Properties

Label 197.10.a.a.1.18
Level 197197
Weight 1010
Character 197.1
Self dual yes
Analytic conductor 101.462101.462
Analytic rank 11
Dimension 7171
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] = [197,10,Mod(1,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: N N == 197 197
Weight: k k == 10 10
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: 101.462059724101.462059724
Analytic rank: 11
Dimension: 7171
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.18
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) == q27.2613q22.80973q3+231.177q4+1123.40q5+76.5969q68481.66q7+7655.60q819675.1q930625.2q10+79300.8q11649.546q1297256.2q13+231221.q143156.44q15327064.q1637665.0q17+536368.q18+584746.q19+259703.q20+23831.2q212.16184e6q22+1.46262e6q2321510.2q24691109.q25+2.65133e6q26+110586.q271.96076e6q285.08723e6q29+86048.6q30226476.q31+4.99651e6q32222814.q33+1.02680e6q349.52825e6q354.54843e6q36+7.07236e6q371.59409e7q38+273264.q39+8.60026e6q402.82852e7q41649669.q42+2.12893e7q43+1.83325e7q442.21029e7q453.98727e7q46+4.37126e6q47+918963.q48+3.15849e7q49+1.88405e7q50+105829.q512.24834e7q52+8.42582e7q533.01471e6q54+8.90861e7q556.49321e7q561.64298e6q57+1.38684e8q584.99543e7q59729696.q60+1.38172e8q61+6.17401e6q62+1.66878e8q63+3.12455e7q641.09257e8q65+6.07420e6q662.30776e7q678.70728e6q684.10956e6q69+2.59752e8q70+1.47748e8q711.50625e8q72+1.64941e8q731.92802e8q74+1.94183e6q75+1.35180e8q766.72602e8q777.44953e6q78+3.82858e8q793.67422e8q80+3.86954e8q81+7.71091e8q824.96417e7q83+5.50922e6q844.23127e7q855.80373e8q86+1.42938e7q87+6.07095e8q882.48081e8q89+6.02554e8q90+8.24894e8q91+3.38123e8q92+636336.q931.19166e8q94+6.56901e8q951.40389e7q961.11825e9q978.61045e8q981.56025e9q99+O(q100)q-27.2613 q^{2} -2.80973 q^{3} +231.177 q^{4} +1123.40 q^{5} +76.5969 q^{6} -8481.66 q^{7} +7655.60 q^{8} -19675.1 q^{9} -30625.2 q^{10} +79300.8 q^{11} -649.546 q^{12} -97256.2 q^{13} +231221. q^{14} -3156.44 q^{15} -327064. q^{16} -37665.0 q^{17} +536368. q^{18} +584746. q^{19} +259703. q^{20} +23831.2 q^{21} -2.16184e6 q^{22} +1.46262e6 q^{23} -21510.2 q^{24} -691109. q^{25} +2.65133e6 q^{26} +110586. q^{27} -1.96076e6 q^{28} -5.08723e6 q^{29} +86048.6 q^{30} -226476. q^{31} +4.99651e6 q^{32} -222814. q^{33} +1.02680e6 q^{34} -9.52825e6 q^{35} -4.54843e6 q^{36} +7.07236e6 q^{37} -1.59409e7 q^{38} +273264. q^{39} +8.60026e6 q^{40} -2.82852e7 q^{41} -649669. q^{42} +2.12893e7 q^{43} +1.83325e7 q^{44} -2.21029e7 q^{45} -3.98727e7 q^{46} +4.37126e6 q^{47} +918963. q^{48} +3.15849e7 q^{49} +1.88405e7 q^{50} +105829. q^{51} -2.24834e7 q^{52} +8.42582e7 q^{53} -3.01471e6 q^{54} +8.90861e7 q^{55} -6.49321e7 q^{56} -1.64298e6 q^{57} +1.38684e8 q^{58} -4.99543e7 q^{59} -729696. q^{60} +1.38172e8 q^{61} +6.17401e6 q^{62} +1.66878e8 q^{63} +3.12455e7 q^{64} -1.09257e8 q^{65} +6.07420e6 q^{66} -2.30776e7 q^{67} -8.70728e6 q^{68} -4.10956e6 q^{69} +2.59752e8 q^{70} +1.47748e8 q^{71} -1.50625e8 q^{72} +1.64941e8 q^{73} -1.92802e8 q^{74} +1.94183e6 q^{75} +1.35180e8 q^{76} -6.72602e8 q^{77} -7.44953e6 q^{78} +3.82858e8 q^{79} -3.67422e8 q^{80} +3.86954e8 q^{81} +7.71091e8 q^{82} -4.96417e7 q^{83} +5.50922e6 q^{84} -4.23127e7 q^{85} -5.80373e8 q^{86} +1.42938e7 q^{87} +6.07095e8 q^{88} -2.48081e8 q^{89} +6.02554e8 q^{90} +8.24894e8 q^{91} +3.38123e8 q^{92} +636336. q^{93} -1.19166e8 q^{94} +6.56901e8 q^{95} -1.40389e7 q^{96} -1.11825e9 q^{97} -8.61045e8 q^{98} -1.56025e9 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 71q32q2892q3+16896q42329q510272q637846q724933q8+419903q9138907q10143074q11496640q12433821q13130143q14670126q15+6380320552q99+O(q100) 71 q - 32 q^{2} - 892 q^{3} + 16896 q^{4} - 2329 q^{5} - 10272 q^{6} - 37846 q^{7} - 24933 q^{8} + 419903 q^{9} - 138907 q^{10} - 143074 q^{11} - 496640 q^{12} - 433821 q^{13} - 130143 q^{14} - 670126 q^{15}+ \cdots - 6380320552 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 −27.2613 −1.20479 −0.602395 0.798198i 0.705787π-0.705787\pi
−0.602395 + 0.798198i 0.705787π0.705787\pi
33 −2.80973 −0.0200272 −0.0100136 0.999950i 0.503187π-0.503187\pi
−0.0100136 + 0.999950i 0.503187π0.503187\pi
44 231.177 0.451517
55 1123.40 0.803836 0.401918 0.915676i 0.368344π-0.368344\pi
0.401918 + 0.915676i 0.368344π0.368344\pi
66 76.5969 0.0241285
77 −8481.66 −1.33518 −0.667590 0.744529i 0.732674π-0.732674\pi
−0.667590 + 0.744529i 0.732674π0.732674\pi
88 7655.60 0.660806
99 −19675.1 −0.999599
1010 −30625.2 −0.968453
1111 79300.8 1.63309 0.816546 0.577281i 0.195886π-0.195886\pi
0.816546 + 0.577281i 0.195886π0.195886\pi
1212 −649.546 −0.00904262
1313 −97256.2 −0.944435 −0.472218 0.881482i 0.656546π-0.656546\pi
−0.472218 + 0.881482i 0.656546π0.656546\pi
1414 231221. 1.60861
1515 −3156.44 −0.0160986
1616 −327064. −1.24765
1717 −37665.0 −0.109375 −0.0546875 0.998504i 0.517416π-0.517416\pi
−0.0546875 + 0.998504i 0.517416π0.517416\pi
1818 536368. 1.20431
1919 584746. 1.02938 0.514691 0.857376i 0.327907π-0.327907\pi
0.514691 + 0.857376i 0.327907π0.327907\pi
2020 259703. 0.362946
2121 23831.2 0.0267399
2222 −2.16184e6 −1.96753
2323 1.46262e6 1.08982 0.544910 0.838495i 0.316564π-0.316564\pi
0.544910 + 0.838495i 0.316564π0.316564\pi
2424 −21510.2 −0.0132341
2525 −691109. −0.353848
2626 2.65133e6 1.13785
2727 110586. 0.0400463
2828 −1.96076e6 −0.602857
2929 −5.08723e6 −1.33564 −0.667822 0.744321i 0.732773π-0.732773\pi
−0.667822 + 0.744321i 0.732773π0.732773\pi
3030 86048.6 0.0193954
3131 −226476. −0.0440447 −0.0220224 0.999757i 0.507011π-0.507011\pi
−0.0220224 + 0.999757i 0.507011π0.507011\pi
3232 4.99651e6 0.842349
3333 −222814. −0.0327062
3434 1.02680e6 0.131774
3535 −9.52825e6 −1.07327
3636 −4.54843e6 −0.451336
3737 7.07236e6 0.620378 0.310189 0.950675i 0.399608π-0.399608\pi
0.310189 + 0.950675i 0.399608π0.399608\pi
