Properties

Label 197.14.a.a.1.19
Level $197$
Weight $14$
Character 197.1
Self dual yes
Analytic conductor $211.245$
Analytic rank $1$
Dimension $104$
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] = [197,14,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, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.1");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 14 \)
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: \(211.244930035\)
Analytic rank: \(1\)
Dimension: \(104\)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
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)
 
\(f(q)\) \(=\) \(q-130.362 q^{2} -354.130 q^{3} +8802.19 q^{4} +43213.6 q^{5} +46165.1 q^{6} -431996. q^{7} -79545.1 q^{8} -1.46891e6 q^{9} +O(q^{10})\) \(q-130.362 q^{2} -354.130 q^{3} +8802.19 q^{4} +43213.6 q^{5} +46165.1 q^{6} -431996. q^{7} -79545.1 q^{8} -1.46891e6 q^{9} -5.63341e6 q^{10} -2.08630e6 q^{11} -3.11712e6 q^{12} -1.11228e7 q^{13} +5.63157e7 q^{14} -1.53033e7 q^{15} -6.17379e7 q^{16} -1.52551e6 q^{17} +1.91490e8 q^{18} -3.65937e8 q^{19} +3.80375e8 q^{20} +1.52983e8 q^{21} +2.71974e8 q^{22} +9.39744e8 q^{23} +2.81693e7 q^{24} +6.46716e8 q^{25} +1.44999e9 q^{26} +1.08479e9 q^{27} -3.80251e9 q^{28} +2.35362e9 q^{29} +1.99496e9 q^{30} +3.30404e9 q^{31} +8.69989e9 q^{32} +7.38822e8 q^{33} +1.98868e8 q^{34} -1.86681e10 q^{35} -1.29297e10 q^{36} +1.67506e10 q^{37} +4.77042e10 q^{38} +3.93892e9 q^{39} -3.43743e9 q^{40} +3.16155e10 q^{41} -1.99431e10 q^{42} +5.12868e10 q^{43} -1.83640e10 q^{44} -6.34771e10 q^{45} -1.22507e11 q^{46} -1.37272e11 q^{47} +2.18633e10 q^{48} +8.97312e10 q^{49} -8.43070e10 q^{50} +5.40230e8 q^{51} -9.79050e10 q^{52} -2.69141e9 q^{53} -1.41415e11 q^{54} -9.01566e10 q^{55} +3.43631e10 q^{56} +1.29590e11 q^{57} -3.06822e11 q^{58} -5.97819e11 q^{59} -1.34702e11 q^{60} -4.79482e11 q^{61} -4.30721e11 q^{62} +6.34565e11 q^{63} -6.28376e11 q^{64} -4.80657e11 q^{65} -9.63142e10 q^{66} +8.58918e11 q^{67} -1.34278e10 q^{68} -3.32792e11 q^{69} +2.43361e12 q^{70} +9.24785e11 q^{71} +1.16845e11 q^{72} +1.02832e12 q^{73} -2.18364e12 q^{74} -2.29022e11 q^{75} -3.22105e12 q^{76} +9.01272e11 q^{77} -5.13485e11 q^{78} +1.12964e12 q^{79} -2.66792e12 q^{80} +1.95777e12 q^{81} -4.12145e12 q^{82} +3.36152e12 q^{83} +1.34658e12 q^{84} -6.59229e10 q^{85} -6.68584e12 q^{86} -8.33489e11 q^{87} +1.65955e11 q^{88} -4.04530e12 q^{89} +8.27499e12 q^{90} +4.80500e12 q^{91} +8.27180e12 q^{92} -1.17006e12 q^{93} +1.78950e13 q^{94} -1.58135e13 q^{95} -3.08090e12 q^{96} +1.29664e13 q^{97} -1.16975e13 q^{98} +3.06460e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 104 q - 128 q^{2} - 8020 q^{3} + 409600 q^{4} - 99004 q^{5} - 83328 q^{6} - 2084037 q^{7} - 2111301 q^{8} + 51549776 q^{9} - 9626347 q^{10} - 10688800 q^{11} - 68157440 q^{12} - 94762650 q^{13} - 52465903 q^{14} - 186128761 q^{15} + 1543503872 q^{16} - 109572251 q^{17} - 449658263 q^{18} - 1495268031 q^{19} - 1194030741 q^{20} - 832275538 q^{21} - 2695120703 q^{22} - 2632554532 q^{23} - 190649667 q^{24} + 22696779124 q^{25} - 2460454754 q^{26} - 16267542277 q^{27} - 18137835250 q^{28} + 47556769 q^{29} - 9613748117 q^{30} - 24774628288 q^{31} - 29246249180 q^{32} - 42367036666 q^{33} - 39395206606 q^{34} - 26216433864 q^{35} + 190013501626 q^{36} - 82419664050 q^{37} - 34593622142 q^{38} - 39498281801 q^{39} - 150303128514 q^{40} - 25862853768 q^{41} - 138889965149 q^{42} - 258164897781 q^{43} - 197365738094 q^{44} - 240782892021 q^{45} - 218441397971 q^{46} - 208905762731 q^{47} - 664063830814 q^{48} + 1113758315863 q^{49} - 1516068087607 q^{50} - 1019253294393 q^{51} - 1162941441840 q^{52} + 161684855900 q^{53} + 1679137315823 q^{54} - 557952233701 q^{55} + 2842561845328 q^{56} + 801593765429 q^{57} - 7249760433 q^{58} - 775487110641 q^{59} - 57598844627 q^{60} - 36786715662 q^{61} + 681529132643 q^{62} - 4349115033663 q^{63} + 4600420238797 q^{64} - 2531819073161 q^{65} - 3958922748734 q^{66} - 7314072405766 q^{67} - 10297353950393 q^{68} - 2089200206275 q^{69} - 14268943913713 q^{70} - 6055724651085 q^{71} - 26860198563805 q^{72} - 7572811533391 q^{73} - 11175265675817 q^{74} - 24431657592434 q^{75} - 26425925198106 q^{76} - 9735327037686 q^{77} - 35310017230907 q^{78} - 8981210762721 q^{79} - 25913753436330 q^{80} + 15437375349812 q^{81} - 19721330628227 q^{82} - 22209909714532 q^{83} - 18837805278768 q^{84} - 5905005171430 q^{85} - 8913876797772 q^{86} - 7341562344401 q^{87} - 35154329886441 q^{88} - 4646484034146 q^{89} + 9564902968095 q^{90} - 22752431457047 q^{91} - 13601121953458 q^{92} - 9615114240293 q^{93} + 15352521272967 q^{94} + 5258551767043 q^{95} + 87277848810881 q^{96} - 42298840804040 q^{97} + 27000102375354 q^{98} - 8666459567773 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −130.362 −1.44031 −0.720154 0.693815i \(-0.755929\pi\)
−0.720154 + 0.693815i \(0.755929\pi\)
\(3\) −354.130 −0.280463 −0.140231 0.990119i \(-0.544785\pi\)
−0.140231 + 0.990119i \(0.544785\pi\)
\(4\) 8802.19 1.07449
\(5\) 43213.6 1.23685 0.618423 0.785845i \(-0.287772\pi\)
0.618423 + 0.785845i \(0.287772\pi\)
\(6\) 46165.1 0.403953
\(7\) −431996. −1.38785 −0.693924 0.720048i \(-0.744120\pi\)
−0.693924 + 0.720048i \(0.744120\pi\)
\(8\) −79545.1 −0.107282
\(9\) −1.46891e6 −0.921341
\(10\) −5.63341e6 −1.78144
\(11\) −2.08630e6 −0.355078 −0.177539 0.984114i \(-0.556814\pi\)
−0.177539 + 0.984114i \(0.556814\pi\)
\(12\) −3.11712e6 −0.301353
\(13\) −1.11228e7 −0.639120 −0.319560 0.947566i \(-0.603535\pi\)
−0.319560 + 0.947566i \(0.603535\pi\)
\(14\) 5.63157e7 1.99893
\(15\) −1.53033e7 −0.346889
\(16\) −6.17379e7 −0.919966
\(17\) −1.52551e6 −0.0153284 −0.00766421 0.999971i \(-0.502440\pi\)
−0.00766421 + 0.999971i \(0.502440\pi\)
\(18\) 1.91490e8 1.32701
\(19\) −3.65937e8 −1.78447 −0.892233 0.451575i \(-0.850862\pi\)
