Properties

Label 7225.2.a.bp.1.11
Level 72257225
Weight 22
Character 7225.1
Self dual yes
Analytic conductor 57.69257.692
Analytic rank 00
Dimension 1212
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [7225,2,Mod(1,7225)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7225, 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("7225.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 7225=52172 7225 = 5^{2} \cdot 17^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7225.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [12,0,0,12,0,0,0] 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: 57.691915460457.6919154604
Analytic rank: 00
Dimension: 1212
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x1230x10+343x81860x6+4823x45230x2+1681 x^{12} - 30x^{10} + 343x^{8} - 1860x^{6} + 4823x^{4} - 5230x^{2} + 1681 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 23 2^{3}
Twist minimal: no (minimal twist has level 85)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.11
Root 3.075923.07592 of defining polynomial
Character χ\chi == 7225.1

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+2.38621q23.15462q3+3.69399q47.52757q6+0.219993q7+4.04223q8+6.95160q9+0.524950q1111.6531q12+1.96713q13+0.524950q14+2.25761q16+16.5880q18+4.00000q190.693995q21+1.25264q220.372668q2312.7517q24+4.69399q2612.4658q27+0.812655q28+7.00262q29+2.92062q312.69733q321.65602q33+25.6792q365.71657q37+9.54484q386.20555q390.797070q411.65602q422.49417q43+1.93916q440.889263q46+6.73955q477.12189q486.95160q49+7.26658q525.92169q5329.7460q54+0.889263q5612.6185q57+16.7097q58+6.00000q59+5.65685q61+6.96921q62+1.52931q6310.9516q643.95160q66+11.5120q67+1.17562q697.16326q71+28.1000q721.18532q7313.6409q74+14.7760q76+0.115486q7714.8078q78+6.73050q79+18.4700q811.90197q826.11732q832.56361q845.95160q8622.0906q87+2.12197q88+15.9852q89+0.432757q911.37663q929.21344q93+16.0820q94+8.50903q96+9.21517q9716.5880q98+3.64925q99+O(q100)q+2.38621 q^{2} -3.15462 q^{3} +3.69399 q^{4} -7.52757 q^{6} +0.219993 q^{7} +4.04223 q^{8} +6.95160 q^{9} +0.524950 q^{11} -11.6531 q^{12} +1.96713 q^{13} +0.524950 q^{14} +2.25761 q^{16} +16.5880 q^{18} +4.00000 q^{19} -0.693995 q^{21} +1.25264 q^{22} -0.372668 q^{23} -12.7517 q^{24} +4.69399 q^{26} -12.4658 q^{27} +0.812655 q^{28} +7.00262 q^{29} +2.92062 q^{31} -2.69733 q^{32} -1.65602 q^{33} +25.6792 q^{36} -5.71657 q^{37} +9.54484 q^{38} -6.20555 q^{39} -0.797070 q^{41} -1.65602 q^{42} -2.49417 q^{43} +1.93916 q^{44} -0.889263 q^{46} +6.73955 q^{47} -7.12189 q^{48} -6.95160 q^{49} +7.26658 q^{52} -5.92169 q^{53} -29.7460 q^{54} +0.889263 q^{56} -12.6185 q^{57} +16.7097 q^{58} +6.00000 q^{59} +5.65685 q^{61} +6.96921 q^{62} +1.52931 q^{63} -10.9516 q^{64} -3.95160 q^{66} +11.5120 q^{67} +1.17562 q^{69} -7.16326 q^{71} +28.1000 q^{72} -1.18532 q^{73} -13.6409 q^{74} +14.7760 q^{76} +0.115486 q^{77} -14.8078 q^{78} +6.73050 q^{79} +18.4700 q^{81} -1.90197 q^{82} -6.11732 q^{83} -2.56361 q^{84} -5.95160 q^{86} -22.0906 q^{87} +2.12197 q^{88} +15.9852 q^{89} +0.432757 q^{91} -1.37663 q^{92} -9.21344 q^{93} +16.0820 q^{94} +8.50903 q^{96} +9.21517 q^{97} -16.5880 q^{98} +3.64925 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+12q4+28q9+4q16+48q19+24q21+24q26+68q3628q49+72q5976q64+8q66+88q69+48q76+60q8140q8416q8616q89++96q94+O(q100) 12 q + 12 q^{4} + 28 q^{9} + 4 q^{16} + 48 q^{19} + 24 q^{21} + 24 q^{26} + 68 q^{36} - 28 q^{49} + 72 q^{59} - 76 q^{64} + 8 q^{66} + 88 q^{69} + 48 q^{76} + 60 q^{81} - 40 q^{84} - 16 q^{86} - 16 q^{89}+ \cdots + 96 q^{94}+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 2.38621 1.68730 0.843652 0.536890i 0.180401π-0.180401\pi
0.843652 + 0.536890i 0.180401π0.180401\pi
33 −3.15462 −1.82132 −0.910659 0.413158i 0.864426π-0.864426\pi
−0.910659 + 0.413158i 0.864426π0.864426\pi
44 3.69399 1.84700
55 0 0
66 −7.52757 −3.07312
77 0.219993 0.0831497 0.0415749 0.999135i 0.486762π-0.486762\pi
0.0415749 + 0.999135i 0.486762π0.486762\pi
88 4.04223 1.42914
99 6.95160 2.31720
1010 0 0
1111 0.524950 0.158278 0.0791392 0.996864i 0.474783π-0.474783\pi
0.0791392 + 0.996864i 0.474783π0.474783\pi
1212 −11.6531 −3.36397
1313 1.96713 0.545585 0.272792 0.962073i 0.412053π-0.412053\pi
0.272792 + 0.962073i 0.412053π0.412053\pi
1414 0.524950 0.140299
1515 0 0
1616 2.25761 0.564402
1717 0 0
1818 16.5880 3.90982
1919 4.00000 0.917663 0.458831 0.888523i 0.348268π-0.348268\pi
0.458831 + 0.888523i 0.348268π0.348268\pi
2020 0 0
2121 −0.693995 −0.151442
2222 1.25264 0.267064
2323 −0.372668 −0.0777066 −0.0388533 0.999245i 0.512371π-0.512371\pi
−0.0388533 + 0.999245i 0.512371π0.512371\pi
2424 −12.7517 −2.60292
2525 0 0
2626 4.69399 0.920568
2727 −12.4658 −2.39904
2828 0.812655 0.153577
2929 7.00262 1.30035 0.650177 0.759783i 0.274695π-0.274695\pi
0.650177 + 0.759783i 0.274695π0.274695\pi
3030 0 0
3131 2.92062 0.524559 0.262279 0.964992i 0.415526π-0.415526\pi
0.262279 + 0.964992i 0.415526π0.415526\pi
3232 −2.69733 −0.476825
3333 −1.65602 −0.288276
3434 0 0
3535 0 0
3636 25.6792 4.27986
