Properties

Label 9025.2.a.cu.1.10
Level 90259025
Weight 22
Character 9025.1
Self dual yes
Analytic conductor 72.06572.065
Analytic rank 00
Dimension 2424
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] = [9025,2,Mod(1,9025)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9025, 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("9025.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 9025=52192 9025 = 5^{2} \cdot 19^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 9025.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0,0,18,0,-12,0,0,12,0,12,0,0,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 72.064987824272.0649878242
Analytic rank: 00
Dimension: 2424
Twist minimal: no (minimal twist has level 95)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.10
Character χ\chi == 9025.1

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) == q0.449373q2+1.95684q31.79806q40.879352q62.06079q7+1.70675q8+0.829224q92.30599q113.51852q124.39611q13+0.926065q14+2.82916q165.47185q170.372631q184.03264q21+1.03625q225.81755q23+3.33983q24+1.97549q264.24786q27+3.70544q28+5.50466q29+0.757832q314.68485q324.51245q33+2.45890q341.49100q366.22555q378.60248q396.53829q41+1.81216q42+3.16680q43+4.14632q44+2.61425q46+6.36116q47+5.53621q482.75314q4910.7075q51+7.90448q523.85028q53+1.90888q543.51725q562.47365q58+2.55023q59+9.94010q610.340550q621.70886q633.55308q64+2.02778q66+1.70269q67+9.83874q6811.3840q69+9.85909q71+1.41528q72+10.2167q73+2.79760q74+4.75216q77+3.86572q78+2.41187q7910.8001q81+2.93813q827.06253q83+7.25095q841.42307q86+10.7717q873.93574q882.33452q89+9.05946q91+10.4603q92+1.48296q932.85854q949.16749q96+6.81539q97+1.23719q981.91218q99+O(q100)q-0.449373 q^{2} +1.95684 q^{3} -1.79806 q^{4} -0.879352 q^{6} -2.06079 q^{7} +1.70675 q^{8} +0.829224 q^{9} -2.30599 q^{11} -3.51852 q^{12} -4.39611 q^{13} +0.926065 q^{14} +2.82916 q^{16} -5.47185 q^{17} -0.372631 q^{18} -4.03264 q^{21} +1.03625 q^{22} -5.81755 q^{23} +3.33983 q^{24} +1.97549 q^{26} -4.24786 q^{27} +3.70544 q^{28} +5.50466 q^{29} +0.757832 q^{31} -4.68485 q^{32} -4.51245 q^{33} +2.45890 q^{34} -1.49100 q^{36} -6.22555 q^{37} -8.60248 q^{39} -6.53829 q^{41} +1.81216 q^{42} +3.16680 q^{43} +4.14632 q^{44} +2.61425 q^{46} +6.36116 q^{47} +5.53621 q^{48} -2.75314 q^{49} -10.7075 q^{51} +7.90448 q^{52} -3.85028 q^{53} +1.90888 q^{54} -3.51725 q^{56} -2.47365 q^{58} +2.55023 q^{59} +9.94010 q^{61} -0.340550 q^{62} -1.70886 q^{63} -3.55308 q^{64} +2.02778 q^{66} +1.70269 q^{67} +9.83874 q^{68} -11.3840 q^{69} +9.85909 q^{71} +1.41528 q^{72} +10.2167 q^{73} +2.79760 q^{74} +4.75216 q^{77} +3.86572 q^{78} +2.41187 q^{79} -10.8001 q^{81} +2.93813 q^{82} -7.06253 q^{83} +7.25095 q^{84} -1.42307 q^{86} +10.7717 q^{87} -3.93574 q^{88} -2.33452 q^{89} +9.05946 q^{91} +10.4603 q^{92} +1.48296 q^{93} -2.85854 q^{94} -9.16749 q^{96} +6.81539 q^{97} +1.23719 q^{98} -1.91218 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+18q412q6+12q9+12q11+24q14+6q16+6q2142q2412q26+36q29+42q31+6q346q36+24q39+60q4130q44+6q46+12q49+120q96+O(q100) 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} + 24 q^{14} + 6 q^{16} + 6 q^{21} - 42 q^{24} - 12 q^{26} + 36 q^{29} + 42 q^{31} + 6 q^{34} - 6 q^{36} + 24 q^{39} + 60 q^{41} - 30 q^{44} + 6 q^{46} + 12 q^{49}+ \cdots - 120 q^{96}+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 −0.449373 −0.317755 −0.158877 0.987298i 0.550787π-0.550787\pi
−0.158877 + 0.987298i 0.550787π0.550787\pi
33 1.95684 1.12978 0.564891 0.825165i 0.308918π-0.308918\pi
0.564891 + 0.825165i 0.308918π0.308918\pi
44 −1.79806 −0.899032
55 0 0
66 −0.879352 −0.358994
77 −2.06079 −0.778906 −0.389453 0.921046i 0.627336π-0.627336\pi
−0.389453 + 0.921046i 0.627336π0.627336\pi
88 1.70675 0.603427
99 0.829224 0.276408
1010 0 0
1111 −2.30599 −0.695282 −0.347641 0.937628i 0.613017π-0.613017\pi
−0.347641 + 0.937628i 0.613017π0.613017\pi
1212 −3.51852 −1.01571
1313 −4.39611 −1.21926 −0.609630 0.792686i 0.708682π-0.708682\pi
−0.609630 + 0.792686i 0.708682π0.708682\pi
1414 0.926065 0.247501
1515 0 0
1616 2.82916 0.707290
1717 −5.47185 −1.32712 −0.663560 0.748123i 0.730955π-0.730955\pi
−0.663560 + 0.748123i 0.730955π0.730955\pi
1818 −0.372631 −0.0878299
1919 0 0
2020 0 0
2121 −4.03264 −0.879994
2222 1.03625 0.220929
2323 −5.81755 −1.21304 −0.606522 0.795067i 0.707436π-0.707436\pi
−0.606522 + 0.795067i 0.707436π0.707436\pi
2424 3.33983 0.681741
2525 0 0
2626 1.97549 0.387426
2727 −4.24786 −0.817502
2828 3.70544 0.700262
2929 5.50466 1.02219 0.511095 0.859524i 0.329240π-0.329240\pi
0.511095 + 0.859524i 0.329240π0.329240\pi
3030 0 0
3131 0.757832 0.136111 0.0680553 0.997682i 0.478321π-0.478321\pi
0.0680553 + 0.997682i 0.478321π0.478321\pi
3232 −4.68485 −0.828171
3333 −4.51245 −0.785517
3434 2.45890 0.421699
3535 0 0
3636 −1.49100 −0.248499
3737 −6.22555 −1.02347 −0.511737 0.859142i 0.670998π-0.670998\pi
−0.511737 + 0.859142i 0.670998π0.670998\pi
3838 0 0
3939 −8.60248 −1.37750
4040 0 0
4141 −6.53829 −1.02111 −0.510554 0.859845i 0.670560π-0.670560\pi
−0.510554 + 0.859845i 0.670560π0.670560\pi
