Properties

Label 197.10.a.b.1.10
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 1.10
Character \(\chi\) \(=\) 197.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-36.2963 q^{2} -223.000 q^{3} +805.418 q^{4} +837.898 q^{5} +8094.08 q^{6} -7154.81 q^{7} -10650.0 q^{8} +30046.2 q^{9} +O(q^{10})\) \(q-36.2963 q^{2} -223.000 q^{3} +805.418 q^{4} +837.898 q^{5} +8094.08 q^{6} -7154.81 q^{7} -10650.0 q^{8} +30046.2 q^{9} -30412.5 q^{10} -48642.2 q^{11} -179609. q^{12} -165417. q^{13} +259693. q^{14} -186851. q^{15} -25819.7 q^{16} +237529. q^{17} -1.09056e6 q^{18} +247911. q^{19} +674858. q^{20} +1.59552e6 q^{21} +1.76553e6 q^{22} +2.19717e6 q^{23} +2.37495e6 q^{24} -1.25105e6 q^{25} +6.00401e6 q^{26} -2.31099e6 q^{27} -5.76261e6 q^{28} -3.47504e6 q^{29} +6.78201e6 q^{30} -8.53092e6 q^{31} +6.38995e6 q^{32} +1.08472e7 q^{33} -8.62143e6 q^{34} -5.99500e6 q^{35} +2.41997e7 q^{36} +9.70151e6 q^{37} -8.99823e6 q^{38} +3.68880e7 q^{39} -8.92359e6 q^{40} -4.25913e6 q^{41} -5.79116e7 q^{42} +1.45669e6 q^{43} -3.91773e7 q^{44} +2.51756e7 q^{45} -7.97489e7 q^{46} -2.59145e7 q^{47} +5.75780e6 q^{48} +1.08377e7 q^{49} +4.54085e7 q^{50} -5.29691e7 q^{51} -1.33230e8 q^{52} -7.22332e7 q^{53} +8.38802e7 q^{54} -4.07571e7 q^{55} +7.61986e7 q^{56} -5.52842e7 q^{57} +1.26131e8 q^{58} +8.95363e7 q^{59} -1.50494e8 q^{60} -1.82830e8 q^{61} +3.09640e8 q^{62} -2.14975e8 q^{63} -2.18712e8 q^{64} -1.38602e8 q^{65} -3.93713e8 q^{66} -1.41642e8 q^{67} +1.91310e8 q^{68} -4.89969e8 q^{69} +2.17596e8 q^{70} +1.72970e8 q^{71} -3.19991e8 q^{72} -3.77861e8 q^{73} -3.52129e8 q^{74} +2.78985e8 q^{75} +1.99672e8 q^{76} +3.48025e8 q^{77} -1.33890e9 q^{78} -5.40375e8 q^{79} -2.16343e7 q^{80} -7.60473e7 q^{81} +1.54591e8 q^{82} +3.32445e8 q^{83} +1.28506e9 q^{84} +1.99025e8 q^{85} -5.28722e7 q^{86} +7.74935e8 q^{87} +5.18038e8 q^{88} -4.21712e8 q^{89} -9.13780e8 q^{90} +1.18352e9 q^{91} +1.76964e9 q^{92} +1.90240e9 q^{93} +9.40601e8 q^{94} +2.07724e8 q^{95} -1.42496e9 q^{96} -4.05306e8 q^{97} -3.93367e8 q^{98} -1.46151e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −36.2963 −1.60408 −0.802042 0.597268i \(-0.796253\pi\)
−0.802042 + 0.597268i \(0.796253\pi\)
\(3\) −223.000 −1.58950 −0.794749 0.606938i \(-0.792397\pi\)
−0.794749 + 0.606938i \(0.792397\pi\)
\(4\) 805.418 1.57308
\(5\) 837.898 0.599551 0.299775 0.954010i \(-0.403088\pi\)
0.299775 + 0.954010i \(0.403088\pi\)
\(6\) 8094.08 2.54969
\(7\) −7154.81 −1.12631 −0.563154 0.826352i \(-0.690412\pi\)
−0.563154 + 0.826352i \(0.690412\pi\)
\(8\) −10650.0 −0.919272
\(9\) 30046.2 1.52650
\(10\) −30412.5 −0.961729
\(11\) −48642.2 −1.00172 −0.500859 0.865529i \(-0.666983\pi\)
−0.500859 + 0.865529i \(0.666983\pi\)
\(12\) −179609. −2.50041
\(13\) −165417. −1.60633 −0.803164 0.595758i \(-0.796852\pi\)
−0.803164 + 0.595758i \(0.796852\pi\)
\(14\) 259693. 1.80669
\(15\) −186851. −0.952985
\(16\) −25819.7 −0.0984943
\(17\) 237529. 0.689759 0.344879 0.938647i \(-0.387920\pi\)
0.344879 + 0.938647i \(0.387920\pi\)
\(18\) −1.09056e6 −2.44864
\(19\) 247911. 0.436420 0.218210 0.975902i \(-0.429978\pi\)
0.218210 + 0.975902i \(0.429978\pi\)
\(20\) 674858. 0.943143
\(21\) 1.59552e6 1.79026
\(22\) 1.76553e6 1.60684
\(23\) 2.19717e6 1.63715 0.818574 0.574402i \(-0.194765\pi\)
0.818574 + 0.574402i \(0.194765\pi\)
\(24\) 2.37495e6 1.46118
\(25\) −1.25105e6 −0.640539
\(26\) 6.00401e6 2.57668
\(27\) −2.31099e6 −0.836876
\(28\) −5.76261e6 −1.77177
\(29\) −3.47504e6 −0.912365 −0.456182 0.889886i \(-0.650784\pi\)
−0.456182 + 0.889886i \(0.650784\pi\)
\(30\) 6.78201e6 1.52867
\(31\) −8.53092e6 −1.65908 −0.829541 0.558445i \(-0.811398\pi\)
−0.829541 + 0.558445i \(0.811398\pi\)
\(32\) 6.38995e6 1.07726
\(33\) 1.08472e7 1.59223
\(34\) −8.62143e6 −1.10643
\(35\) −5.99500e6 −0.675278
\(36\) 2.41997e7 2.40132
\(37\) 9.70151e6 0.851004 0.425502 0.904957i \(-0.360098\pi\)
0.425502 + 0.904957i \(0.360098\pi\)
\(38\) −8.99823e6 −0.700053
\(39\) 3.68880e7 2.55325
\(40\) −8.92359e6 −0.551150
\(41\) −4.25913e6 −0.235393 −0.117697 0.993050i \(-0.537551\pi\)
−0.117697 + 0.993050i \(0.537551\pi\)
\(42\) −5.79116e7 −2.87173
\(43\) 1.45669e6 0.0649767 0.0324883 0.999472i \(-0.489657\pi\)
0.0324883 + 0.999472i \(0.489657\pi\)
\(44\) −3.91773e7 −1.57579
\(45\) 2.51756e7 0.915216
\(46\) −7.97489e7 −2.62612
\(47\) −2.59145e7 −0.774646 −0.387323 0.921944i \(-0.626600\pi\)
−0.387323 + 0.921944i \(0.626600\pi\)
\(48\) 5.75780e6 0.156556
\(49\) 1.08377e7 0.268567
\(50\) 4.54085e7 1.02748
\(51\) −5.29691e7 −1.09637
\(52\) −1.33230e8 −2.52689
\(53\) −7.22332e7 −1.25746 −0.628732 0.777622i \(-0.716426\pi\)
−0.628732 + 0.777622i \(0.716426\pi\)
\(54\) 8.38802e7 1.34242
\(55\) −4.07571e7 −0.600581
\(56\) 7.61986e7 1.03538
\(57\) −5.52842e7 −0.693688
\(58\) 1.26131e8 1.46351
\(59\) 8.95363e7 0.961978 0.480989 0.876727i \(-0.340278\pi\)
0.480989 + 0.876727i \(0.340278\pi\)
\(60\) −1.50494e8 −1.49912
\(61\) −1.82830e8 −1.69068 −0.845342 0.534226i \(-0.820603\pi\)
−0.845342 + 0.534226i \(0.820603\pi\)
\(62\) 3.09640e8 2.66131
\(63\) −2.14975e8 −1.71931
\(64\) −2.18712e8 −1.62953
\(65\) −1.38602e8 −0.963075
\(66\) −3.93713e8 −2.55407
\(67\) −1.41642e8 −0.858727 −0.429363 0.903132i \(-0.641262\pi\)
−0.429363 + 0.903132i \(0.641262\pi\)
\(68\) 1.91310e8 1.08505
\(69\) −4.89969e8 −2.60224
\(70\) 2.17596e8 1.08320
\(71\) 1.72970e8 0.807806 0.403903 0.914802i \(-0.367653\pi\)
0.403903 + 0.914802i \(0.367653\pi\)