3737 −5.71657 −0.939798 −0.469899 0.882720i 0.655710π-0.655710\pi
−0.469899 + 0.882720i 0.655710π0.655710\pi
3838 9.54484 1.54838
3939 −6.20555 −0.993684
4040 0 0
4141 −0.797070 −0.124481 −0.0622407 0.998061i 0.519825π-0.519825\pi
−0.0622407 + 0.998061i 0.519825π0.519825\pi
4242 −1.65602 −0.255529
4343 −2.49417 −0.380357 −0.190178 0.981750i 0.560907π-0.560907\pi
−0.190178 + 0.981750i 0.560907π0.560907\pi
4444 1.93916 0.292340
4545 0 0
4646 −0.889263 −0.131115
4747 6.73955 0.983065 0.491532 0.870859i 0.336437π-0.336437\pi
0.491532 + 0.870859i 0.336437π0.336437\pi
4848 −7.12189 −1.02796
4949 −6.95160 −0.993086
5050 0 0
5151 0 0
5252 7.26658 1.00769
5353 −5.92169 −0.813406 −0.406703 0.913560i 0.633322π-0.633322\pi
−0.406703 + 0.913560i 0.633322π0.633322\pi
5454 −29.7460 −4.04792
5555 0 0
5656 0.889263 0.118833
5757 −12.6185 −1.67136
5858 16.7097 2.19409
5959 6.00000 0.781133 0.390567 0.920575i 0.372279π-0.372279\pi
0.390567 + 0.920575i 0.372279π0.372279\pi
6060 0 0
6161 5.65685 0.724286 0.362143 0.932123i 0.382045π-0.382045\pi
0.362143 + 0.932123i 0.382045π0.382045\pi
6262 6.96921 0.885091
6363 1.52931 0.192675
6464 −10.9516 −1.36895
6565 0 0
6666 −3.95160 −0.486409
6767 11.5120 1.40641 0.703206 0.710987i 0.251751π-0.251751\pi
0.703206 + 0.710987i 0.251751π0.251751\pi
6868 0 0
6969 1.17562 0.141528
7070 0 0
7171 −7.16326 −0.850123 −0.425061 0.905165i 0.639747π-0.639747\pi
−0.425061 + 0.905165i 0.639747π0.639747\pi
7272 28.1000 3.31161
7373 −1.18532 −0.138731 −0.0693657 0.997591i 0.522098π-0.522098\pi
−0.0693657 + 0.997591i 0.522098π0.522098\pi
7474 −13.6409 −1.58573
7575 0 0
7676 14.7760 1.69492
7777 0.115486 0.0131608
7878 −14.8078 −1.67665
7979 6.73050 0.757241 0.378620 0.925552i 0.376399π-0.376399\pi
0.378620 + 0.925552i 0.376399π0.376399\pi
8080 0 0
8181 18.4700 2.05222
8282 −1.90197 −0.210038
8383 −6.11732 −0.671463 −0.335731 0.941958i 0.608983π-0.608983\pi
−0.335731 + 0.941958i 0.608983π0.608983\pi
8484 −2.56361 −0.279713
8585 0 0
8686 −5.95160 −0.641778
8787 −22.0906 −2.36836
8888 2.12197 0.226203
8989 15.9852 1.69443 0.847213 0.531253i 0.178279π-0.178279\pi
0.847213 + 0.531253i 0.178279π0.178279\pi
9090 0 0
9191 0.432757 0.0453652
9292 −1.37663 −0.143524
9393 −9.21344 −0.955389
9494 16.0820 1.65873
9595 0 0
9696 8.50903 0.868449
9797 9.21517 0.935659 0.467829 0.883819i 0.345036π-0.345036\pi
0.467829 + 0.883819i 0.345036π0.345036\pi
9898 −16.5880 −1.67564
9999 3.64925 0.366763
100100 0 0
101101 −7.20921 −0.717343 −0.358672 0.933464i 0.616770π-0.616770\pi
−0.358672 + 0.933464i 0.616770π0.616770\pi
102102 0 0
103103 −9.52456 −0.938482 −0.469241 0.883070i 0.655472π-0.655472\pi
−0.469241 + 0.883070i 0.655472π0.655472\pi
104104 7.95160 0.779719
105105 0 0
106106 −14.1304 −1.37246
107107 10.7838 1.04251 0.521255 0.853401i 0.325464π-0.325464\pi
0.521255 + 0.853401i 0.325464π0.325464\pi
108108 −46.0486 −4.43103
109109 −14.0737 −1.34802 −0.674008 0.738724i 0.735429π-0.735429\pi
−0.674008 + 0.738724i 0.735429π0.735429\pi
110110 0 0
111111 18.0336 1.71167
112112 0.496659 0.0469299
113113 7.18921 0.676304 0.338152 0.941092i 0.390198π-0.390198\pi
0.338152 + 0.941092i 0.390198π0.390198\pi
114114 −30.1103 −2.82009
115115 0 0
116116 25.8677 2.40175
117117 13.6747 1.26423
118118 14.3173 1.31801
119119 0 0
120120 0 0
121121 −10.7244 −0.974948
122122 13.4984 1.22209
123123 2.51445 0.226720
124124 10.7888 0.968859
125125 0 0
126126 3.64925 0.325101
127127 9.74047 0.864327 0.432163 0.901795i 0.357750π-0.357750\pi
0.432163 + 0.901795i 0.357750π0.357750\pi
128128 −20.7382 −1.83301
129129 7.86814 0.692751
130130 0 0
131131 19.6859 1.71996 0.859980 0.510327i 0.170476π-0.170476\pi
0.859980 + 0.510327i 0.170476π0.170476\pi
132132 −6.11732 −0.532444
133133 0.879974 0.0763034
134134 27.4700 2.37304
135135 0 0
136136 0 0
137137 −4.65693 −0.397869 −0.198934 0.980013i 0.563748π-0.563748\pi
−0.198934 + 0.980013i 0.563748π0.563748\pi
138138 2.80528 0.238802
139139 5.24785 0.445117 0.222558 0.974919i 0.428559π-0.428559\pi
0.222558 + 0.974919i 0.428559π0.428559\pi
140140 0 0
141141 −21.2607 −1.79047
142142 −17.0930 −1.43442
143143 1.03265 0.0863544
144144 15.6940 1.30783
145145 0 0
146146 −2.82843 −0.234082
147147 21.9296 1.80873
148148 −21.1170 −1.73581
149149 8.74239 0.716205 0.358102 0.933682i 0.383424π-0.383424\pi
0.358102 + 0.933682i 0.383424π0.383424\pi
150150 0 0
151151 15.9032 1.29418 0.647092 0.762412i 0.275985π-0.275985\pi
0.647092 + 0.762412i 0.275985π0.275985\pi
152152 16.1689 1.31147
153153 0 0
154154 0.275573 0.0222063
155155 0 0
156156 −22.9233 −1.83533
157157 10.0719 0.803823 0.401911 0.915679i 0.368346π-0.368346\pi
0.401911 + 0.915679i 0.368346π0.368346\pi
158158 16.0604 1.27770
159159 18.6806 1.48147
160160 0 0
161161 −0.0819845 −0.00646128
162162 44.0732 3.46272
163163 9.58784 0.750978 0.375489 0.926827i 0.377475π-0.377475\pi
0.375489 + 0.926827i 0.377475π0.377475\pi
164164 −2.94437 −0.229917
165165 0 0
166166 −14.5972 −1.13296
167167 5.34390 0.413524 0.206762 0.978391i 0.433707π-0.433707\pi
0.206762 + 0.978391i 0.433707π0.433707\pi
168168 −2.80528 −0.216432
