Properties

Label 245.10.a.e.1.2
Level 245245
Weight 1010
Character 245.1
Self dual yes
Analytic conductor 126.184126.184
Analytic rank 11
Dimension 44
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] = [245,10,Mod(1,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("245.1"); S:= CuspForms(chi, 10); N := Newforms(S);
 
Level: N N == 245=572 245 = 5 \cdot 7^{2}
Weight: k k == 10 10
Character orbit: [χ][\chi] == 245.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,-19,18] 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: 126.183779860126.183779860
Analytic rank: 11
Dimension: 44
Coefficient field: Q[x]/(x4)\mathbb{Q}[x]/(x^{4} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4x3648x2+6926x8308 x^{4} - x^{3} - 648x^{2} + 6926x - 8308 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 2325 2\cdot 3^{2}\cdot 5
Twist minimal: no (minimal twist has level 35)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 1.376731.37673 of defining polynomial
Character χ\chi == 245.1

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) == q25.9629q2+209.523q3+162.070q4+625.000q55439.82q6+9085.18q8+24216.9q916226.8q10+43490.0q11+33957.4q1267126.8q13+130952.q15318857.q16+261183.q17628740.q18744649.q19+101294.q201.12912e6q222.12319e6q23+1.90355e6q24+390625.q25+1.74280e6q26+949956.q27+2.19162e6q293.39989e6q30+1.20634e6q31+3.62683e6q32+9.11216e6q336.78107e6q34+3.92484e6q367.82577e6q37+1.93332e7q381.40646e7q39+5.67824e6q402.84010e7q41836250.q43+7.04843e6q44+1.51356e7q45+5.51241e7q464.69259e7q476.68079e7q481.01417e7q50+5.47240e7q511.08793e7q521.18469e7q532.46636e7q54+2.71813e7q551.56021e8q575.69006e7q581.31445e8q59+2.12234e7q60+1.79312e8q613.13200e7q62+6.90919e7q644.19543e7q652.36578e8q662.11309e8q67+4.23300e7q684.44857e8q693.50475e8q71+2.20015e8q72+2.82794e8q73+2.03179e8q74+8.18449e7q751.20685e8q76+3.65158e8q783.47506e6q791.99286e8q802.77624e8q81+7.37370e8q821.95999e8q83+1.63240e8q85+2.17115e7q86+4.59194e8q87+3.95115e8q88+3.37238e8q893.92962e8q903.44106e8q92+2.52755e8q93+1.21833e9q944.65406e8q95+7.59905e8q96+1.63718e8q97+1.05319e9q99+O(q100)q-25.9629 q^{2} +209.523 q^{3} +162.070 q^{4} +625.000 q^{5} -5439.82 q^{6} +9085.18 q^{8} +24216.9 q^{9} -16226.8 q^{10} +43490.0 q^{11} +33957.4 q^{12} -67126.8 q^{13} +130952. q^{15} -318857. q^{16} +261183. q^{17} -628740. q^{18} -744649. q^{19} +101294. q^{20} -1.12912e6 q^{22} -2.12319e6 q^{23} +1.90355e6 q^{24} +390625. q^{25} +1.74280e6 q^{26} +949956. q^{27} +2.19162e6 q^{29} -3.39989e6 q^{30} +1.20634e6 q^{31} +3.62683e6 q^{32} +9.11216e6 q^{33} -6.78107e6 q^{34} +3.92484e6 q^{36} -7.82577e6 q^{37} +1.93332e7 q^{38} -1.40646e7 q^{39} +5.67824e6 q^{40} -2.84010e7 q^{41} -836250. q^{43} +7.04843e6 q^{44} +1.51356e7 q^{45} +5.51241e7 q^{46} -4.69259e7 q^{47} -6.68079e7 q^{48} -1.01417e7 q^{50} +5.47240e7 q^{51} -1.08793e7 q^{52} -1.18469e7 q^{53} -2.46636e7 q^{54} +2.71813e7 q^{55} -1.56021e8 q^{57} -5.69006e7 q^{58} -1.31445e8 q^{59} +2.12234e7 q^{60} +1.79312e8 q^{61} -3.13200e7 q^{62} +6.90919e7 q^{64} -4.19543e7 q^{65} -2.36578e8 q^{66} -2.11309e8 q^{67} +4.23300e7 q^{68} -4.44857e8 q^{69} -3.50475e8 q^{71} +2.20015e8 q^{72} +2.82794e8 q^{73} +2.03179e8 q^{74} +8.18449e7 q^{75} -1.20685e8 q^{76} +3.65158e8 q^{78} -3.47506e6 q^{79} -1.99286e8 q^{80} -2.77624e8 q^{81} +7.37370e8 q^{82} -1.95999e8 q^{83} +1.63240e8 q^{85} +2.17115e7 q^{86} +4.59194e8 q^{87} +3.95115e8 q^{88} +3.37238e8 q^{89} -3.92962e8 q^{90} -3.44106e8 q^{92} +2.52755e8 q^{93} +1.21833e9 q^{94} -4.65406e8 q^{95} +7.59905e8 q^{96} +1.63718e8 q^{97} +1.05319e9 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q19q2+18q3+1729q4+2500q5+144q630495q8+5382q911875q10+82438q1141328q12+72962q13+11250q15+64257q16+357542q17965367q18++1222369524q99+O(q100) 4 q - 19 q^{2} + 18 q^{3} + 1729 q^{4} + 2500 q^{5} + 144 q^{6} - 30495 q^{8} + 5382 q^{9} - 11875 q^{10} + 82438 q^{11} - 41328 q^{12} + 72962 q^{13} + 11250 q^{15} + 64257 q^{16} + 357542 q^{17} - 965367 q^{18}+ \cdots + 1222369524 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 −25.9629 −1.14741 −0.573704 0.819063i 0.694494π-0.694494\pi
−0.573704 + 0.819063i 0.694494π0.694494\pi
33 209.523 1.49343 0.746717 0.665142i 0.231629π-0.231629\pi
0.746717 + 0.665142i 0.231629π0.231629\pi
44 162.070 0.316543
55 625.000 0.447214
66 −5439.82 −1.71358
77 0 0
88 9085.18 0.784203
99 24216.9 1.23035
1010 −16226.8 −0.513136
1111 43490.0 0.895617 0.447809 0.894129i 0.352205π-0.352205\pi
0.447809 + 0.894129i 0.352205π0.352205\pi
1212 33957.4 0.472736
1313 −67126.8 −0.651855 −0.325928 0.945395i 0.605677π-0.605677\pi
−0.325928 + 0.945395i 0.605677π0.605677\pi
1414 0 0
1515 130952. 0.667884
1616 −318857. −1.21634
1717 261183. 0.758448 0.379224 0.925305i 0.376191π-0.376191\pi
0.379224 + 0.925305i 0.376191π0.376191\pi
1818 −628740. −1.41171
1919 −744649. −1.31087 −0.655437 0.755250i 0.727515π-0.727515\pi
−0.655437 + 0.755250i 0.727515π0.727515\pi
2020 101294. 0.141562
2121 0 0
2222 −1.12912e6 −1.02764
2323 −2.12319e6 −1.58203 −0.791013 0.611799i 0.790446π-0.790446\pi
−0.791013 + 0.611799i 0.790446π0.790446\pi
2424 1.90355e6 1.17116
2525 390625. 0.200000
2626 1.74280e6 0.747943
2727 949956. 0.344006
2828 0 0
2929 2.19162e6 0.575405 0.287702 0.957720i 0.407109π-0.407109\pi
0.287702 + 0.957720i 0.407109π0.407109\pi
3030 −3.39989e6 −0.766335
3131 1.20634e6 0.234607 0.117303 0.993096i 0.462575π-0.462575\pi
0.117303 + 0.993096i 0.462575π0.462575\pi
3232 3.62683e6 0.611438