\(72\) −3.19991e8 −1.40327
\(73\) −3.77861e8 −1.55732 −0.778662 0.627444i \(-0.784101\pi\)
−0.778662 + 0.627444i \(0.784101\pi\)
\(74\) −3.52129e8 −1.36508
\(75\) 2.78985e8 1.01814
\(76\) 1.99672e8 0.686524
\(77\) 3.48025e8 1.12824
\(78\) −1.33890e9 −4.09563
\(79\) −5.40375e8 −1.56089 −0.780447 0.625222i \(-0.785008\pi\)
−0.780447 + 0.625222i \(0.785008\pi\)
\(80\) −2.16343e7 −0.0590523
\(81\) −7.60473e7 −0.196291
\(82\) 1.54591e8 0.377590
\(83\) 3.32445e8 0.768897 0.384448 0.923146i \(-0.374392\pi\)
0.384448 + 0.923146i \(0.374392\pi\)
\(84\) 1.28506e9 2.81623
\(85\) 1.99025e8 0.413545
\(86\) −5.28722e7 −0.104228
\(87\) 7.74935e8 1.45020
\(88\) 5.18038e8 0.920852
\(89\) −4.21712e8 −0.712460 −0.356230 0.934398i \(-0.615938\pi\)
−0.356230 + 0.934398i \(0.615938\pi\)
\(90\) −9.13780e8 −1.46808
\(91\) 1.18352e9 1.80922
\(92\) 1.76964e9 2.57537
\(93\) 1.90240e9 2.63711
\(94\) 9.40601e8 1.24260
\(95\) 2.07724e8 0.261656
\(96\) −1.42496e9 −1.71231
\(97\) −4.05306e8 −0.464847 −0.232424 0.972615i \(-0.574666\pi\)
−0.232424 + 0.972615i \(0.574666\pi\)
\(98\) −3.93367e8 −0.430805
\(99\) −1.46151e9 −1.52913
\(100\) −1.00762e9 −1.00762
\(101\) −1.51903e9 −1.45252 −0.726259 0.687421i \(-0.758743\pi\)
−0.726259 + 0.687421i \(0.758743\pi\)
\(102\) 1.92258e9 1.75867
\(103\) 5.44230e7 0.0476448 0.0238224 0.999716i \(-0.492416\pi\)
0.0238224 + 0.999716i \(0.492416\pi\)
\(104\) 1.76168e9 1.47665
\(105\) 1.33689e9 1.07335
\(106\) 2.62180e9 2.01708
\(107\) −2.67718e9 −1.97447 −0.987235 0.159268i \(-0.949087\pi\)
−0.987235 + 0.159268i \(0.949087\pi\)
\(108\) −1.86131e9 −1.31647
\(109\) −8.58867e8 −0.582783 −0.291391 0.956604i \(-0.594118\pi\)
−0.291391 + 0.956604i \(0.594118\pi\)
\(110\) 1.47933e9 0.963382
\(111\) −2.16344e9 −1.35267
\(112\) 1.84735e8 0.110935
\(113\) 2.68450e9 1.54885 0.774426 0.632664i \(-0.218039\pi\)
0.774426 + 0.632664i \(0.218039\pi\)
\(114\) 2.00661e9 1.11273
\(115\) 1.84100e9 0.981553
\(116\) −2.79886e9 −1.43523
\(117\) −4.97014e9 −2.45206
\(118\) −3.24983e9 −1.54309
\(119\) −1.69948e9 −0.776880
\(120\) 1.98996e9 0.876052
\(121\) 8.11187e6 0.00344023
\(122\) 6.63603e9 2.71200
\(123\) 9.49788e8 0.374157
\(124\) −6.87095e9 −2.60987
\(125\) −2.68477e9 −0.983586
\(126\) 7.80277e9 2.75792
\(127\) 1.96576e9 0.670522 0.335261 0.942125i \(-0.391176\pi\)
0.335261 + 0.942125i \(0.391176\pi\)
\(128\) 4.66676e9 1.53663
\(129\) −3.24841e8 −0.103280
\(130\) 5.03074e9 1.54485
\(131\) −4.30836e9 −1.27818 −0.639089 0.769133i \(-0.720688\pi\)
−0.639089 + 0.769133i \(0.720688\pi\)
\(132\) 8.73655e9 2.50471
\(133\) −1.77375e9 −0.491542
\(134\) 5.14107e9 1.37747
\(135\) −1.93637e9 −0.501749
\(136\) −2.52968e9 −0.634076
\(137\) −2.01231e9 −0.488037 −0.244019 0.969771i \(-0.578466\pi\)
−0.244019 + 0.969771i \(0.578466\pi\)
\(138\) 1.77840e10 4.17421
\(139\) 7.24917e9 1.64711 0.823553 0.567239i \(-0.191988\pi\)
0.823553 + 0.567239i \(0.191988\pi\)
\(140\) −4.82848e9 −1.06227
\(141\) 5.77895e9 1.23130
\(142\) −6.27815e9 −1.29579
\(143\) 8.04622e9 1.60909
\(144\) −7.75783e8 −0.150352
\(145\) −2.91173e9 −0.547009
\(146\) 1.37149e10 2.49808
\(147\) −2.41680e9 −0.426887
\(148\) 7.81377e9 1.33870
\(149\) −4.57307e9 −0.760098 −0.380049 0.924966i \(-0.624093\pi\)
−0.380049 + 0.924966i \(0.624093\pi\)
\(150\) −1.01261e10 −1.63317
\(151\) −1.05540e10 −1.65204 −0.826018 0.563644i \(-0.809399\pi\)
−0.826018 + 0.563644i \(0.809399\pi\)
\(152\) −2.64025e9 −0.401188
\(153\) 7.13685e9 1.05292
\(154\) −1.26320e10 −1.80979
\(155\) −7.14803e9 −0.994704
\(156\) 2.97102e10 4.01648
\(157\) −5.91949e9 −0.777564 −0.388782 0.921330i \(-0.627104\pi\)
−0.388782 + 0.921330i \(0.627104\pi\)
\(158\) 1.96136e10 2.50380
\(159\) 1.61080e10 1.99874
\(160\) 5.35412e9 0.645875
\(161\) −1.57203e10 −1.84393
\(162\) 2.76023e9 0.314868
\(163\) −5.78478e9 −0.641864 −0.320932 0.947102i \(-0.603996\pi\)
−0.320932 + 0.947102i \(0.603996\pi\)
\(164\) −3.43038e9 −0.370293
\(165\) 9.08886e9 0.954622
\(166\) −1.20665e10 −1.23337
\(167\) −4.50440e9 −0.448139 −0.224069 0.974573i \(-0.571934\pi\)
−0.224069 + 0.974573i \(0.571934\pi\)
\(168\) −1.69923e10 −1.64574
\(169\) 1.67582e10 1.58029
\(170\) −7.22387e9 −0.663361
\(171\) 7.44877e9 0.666196
\(172\) 1.17324e9 0.102214
\(173\) −1.31715e9 −0.111796 −0.0558981 0.998436i \(-0.517802\pi\)
−0.0558981 + 0.998436i \(0.517802\pi\)
\(174\) −2.81272e10 −2.32624
\(175\) 8.95104e9 0.721443
\(176\) 1.25593e9 0.0986636
\(177\) −1.99666e10 −1.52906
\(178\) 1.53066e10 1.14285
\(179\) 1.01850e10 0.741522 0.370761 0.928728i \(-0.379097\pi\)
0.370761 + 0.928728i \(0.379097\pi\)
\(180\) 2.02769e10 1.43971
\(181\) 1.63383e10 1.13149 0.565747 0.824579i \(-0.308588\pi\)
0.565747 + 0.824579i \(0.308588\pi\)
\(182\) −4.29575e10 −2.90214
\(183\) 4.07711e10 2.68734
\(184\) −2.33998e10 −1.50498
\(185\) 8.12887e9 0.510220
\(186\) −6.90499e10 −4.23014
\(187\) −1.15539e10 −0.690944
\(188\) −2.08720e10 −1.21858
\(189\) 1.65347e10 0.942579
\(190\) −7.53960e9 −0.419717
\(191\) −3.27140e10 −1.77862 −0.889309 0.457306i \(-0.848814\pi\)
−0.889309 + 0.457306i \(0.848814\pi\)
\(192\) 4.87727e10 2.59013
\(193\) −1.58246e10 −0.820965 −0.410483 0.911868i \(-0.634640\pi\)
−0.410483 + 0.911868i \(0.634640\pi\)
\(194\) 1.47111e10 0.745653
\(195\) 3.09083e10 1.53081
\(196\) 8.72885e9 0.422479
\(197\) 1.50614e9 0.0712470
\(198\) 5.30473e10 2.45285
\(199\) −2.39794e10 −1.08393 −0.541964 0.840402i \(-0.682319\pi\)