169169 −9.13038 −0.702337
170170 0 0
171171 27.8064 2.12641
172172 −9.21344 −0.702518
173173 −17.4551 −1.32708 −0.663542 0.748139i 0.730948π-0.730948\pi
−0.663542 + 0.748139i 0.730948π0.730948\pi
174174 −52.7128 −3.99614
175175 0 0
176176 1.18513 0.0893327
177177 −18.9277 −1.42269
178178 38.1440 2.85901
179179 −21.3248 −1.59389 −0.796945 0.604052i 0.793552π-0.793552\pi
−0.796945 + 0.604052i 0.793552π0.793552\pi
180180 0 0
181181 14.4380 1.07317 0.536584 0.843847i 0.319714π-0.319714\pi
0.536584 + 0.843847i 0.319714π0.319714\pi
182182 1.03265 0.0765450
183183 −17.8452 −1.31916
184184 −1.50641 −0.111054
185185 0 0
186186 −21.9852 −1.61203
187187 0 0
188188 24.8959 1.81572
189189 −2.74239 −0.199480
190190 0 0
191191 6.74239 0.487862 0.243931 0.969793i 0.421563π-0.421563\pi
0.243931 + 0.969793i 0.421563π0.421563\pi
192192 34.5481 2.49329
193193 14.6551 1.05490 0.527448 0.849587i 0.323149π-0.323149\pi
0.527448 + 0.849587i 0.323149π0.323149\pi
194194 21.9893 1.57874
195195 0 0
196196 −25.6792 −1.83423
197197 0.869327 0.0619370 0.0309685 0.999520i 0.490141π-0.490141\pi
0.0309685 + 0.999520i 0.490141π0.490141\pi
198198 8.70787 0.618841
199199 13.3004 0.942838 0.471419 0.881909i 0.343742π-0.343742\pi
0.471419 + 0.881909i 0.343742π0.343742\pi
200200 0 0
201201 −36.3159 −2.56152
202202 −17.2027 −1.21038
203203 1.54053 0.108124
204204 0 0
205205 0 0
206206 −22.7276 −1.58351
207207 −2.59064 −0.180062
208208 4.44102 0.307929
209209 2.09980 0.145246
210210 0 0
211211 17.7914 1.22481 0.612405 0.790544i 0.290202π-0.290202\pi
0.612405 + 0.790544i 0.290202π0.290202\pi
212212 −21.8747 −1.50236
213213 22.5973 1.54834
214214 25.7324 1.75903
215215 0 0
216216 −50.3895 −3.42857
217217 0.642517 0.0436169
218218 −33.5828 −2.27451
219219 3.73924 0.252674
220220 0 0
221221 0 0
222222 43.0319 2.88811
223223 1.96713 0.131729 0.0658645 0.997829i 0.479019π-0.479019\pi
0.0658645 + 0.997829i 0.479019π0.479019\pi
224224 −0.593394 −0.0396478
225225 0 0
226226 17.1550 1.14113
227227 11.9585 0.793712 0.396856 0.917881i 0.370101π-0.370101\pi
0.396856 + 0.917881i 0.370101π0.370101\pi
228228 −46.6125 −3.08699
229229 9.30601 0.614958 0.307479 0.951555i 0.400515π-0.400515\pi
0.307479 + 0.951555i 0.400515π0.400515\pi
230230 0 0
231231 −0.364313 −0.0239700
232232 28.3062 1.85839
233233 −25.8009 −1.69027 −0.845137 0.534550i 0.820481π-0.820481\pi
−0.845137 + 0.534550i 0.820481π0.820481\pi
234234 32.6308 2.13314
235235 0 0
236236 22.1640 1.44275
237237 −21.2322 −1.37918
238238 0 0
239239 29.2912 1.89469 0.947345 0.320215i 0.103755π-0.103755\pi
0.947345 + 0.320215i 0.103755π0.103755\pi
240240 0 0
241241 8.48528 0.546585 0.273293 0.961931i 0.411887π-0.411887\pi
0.273293 + 0.961931i 0.411887π0.411887\pi
242242 −25.5907 −1.64503
243243 −20.8683 −1.33870
244244 20.8964 1.33775
245245 0 0
246246 6.00000 0.382546
247247 7.86854 0.500663
248248 11.8058 0.749670
249249 19.2978 1.22295
250250 0 0
251251 1.77282 0.111900 0.0559498 0.998434i 0.482181π-0.482181\pi
0.0559498 + 0.998434i 0.482181π0.482181\pi
252252 5.64925 0.355869
253253 −0.195632 −0.0122993
254254 23.2428 1.45838
255255 0 0
256256 −27.5824 −1.72390
257257 −7.40235 −0.461746 −0.230873 0.972984i 0.574158π-0.574158\pi
−0.230873 + 0.972984i 0.574158π0.574158\pi
258258 18.7750 1.16888
259259 −1.25761 −0.0781440
260260 0 0
261261 48.6795 3.01318
262262 46.9746 2.90210
263263 7.67291 0.473132 0.236566 0.971615i 0.423978π-0.423978\pi
0.236566 + 0.971615i 0.423978π0.423978\pi
264264 −6.69399 −0.411987
265265 0 0
266266 2.09980 0.128747
267267 −50.4271 −3.08609
268268 42.5252 2.59764
269269 7.87260 0.480001 0.240000 0.970773i 0.422852π-0.422852\pi
0.240000 + 0.970773i 0.422852π0.422852\pi
270270 0 0
271271 18.0672 1.09750 0.548751 0.835986i 0.315103π-0.315103\pi
0.548751 + 0.835986i 0.315103π0.315103\pi
272272 0 0
273273 −1.36518 −0.0826245
274274 −11.1124 −0.671326
275275 0 0
276276 4.34275 0.261403
277277 −26.5569 −1.59565 −0.797824 0.602890i 0.794016π-0.794016\pi
−0.797824 + 0.602890i 0.794016π0.794016\pi
278278 12.5225 0.751047
279279 20.3030 1.21551
280280 0 0
281281 13.7728 0.821618 0.410809 0.911721i 0.365246π-0.365246\pi
0.410809 + 0.911721i 0.365246π0.365246\pi
282282 −50.7325 −3.02108
283283 13.7471 0.817181 0.408591 0.912718i 0.366020π-0.366020\pi
0.408591 + 0.912718i 0.366020π0.366020\pi
284284 −26.4611 −1.57017
285285 0 0
286286 2.46411 0.145706
287287 −0.175350 −0.0103506
288288 −18.7507 −1.10490
289289 0 0
290290 0 0
291291 −29.0703 −1.70413
292292 −4.37857 −0.256237
293293 19.8873 1.16183 0.580913 0.813966i 0.302696π-0.302696\pi
0.580913 + 0.813966i 0.302696π0.302696\pi
294294 52.3287 3.05187
295295 0 0
296296 −23.1077 −1.34311
297297 −6.54392 −0.379717
298298 20.8612 1.20846
299299 −0.733088 −0.0423955
300300 0 0
301301 −0.548700 −0.0316266
302302 37.9484 2.18368
303303 22.7423 1.30651
304304 9.03043 0.517931
305305 0 0
306306 0 0
307307 −14.9598 −0.853799 −0.426900 0.904299i 0.640394π-0.640394\pi
−0.426900 + 0.904299i 0.640394π0.640394\pi
308308 0.426603 0.0243080
309309 30.0463 1.70928
