(0.635927\pi\)
\(114\) 3.88714e10 0.189083
\(115\) 3.75757e10 0.174208
\(116\) 4.27794e11 1.89111
\(117\) −1.36371e11 −0.575043
\(118\) 2.21264e11 0.890347
\(119\) −3.99489e11 −1.53461
\(120\) −7.49105e10 −0.274818
\(121\) −1.25886e11 −0.441222
\(122\) −3.80000e10 −0.127293
\(123\) 7.86812e10 0.251996
\(124\) 1.72003e11 0.526886
\(125\) −2.11682e11 −0.620410
\(126\) −2.50862e11 −0.703714
\(127\) 4.58813e11 1.23230 0.616149 0.787630i \(-0.288692\pi\)
0.616149 + 0.787630i \(0.288692\pi\)
\(128\) 6.51342e11 1.67554
\(129\) 1.80217e11 0.444173
\(130\) −3.40873e11 −0.805201
\(131\) 6.81888e10 0.154426 0.0772131 0.997015i \(-0.475398\pi\)
0.0772131 + 0.997015i \(0.475398\pi\)
\(132\) 4.47791e11 0.972565
\(133\) 8.02034e10 0.167112
\(134\) 6.62800e11 1.32528
\(135\) −1.85564e11 −0.356171
\(136\) −7.83697e11 −1.44439
\(137\) 1.17320e9 0.00207686 0.00103843 0.999999i \(-0.499669\pi\)
0.00103843 + 0.999999i \(0.499669\pi\)
\(138\) −4.00348e11 −0.680931
\(139\) −3.45355e11 −0.564526 −0.282263 0.959337i \(-0.591085\pi\)
−0.282263 + 0.959337i \(0.591085\pi\)
\(140\) −3.90809e11 −0.614129
\(141\) −3.03180e11 −0.458137
\(142\) −1.55001e12 −2.25293
\(143\) 8.05873e11 1.12699
\(144\) −2.33193e10 −0.0313850
\(145\) 2.89251e11 0.374758
\(146\) −7.04024e11 −0.878308
\(147\) 1.84895e11 0.222167
\(148\) −8.94954e11 −1.03600
\(149\) 1.04364e12 1.16419 0.582097 0.813120i \(-0.302233\pi\)
0.582097 + 0.813120i \(0.302233\pi\)
\(150\) 1.06364e12 1.14365
\(151\) 8.16986e11 0.846918 0.423459 0.905915i \(-0.360816\pi\)
0.423459 + 0.905915i \(0.360816\pi\)
\(152\) 1.57339e11 0.157288
\(153\) −5.36014e11 −0.516861
\(154\) 1.48245e12 1.37916
\(155\) 1.16299e11 0.104412
\(156\) 2.26351e12 1.96154
\(157\) −1.30094e12 −1.08845 −0.544227 0.838938i \(-0.683177\pi\)
−0.544227 + 0.838938i \(0.683177\pi\)
\(158\) 3.38547e11 0.273530
\(159\) 6.38305e11 0.498131
\(160\) 4.05166e11 0.305473
\(161\) −8.26039e11 −0.601808
\(162\) 1.09461e12 0.770771
\(163\) −8.77386e11 −0.597254 −0.298627 0.954370i \(-0.596529\pi\)
−0.298627 + 0.954370i \(0.596529\pi\)
\(164\) 8.05260e11 0.530023
\(165\) 3.02772e11 0.192732
\(166\) −1.09727e12 −0.675644
\(167\) 4.13045e11 0.246069 0.123034 0.992402i \(-0.460737\pi\)
0.123034 + 0.992402i \(0.460737\pi\)
\(168\) 1.64678e12 0.949369
\(169\) 2.28140e12 1.27299
\(170\) −1.33982e12 −0.723732
\(171\) 1.07613e11 0.0562841
\(172\) 1.84442e12 0.934230
\(173\) −1.01662e12 −0.498773 −0.249387 0.968404i \(-0.580229\pi\)
−0.249387 + 0.968404i \(0.580229\pi\)
\(174\) −3.08181e12 −1.46482
\(175\) 2.19462e12 1.01076
\(176\) 1.37803e11 0.0615092
\(177\) −9.93437e11 −0.429821
\(178\) 1.04868e12 0.439879
\(179\) −2.02367e11 −0.0823090 −0.0411545 0.999153i \(-0.513104\pi\)
−0.0411545 + 0.999153i \(0.513104\pi\)
\(180\) −5.24367e11 −0.206841
\(181\) 3.58266e12 1.37080 0.685399 0.728168i \(-0.259628\pi\)
0.685399 + 0.728168i \(0.259628\pi\)
\(182\) 7.49353e12 2.78159
\(183\) 1.70613e11 0.0614515
\(184\) −1.62048e12 −0.566429
\(185\) −6.05119e11 −0.205304
\(186\) −1.23910e12 −0.408118
\(187\) 3.16753e12 1.01296
\(188\) −3.10288e12 −0.963601
\(189\) 4.07932e12 1.23041
\(190\) 2.68989e11 0.0788116
\(191\) −1.34066e12 −0.381622 −0.190811 0.981627i \(-0.561112\pi\)
−0.190811 + 0.981627i \(0.561112\pi\)
\(192\) −4.55079e12 −1.25872
\(193\) −1.08399e8 −2.91381e−5 0 −1.45691e−5 1.00000i \(-0.500005\pi\)
−1.45691e−5 1.00000i \(0.500005\pi\)
\(194\) 8.51203e12 2.22394
\(195\) 1.53046e12 0.388716
\(196\) 1.89230e12 0.467284
\(197\) −2.96709e11 −0.0712470
\(198\) 1.98907e12 0.464506
\(199\) 2.20690e12 0.501292 0.250646 0.968079i \(-0.419357\pi\)
0.250646 + 0.968079i \(0.419357\pi\)
\(200\) 4.30528e12 0.951343
\(201\) −2.97586e12 −0.639785
\(202\) 7.36911e11 0.154164
\(203\) −6.35870e12 −1.29461
\(204\) 8.89686e12 1.76308
\(205\) 5.44472e11 0.105034
\(206\) 6.09349e12 1.14445
\(207\) −1.10834e12 −0.202691
\(208\) 6.96575e11 0.124056
\(209\) −6.35928e11 −0.110307
\(210\) 2.81537e12 0.475695
\(211\) 4.22161e12 0.694904 0.347452 0.937698i \(-0.387047\pi\)
0.347452 + 0.937698i \(0.387047\pi\)
\(212\) 6.53270e12 1.04772
\(213\) 6.95927e12 1.08762
\(214\) −4.50558e12 −0.686238
\(215\) 1.24710e12 0.185135
\(216\) 8.00261e12 1.15807
\(217\) −2.55664e12 −0.360696
\(218\) −1.66142e13 −2.28543
\(219\) 3.16095e12 0.424009
\(220\) 3.09870e12 0.405373
\(221\) 1.60114e13 2.04301
\(222\) 6.44721e12 0.802473
\(223\) 3.85211e12 0.467759 0.233880 0.972266i \(-0.424858\pi\)
0.233880 + 0.972266i \(0.424858\pi\)
\(224\) −8.90689e12 −1.05527
\(225\) 2.94463e12 0.340429
