Properties

Label 8464.2.a.cb.1.4
Level 84648464
Weight 22
Character 8464.1
Self dual yes
Analytic conductor 67.58567.585
Analytic rank 00
Dimension 88
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] = [8464,2,Mod(1,8464)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8464, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 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("8464.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 8464=24232 8464 = 2^{4} \cdot 23^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 8464.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8,0,-4,0,0,0,0,0,20,0,0,0,12] 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: 67.585380270867.5853802708
Analytic rank: 00
Dimension: 88
Coefficient field: 8.8.819879542784.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x84x722x6+80x5+151x4440x3298x2+532x146 x^{8} - 4x^{7} - 22x^{6} + 80x^{5} + 151x^{4} - 440x^{3} - 298x^{2} + 532x - 146 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 1058)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.4
Root 0.4437680.443768 of defining polynomial
Character χ\chi == 8464.1

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) == q2.37562q3+4.07171q5+1.94542q7+2.64357q9+2.44949q11+1.35643q139.67283q155.09341q17+3.55407q194.62158q21+11.5788q25+0.846745q274.40183q293.46410q315.81906q33+7.92118q35+1.94542q373.22236q395.57177q41+1.63579q43+10.7638q45+2.29416q473.21534q49+12.1000q51+8.84555q53+9.97360q558.44312q5714.3300q59+5.96285q61+5.14285q63+5.52299q65+8.83199q67+13.9877q714.92118q7327.5068q75+4.76529q77+7.06114q799.94225q81+4.96828q8320.7389q85+10.4571q87+16.0689q89+2.63883q91+8.22939q93+14.4711q95+8.59175q97+6.47539q99+O(q100)q-2.37562 q^{3} +4.07171 q^{5} +1.94542 q^{7} +2.64357 q^{9} +2.44949 q^{11} +1.35643 q^{13} -9.67283 q^{15} -5.09341 q^{17} +3.55407 q^{19} -4.62158 q^{21} +11.5788 q^{25} +0.846745 q^{27} -4.40183 q^{29} -3.46410 q^{31} -5.81906 q^{33} +7.92118 q^{35} +1.94542 q^{37} -3.22236 q^{39} -5.57177 q^{41} +1.63579 q^{43} +10.7638 q^{45} +2.29416 q^{47} -3.21534 q^{49} +12.1000 q^{51} +8.84555 q^{53} +9.97360 q^{55} -8.44312 q^{57} -14.3300 q^{59} +5.96285 q^{61} +5.14285 q^{63} +5.52299 q^{65} +8.83199 q^{67} +13.9877 q^{71} -4.92118 q^{73} -27.5068 q^{75} +4.76529 q^{77} +7.06114 q^{79} -9.94225 q^{81} +4.96828 q^{83} -20.7389 q^{85} +10.4571 q^{87} +16.0689 q^{89} +2.63883 q^{91} +8.22939 q^{93} +14.4711 q^{95} +8.59175 q^{97} +6.47539 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q4q3+20q9+12q13+32q2540q27+12q35+36q39+12q41+12q47+32q4912q5524q59+12q71+12q73+8q7516q8136q85++84q95+O(q100) 8 q - 4 q^{3} + 20 q^{9} + 12 q^{13} + 32 q^{25} - 40 q^{27} + 12 q^{35} + 36 q^{39} + 12 q^{41} + 12 q^{47} + 32 q^{49} - 12 q^{55} - 24 q^{59} + 12 q^{71} + 12 q^{73} + 8 q^{75} - 16 q^{81} - 36 q^{85}+ \cdots + 84 q^{95}+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 0
