Properties

Label 197.10.a.b.1.1
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 1.1
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)
 
\(f(q)\) \(=\) \(q-44.8173 q^{2} -222.555 q^{3} +1496.59 q^{4} +1221.65 q^{5} +9974.32 q^{6} +2695.26 q^{7} -44126.8 q^{8} +29847.7 q^{9} +O(q^{10})\) \(q-44.8173 q^{2} -222.555 q^{3} +1496.59 q^{4} +1221.65 q^{5} +9974.32 q^{6} +2695.26 q^{7} -44126.8 q^{8} +29847.7 q^{9} -54751.2 q^{10} -67291.8 q^{11} -333074. q^{12} +78776.4 q^{13} -120794. q^{14} -271885. q^{15} +1.21139e6 q^{16} -456849. q^{17} -1.33769e6 q^{18} -1.02396e6 q^{19} +1.82832e6 q^{20} -599844. q^{21} +3.01584e6 q^{22} +1.05716e6 q^{23} +9.82064e6 q^{24} -460690. q^{25} -3.53055e6 q^{26} -2.26221e6 q^{27} +4.03371e6 q^{28} +2.55701e6 q^{29} +1.21852e7 q^{30} +6.29959e6 q^{31} -3.16983e7 q^{32} +1.49761e7 q^{33} +2.04748e7 q^{34} +3.29267e6 q^{35} +4.46699e7 q^{36} -3.63397e6 q^{37} +4.58910e7 q^{38} -1.75321e7 q^{39} -5.39076e7 q^{40} -3.55107e7 q^{41} +2.68834e7 q^{42} +2.23251e7 q^{43} -1.00708e8 q^{44} +3.64635e7 q^{45} -4.73793e7 q^{46} +3.40966e6 q^{47} -2.69601e8 q^{48} -3.30892e7 q^{49} +2.06469e7 q^{50} +1.01674e8 q^{51} +1.17896e8 q^{52} -1.91404e7 q^{53} +1.01386e8 q^{54} -8.22072e7 q^{55} -1.18933e8 q^{56} +2.27887e8 q^{57} -1.14598e8 q^{58} -1.21878e8 q^{59} -4.06901e8 q^{60} -5.35936e7 q^{61} -2.82331e8 q^{62} +8.04474e7 q^{63} +8.00402e8 q^{64} +9.62373e7 q^{65} -6.71190e8 q^{66} +1.59987e8 q^{67} -6.83717e8 q^{68} -2.35277e8 q^{69} -1.47569e8 q^{70} -6.15700e7 q^{71} -1.31708e9 q^{72} +1.80720e7 q^{73} +1.62865e8 q^{74} +1.02529e8 q^{75} -1.53245e9 q^{76} -1.81369e8 q^{77} +7.85740e8 q^{78} +3.43475e8 q^{79} +1.47990e9 q^{80} -8.40272e7 q^{81} +1.59149e9 q^{82} +3.37643e8 q^{83} -8.97722e8 q^{84} -5.58111e8 q^{85} -1.00055e9 q^{86} -5.69075e8 q^{87} +2.96937e9 q^{88} +9.24310e8 q^{89} -1.63420e9 q^{90} +2.12323e8 q^{91} +1.58214e9 q^{92} -1.40201e9 q^{93} -1.52812e8 q^{94} -1.25092e9 q^{95} +7.05461e9 q^{96} +5.26076e8 q^{97} +1.48297e9 q^{98} -2.00851e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −44.8173 −1.98066 −0.990332 0.138716i \(-0.955703\pi\)
−0.990332 + 0.138716i \(0.955703\pi\)
\(3\) −222.555 −1.58632 −0.793162 0.609011i \(-0.791566\pi\)
−0.793162 + 0.609011i \(0.791566\pi\)
\(4\) 1496.59 2.92303
\(5\) 1221.65 0.874143 0.437072 0.899427i \(-0.356016\pi\)
0.437072 + 0.899427i \(0.356016\pi\)
\(6\) 9974.32 3.14197
\(7\) 2695.26 0.424287 0.212144 0.977239i \(-0.431956\pi\)
0.212144 + 0.977239i \(0.431956\pi\)
\(8\) −44126.8 −3.80888
\(9\) 29847.7 1.51642
\(10\) −54751.2 −1.73138
\(11\) −67291.8 −1.38578 −0.692891 0.721042i \(-0.743663\pi\)
−0.692891 + 0.721042i \(0.743663\pi\)
\(12\) −333074. −4.63687
\(13\) 78776.4 0.764981 0.382491 0.923959i \(-0.375066\pi\)
0.382491 + 0.923959i \(0.375066\pi\)
\(14\) −120794. −0.840370
\(15\) −271885. −1.38667
\(16\) 1.21139e6 4.62108
\(17\) −456849. −1.32664 −0.663320 0.748336i \(-0.730853\pi\)
−0.663320 + 0.748336i \(0.730853\pi\)
\(18\) −1.33769e6 −3.00352
\(19\) −1.02396e6 −1.80256 −0.901281 0.433234i \(-0.857372\pi\)
−0.901281 + 0.433234i \(0.857372\pi\)
\(20\) 1.82832e6 2.55515
\(21\) −599844. −0.673056
\(22\) 3.01584e6 2.74477
\(23\) 1.05716e6 0.787711 0.393856 0.919172i \(-0.371141\pi\)
0.393856 + 0.919172i \(0.371141\pi\)
\(24\) 9.82064e6 6.04212
\(25\) −460690. −0.235873
\(26\) −3.53055e6 −1.51517
\(27\) −2.26221e6 −0.819210
\(28\) 4.03371e6 1.24020
\(29\) 2.55701e6 0.671338 0.335669 0.941980i \(-0.391038\pi\)
0.335669 + 0.941980i \(0.391038\pi\)
\(30\) 1.21852e7 2.74654
\(31\) 6.29959e6 1.22514 0.612569 0.790417i \(-0.290136\pi\)
0.612569 + 0.790417i \(0.290136\pi\)
\(32\) −3.16983e7 −5.34393
\(33\) 1.49761e7 2.19830
\(34\) 2.04748e7 2.62763
\(35\) 3.29267e6 0.370888
\(36\) 4.46699e7 4.43255
\(37\) −3.63397e6 −0.318767 −0.159383 0.987217i \(-0.550951\pi\)
−0.159383 + 0.987217i \(0.550951\pi\)
\(38\) 4.58910e7 3.57027
\(39\) −1.75321e7 −1.21351
\(40\) −5.39076e7 −3.32951
\(41\) −3.55107e7 −1.96260 −0.981300 0.192486i \(-0.938345\pi\)
−0.981300 + 0.192486i \(0.938345\pi\)
\(42\) 2.68834e7 1.33310
\(43\) 2.23251e7 0.995831 0.497915 0.867226i \(-0.334099\pi\)
0.497915 + 0.867226i \(0.334099\pi\)
\(44\) −1.00708e8 −4.05069
\(45\) 3.64635e7 1.32557
\(46\) −4.73793e7 −1.56019
\(47\) 3.40966e6 0.101923 0.0509613 0.998701i \(-0.483771\pi\)
0.0509613 + 0.998701i \(0.483771\pi\)
\(48\) −2.69601e8 −7.33053
\(49\) −3.30892e7 −0.819980
\(50\) 2.06469e7 0.467186
\(51\) 1.01674e8 2.10448
\(52\) 1.17896e8 2.23606
\(53\) −1.91404e7 −0.333203 −0.166602 0.986024i \(-0.553279\pi\)
−0.166602 + 0.986024i \(0.553279\pi\)
\(54\) 1.01386e8 1.62258
\(55\) −8.22072e7 −1.21137
\(56\) −1.18933e8 −1.61606
\(57\) 2.27887e8 2.85945
\(58\) −1.14598e8 −1.32970
\(59\) −1.21878e8 −1.30945 −0.654727 0.755866i \(-0.727216\pi\)
−0.654727 + 0.755866i \(0.727216\pi\)
\(60\) −4.06901e8 −4.05329
\(61\) −5.35936e7 −0.495597 −0.247799 0.968812i \(-0.579707\pi\)
−0.247799 + 0.968812i \(0.579707\pi\)
\(62\) −2.82331e8 −2.42659
\(63\) 8.04474e7 0.643398
\(64\) 8.00402e8 5.96346
\(65\) 9.62373e7 0.668703
\(66\) −6.71190e8 −4.35409
\(67\) 1.59987e8 0.969950 0.484975 0.874528i \(-0.338829\pi\)
0.484975 + 0.874528i \(0.338829\pi\)
\(68\) −6.83717e8 −3.87781
\(69\) −2.35277e8 −1.24956
\(70\) −1.47569e8 −0.734604
\(71\) −6.15700e7 −0.287545 −0.143773 0.989611i \(-0.545923\pi\)