3838 −1.59409e7 −1.24019
3939 273264. 0.0189144
4040 8.60026e6 0.531180
4141 −2.82852e7 −1.56326 −0.781632 0.623740i 0.785613π-0.785613\pi
−0.781632 + 0.623740i 0.785613π0.785613\pi
4242 −649669. −0.0322159
4343 2.12893e7 0.949627 0.474813 0.880087i 0.342516π-0.342516\pi
0.474813 + 0.880087i 0.342516π0.342516\pi
4444 1.83325e7 0.737369
4545 −2.21029e7 −0.803514
4646 −3.98727e7 −1.31300
4747 4.37126e6 0.130667 0.0653335 0.997863i 0.479189π-0.479189\pi
0.0653335 + 0.997863i 0.479189π0.479189\pi
4848 918963. 0.0249869
4949 3.15849e7 0.782704
5050 1.88405e7 0.426312
5151 105829. 0.00219047
5252 −2.24834e7 −0.426429
5353 8.42582e7 1.46680 0.733400 0.679797i 0.237932π-0.237932\pi
0.733400 + 0.679797i 0.237932π0.237932\pi
5454 −3.01471e6 −0.0482474
5555 8.90861e7 1.31274
5656 −6.49321e7 −0.882295
5757 −1.64298e6 −0.0206156
5858 1.38684e8 1.60917
5959 −4.99543e7 −0.536709 −0.268354 0.963320i 0.586480π-0.586480\pi
−0.268354 + 0.963320i 0.586480π0.586480\pi
6060 −729696. −0.00726878
6161 1.38172e8 1.27772 0.638860 0.769323i 0.279406π-0.279406\pi
0.638860 + 0.769323i 0.279406π0.279406\pi
6262 6.17401e6 0.0530646
6363 1.66878e8 1.33464
6464 3.12455e7 0.232797
6565 −1.09257e8 −0.759171
6666 6.07420e6 0.0394041
6767 −2.30776e7 −0.139912 −0.0699559 0.997550i 0.522286π-0.522286\pi
−0.0699559 + 0.997550i 0.522286π0.522286\pi
6868 −8.70728e6 −0.0493847
6969 −4.10956e6 −0.0218260
7070 2.59752e8 1.29306
7171 1.47748e8 0.690018 0.345009 0.938599i 0.387876π-0.387876\pi
0.345009 + 0.938599i 0.387876π0.387876\pi
7272 −1.50625e8 −0.660541
7373 1.64941e8 0.679791 0.339896 0.940463i 0.389608π-0.389608\pi
0.339896 + 0.940463i 0.389608π0.389608\pi
7474 −1.92802e8 −0.747425
7575 1.94183e6 0.00708657
7676 1.35180e8 0.464783
7777 −6.72602e8 −2.18047
7878 −7.44953e6 −0.0227878
7979 3.82858e8 1.10590 0.552949 0.833215i 0.313502π-0.313502\pi
0.552949 + 0.833215i 0.313502π0.313502\pi
8080 −3.67422e8 −1.00291
8181 3.86954e8 0.998797
8282 7.71091e8 1.88340
8383 −4.96417e7 −0.114814 −0.0574070 0.998351i 0.518283π-0.518283\pi
−0.0574070 + 0.998351i 0.518283π0.518283\pi
8484 5.50922e6 0.0120735
8585 −4.23127e7 −0.0879196
8686 −5.80373e8 −1.14410
8787 1.42938e7 0.0267492
8888 6.07095e8 1.07916
8989 −2.48081e8 −0.419120 −0.209560 0.977796i 0.567203π-0.567203\pi
−0.209560 + 0.977796i 0.567203π0.567203\pi
9090 6.02554e8 0.968065
9191 8.24894e8 1.26099
9292 3.38123e8 0.492073
9393 636336. 0.000882091 0
9494 −1.19166e8 −0.157426
9595 6.56901e8 0.827454
9696 −1.40389e7 −0.0168699
9797 −1.11825e9 −1.28253 −0.641265 0.767319i 0.721590π-0.721590\pi
−0.641265 + 0.767319i 0.721590π0.721590\pi
9898 −8.61045e8 −0.942993
9999 −1.56025e9 −1.63244
100100 −1.59768e8 −0.159768
101101 −8.40721e7 −0.0803907 −0.0401953 0.999192i 0.512798π-0.512798\pi
−0.0401953 + 0.999192i 0.512798π0.512798\pi
102102 −2.88503e6 −0.00263906
103103 1.40068e8 0.122623 0.0613113 0.998119i 0.480472π-0.480472\pi
0.0613113 + 0.998119i 0.480472π0.480472\pi
104104 −7.44554e8 −0.624089
105105 2.67719e7 0.0214945
106106 −2.29699e9 −1.76719
107107 1.22164e9 0.900985 0.450492 0.892780i 0.351248π-0.351248\pi
0.450492 + 0.892780i 0.351248π0.351248\pi
108108 2.55649e7 0.0180816
109109 −2.76698e9 −1.87753 −0.938765 0.344559i 0.888028π-0.888028\pi
−0.938765 + 0.344559i 0.888028π0.888028\pi
110110 −2.42860e9 −1.58157
111111 −1.98715e7 −0.0124244
112112 2.77404e9 1.66584
113113 6.64574e8 0.383434 0.191717 0.981450i 0.438594π-0.438594\pi
0.191717 + 0.981450i 0.438594π0.438594\pi
114114 4.47898e7 0.0248374
115115 1.64309e9 0.876037
116116 −1.17605e9 −0.603066
117117 1.91353e9 0.944057
118118 1.36182e9 0.646621
119119 3.19462e8 0.146035
120120 −2.41644e7 −0.0106380
121121 3.93067e9 1.66699
122122 −3.76674e9 −1.53938
123123 7.94740e7 0.0313078
124124 −5.23559e7 −0.0198870
125125 −2.97052e9 −1.08827
126126 −4.54929e9 −1.60796
127127 −1.43263e9 −0.488671 −0.244336 0.969691i 0.578570π-0.578570\pi
−0.244336 + 0.969691i 0.578570π0.578570\pi
128128 −3.41000e9 −1.12282
129129 −5.98172e7 −0.0190183
130130 2.97849e9 0.914641
131131 3.69105e9 1.09504 0.547519 0.836793i 0.315572π-0.315572\pi
0.547519 + 0.836793i 0.315572π0.315572\pi
132132 −5.15095e7 −0.0147674
133133 −4.95962e9 −1.37441
134134 6.29125e8 0.168564
135135 1.24232e8 0.0321907
136136 −2.88348e8 −0.0722757
137137 −3.13654e9 −0.760692 −0.380346 0.924844i 0.624195π-0.624195\pi
−0.380346 + 0.924844i 0.624195π0.624195\pi
138138 1.12032e8 0.0262958
139139 −3.50593e9 −0.796594 −0.398297 0.917257i 0.630399π-0.630399\pi
−0.398297 + 0.917257i 0.630399π0.630399\pi
140140 −2.20271e9 −0.484598
141141 −1.22821e7 −0.00261689
142142 −4.02781e9 −0.831326
143143 −7.71250e9 −1.54235
144144 6.43501e9 1.24715
145145 −5.71497e9 −1.07364
146146 −4.49650e9 −0.819005
147147 −8.87453e7 −0.0156753
148148 1.63497e9 0.280112
149149 −3.48521e9 −0.579283 −0.289641 0.957135i 0.593536π-0.593536\pi
−0.289641 + 0.957135i 0.593536π0.593536\pi
150150 −5.29368e7 −0.00853782
151151 9.00940e9 1.41026 0.705131 0.709077i 0.250888π-0.250888\pi
0.705131 + 0.709077i 0.250888π0.250888\pi
152152 4.47658e9 0.680221
153153 7.41063e8 0.109331
154154 1.83360e10 2.62701
155155 −2.54422e8 −0.0354047
156156 6.31724e7 0.00854017
157157 −1.39865e10 −1.83721 −0.918606 0.395174i 0.870684π-0.870684\pi
−0.918606 + 0.395174i 0.870684π0.870684\pi
158158 −1.04372e10 −1.33238
159159 −2.36743e8 −0.0293759
160160 5.61305e9 0.677110
161161 −1.24054e10 −1.45511
162162 −1.05489e10 −1.20334
163163 −9.82245e8 −0.108987 −0.0544936 0.998514i 0.517354π-0.517354\pi
−0.0544936 + 0.998514i 0.517354π0.517354\pi
164164 −6.53889e9 −0.705841
165165 −2.50308e8 −0.0262904
166166 1.35329e9 0.138327
167167 −1.90494e10 −1.89521 −0.947606 0.319441i 0.896505π-0.896505\pi
−0.947606 + 0.319441i 0.896505π0.896505\pi
168168 1.82442e8 0.0176699
