Properties

Label 8649.2.a.r.1.2
Level 86498649
Weight 22
Character 8649.1
Self dual yes
Analytic conductor 69.06369.063
Analytic rank 11
Dimension 44
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] = [8649,2,Mod(1,8649)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8649, 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("8649.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 8649=32312 8649 = 3^{2} \cdot 31^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 8649.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,-6,0,6,0,0,-4,-12,0,10,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 69.062612708269.0626127082
Analytic rank: 11
Dimension: 44
Coefficient field: Q(2,5)\Q(\sqrt{2}, \sqrt{5})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x46x2+4 x^{4} - 6x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 961)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 2.28825-2.28825 of defining polynomial
Character χ\chi == 8649.1

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) == q2.61803q2+4.85410q42.23607q51.00000q77.47214q8+5.85410q10+4.24264q11+2.62210q13+2.61803q14+9.85410q16+3.70246q17+1.00000q1910.8541q2011.1074q222.62210q236.86474q264.85410q280.540182q2910.8541q329.69316q34+2.23607q354.24264q372.61803q38+16.7082q40+1.47214q41+9.69316q43+20.5942q44+6.86474q46+9.70820q476.00000q49+12.7279q5213.7295q539.48683q55+7.47214q56+1.41421q5811.9443q5913.9358q61+8.70820q645.86319q65+6.00000q67+17.9721q685.85410q70+1.47214q714.24264q73+11.1074q74+4.85410q764.24264q77+1.62054q7922.0344q803.85410q823.16228q838.27895q8525.3770q8631.7016q8815.3500q892.62210q9112.7279q9225.4164q942.23607q957.00000q97+15.7082q98+O(q100)q-2.61803 q^{2} +4.85410 q^{4} -2.23607 q^{5} -1.00000 q^{7} -7.47214 q^{8} +5.85410 q^{10} +4.24264 q^{11} +2.62210 q^{13} +2.61803 q^{14} +9.85410 q^{16} +3.70246 q^{17} +1.00000 q^{19} -10.8541 q^{20} -11.1074 q^{22} -2.62210 q^{23} -6.86474 q^{26} -4.85410 q^{28} -0.540182 q^{29} -10.8541 q^{32} -9.69316 q^{34} +2.23607 q^{35} -4.24264 q^{37} -2.61803 q^{38} +16.7082 q^{40} +1.47214 q^{41} +9.69316 q^{43} +20.5942 q^{44} +6.86474 q^{46} +9.70820 q^{47} -6.00000 q^{49} +12.7279 q^{52} -13.7295 q^{53} -9.48683 q^{55} +7.47214 q^{56} +1.41421 q^{58} -11.9443 q^{59} -13.9358 q^{61} +8.70820 q^{64} -5.86319 q^{65} +6.00000 q^{67} +17.9721 q^{68} -5.85410 q^{70} +1.47214 q^{71} -4.24264 q^{73} +11.1074 q^{74} +4.85410 q^{76} -4.24264 q^{77} +1.62054 q^{79} -22.0344 q^{80} -3.85410 q^{82} -3.16228 q^{83} -8.27895 q^{85} -25.3770 q^{86} -31.7016 q^{88} -15.3500 q^{89} -2.62210 q^{91} -12.7279 q^{92} -25.4164 q^{94} -2.23607 q^{95} -7.00000 q^{97} +15.7082 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q6q2+6q44q712q8+10q10+6q14+26q16+4q1930q206q2830q326q38+40q4012q41+12q4724q49+12q5612q59++36q98+O(q100) 4 q - 6 q^{2} + 6 q^{4} - 4 q^{7} - 12 q^{8} + 10 q^{10} + 6 q^{14} + 26 q^{16} + 4 q^{19} - 30 q^{20} - 6 q^{28} - 30 q^{32} - 6 q^{38} + 40 q^{40} - 12 q^{41} + 12 q^{47} - 24 q^{49} + 12 q^{56} - 12 q^{59}+ \cdots + 36 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 −2.61803 −1.85123 −0.925615 0.378467i 0.876451π-0.876451\pi
−0.925615 + 0.378467i 0.876451π0.876451\pi
33 0 0
44 4.85410 2.42705
55 −2.23607 −1.00000 −0.500000 0.866025i 0.666667π-0.666667\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
66 0 0
77 −1.00000 −0.377964 −0.188982 0.981981i 0.560519π-0.560519\pi
−0.188982 + 0.981981i 0.560519π0.560519\pi
88 −7.47214 −2.64180
99 0 0
1010 5.85410 1.85123
1111 4.24264 1.27920 0.639602 0.768706i 0.279099π-0.279099\pi
0.639602 + 0.768706i 0.279099π0.279099\pi
1212 0 0
1313 2.62210 0.727239 0.363619 0.931548i 0.381541π-0.381541\pi
0.363619 + 0.931548i 0.381541π0.381541\pi
1414 2.61803 0.699699
1515 0 0
1616 9.85410 2.46353
1717 3.70246 0.897978 0.448989 0.893537i 0.351784π-0.351784\pi
0.448989 + 0.893537i 0.351784π0.351784\pi
1818 0 0
1919 1.00000 0.229416 0.114708 0.993399i 0.463407π-0.463407\pi
0.114708 + 0.993399i 0.463407π0.463407\pi
2020 −10.8541 −2.42705
2121 0 0
2222 −11.1074 −2.36810
2323 −2.62210 −0.546745 −0.273372 0.961908i 0.588139π-0.588139\pi
−0.273372 + 0.961908i 0.588139π0.588139\pi
2424 0 0
2525 0 0
2626 −6.86474 −1.34629
2727 0 0
2828 −4.85410 −0.917339
2929 −0.540182 −0.100309 −0.0501546 0.998741i 0.515971π-0.515971\pi
−0.0501546 + 0.998741i 0.515971π0.515971\pi
3030 0 0
3131 0 0
3232 −10.8541 −1.91875
3333 0 0
3434 −9.69316 −1.66236
3535 2.23607 0.377964
3636 0 0
3737 −4.24264 −0.697486 −0.348743 0.937218i 0.613391π-0.613391\pi
−0.348743 + 0.937218i 0.613391π0.613391\pi
3838 −2.61803 −0.424701
3939 0 0
4040 16.7082 2.64180
4141 1.47214 0.229909 0.114955 0.993371i 0.463328π-0.463328\pi
0.114955 + 0.993371i 0.463328π0.463328\pi
4242 0 0
4343 9.69316 1.47819 0.739097 0.673599i 0.235253π-0.235253\pi
0.739097 + 0.673599i 0.235253π0.235253\pi
