Properties

Label 197.14.a.a.1.10
Level 197197
Weight 1414
Character 197.1
Self dual yes
Analytic conductor 211.245211.245
Analytic rank 11
Dimension 104104
CM no
Inner twists 11

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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 N == 197 197
Weight: k k == 14 14
Character orbit: [χ][\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: 211.244930035211.244930035
Analytic rank: 11
Dimension: 104104
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.10
Character χ\chi == 197.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q156.182q2+145.398q3+16200.7q442219.2q522708.4q6+140720.q71.25081e6q81.57318e6q9+6.59387e6q10+1.01012e7q11+2.35555e6q12+2.70916e7q132.19779e7q146.13857e6q15+6.26381e7q167.94734e7q17+2.45702e8q183.02415e8q196.83982e8q20+2.04604e7q211.57763e9q22+1.22651e9q231.81865e8q24+5.61759e8q254.23121e9q264.60548e8q27+2.27977e9q282.20816e9q29+9.58733e8q306.83081e8q31+4.63754e8q32+1.46869e9q33+1.24123e10q345.94110e9q352.54867e10q36+2.15026e10q37+4.72317e10q38+3.93906e9q39+5.28084e10q402.01349e10q413.19554e9q427.18113e10q43+1.63647e11q44+6.64185e10q451.91558e11q46+1.65782e10q47+9.10743e9q487.70868e10q498.77365e10q501.15552e10q51+4.38904e11q52+2.28728e11q53+7.19291e10q544.26466e11q551.76015e11q564.39705e10q57+3.44874e11q585.15415e11q599.94493e10q60+1.40601e11q61+1.06685e11q622.21379e11q635.85561e11q641.14379e12q652.29383e11q66+2.53048e11q671.28753e12q68+1.78331e11q69+9.27892e11q701.59034e12q71+1.96776e12q72+1.28348e12q733.35832e12q74+8.16784e10q754.89934e12q76+1.42145e12q776.15208e11q782.01437e12q792.64453e12q80+2.44120e12q81+3.14469e12q82+1.86340e12q83+3.31473e11q84+3.35530e12q85+1.12156e13q863.21061e11q871.26348e13q88+4.05006e12q891.03734e13q90+3.81234e12q91+1.98703e13q929.93184e10q932.58921e12q94+1.27677e13q95+6.74287e10q96+4.35140e12q97+1.20395e13q981.58911e13q99+O(q100)q-156.182 q^{2} +145.398 q^{3} +16200.7 q^{4} -42219.2 q^{5} -22708.4 q^{6} +140720. q^{7} -1.25081e6 q^{8} -1.57318e6 q^{9} +6.59387e6 q^{10} +1.01012e7 q^{11} +2.35555e6 q^{12} +2.70916e7 q^{13} -2.19779e7 q^{14} -6.13857e6 q^{15} +6.26381e7 q^{16} -7.94734e7 q^{17} +2.45702e8 q^{18} -3.02415e8 q^{19} -6.83982e8 q^{20} +2.04604e7 q^{21} -1.57763e9 q^{22} +1.22651e9 q^{23} -1.81865e8 q^{24} +5.61759e8 q^{25} -4.23121e9 q^{26} -4.60548e8 q^{27} +2.27977e9 q^{28} -2.20816e9 q^{29} +9.58733e8 q^{30} -6.83081e8 q^{31} +4.63754e8 q^{32} +1.46869e9 q^{33} +1.24123e10 q^{34} -5.94110e9 q^{35} -2.54867e10 q^{36} +2.15026e10 q^{37} +4.72317e10 q^{38} +3.93906e9 q^{39} +5.28084e10 q^{40} -2.01349e10 q^{41} -3.19554e9 q^{42} -7.18113e10 q^{43} +1.63647e11 q^{44} +6.64185e10 q^{45} -1.91558e11 q^{46} +1.65782e10 q^{47} +9.10743e9 q^{48} -7.70868e10 q^{49} -8.77365e10 q^{50} -1.15552e10 q^{51} +4.38904e11 q^{52} +2.28728e11 q^{53} +7.19291e10 q^{54} -4.26466e11 q^{55} -1.76015e11 q^{56} -4.39705e10 q^{57} +3.44874e11 q^{58} -5.15415e11 q^{59} -9.94493e10 q^{60} +1.40601e11 q^{61} +1.06685e11 q^{62} -2.21379e11 q^{63} -5.85561e11 q^{64} -1.14379e12 q^{65} -2.29383e11 q^{66} +2.53048e11 q^{67} -1.28753e12 q^{68} +1.78331e11 q^{69} +9.27892e11 q^{70} -1.59034e12 q^{71} +1.96776e12 q^{72} +1.28348e12 q^{73} -3.35832e12 q^{74} +8.16784e10 q^{75} -4.89934e12 q^{76} +1.42145e12 q^{77} -6.15208e11 q^{78} -2.01437e12 q^{79} -2.64453e12 q^{80} +2.44120e12 q^{81} +3.14469e12 q^{82} +1.86340e12 q^{83} +3.31473e11 q^{84} +3.35530e12 q^{85} +1.12156e13 q^{86} -3.21061e11 q^{87} -1.26348e13 q^{88} +4.05006e12 q^{89} -1.03734e13 q^{90} +3.81234e12 q^{91} +1.98703e13 q^{92} -9.93184e10 q^{93} -2.58921e12 q^{94} +1.27677e13 q^{95} +6.74287e10 q^{96} +4.35140e12 q^{97} +1.20395e13 q^{98} -1.58911e13 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 104q128q28020q3+409600q499004q583328q62084037q72111301q8+51549776q99626347q1010688800q1168157440q1294762650q1352465903q14+8666459567773q99+O(q100) 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}+ \cdots - 8666459567773 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −156.182 −1.72558 −0.862790 0.505562i 0.831285π-0.831285\pi
−0.862790 + 0.505562i 0.831285π0.831285\pi
33 145.398 0.115151 0.0575757 0.998341i 0.481663π-0.481663\pi
0.0575757 + 0.998341i 0.481663π0.481663\pi
44 16200.7 1.97763
55 −42219.2 −1.20838 −0.604192 0.796839i 0.706504π-0.706504\pi
−0.604192 + 0.796839i 0.706504π0.706504\pi
66 −22708.4 −0.198703
77 140720. 0.452085 0.226042 0.974117i 0.427421π-0.427421\pi
0.226042 + 0.974117i 0.427421π0.427421\pi
88 −1.25081e6 −1.68697
99 −1.57318e6 −0.986740
1010 6.59387e6 2.08516
1111 1.01012e7 1.71918 0.859590 0.510984i 0.170719π-0.170719\pi
0.859590 + 0.510984i 0.170719π0.170719\pi
1212 2.35555e6 0.227726
1313 2.70916e7 1.55669 0.778347 0.627835i 0.216059π-0.216059\pi
0.778347 + 0.627835i 0.216059π0.216059\pi
1414 −2.19779e7 −0.780108
1515 −6.13857e6 −0.139147
1616 6.26381e7 0.933380
1717 −7.94734e7 −0.798553 −0.399276 0.916831i 0.630739π-0.630739\pi
−0.399276 + 0.916831i 0.630739π0.630739\pi
1818 2.45702e8 1.70270
1919 −3.02415e8 −1.47471 −0.737353 0.675508i 0.763924π-0.763924\pi
−0.737353 + 0.675508i 0.763924π0.763924\pi
2020 −6.83982e8 −2.38973
2121 2.04604e7 0.0520582
2222 −1.57763e9 −2.96658
2323 1.22651e9 1.72758 0.863791 0.503850i 0.168084π-0.168084\pi
0.863791 + 0.503850i 0.168084π0.168084\pi
2424 −1.81865e8 −0.194257
2525 5.61759e8 0.460193
2626 −4.23121e9 −2.68620
2727 −4.60548e8 −0.228776
2828 2.27977e9 0.894055
2929 −2.20816e9 −0.689357 −0.344678 0.938721i 0.612012π-0.612012\pi
−0.344678 + 0.938721i 0.612012π0.612012\pi
3030 9.58733e8 0.240110
3131 −6.83081e8 −0.138236 −0.0691181 0.997608i 0.522019π-0.522019\pi
−0.0691181 + 0.997608i 0.522019π0.522019\pi
3232 4.63754e8 0.0763507
3333 1.46869e9 0.197966
3434 1.24123e10 1.37797