169169 −1.14573e9 −0.108042
170170 1.15350e9 0.105925
171171 −1.15049e10 −1.02897
172172 4.92159e9 0.428773
173173 −1.55325e10 −1.31836 −0.659180 0.751985i 0.729097π-0.729097\pi
−0.659180 + 0.751985i 0.729097π0.729097\pi
174174 −3.89666e8 −0.0322271
175175 5.86175e9 0.472450
176176 −2.59364e10 −2.03753
177177 1.40358e8 0.0107488
178178 6.76301e9 0.504952
179179 −7.81980e9 −0.569321 −0.284660 0.958628i 0.591881π-0.591881\pi
−0.284660 + 0.958628i 0.591881π0.591881\pi
180180 −5.10968e9 −0.362800
181181 −2.49172e10 −1.72562 −0.862811 0.505527i 0.831298π-0.831298\pi
−0.862811 + 0.505527i 0.831298π0.831298\pi
182182 −2.24877e10 −1.51923
183183 −3.88227e8 −0.0255891
184184 1.11972e10 0.720160
185185 7.94505e9 0.498682
186186 −1.73473e7 −0.00106273
187187 −2.98687e9 −0.178619
188188 1.01053e9 0.0589984
189189 −9.37951e8 −0.0534690
190190 −1.79080e10 −0.996907
191191 1.77428e10 0.964655 0.482328 0.875991i 0.339792π-0.339792\pi
0.482328 + 0.875991i 0.339792π0.339792\pi
192192 −8.77915e7 −0.00466226
193193 −4.69301e9 −0.243469 −0.121735 0.992563i 0.538846π-0.538846\pi
−0.121735 + 0.992563i 0.538846π0.538846\pi
194194 3.04850e10 1.54518
195195 3.06984e8 0.0152041
196196 7.30170e9 0.353404
197197 −1.50614e9 −0.0712470
198198 4.25344e10 1.96674
199199 −1.32204e10 −0.597594 −0.298797 0.954317i 0.596585π-0.596585\pi
−0.298797 + 0.954317i 0.596585π0.596585\pi
200200 −5.29085e9 −0.233825
201201 6.48420e7 0.00280204
202202 2.29191e9 0.0968538
203203 4.31482e10 1.78332
204204 2.44652e7 0.000989036 0
205205 −3.17755e10 −1.25661
206206 −3.81842e9 −0.147734
207207 −2.87771e10 −1.08938
208208 3.18090e10 1.17832
209209 4.63708e10 1.68107
210210 −7.29835e8 −0.0258963
211211 5.71933e10 1.98643 0.993216 0.116280i 0.0370970π-0.0370970\pi
0.993216 + 0.116280i 0.0370970π0.0370970\pi
212212 1.94786e10 0.662286
213213 −4.15134e8 −0.0138191
214214 −3.33036e10 −1.08550
215215 2.39163e10 0.763344
216216 8.46600e8 0.0264629
217217 1.92089e9 0.0588076
218218 7.54314e10 2.26203
219219 −4.63440e8 −0.0136143
220220 2.05947e10 0.592724
221221 3.66316e9 0.103298
222222 5.41721e8 0.0149688
223223 −5.71649e10 −1.54795 −0.773977 0.633214i 0.781735π-0.781735\pi
−0.773977 + 0.633214i 0.781735π0.781735\pi
224224 −4.23787e10 −1.12469
225225 1.35976e10 0.353706
226226 −1.81171e10 −0.461957
227227 −1.80488e10 −0.451163 −0.225581 0.974224i 0.572428π-0.572428\pi
−0.225581 + 0.974224i 0.572428π0.572428\pi
228228 −3.79819e8 −0.00930830
229229 5.57660e10 1.34002 0.670008 0.742354i 0.266291π-0.266291\pi
0.670008 + 0.742354i 0.266291π0.266291\pi
230230 −4.47928e10 −1.05544
231231 1.88983e9 0.0436687
232232 −3.89458e10 −0.882601
233233 −5.29219e10 −1.17634 −0.588172 0.808736i 0.700152π-0.700152\pi
−0.588172 + 0.808736i 0.700152π0.700152\pi
234234 −5.21652e10 −1.13739
235235 4.91065e9 0.105035
236236 −1.15483e10 −0.242333
237237 −1.07573e9 −0.0221480
238238 −8.70894e9 −0.175942
239239 1.79804e9 0.0356458 0.0178229 0.999841i 0.494327π-0.494327\pi
0.0178229 + 0.999841i 0.494327π0.494327\pi
240240 1.03236e9 0.0200854
241241 −6.95213e10 −1.32752 −0.663760 0.747945i 0.731041π-0.731041\pi
−0.663760 + 0.747945i 0.731041π0.731041\pi
242242 −1.07155e11 −2.00837
243243 −3.26390e9 −0.0600494
244244 3.19422e10 0.576913
245245 3.54824e10 0.629166
246246 −2.16656e9 −0.0377193
247247 −5.68702e10 −0.972184
248248 −1.73381e9 −0.0291050
249249 1.39480e8 0.00229940
250250 8.09801e10 1.31114
251251 1.13858e11 1.81063 0.905317 0.424737i 0.139633π-0.139633\pi
0.905317 + 0.424737i 0.139633π0.139633\pi
252252 3.85782e10 0.602615
253253 1.15987e11 1.77978
254254 3.90553e10 0.588746
255255 1.18887e8 0.00176078
256256 7.69634e10 1.11996
257257 −6.07005e9 −0.0867947 −0.0433974 0.999058i 0.513818π-0.513818\pi
−0.0433974 + 0.999058i 0.513818π0.513818\pi
258258 1.63069e9 0.0229131
259259 −5.99853e10 −0.828316
260260 −2.52577e10 −0.342779
261261 1.00092e11 1.33511
262262 −1.00623e11 −1.31929
263263 8.09083e10 1.04278 0.521390 0.853319i 0.325414π-0.325414\pi
0.521390 + 0.853319i 0.325414π0.325414\pi
264264 −1.70578e9 −0.0216125
265265 9.46553e10 1.17907
266266 1.35205e11 1.65587
267267 6.97042e8 0.00839380
268268 −5.33501e9 −0.0631726
269269 −7.12863e10 −0.830081 −0.415041 0.909803i 0.636233π-0.636233\pi
−0.415041 + 0.909803i 0.636233π0.636233\pi
270270 −3.38671e9 −0.0387830
271271 1.47145e11 1.65723 0.828617 0.559816i 0.189128π-0.189128\pi
0.828617 + 0.559816i 0.189128π0.189128\pi
272272 1.23189e10 0.136462
273273 −2.31773e9 −0.0252541
274274 8.55062e10 0.916474
275275 −5.48055e10 −0.577866
276276 −9.50035e8 −0.00985482
277277 2.60482e10 0.265839 0.132919 0.991127i 0.457565π-0.457565\pi
0.132919 + 0.991127i 0.457565π0.457565\pi
278278 9.55762e10 0.959728
279279 4.45593e9 0.0440271
280280 −7.29445e10 −0.709220
281281 −6.02508e10 −0.576480 −0.288240 0.957558i 0.593070π-0.593070\pi
−0.288240 + 0.957558i 0.593070π0.593070\pi
282282 3.34825e8 0.00315280
283283 −3.43541e10 −0.318376 −0.159188 0.987248i 0.550888π-0.550888\pi
−0.159188 + 0.987248i 0.550888π0.550888\pi
284284 3.41560e10 0.311555
285285 −1.84572e9 −0.0165716
286286 2.10252e11 1.85821
287287 2.39906e11 2.08724
288288 −9.83069e10 −0.842011
289289 −1.17169e11 −0.988037
290290 1.55797e11 1.29351
291291 3.14200e9 0.0256855
292292 3.81305e10 0.306937
293293 −7.28008e10 −0.577075 −0.288537 0.957469i 0.593169π-0.593169\pi
−0.288537 + 0.957469i 0.593169π0.593169\pi
294294 2.41931e9 0.0188855
295295 −5.61184e10 −0.431426
296296 5.41431e10 0.409950
297297 8.76955e9 0.0653993
298298 9.50112e10 0.697914
299299 −1.42248e11 −1.02926
300300 4.48907e8 0.00319971
301301 −1.80568e11 −1.26792
302302 −2.45608e11 −1.69907
303303 2.36220e8 0.00161000
304304 −1.91249e11 −1.28431
305305 1.55222e11 1.02708
306306 −2.02023e10 −0.131721
307307 6.54927e10 0.420795 0.210397 0.977616i 0.432524π-0.432524\pi