−0.892233 + 0.451575i \(0.850862\pi\)
\(20\) 3.80375e8 1.32897
\(21\) 1.52983e8 0.389240
\(22\) 2.71974e8 0.511422
\(23\) 9.39744e8 1.32367 0.661833 0.749651i \(-0.269779\pi\)
0.661833 + 0.749651i \(0.269779\pi\)
\(24\) 2.81693e7 0.0300887
\(25\) 6.46716e8 0.529789
\(26\) 1.44999e9 0.920529
\(27\) 1.08479e9 0.538864
\(28\) −3.80251e9 −1.49122
\(29\) 2.35362e9 0.734767 0.367383 0.930070i \(-0.380254\pi\)
0.367383 + 0.930070i \(0.380254\pi\)
\(30\) 1.99496e9 0.499627
\(31\) 3.30404e9 0.668644 0.334322 0.942459i \(-0.391493\pi\)
0.334322 + 0.942459i \(0.391493\pi\)
\(32\) 8.69989e9 1.43232
\(33\) 7.38822e8 0.0995863
\(34\) 1.98868e8 0.0220776
\(35\) −1.86681e10 −1.71656
\(36\) −1.29297e10 −0.989967
\(37\) 1.67506e10 1.07330 0.536649 0.843806i \(-0.319690\pi\)
0.536649 + 0.843806i \(0.319690\pi\)
\(38\) 4.77042e10 2.57018
\(39\) 3.93892e9 0.179249
\(40\) −3.43743e9 −0.132692
\(41\) 3.16155e10 1.03945 0.519726 0.854333i \(-0.326034\pi\)
0.519726 + 0.854333i \(0.326034\pi\)
\(42\) −1.99431e10 −0.560625
\(43\) 5.12868e10 1.23726 0.618630 0.785683i \(-0.287688\pi\)
0.618630 + 0.785683i \(0.287688\pi\)
\(44\) −1.83640e10 −0.381527
\(45\) −6.34771e10 −1.13956
\(46\) −1.22507e11 −1.90649
\(47\) −1.37272e11 −1.85757 −0.928785 0.370620i \(-0.879145\pi\)
−0.928785 + 0.370620i \(0.879145\pi\)
\(48\) 2.18633e10 0.258016
\(49\) 8.97312e10 0.926123
\(50\) −8.43070e10 −0.763060
\(51\) 5.40230e8 0.00429905
\(52\) −9.79050e10 −0.686725
\(53\) −2.69141e9 −0.0166796 −0.00833981 0.999965i \(-0.502655\pi\)
−0.00833981 + 0.999965i \(0.502655\pi\)
\(54\) −1.41415e11 −0.776130
\(55\) −9.01566e10 −0.439178
\(56\) 3.43631e10 0.148892
\(57\) 1.29590e11 0.500476
\(58\) −3.06822e11 −1.05829
\(59\) −5.97819e11 −1.84515 −0.922576 0.385816i \(-0.873920\pi\)
−0.922576 + 0.385816i \(0.873920\pi\)
\(60\) −1.34702e11 −0.372728
\(61\) −4.79482e11 −1.19159 −0.595797 0.803135i \(-0.703164\pi\)
−0.595797 + 0.803135i \(0.703164\pi\)
\(62\) −4.30721e11 −0.963053
\(63\) 6.34565e11 1.27868
\(64\) −6.28376e11 −1.14301
\(65\) −4.80657e11 −0.790493
\(66\) −9.63142e10 −0.143435
\(67\) 8.58918e11 1.16002 0.580010 0.814609i \(-0.303049\pi\)
0.580010 + 0.814609i \(0.303049\pi\)
\(68\) −1.34278e10 −0.0164702
\(69\) −3.32792e11 −0.371239
\(70\) 2.43361e12 2.47237
\(71\) 9.24785e11 0.856765 0.428382 0.903598i \(-0.359084\pi\)
0.428382 + 0.903598i \(0.359084\pi\)
\(72\) 1.16845e11 0.0988436
\(73\) 1.02832e12 0.795296 0.397648 0.917538i \(-0.369827\pi\)
0.397648 + 0.917538i \(0.369827\pi\)
\(74\) −2.18364e12 −1.54588
\(75\) −2.29022e11 −0.148586
\(76\) −3.22105e12 −1.91738
\(77\) 9.01272e11 0.492795
\(78\) −5.13485e11 −0.258174
\(79\) 1.12964e12 0.522832 0.261416 0.965226i \(-0.415811\pi\)
0.261416 + 0.965226i \(0.415811\pi\)
\(80\) −2.66792e12 −1.13786
\(81\) 1.95777e12 0.770209
\(82\) −4.12145e12 −1.49713
\(83\) 3.36152e12 1.12857 0.564284 0.825581i \(-0.309152\pi\)
0.564284 + 0.825581i \(0.309152\pi\)
\(84\) 1.34658e12 0.418233
\(85\) −6.59229e10 −0.0189589
\(86\) −6.68584e12 −1.78203
\(87\) −8.33489e11 −0.206075
\(88\) 1.65955e11 0.0380937
\(89\) −4.04530e12 −0.862811 −0.431406 0.902158i \(-0.641982\pi\)
−0.431406 + 0.902158i \(0.641982\pi\)
\(90\) 8.27499e12 1.64131
\(91\) 4.80500e12 0.887002
\(92\) 8.27180e12 1.42226
\(93\) −1.17006e12 −0.187530
\(94\) 1.78950e13 2.67547
\(95\) −1.58135e13 −2.20711
\(96\) −3.08090e12 −0.401711
\(97\) 1.29664e13 1.58053 0.790265 0.612765i \(-0.209943\pi\)
0.790265 + 0.612765i \(0.209943\pi\)
\(98\) −1.16975e13 −1.33390
\(99\) 3.06460e12 0.327148
\(100\) 5.69251e12 0.569251
\(101\) 1.69646e13 1.59021 0.795104 0.606474i \(-0.207416\pi\)
0.795104 + 0.606474i \(0.207416\pi\)
\(102\) −7.04253e10 −0.00619195
\(103\) −6.05853e12 −0.499949 −0.249974 0.968252i \(-0.580422\pi\)
−0.249974 + 0.968252i \(0.580422\pi\)
\(104\) 8.84764e11 0.0685663
\(105\) 6.61094e12 0.481430
\(106\) 3.50856e11 0.0240238
\(107\) −2.27509e13 −1.46556 −0.732781 0.680464i \(-0.761778\pi\)
−0.732781 + 0.680464i \(0.761778\pi\)
\(108\) 9.54849e12 0.579002
\(109\) 4.33407e12 0.247528 0.123764 0.992312i \(-0.460503\pi\)
0.123764 + 0.992312i \(0.460503\pi\)
\(110\) 1.17530e13 0.632551
\(111\) −5.93191e12 −0.301020
\(112\) 2.66705e13 1.27677
\(113\) 3.27907e13 1.48163 0.740816 0.671708i \(-0.234439\pi\)
0.740816 + 0.671708i \(0.234439\pi\)
\(114\) −1.68935e13 −0.720840
\(115\) 4.06098e13 1.63717
\(116\) 2.07170e13 0.789496
\(117\) 1.63384e13 0.588847
\(118\) 7.79328e13 2.65759
\(119\) 6.59014e11 0.0212735
\(120\) 1.21730e12 0.0372151
\(121\) −3.01701e13 −0.873919
\(122\) 6.25061e13 1.71626
\(123\) −1.11960e13 −0.291527
\(124\) 2.90828e13 0.718448
\(125\) −2.48041e13 −0.581578
\(126\) −8.27230e13 −1.84169
\(127\) −4.06455e13 −0.859585 −0.429792 0.902928i \(-0.641413\pi\)
−0.429792 + 0.902928i \(0.641413\pi\)
\(128\) 1.06467e13 0.213970
\(129\) −1.81622e13 −0.347005
\(130\) 6.26593e13 1.13855
\(131\) −4.84077e13 −0.836856 −0.418428 0.908250i \(-0.637419\pi\)
−0.418428 + 0.908250i \(0.637419\pi\)
\(132\) 6.50325e12 0.107004
\(133\) 1.58083e14 2.47657
\(134\) −1.11970e14 −1.67079
\(135\) 4.68775e13 0.666493
\(136\) 1.21347e11 0.00164447
\(137\) −4.02215e13 −0.519726 −0.259863 0.965646i \(-0.583677\pi\)
−0.259863 + 0.965646i \(0.583677\pi\)
\(138\) 4.33833e13 0.534698
\(139\) 4.65542e13 0.547473 0.273737 0.961805i \(-0.411740\pi\)
0.273737 + 0.961805i \(0.411740\pi\)
\(140\) −1.64320e14 −1.84441
\(141\) 4.86121e13 0.520979
\(142\) −1.20557e14 −1.23400
\(143\) 2.32055e13 0.226938
\(144\) 9.06877e13 0.847602
\(145\) 1.01708e14 0.908793
\(146\) −1.34053e14 −1.14547
\(147\) −3.17765e13 −0.259743
\(148\) 1.47442e14 1.15324
\(149\) 1.25126e14 0.936778 0.468389 0.883522i \(-0.344835\pi\)
0.468389 + 0.883522i \(0.344835\pi\)
\(150\) 2.98557e13 0.214010