4242 1.81216 0.279623
4343 3.16680 0.482932 0.241466 0.970409i 0.422372π-0.422372\pi
0.241466 + 0.970409i 0.422372π0.422372\pi
4444 4.14632 0.625081
4545 0 0
4646 2.61425 0.385451
4747 6.36116 0.927871 0.463936 0.885869i 0.346437π-0.346437\pi
0.463936 + 0.885869i 0.346437π0.346437\pi
4848 5.53621 0.799084
4949 −2.75314 −0.393305
5050 0 0
5151 −10.7075 −1.49936
5252 7.90448 1.09615
5353 −3.85028 −0.528876 −0.264438 0.964403i 0.585187π-0.585187\pi
−0.264438 + 0.964403i 0.585187π0.585187\pi
5454 1.90888 0.259765
5555 0 0
5656 −3.51725 −0.470013
5757 0 0
5858 −2.47365 −0.324806
5959 2.55023 0.332012 0.166006 0.986125i 0.446913π-0.446913\pi
0.166006 + 0.986125i 0.446913π0.446913\pi
6060 0 0
6161 9.94010 1.27270 0.636350 0.771401i 0.280444π-0.280444\pi
0.636350 + 0.771401i 0.280444π0.280444\pi
6262 −0.340550 −0.0432498
6363 −1.70886 −0.215296
6464 −3.55308 −0.444135
6565 0 0
6666 2.02778 0.249602
6767 1.70269 0.208017 0.104009 0.994576i 0.466833π-0.466833\pi
0.104009 + 0.994576i 0.466833π0.466833\pi
6868 9.83874 1.19312
6969 −11.3840 −1.37048
7070 0 0
7171 9.85909 1.17006 0.585029 0.811012i 0.301083π-0.301083\pi
0.585029 + 0.811012i 0.301083π0.301083\pi
7272 1.41528 0.166792
7373 10.2167 1.19577 0.597886 0.801581i 0.296007π-0.296007\pi
0.597886 + 0.801581i 0.296007π0.296007\pi
7474 2.79760 0.325214
7575 0 0
7676 0 0
7777 4.75216 0.541559
7878 3.86572 0.437707
7979 2.41187 0.271357 0.135679 0.990753i 0.456679π-0.456679\pi
0.135679 + 0.990753i 0.456679π0.456679\pi
8080 0 0
8181 −10.8001 −1.20001
8282 2.93813 0.324462
8383 −7.06253 −0.775213 −0.387607 0.921825i 0.626698π-0.626698\pi
−0.387607 + 0.921825i 0.626698π0.626698\pi
8484 7.25095 0.791143
8585 0 0
8686 −1.42307 −0.153454
8787 10.7717 1.15485
8888 −3.93574 −0.419552
8989 −2.33452 −0.247458 −0.123729 0.992316i 0.539485π-0.539485\pi
−0.123729 + 0.992316i 0.539485π0.539485\pi
9090 0 0
9191 9.05946 0.949689
9292 10.4603 1.09056
9393 1.48296 0.153775
9494 −2.85854 −0.294836
9595 0 0
9696 −9.16749 −0.935653
9797 6.81539 0.691998 0.345999 0.938235i 0.387540π-0.387540\pi
0.345999 + 0.938235i 0.387540π0.387540\pi
9898 1.23719 0.124975
9999 −1.91218 −0.192181
100100 0 0
101101 12.1976 1.21370 0.606851 0.794816i 0.292433π-0.292433\pi
0.606851 + 0.794816i 0.292433π0.292433\pi
102102 4.81168 0.476428
103103 −12.9197 −1.27302 −0.636509 0.771269i 0.719622π-0.719622\pi
−0.636509 + 0.771269i 0.719622π0.719622\pi
104104 −7.50304 −0.735734
105105 0 0
106106 1.73021 0.168053
107107 15.1729 1.46682 0.733412 0.679785i 0.237927π-0.237927\pi
0.733412 + 0.679785i 0.237927π0.237927\pi
108108 7.63793 0.734960
109109 −19.1794 −1.83705 −0.918527 0.395359i 0.870620π-0.870620\pi
−0.918527 + 0.395359i 0.870620π0.870620\pi
110110 0 0
111111 −12.1824 −1.15630
112112 −5.83031 −0.550913
113113 1.91146 0.179815 0.0899075 0.995950i 0.471343π-0.471343\pi
0.0899075 + 0.995950i 0.471343π0.471343\pi
114114 0 0
115115 0 0
116116 −9.89773 −0.918981
117117 −3.64535 −0.337013
118118 −1.14601 −0.105498
119119 11.2764 1.03370
120120 0 0
121121 −5.68241 −0.516583
122122 −4.46682 −0.404406
123123 −12.7944 −1.15363
124124 −1.36263 −0.122368
125125 0 0
126126 0.767915 0.0684113
127127 −21.2359 −1.88438 −0.942191 0.335077i 0.891238π-0.891238\pi
−0.942191 + 0.335077i 0.891238π0.891238\pi
128128 10.9663 0.969297
129129 6.19692 0.545608
130130 0 0
131131 −1.67271 −0.146146 −0.0730728 0.997327i 0.523281π-0.523281\pi
−0.0730728 + 0.997327i 0.523281π0.523281\pi
132132 8.11368 0.706205
133133 0 0
134134 −0.765145 −0.0660984
135135 0 0
136136 −9.33908 −0.800819
137137 17.2880 1.47701 0.738506 0.674247i 0.235532π-0.235532\pi
0.738506 + 0.674247i 0.235532π0.235532\pi
138138 5.11567 0.435475
139139 12.3265 1.04552 0.522761 0.852479i 0.324902π-0.324902\pi
0.522761 + 0.852479i 0.324902π0.324902\pi
140140 0 0
141141 12.4478 1.04829
142142 −4.43041 −0.371792
143143 10.1374 0.847730
144144 2.34601 0.195501
145145 0 0
146146 −4.59111 −0.379963
147147 −5.38745 −0.444349
148148 11.1939 0.920136
149149 4.35901 0.357104 0.178552 0.983930i 0.442859π-0.442859\pi
0.178552 + 0.983930i 0.442859π0.442859\pi
150150 0 0
151151 4.44628 0.361833 0.180917 0.983498i 0.442094π-0.442094\pi
0.180917 + 0.983498i 0.442094π0.442094\pi
152152 0 0
153153 −4.53739 −0.366826
154154 −2.13550 −0.172083
155155 0 0
156156 15.4678 1.23841
157157 19.8432 1.58366 0.791831 0.610740i 0.209128π-0.209128\pi
0.791831 + 0.610740i 0.209128π0.209128\pi
158158 −1.08383 −0.0862250
159159 −7.53438 −0.597515
160160 0 0
161161 11.9888 0.944847
162162 4.85326 0.381308
163163 −1.28088 −0.100326 −0.0501632 0.998741i 0.515974π-0.515974\pi
−0.0501632 + 0.998741i 0.515974π0.515974\pi
164164 11.7563 0.918009
165165 0 0
166166 3.17371 0.246328
167167 −8.03589 −0.621836 −0.310918 0.950437i 0.600636π-0.600636\pi
−0.310918 + 0.950437i 0.600636π0.600636\pi
168168 −6.88270 −0.531012
169169 6.32574 0.486595
170170 0 0
171171 0 0
172172 −5.69410 −0.434171
173173 2.65910 0.202167 0.101084 0.994878i 0.467769π-0.467769\pi
0.101084 + 0.994878i 0.467769π0.467769\pi
174174 −4.84053 −0.366960
