Properties

Label 285.10.a.d.1.8
Level 285285
Weight 1010
Character 285.1
Self dual yes
Analytic conductor 146.785146.785
Analytic rank 11
Dimension 1212
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [285,10,Mod(1,285)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(285, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 10, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("285.1"); S:= CuspForms(chi, 10); N := Newforms(S);
 
Level: N N == 285=3519 285 = 3 \cdot 5 \cdot 19
Weight: k k == 10 10
Character orbit: [χ][\chi] == 285.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,-33,972] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 146.785213307146.785213307
Analytic rank: 11
Dimension: 1212
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x123x114398x10+11376x9+7070146x815274638x75114407260x6++43 ⁣ ⁣00 x^{12} - 3 x^{11} - 4398 x^{10} + 11376 x^{9} + 7070146 x^{8} - 15274638 x^{7} - 5114407260 x^{6} + \cdots + 43\!\cdots\!00 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 2143352 2^{14}\cdot 3^{3}\cdot 5^{2}
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.8
Root 11.501311.5013 of defining polynomial
Character χ\chi == 285.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+8.50131q2+81.0000q3439.728q4+625.000q5+688.606q68602.42q78090.93q8+6561.00q9+5313.32q102144.81q1135617.9q12+70308.7q1373131.8q14+50625.0q15+156357.q16+263687.q17+55777.1q18130321.q19274830.q20696796.q2118233.7q22+295644.q23655366.q24+390625.q25+597716.q26+531441.q27+3.78272e6q28+1.37332e6q29+430379.q30+5.69212e6q31+5.47180e6q32173729.q33+2.24168e6q345.37651e6q352.88505e6q36+2.06086e6q371.10790e6q38+5.69500e6q395.05683e6q40+4.65536e6q415.92368e6q422.99326e7q43+943131.q44+4.10062e6q45+2.51336e6q464.23360e7q47+1.26649e7q48+3.36479e7q49+3.32082e6q50+2.13586e7q513.09167e7q52+1.46136e6q53+4.51795e6q541.34050e6q55+6.96016e7q561.05560e7q57+1.16750e7q581.52959e8q592.22612e7q60+3.93525e7q61+4.83905e7q625.64404e7q633.35374e7q64+4.39429e7q651.47693e6q66+8.09717e7q671.15950e8q68+2.39472e7q694.57074e7q702.70449e8q715.30846e7q722.60740e8q73+1.75200e7q74+3.16406e7q75+5.73058e7q76+1.84505e7q77+4.84150e7q784.52449e8q79+9.77232e7q80+4.30467e7q81+3.95767e7q82+3.90244e8q83+3.06400e8q84+1.64804e8q852.54466e8q86+1.11239e8q87+1.73535e7q88+2.57339e8q89+3.48607e7q906.04825e8q911.30003e8q92+4.61062e8q933.59911e8q948.14506e7q95+4.43216e8q966.90478e8q97+2.86052e8q981.40721e7q99+O(q100)q+8.50131 q^{2} +81.0000 q^{3} -439.728 q^{4} +625.000 q^{5} +688.606 q^{6} -8602.42 q^{7} -8090.93 q^{8} +6561.00 q^{9} +5313.32 q^{10} -2144.81 q^{11} -35617.9 q^{12} +70308.7 q^{13} -73131.8 q^{14} +50625.0 q^{15} +156357. q^{16} +263687. q^{17} +55777.1 q^{18} -130321. q^{19} -274830. q^{20} -696796. q^{21} -18233.7 q^{22} +295644. q^{23} -655366. q^{24} +390625. q^{25} +597716. q^{26} +531441. q^{27} +3.78272e6 q^{28} +1.37332e6 q^{29} +430379. q^{30} +5.69212e6 q^{31} +5.47180e6 q^{32} -173729. q^{33} +2.24168e6 q^{34} -5.37651e6 q^{35} -2.88505e6 q^{36} +2.06086e6 q^{37} -1.10790e6 q^{38} +5.69500e6 q^{39} -5.05683e6 q^{40} +4.65536e6 q^{41} -5.92368e6 q^{42} -2.99326e7 q^{43} +943131. q^{44} +4.10062e6 q^{45} +2.51336e6 q^{46} -4.23360e7 q^{47} +1.26649e7 q^{48} +3.36479e7 q^{49} +3.32082e6 q^{50} +2.13586e7 q^{51} -3.09167e7 q^{52} +1.46136e6 q^{53} +4.51795e6 q^{54} -1.34050e6 q^{55} +6.96016e7 q^{56} -1.05560e7 q^{57} +1.16750e7 q^{58} -1.52959e8 q^{59} -2.22612e7 q^{60} +3.93525e7 q^{61} +4.83905e7 q^{62} -5.64404e7 q^{63} -3.35374e7 q^{64} +4.39429e7 q^{65} -1.47693e6 q^{66} +8.09717e7 q^{67} -1.15950e8 q^{68} +2.39472e7 q^{69} -4.57074e7 q^{70} -2.70449e8 q^{71} -5.30846e7 q^{72} -2.60740e8 q^{73} +1.75200e7 q^{74} +3.16406e7 q^{75} +5.73058e7 q^{76} +1.84505e7 q^{77} +4.84150e7 q^{78} -4.52449e8 q^{79} +9.77232e7 q^{80} +4.30467e7 q^{81} +3.95767e7 q^{82} +3.90244e8 q^{83} +3.06400e8 q^{84} +1.64804e8 q^{85} -2.54466e8 q^{86} +1.11239e8 q^{87} +1.73535e7 q^{88} +2.57339e8 q^{89} +3.48607e7 q^{90} -6.04825e8 q^{91} -1.30003e8 q^{92} +4.61062e8 q^{93} -3.59911e8 q^{94} -8.14506e7 q^{95} +4.43216e8 q^{96} -6.90478e8 q^{97} +2.86052e8 q^{98} -1.40721e7 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q33q2+972q3+2751q4+7500q52673q65100q740215q8+78732q920625q1060416q11+222831q12164042q13444762q14+607500q15+396389376q99+O(q100) 12 q - 33 q^{2} + 972 q^{3} + 2751 q^{4} + 7500 q^{5} - 2673 q^{6} - 5100 q^{7} - 40215 q^{8} + 78732 q^{9} - 20625 q^{10} - 60416 q^{11} + 222831 q^{12} - 164042 q^{13} - 444762 q^{14} + 607500 q^{15}+ \cdots - 396389376 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 8.50131 0.375708 0.187854 0.982197i 0.439847π-0.439847\pi
0.187854 + 0.982197i 0.439847π0.439847\pi
33 81.0000 0.577350
44 −439.728 −0.858843
55 625.000 0.447214
66 688.606 0.216915
77 −8602.42 −1.35419 −0.677094 0.735896i 0.736761π-0.736761\pi
−0.677094 + 0.735896i 0.736761π0.736761\pi
88 −8090.93 −0.698383
99 6561.00 0.333333
1010 5313.32 0.168022
1111 −2144.81 −0.0441694 −0.0220847 0.999756i 0.507030π-0.507030\pi
−0.0220847 + 0.999756i 0.507030π0.507030\pi
1212 −35617.9 −0.495853
1313 70308.7 0.682753 0.341377 0.939927i 0.389107π-0.389107\pi
0.341377 + 0.939927i 0.389107π0.389107\pi
1414 −73131.8 −0.508780
1515 50625.0 0.258199
1616 156357. 0.596455
1717 263687. 0.765717 0.382858 0.923807i 0.374940π-0.374940\pi
0.382858 + 0.923807i 0.374940π0.374940\pi
1818 55777.1 0.125236
1919 −130321. −0.229416
2020 −274830. −0.384086
2121 −696796. −0.781841
2222 −18233.7 −0.0165948
2323 295644. 0.220290 0.110145 0.993916i 0.464869π-0.464869\pi
0.110145 + 0.993916i 0.464869π0.464869\pi
2424 −655366. −0.403212
2525 390625. 0.200000
2626 597716. 0.256516
2727 531441. 0.192450
2828 3.78272e6 1.16304
2929 1.37332e6 0.360562 0.180281 0.983615i 0.442299π-0.442299\pi
0.180281 + 0.983615i 0.442299π0.442299\pi