3535 −5.94110e9 −0.546292
3636 −2.54867e10 −1.95140
3737 2.15026e10 1.37778 0.688890 0.724865i 0.258098π-0.258098\pi
0.688890 + 0.724865i 0.258098π0.258098\pi
3838 4.72317e10 2.54472
3939 3.93906e9 0.179255
4040 5.28084e10 2.03851
4141 −2.01349e10 −0.661993 −0.330996 0.943632i 0.607385π-0.607385\pi
−0.330996 + 0.943632i 0.607385π0.607385\pi
4242 −3.19554e9 −0.0898305
4343 −7.18113e10 −1.73240 −0.866199 0.499700i 0.833444π-0.833444\pi
−0.866199 + 0.499700i 0.833444π0.833444\pi
4444 1.63647e11 3.39990
4545 6.64185e10 1.19236
4646 −1.91558e11 −2.98108
4747 1.65782e10 0.224337 0.112168 0.993689i 0.464220π-0.464220\pi
0.112168 + 0.993689i 0.464220π0.464220\pi
4848 9.10743e9 0.107480
4949 −7.70868e10 −0.795619
5050 −8.77365e10 −0.794100
5151 −1.15552e10 −0.0919545
5252 4.38904e11 3.07856
5353 2.28728e11 1.41751 0.708754 0.705455i 0.249257π-0.249257\pi
0.708754 + 0.705455i 0.249257π0.249257\pi
5454 7.19291e10 0.394771
5555 −4.26466e11 −2.07743
5656 −1.76015e11 −0.762655
5757 −4.39705e10 −0.169814
5858 3.44874e11 1.18954
5959 −5.15415e11 −1.59081 −0.795407 0.606076i 0.792743π-0.792743\pi
−0.795407 + 0.606076i 0.792743π0.792743\pi
6060 −9.94493e10 −0.275181
6161 1.40601e11 0.349418 0.174709 0.984620i 0.444102π-0.444102\pi
0.174709 + 0.984620i 0.444102π0.444102\pi
6262 1.06685e11 0.238537
6363 −2.21379e11 −0.446090
6464 −5.85561e11 −1.06513
6565 −1.14379e12 −1.88108
6666 −2.29383e11 −0.341606
6767 2.53048e11 0.341757 0.170878 0.985292i 0.445339π-0.445339\pi
0.170878 + 0.985292i 0.445339π0.445339\pi
6868 −1.28753e12 −1.57924
6969 1.78331e11 0.198933
7070 9.27892e11 0.942671
7171 −1.59034e12 −1.47337 −0.736685 0.676236i 0.763610π-0.763610\pi
−0.736685 + 0.676236i 0.763610π0.763610\pi
7272 1.96776e12 1.66460
7373 1.28348e12 0.992634 0.496317 0.868141i 0.334685π-0.334685\pi
0.496317 + 0.868141i 0.334685π0.334685\pi
7474 −3.35832e12 −2.37747
7575 8.16784e10 0.0529919
7676 −4.89934e12 −2.91642
7777 1.42145e12 0.777215
7878 −6.15208e11 −0.309320
7979 −2.01437e12 −0.932315 −0.466157 0.884702i 0.654362π-0.654362\pi
−0.466157 + 0.884702i 0.654362π0.654362\pi
8080 −2.64453e12 −1.12788
8181 2.44120e12 0.960396
8282 3.14469e12 1.14232
8383 1.86340e12 0.625602 0.312801 0.949819i 0.398733π-0.398733\pi
0.312801 + 0.949819i 0.398733π0.398733\pi
8484 3.31473e11 0.102952
8585 3.35530e12 0.964959
8686 1.12156e13 2.98939
8787 −3.21061e11 −0.0793804
8888 −1.26348e13 −2.90021
8989 4.05006e12 0.863826 0.431913 0.901915i 0.357839π-0.357839\pi
0.431913 + 0.901915i 0.357839π0.357839\pi
9090 −1.03734e13 −2.05752
9191 3.81234e12 0.703757
9292 1.98703e13 3.41651
9393 −9.93184e10 −0.0159181
9494 −2.58921e12 −0.387111
9595 1.27677e13 1.78201
9696 6.74287e10 0.00879188
9797 4.35140e12 0.530411 0.265206 0.964192i 0.414560π-0.414560\pi
0.265206 + 0.964192i 0.414560π0.414560\pi
9898 1.20395e13 1.37291
9999 −1.58911e13 −1.69638
100100 9.10090e12 0.910090
101101 −1.38940e13 −1.30238 −0.651192 0.758913i 0.725731π-0.725731\pi
−0.651192 + 0.758913i 0.725731π0.725731\pi
102102 1.80472e12 0.158675
103103 −2.39762e13 −1.97851 −0.989255 0.146203i 0.953295π-0.953295\pi
−0.989255 + 0.146203i 0.953295π0.953295\pi
104104 −3.38866e13 −2.62610
105105 −8.63822e11 −0.0629063
106106 −3.57231e13 −2.44602
107107 3.47469e12 0.223832 0.111916 0.993718i 0.464301π-0.464301\pi
0.111916 + 0.993718i 0.464301π0.464301\pi
108108 −7.46120e12 −0.452433
109109 1.17165e12 0.0669154 0.0334577 0.999440i 0.489348π-0.489348\pi
0.0334577 + 0.999440i 0.489348π0.489348\pi
110110 6.66061e13 3.58477
111111 3.12643e12 0.158653
112112 8.81446e12 0.421967
113113 2.58831e13 1.16952 0.584758 0.811208i 0.301190π-0.301190\pi
0.584758 + 0.811208i 0.301190π0.301190\pi
114114 6.86738e12 0.293028
115115 −5.17821e13 −2.08758
116116 −3.57738e13 −1.36329
117117 −4.26201e13 −1.53605
118118 8.04984e13 2.74508
119119 −1.11835e13 −0.361014
120120 7.67822e12 0.234737
121121 6.75120e13 1.95558
122122 −2.19593e13 −0.602949
123123 −2.92756e12 −0.0762294
124124 −1.10664e13 −0.273379
125125 2.78201e13 0.652294
126126 3.45753e13 0.769764
127127 8.07463e13 1.70765 0.853825 0.520561i 0.174277π-0.174277\pi
0.853825 + 0.520561i 0.174277π0.174277\pi
128128 8.76548e13 1.76162
129129 −1.04412e13 −0.199488
130130 1.78639e14 3.24596
131131 8.22895e13 1.42259 0.711297 0.702892i 0.248108π-0.248108\pi
0.711297 + 0.702892i 0.248108π0.248108\pi
132132 2.37939e13 0.391503
133133 −4.25560e13 −0.666692
134134 −3.95215e13 −0.589728
135135 1.94440e13 0.276449
136136 9.94065e13 1.34714
137137 −4.05438e13 −0.523890 −0.261945 0.965083i 0.584364π-0.584364\pi
−0.261945 + 0.965083i 0.584364π0.584364\pi
138138 −2.78520e13 −0.343276
139139 −1.58298e14 −1.86157 −0.930783 0.365572i 0.880873π-0.880873\pi
−0.930783 + 0.365572i 0.880873π0.880873\pi
140140 −9.62501e13 −1.08036
141141 2.41043e12 0.0258327
142142 2.48383e14 2.54242
143143 2.73658e14 2.67624
144144 −9.85411e13 −0.921004
145145 9.32269e13 0.833008
146146 −2.00455e14 −1.71287
147147 −1.12082e13 −0.0916167
148148 3.48358e14 2.72474
149149 1.91701e14 1.43520 0.717602 0.696454i 0.245240π-0.245240\pi
0.717602 + 0.696454i 0.245240π0.245240\pi
150150 −1.27567e13 −0.0914417
151151 1.41076e14 0.968511 0.484255 0.874927i 0.339091π-0.339091\pi
0.484255 + 0.874927i 0.339091π0.339091\pi
152152 3.78265e14 2.48779
153153 1.25026e14 0.787964
154154 −2.22004e14 −1.34115
155155 2.88392e13 0.167042
156156 6.38155e13 0.354500
157157 4.64114e13 0.247330 0.123665 0.992324i 0.460535π-0.460535\pi
0.123665 + 0.992324i 0.460535π0.460535\pi
158158 3.14607e14 1.60878
159159 3.32565e13 0.163228
160160 −1.95793e13 −0.0922610
161161 1.72594e14 0.781013
162162 −3.81270e14 −1.65724
163163 2.55936e14 1.06884 0.534418 0.845220i 0.320531π-0.320531\pi
0.534418 + 0.845220i 0.320531π0.320531\pi