175175 0 0
176176 −6.52401 −0.491766
177177 4.99040 0.375101
178178 1.04907 0.0786311
179179 8.10201 0.605572 0.302786 0.953059i 0.402083π-0.402083\pi
0.302786 + 0.953059i 0.402083π0.402083\pi
180180 0 0
181181 21.5023 1.59826 0.799128 0.601161i 0.205295π-0.205295\pi
0.799128 + 0.601161i 0.205295π0.205295\pi
182182 −4.07108 −0.301768
183183 19.4512 1.43787
184184 −9.92910 −0.731983
185185 0 0
186186 −0.666401 −0.0488629
187187 12.6180 0.922722
188188 −11.4378 −0.834186
189189 8.75396 0.636757
190190 0 0
191191 −19.5939 −1.41777 −0.708884 0.705326i 0.750801π-0.750801\pi
−0.708884 + 0.705326i 0.750801π0.750801\pi
192192 −6.95280 −0.501775
193193 0.483357 0.0347928 0.0173964 0.999849i 0.494462π-0.494462\pi
0.0173964 + 0.999849i 0.494462π0.494462\pi
194194 −3.06265 −0.219886
195195 0 0
196196 4.95031 0.353594
197197 −1.26189 −0.0899060 −0.0449530 0.998989i 0.514314π-0.514314\pi
−0.0449530 + 0.998989i 0.514314π0.514314\pi
198198 0.859283 0.0610666
199199 20.6554 1.46423 0.732113 0.681183i 0.238534π-0.238534\pi
0.732113 + 0.681183i 0.238534π0.238534\pi
200200 0 0
201201 3.33190 0.235014
202202 −5.48125 −0.385660
203203 −11.3440 −0.796190
204204 19.2528 1.34797
205205 0 0
206206 5.80578 0.404508
207207 −4.82405 −0.335295
208208 −12.4373 −0.862371
209209 0 0
210210 0 0
211211 7.01196 0.482723 0.241361 0.970435i 0.422406π-0.422406\pi
0.241361 + 0.970435i 0.422406π0.422406\pi
212212 6.92305 0.475477
213213 19.2927 1.32191
214214 −6.81831 −0.466090
215215 0 0
216216 −7.25003 −0.493302
217217 −1.56173 −0.106017
218218 8.61871 0.583733
219219 19.9924 1.35096
220220 0 0
221221 24.0548 1.61810
222222 5.47445 0.367421
223223 −19.4374 −1.30162 −0.650812 0.759239i 0.725571π-0.725571\pi
−0.650812 + 0.759239i 0.725571π0.725571\pi
224224 9.65449 0.645068
225225 0 0
226226 −0.858959 −0.0571371
227227 −6.53998 −0.434074 −0.217037 0.976163i 0.569639π-0.569639\pi
−0.217037 + 0.976163i 0.569639π0.569639\pi
228228 0 0
229229 −20.4005 −1.34810 −0.674052 0.738684i 0.735448π-0.735448\pi
−0.674052 + 0.738684i 0.735448π0.735448\pi
230230 0 0
231231 9.29923 0.611844
232232 9.39507 0.616816
233233 −12.0490 −0.789357 −0.394679 0.918819i 0.629144π-0.629144\pi
−0.394679 + 0.918819i 0.629144π0.629144\pi
234234 1.63812 0.107088
235235 0 0
236236 −4.58548 −0.298489
237237 4.71965 0.306574
238238 −5.06729 −0.328464
239239 −6.12499 −0.396193 −0.198096 0.980183i 0.563476π-0.563476\pi
−0.198096 + 0.980183i 0.563476π0.563476\pi
240240 0 0
241241 −7.27309 −0.468501 −0.234250 0.972176i 0.575264π-0.575264\pi
−0.234250 + 0.972176i 0.575264π0.575264\pi
242242 2.55352 0.164147
243243 −8.39040 −0.538244
244244 −17.8729 −1.14420
245245 0 0
246246 5.74945 0.366572
247247 0 0
248248 1.29343 0.0821328
249249 −13.8202 −0.875822
250250 0 0
251251 −24.1866 −1.52664 −0.763321 0.646019i 0.776433π-0.776433\pi
−0.763321 + 0.646019i 0.776433π0.776433\pi
252252 3.07263 0.193558
253253 13.4152 0.843407
254254 9.54285 0.598771
255255 0 0
256256 2.17817 0.136136
257257 −12.2379 −0.763382 −0.381691 0.924290i 0.624658π-0.624658\pi
−0.381691 + 0.924290i 0.624658π0.624658\pi
258258 −2.78473 −0.173370
259259 12.8296 0.797191
260260 0 0
261261 4.56459 0.282541
262262 0.751673 0.0464385
263263 12.3859 0.763746 0.381873 0.924215i 0.375279π-0.375279\pi
0.381873 + 0.924215i 0.375279π0.375279\pi
264264 −7.70162 −0.474002
265265 0 0
266266 0 0
267267 −4.56828 −0.279574
268268 −3.06155 −0.187014
269269 −4.93880 −0.301124 −0.150562 0.988601i 0.548108π-0.548108\pi
−0.150562 + 0.988601i 0.548108π0.548108\pi
270270 0 0
271271 −6.90194 −0.419263 −0.209631 0.977780i 0.567226π-0.567226\pi
−0.209631 + 0.977780i 0.567226π0.567226\pi
272272 −15.4808 −0.938658
273273 17.7279 1.07294
274274 −7.76876 −0.469328
275275 0 0
276276 20.4692 1.23210
277277 3.96325 0.238129 0.119064 0.992887i 0.462011π-0.462011\pi
0.119064 + 0.992887i 0.462011π0.462011\pi
278278 −5.53921 −0.332220
279279 0.628412 0.0376221
280280 0 0
281281 31.1993 1.86119 0.930597 0.366045i 0.119289π-0.119289\pi
0.930597 + 0.366045i 0.119289π0.119289\pi
282282 −5.59370 −0.333100
283283 −10.6270 −0.631711 −0.315855 0.948807i 0.602291π-0.602291\pi
−0.315855 + 0.948807i 0.602291π0.602291\pi
284284 −17.7273 −1.05192
285285 0 0
286286 −4.55546 −0.269370
287287 13.4741 0.795348
288288 −3.88478 −0.228913
289289 12.9412 0.761246
290290 0 0
291291 13.3366 0.781807
292292 −18.3703 −1.07504
293293 19.6263 1.14658 0.573289 0.819353i 0.305667π-0.305667\pi
0.573289 + 0.819353i 0.305667π0.305667\pi
294294 2.42097 0.141194
295295 0 0
296296 −10.6255 −0.617592
297297 9.79553 0.568394
298298 −1.95882 −0.113472
299299 25.5746 1.47902
300300 0 0
301301 −6.52611 −0.376159
302302 −1.99804 −0.114974
303303 23.8687 1.37122
304304 0 0
305305 0 0
306306 2.03898 0.116561
307307 22.6258 1.29132 0.645662 0.763623i 0.276581π-0.276581\pi
0.645662 + 0.763623i 0.276581π0.276581\pi
308308 −8.54469 −0.486879
309309 −25.2818 −1.43823
310310 0 0
311311 24.8577 1.40955 0.704776 0.709430i 0.251047π-0.251047\pi
0.704776 + 0.709430i 0.251047π0.251047\pi
312312 −14.6823 −0.831219