−0.541964 + 0.840402i \(0.682319\pi\)
\(200\) 1.33237e10 0.588829
\(201\) 3.15862e10 1.36494
\(202\) 5.51353e10 2.32996
\(203\) 2.48632e10 1.02760
\(204\) −4.26623e10 −1.72468
\(205\) −3.56872e9 −0.141130
\(206\) −1.97535e9 −0.0764262
\(207\) 6.60164e10 2.49911
\(208\) 4.27101e9 0.158214
\(209\) −1.20589e10 −0.437170
\(210\) −4.85240e10 −1.72175
\(211\) −1.76343e10 −0.612473 −0.306237 0.951955i \(-0.599070\pi\)
−0.306237 + 0.951955i \(0.599070\pi\)
\(212\) −5.81779e10 −1.97809
\(213\) −3.85723e10 −1.28401
\(214\) 9.71716e10 3.16722
\(215\) 1.22055e9 0.0389568
\(216\) 2.46120e10 0.769316
\(217\) 6.10371e10 1.86864
\(218\) 3.11737e10 0.934832
\(219\) 8.42631e10 2.47536
\(220\) −3.28265e10 −0.944764
\(221\) −3.92913e10 −1.10798
\(222\) 7.85248e10 2.16979
\(223\) 2.99192e10 0.810173 0.405086 0.914278i \(-0.367241\pi\)
0.405086 + 0.914278i \(0.367241\pi\)
\(224\) −4.57188e10 −1.21333
\(225\) −3.75893e10 −0.977785
\(226\) −9.74372e10 −2.48449
\(227\) 1.49180e10 0.372901 0.186450 0.982464i \(-0.440302\pi\)
0.186450 + 0.982464i \(0.440302\pi\)
\(228\) −4.45269e10 −1.09123
\(229\) 7.56672e9 0.181823 0.0909113 0.995859i \(-0.471022\pi\)
0.0909113 + 0.995859i \(0.471022\pi\)
\(230\) −6.68214e10 −1.57449
\(231\) −7.76098e10 −1.79334
\(232\) 3.70091e10 0.838711
\(233\) −5.29276e10 −1.17647 −0.588234 0.808691i \(-0.700177\pi\)
−0.588234 + 0.808691i \(0.700177\pi\)
\(234\) 1.80397e11 3.93331
\(235\) −2.17137e10 −0.464440
\(236\) 7.21142e10 1.51327
\(237\) 1.20504e11 2.48104
\(238\) 6.16847e10 1.24618
\(239\) 1.19650e8 0.00237204 0.00118602 0.999999i \(-0.499622\pi\)
0.00118602 + 0.999999i \(0.499622\pi\)
\(240\) 4.82445e9 0.0938636
\(241\) −3.90771e10 −0.746184 −0.373092 0.927794i \(-0.621702\pi\)
−0.373092 + 0.927794i \(0.621702\pi\)
\(242\) −2.94431e8 −0.00551841
\(243\) 6.24458e10 1.14888
\(244\) −1.47254e11 −2.65959
\(245\) 9.08085e9 0.161020
\(246\) −3.44737e10 −0.600178
\(247\) −4.10086e10 −0.701033
\(248\) 9.08541e10 1.52515
\(249\) −7.41353e10 −1.22216
\(250\) 9.74472e10 1.57775
\(251\) −3.84879e10 −0.612058 −0.306029 0.952022i \(-0.599001\pi\)
−0.306029 + 0.952022i \(0.599001\pi\)
\(252\) −1.73144e11 −2.70462
\(253\) −1.06875e11 −1.63996
\(254\) −7.13496e10 −1.07557
\(255\) −4.43827e10 −0.657329
\(256\) −5.74054e10 −0.835359
\(257\) −2.78466e10 −0.398174 −0.199087 0.979982i \(-0.563798\pi\)
−0.199087 + 0.979982i \(0.563798\pi\)
\(258\) 1.17905e10 0.165670
\(259\) −6.94125e10 −0.958492
\(260\) −1.11633e11 −1.51500
\(261\) −1.04412e11 −1.39273
\(262\) 1.56377e11 2.05030
\(263\) 9.68880e10 1.24873 0.624366 0.781132i \(-0.285357\pi\)
0.624366 + 0.781132i \(0.285357\pi\)
\(264\) −1.15523e11 −1.46369
\(265\) −6.05240e10 −0.753913
\(266\) 6.43806e10 0.788475
\(267\) 9.40418e10 1.13245
\(268\) −1.14081e11 −1.35085
\(269\) 4.64112e10 0.540428 0.270214 0.962800i \(-0.412906\pi\)
0.270214 + 0.962800i \(0.412906\pi\)
\(270\) 7.02831e10 0.804848
\(271\) −9.49935e10 −1.06987 −0.534936 0.844893i \(-0.679664\pi\)
−0.534936 + 0.844893i \(0.679664\pi\)
\(272\) −6.13294e9 −0.0679373
\(273\) −2.63926e11 −2.87575
\(274\) 7.30394e10 0.782852
\(275\) 6.08539e10 0.641640
\(276\) −3.94630e11 −4.09354
\(277\) −1.40482e10 −0.143371 −0.0716857 0.997427i \(-0.522838\pi\)
−0.0716857 + 0.997427i \(0.522838\pi\)
\(278\) −2.63118e11 −2.64210
\(279\) −2.56321e11 −2.53259
\(280\) 6.38466e10 0.620764
\(281\) −4.90910e10 −0.469703 −0.234852 0.972031i \(-0.575460\pi\)
−0.234852 + 0.972031i \(0.575460\pi\)
\(282\) −2.09754e11 −1.97510
\(283\) 1.99025e11 1.84446 0.922228 0.386646i \(-0.126367\pi\)
0.922228 + 0.386646i \(0.126367\pi\)
\(284\) 1.39313e11 1.27075
\(285\) −4.63225e10 −0.415901
\(286\) −2.92048e11 −2.58111
\(287\) 3.04733e10 0.265125
\(288\) 1.91993e11 1.64445
\(289\) −6.21677e10 −0.524233
\(290\) 1.05685e11 0.877448
\(291\) 9.03834e10 0.738873
\(292\) −3.04336e11 −2.44980
\(293\) 6.27330e10 0.497269 0.248635 0.968597i \(-0.420018\pi\)
0.248635 + 0.968597i \(0.420018\pi\)
\(294\) 8.77209e10 0.684763
\(295\) 7.50223e10 0.576755
\(296\) −1.03321e11 −0.782304
\(297\) 1.12411e11 0.838314
\(298\) 1.65985e11 1.21926
\(299\) −3.63448e11 −2.62979
\(300\) 2.24700e11 1.60161
\(301\) −1.04223e10 −0.0731837
\(302\) 3.83069e11 2.65000
\(303\) 3.38745e11 2.30877
\(304\) −6.40098e9 −0.0429849
\(305\) −1.53193e11 −1.01365
\(306\) −2.59041e11 −1.68897
\(307\) 2.83364e11 1.82063 0.910316 0.413913i \(-0.135838\pi\)
0.910316 + 0.413913i \(0.135838\pi\)
\(308\) 2.80306e11 1.77482
\(309\) −1.21364e10 −0.0757313
\(310\) 2.59447e11 1.59559
\(311\) 1.22406e11 0.741958 0.370979 0.928641i \(-0.379022\pi\)
0.370979 + 0.928641i \(0.379022\pi\)
\(312\) −3.92856e11 −2.34713
\(313\) −3.37873e10 −0.198978 −0.0994888 0.995039i \(-0.531721\pi\)
−0.0994888 + 0.995039i \(0.531721\pi\)
\(314\) 2.14856e11 1.24728
\(315\) −1.80127e11 −1.03081
\(316\) −4.35228e11 −2.45541
\(317\) 1.20564e11 0.670583 0.335291 0.942115i \(-0.391165\pi\)
0.335291 + 0.942115i \(0.391165\pi\)
\(318\) −5.84661e11 −3.20614
\(319\) 1.69033e11 0.913933
\(320\) −1.83258e11 −0.976984
\(321\) 5.97012e11 3.13842
\(322\) 5.70588e11 2.95782
\(323\) 5.88861e10 0.301024
\(324\) −6.12498e10 −0.308782
\(325\) 2.06945e11 1.02892
\(326\) 2.09966e11 1.02960
\(327\) 1.91528e11 0.926332
\(328\) 4.53597e10 0.216390
\(329\) 1.85414e11 0.872489
\(330\) −3.29892e11 −1.53129
\(331\) 1.71475e11 0.785190 0.392595 0.919711i \(-0.371577\pi\)
0.392595 + 0.919711i \(0.371577\pi\)