\(151\) 7.35760e13 0.505110 0.252555 0.967583i \(-0.418729\pi\)
0.252555 + 0.967583i \(0.418729\pi\)
\(152\) 2.91085e13 0.191442
\(153\) 2.24084e12 0.0141227
\(154\) −1.17491e14 −0.709776
\(155\) 1.42780e14 0.827010
\(156\) 3.46711e13 0.192601
\(157\) 1.87382e13 0.0998572 0.0499286 0.998753i \(-0.484101\pi\)
0.0499286 + 0.998753i \(0.484101\pi\)
\(158\) −1.47261e14 −0.753039
\(159\) 9.53109e11 0.00467801
\(160\) 3.75954e14 1.77156
\(161\) −4.05965e14 −1.83705
\(162\) −2.55218e14 −1.10934
\(163\) −9.17220e13 −0.383049 −0.191524 0.981488i \(-0.561343\pi\)
−0.191524 + 0.981488i \(0.561343\pi\)
\(164\) 2.78285e14 1.11688
\(165\) 3.19272e13 0.123173
\(166\) −4.38213e14 −1.62548
\(167\) 2.47054e14 0.881324 0.440662 0.897673i \(-0.354744\pi\)
0.440662 + 0.897673i \(0.354744\pi\)
\(168\) −1.21690e13 −0.0417586
\(169\) −1.79158e14 −0.591526
\(170\) 8.59382e12 0.0273066
\(171\) 5.37531e14 1.64410
\(172\) 4.51436e14 1.32942
\(173\) −1.49888e14 −0.425076 −0.212538 0.977153i \(-0.568173\pi\)
−0.212538 + 0.977153i \(0.568173\pi\)
\(174\) 1.08655e14 0.296811
\(175\) −2.79378e14 −0.735267
\(176\) 1.28804e14 0.326660
\(177\) 2.11706e14 0.517496
\(178\) 5.27353e14 1.24271
\(179\) −3.88315e13 −0.0882346 −0.0441173 0.999026i \(-0.514048\pi\)
−0.0441173 + 0.999026i \(0.514048\pi\)
\(180\) −5.58738e14 −1.22444
\(181\) 1.34399e14 0.284110 0.142055 0.989859i \(-0.454629\pi\)
0.142055 + 0.989859i \(0.454629\pi\)
\(182\) −6.26388e14 −1.27756
\(183\) 1.69799e14 0.334198
\(184\) −7.47520e13 −0.142006
\(185\) 7.23856e14 1.32750
\(186\) 1.52531e14 0.270100
\(187\) 3.18267e12 0.00544279
\(188\) −1.20829e15 −1.99593
\(189\) −4.68623e14 −0.747862
\(190\) 2.06147e15 3.17892
\(191\) 1.63251e14 0.243299 0.121649 0.992573i \(-0.461182\pi\)
0.121649 + 0.992573i \(0.461182\pi\)
\(192\) 2.22527e14 0.320572
\(193\) 4.52436e14 0.630137 0.315068 0.949069i \(-0.397973\pi\)
0.315068 + 0.949069i \(0.397973\pi\)
\(194\) −1.69032e15 −2.27645
\(195\) 1.70215e14 0.221704
\(196\) 7.89831e14 0.995106
\(197\) −5.84517e13 −0.0712470
\(198\) −3.99506e14 −0.471194
\(199\) −1.12221e15 −1.28095 −0.640473 0.767981i \(-0.721262\pi\)
−0.640473 + 0.767981i \(0.721262\pi\)
\(200\) −5.14431e13 −0.0568371
\(201\) −3.04169e14 −0.325342
\(202\) −2.21153e15 −2.29039
\(203\) −1.01675e15 −1.01974
\(204\) 4.75520e12 0.00461927
\(205\) 1.36622e15 1.28564
\(206\) 7.89801e14 0.720080
\(207\) −1.38040e15 −1.21955
\(208\) 6.86698e14 0.587969
\(209\) 7.63455e14 0.633625
\(210\) −8.61814e14 −0.693407
\(211\) 3.23786e14 0.252593 0.126297 0.991993i \(-0.459691\pi\)
0.126297 + 0.991993i \(0.459691\pi\)
\(212\) −2.36903e13 −0.0179220
\(213\) −3.27495e14 −0.240291
\(214\) 2.96585e15 2.11086
\(215\) 2.21629e15 1.53030
\(216\) −8.62894e13 −0.0578107
\(217\) −1.42733e15 −0.927976
\(218\) −5.64997e14 −0.356516
\(219\) −3.64159e14 −0.223051
\(220\) −7.93576e14 −0.471890
\(221\) 1.69679e13 0.00979669
\(222\) 7.73294e14 0.433561
\(223\) 1.72096e15 0.937107 0.468554 0.883435i \(-0.344775\pi\)
0.468554 + 0.883435i \(0.344775\pi\)
\(224\) −3.75831e15 −1.98784
\(225\) −9.49970e14 −0.488117
\(226\) −4.27465e15 −2.13401
\(227\) −1.48303e15 −0.719421 −0.359710 0.933064i \(-0.617124\pi\)
−0.359710 + 0.933064i \(0.617124\pi\)
\(228\) 1.14067e15 0.537755
\(229\) 5.64162e14 0.258507 0.129254 0.991612i \(-0.458742\pi\)
0.129254 + 0.991612i \(0.458742\pi\)
\(230\) −5.29396e15 −2.35803
\(231\) −3.19168e14 −0.138211
\(232\) −1.87219e14 −0.0788275
\(233\) −7.20181e14 −0.294869 −0.147434 0.989072i \(-0.547101\pi\)
−0.147434 + 0.989072i \(0.547101\pi\)
\(234\) −2.12991e15 −0.848121
\(235\) −5.93201e15 −2.29753
\(236\) −5.26212e15 −1.98259
\(237\) −4.00039e14 −0.146635
\(238\) −8.59102e13 −0.0306404
\(239\) 8.69155e14 0.301655 0.150828 0.988560i \(-0.451806\pi\)
0.150828 + 0.988560i \(0.451806\pi\)
\(240\) 9.44791e14 0.319126
\(241\) −4.72685e15 −1.55404 −0.777018 0.629478i \(-0.783269\pi\)
−0.777018 + 0.629478i \(0.783269\pi\)
\(242\) 3.93302e15 1.25871
\(243\) −2.42280e15 −0.754879
\(244\) −4.22049e15 −1.28035
\(245\) 3.87761e15 1.14547
\(246\) 1.45953e15 0.419889
\(247\) 4.07025e15 1.14049
\(248\) −2.62820e14 −0.0717337
\(249\) −1.19041e15 −0.316521
\(250\) 3.23350e15 0.837652
\(251\) 1.70080e15 0.429314 0.214657 0.976689i \(-0.431137\pi\)
0.214657 + 0.976689i \(0.431137\pi\)
\(252\) 5.58556e15 1.37392
\(253\) −1.96059e15 −0.470005
\(254\) 5.29862e15 1.23807
\(255\) 2.33453e13 0.00531726
\(256\) 3.75973e15 0.834828
\(257\) 2.07760e14 0.0449777 0.0224888 0.999747i \(-0.492841\pi\)
0.0224888 + 0.999747i \(0.492841\pi\)
\(258\) 2.36766e15 0.499794
\(259\) −7.23620e15 −1.48957
\(260\) −4.23083e15 −0.849374
\(261\) −3.45727e15 −0.676970
\(262\) 6.31051e15 1.20533
\(263\) −8.78752e13 −0.0163740 −0.00818699 0.999966i \(-0.502606\pi\)
−0.00818699 + 0.999966i \(0.502606\pi\)
\(264\) −5.87697e13 −0.0106839
\(265\) −1.16305e14 −0.0206301
\(266\) −2.06080e16 −3.56702
\(267\) 1.43256e15 0.241986
\(268\) 7.56036e15 1.24642
\(269\) −9.58755e15 −1.54283 −0.771414 0.636333i \(-0.780450\pi\)
−0.771414 + 0.636333i \(0.780450\pi\)
\(270\) −6.11104e15 −0.959954
\(271\) 6.49098e15 0.995429 0.497714 0.867341i \(-0.334173\pi\)
0.497714 + 0.867341i \(0.334173\pi\)
\(272\) 9.41818e13 0.0141016
\(273\) −1.70160e15 −0.248771
\(274\) 5.24334e15 0.748565
\(275\) −1.34924e15 −0.188117
\(276\) −2.92930e15 −0.398891
\(277\) 1.15861e16 1.54105 0.770527 0.637407i \(-0.219993\pi\)
0.770527 + 0.637407i \(0.219993\pi\)
\(278\) −6.06889e15 −0.788530
\(279\) −4.85336e15 −0.616049
\(280\) 1.48496e15 0.184156
\(281\) 1.45285e16 1.76047 0.880235 0.474538i \(-0.157385\pi\)
0.880235 + 0.474538i \(0.157385\pi\)
\(282\) −6.33716e15 −0.750370
\(283\) −1.50963e16 −1.74686 −0.873430 0.486950i \(-0.838109\pi\)
−0.873430 + 0.486950i \(0.838109\pi\)
\(284\) 8.14013e15 0.920581
\(285\) 5.60004e15 0.619012
\(286\) −3.02511e15 −0.326860