4444 20.5942 3.10469
4545 0 0
4646 6.86474 1.01215
4747 9.70820 1.41609 0.708044 0.706169i 0.249578π-0.249578\pi
0.708044 + 0.706169i 0.249578π0.249578\pi
4848 0 0
4949 −6.00000 −0.857143
5050 0 0
5151 0 0
5252 12.7279 1.76505
5353 −13.7295 −1.88589 −0.942944 0.332951i 0.891956π-0.891956\pi
−0.942944 + 0.332951i 0.891956π0.891956\pi
5454 0 0
5555 −9.48683 −1.27920
5656 7.47214 0.998506
5757 0 0
5858 1.41421 0.185695
5959 −11.9443 −1.55501 −0.777506 0.628876i 0.783515π-0.783515\pi
−0.777506 + 0.628876i 0.783515π0.783515\pi
6060 0 0
6161 −13.9358 −1.78430 −0.892148 0.451742i 0.850803π-0.850803\pi
−0.892148 + 0.451742i 0.850803π0.850803\pi
6262 0 0
6363 0 0
6464 8.70820 1.08853
6565 −5.86319 −0.727239
6666 0 0
6767 6.00000 0.733017 0.366508 0.930415i 0.380553π-0.380553\pi
0.366508 + 0.930415i 0.380553π0.380553\pi
6868 17.9721 2.17944
6969 0 0
7070 −5.85410 −0.699699
7171 1.47214 0.174710 0.0873552 0.996177i 0.472158π-0.472158\pi
0.0873552 + 0.996177i 0.472158π0.472158\pi
7272 0 0
7373 −4.24264 −0.496564 −0.248282 0.968688i 0.579866π-0.579866\pi
−0.248282 + 0.968688i 0.579866π0.579866\pi
7474 11.1074 1.29121
7575 0 0
7676 4.85410 0.556804
7777 −4.24264 −0.483494
7878 0 0
7979 1.62054 0.182326 0.0911628 0.995836i 0.470942π-0.470942\pi
0.0911628 + 0.995836i 0.470942π0.470942\pi
8080 −22.0344 −2.46353
8181 0 0
8282 −3.85410 −0.425614
8383 −3.16228 −0.347105 −0.173553 0.984825i 0.555525π-0.555525\pi
−0.173553 + 0.984825i 0.555525π0.555525\pi
8484 0 0
8585 −8.27895 −0.897978
8686 −25.3770 −2.73648
8787 0 0
8888 −31.7016 −3.37940
8989 −15.3500 −1.62710 −0.813549 0.581496i 0.802468π-0.802468\pi
−0.813549 + 0.581496i 0.802468π0.802468\pi
9090 0 0
9191 −2.62210 −0.274870
9292 −12.7279 −1.32698
9393 0 0
9494 −25.4164 −2.62150
9595 −2.23607 −0.229416
9696 0 0
9797 −7.00000 −0.710742 −0.355371 0.934725i 0.615646π-0.615646\pi
−0.355371 + 0.934725i 0.615646π0.615646\pi
9898 15.7082 1.58677
9999 0 0
100100 0 0
101101 −2.23607 −0.222497 −0.111249 0.993793i 0.535485π-0.535485\pi
−0.111249 + 0.993793i 0.535485π0.535485\pi
102102 0 0
103103 10.7082 1.05511 0.527555 0.849521i 0.323109π-0.323109\pi
0.527555 + 0.849521i 0.323109π0.323109\pi
104104 −19.5927 −1.92122
105105 0 0
106106 35.9442 3.49121
107107 −1.47214 −0.142317 −0.0711584 0.997465i 0.522670π-0.522670\pi
−0.0711584 + 0.997465i 0.522670π0.522670\pi
108108 0 0
109109 −1.29180 −0.123732 −0.0618658 0.998084i 0.519705π-0.519705\pi
−0.0618658 + 0.998084i 0.519705π0.519705\pi
110110 24.8369 2.36810
111111 0 0
112112 −9.85410 −0.931125
113113 9.76393 0.918513 0.459257 0.888304i 0.348116π-0.348116\pi
0.459257 + 0.888304i 0.348116π0.348116\pi
114114 0 0
115115 5.86319 0.546745
116116 −2.62210 −0.243456
117117 0 0
118118 31.2705 2.87868
119119 −3.70246 −0.339404
120120 0 0
121121 7.00000 0.636364
122122 36.4844 3.30314
123123 0 0
124124 0 0
125125 11.1803 1.00000
126126 0 0
127127 9.48683 0.841820 0.420910 0.907102i 0.361711π-0.361711\pi
0.420910 + 0.907102i 0.361711π0.361711\pi
128128 −1.09017 −0.0963583
129129 0 0
130130 15.3500 1.34629
131131 −7.41641 −0.647975 −0.323987 0.946061i 0.605024π-0.605024\pi
−0.323987 + 0.946061i 0.605024π0.605024\pi
132132 0 0
133133 −1.00000 −0.0867110
134134 −15.7082 −1.35698
135135 0 0
136136 −27.6653 −2.37228
137137 −2.62210 −0.224021 −0.112010 0.993707i 0.535729π-0.535729\pi
−0.112010 + 0.993707i 0.535729π0.535729\pi
138138 0 0
139139 17.9721 1.52437 0.762187 0.647356i 0.224125π-0.224125\pi
0.762187 + 0.647356i 0.224125π0.224125\pi
140140 10.8541 0.917339
141141 0 0
142142 −3.85410 −0.323429
143143 11.1246 0.930287
144144 0 0
145145 1.20788 0.100309
146146 11.1074 0.919253
147147 0 0
148148 −20.5942 −1.69283
149149 13.4164 1.09911 0.549557 0.835456i 0.314796π-0.314796\pi
0.549557 + 0.835456i 0.314796π0.314796\pi
150150 0 0
151151 −12.5216 −1.01899 −0.509496 0.860473i 0.670168π-0.670168\pi
−0.509496 + 0.860473i 0.670168π0.670168\pi
152152 −7.47214 −0.606070
153153 0 0
154154 11.1074 0.895058
155155 0 0
156156 0 0
157157 8.70820 0.694990 0.347495 0.937682i 0.387032π-0.387032\pi
0.347495 + 0.937682i 0.387032π0.387032\pi
158158 −4.24264 −0.337526
159159 0 0
160160 24.2705 1.91875
161161 2.62210 0.206650
162162 0 0
163163 14.4164 1.12918 0.564590 0.825371i 0.309034π-0.309034\pi
0.564590 + 0.825371i 0.309034π0.309034\pi
164164 7.14590 0.558001
165165 0 0
166166 8.27895 0.642571
167167 −1.08036 −0.0836010 −0.0418005 0.999126i 0.513309π-0.513309\pi
−0.0418005 + 0.999126i 0.513309π0.513309\pi
168168 0 0
169169 −6.12461 −0.471124
170170 21.6746 1.66236
171171 0 0
172172 47.0516 3.58765
173173 −18.0000 −1.36851 −0.684257 0.729241i 0.739873π-0.739873\pi
−0.684257 + 0.729241i 0.739873π0.739873\pi
174174 0 0
175175 0 0
176176 41.8074 3.15135
177177 0 0
178178 40.1869 3.01213
179179 13.2681 0.991705 0.495852 0.868407i 0.334856π-0.334856\pi
0.495852 + 0.868407i 0.334856π0.334856\pi