164164 −3.26199e14 −1.30917
165165 −6.20071e13 −0.239219
166166 −2.91028e14 −1.07953
167167 −9.12125e13 −0.325385 −0.162692 0.986677i 0.552018π-0.552018\pi
−0.162692 + 0.986677i 0.552018π0.552018\pi
168168 −2.55922e13 −0.0878207
169169 4.31081e14 1.42330
170170 −5.24037e14 −1.66511
171171 4.75754e14 1.45515
172172 −1.16339e15 −3.42604
173173 2.19464e13 0.0622392 0.0311196 0.999516i 0.490093π-0.490093\pi
0.0311196 + 0.999516i 0.490093π0.490093\pi
174174 5.01439e13 0.136977
175175 7.90510e13 0.208046
176176 6.32721e14 1.60465
177177 −7.49402e13 −0.183184
178178 −6.32545e14 −1.49060
179179 −1.18994e14 −0.270384 −0.135192 0.990819i 0.543165π-0.543165\pi
−0.135192 + 0.990819i 0.543165π0.543165\pi
180180 1.07603e15 2.35805
181181 −2.24422e14 −0.474412 −0.237206 0.971459i 0.576232π-0.576232\pi
−0.237206 + 0.971459i 0.576232π0.576232\pi
182182 −5.95418e14 −1.21439
183183 2.04431e13 0.0402360
184184 −1.53413e15 −2.91438
185185 −9.07824e14 −1.66489
186186 1.55117e13 0.0274679
187187 −8.02778e14 −1.37286
188188 2.68578e14 0.443655
189189 −6.48085e13 −0.103426
190190 −1.99409e15 −3.07500
191191 1.02189e15 1.52295 0.761474 0.648195i 0.224476π-0.224476\pi
0.761474 + 0.648195i 0.224476π0.224476\pi
192192 −8.51392e13 −0.122651
193193 −1.32634e14 −0.184728 −0.0923640 0.995725i 0.529442π-0.529442\pi
−0.0923640 + 0.995725i 0.529442π0.529442\pi
194194 −6.79609e14 −0.915267
195195 −1.66304e14 −0.216609
196196 −1.24886e15 −1.57344
197197 −5.84517e13 −0.0712470
198198 2.48189e15 2.92725
199199 −1.18083e15 −1.34785 −0.673925 0.738800i 0.735393π-0.735393\pi
−0.673925 + 0.738800i 0.735393π0.735393\pi
200200 −7.02657e14 −0.776333
201201 3.67926e13 0.0393537
202202 2.16999e15 2.24737
203203 −3.10733e14 −0.311648
204204 −1.87203e14 −0.181852
205205 8.50078e14 0.799942
206206 3.74464e15 3.41408
207207 −1.92952e15 −1.70467
208208 1.69697e15 1.45299
209209 −3.05476e15 −2.53529
210210 1.34913e14 0.108550
211211 −2.59301e14 −0.202287 −0.101143 0.994872i 0.532250π-0.532250\pi
−0.101143 + 0.994872i 0.532250π0.532250\pi
212212 3.70555e15 2.80330
213213 −2.31232e14 −0.169661
214214 −5.42683e14 −0.386240
215215 3.03181e15 2.09340
216216 5.76060e14 0.385939
217217 −9.61235e13 −0.0624944
218218 −1.82990e14 −0.115468
219219 1.86614e14 0.114303
220220 −6.90905e15 −4.10838
221221 −2.15306e15 −1.24310
222222 −4.88291e14 −0.273769
223223 −2.70804e15 −1.47460 −0.737299 0.675567i 0.763899π-0.763899\pi
−0.737299 + 0.675567i 0.763899π0.763899\pi
224224 6.52596e13 0.0345170
225225 −8.83750e14 −0.454091
226226 −4.04246e15 −2.01809
227227 6.30594e14 0.305902 0.152951 0.988234i 0.451122π-0.451122\pi
0.152951 + 0.988234i 0.451122π0.451122\pi
228228 −7.12353e14 −0.335829
229229 −1.68684e15 −0.772937 −0.386468 0.922303i 0.626305π-0.626305\pi
−0.386468 + 0.922303i 0.626305π0.626305\pi
230230 8.08742e15 3.60229
231231 2.06675e14 0.0894974
232232 2.76200e15 1.16293
233233 1.12024e15 0.458667 0.229334 0.973348i 0.426345π-0.426345\pi
0.229334 + 0.973348i 0.426345π0.426345\pi
234234 6.65647e15 2.65058
235235 −6.99918e14 −0.271085
236236 −8.35010e15 −3.14603
237237 −2.92884e14 −0.107357
238238 1.74666e15 0.622958
239239 5.25075e15 1.82236 0.911181 0.412006i 0.135172π-0.135172\pi
0.911181 + 0.412006i 0.135172π0.135172\pi
240240 −3.84508e14 −0.129877
241241 2.28199e15 0.750246 0.375123 0.926975i 0.377600π-0.377600\pi
0.375123 + 0.926975i 0.377600π0.377600\pi
242242 −1.05441e16 −3.37451
243243 1.08921e15 0.339367
244244 2.27784e15 0.691018
245245 3.25454e15 0.961414
246246 4.57231e14 0.131540
247247 −8.19292e15 −2.29566
248248 8.54408e14 0.233201
249249 2.70934e14 0.0720389
250250 −4.34499e15 −1.12559
251251 2.18163e15 0.550683 0.275342 0.961346i 0.411209π-0.411209\pi
0.275342 + 0.961346i 0.411209π0.411209\pi
252252 −3.58650e15 −0.882200
253253 1.23892e16 2.97003
254254 −1.26111e16 −2.94669
255255 4.87853e14 0.111116
256256 −8.89316e15 −1.97468
257257 −5.82816e14 −0.126173 −0.0630864 0.998008i 0.520094π-0.520094\pi
−0.0630864 + 0.998008i 0.520094π0.520094\pi
258258 1.63072e15 0.344232
259259 3.02586e15 0.622874
260260 −1.85302e16 −3.72008
261261 3.47384e15 0.680216
262262 −1.28521e16 −2.45480
263263 −8.54114e15 −1.59149 −0.795744 0.605633i 0.792920π-0.792920\pi
−0.795744 + 0.605633i 0.792920π0.792920\pi
264264 −1.83706e15 −0.333963
265265 −9.65671e15 −1.71290
266266 6.64647e15 1.15043
267267 5.88869e14 0.0994707
268268 4.09956e15 0.675867
269269 −2.03560e15 −0.327569 −0.163784 0.986496i 0.552370π-0.552370\pi
−0.163784 + 0.986496i 0.552370π0.552370\pi
270270 −3.03679e15 −0.477035
271271 −9.13857e15 −1.40145 −0.700726 0.713431i 0.747140π-0.747140\pi
−0.700726 + 0.713431i 0.747140π0.747140\pi
272272 −4.97806e15 −0.745353
273273 5.54306e14 0.0810386
274274 6.33219e15 0.904015
275275 5.67445e15 0.791155
276276 2.88909e15 0.393416
277277 −1.68445e15 −0.224048 −0.112024 0.993706i 0.535733π-0.535733\pi
−0.112024 + 0.993706i 0.535733π0.535733\pi
278278 2.47232e16 3.21228
279279 1.07461e15 0.136403
280280 7.43122e15 0.921580
281281 4.98535e15 0.604094 0.302047 0.953293i 0.402330π-0.402330\pi
0.302047 + 0.953293i 0.402330π0.402330\pi
282282 −3.76465e14 −0.0445764
283283 4.42735e15 0.512309 0.256154 0.966636i 0.417544π-0.417544\pi
0.256154 + 0.966636i 0.417544π0.417544\pi
284284 −2.57647e16 −2.91378
285285 1.85640e15 0.205201
286286 −4.27404e16 −4.61806
287287 −2.83338e15 −0.299277
288288 −7.29570e14 −0.0753383
289289 −3.58856e15 −0.362313
290290 −1.45603e16 −1.43742
291291 6.32683e14 0.0610776
292292 2.07932e16 1.96306
293293 1.20468e16 1.11233 0.556165 0.831072i 0.312272π-0.312272\pi
0.556165 + 0.831072i 0.312272π0.312272\pi
294294 1.75052e15 0.158092
295295 2.17604e16 1.92231
296296 −2.68958e16 −2.32428
297297 −4.65210e15 −0.393307
298298 −2.99402e16 −2.47656
299299 3.32280e16 2.68932