\(226\) 1.19611e13 1.34951
\(227\) 1.10232e13 1.21385 0.606927 0.794758i \(-0.292402\pi\)
0.606927 + 0.794758i \(0.292402\pi\)
\(228\) −1.78618e12 −0.191992
\(229\) −7.24160e11 −0.0759870 −0.0379935 0.999278i \(-0.512097\pi\)
−0.0379935 + 0.999278i \(0.512097\pi\)
\(230\) −2.77040e12 −0.283818
\(231\) −6.65593e12 −0.665798
\(232\) −1.24742e13 −1.21851
\(233\) −1.39480e12 −0.133062 −0.0665309 0.997784i \(-0.521193\pi\)
−0.0665309 + 0.997784i \(0.521193\pi\)
\(234\) 1.00544e13 0.936851
\(235\) −2.09800e12 −0.190955
\(236\) −1.01673e13 −0.904043
\(237\) −1.52002e12 −0.132048
\(238\) 2.94537e13 2.50016
\(239\) 3.29448e12 0.273274 0.136637 0.990621i \(-0.456371\pi\)
0.136637 + 0.990621i \(0.456371\pi\)
\(240\) 2.61708e11 0.0212156
\(241\) −1.11368e13 −0.882405 −0.441202 0.897408i \(-0.645448\pi\)
−0.441202 + 0.897408i \(0.645448\pi\)
\(242\) 9.28138e12 0.718833
\(243\) 9.43561e12 0.714390
\(244\) 1.74614e12 0.129251
\(245\) 1.27947e12 0.0926009
\(246\) −5.80105e12 −0.410548
\(247\) −3.21452e12 −0.222476
\(248\) −5.01549e12 −0.339491
\(249\) 4.92654e12 0.326171
\(250\) 1.56070e13 1.01076
\(251\) 2.17570e13 1.37846 0.689229 0.724543i \(-0.257949\pi\)
0.689229 + 0.724543i \(0.257949\pi\)
\(252\) 1.15273e13 0.714539
\(253\) 6.54962e12 0.397240
\(254\) −3.38276e13 −2.00764
\(255\) 6.01557e12 0.349386
\(256\) −1.98677e13 −1.12935
\(257\) 1.61133e13 0.896503 0.448251 0.893908i \(-0.352047\pi\)
0.448251 + 0.893908i \(0.352047\pi\)
\(258\) −1.32871e13 −0.723640
\(259\) 1.33025e13 0.709228
\(260\) 1.56635e13 0.817587
\(261\) −8.53179e12 −0.436031
\(262\) −5.02746e12 −0.251589
\(263\) −5.47457e12 −0.268283 −0.134142 0.990962i \(-0.542828\pi\)
−0.134142 + 0.990962i \(0.542828\pi\)
\(264\) −1.30573e13 −0.626657
\(265\) 4.41705e12 0.207625
\(266\) −5.91328e12 −0.272257
\(267\) −4.70840e12 −0.212354
\(268\) −3.04563e13 −1.34566
\(269\) −1.98053e12 −0.0857320 −0.0428660 0.999081i \(-0.513649\pi\)
−0.0428660 + 0.999081i \(0.513649\pi\)
\(270\) 1.36814e13 0.580269
\(271\) 6.50171e12 0.270207 0.135104 0.990831i \(-0.456863\pi\)
0.135104 + 0.990831i \(0.456863\pi\)
\(272\) 2.73793e12 0.111505
\(273\) −3.36447e13 −1.34283
\(274\) −8.64981e10 −0.00338360
\(275\) −1.74010e13 −0.667182
\(276\) 1.83964e13 0.691405
\(277\) −2.36179e13 −0.870165 −0.435083 0.900390i \(-0.643281\pi\)
−0.435083 + 0.900390i \(0.643281\pi\)
\(278\) 2.54625e13 0.919718
\(279\) −3.43037e12 −0.121484
\(280\) 1.13957e13 0.395705
\(281\) −3.59005e13 −1.22241 −0.611203 0.791474i \(-0.709314\pi\)
−0.611203 + 0.791474i \(0.709314\pi\)
\(282\) 2.23530e13 0.746390
\(283\) 5.22092e13 1.70971 0.854854 0.518869i \(-0.173647\pi\)
0.854854 + 0.518869i \(0.173647\pi\)
\(284\) 7.12243e13 2.28759
\(285\) −1.20772e12 −0.0380468
\(286\) −5.94158e13 −1.83607
\(287\) −1.19693e13 −0.362843
\(288\) −1.19508e13 −0.355417
\(289\) 2.86617e13 0.836303
\(290\) −2.13261e13 −0.610551
\(291\) −3.82176e13 −1.07362
\(292\) 3.23506e13 0.891818
\(293\) 1.79206e13 0.484821 0.242411 0.970174i \(-0.422062\pi\)
0.242411 + 0.970174i \(0.422062\pi\)
\(294\) −1.36320e13 −0.361951
\(295\) −6.87456e12 −0.179153
\(296\) 2.60962e13 0.667534
\(297\) −3.23448e13 −0.812163
\(298\) −7.69458e13 −1.89669
\(299\) 3.31073e13 0.801184
\(300\) −4.88754e13 −1.16124
\(301\) −2.74154e13 −0.639555
\(302\) −6.02352e13 −1.37979
\(303\) −3.30861e12 −0.0744236
\(304\) −5.49679e11 −0.0121424
\(305\) 1.18064e12 0.0256135
\(306\) 3.95196e13 0.842062
\(307\) −4.24972e13 −0.889405 −0.444702 0.895678i \(-0.646691\pi\)
−0.444702 + 0.895678i \(0.646691\pi\)
\(308\) −6.81198e13 −1.40037
\(309\) −2.73587e13 −0.552489
\(310\) −8.57456e12 −0.170107
\(311\) −1.88853e13 −0.368079 −0.184040 0.982919i \(-0.558917\pi\)
−0.184040 + 0.982919i \(0.558917\pi\)
\(312\) −6.60024e13 −1.26389
\(313\) 1.97471e13 0.371543 0.185771 0.982593i \(-0.440522\pi\)
0.185771 + 0.982593i \(0.440522\pi\)
\(314\) 9.59166e13 1.77329
\(315\) 7.79416e12 0.141599
\(316\) −1.55566e13 −0.277738
\(317\) −4.83693e13 −0.848680 −0.424340 0.905503i \(-0.639494\pi\)
−0.424340 + 0.905503i \(0.639494\pi\)
\(318\) −4.70613e13 −0.811548
\(319\) 5.04178e13 0.854546
\(320\) −3.14914e13 −0.524647
\(321\) 2.02293e13 0.331286
\(322\) 6.09026e13 0.980457
\(323\) −1.26349e13 −0.199966
\(324\) −5.02982e13 −0.782627
\(325\) −8.79594e13 −1.34562
\(326\) 6.46884e13 0.973037
\(327\) 7.45949e13 1.10331
\(328\) −2.34808e13 −0.341512
\(329\) 4.61210e13 0.659662
\(330\) −2.23229e13 −0.313996
\(331\) 5.11526e13 0.707642 0.353821 0.935313i \(-0.384882\pi\)
0.353821 + 0.935313i \(0.384882\pi\)