180180 0 0
181181 −8.69161 −0.646042 −0.323021 0.946392i 0.604699π-0.604699\pi
−0.323021 + 0.946392i 0.604699π0.604699\pi
182182 6.86474 0.508848
183183 0 0
184184 19.5927 1.44439
185185 9.48683 0.697486
186186 0 0
187187 15.7082 1.14870
188188 47.1246 3.43692
189189 0 0
190190 5.85410 0.424701
191191 −9.76393 −0.706493 −0.353247 0.935530i 0.614922π-0.614922\pi
−0.353247 + 0.935530i 0.614922π0.614922\pi
192192 0 0
193193 −20.7082 −1.49061 −0.745305 0.666724i 0.767696π-0.767696\pi
−0.745305 + 0.666724i 0.767696π0.767696\pi
194194 18.3262 1.31575
195195 0 0
196196 −29.1246 −2.08033
197197 −1.08036 −0.0769727 −0.0384863 0.999259i 0.512254π-0.512254\pi
−0.0384863 + 0.999259i 0.512254π0.512254\pi
198198 0 0
199199 −23.2163 −1.64576 −0.822880 0.568215i 0.807634π-0.807634\pi
−0.822880 + 0.568215i 0.807634π0.807634\pi
200200 0 0
201201 0 0
202202 5.85410 0.411893
203203 0.540182 0.0379133
204204 0 0
205205 −3.29180 −0.229909
206206 −28.0344 −1.95325
207207 0 0
208208 25.8384 1.79157
209209 4.24264 0.293470
210210 0 0
211211 −5.00000 −0.344214 −0.172107 0.985078i 0.555058π-0.555058\pi
−0.172107 + 0.985078i 0.555058π0.555058\pi
212212 −66.6443 −4.57715
213213 0 0
214214 3.85410 0.263461
215215 −21.6746 −1.47819
216216 0 0
217217 0 0
218218 3.38197 0.229056
219219 0 0
220220 −46.0501 −3.10469
221221 9.70820 0.653044
222222 0 0
223223 −16.1452 −1.08117 −0.540583 0.841291i 0.681796π-0.681796\pi
−0.540583 + 0.841291i 0.681796π0.681796\pi
224224 10.8541 0.725220
225225 0 0
226226 −25.5623 −1.70038
227227 −2.29180 −0.152112 −0.0760559 0.997104i 0.524233π-0.524233\pi
−0.0760559 + 0.997104i 0.524233π0.524233\pi
228228 0 0
229229 −4.24264 −0.280362 −0.140181 0.990126i 0.544768π-0.544768\pi
−0.140181 + 0.990126i 0.544768π0.544768\pi
230230 −15.3500 −1.01215
231231 0 0
232232 4.03631 0.264997
233233 13.4721 0.882589 0.441294 0.897362i 0.354519π-0.354519\pi
0.441294 + 0.897362i 0.354519π0.354519\pi
234234 0 0
235235 −21.7082 −1.41609
236236 −57.9787 −3.77409
237237 0 0
238238 9.69316 0.628314
239239 12.1089 0.783262 0.391631 0.920122i 0.371911π-0.371911\pi
0.391631 + 0.920122i 0.371911π0.371911\pi
240240 0 0
241241 23.2163 1.49549 0.747747 0.663984i 0.231136π-0.231136\pi
0.747747 + 0.663984i 0.231136π0.231136\pi
242242 −18.3262 −1.17806
243243 0 0
244244 −67.6458 −4.33058
245245 13.4164 0.857143
246246 0 0
247247 2.62210 0.166840
248248 0 0
249249 0 0
250250 −29.2705 −1.85123
251251 11.0286 0.696117 0.348058 0.937473i 0.386841π-0.386841\pi
0.348058 + 0.937473i 0.386841π0.386841\pi
252252 0 0
253253 −11.1246 −0.699398
254254 −24.8369 −1.55840
255255 0 0
256256 −14.5623 −0.910144
257257 −6.05573 −0.377746 −0.188873 0.982002i 0.560483π-0.560483\pi
−0.188873 + 0.982002i 0.560483π0.560483\pi
258258 0 0
259259 4.24264 0.263625
260260 −28.4605 −1.76505
261261 0 0
262262 19.4164 1.19955
263263 18.5123 1.14152 0.570759 0.821118i 0.306649π-0.306649\pi
0.570759 + 0.821118i 0.306649π0.306649\pi
264264 0 0
265265 30.7000 1.88589
266266 2.61803 0.160522
267267 0 0
268268 29.1246 1.77907
269269 2.16073 0.131742 0.0658709 0.997828i 0.479017π-0.479017\pi
0.0658709 + 0.997828i 0.479017π0.479017\pi
270270 0 0
271271 18.5911 1.12933 0.564665 0.825320i 0.309006π-0.309006\pi
0.564665 + 0.825320i 0.309006π0.309006\pi
272272 36.4844 2.21219
273273 0 0
274274 6.86474 0.414714
275275 0 0
276276 0 0
277277 −10.1058 −0.607200 −0.303600 0.952800i 0.598189π-0.598189\pi
−0.303600 + 0.952800i 0.598189π0.598189\pi
278278 −47.0516 −2.82197
279279 0 0
280280 −16.7082 −0.998506
281281 −13.3607 −0.797031 −0.398516 0.917162i 0.630475π-0.630475\pi
−0.398516 + 0.917162i 0.630475π0.630475\pi
282282 0 0
283283 24.0000 1.42665 0.713326 0.700832i 0.247188π-0.247188\pi
0.713326 + 0.700832i 0.247188π0.247188\pi
284284 7.14590 0.424031
285285 0 0
286286 −29.1246 −1.72217
287287 −1.47214 −0.0868974
288288 0 0
289289 −3.29180 −0.193635
290290 −3.16228 −0.185695
291291 0 0
292292 −20.5942 −1.20519
293293 2.29180 0.133888 0.0669441 0.997757i 0.478675π-0.478675\pi
0.0669441 + 0.997757i 0.478675π0.478675\pi
294294 0 0
295295 26.7082 1.55501
296296 31.7016 1.84262
297297 0 0
298298 −35.1246 −2.03471
299299 −6.87539 −0.397614
300300 0 0
301301 −9.69316 −0.558705
302302 32.7820 1.88639
303303 0 0
304304 9.85410 0.565172
305305 31.1614 1.78430
306306 0 0
307307 24.1246 1.37686 0.688432 0.725301i 0.258299π-0.258299\pi
0.688432 + 0.725301i 0.258299π0.258299\pi
308308 −20.5942 −1.17346
309309 0 0
310310 0 0
311311 −25.4721 −1.44439 −0.722196 0.691688i 0.756867π-0.756867\pi
−0.722196 + 0.691688i 0.756867π0.756867\pi
312312 0 0
313313 11.5200 0.651151 0.325576 0.945516i 0.394442π-0.394442\pi
0.325576 + 0.945516i 0.394442π0.394442\pi
314314 −22.7984 −1.28659
315315 0 0
316316 7.86629 0.442513
317317 −26.2361 −1.47356 −0.736782 0.676130i 0.763656π-0.763656\pi
−0.736782 + 0.676130i 0.763656π0.763656\pi