300300 1.32325e15 0.104798
301301 −1.01053e16 −0.783190
302302 −2.20336e16 −1.67124
303303 −2.02016e15 −0.149971
304304 −1.89427e16 −1.37646
305305 −5.93608e15 −0.422231
306306 −1.95268e16 −1.35970
307307 −9.26126e14 −0.0631351 −0.0315675 0.999502i 0.510050π-0.510050\pi
−0.0315675 + 0.999502i 0.510050π0.510050\pi
308308 2.30285e16 1.53704
309309 −3.48608e15 −0.227828
310310 −4.50415e15 −0.288245
311311 −2.90105e16 −1.81808 −0.909038 0.416712i 0.863182π-0.863182\pi
−0.909038 + 0.416712i 0.863182π0.863182\pi
312312 −4.92703e15 −0.302399
313313 −5.07394e15 −0.305005 −0.152503 0.988303i 0.548733π-0.548733\pi
−0.152503 + 0.988303i 0.548733π0.548733\pi
314314 −7.24860e15 −0.426788
315315 9.34644e15 0.539048
316316 −3.26342e16 −1.84377
317317 9.04960e15 0.500892 0.250446 0.968131i 0.419423π-0.419423\pi
0.250446 + 0.968131i 0.419423π0.419423\pi
318318 −5.19405e15 −0.281663
319319 −2.23051e16 −1.18513
320320 2.47219e16 1.28709
321321 5.05212e14 0.0257745
322322 −2.69561e16 −1.34770
323323 2.40340e16 1.17763
324324 3.95492e16 1.89931
325325 1.52190e16 0.716380
326326 −3.99724e16 −1.84436
327327 1.70355e14 0.00770540
328328 2.51850e16 1.11676
329329 2.33289e15 0.101419
330330 9.68437e15 0.412792
331331 −3.09772e16 −1.29467 −0.647337 0.762204i 0.724117π-0.724117\pi
−0.647337 + 0.762204i 0.724117π0.724117\pi
332332 3.01884e16 1.23721
333333 −3.38275e16 −1.35951
334334 1.42457e16 0.561478
335335 −1.06835e16 −0.412973
336336 1.28160e15 0.0485901
337337 2.94553e16 1.09539 0.547696 0.836678i 0.315505π-0.315505\pi
0.547696 + 0.836678i 0.315505π0.315505\pi
338338 −6.73269e16 −2.45601
339339 3.76334e15 0.134671
340340 5.43583e16 1.90833
341341 −6.89996e15 −0.237653
342342 −7.43041e16 −2.51098
343343 −2.44819e16 −0.811772
344344 8.98226e16 2.92251
345345 −7.52900e15 −0.240388
346346 −3.42763e15 −0.107399
347347 −5.52018e16 −1.69751 −0.848753 0.528790i 0.822646π-0.822646\pi
−0.848753 + 0.528790i 0.822646π0.822646\pi
348348 −5.20143e15 −0.156985
349349 1.30873e16 0.387689 0.193845 0.981032i 0.437904π-0.437904\pi
0.193845 + 0.981032i 0.437904π0.437904\pi
350350 −1.23463e16 −0.359000
351351 −1.24770e16 −0.356134
352352 4.68448e15 0.131261
353353 6.32311e16 1.73938 0.869692 0.493595i 0.164318π-0.164318\pi
0.869692 + 0.493595i 0.164318π0.164318\pi
354354 1.17043e16 0.316099
355355 6.71431e16 1.78040
356356 6.56138e16 1.70832
357357 −1.62606e15 −0.0415712
358358 1.85847e16 0.466569
359359 −3.74200e14 −0.00922550 −0.00461275 0.999989i 0.501468π-0.501468\pi
−0.00461275 + 0.999989i 0.501468π0.501468\pi
360360 −8.30773e16 −2.01148
361361 4.94020e16 1.17476
362362 3.50507e16 0.818635
363363 9.81608e15 0.225188
364364 6.17627e16 1.39177
365365 −5.41873e16 −1.19948
366366 −3.19284e15 −0.0694304
367367 −3.98708e16 −0.851775 −0.425888 0.904776i 0.640038π-0.640038\pi
−0.425888 + 0.904776i 0.640038π0.640038\pi
368368 7.68260e16 1.61249
369369 3.16758e16 0.653215
370370 1.41785e17 2.87290
371371 3.21867e16 0.640834
372372 −1.60903e15 −0.0314800
373373 −5.55924e16 −1.06883 −0.534414 0.845223i 0.679468π-0.679468\pi
−0.534414 + 0.845223i 0.679468π0.679468\pi
374374 1.25379e17 2.36897
375375 4.04498e15 0.0751126
376376 −2.07362e16 −0.378450
377377 −5.98227e16 −1.07312
378378 1.01219e16 0.178470
379379 −4.87769e16 −0.845394 −0.422697 0.906271i 0.638917π-0.638917\pi
−0.422697 + 0.906271i 0.638917π0.638917\pi
380380 2.06846e17 3.52415
381381 1.17403e16 0.196638
382382 −1.59600e17 −2.62797
383383 −3.53081e16 −0.571587 −0.285793 0.958291i 0.592257π-0.592257\pi
−0.285793 + 0.958291i 0.592257π0.592257\pi
384384 1.27448e16 0.202852
385385 −6.00124e16 −0.939175
386386 2.07150e16 0.318763
387387 1.12972e17 1.70943
388388 7.04958e16 1.04896
389389 4.31504e16 0.631411 0.315706 0.948857i 0.397759π-0.397759\pi
0.315706 + 0.948857i 0.397759π0.397759\pi
390390 2.59736e16 0.373777
391391 −9.74746e16 −1.37957
392392 9.64213e16 1.34219
393393 1.19647e16 0.163814
394394 9.12909e15 0.122942
395395 8.50450e16 1.12659
396396 −2.57447e17 −3.35481
397397 8.33842e15 0.106892 0.0534460 0.998571i 0.482979π-0.482979\pi
0.0534460 + 0.998571i 0.482979π0.482979\pi
398398 1.84424e17 2.32582
399399 −6.18754e15 −0.0767705
400400 3.51875e16 0.429535
401401 6.03120e16 0.724378 0.362189 0.932105i 0.382030π-0.382030\pi
0.362189 + 0.932105i 0.382030π0.382030\pi
402402 −5.74633e15 −0.0679080
403403 −1.85058e16 −0.215191
404404 −2.25093e17 −2.57563
405405 −1.03065e17 −1.16053
406406 4.85309e16 0.537773
407407 2.17203e17 2.36865
408408 1.44535e16 0.155125
409409 −4.61200e16 −0.487178 −0.243589 0.969879i 0.578325π-0.578325\pi
−0.243589 + 0.969879i 0.578325π0.578325\pi
410410 −1.32767e17 −1.38036
411411 −5.89497e15 −0.0603267
412412 −3.88431e17 −3.91275
413413 −7.25294e16 −0.719182
414414 3.01355e17 2.94155
415415 −7.86712e16 −0.755967
416416 1.25638e16 0.118855
417417 −2.30161e16 −0.214362
418418 4.77098e17 4.37484
419419 −1.76604e16 −0.159445 −0.0797223 0.996817i 0.525403π-0.525403\pi
−0.0797223 + 0.996817i 0.525403π0.525403\pi
420420 −1.39945e16 −0.124405
421421 −1.78240e17 −1.56016 −0.780082 0.625677i 0.784823π-0.784823\pi
−0.780082 + 0.625677i 0.784823π0.784823\pi
422422 4.04980e16 0.349062
423423 −2.60805e16 −0.221362
424424 −2.86096e17 −2.39130
425425 −4.46449e16 −0.367489
426426 3.61142e16 0.292763
427427 1.97855e16 0.157967
428428 5.62925e16 0.442656
429429 3.97893e16 0.308172
430430 −4.73514e17 −3.61233
431431 −1.68744e17 −1.26802 −0.634010 0.773325i 0.718592π-0.718592\pi
−0.634010 + 0.773325i 0.718592π0.718592\pi
432432 −2.88478e16 −0.213535
433433 −1.12283e17 −0.818737 −0.409368 0.912369i 0.634251π-0.634251\pi
−0.409368 + 0.912369i 0.634251π0.634251\pi
434434 1.50127e16 0.107839
435435 1.35550e16 0.0959220
436436 1.89816e16 0.132334
437437 −3.70914e17 −2.54767