3030 430379. 0.0970075
3131 5.69212e6 1.10700 0.553499 0.832850i 0.313292π-0.313292\pi
0.553499 + 0.832850i 0.313292π0.313292\pi
3232 5.47180e6 0.922476
3333 −173729. −0.0255012
3434 2.24168e6 0.287686
3535 −5.37651e6 −0.605612
3636 −2.88505e6 −0.286281
3737 2.06086e6 0.180776 0.0903882 0.995907i 0.471189π-0.471189\pi
0.0903882 + 0.995907i 0.471189π0.471189\pi
3838 −1.10790e6 −0.0861934
3939 5.69500e6 0.394188
4040 −5.05683e6 −0.312326
4141 4.65536e6 0.257292 0.128646 0.991691i 0.458937π-0.458937\pi
0.128646 + 0.991691i 0.458937π0.458937\pi
4242 −5.92368e6 −0.293744
4343 −2.99326e7 −1.33517 −0.667585 0.744534i 0.732672π-0.732672\pi
−0.667585 + 0.744534i 0.732672π0.732672\pi
4444 943131. 0.0379346
4545 4.10062e6 0.149071
4646 2.51336e6 0.0827647
4747 −4.23360e7 −1.26552 −0.632760 0.774348i 0.718078π-0.718078\pi
−0.632760 + 0.774348i 0.718078π0.718078\pi
4848 1.26649e7 0.344363
4949 3.36479e7 0.833827
5050 3.32082e6 0.0751417
5151 2.13586e7 0.442087
5252 −3.09167e7 −0.586378
5353 1.46136e6 0.0254400 0.0127200 0.999919i 0.495951π-0.495951\pi
0.0127200 + 0.999919i 0.495951π0.495951\pi
5454 4.51795e6 0.0723051
5555 −1.34050e6 −0.0197531
5656 6.96016e7 0.945743
5757 −1.05560e7 −0.132453
5858 1.16750e7 0.135466
5959 −1.52959e8 −1.64339 −0.821695 0.569928i 0.806971π-0.806971\pi
−0.821695 + 0.569928i 0.806971π0.806971\pi
6060 −2.22612e7 −0.221752
6161 3.93525e7 0.363905 0.181952 0.983307i 0.441758π-0.441758\pi
0.181952 + 0.983307i 0.441758π0.441758\pi
6262 4.83905e7 0.415908
6363 −5.64404e7 −0.451396
6464 −3.35374e7 −0.249873
6565 4.39429e7 0.305337
6666 −1.47693e6 −0.00958101
6767 8.09717e7 0.490904 0.245452 0.969409i 0.421064π-0.421064\pi
0.245452 + 0.969409i 0.421064π0.421064\pi
6868 −1.15950e8 −0.657630
6969 2.39472e7 0.127184
7070 −4.57074e7 −0.227533
7171 −2.70449e8 −1.26306 −0.631529 0.775352i 0.717572π-0.717572\pi
−0.631529 + 0.775352i 0.717572π0.717572\pi
7272 −5.30846e7 −0.232794
7373 −2.60740e8 −1.07462 −0.537310 0.843385i 0.680559π-0.680559\pi
−0.537310 + 0.843385i 0.680559π0.680559\pi
7474 1.75200e7 0.0679192
7575 3.16406e7 0.115470
7676 5.73058e7 0.197032
7777 1.84505e7 0.0598137
7878 4.84150e7 0.148100
7979 −4.52449e8 −1.30691 −0.653457 0.756963i 0.726682π-0.726682\pi
−0.653457 + 0.756963i 0.726682π0.726682\pi
8080 9.77232e7 0.266743
8181 4.30467e7 0.111111
8282 3.95767e7 0.0966667
8383 3.90244e8 0.902578 0.451289 0.892378i 0.350964π-0.350964\pi
0.451289 + 0.892378i 0.350964π0.350964\pi
8484 3.06400e8 0.671479
8585 1.64804e8 0.342439
8686 −2.54466e8 −0.501634
8787 1.11239e8 0.208171
8888 1.73535e7 0.0308471
8989 2.57339e8 0.434760 0.217380 0.976087i 0.430249π-0.430249\pi
0.217380 + 0.976087i 0.430249π0.430249\pi
9090 3.48607e7 0.0560073
9191 −6.04825e8 −0.924577
9292 −1.30003e8 −0.189194
9393 4.61062e8 0.639125
9494 −3.59911e8 −0.475467
9595 −8.14506e7 −0.102598
9696 4.43216e8 0.532592
9797 −6.90478e8 −0.791912 −0.395956 0.918269i 0.629587π-0.629587\pi
−0.395956 + 0.918269i 0.629587π0.629587\pi
9898 2.86052e8 0.313276
9999 −1.40721e7 −0.0147231
100100 −1.71769e8 −0.171769
101101 8.09329e8 0.773889 0.386945 0.922103i 0.373530π-0.373530\pi
0.386945 + 0.922103i 0.373530π0.373530\pi
102102 1.81576e8 0.166096
103103 −4.61235e8 −0.403789 −0.201895 0.979407i 0.564710π-0.564710\pi
−0.201895 + 0.979407i 0.564710π0.564710\pi
104104 −5.68863e8 −0.476823
105105 −4.35497e8 −0.349650
106106 1.24235e7 0.00955801
107107 2.07157e9 1.52782 0.763910 0.645323i 0.223277π-0.223277\pi
0.763910 + 0.645323i 0.223277π0.223277\pi
108108 −2.33689e8 −0.165284
109109 −1.48763e9 −1.00943 −0.504716 0.863286i 0.668403π-0.668403\pi
−0.504716 + 0.863286i 0.668403π0.668403\pi
110110 −1.13960e7 −0.00742142
111111 1.66930e8 0.104371
112112 −1.34505e9 −0.807712
113113 −1.80621e9 −1.04212 −0.521058 0.853521i 0.674462π-0.674462\pi
−0.521058 + 0.853521i 0.674462π0.674462\pi
114114 −8.97398e7 −0.0497638
115115 1.84778e8 0.0985165
116116 −6.03886e8 −0.309666
117117 4.61295e8 0.227584
118118 −1.30035e9 −0.617435
119119 −2.26834e9 −1.03692
120120 −4.09604e8 −0.180322
121121 −2.35335e9 −0.998049
122122 3.34548e8 0.136722
123123 3.77084e8 0.148547
124124 −2.50298e9 −0.950737
125125 2.44141e8 0.0894427
126126 −4.79818e8 −0.169593
127127 5.96178e7 0.0203357 0.0101679 0.999948i 0.496763π-0.496763\pi
0.0101679 + 0.999948i 0.496763π0.496763\pi
128128 −3.08667e9 −1.01636
129129 −2.42454e9 −0.770860
130130 3.73572e8 0.114718
131131 −1.77693e9 −0.527170 −0.263585 0.964636i 0.584905π-0.584905\pi
−0.263585 + 0.964636i 0.584905π0.584905\pi
132132 7.63936e7 0.0219015
133133 1.12108e9 0.310672
134134 6.88365e8 0.184437
135135 3.32151e8 0.0860663
136136 −2.13347e9 −0.534763
137137 5.67513e9 1.37636 0.688182 0.725538i 0.258409π-0.258409\pi
0.688182 + 0.725538i 0.258409π0.258409\pi
138138 2.03582e8 0.0477842
139139 −3.44001e9 −0.781615 −0.390808 0.920472i 0.627804π-0.627804\pi
−0.390808 + 0.920472i 0.627804π0.627804\pi
140140 2.36420e9 0.520125
141141 −3.42921e9 −0.730649
142142 −2.29917e9 −0.474541
143143 −1.50799e8 −0.0301568
144144 1.02586e9 0.198818
145145 8.58323e8 0.161248
146146 −2.21663e9 −0.403744
147147 2.72548e9 0.481411
148148 −9.06219e8 −0.155259
149149 2.87682e9 0.478162 0.239081 0.971000i 0.423154π-0.423154\pi
0.239081 + 0.971000i 0.423154π0.423154\pi
150150 2.68987e8 0.0433831
151151 1.91829e9 0.300274 0.150137 0.988665i 0.452029π-0.452029\pi
0.150137 + 0.988665i 0.452029π0.452029\pi
152152 1.05442e9 0.160220
153153 1.73005e9 0.255239
154154 1.56854e8 0.0224725
155155 3.55758e9 0.495064
156156 −2.50425e9 −0.338546
157157 −8.04093e9 −1.05623 −0.528114 0.849173i 0.677101π-0.677101\pi
−0.528114 + 0.849173i 0.677101π0.677101\pi
158158 −3.84641e9 −0.491019
159159 1.18370e8 0.0146878
160160 3.41987e9 0.412544
161161 −2.54325e9 −0.298314
162162 3.65954e8 0.0417454
163163 1.11263e9 0.123455 0.0617273 0.998093i 0.480339π-0.480339\pi