3333 9.11216e6 1.33755
3434 −6.78107e6 −0.870248
3535 0 0
3636 3.92484e6 0.389458
3737 −7.82577e6 −0.686467 −0.343233 0.939250i 0.611522π-0.611522\pi
−0.343233 + 0.939250i 0.611522π0.611522\pi
3838 1.93332e7 1.50411
3939 −1.40646e7 −0.973503
4040 5.67824e6 0.350706
4141 −2.84010e7 −1.56966 −0.784830 0.619711i 0.787250π-0.787250\pi
−0.784830 + 0.619711i 0.787250π0.787250\pi
4242 0 0
4343 −836250. −0.0373017 −0.0186508 0.999826i 0.505937π-0.505937\pi
−0.0186508 + 0.999826i 0.505937π0.505937\pi
4444 7.04843e6 0.283501
4545 1.51356e7 0.550227
4646 5.51241e7 1.81523
4747 −4.69259e7 −1.40273 −0.701363 0.712804i 0.747425π-0.747425\pi
−0.701363 + 0.712804i 0.747425π0.747425\pi
4848 −6.68079e7 −1.81653
4949 0 0
5050 −1.01417e7 −0.229481
5151 5.47240e7 1.13269
5252 −1.08793e7 −0.206340
5353 −1.18469e7 −0.206235 −0.103118 0.994669i 0.532882π-0.532882\pi
−0.103118 + 0.994669i 0.532882π0.532882\pi
5454 −2.46636e7 −0.394715
5555 2.71813e7 0.400532
5656 0 0
5757 −1.56021e8 −1.95770
5858 −5.69006e7 −0.660224
5959 −1.31445e8 −1.41224 −0.706120 0.708092i 0.749556π-0.749556\pi
−0.706120 + 0.708092i 0.749556π0.749556\pi
6060 2.12234e7 0.211414
6161 1.79312e8 1.65815 0.829077 0.559135i 0.188867π-0.188867\pi
0.829077 + 0.559135i 0.188867π0.188867\pi
6262 −3.13200e7 −0.269190
6363 0 0
6464 6.90919e7 0.514775
6565 −4.19543e7 −0.291518
6666 −2.36578e8 −1.53471
6767 −2.11309e8 −1.28109 −0.640547 0.767919i 0.721292π-0.721292\pi
−0.640547 + 0.767919i 0.721292π0.721292\pi
6868 4.23300e7 0.240081
6969 −4.44857e8 −2.36265
7070 0 0
7171 −3.50475e8 −1.63680 −0.818398 0.574651i 0.805138π-0.805138\pi
−0.818398 + 0.574651i 0.805138π0.805138\pi
7272 2.20015e8 0.964841
7373 2.82794e8 1.16551 0.582757 0.812646i 0.301974π-0.301974\pi
0.582757 + 0.812646i 0.301974π0.301974\pi
7474 2.03179e8 0.787657
7575 8.18449e7 0.298687
7676 −1.20685e8 −0.414948
7777 0 0
7878 3.65158e8 1.11700
7979 −3.47506e6 −0.0100378 −0.00501892 0.999987i 0.501598π-0.501598\pi
−0.00501892 + 0.999987i 0.501598π0.501598\pi
8080 −1.99286e8 −0.543965
8181 −2.77624e8 −0.716595
8282 7.37370e8 1.80104
8383 −1.95999e8 −0.453318 −0.226659 0.973974i 0.572780π-0.572780\pi
−0.226659 + 0.973974i 0.572780π0.572780\pi
8484 0 0
8585 1.63240e8 0.339188
8686 2.17115e7 0.0428002
8787 4.59194e8 0.859330
8888 3.95115e8 0.702346
8989 3.37238e8 0.569747 0.284873 0.958565i 0.408048π-0.408048\pi
0.284873 + 0.958565i 0.408048π0.408048\pi
9090 −3.92962e8 −0.631335
9191 0 0
9292 −3.44106e8 −0.500780
9393 2.52755e8 0.350370
9494 1.21833e9 1.60950
9595 −4.65406e8 −0.586240
9696 7.59905e8 0.913143
9797 1.63718e8 0.187769 0.0938847 0.995583i 0.470072π-0.470072\pi
0.0938847 + 0.995583i 0.470072π0.470072\pi
9898 0 0
9999 1.05319e9 1.10192
100100 6.33086e7 0.0633086
101101 1.76637e9 1.68902 0.844510 0.535540i 0.179892π-0.179892\pi
0.844510 + 0.535540i 0.179892π0.179892\pi
102102 −1.42079e9 −1.29966
103103 1.92191e8 0.168254 0.0841269 0.996455i 0.473190π-0.473190\pi
0.0841269 + 0.996455i 0.473190π0.473190\pi
104104 −6.09859e8 −0.511187
105105 0 0
106106 3.07579e8 0.236636
107107 1.72802e9 1.27445 0.637225 0.770678i 0.280082π-0.280082\pi
0.637225 + 0.770678i 0.280082π0.280082\pi
108108 1.53959e8 0.108893
109109 5.28362e8 0.358519 0.179260 0.983802i 0.442630π-0.442630\pi
0.179260 + 0.983802i 0.442630π0.442630\pi
110110 −7.05703e8 −0.459573
111111 −1.63968e9 −1.02519
112112 0 0
113113 2.74144e9 1.58171 0.790853 0.612006i 0.209637π-0.209637\pi
0.790853 + 0.612006i 0.209637π0.209637\pi
114114 4.05076e9 2.24628
115115 −1.32699e9 −0.707504
116116 3.55196e8 0.182141
117117 −1.62560e9 −0.802007
118118 3.41268e9 1.62041
119119 0 0
120120 1.18972e9 0.523757
121121 −4.66567e8 −0.197870
122122 −4.65545e9 −1.90258
123123 −5.95065e9 −2.34418
124124 1.95511e8 0.0742632
125125 2.44141e8 0.0894427
126126 0 0
127127 2.75922e8 0.0941175 0.0470587 0.998892i 0.485015π-0.485015\pi
0.0470587 + 0.998892i 0.485015π0.485015\pi
128128 −3.65076e9 −1.20209
129129 −1.75214e8 −0.0557076
130130 1.08925e9 0.334490
131131 −4.12137e9 −1.22270 −0.611352 0.791359i 0.709374π-0.709374\pi
−0.611352 + 0.791359i 0.709374π0.709374\pi
132132 1.47681e9 0.423391
133133 0 0
134134 5.48618e9 1.46994
135135 5.93723e8 0.153844
136136 2.37290e9 0.594777
137137 −5.56659e9 −1.35004 −0.675020 0.737799i 0.735865π-0.735865\pi
−0.675020 + 0.737799i 0.735865π0.735865\pi
138138 1.15498e10 2.71093
139139 −1.51553e8 −0.0344349 −0.0172175 0.999852i 0.505481π-0.505481\pi
−0.0172175 + 0.999852i 0.505481π0.505481\pi
140140 0 0
141141 −9.83207e9 −2.09488
142142 9.09934e9 1.87807
143143 −2.91935e9 −0.583813
144144 −7.72173e9 −1.49652
145145 1.36976e9 0.257329
146146 −7.34215e9 −1.33732
147147 0 0
148148 −1.26832e9 −0.217296
149149 −1.49119e9 −0.247853 −0.123927 0.992291i 0.539549π-0.539549\pi
−0.123927 + 0.992291i 0.539549π0.539549\pi
150150 −2.12493e9 −0.342715
151151 −1.06694e10 −1.67010 −0.835051 0.550173i 0.814562π-0.814562\pi
−0.835051 + 0.550173i 0.814562π0.814562\pi
152152 −6.76527e9 −1.02799
153153 6.32505e9 0.933153
154154 0 0
155155 7.53960e8 0.104919
156156 −2.27945e9 −0.308156
157157 9.03073e9 1.18625 0.593123 0.805112i 0.297895π-0.297895\pi
0.593123 + 0.805112i 0.297895π0.297895\pi
158158 9.02225e7 0.0115175
159159 −2.48220e9 −0.307999
160160 2.26677e9 0.273443
161161 0 0
162162 7.20790e9 0.822226
163163 −5.34934e9 −0.593549 −0.296774 0.954948i 0.595911π-0.595911\pi
−0.296774 + 0.954948i 0.595911π0.595911\pi
164164 −4.60295e9 −0.496865
165165 5.69510e9 0.598168
166166 5.08870e9 0.520141