\(332\) 2.67757e11 1.20954
\(333\) 2.91493e11 1.29906
\(334\) 1.63493e11 0.718852
\(335\) −1.18681e11 −0.514850
\(336\) −4.11960e10 −0.176331
\(337\) −4.26686e10 −0.180208 −0.0901039 0.995932i \(-0.528720\pi\)
−0.0901039 + 0.995932i \(0.528720\pi\)
\(338\) −6.08259e11 −2.53491
\(339\) −5.98644e11 −2.46190
\(340\) 1.60299e11 0.650541
\(341\) 4.14962e11 1.66193
\(342\) −2.70362e11 −1.06863
\(343\) 2.11181e11 0.823818
\(344\) −1.55137e10 −0.0597312
\(345\) −4.10544e11 −1.56018
\(346\) 4.78075e10 0.179330
\(347\) −1.40769e11 −0.521224 −0.260612 0.965444i \(-0.583924\pi\)
−0.260612 + 0.965444i \(0.583924\pi\)
\(348\) 6.24147e11 2.28129
\(349\) −1.65686e11 −0.597821 −0.298911 0.954281i \(-0.596623\pi\)
−0.298911 + 0.954281i \(0.596623\pi\)
\(350\) −3.24889e11 −1.15726
\(351\) 3.82276e11 1.34430
\(352\) −3.10821e11 −1.07912
\(353\) −4.59387e11 −1.57468 −0.787341 0.616518i \(-0.788543\pi\)
−0.787341 + 0.616518i \(0.788543\pi\)
\(354\) 7.24714e11 2.45274
\(355\) 1.44931e11 0.484321
\(356\) −3.39654e11 −1.12076
\(357\) 3.78984e11 1.23485
\(358\) −3.69679e11 −1.18946
\(359\) 4.69834e11 1.49286 0.746431 0.665463i \(-0.231766\pi\)
0.746431 + 0.665463i \(0.231766\pi\)
\(360\) −2.68120e11 −0.841332
\(361\) −2.61228e11 −0.809538
\(362\) −5.93017e11 −1.81501
\(363\) −1.80895e9 −0.00546823
\(364\) 9.53232e11 2.84605
\(365\) −3.16609e11 −0.933694
\(366\) −1.47984e12 −4.31071
\(367\) 2.25109e11 0.647732 0.323866 0.946103i \(-0.395017\pi\)
0.323866 + 0.946103i \(0.395017\pi\)
\(368\) −5.67302e10 −0.161250
\(369\) −1.27971e11 −0.359328
\(370\) −2.95048e11 −0.818435
\(371\) 5.16815e11 1.41629
\(372\) 1.53223e12 4.14839
\(373\) 2.42835e11 0.649562 0.324781 0.945789i \(-0.394709\pi\)
0.324781 + 0.945789i \(0.394709\pi\)
\(374\) 4.19365e11 1.10833
\(375\) 5.98705e11 1.56341
\(376\) 2.75989e11 0.712110
\(377\) 5.74829e11 1.46556
\(378\) −6.00147e11 −1.51197
\(379\) −4.12709e10 −0.102747 −0.0513734 0.998680i \(-0.516360\pi\)
−0.0513734 + 0.998680i \(0.516360\pi\)
\(380\) 1.67305e11 0.411606
\(381\) −4.38364e11 −1.06579
\(382\) 1.18739e12 2.85305
\(383\) −2.40285e11 −0.570600 −0.285300 0.958438i \(-0.592093\pi\)
−0.285300 + 0.958438i \(0.592093\pi\)
\(384\) −1.04069e12 −2.44247
\(385\) 2.91610e11 0.676439
\(386\) 5.74374e11 1.31690
\(387\) 4.37678e10 0.0991871
\(388\) −3.26441e11 −0.731243
\(389\) 4.37568e11 0.968885 0.484443 0.874823i \(-0.339022\pi\)
0.484443 + 0.874823i \(0.339022\pi\)
\(390\) −1.12186e12 −2.45554
\(391\) 5.21892e11 1.12924
\(392\) −1.15421e11 −0.246886
\(393\) 9.60766e11 2.03166
\(394\) −5.46672e10 −0.114286
\(395\) −4.52779e11 −0.935835
\(396\) −1.17713e12 −2.40544
\(397\) −3.81340e11 −0.770469 −0.385234 0.922819i \(-0.625879\pi\)
−0.385234 + 0.922819i \(0.625879\pi\)
\(398\) 8.70364e11 1.73871
\(399\) 3.95548e11 0.781306
\(400\) 3.23018e10 0.0630894
\(401\) −6.35926e11 −1.22817 −0.614083 0.789241i \(-0.710474\pi\)
−0.614083 + 0.789241i \(0.710474\pi\)
\(402\) −1.14646e12 −2.18948
\(403\) 1.41116e12 2.66503
\(404\) −1.22346e12 −2.28493
\(405\) −6.37198e10 −0.117687
\(406\) −9.02442e11 −1.64836
\(407\) −4.71902e11 −0.852467
\(408\) 5.64120e11 1.00786
\(409\) −2.14433e11 −0.378910 −0.189455 0.981889i \(-0.560672\pi\)
−0.189455 + 0.981889i \(0.560672\pi\)
\(410\) 1.29531e11 0.226384
\(411\) 4.48746e11 0.775734
\(412\) 4.38333e10 0.0749492
\(413\) −6.40615e11 −1.08348
\(414\) −2.39615e12 −4.00878
\(415\) 2.78555e11 0.460993
\(416\) −1.05700e12 −1.73044
\(417\) −1.61657e12 −2.61807
\(418\) 4.37694e11 0.701256
\(419\) 8.62883e11 1.36769 0.683847 0.729626i \(-0.260306\pi\)
0.683847 + 0.729626i \(0.260306\pi\)
\(420\) 1.07675e12 1.68847
\(421\) −7.11528e11 −1.10388 −0.551941 0.833883i \(-0.686113\pi\)
−0.551941 + 0.833883i \(0.686113\pi\)
\(422\) 6.40059e11 0.982458
\(423\) −7.78633e11 −1.18250
\(424\) 7.69282e11 1.15595
\(425\) −2.97162e11 −0.441817
\(426\) 1.40003e12 2.05965
\(427\) 1.30811e12 1.90423
\(428\) −2.15625e12 −3.10601
\(429\) −1.79431e12 −2.55764
\(430\) −4.43015e10 −0.0624900
\(431\) −1.72211e10 −0.0240388 −0.0120194 0.999928i \(-0.503826\pi\)
−0.0120194 + 0.999928i \(0.503826\pi\)
\(432\) 5.96690e10 0.0824275
\(433\) 1.27905e12 1.74861 0.874304 0.485379i \(-0.161319\pi\)
0.874304 + 0.485379i \(0.161319\pi\)
\(434\) −2.21542e12 −2.99745
\(435\) 6.49316e11 0.869470
\(436\) −6.91747e11 −0.916765
\(437\) 5.44701e11 0.714483
\(438\) −3.05843e12 −3.97069
\(439\) 5.36222e11 0.689056 0.344528 0.938776i \(-0.388039\pi\)
0.344528 + 0.938776i \(0.388039\pi\)
\(440\) 4.34063e11 0.552097
\(441\) 3.25630e11 0.409969
\(442\) 1.42613e12 1.77729
\(443\) −3.86887e10 −0.0477274 −0.0238637 0.999715i \(-0.507597\pi\)
−0.0238637 + 0.999715i \(0.507597\pi\)
\(444\) −1.74247e12 −2.12786
\(445\) −3.53351e11 −0.427156
\(446\) −1.08595e12 −1.29958
\(447\) 1.01980e12 1.20817
\(448\) 1.56484e12 1.83535
\(449\) 1.14374e12 1.32806 0.664031 0.747705i \(-0.268844\pi\)
0.664031 + 0.747705i \(0.268844\pi\)
\(450\) 1.36435e12 1.56845
\(451\) 2.07173e11 0.235798
\(452\) 2.16214e12 2.43647
\(453\) 2.35354e12 2.62591
\(454\) −5.41467e11 −0.598164
\(455\) 9.91672e11 1.08472
\(456\) 5.88776e11 0.637688
\(457\) −1.09433e11 −0.117361 −0.0586806 0.998277i \(-0.518689\pi\)
−0.0586806 + 0.998277i \(0.518689\pi\)
\(458\) −2.74643e11 −0.291658
\(459\) −5.48928e11 −0.577242
\(460\) 1.48278e12 1.54406
\(461\) −8.07098e11 −0.832286 −0.416143 0.909299i \(-0.636618\pi\)
−0.416143 + 0.909299i \(0.636618\pi\)