0.210397 + 0.977616i 0.432524π0.432524\pi
308308 −1.55490e11 −0.984520
309309 −3.93553e8 −0.00245578
310310 6.93586e9 0.0426552
311311 −1.93043e11 −1.17013 −0.585064 0.810987i 0.698930π-0.698930\pi
−0.585064 + 0.810987i 0.698930π0.698930\pi
312312 2.09200e9 0.0124987
313313 −2.03390e11 −1.19779 −0.598895 0.800828i 0.704393π-0.704393\pi
−0.598895 + 0.800828i 0.704393π0.704393\pi
314314 3.81289e11 2.21345
315315 1.87469e11 1.07283
316316 8.85078e10 0.499332
317317 −3.09712e11 −1.72263 −0.861314 0.508073i 0.830358π-0.830358\pi
−0.861314 + 0.508073i 0.830358π0.830358\pi
318318 6.45392e9 0.0353917
319319 −4.03422e11 −2.18123
320320 3.51010e10 0.187130
321321 −3.43249e9 −0.0180442
322322 3.38187e11 1.75310
323323 −2.20245e10 −0.112589
324324 8.94549e10 0.450974
325325 6.72146e10 0.334186
326326 2.67772e10 0.131307
327327 7.77448e9 0.0376016
328328 −2.16540e11 −1.03301
329329 −3.70755e10 −0.174464
330330 6.82372e9 0.0316744
331331 −3.55412e11 −1.62744 −0.813722 0.581255i 0.802562π-0.802562\pi
−0.813722 + 0.581255i 0.802562π0.802562\pi
332332 −1.14760e10 −0.0518405
333333 −1.39149e11 −0.620129
334334 5.19312e11 2.28333
335335 −2.59253e10 −0.112466
336336 −7.79433e9 −0.0333620
337337 −3.56501e10 −0.150566 −0.0752829 0.997162i 0.523986π-0.523986\pi
−0.0752829 + 0.997162i 0.523986π0.523986\pi
338338 3.12340e10 0.130168
339339 −1.86728e9 −0.00767910
340340 −9.78172e9 −0.0396972
341341 −1.79597e10 −0.0719291
342342 3.13639e11 1.23969
343343 7.43729e10 0.290129
344344 1.62982e11 0.627519
345345 −4.61666e9 −0.0175445
346346 4.23436e11 1.58835
347347 −2.35582e11 −0.872288 −0.436144 0.899877i 0.643656π-0.643656\pi
−0.436144 + 0.899877i 0.643656π0.643656\pi
348348 3.30439e9 0.0120777
349349 −1.61378e11 −0.582276 −0.291138 0.956681i 0.594034π-0.594034\pi
−0.291138 + 0.956681i 0.594034π0.594034\pi
350350 −1.59799e11 −0.569203
351351 −1.07552e10 −0.0378212
352352 3.96227e11 1.37563
353353 −3.84760e11 −1.31888 −0.659438 0.751759i 0.729206π-0.729206\pi
−0.659438 + 0.751759i 0.729206π0.729206\pi
354354 −3.82634e9 −0.0129500
355355 1.65980e11 0.554661
356356 −5.73506e10 −0.189240
357357 −8.97603e8 −0.00292467
358358 2.13178e11 0.685912
359359 −2.52817e11 −0.803308 −0.401654 0.915792i 0.631565π-0.631565\pi
−0.401654 + 0.915792i 0.631565π0.631565\pi
360360 −1.69211e11 −0.530967
361361 1.92403e10 0.0596253
362362 6.79274e11 2.07901
363363 −1.10441e10 −0.0333851
364364 1.90696e11 0.569359
365365 1.85294e11 0.546441
366366 1.05836e10 0.0308295
367367 −1.71582e11 −0.493713 −0.246856 0.969052i 0.579398π-0.579398\pi
−0.246856 + 0.969052i 0.579398π0.579398\pi
368368 −4.78368e11 −1.35971
369369 5.56515e11 1.56264
370370 −2.16592e11 −0.600807
371371 −7.14650e11 −1.95844
372372 1.47106e8 0.000398279 0
373373 −5.28558e10 −0.141385 −0.0706924 0.997498i 0.522521π-0.522521\pi
−0.0706924 + 0.997498i 0.522521π0.522521\pi
374374 8.14258e10 0.215199
375375 8.34637e9 0.0217950
376376 3.34646e10 0.0863455
377377 4.94765e11 1.26143
378378 2.55697e10 0.0644189
379379 −4.80261e11 −1.19564 −0.597821 0.801630i 0.703967π-0.703967\pi
−0.597821 + 0.801630i 0.703967π0.703967\pi
380380 1.51860e11 0.373610
381381 4.02531e9 0.00978670
382382 −4.83691e11 −1.16221
383383 −4.19884e11 −0.997092 −0.498546 0.866863i 0.666133π-0.666133\pi
−0.498546 + 0.866863i 0.666133π0.666133\pi
384384 9.58121e9 0.0224869
385385 −7.55598e11 −1.75274
386386 1.27937e11 0.293329
387387 −4.18869e11 −0.949246
388388 −2.58515e11 −0.579085
389389 8.83759e11 1.95686 0.978432 0.206569i 0.0662297π-0.0662297\pi
0.978432 + 0.206569i 0.0662297π0.0662297\pi
390390 −8.36876e9 −0.0183177
391391 −5.50894e10 −0.119199
392392 2.41801e11 0.517216
393393 −1.03709e10 −0.0219305
394394 4.10592e10 0.0858377
395395 4.30100e11 0.888961
396396 −3.60694e11 −0.737073
397397 5.53182e11 1.11766 0.558832 0.829281i 0.311250π-0.311250\pi
0.558832 + 0.829281i 0.311250π0.311250\pi
398398 3.60405e11 0.719975
399399 1.39352e10 0.0275255
400400 2.26037e11 0.441478
401401 3.82922e11 0.739538 0.369769 0.929124i 0.379437π-0.379437\pi
0.369769 + 0.929124i 0.379437π0.379437\pi
402402 −1.76767e9 −0.00337587
403403 2.20262e10 0.0415974
404404 −1.94355e10 −0.0362978
405405 4.34703e11 0.802869
406406 −1.17627e12 −2.14853
407407 5.60844e11 1.01313
408408 8.10182e8 0.00144748
409409 7.80488e11 1.37915 0.689575 0.724214i 0.257797π-0.257797\pi
0.689575 + 0.724214i 0.257797π0.257797\pi
410410 8.66240e11 1.51395
411411 8.81286e9 0.0152345
412412 3.23804e10 0.0553662
413413 4.23695e11 0.716602
414414 7.84501e11 1.31248
415415 −5.57672e10 −0.0922916
416416 −4.85942e11 −0.795544
417417 9.85074e9 0.0159535
418418 −1.26413e12 −2.02534
419419 −2.67523e11 −0.424032 −0.212016 0.977266i 0.568003π-0.568003\pi
−0.212016 + 0.977266i 0.568003π0.568003\pi
420420 6.18904e9 0.00970513
421421 −1.20251e11 −0.186560 −0.0932801 0.995640i 0.529735π-0.529735\pi
−0.0932801 + 0.995640i 0.529735π0.529735\pi
422422 −1.55916e12 −2.39323
423423 −8.60049e10 −0.130615
424424 6.45047e11 0.969271
425425 2.60306e10 0.0387021
426426 1.13171e10 0.0166491
427427 −1.17193e12 −1.70599
428428 2.82416e11 0.406810
429429 2.16701e10 0.0308889
430430 −6.51988e11 −0.919669
431431 5.43676e10 0.0758914 0.0379457 0.999280i 0.487919π-0.487919\pi
0.0379457 + 0.999280i 0.487919π0.487919\pi
432432 −3.61686e10 −0.0499638
433433 7.13709e11 0.975721 0.487860 0.872922i 0.337777π-0.337777\pi
0.487860 + 0.872922i 0.337777π0.337777\pi
434434 −5.23659e10 −0.0708508
435435 1.60576e10 0.0215019
436436 −6.39662e11 −0.847737
437437 8.55259e11 1.12184
438438 1.26340e10 0.0164024
439439 −3.91017e10 −0.0502464 −0.0251232 0.999684i 0.507998π-0.507998\pi
−0.0251232 + 0.999684i 0.507998π0.507998\pi
440440 6.82007e11 0.867465
441441 −6.21437e11 −0.782390
442442 −9.98623e10 −0.124452