167167 −9.41973e9 −0.937162 −0.468581 0.883421i 0.655235π-0.655235\pi
−0.468581 + 0.883421i 0.655235π0.655235\pi
168168 0 0
169169 −6.09849e9 −0.575085
170170 −4.23817e9 −0.389187
171171 −1.80331e10 −1.61283
172172 −1.35531e8 −0.0118076
173173 1.38243e10 1.17337 0.586687 0.809814i 0.300432π-0.300432\pi
0.586687 + 0.809814i 0.300432π0.300432\pi
174174 −1.19220e10 −0.986001
175175 0 0
176176 −1.38671e10 −1.08938
177177 −2.75407e10 −2.10909
178178 −8.75567e9 −0.653731
179179 2.20063e10 1.60217 0.801084 0.598552i 0.204257π-0.204257\pi
0.801084 + 0.598552i 0.204257π0.204257\pi
180180 2.45302e9 0.174171
181181 1.83559e8 0.0127122 0.00635611 0.999980i 0.497977π-0.497977\pi
0.00635611 + 0.999980i 0.497977π0.497977\pi
182182 0 0
183183 3.75700e10 2.47634
184184 −1.92896e10 −1.24063
185185 −4.89111e9 −0.306997
186186 −6.56225e9 −0.402017
187187 1.13589e10 0.679279
188188 −7.60529e9 −0.444023
189189 0 0
190190 1.20833e10 0.672656
191191 −2.04034e10 −1.10931 −0.554654 0.832081i 0.687150π-0.687150\pi
−0.554654 + 0.832081i 0.687150π0.687150\pi
192192 1.44764e10 0.768783
193193 9.14597e9 0.474484 0.237242 0.971451i 0.423756π-0.423756\pi
0.237242 + 0.971451i 0.423756π0.423756\pi
194194 −4.25060e9 −0.215448
195195 −8.79039e9 −0.435364
196196 0 0
197197 −2.08681e10 −0.987152 −0.493576 0.869703i 0.664311π-0.664311\pi
−0.493576 + 0.869703i 0.664311π0.664311\pi
198198 −2.73439e10 −1.26435
199199 −4.12889e10 −1.86635 −0.933177 0.359416i 0.882976π-0.882976\pi
−0.933177 + 0.359416i 0.882976π0.882976\pi
200200 3.54890e9 0.156841
201201 −4.42741e10 −1.91323
202202 −4.58599e10 −1.93799
203203 0 0
204204 8.86912e9 0.358546
205205 −1.77506e10 −0.701973
206206 −4.98982e9 −0.193056
207207 −5.14171e10 −1.94644
208208 2.14039e10 0.792880
209209 −3.23848e10 −1.17404
210210 0 0
211211 −3.01901e10 −1.04856 −0.524280 0.851546i 0.675666π-0.675666\pi
−0.524280 + 0.851546i 0.675666π0.675666\pi
212212 −1.92003e9 −0.0652823
213213 −7.34326e10 −2.44445
214214 −4.48644e10 −1.46231
215215 −5.22657e8 −0.0166818
216216 8.63052e9 0.269771
217217 0 0
218218 −1.37178e10 −0.411367
219219 5.92519e10 1.74062
220220 4.40527e9 0.126786
221221 −1.75324e10 −0.494398
222222 4.25708e10 1.17631
223223 −8.91955e9 −0.241530 −0.120765 0.992681i 0.538535π-0.538535\pi
−0.120765 + 0.992681i 0.538535π0.538535\pi
224224 0 0
225225 9.45973e9 0.246069
226226 −7.11756e10 −1.81486
227227 −1.85212e10 −0.462971 −0.231486 0.972838i 0.574359π-0.574359\pi
−0.231486 + 0.972838i 0.574359π0.574359\pi
228228 −2.52864e10 −0.619697
229229 6.14911e10 1.47758 0.738792 0.673933i 0.235396π-0.235396\pi
0.738792 + 0.673933i 0.235396π0.235396\pi
230230 3.44526e10 0.811795
231231 0 0
232232 1.99112e10 0.451234
233233 7.22531e10 1.60603 0.803017 0.595956i 0.203227π-0.203227\pi
0.803017 + 0.595956i 0.203227π0.203227\pi
234234 4.22053e10 0.920229
235235 −2.93287e10 −0.627318
236236 −2.13032e10 −0.447035
237237 −7.28105e8 −0.0149909
238238 0 0
239239 −5.51824e10 −1.09398 −0.546991 0.837139i 0.684227π-0.684227\pi
−0.546991 + 0.837139i 0.684227π0.684227\pi
240240 −4.17550e10 −0.812377
241241 −6.33057e10 −1.20883 −0.604416 0.796669i 0.706594π-0.706594\pi
−0.604416 + 0.796669i 0.706594π0.706594\pi
242242 1.21134e10 0.227038
243243 −7.68665e10 −1.41419
244244 2.90611e10 0.524877
245245 0 0
246246 1.54496e11 2.68973
247247 4.99860e10 0.854499
248248 1.09598e10 0.183980
249249 −4.10664e10 −0.677001
250250 −6.33859e9 −0.102627
251251 6.18704e10 0.983900 0.491950 0.870623i 0.336284π-0.336284\pi
0.491950 + 0.870623i 0.336284π0.336284\pi
252252 0 0
253253 −9.23376e10 −1.41689
254254 −7.16373e9 −0.107991
255255 3.42025e10 0.506555
256256 5.94092e10 0.864517
257257 −1.05744e10 −0.151202 −0.0756010 0.997138i 0.524088π-0.524088\pi
−0.0756010 + 0.997138i 0.524088π0.524088\pi
258258 4.54905e9 0.0639193
259259 0 0
260260 −6.79953e9 −0.0922782
261261 5.30742e10 0.707947
262262 1.07003e11 1.40294
263263 −9.17838e10 −1.18295 −0.591473 0.806325i 0.701453π-0.701453\pi
−0.591473 + 0.806325i 0.701453π0.701453\pi
264264 8.27856e10 1.04891
265265 −7.40430e9 −0.0922312
266266 0 0
267267 7.06592e10 0.850879
268268 −3.42469e10 −0.405522
269269 1.18137e11 1.37562 0.687811 0.725890i 0.258572π-0.258572\pi
0.687811 + 0.725890i 0.258572π0.258572\pi
270270 −1.54147e10 −0.176522
271271 7.96797e10 0.897399 0.448700 0.893683i 0.351887π-0.351887\pi
0.448700 + 0.893683i 0.351887π0.351887\pi
272272 −8.32802e10 −0.922533
273273 0 0
274274 1.44525e11 1.54905
275275 1.69883e10 0.179123
276276 −7.20981e10 −0.747882
277277 3.15470e9 0.0321958 0.0160979 0.999870i 0.494876π-0.494876\pi
0.0160979 + 0.999870i 0.494876π0.494876\pi
278278 3.93476e9 0.0395109
279279 2.92137e10 0.288648
280280 0 0
281281 −1.15513e11 −1.10523 −0.552614 0.833438i 0.686369π-0.686369\pi
−0.552614 + 0.833438i 0.686369π0.686369\pi
282282 2.55269e11 2.40368
283283 6.39337e10 0.592504 0.296252 0.955110i 0.404263π-0.404263\pi
0.296252 + 0.955110i 0.404263π0.404263\pi
284284 −5.68016e10 −0.518117
285285 −9.75132e10 −0.875511
286286 7.57946e10 0.669871
287287 0 0
288288 8.78306e10 0.752280
289289 −5.03711e10 −0.424757
290290 −3.55629e10 −0.295261
291291 3.43028e10 0.280421
292292 4.58325e10 0.368936
293293 −8.43668e10 −0.668756 −0.334378 0.942439i 0.608526π-0.608526\pi
−0.334378 + 0.942439i 0.608526π0.608526\pi
294294 0 0
295295 −8.21528e10 −0.631573
296296 −7.10986e10 −0.538329
297297 4.13136e10 0.308098
298298 3.87156e10 0.284389
299299 1.42523e11 1.03125
300300 1.32646e10 0.0945473
301301 0 0