\(332\) 5.04205e13 0.686037
\(333\) 1.78487e13 0.238871
\(334\) −3.04532e13 −0.400892
\(335\) −2.05929e13 −0.266668
\(336\) −5.75320e12 −0.0732898
\(337\) −4.06419e12 −0.0509342 −0.0254671 0.999676i \(-0.508107\pi\)
−0.0254671 + 0.999676i \(0.508107\pi\)
\(338\) −1.68204e14 −2.07394
\(339\) −5.37033e13 −0.651483
\(340\) 6.15661e13 0.734865
\(341\) 2.02715e13 0.238087
\(342\) −7.93414e12 −0.0916972
\(343\) 7.14462e13 0.812571
\(344\) −5.37820e13 −0.601957
\(345\) 1.24386e13 0.137015
\(346\) 7.49536e13 0.812595
\(347\) 9.12072e13 0.973233 0.486616 0.873616i \(-0.338231\pi\)
0.486616 + 0.873616i \(0.338231\pi\)
\(348\) 1.41612e14 1.48735
\(349\) 4.78457e13 0.494656 0.247328 0.968932i \(-0.420447\pi\)
0.247328 + 0.968932i \(0.420447\pi\)
\(350\) −1.61806e14 −1.64672
\(351\) −1.63498e14 −1.63803
\(352\) 7.06223e13 0.696558
\(353\) 1.28016e14 1.24309 0.621547 0.783377i \(-0.286505\pi\)
0.621547 + 0.783377i \(0.286505\pi\)
\(354\) 7.32447e13 0.700258
\(355\) 4.81580e13 0.453328
\(356\) −4.81879e13 −0.446645
\(357\) −1.32242e14 −1.20697
\(358\) 1.49202e13 0.134097
\(359\) 1.37467e14 1.21669 0.608344 0.793674i \(-0.291834\pi\)
0.608344 + 0.793674i \(0.291834\pi\)
\(360\) 1.52902e13 0.133275
\(361\) −1.13954e14 −0.978224
\(362\) −2.64144e14 −2.23328
\(363\) −4.16718e13 −0.347021
\(364\) −3.44335e14 −2.82438
\(365\) 2.18737e13 0.176730
\(366\) −1.25791e13 −0.100116
\(367\) 1.70128e14 1.33386 0.666932 0.745119i \(-0.267607\pi\)
0.666932 + 0.745119i \(0.267607\pi\)
\(368\) 5.66131e12 0.0437275
\(369\) −1.60598e13 −0.122207
\(370\) 4.46145e13 0.334478
\(371\) −9.71016e13 −0.717249
\(372\) 5.69379e13 0.414396
\(373\) 1.42254e14 1.02016 0.510079 0.860128i \(-0.329616\pi\)
0.510079 + 0.860128i \(0.329616\pi\)
\(374\) −2.33537e14 −1.65030
\(375\) −7.00728e13 −0.487952
\(376\) 9.04778e13 0.620882
\(377\) 2.54854e14 1.72351
\(378\) −3.00763e14 −2.00456
\(379\) 4.38157e13 0.287815 0.143908 0.989591i \(-0.454033\pi\)
0.143908 + 0.989591i \(0.454033\pi\)
\(380\) −1.23603e13 −0.0800239
\(381\) 1.51880e14 0.969202
\(382\) 9.88445e13 0.621733
\(383\) 1.88156e14 1.16661 0.583303 0.812255i \(-0.301760\pi\)
0.583303 + 0.812255i \(0.301760\pi\)
\(384\) 2.15613e14 1.31781
\(385\) −4.60589e13 −0.277510
\(386\) 7.99213e9 4.74715e−5 0
\(387\) −3.67845e13 −0.215405
\(388\) −3.91136e14 −2.25815
\(389\) 1.24223e14 0.707095 0.353548 0.935417i \(-0.384975\pi\)
0.353548 + 0.935417i \(0.384975\pi\)
\(390\) −1.12839e14 −0.633291
\(391\) 1.30130e14 0.720121
\(392\) −5.51780e13 −0.301087
\(393\) 2.25724e13 0.121456
\(394\) 2.18759e13 0.116075
\(395\) −1.05185e13 −0.0550389
\(396\) −9.13997e13 −0.471651
\(397\) 3.33821e14 1.69889 0.849445 0.527676i \(-0.176937\pi\)
0.849445 + 0.527676i \(0.176937\pi\)
\(398\) −1.62711e14 −0.816698
\(399\) 2.65496e13 0.131434
\(400\) −1.50410e13 −0.0734422
\(401\) 1.61490e14 0.777772 0.388886 0.921286i \(-0.372860\pi\)
0.388886 + 0.921286i \(0.372860\pi\)
\(402\) 2.19406e14 1.04233
\(403\) 1.02469e14 0.480193
\(404\) −3.38618e13 −0.156535
\(405\) −3.40089e13 −0.155092
\(406\) 4.68818e14 2.10917
\(407\) −1.05475e14 −0.468145
\(408\) −2.59426e14 −1.13601
\(409\) 3.11378e14 1.34527 0.672636 0.739973i \(-0.265162\pi\)
0.672636 + 0.739973i \(0.265162\pi\)
\(410\) −4.01432e13 −0.171120
\(411\) 3.88362e11 0.00163345
\(412\) −2.80001e14 −1.16205
\(413\) 1.51126e14 0.618890
\(414\) 8.17161e13 0.330222
\(415\) 3.40916e13 0.135951
\(416\) 3.56985e14 1.40487
\(417\) −1.14322e14 −0.444000
\(418\) 4.68861e13 0.179711
\(419\) 3.23883e14 1.22521 0.612607 0.790388i \(-0.290121\pi\)
0.612607 + 0.790388i \(0.290121\pi\)
\(420\) −1.29369e14 −0.483013
\(421\) 2.72604e14 1.00457 0.502285 0.864702i \(-0.332493\pi\)
0.502285 + 0.864702i \(0.332493\pi\)
\(422\) −3.11253e14 −1.13213
\(423\) 6.18828e13 0.222177
\(424\) −1.90489e14 −0.675083
\(425\) −3.45729e14 −1.20948
\(426\) −5.13097e14 −1.77193
\(427\) −2.59544e13 −0.0884827
\(428\) 2.07036e14 0.696794
\(429\) 2.66767e14 0.886374
\(430\) −9.19467e13 −0.301620
\(431\) −3.41043e14 −1.10455 −0.552273 0.833664i \(-0.686239\pi\)
−0.552273 + 0.833664i \(0.686239\pi\)
\(432\) −2.79579e13 −0.0894014
\(433\) 2.01034e14 0.634724 0.317362 0.948304i \(-0.397203\pi\)
0.317362 + 0.948304i \(0.397203\pi\)
\(434\) 1.88497e14 0.587641
\(435\) 9.57504e13 0.294747
\(436\) 7.63438e14 2.32059
\(437\) −2.61256e13 −0.0784183
\(438\) −2.33052e14 −0.690789
\(439\) −3.96585e14 −1.16086 −0.580432 0.814309i \(-0.697116\pi\)
−0.580432 + 0.814309i \(0.697116\pi\)
\(440\) −9.03559e13 −0.261196
\(441\) −3.77393e13 −0.107741