318318 0 0
319319 −2.29180 −0.128316
320320 −19.4721 −1.08853
321321 0 0
322322 −6.86474 −0.382557
323323 3.70246 0.206010
324324 0 0
325325 0 0
326326 −37.7426 −2.09037
327327 0 0
328328 −11.0000 −0.607373
329329 −9.70820 −0.535231
330330 0 0
331331 −31.2889 −1.71979 −0.859897 0.510467i 0.829473π-0.829473\pi
−0.859897 + 0.510467i 0.829473π0.829473\pi
332332 −15.3500 −0.842442
333333 0 0
334334 2.82843 0.154765
335335 −13.4164 −0.733017
336336 0 0
337337 15.3500 0.836169 0.418084 0.908408i 0.362702π-0.362702\pi
0.418084 + 0.908408i 0.362702π0.362702\pi
338338 16.0344 0.872159
339339 0 0
340340 −40.1869 −2.17944
341341 0 0
342342 0 0
343343 13.0000 0.701934
344344 −72.4286 −3.90509
345345 0 0
346346 47.1246 2.53343
347347 −21.5958 −1.15932 −0.579661 0.814858i 0.696815π-0.696815\pi
−0.579661 + 0.814858i 0.696815π0.696815\pi
348348 0 0
349349 6.00000 0.321173 0.160586 0.987022i 0.448662π-0.448662\pi
0.160586 + 0.987022i 0.448662π0.448662\pi
350350 0 0
351351 0 0
352352 −46.0501 −2.45448
353353 9.56564 0.509128 0.254564 0.967056i 0.418068π-0.418068\pi
0.254564 + 0.967056i 0.418068π0.418068\pi
354354 0 0
355355 −3.29180 −0.174710
356356 −74.5106 −3.94905
357357 0 0
358358 −34.7363 −1.83587
359359 −14.2361 −0.751351 −0.375675 0.926751i 0.622589π-0.622589\pi
−0.375675 + 0.926751i 0.622589π0.622589\pi
360360 0 0
361361 −18.0000 −0.947368
362362 22.7549 1.19597
363363 0 0
364364 −12.7279 −0.667124
365365 9.48683 0.496564
366366 0 0
367367 −6.65841 −0.347566 −0.173783 0.984784i 0.555599π-0.555599\pi
−0.173783 + 0.984784i 0.555599π0.555599\pi
368368 −25.8384 −1.34692
369369 0 0
370370 −24.8369 −1.29121
371371 13.7295 0.712799
372372 0 0
373373 −9.29180 −0.481111 −0.240555 0.970635i 0.577330π-0.577330\pi
−0.240555 + 0.970635i 0.577330π0.577330\pi
374374 −41.1246 −2.12650
375375 0 0
376376 −72.5410 −3.74102
377377 −1.41641 −0.0729487
378378 0 0
379379 7.41641 0.380955 0.190478 0.981692i 0.438996π-0.438996\pi
0.190478 + 0.981692i 0.438996π0.438996\pi
380380 −10.8541 −0.556804
381381 0 0
382382 25.5623 1.30788
383383 −6.40337 −0.327197 −0.163598 0.986527i 0.552310π-0.552310\pi
−0.163598 + 0.986527i 0.552310π0.552310\pi
384384 0 0
385385 9.48683 0.483494
386386 54.2148 2.75946
387387 0 0
388388 −33.9787 −1.72501
389389 −16.8129 −0.852450 −0.426225 0.904617i 0.640157π-0.640157\pi
−0.426225 + 0.904617i 0.640157π0.640157\pi
390390 0 0
391391 −9.70820 −0.490965
392392 44.8328 2.26440
393393 0 0
394394 2.82843 0.142494
395395 −3.62365 −0.182326
396396 0 0
397397 14.7082 0.738184 0.369092 0.929393i 0.379669π-0.379669\pi
0.369092 + 0.929393i 0.379669π0.379669\pi
398398 60.7811 3.04668
399399 0 0
400400 0 0
401401 −0.540182 −0.0269754 −0.0134877 0.999909i 0.504293π-0.504293\pi
−0.0134877 + 0.999909i 0.504293π0.504293\pi
402402 0 0
403403 0 0
404404 −10.8541 −0.540012
405405 0 0
406406 −1.41421 −0.0701862
407407 −18.0000 −0.892227
408408 0 0
409409 −30.0810 −1.48741 −0.743706 0.668507i 0.766934π-0.766934\pi
−0.743706 + 0.668507i 0.766934π0.766934\pi
410410 8.61803 0.425614
411411 0 0
412412 51.9787 2.56081
413413 11.9443 0.587739
414414 0 0
415415 7.07107 0.347105
416416 −28.4605 −1.39539
417417 0 0
418418 −11.1074 −0.543280
419419 −30.5967 −1.49475 −0.747374 0.664403i 0.768686π-0.768686\pi
−0.747374 + 0.664403i 0.768686π0.768686\pi
420420 0 0
421421 26.4164 1.28746 0.643728 0.765254i 0.277387π-0.277387\pi
0.643728 + 0.765254i 0.277387π0.277387\pi
422422 13.0902 0.637220
423423 0 0
424424 102.588 4.98214
425425 0 0
426426 0 0
427427 13.9358 0.674401
428428 −7.14590 −0.345410
429429 0 0
430430 56.7448 2.73648
431431 35.8885 1.72869 0.864345 0.502899i 0.167733π-0.167733\pi
0.864345 + 0.502899i 0.167733π0.167733\pi
432432 0 0
433433 25.8384 1.24171 0.620857 0.783924i 0.286785π-0.286785\pi
0.620857 + 0.783924i 0.286785π0.286785\pi
434434 0 0
435435 0 0
436436 −6.27051 −0.300303
437437 −2.62210 −0.125432
438438 0 0
439439 −25.0000 −1.19318 −0.596592 0.802544i 0.703479π-0.703479\pi
−0.596592 + 0.802544i 0.703479π0.703479\pi
440440 70.8869 3.37940
441441 0 0
442442 −25.4164 −1.20894
443443 −6.05573 −0.287716 −0.143858 0.989598i 0.545951π-0.545951\pi
−0.143858 + 0.989598i 0.545951π0.545951\pi
444444 0 0
445445 34.3237 1.62710
446446 42.2688 2.00148
447447 0 0
448448 −8.70820 −0.411424
449449 33.7047 1.59062 0.795311 0.606201i 0.207307π-0.207307\pi
0.795311 + 0.606201i 0.207307π0.207307\pi
450450 0 0
451451 6.24574 0.294101
452452 47.3951 2.22928
453453 0 0
454454 6.00000 0.281594
455455 5.86319 0.274870
456456 0 0
457457 −11.3137 −0.529233 −0.264616 0.964354i 0.585245π-0.585245\pi
−0.264616 + 0.964354i 0.585245π0.585245\pi
458458 11.1074 0.519014
459459 0 0
460460 28.4605 1.32698
461461 5.16538 0.240576 0.120288 0.992739i 0.461618π-0.461618\pi
0.120288 + 0.992739i 0.461618π0.461618\pi
462462 0 0
463463 3.82998 0.177994 0.0889971 0.996032i 0.471634π-0.471634\pi