313313 22.2026 1.25497 0.627484 0.778630i 0.284085π-0.284085\pi
0.627484 + 0.778630i 0.284085π0.284085\pi
314314 −8.91701 −0.503216
315315 0 0
316316 −4.33670 −0.243959
317317 2.03957 0.114554 0.0572769 0.998358i 0.481758π-0.481758\pi
0.0572769 + 0.998358i 0.481758π0.481758\pi
318318 3.38575 0.189863
319319 −12.6937 −0.710710
320320 0 0
321321 29.6910 1.65719
322322 −5.38743 −0.300230
323323 0 0
324324 19.4192 1.07884
325325 0 0
326326 0.575594 0.0318792
327327 −37.5310 −2.07547
328328 −11.1592 −0.616164
329329 −13.1090 −0.722725
330330 0 0
331331 33.6525 1.84971 0.924855 0.380321i 0.124186π-0.124186\pi
0.924855 + 0.380321i 0.124186π0.124186\pi
332332 12.6989 0.696941
333333 −5.16237 −0.282896
334334 3.61111 0.197591
335335 0 0
336336 −11.4090 −0.622411
337337 −2.58877 −0.141019 −0.0705096 0.997511i 0.522463π-0.522463\pi
−0.0705096 + 0.997511i 0.522463π0.522463\pi
338338 −2.84262 −0.154618
339339 3.74042 0.203152
340340 0 0
341341 −1.74755 −0.0946353
342342 0 0
343343 20.0992 1.08525
344344 5.40493 0.291414
345345 0 0
346346 −1.19493 −0.0642397
347347 −23.8033 −1.27783 −0.638913 0.769279i 0.720616π-0.720616\pi
−0.638913 + 0.769279i 0.720616π0.720616\pi
348348 −19.3683 −1.03825
349349 −2.48241 −0.132880 −0.0664402 0.997790i 0.521164π-0.521164\pi
−0.0664402 + 0.997790i 0.521164π0.521164\pi
350350 0 0
351351 18.6741 0.996747
352352 10.8032 0.575813
353353 −35.7434 −1.90243 −0.951216 0.308527i 0.900164π-0.900164\pi
−0.951216 + 0.308527i 0.900164π0.900164\pi
354354 −2.24255 −0.119190
355355 0 0
356356 4.19761 0.222473
357357 22.0660 1.16786
358358 −3.64082 −0.192424
359359 −5.76436 −0.304231 −0.152116 0.988363i 0.548609π-0.548609\pi
−0.152116 + 0.988363i 0.548609π0.548609\pi
360360 0 0
361361 0 0
362362 −9.66258 −0.507854
363363 −11.1196 −0.583626
364364 −16.2895 −0.853801
365365 0 0
366366 −8.74084 −0.456891
367367 5.95729 0.310968 0.155484 0.987838i 0.450306π-0.450306\pi
0.155484 + 0.987838i 0.450306π0.450306\pi
368368 −16.4588 −0.857974
369369 −5.42170 −0.282243
370370 0 0
371371 7.93462 0.411945
372372 −2.66645 −0.138249
373373 4.46841 0.231365 0.115683 0.993286i 0.463094π-0.463094\pi
0.115683 + 0.993286i 0.463094π0.463094\pi
374374 −5.67021 −0.293199
375375 0 0
376376 10.8569 0.559902
377377 −24.1991 −1.24631
378378 −3.93380 −0.202333
379379 13.3179 0.684095 0.342047 0.939683i 0.388880π-0.388880\pi
0.342047 + 0.939683i 0.388880π0.388880\pi
380380 0 0
381381 −41.5553 −2.12894
382382 8.80499 0.450502
383383 −10.1737 −0.519849 −0.259925 0.965629i 0.583698π-0.583698\pi
−0.259925 + 0.965629i 0.583698π0.583698\pi
384384 21.4594 1.09509
385385 0 0
386386 −0.217208 −0.0110556
387387 2.62598 0.133486
388388 −12.2545 −0.622128
389389 −11.4104 −0.578530 −0.289265 0.957249i 0.593411π-0.593411\pi
−0.289265 + 0.957249i 0.593411π0.593411\pi
390390 0 0
391391 31.8328 1.60985
392392 −4.69891 −0.237331
393393 −3.27323 −0.165113
394394 0.567060 0.0285681
395395 0 0
396396 3.43822 0.172777
397397 −5.14253 −0.258096 −0.129048 0.991638i 0.541192π-0.541192\pi
−0.129048 + 0.991638i 0.541192π0.541192\pi
398398 −9.28201 −0.465265
399399 0 0
400400 0 0
401401 17.0822 0.853043 0.426522 0.904477i 0.359739π-0.359739\pi
0.426522 + 0.904477i 0.359739π0.359739\pi
402402 −1.49727 −0.0746768
403403 −3.33151 −0.165954
404404 −21.9320 −1.09116
405405 0 0
406406 5.09767 0.252993
407407 14.3561 0.711603
408408 −18.2751 −0.904751
409409 −26.0696 −1.28906 −0.644529 0.764580i 0.722947π-0.722947\pi
−0.644529 + 0.764580i 0.722947π0.722947\pi
410410 0 0
411411 33.8298 1.66870
412412 23.2305 1.14448
413413 −5.25550 −0.258606
414414 2.16780 0.106542
415415 0 0
416416 20.5951 1.00976
417417 24.1211 1.18121
418418 0 0
419419 5.77281 0.282020 0.141010 0.990008i 0.454965π-0.454965\pi
0.141010 + 0.990008i 0.454965π0.454965\pi
420420 0 0
421421 25.3007 1.23308 0.616540 0.787323i 0.288534π-0.288534\pi
0.616540 + 0.787323i 0.288534π0.288534\pi
422422 −3.15099 −0.153388
423423 5.27483 0.256471
424424 −6.57146 −0.319138
425425 0 0
426426 −8.66960 −0.420044
427427 −20.4845 −0.991314
428428 −27.2819 −1.31872
429429 19.8372 0.957750
430430 0 0
431431 −18.7629 −0.903777 −0.451888 0.892074i 0.649249π-0.649249\pi
−0.451888 + 0.892074i 0.649249π0.649249\pi
432432 −12.0179 −0.578211
433433 8.51298 0.409108 0.204554 0.978855i 0.434426π-0.434426\pi
0.204554 + 0.978855i 0.434426π0.434426\pi
434434 0.701802 0.0336876
435435 0 0
436436 34.4858 1.65157
437437 0 0
438438 −8.98406 −0.429275
439439 −2.05530 −0.0980941 −0.0490470 0.998796i 0.515618π-0.515618\pi
−0.0490470 + 0.998796i 0.515618π0.515618\pi
440440 0 0
441441 −2.28296 −0.108713
442442 −10.8096 −0.514160
443443 −12.0403 −0.572054 −0.286027 0.958222i 0.592335π-0.592335\pi
−0.286027 + 0.958222i 0.592335π0.592335\pi
444444 21.9048 1.03955
445445 0 0
446446 8.73464 0.413597
447447 8.52989 0.403450
448448 7.32215 0.345939
449449 7.49400 0.353664 0.176832 0.984241i 0.443415π-0.443415\pi
0.176832 + 0.984241i 0.443415π0.443415\pi
450450 0 0
451451 15.0772 0.709959
452452 −3.43693 −0.161659
453453 8.70066 0.408793
454454 2.93889 0.137929
