Properties

Label 197.10.a.b.1.9
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 1.9
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)
 
\(f(q)\) \(=\) \(q-37.7253 q^{2} -206.276 q^{3} +911.195 q^{4} -2075.65 q^{5} +7781.80 q^{6} -5253.06 q^{7} -15059.7 q^{8} +22866.6 q^{9} +O(q^{10})\) \(q-37.7253 q^{2} -206.276 q^{3} +911.195 q^{4} -2075.65 q^{5} +7781.80 q^{6} -5253.06 q^{7} -15059.7 q^{8} +22866.6 q^{9} +78304.4 q^{10} -12772.0 q^{11} -187957. q^{12} +107848. q^{13} +198173. q^{14} +428156. q^{15} +101600. q^{16} -149863. q^{17} -862649. q^{18} +434522. q^{19} -1.89132e6 q^{20} +1.08358e6 q^{21} +481826. q^{22} +1.41689e6 q^{23} +3.10645e6 q^{24} +2.35520e6 q^{25} -4.06861e6 q^{26} -656706. q^{27} -4.78656e6 q^{28} -162161. q^{29} -1.61523e7 q^{30} +6.06824e6 q^{31} +3.87769e6 q^{32} +2.63455e6 q^{33} +5.65364e6 q^{34} +1.09035e7 q^{35} +2.08360e7 q^{36} +1.36648e7 q^{37} -1.63924e7 q^{38} -2.22465e7 q^{39} +3.12587e7 q^{40} +1.98891e6 q^{41} -4.08782e7 q^{42} -1.33138e7 q^{43} -1.16377e7 q^{44} -4.74631e7 q^{45} -5.34524e7 q^{46} -8.33704e6 q^{47} -2.09576e7 q^{48} -1.27590e7 q^{49} -8.88505e7 q^{50} +3.09132e7 q^{51} +9.82709e7 q^{52} +4.16397e7 q^{53} +2.47744e7 q^{54} +2.65101e7 q^{55} +7.91095e7 q^{56} -8.96313e7 q^{57} +6.11755e6 q^{58} -1.51523e8 q^{59} +3.90134e8 q^{60} +1.06168e6 q^{61} -2.28926e8 q^{62} -1.20120e8 q^{63} -1.98306e8 q^{64} -2.23856e8 q^{65} -9.93889e7 q^{66} -3.49032e7 q^{67} -1.36555e8 q^{68} -2.92269e8 q^{69} -4.11338e8 q^{70} -1.45435e8 q^{71} -3.44365e8 q^{72} +9.14830e7 q^{73} -5.15506e8 q^{74} -4.85820e8 q^{75} +3.95934e8 q^{76} +6.70919e7 q^{77} +8.39255e8 q^{78} +1.99332e8 q^{79} -2.10886e8 q^{80} -3.14621e8 q^{81} -7.50323e7 q^{82} +2.80259e7 q^{83} +9.87350e8 q^{84} +3.11064e8 q^{85} +5.02266e8 q^{86} +3.34498e7 q^{87} +1.92342e8 q^{88} -7.74302e8 q^{89} +1.79056e9 q^{90} -5.66534e8 q^{91} +1.29106e9 q^{92} -1.25173e9 q^{93} +3.14517e8 q^{94} -9.01916e8 q^{95} -7.99873e8 q^{96} +4.57437e8 q^{97} +4.81337e8 q^{98} -2.92052e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −37.7253 −1.66724 −0.833618 0.552341i \(-0.813735\pi\)
−0.833618 + 0.552341i \(0.813735\pi\)
\(3\) −206.276 −1.47029 −0.735144 0.677911i \(-0.762885\pi\)
−0.735144 + 0.677911i \(0.762885\pi\)
\(4\) 911.195 1.77968
\(5\) −2075.65 −1.48521 −0.742607 0.669727i \(-0.766411\pi\)
−0.742607 + 0.669727i \(0.766411\pi\)
\(6\) 7781.80 2.45132
\(7\) −5253.06 −0.826934 −0.413467 0.910519i \(-0.635682\pi\)
−0.413467 + 0.910519i \(0.635682\pi\)
\(8\) −15059.7 −1.29991
\(9\) 22866.6 1.16175
\(10\) 78304.4 2.47620
\(11\) −12772.0 −0.263021 −0.131511 0.991315i \(-0.541983\pi\)
−0.131511 + 0.991315i \(0.541983\pi\)
\(12\) −187957. −2.61664
\(13\) 107848. 1.04729 0.523647 0.851935i \(-0.324571\pi\)
0.523647 + 0.851935i \(0.324571\pi\)
\(14\) 198173. 1.37869
\(15\) 428156. 2.18369
\(16\) 101600. 0.387573
\(17\) −149863. −0.435187 −0.217593 0.976040i \(-0.569821\pi\)
−0.217593 + 0.976040i \(0.569821\pi\)
\(18\) −862649. −1.93690
\(19\) 434522. 0.764928 0.382464 0.923970i \(-0.375076\pi\)
0.382464 + 0.923970i \(0.375076\pi\)
\(20\) −1.89132e6 −2.64320
\(21\) 1.08358e6 1.21583
\(22\) 481826. 0.438519
\(23\) 1.41689e6 1.05575 0.527874 0.849323i \(-0.322989\pi\)
0.527874 + 0.849323i \(0.322989\pi\)
\(24\) 3.10645e6 1.91123
\(25\) 2.35520e6 1.20586
\(26\) −4.06861e6 −1.74609
\(27\) −656706. −0.237812
\(28\) −4.78656e6 −1.47168
\(29\) −162161. −0.0425750 −0.0212875 0.999773i \(-0.506777\pi\)
−0.0212875 + 0.999773i \(0.506777\pi\)
\(30\) −1.61523e7 −3.64073
\(31\) 6.06824e6 1.18015 0.590073 0.807350i \(-0.299099\pi\)
0.590073 + 0.807350i \(0.299099\pi\)
\(32\) 3.87769e6 0.653730
\(33\) 2.63455e6 0.386717
\(34\) 5.65364e6 0.725559
\(35\) 1.09035e7 1.22817
\(36\) 2.08360e7 2.06753
\(37\) 1.36648e7 1.19865 0.599327 0.800504i \(-0.295435\pi\)
0.599327 + 0.800504i \(0.295435\pi\)
\(38\) −1.63924e7 −1.27532
\(39\) −2.22465e7 −1.53982
\(40\) 3.12587e7 1.93064
\(41\) 1.98891e6 0.109923 0.0549615 0.998488i \(-0.482496\pi\)
0.0549615 + 0.998488i \(0.482496\pi\)
\(42\) −4.08782e7 −2.02708
\(43\) −1.33138e7 −0.593873 −0.296936 0.954897i \(-0.595965\pi\)
−0.296936 + 0.954897i \(0.595965\pi\)
\(44\) −1.16377e7 −0.468093
\(45\) −4.74631e7 −1.72544
\(46\) −5.34524e7 −1.76018
\(47\) −8.33704e6 −0.249213 −0.124607 0.992206i \(-0.539767\pi\)
−0.124607 + 0.992206i \(0.539767\pi\)
\(48\) −2.09576e7 −0.569843
\(49\) −1.27590e7 −0.316180
\(50\) −8.88505e7 −2.01046
\(51\) 3.09132e7 0.639850
\(52\) 9.82709e7 1.86385
\(53\) 4.16397e7 0.724879 0.362440 0.932007i \(-0.381944\pi\)
0.362440 + 0.932007i \(0.381944\pi\)
\(54\) 2.47744e7 0.396489
\(55\) 2.65101e7 0.390643
\(56\) 7.91095e7 1.07494
\(57\) −8.96313e7 −1.12466
\(58\) 6.11755e6 0.0709825
\(59\) −1.51523e8 −1.62797 −0.813983 0.580888i \(-0.802705\pi\)
−0.813983 + 0.580888i \(0.802705\pi\)
\(60\) 3.90134e8 3.88627
\(61\) 1.06168e6 0.00981770 0.00490885 0.999988i \(-0.498437\pi\)
0.00490885 + 0.999988i \(0.498437\pi\)
\(62\) −2.28926e8 −1.96758
\(63\) −1.20120e8 −0.960687
\(64\) −1.98306e8 −1.47750
\(65\) −2.23856e8 −1.55546
\(66\) −9.93889e7 −0.644748
\(67\) −3.49032e7 −0.211606 −0.105803 0.994387i \(-0.533741\pi\)
−0.105803 + 0.994387i \(0.533741\pi\)
\(68\) −1.36555e8 −0.774492
\(69\) −2.92269e8 −1.55225
\(70\) −4.11338e8 −2.04766
\(71\) −1.45435e8 −0.679216 −0.339608 0.940567i \(-0.610294\pi\)
−0.339608 + 0.940567i \(0.610294\pi\)
