Properties

Label 1587.2.a.s.1.5
Level 15871587
Weight 22
Character 1587.1
Self dual yes
Analytic conductor 12.67212.672
Analytic rank 00
Dimension 66
Inner twists 22

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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] = [1587,2,Mod(1,1587)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1587, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1587.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 1587=3232 1587 = 3 \cdot 23^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1587.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,2,6,10,0,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 12.672258800812.6722588008
Analytic rank: 00
Dimension: 66
Coefficient field: 6.6.2803712.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x66x4+8x22 x^{6} - 6x^{4} + 8x^{2} - 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 22 2^{2}
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.5
Root 1.20864-1.20864 of defining polynomial
Character χ\chi == 1587.1

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+2.70928q2+1.00000q3+5.34017q40.762528q5+2.70928q60.651685q7+9.04945q8+1.00000q92.06590q10+6.13793q11+5.34017q123.41855q131.76560q140.762528q15+13.8371q163.59096q17+2.70928q183.96119q194.07203q200.651685q21+16.6293q22+9.04945q244.41855q259.26180q26+1.00000q273.48011q28+0.921622q292.06590q30+3.07838q31+19.3896q32+6.13793q339.72889q34+0.496928q35+5.34017q361.89529q3710.7320q383.41855q396.90046q406.68035q411.76560q42+3.48011q43+32.7776q440.762528q450.183417q47+13.8371q486.57531q4911.9711q503.59096q5118.2557q52+10.2100q53+2.70928q544.68035q555.89739q563.96119q57+2.49693q58+5.65983q594.07203q602.93927q61+8.34017q620.651685q63+24.8576q64+2.60674q65+16.6293q667.01130q6719.1763q68+1.34632q704.00000q71+9.04945q720.680346q735.13486q744.41855q7521.1534q764.00000q779.26180q78+11.1431q7910.5512q80+1.00000q8118.0989q82+12.4975q833.48011q84+2.73820q85+9.42858q86+0.921622q87+55.5449q883.36927q892.06590q90+2.22782q91+3.07838q930.496928q94+3.02052q95+19.3896q965.54601q9717.8143q98+6.13793q99+O(q100)q+2.70928 q^{2} +1.00000 q^{3} +5.34017 q^{4} -0.762528 q^{5} +2.70928 q^{6} -0.651685 q^{7} +9.04945 q^{8} +1.00000 q^{9} -2.06590 q^{10} +6.13793 q^{11} +5.34017 q^{12} -3.41855 q^{13} -1.76560 q^{14} -0.762528 q^{15} +13.8371 q^{16} -3.59096 q^{17} +2.70928 q^{18} -3.96119 q^{19} -4.07203 q^{20} -0.651685 q^{21} +16.6293 q^{22} +9.04945 q^{24} -4.41855 q^{25} -9.26180 q^{26} +1.00000 q^{27} -3.48011 q^{28} +0.921622 q^{29} -2.06590 q^{30} +3.07838 q^{31} +19.3896 q^{32} +6.13793 q^{33} -9.72889 q^{34} +0.496928 q^{35} +5.34017 q^{36} -1.89529 q^{37} -10.7320 q^{38} -3.41855 q^{39} -6.90046 q^{40} -6.68035 q^{41} -1.76560 q^{42} +3.48011 q^{43} +32.7776 q^{44} -0.762528 q^{45} -0.183417 q^{47} +13.8371 q^{48} -6.57531 q^{49} -11.9711 q^{50} -3.59096 q^{51} -18.2557 q^{52} +10.2100 q^{53} +2.70928 q^{54} -4.68035 q^{55} -5.89739 q^{56} -3.96119 q^{57} +2.49693 q^{58} +5.65983 q^{59} -4.07203 q^{60} -2.93927 q^{61} +8.34017 q^{62} -0.651685 q^{63} +24.8576 q^{64} +2.60674 q^{65} +16.6293 q^{66} -7.01130 q^{67} -19.1763 q^{68} +1.34632 q^{70} -4.00000 q^{71} +9.04945 q^{72} -0.680346 q^{73} -5.13486 q^{74} -4.41855 q^{75} -21.1534 q^{76} -4.00000 q^{77} -9.26180 q^{78} +11.1431 q^{79} -10.5512 q^{80} +1.00000 q^{81} -18.0989 q^{82} +12.4975 q^{83} -3.48011 q^{84} +2.73820 q^{85} +9.42858 q^{86} +0.921622 q^{87} +55.5449 q^{88} -3.36927 q^{89} -2.06590 q^{90} +2.22782 q^{91} +3.07838 q^{93} -0.496928 q^{94} +3.02052 q^{95} +19.3896 q^{96} -5.54601 q^{97} -17.8143 q^{98} +6.13793 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+2q2+6q3+10q4+2q6+18q8+6q9+10q12+8q13+26q16+2q18+18q24+2q2540q26+6q27+12q29+12q31+58q3232q35+90q98+O(q100) 6 q + 2 q^{2} + 6 q^{3} + 10 q^{4} + 2 q^{6} + 18 q^{8} + 6 q^{9} + 10 q^{12} + 8 q^{13} + 26 q^{16} + 2 q^{18} + 18 q^{24} + 2 q^{25} - 40 q^{26} + 6 q^{27} + 12 q^{29} + 12 q^{31} + 58 q^{32} - 32 q^{35}+ \cdots - 90 q^{98}+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 2.70928 1.91575 0.957873 0.287190i 0.0927213π-0.0927213\pi
0.957873 + 0.287190i 0.0927213π0.0927213\pi
33 1.00000 0.577350
44 5.34017 2.67009
55 −0.762528 −0.341013 −0.170506 0.985357i 0.554540π-0.554540\pi
−0.170506 + 0.985357i 0.554540π0.554540\pi
66 2.70928 1.10606
77 −0.651685 −0.246314 −0.123157 0.992387i 0.539302π-0.539302\pi
−0.123157 + 0.992387i 0.539302π0.539302\pi
88 9.04945 3.19946
99 1.00000 0.333333
1010 −2.06590 −0.653295
1111 6.13793 1.85066 0.925328 0.379168i 0.123790π-0.123790\pi
0.925328 + 0.379168i 0.123790π0.123790\pi
1212 5.34017 1.54158
1313 −3.41855 −0.948135 −0.474068 0.880488i 0.657215π-0.657215\pi
−0.474068 + 0.880488i 0.657215π0.657215\pi
1414 −1.76560 −0.471875
1515 −0.762528 −0.196884
1616 13.8371 3.45928
1717 −3.59096 −0.870935 −0.435467 0.900205i 0.643417π-0.643417\pi
−0.435467 + 0.900205i 0.643417π0.643417\pi
1818 2.70928 0.638582
1919 −3.96119 −0.908759 −0.454380 0.890808i 0.650139π-0.650139\pi
−0.454380 + 0.890808i 0.650139π0.650139\pi
2020 −4.07203 −0.910534
2121 −0.651685 −0.142209
2222 16.6293 3.54539
2323 0 0
2424 9.04945 1.84721
2525 −4.41855 −0.883710
2626 −9.26180 −1.81639
2727 1.00000 0.192450
2828 −3.48011 −0.657679
2929 0.921622 0.171141 0.0855705 0.996332i 0.472729π-0.472729\pi