455455 0 0
456456 0 0
457457 14.0052 0.655137 0.327568 0.944827i 0.393771π-0.393771\pi
0.327568 + 0.944827i 0.393771π0.393771\pi
458458 9.16745 0.428367
459459 23.2437 1.08492
460460 0 0
461461 −17.6751 −0.823210 −0.411605 0.911362i 0.635032π-0.635032\pi
−0.411605 + 0.911362i 0.635032π0.635032\pi
462462 −4.17882 −0.194416
463463 −16.5926 −0.771123 −0.385562 0.922682i 0.625992π-0.625992\pi
−0.385562 + 0.922682i 0.625992π0.625992\pi
464464 15.5736 0.722984
465465 0 0
466466 5.41451 0.250822
467467 −15.9904 −0.739949 −0.369975 0.929042i 0.620634π-0.620634\pi
−0.369975 + 0.929042i 0.620634π0.620634\pi
468468 6.55458 0.302985
469469 −3.50890 −0.162026
470470 0 0
471471 38.8300 1.78919
472472 4.35261 0.200345
473473 −7.30260 −0.335774
474474 −2.12089 −0.0974155
475475 0 0
476476 −20.2756 −0.929331
477477 −3.19274 −0.146186
478478 2.75241 0.125892
479479 7.39591 0.337928 0.168964 0.985622i 0.445958π-0.445958\pi
0.168964 + 0.985622i 0.445958π0.445958\pi
480480 0 0
481481 27.3682 1.24788
482482 3.26833 0.148868
483483 23.4601 1.06747
484484 10.2173 0.464425
485485 0 0
486486 3.77042 0.171030
487487 −20.1881 −0.914811 −0.457406 0.889258i 0.651221π-0.651221\pi
−0.457406 + 0.889258i 0.651221π0.651221\pi
488488 16.9652 0.767981
489489 −2.50648 −0.113347
490490 0 0
491491 9.33307 0.421195 0.210598 0.977573i 0.432459π-0.432459\pi
0.210598 + 0.977573i 0.432459π0.432459\pi
492492 23.0051 1.03715
493493 −30.1207 −1.35657
494494 0 0
495495 0 0
496496 2.14403 0.0962697
497497 −20.3175 −0.911366
498498 6.21044 0.278297
499499 −23.9612 −1.07265 −0.536326 0.844011i 0.680188π-0.680188\pi
−0.536326 + 0.844011i 0.680188π0.680188\pi
500500 0 0
501501 −15.7249 −0.702539
502502 10.8688 0.485098
503503 −10.3338 −0.460763 −0.230382 0.973100i 0.573997π-0.573997\pi
−0.230382 + 0.973100i 0.573997π0.573997\pi
504504 −2.91659 −0.129915
505505 0 0
506506 −6.02844 −0.267997
507507 12.3785 0.549747
508508 38.1835 1.69412
509509 27.7116 1.22829 0.614147 0.789192i 0.289500π-0.289500\pi
0.614147 + 0.789192i 0.289500π0.289500\pi
510510 0 0
511511 −21.0545 −0.931395
512512 −22.9115 −1.01256
513513 0 0
514514 5.49940 0.242568
515515 0 0
516516 −11.1424 −0.490519
517517 −14.6688 −0.645132
518518 −5.76527 −0.253311
519519 5.20343 0.228405
520520 0 0
521521 −10.5729 −0.463209 −0.231604 0.972810i 0.574398π-0.574398\pi
−0.231604 + 0.972810i 0.574398π0.574398\pi
522522 −2.05121 −0.0897788
523523 18.1596 0.794065 0.397032 0.917805i 0.370040π-0.370040\pi
0.397032 + 0.917805i 0.370040π0.370040\pi
524524 3.00765 0.131390
525525 0 0
526526 −5.56588 −0.242684
527527 −4.14675 −0.180635
528528 −12.7665 −0.555588
529529 10.8439 0.471475
530530 0 0
531531 2.11471 0.0917707
532532 0 0
533533 28.7430 1.24500
534534 2.05286 0.0888360
535535 0 0
536536 2.90607 0.125523
537537 15.8543 0.684165
538538 2.21936 0.0956835
539539 6.34870 0.273458
540540 0 0
541541 6.10507 0.262478 0.131239 0.991351i 0.458105π-0.458105\pi
0.131239 + 0.991351i 0.458105π0.458105\pi
542542 3.10155 0.133223
543543 42.0766 1.80568
544544 25.6348 1.09908
545545 0 0
546546 −7.96645 −0.340933
547547 −10.9019 −0.466132 −0.233066 0.972461i 0.574876π-0.574876\pi
−0.233066 + 0.972461i 0.574876π0.574876\pi
548548 −31.0849 −1.32788
549549 8.24256 0.351784
550550 0 0
551551 0 0
552552 −19.4297 −0.826981
553553 −4.97037 −0.211362
554554 −1.78098 −0.0756665
555555 0 0
556556 −22.1639 −0.939958
557557 12.2157 0.517595 0.258798 0.965932i 0.416674π-0.416674\pi
0.258798 + 0.965932i 0.416674π0.416674\pi
558558 −0.282392 −0.0119546
559559 −13.9216 −0.588820
560560 0 0
561561 24.6915 1.04247
562562 −14.0201 −0.591403
563563 −18.3200 −0.772095 −0.386048 0.922479i 0.626160π-0.626160\pi
−0.386048 + 0.922479i 0.626160π0.626160\pi
564564 −22.3819 −0.942448
565565 0 0
566566 4.77550 0.200729
567567 22.2567 0.934693
568568 16.8270 0.706044
569569 32.3240 1.35509 0.677546 0.735480i 0.263043π-0.263043\pi
0.677546 + 0.735480i 0.263043π0.263043\pi
570570 0 0
571571 −13.2641 −0.555083 −0.277542 0.960714i 0.589520π-0.589520\pi
−0.277542 + 0.960714i 0.589520π0.589520\pi
572572 −18.2276 −0.762136
573573 −38.3422 −1.60177
574574 −6.05488 −0.252726
575575 0 0
576576 −2.94629 −0.122762
577577 21.7627 0.905993 0.452996 0.891512i 0.350355π-0.350355\pi
0.452996 + 0.891512i 0.350355π0.350355\pi
578578 −5.81542 −0.241890
579579 0.945853 0.0393083
580580 0 0
581581 14.5544 0.603818
582582 −5.99312 −0.248423
583583 8.87870 0.367718
584584 17.4373 0.721561
585585 0 0
586586 −8.81952 −0.364331
587587 41.5762 1.71604 0.858018 0.513620i 0.171696π-0.171696\pi
0.858018 + 0.513620i 0.171696π0.171696\pi
588588 9.68697 0.399484
589589 0 0
590590 0 0
591591 −2.46932 −0.101574
592592 −17.6131 −0.723893
593593 −8.58712 −0.352631 −0.176315 0.984334i 0.556418π-0.556418\pi
−0.176315 + 0.984334i 0.556418π0.556418\pi
594594 −4.40185 −0.180610
595595 0 0
596596 −7.83778 −0.321048
597597 40.4194 1.65426
598598 −11.4925 −0.469964
599599 41.2980 1.68739 0.843696 0.536822i 0.180375π-0.180375\pi
0.843696 + 0.536822i 0.180375π0.180375\pi
600600 0 0