\(72\) −3.44365e8 −1.51016
\(73\) 9.14830e7 0.377040 0.188520 0.982069i \(-0.439631\pi\)
0.188520 + 0.982069i \(0.439631\pi\)
\(74\) −5.15506e8 −1.99844
\(75\) −4.85820e8 −1.77296
\(76\) 3.95934e8 1.36132
\(77\) 6.70919e7 0.217501
\(78\) 8.39255e8 2.56725
\(79\) 1.99332e8 0.575778 0.287889 0.957664i \(-0.407047\pi\)
0.287889 + 0.957664i \(0.407047\pi\)
\(80\) −2.10886e8 −0.575629
\(81\) −3.14621e8 −0.812093
\(82\) −7.50323e7 −0.183268
\(83\) 2.80259e7 0.0648199 0.0324100 0.999475i \(-0.489682\pi\)
0.0324100 + 0.999475i \(0.489682\pi\)
\(84\) 9.87350e8 2.16379
\(85\) 3.11064e8 0.646346
\(86\) 5.02266e8 0.990126
\(87\) 3.34498e7 0.0625974
\(88\) 1.92342e8 0.341903
\(89\) −7.74302e8 −1.30814 −0.654072 0.756432i \(-0.726941\pi\)
−0.654072 + 0.756432i \(0.726941\pi\)
\(90\) 1.79056e9 2.87672
\(91\) −5.66534e8 −0.866043
\(92\) 1.29106e9 1.87889
\(93\) −1.25173e9 −1.73515
\(94\) 3.14517e8 0.415498
\(95\) −9.01916e8 −1.13608
\(96\) −7.99873e8 −0.961171
\(97\) 4.57437e8 0.524637 0.262318 0.964981i \(-0.415513\pi\)
0.262318 + 0.964981i \(0.415513\pi\)
\(98\) 4.81337e8 0.527147
\(99\) −2.92052e8 −0.305564
\(100\) 2.14605e9 2.14605
\(101\) 1.11363e9 1.06487 0.532435 0.846471i \(-0.321277\pi\)
0.532435 + 0.846471i \(0.321277\pi\)
\(102\) −1.16621e9 −1.06678
\(103\) 1.98792e9 1.74033 0.870164 0.492762i \(-0.164013\pi\)
0.870164 + 0.492762i \(0.164013\pi\)
\(104\) −1.62417e9 −1.36138
\(105\) −2.24913e9 −1.80577
\(106\) −1.57087e9 −1.20854
\(107\) −7.22563e8 −0.532903 −0.266452 0.963848i \(-0.585851\pi\)
−0.266452 + 0.963848i \(0.585851\pi\)
\(108\) −5.98387e8 −0.423229
\(109\) 2.93596e8 0.199219 0.0996096 0.995027i \(-0.468241\pi\)
0.0996096 + 0.995027i \(0.468241\pi\)
\(110\) −1.00010e9 −0.651294
\(111\) −2.81871e9 −1.76237
\(112\) −5.33710e8 −0.320497
\(113\) 5.00057e6 0.00288514 0.00144257 0.999999i \(-0.499541\pi\)
0.00144257 + 0.999999i \(0.499541\pi\)
\(114\) 3.38136e9 1.87508
\(115\) −2.94096e9 −1.56801
\(116\) −1.47760e8 −0.0757697
\(117\) 2.46613e9 1.21669
\(118\) 5.71626e9 2.71421
\(119\) 7.87241e8 0.359871
\(120\) −6.44791e9 −2.83859
\(121\) −2.19482e9 −0.930820
\(122\) −4.00522e7 −0.0163684
\(123\) −4.10264e8 −0.161618
\(124\) 5.52935e9 2.10028
\(125\) −8.34568e8 −0.305750
\(126\) 4.53155e9 1.60169
\(127\) 3.36285e9 1.14707 0.573535 0.819181i \(-0.305571\pi\)
0.573535 + 0.819181i \(0.305571\pi\)
\(128\) 5.49577e9 1.80960
\(129\) 2.74631e9 0.873164
\(130\) 8.44501e9 2.59331
\(131\) 4.07101e9 1.20776 0.603881 0.797075i \(-0.293620\pi\)
0.603881 + 0.797075i \(0.293620\pi\)
\(132\) 2.40058e9 0.688231
\(133\) −2.28257e9 −0.632545
\(134\) 1.31673e9 0.352797
\(135\) 1.36309e9 0.353202
\(136\) 2.25690e9 0.565702
\(137\) 2.88528e9 0.699754 0.349877 0.936796i \(-0.386223\pi\)
0.349877 + 0.936796i \(0.386223\pi\)
\(138\) 1.10259e10 2.58797
\(139\) −5.51965e9 −1.25414 −0.627068 0.778964i \(-0.715745\pi\)
−0.627068 + 0.778964i \(0.715745\pi\)
\(140\) 9.93522e9 2.18575
\(141\) 1.71973e9 0.366415
\(142\) 5.48659e9 1.13241
\(143\) −1.37744e9 −0.275461
\(144\) 2.32325e9 0.450261
\(145\) 3.36589e8 0.0632329
\(146\) −3.45122e9 −0.628615
\(147\) 2.63187e9 0.464876
\(148\) 1.24513e10 2.13322
\(149\) 5.38947e9 0.895793 0.447897 0.894085i \(-0.352173\pi\)
0.447897 + 0.894085i \(0.352173\pi\)
\(150\) 1.83277e10 2.95595
\(151\) 7.90820e8 0.123789 0.0618944 0.998083i \(-0.480286\pi\)
0.0618944 + 0.998083i \(0.480286\pi\)
\(152\) −6.54378e9 −0.994334
\(153\) −3.42687e9 −0.505576
\(154\) −2.53106e9 −0.362626
\(155\) −1.25956e10 −1.75277
\(156\) −2.02709e10 −2.74039
\(157\) 2.69380e9 0.353848 0.176924 0.984225i \(-0.443385\pi\)
0.176924 + 0.984225i \(0.443385\pi\)
\(158\) −7.51985e9 −0.959958
\(159\) −8.58925e9 −1.06578
\(160\) −8.04873e9 −0.970929
\(161\) −7.44299e9 −0.873034
\(162\) 1.18692e10 1.35395
\(163\) −1.45994e9 −0.161991 −0.0809955 0.996714i \(-0.525810\pi\)
−0.0809955 + 0.996714i \(0.525810\pi\)
\(164\) 1.81229e9 0.195627
\(165\) −5.46840e9 −0.574358
\(166\) −1.05729e9 −0.108070
\(167\) −1.00431e9 −0.0999182 −0.0499591 0.998751i \(-0.515909\pi\)
−0.0499591 + 0.998751i \(0.515909\pi\)
\(168\) −1.63184e10 −1.58047
\(169\) 1.02678e9 0.0968249
\(170\) −1.17350e10 −1.07761
\(171\) 9.93605e9 0.888651
\(172\) −1.21314e10 −1.05690
\(173\) −1.72999e10 −1.46838 −0.734188 0.678946i \(-0.762437\pi\)
−0.734188 + 0.678946i \(0.762437\pi\)
\(174\) −1.26190e9 −0.104365
\(175\) −1.23720e10 −0.997169
\(176\) −1.29763e9 −0.101940
\(177\) 3.12556e10 2.39358
\(178\) 2.92107e10 2.18098
\(179\) 3.55457e9 0.258790 0.129395 0.991593i \(-0.458696\pi\)
0.129395 + 0.991593i \(0.458696\pi\)
\(180\) −4.32482e10 −3.07073
\(181\) −9.12520e9 −0.631959 −0.315980 0.948766i \(-0.602333\pi\)
−0.315980 + 0.948766i \(0.602333\pi\)
\(182\) 2.13726e10 1.44390
\(183\) −2.18999e8 −0.0144348
\(184\) −2.13379e10 −1.37237
\(185\) −2.83633e10 −1.78026
\(186\) 4.72219e10 2.89291
\(187\) 1.91405e9 0.114463
\(188\) −7.59666e9 −0.443519
\(189\) 3.44971e9 0.196655
\(190\) 3.40250e10 1.89412
\(191\) −1.75219e10 −0.952643 −0.476322 0.879271i \(-0.658030\pi\)
−0.476322 + 0.879271i \(0.658030\pi\)
\(192\) 4.09057e10 2.17234
\(193\) 2.96074e10 1.53600 0.768002 0.640447i \(-0.221251\pi\)
0.768002 + 0.640447i \(0.221251\pi\)
\(194\) −1.72569e10 −0.874693
\(195\) 4.61760e10 2.28697
\(196\) −1.16259e10 −0.562698
\(197\) 1.50614e9 0.0712470
\(198\) 1.10177e10 0.509447
\(199\) 3.92021e10 1.77203 0.886014 0.463658i \(-0.153464\pi\)