302302 2.77008e11 1.91629
303303 3.70094e11 2.52244
304304 2.37437e11 1.59447
305305 1.12070e11 0.741549
306306 −1.64216e11 −1.07071
307307 −9.93740e10 −0.638484 −0.319242 0.947673i 0.603428π-0.603428\pi
−0.319242 + 0.947673i 0.603428π0.603428\pi
308308 0 0
309309 4.02684e10 0.251276
310310 −1.95750e10 −0.120385
311311 −2.24958e11 −1.36358 −0.681788 0.731550i 0.738797π-0.738797\pi
−0.681788 + 0.731550i 0.738797π0.738797\pi
312312 −1.27780e11 −0.763424
313313 −1.79613e11 −1.05776 −0.528881 0.848696i 0.677388π-0.677388\pi
−0.528881 + 0.848696i 0.677388π0.677388\pi
314314 −2.34464e11 −1.36111
315315 0 0
316316 −5.63204e8 −0.00317741
317317 1.89181e11 1.05223 0.526114 0.850414i 0.323649π-0.323649\pi
0.526114 + 0.850414i 0.323649π0.323649\pi
318318 6.44449e10 0.353400
319319 9.53134e10 0.515343
320320 4.31825e10 0.230214
321321 3.62061e11 1.90331
322322 0 0
323323 −1.94490e11 −0.994228
324324 −4.49945e10 −0.226833
325325 −2.62214e10 −0.130371
326326 1.38884e11 0.681042
327327 1.10704e11 0.535425
328328 −2.58028e11 −1.23093
329329 0 0
330330 −1.47861e11 −0.686343
331331 −2.82309e11 −1.29270 −0.646351 0.763040i 0.723706π-0.723706\pi
−0.646351 + 0.763040i 0.723706π0.723706\pi
332332 −3.17656e10 −0.143495
333333 −1.89516e11 −0.844591
334334 2.44563e11 1.07531
335335 −1.32068e11 −0.572923
336336 0 0
337337 −2.97708e11 −1.25735 −0.628675 0.777668i 0.716403π-0.716403\pi
−0.628675 + 0.777668i 0.716403π0.716403\pi
338338 1.58334e11 0.659857
339339 5.74395e11 2.36217
340340 2.64563e10 0.107368
341341 5.24636e10 0.210118
342342 4.68191e11 1.85057
343343 0 0
344344 −7.59749e9 −0.0292521
345345 −2.78036e11 −1.05661
346346 −3.58919e11 −1.34634
347347 −3.44149e11 −1.27428 −0.637139 0.770749i 0.719882π-0.719882\pi
−0.637139 + 0.770749i 0.719882π0.719882\pi
348348 7.44217e10 0.272015
349349 3.88686e11 1.40244 0.701220 0.712945i 0.252639π-0.252639\pi
0.701220 + 0.712945i 0.252639π0.252639\pi
350350 0 0
351351 −6.37675e10 −0.224242
352352 1.57731e11 0.547614
353353 −1.33667e11 −0.458181 −0.229091 0.973405i 0.573575π-0.573575\pi
−0.229091 + 0.973405i 0.573575π0.573575\pi
354354 7.15034e11 2.41998
355355 −2.19047e11 −0.731998
356356 5.46562e10 0.180349
357357 0 0
358358 −5.71346e11 −1.83834
359359 1.55733e11 0.494831 0.247415 0.968909i 0.420419π-0.420419\pi
0.247415 + 0.968909i 0.420419π0.420419\pi
360360 1.37509e11 0.431490
361361 2.31815e11 0.718388
362362 −4.76571e9 −0.0145861
363363 −9.77566e10 −0.295506
364364 0 0
365365 1.76746e11 0.521234
366366 −9.75424e11 −2.84137
367367 −4.25431e11 −1.22414 −0.612071 0.790803i 0.709663π-0.709663\pi
−0.612071 + 0.790803i 0.709663π0.709663\pi
368368 6.76995e11 1.92429
369369 −6.87783e11 −1.93122
370370 1.26987e11 0.352251
371371 0 0
372372 4.09641e10 0.110907
373373 −4.92563e11 −1.31757 −0.658783 0.752333i 0.728929π-0.728929\pi
−0.658783 + 0.752333i 0.728929π0.728929\pi
374374 −2.94909e11 −0.779409
375375 5.11531e10 0.133577
376376 −4.26331e11 −1.10002
377377 −1.47116e11 −0.375081
378378 0 0
379379 3.59952e11 0.896124 0.448062 0.894003i 0.352114π-0.352114\pi
0.448062 + 0.894003i 0.352114π0.352114\pi
380380 −7.54284e10 −0.185570
381381 5.78121e10 0.140558
382382 5.29731e11 1.27283
383383 −1.79352e11 −0.425905 −0.212953 0.977063i 0.568308π-0.568308\pi
−0.212953 + 0.977063i 0.568308π0.568308\pi
384384 −7.64919e11 −1.79525
385385 0 0
386386 −2.37456e11 −0.544427
387387 −2.02514e10 −0.0458940
388388 2.65339e10 0.0594371
389389 4.87473e11 1.07939 0.539694 0.841861i 0.318540π-0.318540\pi
0.539694 + 0.841861i 0.318540π0.318540\pi
390390 2.28224e11 0.499539
391391 −5.54542e11 −1.19988
392392 0 0
393393 −8.63522e11 −1.82603
394394 5.41795e11 1.13267
395395 −2.17191e9 −0.00448906
396396 1.70691e11 0.348805
397397 3.74858e11 0.757372 0.378686 0.925525i 0.376376π-0.376376\pi
0.378686 + 0.925525i 0.376376π0.376376\pi
398398 1.07198e12 2.14147
399399 0 0
400400 −1.24554e11 −0.243269
401401 −1.53956e11 −0.297336 −0.148668 0.988887i 0.547499π-0.547499\pi
−0.148668 + 0.988887i 0.547499π0.547499\pi
402402 1.14948e12 2.19525
403403 −8.09776e10 −0.152930
404404 2.86275e11 0.534648
405405 −1.73515e11 −0.320471
406406 0 0
407407 −3.40343e11 −0.614811
408408 4.97177e11 0.888260
409409 9.95183e11 1.75852 0.879261 0.476340i 0.158037π-0.158037\pi
0.879261 + 0.476340i 0.158037π0.158037\pi
410410 4.60856e11 0.805449
411411 −1.16633e12 −2.01620
412412 3.11484e10 0.0532596
413413 0 0
414414 1.33494e12 2.23336
415415 −1.22500e11 −0.202730
416416 −2.43458e11 −0.398569
417417 −3.17539e10 −0.0514263
418418 8.40802e11 1.34710
419419 −1.86666e11 −0.295870 −0.147935 0.988997i 0.547263π-0.547263\pi
−0.147935 + 0.988997i 0.547263π0.547263\pi
420420 0 0
421421 1.54125e11 0.239114 0.119557 0.992827i 0.461853π-0.461853\pi
0.119557 + 0.992827i 0.461853π0.461853\pi
422422 7.83822e11 1.20313
423423 −1.13640e12 −1.72584
424424 −1.07631e11 −0.161730
425425 1.02025e11 0.151690
426426 1.90652e12 2.80478
427427 0 0
428428 2.80061e11 0.403418
429429 −6.11670e11 −0.871886
430430 1.35697e10 0.0191408
431431 8.64666e11 1.20698 0.603491 0.797370i 0.293776π-0.293776\pi
0.603491 + 0.797370i 0.293776π0.293776\pi
432432 −3.02900e11 −0.418430
433433 9.90737e11 1.35445 0.677225 0.735776i 0.263182π-0.263182\pi
0.677225 + 0.735776i 0.263182π0.263182\pi
434434 0 0
435435 2.86996e11 0.384304
436436 8.56317e10 0.113487
437437 1.58103e12 2.07384
438438 −1.53835e12 −1.99720
439439 −5.91950e11 −0.760668 −0.380334 0.924849i 0.624191π-0.624191\pi
−0.380334 + 0.924849i 0.624191π0.624191\pi