0.0617273 + 0.998093i 0.480339π0.480339\pi
164164 −2.04709e9 −0.220973
165165 −1.08581e8 −0.0114045
166166 3.31759e9 0.339106
167167 2.76400e9 0.274988 0.137494 0.990503i 0.456095π-0.456095\pi
0.137494 + 0.990503i 0.456095π0.456095\pi
168168 5.63773e9 0.546025
169169 −5.66119e9 −0.533848
170170 1.40105e9 0.128657
171171 −8.55036e8 −0.0764719
172172 1.31622e10 1.14670
173173 3.79638e9 0.322227 0.161114 0.986936i 0.448491π-0.448491\pi
0.161114 + 0.986936i 0.448491π0.448491\pi
174174 9.45675e8 0.0782114
175175 −3.36032e9 −0.270838
176176 −3.35356e8 −0.0263450
177177 −1.23897e10 −0.948811
178178 2.18772e9 0.163343
179179 1.07013e10 0.779107 0.389554 0.921004i 0.372629π-0.372629\pi
0.389554 + 0.921004i 0.372629π0.372629\pi
180180 −1.80316e9 −0.128029
181181 2.07548e10 1.43736 0.718679 0.695342i 0.244747π-0.244747\pi
0.718679 + 0.695342i 0.244747π0.244747\pi
182182 −5.14180e9 −0.347371
183183 3.18755e9 0.210101
184184 −2.39204e9 −0.153847
185185 1.28804e9 0.0808456
186186 3.91963e9 0.240125
187187 −5.65557e8 −0.0338212
188188 1.86163e10 1.08688
189189 −4.57168e9 −0.260614
190190 −6.92437e8 −0.0385469
191191 −1.39914e10 −0.760695 −0.380348 0.924844i 0.624196π-0.624196\pi
−0.380348 + 0.924844i 0.624196π0.624196\pi
192192 −2.71653e9 −0.144264
193193 −2.41922e10 −1.25507 −0.627535 0.778588i 0.715936π-0.715936\pi
−0.627535 + 0.778588i 0.715936π0.715936\pi
194194 −5.86997e9 −0.297528
195195 3.55938e9 0.176286
196196 −1.47959e10 −0.716127
197197 6.24104e9 0.295229 0.147615 0.989045i 0.452840π-0.452840\pi
0.147615 + 0.989045i 0.452840π0.452840\pi
198198 −1.19631e8 −0.00553160
199199 −3.55762e10 −1.60813 −0.804064 0.594543i 0.797333π-0.797333\pi
−0.804064 + 0.594543i 0.797333π0.797333\pi
200200 −3.16052e9 −0.139677
201201 6.55871e9 0.283424
202202 6.88035e9 0.290757
203203 −1.18138e10 −0.488269
204204 −9.39198e9 −0.379683
205205 2.90960e9 0.115064
206206 −3.92110e9 −0.151707
207207 1.93972e9 0.0734299
208208 1.09933e10 0.407232
209209 2.79513e8 0.0101331
210210 −3.70230e9 −0.131366
211211 −1.51159e10 −0.525003 −0.262501 0.964932i 0.584547π-0.584547\pi
−0.262501 + 0.964932i 0.584547π0.584547\pi
212212 −6.42602e8 −0.0218489
213213 −2.19064e10 −0.729227
214214 1.76110e10 0.574015
215215 −1.87079e10 −0.597106
216216 −4.29985e9 −0.134404
217217 −4.89660e10 −1.49908
218218 −1.26468e10 −0.379252
219219 −2.11199e10 −0.620432
220220 5.89457e8 0.0169649
221221 1.85395e10 0.522796
222222 1.41912e9 0.0392132
223223 −2.92879e10 −0.793080 −0.396540 0.918018i 0.629789π-0.629789\pi
−0.396540 + 0.918018i 0.629789π0.629789\pi
224224 −4.70707e10 −1.24921
225225 2.56289e9 0.0666667
226226 −1.53552e10 −0.391531
227227 −6.62027e10 −1.65485 −0.827426 0.561574i 0.810196π-0.810196\pi
−0.827426 + 0.561574i 0.810196π0.810196\pi
228228 4.64177e9 0.113757
229229 −2.98555e10 −0.717406 −0.358703 0.933452i 0.616781π-0.616781\pi
−0.358703 + 0.933452i 0.616781π0.616781\pi
230230 1.57085e9 0.0370135
231231 1.49449e9 0.0345334
232232 −1.11114e10 −0.251810
233233 −1.62148e10 −0.360421 −0.180211 0.983628i 0.557678π-0.557678\pi
−0.180211 + 0.983628i 0.557678π0.557678\pi
234234 3.92161e9 0.0855054
235235 −2.64600e10 −0.565958
236236 6.72602e10 1.41141
237237 −3.66483e10 −0.754548
238238 −1.92839e10 −0.389581
239239 −8.99004e10 −1.78226 −0.891130 0.453749i 0.850086π-0.850086\pi
−0.891130 + 0.453749i 0.850086π0.850086\pi
240240 7.91558e9 0.154004
241241 9.07409e10 1.73271 0.866356 0.499426i 0.166456π-0.166456\pi
0.866356 + 0.499426i 0.166456π0.166456\pi
242242 −2.00065e10 −0.374975
243243 3.48678e9 0.0641500
244244 −1.73044e10 −0.312537
245245 2.10300e10 0.372899
246246 3.20571e9 0.0558105
247247 −9.16270e9 −0.156634
248248 −4.60546e10 −0.773108
249249 3.16098e10 0.521104
250250 2.07552e9 0.0336044
251251 −1.91156e10 −0.303987 −0.151994 0.988381i 0.548569π-0.548569\pi
−0.151994 + 0.988381i 0.548569π0.548569\pi
252252 2.48184e10 0.387679
253253 −6.34100e8 −0.00973005
254254 5.06830e8 0.00764030
255255 1.33491e10 0.197707
256256 −9.06964e9 −0.131981
257257 4.66528e10 0.667081 0.333541 0.942736i 0.391757π-0.391757\pi
0.333541 + 0.942736i 0.391757π0.391757\pi
258258 −2.06118e10 −0.289619
259259 −1.77284e10 −0.244805
260260 −1.93229e10 −0.262236
261261 9.01034e9 0.120187
262262 −1.51063e10 −0.198062
263263 −3.87982e10 −0.500047 −0.250023 0.968240i 0.580438π-0.580438\pi
−0.250023 + 0.968240i 0.580438π0.580438\pi
264264 1.40563e9 0.0178096
265265 9.13352e8 0.0113771
266266 9.53061e9 0.116722
267267 2.08444e10 0.251009
268268 −3.56055e10 −0.421609
269269 3.81888e10 0.444683 0.222342 0.974969i 0.428630π-0.428630\pi
0.222342 + 0.974969i 0.428630π0.428630\pi
270270 2.82372e9 0.0323358
271271 1.12956e11 1.27218 0.636088 0.771617i 0.280552π-0.280552\pi
0.636088 + 0.771617i 0.280552π0.280552\pi
272272 4.12293e10 0.456715
273273 −4.89908e10 −0.533805
274274 4.82460e10 0.517111
275275 −8.37815e8 −0.00883387
276276 −1.05302e10 −0.109231
277277 −1.75341e11 −1.78947 −0.894737 0.446594i 0.852637π-0.852637\pi
−0.894737 + 0.446594i 0.852637π0.852637\pi
278278 −2.92446e10 −0.293659
279279 3.73460e10 0.368999
280280 4.35010e10 0.422949
281281 −7.22309e10 −0.691105 −0.345553 0.938399i 0.612309π-0.612309\pi
−0.345553 + 0.938399i 0.612309π0.612309\pi
282282 −2.91528e10 −0.274511
283283 −8.68728e10 −0.805090 −0.402545 0.915400i 0.631874π-0.631874\pi
−0.402545 + 0.915400i 0.631874π0.631874\pi
284284 1.18924e11 1.08477
285285 −6.59750e9 −0.0592349
286286 −1.28199e9 −0.0113302
287287 −4.00473e10 −0.348422
288288 3.59005e10 0.307492
289289 −4.90572e10 −0.413678
290290 7.29688e9 0.0605823
291291 −5.59287e10 −0.457211
292292 1.14655e11 0.922930
293293 −1.30875e11 −1.03742 −0.518708 0.854951i 0.673587π-0.673587\pi
−0.518708 + 0.854951i 0.673587π0.673587\pi
294294 2.31702e10 0.180870
295295 −9.55993e10 −0.734946
296296 −1.66743e10 −0.126251