0.886014 + 0.463658i \(0.153464\pi\)
\(200\) −3.54686e10 −1.56751
\(201\) 7.19967e9 0.311122
\(202\) −4.20121e10 −1.77539
\(203\) 8.51838e8 0.0352067
\(204\) 2.81679e10 1.13873
\(205\) −4.12829e9 −0.163259
\(206\) −7.49947e10 −2.90154
\(207\) 3.23994e10 1.22651
\(208\) 1.09574e10 0.405903
\(209\) −5.54970e9 −0.201192
\(210\) 8.48489e10 3.01064
\(211\) 2.37581e9 0.0825164 0.0412582 0.999149i \(-0.486863\pi\)
0.0412582 + 0.999149i \(0.486863\pi\)
\(212\) 3.79418e10 1.29005
\(213\) 2.99998e10 0.998642
\(214\) 2.72589e10 0.888476
\(215\) 2.76348e10 0.882029
\(216\) 9.88981e9 0.309133
\(217\) −3.18768e10 −0.975902
\(218\) −1.10760e10 −0.332145
\(219\) −1.88707e10 −0.554358
\(220\) 2.41559e10 0.695218
\(221\) −1.61625e10 −0.455769
\(222\) 1.06336e11 2.93828
\(223\) 1.31894e9 0.0357151 0.0178576 0.999841i \(-0.494315\pi\)
0.0178576 + 0.999841i \(0.494315\pi\)
\(224\) −2.03697e10 −0.540592
\(225\) 5.38555e10 1.40091
\(226\) −1.88648e8 −0.00481020
\(227\) −6.43494e10 −1.60853 −0.804263 0.594273i \(-0.797440\pi\)
−0.804263 + 0.594273i \(0.797440\pi\)
\(228\) −8.16715e10 −2.00154
\(229\) 6.63740e10 1.59492 0.797459 0.603373i \(-0.206177\pi\)
0.797459 + 0.603373i \(0.206177\pi\)
\(230\) 1.10949e11 2.61425
\(231\) −1.38394e10 −0.319789
\(232\) 2.44209e9 0.0553434
\(233\) −3.44486e10 −0.765721 −0.382860 0.923806i \(-0.625061\pi\)
−0.382860 + 0.923806i \(0.625061\pi\)
\(234\) −9.30354e10 −2.02851
\(235\) 1.73048e10 0.370135
\(236\) −1.38067e11 −2.89725
\(237\) −4.11173e10 −0.846559
\(238\) −2.96989e10 −0.599990
\(239\) 1.96234e9 0.0389030 0.0194515 0.999811i \(-0.493808\pi\)
0.0194515 + 0.999811i \(0.493808\pi\)
\(240\) 4.35006e10 0.846340
\(241\) −3.35622e10 −0.640876 −0.320438 0.947269i \(-0.603830\pi\)
−0.320438 + 0.947269i \(0.603830\pi\)
\(242\) 8.28003e10 1.55190
\(243\) 7.78247e10 1.43182
\(244\) 9.67398e8 0.0174723
\(245\) 2.64832e10 0.469595
\(246\) 1.54773e10 0.269456
\(247\) 4.68625e10 0.801104
\(248\) −9.13860e10 −1.53408
\(249\) −5.78107e9 −0.0953039
\(250\) 3.14843e10 0.509758
\(251\) 6.31282e10 1.00390 0.501952 0.864896i \(-0.332616\pi\)
0.501952 + 0.864896i \(0.332616\pi\)
\(252\) −1.09452e11 −1.70971
\(253\) −1.80964e10 −0.277684
\(254\) −1.26864e11 −1.91244
\(255\) −6.41650e10 −0.950314
\(256\) −1.05796e11 −1.53954
\(257\) 1.10368e11 1.57814 0.789070 0.614303i \(-0.210563\pi\)
0.789070 + 0.614303i \(0.210563\pi\)
\(258\) −1.03605e11 −1.45577
\(259\) −7.17817e10 −0.991209
\(260\) −2.03976e11 −2.76821
\(261\) −3.70807e9 −0.0494613
\(262\) −1.53580e11 −2.01362
\(263\) 2.94937e10 0.380127 0.190063 0.981772i \(-0.439131\pi\)
0.190063 + 0.981772i \(0.439131\pi\)
\(264\) −3.96755e10 −0.502695
\(265\) −8.64294e10 −1.07660
\(266\) 8.61104e10 1.05460
\(267\) 1.59720e11 1.92335
\(268\) −3.18036e10 −0.376591
\(269\) −1.38102e11 −1.60811 −0.804054 0.594556i \(-0.797328\pi\)
−0.804054 + 0.594556i \(0.797328\pi\)
\(270\) −5.14230e10 −0.588871
\(271\) −3.76108e10 −0.423595 −0.211797 0.977314i \(-0.567932\pi\)
−0.211797 + 0.977314i \(0.567932\pi\)
\(272\) −1.52261e10 −0.168667
\(273\) 1.16862e11 1.27333
\(274\) −1.08848e11 −1.16666
\(275\) −3.00805e10 −0.317167
\(276\) −2.66314e11 −2.76251
\(277\) −4.03699e10 −0.412001 −0.206000 0.978552i \(-0.566045\pi\)
−0.206000 + 0.978552i \(0.566045\pi\)
\(278\) 2.08230e11 2.09094
\(279\) 1.38760e11 1.37103
\(280\) −1.64204e11 −1.59651
\(281\) −1.61017e11 −1.54061 −0.770307 0.637673i \(-0.779897\pi\)
−0.770307 + 0.637673i \(0.779897\pi\)
\(282\) −6.48771e10 −0.610901
\(283\) −2.06961e11 −1.91801 −0.959004 0.283394i \(-0.908540\pi\)
−0.959004 + 0.283394i \(0.908540\pi\)
\(284\) −1.32520e11 −1.20878
\(285\) 1.86043e11 1.67037
\(286\) 5.19641e10 0.459258
\(287\) −1.04479e10 −0.0908991
\(288\) 8.86698e10 0.759468
\(289\) −9.61288e10 −0.810612
\(290\) −1.26979e10 −0.105424
\(291\) −9.43581e10 −0.771367
\(292\) 8.33588e10 0.671010
\(293\) −2.23194e11 −1.76921 −0.884603 0.466345i \(-0.845570\pi\)
−0.884603 + 0.466345i \(0.845570\pi\)
\(294\) −9.92880e10 −0.775058
\(295\) 3.14510e11 2.41788
\(296\) −2.05787e11 −1.55814
\(297\) 8.38743e9 0.0625497
\(298\) −2.03319e11 −1.49350
\(299\) 1.52809e11 1.10568
\(300\) −4.42677e11 −3.15530
\(301\) 6.99381e10 0.491094
\(302\) −2.98339e10 −0.206385
\(303\) −2.29716e11 −1.56566
\(304\) 4.41474e10 0.296465
\(305\) −2.20368e9 −0.0145814
\(306\) 1.29280e11 0.842915
\(307\) 2.70294e11 1.73666 0.868329 0.495989i \(-0.165195\pi\)
0.868329 + 0.495989i \(0.165195\pi\)
\(308\) 6.11338e10 0.387082
\(309\) −4.10059e11 −2.55878
\(310\) 4.75170e11 2.92228
\(311\) −1.91974e10 −0.116365 −0.0581823 0.998306i \(-0.518530\pi\)
−0.0581823 + 0.998306i \(0.518530\pi\)
\(312\) 3.35026e11 2.00162
\(313\) −3.44294e10 −0.202759 −0.101379 0.994848i \(-0.532326\pi\)
−0.101379 + 0.994848i \(0.532326\pi\)
\(314\) −1.01624e11 −0.589948
\(315\) 2.49327e11 1.42683
\(316\) 1.81630e11 1.02470
\(317\) 1.25656e11 0.698901 0.349450 0.936955i \(-0.386368\pi\)
0.349450 + 0.936955i \(0.386368\pi\)
\(318\) 3.24031e11 1.77691
\(319\) 2.07111e9 0.0111981
\(320\) 4.11614e11 2.19440
\(321\) 1.49047e11 0.783521
\(322\) 2.80789e11 1.45555
\(323\) −6.51190e10 −0.332886
\(324\) −2.86681e11 −1.44526
\(325\) 2.54005e11 1.26289
\(326\) 5.50766e10 0.270077
\(327\) −6.05617e10 −0.292909
\(328\) −2.99525e10 −0.142890
\(329\) 4.37949e10 0.206083
\(330\) 2.06297e11 0.957590
\(331\) −3.60390e10 −0.165024 −0.0825119 0.996590i \(-0.526294\pi\)
−0.0825119 + 0.996590i \(0.526294\pi\)