0.0855705 + 0.996332i 0.472729π0.472729\pi
3030 −2.06590 −0.377180
3131 3.07838 0.552893 0.276446 0.961029i 0.410843π-0.410843\pi
0.276446 + 0.961029i 0.410843π0.410843\pi
3232 19.3896 3.42763
3333 6.13793 1.06848
3434 −9.72889 −1.66849
3535 0.496928 0.0839962
3636 5.34017 0.890029
3737 −1.89529 −0.311584 −0.155792 0.987790i 0.549793π-0.549793\pi
−0.155792 + 0.987790i 0.549793π0.549793\pi
3838 −10.7320 −1.74095
3939 −3.41855 −0.547406
4040 −6.90046 −1.09106
4141 −6.68035 −1.04329 −0.521647 0.853161i 0.674682π-0.674682\pi
−0.521647 + 0.853161i 0.674682π0.674682\pi
4242 −1.76560 −0.272437
4343 3.48011 0.530712 0.265356 0.964150i 0.414510π-0.414510\pi
0.265356 + 0.964150i 0.414510π0.414510\pi
4444 32.7776 4.94141
4545 −0.762528 −0.113671
4646 0 0
4747 −0.183417 −0.0267542 −0.0133771 0.999911i 0.504258π-0.504258\pi
−0.0133771 + 0.999911i 0.504258π0.504258\pi
4848 13.8371 1.99721
4949 −6.57531 −0.939329
5050 −11.9711 −1.69297
5151 −3.59096 −0.502834
5252 −18.2557 −2.53160
5353 10.2100 1.40245 0.701223 0.712942i 0.252638π-0.252638\pi
0.701223 + 0.712942i 0.252638π0.252638\pi
5454 2.70928 0.368686
5555 −4.68035 −0.631098
5656 −5.89739 −0.788072
5757 −3.96119 −0.524672
5858 2.49693 0.327863
5959 5.65983 0.736847 0.368423 0.929658i 0.379898π-0.379898\pi
0.368423 + 0.929658i 0.379898π0.379898\pi
6060 −4.07203 −0.525697
6161 −2.93927 −0.376335 −0.188167 0.982137i 0.560255π-0.560255\pi
−0.188167 + 0.982137i 0.560255π0.560255\pi
6262 8.34017 1.05920
6363 −0.651685 −0.0821046
6464 24.8576 3.10720
6565 2.60674 0.323326
6666 16.6293 2.04693
6767 −7.01130 −0.856567 −0.428283 0.903644i 0.640882π-0.640882\pi
−0.428283 + 0.903644i 0.640882π0.640882\pi
6868 −19.1763 −2.32547
6969 0 0
7070 1.34632 0.160916
7171 −4.00000 −0.474713 −0.237356 0.971423i 0.576281π-0.576281\pi
−0.237356 + 0.971423i 0.576281π0.576281\pi
7272 9.04945 1.06649
7373 −0.680346 −0.0796285 −0.0398142 0.999207i 0.512677π-0.512677\pi
−0.0398142 + 0.999207i 0.512677π0.512677\pi
7474 −5.13486 −0.596916
7575 −4.41855 −0.510210
7676 −21.1534 −2.42647
7777 −4.00000 −0.455842
7878 −9.26180 −1.04869
7979 11.1431 1.25370 0.626848 0.779141i 0.284345π-0.284345\pi
0.626848 + 0.779141i 0.284345π0.284345\pi
8080 −10.5512 −1.17966
8181 1.00000 0.111111
8282 −18.0989 −1.99869
8383 12.4975 1.37178 0.685892 0.727703i 0.259412π-0.259412\pi
0.685892 + 0.727703i 0.259412π0.259412\pi
8484 −3.48011 −0.379711
8585 2.73820 0.297000
8686 9.42858 1.01671
8787 0.921622 0.0988083
8888 55.5449 5.92111
8989 −3.36927 −0.357142 −0.178571 0.983927i 0.557147π-0.557147\pi
−0.178571 + 0.983927i 0.557147π0.557147\pi
9090 −2.06590 −0.217765
9191 2.22782 0.233539
9292 0 0
9393 3.07838 0.319213
9494 −0.496928 −0.0512543
9595 3.02052 0.309899
9696 19.3896 1.97894
9797 −5.54601 −0.563112 −0.281556 0.959545i 0.590851π-0.590851\pi
−0.281556 + 0.959545i 0.590851π0.590851\pi
9898 −17.8143 −1.79952
9999 6.13793 0.616885
100100 −23.5958 −2.35958
101101 −9.51745 −0.947021 −0.473511 0.880788i 0.657013π-0.657013\pi
−0.473511 + 0.880788i 0.657013π0.657013\pi
102102 −9.72889 −0.963303
103103 15.4966 1.52692 0.763462 0.645853i 0.223498π-0.223498\pi
0.763462 + 0.645853i 0.223498π0.223498\pi
104104 −30.9360 −3.03352
105105 0.496928 0.0484953
106106 27.6616 2.68673
107107 −12.7569 −1.23326 −0.616630 0.787253i 0.711503π-0.711503\pi
−0.616630 + 0.787253i 0.711503π0.711503\pi
108108 5.34017 0.513858
109109 −16.7402 −1.60342 −0.801710 0.597714i 0.796076π-0.796076\pi
−0.801710 + 0.597714i 0.796076π0.796076\pi
110110 −12.6803 −1.20902
111111 −1.89529 −0.179893
112112 −9.01744 −0.852068
113113 −7.38154 −0.694397 −0.347198 0.937792i 0.612867π-0.612867\pi
−0.347198 + 0.937792i 0.612867π0.612867\pi
114114 −10.7320 −1.00514
115115 0 0
116116 4.92162 0.456961
117117 −3.41855 −0.316045
118118 15.3340 1.41161
119119 2.34017 0.214523
120120 −6.90046 −0.629923
121121 26.6742 2.42493
122122 −7.96329 −0.720963
123123 −6.68035 −0.602347
124124 16.4391 1.47627
125125 7.18191 0.642370
126126 −1.76560 −0.157292
127127 7.44521 0.660656 0.330328 0.943866i 0.392841π-0.392841\pi
0.330328 + 0.943866i 0.392841π0.392841\pi
128128 28.5669 2.52498
129129 3.48011 0.306407
130130 7.06238 0.619412
131131 −18.8371 −1.64581 −0.822903 0.568182i 0.807647π-0.807647\pi
−0.822903 + 0.568182i 0.807647π0.807647\pi
132132 32.7776 2.85293
133133 2.58145 0.223840
134134 −18.9955 −1.64097
135135 −0.762528 −0.0656280
136136 −32.4962 −2.78652
137137 −3.81264 −0.325736 −0.162868 0.986648i 0.552074π-0.552074\pi
−0.162868 + 0.986648i 0.552074π0.552074\pi
138138 0 0
139139 6.15676 0.522209 0.261105 0.965311i 0.415913π-0.415913\pi
0.261105 + 0.965311i 0.415913π0.415913\pi
140140 2.65368 0.224277
141141 −0.183417 −0.0154465
142142 −10.8371 −0.909429
143143 −20.9828 −1.75467
144144 13.8371 1.15309
145145 −0.702763 −0.0583613
146146 −1.84324 −0.152548
147147 −6.57531 −0.542322
148148 −10.1212 −0.831956
149149 −7.94444 −0.650834 −0.325417 0.945571i 0.605505π-0.605505\pi
−0.325417 + 0.945571i 0.605505π0.605505\pi
150150 −11.9711 −0.977434
151151 10.5236 0.856398 0.428199 0.903685i 0.359148π-0.359148\pi
0.428199 + 0.903685i 0.359148π0.359148\pi
152152 −35.8466 −2.90754
153153 −3.59096 −0.290312
154154 −10.8371 −0.873279
155155 −2.34735 −0.188544
156156 −18.2557 −1.46162
157157 −20.0497 −1.60014 −0.800070 0.599907i 0.795204π-0.795204\pi
−0.800070 + 0.599907i 0.795204π0.795204\pi