\(442\) −1.18049e15 −3.32845
\(443\) 3.34805e14 0.932334 0.466167 0.884697i \(-0.345635\pi\)
0.466167 + 0.884697i \(0.345635\pi\)
\(444\) −2.96255e14 −0.814817
\(445\) −3.25820e13 −0.0885111
\(446\) −2.84011e14 −0.762066
\(447\) 3.45474e14 0.915638
\(448\) 6.92286e14 1.81241
\(449\) 6.12342e13 0.158358 0.0791788 0.996860i \(-0.474770\pi\)
0.0791788 + 0.996860i \(0.474770\pi\)
\(450\) −2.17103e14 −0.554622
\(451\) 9.49041e13 0.239505
\(452\) −5.49624e14 −1.37027
\(453\) 2.70446e14 0.666101
\(454\) −8.12726e14 −1.97759
\(455\) −2.32820e14 −0.559704
\(456\) 5.20836e13 0.123707
\(457\) −5.14743e14 −1.20796 −0.603978 0.797001i \(-0.706418\pi\)
−0.603978 + 0.797001i \(0.706418\pi\)
\(458\) 5.33913e13 0.123797
\(459\) −6.42637e14 −1.47230
\(460\) 1.27303e14 0.288183
\(461\) 2.87114e14 0.642242 0.321121 0.947038i \(-0.395940\pi\)
0.321121 + 0.947038i \(0.395940\pi\)
\(462\) 4.90732e14 1.08471
\(463\) −1.72267e14 −0.376276 −0.188138 0.982143i \(-0.560245\pi\)
−0.188138 + 0.982143i \(0.560245\pi\)
\(464\) 4.35798e13 0.0940668
\(465\) 3.84983e13 0.0821203
\(466\) 1.02836e14 0.216782
\(467\) −6.00139e14 −1.25029 −0.625143 0.780510i \(-0.714959\pi\)
−0.625143 + 0.780510i \(0.714959\pi\)
\(468\) −4.62011e14 −0.951262
\(469\) 4.52700e14 0.921213
\(470\) 1.54682e14 0.311102
\(471\) −4.30649e14 −0.856069
\(472\) 2.96471e14 0.582507
\(473\) 2.17375e14 0.422156
\(474\) 1.12069e14 0.215131
\(475\) 6.94103e13 0.131707
\(476\) −1.35343e15 −2.53862
\(477\) −1.30286e14 −0.241572
\(478\) −2.42897e14 −0.445214
\(479\) 4.83658e14 0.876381 0.438190 0.898882i \(-0.355620\pi\)
0.438190 + 0.898882i \(0.355620\pi\)
\(480\) 1.34121e14 0.240254
\(481\) −5.33160e14 −0.944191
\(482\) 8.21102e14 1.43760
\(483\) −2.73442e14 −0.473322
\(484\) −4.26488e14 −0.729890
\(485\) −2.64465e14 −0.447495
\(486\) −6.95674e14 −1.16387
\(487\) 8.09121e14 1.33846 0.669229 0.743057i \(-0.266625\pi\)
0.669229 + 0.743057i \(0.266625\pi\)
\(488\) −5.09161e13 −0.0832810
\(489\) −2.90440e14 −0.469740
\(490\) −9.43332e13 −0.150864
\(491\) −5.64967e14 −0.893460 −0.446730 0.894669i \(-0.647412\pi\)
−0.446730 + 0.894669i \(0.647412\pi\)
\(492\) 2.66564e14 0.416863
\(493\) 1.00172e15 1.54913
\(494\) 2.37002e14 0.362454
\(495\) −6.17995e13 −0.0934665
\(496\) 1.75221e13 0.0262082
\(497\) −1.05867e15 −1.56604
\(498\) −3.63227e14 −0.531394
\(499\) 8.81666e14 1.27571 0.637853 0.770158i \(-0.279823\pi\)
0.637853 + 0.770158i \(0.279823\pi\)
\(500\) −7.17157e14 −1.02631
\(501\) 1.36730e14 0.193533
\(502\) −1.60411e15 −2.24577
\(503\) 2.53182e14 0.350597 0.175298 0.984515i \(-0.443911\pi\)
0.175298 + 0.984515i \(0.443911\pi\)
\(504\) −3.36129e14 −0.460403
\(505\) −2.28955e13 −0.0310204
\(506\) −4.82894e14 −0.647178
\(507\) 7.55209e14 1.00121
\(508\) 1.55441e15 2.03852
\(509\) −5.59138e13 −0.0725390 −0.0362695 0.999342i \(-0.511547\pi\)
−0.0362695 + 0.999342i \(0.511547\pi\)
\(510\) −4.43519e14 −0.569215
\(511\) −4.80857e14 −0.610521
\(512\) 1.30870e14 0.164382
\(513\) 1.29019e14 0.160327
\(514\) −1.18801e15 −1.46057
\(515\) −1.89322e14 −0.230282
\(516\) 6.10556e14 0.734772
\(517\) −3.65691e14 −0.435428
\(518\) −9.80776e14 −1.15546
\(519\) −3.36529e14 −0.392285
\(520\) −4.56735e14 −0.526800
\(521\) −1.50269e15 −1.71500 −0.857498 0.514487i \(-0.827982\pi\)
−0.857498 + 0.514487i \(0.827982\pi\)
\(522\) 6.29036e14 0.710375
\(523\) 1.49288e15 1.66827 0.834134 0.551562i \(-0.185968\pi\)
0.834134 + 0.551562i \(0.185968\pi\)
\(524\) 2.31017e14 0.255459
\(525\) 7.26481e14 0.794965
\(526\) 4.03632e14 0.437083
\(527\) 4.02761e14 0.431607
\(528\) 4.56169e13 0.0483770
\(529\) −6.83735e14 −0.717598
\(530\) −3.25663e14 −0.338260
\(531\) 2.02773e14 0.208444
\(532\) 2.71721e14 0.276445
\(533\) 4.79726e14 0.483051
\(534\) 3.47143e14 0.345965
\(535\) 1.39986e14 0.138083
\(536\) 8.88084e14 0.867057
\(537\) −6.69891e13 −0.0647360
\(538\) 1.46021e14 0.139673
\(539\) 2.23017e14 0.211154
\(540\) −6.28673e14 −0.589195
\(541\) −3.42334e14 −0.317589 −0.158794 0.987312i \(-0.550761\pi\)
−0.158794 + 0.987312i \(0.550761\pi\)
\(542\) −4.79362e14 −0.440218
\(543\) 1.18596e15 1.07813
\(544\) 1.40315e15 1.26273
\(545\) 5.16195e14 0.459868
\(546\) 2.48057e15 2.18772
\(547\) 2.06884e15 1.80633 0.903165 0.429294i \(-0.141238\pi\)
0.903165 + 0.429294i \(0.141238\pi\)
\(548\) 3.97467e12 0.00343564
\(549\) −3.48243e13 −0.0298013
\(550\) 1.28295e15 1.08696
\(551\) −2.01110e14 −0.168694
\(552\) −5.36425e14 −0.445496
\(553\) 2.31231e14 0.190134
\(554\) 1.74131e15 1.41766
\(555\) −2.00312e14 −0.161471