\(462\) 2.81694e12 2.87667
\(463\) −1.47892e12 −1.49565 −0.747825 0.663896i \(-0.768902\pi\)
−0.747825 + 0.663896i \(0.768902\pi\)
\(464\) 8.97244e10 0.0898628
\(465\) 1.59401e12 1.58108
\(466\) 1.92107e12 1.88715
\(467\) 6.69178e11 0.651052 0.325526 0.945533i \(-0.394459\pi\)
0.325526 + 0.945533i \(0.394459\pi\)
\(468\) −4.00304e12 −3.85730
\(469\) 1.01342e12 0.967190
\(470\) 7.88127e11 0.745000
\(471\) 1.32005e12 1.23594
\(472\) −9.53560e11 −0.884319
\(473\) −7.08563e10 −0.0650884
\(474\) −4.37384e12 −3.97979
\(475\) −3.10149e11 −0.279544
\(476\) −1.36879e12 −1.22210
\(477\) −2.17033e12 −1.91952
\(478\) −4.34285e9 −0.00380495
\(479\) −1.60620e12 −1.39409 −0.697044 0.717028i \(-0.745502\pi\)
−0.697044 + 0.717028i \(0.745502\pi\)
\(480\) −1.19397e12 −1.02662
\(481\) −1.60479e12 −1.36699
\(482\) 1.41835e12 1.19694
\(483\) 3.50563e12 2.93092
\(484\) 6.53345e9 0.00541176
\(485\) −3.39605e11 −0.278699
\(486\) −2.26655e12 −1.84290
\(487\) −2.11418e11 −0.170319 −0.0851593 0.996367i \(-0.527140\pi\)
−0.0851593 + 0.996367i \(0.527140\pi\)
\(488\) 1.94713e12 1.55420
\(489\) 1.29001e12 1.02024
\(490\) −3.29601e11 −0.258289
\(491\) −3.60341e11 −0.279800 −0.139900 0.990166i \(-0.544678\pi\)
−0.139900 + 0.990166i \(0.544678\pi\)
\(492\) 7.64976e11 0.588579
\(493\) −8.25424e11 −0.629312
\(494\) 1.48846e12 1.12451
\(495\) −1.22460e12 −0.916789
\(496\) 2.20266e11 0.163410
\(497\) −1.23756e12 −0.909837
\(498\) 2.69083e12 1.96045
\(499\) 1.52358e11 0.110005 0.0550026 0.998486i \(-0.482483\pi\)
0.0550026 + 0.998486i \(0.482483\pi\)
\(500\) −2.16236e12 −1.54726
\(501\) 1.00448e12 0.712315
\(502\) 1.39697e12 0.981792
\(503\) −2.07644e12 −1.44632 −0.723159 0.690682i \(-0.757310\pi\)
−0.723159 + 0.690682i \(0.757310\pi\)
\(504\) 2.28947e12 1.58051
\(505\) −1.27280e12 −0.870858
\(506\) 3.87916e12 2.63063
\(507\) −3.73708e12 −2.51187
\(508\) 1.58326e12 1.05479
\(509\) 1.38430e12 0.914115 0.457058 0.889437i \(-0.348903\pi\)
0.457058 + 0.889437i \(0.348903\pi\)
\(510\) 1.61093e12 1.05441
\(511\) 2.70352e12 1.75402
\(512\) −3.05776e11 −0.196647
\(513\) −5.72919e11 −0.365229
\(514\) 1.01073e12 0.638704
\(515\) 4.56009e10 0.0285655
\(516\) −2.61633e11 −0.162468
\(517\) 1.26054e12 0.775977
\(518\) 2.51941e12 1.53750
\(519\) 2.93724e11 0.177700
\(520\) 1.47611e12 0.885327
\(521\) −1.04843e12 −0.623403 −0.311702 0.950180i \(-0.600899\pi\)
−0.311702 + 0.950180i \(0.600899\pi\)
\(522\) 3.78975e12 2.23405
\(523\) 1.59947e12 0.934800 0.467400 0.884046i \(-0.345191\pi\)
0.467400 + 0.884046i \(0.345191\pi\)
\(524\) −3.47003e12 −2.01068
\(525\) −1.99609e12 −1.14673
\(526\) −3.51667e12 −2.00307
\(527\) −2.02634e12 −1.14437
\(528\) −2.80072e11 −0.156826
\(529\) 3.02639e12 1.68025
\(530\) 2.19680e12 1.20934
\(531\) 2.69022e12 1.46846
\(532\) −1.42861e12 −0.773237
\(533\) 7.04531e11 0.378118
\(534\) −3.41337e12 −1.81655
\(535\) −2.24320e12 −1.18380
\(536\) 1.50848e12 0.789403
\(537\) −2.27127e12 −1.17865
\(538\) −1.68455e12 −0.866891
\(539\) −5.27167e11 −0.269029
\(540\) −1.55959e12 −0.789293
\(541\) 3.48281e12 1.74800 0.874001 0.485924i \(-0.161517\pi\)
0.874001 + 0.485924i \(0.161517\pi\)
\(542\) 3.44791e12 1.71616
\(543\) −3.64344e12 −1.79851
\(544\) 1.51780e12 0.743053
\(545\) −7.19642e11 −0.349408
\(546\) 9.57954e12 4.61294
\(547\) −2.74309e11 −0.131008 −0.0655040 0.997852i \(-0.520865\pi\)
−0.0655040 + 0.997852i \(0.520865\pi\)
\(548\) −1.62075e12 −0.767723
\(549\) −5.49333e12 −2.58083
\(550\) −2.20877e12 −1.02924
\(551\) −8.61499e11 −0.398174
\(552\) 5.21816e12 2.39217
\(553\) 3.86628e12 1.75805
\(554\) 5.09898e11 0.229980
\(555\) −1.81274e12 −0.810994
\(556\) 5.83861e12 2.59103
\(557\) −2.37068e11 −0.104358 −0.0521789 0.998638i \(-0.516617\pi\)
−0.0521789 + 0.998638i \(0.516617\pi\)
\(558\) 9.30350e12 4.06249
\(559\) −2.40960e11 −0.104374
\(560\) 1.54789e11 0.0665111
\(561\) 2.57653e12 1.09825
\(562\) 1.78182e12 0.753443
\(563\) −2.68204e12 −1.12507 −0.562533 0.826775i \(-0.690173\pi\)
−0.562533 + 0.826775i \(0.690173\pi\)
\(564\) 4.65447e12 1.93693
\(565\) 2.24933e12 0.928615
\(566\) −7.22386e12 −2.95866
\(567\) 5.44104e11 0.221084
\(568\) −1.84212e12 −0.742593
\(569\) 3.06021e12 1.22390 0.611949 0.790897i \(-0.290386\pi\)
0.611949 + 0.790897i \(0.290386\pi\)
\(570\) 1.68133e12 0.667140
\(571\) −4.43210e12 −1.74480 −0.872402 0.488789i \(-0.837439\pi\)
−0.872402 + 0.488789i \(0.837439\pi\)
\(572\) 6.48057e12 2.53123
\(573\) 7.29522e12 2.82711
\(574\) −1.10607e12 −0.425282
\(575\) −2.74877e12 −1.04866
\(576\) −6.57144e12 −2.48748
\(577\) −4.06079e12 −1.52517 −0.762586 0.646887i \(-0.776071\pi\)
−0.762586 + 0.646887i \(0.776071\pi\)
\(578\) 2.25645e12 0.840913
\(579\) 3.52889e12 1.30492
\(580\) −2.34516e12 −0.860490
\(581\) −2.37858e12 −0.866014
\(582\) −3.28058e12 −1.18521
\(583\) 3.51358e12 1.25962
\(584\) 4.02421e12 1.43160
\(585\) −4.16446e12 −1.47014
\(586\) −2.27697e12 −0.797662
\(587\) −1.69116e12 −0.587915 −0.293957 0.955819i \(-0.594972\pi\)
−0.293957 + 0.955819i \(0.594972\pi\)
\(588\) −1.94654e12 −0.671529
\(589\) −2.11491e12 −0.724056
\(590\) −2.72303e12 −0.925162
\(591\) −3.35869e11 −0.113247
\(592\) −2.50490e11 −0.0838191
\(593\) 2.63198e12 0.874050 0.437025 0.899449i \(-0.356032\pi\)
0.437025 + 0.899449i \(0.356032\pi\)
\(594\) −4.08012e12 −1.34473
\(595\) −1.42399e12 −0.465779
\(596\) −3.68323e12 −1.19570
\(597\) 5.34742e12 1.72290
\(598\) 1.31918e13 4.21841