33 −2.37562 −1.37156 −0.685782 0.727807i 0.740540π-0.740540\pi
−0.685782 + 0.727807i 0.740540π0.740540\pi
44 0 0
55 4.07171 1.82092 0.910461 0.413594i 0.135727π-0.135727\pi
0.910461 + 0.413594i 0.135727π0.135727\pi
66 0 0
77 1.94542 0.735300 0.367650 0.929964i 0.380163π-0.380163\pi
0.367650 + 0.929964i 0.380163π0.380163\pi
88 0 0
99 2.64357 0.881190
1010 0 0
1111 2.44949 0.738549 0.369274 0.929320i 0.379606π-0.379606\pi
0.369274 + 0.929320i 0.379606π0.379606\pi
1212 0 0
1313 1.35643 0.376206 0.188103 0.982149i 0.439766π-0.439766\pi
0.188103 + 0.982149i 0.439766π0.439766\pi
1414 0 0
1515 −9.67283 −2.49751
1616 0 0
1717 −5.09341 −1.23533 −0.617667 0.786440i 0.711922π-0.711922\pi
−0.617667 + 0.786440i 0.711922π0.711922\pi
1818 0 0
1919 3.55407 0.815359 0.407680 0.913125i 0.366338π-0.366338\pi
0.407680 + 0.913125i 0.366338π0.366338\pi
2020 0 0
2121 −4.62158 −1.00851
2222 0 0
2323 0 0
2424 0 0
2525 11.5788 2.31576
2626 0 0
2727 0.846745 0.162956
2828 0 0
2929 −4.40183 −0.817400 −0.408700 0.912669i 0.634018π-0.634018\pi
−0.408700 + 0.912669i 0.634018π0.634018\pi
3030 0 0
3131 −3.46410 −0.622171 −0.311086 0.950382i 0.600693π-0.600693\pi
−0.311086 + 0.950382i 0.600693π0.600693\pi
3232 0 0
3333 −5.81906 −1.01297
3434 0 0
3535 7.92118 1.33892
3636 0 0
3737 1.94542 0.319825 0.159913 0.987131i 0.448879π-0.448879\pi
0.159913 + 0.987131i 0.448879π0.448879\pi
3838 0 0
3939 −3.22236 −0.515991
4040 0 0
4141 −5.57177 −0.870165 −0.435082 0.900391i 0.643281π-0.643281\pi
−0.435082 + 0.900391i 0.643281π0.643281\pi
4242 0 0
4343 1.63579 0.249455 0.124727 0.992191i 0.460194π-0.460194\pi
0.124727 + 0.992191i 0.460194π0.460194\pi
4444 0 0
4545 10.7638 1.60458
4646 0 0
4747 2.29416 0.334638 0.167319 0.985903i 0.446489π-0.446489\pi
0.167319 + 0.985903i 0.446489π0.446489\pi
4848 0 0
4949 −3.21534 −0.459334
5050 0 0
5151 12.1000 1.69434
5252 0 0
5353 8.84555 1.21503 0.607515 0.794308i 0.292166π-0.292166\pi
0.607515 + 0.794308i 0.292166π0.292166\pi
5454 0 0
5555 9.97360 1.34484
5656 0 0
5757 −8.44312 −1.11832
5858 0 0
5959 −14.3300 −1.86561 −0.932806 0.360379i 0.882647π-0.882647\pi
−0.932806 + 0.360379i 0.882647π0.882647\pi
6060 0 0
6161 5.96285 0.763465 0.381733 0.924273i 0.375328π-0.375328\pi
0.381733 + 0.924273i 0.375328π0.375328\pi
6262 0 0
6363 5.14285 0.647938
6464 0 0
6565 5.52299 0.685043
6666 0 0
6767 8.83199 1.07900 0.539499 0.841986i 0.318614π-0.318614\pi