443443 9.76650e10 0.120482 0.0602410 0.998184i 0.480813π-0.480813\pi
0.0602410 + 0.998184i 0.480813π0.480813\pi
444444 −4.59382e9 −0.00560984
445445 −2.78693e11 −0.336904
446446 1.55839e12 1.86496
447447 9.79251e9 0.0116014
448448 −2.65013e11 −0.310826
449449 −4.90259e11 −0.569268 −0.284634 0.958636i 0.591872π-0.591872\pi
−0.284634 + 0.958636i 0.591872π0.591872\pi
450450 −3.70689e11 −0.426141
451451 −2.24304e12 −2.55295
452452 1.53634e11 0.173127
453453 −2.53140e10 −0.0282436
454454 4.92035e11 0.543556
455455 9.26682e11 1.01363
456456 −1.25780e10 −0.0136229
457457 1.12239e12 1.20371 0.601855 0.798606i 0.294429π-0.294429\pi
0.601855 + 0.798606i 0.294429π0.294429\pi
458458 −1.52025e12 −1.61444
459459 −4.16522e9 −0.00438007
460460 3.79845e11 0.395546
461461 −5.53487e11 −0.570759 −0.285380 0.958415i 0.592120π-0.592120\pi
−0.285380 + 0.958415i 0.592120π0.592120\pi
462462 −5.15193e10 −0.0526115
463463 −1.15064e12 −1.16366 −0.581829 0.813311i 0.697663π-0.697663\pi
−0.581829 + 0.813311i 0.697663π0.697663\pi
464464 1.66385e12 1.66641
465465 7.14857e8 0.000709057 0
466466 1.44272e12 1.41725
467467 −1.20682e12 −1.17413 −0.587067 0.809538i 0.699718π-0.699718\pi
−0.587067 + 0.809538i 0.699718π0.699718\pi
468468 4.42363e11 0.426258
469469 1.95736e11 0.186807
470470 −1.33870e11 −0.126545
471471 3.92982e10 0.0367942
472472 −3.82430e11 −0.354660
473473 1.68826e12 1.55083
474474 2.93257e10 0.0266837
475475 −4.04123e11 −0.364244
476476 7.38522e10 0.0659375
477477 −1.65779e12 −1.46621
478478 −4.90167e10 −0.0429456
479479 −5.88600e11 −0.510870 −0.255435 0.966826i 0.582219π-0.582219\pi
−0.255435 + 0.966826i 0.582219π0.582219\pi
480480 −1.57712e10 −0.0135606
481481 −6.87831e11 −0.585907
482482 1.89524e12 1.59938
483483 3.48559e10 0.0291416
484484 9.08680e11 0.752674
485485 −1.25624e12 −1.03094
486486 8.89781e10 0.0723469
487487 8.90630e11 0.717492 0.358746 0.933435i 0.383204π-0.383204\pi
0.358746 + 0.933435i 0.383204π0.383204\pi
488488 1.05779e12 0.844325
489489 2.75985e9 0.00218271
490490 −9.67294e11 −0.758012
491491 −1.75078e11 −0.135946 −0.0679729 0.997687i 0.521653π-0.521653\pi
−0.0679729 + 0.997687i 0.521653π0.521653\pi
492492 1.83726e10 0.0141360
493493 1.91611e11 0.146086
494494 1.55035e12 1.17128
495495 −1.75278e12 −1.31221
496496 7.40720e10 0.0549524
497497 −1.25315e12 −0.921298
498498 −3.80240e9 −0.00277029
499499 2.13513e12 1.54160 0.770801 0.637076i 0.219856π-0.219856\pi
0.770801 + 0.637076i 0.219856π0.219856\pi
500500 −6.86715e11 −0.491373
501501 5.35239e10 0.0379558
502502 −3.10391e12 −2.18143
503503 −1.85502e12 −1.29209 −0.646044 0.763300i 0.723578π-0.723578\pi
−0.646044 + 0.763300i 0.723578π0.723578\pi
504504 1.27755e12 0.881941
505505 −9.44462e10 −0.0646209
506506 −3.16194e12 −2.14425
507507 3.21919e9 0.00216377
508508 −3.31191e11 −0.220644
509509 −6.25773e11 −0.413225 −0.206613 0.978423i 0.566244π-0.566244\pi
−0.206613 + 0.978423i 0.566244π0.566244\pi
510510 −3.24102e9 −0.00212137
511511 −1.39897e12 −0.907643
512512 −3.52197e11 −0.226501
513513 6.46646e10 0.0412229
514514 1.65477e11 0.104569
515515 1.57351e11 0.0985685
516516 −1.38284e10 −0.00858711
517517 3.46644e11 0.213391
518518 1.63528e12 0.997947
519519 4.36422e10 0.0264030
520520 −8.36429e11 −0.501665
521521 −7.06921e11 −0.420341 −0.210170 0.977665i 0.567402π-0.567402\pi
−0.210170 + 0.977665i 0.567402π0.567402\pi
522522 −2.72863e12 −1.60852
523523 8.82998e11 0.516062 0.258031 0.966137i 0.416926π-0.416926\pi
0.258031 + 0.966137i 0.416926π0.416926\pi
524524 8.53286e11 0.494429
525525 −1.64700e10 −0.00946184
526526 −2.20566e12 −1.25633
527527 8.53021e9 0.00481739
528528 7.28745e10 0.0408059
529529 3.38090e11 0.187708
530530 −2.58042e12 −1.42053
531531 9.82856e11 0.536493
532532 −1.14655e12 −0.620569
533533 2.75092e12 1.47640
534534 −1.90023e10 −0.0101128
535535 1.37239e12 0.724244
536536 −1.76673e11 −0.0924546
537537 2.19716e10 0.0114019
538538 1.94335e12 1.00007
539539 2.50471e12 1.27823
540540 2.87195e10 0.0145346
541541 1.66056e12 0.833427 0.416713 0.909038i 0.363182π-0.363182\pi
0.416713 + 0.909038i 0.363182π0.363182\pi
542542 −4.01136e12 −1.99662
543543 7.00107e10 0.0345593
544544 −1.88194e11 −0.0921319
545545 −3.10841e12 −1.50923
546546 6.31844e10 0.0304258
547547 −2.25202e12 −1.07555 −0.537773 0.843090i 0.680734π-0.680734\pi
−0.537773 + 0.843090i 0.680734π0.680734\pi
548548 −7.25096e11 −0.343466
549549 −2.71855e12 −1.27721
550550 1.49407e12 0.696206
551551 −2.97474e12 −1.37489
552552 −3.14611e10 −0.0144228
553553 −3.24727e12 −1.47657
554554 −7.10106e11 −0.320279
555555 −2.23235e10 −0.00998720
556556 −8.10491e11 −0.359676
557557 2.43310e12 1.07105 0.535527 0.844518i 0.320113π-0.320113\pi
0.535527 + 0.844518i 0.320113π0.320113\pi
558558 −1.21474e11 −0.0530433
559559 −2.07051e12 −0.896861
560560 3.11635e12 1.33906
561561 8.39230e9 0.00357724
562562 1.64251e12 0.694537
563563 −1.87650e12 −0.787154 −0.393577 0.919292i 0.628763π-0.628763\pi
−0.393577 + 0.919292i 0.628763π0.628763\pi
564564 −2.83933e9 −0.00118157
565565 7.46579e11 0.308218
566566 9.36536e11 0.383575
567567 −3.28202e12 −1.33357
568568 1.13110e12 0.455968
569569 6.80557e11 0.272182 0.136091 0.990696i 0.456546π-0.456546\pi
0.136091 + 0.990696i 0.456546π0.456546\pi
570570 5.03166e10 0.0199652
571571 −1.66287e12 −0.654628 −0.327314 0.944916i 0.606143π-0.606143\pi
−0.327314 + 0.944916i 0.606143π0.606143\pi
572572 −1.78295e12 −0.696397
573573 −4.98526e10 −0.0193193
574574 −6.54013e12 −2.51468
575575 −1.01083e12 −0.385630
576576 −6.14758e11 −0.232703
577577 2.72131e12 1.02208 0.511042 0.859556i 0.329260π-0.329260\pi
0.511042 + 0.859556i 0.329260π0.329260\pi
578578 3.19418e12 1.19038
579579 1.31861e10 0.00487600
580580 −1.32117e12 −0.484766
581581 4.21044e11 0.153297
582582 −8.56549e10 −0.0309456