\(556\) −1.17003e15 −0.933865
\(557\) −1.93311e15 −1.52775 −0.763875 0.645364i \(-0.776706\pi\)
−0.763875 + 0.645364i \(0.776706\pi\)
\(558\) 2.52916e14 0.197920
\(559\) 1.09880e15 0.851437
\(560\) −3.98120e13 −0.0305478
\(561\) 1.04854e15 0.796692
\(562\) 2.64689e15 1.99153
\(563\) −4.76413e14 −0.354966 −0.177483 0.984124i \(-0.556796\pi\)
−0.177483 + 0.984124i \(0.556796\pi\)
\(564\) −1.02714e15 −0.757872
\(565\) −3.71626e14 −0.271544
\(566\) −3.84931e15 −2.78543
\(567\) 7.47629e14 0.535771
\(568\) −2.07685e15 −1.47397
\(569\) −1.92878e14 −0.135571 −0.0677854 0.997700i \(-0.521593\pi\)
−0.0677854 + 0.997700i \(0.521593\pi\)
\(570\) 8.90431e13 0.0619853
\(571\) 7.17628e14 0.494767 0.247384 0.968918i \(-0.420429\pi\)
0.247384 + 0.968918i \(0.420429\pi\)
\(572\) 2.73021e15 1.86431
\(573\) −4.43795e14 −0.300146
\(574\) 8.82480e14 0.591139
\(575\) −7.14877e14 −0.474306
\(576\) 9.28874e14 0.610426
\(577\) −4.07758e14 −0.265421 −0.132710 0.991155i \(-0.542368\pi\)
−0.132710 + 0.991155i \(0.542368\pi\)
\(578\) −2.11318e15 −1.36249
\(579\) −3.58833e10 −2.29171e−5 0
\(580\) 9.79953e14 0.619942
\(581\) −7.49446e14 −0.469647
\(582\) 2.81773e15 1.74913
\(583\) 7.69913e14 0.473440
\(584\) −9.43320e14 −0.574630
\(585\) −3.12387e14 −0.188510
\(586\) −1.32126e15 −0.789864
\(587\) 2.14190e15 1.26850 0.634248 0.773130i \(-0.281310\pi\)
0.634248 + 0.773130i \(0.281310\pi\)
\(588\) 6.26404e14 0.367518
\(589\) −8.08602e13 −0.0470003
\(590\) 5.06852e14 0.291874
\(591\) −9.82193e13 −0.0560358
\(592\) −9.11699e13 −0.0515326
\(593\) −2.99983e15 −1.67995 −0.839974 0.542627i \(-0.817430\pi\)
−0.839974 + 0.542627i \(0.817430\pi\)
\(594\) 2.38473e15 1.32316
\(595\) −9.15114e14 −0.503074
\(596\) 3.53573e15 1.92586
\(597\) 7.30547e14 0.394266
\(598\) −2.44095e15 −1.30528
\(599\) 1.17931e15 0.624855 0.312427 0.949942i \(-0.398858\pi\)
0.312427 + 0.949942i \(0.398858\pi\)
\(600\) 1.42517e15 0.748231
\(601\) 2.22042e15 1.15512 0.577558 0.816349i \(-0.304006\pi\)
0.577558 + 0.816349i \(0.304006\pi\)
\(602\) 2.02129e15 1.04195
\(603\) 6.07410e14 0.310268
\(604\) 2.76786e15 1.40101
\(605\) −2.88368e14 −0.144641
\(606\) 2.43939e14 0.121250
\(607\) −9.57108e14 −0.471437 −0.235718 0.971821i \(-0.575744\pi\)
−0.235718 + 0.971821i \(0.575744\pi\)
\(608\) −2.81703e14 −0.137506
\(609\) −2.10491e15 −1.01821
\(610\) −8.70470e13 −0.0417292
\(611\) −1.84851e15 −0.878204
\(612\) −1.81596e15 −0.855015
\(613\) 2.26404e15 1.05646 0.528229 0.849102i \(-0.322856\pi\)
0.528229 + 0.849102i \(0.322856\pi\)
\(614\) 3.13326e15 1.44901
\(615\) 1.80236e14 0.0826092
\(616\) 1.98632e15 0.902311
\(617\) −2.19161e15 −0.986724 −0.493362 0.869824i \(-0.664232\pi\)
−0.493362 + 0.869824i \(0.664232\pi\)
\(618\) 2.01712e15 0.900108
\(619\) −3.40666e15 −1.50671 −0.753355 0.657614i \(-0.771566\pi\)
−0.753355 + 0.657614i \(0.771566\pi\)
\(620\) 3.94009e14 0.172724
\(621\) −1.32880e15 −0.577374
\(622\) 1.39238e15 0.599669
\(623\) 7.16261e14 0.305765
\(624\) 2.30586e14 0.0975704
\(625\) 1.64307e15 0.689151
\(626\) −1.45592e15 −0.605313
\(627\) −2.10510e14 −0.0867565
\(628\) −4.40746e15 −1.80057
\(629\) −2.09562e15 −0.848659
\(630\) −5.74652e14 −0.230692
\(631\) −2.25820e15 −0.898672 −0.449336 0.893363i \(-0.648339\pi\)
−0.449336 + 0.893363i \(0.648339\pi\)
\(632\) 4.53618e14 0.178956
\(633\) 1.39748e15 0.546542
\(634\) 3.56620e15 1.38266
\(635\) 1.05101e15 0.403972
\(636\) 2.16251e15 0.824032
\(637\) 1.12732e15 0.425872
\(638\) −3.71723e15 −1.39221
\(639\) −1.42047e15 −0.527447
\(640\) 1.49203e15 0.549274
\(641\) −3.54602e15 −1.29426 −0.647130 0.762380i \(-0.724031\pi\)
−0.647130 + 0.762380i \(0.724031\pi\)
\(642\) −1.49148e15 −0.539726
\(643\) 1.96644e15 0.705539 0.352770 0.935710i \(-0.385240\pi\)
0.352770 + 0.935710i \(0.385240\pi\)
\(644\) −2.79853e15 −0.995539
\(645\) 4.12825e14 0.145609
\(646\) 9.31549e14 0.325782
\(647\) 5.18068e15 1.79644 0.898221 0.439544i \(-0.144860\pi\)
0.898221 + 0.439544i \(0.144860\pi\)
\(648\) 1.46666e15 0.504274
\(649\) −1.19827e15 −0.408515
\(650\) 6.48512e15 2.19227
\(651\) −8.46321e14 −0.283687
\(652\) −2.97249e15 −0.988005
\(653\) −1.91238e14 −0.0630305 −0.0315153 0.999503i \(-0.510033\pi\)
−0.0315153 + 0.999503i \(0.510033\pi\)
\(654\) −5.49977e15 −1.79749
\(655\) 1.56201e14 0.0506240
\(656\) 8.20326e13 0.0263642
\(657\) −6.45189e14 −0.205626
\(658\) −3.40043e15 −1.07471
\(659\) −4.48314e15 −1.40512 −0.702559 0.711625i \(-0.747959\pi\)
−0.702559 + 0.711625i \(0.747959\pi\)
\(660\) 1.02576e15 0.318826
\(661\) 5.33081e15 1.64318 0.821590 0.570079i \(-0.193087\pi\)