\(599\) 1.24241e12 0.394316 0.197158 0.980372i \(-0.436829\pi\)
0.197158 + 0.980372i \(0.436829\pi\)
\(600\) −2.97119e12 −0.935943
\(601\) 5.97867e12 1.86926 0.934630 0.355622i \(-0.115731\pi\)
0.934630 + 0.355622i \(0.115731\pi\)
\(602\) 3.78291e11 0.117393
\(603\) −4.25579e12 −1.31085
\(604\) −8.50035e12 −2.59879
\(605\) 6.79692e9 0.00206259
\(606\) −1.22952e13 −3.70347
\(607\) −4.12922e12 −1.23458 −0.617289 0.786736i \(-0.711769\pi\)
−0.617289 + 0.786736i \(0.711769\pi\)
\(608\) 1.58414e12 0.470139
\(609\) −5.54451e12 −1.63337
\(610\) 5.56032e12 1.62598
\(611\) 4.28670e12 1.24434
\(612\) 5.74815e12 1.65633
\(613\) −4.24710e12 −1.21484 −0.607422 0.794379i \(-0.707796\pi\)
−0.607422 + 0.794379i \(0.707796\pi\)
\(614\) −1.02851e13 −2.92045
\(615\) 7.95825e11 0.224326
\(616\) −3.70646e12 −1.03716
\(617\) 1.22102e12 0.339186 0.169593 0.985514i \(-0.445755\pi\)
0.169593 + 0.985514i \(0.445755\pi\)
\(618\) 4.40504e11 0.121479
\(619\) 6.04820e11 0.165584 0.0827920 0.996567i \(-0.473616\pi\)
0.0827920 + 0.996567i \(0.473616\pi\)
\(620\) −5.75716e12 −1.56475
\(621\) −5.07763e12 −1.37009
\(622\) −4.44286e12 −1.19016
\(623\) 3.01727e12 0.802449
\(624\) −9.52436e11 −0.251481
\(625\) 1.93897e11 0.0508291
\(626\) 1.22635e12 0.319177
\(627\) 2.68914e12 0.694880
\(628\) −4.76767e12 −1.22317
\(629\) 2.30439e12 0.586987
\(630\) 6.53792e12 1.65351
\(631\) 3.22615e12 0.810125 0.405063 0.914289i \(-0.367250\pi\)
0.405063 + 0.914289i \(0.367250\pi\)
\(632\) 5.75498e12 1.43489
\(633\) 3.93245e12 0.973525
\(634\) −4.37603e12 −1.07567
\(635\) 1.64710e12 0.402012
\(636\) 1.29737e13 3.14418
\(637\) −1.79273e12 −0.431407
\(638\) −6.13528e12 −1.46602
\(639\) 5.19707e12 1.23312
\(640\) 3.91026e12 0.921289
\(641\) −5.23129e12 −1.22391 −0.611953 0.790894i \(-0.709616\pi\)
−0.611953 + 0.790894i \(0.709616\pi\)
\(642\) −2.16693e13 −5.03428
\(643\) 5.33218e12 1.23014 0.615072 0.788471i \(-0.289127\pi\)
0.615072 + 0.788471i \(0.289127\pi\)
\(644\) −1.26614e13 −2.90065
\(645\) −2.72184e11 −0.0619218
\(646\) −2.13734e12 −0.482868
\(647\) 1.58217e12 0.354964 0.177482 0.984124i \(-0.443205\pi\)
0.177482 + 0.984124i \(0.443205\pi\)
\(648\) 8.09902e11 0.180445
\(649\) −4.35524e12 −0.963631
\(650\) −7.51133e12 −1.65047
\(651\) −1.36113e13 −2.97019
\(652\) −4.65917e12 −1.00970
\(653\) −7.13212e12 −1.53500 −0.767502 0.641046i \(-0.778501\pi\)
−0.767502 + 0.641046i \(0.778501\pi\)
\(654\) −6.95174e12 −1.48591
\(655\) −3.60996e12 −0.766332
\(656\) 1.09969e11 0.0231849
\(657\) −1.13533e13 −2.37726
\(658\) −6.72982e12 −1.39955
\(659\) −4.48841e12 −0.927062 −0.463531 0.886081i \(-0.653418\pi\)
−0.463531 + 0.886081i \(0.653418\pi\)
\(660\) 7.32033e12 1.50170
\(661\) −2.71638e12 −0.553458 −0.276729 0.960948i \(-0.589250\pi\)
−0.276729 + 0.960948i \(0.589250\pi\)
\(662\) −6.22390e12 −1.25951
\(663\) 8.76198e12 1.76113
\(664\) −3.54053e12 −0.706825
\(665\) −1.48622e12 −0.294705
\(666\) −1.05801e13 −2.08380
\(667\) −7.63524e12 −1.49368
\(668\) −3.62792e12 −0.704959
\(669\) −6.67199e12 −1.28777
\(670\) 4.30769e12 0.825862
\(671\) 8.89323e12 1.69359
\(672\) 1.01953e13 1.92859
\(673\) 4.83949e12 0.909351 0.454676 0.890657i \(-0.349755\pi\)
0.454676 + 0.890657i \(0.349755\pi\)
\(674\) 1.54871e12 0.289068
\(675\) 2.89117e12 0.536051
\(676\) 1.34973e13 2.48592
\(677\) −1.01283e13 −1.85305 −0.926523 0.376238i \(-0.877218\pi\)
−0.926523 + 0.376238i \(0.877218\pi\)
\(678\) 2.17285e13 3.94909
\(679\) 2.89989e12 0.523560
\(680\) −2.11962e12 −0.380160
\(681\) −3.32671e12 −0.592725
\(682\) −1.50616e13 −2.66588
\(683\) −2.10573e12 −0.370262 −0.185131 0.982714i \(-0.559271\pi\)
−0.185131 + 0.982714i \(0.559271\pi\)
\(684\) 5.99937e12 1.04798
\(685\) −1.68611e12 −0.292603
\(686\) −7.66508e12 −1.32147
\(687\) −1.68738e12 −0.289007
\(688\) −3.76112e10 −0.00639984
\(689\) 1.19486e13 2.01990
\(690\) 1.49012e13 2.50265
\(691\) 6.50389e12 1.08523 0.542615 0.839982i \(-0.317434\pi\)
0.542615 + 0.839982i \(0.317434\pi\)
\(692\) −1.06085e12 −0.175865
\(693\) 1.04568e13 1.72227
\(694\) 5.10939e12 0.836087
\(695\) 6.07406e12 0.987524
\(696\) −8.25304e12 −1.33313
\(697\) −1.01167e12 −0.162364
\(698\) 6.01378e12 0.958955
\(699\) 1.18029e13 1.86999
\(700\) 7.20933e12 1.13489
\(701\) 4.33793e12 0.678503 0.339252 0.940696i \(-0.389826\pi\)
0.339252 + 0.940696i \(0.389826\pi\)
\(702\) −1.38752e13 −2.15636
\(703\) 2.40511e12 0.371395
\(704\) 1.06386e13 1.63233
\(705\) 4.84217e12 0.738226
\(706\) 1.66740e13 2.52592
\(707\) 1.08684e13 1.63598
\(708\) −1.60815e13 −2.40534
\(709\) −1.14641e13 −1.70386 −0.851929 0.523658i \(-0.824567\pi\)
−0.851929 + 0.523658i \(0.824567\pi\)
\(710\) −5.26044e12 −0.776890
\(711\) −1.62362e13 −2.38271
\(712\) 4.49122e12 0.654944
\(713\) −1.87438e13 −2.71616
\(714\) −1.37557e13 −1.98080
\(715\) 6.74191e12 0.964730
\(716\) 8.20322e12 1.16648
\(717\) −2.66820e10 −0.00377036
\(718\) −1.70532e13 −2.39467
\(719\) −3.02789e12 −0.422533 −0.211266 0.977429i \(-0.567759\pi\)
−0.211266 + 0.977429i \(0.567759\pi\)
\(720\) −6.50026e11 −0.0901436
\(721\) −3.89386e11 −0.0536627
\(722\) 9.48160e12 1.29857
\(723\) 8.71421e12 1.18606
\(724\) 1.31591e13 1.77993
\(725\) 4.34746e12 0.584405
\(726\) 6.56581e10 0.00877150
\(727\) −2.43179e12 −0.322865 −0.161433 0.986884i \(-0.551611\pi\)
−0.161433 + 0.986884i \(0.551611\pi\)
\(728\) −1.26045e13 −1.66316
\(729\) −1.24286e13 −1.62985
\(730\) 1.14917e13 1.49772
\(731\) 3.46006e11 0.0448182