0.0889971 + 0.996032i 0.471634π0.471634\pi
464464 −5.32300 −0.247114
465465 0 0
466466 −35.2705 −1.63387
467467 15.6525 0.724310 0.362155 0.932118i 0.382041π-0.382041\pi
0.362155 + 0.932118i 0.382041π0.382041\pi
468468 0 0
469469 −6.00000 −0.277054
470470 56.8328 2.62150
471471 0 0
472472 89.2492 4.10803
473473 41.1246 1.89091
474474 0 0
475475 0 0
476476 −17.9721 −0.823751
477477 0 0
478478 −31.7016 −1.45000
479479 −16.5279 −0.755177 −0.377589 0.925973i 0.623247π-0.623247\pi
−0.377589 + 0.925973i 0.623247π0.623247\pi
480480 0 0
481481 −11.1246 −0.507239
482482 −60.7811 −2.76850
483483 0 0
484484 33.9787 1.54449
485485 15.6525 0.710742
486486 0 0
487487 −28.0779 −1.27233 −0.636166 0.771552i 0.719481π-0.719481\pi
−0.636166 + 0.771552i 0.719481π0.719481\pi
488488 104.130 4.71375
489489 0 0
490490 −35.1246 −1.58677
491491 −15.8902 −0.717115 −0.358557 0.933508i 0.616731π-0.616731\pi
−0.358557 + 0.933508i 0.616731π0.616731\pi
492492 0 0
493493 −2.00000 −0.0900755
494494 −6.86474 −0.308859
495495 0 0
496496 0 0
497497 −1.47214 −0.0660343
498498 0 0
499499 −18.3848 −0.823016 −0.411508 0.911406i 0.634998π-0.634998\pi
−0.411508 + 0.911406i 0.634998π0.634998\pi
500500 54.2705 2.42705
501501 0 0
502502 −28.8732 −1.28867
503503 32.8885 1.46643 0.733214 0.679998i 0.238019π-0.238019\pi
0.733214 + 0.679998i 0.238019π0.238019\pi
504504 0 0
505505 5.00000 0.222497
506506 29.1246 1.29475
507507 0 0
508508 46.0501 2.04314
509509 −7.94510 −0.352160 −0.176080 0.984376i 0.556342π-0.556342\pi
−0.176080 + 0.984376i 0.556342π0.556342\pi
510510 0 0
511511 4.24264 0.187683
512512 40.3050 1.78124
513513 0 0
514514 15.8541 0.699294
515515 −23.9443 −1.05511
516516 0 0
517517 41.1884 1.81146
518518 −11.1074 −0.488030
519519 0 0
520520 43.8105 1.92122
521521 13.4164 0.587784 0.293892 0.955839i 0.405049π-0.405049\pi
0.293892 + 0.955839i 0.405049π0.405049\pi
522522 0 0
523523 −0.618993 −0.0270667 −0.0135333 0.999908i 0.504308π-0.504308\pi
−0.0135333 + 0.999908i 0.504308π0.504308\pi
524524 −36.0000 −1.57267
525525 0 0
526526 −48.4658 −2.11321
527527 0 0
528528 0 0
529529 −16.1246 −0.701070
530530 −80.3737 −3.49121
531531 0 0
532532 −4.85410 −0.210452
533533 3.86008 0.167199
534534 0 0
535535 3.29180 0.142317
536536 −44.8328 −1.93648
537537 0 0
538538 −5.65685 −0.243884
539539 −25.4558 −1.09646
540540 0 0
541541 25.8328 1.11064 0.555320 0.831637i 0.312596π-0.312596\pi
0.555320 + 0.831637i 0.312596π0.312596\pi
542542 −48.6722 −2.09065
543543 0 0
544544 −40.1869 −1.72300
545545 2.88854 0.123732
546546 0 0
547547 2.41641 0.103318 0.0516591 0.998665i 0.483549π-0.483549\pi
0.0516591 + 0.998665i 0.483549π0.483549\pi
548548 −12.7279 −0.543710
549549 0 0
550550 0 0
551551 −0.540182 −0.0230125
552552 0 0
553553 −1.62054 −0.0689126
554554 26.4574 1.12407
555555 0 0
556556 87.2385 3.69974
557557 −10.6460 −0.451086 −0.225543 0.974233i 0.572416π-0.572416\pi
−0.225543 + 0.974233i 0.572416π0.572416\pi
558558 0 0
559559 25.4164 1.07500
560560 22.0344 0.931125
561561 0 0
562562 34.9787 1.47549
563563 −9.76393 −0.411501 −0.205750 0.978605i 0.565963π-0.565963\pi
−0.205750 + 0.978605i 0.565963π0.565963\pi
564564 0 0
565565 −21.8328 −0.918513
566566 −62.8328 −2.64106
567567 0 0
568568 −11.0000 −0.461550
569569 −11.7264 −0.491595 −0.245798 0.969321i 0.579050π-0.579050\pi
−0.245798 + 0.969321i 0.579050π0.579050\pi
570570 0 0
571571 2.62210 0.109731 0.0548657 0.998494i 0.482527π-0.482527\pi
0.0548657 + 0.998494i 0.482527π0.482527\pi
572572 54.0000 2.25785
573573 0 0
574574 3.85410 0.160867
575575 0 0
576576 0 0
577577 −30.0000 −1.24892 −0.624458 0.781058i 0.714680π-0.714680\pi
−0.624458 + 0.781058i 0.714680π0.714680\pi
578578 8.61803 0.358463
579579 0 0
580580 5.86319 0.243456
581581 3.16228 0.131193
582582 0 0
583583 −58.2492 −2.41244
584584 31.7016 1.31182
585585 0 0
586586 −6.00000 −0.247858
587587 −15.7326 −0.649353 −0.324676 0.945825i 0.605255π-0.605255\pi
−0.324676 + 0.945825i 0.605255π0.605255\pi
588588 0 0
589589 0 0
590590 −69.9230 −2.87868
591591 0 0
592592 −41.8074 −1.71827
593593 −5.18034 −0.212731 −0.106366 0.994327i 0.533921π-0.533921\pi
−0.106366 + 0.994327i 0.533921π0.533921\pi
594594 0 0
595595 8.27895 0.339404
596596 65.1246 2.66761
597597 0 0
598598 18.0000 0.736075
599599 −6.05573 −0.247430 −0.123715 0.992318i 0.539481π-0.539481\pi
−0.123715 + 0.992318i 0.539481π0.539481\pi
600600 0 0
601601 −18.1784 −0.741514 −0.370757 0.928730i 0.620902π-0.620902\pi
−0.370757 + 0.928730i 0.620902π0.620902\pi
602602 25.3770 1.03429
603603 0 0
604604 −60.7811 −2.47315
605605 −15.6525 −0.636364
606606 0 0
607607 15.1246 0.613889 0.306945 0.951727i 0.400693π-0.400693\pi
0.306945 + 0.951727i 0.400693π0.400693\pi
608608 −10.8541 −0.440192
609609 0 0
610610 −81.5816 −3.30314
611611 25.4558 1.02983
612612 0 0
613613 −0.588890 −0.0237850 −0.0118925 0.999929i 0.503786π-0.503786\pi