\(287\) −1.36577e16 −1.44260
\(288\) −1.27794e16 −1.31965
\(289\) −9.90225e15 −0.999765
\(290\) −1.32589e16 −1.30894
\(291\) −4.59179e15 −0.443280
\(292\) 9.05144e15 0.854534
\(293\) −7.51198e15 −0.693609 −0.346805 0.937937i \(-0.612733\pi\)
−0.346805 + 0.937937i \(0.612733\pi\)
\(294\) 4.14245e15 0.374110
\(295\) −2.58340e16 −2.28217
\(296\) −1.33243e15 −0.115146
\(297\) −2.26319e15 −0.191339
\(298\) −1.63116e16 −1.34925
\(299\) −1.04526e16 −0.845982
\(300\) −2.01589e15 −0.159654
\(301\) −2.21557e16 −1.71713
\(302\) −9.59150e15 −0.727514
\(303\) −6.00767e15 −0.445994
\(304\) 2.25922e16 1.64165
\(305\) −2.07202e16 −1.47382
\(306\) −2.92120e14 −0.0203410
\(307\) 1.71489e15 0.116906 0.0584530 0.998290i \(-0.481383\pi\)
0.0584530 + 0.998290i \(0.481383\pi\)
\(308\) 7.93317e15 0.529501
\(309\) 2.14551e15 0.140217
\(310\) −1.86130e16 −1.19115
\(311\) 1.38605e16 0.868631 0.434316 0.900761i \(-0.356990\pi\)
0.434316 + 0.900761i \(0.356990\pi\)
\(312\) −3.13322e14 −0.0192303
\(313\) −2.39233e16 −1.43808 −0.719040 0.694969i \(-0.755418\pi\)
−0.719040 + 0.694969i \(0.755418\pi\)
\(314\) −2.44274e15 −0.143825
\(315\) 2.74218e16 1.58153
\(316\) 9.94327e15 0.561776
\(317\) −2.31923e16 −1.28369 −0.641843 0.766836i \(-0.721830\pi\)
−0.641843 + 0.766836i \(0.721830\pi\)
\(318\) −1.24249e14 −0.00673777
\(319\) −4.91036e15 −0.260900
\(320\) −2.71544e16 −1.41373
\(321\) 8.05679e15 0.411036
\(322\) 5.29223e16 2.64591
\(323\) 5.58241e14 0.0273530
\(324\) 1.72326e16 0.827579
\(325\) −7.19329e15 −0.338599
\(326\) 1.19570e16 0.551708
\(327\) −1.53483e15 −0.0694223
\(328\) −2.51485e15 −0.111515
\(329\) 5.93008e16 2.57802
\(330\) −4.16209e15 −0.177407
\(331\) −1.97820e16 −0.826775 −0.413387 0.910555i \(-0.635654\pi\)
−0.413387 + 0.910555i \(0.635654\pi\)
\(332\) 2.95887e16 1.21263
\(333\) −2.46053e16 −0.988873
\(334\) −3.22064e16 −1.26938
\(335\) 3.71170e16 1.43477
\(336\) −9.44483e15 −0.358087
\(337\) 4.12798e16 1.53512 0.767561 0.640976i \(-0.221470\pi\)
0.767561 + 0.640976i \(0.221470\pi\)
\(338\) 2.33554e16 0.851979
\(339\) −1.16122e16 −0.415543
\(340\) −5.80265e14 −0.0203711
\(341\) −6.89323e15 −0.237421
\(342\) −7.00734e16 −2.36801
\(343\) 3.09216e15 0.102530
\(344\) −4.07961e15 −0.132736
\(345\) −1.43812e16 −0.459166
\(346\) 1.95397e16 0.612241
\(347\) −4.98693e16 −1.53353 −0.766764 0.641929i \(-0.778134\pi\)
−0.766764 + 0.641929i \(0.778134\pi\)
\(348\) −7.33652e15 −0.221424
\(349\) −8.69199e15 −0.257486 −0.128743 0.991678i \(-0.541094\pi\)
−0.128743 + 0.991678i \(0.541094\pi\)
\(350\) 3.64202e16 1.05901
\(351\) −1.20659e16 −0.344399
\(352\) −1.81506e16 −0.508585
\(353\) 5.78772e16 1.59211 0.796053 0.605228i \(-0.206918\pi\)
0.796053 + 0.605228i \(0.206918\pi\)
\(354\) −2.75984e16 −0.745354
\(355\) 3.99633e16 1.05969
\(356\) −3.56075e16 −0.927078
\(357\) −2.33377e14 −0.00596643
\(358\) 5.06214e15 0.127085
\(359\) −3.73927e16 −0.921877 −0.460938 0.887432i \(-0.652487\pi\)
−0.460938 + 0.887432i \(0.652487\pi\)
\(360\) 5.04930e15 0.122254
\(361\) 9.18571e16 2.18432
\(362\) −1.75205e16 −0.409205
\(363\) 1.06841e16 0.245102
\(364\) 4.22945e16 0.953071
\(365\) 4.44374e16 0.983659
\(366\) −2.21353e16 −0.481347
\(367\) 6.55093e16 1.39950 0.699751 0.714387i \(-0.253294\pi\)
0.699751 + 0.714387i \(0.253294\pi\)
\(368\) −5.80178e16 −1.21773
\(369\) −4.64404e16 −0.957689
\(370\) −9.43631e16 −1.91201
\(371\) 1.16268e15 0.0231488
\(372\) −1.02991e16 −0.201498
\(373\) 6.89000e16 1.32468 0.662341 0.749202i \(-0.269563\pi\)
0.662341 + 0.749202i \(0.269563\pi\)
\(374\) −4.14899e14 −0.00783929
\(375\) 8.78388e15 0.163111
\(376\) 1.09193e16 0.199284
\(377\) −2.61788e16 −0.469604
\(378\) 6.10905e16 1.07715
\(379\) 7.69091e16 1.33298 0.666489 0.745515i \(-0.267796\pi\)
0.666489 + 0.745515i \(0.267796\pi\)
\(380\) −1.39193e17 −2.37151
\(381\) 1.43938e16 0.241082
\(382\) −2.12817e16 −0.350425
\(383\) 7.74236e16 1.25338 0.626688 0.779270i \(-0.284410\pi\)
0.626688 + 0.779270i \(0.284410\pi\)
\(384\) −3.77034e15 −0.0600105
\(385\) 3.89473e16 0.609512
\(386\) −5.89804e16 −0.907590
\(387\) −7.53359e16 −1.13994
\(388\) 1.14133e17 1.69826
\(389\) 2.01646e16 0.295065 0.147532 0.989057i \(-0.452867\pi\)
0.147532 + 0.989057i \(0.452867\pi\)
\(390\) −2.21896e16 −0.319322
\(391\) −1.43359e15 −0.0202897
\(392\) −7.13767e15 −0.0993567
\(393\) 1.71426e16 0.234707
\(394\) 7.61987e15 0.102618
\(395\) 4.88157e16 0.646663
\(396\) 2.69752e16 0.351516
\(397\) −9.16217e14 −0.0117452 −0.00587259 0.999983i \(-0.501869\pi\)
−0.00587259 + 0.999983i \(0.501869\pi\)
\(398\) 1.46294e17 1.84496
\(399\) −5.59821e16 −0.694585
\(400\) −3.99269e16 −0.487388
\(401\) −6.44125e16 −0.773627 −0.386813 0.922158i \(-0.626424\pi\)
−0.386813 + 0.922158i \(0.626424\pi\)
\(402\) 3.96520e16 0.468593
\(403\) −3.67502e16 −0.427344
\(404\) 1.49325e17 1.70865
\(405\) 8.46023e16 0.952631
\(406\) 1.32546e17 1.46875
\(407\) −3.49469e16 −0.381105
\(408\) −4.29726e13 −0.000461212 0
\(409\) −5.87064e16 −0.620132 −0.310066 0.950715i \(-0.600351\pi\)
−0.310066 + 0.950715i \(0.600351\pi\)
\(410\) −1.78103e17 −1.85172
\(411\) 1.42436e16 0.145764
\(412\) −5.33283e16 −0.537188
\(413\) 2.58255e17 2.56079
\(414\) 1.79952e17 1.75652
\(415\) 1.45263e17 1.39586
\(416\) −9.67672e16 −0.915422
\(417\) −1.64863e16 −0.153546
\(418\) −9.95253e16 −0.912616
\(419\) −1.69233e17 −1.52790 −0.763948 0.645278i \(-0.776742\pi\)
−0.763948 + 0.645278i \(0.776742\pi\)
\(420\) 5.81908e16 0.517290
\(421\) −1.23495e17 −1.08098 −0.540488 0.841351i \(-0.681761\pi\)
−0.540488 + 0.841351i \(0.681761\pi\)
\(422\) −4.22093e16 −0.363812
\(423\) 2.01640e17 1.71145
\(424\) 2.14088e14 0.00178943
\(425\) −9.86571e14 −0.00812083
\(426\) 4.26928e16 0.346092
\(427\) 2.07134e17 1.65375
\(428\) −2.00258e17 −1.57473
\(429\) −8.21778e15 −0.0636476
\(430\) −2.88919e17 −2.20410