−0.143773 + 0.989611i \(0.545923\pi\)
\(72\) −1.31708e9 −5.77587
\(73\) 1.80720e7 0.0744825 0.0372412 0.999306i \(-0.488143\pi\)
0.0372412 + 0.999306i \(0.488143\pi\)
\(74\) 1.62865e8 0.631370
\(75\) 1.02529e8 0.374171
\(76\) −1.53245e9 −5.26895
\(77\) −1.81369e8 −0.587970
\(78\) 7.85740e8 2.40355
\(79\) 3.43475e8 0.992140 0.496070 0.868282i \(-0.334776\pi\)
0.496070 + 0.868282i \(0.334776\pi\)
\(80\) 1.47990e9 4.03949
\(81\) −8.40272e7 −0.216889
\(82\) 1.59149e9 3.88725
\(83\) 3.37643e8 0.780920 0.390460 0.920620i \(-0.372316\pi\)
0.390460 + 0.920620i \(0.372316\pi\)
\(84\) −8.97722e8 −1.96737
\(85\) −5.58111e8 −1.15967
\(86\) −1.00055e9 −1.97241
\(87\) −5.69075e8 −1.06496
\(88\) 2.96937e9 5.27828
\(89\) 9.24310e8 1.56157 0.780787 0.624797i \(-0.214818\pi\)
0.780787 + 0.624797i \(0.214818\pi\)
\(90\) −1.63420e9 −2.62551
\(91\) 2.12323e8 0.324572
\(92\) 1.58214e9 2.30251
\(93\) −1.40201e9 −1.94346
\(94\) −1.52812e8 −0.201875
\(95\) −1.25092e9 −1.57570
\(96\) 7.05461e9 8.47721
\(97\) 5.26076e8 0.603359 0.301680 0.953409i \(-0.402453\pi\)
0.301680 + 0.953409i \(0.402453\pi\)
\(98\) 1.48297e9 1.62411
\(99\) −2.00851e9 −2.10143
\(100\) −6.89465e8 −0.689465
\(101\) −1.20559e9 −1.15280 −0.576400 0.817167i \(-0.695543\pi\)
−0.576400 + 0.817167i \(0.695543\pi\)
\(102\) −4.55676e9 −4.16827
\(103\) −1.48252e9 −1.29787 −0.648937 0.760842i \(-0.724786\pi\)
−0.648937 + 0.760842i \(0.724786\pi\)
\(104\) −3.47615e9 −2.91372
\(105\) −7.32801e8 −0.588348
\(106\) 8.57821e8 0.659964
\(107\) 1.39441e9 1.02841 0.514203 0.857668i \(-0.328088\pi\)
0.514203 + 0.857668i \(0.328088\pi\)
\(108\) −3.38560e9 −2.39458
\(109\) −1.59761e9 −1.08406 −0.542028 0.840360i \(-0.682343\pi\)
−0.542028 + 0.840360i \(0.682343\pi\)
\(110\) 3.68431e9 2.39932
\(111\) 8.08757e8 0.505667
\(112\) 3.26501e9 1.96067
\(113\) −1.00787e8 −0.0581503 −0.0290752 0.999577i \(-0.509256\pi\)
−0.0290752 + 0.999577i \(0.509256\pi\)
\(114\) −1.02133e10 −5.66360
\(115\) 1.29149e9 0.688573
\(116\) 3.82680e9 1.96234
\(117\) 2.35129e9 1.16003
\(118\) 5.46223e9 2.59359
\(119\) −1.23133e9 −0.562876
\(120\) 1.19974e10 5.28168
\(121\) 2.17024e9 0.920393
\(122\) 2.40192e9 0.981611
\(123\) 7.90308e9 3.11332
\(124\) 9.42792e9 3.58111
\(125\) −2.94884e9 −1.08033
\(126\) −3.60544e9 −1.27436
\(127\) −1.65424e9 −0.564265 −0.282132 0.959375i \(-0.591042\pi\)
−0.282132 + 0.959375i \(0.591042\pi\)
\(128\) −1.96423e10 −6.46767
\(129\) −4.96856e9 −1.57971
\(130\) −4.31310e9 −1.32448
\(131\) −1.98621e9 −0.589257 −0.294628 0.955612i \(-0.595196\pi\)
−0.294628 + 0.955612i \(0.595196\pi\)
\(132\) 2.24132e10 6.42570
\(133\) −2.75983e9 −0.764804
\(134\) −7.17021e9 −1.92115
\(135\) −2.76363e9 −0.716107
\(136\) 2.01593e10 5.05301
\(137\) −6.89669e9 −1.67262 −0.836312 0.548254i \(-0.815293\pi\)
−0.836312 + 0.548254i \(0.815293\pi\)
\(138\) 1.05445e10 2.47497
\(139\) 4.02813e9 0.915243 0.457621 0.889147i \(-0.348702\pi\)
0.457621 + 0.889147i \(0.348702\pi\)
\(140\) 4.92779e9 1.08412
\(141\) −7.58837e8 −0.161682
\(142\) 2.75940e9 0.569531
\(143\) −5.30100e9 −1.06010
\(144\) 3.61572e10 7.00751
\(145\) 3.12378e9 0.586846
\(146\) −8.09940e8 −0.147525
\(147\) 7.36416e9 1.30075
\(148\) −5.43857e9 −0.931765
\(149\) −5.67750e9 −0.943668 −0.471834 0.881687i \(-0.656408\pi\)
−0.471834 + 0.881687i \(0.656408\pi\)
\(150\) −4.59507e9 −0.741107
\(151\) −1.05118e10 −1.64544 −0.822720 0.568447i \(-0.807544\pi\)
−0.822720 + 0.568447i \(0.807544\pi\)
\(152\) 4.51839e10 6.86575
\(153\) −1.36359e10 −2.01174
\(154\) 8.12847e9 1.16457
\(155\) 7.69591e9 1.07095
\(156\) −2.62384e10 −3.54712
\(157\) 2.32592e9 0.305525 0.152762 0.988263i \(-0.451183\pi\)
0.152762 + 0.988263i \(0.451183\pi\)
\(158\) −1.53936e10 −1.96510
\(159\) 4.25979e9 0.528568
\(160\) −3.87243e10 −4.67137
\(161\) 2.84933e9 0.334216
\(162\) 3.76587e9 0.429584
\(163\) 9.30960e8 0.103297 0.0516484 0.998665i \(-0.483552\pi\)
0.0516484 + 0.998665i \(0.483552\pi\)
\(164\) −5.31450e10 −5.73674
\(165\) 1.82956e10 1.92163
\(166\) −1.51323e10 −1.54674
\(167\) 8.47247e9 0.842919 0.421459 0.906847i \(-0.361518\pi\)
0.421459 + 0.906847i \(0.361518\pi\)
\(168\) 2.64692e10 2.56359
\(169\) −4.39878e9 −0.414804
\(170\) 2.50130e10 2.29692
\(171\) −3.05628e10 −2.73344
\(172\) 3.34116e10 2.91084
\(173\) 3.24372e9 0.275319 0.137659 0.990480i \(-0.456042\pi\)
0.137659 + 0.990480i \(0.456042\pi\)
\(174\) 2.55044e10 2.10933
\(175\) −1.24168e9 −0.100078
\(176\) −8.15166e10 −6.40382
\(177\) 2.71245e10 2.07722
\(178\) −4.14251e10 −3.09295
\(179\) −1.90933e9 −0.139009 −0.0695046 0.997582i \(-0.522142\pi\)
−0.0695046 + 0.997582i \(0.522142\pi\)
\(180\) 5.45710e10 3.87468
\(181\) −2.24205e10 −1.55272 −0.776359 0.630291i \(-0.782935\pi\)
−0.776359 + 0.630291i \(0.782935\pi\)
\(182\) −9.51575e9 −0.642868
\(183\) 1.19275e10 0.786177
\(184\) −4.66493e10 −3.00030
\(185\) −4.43944e9 −0.278648
\(186\) 6.28341e10 3.84935
\(187\) 3.07422e10 1.83843
\(188\) 5.10287e9 0.297923
\(189\) −6.09724e9 −0.347580
\(190\) 5.60629e10 3.12093
\(191\) 1.53199e10 0.832922 0.416461 0.909153i \(-0.363270\pi\)
0.416461 + 0.909153i \(0.363270\pi\)
\(192\) −1.78133e11 −9.45997
\(193\) −6.62203e9 −0.343545 −0.171772 0.985137i \(-0.554949\pi\)
−0.171772 + 0.985137i \(0.554949\pi\)
\(194\) −2.35773e10 −1.19505
\(195\) −2.14181e10 −1.06078
\(196\) −4.95210e10 −2.39683
\(197\) 1.50614e9 0.0712470
\(198\) 9.00159e10 4.16223
\(199\) 1.04676e10 0.473162 0.236581 0.971612i \(-0.423973\pi\)