297297 −1.13984e9 −0.00850040
298298 2.44568e10 0.179650
299299 2.07863e10 0.150403
300300 −1.39133e10 −0.0991707
301301 2.57493e11 1.80807
302302 1.63080e10 0.112815
303303 6.55556e10 0.446805
304304 −2.03766e10 −0.136836
305305 2.45953e10 0.162743
306306 1.47077e10 0.0958954
307307 −1.56180e11 −1.00346 −0.501732 0.865023i 0.667304π-0.667304\pi
−0.501732 + 0.865023i 0.667304π0.667304\pi
308308 −8.11321e9 −0.0513706
309309 −3.73600e10 −0.233128
310310 3.02441e10 0.186000
311311 2.89274e10 0.175343 0.0876713 0.996149i 0.472057π-0.472057\pi
0.0876713 + 0.996149i 0.472057π0.472057\pi
312312 −4.60779e10 −0.275294
313313 9.15012e10 0.538862 0.269431 0.963020i 0.413164π-0.413164\pi
0.269431 + 0.963020i 0.413164π0.413164\pi
314314 −6.83585e10 −0.396834
315315 −3.52753e10 −0.201871
316316 1.98954e11 1.12244
317317 −5.26556e10 −0.292872 −0.146436 0.989220i 0.546780π-0.546780\pi
−0.146436 + 0.989220i 0.546780π0.546780\pi
318318 1.00630e9 0.00551832
319319 −2.94550e9 −0.0159258
320320 −2.09608e10 −0.111746
321321 1.67797e11 0.882087
322322 −2.16210e10 −0.112079
323323 −3.43639e10 −0.175667
324324 −1.89288e10 −0.0954270
325325 2.74643e10 0.136551
326326 9.45882e9 0.0463829
327327 −1.20498e11 −0.582795
328328 −3.76662e10 −0.179688
329329 3.64192e11 1.71375
330330 −9.23080e8 −0.00428476
331331 −1.18390e11 −0.542111 −0.271056 0.962564i 0.587373π-0.587373\pi
−0.271056 + 0.962564i 0.587373π0.587373\pi
332332 −1.71601e11 −0.775173
333333 1.35213e10 0.0602588
334334 2.34977e10 0.103315
335335 5.06073e10 0.219539
336336 −1.08949e11 −0.466333
337337 5.53843e10 0.233912 0.116956 0.993137i 0.462686π-0.462686\pi
0.116956 + 0.993137i 0.462686π0.462686\pi
338338 −4.81275e10 −0.200571
339339 −1.46303e11 −0.601666
340340 −7.24690e10 −0.294101
341341 −1.22085e10 −0.0488954
342342 −7.26893e9 −0.0287311
343343 5.76849e10 0.225029
344344 2.42183e11 0.932459
345345 1.49670e10 0.0568785
346346 3.22742e10 0.121063
347347 1.58194e11 0.585744 0.292872 0.956152i 0.405389π-0.405389\pi
0.292872 + 0.956152i 0.405389π0.405389\pi
348348 −4.89147e10 −0.178786
349349 −3.34223e11 −1.20593 −0.602964 0.797768i 0.706014π-0.706014\pi
−0.602964 + 0.797768i 0.706014π0.706014\pi
350350 −2.85671e10 −0.101756
351351 3.73649e10 0.131396
352352 −1.17360e10 −0.0407452
353353 2.89176e11 0.991233 0.495616 0.868542i 0.334942π-0.334942\pi
0.495616 + 0.868542i 0.334942π0.334942\pi
354354 −1.05328e11 −0.356476
355355 −1.69031e11 −0.564857
356356 −1.13159e11 −0.373391
357357 −1.83736e11 −0.598669
358358 9.09749e10 0.292717
359359 5.54463e11 1.76176 0.880882 0.473336i 0.156950π-0.156950\pi
0.880882 + 0.473336i 0.156950π0.156950\pi
360360 −3.31779e10 −0.104109
361361 1.69836e10 0.0526316
362362 1.76443e11 0.540027
363363 −1.90621e11 −0.576224
364364 2.65958e11 0.794067
365365 −1.62963e11 −0.480585
366366 2.70984e10 0.0789365
367367 −1.93025e11 −0.555414 −0.277707 0.960666i 0.589574π-0.589574\pi
−0.277707 + 0.960666i 0.589574π0.589574\pi
368368 4.62260e10 0.131393
369369 3.05438e10 0.0857639
370370 1.09500e10 0.0303744
371371 −1.25712e10 −0.0344505
372372 −2.02742e11 −0.548908
373373 2.11386e11 0.565441 0.282720 0.959202i 0.408763π-0.408763\pi
0.282720 + 0.959202i 0.408763π0.408763\pi
374374 −4.80798e9 −0.0127069
375375 1.97754e10 0.0516398
376376 3.42538e11 0.883818
377377 9.65562e10 0.246175
378378 −3.88652e10 −0.0979148
379379 3.57260e11 0.889422 0.444711 0.895674i 0.353306π-0.353306\pi
0.444711 + 0.895674i 0.353306π0.353306\pi
380380 3.58161e10 0.0881155
381381 4.82905e9 0.0117408
382382 −1.18945e11 −0.285800
383383 −5.89233e11 −1.39924 −0.699621 0.714515i 0.746648π-0.746648\pi
−0.699621 + 0.714515i 0.746648π0.746648\pi
384384 −2.50020e11 −0.586793
385385 1.15316e10 0.0267495
386386 −2.05666e11 −0.471541
387387 −1.96388e11 −0.445056
388388 3.03622e11 0.680128
389389 −6.40517e11 −1.41827 −0.709133 0.705075i 0.750913π-0.750913\pi
−0.709133 + 0.705075i 0.750913π0.750913\pi
390390 3.02594e10 0.0662322
391391 7.79574e10 0.168679
392392 −2.72243e11 −0.582331
393393 −1.43932e11 −0.304362
394394 5.30570e10 0.110920
395395 −2.82780e11 −0.584470
396396 6.18788e9 0.0126449
397397 5.48741e11 1.10869 0.554345 0.832287i 0.312969π-0.312969\pi
0.554345 + 0.832287i 0.312969π0.312969\pi
398398 −3.02444e11 −0.604187
399399 9.08071e10 0.179367
400400 6.10770e10 0.119291
401401 2.21962e11 0.428676 0.214338 0.976760i 0.431241π-0.431241\pi
0.214338 + 0.976760i 0.431241π0.431241\pi
402402 5.57576e10 0.106485
403403 4.00205e11 0.755806
404404 −3.55884e11 −0.664649
405405 2.69042e10 0.0496904
406406 −1.00433e11 −0.183447
407407 −4.42016e9 −0.00798478
408408 −1.72811e11 −0.308746
409409 −9.17718e10 −0.162164 −0.0810820 0.996707i 0.525838π-0.525838\pi
−0.0810820 + 0.996707i 0.525838π0.525838\pi
410410 2.47354e10 0.0432306
411411 4.59685e11 0.794644
412412 2.02818e11 0.346792
413413 1.31582e12 2.22546
414414 1.64902e10 0.0275882
415415 2.43903e11 0.403645
416416 3.84715e11 0.629824
417417 −2.78641e11 −0.451266
418418 2.37623e9 0.00380711
419419 8.34752e11 1.32311 0.661553 0.749899i 0.269898π-0.269898\pi
0.661553 + 0.749899i 0.269898π0.269898\pi
420420 1.91500e11 0.300295
421421 −3.68245e11 −0.571304 −0.285652 0.958333i 0.592210π-0.592210\pi
−0.285652 + 0.958333i 0.592210π0.592210\pi
422422 −1.28505e11 −0.197248
423423 −2.77766e11 −0.421840
424424 −1.18238e10 −0.0177668
425425 1.03003e11 0.153143
426426 −1.86233e11 −0.273977
427427 −3.38526e11 −0.492796
428428 −9.10926e11 −1.31216
429429 −1.22147e10 −0.0174110
430430 −1.59041e11 −0.224338
431431 −5.03089e11 −0.702259 −0.351129 0.936327i 0.614202π-0.614202\pi
−0.351129 + 0.936327i 0.614202π0.614202\pi
432432 8.30945e10 0.114788
433433 8.95533e11 1.22430 0.612148 0.790743i 0.290306π-0.290306\pi
0.612148 + 0.790743i 0.290306π0.290306\pi
434434 −4.16275e11 −0.563218
435435 6.95242e10 0.0930967
436436 6.54154e11 0.866943