\(332\) 2.55371e10 0.115359
\(333\) 3.12467e11 1.39253
\(334\) 3.78879e10 0.166587
\(335\) 7.24468e10 0.314281
\(336\) 1.10091e11 0.471223
\(337\) −3.32706e11 −1.40516 −0.702580 0.711604i \(-0.747969\pi\)
−0.702580 + 0.711604i \(0.747969\pi\)
\(338\) −3.87355e10 −0.161430
\(339\) −1.03150e9 −0.00424198
\(340\) 2.83440e11 1.15029
\(341\) −7.75034e10 −0.310403
\(342\) −3.74840e11 −1.48159
\(343\) 2.79004e11 1.08839
\(344\) 2.00502e11 0.771979
\(345\) 6.06649e11 2.30543
\(346\) 6.52645e11 2.44813
\(347\) 2.61204e11 0.967157 0.483578 0.875301i \(-0.339337\pi\)
0.483578 + 0.875301i \(0.339337\pi\)
\(348\) 3.04792e10 0.111403
\(349\) −1.42093e11 −0.512695 −0.256347 0.966585i \(-0.582519\pi\)
−0.256347 + 0.966585i \(0.582519\pi\)
\(350\) 4.66737e11 1.66252
\(351\) −7.08247e10 −0.249059
\(352\) −4.95258e10 −0.171945
\(353\) −4.00093e11 −1.37143 −0.685716 0.727869i \(-0.740511\pi\)
−0.685716 + 0.727869i \(0.740511\pi\)
\(354\) −1.17912e12 −3.99066
\(355\) 3.01873e11 1.00878
\(356\) −7.05540e11 −2.32807
\(357\) −1.62389e11 −0.529113
\(358\) −1.34097e11 −0.431465
\(359\) 4.36609e10 0.138729 0.0693645 0.997591i \(-0.477903\pi\)
0.0693645 + 0.997591i \(0.477903\pi\)
\(360\) 7.14781e11 2.24291
\(361\) −1.33878e11 −0.414885
\(362\) 3.44251e11 1.05363
\(363\) 4.52739e11 1.36857
\(364\) −5.16222e11 −1.54128
\(365\) −1.89887e11 −0.559986
\(366\) 8.26179e9 0.0240663
\(367\) 2.27984e11 0.656006 0.328003 0.944677i \(-0.393624\pi\)
0.328003 + 0.944677i \(0.393624\pi\)
\(368\) 1.43956e11 0.409179
\(369\) 4.54798e10 0.127703
\(370\) 1.07001e12 2.96811
\(371\) −2.18735e11 −0.599427
\(372\) −1.14057e12 −3.08801
\(373\) 2.72543e11 0.729030 0.364515 0.931198i \(-0.381235\pi\)
0.364515 + 0.931198i \(0.381235\pi\)
\(374\) −7.22081e10 −0.190837
\(375\) 1.72151e11 0.449541
\(376\) 1.25553e11 0.323954
\(377\) −1.74888e10 −0.0445885
\(378\) −1.30141e11 −0.327870
\(379\) −1.97263e11 −0.491099 −0.245549 0.969384i \(-0.578968\pi\)
−0.245549 + 0.969384i \(0.578968\pi\)
\(380\) −8.21821e11 −2.02186
\(381\) −6.93673e11 −1.68652
\(382\) 6.61017e11 1.58828
\(383\) 3.57275e11 0.848415 0.424208 0.905565i \(-0.360553\pi\)
0.424208 + 0.905565i \(0.360553\pi\)
\(384\) −1.13364e12 −2.66064
\(385\) −1.39259e11 −0.323036
\(386\) −1.11695e12 −2.56088
\(387\) −3.04441e11 −0.689929
\(388\) 4.16814e11 0.933684
\(389\) 7.13622e11 1.58014 0.790069 0.613018i \(-0.210045\pi\)
0.790069 + 0.613018i \(0.210045\pi\)
\(390\) −1.74200e12 −3.81292
\(391\) −2.12340e11 −0.459447
\(392\) 1.92147e11 0.411004
\(393\) −8.39750e11 −1.77576
\(394\) −5.68195e10 −0.118786
\(395\) −4.13743e11 −0.855154
\(396\) −2.66116e11 −0.543805
\(397\) 5.92892e11 1.19789 0.598947 0.800789i \(-0.295586\pi\)
0.598947 + 0.800789i \(0.295586\pi\)
\(398\) −1.47891e12 −2.95439
\(399\) 4.70838e11 0.930023
\(400\) 2.39288e11 0.467360
\(401\) 1.93675e11 0.374045 0.187023 0.982356i \(-0.440116\pi\)
0.187023 + 0.982356i \(0.440116\pi\)
\(402\) −2.71610e11 −0.518714
\(403\) 6.54450e11 1.23596
\(404\) 1.01474e12 1.89512
\(405\) 6.53044e11 1.20613
\(406\) −3.21358e10 −0.0586979
\(407\) −1.74526e11 −0.315272
\(408\) −4.65544e11 −0.831744
\(409\) 7.57275e11 1.33813 0.669065 0.743204i \(-0.266695\pi\)
0.669065 + 0.743204i \(0.266695\pi\)
\(410\) 1.55741e11 0.272192
\(411\) −5.95163e11 −1.02884
\(412\) 1.81138e12 3.09722
\(413\) 7.95961e11 1.34622
\(414\) −1.22228e12 −2.04488
\(415\) −5.81720e10 −0.0962715
\(416\) 4.18203e11 0.684648
\(417\) 1.13857e12 1.84394
\(418\) 2.09364e11 0.335435
\(419\) 6.09257e11 0.965689 0.482844 0.875706i \(-0.339604\pi\)
0.482844 + 0.875706i \(0.339604\pi\)
\(420\) −2.04939e12 −3.21369
\(421\) 1.21601e12 1.88655 0.943273 0.332019i \(-0.107730\pi\)
0.943273 + 0.332019i \(0.107730\pi\)
\(422\) −8.96279e10 −0.137574
\(423\) −1.90640e11 −0.289522
\(424\) −6.27081e11 −0.942275
\(425\) −3.52959e11 −0.524775
\(426\) −1.13175e12 −1.66497
\(427\) −5.57707e9 −0.00811859
\(428\) −6.58395e11 −0.948396
\(429\) 2.84132e11 0.405006
\(430\) −1.04253e12 −1.47055
\(431\) −1.35749e12 −1.89492 −0.947458 0.319880i \(-0.896357\pi\)
−0.947458 + 0.319880i \(0.896357\pi\)
\(432\) −6.67213e10 −0.0921695
\(433\) −1.07630e12 −1.47142 −0.735712 0.677295i \(-0.763152\pi\)
−0.735712 + 0.677295i \(0.763152\pi\)
\(434\) 1.20256e12 1.62706
\(435\) −6.94300e10 −0.0929706
\(436\) 2.67523e11 0.354546
\(437\) 6.15669e11 0.807571
\(438\) 7.11903e11 0.924245
\(439\) 1.41075e12 1.81283 0.906417 0.422383i \(-0.138806\pi\)
0.906417 + 0.422383i \(0.138806\pi\)
\(440\) −3.99235e11 −0.507799
\(441\) −2.91756e11 −0.367321
\(442\) 6.09736e11 0.759874
\(443\) −1.32083e12 −1.62941 −0.814706 0.579874i \(-0.803102\pi\)
−0.814706 + 0.579874i \(0.803102\pi\)
\(444\) −2.56839e12 −3.13644
\(445\) 1.60718e12 1.94287
\(446\) −4.97572e10 −0.0595456
\(447\) −1.11172e12 −1.31707
\(448\) 1.04171e12 1.22179
\(449\) −5.52487e11 −0.641524 −0.320762 0.947160i \(-0.603939\pi\)
−0.320762 + 0.947160i \(0.603939\pi\)
\(450\) −2.03171e12 −2.33564
\(451\) −2.54023e10 −0.0289121
\(452\) 4.55649e9 0.00513461
\(453\) −1.63127e11 −0.182005
\(454\) 2.42760e12 2.68179
\(455\) 1.17593e12 1.28626
\(456\) 1.34982e12 1.46196
\(457\) 5.84967e11 0.627348 0.313674 0.949531i \(-0.398440\pi\)
0.313674 + 0.949531i \(0.398440\pi\)
\(458\) −2.50398e12 −2.65911
\(459\) 9.84163e10 0.103493
\(460\) −2.67979e12 −2.79055
\(461\) 5.24862e11 0.541242 0.270621 0.962686i \(-0.412771\pi\)
0.270621 + 0.962686i \(0.412771\pi\)