440440 2.46947e11 0.314099
441441 0 0
442442 4.55192e11 0.567276
443443 −9.35260e11 −1.15376 −0.576880 0.816829i 0.695730π-0.695730\pi
−0.576880 + 0.816829i 0.695730π0.695730\pi
444444 −2.65743e11 −0.324518
445445 2.10774e11 0.254798
446446 2.31577e11 0.277133
447447 −3.12439e11 −0.370153
448448 0 0
449449 −9.09288e11 −1.05583 −0.527913 0.849298i 0.677025π-0.677025\pi
−0.527913 + 0.849298i 0.677025π0.677025\pi
450450 −2.45602e11 −0.282342
451451 −1.23516e12 −1.40581
452452 4.44305e11 0.500678
453453 −2.23548e12 −2.49419
454454 4.80865e11 0.531216
455455 0 0
456456 −1.41748e12 −1.53524
457457 2.30997e11 0.247733 0.123866 0.992299i 0.460471π-0.460471\pi
0.123866 + 0.992299i 0.460471π0.460471\pi
458458 −1.59648e12 −1.69539
459459 2.48113e11 0.260911
460460 −2.15066e11 −0.223956
461461 1.22394e12 1.26213 0.631066 0.775729i 0.282618π-0.282618\pi
0.631066 + 0.775729i 0.282618π0.282618\pi
462462 0 0
463463 7.72436e10 0.0781175 0.0390587 0.999237i 0.487564π-0.487564\pi
0.0390587 + 0.999237i 0.487564π0.487564\pi
464464 −6.98813e11 −0.699890
465465 1.57972e11 0.156690
466466 −1.87590e12 −1.84278
467467 −3.92470e11 −0.381839 −0.190920 0.981606i 0.561147π-0.561147\pi
−0.190920 + 0.981606i 0.561147π0.561147\pi
468468 −2.63462e11 −0.253870
469469 0 0
470470 7.61457e11 0.719789
471471 1.89215e12 1.77158
472472 −1.19420e12 −1.10748
473473 −3.63685e10 −0.0334080
474474 1.89037e10 0.0172006
475475 −2.90879e11 −0.262175
476476 0 0
477477 −2.86895e11 −0.253741
478478 1.43269e12 1.25524
479479 1.62209e12 1.40788 0.703941 0.710259i 0.251422π-0.251422\pi
0.703941 + 0.710259i 0.251422π0.251422\pi
480480 4.74940e11 0.408370
481481 5.25319e11 0.447477
482482 1.64360e12 1.38702
483483 0 0
484484 −7.56166e10 −0.0626344
485485 1.02324e11 0.0839730
486486 1.99567e12 1.62266
487487 6.21478e11 0.500663 0.250332 0.968160i 0.419460π-0.419460\pi
0.250332 + 0.968160i 0.419460π0.419460\pi
488488 1.62908e12 1.30033
489489 −1.12081e12 −0.886426
490490 0 0
491491 −2.43192e12 −1.88835 −0.944176 0.329442i 0.893139π-0.893139\pi
−0.944176 + 0.329442i 0.893139π0.893139\pi
492492 −9.64423e11 −0.742035
493493 5.72414e11 0.436415
494494 −1.29778e12 −0.980459
495495 6.58246e11 0.492793
496496 −3.84649e11 −0.285363
497497 0 0
498498 1.06620e12 0.776796
499499 −1.10777e11 −0.0799827 −0.0399913 0.999200i 0.512733π-0.512733\pi
−0.0399913 + 0.999200i 0.512733π0.512733\pi
500500 3.95679e10 0.0283125
501501 −1.97365e12 −1.39959
502502 −1.60633e12 −1.12893
503503 7.14662e11 0.497788 0.248894 0.968531i 0.419933π-0.419933\pi
0.248894 + 0.968531i 0.419933π0.419933\pi
504504 0 0
505505 1.10398e12 0.755353
506506 2.39735e12 1.62575
507507 −1.27777e12 −0.858851
508508 4.47188e10 0.0297922
509509 1.21131e12 0.799884 0.399942 0.916541i 0.369030π-0.369030\pi
0.399942 + 0.916541i 0.369030π0.369030\pi
510510 −8.87994e11 −0.581225
511511 0 0
512512 3.26759e11 0.210142
513513 −7.07384e11 −0.450949
514514 2.74542e11 0.173490
515515 1.20119e11 0.0752454
516516 −2.83969e10 −0.0176339
517517 −2.04081e12 −1.25630
518518 0 0
519519 2.89651e12 1.75236
520520 −3.81162e11 −0.228610
521521 7.89014e11 0.469154 0.234577 0.972098i 0.424630π-0.424630\pi
0.234577 + 0.972098i 0.424630π0.424630\pi
522522 −1.37796e12 −0.812304
523523 2.34542e12 1.37077 0.685383 0.728183i 0.259635π-0.259635\pi
0.685383 + 0.728183i 0.259635π0.259635\pi
524524 −6.67951e11 −0.387038
525525 0 0
526526 2.38297e12 1.35732
527527 3.15075e11 0.177937
528528 −2.90548e12 −1.62691
529529 2.70679e12 1.50281
530530 1.92237e11 0.105827
531531 −3.18318e12 −1.73754
532532 0 0
533533 1.90647e12 1.02319
534534 −1.83451e12 −0.976305
535535 1.08001e12 0.569951
536536 −1.91978e12 −1.00464
537537 4.61082e12 2.39273
538538 −3.06716e12 −1.57840
539539 0 0
540540 9.62247e10 0.0486984
541541 1.88358e12 0.945357 0.472678 0.881235i 0.343287π-0.343287\pi
0.472678 + 0.881235i 0.343287π0.343287\pi
542542 −2.06871e12 −1.02968
543543 3.84598e10 0.0189849
544544 9.47269e11 0.463744
545545 3.30226e11 0.160335
546546 0 0
547547 −2.08933e12 −0.997846 −0.498923 0.866646i 0.666271π-0.666271\pi
−0.498923 + 0.866646i 0.666271π0.666271\pi
548548 −9.02178e11 −0.427346
549549 4.34238e12 2.04010
550550 −4.41064e11 −0.205527
551551 −1.63199e12 −0.754283
552552 −4.04161e12 −1.85280
553553 0 0
554554 −8.19051e10 −0.0369417
555555 −1.02480e12 −0.458480
556556 −2.45623e10 −0.0109001
557557 −2.51383e12 −1.10659 −0.553297 0.832984i 0.686630π-0.686630\pi
−0.553297 + 0.832984i 0.686630π0.686630\pi
558558 −7.58472e11 −0.331196
559559 5.61348e10 0.0243153
560560 0 0
561561 2.37994e12 1.01446
562562 2.99904e12 1.26815
563563 −8.76468e11 −0.367662 −0.183831 0.982958i 0.558850π-0.558850\pi
−0.183831 + 0.982958i 0.558850π0.558850\pi
564564 −1.59348e12 −0.663120
565565 1.71340e12 0.707360
566566 −1.65990e12 −0.679843
567567 0 0
568568 −3.18413e12 −1.28358
569569 −1.75549e12 −0.702091 −0.351046 0.936358i 0.614174π-0.614174\pi
−0.351046 + 0.936358i 0.614174π0.614174\pi
570570 2.53172e12 1.00457
571571 2.32441e12 0.915060 0.457530 0.889194i 0.348734π-0.348734\pi
0.457530 + 0.889194i 0.348734π0.348734\pi
572572 −4.73139e11 −0.184802
573573 −4.27498e12 −1.65668
574574 0 0
575575 −8.29372e11 −0.316405
576576 1.67319e12 0.633351
577577 −3.74722e12 −1.40740 −0.703700 0.710497i 0.748470π-0.748470\pi
−0.703700 + 0.710497i 0.748470π0.748470\pi
578578 1.30778e12 0.487370
579579 1.91629e12 0.708611
580580 2.21997e11 0.0814557
581581 0 0
582582 −8.90598e11 −0.321757