158158 30.1897 2.40177
159159 10.2100 0.809703
160160 −14.7851 −1.16887
161161 0 0
162162 2.70928 0.212861
163163 −14.5958 −1.14323 −0.571617 0.820521i 0.693684π-0.693684\pi
−0.571617 + 0.820521i 0.693684π0.693684\pi
164164 −35.6742 −2.78569
165165 −4.68035 −0.364364
166166 33.8593 2.62799
167167 14.8371 1.14813 0.574065 0.818810i 0.305366π-0.305366\pi
0.574065 + 0.818810i 0.305366π0.305366\pi
168168 −5.89739 −0.454994
169169 −1.31351 −0.101039
170170 7.41855 0.568977
171171 −3.96119 −0.302920
172172 18.5844 1.41705
173173 −9.23513 −0.702134 −0.351067 0.936350i 0.614181π-0.614181\pi
−0.351067 + 0.936350i 0.614181π0.614181\pi
174174 2.49693 0.189292
175175 2.87950 0.217670
176176 84.9312 6.40193
177177 5.65983 0.425419
178178 −9.12828 −0.684193
179179 2.02666 0.151480 0.0757399 0.997128i 0.475868π-0.475868\pi
0.0757399 + 0.997128i 0.475868π0.475868\pi
180180 −4.07203 −0.303511
181181 −22.9977 −1.70940 −0.854701 0.519121i 0.826260π-0.826260\pi
−0.854701 + 0.519121i 0.826260π0.826260\pi
182182 6.03578 0.447402
183183 −2.93927 −0.217277
184184 0 0
185185 1.44521 0.106254
186186 8.34017 0.611531
187187 −22.0410 −1.61180
188188 −0.979481 −0.0714360
189189 −0.651685 −0.0474031
190190 8.18342 0.593688
191191 −11.2319 −0.812711 −0.406355 0.913715i 0.633200π-0.633200\pi
−0.406355 + 0.913715i 0.633200π0.633200\pi
192192 24.8576 1.79394
193193 14.0989 1.01486 0.507430 0.861693i 0.330595π-0.330595\pi
0.507430 + 0.861693i 0.330595π0.330595\pi
194194 −15.0257 −1.07878
195195 2.60674 0.186673
196196 −35.1133 −2.50809
197197 2.39803 0.170853 0.0854263 0.996344i 0.472775π-0.472775\pi
0.0854263 + 0.996344i 0.472775π0.472775\pi
198198 16.6293 1.18180
199199 17.2810 1.22502 0.612510 0.790463i 0.290160π-0.290160\pi
0.612510 + 0.790463i 0.290160π0.290160\pi
200200 −39.9854 −2.82740
201201 −7.01130 −0.494539
202202 −25.7854 −1.81425
203203 −0.600608 −0.0421544
204204 −19.1763 −1.34261
205205 5.09395 0.355777
206206 41.9845 2.92520
207207 0 0
208208 −47.3028 −3.27986
209209 −24.3135 −1.68180
210210 1.34632 0.0929046
211211 13.6020 0.936398 0.468199 0.883623i 0.344903π-0.344903\pi
0.468199 + 0.883623i 0.344903π0.344903\pi
212212 54.5230 3.74465
213213 −4.00000 −0.274075
214214 −34.5621 −2.36261
215215 −2.65368 −0.180980
216216 9.04945 0.615737
217217 −2.00613 −0.136185
218218 −45.3538 −3.07175
219219 −0.680346 −0.0459735
220220 −24.9939 −1.68509
221221 12.2759 0.825764
222222 −5.13486 −0.344630
223223 15.2039 1.01813 0.509065 0.860728i 0.329991π-0.329991\pi
0.509065 + 0.860728i 0.329991π0.329991\pi
224224 −12.6359 −0.844274
225225 −4.41855 −0.294570
226226 −19.9986 −1.33029
227227 7.44130 0.493897 0.246948 0.969029i 0.420572π-0.420572\pi
0.246948 + 0.969029i 0.420572π0.420572\pi
228228 −21.1534 −1.40092
229229 22.3970 1.48004 0.740019 0.672586i 0.234816π-0.234816\pi
0.740019 + 0.672586i 0.234816π0.234816\pi
230230 0 0
231231 −4.00000 −0.263181
232232 8.34017 0.547559
233233 16.8371 1.10304 0.551518 0.834163i 0.314049π-0.314049\pi
0.551518 + 0.834163i 0.314049π0.314049\pi
234234 −9.26180 −0.605462
235235 0.139861 0.00912353
236236 30.2245 1.96744
237237 11.1431 0.723822
238238 6.34017 0.410972
239239 −9.84324 −0.636707 −0.318353 0.947972i 0.603130π-0.603130\pi
−0.318353 + 0.947972i 0.603130π0.603130\pi
240240 −10.5512 −0.681076
241241 13.4307 0.865146 0.432573 0.901599i 0.357606π-0.357606\pi
0.432573 + 0.901599i 0.357606π0.357606\pi
242242 72.2678 4.64555
243243 1.00000 0.0641500
244244 −15.6962 −1.00485
245245 5.01386 0.320324
246246 −18.0989 −1.15394
247247 13.5415 0.861627
248248 27.8576 1.76896
249249 12.4975 0.792000
250250 19.4578 1.23062
251251 −13.3575 −0.843121 −0.421560 0.906800i 0.638517π-0.638517\pi
−0.421560 + 0.906800i 0.638517π0.638517\pi
252252 −3.48011 −0.219226
253253 0 0
254254 20.1711 1.26565
255255 2.73820 0.171473
256256 27.6803 1.73002
257257 4.52359 0.282174 0.141087 0.989997i 0.454940π-0.454940\pi
0.141087 + 0.989997i 0.454940π0.454940\pi
258258 9.42858 0.586998
259259 1.23513 0.0767474
260260 13.9204 0.863310
261261 0.921622 0.0570470
262262 −51.0349 −3.15295
263263 25.5957 1.57830 0.789149 0.614201i 0.210522π-0.210522\pi
0.789149 + 0.614201i 0.210522π0.210522\pi
264264 55.5449 3.41855
265265 −7.78539 −0.478252
266266 6.99386 0.428821
267267 −3.36927 −0.206196
268268 −37.4416 −2.28711
269269 25.4329 1.55067 0.775336 0.631548i 0.217580π-0.217580\pi
0.775336 + 0.631548i 0.217580π0.217580\pi
270270 −2.06590 −0.125727
271271 −31.6430 −1.92218 −0.961088 0.276243i 0.910911π-0.910911\pi
−0.961088 + 0.276243i 0.910911π0.910911\pi
272272 −49.6884 −3.01280
273273 2.22782 0.134834
274274 −10.3295 −0.624028
275275 −27.1208 −1.63544
276276 0 0
277277 13.0472 0.783929 0.391965 0.919980i 0.371796π-0.371796\pi
0.391965 + 0.919980i 0.371796π0.371796\pi
278278 16.6803 1.00042
279279 3.07838 0.184298
280280 4.49693 0.268743
281281 3.93217 0.234574 0.117287 0.993098i 0.462580π-0.462580\pi
0.117287 + 0.993098i 0.462580π0.462580\pi
282282 −0.496928 −0.0295917
283283 20.9318 1.24426 0.622132 0.782913i 0.286267π-0.286267\pi
0.622132 + 0.782913i 0.286267π0.286267\pi
284284 −21.3607 −1.26752
285285 3.02052 0.178920
286286 −56.8483 −3.36151
287287 4.35348 0.256978
288288 19.3896 1.14254
289289 −4.10504 −0.241473
290290 −1.90398 −0.111805
291291 −5.54601 −0.325113
292292 −3.63317 −0.212615