583583 6.68175e12 2.39542
584584 1.26272e12 0.449210
585585 2.14965e12 0.758867
586586 1.98464e12 0.695253
587587 4.16725e12 1.44870 0.724349 0.689433i 0.242140π-0.242140\pi
0.724349 + 0.689433i 0.242140π0.242140\pi
588588 −2.05159e10 −0.00707769
589589 −1.32431e11 −0.0453388
590590 1.52986e12 0.519777
591591 4.23185e9 0.00142688
592592 −2.31311e12 −0.774015
593593 −3.32259e11 −0.110339 −0.0551696 0.998477i 0.517570π-0.517570\pi
−0.0551696 + 0.998477i 0.517570π0.517570\pi
594594 −2.39069e11 −0.0787924
595595 3.58882e11 0.117388
596596 −8.05700e11 −0.261556
597597 3.71459e10 0.0119681
598598 3.87787e12 1.24005
599599 3.49811e12 1.11023 0.555115 0.831773i 0.312674π-0.312674\pi
0.555115 + 0.831773i 0.312674π0.312674\pi
600600 1.48659e10 0.00468285
601601 4.68251e12 1.46401 0.732004 0.681301i 0.238585π-0.238585\pi
0.732004 + 0.681301i 0.238585π0.238585\pi
602602 4.92252e12 1.52758
603603 4.54054e11 0.139856
604604 2.08277e12 0.636758
605605 4.41570e12 1.33998
606606 −6.43967e9 −0.00193971
607607 −3.49070e12 −1.04367 −0.521836 0.853046i 0.674753π-0.674753\pi
−0.521836 + 0.853046i 0.674753π0.674753\pi
608608 2.92169e12 0.867098
609609 −1.21235e11 −0.0357149
610610 −4.23154e12 −1.23741
611611 −4.25132e11 −0.123407
612612 1.71317e11 0.0493649
613613 3.63680e12 1.04027 0.520136 0.854084i 0.325881π-0.325881\pi
0.520136 + 0.854084i 0.325881π0.325881\pi
614614 −1.78542e12 −0.506969
615615 8.92807e10 0.0251663
616616 −5.14917e12 −1.44087
617617 6.36043e11 0.176686 0.0883432 0.996090i 0.471843π-0.471843\pi
0.0883432 + 0.996090i 0.471843π0.471843\pi
618618 1.07288e10 0.00295870
619619 1.92995e12 0.528369 0.264185 0.964472i 0.414897π-0.414897\pi
0.264185 + 0.964472i 0.414897π0.414897\pi
620620 −5.88164e10 −0.0159858
621621 1.61745e11 0.0436433
622622 5.26261e12 1.40976
623623 2.10414e12 0.559601
624624 −8.93748e10 −0.0235985
625625 −1.98724e12 −0.520944
626626 5.54468e12 1.44308
627627 −1.30290e11 −0.0336671
628628 −3.23335e12 −0.829533
629629 −2.66381e11 −0.0678539
630630 −5.11065e12 −1.29254
631631 −3.98525e11 −0.100075 −0.0500373 0.998747i 0.515934π-0.515934\pi
−0.0500373 + 0.998747i 0.515934π0.515934\pi
632632 2.93100e12 0.730785
633633 −1.60698e11 −0.0397826
634634 8.44315e12 2.07540
635635 −1.60941e12 −0.392812
636636 −5.47296e10 −0.0132637
637637 −3.07183e12 −0.739213
638638 1.09978e13 2.62792
639639 −2.90697e12 −0.689741
640640 −3.83078e12 −0.902563
641641 −5.02329e12 −1.17524 −0.587621 0.809136i 0.699935π-0.699935\pi
−0.587621 + 0.809136i 0.699935π0.699935\pi
642642 9.35742e10 0.0217394
643643 5.97878e10 0.0137931 0.00689657 0.999976i 0.497805π-0.497805\pi
0.00689657 + 0.999976i 0.497805π0.497805\pi
644644 −2.86784e12 −0.657005
645645 −6.71984e10 −0.0152876
646646 6.00415e11 0.135646
647647 −7.37249e12 −1.65404 −0.827018 0.562176i 0.809964π-0.809964\pi
−0.827018 + 0.562176i 0.809964π0.809964\pi
648648 2.96237e12 0.660011
649649 −3.96141e12 −0.876494
650650 −1.83236e12 −0.402624
651651 −5.39719e9 −0.00117775
652652 −2.27072e11 −0.0492096
653653 8.15737e12 1.75566 0.877831 0.478971i 0.158990π-0.158990\pi
0.877831 + 0.478971i 0.158990π0.158990\pi
654654 −2.11942e11 −0.0453020
655655 4.14651e12 0.880232
656656 9.25108e12 1.95041
657657 −3.24523e12 −0.679519
658658 1.01073e12 0.210192
659659 6.17339e12 1.27508 0.637542 0.770415i 0.279951π-0.279951\pi
0.637542 + 0.770415i 0.279951π0.279951\pi
660660 −5.78655e10 −0.0118706
661661 −1.02154e12 −0.208136 −0.104068 0.994570i 0.533186π-0.533186\pi
−0.104068 + 0.994570i 0.533186π0.533186\pi
662662 9.68898e12 1.96073
663663 −1.02925e10 −0.00206876
664664 −3.80036e11 −0.0758698
665665 −5.57161e12 −1.10480
666666 3.79339e12 0.747125
667667 −7.44066e12 −1.45561
668668 −4.40379e12 −0.855721
669669 1.60618e11 0.0310011
670670 7.06756e11 0.135498
671671 1.09572e13 2.08663
672672 1.19073e11 0.0225243
673673 −8.94337e12 −1.68048 −0.840241 0.542214i 0.817586π-0.817586\pi
−0.840241 + 0.542214i 0.817586π0.817586\pi
674674 9.71867e11 0.181400
675675 −7.64268e10 −0.0141703
676676 −2.64866e11 −0.0487827
677677 −6.62513e12 −1.21212 −0.606060 0.795419i 0.707251π-0.707251\pi
−0.606060 + 0.795419i 0.707251π0.707251\pi
678678 5.09044e10 0.00925169
679679 9.48465e12 1.71241
680680 −3.23929e11 −0.0580978
681681 5.07125e10 0.00903551
682682 4.89604e11 0.0866594
683683 −4.28043e11 −0.0752653 −0.0376326 0.999292i 0.511982π-0.511982\pi
−0.0376326 + 0.999292i 0.511982π0.511982\pi
684684 −2.65968e12 −0.464597
685685 −3.52358e12 −0.611472
686686 −2.02750e12 −0.349545
687687 −1.56688e11 −0.0268367
688688 −6.96295e12 −1.18480
689689 −8.19464e12 −1.38530
690690 1.25856e11 0.0211375
691691 2.03772e12 0.340012 0.170006 0.985443i 0.445621π-0.445621\pi
0.170006 + 0.985443i 0.445621π0.445621\pi
692692 −3.59076e12 −0.595263
693693 1.32335e13 2.17960
694694 6.42227e12 1.05092
695695 −3.93855e12 −0.640331
696696 1.09427e11 0.0176760
697697 1.06536e12 0.170982
698698 4.39936e12 0.701520
699699 1.48697e11 0.0235588
700700 1.35510e12 0.213319
701701 9.06293e12 1.41755 0.708774 0.705436i 0.249249π-0.249249\pi
0.708774 + 0.705436i 0.249249π0.249249\pi
702702 2.93199e11 0.0455665
703703 4.13553e12 0.638606
704704 2.47779e12 0.380179
705705 −1.37976e10 −0.00210355
706706 1.04891e13 1.58897
707707 7.13071e11 0.107336
708708 3.24476e10 0.00485325
709709 −1.97637e12 −0.293738 −0.146869 0.989156i 0.546920π-0.546920\pi
−0.146869 + 0.989156i 0.546920π0.546920\pi
710710 −4.52482e12 −0.668250
711711 −7.53276e12 −1.10546
712712 −1.89921e12 −0.276957
713713 −3.31247e11 −0.0480008
714714 2.44698e10 0.00352362
715715 −8.66418e12 −1.23980
716716 −1.80776e12 −0.257058
717717 −5.05200e9 −0.000713884 0
718718 6.89213e12 0.967817
719719 −1.30533e12 −0.182154 −0.0910771 0.995844i 0.529031π-0.529031\pi
−0.0910771 + 0.995844i 0.529031π0.529031\pi