310310 0 0
311311 29.6538 1.68151 0.840756 0.541414i 0.182111π-0.182111\pi
0.840756 + 0.541414i 0.182111π0.182111\pi
312312 −25.0843 −1.42012
313313 14.3784 0.812716 0.406358 0.913714i 0.366799π-0.366799\pi
0.406358 + 0.913714i 0.366799π0.366799\pi
314314 24.0336 1.35629
315315 0 0
316316 24.8624 1.39862
317317 −13.7751 −0.773687 −0.386843 0.922145i 0.626435π-0.626435\pi
−0.386843 + 0.922145i 0.626435π0.626435\pi
318318 44.5759 2.49969
319319 3.67603 0.205818
320320 0 0
321321 −34.0188 −1.89874
322322 −0.195632 −0.0109021
323323 0 0
324324 68.2280 3.79044
325325 0 0
326326 22.8786 1.26713
327327 44.3971 2.45516
328328 −3.22194 −0.177902
329329 1.48266 0.0817415
330330 0 0
331331 −20.1640 −1.10831 −0.554156 0.832413i 0.686959π-0.686959\pi
−0.554156 + 0.832413i 0.686959π0.686959\pi
332332 −22.5973 −1.24019
333333 −39.7393 −2.17770
334334 12.7517 0.697740
335335 0 0
336336 −1.56677 −0.0854742
337337 −28.5829 −1.55701 −0.778504 0.627640i 0.784021π-0.784021\pi
−0.778504 + 0.627640i 0.784021π0.784021\pi
338338 −21.7870 −1.18506
339339 −22.6792 −1.23176
340340 0 0
341341 1.53318 0.0830264
342342 66.3519 3.58790
343343 −3.06926 −0.165725
344344 −10.0820 −0.543584
345345 0 0
346346 −41.6514 −2.23919
347347 −10.9365 −0.587101 −0.293551 0.955944i 0.594837π-0.594837\pi
−0.293551 + 0.955944i 0.594837π0.594837\pi
348348 −81.6025 −4.37435
349349 0.645598 0.0345581 0.0172790 0.999851i 0.494500π-0.494500\pi
0.0172790 + 0.999851i 0.494500π0.494500\pi
350350 0 0
351351 −24.5219 −1.30888
352352 −1.41596 −0.0754711
353353 14.3022 0.761229 0.380615 0.924734i 0.375712π-0.375712\pi
0.380615 + 0.924734i 0.375712π0.375712\pi
354354 −45.1654 −2.40052
355355 0 0
356356 59.0492 3.12960
357357 0 0
358358 −50.8854 −2.68938
359359 −15.6760 −0.827349 −0.413675 0.910425i 0.635755π-0.635755\pi
−0.413675 + 0.910425i 0.635755π0.635755\pi
360360 0 0
361361 −3.00000 −0.157895
362362 34.4521 1.81076
363363 33.8315 1.77569
364364 1.59860 0.0837895
365365 0 0
366366 −42.5824 −2.22582
367367 −21.9010 −1.14322 −0.571610 0.820525i 0.693681π-0.693681\pi
−0.571610 + 0.820525i 0.693681π0.693681\pi
368368 −0.841338 −0.0438578
369369 −5.54091 −0.288448
370370 0 0
371371 −1.30273 −0.0676345
372372 −34.0344 −1.76460
373373 6.50858 0.337002 0.168501 0.985702i 0.446107π-0.446107\pi
0.168501 + 0.985702i 0.446107π0.446107\pi
374374 0 0
375375 0 0
376376 27.2428 1.40494
377377 13.7751 0.709454
378378 −6.54392 −0.336583
379379 −7.52757 −0.386666 −0.193333 0.981133i 0.561930π-0.561930\pi
−0.193333 + 0.981133i 0.561930π0.561930\pi
380380 0 0
381381 −30.7274 −1.57421
382382 16.0888 0.823172
383383 −24.7752 −1.26595 −0.632976 0.774172i 0.718167π-0.718167\pi
−0.632976 + 0.774172i 0.718167π0.718167\pi
384384 65.4209 3.33850
385385 0 0
386386 34.9701 1.77993
387387 −17.3385 −0.881363
388388 34.0408 1.72816
389389 23.6971 1.20149 0.600747 0.799440i 0.294870π-0.294870\pi
0.600747 + 0.799440i 0.294870π0.294870\pi
390390 0 0
391391 0 0
392392 −28.1000 −1.41926
393393 −62.1013 −3.13260
394394 2.07440 0.104507
395395 0 0
396396 13.4803 0.677410
397397 27.7135 1.39090 0.695451 0.718573i 0.255205π-0.255205\pi
0.695451 + 0.718573i 0.255205π0.255205\pi
398398 31.7375 1.59086
399399 −2.77598 −0.138973
400400 0 0
401401 30.5431 1.52525 0.762624 0.646842i 0.223911π-0.223911\pi
0.762624 + 0.646842i 0.223911π0.223911\pi
402402 −86.6572 −4.32207
403403 5.74525 0.286191
404404 −26.6308 −1.32493
405405 0 0
406406 3.67603 0.182438
407407 −3.00092 −0.148750
408408 0 0
409409 −5.90321 −0.291895 −0.145947 0.989292i 0.546623π-0.546623\pi
−0.145947 + 0.989292i 0.546623π0.546623\pi
410410 0 0
411411 14.6908 0.724645
412412 −35.1837 −1.73337
413413 1.31996 0.0649510
414414 −6.18180 −0.303819
415415 0 0
416416 −5.30601 −0.260148
417417 −16.5549 −0.810699
418418 5.01057 0.245075
419419 −32.4867 −1.58708 −0.793539 0.608519i 0.791764π-0.791764\pi
−0.793539 + 0.608519i 0.791764π0.791764\pi
420420 0 0
421421 −30.1156 −1.46774 −0.733872 0.679288i 0.762289π-0.762289\pi
−0.733872 + 0.679288i 0.762289π0.762289\pi
422422 42.4540 2.06663
423423 46.8507 2.27796
424424 −23.9368 −1.16247
425425 0 0
426426 53.9220 2.61253
427427 1.24447 0.0602242
428428 39.8353 1.92551
429429 −3.25761 −0.157279
430430 0 0
431431 −8.32464 −0.400984 −0.200492 0.979695i 0.564254π-0.564254\pi
−0.200492 + 0.979695i 0.564254π0.564254\pi
432432 −28.1429 −1.35402
433433 −13.5795 −0.652591 −0.326295 0.945268i 0.605800π-0.605800\pi
−0.326295 + 0.945268i 0.605800π0.605800\pi
434434 1.53318 0.0735950
435435 0 0
436436 −51.9881 −2.48978
437437 −1.49067 −0.0713085
438438 8.92260 0.426338
439439 −20.3714 −0.972276 −0.486138 0.873882i 0.661595π-0.661595\pi
−0.486138 + 0.873882i 0.661595π0.661595\pi
440440 0 0
441441 −48.3248 −2.30118
442442 0 0
443443 2.45360 0.116574 0.0582871 0.998300i 0.481436π-0.481436\pi
0.0582871 + 0.998300i 0.481436π0.481436\pi
444444 66.6160 3.16145
445445 0 0
446446 4.69399 0.222267
447447 −27.5789 −1.30444
448448 −2.40928 −0.113828
449449 3.19720 0.150885 0.0754426 0.997150i 0.475963π-0.475963\pi
0.0754426 + 0.997150i 0.475963π0.475963\pi