\(732\) 3.28378e13 4.22740
\(733\) −3.52706e11 −0.0451279 −0.0225639 0.999745i \(-0.507183\pi\)
−0.0225639 + 0.999745i \(0.507183\pi\)
\(734\) −8.17061e12 −1.03902
\(735\) −2.02503e12 −0.255941
\(736\) 1.40398e13 1.76364
\(737\) 6.88976e12 0.860203
\(738\) 4.64485e12 0.576392
\(739\) −6.46135e12 −0.796936 −0.398468 0.917182i \(-0.630458\pi\)
−0.398468 + 0.917182i \(0.630458\pi\)
\(740\) 6.54714e12 0.802618
\(741\) 9.14493e12 1.11429
\(742\) −1.87584e13 −2.27185
\(743\) −1.26195e13 −1.51912 −0.759559 0.650439i \(-0.774585\pi\)
−0.759559 + 0.650439i \(0.774585\pi\)
\(744\) −2.02605e13 −2.42422
\(745\) −3.83176e12 −0.455717
\(746\) −8.81398e12 −1.04195
\(747\) 9.98869e12 1.17372
\(748\) −9.30575e12 −1.08691
\(749\) 1.91547e13 2.22386
\(750\) −2.17308e13 −2.50784
\(751\) −8.97948e12 −1.03008 −0.515041 0.857166i \(-0.672223\pi\)
−0.515041 + 0.857166i \(0.672223\pi\)
\(752\) 6.69106e11 0.0762982
\(753\) 8.58282e12 0.972865
\(754\) −2.08641e13 −2.35088
\(755\) −8.84314e12 −0.990479
\(756\) 1.33173e13 1.48275
\(757\) −1.60509e13 −1.77651 −0.888255 0.459351i \(-0.848082\pi\)
−0.888255 + 0.459351i \(0.848082\pi\)
\(758\) 1.49798e12 0.164814
\(759\) 2.38331e13 2.60671
\(760\) −2.21226e12 −0.240533
\(761\) −1.21379e13 −1.31194 −0.655969 0.754788i \(-0.727740\pi\)
−0.655969 + 0.754788i \(0.727740\pi\)
\(762\) 1.59110e13 1.70962
\(763\) 6.14503e12 0.656392
\(764\) −2.63484e13 −2.79791
\(765\) 5.97995e12 0.631278
\(766\) 8.72144e12 0.915290
\(767\) −1.48108e13 −1.54525
\(768\) 1.28014e13 1.32780
\(769\) 1.17141e13 1.20792 0.603962 0.797013i \(-0.293588\pi\)
0.603962 + 0.797013i \(0.293588\pi\)
\(770\) −1.05843e13 −1.08506
\(771\) 6.20980e12 0.632897
\(772\) −1.27454e13 −1.29145
\(773\) 1.06869e13 1.07657 0.538285 0.842763i \(-0.319072\pi\)
0.538285 + 0.842763i \(0.319072\pi\)
\(774\) −1.58861e12 −0.159104
\(775\) 1.06726e13 1.06271
\(776\) 4.31650e12 0.427321
\(777\) 1.54790e13 1.52352
\(778\) −1.58821e13 −1.55417
\(779\) −1.05588e12 −0.102730
\(780\) 2.48941e13 2.40808
\(781\) −8.41361e12 −0.809194
\(782\) −1.89427e13 −1.81139
\(783\) 8.03077e12 0.763536
\(784\) −2.79825e11 −0.0264524
\(785\) −4.95993e12 −0.466189
\(786\) −3.48722e13 −3.25895
\(787\) 1.05523e13 0.980534 0.490267 0.871572i \(-0.336899\pi\)
0.490267 + 0.871572i \(0.336899\pi\)
\(788\) 1.21307e12 0.112077
\(789\) −2.16061e13 −1.98486
\(790\) 1.64342e13 1.50116
\(791\) −1.92071e13 −1.74448
\(792\) 1.55651e13 1.40568
\(793\) 3.02431e13 2.71579
\(794\) 1.38412e13 1.23590
\(795\) 1.34969e13 1.19834
\(796\) −1.93135e13 −1.70511
\(797\) −1.09660e12 −0.0962692 −0.0481346 0.998841i \(-0.515328\pi\)
−0.0481346 + 0.998841i \(0.515328\pi\)
\(798\) −1.43569e13 −1.25328
\(799\) −6.15547e12 −0.534319
\(800\) −7.99416e12 −0.690030
\(801\) −1.26708e13 −1.08757
\(802\) 2.30817e13 1.97008
\(803\) 1.83800e13 1.56000
\(804\) 2.54401e13 2.14717
\(805\) −1.31720e13 −1.10553
\(806\) −5.12197e13 −4.27493
\(807\) −1.03497e13 −0.859009
\(808\) 1.61777e13 1.33526
\(809\) 6.68419e12 0.548631 0.274316 0.961640i \(-0.411549\pi\)
0.274316 + 0.961640i \(0.411549\pi\)
\(810\) 2.31279e12 0.188779
\(811\) −2.62878e12 −0.213384 −0.106692 0.994292i \(-0.534026\pi\)
−0.106692 + 0.994292i \(0.534026\pi\)
\(812\) 2.00253e13 1.61650
\(813\) 2.11836e13 1.70056
\(814\) 1.71283e13 1.36743
\(815\) −4.84706e12 −0.384830
\(816\) 1.36765e12 0.107986
\(817\) 3.61128e11 0.0283571
\(818\) 7.78310e12 0.607803
\(819\) 3.55604e13 2.76178
\(820\) −2.87431e12 −0.222009
\(821\) 3.71457e12 0.285341 0.142671 0.989770i \(-0.454431\pi\)
0.142671 + 0.989770i \(0.454431\pi\)
\(822\) −1.62878e13 −1.24434
\(823\) −8.98302e12 −0.682532 −0.341266 0.939967i \(-0.610856\pi\)
−0.341266 + 0.939967i \(0.610856\pi\)
\(824\) −5.79604e11 −0.0437985
\(825\) −1.35704e13 −1.01989
\(826\) 2.32519e13 1.73800
\(827\) 1.43496e13 1.06676 0.533379 0.845876i \(-0.320922\pi\)
0.533379 + 0.845876i \(0.320922\pi\)
\(828\) 5.31708e13 3.93131
\(829\) −2.23056e13 −1.64028 −0.820141 0.572162i \(-0.806105\pi\)
−0.820141 + 0.572162i \(0.806105\pi\)
\(830\) −1.01105e13 −0.739470
\(831\) 3.13276e12 0.227888
\(832\) 3.61785e13 2.61756
\(833\) 2.57426e12 0.185247
\(834\) 5.86754e13 4.19961
\(835\) −3.77422e12 −0.268682
\(836\) −9.71247e12 −0.687704
\(837\) 1.97149e13 1.38845
\(838\) −3.13194e13 −2.19389
\(839\) −1.73183e13 −1.20664 −0.603320 0.797500i \(-0.706156\pi\)
−0.603320 + 0.797500i \(0.706156\pi\)
\(840\) −1.42378e13 −0.986703
\(841\) −2.43126e12 −0.167590
\(842\) 2.58258e13 1.77072
\(843\) 1.09473e13 0.746592
\(844\) −1.42030e13 −0.963471
\(845\) 1.40416e13 0.947463
\(846\) 2.82615e13 1.89683
\(847\) −5.80389e10 −0.00387475
\(848\) 1.86504e12 0.123853
\(849\) −4.43826e13 −2.93176
\(850\) 1.07859e13 0.708712
\(851\) 2.13158e13 1.39322
\(852\) −3.10668e13 −2.01985
\(853\) −7.93401e12 −0.513124 −0.256562 0.966528i \(-0.582590\pi\)
−0.256562 + 0.966528i \(0.582590\pi\)
\(854\) −4.74795e13 −3.05454
\(855\) 6.24131e12 0.399418
\(856\) 2.85119e13 1.81507
\(857\) 1.08137e13 0.684795 0.342397 0.939555i \(-0.388761\pi\)
0.342397 + 0.939555i \(0.388761\pi\)
\(858\) 6.51268e13 4.10267
\(859\) 8.64575e12 0.541793 0.270896 0.962609i \(-0.412680\pi\)
0.270896 + 0.962609i \(0.412680\pi\)
\(860\) 9.83056e11 0.0612823
\(861\) −6.79555e12 −0.421415
\(862\) 6.25062e11 0.0385603
\(863\) 2.44385e13 1.49978 0.749888 0.661565i \(-0.230107\pi\)
0.749888 + 0.661565i \(0.230107\pi\)
\(864\) −1.47671e13 −0.901537