0.821590 + 0.570079i \(0.193087\pi\)
\(662\) −3.77141e15 −1.15288
\(663\) 5.30022e15 1.60683
\(664\) −1.47022e15 −0.442038
\(665\) 1.83723e14 0.0547827
\(666\) −1.31596e15 −0.389164
\(667\) 2.07129e15 0.607504
\(668\) 1.39935e15 0.407058
\(669\) 1.27516e15 0.367892
\(670\) 1.51828e15 0.434452
\(671\) 2.05791e14 0.0584054
\(672\) −2.94843e15 −0.829966
\(673\) −8.39608e13 −0.0234419 −0.0117210 0.999931i \(-0.503731\pi\)
−0.0117210 + 0.999931i \(0.503731\pi\)
\(674\) 2.99647e14 0.0829813
\(675\) 3.53036e15 0.969725
\(676\) 7.72915e15 2.10584
\(677\) −6.79837e15 −1.83724 −0.918622 0.395137i \(-0.870697\pi\)
−0.918622 + 0.395137i \(0.870697\pi\)
\(678\) 3.95947e15 1.06139
\(679\) 5.81382e15 1.54589
\(680\) −1.79522e15 −0.473499
\(681\) 3.64900e15 0.954696
\(682\) −1.49459e15 −0.387889
\(683\) 2.14600e15 0.552478 0.276239 0.961089i \(-0.410912\pi\)
0.276239 + 0.961089i \(0.410912\pi\)
\(684\) 3.64581e14 0.0931077
\(685\) 2.68746e12 0.000680837 0
\(686\) −5.26762e15 −1.32383
\(687\) −2.39718e14 −0.0597638
\(688\) 1.87893e14 0.0464702
\(689\) 3.89179e15 0.954869
\(690\) −9.17082e14 −0.223223
\(691\) −4.37783e15 −1.05713 −0.528566 0.848892i \(-0.677270\pi\)
−0.528566 + 0.848892i \(0.677270\pi\)
\(692\) −3.44419e15 −0.825094
\(693\) 1.35856e15 0.322883
\(694\) −6.72457e15 −1.58558
\(695\) −7.91108e14 −0.185063
\(696\) −4.12931e15 −0.958355
\(697\) 1.88559e15 0.434177
\(698\) −3.52760e15 −0.805887
\(699\) −4.61718e14 −0.104653
\(700\) 7.43513e15 1.67205
\(701\) 6.04215e15 1.34816 0.674081 0.738657i \(-0.264540\pi\)
0.674081 + 0.738657i \(0.264540\pi\)
\(702\) 1.20544e16 2.66866
\(703\) 4.20726e14 0.0924156
\(704\) −5.48910e15 −1.19633
\(705\) −6.94498e14 −0.150186
\(706\) −9.43844e15 −2.02523
\(707\) 5.03319e14 0.107161
\(708\) −3.36566e15 −0.711030
\(709\) 3.12868e15 0.655853 0.327926 0.944703i \(-0.393650\pi\)
0.327926 + 0.944703i \(0.393650\pi\)
\(710\) −3.55062e15 −0.738555
\(711\) 3.10255e14 0.0640377
\(712\) 1.40512e15 0.287789
\(713\) 8.32804e14 0.169258
\(714\) 9.75003e15 1.96637
\(715\) 1.84602e15 0.369448
\(716\) −6.85597e14 −0.136159
\(717\) 1.09057e15 0.214930
\(718\) −1.01352e16 −1.98221
\(719\) −4.67906e15 −0.908133 −0.454067 0.890968i \(-0.650027\pi\)
−0.454067 + 0.890968i \(0.650027\pi\)
\(720\) −5.34178e13 −0.0102886
\(721\) 4.16192e15 0.795518
\(722\) 8.40163e15 1.59371
\(723\) −3.68661e15 −0.694011
\(724\) 1.21377e16 2.26764
\(725\) −5.50300e15 −1.02033
\(726\) 3.07240e15 0.565362
\(727\) 6.26366e14 0.114390 0.0571951 0.998363i \(-0.481784\pi\)
0.0571951 + 0.998363i \(0.481784\pi\)
\(728\) 1.00406e16 1.81985
\(729\) 5.75346e15 1.03497
\(730\) −1.61272e15 −0.287927
\(731\) 4.31888e15 0.765290
\(732\) 5.78021e14 0.101656
\(733\) −1.75098e15 −0.305639 −0.152820 0.988254i \(-0.548835\pi\)
−0.152820 + 0.988254i \(0.548835\pi\)
\(734\) −1.25433e16 −2.17311
\(735\) 4.23540e14 0.0728306
\(736\) 2.90134e15 0.495189
\(737\) −3.58944e15 −0.608072
\(738\) 1.18407e15 0.199098
\(739\) 8.05370e14 0.134416 0.0672080 0.997739i \(-0.478591\pi\)
0.0672080 + 0.997739i \(0.478591\pi\)
\(740\) −2.05008e15 −0.339623
\(741\) −1.06410e15 −0.174977
\(742\) 7.15916e15 1.16853
\(743\) 7.19998e15 1.16652 0.583261 0.812285i \(-0.301777\pi\)
0.583261 + 0.812285i \(0.301777\pi\)
\(744\) −1.66027e15 −0.267010
\(745\) 2.39067e15 0.381646
\(746\) −1.04882e16 −1.66203
\(747\) −1.00557e15 −0.158179
\(748\) 1.07313e16 1.67568
\(749\) −3.07736e15 −0.477011
\(750\) 5.16636e15 0.794965
\(751\) −7.94398e15 −1.21344 −0.606720 0.794915i \(-0.707515\pi\)
−0.606720 + 0.794915i \(0.707515\pi\)
\(752\) −3.16094e14 −0.0479311
\(753\) 7.20219e15 1.08416
\(754\) −1.87900e16 −2.80792
\(755\) 1.87148e15 0.277636
\(756\) 1.38203e16 2.03539
\(757\) 1.80773e15 0.264305 0.132153 0.991229i \(-0.457811\pi\)
0.132153 + 0.991229i \(0.457811\pi\)
\(758\) −3.23047e15 −0.468905
\(759\) 2.16811e15 0.312429
\(760\) 3.60418e14 0.0515622
\(761\) −9.95318e15 −1.41366 −0.706832 0.707382i \(-0.749876\pi\)
−0.706832 + 0.707382i \(0.749876\pi\)
\(762\) −1.11979e16 −1.57901
\(763\) −1.13477e16 −1.58863
\(764\) −4.54200e15 −0.631297
\(765\) −1.22785e15 −0.169437
\(766\) −1.38724e16 −1.90062
\(767\) −6.05706e15 −0.823925
\(768\) −6.57678e15 −0.888233
\(769\) −1.61413e15 −0.216443 −0.108221 0.994127i \(-0.534516\pi\)
−0.108221 + 0.994127i \(0.534516\pi\)
\(770\) 3.39585e15 0.452116
\(771\) 5.33395e15 0.705099
\(772\) −3.67246e11 −4.82017e−5 0
\(773\) 9.02775e15 1.17650 0.588251 0.808679i \(-0.299817\pi\)
0.588251 + 0.808679i \(0.299817\pi\)