\(462\) 5.22096e11 0.533164
\(463\) 5.08969e11 0.514727 0.257363 0.966315i \(-0.417146\pi\)
0.257363 + 0.966315i \(0.417146\pi\)
\(464\) −1.64755e10 −0.0165009
\(465\) 2.59816e12 2.57707
\(466\) 1.29958e12 1.27664
\(467\) 9.74520e10 0.0948123 0.0474062 0.998876i \(-0.484904\pi\)
0.0474062 + 0.998876i \(0.484904\pi\)
\(468\) 2.24712e12 2.16531
\(469\) 1.83348e11 0.174984
\(470\) −6.52827e11 −0.617103
\(471\) −5.55665e11 −0.520259
\(472\) 2.28190e12 2.11620
\(473\) 1.70043e11 0.156201
\(474\) 1.55116e12 1.41141
\(475\) 1.02339e12 0.922398
\(476\) 7.17330e11 0.640454
\(477\) 9.52159e11 0.842125
\(478\) −7.40297e10 −0.0648605
\(479\) −9.32524e11 −0.809376 −0.404688 0.914455i \(-0.632620\pi\)
−0.404688 + 0.914455i \(0.632620\pi\)
\(480\) 1.66026e12 1.42755
\(481\) 1.47372e12 1.25534
\(482\) 1.26614e12 1.06849
\(483\) 1.53531e12 1.28361
\(484\) −1.99991e12 −1.65656
\(485\) −9.49480e11 −0.779198
\(486\) −2.93596e12 −2.38719
\(487\) −2.38809e12 −1.92384 −0.961922 0.273323i \(-0.911877\pi\)
−0.961922 + 0.273323i \(0.911877\pi\)
\(488\) −1.59886e10 −0.0127621
\(489\) 3.01150e11 0.238173
\(490\) −9.99087e11 −0.782926
\(491\) −4.08754e11 −0.317392 −0.158696 0.987328i \(-0.550729\pi\)
−0.158696 + 0.987328i \(0.550729\pi\)
\(492\) −3.73831e11 −0.287629
\(493\) 2.43019e10 0.0185281
\(494\) −1.76790e12 −1.33563
\(495\) 6.06198e11 0.453828
\(496\) 6.16533e11 0.457392
\(497\) 7.63981e11 0.561667
\(498\) 2.18092e11 0.158894
\(499\) −1.26604e12 −0.914103 −0.457052 0.889440i \(-0.651095\pi\)
−0.457052 + 0.889440i \(0.651095\pi\)
\(500\) −7.60454e11 −0.544136
\(501\) 2.07165e11 0.146908
\(502\) −2.38153e12 −1.67374
\(503\) 1.10610e12 0.770440 0.385220 0.922825i \(-0.374126\pi\)
0.385220 + 0.922825i \(0.374126\pi\)
\(504\) 1.80897e12 1.24880
\(505\) −2.31151e12 −1.58156
\(506\) 6.82693e11 0.462965
\(507\) −2.11800e11 −0.142360
\(508\) 3.06421e12 2.04142
\(509\) −4.72966e11 −0.312320 −0.156160 0.987732i \(-0.549912\pi\)
−0.156160 + 0.987732i \(0.549912\pi\)
\(510\) 2.42064e12 1.58440
\(511\) −4.80566e11 −0.311787
\(512\) 1.17737e12 0.757176
\(513\) −2.85353e11 −0.181909
\(514\) −4.16368e12 −2.63113
\(515\) −4.12622e12 −2.58476
\(516\) 2.50242e12 1.55395
\(517\) 1.06480e11 0.0655484
\(518\) 2.70798e12 1.65258
\(519\) 3.56856e12 2.15894
\(520\) 3.37120e12 2.02195
\(521\) −2.21607e12 −1.31769 −0.658845 0.752278i \(-0.728955\pi\)
−0.658845 + 0.752278i \(0.728955\pi\)
\(522\) 1.39888e11 0.0824636
\(523\) −2.30683e12 −1.34821 −0.674107 0.738634i \(-0.735471\pi\)
−0.674107 + 0.738634i \(0.735471\pi\)
\(524\) 3.70948e12 2.14942
\(525\) 2.55204e12 1.46612
\(526\) −1.11266e12 −0.633761
\(527\) −9.09408e11 −0.513584
\(528\) 2.67670e11 0.149881
\(529\) 2.06417e11 0.114603
\(530\) 3.26057e12 1.79495
\(531\) −3.46483e12 −1.89128
\(532\) −2.07986e12 −1.12573
\(533\) 2.14501e11 0.115122
\(534\) −6.02546e12 −3.20667
\(535\) 1.49979e12 0.791476
\(536\) 5.25632e11 0.275068
\(537\) −7.33220e11 −0.380496
\(538\) 5.20994e12 2.68110
\(539\) 1.62958e11 0.0831621
\(540\) 1.24204e12 0.628586
\(541\) −9.20712e11 −0.462100 −0.231050 0.972942i \(-0.574216\pi\)
−0.231050 + 0.972942i \(0.574216\pi\)
\(542\) 1.41888e12 0.706233
\(543\) 1.88231e12 0.929161
\(544\) −5.81125e11 −0.284495
\(545\) −6.09403e11 −0.295883
\(546\) −4.40865e12 −2.12295
\(547\) −1.99861e11 −0.0954519 −0.0477259 0.998860i \(-0.515197\pi\)
−0.0477259 + 0.998860i \(0.515197\pi\)
\(548\) 2.62905e12 1.24534
\(549\) 2.42771e10 0.0114057
\(550\) 1.13480e12 0.528793
\(551\) −7.04623e10 −0.0325668
\(552\) 4.40149e12 2.01778
\(553\) −1.04710e12 −0.476130
\(554\) 1.52296e12 0.686903
\(555\) 5.85065e12 2.61749
\(556\) −5.02947e12 −2.23196
\(557\) −1.16526e12 −0.512947 −0.256474 0.966551i \(-0.582561\pi\)
−0.256474 + 0.966551i \(0.582561\pi\)
\(558\) −5.23477e12 −2.28583
\(559\) −1.43587e12 −0.621960
\(560\) 1.10780e12 0.476007
\(561\) −3.94822e11 −0.168294
\(562\) 6.07442e12 2.56857
\(563\) 3.38943e12 1.42180 0.710900 0.703293i \(-0.248288\pi\)
0.710900 + 0.703293i \(0.248288\pi\)
\(564\) 1.56701e12 0.652101
\(565\) −1.03794e10 −0.00428505
\(566\) 7.80767e12 3.19777
\(567\) 1.65272e12 0.671547
\(568\) 2.19022e12 0.882916
\(569\) 5.58181e11 0.223239 0.111619 0.993751i \(-0.464396\pi\)
0.111619 + 0.993751i \(0.464396\pi\)
\(570\) −7.01853e12 −2.78490
\(571\) 3.83146e11 0.150835 0.0754174 0.997152i \(-0.475971\pi\)
0.0754174 + 0.997152i \(0.475971\pi\)
\(572\) −1.25511e12 −0.490231
\(573\) 3.61434e12 1.40066
\(574\) 3.94149e11 0.151550
\(575\) 3.33705e12 1.27309
\(576\) −4.53459e12 −1.71647
\(577\) −4.27490e12 −1.60559 −0.802795 0.596255i \(-0.796655\pi\)
−0.802795 + 0.596255i \(0.796655\pi\)
\(578\) 3.62648e12 1.35148
\(579\) −6.10729e12 −2.25837
\(580\) 3.06698e11 0.112534
\(581\) −1.47222e11 −0.0536018
\(582\) 3.55968e12 1.28605
\(583\) −5.31820e11 −0.190659
\(584\) −1.37771e12 −0.490117
\(585\) −5.11882e12 −1.80704
\(586\) 8.42005e12 2.94968
\(587\) 6.39907e11 0.222457 0.111228 0.993795i \(-0.464521\pi\)
0.111228 + 0.993795i \(0.464521\pi\)
\(588\) 2.39815e12 0.827328
\(589\) 2.63678e12 0.902726
\(590\) −1.18650e13 −4.03118
\(591\) −3.10680e11 −0.104754
\(592\) 1.38834e12 0.464566
\(593\) 3.15740e12 1.04854 0.524269 0.851553i \(-0.324339\pi\)
0.524269 + 0.851553i \(0.324339\pi\)
\(594\) −3.16418e11 −0.104285
\(595\) −1.63404e12 −0.534485
\(596\) 4.91086e12 1.59422
\(597\) −8.08644e12 −2.60539
\(598\) −5.76476e12 −1.84343