601601 −1.60121 −0.0653145 −0.0326573 0.999467i 0.510397π-0.510397\pi
−0.0326573 + 0.999467i 0.510397π0.510397\pi
602602 2.93266 0.119526
603603 1.41191 0.0574975
604604 −7.99470 −0.325300
605605 0 0
606606 −10.7259 −0.435711
607607 32.4708 1.31795 0.658975 0.752165i 0.270990π-0.270990\pi
0.658975 + 0.752165i 0.270990π0.270990\pi
608608 0 0
609609 −22.1983 −0.899521
610610 0 0
611611 −27.9643 −1.13132
612612 8.15852 0.329788
613613 13.9352 0.562839 0.281420 0.959585i 0.409195π-0.409195\pi
0.281420 + 0.959585i 0.409195π0.409195\pi
614614 −10.1674 −0.410325
615615 0 0
616616 8.11075 0.326791
617617 −14.4224 −0.580625 −0.290313 0.956932i 0.593759π-0.593759\pi
−0.290313 + 0.956932i 0.593759π0.593759\pi
618618 11.3610 0.457005
619619 −4.71305 −0.189434 −0.0947168 0.995504i 0.530195π-0.530195\pi
−0.0947168 + 0.995504i 0.530195π0.530195\pi
620620 0 0
621621 24.7122 0.991665
622622 −11.1704 −0.447892
623623 4.81095 0.192747
624624 −24.3378 −0.974291
625625 0 0
626626 −9.97728 −0.398772
627627 0 0
628628 −35.6794 −1.42376
629629 34.0653 1.35827
630630 0 0
631631 3.31273 0.131878 0.0659388 0.997824i 0.478996π-0.478996\pi
0.0659388 + 0.997824i 0.478996π0.478996\pi
632632 4.11646 0.163744
633633 13.7213 0.545372
634634 −0.916530 −0.0364000
635635 0 0
636636 13.5473 0.537185
637637 12.1031 0.479541
638638 5.70420 0.225831
639639 8.17539 0.323413
640640 0 0
641641 −0.0491989 −0.00194324 −0.000971620 1.00000i 0.500309π-0.500309\pi
−0.000971620 1.00000i 0.500309π0.500309\pi
642642 −13.3424 −0.526581
643643 −12.0003 −0.473246 −0.236623 0.971602i 0.576041π-0.576041\pi
−0.236623 + 0.971602i 0.576041π0.576041\pi
644644 −21.5566 −0.849448
645645 0 0
646646 0 0
647647 36.3971 1.43092 0.715458 0.698656i 0.246218π-0.246218\pi
0.715458 + 0.698656i 0.246218π0.246218\pi
648648 −18.4330 −0.724116
649649 −5.88081 −0.230842
650650 0 0
651651 −3.05607 −0.119777
652652 2.30311 0.0901967
653653 31.7999 1.24443 0.622214 0.782847i 0.286233π-0.286233\pi
0.622214 + 0.782847i 0.286233π0.286233\pi
654654 16.8654 0.659491
655655 0 0
656656 −18.4979 −0.722220
657657 8.47192 0.330521
658658 5.89085 0.229649
659659 26.8414 1.04559 0.522796 0.852458i 0.324889π-0.324889\pi
0.522796 + 0.852458i 0.324889π0.324889\pi
660660 0 0
661661 −34.2970 −1.33400 −0.667000 0.745057i 0.732422π-0.732422\pi
−0.667000 + 0.745057i 0.732422π0.732422\pi
662662 −15.1225 −0.587754
663663 47.0715 1.82810
664664 −12.0540 −0.467784
665665 0 0
666666 2.31983 0.0898917
667667 −32.0236 −1.23996
668668 14.4490 0.559050
669669 −38.0358 −1.47055
670670 0 0
671671 −22.9218 −0.884885
672672 18.8923 0.728786
673673 −21.7196 −0.837230 −0.418615 0.908164i 0.637484π-0.637484\pi
−0.418615 + 0.908164i 0.637484π0.637484\pi
674674 1.16332 0.0448096
675675 0 0
676676 −11.3741 −0.437465
677677 −8.53064 −0.327859 −0.163930 0.986472i 0.552417π-0.552417\pi
−0.163930 + 0.986472i 0.552417π0.552417\pi
678678 −1.68085 −0.0645525
679679 −14.0451 −0.539001
680680 0 0
681681 −12.7977 −0.490409
682682 0.785303 0.0300708
683683 17.3190 0.662695 0.331347 0.943509i 0.392497π-0.392497\pi
0.331347 + 0.943509i 0.392497π0.392497\pi
684684 0 0
685685 0 0
686686 −9.03204 −0.344845
687687 −39.9206 −1.52306
688688 8.95938 0.341573
689689 16.9262 0.644838
690690 0 0
691691 17.2709 0.657014 0.328507 0.944501i 0.393454π-0.393454\pi
0.328507 + 0.944501i 0.393454π0.393454\pi
692692 −4.78122 −0.181755
693693 3.94061 0.149691
694694 10.6966 0.406036
695695 0 0
696696 18.3846 0.696868
697697 35.7765 1.35513
698698 1.11553 0.0422234
699699 −23.5780 −0.891802
700700 0 0
701701 21.8816 0.826457 0.413228 0.910627i 0.364401π-0.364401\pi
0.413228 + 0.910627i 0.364401π0.364401\pi
702702 −8.39162 −0.316721
703703 0 0
704704 8.19336 0.308799
705705 0 0
706706 16.0621 0.604507
707707 −25.1366 −0.945360
708708 −8.97305 −0.337228
709709 20.5621 0.772224 0.386112 0.922452i 0.373818π-0.373818\pi
0.386112 + 0.922452i 0.373818π0.373818\pi
710710 0 0
711711 1.99998 0.0750052
712712 −3.98443 −0.149323
713713 −4.40873 −0.165108
714714 −9.91588 −0.371092
715715 0 0
716716 −14.5679 −0.544429
717717 −11.9856 −0.447612
718718 2.59035 0.0966709
719719 15.6722 0.584473 0.292237 0.956346i 0.405600π-0.405600\pi
0.292237 + 0.956346i 0.405600π0.405600\pi
720720 0 0
721721 26.6249 0.991561
722722 0 0
723723 −14.2323 −0.529304
724724 −38.6626 −1.43688
725725 0 0
726726 4.99684 0.185450
727727 −43.5233 −1.61419 −0.807095 0.590421i 0.798962π-0.798962\pi
−0.807095 + 0.590421i 0.798962π0.798962\pi
728728 15.4622 0.573068
729729 15.9815 0.591907
730730 0 0
731731 −17.3282 −0.640908
732732 −34.9745 −1.29269
733733 −12.6904 −0.468729 −0.234364 0.972149i 0.575301π-0.575301\pi
−0.234364 + 0.972149i 0.575301π0.575301\pi
734734 −2.67705 −0.0988116
735735 0 0
736736 27.2543 1.00461
737737 −3.92639 −0.144630
738738 2.43637 0.0896839
739739 28.1664 1.03612 0.518059 0.855345i 0.326655π-0.326655\pi
0.518059 + 0.855345i 0.326655π0.326655\pi
740740 0 0
741741 0 0
742742 −3.56561 −0.130898
743743 −25.5639 −0.937849 −0.468924 0.883238i 0.655358π-0.655358\pi
−0.468924 + 0.883238i 0.655358π0.655358\pi