438438 −2.91457e16 −0.197239
439439 1.39313e17 0.928907 0.464453 0.885598i 0.346251π-0.346251\pi
0.464453 + 0.885598i 0.346251π0.346251\pi
440440 5.33430e17 3.50457
441441 1.21272e17 0.785070
442442 3.36269e17 2.14507
443443 2.87843e17 1.80939 0.904694 0.426061i 0.140099π-0.140099\pi
0.904694 + 0.426061i 0.140099π0.140099\pi
444444 5.06504e16 0.313757
445445 −1.70990e17 −1.04383
446446 4.22946e17 2.54454
447447 2.78728e16 0.165266
448448 −8.24004e16 −0.481529
449449 −1.92688e17 −1.10982 −0.554911 0.831910i 0.687248π-0.687248\pi
−0.554911 + 0.831910i 0.687248π0.687248\pi
450450 1.38025e17 0.783570
451451 −2.03387e17 −1.13809
452452 4.19324e17 2.31286
453453 2.05122e16 0.111525
454454 −9.84873e16 −0.527858
455455 −1.60954e17 −0.850409
456456 5.49989e16 0.286472
457457 −1.94202e17 −0.997237 −0.498618 0.866822i 0.666159π-0.666159\pi
−0.498618 + 0.866822i 0.666159π0.666159\pi
458458 2.63454e17 1.33376
459459 3.66013e16 0.182690
460460 −8.38907e17 −4.12846
461461 −1.54263e17 −0.748524 −0.374262 0.927323i 0.622104π-0.622104\pi
−0.374262 + 0.927323i 0.622104π0.622104\pi
462462 −3.22789e16 −0.154435
463463 −5.96965e16 −0.281626 −0.140813 0.990036i 0.544972π-0.544972\pi
−0.140813 + 0.990036i 0.544972π0.544972\pi
464464 −1.38315e17 −0.643432
465465 4.19315e15 0.0192352
466466 −1.74961e17 −0.791467
467467 −2.22537e16 −0.0992754 −0.0496377 0.998767i 0.515807π-0.515807\pi
−0.0496377 + 0.998767i 0.515807π0.515807\pi
468468 −6.90476e17 −3.03774
469469 3.56090e16 0.154503
470470 1.09314e17 0.467779
471471 6.74810e15 0.0284804
472472 6.44689e17 2.68366
473473 −7.25381e17 −2.97830
474474 4.57431e16 0.185254
475475 −1.69885e17 −0.678649
476476 −1.81181e17 −0.713950
477477 −3.59831e17 −1.39871
478478 −8.20071e17 −3.14463
479479 −7.45601e16 −0.282050 −0.141025 0.990006i 0.545040π-0.545040\pi
−0.141025 + 0.990006i 0.545040π0.545040\pi
480480 −2.84679e15 −0.0106240
481481 5.82541e17 2.14478
482482 −3.56406e17 −1.29461
483483 2.50948e16 0.0899348
484484 1.09374e18 3.86741
485485 −1.83713e17 −0.640941
486486 −1.70114e17 −0.585605
487487 4.65421e16 0.158091 0.0790456 0.996871i 0.474813π-0.474813\pi
0.0790456 + 0.996871i 0.474813π0.474813\pi
488488 −1.75866e17 −0.589459
489489 3.72124e16 0.123078
490490 −5.08300e17 −1.65900
491491 −5.75242e17 −1.85277 −0.926383 0.376583i 0.877099π-0.877099\pi
−0.926383 + 0.376583i 0.877099π0.877099\pi
492492 −4.74286e16 −0.150753
493493 1.75490e17 0.550488
494494 1.27958e18 3.96135
495495 6.70908e17 2.04988
496496 −4.27869e16 −0.129027
497497 −2.23794e17 −0.666088
498498 −4.23148e16 −0.124309
499499 −2.60876e16 −0.0756450 −0.0378225 0.999284i 0.512042π-0.512042\pi
−0.0378225 + 0.999284i 0.512042π0.512042\pi
500500 4.50706e17 1.28999
501501 −1.32621e16 −0.0374685
502502 −3.40731e17 −0.950248
503503 −2.00565e17 −0.552159 −0.276080 0.961135i 0.589035π-0.589035\pi
−0.276080 + 0.961135i 0.589035π0.589035\pi
504504 2.76904e17 0.752542
505505 5.86594e17 1.57378
506506 −1.93497e18 −5.12502
507507 6.26781e16 0.163894
508508 1.30815e18 3.37709
509509 −2.45371e17 −0.625399 −0.312700 0.949852i 0.601233π-0.601233\pi
−0.312700 + 0.949852i 0.601233π0.601233\pi
510510 −7.61937e16 −0.191740
511511 1.80611e17 0.448755
512512 6.70881e17 1.64585
513513 1.39277e17 0.337377
514514 9.10251e16 0.217721
515515 1.01226e18 2.39080
516516 −1.69155e17 −0.394513
517517 1.67460e17 0.385676
518518 −4.72583e17 −1.07482
519519 3.19096e15 0.00716693
520520 1.43067e18 3.17334
521521 −1.71991e17 −0.376755 −0.188378 0.982097i 0.560323π-0.560323\pi
−0.188378 + 0.982097i 0.560323π0.560323\pi
522522 −5.42550e17 −1.17377
523523 −1.09598e17 −0.234176 −0.117088 0.993122i 0.537356π-0.537356\pi
−0.117088 + 0.993122i 0.537356π0.537356\pi
524524 1.33315e18 2.81336
525525 1.14938e16 0.0239568
526526 1.33397e18 2.74624
527527 5.42868e16 0.110389
528528 9.19962e16 0.184778
529529 1.00028e18 1.98454
530530 1.50820e18 2.95574
531531 8.10842e17 1.56972
532532 −6.89438e17 −1.31847
533533 −5.45486e17 −1.03052
534534 −9.19705e16 −0.171645
535535 −1.46699e17 −0.270475
536536 −3.16516e17 −0.576534
537537 −1.73014e16 −0.0311351
538538 3.17923e17 0.565246
539539 −7.78671e17 −1.36781
540540 3.15006e17 0.546713
541541 −1.00640e18 −1.72579 −0.862896 0.505381i 0.831352π-0.831352\pi
−0.862896 + 0.505381i 0.831352π0.831352\pi
542542 1.42728e18 2.41832
543543 −3.26305e16 −0.0546292
544544 −3.68561e16 −0.0609701
545545 −4.94662e16 −0.0808595
546546 −8.65724e16 −0.139839
547547 1.56743e17 0.250190 0.125095 0.992145i 0.460076π-0.460076\pi
0.125095 + 0.992145i 0.460076π0.460076\pi
548548 −6.56838e17 −1.03606
549549 −2.21191e17 −0.344785
550550 −8.86246e17 −1.36520
551551 6.67782e17 1.01660
552552 −2.23059e17 −0.335595
553553 −2.83463e17 −0.421485
554554 2.63081e17 0.386612
555555 −1.31995e17 −0.191714
556556 −2.56454e18 −3.68148
557557 7.98265e17 1.13263 0.566316 0.824188i 0.308368π-0.308368\pi
0.566316 + 0.824188i 0.308368π0.308368\pi
558558 −1.67835e17 −0.235375
559559 −1.94548e18 −2.69681
560560 −3.72139e17 −0.509898
561561 −1.16722e17 −0.158086
562562 −7.78621e17 −1.04241
563563 6.49635e17 0.859735 0.429867 0.902892i 0.358560π-0.358560\pi
0.429867 + 0.902892i 0.358560π0.358560\pi
564564 3.90507e16 0.0510874
565565 −1.09276e18 −1.41322
566566 −6.91470e17 −0.884029
567567 3.43526e17 0.434180
568568 1.98923e18 2.48554
569569 5.45655e17 0.674045 0.337022 0.941497i 0.390580π-0.390580\pi
0.337022 + 0.941497i 0.390580π0.390580\pi
570570 −2.89935e17 −0.354091
571571 5.26721e17 0.635983 0.317992 0.948094i 0.396992π-0.396992\pi
0.317992 + 0.948094i 0.396992π0.396992\pi
572572 4.43346e18 5.29260
573573 1.48580e17 0.175370
574574 4.42523e17 0.516426
575575 6.89001e17 0.795021
576576 9.21194e17 1.05101
577577 −1.14653e18 −1.29343 −0.646717 0.762730i 0.723858π-0.723858\pi