\(599\) −3.82726e12 −1.21470 −0.607348 0.794436i \(-0.707767\pi\)
−0.607348 + 0.794436i \(0.707767\pi\)
\(600\) 7.31632e12 2.30469
\(601\) −3.13182e12 −0.979178 −0.489589 0.871953i \(-0.662853\pi\)
−0.489589 + 0.871953i \(0.662853\pi\)
\(602\) −2.63843e12 −0.818769
\(603\) −7.98118e11 −0.245832
\(604\) 7.20591e11 0.220304
\(605\) 4.55569e12 1.38247
\(606\) 8.66608e12 2.61033
\(607\) 2.48901e12 0.744178 0.372089 0.928197i \(-0.378642\pi\)
0.372089 + 0.928197i \(0.378642\pi\)
\(608\) 1.68494e12 0.500056
\(609\) −1.75714e11 −0.0517639
\(610\) 8.31344e10 0.0243106
\(611\) −8.99136e11 −0.261000
\(612\) −3.12255e12 −0.899762
\(613\) 5.51889e12 1.57863 0.789313 0.613991i \(-0.210437\pi\)
0.789313 + 0.613991i \(0.210437\pi\)
\(614\) −1.01969e13 −2.89542
\(615\) 8.51566e11 0.240038
\(616\) −1.01038e12 −0.282731
\(617\) 2.13114e12 0.592010 0.296005 0.955186i \(-0.404345\pi\)
0.296005 + 0.955186i \(0.404345\pi\)
\(618\) 1.54696e13 4.26610
\(619\) 2.15468e12 0.589896 0.294948 0.955513i \(-0.404698\pi\)
0.294948 + 0.955513i \(0.404698\pi\)
\(620\) −1.14770e13 −3.11936
\(621\) −9.30479e11 −0.251070
\(622\) 7.24227e11 0.194007
\(623\) 4.06745e12 1.08175
\(624\) −2.26024e12 −0.596794
\(625\) −2.86773e12 −0.751758
\(626\) 1.29886e12 0.338047
\(627\) 1.14477e12 0.295810
\(628\) 2.45458e12 0.629735
\(629\) −2.04785e12 −0.521639
\(630\) −9.40591e12 −2.37886
\(631\) −5.88766e12 −1.47846 −0.739231 0.673452i \(-0.764811\pi\)
−0.739231 + 0.673452i \(0.764811\pi\)
\(632\) −3.00188e12 −0.748457
\(633\) −4.90071e11 −0.121323
\(634\) −4.74039e12 −1.16523
\(635\) −6.98009e12 −1.70365
\(636\) −7.82647e12 −1.89675
\(637\) −1.37604e12 −0.331134
\(638\) −7.81331e10 −0.0186699
\(639\) −3.32562e12 −0.789076
\(640\) −1.14073e13 −2.68765
\(641\) −4.94911e12 −1.15789 −0.578944 0.815367i \(-0.696535\pi\)
−0.578944 + 0.815367i \(0.696535\pi\)
\(642\) −5.62284e12 −1.30632
\(643\) 1.63185e12 0.376471 0.188235 0.982124i \(-0.439723\pi\)
0.188235 + 0.982124i \(0.439723\pi\)
\(644\) −6.78201e12 −1.55372
\(645\) −5.70038e12 −1.29684
\(646\) 2.45663e12 0.555000
\(647\) 1.18883e12 0.266718 0.133359 0.991068i \(-0.457424\pi\)
0.133359 + 0.991068i \(0.457424\pi\)
\(648\) 4.73811e12 1.05564
\(649\) 1.93525e12 0.428190
\(650\) −9.58239e12 −2.10554
\(651\) 6.57541e12 1.43486
\(652\) −1.33029e12 −0.288292
\(653\) 2.46630e12 0.530807 0.265404 0.964137i \(-0.414495\pi\)
0.265404 + 0.964137i \(0.414495\pi\)
\(654\) 2.28471e12 0.488349
\(655\) −8.44999e12 −1.79378
\(656\) 2.02073e11 0.0426032
\(657\) 2.09191e12 0.438025
\(658\) −1.65217e12 −0.343589
\(659\) −8.71065e12 −1.79914 −0.899572 0.436772i \(-0.856122\pi\)
−0.899572 + 0.436772i \(0.856122\pi\)
\(660\) −4.98277e12 −1.02217
\(661\) 8.35219e10 0.0170174 0.00850871 0.999964i \(-0.497292\pi\)
0.00850871 + 0.999964i \(0.497292\pi\)
\(662\) 1.35958e12 0.275134
\(663\) 3.33394e12 0.670111
\(664\) −4.22062e11 −0.0842598
\(665\) 4.73781e12 0.939465
\(666\) −1.17879e13 −2.32168
\(667\) −2.29763e11 −0.0449484
\(668\) −9.15124e11 −0.177822
\(669\) −2.72065e11 −0.0525115
\(670\) −2.73307e12 −0.523980
\(671\) −1.35598e10 −0.00258226
\(672\) 4.20178e12 0.794825
\(673\) −3.26734e12 −0.613941 −0.306970 0.951719i \(-0.599315\pi\)
−0.306970 + 0.951719i \(0.599315\pi\)
\(674\) 1.25514e13 2.34273
\(675\) −1.54667e12 −0.286769
\(676\) 9.35596e11 0.172317
\(677\) 6.31103e12 1.15465 0.577327 0.816513i \(-0.304096\pi\)
0.577327 + 0.816513i \(0.304096\pi\)
\(678\) 3.89134e10 0.00707238
\(679\) −2.40294e12 −0.433840
\(680\) −4.68454e12 −0.840188
\(681\) 1.32737e13 2.36500
\(682\) 2.92384e12 0.517516
\(683\) 4.01246e12 0.705533 0.352766 0.935711i \(-0.385241\pi\)
0.352766 + 0.935711i \(0.385241\pi\)
\(684\) 9.05368e12 1.58151
\(685\) −5.98883e12 −1.03929
\(686\) −1.05255e13 −1.81461
\(687\) −1.36913e13 −2.34499
\(688\) −1.35268e12 −0.230169
\(689\) 4.49077e12 0.759162
\(690\) −2.28860e13 −3.84369
\(691\) 8.60086e12 1.43513 0.717564 0.696492i \(-0.245257\pi\)
0.717564 + 0.696492i \(0.245257\pi\)
\(692\) −1.57636e13 −2.61324
\(693\) 1.53417e12 0.252681
\(694\) −9.85398e12 −1.61248
\(695\) 1.14569e13 1.86266
\(696\) −5.03744e11 −0.0813707
\(697\) −2.98066e11 −0.0478370
\(698\) 5.36050e12 0.854783
\(699\) 7.10592e12 1.12583
\(700\) −1.12733e13 −1.77464
\(701\) −8.66222e12 −1.35487 −0.677436 0.735582i \(-0.736909\pi\)
−0.677436 + 0.735582i \(0.736909\pi\)
\(702\) 2.67188e12 0.415241
\(703\) 5.93764e12 0.916885
\(704\) 2.53276e12 0.388613
\(705\) −3.56955e12 −0.544205
\(706\) 1.50936e13 2.28650
\(707\) −5.84998e12 −0.880577
\(708\) 2.84799e13 4.25980
\(709\) −3.10340e12 −0.461244 −0.230622 0.973043i \(-0.574076\pi\)
−0.230622 + 0.973043i \(0.574076\pi\)
\(710\) −1.13882e13 −1.68188
\(711\) 4.55805e12 0.668907
\(712\) 1.16608e13 1.70046
\(713\) 8.59802e12 1.24594
\(714\) 6.12615e12 0.882157
\(715\) 2.85908e12 0.409118
\(716\) 3.23890e12 0.460563
\(717\) −4.04782e11 −0.0571986
\(718\) −1.64712e12 −0.231294
\(719\) 7.46663e12 1.04194 0.520972 0.853574i \(-0.325570\pi\)
0.520972 + 0.853574i \(0.325570\pi\)
\(720\) −4.82225e12 −0.668734
\(721\) −1.04426e13 −1.43914
\(722\) 5.05060e12 0.691712
\(723\) 6.92307e12 0.942272
\(724\) −8.31484e12 −1.12468
\(725\) −3.81921e11 −0.0513395
\(726\) −1.70797e13 −2.28173
\(727\) −2.77617e12 −0.368587 −0.184294 0.982871i \(-0.559000\pi\)
−0.184294 + 0.982871i \(0.559000\pi\)
\(728\) 8.53184e12 1.12577
\(729\) −9.86064e12 −1.29310
\(730\) 7.16353e12 0.933629
\(731\) 1.99525e12 0.258446