293293 15.8668 0.926949 0.463475 0.886110i 0.346602π-0.346602\pi
0.463475 + 0.886110i 0.346602π0.346602\pi
294294 −17.8143 −1.03895
295295 −4.31578 −0.251274
296296 −17.1513 −0.996901
297297 6.13793 0.356159
298298 −21.5237 −1.24683
299299 0 0
300300 −23.5958 −1.36231
301301 −2.26794 −0.130722
302302 28.5113 1.64064
303303 −9.51745 −0.546763
304304 −54.8114 −3.14365
305305 2.24128 0.128335
306306 −9.72889 −0.556163
307307 32.7526 1.86929 0.934644 0.355584i 0.115718π-0.115718\pi
0.934644 + 0.355584i 0.115718π0.115718\pi
308308 −21.3607 −1.21714
309309 15.4966 0.881570
310310 −6.35962 −0.361202
311311 −14.0267 −0.795379 −0.397690 0.917520i 0.630188π-0.630188\pi
−0.397690 + 0.917520i 0.630188π0.630188\pi
312312 −30.9360 −1.75141
313313 15.4745 0.874672 0.437336 0.899298i 0.355922π-0.355922\pi
0.437336 + 0.899298i 0.355922π0.355922\pi
314314 −54.3201 −3.06546
315315 0.496928 0.0279987
316316 59.5061 3.34748
317317 19.4452 1.09215 0.546076 0.837736i 0.316121π-0.316121\pi
0.546076 + 0.837736i 0.316121π0.316121\pi
318318 27.6616 1.55119
319319 5.65685 0.316723
320320 −18.9546 −1.05960
321321 −12.7569 −0.712023
322322 0 0
323323 14.2245 0.791470
324324 5.34017 0.296676
325325 15.1050 0.837877
326326 −39.5441 −2.19015
327327 −16.7402 −0.925735
328328 −60.4534 −3.33798
329329 0.119530 0.00658993
330330 −12.6803 −0.698030
331331 17.1194 0.940968 0.470484 0.882408i 0.344079π-0.344079\pi
0.470484 + 0.882408i 0.344079π0.344079\pi
332332 66.7391 3.66278
333333 −1.89529 −0.103861
334334 40.1978 2.19953
335335 5.34632 0.292100
336336 −9.01744 −0.491941
337337 −11.2029 −0.610259 −0.305129 0.952311i 0.598700π-0.598700\pi
−0.305129 + 0.952311i 0.598700π0.598700\pi
338338 −3.55866 −0.193566
339339 −7.38154 −0.400910
340340 14.6225 0.793016
341341 18.8949 1.02321
342342 −10.7320 −0.580318
343343 8.84683 0.477684
344344 31.4931 1.69799
345345 0 0
346346 −25.0205 −1.34511
347347 9.17727 0.492662 0.246331 0.969186i 0.420775π-0.420775\pi
0.246331 + 0.969186i 0.420775π0.420775\pi
348348 4.92162 0.263827
349349 29.2495 1.56569 0.782845 0.622217i 0.213768π-0.213768\pi
0.782845 + 0.622217i 0.213768π0.213768\pi
350350 7.80137 0.417001
351351 −3.41855 −0.182469
352352 119.012 6.34337
353353 −30.2823 −1.61176 −0.805882 0.592076i 0.798309π-0.798309\pi
−0.805882 + 0.592076i 0.798309π0.798309\pi
354354 15.3340 0.814994
355355 3.05011 0.161883
356356 −17.9925 −0.953600
357357 2.34017 0.123855
358358 5.49079 0.290197
359359 −7.66299 −0.404437 −0.202219 0.979340i 0.564815π-0.564815\pi
−0.202219 + 0.979340i 0.564815π0.564815\pi
360360 −6.90046 −0.363686
361361 −3.30898 −0.174157
362362 −62.3070 −3.27478
363363 26.6742 1.40003
364364 11.8969 0.623569
365365 0.518783 0.0271543
366366 −7.96329 −0.416248
367367 25.1657 1.31364 0.656820 0.754048i 0.271901π-0.271901\pi
0.656820 + 0.754048i 0.271901π0.271901\pi
368368 0 0
369369 −6.68035 −0.347765
370370 3.91548 0.203556
371371 −6.65368 −0.345442
372372 16.4391 0.852326
373373 −3.07913 −0.159431 −0.0797157 0.996818i 0.525401π-0.525401\pi
−0.0797157 + 0.996818i 0.525401π0.525401\pi
374374 −59.7152 −3.08780
375375 7.18191 0.370872
376376 −1.65983 −0.0855990
377377 −3.15061 −0.162265
378378 −1.76560 −0.0908124
379379 −11.0613 −0.568180 −0.284090 0.958798i 0.591691π-0.591691\pi
−0.284090 + 0.958798i 0.591691π0.591691\pi
380380 16.1301 0.827456
381381 7.44521 0.381430
382382 −30.4303 −1.55695
383383 24.3742 1.24546 0.622731 0.782436i 0.286023π-0.286023\pi
0.622731 + 0.782436i 0.286023π0.286023\pi
384384 28.5669 1.45780
385385 3.05011 0.155448
386386 38.1978 1.94422
387387 3.48011 0.176904
388388 −29.6167 −1.50356
389389 −1.10374 −0.0559621 −0.0279810 0.999608i 0.508908π-0.508908\pi
−0.0279810 + 0.999608i 0.508908π0.508908\pi
390390 7.06238 0.357618
391391 0 0
392392 −59.5029 −3.00535
393393 −18.8371 −0.950206
394394 6.49693 0.327311
395395 −8.49693 −0.427527
396396 32.7776 1.64714
397397 3.47641 0.174476 0.0872380 0.996187i 0.472196π-0.472196\pi
0.0872380 + 0.996187i 0.472196π0.472196\pi
398398 46.8191 2.34683
399399 2.58145 0.129234
400400 −61.1399 −3.05700
401401 −21.5237 −1.07484 −0.537420 0.843314i 0.680601π-0.680601\pi
−0.537420 + 0.843314i 0.680601π0.680601\pi
402402 −18.9955 −0.947412
403403 −10.5236 −0.524217
404404 −50.8248 −2.52863
405405 −0.762528 −0.0378903
406406 −1.62721 −0.0807572
407407 −11.6332 −0.576635
408408 −32.4962 −1.60880
409409 25.3028 1.25114 0.625572 0.780166i 0.284866π-0.284866\pi
0.625572 + 0.780166i 0.284866π0.284866\pi
410410 13.8009 0.681579
411411 −3.81264 −0.188064
412412 82.7544 4.07702
413413 −3.68843 −0.181496
414414 0 0
415415 −9.52973 −0.467796
416416 −66.2844 −3.24986
417417 6.15676 0.301498
418418 −65.8720 −3.22190
419419 −25.4558 −1.24360 −0.621800 0.783176i 0.713598π-0.713598\pi
−0.621800 + 0.783176i 0.713598π0.713598\pi
420420 2.65368 0.129487
421421 −27.5287 −1.34167 −0.670833 0.741608i 0.734063π-0.734063\pi
−0.670833 + 0.741608i 0.734063π0.734063\pi
422422 36.8515 1.79390
423423 −0.183417 −0.00891806
424424 92.3945 4.48708
425425 15.8668 0.769654
426426 −10.8371 −0.525059
427427 1.91548 0.0926965
428428 −68.1243 −3.29291
429429 −20.9828 −1.01306
430430 −7.18956 −0.346711
431431 −28.3046 −1.36338 −0.681692 0.731639i 0.738756π-0.738756\pi
−0.681692 + 0.731639i 0.738756π0.738756\pi
432432 13.8371 0.665738
433433 −29.0161 −1.39442 −0.697211 0.716866i 0.745576π-0.745576\pi