−0.646717 + 0.762730i 0.723858π0.723858\pi
578578 5.60467e17 0.625200
579579 −1.92847e16 −0.0212717
580580 1.51034e18 1.64738
581581 2.62218e17 0.282825
582582 −9.88135e16 −0.105394
583583 2.31043e18 2.43695
584584 −1.60539e18 −1.67455
585585 1.79939e18 1.85614
586586 −1.88150e18 −1.91942
587587 −2.89181e17 −0.291758 −0.145879 0.989302i 0.546601π-0.546601\pi
−0.145879 + 0.989302i 0.546601π0.546601\pi
588588 −1.81581e17 −0.181184
589589 2.06574e17 0.203858
590590 −3.39858e18 −3.31711
591591 −8.49874e15 −0.00820420
592592 1.34688e18 1.28599
593593 −7.69437e17 −0.726637 −0.363319 0.931665i 0.618356π-0.618356\pi
−0.363319 + 0.931665i 0.618356π0.618356\pi
594594 7.26572e17 0.678683
595595 4.72160e17 0.436243
596596 3.10569e18 2.83830
597597 −1.71689e17 −0.155207
598598 −5.18961e18 −4.64063
599599 −1.27078e18 −1.12407 −0.562037 0.827112i 0.689982π-0.689982\pi
−0.562037 + 0.827112i 0.689982π0.689982\pi
600600 −1.02165e17 −0.0893958
601601 −1.71100e18 −1.48104 −0.740519 0.672035i 0.765420π-0.765420\pi
−0.740519 + 0.672035i 0.765420π0.765420\pi
602602 1.57826e18 1.35146
603603 −3.98091e17 −0.337225
604604 2.28554e18 1.91535
605605 −2.85030e18 −2.36309
606606 3.15511e17 0.258787
607607 −1.97449e18 −1.60225 −0.801123 0.598500i 0.795764π-0.795764\pi
−0.801123 + 0.598500i 0.795764π0.795764\pi
608608 −1.40246e17 −0.112595
609609 −4.51799e16 −0.0358866
610610 9.27106e17 0.728594
611611 4.49130e17 0.349224
612612 2.02551e18 1.55830
613613 −1.66843e18 −1.27003 −0.635016 0.772499i 0.719007π-0.719007\pi
−0.635016 + 0.772499i 0.719007π0.719007\pi
614614 1.44644e17 0.108945
615615 1.23599e17 0.0921144
616616 −1.77797e18 −1.31114
617617 7.95080e17 0.580173 0.290086 0.957000i 0.406316π-0.406316\pi
0.290086 + 0.957000i 0.406316π0.406316\pi
618618 5.44462e17 0.393136
619619 1.95212e18 1.39482 0.697409 0.716673i 0.254336π-0.254336\pi
0.697409 + 0.716673i 0.254336π0.254336\pi
620620 4.67215e17 0.330347
621621 −5.64864e17 −0.395229
622622 4.53090e18 3.13724
623623 5.69926e17 0.390522
624624 2.46735e17 0.167313
625625 −1.86028e18 −1.24842
626626 7.92457e17 0.526311
627627 −4.44155e17 −0.291942
628628 7.51897e17 0.489126
629629 −1.70889e18 −1.10023
630630 −1.45974e18 −0.930171
631631 2.25291e18 1.42087 0.710434 0.703764i 0.248499π-0.248499\pi
0.710434 + 0.703764i 0.248499π0.248499\pi
632632 2.51960e18 1.57279
633633 −3.77017e16 −0.0232936
634634 −1.41338e18 −0.864330
635635 −3.40905e18 −2.06350
636636 5.38779e17 0.322804
637637 −2.08841e18 −1.23854
638638 3.48365e18 2.04503
639639 2.50190e18 1.45383
640640 −3.70072e18 −2.12871
641641 7.02648e17 0.400093 0.200046 0.979786i 0.435891π-0.435891\pi
0.200046 + 0.979786i 0.435891π0.435891\pi
642642 −7.89049e16 −0.0444760
643643 3.25156e17 0.181435 0.0907174 0.995877i 0.471084π-0.471084\pi
0.0907174 + 0.995877i 0.471084π0.471084\pi
644644 2.79615e18 1.54455
645645 4.40819e17 0.241058
646646 −3.75367e18 −2.03210
647647 7.77446e16 0.0416670 0.0208335 0.999783i 0.493368π-0.493368\pi
0.0208335 + 0.999783i 0.493368π0.493368\pi
648648 −3.05349e18 −1.62016
649649 −5.20632e18 −2.73490
650650 −2.37692e18 −1.23617
651651 −1.39761e16 −0.00719632
652652 4.14634e18 2.11376
653653 3.53906e18 1.78629 0.893145 0.449769i 0.148494π-0.148494\pi
0.893145 + 0.449769i 0.148494π0.148494\pi
654654 −2.66064e16 −0.0132963
655655 −3.47420e18 −1.71904
656656 −1.26121e18 −0.617891
657657 −2.01914e18 −0.979472
658658 −3.64354e17 −0.175007
659659 −2.41172e18 −1.14702 −0.573512 0.819197i 0.694419π-0.694419\pi
−0.573512 + 0.819197i 0.694419π0.694419\pi
660660 −1.00456e18 −0.473086
661661 3.41467e18 1.59235 0.796175 0.605066i 0.206853π-0.206853\pi
0.796175 + 0.605066i 0.206853π0.206853\pi
662662 4.83807e18 2.23406
663663 −3.13050e17 −0.143145
664664 −2.33076e18 −1.05537
665665 1.79668e18 0.805620
666666 5.28324e18 2.34595
667667 −2.70832e18 −1.19092
668668 −1.47771e18 −0.643490
669669 −3.93743e17 −0.169802
670670 1.66857e18 0.712619
671671 1.42024e18 0.600713
672672 9.48860e15 0.00397468
673673 5.31727e17 0.220592 0.110296 0.993899i 0.464820π-0.464820\pi
0.110296 + 0.993899i 0.464820π0.464820\pi
674674 −4.60038e18 −1.89018
675675 −2.58717e17 −0.105281
676676 6.98382e18 2.81475
677677 −3.10744e18 −1.24044 −0.620221 0.784427i 0.712957π-0.712957\pi
−0.620221 + 0.784427i 0.712957π0.712957\pi
678678 −5.87764e17 −0.232386
679679 6.12331e17 0.239791
680680 −4.19686e18 −1.62786
681681 9.16869e16 0.0352250
682682 1.07765e18 0.410089
683683 2.49420e18 0.940151 0.470075 0.882626i 0.344227π-0.344227\pi
0.470075 + 0.882626i 0.344227π0.344227\pi
684684 7.70756e18 2.87775
685685 1.71173e18 0.633061
686686 3.82363e18 1.40078
687687 −2.45263e17 −0.0890047
688688 −4.49812e18 −1.61699
689689 6.19661e18 2.20663
690690 1.17589e18 0.414809
691691 6.96468e17 0.243385 0.121693 0.992568i 0.461168π-0.461168\pi
0.121693 + 0.992568i 0.461168π0.461168\pi
692692 3.55548e17 0.123086
693693 −2.23620e18 −0.766909
694694 8.62150e18 2.92918
695695 6.68321e18 2.24949
696696 4.01588e17 0.133913
697697 1.60018e18 0.528636
698698 −2.04399e18 −0.668989
699699 1.62880e17 0.0528162
700700 1.28068e18 0.411438
701701 1.48603e18 0.473000 0.236500 0.971632i 0.424000π-0.424000\pi
0.236500 + 0.971632i 0.424000π0.424000\pi
702702 1.94868e18 0.614538
703703 −6.50272e18 −2.03182
704704 −5.91488e18 −1.83115
705705 −1.01766e17 −0.0312158
706706 −9.87554e18 −3.00145
707707 −1.95517e18 −0.588787
708708 −1.21408e18 −0.362270
709709 −1.31649e18 −0.389240 −0.194620 0.980879i 0.562347π-0.562347\pi
−0.194620 + 0.980879i 0.562347π0.562347\pi
710710 −1.04865e19 −3.07222
711711 3.16897e18 0.919952
712712 −5.06587e18 −1.45725
713713 −8.37803e17 −0.238814
714714 2.53960e17 0.0717344
715715 −1.15536e19 −3.23392
716716 −1.92779e18 −0.534718
717717 7.63446e17 0.209848
718718 5.84432e16 0.0159193