\(732\) −1.99551e11 −0.0256894
\(733\) −7.50272e12 −0.959955 −0.479977 0.877281i \(-0.659355\pi\)
−0.479977 + 0.877281i \(0.659355\pi\)
\(734\) −8.60077e12 −1.09372
\(735\) −5.46285e12 −0.690440
\(736\) 5.49425e12 0.690174
\(737\) 4.45782e11 0.0556569
\(738\) −1.71574e12 −0.212910
\(739\) 1.01345e13 1.24997 0.624986 0.780636i \(-0.285105\pi\)
0.624986 + 0.780636i \(0.285105\pi\)
\(740\) −2.58445e13 −3.16829
\(741\) −9.66659e12 −1.17785
\(742\) 8.25185e12 0.999387
\(743\) 8.50223e11 0.102349 0.0511745 0.998690i \(-0.483704\pi\)
0.0511745 + 0.998690i \(0.483704\pi\)
\(744\) 1.88507e13 2.25553
\(745\) −1.11867e13 −1.33045
\(746\) −1.02818e13 −1.21546
\(747\) 6.40859e11 0.0753043
\(748\) 1.74407e12 0.203708
\(749\) 3.79566e12 0.440676
\(750\) −6.49444e12 −0.749490
\(751\) 1.24461e13 1.42775 0.713877 0.700271i \(-0.246937\pi\)
0.713877 + 0.700271i \(0.246937\pi\)
\(752\) −8.47042e11 −0.0965883
\(753\) −1.30218e13 −1.47603
\(754\) 6.59768e11 0.0743396
\(755\) −1.64147e12 −0.183853
\(756\) 3.14336e12 0.349982
\(757\) 3.37433e12 0.373470 0.186735 0.982410i \(-0.440209\pi\)
0.186735 + 0.982410i \(0.440209\pi\)
\(758\) 7.44179e12 0.818777
\(759\) 3.73286e12 0.408275
\(760\) 1.35826e13 1.47680
\(761\) −9.72420e12 −1.05105 −0.525524 0.850779i \(-0.676131\pi\)
−0.525524 + 0.850779i \(0.676131\pi\)
\(762\) 2.61690e13 2.81183
\(763\) −1.54228e12 −0.164741
\(764\) −1.59658e13 −1.69540
\(765\) 7.11299e12 0.750889
\(766\) −1.34783e13 −1.41451
\(767\) −1.63416e13 −1.70496
\(768\) 2.18232e13 2.26357
\(769\) 2.91544e11 0.0300632 0.0150316 0.999887i \(-0.495215\pi\)
0.0150316 + 0.999887i \(0.495215\pi\)
\(770\) 5.25359e12 0.538577
\(771\) −2.27663e13 −2.32032
\(772\) 2.69781e13 2.73359
\(773\) 6.57221e11 0.0662069 0.0331035 0.999452i \(-0.489461\pi\)
0.0331035 + 0.999452i \(0.489461\pi\)
\(774\) 1.14851e13 1.15027
\(775\) 1.42919e13 1.42309
\(776\) −6.88887e12 −0.681978
\(777\) 1.48068e13 1.45736
\(778\) −2.69216e13 −2.63446
\(779\) 8.64227e11 0.0840832
\(780\) 4.20753e13 4.07006
\(781\) 1.85750e12 0.178648
\(782\) 8.01057e12 0.766007
\(783\) 1.06492e11 0.0101248
\(784\) −1.29631e12 −0.122543
\(785\) −5.59139e12 −0.525540
\(786\) 3.16798e13 2.96061
\(787\) −1.43680e13 −1.33509 −0.667544 0.744570i \(-0.732655\pi\)
−0.667544 + 0.744570i \(0.732655\pi\)
\(788\) 1.37239e12 0.126797
\(789\) −6.08383e12 −0.558896
\(790\) 1.56086e13 1.42574
\(791\) −2.62683e10 −0.00238582
\(792\) 4.39822e12 0.397204
\(793\) 1.14501e11 0.0102820
\(794\) −2.23670e13 −1.99717
\(795\) 1.78283e13 1.58291
\(796\) 3.57207e13 3.15364
\(797\) −1.41338e11 −0.0124079 −0.00620393 0.999981i \(-0.501975\pi\)
−0.00620393 + 0.999981i \(0.501975\pi\)
\(798\) −1.77625e13 −1.55057
\(799\) 1.24942e12 0.108454
\(800\) 9.13274e12 0.788309
\(801\) −1.77057e13 −1.51973
\(802\) −7.30644e12 −0.623622
\(803\) −1.16842e12 −0.0991696
\(804\) 6.56030e12 0.553696
\(805\) 1.54490e13 1.29664
\(806\) −2.46893e13 −2.06064
\(807\) 2.84871e13 2.36438
\(808\) −1.67710e13 −1.38423
\(809\) 1.19441e13 0.980361 0.490180 0.871621i \(-0.336931\pi\)
0.490180 + 0.871621i \(0.336931\pi\)
\(810\) −2.46363e13 −2.01091
\(811\) −4.81505e12 −0.390847 −0.195424 0.980719i \(-0.562608\pi\)
−0.195424 + 0.980719i \(0.562608\pi\)
\(812\) 7.76191e11 0.0626565
\(813\) 7.75819e12 0.622806
\(814\) 6.58403e12 0.525632
\(815\) 3.03033e12 0.240591
\(816\) 3.14078e12 0.247988
\(817\) −5.78513e12 −0.454270
\(818\) −2.85684e13 −2.23098
\(819\) −1.29547e13 −1.00612
\(820\) −3.76168e12 −0.290549
\(821\) 1.00327e13 0.770679 0.385340 0.922775i \(-0.374084\pi\)
0.385340 + 0.922775i \(0.374084\pi\)
\(822\) 2.24527e13 1.71532
\(823\) 1.10769e13 0.841624 0.420812 0.907148i \(-0.361745\pi\)
0.420812 + 0.907148i \(0.361745\pi\)
\(824\) −2.99375e13 −2.26226
\(825\) 6.20488e12 0.466327
\(826\) −3.00278e13 −2.24447
\(827\) 1.69072e13 1.25689 0.628444 0.777855i \(-0.283692\pi\)
0.628444 + 0.777855i \(0.283692\pi\)
\(828\) 2.95222e13 2.18279
\(829\) −1.41723e13 −1.04219 −0.521094 0.853499i \(-0.674476\pi\)
−0.521094 + 0.853499i \(0.674476\pi\)
\(830\) 2.19455e12 0.160507
\(831\) 8.32732e12 0.605760
\(832\) −2.13870e13 −1.54737
\(833\) 1.91211e12 0.137597
\(834\) −4.29528e13 −3.07428
\(835\) 2.08460e12 0.148400
\(836\) −5.05686e12 −0.358057
\(837\) −3.98505e12 −0.280653
\(838\) −2.29844e13 −1.61003
\(839\) −4.27646e12 −0.297959 −0.148979 0.988840i \(-0.547599\pi\)
−0.148979 + 0.988840i \(0.547599\pi\)
\(840\) 3.38712e13 2.34733
\(841\) −1.44808e13 −0.998187
\(842\) −4.58742e13 −3.14532
\(843\) 3.32139e13 2.26515
\(844\) 2.16482e12 0.146853
\(845\) −2.13124e12 −0.143806
\(846\) 7.19194e12 0.482702
\(847\) 1.15295e13 0.769727
\(848\) 4.23058e12 0.280944
\(849\) 4.26911e13 2.82002
\(850\) 1.33154e13 0.874925
\(851\) 1.93614e13 1.26548
\(852\) 2.73356e13 1.77726
\(853\) 4.74625e12 0.306959 0.153479 0.988152i \(-0.450952\pi\)
0.153479 + 0.988152i \(0.450952\pi\)
\(854\) 2.10396e11 0.0135356
\(855\) −2.06238e13 −1.31984
\(856\) 1.08816e13 0.692724
\(857\) 7.59340e12 0.480864 0.240432 0.970666i \(-0.422711\pi\)
0.240432 + 0.970666i \(0.422711\pi\)
\(858\) −1.07189e13 −0.675241
\(859\) 9.14456e12 0.573052 0.286526 0.958073i \(-0.407500\pi\)
0.286526 + 0.958073i \(0.407500\pi\)
\(860\) 2.51806e13 1.56973
\(861\) 2.15514e12 0.133648
\(862\) 5.12118e13 3.15927
\(863\) 1.27626e13 0.783232 0.391616 0.920129i \(-0.371916\pi\)
0.391616 + 0.920129i \(0.371916\pi\)
\(864\) −2.54650e12 −0.155465