450450 0 0
451451 −0.418422 −0.0197027
452452 26.5569 1.24913
453453 −50.1685 −2.35712
454454 28.5354 1.33923
455455 0 0
456456 −51.0067 −2.38861
457457 30.1803 1.41177 0.705887 0.708325i 0.250549π-0.250549\pi
0.705887 + 0.708325i 0.250549π0.250549\pi
458458 22.2061 1.03762
459459 0 0
460460 0 0
461461 5.41527 0.252214 0.126107 0.992017i 0.459752π-0.459752\pi
0.126107 + 0.992017i 0.459752π0.459752\pi
462462 −0.869327 −0.0404447
463463 −15.7574 −0.732307 −0.366153 0.930555i 0.619325π-0.619325\pi
−0.366153 + 0.930555i 0.619325π0.619325\pi
464464 15.8092 0.733923
465465 0 0
466466 −61.5664 −2.85201
467467 10.7690 0.498331 0.249166 0.968461i 0.419844π-0.419844\pi
0.249166 + 0.968461i 0.419844π0.419844\pi
468468 50.5144 2.33503
469469 2.53256 0.116943
470470 0 0
471471 −31.7729 −1.46402
472472 24.2534 1.11635
473473 −1.30931 −0.0602023
474474 −50.6644 −2.32709
475475 0 0
476476 0 0
477477 −41.1652 −1.88483
478478 69.8949 3.19692
479479 −36.9092 −1.68643 −0.843213 0.537579i 0.819339π-0.819339\pi
−0.843213 + 0.537579i 0.819339π0.819339\pi
480480 0 0
481481 −11.2453 −0.512740
482482 20.2477 0.922256
483483 0.258629 0.0117680
484484 −39.6160 −1.80073
485485 0 0
486486 −49.7961 −2.25880
487487 38.3234 1.73660 0.868299 0.496041i 0.165214π-0.165214\pi
0.868299 + 0.496041i 0.165214π0.165214\pi
488488 22.8663 1.03511
489489 −30.2460 −1.36777
490490 0 0
491491 38.0336 1.71643 0.858216 0.513289i 0.171573π-0.171573\pi
0.858216 + 0.513289i 0.171573π0.171573\pi
492492 9.28836 0.418752
493493 0 0
494494 18.7760 0.844771
495495 0 0
496496 6.59362 0.296062
497497 −1.57587 −0.0706875
498498 46.0486 2.06349
499499 −9.30610 −0.416598 −0.208299 0.978065i 0.566793π-0.566793\pi
−0.208299 + 0.978065i 0.566793π0.566793\pi
500500 0 0
501501 −16.8580 −0.753158
502502 4.23033 0.188809
503503 −1.56864 −0.0699421 −0.0349710 0.999388i 0.511134π-0.511134\pi
−0.0349710 + 0.999388i 0.511134π0.511134\pi
504504 6.18180 0.275359
505505 0 0
506506 −0.466819 −0.0207526
507507 28.8028 1.27918
508508 35.9812 1.59641
509509 24.4247 1.08261 0.541304 0.840827i 0.317931π-0.317931\pi
0.541304 + 0.840827i 0.317931π0.317931\pi
510510 0 0
511511 −0.260763 −0.0115355
512512 −24.3410 −1.07573
513513 −49.8632 −2.20151
514514 −17.6636 −0.779106
515515 0 0
516516 29.0649 1.27951
517517 3.53793 0.155598
518518 −3.00092 −0.131853
519519 55.0640 2.41704
520520 0 0
521521 −7.50829 −0.328944 −0.164472 0.986382i 0.552592π-0.552592\pi
−0.164472 + 0.986382i 0.552592π0.552592\pi
522522 116.159 5.08416
523523 −8.98247 −0.392776 −0.196388 0.980526i 0.562921π-0.562921\pi
−0.196388 + 0.980526i 0.562921π0.562921\pi
524524 72.7194 3.17676
525525 0 0
526526 18.3092 0.798317
527527 0 0
528528 −3.73864 −0.162703
529529 −22.8611 −0.993962
530530 0 0
531531 41.7096 1.81004
532532 3.25062 0.140932
533533 −1.56794 −0.0679152
534534 −120.330 −5.20718
535535 0 0
536536 46.5340 2.00996
537537 67.2715 2.90298
538538 18.7857 0.809908
539539 −3.64925 −0.157184
540540 0 0
541541 −12.7279 −0.547216 −0.273608 0.961841i 0.588217π-0.588217\pi
−0.273608 + 0.961841i 0.588217π0.588217\pi
542542 43.1121 1.85182
543543 −45.5464 −1.95458
544544 0 0
545545 0 0
546546 −3.25761 −0.139413
547547 −2.57260 −0.109997 −0.0549983 0.998486i 0.517515π-0.517515\pi
−0.0549983 + 0.998486i 0.517515π0.517515\pi
548548 −17.2027 −0.734862
549549 39.3242 1.67832
550550 0 0
551551 28.0105 1.19329
552552 4.75214 0.202264
553553 1.48067 0.0629644
554554 −63.3703 −2.69235
555555 0 0
556556 19.3855 0.822129
557557 −21.0162 −0.890487 −0.445243 0.895410i 0.646883π-0.646883\pi
−0.445243 + 0.895410i 0.646883π0.646883\pi
558558 48.4472 2.05093
559559 −4.90636 −0.207517
560560 0 0
561561 0 0
562562 32.8648 1.38632
563563 −40.5377 −1.70846 −0.854231 0.519893i 0.825972π-0.825972\pi
−0.854231 + 0.519893i 0.825972π0.825972\pi
564564 −78.5369 −3.30700
565565 0 0
566566 32.8035 1.37883
567567 4.06327 0.170641
568568 −28.9555 −1.21495
569569 −0.612010 −0.0256568 −0.0128284 0.999918i 0.504084π-0.504084\pi
−0.0128284 + 0.999918i 0.504084π0.504084\pi
570570 0 0
571571 14.8945 0.623316 0.311658 0.950194i 0.399116π-0.399116\pi
0.311658 + 0.950194i 0.399116π0.399116\pi
572572 3.81460 0.159496
573573 −21.2697 −0.888553
574574 −0.418422 −0.0174646
575575 0 0
576576 −76.1312 −3.17213
577577 37.2107 1.54910 0.774550 0.632513i 0.217976π-0.217976\pi
0.774550 + 0.632513i 0.217976π0.217976\pi
578578 0 0
579579 −46.2311 −1.92130
580580 0 0
581581 −1.34577 −0.0558319
582582 −69.3679 −2.87539
583583 −3.10859 −0.128745
584584 −4.79134 −0.198267
585585 0 0
586586 47.4552 1.96035
587587 9.60470 0.396428 0.198214 0.980159i 0.436486π-0.436486\pi
0.198214 + 0.980159i 0.436486π0.436486\pi
588588 81.0080 3.34071
589589 11.6825 0.481368
590590 0 0
591591 −2.74239 −0.112807
592592 −12.9058 −0.530424
593593 16.5206 0.678419 0.339210 0.940711i 0.389840π-0.389840\pi
0.339210 + 0.940711i 0.389840π0.389840\pi
594594 −15.6152 −0.640698
595595 0 0
596596 32.2944 1.32283
597597 −41.9576 −1.71721
598598 −1.74930 −0.0715342
599599 34.8096 1.42228 0.711140 0.703050i 0.248179π-0.248179\pi