0.539499 + 0.841986i 0.318614π0.318614\pi
6868 0 0
6969 0 0
7070 0 0
7171 13.9877 1.66003 0.830014 0.557742i 0.188332π-0.188332\pi
0.830014 + 0.557742i 0.188332π0.188332\pi
7272 0 0
7373 −4.92118 −0.575981 −0.287990 0.957633i 0.592987π-0.592987\pi
−0.287990 + 0.957633i 0.592987π0.592987\pi
7474 0 0
7575 −27.5068 −3.17621
7676 0 0
7777 4.76529 0.543055
7878 0 0
7979 7.06114 0.794440 0.397220 0.917723i 0.369975π-0.369975\pi
0.397220 + 0.917723i 0.369975π0.369975\pi
8080 0 0
8181 −9.94225 −1.10469
8282 0 0
8383 4.96828 0.545340 0.272670 0.962108i 0.412093π-0.412093\pi
0.272670 + 0.962108i 0.412093π0.412093\pi
8484 0 0
8585 −20.7389 −2.24945
8686 0 0
8787 10.4571 1.12112
8888 0 0
8989 16.0689 1.70330 0.851650 0.524112i 0.175603π-0.175603\pi
0.851650 + 0.524112i 0.175603π0.175603\pi
9090 0 0
9191 2.63883 0.276624
9292 0 0
9393 8.22939 0.853348
9494 0 0
9595 14.4711 1.48471
9696 0 0
9797 8.59175 0.872360 0.436180 0.899859i 0.356331π-0.356331\pi
0.436180 + 0.899859i 0.356331π0.356331\pi
9898 0 0
9999 6.47539 0.650802
100100 0 0
101101 15.5858 1.55085 0.775423 0.631442i 0.217536π-0.217536\pi
0.775423 + 0.631442i 0.217536π0.217536\pi
102102 0 0
103103 −9.82510 −0.968095 −0.484048 0.875042i 0.660834π-0.660834\pi
−0.484048 + 0.875042i 0.660834π0.660834\pi
104104 0 0
105105 −18.8177 −1.83642
106106 0 0
107107 −2.10762 −0.203751 −0.101876 0.994797i 0.532484π-0.532484\pi
−0.101876 + 0.994797i 0.532484π0.532484\pi
108108 0 0
109109 11.1328 1.06633 0.533166 0.846010i 0.321002π-0.321002\pi
0.533166 + 0.846010i 0.321002π0.321002\pi
110110 0 0
111111 −4.62158 −0.438661
112112 0 0
113113 11.6146 1.09261 0.546305 0.837586i 0.316034π-0.316034\pi
0.546305 + 0.837586i 0.316034π0.316034\pi
114114 0 0
115115 0 0
116116 0 0
117117 3.58582 0.331509
118118 0 0
119119 −9.90883 −0.908341
120120 0 0
121121 −5.00000 −0.454545
122122 0 0
123123 13.2364 1.19349
124124 0 0
125125 26.7869 2.39590
126126 0 0
127127 −8.22939 −0.730240 −0.365120 0.930960i 0.618972π-0.618972\pi
−0.365120 + 0.930960i 0.618972π0.618972\pi
128128 0 0
129129 −3.88600 −0.342144
130130 0 0
131131 8.81351 0.770040 0.385020 0.922908i 0.374195π-0.374195\pi
0.385020 + 0.922908i 0.374195π0.374195\pi
132132 0 0
133133 6.91416 0.599533
134134 0 0
135135 3.44770 0.296730
136136 0 0
137137 3.87727 0.331258 0.165629 0.986188i 0.447035π-0.447035\pi
0.165629 + 0.986188i 0.447035π0.447035\pi
138138 0 0
139139 0.533395 0.0452420 0.0226210 0.999744i 0.492799π-0.492799\pi
0.0226210 + 0.999744i 0.492799π0.492799\pi
140140 0 0
141141 −5.45005 −0.458977
142142 0 0
143143 3.32256 0.277847
144144 0 0
145145 −17.9230 −1.48842
146146 0 0
147147 7.63843 0.630007