0.236581 + 0.971612i \(0.423973\pi\)
\(200\) 2.03288e10 0.898413
\(201\) −3.56060e10 −1.53865
\(202\) 5.40314e10 2.28331
\(203\) 6.89181e9 0.284840
\(204\) 1.52165e11 6.15146
\(205\) −4.33817e10 −1.71559
\(206\) 6.64425e10 2.57065
\(207\) 3.15539e10 1.19450
\(208\) 9.54288e10 3.53504
\(209\) 6.89039e10 2.49796
\(210\) 3.28422e10 1.16532
\(211\) 3.16980e9 0.110093 0.0550466 0.998484i \(-0.482469\pi\)
0.0550466 + 0.998484i \(0.482469\pi\)
\(212\) −2.86453e10 −0.973964
\(213\) 1.37027e10 0.456140
\(214\) −6.24939e10 −2.03693
\(215\) 2.72735e10 0.870499
\(216\) 9.98239e10 3.12027
\(217\) 1.69790e10 0.519810
\(218\) 7.16006e10 2.14715
\(219\) −4.02202e9 −0.118153
\(220\) −1.23031e11 −3.54088
\(221\) −3.59889e10 −1.01485
\(222\) −3.62463e10 −1.00156
\(223\) 6.25531e10 1.69386 0.846929 0.531706i \(-0.178449\pi\)
0.846929 + 0.531706i \(0.178449\pi\)
\(224\) −8.54352e10 −2.26736
\(225\) −1.37505e10 −0.357683
\(226\) 4.51701e9 0.115176
\(227\) 5.40615e10 1.35136 0.675681 0.737194i \(-0.263850\pi\)
0.675681 + 0.737194i \(0.263850\pi\)
\(228\) 3.41053e11 8.35825
\(229\) −1.02334e10 −0.245901 −0.122950 0.992413i \(-0.539236\pi\)
−0.122950 + 0.992413i \(0.539236\pi\)
\(230\) −5.78810e10 −1.36383
\(231\) 4.03646e10 0.932710
\(232\) −1.12833e11 −2.55705
\(233\) −7.22261e10 −1.60544 −0.802718 0.596359i \(-0.796613\pi\)
−0.802718 + 0.596359i \(0.796613\pi\)
\(234\) −1.05379e11 −2.29764
\(235\) 4.16542e9 0.0890950
\(236\) −1.82401e11 −3.82757
\(237\) −7.64420e10 −1.57385
\(238\) 5.51849e10 1.11487
\(239\) 7.08890e10 1.40536 0.702681 0.711505i \(-0.251986\pi\)
0.702681 + 0.711505i \(0.251986\pi\)
\(240\) −3.29358e11 −6.40794
\(241\) 4.67626e10 0.892940 0.446470 0.894799i \(-0.352681\pi\)
0.446470 + 0.894799i \(0.352681\pi\)
\(242\) −9.72643e10 −1.82299
\(243\) 6.32277e10 1.16327
\(244\) −8.02078e10 −1.44865
\(245\) −4.04235e10 −0.716781
\(246\) −3.54195e11 −6.16644
\(247\) −8.06636e10 −1.37893
\(248\) −2.77981e11 −4.66640
\(249\) −7.51442e10 −1.23879
\(250\) 1.32159e11 2.13977
\(251\) 4.40203e10 0.700037 0.350019 0.936743i \(-0.386175\pi\)
0.350019 + 0.936743i \(0.386175\pi\)
\(252\) 1.20397e11 1.88067
\(253\) −7.11385e10 −1.09160
\(254\) 7.41388e10 1.11762
\(255\) 1.24210e11 1.83962
\(256\) 4.70511e11 6.84684
\(257\) 8.86934e9 0.126821 0.0634106 0.997988i \(-0.479802\pi\)
0.0634106 + 0.997988i \(0.479802\pi\)
\(258\) 2.22678e11 3.12887
\(259\) −9.79449e9 −0.135249
\(260\) 1.44028e11 1.95464
\(261\) 7.63209e10 1.01803
\(262\) 8.90166e10 1.16712
\(263\) −9.73763e10 −1.25503 −0.627513 0.778606i \(-0.715927\pi\)
−0.627513 + 0.778606i \(0.715927\pi\)
\(264\) −6.60848e11 −8.37306
\(265\) −2.33829e10 −0.291267
\(266\) 1.23688e11 1.51482
\(267\) −2.05710e11 −2.47716
\(268\) 2.39436e11 2.83519
\(269\) −5.05560e10 −0.588691 −0.294345 0.955699i \(-0.595102\pi\)
−0.294345 + 0.955699i \(0.595102\pi\)
\(270\) 1.23859e11 1.41837
\(271\) −1.51161e10 −0.170247 −0.0851233 0.996370i \(-0.527128\pi\)
−0.0851233 + 0.996370i \(0.527128\pi\)
\(272\) −5.53422e11 −6.13051
\(273\) −4.72535e10 −0.514876
\(274\) 3.09091e11 3.31291
\(275\) 3.10006e10 0.326869
\(276\) −3.52114e11 −3.65252
\(277\) −7.29515e10 −0.744518 −0.372259 0.928129i \(-0.621417\pi\)
−0.372259 + 0.928129i \(0.621417\pi\)
\(278\) −1.80530e11 −1.81279
\(279\) 1.88028e11 1.85782
\(280\) −1.45295e11 −1.41267
\(281\) −1.82658e10 −0.174767 −0.0873835 0.996175i \(-0.527851\pi\)
−0.0873835 + 0.996175i \(0.527851\pi\)
\(282\) 3.40090e10 0.320238
\(283\) 5.96501e10 0.552805 0.276402 0.961042i \(-0.410858\pi\)
0.276402 + 0.961042i \(0.410858\pi\)
\(284\) −9.21452e10 −0.840505
\(285\) 2.78398e11 2.49957
\(286\) 2.37577e11 2.09970
\(287\) −9.57106e10 −0.832706
\(288\) −9.46122e11 −8.10365
\(289\) 9.01234e10 0.759972
\(290\) −1.39999e11 −1.16234
\(291\) −1.17081e11 −0.957122
\(292\) 2.70465e10 0.217715
\(293\) −7.96661e10 −0.631494 −0.315747 0.948843i \(-0.602255\pi\)
−0.315747 + 0.948843i \(0.602255\pi\)
\(294\) −3.30042e11 −2.57636
\(295\) −1.48892e11 −1.14465
\(296\) 1.60355e11 1.21414
\(297\) 1.52228e11 1.13525
\(298\) 2.54450e11 1.86909
\(299\) 8.32795e10 0.602585
\(300\) 1.53444e11 1.09371
\(301\) 6.01720e10 0.422518
\(302\) 4.71112e11 3.25906
\(303\) 2.68311e11 1.82871
\(304\) −1.24041e12 −8.32979
\(305\) −6.54728e10 −0.433223
\(306\) 6.11125e11 3.98459
\(307\) −1.04450e11 −0.671099 −0.335549 0.942023i \(-0.608922\pi\)
−0.335549 + 0.942023i \(0.608922\pi\)
\(308\) −2.71435e11 −1.71865
\(309\) 3.29942e11 2.05885
\(310\) −3.44910e11 −2.12118
\(311\) −1.32059e11 −0.800472 −0.400236 0.916412i \(-0.631072\pi\)
−0.400236 + 0.916412i \(0.631072\pi\)
\(312\) 7.73634e11 4.62211
\(313\) −7.55896e10 −0.445156 −0.222578 0.974915i \(-0.571447\pi\)
−0.222578 + 0.974915i \(0.571447\pi\)
\(314\) −1.04241e11 −0.605142
\(315\) 9.82788e10 0.562422
\(316\) 5.14042e11 2.90006
\(317\) 3.22598e11 1.79430 0.897149 0.441727i \(-0.145634\pi\)
0.897149 + 0.441727i \(0.145634\pi\)
\(318\) −1.90912e11 −1.04692
\(319\) −1.72066e11 −0.930329
\(320\) 9.77813e11 5.21292
\(321\) −3.10334e11 −1.63138
\(322\) −1.27700e11 −0.661969
\(323\) 4.67794e11 2.39135
\(324\) −1.25754e11 −0.633973
\(325\) −3.62915e10 −0.180439
\(326\) −4.17232e10 −0.204596
\(327\) 3.55556e11 1.71966
\(328\) 1.56697e12 7.47531
\(329\) 9.18993e9 0.0432445
\(330\) −8.19961e11 −3.80610
\(331\) 6.11091e10 0.279821 0.139910 0.990164i \(-0.455319\pi\)