0.711140 + 0.703050i 0.248179π0.248179\pi
600600 0 0
601601 −11.6825 −0.476538 −0.238269 0.971199i 0.576580π-0.576580\pi
−0.238269 + 0.971199i 0.576580π0.576580\pi
602602 −1.30931 −0.0533636
603603 80.0267 3.25894
604604 58.7464 2.39036
605605 0 0
606606 54.2679 2.20448
607607 26.9296 1.09304 0.546519 0.837447i 0.315953π-0.315953\pi
0.546519 + 0.837447i 0.315953π0.315953\pi
608608 −10.7893 −0.437564
609609 −4.85978 −0.196928
610610 0 0
611611 13.2576 0.536345
612612 0 0
613613 −5.43522 −0.219526 −0.109763 0.993958i 0.535009π-0.535009\pi
−0.109763 + 0.993958i 0.535009π0.535009\pi
614614 −35.6971 −1.44062
615615 0 0
616616 0.466819 0.0188087
617617 3.49860 0.140848 0.0704242 0.997517i 0.477565π-0.477565\pi
0.0704242 + 0.997517i 0.477565π0.477565\pi
618618 71.6968 2.88407
619619 12.1301 0.487549 0.243774 0.969832i 0.421614π-0.421614\pi
0.243774 + 0.969832i 0.421614π0.421614\pi
620620 0 0
621621 4.64560 0.186421
622622 70.7602 2.83722
623623 3.51664 0.140891
624624 −14.0097 −0.560837
625625 0 0
626626 34.3099 1.37130
627627 −6.62407 −0.264540
628628 37.2054 1.48466
629629 0 0
630630 0 0
631631 12.6183 0.502327 0.251164 0.967945i 0.419187π-0.419187\pi
0.251164 + 0.967945i 0.419187π0.419187\pi
632632 27.2062 1.08221
633633 −56.1250 −2.23077
634634 −32.8703 −1.30545
635635 0 0
636636 69.0062 2.73627
637637 −13.6747 −0.541813
638638 8.77178 0.347278
639639 −49.7961 −1.96991
640640 0 0
641641 −30.1997 −1.19282 −0.596408 0.802681i 0.703406π-0.703406\pi
−0.596408 + 0.802681i 0.703406π0.703406\pi
642642 −81.1759 −3.20376
643643 19.7117 0.777352 0.388676 0.921374i 0.372932π-0.372932\pi
0.388676 + 0.921374i 0.372932π0.372932\pi
644644 −0.302850 −0.0119340
645645 0 0
646646 0 0
647647 21.0418 0.827237 0.413618 0.910450i 0.364265π-0.364265\pi
0.413618 + 0.910450i 0.364265π0.364265\pi
648648 74.6598 2.93291
649649 3.14970 0.123637
650650 0 0
651651 −2.02690 −0.0794403
652652 35.4174 1.38705
653653 −38.7173 −1.51513 −0.757563 0.652762i 0.773610π-0.773610\pi
−0.757563 + 0.652762i 0.773610π0.773610\pi
654654 105.941 4.14261
655655 0 0
656656 −1.79947 −0.0702575
657657 −8.23989 −0.321469
658658 3.53793 0.137923
659659 −24.1577 −0.941049 −0.470524 0.882387i 0.655935π-0.655935\pi
−0.470524 + 0.882387i 0.655935π0.655935\pi
660660 0 0
661661 −25.7432 −1.00129 −0.500647 0.865651i 0.666905π-0.666905\pi
−0.500647 + 0.865651i 0.666905π0.666905\pi
662662 −48.1155 −1.87006
663663 0 0
664664 −24.7276 −0.959616
665665 0 0
666666 −94.8264 −3.67445
667667 −2.60965 −0.101046
668668 19.7404 0.763777
669669 −6.20555 −0.239921
670670 0 0
671671 2.96957 0.114639
672672 1.87193 0.0722113
673673 −10.4958 −0.404583 −0.202292 0.979325i 0.564839π-0.564839\pi
−0.202292 + 0.979325i 0.564839π0.564839\pi
674674 −68.2047 −2.62715
675675 0 0
676676 −33.7276 −1.29721
677677 8.48787 0.326215 0.163108 0.986608i 0.447848π-0.447848\pi
0.163108 + 0.986608i 0.447848π0.447848\pi
678678 −54.1173 −2.07836
679679 2.02728 0.0777998
680680 0 0
681681 −37.7244 −1.44560
682682 3.65849 0.140091
683683 14.2898 0.546784 0.273392 0.961903i 0.411854π-0.411854\pi
0.273392 + 0.961903i 0.411854π0.411854\pi
684684 102.717 3.92747
685685 0 0
686686 −7.32390 −0.279628
687687 −29.3569 −1.12003
688688 −5.63085 −0.214674
689689 −11.6488 −0.443782
690690 0 0
691691 −8.82584 −0.335751 −0.167875 0.985808i 0.553691π-0.553691\pi
−0.167875 + 0.985808i 0.553691π0.553691\pi
692692 −64.4789 −2.45112
693693 0.802810 0.0304962
694694 −26.0967 −0.990619
695695 0 0
696696 −89.2952 −3.38472
697697 0 0
698698 1.54053 0.0583100
699699 81.3920 3.07853
700700 0 0
701701 −18.5340 −0.700019 −0.350010 0.936746i 0.613822π-0.613822\pi
−0.350010 + 0.936746i 0.613822π0.613822\pi
702702 −58.5144 −2.20848
703703 −22.8663 −0.862418
704704 −5.74905 −0.216675
705705 0 0
706706 34.1280 1.28443
707707 −1.58598 −0.0596469
708708 −69.9188 −2.62771
709709 −25.4989 −0.957631 −0.478815 0.877916i 0.658934π-0.658934\pi
−0.478815 + 0.877916i 0.658934π0.658934\pi
710710 0 0
711711 46.7878 1.75468
712712 64.6158 2.42158
713713 −1.08842 −0.0407617
714714 0 0
715715 0 0
716716 −78.7736 −2.94391
717717 −92.4025 −3.45083
718718 −37.4063 −1.39599
719719 4.76313 0.177635 0.0888174 0.996048i 0.471691π-0.471691\pi
0.0888174 + 0.996048i 0.471691π0.471691\pi
720720 0 0
721721 −2.09534 −0.0780345
722722 −7.15863 −0.266417
723723 −26.7678 −0.995505
724724 53.3339 1.98214
725725 0 0
726726 80.7289 2.99613
727727 11.1858 0.414858 0.207429 0.978250i 0.433490π-0.433490\pi
0.207429 + 0.978250i 0.433490π0.433490\pi
728728 1.74930 0.0648334
729729 10.4216 0.385984
730730 0 0
731731 0 0
732732 −65.9201 −2.43648
733733 26.2804 0.970687 0.485344 0.874324i 0.338695π-0.338695\pi
0.485344 + 0.874324i 0.338695π0.338695\pi
734734 −52.2603 −1.92896
735735 0 0
736736 1.00521 0.0370524
737737 6.04321 0.222605
738738 −13.2218 −0.486700
739739 6.00000 0.220714 0.110357 0.993892i 0.464801π-0.464801\pi
0.110357 + 0.993892i 0.464801π0.464801\pi
740740 0 0
741741 −24.8222 −0.911867
742742 −3.10859 −0.114120