720720 7.22906e12 1.00250
721721 −1.18801e12 −0.163723
722722 −5.24516e11 −0.0718359
723723 1.95336e11 0.0265865
724724 −5.76028e12 −0.779148
725725 3.51583e12 0.472614
726726 3.01077e11 0.0402220
727727 1.26168e13 1.67511 0.837557 0.546350i 0.183983π-0.183983\pi
0.837557 + 0.546350i 0.183983π0.183983\pi
728728 6.31505e12 0.833270
729729 −7.60725e12 −0.997594
730730 −5.05134e12 −0.658346
731731 −8.01861e11 −0.103865
732732 −8.97490e10 −0.0115539
733733 −1.05610e13 −1.35125 −0.675627 0.737243i 0.736127π-0.736127\pi
−0.675627 + 0.737243i 0.736127π0.736127\pi
734734 4.67754e12 0.594820
735735 −9.96960e10 −0.0126004
736736 7.30797e12 0.918008
737737 −1.83007e12 −0.228489
738738 −1.51713e13 −1.88265
739739 3.02384e12 0.372957 0.186479 0.982459i 0.440293π-0.440293\pi
0.186479 + 0.982459i 0.440293π0.440293\pi
740740 1.83671e12 0.225164
741741 1.59790e11 0.0194701
742742 1.94823e13 2.35951
743743 1.45200e13 1.74790 0.873952 0.486012i 0.161549π-0.161549\pi
0.873952 + 0.486012i 0.161549π0.161549\pi
744744 4.87153e9 0.000582891 0
745745 −3.91527e12 −0.465648
746746 1.44091e12 0.170339
747747 9.76705e11 0.114768
748748 −6.90495e11 −0.0806498
749749 −1.03616e13 −1.20298
750750 −2.27533e11 −0.0262584
751751 4.67153e12 0.535895 0.267948 0.963434i 0.413655π-0.413655\pi
0.267948 + 0.963434i 0.413655π0.413655\pi
752752 −1.42968e12 −0.163027
753753 −3.19910e11 −0.0362619
754754 −1.34879e13 −1.51976
755755 1.01211e13 1.13362
756756 −2.16833e11 −0.0241422
757757 5.33315e12 0.590272 0.295136 0.955455i 0.404635π-0.404635\pi
0.295136 + 0.955455i 0.404635π0.404635\pi
758758 1.30925e13 1.44050
759759 −3.25891e11 −0.0356439
760760 5.02897e12 0.546786
761761 −2.66730e12 −0.288298 −0.144149 0.989556i 0.546044π-0.546044\pi
−0.144149 + 0.989556i 0.546044π0.546044\pi
762762 −1.09735e11 −0.0117909
763763 2.34686e13 2.50684
764764 4.10173e12 0.435558
765765 8.32507e11 0.0878843
766766 1.14466e13 1.20129
767767 4.85836e12 0.506887
768768 −2.16247e11 −0.0224297
769769 −1.16350e13 −1.19977 −0.599883 0.800087i 0.704786π-0.704786\pi
−0.599883 + 0.800087i 0.704786π0.704786\pi
770770 2.05986e13 2.11168
771771 1.70552e10 0.00173825
772772 −1.08492e12 −0.109930
773773 −5.34961e12 −0.538908 −0.269454 0.963013i 0.586843π-0.586843\pi
−0.269454 + 0.963013i 0.586843π0.586843\pi
774774 1.14189e13 1.14364
775775 1.56519e11 0.0155851
776776 −8.56090e12 −0.847504
777777 1.68543e11 0.0165888
778778 −2.40924e13 −2.35761
779779 −1.65397e13 −1.60919
780780 7.09675e10 0.00686489
781781 1.17166e13 1.12686
782782 1.50181e12 0.143610
783783 −5.62576e11 −0.0534876
784784 −1.03303e13 −0.976540
785785 −1.57123e13 −1.47682
786786 2.82723e11 0.0264217
787787 −1.16579e13 −1.08326 −0.541632 0.840615i 0.682194π-0.682194\pi
−0.541632 + 0.840615i 0.682194π0.682194\pi
788788 −3.48184e11 −0.0321693
789789 −2.27331e11 −0.0208839
790790 −1.17251e13 −1.07101
791791 −5.63669e12 −0.511953
792792 −1.19447e13 −1.07872
793793 −1.34381e13 −1.20672
794794 −1.50805e13 −1.34655
795795 −2.65956e11 −0.0236134
796796 −3.05625e12 −0.269824
797797 −1.16078e13 −1.01903 −0.509514 0.860463i 0.670175π-0.670175\pi
−0.509514 + 0.860463i 0.670175π0.670175\pi
798798 −3.79891e11 −0.0331624
799799 −1.64643e11 −0.0142917
800800 −3.45313e12 −0.298063
801801 4.88102e12 0.418952
802802 −1.04389e13 −0.890988
803803 1.30799e13 1.11016
804804 1.49900e10 0.00126517
805805 −1.39362e13 −1.16967
806806 −6.00461e11 −0.0501161
807807 2.00296e11 0.0166242
808808 −6.43622e11 −0.0531227
809809 3.30393e12 0.271183 0.135591 0.990765i 0.456707π-0.456707\pi
0.135591 + 0.990765i 0.456707π0.456707\pi
810810 −1.18505e13 −0.967288
811811 −3.66102e12 −0.297172 −0.148586 0.988899i 0.547472π-0.547472\pi
−0.148586 + 0.988899i 0.547472π0.547472\pi
812812 9.97486e12 0.805201
813813 −4.13438e11 −0.0331897
814814 −1.52893e13 −1.22061
815815 −1.10345e12 −0.0876078
816816 −3.46128e10 −0.00273294
817817 1.24488e13 0.977528
818818 −2.12771e13 −1.66159
819819 −1.62299e13 −1.26048
820820 −7.34576e12 −0.567380
821821 1.09783e13 0.843321 0.421660 0.906754i 0.361447π-0.361447\pi
0.421660 + 0.906754i 0.361447π0.361447\pi
822822 −2.40250e11 −0.0183544
823823 −1.81105e13 −1.37604 −0.688019 0.725693i 0.741519π-0.741519\pi
−0.688019 + 0.725693i 0.741519π0.741519\pi
824824 1.07230e12 0.0810298
825825 1.53989e11 0.0115730
826826 −1.15505e13 −0.863355
827827 −5.02389e12 −0.373478 −0.186739 0.982410i 0.559792π-0.559792\pi
−0.186739 + 0.982410i 0.559792π0.559792\pi
828828 −6.65260e12 −0.491875
829829 2.49772e13 1.83674 0.918371 0.395721i 0.129505π-0.129505\pi
0.918371 + 0.395721i 0.129505π0.129505\pi
830830 1.52028e12 0.111192
831831 −7.31884e10 −0.00532400
832832 −3.03882e12 −0.219862
833833 −1.18965e12 −0.0856083
834834 −2.68544e11 −0.0192206
835835 −2.14000e13 −1.52344
836836 1.07199e13 0.759034
837837 −2.50450e10 −0.00176383
838838 7.29302e12 0.510869
839839 −1.68612e13 −1.17479 −0.587393 0.809302i 0.699846π-0.699846\pi
−0.587393 + 0.809302i 0.699846π0.699846\pi
840840 2.04955e11 0.0142037
841841 1.13728e13 0.783944
842842 3.27819e12 0.224766
843843 1.69289e11 0.0115453
844844 1.32218e13 0.896909
845845 −1.28711e12 −0.0868479
846846 2.34460e12 0.157363
847847 −3.33386e13 −2.22573
848848 −2.75578e13 −1.83005
849849 9.65259e10 0.00637616
850850 −7.09628e11 −0.0466279
851851 1.03441e13 0.676101
852852 −9.59694e10 −0.00623957
853853 −2.96077e12 −0.191485 −0.0957424 0.995406i 0.530523π-0.530523\pi
−0.0957424 + 0.995406i 0.530523π0.530523\pi
854854 3.19482e13 2.05535
855855 −1.29246e13 −0.827122
856856 9.35241e12 0.595376
857857 −2.12923e13 −1.34837 −0.674186 0.738562i 0.735505π-0.735505\pi
−0.674186 + 0.738562i 0.735505π0.735505\pi
858858 −5.90754e11 −0.0372146
859859 1.10479e13 0.692325 0.346163 0.938174i 0.387485π-0.387485\pi
0.346163 + 0.938174i 0.387485π0.387485\pi