148148 0 0
149149 −2.79256 −0.228775 −0.114388 0.993436i 0.536491π-0.536491\pi
−0.114388 + 0.993436i 0.536491π0.536491\pi
150150 0 0
151151 −22.2030 −1.80685 −0.903427 0.428742i 0.858957π-0.858957\pi
−0.903427 + 0.428742i 0.858957π0.858957\pi
152152 0 0
153153 −13.4648 −1.08856
154154 0 0
155155 −14.1048 −1.13293
156156 0 0
157157 −12.4925 −0.997012 −0.498506 0.866886i 0.666118π-0.666118\pi
−0.498506 + 0.866886i 0.666118π0.666118\pi
158158 0 0
159159 −21.0137 −1.66649
160160 0 0
161161 0 0
162162 0 0
163163 −6.33254 −0.496003 −0.248001 0.968760i 0.579774π-0.579774\pi
−0.248001 + 0.968760i 0.579774π0.579774\pi
164164 0 0
165165 −23.6935 −1.84454
166166 0 0
167167 20.6741 1.59981 0.799906 0.600126i 0.204883π-0.204883\pi
0.799906 + 0.600126i 0.204883π0.204883\pi
168168 0 0
169169 −11.1601 −0.858469
170170 0 0
171171 9.39543 0.718486
172172 0 0
173173 1.59817 0.121506 0.0607532 0.998153i 0.480650π-0.480650\pi
0.0607532 + 0.998153i 0.480650π0.480650\pi
174174 0 0
175175 22.5256 1.70278
176176 0 0
177177 34.0427 2.55881
178178 0 0
179179 −8.87107 −0.663055 −0.331528 0.943446i 0.607564π-0.607564\pi
−0.331528 + 0.943446i 0.607564π0.607564\pi
180180 0 0
181181 4.26624 0.317107 0.158553 0.987350i 0.449317π-0.449317\pi
0.158553 + 0.987350i 0.449317π0.449317\pi
182182 0 0
183183 −14.1655 −1.04714
184184 0 0
185185 7.92118 0.582377
186186 0 0
187187 −12.4763 −0.912355
188188 0 0
189189 1.64727 0.119822
190190 0 0
191191 −3.58630 −0.259496 −0.129748 0.991547i 0.541417π-0.541417\pi
−0.129748 + 0.991547i 0.541417π0.541417\pi
192192 0 0
193193 15.2870 1.10038 0.550190 0.835040i 0.314555π-0.314555\pi
0.550190 + 0.835040i 0.314555π0.314555\pi
194194 0 0
195195 −13.1205 −0.939580
196196 0 0
197197 −7.79946 −0.555689 −0.277844 0.960626i 0.589620π-0.589620\pi
−0.277844 + 0.960626i 0.589620π0.589620\pi
198198 0 0
199199 24.1394 1.71119 0.855597 0.517642i 0.173190π-0.173190\pi
0.855597 + 0.517642i 0.173190π0.173190\pi
200200 0 0
201201 −20.9814 −1.47992
202202 0 0
203203 −8.56341 −0.601034
204204 0 0
205205 −22.6866 −1.58450
206206 0 0
207207 0 0
208208 0 0
209209 8.70565 0.602183
210210 0 0
211211 0.100647 0.00692882 0.00346441 0.999994i 0.498897π-0.498897\pi
0.00346441 + 0.999994i 0.498897π0.498897\pi
212212 0 0
213213 −33.2293 −2.27684
214214 0 0
215215 6.66044 0.454238
216216 0 0
217217 −6.73913 −0.457482
218218 0 0
219219 11.6909 0.789995
220220 0 0
221221 −6.90887 −0.464741
222222 0 0
223223 −6.11720 −0.409638 −0.204819 0.978800i 0.565661π-0.565661\pi
−0.204819 + 0.978800i 0.565661π0.565661\pi
224224 0 0
225225 30.6093 2.04062
226226 0 0
227227 24.5033 1.62634 0.813170 0.582027i 0.197740π-0.197740\pi