\(774\) 2.71207e15 0.350934
\(775\) −2.21259e15 −0.284277
\(776\) 1.14052e16 1.45501
\(777\) 4.40352e15 0.557807
\(778\) −9.15875e15 −1.15199
\(779\) −3.78560e14 −0.0472801
\(780\) 5.18505e15 0.643032
\(781\) 8.39417e15 1.03371
\(782\) −9.59431e15 −1.17321
\(783\) −1.02289e16 −1.24205
\(784\) 1.92770e14 0.0232435
\(785\) −2.98008e15 −0.356817
\(786\) −1.66423e15 −0.197875
\(787\) 1.46678e16 1.73182 0.865909 0.500201i \(-0.166740\pi\)
0.865909 + 0.500201i \(0.166740\pi\)
\(788\) −1.00522e15 −0.117860
\(789\) −1.81224e15 −0.211005
\(790\) 7.75513e14 0.0896685
\(791\) 8.16958e15 0.938056
\(792\) 2.66515e15 0.303902
\(793\) 1.04024e15 0.117797
\(794\) −2.46121e16 −2.76781
\(795\) 1.46217e15 0.163297
\(796\) 7.47675e15 0.829260
\(797\) −1.53657e16 −1.69252 −0.846258 0.532773i \(-0.821150\pi\)
−0.846258 + 0.532773i \(0.821150\pi\)
\(798\) −1.95746e15 −0.214130
\(799\) −7.26568e15 −0.789349
\(800\) −7.70828e15 −0.831692
\(801\) 9.61043e14 0.102983
\(802\) −1.19064e16 −1.26713
\(803\) 3.81269e15 0.402991
\(804\) −1.00819e16 −1.05836
\(805\) −1.89222e15 −0.197285
\(806\) −7.55490e15 −0.782323
\(807\) −6.55611e14 −0.0674282
\(808\) 9.87385e14 0.100861
\(809\) 2.05032e15 0.208020 0.104010 0.994576i \(-0.466833\pi\)
0.104010 + 0.994576i \(0.466833\pi\)
\(810\) 2.50743e15 0.252674
\(811\) −1.78243e16 −1.78401 −0.892005 0.452025i \(-0.850702\pi\)
−0.892005 + 0.452025i \(0.850702\pi\)
\(812\) −2.15426e16 −2.14161
\(813\) 2.15225e15 0.212518
\(814\) 7.77653e15 0.762696
\(815\) −2.00984e15 −0.195792
\(816\) 9.06332e14 0.0876984
\(817\) −8.67080e14 −0.0833370
\(818\) −2.29575e16 −2.19170
\(819\) 6.86730e15 0.651215
\(820\) 1.84462e15 0.173752
\(821\) −9.30037e15 −0.870188 −0.435094 0.900385i \(-0.643285\pi\)
−0.435094 + 0.900385i \(0.643285\pi\)
\(822\) −2.86333e13 −0.00266120
\(823\) −7.97756e15 −0.736497 −0.368249 0.929727i \(-0.620042\pi\)
−0.368249 + 0.929727i \(0.620042\pi\)
\(824\) 8.16464e15 0.748751
\(825\) −5.76023e15 −0.524739
\(826\) −1.11423e16 −1.00829
\(827\) −2.22714e15 −0.200201 −0.100101 0.994977i \(-0.531916\pi\)
−0.100101 + 0.994977i \(0.531916\pi\)
\(828\) −3.75493e15 −0.335301
\(829\) −1.30117e16 −1.15421 −0.577106 0.816669i \(-0.695818\pi\)
−0.577106 + 0.816669i \(0.695818\pi\)
\(830\) −2.51352e15 −0.221489
\(831\) −7.81819e15 −0.684385
\(832\) −2.77465e16 −2.41285
\(833\) 4.43098e15 0.382783
\(834\) 8.42882e15 0.723358
\(835\) 9.46166e14 0.0806662
\(836\) −2.15446e15 −0.182475
\(837\) −4.11273e15 −0.346051
\(838\) −2.38795e16 −1.99610
\(839\) −6.51934e15 −0.541394 −0.270697 0.962665i \(-0.587254\pi\)
−0.270697 + 0.962665i \(0.587254\pi\)
\(840\) 3.77230e15 0.311222
\(841\) 3.74394e15 0.306868
\(842\) −2.00987e16 −1.63663
\(843\) −1.18841e16 −0.961422
\(844\) 1.43024e16 1.14954
\(845\) 5.22603e15 0.417311
\(846\) −4.56253e15 −0.361967
\(847\) 6.33929e15 0.499668
\(848\) 6.65493e14 0.0521154
\(849\) 1.72827e16 1.34468
\(850\) 2.54901e16 1.97046
\(851\) −4.33319e15 −0.332809
\(852\) 2.35773e16 1.79919
\(853\) −2.49420e16 −1.89108 −0.945542 0.325500i \(-0.894467\pi\)
−0.945542 + 0.325500i \(0.894467\pi\)
\(854\) 1.91358e15 0.144155
\(855\) 2.46510e14 0.0184510
\(856\) −6.03701e15 −0.448969
\(857\) 1.18643e16 0.876692 0.438346 0.898806i \(-0.355564\pi\)
0.438346 + 0.898806i \(0.355564\pi\)
\(858\) −1.96683e16 −1.44407
\(859\) −3.39126e15 −0.247399 −0.123700 0.992320i \(-0.539476\pi\)
−0.123700 + 0.992320i \(0.539476\pi\)
\(860\) 4.22504e15 0.306259
\(861\) −3.96219e15 −0.285376
\(862\) 2.51446e16 1.79951
\(863\) 5.01659e14 0.0356738 0.0178369 0.999841i \(-0.494322\pi\)
0.0178369 + 0.999841i \(0.494322\pi\)
\(864\) −1.43280e16 −1.01242
\(865\) −2.32877e15 −0.163508
\(866\) −1.48219e16 −1.03408
\(867\) 9.48784e15 0.657752
\(868\) −8.66164e15 −0.596680
\(869\) −1.83342e15 −0.125503
\(870\) −7.05953e15 −0.480198
\(871\) −1.81440e16 −1.22641
\(872\) −2.22613e16 −1.49524
\(873\) 7.80069e15 0.520660
\(874\) 1.92620e15 0.127758
\(875\) 1.06598e16 0.702592
\(876\) 1.07090e16 0.701415
\(877\) 2.06847e16 1.34633 0.673164 0.739493i \(-0.264935\pi\)
0.673164 + 0.739493i \(0.264935\pi\)
\(878\) 2.92396e16 1.89126
\(879\) 5.93225e15 0.381312
\(880\) 3.15668e14 0.0201639
\(881\) 1.42453e16 0.904280 0.452140 0.891947i \(-0.350661\pi\)
0.452140 + 0.891947i \(0.350661\pi\)
\(882\) 2.78246e15 0.175530
\(883\) −7.17959e14 −0.0450107 −0.0225054 0.999747i \(-0.507164\pi\)
−0.0225054 + 0.999747i \(0.507164\pi\)
\(884\) 5.42449e16 3.37965
\(885\) −2.27568e15 −0.140904
\(886\) −2.46847e16 −1.51895
\(887\) 1.71047e16 1.04601 0.523005 0.852329i \(-0.324811\pi\)