0.139910 + 0.990164i \(0.455319\pi\)
\(332\) 5.05314e11 2.28265
\(333\) −1.08466e11 −0.483385
\(334\) −3.79713e11 −1.66954
\(335\) 1.95449e11 0.847876
\(336\) −7.26644e11 −3.11025
\(337\) 1.02396e11 0.432463 0.216231 0.976342i \(-0.430623\pi\)
0.216231 + 0.976342i \(0.430623\pi\)
\(338\) 1.97142e11 0.821587
\(339\) 2.24307e10 0.0922452
\(340\) −8.35265e11 −3.38976
\(341\) −4.23911e11 −1.69777
\(342\) 1.36974e12 5.41403
\(343\) −1.97948e11 −0.772194
\(344\) −9.85135e11 −3.79300
\(345\) −2.87427e11 −1.09230
\(346\) −1.45375e11 −0.545314
\(347\) −2.15746e11 −0.798842 −0.399421 0.916768i \(-0.630789\pi\)
−0.399421 + 0.916768i \(0.630789\pi\)
\(348\) −8.51673e11 −3.11291
\(349\) 5.15468e11 1.85989 0.929945 0.367699i \(-0.119854\pi\)
0.929945 + 0.367699i \(0.119854\pi\)
\(350\) 5.56488e10 0.198221
\(351\) −1.78208e11 −0.626680
\(352\) 2.13304e12 7.40553
\(353\) 6.74884e10 0.231336 0.115668 0.993288i \(-0.463099\pi\)
0.115668 + 0.993288i \(0.463099\pi\)
\(354\) −1.21565e12 −4.11427
\(355\) −7.52171e10 −0.251356
\(356\) 1.38331e12 4.56453
\(357\) 2.74038e11 0.892903
\(358\) 8.55713e10 0.275331
\(359\) −2.26879e11 −0.720892 −0.360446 0.932780i \(-0.617375\pi\)
−0.360446 + 0.932780i \(0.617375\pi\)
\(360\) −1.60902e12 −5.04894
\(361\) 7.25800e11 2.24923
\(362\) 1.00483e12 3.07541
\(363\) −4.82997e11 −1.46004
\(364\) 3.17761e11 0.948733
\(365\) 2.20777e10 0.0651084
\(366\) −5.34560e11 −1.55715
\(367\) 4.09124e11 1.17722 0.588611 0.808417i \(-0.299675\pi\)
0.588611 + 0.808417i \(0.299675\pi\)
\(368\) 1.28064e12 3.64008
\(369\) −1.05991e12 −2.97613
\(370\) 1.98964e11 0.551908
\(371\) −5.15883e10 −0.141374
\(372\) −2.09823e12 −5.68080
\(373\) 1.37033e11 0.366552 0.183276 0.983062i \(-0.441330\pi\)
0.183276 + 0.983062i \(0.441330\pi\)
\(374\) −1.37778e12 −3.64132
\(375\) 6.56280e11 1.71375
\(376\) −1.50457e11 −0.388211
\(377\) 2.01432e11 0.513561
\(378\) 2.73262e11 0.688440
\(379\) 4.52490e11 1.12650 0.563251 0.826286i \(-0.309550\pi\)
0.563251 + 0.826286i \(0.309550\pi\)
\(380\) −1.87212e12 −4.60582
\(381\) 3.68160e11 0.895106
\(382\) −6.86595e11 −1.64974
\(383\) 3.36445e11 0.798950 0.399475 0.916744i \(-0.369192\pi\)
0.399475 + 0.916744i \(0.369192\pi\)
\(384\) 4.37150e12 10.2598
\(385\) −2.21570e11 −0.513970
\(386\) 2.96782e11 0.680447
\(387\) 6.66353e11 1.51010
\(388\) 7.87322e11 1.76364
\(389\) 4.52622e11 1.00222 0.501109 0.865384i \(-0.332926\pi\)
0.501109 + 0.865384i \(0.332926\pi\)
\(390\) 9.59902e11 2.10105
\(391\) −4.82965e11 −1.04501
\(392\) 1.46012e12 3.12321
\(393\) 4.42041e11 0.934751
\(394\) −6.75011e10 −0.141117
\(395\) 4.19607e11 0.867273
\(396\) −3.00591e12 −6.14254
\(397\) 1.78064e11 0.359766 0.179883 0.983688i \(-0.442428\pi\)
0.179883 + 0.983688i \(0.442428\pi\)
\(398\) −4.69131e11 −0.937175
\(399\) 6.14214e11 1.21323
\(400\) −5.58075e11 −1.08999
\(401\) 1.71522e11 0.331261 0.165630 0.986188i \(-0.447034\pi\)
0.165630 + 0.986188i \(0.447034\pi\)
\(402\) 1.59577e12 3.04756
\(403\) 4.96259e11 0.937207
\(404\) −1.80428e12 −3.36967
\(405\) −1.02652e11 −0.189592
\(406\) −3.08872e11 −0.564173
\(407\) 2.44536e11 0.441741
\(408\) −4.48655e12 −8.01571
\(409\) 8.48987e11 1.50019 0.750094 0.661331i \(-0.230008\pi\)
0.750094 + 0.661331i \(0.230008\pi\)
\(410\) 1.94425e12 3.39801
\(411\) 1.53489e12 2.65332
\(412\) −2.21873e12 −3.79373
\(413\) −3.28492e11 −0.555584
\(414\) −1.41416e12 −2.36591
\(415\) 4.12483e11 0.682636
\(416\) −2.49708e12 −4.08801
\(417\) −8.96479e11 −1.45187
\(418\) −3.08809e12 −4.94762
\(419\) −7.15732e11 −1.13445 −0.567227 0.823561i \(-0.691984\pi\)
−0.567227 + 0.823561i \(0.691984\pi\)
\(420\) −1.09670e12 −1.71976
\(421\) 8.23979e11 1.27834 0.639170 0.769065i \(-0.279278\pi\)
0.639170 + 0.769065i \(0.279278\pi\)
\(422\) −1.42062e11 −0.218058
\(423\) 1.01771e11 0.154558
\(424\) 8.44604e11 1.26913
\(425\) 2.10466e11 0.312919
\(426\) −6.14119e11 −0.903460
\(427\) −1.44449e11 −0.210275
\(428\) 2.08687e12 3.00606
\(429\) 1.17976e12 1.68166
\(430\) −1.22233e12 −1.72417
\(431\) −8.64097e11 −1.20619 −0.603094 0.797670i \(-0.706066\pi\)
−0.603094 + 0.797670i \(0.706066\pi\)
\(432\) −2.74041e12 −3.78564
\(433\) 1.09124e12 1.49184 0.745921 0.666034i \(-0.232010\pi\)
0.745921 + 0.666034i \(0.232010\pi\)
\(434\) −7.60955e11 −1.02957
\(435\) −6.95212e11 −0.930927
\(436\) −2.39097e12 −3.16873
\(437\) −1.08249e12 −1.41990
\(438\) 1.80256e11 0.234022
\(439\) −1.39581e12 −1.79364 −0.896821 0.442393i \(-0.854130\pi\)
−0.896821 + 0.442393i \(0.854130\pi\)
\(440\) 3.62754e12 4.61397
\(441\) −9.87636e11 −1.24344
\(442\) 1.61293e12 2.01009
\(443\) −7.88480e11 −0.972688 −0.486344 0.873767i \(-0.661670\pi\)
−0.486344 + 0.873767i \(0.661670\pi\)
\(444\) 1.21038e12 1.47808
\(445\) 1.12919e12 1.36504
\(446\) −2.80346e12 −3.35496
\(447\) 1.26356e12 1.49696
\(448\) 2.15729e12 2.53022
\(449\) 2.71552e11 0.315315 0.157658 0.987494i \(-0.449606\pi\)
0.157658 + 0.987494i \(0.449606\pi\)
\(450\) 6.16262e11 0.708450
\(451\) 2.38958e12 2.71974
\(452\) −1.50837e11 −0.169975
\(453\) 2.33946e12 2.61020
\(454\) −2.42289e12 −2.67660
\(455\) 2.59385e11 0.283722
\(456\) −1.00559e13 −10.8913
\(457\) −1.08795e12 −1.16678 −0.583388 0.812193i \(-0.698273\pi\)
−0.583388 + 0.812193i \(0.698273\pi\)
\(458\) 4.58633e11 0.487047
\(459\) 1.03349e12 1.08680
\(460\) 1.93283e12 2.01272
\(461\) 9.84892e11 1.01563 0.507814 0.861467i \(-0.330454\pi\)
0.507814 + 0.861467i \(0.330454\pi\)