719719 −4.49679e18 −1.21385 −0.606925 0.794759i 0.707597π-0.707597\pi
−0.606925 + 0.794759i 0.707597π0.707597\pi
720720 4.16033e18 1.11293
721721 −3.37394e18 −0.894454
722722 −7.71569e18 −2.02714
723723 3.31796e17 0.0863919
724724 −3.63580e18 −0.938209
725725 −1.24046e18 −0.317237
726726 −1.53309e18 −0.388580
727727 1.98219e18 0.497934 0.248967 0.968512i 0.419909π-0.419909\pi
0.248967 + 0.968512i 0.419909π0.419909\pi
728728 −4.76854e18 −1.18722
729729 −3.73369e18 −0.921318
730730 8.46307e18 2.06980
731731 5.70708e18 1.38341
732732 3.31193e17 0.0795717
733733 4.46397e18 1.06303 0.531515 0.847049i 0.321623π-0.321623\pi
0.531515 + 0.847049i 0.321623π0.321623\pi
734734 6.22708e18 1.46981
735735 4.73203e17 0.110708
736736 5.68797e17 0.131902
737737 2.55610e18 0.587541
738738 −4.94718e18 −1.12717
739739 7.78019e17 0.175712 0.0878560 0.996133i 0.471998π-0.471998\pi
0.0878560 + 0.996133i 0.471998π0.471998\pi
740740 −1.47074e19 −3.29253
741741 −1.19123e18 −0.264349
742742 −5.02697e18 −1.10581
743743 4.44055e18 0.968299 0.484150 0.874985i 0.339129π-0.339129\pi
0.484150 + 0.874985i 0.339129π0.339129\pi
744744 1.24229e17 0.0268534
745745 −8.09346e18 −1.73428
746746 8.68251e18 1.84435
747747 −2.93146e18 −0.617306
748748 −1.30056e19 −2.71500
749749 4.88960e17 0.101191
750750 −6.31751e17 −0.129613
751751 6.91924e18 1.40734 0.703670 0.710527i 0.251543π-0.251543\pi
0.703670 + 0.710527i 0.251543π0.251543\pi
752752 1.03843e18 0.209392
753753 3.17204e17 0.0634120
754754 9.34321e18 1.85175
755755 −5.95614e18 −1.17033
756756 −1.04994e18 −0.204538
757757 7.26685e17 0.140353 0.0701767 0.997535i 0.477644π-0.477644\pi
0.0701767 + 0.997535i 0.477644π0.477644\pi
758758 7.61806e18 1.45880
759759 1.80136e18 0.342002
760760 −1.59701e19 −3.00620
761761 3.74540e17 0.0699033 0.0349517 0.999389i 0.488872π-0.488872\pi
0.0349517 + 0.999389i 0.488872π0.488872\pi
762762 −1.83362e18 −0.339315
763763 1.64875e17 0.0302514
764764 1.65553e19 3.01182
765765 −5.27851e18 −0.952164
766766 5.51448e18 0.986319
767767 −1.39634e19 −2.47641
768768 −1.29304e18 −0.227387
769769 6.50731e18 1.13470 0.567349 0.823478i 0.307969π-0.307969\pi
0.567349 + 0.823478i 0.307969π0.307969\pi
770770 9.37284e18 1.62062
771771 −8.47400e16 −0.0145290
772772 −2.14877e18 −0.365323
773773 −3.07419e18 −0.518279 −0.259140 0.965840i 0.583439π-0.583439\pi
−0.259140 + 0.965840i 0.583439π0.583439\pi
774774 −1.76442e19 −2.94975
775775 −3.83727e17 −0.0636153
776776 −5.44280e18 −0.894789
777777 4.39952e17 0.0717248
778778 −6.73930e18 −1.08955
779779 6.08909e18 0.976245
780780 −2.69424e18 −0.428373
781781 −1.60644e19 −2.53299
782782 1.52237e19 2.38055
783783 1.01696e18 0.157708
784784 −4.82857e18 −0.742615
785785 −1.95945e18 −0.298870
786786 −1.86867e18 −0.282674
787787 −6.74413e18 −1.01179 −0.505895 0.862595i 0.668838π-0.668838\pi
−0.505895 + 0.862595i 0.668838π0.668838\pi
788788 −9.46960e17 −0.140900
789789 −1.24186e18 −0.183262
790790 −1.32825e19 −1.94403
791791 3.64228e18 0.528720
792792 1.98768e19 2.86175
793793 3.80912e18 0.543937
794794 −1.30231e18 −0.184451
795795 −1.40406e18 −0.197242
796796 −1.91302e19 −2.66554
797797 −9.65539e18 −1.33442 −0.667208 0.744872i 0.732511π-0.732511\pi
−0.667208 + 0.744872i 0.732511π0.732511\pi
798798 9.66380e17 0.132474
799799 −1.31752e18 −0.179145
800800 2.60518e17 0.0351360
801801 −6.37148e18 −0.852372
802802 −9.41962e18 −1.24997
803803 1.29647e19 1.70652
804804 5.96066e17 0.0778270
805805 −7.28680e18 −0.943764
806806 2.89026e18 0.371330
807807 −2.95971e17 −0.0377200
808808 1.73788e19 2.19709
809809 −6.40206e18 −0.802886 −0.401443 0.915884i 0.631491π-0.631491\pi
−0.401443 + 0.915884i 0.631491π0.631491\pi
810810 1.60969e19 2.00258
811811 4.02888e18 0.497220 0.248610 0.968604i 0.420026π-0.420026\pi
0.248610 + 0.968604i 0.420026π0.420026\pi
812812 −5.03410e18 −0.616322
813813 −1.32873e18 −0.161379
814814 −3.39231e19 −4.08730
815815 −1.08054e19 −1.29156
816816 −7.23798e17 −0.0858285
817817 2.17168e19 2.55478
818818 7.20310e18 0.840665
819819 −5.99751e18 −0.694426
820820 1.37719e19 1.58199
821821 3.37777e18 0.384946 0.192473 0.981302i 0.438349π-0.438349\pi
0.192473 + 0.981302i 0.438349π0.438349\pi
822822 9.20686e17 0.104099
823823 −8.89092e17 −0.0997351 −0.0498675 0.998756i 0.515880π-0.515880\pi
−0.0498675 + 0.998756i 0.515880π0.515880\pi
824824 2.99898e19 3.33769
825825 8.25052e17 0.0911026
826826 1.13278e19 1.24101
827827 4.34146e18 0.471900 0.235950 0.971765i 0.424180π-0.424180\pi
0.235950 + 0.971765i 0.424180π0.424180\pi
828828 −3.12596e19 −3.37121
829829 1.34365e19 1.43774 0.718870 0.695144i 0.244659π-0.244659\pi
0.718870 + 0.695144i 0.244659π0.244659\pi
830830 1.22870e19 1.30448
831831 −2.44916e17 −0.0257994
832832 −1.58638e19 −1.65808
833833 6.12635e18 0.635344
834834 3.59470e18 0.369899
835835 3.85092e18 0.393190
836836 −4.94894e19 −5.01385
837837 3.14592e17 0.0316251
838838 2.75823e18 0.275135
839839 −1.72037e19 −1.70282 −0.851412 0.524497i 0.824253π-0.824253\pi
−0.851412 + 0.524497i 0.824253π0.824253\pi
840840 1.08048e18 0.106121
841841 −5.38465e18 −0.524788
842842 2.78377e19 2.69219
843843 7.24858e17 0.0695623
844844 −4.20086e18 −0.400048
845845 −1.81999e19 −1.71989
846846 4.07330e18 0.381978
847847 9.50031e18 0.884088
848848 1.43271e19 1.32307
849849 6.43726e17 0.0589930
850850 6.97271e18 0.634131
851851 2.63731e19 2.38023
852852 −3.74613e18 −0.335525
853853 8.79218e18 0.781498 0.390749 0.920497i 0.372216π-0.372216\pi
0.390749 + 0.920497i 0.372216π0.372216\pi
854854 −3.09013e18 −0.272584
855855 −2.00860e19 −1.75838
856856 −4.34620e18 −0.377598
857857 7.90188e18 0.681326 0.340663 0.940185i 0.389348π-0.389348\pi
0.340663 + 0.940185i 0.389348π0.389348\pi
858858 −6.21436e18 −0.531776
859859 −1.16614e19 −0.990368 −0.495184 0.868788i 0.664899π-0.664899\pi