743743 34.0401 1.24881 0.624405 0.781101i 0.285341π-0.285341\pi
0.624405 + 0.781101i 0.285341π0.285341\pi
744744 −37.2428 −1.36539
745745 0 0
746746 15.5308 0.568624
747747 −42.5252 −1.55591
748748 0 0
749749 2.37237 0.0866844
750750 0 0
751751 −13.0431 −0.475949 −0.237974 0.971271i 0.576483π-0.576483\pi
−0.237974 + 0.971271i 0.576483π0.576483\pi
752752 15.2153 0.554844
753753 −5.59258 −0.203805
754754 32.8703 1.19707
755755 0 0
756756 −10.1304 −0.368438
757757 −31.8716 −1.15839 −0.579197 0.815188i 0.696634π-0.696634\pi
−0.579197 + 0.815188i 0.696634π0.696634\pi
758758 −17.9624 −0.652423
759759 0.617144 0.0224009
760760 0 0
761761 −18.7549 −0.679863 −0.339932 0.940450i 0.610404π-0.610404\pi
−0.339932 + 0.940450i 0.610404π0.610404\pi
762762 −73.3221 −2.65618
763763 −3.09612 −0.112087
764764 24.9064 0.901081
765765 0 0
766766 −59.1187 −2.13605
767767 11.8028 0.426175
768768 87.0119 3.13977
769769 −47.7916 −1.72341 −0.861705 0.507410i 0.830603π-0.830603\pi
−0.861705 + 0.507410i 0.830603π0.830603\pi
770770 0 0
771771 23.3516 0.840987
772772 54.1358 1.94839
773773 −28.3286 −1.01891 −0.509455 0.860497i 0.670153π-0.670153\pi
−0.509455 + 0.860497i 0.670153π0.670153\pi
774774 −41.3732 −1.48713
775775 0 0
776776 37.2498 1.33719
777777 3.96727 0.142325
778778 56.5464 2.02729
779779 −3.18828 −0.114232
780780 0 0
781781 −3.76036 −0.134556
782782 0 0
783783 −87.2932 −3.11961
784784 −15.6940 −0.560500
785785 0 0
786786 −148.187 −5.28565
787787 −42.3119 −1.50826 −0.754129 0.656727i 0.771941π-0.771941\pi
−0.754129 + 0.656727i 0.771941π0.771941\pi
788788 3.21129 0.114397
789789 −24.2051 −0.861723
790790 0 0
791791 1.58158 0.0562344
792792 14.7511 0.524157
793793 11.1278 0.395160
794794 66.1303 2.34688
795795 0 0
796796 49.1315 1.74142
797797 −54.1578 −1.91837 −0.959185 0.282780i 0.908743π-0.908743\pi
−0.959185 + 0.282780i 0.908743π0.908743\pi
798798 −6.62407 −0.234489
799799 0 0
800800 0 0
801801 111.123 3.92633
802802 72.8821 2.57356
803803 −0.622235 −0.0219582
804804 −134.151 −4.73113
805805 0 0
806806 13.7094 0.482892
807807 −24.8350 −0.874234
808808 −29.1413 −1.02519
809809 30.9803 1.08921 0.544604 0.838693i 0.316680π-0.316680\pi
0.544604 + 0.838693i 0.316680π0.316680\pi
810810 0 0
811811 4.15045 0.145742 0.0728710 0.997341i 0.476784π-0.476784\pi
0.0728710 + 0.997341i 0.476784π0.476784\pi
812812 5.69071 0.199705
813813 −56.9950 −1.99890
814814 −7.16081 −0.250986
815815 0 0
816816 0 0
817817 −9.97667 −0.349039
818818 −14.0863 −0.492515
819819 3.00835 0.105120
820820 0 0
821821 1.40975 0.0492007 0.0246003 0.999697i 0.492169π-0.492169\pi
0.0246003 + 0.999697i 0.492169π0.492169\pi
822822 35.0554 1.22270
823823 20.2090 0.704442 0.352221 0.935917i 0.385427π-0.385427\pi
0.352221 + 0.935917i 0.385427π0.385427\pi
824824 −38.5004 −1.34123
825825 0 0
826826 3.14970 0.109592
827827 −11.3584 −0.394971 −0.197486 0.980306i 0.563278π-0.563278\pi
−0.197486 + 0.980306i 0.563278π0.563278\pi
828828 −9.56980 −0.332574
829829 −10.9336 −0.379741 −0.189870 0.981809i 0.560807π-0.560807\pi
−0.189870 + 0.981809i 0.560807π0.560807\pi
830830 0 0
831831 83.7768 2.90618
832832 −21.5433 −0.746879
833833 0 0
834834 −39.5036 −1.36790
835835 0 0
836836 7.75666 0.268270
837837 −36.4078 −1.25844
838838 −77.5200 −2.67788
839839 −38.8677 −1.34186 −0.670931 0.741520i 0.734105π-0.734105\pi
−0.670931 + 0.741520i 0.734105π0.734105\pi
840840 0 0
841841 20.0367 0.690922
842842 −71.8621 −2.47653
843843 −43.4480 −1.49643
844844 65.7213 2.26222
845845 0 0
846846 111.796 3.84361
847847 −2.35930 −0.0810666
848848 −13.3688 −0.459088
849849 −43.3669 −1.48835
850850 0 0
851851 2.13038 0.0730285
852852 83.4745 2.85979
853853 −32.0255 −1.09653 −0.548266 0.836304i 0.684712π-0.684712\pi
−0.548266 + 0.836304i 0.684712π0.684712\pi
854854 2.96957 0.101617
855855 0 0
856856 43.5906 1.48990
857857 25.6769 0.877107 0.438553 0.898705i 0.355491π-0.355491\pi
0.438553 + 0.898705i 0.355491π0.355491\pi
858858 −7.77333 −0.265377
859859 −38.7065 −1.32065 −0.660324 0.750981i 0.729581π-0.729581\pi
−0.660324 + 0.750981i 0.729581π0.729581\pi
860860 0 0
861861 0.553162 0.0188517
862862 −19.8643 −0.676582
863863 −29.5881 −1.00719 −0.503596 0.863939i 0.667990π-0.667990\pi
−0.503596 + 0.863939i 0.667990π0.667990\pi
864864 33.6243 1.14392
865865 0 0
866866 −32.4036 −1.10112
867867 0 0
868868 2.37346 0.0805603
869869 3.53318 0.119855
870870 0 0
871871 22.6456 0.767317
872872 −56.8890 −1.92651
873873 64.0602 2.16811
874874 −3.55705 −0.120319
875875 0 0
876876 13.8127 0.466689
877877 −26.4995 −0.894825 −0.447413 0.894328i 0.647654π-0.647654\pi
−0.447413 + 0.894328i 0.647654π0.647654\pi
878878 −48.6105 −1.64053
879879 −62.7367 −2.11606
880880 0 0
881881 −10.9924 −0.370344 −0.185172 0.982706i 0.559284π-0.559284\pi
−0.185172 + 0.982706i 0.559284π0.559284\pi
882882 −115.313 −3.88279
883883 −56.2202 −1.89196 −0.945980 0.324225i 0.894896π-0.894896\pi
−0.945980 + 0.324225i 0.894896π0.894896\pi
884884 0 0
885885 0 0
886886 5.85481 0.196696
887887 −6.90120 −0.231720 −0.115860 0.993266i 0.536962π-0.536962\pi
−0.115860 + 0.993266i 0.536962π0.536962\pi