860860 5.52889e12 0.344663
861861 −6.74071e11 −0.0418015
862862 −1.48213e12 −0.0914332
863863 −5.45410e12 −0.334714 −0.167357 0.985896i 0.553523π-0.553523\pi
−0.167357 + 0.985896i 0.553523π0.553523\pi
864864 5.52543e11 0.0337330
865865 −1.74491e13 −1.05975
866866 −1.94566e13 −1.17554
867867 3.29214e11 0.0197876
868868 4.44065e11 0.0265526
869869 3.03609e13 1.80603
870870 −4.37749e11 −0.0259053
871871 2.24444e12 0.132138
872872 −2.11829e13 −1.24068
873873 2.20018e13 1.28202
874874 −2.33154e13 −1.35158
875875 2.51949e13 1.45304
876876 −1.07137e11 −0.00614709
877877 −6.93874e12 −0.396079 −0.198040 0.980194i 0.563458π-0.563458\pi
−0.198040 + 0.980194i 0.563458π0.563458\pi
878878 1.06596e12 0.0605363
879879 2.04551e11 0.0115572
880880 −2.91368e13 −1.63784
881881 −1.10273e13 −0.616705 −0.308352 0.951272i 0.599778π-0.599778\pi
−0.308352 + 0.951272i 0.599778π0.599778\pi
882882 1.69412e13 0.942615
883883 −1.09368e13 −0.605434 −0.302717 0.953081i 0.597894π-0.597894\pi
−0.302717 + 0.953081i 0.597894π0.597894\pi
884884 8.46837e11 0.0466407
885885 1.57678e11 0.00864024
886886 −2.66247e12 −0.145155
887887 −2.59031e13 −1.40506 −0.702532 0.711653i 0.747947π-0.747947\pi
−0.702532 + 0.711653i 0.747947π0.747947\pi
888888 −1.52128e11 −0.00821014
889889 1.21511e13 0.652464
890890 7.59753e12 0.405898
891891 3.06858e13 1.63113
892892 −1.32152e13 −0.698928
893893 2.55608e12 0.134506
894894 −2.66956e11 −0.0139772
895895 −8.78473e12 −0.457641
896896 2.89225e13 1.49917
897897 3.99680e11 0.0206133
898898 1.33651e13 0.685848
899899 1.15213e12 0.0588280
900900 3.14346e12 0.159704
901901 −3.17359e12 −0.160431
902902 6.11482e13 3.07577
903903 5.07349e11 0.0253929
904904 5.08771e12 0.253375
905905 −2.79919e13 −1.38712
906906 6.90093e11 0.0340275
907907 −1.56389e12 −0.0767316 −0.0383658 0.999264i 0.512215π-0.512215\pi
−0.0383658 + 0.999264i 0.512215π0.512215\pi
908908 −4.17248e12 −0.203708
909909 1.65413e12 0.0803585
910910 −2.52625e13 −1.22121
911911 2.44644e13 1.17680 0.588398 0.808571i 0.299759π-0.299759\pi
0.588398 + 0.808571i 0.299759π0.299759\pi
912912 5.37360e11 0.0257210
913913 −3.93662e12 −0.187502
914914 −3.05978e13 −1.45022
915915 −4.36132e11 −0.0205695
916916 1.28918e13 0.605040
917917 −3.13063e13 −1.46207
918918 1.13549e11 0.00527706
919919 −9.29278e12 −0.429760 −0.214880 0.976640i 0.568936π-0.568936\pi
−0.214880 + 0.976640i 0.568936π0.568936\pi
920920 1.25789e13 0.578890
921921 −1.84017e11 −0.00842733
922922 1.50888e13 0.687645
923923 −1.43695e13 −0.651678
924924 4.36886e11 0.0197172
925925 −4.88777e12 −0.219519
926926 3.13679e13 1.40196
927927 −2.75585e12 −0.122573
928928 −2.54184e13 −1.12508
929929 3.95256e12 0.174104 0.0870518 0.996204i 0.472255π-0.472255\pi
0.0870518 + 0.996204i 0.472255π0.472255\pi
930930 −1.94879e10 −0.000854264 0
931931 1.84692e13 0.805701
932932 −1.22343e13 −0.531139
933933 5.42401e11 0.0234343
934934 3.28996e13 1.41459
935935 −3.35543e12 −0.143581
936936 1.46492e13 0.623838
937937 3.11102e12 0.131848 0.0659242 0.997825i 0.479000π-0.479000\pi
0.0659242 + 0.997825i 0.479000π0.479000\pi
938938 −5.33602e12 −0.225063
939939 5.71473e11 0.0239884
940940 1.13523e12 0.0474250
941941 −2.78496e13 −1.15789 −0.578943 0.815368i 0.696534π-0.696534\pi
−0.578943 + 0.815368i 0.696534π0.696534\pi
942942 −1.07132e12 −0.0443292
943943 −4.13704e13 −1.70368
944944 1.63382e13 0.669624
945945 −1.05369e12 −0.0429803
946946 −4.60240e13 −1.86842
947947 4.90336e12 0.198116 0.0990578 0.995082i 0.468417π-0.468417\pi
0.0990578 + 0.995082i 0.468417π0.468417\pi
948948 −2.48684e11 −0.0100002
949949 −1.60415e13 −0.642019
950950 1.10169e13 0.438837
951951 8.70209e11 0.0344994
952952 2.44567e12 0.0965010
953953 3.31980e13 1.30375 0.651875 0.758327i 0.273983π-0.273983\pi
0.651875 + 0.758327i 0.273983π0.273983\pi
954954 4.51935e13 1.76648
955955 1.99322e13 0.775425
956956 4.15664e11 0.0160947
957957 1.13351e12 0.0436838
958958 1.60460e13 0.615490
959959 2.66031e13 1.01566
960960 −9.86245e10 −0.00374769
961961 −2.63883e13 −0.998060
962962 1.87511e13 0.705895
963963 −2.40360e13 −0.900624
964964 −1.60717e13 −0.599399
965965 −5.27211e12 −0.195709
966966 −9.50216e11 −0.0351095
967967 −4.01878e13 −1.47800 −0.739001 0.673704i 0.764702π-0.764702\pi
−0.739001 + 0.673704i 0.764702π0.764702\pi
968968 3.00916e13 1.10156
969969 6.18829e10 0.00225483
970970 3.42467e13 1.24207
971971 8.15723e12 0.294480 0.147240 0.989101i 0.452961π-0.452961\pi
0.147240 + 0.989101i 0.452961π0.452961\pi
972972 −7.54538e11 −0.0271133
973973 2.97361e13 1.06360
974974 −2.42797e13 −0.864427
975975 −1.88855e11 −0.00669281
976976 −4.51911e13 −1.59415
977977 9.16012e12 0.321644 0.160822 0.986983i 0.448585π-0.448585\pi
0.160822 + 0.986983i 0.448585π0.448585\pi
978978 −7.52369e10 −0.00262970
979979 −1.96730e13 −0.684462
980980 8.20270e12 0.284079
981981 5.44406e13 1.87678
982982 4.77286e12 0.163786
983983 −3.83289e13 −1.30929 −0.654645 0.755937i 0.727182π-0.727182\pi
−0.654645 + 0.755937i 0.727182π0.727182\pi
984984 6.08421e11 0.0206884
985985 −1.69199e12 −0.0572709
986986 −5.22355e12 −0.176003
987987 1.04172e11 0.00349402
988988 −1.31471e13 −0.438958
989989 3.11380e13 1.03492
990990 4.77830e13 1.58094
991991 5.86162e13 1.93057 0.965287 0.261191i 0.0841152π-0.0841152\pi
0.965287 + 0.261191i 0.0841152π0.0841152\pi
992992 −1.13159e12 −0.0371010
993993 9.98613e11 0.0325931
994994 3.41625e13 1.10997
995995 −1.48518e13 −0.480368
996996 3.22445e10 0.00103822
997997 2.00858e13 0.643814 0.321907 0.946771i 0.395676π-0.395676\pi
0.321907 + 0.946771i 0.395676π0.395676\pi
998998 −5.82064e13 −1.85730
999999 7.82103e11 0.0248439
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 197.10.a.a.1.18 71
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
197.10.a.a.1.18 71 1.1 even 1 trivial