\(462\) −1.80903e12 −1.84738
\(463\) 9.87306e11 0.998475 0.499238 0.866465i \(-0.333614\pi\)
0.499238 + 0.866465i \(0.333614\pi\)
\(464\) 3.09753e12 3.10231
\(465\) −1.71276e12 −1.69887
\(466\) 3.23698e12 3.17983
\(467\) −1.47391e12 −1.43399 −0.716994 0.697079i \(-0.754483\pi\)
−0.716994 + 0.697079i \(0.754483\pi\)
\(468\) 3.51893e12 3.39081
\(469\) 4.31208e11 0.411537
\(470\) −1.86683e11 −0.176467
\(471\) −5.17645e11 −0.484661
\(472\) 5.37807e12 4.98755
\(473\) −1.50230e12 −1.38000
\(474\) 3.42593e12 3.11728
\(475\) 4.71726e11 0.425176
\(476\) −1.84280e12 −1.64530
\(477\) −5.71297e11 −0.505276
\(478\) −3.17705e12 −2.78355
\(479\) 2.90657e11 0.252273 0.126136 0.992013i \(-0.459742\pi\)
0.126136 + 0.992013i \(0.459742\pi\)
\(480\) 8.61829e12 7.41029
\(481\) −2.86271e11 −0.243851
\(482\) −2.09578e12 −1.76861
\(483\) −6.34133e11 −0.530174
\(484\) 3.24796e12 2.69034
\(485\) 6.42682e11 0.527422
\(486\) −2.83370e12 −2.30404
\(487\) 1.52538e11 0.122885 0.0614425 0.998111i \(-0.480430\pi\)
0.0614425 + 0.998111i \(0.480430\pi\)
\(488\) 2.36491e12 1.88767
\(489\) −2.07190e11 −0.163862
\(490\) 1.81167e12 1.41970
\(491\) −8.75599e11 −0.679890 −0.339945 0.940445i \(-0.610408\pi\)
−0.339945 + 0.940445i \(0.610408\pi\)
\(492\) 1.18277e13 9.10032
\(493\) −1.16817e12 −0.890623
\(494\) 3.61513e12 2.73119
\(495\) −2.45370e12 −1.83695
\(496\) 7.63126e12 5.66146
\(497\) −1.65947e11 −0.122002
\(498\) 3.36776e12 2.45363
\(499\) 2.97579e11 0.214857 0.107428 0.994213i \(-0.465738\pi\)
0.107428 + 0.994213i \(0.465738\pi\)
\(500\) −4.41322e12 −3.15784
\(501\) −1.88559e12 −1.33714
\(502\) −1.97287e12 −1.38654
\(503\) 1.70664e11 0.118873 0.0594367 0.998232i \(-0.481070\pi\)
0.0594367 + 0.998232i \(0.481070\pi\)
\(504\) −3.54989e12 −2.45063
\(505\) −1.47281e12 −1.00771
\(506\) 3.18824e12 2.16209
\(507\) 9.78971e11 0.658012
\(508\) −2.47573e12 −1.64936
\(509\) 1.12422e12 0.742372 0.371186 0.928558i \(-0.378951\pi\)
0.371186 + 0.928558i \(0.378951\pi\)
\(510\) −5.56678e12 −3.64366
\(511\) 4.87089e10 0.0316020
\(512\) −1.10302e13 −7.09361
\(513\) 2.31640e12 1.47668
\(514\) −3.97500e11 −0.251190
\(515\) −1.81112e12 −1.13453
\(516\) −7.43591e12 −4.61754
\(517\) −2.29442e11 −0.141243
\(518\) 4.38963e11 0.267882
\(519\) −7.21906e11 −0.436745
\(520\) −4.24665e12 −2.54701
\(521\) −2.17786e12 −1.29497 −0.647486 0.762078i \(-0.724179\pi\)
−0.647486 + 0.762078i \(0.724179\pi\)
\(522\) −3.42050e12 −2.01638
\(523\) 3.09707e12 1.81006 0.905030 0.425348i \(-0.139848\pi\)
0.905030 + 0.425348i \(0.139848\pi\)
\(524\) −2.97255e12 −1.72242
\(525\) 2.76342e11 0.158756
\(526\) 4.36415e12 2.48578
\(527\) −2.87796e12 −1.62531
\(528\) 1.81419e13 10.1585
\(529\) −6.83557e11 −0.379511
\(530\) 1.04796e12 0.576903
\(531\) −3.63777e12 −1.98568
\(532\) −4.13034e12 −2.23555
\(533\) −2.79740e12 −1.50135
\(534\) 9.21936e12 4.90642
\(535\) 1.70349e12 0.898975
\(536\) −7.05973e12 −3.69442
\(537\) 4.24932e11 0.220513
\(538\) 2.26578e12 1.16600
\(539\) 2.22663e12 1.13631
\(540\) −4.13603e12 −2.09320
\(541\) 1.45425e12 0.729882 0.364941 0.931031i \(-0.381089\pi\)
0.364941 + 0.931031i \(0.381089\pi\)
\(542\) 6.77464e11 0.337201
\(543\) 4.98980e12 2.46311
\(544\) 1.44813e13 7.08947
\(545\) −1.95173e12 −0.947620
\(546\) 2.11778e12 1.01980
\(547\) −1.55288e12 −0.741645 −0.370822 0.928704i \(-0.620924\pi\)
−0.370822 + 0.928704i \(0.620924\pi\)
\(548\) −1.03215e13 −4.88913
\(549\) −1.59965e12 −0.751534
\(550\) −1.38937e12 −0.647418
\(551\) −2.61827e12 −1.21013
\(552\) 1.03820e13 4.75944
\(553\) 9.25755e11 0.420952
\(554\) 3.26949e12 1.47464
\(555\) 9.88020e11 0.442026
\(556\) 6.02846e12 2.67528
\(557\) 3.78885e12 1.66786 0.833929 0.551872i \(-0.186086\pi\)
0.833929 + 0.551872i \(0.186086\pi\)
\(558\) −8.42693e12 −3.67972
\(559\) 1.75869e12 0.761792
\(560\) 3.98871e12 1.71390
\(561\) −6.84183e12 −2.91635
\(562\) 8.18623e11 0.346155
\(563\) 5.74431e11 0.240963 0.120481 0.992716i \(-0.461556\pi\)
0.120481 + 0.992716i \(0.461556\pi\)
\(564\) −1.13567e12 −0.472602
\(565\) −1.23127e11 −0.0508317
\(566\) −2.67336e12 −1.09492
\(567\) −2.26475e11 −0.0920231
\(568\) 2.71689e12 1.09523
\(569\) 1.18683e12 0.474659 0.237330 0.971429i \(-0.423728\pi\)
0.237330 + 0.971429i \(0.423728\pi\)
\(570\) −1.24771e13 −4.95080
\(571\) −3.85781e12 −1.51872 −0.759362 0.650669i \(-0.774489\pi\)
−0.759362 + 0.650669i \(0.774489\pi\)
\(572\) −7.93344e12 −3.09870
\(573\) −3.40951e12 −1.32128
\(574\) 4.28949e12 1.64931
\(575\) −4.87025e11 −0.185800
\(576\) 2.38902e13 9.04311
\(577\) 1.08972e12 0.409285 0.204642 0.978837i \(-0.434397\pi\)
0.204642 + 0.978837i \(0.434397\pi\)
\(578\) −4.03909e12 −1.50525
\(579\) 1.47377e12 0.544973
\(580\) 4.67502e12 1.71537
\(581\) 9.10037e11 0.331334
\(582\) 5.24725e12 1.89574
\(583\) 1.28799e12 0.461747
\(584\) −7.97461e11 −0.283695
\(585\) 2.87246e12 1.01404
\(586\) 3.57042e12 1.25078
\(587\) 4.09283e12 1.42283 0.711415 0.702773i \(-0.248055\pi\)
0.711415 + 0.702773i \(0.248055\pi\)
\(588\) 1.10211e13 3.80215
\(589\) −6.45051e12 −2.20839
\(590\) 6.67295e12 2.26717
\(591\) −3.35199e11 −0.113021
\(592\) −4.40215e12 −1.47305
\(593\) 5.77011e10 0.0191619 0.00958094 0.999954i \(-0.496950\pi\)
0.00958094 + 0.999954i \(0.496950\pi\)
\(594\) −6.82245e12 −2.24854
\(595\) −1.50426e12 −0.492034
\(596\) −8.49691e12 −2.75837
\(597\) −2.32962e12 −0.750588
\(598\) −3.73237e12 −1.19352