0.813170 + 0.582027i 0.197740π0.197740\pi
228228 0 0
229229 −13.9724 −0.923322 −0.461661 0.887056i 0.652746π-0.652746\pi
−0.461661 + 0.887056i 0.652746π0.652746\pi
230230 0 0
231231 −11.3205 −0.744835
232232 0 0
233233 4.85641 0.318154 0.159077 0.987266i 0.449148π-0.449148\pi
0.159077 + 0.987266i 0.449148π0.449148\pi
234234 0 0
235235 9.34115 0.609350
236236 0 0
237237 −16.7746 −1.08963
238238 0 0
239239 −10.6601 −0.689543 −0.344771 0.938687i 0.612044π-0.612044\pi
−0.344771 + 0.938687i 0.612044π0.612044\pi
240240 0 0
241241 13.3806 0.861922 0.430961 0.902371i 0.358175π-0.358175\pi
0.430961 + 0.902371i 0.358175π0.358175\pi
242242 0 0
243243 21.0788 1.35220
244244 0 0
245245 −13.0919 −0.836412
246246 0 0
247247 4.82085 0.306743
248248 0 0
249249 −11.8027 −0.747969
250250 0 0
251251 −3.44260 −0.217295 −0.108647 0.994080i 0.534652π-0.534652\pi
−0.108647 + 0.994080i 0.534652π0.534652\pi
252252 0 0
253253 0 0
254254 0 0
255255 49.2677 3.08526
256256 0 0
257257 −8.79150 −0.548399 −0.274199 0.961673i 0.588413π-0.588413\pi
−0.274199 + 0.961673i 0.588413π0.588413\pi
258258 0 0
259259 3.78466 0.235167
260260 0 0
261261 −11.6365 −0.720284
262262 0 0
263263 −17.0957 −1.05417 −0.527083 0.849814i 0.676714π-0.676714\pi
−0.527083 + 0.849814i 0.676714π0.676714\pi
264264 0 0
265265 36.0165 2.21248
266266 0 0
267267 −38.1736 −2.33618
268268 0 0
269269 −4.28181 −0.261067 −0.130533 0.991444i 0.541669π-0.541669\pi
−0.130533 + 0.991444i 0.541669π0.541669\pi
270270 0 0
271271 13.6337 0.828190 0.414095 0.910234i 0.364098π-0.364098\pi
0.414095 + 0.910234i 0.364098π0.364098\pi
272272 0 0
273273 −6.26885 −0.379408
274274 0 0
275275 28.3621 1.71030
276276 0 0
277277 −30.3395 −1.82292 −0.911462 0.411384i 0.865046π-0.865046\pi
−0.911462 + 0.411384i 0.865046π0.865046\pi
278278 0 0
279279 −9.15759 −0.548251
280280 0 0
281281 −9.25793 −0.552282 −0.276141 0.961117i 0.589056π-0.589056\pi
−0.276141 + 0.961117i 0.589056π0.589056\pi
282282 0 0
283283 14.7391 0.876149 0.438074 0.898939i 0.355661π-0.355661\pi
0.438074 + 0.898939i 0.355661π0.355661\pi
284284 0 0
285285 −34.3779 −2.03637
286286 0 0
287287 −10.8394 −0.639832
288288 0 0
289289 8.94287 0.526051
290290 0 0
291291 −20.4107 −1.19650
292292 0 0
293293 −15.7879 −0.922342 −0.461171 0.887311i 0.652571π-0.652571\pi
−0.461171 + 0.887311i 0.652571π0.652571\pi
294294 0 0
295295 −58.3477 −3.39713
296296 0 0
297297 2.07409 0.120351
298298 0 0
299299 0 0
300300 0 0
301301 3.18229 0.183424
302302 0 0
303303 −37.0260 −2.12709
304304 0 0
305305 24.2790 1.39021
306306 0 0
307307 −32.9589 −1.88107 −0.940533 0.339703i 0.889674π-0.889674\pi
−0.940533 + 0.339703i 0.889674π0.889674\pi
308308 0 0