437437 −3.85286e10 −0.0505379
438438 −1.79547e11 −0.233102
439439 4.16326e11 0.534987 0.267494 0.963560i 0.413805π-0.413805\pi
0.267494 + 0.963560i 0.413805π0.413805\pi
440440 1.08459e10 0.0137953
441441 2.20764e11 0.277942
442442 1.57610e11 0.196419
443443 8.58126e11 1.05861 0.529303 0.848433i 0.322453π-0.322453\pi
0.529303 + 0.848433i 0.322453π0.322453\pi
444444 −7.34037e10 −0.0896386
445445 1.60837e11 0.194431
446446 −2.48986e11 −0.297967
447447 2.33023e11 0.276067
448448 2.88502e11 0.338375
449449 8.93036e11 1.03696 0.518478 0.855091i 0.326499π-0.326499\pi
0.518478 + 0.855091i 0.326499π0.326499\pi
450450 2.17879e10 0.0250472
451451 −9.98485e9 −0.0113644
452452 7.94242e11 0.895014
453453 1.55381e11 0.173363
454454 −5.62810e11 −0.621742
455455 −3.78015e11 −0.413483
456456 8.54079e10 0.0925031
457457 9.88248e11 1.05985 0.529924 0.848045i 0.322221π-0.322221\pi
0.529924 + 0.848045i 0.322221π0.322221\pi
458458 −2.53811e11 −0.269535
459459 1.40134e11 0.147362
460460 −8.12518e10 −0.0846102
461461 5.23638e11 0.539979 0.269989 0.962863i 0.412980π-0.412980\pi
0.269989 + 0.962863i 0.412980π0.412980\pi
462462 1.27051e10 0.0129745
463463 −2.36334e11 −0.239008 −0.119504 0.992834i 0.538130π-0.538130\pi
−0.119504 + 0.992834i 0.538130π0.538130\pi
464464 2.14728e11 0.215059
465465 2.88164e11 0.285825
466466 −1.37847e11 −0.135413
467467 −3.42883e11 −0.333595 −0.166798 0.985991i 0.553343π-0.553343\pi
−0.166798 + 0.985991i 0.553343π0.553343\pi
468468 −2.02844e11 −0.195459
469469 −6.96552e11 −0.664777
470470 −2.24945e11 −0.212635
471471 −6.51316e11 −0.609814
472472 1.23758e12 1.14772
473473 6.41996e10 0.0589736
474474 −3.11559e11 −0.283490
475475 −5.09066e10 −0.0458831
476476 9.97453e11 0.890556
477477 9.58800e9 0.00847999
478478 −7.64271e11 −0.669610
479479 −9.37114e11 −0.813359 −0.406680 0.913571i 0.633313π-0.633313\pi
−0.406680 + 0.913571i 0.633313π0.633313\pi
480480 2.77010e11 0.238182
481481 1.44897e11 0.123426
482482 7.71417e11 0.650995
483483 −2.06004e11 −0.172232
484484 1.03483e12 0.857168
485485 −4.31549e11 −0.354154
486486 2.96422e10 0.0241017
487487 7.19365e11 0.579520 0.289760 0.957099i 0.406424π-0.406424\pi
0.289760 + 0.957099i 0.406424π0.406424\pi
488488 −3.18398e11 −0.254145
489489 9.01231e10 0.0712765
490490 1.78782e11 0.140101
491491 −3.72813e11 −0.289484 −0.144742 0.989469i 0.546235π-0.546235\pi
−0.144742 + 0.989469i 0.546235π0.546235\pi
492492 −1.65814e11 −0.127579
493493 3.62126e11 0.276088
494494 −7.78949e10 −0.0588489
495495 −8.79505e9 −0.00658438
496496 8.90003e11 0.660274
497497 2.32652e12 1.71042
498498 2.68725e11 0.195783
499499 1.06787e11 0.0771022 0.0385511 0.999257i 0.487726π-0.487726\pi
0.0385511 + 0.999257i 0.487726π0.487726\pi
500500 −1.07355e11 −0.0768173
501501 2.23884e11 0.158765
502502 −1.62507e11 −0.114211
503503 4.25008e11 0.296034 0.148017 0.988985i 0.452711π-0.452711\pi
0.148017 + 0.988985i 0.452711π0.452711\pi
504504 4.56656e11 0.315248
505505 5.05830e11 0.346094
506506 −5.39068e9 −0.00365566
507507 −4.58556e11 −0.308217
508508 −2.62156e10 −0.0174652
509509 1.79395e12 1.18462 0.592310 0.805710i 0.298216π-0.298216\pi
0.592310 + 0.805710i 0.298216π0.298216\pi
510510 1.13485e11 0.0742802
511511 2.24299e12 1.45524
512512 1.50327e12 0.966769
513513 −6.92579e10 −0.0441511
514514 3.96610e11 0.250628
515515 −2.88272e11 −0.180580
516516 1.06614e12 0.662048
517517 9.08025e10 0.0558972
518518 −1.50715e11 −0.0919754
519519 3.07507e11 0.186038
520520 −3.55539e11 −0.213242
521521 −6.85487e11 −0.407596 −0.203798 0.979013i 0.565329π-0.565329\pi
−0.203798 + 0.979013i 0.565329π0.565329\pi
522522 7.65997e10 0.0451554
523523 −2.20856e12 −1.29078 −0.645390 0.763853i 0.723305π-0.723305\pi
−0.645390 + 0.763853i 0.723305π0.723305\pi
524524 7.81368e11 0.452756
525525 −2.72186e11 −0.156368
526526 −3.29836e11 −0.187872
527527 1.50094e12 0.847646
528528 −2.71638e10 −0.0152103
529529 −1.71375e12 −0.951472
530530 7.76469e9 0.00427447
531531 −1.00356e12 −0.547796
532532 −4.92968e11 −0.266819
533533 3.27312e11 0.175667
534534 1.77205e11 0.0943062
535535 1.29473e12 0.683262
536536 −6.55136e11 −0.342839
537537 8.66804e11 0.449818
538538 3.24655e11 0.167071
539539 −7.21684e10 −0.0368296
540540 −1.46056e11 −0.0739175
541541 −4.05993e11 −0.203765 −0.101883 0.994796i 0.532487π-0.532487\pi
−0.101883 + 0.994796i 0.532487π0.532487\pi
542542 9.60273e11 0.477967
543543 1.68114e12 0.829859
544544 1.44284e12 0.706355
545545 −9.29771e11 −0.451431
546546 −4.16486e11 −0.200555
547547 −6.34987e11 −0.303265 −0.151632 0.988437i 0.548453π-0.548453\pi
−0.151632 + 0.988437i 0.548453π0.548453\pi
548548 −2.49551e12 −1.18208
549549 2.58192e11 0.121302
550550 −7.12253e9 −0.00331896
551551 −1.78972e11 −0.0827186
552552 −1.93755e11 −0.0888233
553553 3.89215e12 1.76981
554554 −1.49063e12 −0.672320
555555 1.04331e11 0.0466763
556556 1.51267e12 0.671285
557557 −1.86712e11 −0.0821909 −0.0410955 0.999155i 0.513085π-0.513085\pi
−0.0410955 + 0.999155i 0.513085π0.513085\pi
558558 3.17490e11 0.138636
559559 −2.10452e12 −0.911591
560560 −8.40655e11 −0.361220
561561 −4.58101e10 −0.0195267
562562 −6.14057e11 −0.259654
563563 6.11205e11 0.256389 0.128194 0.991749i 0.459082π-0.459082\pi
0.128194 + 0.991749i 0.459082π0.459082\pi
564564 1.50792e12 0.627513
565565 −1.12888e12 −0.466048
566566 −7.38532e11 −0.302479
567567 −3.70306e11 −0.150465
568568 2.18819e12 0.882098
569569 −2.16442e12 −0.865638 −0.432819 0.901481i 0.642481π-0.642481\pi
−0.432819 + 0.901481i 0.642481π0.642481\pi
570570 −5.60874e10 −0.0222550
571571 7.99521e11 0.314751 0.157376 0.987539i 0.449697π-0.449697\pi
0.157376 + 0.987539i 0.449697π0.449697\pi
572572 6.63103e10 0.0258999
573573 −1.13330e12 −0.439188
574574 −3.40455e11 −0.130905
575575 1.15486e11 0.0440579
576576 −2.20039e11 −0.0832909
577577 −2.52485e12 −0.948296 −0.474148 0.880445i 0.657244π-0.657244\pi