−0.0118925 + 0.999929i 0.503786π0.503786\pi
614614 −63.1591 −2.54889
615615 0 0
616616 31.7016 1.27729
617617 6.87539 0.276793 0.138396 0.990377i 0.455805π-0.455805\pi
0.138396 + 0.990377i 0.455805π0.455805\pi
618618 0 0
619619 −25.8384 −1.03853 −0.519267 0.854612i 0.673795π-0.673795\pi
−0.519267 + 0.854612i 0.673795π0.673795\pi
620620 0 0
621621 0 0
622622 66.6869 2.67390
623623 15.3500 0.614985
624624 0 0
625625 −25.0000 −1.00000
626626 −30.1599 −1.20543
627627 0 0
628628 42.2705 1.68678
629629 −15.7082 −0.626327
630630 0 0
631631 23.6290 0.940654 0.470327 0.882492i 0.344136π-0.344136\pi
0.470327 + 0.882492i 0.344136π0.344136\pi
632632 −12.1089 −0.481667
633633 0 0
634634 68.6869 2.72791
635635 −21.2132 −0.841820
636636 0 0
637637 −15.7326 −0.623347
638638 6.00000 0.237542
639639 0 0
640640 2.43769 0.0963583
641641 −8.48528 −0.335148 −0.167574 0.985859i 0.553593π-0.553593\pi
−0.167574 + 0.985859i 0.553593π0.553593\pi
642642 0 0
643643 4.65530 0.183587 0.0917936 0.995778i 0.470740π-0.470740\pi
0.0917936 + 0.995778i 0.470740π0.470740\pi
644644 12.7279 0.501550
645645 0 0
646646 −9.69316 −0.381372
647647 31.7804 1.24942 0.624708 0.780858i 0.285218π-0.285218\pi
0.624708 + 0.780858i 0.285218π0.285218\pi
648648 0 0
649649 −50.6753 −1.98918
650650 0 0
651651 0 0
652652 69.9787 2.74058
653653 −24.6525 −0.964726 −0.482363 0.875971i 0.660221π-0.660221\pi
−0.482363 + 0.875971i 0.660221π0.660221\pi
654654 0 0
655655 16.5836 0.647975
656656 14.5066 0.566387
657657 0 0
658658 25.4164 0.990835
659659 −24.8197 −0.966837 −0.483418 0.875389i 0.660605π-0.660605\pi
−0.483418 + 0.875389i 0.660605π0.660605\pi
660660 0 0
661661 7.83282 0.304661 0.152331 0.988330i 0.451322π-0.451322\pi
0.152331 + 0.988330i 0.451322π0.451322\pi
662662 81.9155 3.18374
663663 0 0
664664 23.6290 0.916982
665665 2.23607 0.0867110
666666 0 0
667667 1.41641 0.0548435
668668 −5.24419 −0.202904
669669 0 0
670670 35.1246 1.35698
671671 −59.1246 −2.28248
672672 0 0
673673 −39.9805 −1.54114 −0.770568 0.637357i 0.780027π-0.780027\pi
−0.770568 + 0.637357i 0.780027π0.780027\pi
674674 −40.1869 −1.54794
675675 0 0
676676 −29.7295 −1.14344
677677 −21.2132 −0.815290 −0.407645 0.913141i 0.633650π-0.633650\pi
−0.407645 + 0.913141i 0.633650π0.633650\pi
678678 0 0
679679 7.00000 0.268635
680680 61.8614 2.37228
681681 0 0
682682 0 0
683683 41.1803 1.57572 0.787861 0.615853i 0.211189π-0.211189\pi
0.787861 + 0.615853i 0.211189π0.211189\pi
684684 0 0
685685 5.86319 0.224021
686686 −34.0344 −1.29944
687687 0 0
688688 95.5174 3.64157
689689 −36.0000 −1.37149
690690 0 0
691691 −48.4164 −1.84185 −0.920923 0.389743i 0.872564π-0.872564\pi
−0.920923 + 0.389743i 0.872564π0.872564\pi
692692 −87.3738 −3.32145
693693 0 0
694694 56.5384 2.14617
695695 −40.1869 −1.52437
696696 0 0
697697 5.45052 0.206453
698698 −15.7082 −0.594564
699699 0 0
700700 0 0
701701 3.65248 0.137952 0.0689761 0.997618i 0.478027π-0.478027\pi
0.0689761 + 0.997618i 0.478027π0.478027\pi
702702 0 0
703703 −4.24264 −0.160014
704704 36.9458 1.39245
705705 0 0
706706 −25.0432 −0.942513
707707 2.23607 0.0840960
708708 0 0
709709 41.1884 1.54686 0.773432 0.633880i 0.218538π-0.218538\pi
0.773432 + 0.633880i 0.218538π0.218538\pi
710710 8.61803 0.323429
711711 0 0
712712 114.697 4.29847
713713 0 0
714714 0 0
715715 −24.8754 −0.930287
716716 64.4047 2.40692
717717 0 0
718718 37.2705 1.39092
719719 −37.5648 −1.40093 −0.700465 0.713687i 0.747024π-0.747024\pi
−0.700465 + 0.713687i 0.747024π0.747024\pi
720720 0 0
721721 −10.7082 −0.398794
722722 47.1246 1.75380
723723 0 0
724724 −42.1900 −1.56798
725725 0 0
726726 0 0
727727 −30.4164 −1.12808 −0.564041 0.825747i 0.690754π-0.690754\pi
−0.564041 + 0.825747i 0.690754π0.690754\pi
728728 19.5927 0.726152
729729 0 0
730730 −24.8369 −0.919253
731731 35.8885 1.32739
732732 0 0
733733 −14.4164 −0.532482 −0.266241 0.963906i 0.585782π-0.585782\pi
−0.266241 + 0.963906i 0.585782π0.585782\pi
734734 17.4319 0.643424
735735 0 0
736736 28.4605 1.04907
737737 25.4558 0.937678
738738 0 0
739739 35.1490 1.29298 0.646489 0.762924i 0.276237π-0.276237\pi
0.646489 + 0.762924i 0.276237π0.276237\pi
740740 46.0501 1.69283
741741 0 0
742742 −35.9442 −1.31955
743743 −36.4844 −1.33848 −0.669242 0.743045i 0.733381π-0.733381\pi
−0.669242 + 0.743045i 0.733381π0.733381\pi
744744 0 0
745745 −30.0000 −1.09911
746746 24.3262 0.890647
747747 0 0
748748 76.2492 2.78795
749749 1.47214 0.0537907
750750 0 0
751751 −37.5410 −1.36989 −0.684946 0.728594i 0.740174π-0.740174\pi
−0.684946 + 0.728594i 0.740174π0.740174\pi
752752 95.6656 3.48857
753753 0 0
754754 3.70820 0.135045
755755 27.9991 1.01899
756756 0 0
757757 −9.28050 −0.337306 −0.168653 0.985676i 0.553942π-0.553942\pi
−0.168653 + 0.985676i 0.553942π0.553942\pi
758758 −19.4164 −0.705236
759759 0 0
760760 16.7082 0.606070