744744 2.53103 0.0927922
745745 0 0
746746 −2.00798 −0.0735175
747747 −5.85641 −0.214275
748748 −22.6880 −0.829557
749749 −31.2683 −1.14252
750750 0 0
751751 34.6687 1.26508 0.632539 0.774529i 0.282013π-0.282013\pi
0.632539 + 0.774529i 0.282013π0.282013\pi
752752 17.9968 0.656274
753753 −47.3293 −1.72477
754754 10.8744 0.396023
755755 0 0
756756 −15.7402 −0.572465
757757 −45.7467 −1.66269 −0.831346 0.555755i 0.812429π-0.812429\pi
−0.831346 + 0.555755i 0.812429π0.812429\pi
758758 −5.98471 −0.217374
759759 26.2514 0.952867
760760 0 0
761761 2.85442 0.103472 0.0517362 0.998661i 0.483524π-0.483524\pi
0.0517362 + 0.998661i 0.483524π0.483524\pi
762762 18.6738 0.676481
763763 39.5248 1.43089
764764 35.2311 1.27462
765765 0 0
766766 4.57177 0.165185
767767 −11.2111 −0.404809
768768 4.26233 0.153804
769769 19.5208 0.703937 0.351969 0.936012i 0.385512π-0.385512\pi
0.351969 + 0.936012i 0.385512π0.385512\pi
770770 0 0
771771 −23.9477 −0.862455
772772 −0.869107 −0.0312798
773773 −7.24881 −0.260722 −0.130361 0.991467i 0.541614π-0.541614\pi
−0.130361 + 0.991467i 0.541614π0.541614\pi
774774 −1.18005 −0.0424159
775775 0 0
776776 11.6322 0.417570
777777 25.1054 0.900652
778778 5.12753 0.183831
779779 0 0
780780 0 0
781781 −22.7349 −0.813520
782782 −14.3048 −0.511539
783783 −23.3830 −0.835641
784784 −7.78906 −0.278181
785785 0 0
786786 1.47090 0.0524654
787787 −4.20711 −0.149967 −0.0749837 0.997185i 0.523890π-0.523890\pi
−0.0749837 + 0.997185i 0.523890π0.523890\pi
788788 2.26896 0.0808283
789789 24.2372 0.862867
790790 0 0
791791 −3.93912 −0.140059
792792 −3.26361 −0.115967
793793 −43.6977 −1.55175
794794 2.31091 0.0820113
795795 0 0
796796 −37.1398 −1.31639
797797 −25.6411 −0.908253 −0.454127 0.890937i 0.650049π-0.650049\pi
−0.454127 + 0.890937i 0.650049π0.650049\pi
798798 0 0
799799 −34.8074 −1.23140
800800 0 0
801801 −1.93584 −0.0683994
802802 −7.67627 −0.271059
803803 −23.5596 −0.831399
804804 −5.99096 −0.211285
805805 0 0
806806 1.49709 0.0527328
807807 −9.66444 −0.340204
808808 20.8181 0.732380
809809 −0.516056 −0.0181436 −0.00907179 0.999959i 0.502888π-0.502888\pi
−0.00907179 + 0.999959i 0.502888π0.502888\pi
810810 0 0
811811 −24.0377 −0.844078 −0.422039 0.906578i 0.638685π-0.638685\pi
−0.422039 + 0.906578i 0.638685π0.638685\pi
812812 20.3972 0.715800
813813 −13.5060 −0.473676
814814 −6.45123 −0.226115
815815 0 0
816816 −30.2934 −1.06048
817817 0 0
818818 11.7150 0.409605
819819 7.51232 0.262502
820820 0 0
821821 38.7573 1.35264 0.676320 0.736608i 0.263574π-0.263574\pi
0.676320 + 0.736608i 0.263574π0.263574\pi
822822 −15.2022 −0.530238
823823 3.48827 0.121593 0.0607967 0.998150i 0.480636π-0.480636\pi
0.0607967 + 0.998150i 0.480636π0.480636\pi
824824 −22.0507 −0.768173
825825 0 0
826826 2.36168 0.0821734
827827 −27.4821 −0.955645 −0.477823 0.878456i 0.658574π-0.658574\pi
−0.477823 + 0.878456i 0.658574π0.658574\pi
828828 8.67395 0.301441
829829 −8.60945 −0.299019 −0.149509 0.988760i 0.547769π-0.547769\pi
−0.149509 + 0.988760i 0.547769π0.547769\pi
830830 0 0
831831 7.75545 0.269034
832832 15.6197 0.541516
833833 15.0648 0.521963
834834 −10.8394 −0.375336
835835 0 0
836836 0 0
837837 −3.21917 −0.111271
838838 −2.59415 −0.0896133
839839 11.9397 0.412206 0.206103 0.978530i 0.433922π-0.433922\pi
0.206103 + 0.978530i 0.433922π0.433922\pi
840840 0 0
841841 1.30126 0.0448710
842842 −11.3695 −0.391817
843843 61.0520 2.10274
844844 −12.6079 −0.433983
845845 0 0
846846 −2.37037 −0.0814949
847847 11.7103 0.402370
848848 −10.8931 −0.374069
849849 −20.7954 −0.713695
850850 0 0
851851 36.2175 1.24152
852852 −34.6894 −1.18844
853853 28.9175 0.990117 0.495059 0.868860i 0.335147π-0.335147\pi
0.495059 + 0.868860i 0.335147π0.335147\pi
854854 9.20518 0.314995
855855 0 0
856856 25.8964 0.885121
857857 −55.2147 −1.88610 −0.943050 0.332651i 0.892057π-0.892057\pi
−0.943050 + 0.332651i 0.892057π0.892057\pi
858858 −8.91431 −0.304330
859859 −26.6572 −0.909532 −0.454766 0.890611i 0.650277π-0.650277\pi
−0.454766 + 0.890611i 0.650277π0.650277\pi
860860 0 0
861861 26.3666 0.898570
862862 8.43154 0.287180
863863 −1.21123 −0.0412307 −0.0206154 0.999787i 0.506563π-0.506563\pi
−0.0206154 + 0.999787i 0.506563π0.506563\pi
864864 19.9006 0.677031
865865 0 0
866866 −3.82551 −0.129996
867867 25.3238 0.860042
868868 2.80810 0.0953131
869869 −5.56176 −0.188670
870870 0 0
871871 −7.48522 −0.253627
872872 −32.7344 −1.10853
873873 5.65148 0.191274
874874 0 0
875875 0 0
876876 −35.9476 −1.21456
877877 49.5420 1.67291 0.836457 0.548032i 0.184623π-0.184623\pi
0.836457 + 0.548032i 0.184623π0.184623\pi
878878 0.923597 0.0311699
879879 38.4055 1.29538
880880 0 0
881881 −30.5639 −1.02972 −0.514861 0.857273i 0.672157π-0.672157\pi
−0.514861 + 0.857273i 0.672157π0.672157\pi
882882 1.02590 0.0345440
883883 5.57841 0.187729 0.0938643 0.995585i 0.470078π-0.470078\pi
0.0938643 + 0.995585i 0.470078π0.470078\pi
884884 −43.2521 −1.45473
885885 0 0
886886 5.41061 0.181773
887887 −0.666360 −0.0223742 −0.0111871 0.999937i 0.503561π-0.503561\pi
−0.0111871 + 0.999937i 0.503561π0.503561\pi