−0.474148 + 0.880445i 0.657244π0.657244\pi
578578 −4.17051e11 −0.155422
579579 −1.95957e12 −0.724615
580580 −3.77429e11 −0.138487
581581 −3.35704e12 −1.22226
582582 −4.75467e11 −0.171778
583583 −3.13434e9 −0.00112367
584584 2.10963e12 0.750496
585585 2.88310e11 0.101779
586586 −1.11261e12 −0.389766
587587 −3.03439e12 −1.05487 −0.527436 0.849595i 0.676846π-0.676846\pi
−0.527436 + 0.849595i 0.676846π0.676846\pi
588588 −1.19847e12 −0.413456
589589 −7.41803e11 −0.253963
590590 −8.12719e11 −0.276125
591591 5.05524e11 0.170451
592592 3.22231e11 0.107825
593593 3.40070e12 1.12933 0.564667 0.825319i 0.309005π-0.309005\pi
0.564667 + 0.825319i 0.309005π0.309005\pi
594594 −9.69012e9 −0.00319367
595595 −1.41771e12 −0.463727
596596 −1.26502e12 −0.410666
597597 −2.88167e12 −0.928453
598598 1.76711e11 0.0565079
599599 −4.61319e12 −1.46413 −0.732066 0.681234i 0.761444π-0.761444\pi
−0.732066 + 0.681234i 0.761444π0.761444\pi
600600 −2.56002e11 −0.0806423
601601 −5.97933e11 −0.186947 −0.0934733 0.995622i 0.529797π-0.529797\pi
−0.0934733 + 0.995622i 0.529797π0.529797\pi
602602 2.18902e12 0.679308
603603 5.31255e11 0.163635
604604 −8.43524e11 −0.257888
605605 −1.47084e12 −0.446341
606606 5.57309e11 0.167868
607607 −5.36203e12 −1.60317 −0.801586 0.597880i 0.796010π-0.796010\pi
−0.801586 + 0.597880i 0.796010π0.796010\pi
608608 −7.13090e11 −0.211631
609609 −9.56922e11 −0.281902
610610 2.09092e11 0.0611440
611611 −2.97659e12 −0.864039
612612 −7.60750e11 −0.219210
613613 4.13132e12 1.18173 0.590864 0.806772i 0.298787π-0.298787\pi
0.590864 + 0.806772i 0.298787π0.298787\pi
614614 −1.32773e12 −0.377010
615615 2.35678e11 0.0664324
616616 −1.49282e11 −0.0417728
617617 −4.64600e12 −1.29061 −0.645307 0.763923i 0.723271π-0.723271\pi
−0.645307 + 0.763923i 0.723271π0.723271\pi
618618 −3.17609e11 −0.0875881
619619 6.83793e12 1.87205 0.936023 0.351939i 0.114478π-0.114478\pi
0.936023 + 0.351939i 0.114478π0.114478\pi
620620 −1.56436e12 −0.425182
621621 1.57117e11 0.0423948
622622 2.45921e11 0.0658777
623623 −2.21373e12 −0.588748
624624 8.90454e11 0.235115
625625 1.52588e11 0.0400000
626626 7.77880e11 0.202455
627627 2.26406e10 0.00585038
628628 3.53582e12 0.907135
629629 5.43422e11 0.138423
630630 −2.99886e11 −0.0758445
631631 −3.00641e12 −0.754947 −0.377473 0.926020i 0.623207π-0.623207\pi
−0.377473 + 0.926020i 0.623207π0.623207\pi
632632 3.66073e12 0.912727
633633 −1.22438e12 −0.303111
634634 −4.47641e11 −0.110034
635635 3.72612e10 0.00909441
636636 −5.20507e10 −0.0126145
637637 2.36574e12 0.569299
638638 −2.50406e10 −0.00598346
639639 −1.77442e12 −0.421019
640640 −1.92917e12 −0.454528
641641 −5.29420e12 −1.23862 −0.619311 0.785145i 0.712588π-0.712588\pi
−0.619311 + 0.785145i 0.712588π0.712588\pi
642642 1.42649e12 0.331408
643643 −9.52256e11 −0.219687 −0.109843 0.993949i 0.535035π-0.535035\pi
−0.109843 + 0.993949i 0.535035π0.535035\pi
644644 1.11834e12 0.256205
645645 −1.51534e12 −0.344739
646646 −2.92138e11 −0.0659997
647647 −2.22683e12 −0.499595 −0.249797 0.968298i 0.580364π-0.580364\pi
−0.249797 + 0.968298i 0.580364π0.580364\pi
648648 −3.48288e11 −0.0775981
649649 3.28067e11 0.0725875
650650 2.33483e11 0.0513032
651651 −3.96624e12 −0.865496
652652 −4.89255e11 −0.106028
653653 −8.67231e12 −1.86649 −0.933244 0.359242i 0.883035π-0.883035\pi
−0.933244 + 0.359242i 0.883035π0.883035\pi
654654 −1.02439e12 −0.218961
655655 −1.11058e12 −0.235758
656656 7.27898e11 0.153463
657657 −1.71072e12 −0.358207
658658 3.09611e12 0.643872
659659 −3.26232e12 −0.673817 −0.336909 0.941537i 0.609381π-0.609381\pi
−0.336909 + 0.941537i 0.609381π0.609381\pi
660660 4.77460e10 0.00979466
661661 9.63423e12 1.96296 0.981478 0.191575i 0.0613595π-0.0613595\pi
0.981478 + 0.191575i 0.0613595π0.0613595\pi
662662 −1.00647e12 −0.203676
663663 1.50170e12 0.301836
664664 −3.15744e12 −0.630345
665665 7.00672e11 0.138937
666666 1.14949e11 0.0226397
667667 4.06013e11 0.0794281
668668 −1.21541e12 −0.236172
669669 −2.37232e12 −0.457885
670670 4.30228e11 0.0824826
671671 −8.44035e10 −0.0160734
672672 −3.81272e12 −0.721230
673673 6.68101e12 1.25538 0.627689 0.778464i 0.284001π-0.284001\pi
0.627689 + 0.778464i 0.284001π0.284001\pi
674674 4.70839e11 0.0878827
675675 2.07594e11 0.0384900
676676 2.48938e12 0.458492
677677 −1.83095e12 −0.334987 −0.167494 0.985873i 0.553567π-0.553567\pi
−0.167494 + 0.985873i 0.553567π0.553567\pi
678678 −1.24377e12 −0.226051
679679 5.93978e12 1.07240
680680 −1.33342e12 −0.239153
681681 −5.36242e12 −0.955430
682682 −1.03788e11 −0.0183704
683683 −1.57939e12 −0.277712 −0.138856 0.990313i 0.544343π-0.544343\pi
−0.138856 + 0.990313i 0.544343π0.544343\pi
684684 3.75983e11 0.0656774
685685 3.54695e12 0.615528
686686 4.90397e11 0.0845453
687687 −2.41830e12 −0.414195
688688 −4.68017e12 −0.796368
689689 1.02746e11 0.0173692
690690 1.27239e11 0.0213697
691691 −3.29925e12 −0.550509 −0.275255 0.961371i 0.588762π-0.588762\pi
−0.275255 + 0.961371i 0.588762π0.588762\pi
692692 −1.66937e12 −0.276743
693693 1.21054e11 0.0199379
694694 1.34486e12 0.220069
695695 −2.15001e12 −0.349549
696696 −9.00025e11 −0.145383
697697 1.22756e12 0.197013
698698 −2.84133e12 −0.453078
699699 −1.31340e12 −0.208089
700700 1.47763e12 0.232607
701701 5.89829e12 0.922561 0.461280 0.887254i 0.347390π-0.347390\pi
0.461280 + 0.887254i 0.347390π0.347390\pi
702702 3.17651e11 0.0493666
703703 −2.68574e11 −0.0414729
704704 7.19311e10 0.0110367
705705 −2.14326e12 −0.326756
706706 2.45837e12 0.372415
707707 −6.96218e12 −1.04799
708708 5.44808e12 0.814880
709709 1.10767e13 1.64628 0.823138 0.567842i 0.192222π-0.192222\pi
0.823138 + 0.567842i 0.192222π0.192222\pi
710710 −1.43698e12 −0.212221
711711 −2.96852e12 −0.435638
712712 −2.08211e12 −0.303629
713713 1.68284e12 0.243860
714714 −1.56199e12 −0.224925
715715 −9.42491e10 −0.0134865
716716 −4.70565e12 −0.669131
717717 −7.28193e12 −1.02899