888888 72.8958 2.44622
889889 2.14284 0.0718685
890890 0 0
891891 9.69582 0.324822
892892 7.26658 0.243303
893893 26.9582 0.902122
894894 −65.8090 −2.20098
895895 0 0
896896 −4.56226 −0.152414
897897 2.31261 0.0772158
898898 7.62919 0.254589
899899 20.4520 0.682113
900900 0 0
901901 0 0
902902 −0.998442 −0.0332445
903903 1.73094 0.0576020
904904 29.0604 0.966534
905905 0 0
906906 −119.713 −3.97718
907907 −31.2128 −1.03640 −0.518202 0.855258i 0.673399π-0.673399\pi
−0.518202 + 0.855258i 0.673399π0.673399\pi
908908 44.1746 1.46598
909909 −50.1156 −1.66223
910910 0 0
911911 −42.4932 −1.40786 −0.703931 0.710268i 0.748574π-0.748574\pi
−0.703931 + 0.710268i 0.748574π0.748574\pi
912912 −28.4875 −0.943317
913913 −3.21129 −0.106278
914914 72.0164 2.38209
915915 0 0
916916 34.3763 1.13583
917917 4.33076 0.143014
918918 0 0
919919 29.1312 0.960949 0.480475 0.877009i 0.340464π-0.340464\pi
0.480475 + 0.877009i 0.340464π0.340464\pi
920920 0 0
921921 47.1923 1.55504
922922 12.9220 0.425562
923923 −14.0911 −0.463814
924924 −1.34577 −0.0442726
925925 0 0
926926 −37.6004 −1.23562
927927 −66.2109 −2.17465
928928 −18.8884 −0.620041
929929 −1.30273 −0.0427412 −0.0213706 0.999772i 0.506803π-0.506803\pi
−0.0213706 + 0.999772i 0.506803π0.506803\pi
930930 0 0
931931 −27.8064 −0.911318
932932 −95.3084 −3.12193
933933 −93.5463 −3.06257
934934 25.6971 0.840836
935935 0 0
936936 55.2764 1.80677
937937 −9.43458 −0.308214 −0.154107 0.988054i 0.549250π-0.549250\pi
−0.154107 + 0.988054i 0.549250π0.549250\pi
938938 6.04321 0.197318
939939 −45.3584 −1.48021
940940 0 0
941941 −25.1776 −0.820767 −0.410383 0.911913i 0.634605π-0.634605\pi
−0.410383 + 0.911913i 0.634605π0.634605\pi
942942 −75.8167 −2.47024
943943 0.297042 0.00967302
944944 13.5456 0.440873
945945 0 0
946946 −3.12430 −0.101580
947947 27.6569 0.898727 0.449364 0.893349i 0.351651π-0.351651\pi
0.449364 + 0.893349i 0.351651π0.351651\pi
948948 −78.4315 −2.54734
949949 −2.33169 −0.0756898
950950 0 0
951951 43.4552 1.40913
952952 0 0
953953 −16.0279 −0.519195 −0.259598 0.965717i 0.583590π-0.583590\pi
−0.259598 + 0.965717i 0.583590π0.583590\pi
954954 −98.2288 −3.18027
955955 0 0
956956 108.202 3.49949
957957 −11.5965 −0.374860
958958 −88.0732 −2.84552
959959 −1.02449 −0.0330827
960960 0 0
961961 −22.4700 −0.724838
962962 −26.8336 −0.865149
963963 74.9648 2.41571
964964 31.3446 1.00954
965965 0 0
966966 0.617144 0.0198563
967967 10.9849 0.353252 0.176626 0.984278i 0.443482π-0.443482\pi
0.176626 + 0.984278i 0.443482π0.443482\pi
968968 −43.3506 −1.39334
969969 0 0
970970 0 0
971971 32.2944 1.03638 0.518188 0.855267i 0.326607π-0.326607\pi
0.518188 + 0.855267i 0.326607π0.326607\pi
972972 −77.0874 −2.47258
973973 1.15449 0.0370113
974974 91.4476 2.93017
975975 0 0
976976 12.7710 0.408788
977977 −2.59459 −0.0830084 −0.0415042 0.999138i 0.513215π-0.513215\pi
−0.0415042 + 0.999138i 0.513215π0.513215\pi
978978 −72.1732 −2.30784
979979 8.39143 0.268191
980980 0 0
981981 −97.8347 −3.12362
982982 90.7561 2.89614
983983 −9.61652 −0.306719 −0.153360 0.988170i 0.549009π-0.549009\pi
−0.153360 + 0.988170i 0.549009π0.549009\pi
984984 10.1640 0.324015
985985 0 0
986986 0 0
987987 −4.67721 −0.148877
988988 29.0663 0.924723
989989 0.929495 0.0295562
990990 0 0
991991 −28.2650 −0.897867 −0.448933 0.893565i 0.648196π-0.648196\pi
−0.448933 + 0.893565i 0.648196π0.648196\pi
992992 −7.87787 −0.250123
993993 63.6096 2.01859
994994 −3.76036 −0.119271
995995 0 0
996996 71.2859 2.25878
997997 −3.34593 −0.105967 −0.0529833 0.998595i 0.516873π-0.516873\pi
−0.0529833 + 0.998595i 0.516873π0.516873\pi
998998 −22.2063 −0.702928
999999 71.2616 2.25462
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 7225.2.a.bp.1.11 12
5.2 odd 4 1445.2.b.f.579.12 12
5.3 odd 4 1445.2.b.f.579.1 12
5.4 even 2 inner 7225.2.a.bp.1.2 12
17.2 even 8 425.2.e.d.276.6 12
17.9 even 8 425.2.e.d.251.1 12
17.16 even 2 inner 7225.2.a.bp.1.12 12
85.2 odd 8 85.2.j.c.4.1 12
85.9 even 8 425.2.e.d.251.6 12
85.19 even 8 425.2.e.d.276.1 12
85.33 odd 4 1445.2.b.f.579.2 12
85.43 odd 8 85.2.j.c.64.1 yes 12
85.53 odd 8 85.2.j.c.4.6 yes 12
85.67 odd 4 1445.2.b.f.579.11 12
85.77 odd 8 85.2.j.c.64.6 yes 12
85.84 even 2 inner 7225.2.a.bp.1.1 12
255.2 even 8 765.2.t.e.514.6 12
255.53 even 8 765.2.t.e.514.1 12
255.77 even 8 765.2.t.e.64.1 12
255.128 even 8 765.2.t.e.64.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
85.2.j.c.4.1 12 85.2 odd 8
85.2.j.c.4.6 yes 12 85.53 odd 8
85.2.j.c.64.1 yes 12 85.43 odd 8
85.2.j.c.64.6 yes 12 85.77 odd 8
425.2.e.d.251.1 12 17.9 even 8
425.2.e.d.251.6 12 85.9 even 8
425.2.e.d.276.1 12 85.19 even 8
425.2.e.d.276.6 12 17.2 even 8
765.2.t.e.64.1 12 255.77 even 8
765.2.t.e.64.6 12 255.128 even 8
765.2.t.e.514.1 12 255.53 even 8
765.2.t.e.514.6 12 255.2 even 8
1445.2.b.f.579.1 12 5.3 odd 4
1445.2.b.f.579.2 12 85.33 odd 4
1445.2.b.f.579.11 12 85.67 odd 4
1445.2.b.f.579.12 12 5.2 odd 4
7225.2.a.bp.1.1 12 85.84 even 2 inner
7225.2.a.bp.1.2 12 5.4 even 2 inner
7225.2.a.bp.1.11 12 1.1 even 1 trivial
7225.2.a.bp.1.12 12 17.16 even 2 inner