761761 40.1869 1.45677 0.728386 0.685167i 0.240271π-0.240271\pi
0.728386 + 0.685167i 0.240271π0.240271\pi
762762 0 0
763763 1.29180 0.0467662
764764 −47.3951 −1.71470
765765 0 0
766766 16.7642 0.605716
767767 −31.3190 −1.13086
768768 0 0
769769 54.1246 1.95178 0.975892 0.218255i 0.0700365π-0.0700365\pi
0.975892 + 0.218255i 0.0700365π0.0700365\pi
770770 −24.8369 −0.895058
771771 0 0
772772 −100.520 −3.61778
773773 −11.1862 −0.402339 −0.201170 0.979556i 0.564474π-0.564474\pi
−0.201170 + 0.979556i 0.564474π0.564474\pi
774774 0 0
775775 0 0
776776 52.3050 1.87764
777777 0 0
778778 44.0168 1.57808
779779 1.47214 0.0527447
780780 0 0
781781 6.24574 0.223490
782782 25.4164 0.908889
783783 0 0
784784 −59.1246 −2.11159
785785 −19.4721 −0.694990
786786 0 0
787787 37.5648 1.33904 0.669520 0.742794i 0.266500π-0.266500\pi
0.669520 + 0.742794i 0.266500π0.266500\pi
788788 −5.24419 −0.186817
789789 0 0
790790 9.48683 0.337526
791791 −9.76393 −0.347165
792792 0 0
793793 −36.5410 −1.29761
794794 −38.5066 −1.36655
795795 0 0
796796 −112.694 −3.99434
797797 −13.7295 −0.486323 −0.243161 0.969986i 0.578184π-0.578184\pi
−0.243161 + 0.969986i 0.578184π0.578184\pi
798798 0 0
799799 35.9442 1.27162
800800 0 0
801801 0 0
802802 1.41421 0.0499376
803803 −18.0000 −0.635206
804804 0 0
805805 −5.86319 −0.206650
806806 0 0
807807 0 0
808808 16.7082 0.587793
809809 47.5130 1.67047 0.835234 0.549895i 0.185332π-0.185332\pi
0.835234 + 0.549895i 0.185332π0.185332\pi
810810 0 0
811811 −16.5836 −0.582329 −0.291164 0.956673i 0.594043π-0.594043\pi
−0.291164 + 0.956673i 0.594043π0.594043\pi
812812 2.62210 0.0920175
813813 0 0
814814 47.1246 1.65172
815815 −32.2361 −1.12918
816816 0 0
817817 9.69316 0.339121
818818 78.7532 2.75354
819819 0 0
820820 −15.9787 −0.558001
821821 23.8353 0.831858 0.415929 0.909397i 0.363457π-0.363457\pi
0.415929 + 0.909397i 0.363457π0.363457\pi
822822 0 0
823823 13.5231 0.471387 0.235694 0.971827i 0.424264π-0.424264\pi
0.235694 + 0.971827i 0.424264π0.424264\pi
824824 −80.0132 −2.78739
825825 0 0
826826 −31.2705 −1.08804
827827 −18.3547 −0.638255 −0.319127 0.947712i 0.603390π-0.603390\pi
−0.319127 + 0.947712i 0.603390π0.603390\pi
828828 0 0
829829 −51.0879 −1.77436 −0.887178 0.461427i 0.847338π-0.847338\pi
−0.887178 + 0.461427i 0.847338π0.847338\pi
830830 −18.5123 −0.642571
831831 0 0
832832 22.8337 0.791618
833833 −22.2148 −0.769696
834834 0 0
835835 2.41577 0.0836010
836836 20.5942 0.712266
837837 0 0
838838 80.1033 2.76712
839839 19.4164 0.670329 0.335164 0.942160i 0.391208π-0.391208\pi
0.335164 + 0.942160i 0.391208π0.391208\pi
840840 0 0
841841 −28.7082 −0.989938
842842 −69.1591 −2.38338
843843 0 0
844844 −24.2705 −0.835425
845845 13.6950 0.471124
846846 0 0
847847 −7.00000 −0.240523
848848 −135.292 −4.64593
849849 0 0
850850 0 0
851851 11.1246 0.381347
852852 0 0
853853 −32.2918 −1.10565 −0.552825 0.833297i 0.686450π-0.686450\pi
−0.552825 + 0.833297i 0.686450π0.686450\pi
854854 −36.4844 −1.24847
855855 0 0
856856 11.0000 0.375972
857857 6.00000 0.204956 0.102478 0.994735i 0.467323π-0.467323\pi
0.102478 + 0.994735i 0.467323π0.467323\pi
858858 0 0
859859 41.6011 1.41941 0.709705 0.704499i 0.248828π-0.248828\pi
0.709705 + 0.704499i 0.248828π0.248828\pi
860860 −105.211 −3.58765
861861 0 0
862862 −93.9574 −3.20020
863863 −31.0826 −1.05806 −0.529032 0.848602i 0.677445π-0.677445\pi
−0.529032 + 0.848602i 0.677445π0.677445\pi
864864 0 0
865865 40.2492 1.36851
866866 −67.6458 −2.29870
867867 0 0
868868 0 0
869869 6.87539 0.233232
870870 0 0
871871 15.7326 0.533078
872872 9.65248 0.326874
873873 0 0
874874 6.86474 0.232203
875875 −11.1803 −0.377964
876876 0 0
877877 −28.7082 −0.969407 −0.484704 0.874678i 0.661073π-0.661073\pi
−0.484704 + 0.874678i 0.661073π0.661073\pi
878878 65.4508 2.20886
879879 0 0
880880 −93.4842 −3.15135
881881 7.24730 0.244168 0.122084 0.992520i 0.461042π-0.461042\pi
0.122084 + 0.992520i 0.461042π0.461042\pi
882882 0 0
883883 33.9411 1.14221 0.571105 0.820877i 0.306515π-0.306515\pi
0.571105 + 0.820877i 0.306515π0.306515\pi
884884 47.1246 1.58497
885885 0 0
886886 15.8541 0.532629
887887 −25.3607 −0.851528 −0.425764 0.904834i 0.639995π-0.639995\pi
−0.425764 + 0.904834i 0.639995π0.639995\pi
888888 0 0
889889 −9.48683 −0.318178
890890 −89.8606 −3.01213
891891 0 0
892892 −78.3706 −2.62404
893893 9.70820 0.324873
894894 0 0
895895 −29.6684 −0.991705
896896 1.09017 0.0364200
897897 0 0
898898 −88.2400 −2.94461
899899 0 0
900900 0 0
901901 −50.8328 −1.69349
902902 −16.3516 −0.544448
903903 0 0
904904 −72.9574 −2.42653
905905 19.4350 0.646042
906906 0 0
907907 11.5410 0.383213 0.191607 0.981472i 0.438630π-0.438630\pi
0.191607 + 0.981472i 0.438630π0.438630\pi
908908 −11.1246 −0.369183
909909 0 0
910910 −15.3500 −0.508848
911911 −26.9188 −0.891859 −0.445929 0.895068i 0.647127π-0.647127\pi
−0.445929 + 0.895068i 0.647127π0.647127\pi
912912 0 0