−0.697211 + 0.716866i 0.745576π0.745576\pi
434434 −5.43517 −0.260896
435435 −0.702763 −0.0336949
436436 −89.3955 −4.28127
437437 0 0
438438 −1.84324 −0.0880736
439439 34.3545 1.63965 0.819827 0.572612i 0.194070π-0.194070\pi
0.819827 + 0.572612i 0.194070π0.194070\pi
440440 −42.3545 −2.01917
441441 −6.57531 −0.313110
442442 33.2587 1.58195
443443 −22.8371 −1.08502 −0.542512 0.840048i 0.682527π-0.682527\pi
−0.542512 + 0.840048i 0.682527π0.682527\pi
444444 −10.1212 −0.480330
445445 2.56916 0.121790
446446 41.1917 1.95048
447447 −7.94444 −0.375759
448448 −16.1993 −0.765347
449449 −16.4703 −0.777280 −0.388640 0.921390i 0.627055π-0.627055\pi
−0.388640 + 0.921390i 0.627055π0.627055\pi
450450 −11.9711 −0.564322
451451 −41.0035 −1.93078
452452 −39.4187 −1.85410
453453 10.5236 0.494441
454454 20.1605 0.946181
455455 −1.69878 −0.0796398
456456 −35.8466 −1.67867
457457 −15.0753 −0.705191 −0.352596 0.935776i 0.614701π-0.614701\pi
−0.352596 + 0.935776i 0.614701π0.614701\pi
458458 60.6798 2.83538
459459 −3.59096 −0.167611
460460 0 0
461461 −15.8120 −0.736440 −0.368220 0.929739i 0.620033π-0.620033\pi
−0.368220 + 0.929739i 0.620033π0.620033\pi
462462 −10.8371 −0.504188
463463 −8.00000 −0.371792 −0.185896 0.982569i 0.559519π-0.559519\pi
−0.185896 + 0.982569i 0.559519π0.559519\pi
464464 12.7526 0.592024
465465 −2.34735 −0.108856
466466 45.6163 2.11314
467467 29.1269 1.34783 0.673916 0.738808i 0.264611π-0.264611\pi
0.673916 + 0.738808i 0.264611π0.264611\pi
468468 −18.2557 −0.843868
469469 4.56916 0.210984
470470 0.378922 0.0174784
471471 −20.0497 −0.923841
472472 51.2183 2.35751
473473 21.3607 0.982166
474474 30.1897 1.38666
475475 17.5027 0.803080
476476 12.4969 0.572796
477477 10.2100 0.467482
478478 −26.6681 −1.21977
479479 10.3719 0.473904 0.236952 0.971521i 0.423852π-0.423852\pi
0.236952 + 0.971521i 0.423852π0.423852\pi
480480 −14.7851 −0.674846
481481 6.47915 0.295424
482482 36.3874 1.65740
483483 0 0
484484 142.445 6.47477
485485 4.22899 0.192029
486486 2.70928 0.122895
487487 17.1629 0.777725 0.388863 0.921296i 0.372868π-0.372868\pi
0.388863 + 0.921296i 0.372868π0.372868\pi
488488 −26.5988 −1.20407
489489 −14.5958 −0.660046
490490 13.5839 0.613659
491491 −3.50307 −0.158091 −0.0790457 0.996871i 0.525187π-0.525187\pi
−0.0790457 + 0.996871i 0.525187π0.525187\pi
492492 −35.6742 −1.60832
493493 −3.30950 −0.149053
494494 36.6877 1.65066
495495 −4.68035 −0.210366
496496 42.5958 1.91261
497497 2.60674 0.116928
498498 33.8593 1.51727
499499 −8.92162 −0.399387 −0.199693 0.979858i 0.563995π-0.563995\pi
−0.199693 + 0.979858i 0.563995π0.563995\pi
500500 38.3526 1.71518
501501 14.8371 0.662873
502502 −36.1893 −1.61521
503503 11.0543 0.492888 0.246444 0.969157i 0.420738π-0.420738\pi
0.246444 + 0.969157i 0.420738π0.420738\pi
504504 −5.89739 −0.262691
505505 7.25732 0.322947
506506 0 0
507507 −1.31351 −0.0583351
508508 39.7587 1.76401
509509 6.71154 0.297484 0.148742 0.988876i 0.452478π-0.452478\pi
0.148742 + 0.988876i 0.452478π0.452478\pi
510510 7.41855 0.328499
511511 0.443371 0.0196136
512512 17.8599 0.789303
513513 −3.96119 −0.174891
514514 12.2557 0.540574
515515 −11.8166 −0.520701
516516 18.5844 0.818133
517517 −1.12580 −0.0495128
518518 3.34632 0.147029
519519 −9.23513 −0.405377
520520 23.5896 1.03447
521521 26.9588 1.18109 0.590544 0.807005i 0.298913π-0.298913\pi
0.590544 + 0.807005i 0.298913π0.298913\pi
522522 2.49693 0.109288
523523 −15.2749 −0.667925 −0.333962 0.942586i 0.608386π-0.608386\pi
−0.333962 + 0.942586i 0.608386π0.608386\pi
524524 −100.593 −4.39444
525525 2.87950 0.125672
526526 69.3458 3.02362
527527 −11.0543 −0.481534
528528 84.9312 3.69616
529529 0 0
530530 −21.0928 −0.916211
531531 5.65983 0.245616
532532 13.7854 0.597672
533533 22.8371 0.989185
534534 −9.12828 −0.395019
535535 9.72753 0.420558
536536 −63.4484 −2.74055
537537 2.02666 0.0874569
538538 68.9048 2.97070
539539 −40.3588 −1.73838
540540 −4.07203 −0.175232
541541 33.9299 1.45876 0.729379 0.684110i 0.239809π-0.239809\pi
0.729379 + 0.684110i 0.239809π0.239809\pi
542542 −85.7296 −3.68240
543543 −22.9977 −0.986924
544544 −69.6273 −2.98524
545545 12.7649 0.546787
546546 6.03578 0.258307
547547 2.45136 0.104812 0.0524062 0.998626i 0.483311π-0.483311\pi
0.0524062 + 0.998626i 0.483311π0.483311\pi
548548 −20.3602 −0.869743
549549 −2.93927 −0.125445
550550 −73.4776 −3.13310
551551 −3.65072 −0.155526
552552 0 0
553553 −7.26180 −0.308803
554554 35.3484 1.50181
555555 1.44521 0.0613459
556556 32.8781 1.39434
557557 27.6239 1.17046 0.585231 0.810867i 0.301004π-0.301004\pi
0.585231 + 0.810867i 0.301004π0.301004\pi
558558 8.34017 0.353068
559559 −11.8969 −0.503187
560560 6.87605 0.290566
561561 −22.0410 −0.930573
562562 10.6533 0.449384
563563 −2.22782 −0.0938914 −0.0469457 0.998897i 0.514949π-0.514949\pi
−0.0469457 + 0.998897i 0.514949π0.514949\pi
564564 −0.979481 −0.0412436
565565 5.62863 0.236798
566566 56.7099 2.38369
567567 −0.651685 −0.0273682
568568 −36.1978 −1.51883
569569 40.9814 1.71803 0.859016 0.511949i 0.171076π-0.171076\pi
0.859016 + 0.511949i 0.171076π0.171076\pi
570570 8.18342 0.342766
571571 19.5907 0.819844 0.409922 0.912121i 0.365556π-0.365556\pi
0.409922 + 0.912121i 0.365556π0.365556\pi
572572 −112.052 −4.68513
573573 −11.2319 −0.469219
574574 11.7948 0.492305
575575 0 0
576576 24.8576 1.03573
577577 7.45959 0.310547 0.155273 0.987872i 0.450374π-0.450374\pi