\(431\) −2.22328e16 −0.167068 −0.0835338 0.996505i \(-0.526621\pi\)
−0.0835338 + 0.996505i \(0.526621\pi\)
\(432\) −6.69724e16 −0.495737
\(433\) −2.25406e17 −1.64359 −0.821796 0.569782i \(-0.807028\pi\)
−0.821796 + 0.569782i \(0.807028\pi\)
\(434\) 1.86070e17 1.33657
\(435\) −3.60181e16 −0.254883
\(436\) 3.81493e16 0.265965
\(437\) −3.43887e17 −2.36204
\(438\) 4.74724e16 0.321262
\(439\) 5.26523e16 0.351073 0.175537 0.984473i \(-0.443834\pi\)
0.175537 + 0.984473i \(0.443834\pi\)
\(440\) 7.17152e15 0.0471160
\(441\) −1.31807e17 −0.853275
\(442\) −2.21197e15 −0.0141103
\(443\) 7.62979e16 0.479610 0.239805 0.970821i \(-0.422916\pi\)
0.239805 + 0.970821i \(0.422916\pi\)
\(444\) −5.22138e16 −0.323442
\(445\) −1.74812e17 −1.06717
\(446\) −2.24347e17 −1.34972
\(447\) −4.43109e16 −0.262731
\(448\) 2.71456e17 1.58632
\(449\) −7.06286e16 −0.406799 −0.203399 0.979096i \(-0.565199\pi\)
−0.203399 + 0.979096i \(0.565199\pi\)
\(450\) 1.23840e17 0.703038
\(451\) −6.59593e16 −0.369087
\(452\) 2.88630e17 1.59199
\(453\) −2.60555e16 −0.141665
\(454\) 1.93331e17 1.03619
\(455\) 2.07642e17 1.09708
\(456\) −1.03082e16 −0.0536923
\(457\) −1.37388e17 −0.705497 −0.352748 0.935718i \(-0.614753\pi\)
−0.352748 + 0.935718i \(0.614753\pi\)
\(458\) −7.35451e16 −0.372330
\(459\) −1.65485e15 −0.00825994
\(460\) 3.57455e17 1.75912
\(461\) −1.74298e17 −0.845739 −0.422869 0.906191i \(-0.638977\pi\)
−0.422869 + 0.906191i \(0.638977\pi\)
\(462\) 4.16073e16 0.199066
\(463\) 3.38040e17 1.59475 0.797374 0.603485i \(-0.206222\pi\)
0.797374 + 0.603485i \(0.206222\pi\)
\(464\) −1.45308e17 −0.675960
\(465\) −5.05627e16 −0.231945
\(466\) 9.38841e16 0.424701
\(467\) −3.13179e17 −1.39712 −0.698559 0.715552i \(-0.746175\pi\)
−0.698559 + 0.715552i \(0.746175\pi\)
\(468\) 1.43814e17 0.632708
\(469\) −3.71049e17 −1.60993
\(470\) 7.73307e17 3.30915
\(471\) −6.63575e15 −0.0280062
\(472\) 4.75536e16 0.197952
\(473\) −1.07000e17 −0.439324
\(474\) 5.21497e16 0.211199
\(475\) −2.36657e17 −0.945391
\(476\) 5.80076e15 0.0228581
\(477\) 3.95344e15 0.0153676
\(478\) −1.13305e17 −0.434476
\(479\) −4.95167e17 −1.87314 −0.936572 0.350475i \(-0.886020\pi\)
−0.936572 + 0.350475i \(0.886020\pi\)
\(480\) −1.33137e17 −0.496855
\(481\) −1.86314e17 −0.685966
\(482\) 6.16200e17 2.23829
\(483\) 1.43765e17 0.515224
\(484\) −2.65563e17 −0.939014
\(485\) 5.60325e17 1.95487
\(486\) 3.15841e17 1.08726
\(487\) 2.13238e16 0.0724313 0.0362156 0.999344i \(-0.488470\pi\)
0.0362156 + 0.999344i \(0.488470\pi\)
\(488\) 3.81404e16 0.127837
\(489\) 3.24816e16 0.107431
\(490\) −5.05492e17 −1.64983
\(491\) 2.36164e17 0.760649 0.380324 0.924853i \(-0.375812\pi\)
0.380324 + 0.924853i \(0.375812\pi\)
\(492\) −9.85492e16 −0.313242
\(493\) −3.59047e15 −0.0112628
\(494\) −5.30605e17 −1.64265
\(495\) 1.32432e17 0.404632
\(496\) −2.03985e17 −0.615130
\(497\) −3.99503e17 −1.18906
\(498\) 1.55185e17 0.455888
\(499\) −2.84757e17 −0.825698 −0.412849 0.910799i \(-0.635466\pi\)
−0.412849 + 0.910799i \(0.635466\pi\)
\(500\) −2.18330e17 −0.624898
\(501\) −8.74895e16 −0.247178
\(502\) −2.21720e17 −0.618344
\(503\) −4.44490e17 −1.22369 −0.611844 0.790979i \(-0.709572\pi\)
−0.611844 + 0.790979i \(0.709572\pi\)
\(504\) −5.04765e16 −0.137180
\(505\) 7.33100e17 1.96684
\(506\) 2.55586e17 0.676952
\(507\) 6.34454e16 0.165901
\(508\) −3.57770e17 −0.923612
\(509\) 2.80337e17 0.714519 0.357260 0.934005i \(-0.383711\pi\)
0.357260 + 0.934005i \(0.383711\pi\)
\(510\) −3.04333e15 −0.00765849
\(511\) −4.44229e17 −1.10375
\(512\) −5.77343e17 −1.41638
\(513\) −3.96964e17 −0.961585
\(514\) −2.70840e16 −0.0647817
\(515\) −2.61811e17 −0.618360
\(516\) −1.59867e17 −0.372852
\(517\) 2.86390e17 0.659583
\(518\) 9.43324e17 2.14545
\(519\) 5.30799e16 0.119218
\(520\) 3.82339e16 0.0848060
\(521\) 5.77857e17 1.26583 0.632915 0.774221i \(-0.281858\pi\)
0.632915 + 0.774221i \(0.281858\pi\)
\(522\) 4.50695e17 0.975045
\(523\) −8.49227e16 −0.181452 −0.0907262 0.995876i \(-0.528919\pi\)
−0.0907262 + 0.995876i \(0.528919\pi\)
\(524\) −4.26093e17 −0.899190
\(525\) 9.89364e16 0.206215
\(526\) 1.14556e16 0.0235836
\(527\) −5.04035e15 −0.0102492
\(528\) −4.56133e16 −0.0916160
\(529\) 3.79082e17 0.752093
\(530\) 1.51618e16 0.0297137
\(531\) 8.78146e17 1.70001
\(532\) 1.39148e18 2.66104
\(533\) −3.51652e17 −0.664334
\(534\) −1.86752e17 −0.348535
\(535\) −9.83150e17 −1.81268
\(536\) −6.83227e16 −0.124450
\(537\) 1.37514e16 0.0247465
\(538\) 1.24985e18 2.22215
\(539\) −1.87206e17 −0.328846
\(540\) 4.12625e17 0.716137
\(541\) −3.20352e17 −0.549346 −0.274673 0.961538i \(-0.588570\pi\)
−0.274673 + 0.961538i \(0.588570\pi\)
\(542\) −8.46176e17 −1.43372
\(543\) −4.75949e16 −0.0796822
\(544\) −1.32718e16 −0.0219551
\(545\) 1.87291e17 0.306154
\(546\) 2.21823e17 0.358307
\(547\) 8.83411e17 1.41008 0.705042 0.709165i \(-0.250928\pi\)
0.705042 + 0.709165i \(0.250928\pi\)
\(548\) −3.54037e17 −0.558438
\(549\) 7.04318e17 1.09786
\(550\) 1.75890e17 0.270946
\(551\) −8.61277e17 −1.31117
\(552\) 2.64720e16 0.0398274
\(553\) −4.87998e17 −0.725612
\(554\) −1.51038e18 −2.21959
\(555\) −2.56339e17 −0.372316
\(556\) 4.09779e17 0.588252
\(557\) 3.21388e17 0.456006 0.228003 0.973660i \(-0.426780\pi\)
0.228003 + 0.973660i \(0.426780\pi\)
\(558\) 6.32692e17 0.887299
\(559\) −5.70453e17 −0.790757
\(560\) 1.15253e18 1.57917
\(561\) −1.12708e15 −0.00152650
\(562\) −1.89396e18 −2.53562
\(563\) −1.00802e18 −1.33403 −0.667015 0.745044i \(-0.732428\pi\)
−0.667015 + 0.745044i \(0.732428\pi\)
\(564\) 4.27893e17 0.559784
\(565\) 1.41700e18 1.83255
\(566\) 1.96798e18 2.51601
\(567\) −8.45747e17 −1.06893
\(568\) −7.35621e16 −0.0919158
\(569\) 1.09784e18 1.35615 0.678077 0.734991i \(-0.262813\pi\)
0.678077 + 0.734991i \(0.262813\pi\)
\(570\) −7.30031e17 −0.891568
\(571\) 4.95212e17 0.597938 0.298969 0.954263i \(-0.403357\pi\)