718718 4.71366e12 0.661910
719719 4.32684e12 0.603797 0.301898 0.953340i 0.402380π-0.402380\pi
0.301898 + 0.953340i 0.402380π0.402380\pi
720720 6.41162e11 0.0889142
721721 3.96774e12 0.546807
722722 1.44383e11 0.0197741
723723 7.35002e12 1.00038
724724 −9.12646e12 −1.23446
725725 5.36452e11 0.0721124
726726 −1.62053e12 −0.216492
727727 3.86448e12 0.513081 0.256541 0.966533i 0.417417π-0.417417\pi
0.256541 + 0.966533i 0.417417π0.417417\pi
728728 4.89359e12 0.645709
729729 2.82430e11 0.0370370
730730 −1.38540e12 −0.180560
731731 −7.89282e12 −1.02236
732732 −1.40165e12 −0.180443
733733 4.95097e12 0.633465 0.316732 0.948515i 0.397414π-0.397414\pi
0.316732 + 0.948515i 0.397414π0.397414\pi
734734 −1.64097e12 −0.208674
735735 1.70343e12 0.215293
736736 1.61770e12 0.203212
737737 −1.73669e11 −0.0216829
738738 2.59662e11 0.0322222
739739 5.28526e11 0.0651878 0.0325939 0.999469i 0.489623π-0.489623\pi
0.0325939 + 0.999469i 0.489623π0.489623\pi
740740 −5.66387e11 −0.0694337
741741 −7.42179e11 −0.0904329
742742 −1.06872e11 −0.0129434
743743 1.87009e11 0.0225119 0.0112560 0.999937i 0.496417π-0.496417\pi
0.0112560 + 0.999937i 0.496417π0.496417\pi
744744 −3.73042e12 −0.446354
745745 1.79802e12 0.213841
746746 1.79706e12 0.212441
747747 2.56039e12 0.300859
748748 2.48691e11 0.0290471
749749 −1.78205e13 −2.06896
750750 1.68117e11 0.0194015
751751 −3.65018e12 −0.418730 −0.209365 0.977838i 0.567140π-0.567140\pi
−0.209365 + 0.977838i 0.567140π0.567140\pi
752752 −6.61953e12 −0.754826
753753 −1.54836e12 −0.175507
754754 8.20854e11 0.0924900
755755 1.19893e12 0.134286
756756 2.01029e12 0.223826
757757 1.00306e13 1.11019 0.555095 0.831787i 0.312682π-0.312682\pi
0.555095 + 0.831787i 0.312682π0.312682\pi
758758 3.03718e12 0.334163
759759 −5.13621e10 −0.00561765
760760 6.59012e11 0.0716526
761761 3.29762e12 0.356426 0.178213 0.983992i 0.442968π-0.442968\pi
0.178213 + 0.983992i 0.442968π0.442968\pi
762762 4.10532e10 0.00441113
763763 1.27972e13 1.36696
764764 6.15240e12 0.653318
765765 1.08128e12 0.114146
766766 −5.00925e12 −0.525707
767767 −1.07543e13 −1.12203
768768 −7.34640e11 −0.0761990
769769 −1.76109e12 −0.181599 −0.0907994 0.995869i 0.528942π-0.528942\pi
−0.0907994 + 0.995869i 0.528942π0.528942\pi
770770 9.80335e10 0.0100500
771771 3.77888e12 0.385139
772772 1.06380e13 1.07791
773773 1.71547e12 0.172813 0.0864063 0.996260i 0.472462π-0.472462\pi
0.0864063 + 0.996260i 0.472462π0.472462\pi
774774 −1.66955e12 −0.167211
775775 2.22348e12 0.221399
776776 5.58661e12 0.553058
777777 −1.43600e12 −0.141338
778778 −5.44524e12 −0.532854
779779 −6.06691e11 −0.0590268
780780 −1.56516e12 −0.151402
781781 5.80061e11 0.0557885
782782 6.62740e11 0.0633743
783783 7.29837e11 0.0693902
784784 5.26109e12 0.497340
785785 −5.02558e12 −0.472360
786786 −1.22361e12 −0.114351
787787 −2.08698e13 −1.93924 −0.969619 0.244618i 0.921337π-0.921337\pi
−0.969619 + 0.244618i 0.921337π0.921337\pi
788788 −2.74436e12 −0.253555
789789 −3.14265e12 −0.288702
790790 −2.40400e12 −0.219590
791791 1.55378e13 1.41122
792792 1.13856e11 0.0102824
793793 2.76682e12 0.248457
794794 4.66502e12 0.416544
795795 7.39815e10 0.00656857
796796 1.56438e13 1.38113
797797 −9.92675e12 −0.871454 −0.435727 0.900079i 0.643509π-0.643509\pi
−0.435727 + 0.900079i 0.643509π0.643509\pi
798798 7.71979e11 0.0673896
799799 −1.11634e13 −0.969030
800800 2.13742e12 0.184495
801801 1.68840e12 0.144920
802802 1.88697e12 0.161057
803803 5.59237e11 0.0474653
804804 −2.88404e12 −0.243416
805805 −1.58953e12 −0.133410
806806 3.40227e12 0.283963
807807 3.09329e12 0.256738
808808 −6.54822e12 −0.540471
809809 −1.97003e13 −1.61698 −0.808490 0.588510i 0.799715π-0.799715\pi
−0.808490 + 0.588510i 0.799715π0.799715\pi
810810 2.28721e11 0.0186691
811811 −1.49518e13 −1.21366 −0.606832 0.794830i 0.707560π-0.707560\pi
−0.606832 + 0.794830i 0.707560π0.707560\pi
812812 5.19488e12 0.419347
813813 9.14943e12 0.734491
814814 −3.75771e10 −0.00299995
815815 6.95394e11 0.0552105
816816 3.33957e12 0.263685
817817 3.90085e12 0.306309
818818 −7.80180e11 −0.0609264
819819 −3.96825e12 −0.308192
820820 −1.27943e12 −0.0988222
821821 5.64204e11 0.0433403 0.0216701 0.999765i 0.493102π-0.493102\pi
0.0216701 + 0.999765i 0.493102π0.493102\pi
822822 3.90793e12 0.298554
823823 2.11916e13 1.61015 0.805073 0.593175i 0.202126π-0.202126\pi
0.805073 + 0.593175i 0.202126π0.202126\pi
824824 3.73182e12 0.282000
825825 −6.78630e10 −0.00510024
826826 1.11862e13 0.836124
827827 2.90210e12 0.215743 0.107872 0.994165i 0.465596π-0.465596\pi
0.107872 + 0.994165i 0.465596π0.465596\pi
828828 −8.52949e11 −0.0630647
829829 −1.48771e13 −1.09401 −0.547006 0.837128i 0.684233π-0.684233\pi
−0.547006 + 0.837128i 0.684233π0.684233\pi
830830 2.07349e12 0.151653
831831 −1.42026e13 −1.03315
832832 −2.35797e12 −0.170601
833833 8.87251e12 0.638475
834834 −2.36881e12 −0.169544
835835 1.72750e12 0.122979
836836 −1.22910e11 −0.00870278
837837 3.02503e12 0.213042
838838 7.09649e12 0.497102
839839 −1.09689e13 −0.764248 −0.382124 0.924111i 0.624807π-0.624807\pi
−0.382124 + 0.924111i 0.624807π0.624807\pi
840840 3.52358e12 0.244190
841841 −1.26211e13 −0.869995
842842 −3.13056e12 −0.214644
843843 −5.85070e12 −0.399010
844844 6.64686e12 0.450895
845845 −3.53824e12 −0.238744
846846 −2.36138e12 −0.158489
847847 2.02445e13 1.35155
848848 2.28494e11 0.0151738
849849 −7.03669e12 −0.464819
850850 8.75657e11 0.0575372
851851 6.09282e11 0.0398231
852852 9.63285e12 0.626291
853853 −1.82093e13 −1.17767 −0.588835 0.808254i 0.700413π-0.700413\pi
−0.588835 + 0.808254i 0.700413π0.700413\pi
854854 −2.87792e12 −0.185148
855855 −5.34398e11 −0.0341993
856856 −1.67609e13 −1.06700
857857 −3.77462e12 −0.239034 −0.119517 0.992832i 0.538135π-0.538135\pi
−0.119517 + 0.992832i 0.538135π0.538135\pi
858858 −1.03841e11 −0.00654147
859859 −7.89410e12 −0.494690 −0.247345 0.968927i 0.579558π-0.579558\pi