0.155273 + 0.987872i 0.450374π0.450374\pi
578578 −11.1217 −0.462601
579579 14.0989 0.585930
580580 −3.75288 −0.155830
581581 −8.14447 −0.337890
582582 −15.0257 −0.622834
583583 62.6681 2.59545
584584 −6.15676 −0.254768
585585 2.60674 0.107775
586586 42.9876 1.77580
587587 −17.8432 −0.736470 −0.368235 0.929733i 0.620038π-0.620038\pi
−0.368235 + 0.929733i 0.620038π0.620038\pi
588588 −35.1133 −1.44805
589589 −12.1940 −0.502447
590590 −11.6926 −0.481378
591591 2.39803 0.0986418
592592 −26.2253 −1.07785
593593 −6.73367 −0.276519 −0.138259 0.990396i 0.544151π-0.544151\pi
−0.138259 + 0.990396i 0.544151π0.544151\pi
594594 16.6293 0.682310
595595 −1.78445 −0.0731552
596596 −42.4247 −1.73778
597597 17.2810 0.707266
598598 0 0
599599 −33.8720 −1.38397 −0.691986 0.721911i 0.743264π-0.743264\pi
−0.691986 + 0.721911i 0.743264π0.743264\pi
600600 −39.9854 −1.63240
601601 −19.2618 −0.785705 −0.392853 0.919601i 0.628512π-0.628512\pi
−0.392853 + 0.919601i 0.628512π0.628512\pi
602602 −6.14447 −0.250430
603603 −7.01130 −0.285522
604604 56.1978 2.28666
605605 −20.3398 −0.826932
606606 −25.7854 −1.04746
607607 11.6865 0.474340 0.237170 0.971468i 0.423780π-0.423780\pi
0.237170 + 0.971468i 0.423780π0.423780\pi
608608 −76.8060 −3.11489
609609 −0.600608 −0.0243379
610610 6.07223 0.245858
611611 0.627022 0.0253666
612612 −19.1763 −0.775157
613613 34.6352 1.39890 0.699451 0.714680i 0.253428π-0.253428\pi
0.699451 + 0.714680i 0.253428π0.253428\pi
614614 88.7358 3.58108
615615 5.09395 0.205408
616616 −36.1978 −1.45845
617617 23.2704 0.936832 0.468416 0.883508i 0.344825π-0.344825\pi
0.468416 + 0.883508i 0.344825π0.344825\pi
618618 41.9845 1.68886
619619 −16.7181 −0.671958 −0.335979 0.941869i 0.609067π-0.609067\pi
−0.335979 + 0.941869i 0.609067π0.609067\pi
620620 −12.5353 −0.503428
621621 0 0
622622 −38.0021 −1.52374
623623 2.19570 0.0879690
624624 −47.3028 −1.89363
625625 16.6163 0.664654
626626 41.9247 1.67565
627627 −24.3135 −0.970988
628628 −107.069 −4.27251
629629 6.80590 0.271369
630630 1.34632 0.0536385
631631 −5.10732 −0.203319 −0.101660 0.994819i 0.532415π-0.532415\pi
−0.101660 + 0.994819i 0.532415π0.532415\pi
632632 100.839 4.01116
633633 13.6020 0.540630
634634 52.6824 2.09229
635635 −5.67718 −0.225292
636636 54.5230 2.16198
637637 22.4780 0.890611
638638 15.3260 0.606761
639639 −4.00000 −0.158238
640640 −21.7831 −0.861051
641641 −28.2622 −1.11629 −0.558145 0.829743i 0.688487π-0.688487\pi
−0.558145 + 0.829743i 0.688487π0.688487\pi
642642 −34.5621 −1.36406
643643 −4.88564 −0.192671 −0.0963354 0.995349i 0.530712π-0.530712\pi
−0.0963354 + 0.995349i 0.530712π0.530712\pi
644644 0 0
645645 −2.65368 −0.104489
646646 38.5380 1.51626
647647 1.49079 0.0586088 0.0293044 0.999571i 0.490671π-0.490671\pi
0.0293044 + 0.999571i 0.490671π0.490671\pi
648648 9.04945 0.355496
649649 34.7396 1.36365
650650 40.9237 1.60516
651651 −2.00613 −0.0786266
652652 −77.9442 −3.05253
653653 40.6681 1.59146 0.795732 0.605649i 0.207086π-0.207086\pi
0.795732 + 0.605649i 0.207086π0.207086\pi
654654 −45.3538 −1.77347
655655 14.3638 0.561241
656656 −92.4366 −3.60904
657657 −0.680346 −0.0265428
658658 0.323841 0.0126246
659659 −3.61301 −0.140743 −0.0703715 0.997521i 0.522418π-0.522418\pi
−0.0703715 + 0.997521i 0.522418π0.522418\pi
660660 −24.9939 −0.972885
661661 13.2090 0.513771 0.256885 0.966442i 0.417304π-0.417304\pi
0.256885 + 0.966442i 0.417304π0.417304\pi
662662 46.3812 1.80266
663663 12.2759 0.476755
664664 113.096 4.38897
665665 −1.96843 −0.0763324
666666 −5.13486 −0.198972
667667 0 0
668668 79.2327 3.06560
669669 15.2039 0.587818
670670 14.4846 0.559591
671671 −18.0410 −0.696467
672672 −12.6359 −0.487442
673673 14.9360 0.575740 0.287870 0.957669i 0.407053π-0.407053\pi
0.287870 + 0.957669i 0.407053π0.407053\pi
674674 −30.3516 −1.16910
675675 −4.41855 −0.170070
676676 −7.01438 −0.269784
677677 −7.10181 −0.272945 −0.136472 0.990644i 0.543577π-0.543577\pi
−0.136472 + 0.990644i 0.543577π0.543577\pi
678678 −19.9986 −0.768042
679679 3.61425 0.138702
680680 24.7792 0.950241
681681 7.44130 0.285151
682682 51.1914 1.96022
683683 −41.7275 −1.59666 −0.798330 0.602221i 0.794283π-0.794283\pi
−0.798330 + 0.602221i 0.794283π0.794283\pi
684684 −21.1534 −0.808822
685685 2.90725 0.111080
686686 23.9685 0.915121
687687 22.3970 0.854501
688688 48.1547 1.83588
689689 −34.9033 −1.32971
690690 0 0
691691 11.7587 0.447323 0.223661 0.974667i 0.428199π-0.428199\pi
0.223661 + 0.974667i 0.428199π0.428199\pi
692692 −49.3172 −1.87476
693693 −4.00000 −0.151947
694694 24.8638 0.943816
695695 −4.69470 −0.178080
696696 8.34017 0.316133
697697 23.9888 0.908642
698698 79.2450 2.99947
699699 16.8371 0.636838
700700 15.3771 0.581198
701701 −52.0735 −1.96679 −0.983394 0.181484i 0.941910π-0.941910\pi
−0.983394 + 0.181484i 0.941910π0.941910\pi
702702 −9.26180 −0.349564
703703 7.50761 0.283155
704704 152.574 5.75036
705705 0.139861 0.00526747
706706 −82.0431 −3.08773
707707 6.20238 0.233265
708708 30.2245 1.13590
709709 −6.10891 −0.229425 −0.114713 0.993399i 0.536595π-0.536595\pi
−0.114713 + 0.993399i 0.536595π0.536595\pi
710710 8.26360 0.310127
711711 11.1431 0.417899
712712 −30.4900 −1.14266
713713 0 0
714714 6.34017 0.237275
715715 16.0000 0.598366
716716 10.8227 0.404464
717717 −9.84324 −0.367603
718718 −20.7611 −0.774799
719719 3.81658 0.142335 0.0711673 0.997464i 0.477328π-0.477328\pi