0.298969 + 0.954263i \(0.403357\pi\)
\(572\) 2.04259e17 0.243841
\(573\) −5.78122e16 −0.0682362
\(574\) 1.78045e18 2.07779
\(575\) 6.07747e17 0.701264
\(576\) 9.23031e17 1.05310
\(577\) −4.70532e17 −0.530819 −0.265410 0.964136i \(-0.585507\pi\)
−0.265410 + 0.964136i \(0.585507\pi\)
\(578\) 1.29087e18 1.43997
\(579\) −1.60221e17 −0.176730
\(580\) 8.95257e17 0.976486
\(581\) −1.45216e18 −1.56628
\(582\) 5.98594e17 0.638459
\(583\) 5.61508e15 0.00592257
\(584\) −8.17976e16 −0.0853212
\(585\) 7.06044e17 0.728314
\(586\) 9.79275e17 0.999010
\(587\) −1.48009e18 −1.49327 −0.746637 0.665231i \(-0.768333\pi\)
−0.746637 + 0.665231i \(0.768333\pi\)
\(588\) −2.79703e17 −0.279090
\(589\) −1.20907e18 −1.19317
\(590\) 3.36776e18 3.28702
\(591\) 2.06995e16 0.0199821
\(592\) −1.03415e18 −0.987397
\(593\) −8.73156e17 −0.824587 −0.412293 0.911051i \(-0.635272\pi\)
−0.412293 + 0.911051i \(0.635272\pi\)
\(594\) 2.95033e17 0.275587
\(595\) 2.84784e16 0.0263121
\(596\) 1.10138e18 1.00656
\(597\) 3.97410e17 0.359258
\(598\) 1.36262e18 1.21847
\(599\) 6.21604e17 0.549844 0.274922 0.961466i \(-0.411348\pi\)
0.274922 + 0.961466i \(0.411348\pi\)
\(600\) 1.82176e16 0.0159407
\(601\) 1.31450e18 1.13783 0.568913 0.822398i \(-0.307364\pi\)
0.568913 + 0.822398i \(0.307364\pi\)
\(602\) 2.88825e18 2.47319
\(603\) −1.26168e18 −1.06877
\(604\) 6.47630e17 0.542733
\(605\) −1.30376e18 −1.08090
\(606\) 7.83170e17 0.642368
\(607\) −6.74618e16 −0.0547434 −0.0273717 0.999625i \(-0.508714\pi\)
−0.0273717 + 0.999625i \(0.508714\pi\)
\(608\) −3.18362e18 −2.55592
\(609\) 3.60063e17 0.286000
\(610\) 2.70112e18 2.12275
\(611\) 1.52685e18 1.18721
\(612\) 1.97243e16 0.0151746
\(613\) −1.81911e18 −1.38473 −0.692367 0.721546i \(-0.743432\pi\)
−0.692367 + 0.721546i \(0.743432\pi\)
\(614\) −2.23556e17 −0.168381
\(615\) −4.83820e17 −0.360575
\(616\) −7.16918e16 −0.0528682
\(617\) 1.86705e17 0.136239 0.0681197 0.997677i \(-0.478300\pi\)
0.0681197 + 0.997677i \(0.478300\pi\)
\(618\) −2.79692e17 −0.201955
\(619\) −8.32368e16 −0.0594739 −0.0297369 0.999558i \(-0.509467\pi\)
−0.0297369 + 0.999558i \(0.509467\pi\)
\(620\) 1.25677e18 0.888610
\(621\) 1.01942e18 0.713277
\(622\) −1.80688e18 −1.25110
\(623\) 1.74755e18 1.19745
\(624\) −2.43181e17 −0.164903
\(625\) −1.86132e18 −1.24911
\(626\) 3.11868e18 2.07128
\(627\) −2.70363e17 −0.177708
\(628\) 1.64937e17 0.107295
\(629\) −2.55533e16 −0.0164519
\(630\) −3.57476e18 −2.27789
\(631\) −6.61200e17 −0.417005 −0.208503 0.978022i \(-0.566859\pi\)
−0.208503 + 0.978022i \(0.566859\pi\)
\(632\) −8.98570e16 −0.0560907
\(633\) −1.14662e17 −0.0708430
\(634\) 3.02339e18 1.84890
\(635\) −1.75644e18 −1.06317
\(636\) 8.38944e15 0.00502645
\(637\) −9.98062e17 −0.591904
\(638\) 6.40123e17 0.375776
\(639\) −1.35843e18 −0.789372
\(640\) 4.60085e17 0.264648
\(641\) 3.30693e18 1.88299 0.941495 0.337027i \(-0.109421\pi\)
0.941495 + 0.337027i \(0.109421\pi\)
\(642\) −1.05030e18 −0.592018
\(643\) −2.70105e18 −1.50717 −0.753584 0.657351i \(-0.771677\pi\)
−0.753584 + 0.657351i \(0.771677\pi\)
\(644\) −3.57338e18 −1.97388
\(645\) −7.84856e17 −0.429192
\(646\) −7.27733e16 −0.0393968
\(647\) −2.86266e18 −1.53424 −0.767118 0.641507i \(-0.778310\pi\)
−0.767118 + 0.641507i \(0.778310\pi\)
\(648\) −1.55731e17 −0.0826299
\(649\) 1.24723e18 0.655173
\(650\) 9.37730e17 0.487687
\(651\) 5.05462e17 0.260263
\(652\) −8.07355e17 −0.411581
\(653\) −3.82428e18 −1.93025 −0.965126 0.261784i \(-0.915689\pi\)
−0.965126 + 0.261784i \(0.915689\pi\)
\(654\) 2.00083e17 0.0999894
\(655\) −2.09187e18 −1.03506
\(656\) −1.95187e18 −0.956260
\(657\) −1.51051e18 −0.732738
\(658\) −7.73055e18 −3.71315
\(659\) −7.48217e17 −0.355854 −0.177927 0.984044i \(-0.556939\pi\)
−0.177927 + 0.984044i \(0.556939\pi\)
\(660\) 2.81029e17 0.132348
\(661\) 2.00527e18 0.935110 0.467555 0.883964i \(-0.345135\pi\)
0.467555 + 0.883964i \(0.345135\pi\)
\(662\) 2.57881e18 1.19081
\(663\) −6.00887e15 −0.00274761
\(664\) −2.67392e17 −0.121075
\(665\) 6.83135e18 3.06314
\(666\) 3.20758e18 1.42428
\(667\) 2.21180e18 0.972586
\(668\) 2.17462e18 0.946970
\(669\) −6.09444e17 −0.262824
\(670\) −4.83863e18 −2.06651
\(671\) 1.00034e18 0.423109
\(672\) 1.33093e18 0.557515
\(673\) 9.39797e17 0.389885 0.194942 0.980815i \(-0.437548\pi\)
0.194942 + 0.980815i \(0.437548\pi\)
\(674\) −5.38130e18 −2.21105
\(675\) 7.01548e17 0.285485
\(676\) −1.57699e18 −0.635586
\(677\) 7.53077e16 0.0300617 0.0150308 0.999887i \(-0.495215\pi\)
0.0150308 + 0.999887i \(0.495215\pi\)
\(678\) 1.51378e18 0.598509
\(679\) −5.60142e18 −2.19354
\(680\) 5.24384e15 0.00203396
\(681\) 5.25187e17 0.201771
\(682\) 8.98613e17 0.341959
\(683\) 3.21238e18 1.21085 0.605427 0.795901i \(-0.293002\pi\)
0.605427 + 0.795901i \(0.293002\pi\)
\(684\) 4.73145e18 1.76656
\(685\) −1.73812e18 −0.642821
\(686\) −4.03099e17 −0.147674
\(687\) −1.99787e17 −0.0725017
\(688\) −3.16634e18 −1.13824
\(689\) 2.99360e16 0.0106603
\(690\) 1.87475e18 0.661340
\(691\) −1.98052e18 −0.692105 −0.346052 0.938215i \(-0.612478\pi\)
−0.346052 + 0.938215i \(0.612478\pi\)
\(692\) −1.31934e18 −0.456739
\(693\) −1.32389e18 −0.454032
\(694\) 6.50105e18 2.20875
\(695\) 2.01178e18 0.677141
\(696\) 6.62999e16 0.0221082
\(697\) −4.82297e16 −0.0159331
\(698\) 1.13310e18 0.370859
\(699\) 2.55038e17 0.0826996
\(700\) −2.45914e18 −0.790034
\(701\) −2.04579e18 −0.651168 −0.325584 0.945513i \(-0.605561\pi\)
−0.325584 + 0.945513i \(0.605561\pi\)
\(702\) 1.57293e18 0.496040
\(703\) −6.12968e18 −1.91526
\(704\) 1.31098e18 0.405858
\(705\) 2.10071e18 0.644371
\(706\) −7.54497e18 −2.29312
\(707\) −7.32862e18 −2.20697
\(708\) 1.86348e18 0.556042
\(709\) −2.92951e18 −0.866151 −0.433076 0.901358i \(-0.642572\pi\)
−0.433076 + 0.901358i \(0.642572\pi\)
\(710\) −5.20969e18 −1.52627
\(711\) −1.65934e18 −0.481707