583583 −5.15221e11 −0.184708
584584 2.56924e12 0.914000
585585 −1.01600e12 −0.358669
586586 2.19040e12 0.767335
587587 5.13023e12 1.78347 0.891734 0.452561i 0.149489π-0.149489\pi
0.891734 + 0.452561i 0.149489π0.149489\pi
588588 0 0
589589 −8.98298e11 −0.307540
590590 2.13292e12 0.724671
591591 −4.37234e12 −1.47425
592592 2.49530e12 0.834979
593593 −5.25654e11 −0.174564 −0.0872819 0.996184i 0.527818π-0.527818\pi
−0.0872819 + 0.996184i 0.527818π0.527818\pi
594594 −1.07262e12 −0.353514
595595 0 0
596596 −2.41677e11 −0.0784563
597597 −8.65097e12 −2.78728
598598 −3.70031e12 −1.18327
599599 4.45408e12 1.41364 0.706818 0.707396i 0.250130π-0.250130\pi
0.706818 + 0.707396i 0.250130π0.250130\pi
600600 7.43576e11 0.234231
601601 1.48564e12 0.464491 0.232245 0.972657i 0.425393π-0.425393\pi
0.232245 + 0.972657i 0.425393π0.425393\pi
602602 0 0
603603 −5.11725e12 −1.57619
604604 −1.72919e12 −0.528659
605605 −2.91605e11 −0.0884902
606606 −9.60871e12 −2.89427
607607 −1.33914e12 −0.400385 −0.200192 0.979757i 0.564157π-0.564157\pi
−0.200192 + 0.979757i 0.564157π0.564157\pi
608608 −2.70072e12 −0.801518
609609 0 0
610610 −2.90966e12 −0.850859
611611 3.14999e12 0.914374
612612 1.02510e12 0.295383
613613 −3.77297e12 −1.07922 −0.539612 0.841914i 0.681429π-0.681429\pi
−0.539612 + 0.841914i 0.681429π0.681429\pi
614614 2.58003e12 0.732602
615615 −3.71916e12 −1.04835
616616 0 0
617617 8.47795e11 0.235509 0.117755 0.993043i 0.462430π-0.462430\pi
0.117755 + 0.993043i 0.462430π0.462430\pi
618618 −1.04548e12 −0.288316
619619 −1.05795e12 −0.289640 −0.144820 0.989458i 0.546260π-0.546260\pi
−0.144820 + 0.989458i 0.546260π0.546260\pi
620620 1.22194e11 0.0332115
621621 −2.01694e12 −0.544227
622622 5.84055e12 1.56458
623623 0 0
624624 4.48460e12 1.18411
625625 1.52588e11 0.0400000
626626 4.66327e12 1.21368
627627 −6.78536e12 −1.75335
628628 1.46361e12 0.375498
629629 −2.04396e12 −0.520649
630630 0 0
631631 6.07455e12 1.52539 0.762696 0.646757i 0.223875π-0.223875\pi
0.762696 + 0.646757i 0.223875π0.223875\pi
632632 −3.15716e10 −0.00787171
633633 −6.32552e12 −1.56596
634634 −4.91167e12 −1.20733
635635 1.72451e11 0.0420906
636636 −4.02290e11 −0.0974949
637637 0 0
638638 −2.47461e12 −0.591308
639639 −8.48742e12 −2.01383
640640 −2.28173e12 −0.537593
641641 1.55196e12 0.363094 0.181547 0.983382i 0.441890π-0.441890\pi
0.181547 + 0.983382i 0.441890π0.441890\pi
642642 −9.40013e12 −2.18387
643643 7.39291e12 1.70556 0.852778 0.522273i 0.174916π-0.174916\pi
0.852778 + 0.522273i 0.174916π0.174916\pi
644644 0 0
645645 −1.09509e11 −0.0249132
646646 5.04952e12 1.14078
647647 −3.70849e11 −0.0832009 −0.0416004 0.999134i 0.513246π-0.513246\pi
−0.0416004 + 0.999134i 0.513246π0.513246\pi
648648 −2.52226e12 −0.561956
649649 −5.71652e12 −1.26483
650650 6.80783e11 0.149589
651651 0 0
652652 −8.66969e11 −0.187884
653653 5.70367e12 1.22757 0.613783 0.789475i 0.289647π-0.289647\pi
0.613783 + 0.789475i 0.289647π0.289647\pi
654654 −2.87419e12 −0.614350
655655 −2.57586e12 −0.546810
656656 9.05585e12 1.90925
657657 6.84840e12 1.43399
658658 0 0
659659 −1.72578e12 −0.356451 −0.178226 0.983990i 0.557036π-0.557036\pi
−0.178226 + 0.983990i 0.557036π0.557036\pi
660660 9.23005e11 0.189346
661661 −6.91726e11 −0.140938 −0.0704690 0.997514i 0.522450π-0.522450\pi
−0.0704690 + 0.997514i 0.522450π0.522450\pi
662662 7.32955e12 1.48326
663663 −3.67345e12 −0.738351
664664 −1.78069e12 −0.355494
665665 0 0
666666 4.92038e12 0.969090
667667 −4.65322e12 −0.910306
668668 −1.52666e12 −0.296652
669669 −1.86885e12 −0.360709
670670 3.42886e12 0.657376
671671 7.79827e12 1.48507
672672 0 0
673673 −3.11235e12 −0.584818 −0.292409 0.956293i 0.594457π-0.594457\pi
−0.292409 + 0.956293i 0.594457π0.594457\pi
674674 7.72936e12 1.44269
675675 3.71077e11 0.0688013
676676 −9.88383e11 −0.182039
677677 −6.18272e12 −1.13118 −0.565589 0.824687i 0.691351π-0.691351\pi
−0.565589 + 0.824687i 0.691351π0.691351\pi
678678 −1.49129e13 −2.71037
679679 0 0
680680 1.48306e12 0.265992
681681 −3.88063e12 −0.691417
682682 −1.36210e12 −0.241091
683683 9.17110e12 1.61261 0.806303 0.591503i 0.201465π-0.201465\pi
0.806303 + 0.591503i 0.201465π0.201465\pi
684684 −2.92263e12 −0.510530
685685 −3.47912e12 −0.603756
686686 0 0
687687 1.28838e13 2.20668
688688 2.66644e11 0.0453716
689689 7.95244e11 0.134435
690690 7.21861e12 1.21236
691691 6.21607e12 1.03721 0.518603 0.855015i 0.326452π-0.326452\pi
0.518603 + 0.855015i 0.326452π0.326452\pi
692692 2.24051e12 0.371423
693693 0 0
694694 8.93509e12 1.46211
695695 −9.47209e10 −0.0153998
696696 4.17186e12 0.673889
697697 −7.41786e12 −1.19050
698698 −1.00914e13 −1.60917
699699 1.51387e13 2.39851
700700 0 0
701701 9.62999e12 1.50624 0.753121 0.657882i 0.228547π-0.228547\pi
0.753121 + 0.657882i 0.228547π0.228547\pi
702702 1.65559e12 0.257297
703703 5.82746e12 0.899871
704704 3.00481e12 0.461041
705705 −6.14504e12 −0.936858
706706 3.47037e12 0.525721
707707 0 0
708708 −4.46352e12 −0.667617
709709 −8.38186e12 −1.24575 −0.622877 0.782320i 0.714036π-0.714036\pi
−0.622877 + 0.782320i 0.714036π0.714036\pi
710710 5.68709e12 0.839899
711711 −8.41552e10 −0.0123500
712712 3.06387e12 0.446797
713713 −2.56128e12 −0.371155
714714 0 0
715715 −1.82459e12 −0.261089
716716 3.56656e12 0.507156
717717 −1.15620e13 −1.63379
718718 −4.04328e12 −0.567773
719719 2.10248e12 0.293395 0.146697 0.989181i 0.453136π-0.453136\pi
0.146697 + 0.989181i 0.453136π0.453136\pi
720720 −4.82608e12 −0.669266
721721 0 0
722722 −6.01858e12 −0.824284