\(865\) 3.59086e13 2.18085
\(866\) 4.06037e13 2.45321
\(867\) 1.98290e13 1.19183
\(868\) −2.90460e13 −1.73679
\(869\) −2.54586e12 −0.151442
\(870\) 2.61927e12 0.155004
\(871\) −3.76425e12 −0.221614
\(872\) −4.42147e12 −0.258966
\(873\) 1.04600e13 0.609494
\(874\) −2.32263e13 −1.34641
\(875\) 4.38403e12 0.252835
\(876\) −1.71949e13 −0.986577
\(877\) 2.34914e13 1.34094 0.670472 0.741935i \(-0.266092\pi\)
0.670472 + 0.741935i \(0.266092\pi\)
\(878\) −5.32207e13 −3.02242
\(879\) 4.60395e13 2.60124
\(880\) 2.69343e12 0.151403
\(881\) 1.89053e13 1.05728 0.528641 0.848845i \(-0.322702\pi\)
0.528641 + 0.848845i \(0.322702\pi\)
\(882\) 1.10066e13 0.612410
\(883\) 1.68521e13 0.932892 0.466446 0.884550i \(-0.345534\pi\)
0.466446 + 0.884550i \(0.345534\pi\)
\(884\) −1.47272e13 −0.811121
\(885\) −6.48757e13 −3.55498
\(886\) 4.98288e13 2.71662
\(887\) 2.06874e13 1.12215 0.561073 0.827767i \(-0.310389\pi\)
0.561073 + 0.827767i \(0.310389\pi\)
\(888\) 4.24489e13 2.29091
\(889\) −1.76652e13 −0.948552
\(890\) −6.06313e13 −3.23923
\(891\) 4.01834e12 0.213598
\(892\) 1.20181e12 0.0635614
\(893\) −3.62262e12 −0.190630
\(894\) 4.19398e13 2.19587
\(895\) −7.37804e12 −0.384359
\(896\) −2.88696e13 −1.49642
\(897\) −3.15208e13 −1.62566
\(898\) 2.08427e13 1.06957
\(899\) −9.84030e11 −0.0502446
\(900\) 4.90728e13 2.49316
\(901\) −6.24026e12 −0.315458
\(902\) 9.58310e11 0.0482033
\(903\) −1.44265e13 −0.722049
\(904\) −7.53071e10 −0.00375040
\(905\) 1.89407e13 0.938595
\(906\) 6.15400e12 0.303446
\(907\) 1.83836e13 0.901980 0.450990 0.892529i \(-0.351071\pi\)
0.450990 + 0.892529i \(0.351071\pi\)
\(908\) −5.86348e13 −2.86266
\(909\) 2.54651e13 1.23711
\(910\) −4.43621e13 −2.14450
\(911\) −3.49240e13 −1.67993 −0.839964 0.542642i \(-0.817424\pi\)
−0.839964 + 0.542642i \(0.817424\pi\)
\(912\) −9.10653e12 −0.435889
\(913\) −3.57946e11 −0.0170490
\(914\) −2.20680e13 −1.04594
\(915\) 4.54565e11 0.0214388
\(916\) 6.04796e13 2.83844
\(917\) −2.13852e13 −0.998739
\(918\) −3.71278e12 −0.172547
\(919\) 1.01770e13 0.470650 0.235325 0.971917i \(-0.424384\pi\)
0.235325 + 0.971917i \(0.424384\pi\)
\(920\) 4.42901e13 2.03827
\(921\) −5.57551e13 −2.55339
\(922\) −1.98006e13 −0.902378
\(923\) −1.56850e13 −0.711339
\(924\) −1.26104e13 −0.569122
\(925\) 3.21832e13 1.44541
\(926\) −1.92010e13 −0.858171
\(927\) 4.54570e13 2.02182
\(928\) −6.28809e11 −0.0278325
\(929\) 1.16393e13 0.512690 0.256345 0.966585i \(-0.417482\pi\)
0.256345 + 0.966585i \(0.417482\pi\)
\(930\) −9.80161e13 −4.29659
\(931\) −5.54407e12 −0.241855
\(932\) −3.13894e13 −1.36274
\(933\) 3.95996e12 0.171089
\(934\) −3.67640e12 −0.158075
\(935\) −3.97290e12 −0.170003
\(936\) −3.71392e13 −1.58158
\(937\) −4.07911e13 −1.72877 −0.864384 0.502832i \(-0.832291\pi\)
−0.864384 + 0.502832i \(0.832291\pi\)
\(938\) −6.91686e12 −0.291740
\(939\) 7.10194e12 0.298114
\(940\) 1.57680e13 0.658721
\(941\) 8.56043e12 0.355912 0.177956 0.984038i \(-0.443052\pi\)
0.177956 + 0.984038i \(0.443052\pi\)
\(942\) 2.09626e13 0.867394
\(943\) 2.81807e12 0.116051
\(944\) −1.53948e13 −0.630956
\(945\) −7.16040e12 −0.292075
\(946\) −6.41492e12 −0.260424
\(947\) −1.43826e12 −0.0581117 −0.0290558 0.999578i \(-0.509250\pi\)
−0.0290558 + 0.999578i \(0.509250\pi\)
\(948\) −3.74659e13 −1.50660
\(949\) 9.86630e12 0.394872
\(950\) −3.86075e13 −1.53786
\(951\) −2.59197e13 −1.02759
\(952\) −1.18556e13 −0.467798
\(953\) −1.77380e13 −0.696605 −0.348303 0.937382i \(-0.613242\pi\)
−0.348303 + 0.937382i \(0.613242\pi\)
\(954\) −3.59204e13 −1.40402
\(955\) 3.63693e13 1.41488
\(956\) 1.78807e12 0.0692348
\(957\) −4.27219e11 −0.0164645
\(958\) 3.51797e13 1.34942
\(959\) −1.51565e13 −0.578650
\(960\) −8.49060e13 −3.22640
\(961\) 1.03840e13 0.392742
\(962\) −5.55965e13 −2.09296
\(963\) −1.65226e13 −0.619098
\(964\) −3.05817e13 −1.14055
\(965\) −6.14546e13 −2.28130
\(966\) −5.79199e13 −2.14008
\(967\) −4.73857e12 −0.174272 −0.0871361 0.996196i \(-0.527771\pi\)
−0.0871361 + 0.996196i \(0.527771\pi\)
\(968\) 3.30534e13 1.20998
\(969\) 1.34325e13 0.489439
\(970\) 3.58194e13 1.29911
\(971\) 1.29945e13 0.469107 0.234554 0.972103i \(-0.424637\pi\)
0.234554 + 0.972103i \(0.424637\pi\)
\(972\) 7.09134e13 2.54818
\(973\) 2.89950e13 1.03709
\(974\) 9.00912e13 3.20750
\(975\) −5.23950e13 −1.85682
\(976\) 1.07867e11 0.00380507
\(977\) 3.68324e13 1.29331 0.646657 0.762780i \(-0.276166\pi\)
0.646657 + 0.762780i \(0.276166\pi\)
\(978\) −1.13610e13 −0.397091
\(979\) 9.88937e12 0.344070
\(980\) 2.41314e13 0.835728
\(981\) 6.71356e12 0.231442
\(982\) 1.54204e13 0.529167
\(983\) −3.14481e13 −1.07424 −0.537122 0.843504i \(-0.680489\pi\)
−0.537122 + 0.843504i \(0.680489\pi\)
\(984\) 6.17847e12 0.210089
\(985\) −3.12622e12 −0.105817
\(986\) −9.16797e11 −0.0308906
\(987\) −9.03382e12 −0.303001
\(988\) 4.27008e13 1.42571
\(989\) −1.88641e13 −0.626980
\(990\) −2.28690e13 −0.756638
\(991\) 2.75782e13 0.908309 0.454155 0.890923i \(-0.349941\pi\)
0.454155 + 0.890923i \(0.349941\pi\)
\(992\) 2.35308e13 0.771496
\(993\) 7.43397e12 0.242633
\(994\) −2.88214e13 −0.936431
\(995\) −8.13699e13 −2.63184
\(996\) −5.26768e12 −0.169610
\(997\) 3.87369e13 1.24164 0.620821 0.783953i \(-0.286800\pi\)
0.620821 + 0.783953i \(0.286800\pi\)
\(998\) 4.77617e13 1.52403
\(999\) −8.97373e12 −0.285055
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.1.9 76
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.10.a.b.1.9 76 1.1 even 1 trivial