\(712\) 3.21784e17 0.0925645
\(713\) 3.10495e18 0.885061
\(714\) 3.04234e16 0.00859349
\(715\) 1.00279e18 0.280687
\(716\) −3.41802e17 −0.0948068
\(717\) −3.07794e17 −0.0846031
\(718\) 4.87458e18 1.32779
\(719\) 3.18410e18 0.859506 0.429753 0.902946i \(-0.358601\pi\)
0.429753 + 0.902946i \(0.358601\pi\)
\(720\) 3.91894e18 1.04835
\(721\) 2.61726e18 0.693853
\(722\) −1.19747e19 −3.14609
\(723\) 1.67392e18 0.435849
\(724\) 1.18301e18 0.305272
\(725\) 1.52212e18 0.389272
\(726\) −1.39280e18 −0.353022
\(727\) −5.57646e18 −1.40083 −0.700415 0.713736i \(-0.747002\pi\)
−0.700415 + 0.713736i \(0.747002\pi\)
\(728\) −3.82214e17 −0.0951597
\(729\) −2.26333e18 −0.558494
\(730\) −5.79293e18 −1.41677
\(731\) −7.82386e16 −0.0189652
\(732\) 1.49460e18 0.359091
\(733\) −3.54256e18 −0.843610 −0.421805 0.906687i \(-0.638603\pi\)
−0.421805 + 0.906687i \(0.638603\pi\)
\(734\) −8.53990e18 −2.01571
\(735\) −1.37318e18 −0.321262
\(736\) 8.17567e18 1.89591
\(737\) −1.79196e18 −0.411898
\(738\) 6.05405e18 1.37937
\(739\) 6.53089e18 1.47497 0.737486 0.675363i \(-0.236013\pi\)
0.737486 + 0.675363i \(0.236013\pi\)
\(740\) 6.37152e18 1.42638
\(741\) −1.44140e18 −0.319864
\(742\) −1.51568e17 −0.0333414
\(743\) 1.75730e18 0.383193 0.191596 0.981474i \(-0.438634\pi\)
0.191596 + 0.981474i \(0.438634\pi\)
\(744\) 9.30727e16 0.0201186
\(745\) 5.40715e18 1.15865
\(746\) −8.98193e18 −1.90795
\(747\) −4.93778e18 −1.03980
\(748\) 2.80145e16 0.00584820
\(749\) 9.82830e18 2.03398
\(750\) −1.14508e18 −0.234930
\(751\) −1.77683e18 −0.361399 −0.180700 0.983538i \(-0.557836\pi\)
−0.180700 + 0.983538i \(0.557836\pi\)
\(752\) 8.47487e18 1.70890
\(753\) −6.02307e17 −0.120407
\(754\) 3.41272e18 0.676374
\(755\) 3.17949e18 0.624744
\(756\) −4.12490e18 −0.803567
\(757\) −8.48499e18 −1.63881 −0.819404 0.573216i \(-0.805696\pi\)
−0.819404 + 0.573216i \(0.805696\pi\)
\(758\) −1.00260e19 −1.91990
\(759\) 6.94304e17 0.131819
\(760\) 1.25788e18 0.236784
\(761\) 4.01095e18 0.748595 0.374298 0.927309i \(-0.377884\pi\)
0.374298 + 0.927309i \(0.377884\pi\)
\(762\) −1.87640e18 −0.347231
\(763\) −1.87230e18 −0.343531
\(764\) 1.43697e18 0.261421
\(765\) 9.68351e16 0.0174676
\(766\) −1.00931e19 −1.80525
\(767\) 6.64943e18 1.17927
\(768\) −1.33144e18 −0.234138
\(769\) 4.76798e18 0.831406 0.415703 0.909500i \(-0.363536\pi\)
0.415703 + 0.909500i \(0.363536\pi\)
\(770\) −5.07723e18 −0.877885
\(771\) −7.35742e16 −0.0126146
\(772\) 3.98243e18 0.677073
\(773\) −9.55748e16 −0.0161130 −0.00805650 0.999968i \(-0.502564\pi\)
−0.00805650 + 0.999968i \(0.502564\pi\)
\(774\) 9.82092e18 1.64186
\(775\) 2.13678e18 0.354240
\(776\) −1.03141e18 −0.169563
\(777\) 2.56256e18 0.417770
\(778\) −2.62869e18 −0.424984
\(779\) −1.15693e19 −1.85487
\(780\) 1.49827e18 0.238218
\(781\) −1.92938e18 −0.304219
\(782\) 1.86885e17 0.0292234
\(783\) 2.55317e18 0.395940
\(784\) −5.53981e18 −0.852002
\(785\) 8.09744e17 0.123508
\(786\) −2.23474e18 −0.338050
\(787\) −1.89933e18 −0.284948 −0.142474 0.989799i \(-0.545506\pi\)
−0.142474 + 0.989799i \(0.545506\pi\)
\(788\) −5.14503e17 −0.0765539
\(789\) 3.11193e16 0.00459229
\(790\) −6.36370e18 −0.931394
\(791\) −1.41654e19 −2.05628
\(792\) −2.43774e17 −0.0350972
\(793\) 5.33318e18 0.761571
\(794\) 1.19440e17 0.0169167
\(795\) 4.11873e16 0.00578598
\(796\) −9.87794e18 −1.37636
\(797\) −2.00304e18 −0.276828 −0.138414 0.990374i \(-0.544201\pi\)
−0.138414 + 0.990374i \(0.544201\pi\)
\(798\) 7.29793e18 1.00042
\(799\) 2.09409e17 0.0284736
\(800\) 5.62636e18 0.758826
\(801\) 5.94220e18 0.794943
\(802\) 8.39692e18 1.11426
\(803\) −2.14538e18 −0.282392
\(804\) −2.67735e18 −0.349576
\(805\) −1.75432e19 −2.27215
\(806\) 4.79082e18 0.615506
\(807\) 3.39524e18 0.432706
\(808\) −1.34945e18 −0.170601
\(809\) 1.82735e18 0.229170 0.114585 0.993413i \(-0.463446\pi\)
0.114585 + 0.993413i \(0.463446\pi\)
\(810\) −1.10289e19 −1.37208
\(811\) −9.26601e18 −1.14356 −0.571778 0.820409i \(-0.693746\pi\)
−0.571778 + 0.820409i \(0.693746\pi\)
\(812\) −8.94965e18 −1.09570
\(813\) −2.29865e18 −0.279181
\(814\) 4.55573e18 0.548908
\(815\) −3.96364e18 −0.473773
\(816\) −3.33526e16 −0.00395498
\(817\) −1.87678e19 −2.20785
\(818\) 7.65307e18 0.893181
\(819\) −7.05814e18 −0.817231
\(820\) 1.20257e19 1.38140
\(821\) 4.51238e18 0.514251 0.257125 0.966378i \(-0.417225\pi\)
0.257125 + 0.966378i \(0.417225\pi\)
\(822\) −1.85683e18 −0.209945
\(823\) −1.65659e19 −1.85830 −0.929152 0.369698i \(-0.879461\pi\)
−0.929152 + 0.369698i \(0.879461\pi\)
\(824\) 4.81926e17 0.0536357
\(825\) 4.77808e17 0.0527598
\(826\) −3.36666e19 −3.68833
\(827\) −7.96052e18 −0.865278 −0.432639 0.901567i \(-0.642418\pi\)
−0.432639 + 0.901567i \(0.642418\pi\)
\(828\) −1.21506e19 −1.31039
\(829\) 2.51596e18 0.269215 0.134608 0.990899i \(-0.457023\pi\)
0.134608 + 0.990899i \(0.457023\pi\)
\(830\) −1.89368e19 −2.01047
\(831\) −4.10298e18 −0.432208
\(832\) 6.98931e18 0.730521
\(833\) −1.36886e17 −0.0141960
\(834\) 2.14918e18 0.221153
\(835\) 1.06761e19 1.09006
\(836\) 6.72007e18 0.680822
\(837\) 3.58418e18 0.360308
\(838\) 2.20615e19 2.20064
\(839\) −1.07160e19 −1.06067 −0.530334 0.847789i \(-0.677934\pi\)
−0.530334 + 0.847789i \(0.677934\pi\)
\(840\) −5.25868e17 −0.0516489
\(841\) −4.72110e18 −0.460118
\(842\) 1.60990e19 1.55694
\(843\) −5.14497e18 −0.493746
\(844\) 2.85002e18 0.271408
\(845\) −7.74209e18 −0.731627
\(846\) −2.62862e19 −2.46502
\(847\) 1.30333e19 1.21287
\(848\) 1.66162e17 0.0153447
\(849\) 5.34605e18 0.489929
\(850\) 1.28611e17 0.0116965
\(851\) 1.57413e19 1.42069
\(852\) −2.88267e18 −0.258189
\(853\) −5.39090e17 −0.0479174 −0.0239587 0.999713i \(-0.507627\pi\)
−0.0239587 + 0.999713i \(0.507627\pi\)
\(854\) −2.70024e19 −2.38191
\(855\) 2.32287e19 2.03350
\(856\) 1.80972e18 0.157229
\(857\) 1.40302e19 1.20973 0.604867 0.796327i \(-0.293226\pi\)