888888 −20.7923 −0.697744
889889 43.7628 1.46776
890890 0 0
891891 24.9048 0.834343
892892 34.9497 1.17020
893893 0 0
894894 −3.83310 −0.128198
895895 0 0
896896 −22.5994 −0.754992
897897 50.0454 1.67097
898898 −3.36760 −0.112378
899899 4.17161 0.139131
900900 0 0
901901 21.0682 0.701882
902902 −6.77530 −0.225593
903903 −12.7706 −0.424978
904904 3.26238 0.108505
905905 0 0
906906 −3.90984 −0.129896
907907 52.7812 1.75257 0.876286 0.481792i 0.160014π-0.160014\pi
0.876286 + 0.481792i 0.160014π0.160014\pi
908908 11.7593 0.390246
909909 10.1145 0.335477
910910 0 0
911911 −13.0586 −0.432650 −0.216325 0.976321i 0.569407π-0.569407\pi
−0.216325 + 0.976321i 0.569407π0.569407\pi
912912 0 0
913913 16.2861 0.538992
914914 −6.29357 −0.208173
915915 0 0
916916 36.6814 1.21199
917917 3.44712 0.113834
918918 −10.4451 −0.344739
919919 −46.0539 −1.51918 −0.759589 0.650403i 0.774600π-0.774600\pi
−0.759589 + 0.650403i 0.774600π0.774600\pi
920920 0 0
921921 44.2751 1.45892
922922 7.94271 0.261579
923923 −43.3416 −1.42661
924924 −16.7206 −0.550067
925925 0 0
926926 7.45627 0.245028
927927 −10.7133 −0.351872
928928 −25.7885 −0.846548
929929 30.9736 1.01621 0.508105 0.861295i 0.330346π-0.330346\pi
0.508105 + 0.861295i 0.330346π0.330346\pi
930930 0 0
931931 0 0
932932 21.6649 0.709657
933933 48.6426 1.59249
934934 7.18568 0.235123
935935 0 0
936936 −6.22170 −0.203363
937937 −34.8133 −1.13730 −0.568650 0.822580i 0.692534π-0.692534\pi
−0.568650 + 0.822580i 0.692534π0.692534\pi
938938 1.57680 0.0514845
939939 43.4470 1.41784
940940 0 0
941941 −16.2153 −0.528604 −0.264302 0.964440i 0.585142π-0.585142\pi
−0.264302 + 0.964440i 0.585142π0.585142\pi
942942 −17.4492 −0.568525
943943 38.0368 1.23865
944944 7.21502 0.234829
945945 0 0
946946 3.28159 0.106694
947947 14.6403 0.475746 0.237873 0.971296i 0.423550π-0.423550\pi
0.237873 + 0.971296i 0.423550π0.423550\pi
948948 −8.48624 −0.275620
949949 −44.9136 −1.45796
950950 0 0
951951 3.99112 0.129421
952952 19.2459 0.623763
953953 40.8271 1.32252 0.661260 0.750156i 0.270022π-0.270022\pi
0.661260 + 0.750156i 0.270022π0.270022\pi
954954 1.43473 0.0464512
955955 0 0
956956 11.0131 0.356190
957957 −24.8395 −0.802947
958958 −3.32352 −0.107378
959959 −35.6269 −1.15045
960960 0 0
961961 −30.4257 −0.981474
962962 −12.2985 −0.396520
963963 12.5818 0.405442
964964 13.0775 0.421197
965965 0 0
966966 −10.5423 −0.339194
967967 −24.1608 −0.776958 −0.388479 0.921458i 0.626999π-0.626999\pi
−0.388479 + 0.921458i 0.626999π0.626999\pi
968968 −9.69845 −0.311720
969969 0 0
970970 0 0
971971 27.7592 0.890836 0.445418 0.895323i 0.353055π-0.353055\pi
0.445418 + 0.895323i 0.353055π0.353055\pi
972972 15.0865 0.483899
973973 −25.4024 −0.814364
974974 9.07201 0.290686
975975 0 0
976976 28.1221 0.900168
977977 −3.56499 −0.114054 −0.0570270 0.998373i 0.518162π-0.518162\pi
−0.0570270 + 0.998373i 0.518162π0.518162\pi
978978 1.12635 0.0360166
979979 5.38337 0.172053
980980 0 0
981981 −15.9040 −0.507776
982982 −4.19403 −0.133837
983983 1.63550 0.0521643 0.0260822 0.999660i 0.491697π-0.491697\pi
0.0260822 + 0.999660i 0.491697π0.491697\pi
984984 −21.8368 −0.696131
985985 0 0
986986 13.5354 0.431056
987987 −25.6523 −0.816521
988988 0 0
989989 −18.4230 −0.585818
990990 0 0
991991 1.50405 0.0477778 0.0238889 0.999715i 0.492395π-0.492395\pi
0.0238889 + 0.999715i 0.492395π0.492395\pi
992992 −3.55033 −0.112723
993993 65.8526 2.08977
994994 9.13015 0.289591
995995 0 0
996996 24.8497 0.787392
997997 51.4138 1.62829 0.814146 0.580660i 0.197205π-0.197205\pi
0.814146 + 0.580660i 0.197205π0.197205\pi
998998 10.7675 0.340841
999999 26.4453 0.836692
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 9025.2.a.cu.1.10 24
5.2 odd 4 1805.2.b.k.1084.10 24
5.3 odd 4 1805.2.b.k.1084.15 24
5.4 even 2 inner 9025.2.a.cu.1.15 24
19.4 even 9 475.2.l.f.301.4 48
19.5 even 9 475.2.l.f.101.4 48
19.18 odd 2 9025.2.a.ct.1.15 24
95.4 even 18 475.2.l.f.301.5 48
95.18 even 4 1805.2.b.l.1084.10 24
95.23 odd 36 95.2.p.a.54.4 yes 48
95.24 even 18 475.2.l.f.101.5 48
95.37 even 4 1805.2.b.l.1084.15 24
95.42 odd 36 95.2.p.a.54.5 yes 48
95.43 odd 36 95.2.p.a.44.5 yes 48
95.62 odd 36 95.2.p.a.44.4 48
95.94 odd 2 9025.2.a.ct.1.10 24
285.23 even 36 855.2.da.b.244.5 48
285.62 even 36 855.2.da.b.424.5 48
285.137 even 36 855.2.da.b.244.4 48
285.233 even 36 855.2.da.b.424.4 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.p.a.44.4 48 95.62 odd 36
95.2.p.a.44.5 yes 48 95.43 odd 36
95.2.p.a.54.4 yes 48 95.23 odd 36
95.2.p.a.54.5 yes 48 95.42 odd 36
475.2.l.f.101.4 48 19.5 even 9
475.2.l.f.101.5 48 95.24 even 18
475.2.l.f.301.4 48 19.4 even 9
475.2.l.f.301.5 48 95.4 even 18
855.2.da.b.244.4 48 285.137 even 36
855.2.da.b.244.5 48 285.23 even 36
855.2.da.b.424.4 48 285.233 even 36
855.2.da.b.424.5 48 285.62 even 36
1805.2.b.k.1084.10 24 5.2 odd 4
1805.2.b.k.1084.15 24 5.3 odd 4
1805.2.b.l.1084.10 24 95.18 even 4
1805.2.b.l.1084.15 24 95.37 even 4
9025.2.a.ct.1.10 24 95.94 odd 2
9025.2.a.ct.1.15 24 19.18 odd 2
9025.2.a.cu.1.10 24 1.1 even 1 trivial
9025.2.a.cu.1.15 24 5.4 even 2 inner