0.523005 + 0.852329i \(0.324811\pi\)
\(888\) 8.63860e15 0.525015
\(889\) −2.31047e16 −1.39553
\(890\) 2.40222e15 0.144201
\(891\) −5.92791e15 −0.353651
\(892\) 1.30506e16 0.773789
\(893\) 1.45869e15 0.0859569
\(894\) −2.54713e16 −1.49174
\(895\) −4.63563e14 −0.0269825
\(896\) −3.27999e16 −1.89749
\(897\) 1.09595e16 0.630131
\(898\) −4.51471e15 −0.257994
\(899\) 6.41078e15 0.364110
\(900\) 9.97609e15 0.563153
\(901\) 1.52969e16 0.858257
\(902\) −6.99714e15 −0.390198
\(903\) −9.07527e15 −0.503010
\(904\) 1.60267e16 0.882910
\(905\) 8.20683e15 0.449375
\(906\) −1.99396e16 −1.08520
\(907\) −1.89857e16 −1.02704 −0.513519 0.858078i \(-0.671658\pi\)
−0.513519 + 0.858078i \(0.671658\pi\)
\(908\) 3.73455e16 2.00801
\(909\) 6.75328e14 0.0360922
\(910\) 1.71655e16 0.911862
\(911\) −3.33554e16 −1.76123 −0.880613 0.473836i \(-0.842869\pi\)
−0.880613 + 0.473836i \(0.842869\pi\)
\(912\) −1.81960e14 −0.00955000
\(913\) 5.94232e15 0.310004
\(914\) 3.79512e16 1.96798
\(915\) 3.90826e14 0.0201450
\(916\) −2.45338e15 −0.125701
\(917\) −3.43381e15 −0.174882
\(918\) 4.73807e16 2.39865
\(919\) −1.26006e15 −0.0634098 −0.0317049 0.999497i \(-0.510094\pi\)
−0.0317049 + 0.999497i \(0.510094\pi\)
\(920\) −3.71205e15 −0.185687
\(921\) −1.40678e16 −0.699516
\(922\) −2.11685e16 −1.04633
\(923\) 4.24312e16 2.08486
\(924\) −2.25496e16 −1.10139
\(925\) 1.15124e16 0.558967
\(926\) 1.27010e16 0.613024
\(927\) 5.58426e15 0.267933
\(928\) 2.23340e16 1.06525
\(929\) 2.58888e16 1.22751 0.613756 0.789496i \(-0.289658\pi\)
0.613756 + 0.789496i \(0.289658\pi\)
\(930\) −2.83842e15 −0.133789
\(931\) −8.89585e14 −0.0416835
\(932\) −4.72543e15 −0.220117
\(933\) −6.25157e15 −0.289494
\(934\) 4.42474e16 2.03695
\(935\) 7.25589e15 0.332068
\(936\) 1.34719e16 0.612932
\(937\) −1.04329e16 −0.471887 −0.235943 0.971767i \(-0.575818\pi\)
−0.235943 + 0.971767i \(0.575818\pi\)
\(938\) −3.33769e16 −1.50083
\(939\) 6.53685e15 0.292218
\(940\) −7.10780e15 −0.315887
\(941\) 2.54394e16 1.12400 0.561998 0.827139i \(-0.310033\pi\)
0.561998 + 0.827139i \(0.310033\pi\)
\(942\) 3.17511e16 1.39470
\(943\) 3.89890e15 0.170266
\(944\) −1.03575e15 −0.0449686
\(945\) 9.34455e15 0.403351
\(946\) −1.60267e16 −0.687771
\(947\) 1.28374e16 0.547712 0.273856 0.961771i \(-0.411701\pi\)
0.273856 + 0.961771i \(0.411701\pi\)
\(948\) −5.14966e15 −0.218440
\(949\) 1.92725e16 0.812784
\(950\) −5.11752e15 −0.214575
\(951\) −1.60116e16 −0.667486
\(952\) 3.94650e16 1.63572
\(953\) 2.82424e16 1.16383 0.581917 0.813248i \(-0.302303\pi\)
0.581917 + 0.813248i \(0.302303\pi\)
\(954\) 9.60579e15 0.393566
\(955\) −3.07105e15 −0.125103
\(956\) 1.11614e16 0.452062
\(957\) 1.66897e16 0.672100
\(958\) −3.56594e16 −1.42779
\(959\) −5.90792e13 −0.00235197
\(960\) −1.04245e16 −0.412634
\(961\) −2.28309e16 −0.898554
\(962\) 3.93091e16 1.53826
\(963\) −4.12905e15 −0.160659
\(964\) −3.77304e16 −1.45971
\(965\) −2.48312e11 −9.55206e−6 0
\(966\) 2.01605e16 0.771129
\(967\) 1.74832e16 0.664929 0.332465 0.943116i \(-0.392120\pi\)
0.332465 + 0.943116i \(0.392120\pi\)
\(968\) 1.24361e16 0.470294
\(969\) −4.18250e15 −0.157273
\(970\) 1.94986e16 0.729053
\(971\) 2.35331e15 0.0874931 0.0437466 0.999043i \(-0.486071\pi\)
0.0437466 + 0.999043i \(0.486071\pi\)
\(972\) 3.19669e16 1.18178
\(973\) 1.73912e16 0.639306
\(974\) −5.96553e16 −2.18060
\(975\) −2.91171e16 −1.05833
\(976\) 1.77881e14 0.00642916
\(977\) 1.83471e16 0.659397 0.329698 0.944086i \(-0.393053\pi\)
0.329698 + 0.944086i \(0.393053\pi\)
\(978\) 2.14137e16 0.765294
\(979\) −5.67920e15 −0.201828
\(980\) 4.33470e15 0.153185
\(981\) −1.52258e16 −0.535056
\(982\) 4.16542e16 1.45561
\(983\) 1.35715e16 0.471611 0.235805 0.971800i \(-0.424227\pi\)
0.235805 + 0.971800i \(0.424227\pi\)
\(984\) −7.77281e15 −0.268599
\(985\) −6.79675e14 −0.0233562
\(986\) −7.38553e16 −2.52382
\(987\) 1.52674e16 0.518824
\(988\) −1.08905e16 −0.368030
\(989\) 8.93032e15 0.300115
\(990\) 4.55638e15 0.152274
\(991\) 7.33626e15 0.243820 0.121910 0.992541i \(-0.461098\pi\)
0.121910 + 0.992541i \(0.461098\pi\)
\(992\) 8.97984e15 0.296793
\(993\) 1.69330e16 0.556560
\(994\) 7.80544e16 2.55136
\(995\) 5.05537e15 0.164333
\(996\) 1.66906e16 0.539568
\(997\) 2.93527e16 0.943679 0.471840 0.881684i \(-0.343590\pi\)
0.471840 + 0.881684i \(0.343590\pi\)
\(998\) −6.50039e16 −2.07836
\(999\) 2.13991e16 0.680432
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 197.12.a.b.1.11 92
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.12.a.b.1.11 92 1.1 even 1 trivial