723723 −1.32640e13 −1.80531
724724 2.97494e10 0.00402397
725725 8.56100e11 0.115081
726726 2.53804e12 0.339066
727727 1.36288e12 0.180947 0.0904736 0.995899i 0.471162π-0.471162\pi
0.0904736 + 0.995899i 0.471162π0.471162\pi
728728 0 0
729729 −1.06408e13 −1.39541
730730 −4.58884e12 −0.598068
731731 −2.18415e11 −0.0282914
732732 6.08897e12 0.783870
733733 6.10310e12 0.780878 0.390439 0.920629i 0.372323π-0.372323\pi
0.390439 + 0.920629i 0.372323π0.372323\pi
734734 1.10454e13 1.40459
735735 0 0
736736 −7.70046e12 −0.967312
737737 −9.18982e12 −1.14737
738738 1.78568e13 2.21590
739739 5.95459e12 0.734432 0.367216 0.930136i 0.380311π-0.380311\pi
0.367216 + 0.930136i 0.380311π0.380311\pi
740740 −7.92702e11 −0.0971779
741741 1.04732e13 1.27614
742742 0 0
743743 −1.59757e13 −1.92314 −0.961569 0.274563i 0.911467π-0.911467\pi
−0.961569 + 0.274563i 0.911467π0.911467\pi
744744 2.29633e12 0.274761
745745 −9.31994e11 −0.110843
746746 1.27884e13 1.51178
747747 −4.74650e12 −0.557738
748748 1.84093e12 0.215021
749749 0 0
750750 −1.32808e12 −0.153267
751751 6.94141e12 0.796284 0.398142 0.917324i 0.369655π-0.369655\pi
0.398142 + 0.917324i 0.369655π0.369655\pi
752752 1.49627e13 1.70620
753753 1.29633e13 1.46939
754754 3.81956e12 0.430370
755755 −6.66836e12 −0.746892
756756 0 0
757757 8.41151e12 0.930984 0.465492 0.885052i 0.345877π-0.345877\pi
0.465492 + 0.885052i 0.345877π0.345877\pi
758758 −9.34538e12 −1.02822
759759 −1.93469e13 −2.11603
760760 −4.22830e12 −0.459731
761761 −1.50892e13 −1.63093 −0.815467 0.578803i 0.803520π-0.803520\pi
−0.815467 + 0.578803i 0.803520π0.803520\pi
762762 −1.50097e12 −0.161278
763763 0 0
764764 −3.30678e12 −0.351144
765765 3.95316e12 0.417319
766766 4.65650e12 0.488687
767767 8.82346e12 0.920576
768768 1.24476e13 1.29110
769769 −8.73448e12 −0.900676 −0.450338 0.892858i 0.648697π-0.648697\pi
−0.450338 + 0.892858i 0.648697π0.648697\pi
770770 0 0
771771 −2.21559e12 −0.225810
772772 1.48229e12 0.150195
773773 −9.26595e12 −0.933431 −0.466716 0.884407i 0.654563π-0.654563\pi
−0.466716 + 0.884407i 0.654563π0.654563\pi
774774 5.25784e11 0.0526591
775775 4.71225e11 0.0469214
776776 1.48741e12 0.147249
777777 0 0
778778 −1.26562e13 −1.23850
779779 2.11488e13 2.05762
780780 −1.42466e12 −0.137811
781781 −1.52422e13 −1.46594
782782 1.43975e13 1.37676
783783 2.08194e12 0.197943
784784 0 0
785785 5.64421e12 0.530505
786786 2.24195e13 2.09520
787787 −8.04278e12 −0.747343 −0.373671 0.927561i 0.621901π-0.621901\pi
−0.373671 + 0.927561i 0.621901π0.621901\pi
788788 −3.38209e12 −0.312476
789789 −1.92308e13 −1.76665
790790 5.63891e10 0.00515078
791791 0 0
792792 9.56845e12 0.864128
793793 −1.20366e13 −1.08088
794794 −9.73239e12 −0.869015
795795 −1.55137e12 −0.137741
796796 −6.69169e12 −0.590782
797797 3.62841e12 0.318533 0.159266 0.987236i 0.449087π-0.449087\pi
0.159266 + 0.987236i 0.449087π0.449087\pi
798798 0 0
799799 −1.22563e13 −1.06389
800800 1.41673e12 0.122288
801801 8.16686e12 0.700985
802802 3.99714e12 0.341165
803803 1.22987e13 1.04385
804804 −7.17550e12 −0.605620
805805 0 0
806806 2.10241e12 0.175473
807807 2.47523e13 2.05440
808808 1.60478e13 1.32453
809809 1.27049e13 1.04280 0.521402 0.853311i 0.325409π-0.325409\pi
0.521402 + 0.853311i 0.325409π0.325409\pi
810810 4.50494e12 0.367711
811811 −6.90849e12 −0.560776 −0.280388 0.959887i 0.590463π-0.590463\pi
−0.280388 + 0.959887i 0.590463π0.590463\pi
812812 0 0
813813 1.66947e13 1.34021
814814 8.83627e12 0.705439
815815 −3.34334e12 −0.265443
816816 −1.74491e13 −1.37774
817817 6.22713e11 0.0488978
818818 −2.58378e13 −2.01774
819819 0 0
820820 −2.87684e12 −0.222205
821821 −1.57014e13 −1.20613 −0.603067 0.797691i 0.706055π-0.706055\pi
−0.603067 + 0.797691i 0.706055π0.706055\pi
822822 3.02812e13 2.31340
823823 1.02697e13 0.780295 0.390147 0.920752i 0.372424π-0.372424\pi
0.390147 + 0.920752i 0.372424π0.372424\pi
824824 1.74609e12 0.131945
825825 3.55944e12 0.267509
826826 0 0
827827 −2.06564e13 −1.53561 −0.767804 0.640684i 0.778651π-0.778651\pi
−0.767804 + 0.640684i 0.778651π0.778651\pi
828828 −8.33318e12 −0.616132
829829 9.01114e12 0.662650 0.331325 0.943517i 0.392504π-0.392504\pi
0.331325 + 0.943517i 0.392504π0.392504\pi
830830 3.18044e12 0.232614
831831 6.60983e11 0.0480823
832832 −4.63792e12 −0.335559
833833 0 0
834834 8.24423e11 0.0590069
835835 −5.88733e12 −0.419111
836836 −5.24861e12 −0.371634
837837 1.14597e12 0.0807063
838838 4.84637e12 0.339483
839839 5.25303e12 0.366000 0.183000 0.983113i 0.441419π-0.441419\pi
0.183000 + 0.983113i 0.441419π0.441419\pi
840840 0 0
841841 −9.70396e12 −0.668909
842842 −4.00153e12 −0.274361
843843 −2.42026e13 −1.65058
844844 −4.89291e12 −0.331915
845845 −3.81155e12 −0.257186
846846 2.95042e13 1.98024
847847 0 0
848848 3.77746e12 0.250853
849849 1.33956e13 0.884865
850850 −2.64886e12 −0.174050
851851 1.66156e13 1.08601
852852 −1.19012e13 −0.773773
853853 −2.16481e13 −1.40007 −0.700035 0.714109i 0.746832π-0.746832\pi
−0.700035 + 0.714109i 0.746832π0.746832\pi
854854 0 0
855855 −1.12707e13 −0.721278
856856 1.56994e13 0.999427
857857 2.18253e13 1.38212 0.691061 0.722796i 0.257143π-0.257143\pi
0.691061 + 0.722796i 0.257143π0.257143\pi
858858 1.58807e13 1.00041
859859 8.56506e12 0.536737 0.268368 0.963316i 0.413516π-0.413516\pi
0.268368 + 0.963316i 0.413516π0.413516\pi
860860 −8.47070e10 −0.00528052
861861 0 0
862862 −2.24492e13 −1.38490
863863 −3.29505e12 −0.202215 −0.101108 0.994876i 0.532239π-0.532239\pi
−0.101108 + 0.994876i 0.532239π0.532239\pi