0.0711673 + 0.997464i 0.477328π0.477328\pi
720720 −10.5512 −0.393219
721721 −10.0989 −0.376103
722722 −8.96493 −0.333640
723723 13.4307 0.499493
724724 −122.811 −4.56425
725725 −4.07223 −0.151239
726726 72.2678 2.68211
727727 −44.8452 −1.66322 −0.831608 0.555364i 0.812579π-0.812579\pi
−0.831608 + 0.555364i 0.812579π0.812579\pi
728728 20.1605 0.747199
729729 1.00000 0.0370370
730730 1.40553 0.0520208
731731 −12.4969 −0.462216
732732 −15.6962 −0.580149
733733 −28.4154 −1.04955 −0.524774 0.851241i 0.675850π-0.675850\pi
−0.524774 + 0.851241i 0.675850π0.675850\pi
734734 68.1808 2.51660
735735 5.01386 0.184939
736736 0 0
737737 −43.0349 −1.58521
738738 −18.0989 −0.666230
739739 6.52359 0.239974 0.119987 0.992775i 0.461715π-0.461715\pi
0.119987 + 0.992775i 0.461715π0.461715\pi
740740 7.71769 0.283708
741741 13.5415 0.497460
742742 −18.0267 −0.661780
743743 3.22768 0.118412 0.0592060 0.998246i 0.481143π-0.481143\pi
0.0592060 + 0.998246i 0.481143π0.481143\pi
744744 27.8576 1.02131
745745 6.05786 0.221943
746746 −8.34221 −0.305430
747747 12.4975 0.457261
748748 −117.703 −4.30365
749749 8.31351 0.303769
750750 19.4578 0.710497
751751 9.87744 0.360433 0.180216 0.983627i 0.442320π-0.442320\pi
0.180216 + 0.983627i 0.442320π0.442320\pi
752752 −2.53797 −0.0925501
753753 −13.3575 −0.486776
754754 −8.53588 −0.310858
755755 −8.02453 −0.292043
756756 −3.48011 −0.126570
757757 11.1652 0.405805 0.202902 0.979199i 0.434963π-0.434963\pi
0.202902 + 0.979199i 0.434963π0.434963\pi
758758 −29.9680 −1.08849
759759 0 0
760760 27.3340 0.991509
761761 −4.12556 −0.149551 −0.0747757 0.997200i 0.523824π-0.523824\pi
−0.0747757 + 0.997200i 0.523824π0.523824\pi
762762 20.1711 0.730723
763763 10.9093 0.394944
764764 −59.9802 −2.17001
765765 2.73820 0.0990000
766766 66.0363 2.38599
767767 −19.3484 −0.698630
768768 27.6803 0.998828
769769 −23.8844 −0.861293 −0.430647 0.902521i 0.641714π-0.641714\pi
−0.430647 + 0.902521i 0.641714π0.641714\pi
770770 8.26360 0.297799
771771 4.52359 0.162913
772772 75.2905 2.70977
773773 8.38781 0.301689 0.150844 0.988558i 0.451801π-0.451801\pi
0.150844 + 0.988558i 0.451801π0.451801\pi
774774 9.42858 0.338903
775775 −13.6020 −0.488597
776776 −50.1883 −1.80166
777777 1.23513 0.0443102
778778 −2.99035 −0.107209
779779 26.4621 0.948104
780780 13.9204 0.498432
781781 −24.5517 −0.878530
782782 0 0
783783 0.921622 0.0329361
784784 −90.9832 −3.24940
785785 15.2885 0.545668
786786 −51.0349 −1.82035
787787 5.67023 0.202122 0.101061 0.994880i 0.467776π-0.467776\pi
0.101061 + 0.994880i 0.467776π0.467776\pi
788788 12.8059 0.456191
789789 25.5957 0.911231
790790 −23.0205 −0.819033
791791 4.81044 0.171040
792792 55.5449 1.97370
793793 10.0480 0.356816
794794 9.41855 0.334252
795795 −7.78539 −0.276119
796796 92.2837 3.27091
797797 14.2664 0.505340 0.252670 0.967553i 0.418691π-0.418691\pi
0.252670 + 0.967553i 0.418691π0.418691\pi
798798 6.99386 0.247580
799799 0.658644 0.0233011
800800 −85.6740 −3.02903
801801 −3.36927 −0.119047
802802 −58.3136 −2.05912
803803 −4.17592 −0.147365
804804 −37.4416 −1.32046
805805 0 0
806806 −28.5113 −1.00427
807807 25.4329 0.895281
808808 −86.1276 −3.02996
809809 −48.6369 −1.70998 −0.854991 0.518644i 0.826437π-0.826437\pi
−0.854991 + 0.518644i 0.826437π0.826437\pi
810810 −2.06590 −0.0725883
811811 −40.1256 −1.40900 −0.704499 0.709705i 0.748828π-0.748828\pi
−0.704499 + 0.709705i 0.748828π0.748828\pi
812812 −3.20735 −0.112556
813813 −31.6430 −1.10977
814814 −31.5174 −1.10469
815815 11.1297 0.389857
816816 −49.6884 −1.73944
817817 −13.7854 −0.482290
818818 68.5523 2.39688
819819 2.22782 0.0778463
820820 27.2026 0.949956
821821 −46.7091 −1.63016 −0.815079 0.579349i 0.803307π-0.803307\pi
−0.815079 + 0.579349i 0.803307π0.803307\pi
822822 −10.3295 −0.360282
823823 23.2762 0.811356 0.405678 0.914016i 0.367035π-0.367035\pi
0.405678 + 0.914016i 0.367035π0.367035\pi
824824 140.236 4.88534
825825 −27.1208 −0.944224
826826 −9.99296 −0.347700
827827 −8.58744 −0.298614 −0.149307 0.988791i 0.547704π-0.547704\pi
−0.149307 + 0.988791i 0.547704π0.547704\pi
828828 0 0
829829 21.2208 0.737027 0.368514 0.929622i 0.379867π-0.379867\pi
0.368514 + 0.929622i 0.379867π0.379867\pi
830830 −25.8187 −0.896179
831831 13.0472 0.452602
832832 −84.9770 −2.94605
833833 23.6116 0.818095
834834 16.6803 0.577593
835835 −11.3137 −0.391527
836836 −129.838 −4.49055
837837 3.07838 0.106404
838838 −68.9669 −2.38242
839839 18.9767 0.655148 0.327574 0.944825i 0.393769π-0.393769\pi
0.327574 + 0.944825i 0.393769π0.393769\pi
840840 4.49693 0.155159
841841 −28.1506 −0.970711
842842 −74.5828 −2.57029
843843 3.93217 0.135431
844844 72.6369 2.50026
845845 1.00159 0.0344557
846846 −0.496928 −0.0170848
847847 −17.3832 −0.597293
848848 141.276 4.85145
849849 20.9318 0.718376
850850 42.9876 1.47446
851851 0 0
852852 −21.3607 −0.731805
853853 −17.8843 −0.612346 −0.306173 0.951976i 0.599049π-0.599049\pi
−0.306173 + 0.951976i 0.599049π0.599049\pi
854854 5.18956 0.177583
855855 3.02052 0.103300
856856 −115.443 −3.94577
857857 −3.72753 −0.127330 −0.0636649 0.997971i 0.520279π-0.520279\pi
−0.0636649 + 0.997971i 0.520279π0.520279\pi
858858 −56.8483 −1.94077
859859 −20.9939 −0.716301 −0.358151 0.933664i 0.616593π-0.616593\pi
−0.358151 + 0.933664i 0.616593π0.616593\pi
860860 −14.1711 −0.483232
861861 4.35348 0.148366