\(865\) −1.10363e12 −0.0670275
\(866\) −4.64248e13 −2.80491
\(867\) 1.38634e13 0.833267
\(868\) 4.91604e13 2.93952
\(869\) 2.62850e13 1.56358
\(870\) −2.35677e13 −1.39470
\(871\) 2.34299e13 1.37940
\(872\) 9.14691e12 0.535736
\(873\) −1.21779e13 −0.709590
\(874\) −1.97706e13 −1.14609
\(875\) 1.92090e13 1.10782
\(876\) 6.78670e13 3.89395
\(877\) 2.14237e13 1.22292 0.611458 0.791277i \(-0.290583\pi\)
0.611458 + 0.791277i \(0.290583\pi\)
\(878\) −1.94629e13 −1.10530
\(879\) −1.39895e13 −0.790409
\(880\) 1.05234e12 0.0591538
\(881\) −8.21905e12 −0.459653 −0.229826 0.973232i \(-0.573816\pi\)
−0.229826 + 0.973232i \(0.573816\pi\)
\(882\) −1.18192e13 −0.657624
\(883\) 3.88822e12 0.215242 0.107621 0.994192i \(-0.465677\pi\)
0.107621 + 0.994192i \(0.465677\pi\)
\(884\) −3.16459e13 −1.74294
\(885\) −1.67300e13 −0.916750
\(886\) 1.40425e12 0.0765586
\(887\) −5.49999e12 −0.298336 −0.149168 0.988812i \(-0.547660\pi\)
−0.149168 + 0.988812i \(0.547660\pi\)
\(888\) 2.30406e13 1.24347
\(889\) −1.40646e13 −0.755213
\(890\) 1.28253e13 0.685194
\(891\) 3.69910e12 0.196629
\(892\) 2.40974e13 1.27447
\(893\) −6.42450e12 −0.338071
\(894\) −3.70148e13 −1.93801
\(895\) 8.53402e12 0.444580
\(896\) −3.33897e13 −1.73072
\(897\) 8.10490e13 4.18005
\(898\) −4.15134e13 −2.13032
\(899\) 2.96453e13 1.51369
\(900\) −3.02751e13 −1.53814
\(901\) −1.71575e13 −0.867347
\(902\) −7.51962e12 −0.378239
\(903\) 2.32418e12 0.116325
\(904\) −2.85898e13 −1.42382
\(905\) 1.36898e13 0.678388
\(906\) −8.54246e13 −4.21217
\(907\) 1.38465e13 0.679370 0.339685 0.940539i \(-0.389680\pi\)
0.339685 + 0.940539i \(0.389680\pi\)
\(908\) 1.20152e13 0.586604
\(909\) −4.56412e13 −2.21727
\(910\) −3.59940e13 −1.73998
\(911\) 3.12545e13 1.50342 0.751710 0.659494i \(-0.229229\pi\)
0.751710 + 0.659494i \(0.229229\pi\)
\(912\) 1.42742e12 0.0683243
\(913\) −1.61708e13 −0.770218
\(914\) 3.97200e12 0.188257
\(915\) 3.41620e13 1.61120
\(916\) 6.09437e12 0.286022
\(917\) 3.08255e13 1.43962
\(918\) 1.99240e13 0.925944
\(919\) 1.04138e12 0.0481604 0.0240802 0.999710i \(-0.492334\pi\)
0.0240802 + 0.999710i \(0.492334\pi\)
\(920\) −1.96066e13 −0.902314
\(921\) −6.31903e13 −2.89389
\(922\) 2.92947e13 1.33506
\(923\) −2.86120e13 −1.29760
\(924\) −6.25083e13 −2.82107
\(925\) −1.21371e13 −0.545101
\(926\) 5.36792e13 2.39915
\(927\) 1.63520e12 0.0727299
\(928\) −2.22053e13 −0.982858
\(929\) 7.79811e11 0.0343494 0.0171747 0.999853i \(-0.494533\pi\)
0.0171747 + 0.999853i \(0.494533\pi\)
\(930\) −5.78567e13 −2.53618
\(931\) 2.68677e12 0.117208
\(932\) −4.26288e13 −1.85068
\(933\) −2.72965e13 −1.17934
\(934\) −2.42887e13 −1.04434
\(935\) −9.68102e12 −0.414256
\(936\) 5.29318e13 2.25411
\(937\) −1.40171e12 −0.0594060 −0.0297030 0.999559i \(-0.509456\pi\)
−0.0297030 + 0.999559i \(0.509456\pi\)
\(938\) −3.67834e13 −1.55145
\(939\) 7.53459e12 0.316275
\(940\) −1.74886e13 −0.730602
\(941\) −2.41785e13 −1.00525 −0.502627 0.864504i \(-0.667633\pi\)
−0.502627 + 0.864504i \(0.667633\pi\)
\(942\) −4.79129e13 −1.98254
\(943\) −9.35802e12 −0.385373
\(944\) −2.31180e12 −0.0947494
\(945\) 1.38544e13 0.565124
\(946\) 2.57182e12 0.104407
\(947\) 3.03758e12 0.122730 0.0613652 0.998115i \(-0.480455\pi\)
0.0613652 + 0.998115i \(0.480455\pi\)
\(948\) 9.70560e13 3.90288
\(949\) 6.25045e13 2.50157
\(950\) 1.12573e13 0.448411
\(951\) −2.68859e13 −1.06589
\(952\) 1.80994e13 0.714164
\(953\) −2.51073e13 −0.986011 −0.493006 0.870026i \(-0.664102\pi\)
−0.493006 + 0.870026i \(0.664102\pi\)
\(954\) 7.87749e13 3.07907
\(955\) −2.74109e13 −1.06637
\(956\) 9.63684e10 0.00373142
\(957\) −3.76945e13 −1.45269
\(958\) 5.82991e13 2.23623
\(959\) 1.43977e13 0.549680
\(960\) 4.08666e13 1.55291
\(961\) 4.63369e13 1.75256
\(962\) 5.82479e13 2.19277
\(963\) −8.04390e13 −3.01404
\(964\) −3.14734e13 −1.17381
\(965\) −1.32594e13 −0.492210
\(966\) −1.27241e14 −4.70144
\(967\) −8.20610e11 −0.0301799 −0.0150899 0.999886i \(-0.504803\pi\)
−0.0150899 + 0.999886i \(0.504803\pi\)
\(968\) −8.63913e10 −0.00316250
\(969\) −1.31316e13 −0.478477
\(970\) 1.23264e13 0.447057
\(971\) 3.07977e13 1.11181 0.555907 0.831245i \(-0.312371\pi\)
0.555907 + 0.831245i \(0.312371\pi\)
\(972\) 5.02949e13 1.80728
\(973\) −5.18664e13 −1.85515
\(974\) 7.67369e12 0.273205
\(975\) −4.61488e13 −1.63546
\(976\) 4.72061e12 0.166523
\(977\) 1.54215e13 0.541505 0.270753 0.962649i \(-0.412727\pi\)
0.270753 + 0.962649i \(0.412727\pi\)
\(978\) −4.68225e13 −1.63655
\(979\) 2.05130e13 0.713685
\(980\) 7.31389e12 0.253297
\(981\) −2.58057e13 −0.889620
\(982\) 1.30790e13 0.448822
\(983\) 8.73130e12 0.298255 0.149128 0.988818i \(-0.452353\pi\)
0.149128 + 0.988818i \(0.452353\pi\)
\(984\) −1.01152e13 −0.343952
\(985\) 1.26199e12 0.0427162
\(986\) 2.99598e13 1.00947
\(987\) −4.13473e13 −1.38682
\(988\) −3.30291e13 −1.10278
\(989\) 3.20058e12 0.106376
\(990\) 4.44482e13 1.47061
\(991\) −1.88055e13 −0.619376 −0.309688 0.950838i \(-0.600225\pi\)
−0.309688 + 0.950838i \(0.600225\pi\)
\(992\) −5.45121e13 −1.78727
\(993\) −3.82390e13 −1.24806
\(994\) 4.49189e13 1.45945
\(995\) −2.00923e13 −0.649870
\(996\) −5.97099e13 −1.92256
\(997\) 2.93778e12 0.0941655 0.0470827 0.998891i \(-0.485008\pi\)
0.0470827 + 0.998891i \(0.485008\pi\)
\(998\) −5.53003e12 −0.176458
\(999\) −2.24201e13 −0.712185
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.1.10 76
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.10.a.b.1.10 76 1.1 even 1 trivial