\(599\) 2.66229e12 0.844959 0.422479 0.906373i \(-0.361160\pi\)
0.422479 + 0.906373i \(0.361160\pi\)
\(600\) −4.52427e12 −1.42517
\(601\) 1.09906e12 0.343628 0.171814 0.985129i \(-0.445037\pi\)
0.171814 + 0.985129i \(0.445037\pi\)
\(602\) −2.69675e12 −0.836867
\(603\) 4.77526e12 1.47085
\(604\) −1.57319e13 −4.80967
\(605\) 2.65128e12 0.804555
\(606\) −1.20250e13 −3.62207
\(607\) −3.35207e12 −1.00222 −0.501111 0.865383i \(-0.667075\pi\)
−0.501111 + 0.865383i \(0.667075\pi\)
\(608\) 3.24577e13 9.63278
\(609\) −1.53381e12 −0.451848
\(610\) 2.93431e12 0.858069
\(611\) 2.68601e11 0.0779689
\(612\) −2.04074e13 −5.88039
\(613\) 1.83381e12 0.524543 0.262272 0.964994i \(-0.415528\pi\)
0.262272 + 0.964994i \(0.415528\pi\)
\(614\) 4.68117e12 1.32922
\(615\) 9.65482e12 2.72149
\(616\) 8.00323e12 2.23951
\(617\) −3.83331e11 −0.106486 −0.0532428 0.998582i \(-0.516956\pi\)
−0.0532428 + 0.998582i \(0.516956\pi\)
\(618\) −1.47871e13 −4.07789
\(619\) −3.21657e12 −0.880614 −0.440307 0.897847i \(-0.645130\pi\)
−0.440307 + 0.897847i \(0.645130\pi\)
\(620\) 1.15176e13 3.13041
\(621\) −2.39152e12 −0.645301
\(622\) 5.91853e12 1.58547
\(623\) 2.49126e12 0.662556
\(624\) −2.12382e13 −5.60772
\(625\) −2.70268e12 −0.708491
\(626\) 3.38772e12 0.881705
\(627\) −1.53349e13 −3.96257
\(628\) 3.48095e12 0.893058
\(629\) 1.66017e12 0.422889
\(630\) −4.40459e12 −1.11397
\(631\) −1.73641e12 −0.436033 −0.218017 0.975945i \(-0.569959\pi\)
−0.218017 + 0.975945i \(0.569959\pi\)
\(632\) −1.51564e13 −3.77894
\(633\) −7.05455e11 −0.174643
\(634\) −1.44580e13 −3.55390
\(635\) −2.02091e12 −0.493248
\(636\) 6.37516e12 1.54502
\(637\) −2.60664e12 −0.627270
\(638\) 7.71153e12 1.84267
\(639\) −1.83772e12 −0.436040
\(640\) −2.39961e13 −5.65368
\(641\) 3.58482e12 0.838699 0.419349 0.907825i \(-0.362258\pi\)
0.419349 + 0.907825i \(0.362258\pi\)
\(642\) 1.39083e13 3.23123
\(643\) 5.75914e12 1.32864 0.664322 0.747447i \(-0.268720\pi\)
0.664322 + 0.747447i \(0.268720\pi\)
\(644\) 4.26429e12 0.976923
\(645\) −6.06986e12 −1.38089
\(646\) −2.09653e13 −4.73646
\(647\) −6.62154e12 −1.48556 −0.742779 0.669537i \(-0.766493\pi\)
−0.742779 + 0.669537i \(0.766493\pi\)
\(648\) 3.70785e12 0.826104
\(649\) 8.20137e12 1.81462
\(650\) 1.62649e12 0.357388
\(651\) −3.77877e12 −0.824586
\(652\) 1.39327e12 0.301940
\(653\) 6.05429e12 1.30303 0.651515 0.758636i \(-0.274134\pi\)
0.651515 + 0.758636i \(0.274134\pi\)
\(654\) −1.59351e13 −3.40608
\(655\) −2.42646e12 −0.515095
\(656\) −4.30173e13 −9.06933
\(657\) 5.39409e11 0.112947
\(658\) −4.11868e11 −0.0856528
\(659\) −1.17210e12 −0.242092 −0.121046 0.992647i \(-0.538625\pi\)
−0.121046 + 0.992647i \(0.538625\pi\)
\(660\) 2.73811e13 5.61698
\(661\) 5.80806e12 1.18338 0.591691 0.806165i \(-0.298461\pi\)
0.591691 + 0.806165i \(0.298461\pi\)
\(662\) −2.73875e12 −0.554231
\(663\) 8.00951e12 1.60989
\(664\) −1.48991e13 −2.97443
\(665\) −3.37156e12 −0.668548
\(666\) 4.86114e12 0.957423
\(667\) 2.70318e12 0.528821
\(668\) 1.26798e13 2.46388
\(669\) −1.39215e13 −2.68701
\(670\) −8.75951e12 −1.67936
\(671\) 3.60641e12 0.686790
\(672\) 1.90140e13 3.59677
\(673\) −5.92596e11 −0.111350 −0.0556751 0.998449i \(-0.517731\pi\)
−0.0556751 + 0.998449i \(0.517731\pi\)
\(674\) −4.58911e12 −0.856563
\(675\) 1.04218e12 0.193230
\(676\) −6.58319e12 −1.21248
\(677\) −3.03014e12 −0.554388 −0.277194 0.960814i \(-0.589404\pi\)
−0.277194 + 0.960814i \(0.589404\pi\)
\(678\) −1.00528e12 −0.182707
\(679\) 1.41791e12 0.255997
\(680\) 2.46277e13 4.41706
\(681\) −1.20317e13 −2.14370
\(682\) 1.89985e13 3.36272
\(683\) 2.26695e12 0.398611 0.199306 0.979937i \(-0.436131\pi\)
0.199306 + 0.979937i \(0.436131\pi\)
\(684\) −4.57400e13 −7.98994
\(685\) −8.42536e12 −1.46211
\(686\) 8.87148e12 1.52946
\(687\) 2.27749e12 0.390078
\(688\) 2.70444e13 4.60182
\(689\) −1.50781e12 −0.254894
\(690\) 1.28817e13 2.16348
\(691\) 1.93380e12 0.322671 0.161335 0.986900i \(-0.448420\pi\)
0.161335 + 0.986900i \(0.448420\pi\)
\(692\) 4.85453e12 0.804766
\(693\) −5.41345e12 −0.891609
\(694\) 9.66918e12 1.58224
\(695\) 4.92097e12 0.800054
\(696\) 2.51115e13 4.05630
\(697\) 1.62230e13 2.60366
\(698\) −2.31019e13 −3.68382
\(699\) 1.60743e13 2.54674
\(700\) −1.85829e12 −0.292531
\(701\) −5.12984e12 −0.802366 −0.401183 0.915998i \(-0.631401\pi\)
−0.401183 + 0.915998i \(0.631401\pi\)
\(702\) 7.98682e12 1.24124
\(703\) 3.72102e12 0.574597
\(704\) −5.38605e13 −8.26405
\(705\) −9.27035e11 −0.141333
\(706\) −3.02465e12 −0.458198
\(707\) −3.24939e12 −0.489118
\(708\) 4.05943e13 6.07177
\(709\) 2.22190e12 0.330229 0.165115 0.986274i \(-0.447201\pi\)
0.165115 + 0.986274i \(0.447201\pi\)
\(710\) 3.37103e12 0.497852
\(711\) 1.02519e13 1.50450
\(712\) −4.07868e13 −5.94785
\(713\) 6.65970e12 0.965054
\(714\) −1.22817e13 −1.76854
\(715\) −6.47598e12 −0.926677
\(716\) −2.85750e12 −0.406328
\(717\) −1.57767e13 −2.22936
\(718\) 1.01681e13 1.42784
\(719\) 9.71447e12 1.35562 0.677812 0.735235i \(-0.262928\pi\)
0.677812 + 0.735235i \(0.262928\pi\)
\(720\) 4.41715e13 6.12557
\(721\) −3.99578e12 −0.550671
\(722\) −3.25284e13 −4.45497
\(723\) −1.04073e13 −1.41649
\(724\) −3.35544e13 −4.53864
\(725\) −1.17799e12 −0.158351
\(726\) 2.16466e13 2.89185
\(727\) 1.33708e13 1.77522 0.887611 0.460594i \(-0.152364\pi\)
0.887611 + 0.460594i \(0.152364\pi\)
\(728\) −9.36913e12 −1.23625
\(729\) −1.24177e13 −1.62843
\(730\) −9.89465e11 −0.128958
\(731\) −1.01992e13 −1.32111