864864 3.44533e12 0.210339
865865 8.64020e12 0.524749
866866 −2.57224e13 −1.55411
867867 −1.05539e13 −0.634347
868868 0 0
869869 −1.51130e11 −0.00899007
870870 −7.45125e12 −0.440953
871871 1.41845e13 0.835088
872872 4.80026e12 0.281152
873873 3.96475e12 0.231021
874874 −4.10481e13 −2.37953
875875 0 0
876876 9.60296e12 0.550981
877877 −5.03789e12 −0.287574 −0.143787 0.989609i 0.545928π-0.545928\pi
−0.143787 + 0.989609i 0.545928π0.545928\pi
878878 1.53687e13 0.872796
879879 −1.76768e13 −0.998742
880880 −8.66694e12 −0.487185
881881 1.87408e13 1.04808 0.524042 0.851692i 0.324423π-0.324423\pi
0.524042 + 0.851692i 0.324423π0.324423\pi
882882 0 0
883883 3.35081e13 1.85493 0.927463 0.373914i 0.121984π-0.121984\pi
0.927463 + 0.373914i 0.121984π0.121984\pi
884884 −2.84148e12 −0.156498
885885 −1.72129e13 −0.943213
886886 2.42820e13 1.32383
887887 1.04883e13 0.568917 0.284459 0.958688i 0.408186π-0.408186\pi
0.284459 + 0.958688i 0.408186π0.408186\pi
888888 −1.48968e13 −0.803959
889889 0 0
890890 −5.47229e12 −0.292358
891891 −1.20738e13 −0.641795
892892 −1.44559e12 −0.0764547
893893 3.49434e13 1.83880
894894 8.11180e12 0.424716
895895 1.37539e13 0.716512
896896 0 0
897897 2.98619e13 1.54011
898898 2.36077e13 1.21146
899899 2.64383e12 0.134994
900900 1.53314e12 0.0778915
901901 −3.09421e12 −0.156419
902902 3.20682e13 1.61304
903903 0 0
904904 2.49065e13 1.24038
905905 1.14724e11 0.00568508
906906 5.80395e13 2.86185
907907 −3.18949e13 −1.56491 −0.782454 0.622709i 0.786032π-0.786032\pi
−0.782454 + 0.622709i 0.786032π0.786032\pi
908908 −3.00174e12 −0.146550
909909 4.27759e13 2.07808
910910 0 0
911911 2.29508e13 1.10399 0.551995 0.833848i 0.313867π-0.313867\pi
0.551995 + 0.833848i 0.313867π0.313867\pi
912912 4.97485e13 2.38124
913913 −8.52401e12 −0.405999
914914 −5.99734e12 −0.284250
915915 2.34812e13 1.10745
916916 9.96587e12 0.467719
917917 0 0
918918 −6.44172e12 −0.299371
919919 1.75653e13 0.812334 0.406167 0.913799i 0.366865π-0.366865\pi
0.406167 + 0.913799i 0.366865π0.366865\pi
920920 −1.20560e13 −0.554827
921921 −2.08212e13 −0.953534
922922 −3.17769e13 −1.44818
923923 2.35263e13 1.06695
924924 0 0
925925 −3.05694e12 −0.137293
926926 −2.00547e12 −0.0896326
927927 4.65426e12 0.207010
928928 7.94863e12 0.351825
929929 −1.93752e13 −0.853446 −0.426723 0.904382i 0.640332π-0.640332\pi
−0.426723 + 0.904382i 0.640332π0.640332\pi
930930 −4.10141e12 −0.179788
931931 0 0
932932 1.17101e13 0.508379
933933 −4.71338e13 −2.03641
934934 1.01896e13 0.438125
935935 7.09929e12 0.303783
936936 −1.47689e13 −0.628937
937937 −4.08529e12 −0.173139 −0.0865696 0.996246i 0.527590π-0.527590\pi
−0.0865696 + 0.996246i 0.527590π0.527590\pi
938938 0 0
939939 −3.76331e13 −1.57970
940940 −4.75331e12 −0.198573
941941 1.06000e12 0.0440709 0.0220355 0.999757i 0.492985π-0.492985\pi
0.0220355 + 0.999757i 0.492985π0.492985\pi
942942 −4.91255e13 −2.03272
943943 6.03006e13 2.48324
944944 4.19120e13 1.71777
945945 0 0
946946 9.44231e11 0.0383326
947947 −1.29151e13 −0.521824 −0.260912 0.965363i 0.584023π-0.584023\pi
−0.260912 + 0.965363i 0.584023π0.584023\pi
948948 −1.18004e11 −0.00474526
949949 −1.89831e13 −0.759747
950950 7.55204e12 0.300821
951951 3.96377e13 1.57143
952952 0 0
953953 8.70094e12 0.341702 0.170851 0.985297i 0.445348π-0.445348\pi
0.170851 + 0.985297i 0.445348π0.445348\pi
954954 7.44861e12 0.291144
955955 −1.27521e13 −0.496098
956956 −8.94342e12 −0.346292
957957 1.99704e13 0.769630
958958 −4.21142e13 −1.61541
959959 0 0
960960 9.04772e12 0.343810
961961 −2.49844e13 −0.944960
962962 −1.36388e13 −0.513438
963963 4.18474e13 1.56801
964964 −1.02600e13 −0.382648
965965 5.71623e12 0.212196
966966 0 0
967967 −4.84084e13 −1.78033 −0.890167 0.455635i 0.849412π-0.849412\pi
−0.890167 + 0.455635i 0.849412π0.849412\pi
968968 −4.23885e12 −0.155170
969969 −4.07502e13 −1.48481
970970 −2.65662e12 −0.0963512
971971 −2.67952e13 −0.967319 −0.483660 0.875256i 0.660693π-0.660693\pi
−0.483660 + 0.875256i 0.660693π0.660693\pi
972972 −1.24578e13 −0.447653
973973 0 0
974974 −1.61354e13 −0.574465
975975 −5.49399e12 −0.194701
976976 −5.71749e13 −2.01688
977977 4.21970e12 0.148169 0.0740843 0.997252i 0.476397π-0.476397\pi
0.0740843 + 0.997252i 0.476397π0.476397\pi
978978 2.90994e13 1.01709
979979 1.46665e13 0.510275
980980 0 0
981981 1.27953e13 0.441103
982982 6.31396e13 2.16671
983983 4.74505e13 1.62088 0.810438 0.585825i 0.199229π-0.199229\pi
0.810438 + 0.585825i 0.199229π0.199229\pi
984984 −5.40628e13 −1.83832
985985 −1.30425e13 −0.441468
986986 −1.48615e13 −0.500745
987987 0 0
988988 8.10123e12 0.270486
989989 1.77552e12 0.0590122
990990 −1.70899e13 −0.565434
991991 −1.04090e13 −0.342830 −0.171415 0.985199i 0.554834π-0.554834\pi
−0.171415 + 0.985199i 0.554834π0.554834\pi
992992 4.37518e12 0.143448
993993 −5.91502e13 −1.93057
994994 0 0
995995 −2.58055e13 −0.834659
996996 −6.65563e12 −0.214300
997997 −2.11445e13 −0.677749 −0.338874 0.940832i 0.610046π-0.610046\pi
−0.338874 + 0.940832i 0.610046π0.610046\pi
998998 2.87608e12 0.0917727
999999 −7.43414e12 −0.236149
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 245.10.a.e.1.2 4
7.6 odd 2 35.10.a.c.1.2 4
21.20 even 2 315.10.a.g.1.3 4
35.13 even 4 175.10.b.e.99.6 8
35.27 even 4 175.10.b.e.99.3 8
35.34 odd 2 175.10.a.e.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.10.a.c.1.2 4 7.6 odd 2
175.10.a.e.1.3 4 35.34 odd 2
175.10.b.e.99.3 8 35.27 even 4
175.10.b.e.99.6 8 35.13 even 4
245.10.a.e.1.2 4 1.1 even 1 trivial
315.10.a.g.1.3 4 21.20 even 2