0.604867 + 0.796327i \(0.293226\pi\)
\(858\) 1.07128e18 0.0916721
\(859\) −5.15612e18 −0.437893 −0.218946 0.975737i \(-0.570262\pi\)
−0.218946 + 0.975737i \(0.570262\pi\)
\(860\) 1.95082e19 1.64429
\(861\) 4.83662e18 0.404596
\(862\) 2.89831e18 0.240629
\(863\) 7.53893e18 0.621212 0.310606 0.950539i \(-0.399468\pi\)
0.310606 + 0.950539i \(0.399468\pi\)
\(864\) 9.43752e18 0.771824
\(865\) −6.47720e18 −0.525754
\(866\) 2.93843e19 2.36728
\(867\) 3.50669e18 0.280397
\(868\) −1.25636e19 −0.997097
\(869\) −2.35676e18 −0.185647
\(870\) 4.69538e18 0.367109
\(871\) −9.55357e18 −0.741392
\(872\) −3.44754e17 −0.0265553
\(873\) −1.90465e19 −1.45621
\(874\) 4.48298e19 3.40206
\(875\) 1.07153e19 0.807143
\(876\) −3.20539e18 −0.239665
\(877\) 1.36024e19 1.00953 0.504766 0.863256i \(-0.331579\pi\)
0.504766 + 0.863256i \(0.331579\pi\)
\(878\) −6.86384e18 −0.505654
\(879\) 2.66022e18 0.194531
\(880\) 5.56608e18 0.404028
\(881\) 2.72051e19 1.96023 0.980113 0.198438i \(-0.0635870\pi\)
0.980113 + 0.198438i \(0.0635870\pi\)
\(882\) 1.71826e19 1.22898
\(883\) 7.54359e18 0.535591 0.267796 0.963476i \(-0.413705\pi\)
0.267796 + 0.963476i \(0.413705\pi\)
\(884\) 1.49355e17 0.0105264
\(885\) 9.14859e18 0.640063
\(886\) −9.94633e18 −0.690786
\(887\) −1.91787e19 −1.32225 −0.661127 0.750274i \(-0.729921\pi\)
−0.661127 + 0.750274i \(0.729921\pi\)
\(888\) 4.71854e17 0.0322941
\(889\) 1.75587e19 1.19297
\(890\) 2.27888e19 1.53705
\(891\) −4.08449e18 −0.273485
\(892\) 1.51482e19 1.00691
\(893\) 5.02328e19 3.31477
\(894\) 5.77645e18 0.378414
\(895\) −1.67805e18 −0.109133
\(896\) −4.59935e18 −0.296957
\(897\) 3.70158e18 0.237266
\(898\) 9.20727e18 0.585915
\(899\) 7.77646e18 0.491297
\(900\) −8.36181e18 −0.524474
\(901\) 4.10577e15 0.000255672 0
\(902\) 8.59857e18 0.531599
\(903\) 7.84600e18 0.481590
\(904\) −2.60834e18 −0.158953
\(905\) 5.80788e18 0.351400
\(906\) 3.39664e18 0.204040
\(907\) −2.12971e19 −1.27021 −0.635103 0.772428i \(-0.719042\pi\)
−0.635103 + 0.772428i \(0.719042\pi\)
\(908\) −1.30539e19 −0.773007
\(909\) −2.49195e19 −1.46512
\(910\) −2.70685e19 −1.58014
\(911\) −7.70001e18 −0.446295 −0.223147 0.974785i \(-0.571633\pi\)
−0.223147 + 0.974785i \(0.571633\pi\)
\(912\) −8.00058e18 −0.460421
\(913\) −7.01313e18 −0.400730
\(914\) 1.79102e19 1.01613
\(915\) 7.33764e18 0.413351
\(916\) 4.96586e18 0.277763
\(917\) 2.09119e19 1.16143
\(918\) 2.15729e17 0.0118968
\(919\) −1.27519e19 −0.698274 −0.349137 0.937072i \(-0.613525\pi\)
−0.349137 + 0.937072i \(0.613525\pi\)
\(920\) −3.23031e18 −0.175640
\(921\) −6.07295e17 −0.0327878
\(922\) 2.27218e19 1.21812
\(923\) −1.02862e19 −0.547575
\(924\) −2.80938e18 −0.148505
\(925\) 1.08329e19 0.568622
\(926\) −4.40675e19 −2.29693
\(927\) 8.89946e18 0.460623
\(928\) 2.04762e19 1.05242
\(929\) 1.83918e19 0.938690 0.469345 0.883015i \(-0.344490\pi\)
0.469345 + 0.883015i \(0.344490\pi\)
\(930\) 6.59144e18 0.334073
\(931\) −3.28360e19 −1.65264
\(932\) −6.33917e18 −0.316832
\(933\) −4.90841e18 −0.243619
\(934\) 4.08266e19 2.01228
\(935\) 1.37535e17 0.00673190
\(936\) −1.29964e18 −0.0631729
\(937\) −2.05015e19 −0.989644 −0.494822 0.868994i \(-0.664767\pi\)
−0.494822 + 0.868994i \(0.664767\pi\)
\(938\) 4.83706e19 2.31880
\(939\) 8.47197e18 0.403328
\(940\) −5.22147e19 −2.46866
\(941\) −1.54458e19 −0.725234 −0.362617 0.931938i \(-0.618117\pi\)
−0.362617 + 0.931938i \(0.618117\pi\)
\(942\) 8.65048e17 0.0403376
\(943\) 2.97104e19 1.37589
\(944\) 3.69081e19 1.69748
\(945\) −2.02509e19 −0.924991
\(946\) 1.39487e19 0.632762
\(947\) 1.02449e19 0.461563 0.230782 0.973006i \(-0.425872\pi\)
0.230782 + 0.973006i \(0.425872\pi\)
\(948\) −3.52121e18 −0.157557
\(949\) −1.14378e19 −0.508289
\(950\) 3.08511e19 1.36165
\(951\) 8.21311e18 0.360026
\(952\) −5.24213e16 −0.00228227
\(953\) 3.86166e19 1.66982 0.834911 0.550385i \(-0.185519\pi\)
0.834911 + 0.550385i \(0.185519\pi\)
\(954\) −5.15378e17 −0.0221341
\(955\) 7.05468e18 0.300923
\(956\) 7.65047e18 0.324124
\(957\) 1.73891e18 0.0731727
\(958\) 6.45509e19 2.69790
\(959\) 1.73755e19 0.721301
\(960\) 9.61621e18 0.396498
\(961\) −1.35008e19 −0.552916
\(962\) 2.42882e19 0.988002
\(963\) 3.34192e19 1.35028
\(964\) −4.16066e19 −1.66979
\(965\) 1.95514e19 0.779382
\(966\) −1.87414e19 −0.742080
\(967\) 3.72062e19 1.46333 0.731667 0.681662i \(-0.238742\pi\)
0.731667 + 0.681662i \(0.238742\pi\)
\(968\) 2.39988e18 0.0937562
\(969\) −1.97690e17 −0.00767151
\(970\) −7.30449e19 −2.81562
\(971\) 1.13456e19 0.434411 0.217206 0.976126i \(-0.430306\pi\)
0.217206 + 0.976126i \(0.430306\pi\)
\(972\) −2.13260e19 −0.811107
\(973\) −2.01112e19 −0.759810
\(974\) −2.77981e18 −0.104323
\(975\) 2.54736e18 0.0949644
\(976\) 2.96022e19 1.09623
\(977\) −2.40491e19 −0.884677 −0.442338 0.896848i \(-0.645851\pi\)
−0.442338 + 0.896848i \(0.645851\pi\)
\(978\) −4.23435e18 −0.154734
\(979\) 8.43971e18 0.306366
\(980\) 3.41315e19 1.23079
\(981\) −6.36638e18 −0.228057
\(982\) −3.07868e19 −1.09557
\(983\) −5.06524e19 −1.79062 −0.895308 0.445448i \(-0.853045\pi\)
−0.895308 + 0.445448i \(0.853045\pi\)
\(984\) 8.90586e17 0.0312758
\(985\) −2.52591e18 −0.0881217
\(986\) 4.68060e17 0.0162219
\(987\) −2.10002e19 −0.723040
\(988\) 3.58271e19 1.22544
\(989\) 4.81965e19 1.63772
\(990\) −1.72641e19 −0.582795
\(991\) −9.17044e18 −0.307547 −0.153774 0.988106i \(-0.549143\pi\)
−0.153774 + 0.988106i \(0.549143\pi\)
\(992\) 2.87448e19 0.957709
\(993\) 7.00539e18 0.231880
\(994\) 5.20799e19 1.71261
\(995\) −4.84950e19 −1.58433
\(996\) −1.04783e19 −0.340097
\(997\) 1.48626e19 0.479267 0.239633 0.970863i \(-0.422973\pi\)
0.239633 + 0.970863i \(0.422973\pi\)
\(998\) 3.71215e19 1.18926
\(999\) 1.81709e19 0.578362
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 197.14.a.a.1.19 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.14.a.a.1.19 104 1.1 even 1 trivial