\(732\) 1.78506e13 2.29802
\(733\) 3.68952e12 0.472065 0.236032 0.971745i \(-0.424153\pi\)
0.236032 + 0.971745i \(0.424153\pi\)
\(734\) −1.83359e13 −2.33168
\(735\) 8.99644e12 1.13705
\(736\) −3.35103e13 −4.20948
\(737\) −1.07658e13 −1.34414
\(738\) 4.75024e13 5.89471
\(739\) 8.68235e12 1.07087 0.535436 0.844576i \(-0.320147\pi\)
0.535436 + 0.844576i \(0.320147\pi\)
\(740\) −6.64404e12 −0.814497
\(741\) 1.79521e13 2.18742
\(742\) 2.31205e12 0.280014
\(743\) 1.16035e13 1.39682 0.698409 0.715699i \(-0.253892\pi\)
0.698409 + 0.715699i \(0.253892\pi\)
\(744\) 6.18660e13 7.40242
\(745\) −6.93594e12 −0.824901
\(746\) −6.14145e12 −0.726016
\(747\) 1.00779e13 1.18420
\(748\) 4.60086e13 5.37380
\(749\) 3.75831e12 0.436339
\(750\) −2.94127e13 −3.39437
\(751\) 1.32142e12 0.151587 0.0757935 0.997124i \(-0.475851\pi\)
0.0757935 + 0.997124i \(0.475851\pi\)
\(752\) 4.13043e12 0.470993
\(753\) −9.79693e12 −1.11048
\(754\) −9.02764e12 −1.01719
\(755\) −1.28418e13 −1.43835
\(756\) −9.12508e12 −1.01599
\(757\) −2.71976e12 −0.301022 −0.150511 0.988608i \(-0.548092\pi\)
−0.150511 + 0.988608i \(0.548092\pi\)
\(758\) −2.02794e13 −2.23122
\(759\) 1.58322e13 1.73162
\(760\) 5.51991e13 6.00165
\(761\) 4.08482e12 0.441512 0.220756 0.975329i \(-0.429148\pi\)
0.220756 + 0.975329i \(0.429148\pi\)
\(762\) −1.65000e13 −1.77290
\(763\) −4.30598e12 −0.459951
\(764\) 2.29276e13 2.43466
\(765\) −1.66583e13 −1.75855
\(766\) −1.50786e13 −1.58245
\(767\) −9.60108e12 −1.00171
\(768\) −1.04715e14 −10.8613
\(769\) 6.25441e12 0.644938 0.322469 0.946580i \(-0.395487\pi\)
0.322469 + 0.946580i \(0.395487\pi\)
\(770\) 9.93017e12 1.01800
\(771\) −1.97392e12 −0.201180
\(772\) −9.91048e12 −1.00419
\(773\) 9.39092e12 0.946020 0.473010 0.881057i \(-0.343167\pi\)
0.473010 + 0.881057i \(0.343167\pi\)
\(774\) −2.98642e13 −2.99100
\(775\) −2.90216e12 −0.288977
\(776\) −2.32141e13 −2.29812
\(777\) 2.17981e12 0.214548
\(778\) −2.02853e13 −1.98506
\(779\) 3.63614e13 3.53771
\(780\) −3.20542e13 −3.10069
\(781\) 4.14316e12 0.398475
\(782\) 2.16452e13 2.06981
\(783\) −5.78448e12 −0.549967
\(784\) −4.00839e13 −3.78920
\(785\) 2.84147e12 0.267072
\(786\) −1.98111e13 −1.85143
\(787\) −4.53235e12 −0.421151 −0.210575 0.977578i \(-0.567534\pi\)
−0.210575 + 0.977578i \(0.567534\pi\)
\(788\) 2.25408e12 0.208257
\(789\) 2.16716e13 1.99088
\(790\) −1.88057e13 −1.71778
\(791\) −2.71648e11 −0.0246724
\(792\) 8.86289e13 8.00409
\(793\) −4.22191e12 −0.379122
\(794\) −7.98037e12 −0.712575
\(795\) 5.20398e12 0.462044
\(796\) 1.56658e13 1.38307
\(797\) 8.62990e12 0.757606 0.378803 0.925477i \(-0.376336\pi\)
0.378803 + 0.925477i \(0.376336\pi\)
\(798\) −2.75274e13 −2.40299
\(799\) −1.55770e12 −0.135215
\(800\) 1.46031e13 1.26049
\(801\) 2.75885e13 2.36800
\(802\) −7.68715e12 −0.656116
\(803\) −1.21610e12 −0.103216
\(804\) −5.32877e13 −4.49754
\(805\) 3.48090e12 0.292153
\(806\) −2.22410e13 −1.85629
\(807\) 1.12515e13 0.933854
\(808\) 5.31989e13 4.39088
\(809\) 1.97247e13 1.61898 0.809492 0.587131i \(-0.199743\pi\)
0.809492 + 0.587131i \(0.199743\pi\)
\(810\) 4.60059e12 0.375518
\(811\) −1.75013e12 −0.142062 −0.0710308 0.997474i \(-0.522629\pi\)
−0.0710308 + 0.997474i \(0.522629\pi\)
\(812\) 1.03142e13 0.832597
\(813\) 3.36417e12 0.270066
\(814\) −1.09595e13 −0.874942
\(815\) 1.13731e12 0.0902962
\(816\) 1.23167e14 9.72497
\(817\) −2.28599e13 −1.79505
\(818\) −3.80493e13 −2.97137
\(819\) 6.33735e12 0.492187
\(820\) −6.49247e13 −5.01473
\(821\) 2.78743e12 0.214121 0.107060 0.994253i \(-0.465856\pi\)
0.107060 + 0.994253i \(0.465856\pi\)
\(822\) −6.87898e13 −5.25534
\(823\) −1.19850e13 −0.910620 −0.455310 0.890333i \(-0.650472\pi\)
−0.455310 + 0.890333i \(0.650472\pi\)
\(824\) 6.54188e13 4.94345
\(825\) −6.89935e12 −0.518520
\(826\) 1.47221e13 1.10043
\(827\) 1.38928e13 1.03279 0.516397 0.856349i \(-0.327273\pi\)
0.516397 + 0.856349i \(0.327273\pi\)
\(828\) 4.72234e13 3.49157
\(829\) −2.18676e13 −1.60808 −0.804038 0.594578i \(-0.797319\pi\)
−0.804038 + 0.594578i \(0.797319\pi\)
\(830\) −1.84864e13 −1.35207
\(831\) 1.62357e13 1.18105
\(832\) 6.30527e13 4.56193
\(833\) 1.51168e13 1.08782
\(834\) 4.01778e13 2.87567
\(835\) 1.03504e13 0.736832
\(836\) 1.03121e14 7.30162
\(837\) −1.42510e13 −1.00364
\(838\) 3.20772e13 2.24697
\(839\) −1.67339e13 −1.16592 −0.582960 0.812501i \(-0.698105\pi\)
−0.582960 + 0.812501i \(0.698105\pi\)
\(840\) 3.23362e13 2.24095
\(841\) −7.96885e12 −0.549305
\(842\) −3.69285e13 −2.53196
\(843\) 4.06514e12 0.277237
\(844\) 4.74390e12 0.321806
\(845\) −5.37379e12 −0.362598
\(846\) −4.56108e12 −0.306127
\(847\) 5.84936e12 0.390511
\(848\) −2.31865e13 −1.53976
\(849\) −1.32754e13 −0.876927
\(850\) −9.43252e12 −0.619787
\(851\) −3.84170e12 −0.251096
\(852\) 2.05074e13 1.33331
\(853\) −2.38228e13 −1.54072 −0.770358 0.637612i \(-0.779923\pi\)
−0.770358 + 0.637612i \(0.779923\pi\)
\(854\) 6.47381e12 0.416485
\(855\) −3.73371e13 −2.38942
\(856\) −6.15310e13 −3.91708
\(857\) 1.50682e13 0.954218 0.477109 0.878844i \(-0.341685\pi\)
0.477109 + 0.878844i \(0.341685\pi\)
\(858\) −5.28739e13 −3.33080
\(859\) 2.51544e13 1.57632 0.788161 0.615470i \(-0.211034\pi\)
0.788161 + 0.615470i \(0.211034\pi\)
\(860\) 4.08173e13 2.54450
\(861\) 2.13009e13 1.32094
\(862\) 3.87265e13 2.38905
\(863\) −4.61597e12 −0.283279 −0.141639 0.989918i \(-0.545237\pi\)
−0.141639 + 0.989918i \(0.545237\pi\)
\(864\) 7.17081e13 4.37781