−0.247345 + 0.968927i 0.579558π0.579558\pi
860860 8.22637e12 0.512820
861861 −3.24383e12 −0.201161
862862 −4.27692e12 −0.263845
863863 −6.96799e12 −0.427621 −0.213810 0.976875i 0.568587π-0.568587\pi
−0.213810 + 0.976875i 0.568587π0.568587\pi
864864 2.90794e12 0.177531
865865 2.37274e12 0.144104
866866 7.61321e12 0.459978
867867 −3.97364e12 −0.238837
868868 2.15317e13 1.28748
869869 9.70415e11 0.0577256
870870 5.91047e11 0.0349772
871871 5.69301e12 0.335166
872872 1.20363e13 0.704970
873873 −4.53023e12 −0.263971
874874 −3.27544e11 −0.0189875
875875 −2.10020e12 −0.121122
876876 9.28702e12 0.532854
877877 −2.60614e13 −1.48765 −0.743824 0.668375i 0.766990π-0.766990\pi
−0.743824 + 0.668375i 0.766990π0.766990\pi
878878 3.53932e12 0.200999
879879 −1.06009e13 −0.598953
880880 −2.09597e11 −0.0117819
881881 1.73552e13 0.970593 0.485296 0.874350i 0.338712π-0.338712\pi
0.485296 + 0.874350i 0.338712π0.338712\pi
882882 1.87678e12 0.104425
883883 −3.13519e12 −0.173556 −0.0867782 0.996228i 0.527657π-0.527657\pi
−0.0867782 + 0.996228i 0.527657π0.527657\pi
884884 −8.15231e12 −0.448999
885885 −7.74354e12 −0.424321
886886 7.29520e12 0.397727
887887 2.15561e13 1.16927 0.584633 0.811298i 0.301238π-0.301238\pi
0.584633 + 0.811298i 0.301238π0.301238\pi
888888 −1.35062e12 −0.0728911
889889 −5.12857e11 −0.0275384
890890 1.36732e12 0.0730493
891891 −9.23269e10 −0.00490771
892892 1.28787e13 0.681131
893893 5.51727e12 0.290330
894894 1.98100e12 0.103721
895895 6.68830e12 0.348427
896896 2.65528e13 1.37634
897897 1.68369e12 0.0868355
898898 7.59198e12 0.389593
899899 7.81709e12 0.399141
900900 −1.12697e12 −0.0572562
901901 3.85342e11 0.0194798
902902 −8.48843e10 −0.00426971
903903 2.08569e13 1.04389
904904 1.46139e13 0.727796
905905 1.29717e13 0.642806
906906 1.32094e12 0.0651340
907907 1.84546e13 0.905467 0.452734 0.891646i 0.350449π-0.350449\pi
0.452734 + 0.891646i 0.350449π0.350449\pi
908908 2.91112e13 1.42126
909909 5.31001e12 0.257963
910910 −3.21363e12 −0.155349
911911 1.94952e13 0.937766 0.468883 0.883260i 0.344657π-0.344657\pi
0.468883 + 0.883260i 0.344657π0.344657\pi
912912 −1.65051e12 −0.0790024
913913 −8.36998e11 −0.0398663
914914 8.40141e12 0.398194
915915 1.99222e12 0.0939598
916916 1.31283e13 0.616139
917917 1.52859e13 0.713888
918918 1.19132e12 0.0553652
919919 1.25306e13 0.579498 0.289749 0.957103i 0.406428π-0.406428\pi
0.289749 + 0.957103i 0.406428π0.406428\pi
920920 −1.49502e12 −0.0688023
921921 −1.26506e13 −0.579351
922922 4.45161e12 0.202875
923923 −1.90149e13 −0.862357
924924 −6.57170e11 −0.0296588
925925 8.05025e11 0.0361553
926926 −2.00915e12 −0.0897974
927927 −3.02616e12 −0.134596
928928 7.51452e12 0.332610
929929 −3.45751e13 −1.52298 −0.761488 0.648179i 0.775531π-0.775531\pi
−0.761488 + 0.648179i 0.775531π0.775531\pi
930930 2.44977e12 0.107387
931931 −4.38503e12 −0.191293
932932 7.13010e12 0.309545
933933 2.34312e12 0.101234
934934 −2.91496e12 −0.125335
935935 −3.53473e11 −0.0151253
936936 −3.73231e12 −0.158941
937937 5.46318e12 0.231535 0.115768 0.993276i 0.463067π-0.463067\pi
0.115768 + 0.993276i 0.463067π0.463067\pi
938938 −5.92161e12 −0.249762
939939 7.41160e12 0.311112
940940 1.16352e13 0.486069
941941 −3.27531e12 −0.136176 −0.0680879 0.997679i 0.521690π-0.521690\pi
−0.0680879 + 0.997679i 0.521690π0.521690\pi
942942 −5.53704e12 −0.229112
943943 1.37633e12 0.0566787
944944 −2.39162e13 −0.980208
945945 −2.85730e12 −0.116550
946946 5.45781e11 0.0221569
947947 −2.09027e13 −0.844555 −0.422278 0.906467i 0.638769π-0.638769\pi
−0.422278 + 0.906467i 0.638769π0.638769\pi
948948 1.61153e13 0.648038
949949 −1.83323e13 −0.733700
950950 −4.32773e11 −0.0172387
951951 −4.26510e12 −0.169090
952952 1.83530e13 0.724171
953953 −2.97285e13 −1.16750 −0.583748 0.811935i 0.698414π-0.698414\pi
−0.583748 + 0.811935i 0.698414π0.698414\pi
954954 8.15106e10 0.00318600
955955 −8.74462e12 −0.340193
956956 3.95317e13 1.53068
957957 −2.38586e11 −0.00919476
958958 −7.96669e12 −0.305586
959959 −4.88198e13 −1.86386
960960 −1.69783e12 −0.0645169
961961 5.96061e12 0.225442
962962 1.23181e12 0.0463721
963963 1.35916e13 0.509273
964964 −3.99013e13 −1.48813
965965 −1.51202e13 −0.561285
966966 −1.75130e12 −0.0647088
967967 6.55213e12 0.240970 0.120485 0.992715i 0.461555π-0.461555\pi
0.120485 + 0.992715i 0.461555π0.461555\pi
968968 1.90408e13 0.697021
969969 −2.78348e12 −0.101422
970970 −3.66873e12 −0.133059
971971 4.42665e13 1.59804 0.799021 0.601302i 0.205351π-0.205351\pi
0.799021 + 0.601302i 0.205351π0.205351\pi
972972 −1.53324e12 −0.0550948
973973 2.95924e13 1.05845
974974 6.11554e12 0.217731
975975 2.22461e12 0.0788376
976976 6.15304e12 0.217053
977977 −2.13009e13 −0.747948 −0.373974 0.927439i 0.622005π-0.622005\pi
−0.373974 + 0.927439i 0.622005π0.622005\pi
978978 7.66165e11 0.0267792
979979 −5.51942e11 −0.0192031
980980 −9.24746e12 −0.320262
981981 −9.76036e12 −0.336477
982982 −3.16940e12 −0.108762
983983 1.38841e13 0.474272 0.237136 0.971476i 0.423791π-0.423791\pi
0.237136 + 0.971476i 0.423791π0.423791\pi
984984 −3.05096e12 −0.103743
985985 3.90065e12 0.132030
986986 3.07854e12 0.103729
987987 2.94995e13 0.989436
988988 4.02909e12 0.134524
989989 −8.84939e12 −0.294124
990990 −7.47695e10 −0.00247381
991991 −1.55882e13 −0.513409 −0.256705 0.966490i 0.582637π-0.582637\pi
−0.256705 + 0.966490i 0.582637π0.582637\pi
992992 3.11461e13 1.02118
993993 −9.58958e12 −0.312988
994994 1.97784e13 0.642619
995995 −2.22351e13 −0.719177
996996 −1.38997e13 −0.447547
997997 −2.00048e13 −0.641219 −0.320610 0.947211i 0.603888π-0.603888\pi
−0.320610 + 0.947211i 0.603888π0.603888\pi
998998 9.07832e11 0.0289680
999999 1.09523e12 0.0347904
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 285.10.a.d.1.8 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
285.10.a.d.1.8 12 1.1 even 1 trivial