913913 −13.4164 −0.444018
914914 29.6197 0.979732
915915 0 0
916916 −20.5942 −0.680452
917917 7.41641 0.244911
918918 0 0
919919 −42.5410 −1.40330 −0.701649 0.712522i 0.747553π-0.747553\pi
−0.701649 + 0.712522i 0.747553π0.747553\pi
920920 −43.8105 −1.44439
921921 0 0
922922 −13.5231 −0.445361
923923 3.86008 0.127056
924924 0 0
925925 0 0
926926 −10.0270 −0.329508
927927 0 0
928928 5.86319 0.192468
929929 10.6460 0.349284 0.174642 0.984632i 0.444123π-0.444123\pi
0.174642 + 0.984632i 0.444123π0.444123\pi
930930 0 0
931931 −6.00000 −0.196642
932932 65.3951 2.14209
933933 0 0
934934 −40.9787 −1.34086
935935 −35.1246 −1.14870
936936 0 0
937937 24.2492 0.792188 0.396094 0.918210i 0.370366π-0.370366\pi
0.396094 + 0.918210i 0.370366π0.370366\pi
938938 15.7082 0.512891
939939 0 0
940940 −105.374 −3.43692
941941 25.5347 0.832406 0.416203 0.909272i 0.363361π-0.363361\pi
0.416203 + 0.909272i 0.363361π0.363361\pi
942942 0 0
943943 −3.86008 −0.125702
944944 −117.700 −3.83081
945945 0 0
946946 −107.666 −3.50051
947947 40.1869 1.30590 0.652949 0.757402i 0.273532π-0.273532\pi
0.652949 + 0.757402i 0.273532π0.273532\pi
948948 0 0
949949 −11.1246 −0.361120
950950 0 0
951951 0 0
952952 27.6653 0.896637
953953 18.6699 0.604778 0.302389 0.953185i 0.402216π-0.402216\pi
0.302389 + 0.953185i 0.402216π0.402216\pi
954954 0 0
955955 21.8328 0.706493
956956 58.7780 1.90102
957957 0 0
958958 43.2705 1.39801
959959 2.62210 0.0846719
960960 0 0
961961 0 0
962962 29.1246 0.939015
963963 0 0
964964 112.694 3.62964
965965 46.3050 1.49061
966966 0 0
967967 −44.0168 −1.41549 −0.707743 0.706470i 0.750287π-0.750287\pi
−0.707743 + 0.706470i 0.750287π0.750287\pi
968968 −52.3050 −1.68114
969969 0 0
970970 −40.9787 −1.31575
971971 −53.8885 −1.72937 −0.864683 0.502318i 0.832481π-0.832481\pi
−0.864683 + 0.502318i 0.832481π0.832481\pi
972972 0 0
973973 −17.9721 −0.576160
974974 73.5090 2.35538
975975 0 0
976976 −137.325 −4.39566
977977 42.4853 1.35922 0.679612 0.733571i 0.262148π-0.262148\pi
0.679612 + 0.733571i 0.262148π0.262148\pi
978978 0 0
979979 −65.1246 −2.08139
980980 65.1246 2.08033
981981 0 0
982982 41.6011 1.32754
983983 53.9163 1.71966 0.859832 0.510577i 0.170568π-0.170568\pi
0.859832 + 0.510577i 0.170568π0.170568\pi
984984 0 0
985985 2.41577 0.0769727
986986 5.23607 0.166750
987987 0 0
988988 12.7279 0.404929
989989 −25.4164 −0.808195
990990 0 0
991991 13.9358 0.442685 0.221343 0.975196i 0.428956π-0.428956\pi
0.221343 + 0.975196i 0.428956π0.428956\pi
992992 0 0
993993 0 0
994994 3.85410 0.122245
995995 51.9132 1.64576
996996 0 0
997997 −58.6656 −1.85796 −0.928980 0.370131i 0.879313π-0.879313\pi
−0.928980 + 0.370131i 0.879313π0.879313\pi
998998 48.1320 1.52359
999999 0 0
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 8649.2.a.r.1.2 4
3.2 odd 2 961.2.a.h.1.4 yes 4
31.30 odd 2 inner 8649.2.a.r.1.1 4
93.2 odd 10 961.2.d.j.531.2 8
93.5 odd 6 961.2.c.h.521.3 8
93.8 odd 10 961.2.d.h.374.1 8
93.11 even 30 961.2.g.i.338.2 16
93.14 odd 30 961.2.g.i.816.1 16
93.17 even 30 961.2.g.i.816.2 16
93.20 odd 30 961.2.g.i.338.1 16
93.23 even 10 961.2.d.h.374.2 8
93.26 even 6 961.2.c.h.521.4 8
93.29 even 10 961.2.d.j.531.1 8
93.35 odd 10 961.2.d.h.388.1 8
93.38 odd 30 961.2.g.i.235.2 16
93.41 odd 30 961.2.g.p.844.1 16
93.44 even 30 961.2.g.p.448.1 16
93.47 odd 10 961.2.d.j.628.2 8
93.50 odd 30 961.2.g.p.547.2 16
93.53 even 30 961.2.g.i.732.1 16
93.56 odd 6 961.2.c.h.439.3 8
93.59 odd 30 961.2.g.p.846.1 16
93.65 even 30 961.2.g.p.846.2 16
93.68 even 6 961.2.c.h.439.4 8
93.71 odd 30 961.2.g.i.732.2 16
93.74 even 30 961.2.g.p.547.1 16
93.77 even 10 961.2.d.j.628.1 8
93.80 odd 30 961.2.g.p.448.2 16
93.83 even 30 961.2.g.p.844.2 16
93.86 even 30 961.2.g.i.235.1 16
93.89 even 10 961.2.d.h.388.2 8
93.92 even 2 961.2.a.h.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
961.2.a.h.1.3 4 93.92 even 2
961.2.a.h.1.4 yes 4 3.2 odd 2
961.2.c.h.439.3 8 93.56 odd 6
961.2.c.h.439.4 8 93.68 even 6
961.2.c.h.521.3 8 93.5 odd 6
961.2.c.h.521.4 8 93.26 even 6
961.2.d.h.374.1 8 93.8 odd 10
961.2.d.h.374.2 8 93.23 even 10
961.2.d.h.388.1 8 93.35 odd 10
961.2.d.h.388.2 8 93.89 even 10
961.2.d.j.531.1 8 93.29 even 10
961.2.d.j.531.2 8 93.2 odd 10
961.2.d.j.628.1 8 93.77 even 10
961.2.d.j.628.2 8 93.47 odd 10
961.2.g.i.235.1 16 93.86 even 30
961.2.g.i.235.2 16 93.38 odd 30
961.2.g.i.338.1 16 93.20 odd 30
961.2.g.i.338.2 16 93.11 even 30
961.2.g.i.732.1 16 93.53 even 30
961.2.g.i.732.2 16 93.71 odd 30
961.2.g.i.816.1 16 93.14 odd 30
961.2.g.i.816.2 16 93.17 even 30
961.2.g.p.448.1 16 93.44 even 30
961.2.g.p.448.2 16 93.80 odd 30
961.2.g.p.547.1 16 93.74 even 30
961.2.g.p.547.2 16 93.50 odd 30
961.2.g.p.844.1 16 93.41 odd 30
961.2.g.p.844.2 16 93.83 even 30
961.2.g.p.846.1 16 93.59 odd 30
961.2.g.p.846.2 16 93.65 even 30
8649.2.a.r.1.1 4 31.30 odd 2 inner
8649.2.a.r.1.2 4 1.1 even 1 trivial