−0.495184 + 0.868788i 0.664899π0.664899\pi
860860 4.91176e19 4.13997
861861 −4.11967e17 −0.0344621
862862 2.63547e19 2.18807
863863 3.51764e18 0.289855 0.144928 0.989442i 0.453705π-0.453705\pi
0.144928 + 0.989442i 0.453705π0.453705\pi
864864 −2.13581e17 −0.0174672
865865 −9.26561e17 −0.0752089
866866 1.75366e19 1.41280
867867 −5.21768e17 −0.0417209
868868 −1.55727e18 −0.123591
869869 −2.03476e19 −1.60282
870870 −2.11704e18 −0.165521
871871 6.85548e18 0.532010
872872 −1.46552e18 −0.112884
873873 −6.84555e18 −0.523378
874874 5.79300e19 4.39622
875875 3.91486e18 0.294892
876876 3.02329e18 0.226049
877877 −3.25045e18 −0.241238 −0.120619 0.992699i 0.538488π-0.538488\pi
−0.120619 + 0.992699i 0.538488π0.538488\pi
878878 −2.17581e19 −1.60290
879879 1.75158e18 0.128086
880880 −2.67130e19 −1.93903
881881 −1.04161e19 −0.750522 −0.375261 0.926919i 0.622447π-0.622447\pi
−0.375261 + 0.926919i 0.622447π0.622447\pi
882882 −1.89404e19 −1.35470
883883 −5.27239e18 −0.374337 −0.187169 0.982328i 0.559931π-0.559931\pi
−0.187169 + 0.982328i 0.559931π0.559931\pi
884884 −3.48812e19 −2.45839
885885 3.16391e18 0.221357
886886 −4.49558e19 −3.12225
887887 −1.33763e19 −0.922214 −0.461107 0.887344i 0.652548π-0.652548\pi
−0.461107 + 0.887344i 0.652548π0.652548\pi
888888 −3.91058e18 −0.267644
889889 1.13627e19 0.772002
890890 2.67055e19 1.80122
891891 2.46591e19 1.65109
892892 −4.38722e19 −2.91620
893893 −5.01349e18 −0.330831
894894 −4.35323e18 −0.285179
895895 5.02383e18 0.326727
896896 1.23348e19 0.796399
897897 4.83128e18 0.309678
898898 3.00943e19 1.91509
899899 1.50835e18 0.0952940
900900 −1.43174e19 −0.898022
901901 −1.81778e19 −1.13196
902902 3.17653e19 1.96386
903903 −1.46929e18 −0.0901854
904904 −3.23749e19 −1.97294
905905 9.47494e18 0.573272
906906 −3.20363e18 −0.192446
907907 −1.98060e19 −1.18127 −0.590634 0.806939i 0.701122π-0.701122\pi
−0.590634 + 0.806939i 0.701122π0.701122\pi
908908 1.02161e19 0.604959
909909 2.18578e19 1.28511
910910 2.51381e19 1.46745
911911 9.01891e18 0.522739 0.261369 0.965239i 0.415826π-0.415826\pi
0.261369 + 0.965239i 0.415826π0.415826\pi
912912 −2.75423e18 −0.158501
913913 1.88226e19 1.07552
914914 3.03308e19 1.72081
915915 −8.63091e17 −0.0486205
916916 −2.73281e19 −1.52858
917917 1.15798e19 0.643133
918918 −5.71645e18 −0.315246
919919 3.82062e18 0.209210 0.104605 0.994514i 0.466642π-0.466642\pi
0.104605 + 0.994514i 0.466642π0.466642\pi
920920 6.47698e19 3.52170
921921 −1.34657e17 −0.00727009
922922 2.40931e19 1.29164
923923 −4.30850e19 −2.29359
924924 3.34829e18 0.176992
925925 1.20793e19 0.634045
926926 9.32350e18 0.485968
927927 3.77189e19 1.95227
928928 −1.02404e18 −0.0526328
929929 1.13165e19 0.577578 0.288789 0.957393i 0.406747π-0.406747\pi
0.288789 + 0.957393i 0.406747π0.406747\pi
930930 −6.54893e17 −0.0331918
931931 2.33122e19 1.17330
932932 1.81487e19 0.907073
933933 −4.21805e18 −0.209354
934934 3.47561e18 0.171308
935935 3.38927e19 1.65894
936936 5.33098e19 2.59128
937937 2.91885e19 1.40898 0.704489 0.709714i 0.251176π-0.251176\pi
0.704489 + 0.709714i 0.251176π0.251176\pi
938938 −5.56148e18 −0.266607
939939 −7.37739e17 −0.0351218
940940 −1.13392e19 −0.536105
941941 2.04885e19 0.962005 0.481003 0.876719i 0.340273π-0.340273\pi
0.481003 + 0.876719i 0.340273π0.340273\pi
942942 −1.05393e18 −0.0491452
943943 −2.46955e19 −1.14365
944944 −3.22846e19 −1.48483
945945 2.73616e18 0.124978
946946 1.13291e20 5.13930
947947 −3.42151e19 −1.54150 −0.770749 0.637139i 0.780118π-0.780118\pi
−0.770749 + 0.637139i 0.780118π0.780118\pi
948948 −4.74493e18 −0.212313
949949 3.47714e19 1.54523
950950 2.65329e19 1.17106
951951 1.31579e18 0.0576784
952952 1.39885e19 0.609020
953953 −2.46294e19 −1.06500 −0.532500 0.846430i 0.678747π-0.678747\pi
−0.532500 + 0.846430i 0.678747π0.678747\pi
954954 5.61989e19 2.41359
955955 −4.31432e19 −1.84031
956956 8.50659e19 3.60395
957957 −3.24311e18 −0.136469
958958 1.16449e19 0.486699
959959 −5.70533e18 −0.236843
960960 3.59451e18 0.148210
961961 −2.39509e19 −0.980891
962962 −9.09822e19 −3.70099
963963 −5.46633e18 −0.220864
964964 3.69699e19 1.48371
965965 5.59971e18 0.223222
966966 −3.91935e18 −0.155190
967967 2.16923e19 0.853166 0.426583 0.904449i 0.359717π-0.359717\pi
0.426583 + 0.904449i 0.359717π0.359717\pi
968968 −8.44450e19 −3.29901
969969 3.49448e18 0.135606
970970 2.86926e19 1.10599
971971 2.58227e19 0.988729 0.494365 0.869255i 0.335401π-0.335401\pi
0.494365 + 0.869255i 0.335401π0.335401\pi
972972 1.76459e19 0.671141
973973 −2.22757e19 −0.841585
974974 −7.26903e18 −0.272799
975975 2.21280e18 0.0824921
976976 8.80699e18 0.326140
977977 −4.80925e18 −0.176914 −0.0884571 0.996080i 0.528194π-0.528194\pi
−0.0884571 + 0.996080i 0.528194π0.528194\pi
978978 −5.81190e18 −0.212381
979979 4.09105e19 1.48507
980980 5.27259e19 1.90132
981981 −1.84322e18 −0.0660281
982982 8.98422e19 3.19710
983983 2.45382e18 0.0867451 0.0433725 0.999059i 0.486190π-0.486190\pi
0.0433725 + 0.999059i 0.486190π0.486190\pi
984984 3.66183e18 0.128597
985985 2.46779e18 0.0860938
986986 −2.74083e19 −0.949911
987987 3.39196e17 0.0116786
988988 −1.32731e20 −4.53997
989989 −8.80769e19 −2.99286
990990 −1.04784e20 −3.53724
991991 −5.42214e19 −1.81841 −0.909205 0.416348i 0.863310π-0.863310\pi
−0.909205 + 0.416348i 0.863310π0.863310\pi
992992 −3.16782e17 −0.0105544
993993 −4.50401e18 −0.149083
994994 3.49525e19 1.14939
995995 4.98536e19 1.62872
996996 4.38932e18 0.142466
997997 −5.05255e18 −0.162927 −0.0814633 0.996676i 0.525959π-0.525959\pi
−0.0814633 + 0.996676i 0.525959π0.525959\pi
998998 4.07440e18 0.130532
999999 −9.90298e18 −0.315203
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 197.14.a.a.1.10 104
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.14.a.a.1.10 104 1.1 even 1 trivial