\(865\) 3.96270e12 0.240668
\(866\) −4.89062e13 −2.95484
\(867\) −2.00574e13 −1.20556
\(868\) 2.54107e13 1.51942
\(869\) −2.31130e13 −1.37489
\(870\) 3.11575e13 1.84385
\(871\) 1.26032e13 0.741994
\(872\) 7.04974e13 4.12904
\(873\) 1.57022e13 0.914946
\(874\) 4.85143e13 2.81234
\(875\) −7.94791e12 −0.458370
\(876\) −6.01932e12 −0.345366
\(877\) 2.51807e13 1.43738 0.718688 0.695333i \(-0.244743\pi\)
0.718688 + 0.695333i \(0.244743\pi\)
\(878\) 6.25565e13 3.55260
\(879\) 1.77301e13 1.00175
\(880\) −9.95849e13 −5.59785
\(881\) −1.18325e13 −0.661736 −0.330868 0.943677i \(-0.607342\pi\)
−0.330868 + 0.943677i \(0.607342\pi\)
\(882\) 4.42632e13 2.46283
\(883\) −1.66652e13 −0.922544 −0.461272 0.887259i \(-0.652607\pi\)
−0.461272 + 0.887259i \(0.652607\pi\)
\(884\) −5.38608e13 −2.96645
\(885\) 3.31367e13 1.81579
\(886\) 3.53375e13 1.92657
\(887\) 3.54685e11 0.0192392 0.00961958 0.999954i \(-0.496938\pi\)
0.00961958 + 0.999954i \(0.496938\pi\)
\(888\) −3.56879e13 −1.92603
\(889\) −4.45862e12 −0.239410
\(890\) −5.06071e13 −2.70369
\(891\) 5.65434e12 0.300561
\(892\) 9.36165e13 4.95120
\(893\) −3.49134e12 −0.183722
\(894\) −5.66292e13 −2.96498
\(895\) −2.33254e12 −0.121514
\(896\) −5.29412e13 −2.74415
\(897\) −1.85343e13 −0.955894
\(898\) −1.21703e13 −0.624534
\(899\) 1.61081e13 0.822481
\(900\) −2.05789e13 −1.04552
\(901\) 8.74427e12 0.442040
\(902\) −1.07094e14 −5.38688
\(903\) −1.33916e13 −0.670250
\(904\) 4.44741e12 0.221488
\(905\) −2.73901e13 −1.35730
\(906\) −1.04848e14 −5.16993
\(907\) 3.20467e13 1.57236 0.786178 0.618001i \(-0.212057\pi\)
0.786178 + 0.618001i \(0.212057\pi\)
\(908\) 8.09080e13 3.95007
\(909\) −3.59842e13 −1.74813
\(910\) −1.16249e13 −0.561959
\(911\) 3.62046e12 0.174153 0.0870764 0.996202i \(-0.472248\pi\)
0.0870764 + 0.996202i \(0.472248\pi\)
\(912\) 2.76059e14 13.2137
\(913\) −2.27206e13 −1.08219
\(914\) 4.87592e13 2.31099
\(915\) 1.45713e13 0.687231
\(916\) −1.53152e13 −0.718776
\(917\) −5.35336e12 −0.250014
\(918\) −4.63181e13 −2.15258
\(919\) 5.46114e12 0.252559 0.126280 0.991995i \(-0.459696\pi\)
0.126280 + 0.991995i \(0.459696\pi\)
\(920\) −5.69892e13 −2.62269
\(921\) 2.32459e13 1.06458
\(922\) −4.41402e13 −2.01162
\(923\) −4.85026e12 −0.219967
\(924\) 6.04093e13 2.72634
\(925\) 1.67413e12 0.0751885
\(926\) −4.42484e13 −1.97764
\(927\) −4.42498e13 −1.96812
\(928\) −8.10528e13 −3.58759
\(929\) 2.23394e13 0.984013 0.492006 0.870592i \(-0.336264\pi\)
0.492006 + 0.870592i \(0.336264\pi\)
\(930\) 7.67615e13 3.36488
\(931\) 3.38819e13 1.47807
\(932\) −1.08093e14 −4.69274
\(933\) 2.93904e13 1.26981
\(934\) 6.60568e13 2.84025
\(935\) 3.75563e13 1.60705
\(936\) −1.03755e14 −4.41843
\(937\) −3.42060e13 −1.44969 −0.724844 0.688913i \(-0.758088\pi\)
−0.724844 + 0.688913i \(0.758088\pi\)
\(938\) −1.93256e13 −0.815117
\(939\) 1.68228e13 0.706161
\(940\) 6.23394e12 0.260428
\(941\) −3.53611e13 −1.47019 −0.735094 0.677965i \(-0.762862\pi\)
−0.735094 + 0.677965i \(0.762862\pi\)
\(942\) 2.31995e13 0.959950
\(943\) −3.75406e13 −1.54596
\(944\) −1.47641e14 −6.05109
\(945\) −7.44871e12 −0.303835
\(946\) 6.73289e13 2.73333
\(947\) 4.68361e13 1.89237 0.946185 0.323627i \(-0.104902\pi\)
0.946185 + 0.323627i \(0.104902\pi\)
\(948\) −1.14403e14 −4.60043
\(949\) 1.42365e12 0.0569777
\(950\) −2.11415e13 −0.842131
\(951\) −7.17957e13 −2.84634
\(952\) 5.43346e13 2.14393
\(953\) 3.94090e13 1.54767 0.773833 0.633390i \(-0.218337\pi\)
0.773833 + 0.633390i \(0.218337\pi\)
\(954\) 2.56040e13 1.00078
\(955\) 1.87155e13 0.728094
\(956\) 1.06092e14 4.10792
\(957\) 3.82941e13 1.47580
\(958\) −1.30264e13 −0.499668
\(959\) −1.85884e13 −0.709673
\(960\) −2.17617e14 −8.26937
\(961\) 1.32452e13 0.500961
\(962\) 1.28299e13 0.482986
\(963\) 4.16201e13 1.55950
\(964\) 6.99846e13 2.61009
\(965\) −8.08982e12 −0.300307
\(966\) 2.84202e13 1.05010
\(967\) −2.58756e13 −0.951637 −0.475819 0.879543i \(-0.657848\pi\)
−0.475819 + 0.879543i \(0.657848\pi\)
\(968\) −9.57656e13 −3.50567
\(969\) −1.04110e14 −3.79345
\(970\) −2.88033e13 −1.04465
\(971\) 8.30034e12 0.299646 0.149823 0.988713i \(-0.452130\pi\)
0.149823 + 0.988713i \(0.452130\pi\)
\(972\) 9.46261e13 3.40026
\(973\) 1.08569e13 0.388326
\(974\) −6.83636e12 −0.243394
\(975\) 8.07685e12 0.286234
\(976\) −6.49227e13 −2.29020
\(977\) −2.36004e13 −0.828694 −0.414347 0.910119i \(-0.635990\pi\)
−0.414347 + 0.910119i \(0.635990\pi\)
\(978\) 9.28569e12 0.324556
\(979\) −6.21985e13 −2.16400
\(980\) −6.04975e13 −2.09517
\(981\) −4.76850e13 −1.64388
\(982\) 3.92420e13 1.34663
\(983\) −4.25392e12 −0.145311 −0.0726555 0.997357i \(-0.523147\pi\)
−0.0726555 + 0.997357i \(0.523147\pi\)
\(984\) −3.48737e14 −11.8583
\(985\) 1.83998e12 0.0622801
\(986\) 5.23542e13 1.76403
\(987\) −2.04526e12 −0.0685997
\(988\) −1.20720e14 −4.03065
\(989\) 2.36013e13 0.784427
\(990\) 1.09968e14 3.63838
\(991\) −4.80502e13 −1.58257 −0.791287 0.611445i \(-0.790589\pi\)
−0.791287 + 0.611445i \(0.790589\pi\)
\(992\) −1.99686e14 −6.54705
\(993\) −1.36001e13 −0.443886
\(994\) 7.43731e12 0.241645
\(995\) 1.27878e13 0.413611
\(996\) −1.12460e14 −3.62103
\(997\) 8.87826e12 0.284577 0.142288 0.989825i \(-0.454554\pi\)
0.142288 + 0.989825i \(0.454554\pi\)
\(998\) −1.33367e13 −0.425559
\(999\) 8.22078e12 0.261137
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.1.1 76
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.10.a.b.1.1 76 1.1 even 1 trivial