862862 −76.6850 −2.61190
863863 −21.1773 −0.720883 −0.360441 0.932782i 0.617374π-0.617374\pi
−0.360441 + 0.932782i 0.617374π0.617374\pi
864864 19.3896 0.659648
865865 7.04205 0.239437
866866 −78.6125 −2.67136
867867 −4.10504 −0.139414
868868 −10.7131 −0.363626
869869 68.3956 2.32016
870870 −1.90398 −0.0645509
871871 23.9685 0.812141
872872 −151.489 −5.13008
873873 −5.54601 −0.187704
874874 0 0
875875 −4.68035 −0.158225
876876 −3.63317 −0.122753
877877 38.3545 1.29514 0.647571 0.762006i 0.275785π-0.275785\pi
0.647571 + 0.762006i 0.275785π0.275785\pi
878878 93.0759 3.14116
879879 15.8668 0.535174
880880 −64.7624 −2.18314
881881 −29.0468 −0.978612 −0.489306 0.872112i 0.662750π-0.662750\pi
−0.489306 + 0.872112i 0.662750π0.662750\pi
882882 −17.8143 −0.599839
883883 −19.6430 −0.661040 −0.330520 0.943799i 0.607224π-0.607224\pi
−0.330520 + 0.943799i 0.607224π0.607224\pi
884884 65.5552 2.20486
885885 −4.31578 −0.145073
886886 −61.8720 −2.07863
887887 −22.9672 −0.771163 −0.385581 0.922674i 0.625999π-0.625999\pi
−0.385581 + 0.922674i 0.625999π0.625999\pi
888888 −17.1513 −0.575561
889889 −4.85194 −0.162729
890890 6.96057 0.233319
891891 6.13793 0.205628
892892 81.1917 2.71850
893893 0.726551 0.0243131
894894 −21.5237 −0.719859
895895 −1.54539 −0.0516566
896896 −18.6166 −0.621938
897897 0 0
898898 −44.6225 −1.48907
899899 2.83710 0.0946226
900900 −23.5958 −0.786528
901901 −36.6635 −1.22144
902902 −111.090 −3.69889
903903 −2.26794 −0.0754723
904904 −66.7988 −2.22170
905905 17.5364 0.582928
906906 28.5113 0.947225
907907 −23.9819 −0.796305 −0.398152 0.917319i 0.630348π-0.630348\pi
−0.398152 + 0.917319i 0.630348π0.630348\pi
908908 39.7378 1.31875
909909 −9.51745 −0.315674
910910 −4.60245 −0.152570
911911 8.96636 0.297069 0.148534 0.988907i 0.452544π-0.452544\pi
0.148534 + 0.988907i 0.452544π0.452544\pi
912912 −54.8114 −1.81499
913913 76.7091 2.53870
914914 −40.8431 −1.35097
915915 2.24128 0.0740943
916916 119.604 3.95183
917917 12.2759 0.405385
918918 −9.72889 −0.321101
919919 16.6601 0.549566 0.274783 0.961506i 0.411394π-0.411394\pi
0.274783 + 0.961506i 0.411394π0.411394\pi
920920 0 0
921921 32.7526 1.07923
922922 −42.8392 −1.41083
923923 13.6742 0.450092
924924 −21.3607 −0.702715
925925 8.37444 0.275350
926926 −21.6742 −0.712259
927927 15.4966 0.508975
928928 17.8699 0.586608
929929 17.8843 0.586764 0.293382 0.955995i 0.405219π-0.405219\pi
0.293382 + 0.955995i 0.405219π0.405219\pi
930930 −6.35962 −0.208540
931931 26.0460 0.853624
932932 89.9130 2.94520
933933 −14.0267 −0.459212
934934 78.9128 2.58211
935935 16.8069 0.549645
936936 −30.9360 −1.01117
937937 44.6391 1.45830 0.729148 0.684356i 0.239916π-0.239916\pi
0.729148 + 0.684356i 0.239916π0.239916\pi
938938 12.3791 0.404193
939939 15.4745 0.504992
940940 0.746882 0.0243606
941941 −8.58275 −0.279790 −0.139895 0.990166i 0.544676π-0.544676\pi
−0.139895 + 0.990166i 0.544676π0.544676\pi
942942 −54.3201 −1.76985
943943 0 0
944944 78.3156 2.54896
945945 0.496928 0.0161651
946946 57.8720 1.88158
947947 2.65368 0.0862331 0.0431166 0.999070i 0.486271π-0.486271\pi
0.0431166 + 0.999070i 0.486271π0.486271\pi
948948 59.5061 1.93267
949949 2.32580 0.0754986
950950 47.4197 1.53850
951951 19.4452 0.630554
952952 21.1773 0.686359
953953 −29.3880 −0.951971 −0.475986 0.879453i 0.657909π-0.657909\pi
−0.475986 + 0.879453i 0.657909π0.657909\pi
954954 27.6616 0.895577
955955 8.56463 0.277145
956956 −52.5646 −1.70006
957957 5.65685 0.182860
958958 28.1003 0.907879
959959 2.48464 0.0802333
960960 −18.9546 −0.611758
961961 −21.5236 −0.694309
962962 17.5538 0.565957
963963 −12.7569 −0.411087
964964 71.7222 2.31002
965965 −10.7508 −0.346081
966966 0 0
967967 −17.9155 −0.576123 −0.288061 0.957612i 0.593011π-0.593011\pi
−0.288061 + 0.957612i 0.593011π0.593011\pi
968968 241.387 7.75847
969969 14.2245 0.456955
970970 11.4575 0.367878
971971 21.1227 0.677859 0.338930 0.940812i 0.389935π-0.389935\pi
0.338930 + 0.940812i 0.389935π0.389935\pi
972972 5.34017 0.171286
973973 −4.01227 −0.128627
974974 46.4990 1.48992
975975 15.1050 0.483748
976976 −40.6710 −1.30185
977977 −42.5645 −1.36176 −0.680880 0.732395i 0.738403π-0.738403\pi
−0.680880 + 0.732395i 0.738403π0.738403\pi
978978 −39.5441 −1.26448
979979 −20.6803 −0.660947
980980 26.7749 0.855292
981981 −16.7402 −0.534473
982982 −9.49079 −0.302863
983983 18.1921 0.580238 0.290119 0.956991i 0.406305π-0.406305\pi
0.290119 + 0.956991i 0.406305π0.406305\pi
984984 −60.4534 −1.92719
985985 −1.82857 −0.0582630
986986 −8.96636 −0.285547
987987 0.119530 0.00380470
988988 72.3141 2.30062
989989 0 0
990990 −12.6803 −0.403008
991991 29.9155 0.950297 0.475148 0.879906i 0.342394π-0.342394\pi
0.475148 + 0.879906i 0.342394π0.342394\pi
992992 59.6886 1.89511
993993 17.1194 0.543268
994994 7.06238 0.224005
995995 −13.1773 −0.417748
996996 66.7391 2.11471
997997 −2.52813 −0.0800665 −0.0400333 0.999198i 0.512746π-0.512746\pi
−0.0400333 + 0.999198i 0.512746π0.512746\pi
998998 −24.1711 −0.765124
999999 −1.89529 −0.0599643
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 1587.2.a.s.1.5 6
3.2 odd 2 4761.2.a.bs.1.2 6
23.22 odd 2 inner 1587.2.a.s.1.6 yes 6
69.68 even 2 4761.2.a.bs.1.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1587.2.a.s.1.5 6 1.1 even 1 trivial
1587.2.a.s.1.6 yes 6 23.22 odd 2 inner
4761.2.a.bs.1.1 6 69.68 even 2
4761.2.a.bs.1.2 6 3.2 odd 2