309309 23.3407 1.32781
310310 0 0
311311 19.9212 1.12963 0.564813 0.825219i 0.308948π-0.308948\pi
0.564813 + 0.825219i 0.308948π0.308948\pi
312312 0 0
313313 9.67273 0.546735 0.273368 0.961910i 0.411862π-0.411862\pi
0.273368 + 0.961910i 0.411862π0.411862\pi
314314 0 0
315315 20.9402 1.17985
316316 0 0
317317 −18.3490 −1.03058 −0.515292 0.857014i 0.672317π-0.672317\pi
−0.515292 + 0.857014i 0.672317π0.672317\pi
318318 0 0
319319 −10.7822 −0.603690
320320 0 0
321321 5.00691 0.279458
322322 0 0
323323 −18.1023 −1.00724
324324 0 0
325325 15.7058 0.871203
326326 0 0
327327 −26.4474 −1.46254
328328 0 0
329329 4.46311 0.246059
330330 0 0
331331 25.5384 1.40371 0.701857 0.712317i 0.252354π-0.252354\pi
0.701857 + 0.712317i 0.252354π0.252354\pi
332332 0 0
333333 5.14285 0.281827
334334 0 0
335335 35.9613 1.96477
336336 0 0
337337 32.6280 1.77736 0.888681 0.458526i 0.151623π-0.151623\pi
0.888681 + 0.458526i 0.151623π0.151623\pi
338338 0 0
339339 −27.5919 −1.49859
340340 0 0
341341 −8.48528 −0.459504
342342 0 0
343343 −19.8731 −1.07305
344344 0 0
345345 0 0
346346 0 0
347347 −11.6909 −0.627598 −0.313799 0.949489i 0.601602π-0.601602\pi
−0.313799 + 0.949489i 0.601602π0.601602\pi
348348 0 0
349349 11.3012 0.604939 0.302469 0.953159i 0.402189π-0.402189\pi
0.302469 + 0.953159i 0.402189π0.402189\pi
350350 0 0
351351 1.14855 0.0613051
352352 0 0
353353 −25.1190 −1.33695 −0.668476 0.743734i 0.733053π-0.733053\pi
−0.668476 + 0.743734i 0.733053π0.733053\pi
354354 0 0
355355 56.9536 3.02278
356356 0 0
357357 23.5396 1.24585
358358 0 0
359359 −15.9761 −0.843186 −0.421593 0.906785i 0.638529π-0.638529\pi
−0.421593 + 0.906785i 0.638529π0.638529\pi
360360 0 0
361361 −6.36860 −0.335189
362362 0 0
363363 11.8781 0.623438
364364 0 0
365365 −20.0376 −1.04882
366366 0 0
367367 −0.337877 −0.0176370 −0.00881851 0.999961i 0.502807π-0.502807\pi
−0.00881851 + 0.999961i 0.502807π0.502807\pi
368368 0 0
369369 −14.7294 −0.766780
370370 0 0
371371 17.2083 0.893411
372372 0 0
373373 2.17582 0.112660 0.0563298 0.998412i 0.482060π-0.482060\pi
0.0563298 + 0.998412i 0.482060π0.482060\pi
374374 0 0
375375 −63.6355 −3.28613
376376 0 0
377377 −5.97078 −0.307511
378378 0 0
379379 −3.99367 −0.205141 −0.102571 0.994726i 0.532707π-0.532707\pi
−0.102571 + 0.994726i 0.532707π0.532707\pi
380380 0 0
381381 19.5499 1.00157
382382 0 0
383383 16.2398 0.829816 0.414908 0.909863i 0.363814π-0.363814\pi
0.414908 + 0.909863i 0.363814π0.363814\pi
384384 0 0
385385 19.4028 0.988861
386386 0 0
387387 4.32431 0.219817
388388 0 0
389389 3.96170 0.200866 0.100433 0.994944i 0.467977π-0.467977\pi
0.100433 + 0.994944i 0.467977π0.467977\pi
390390 0 0
391391 0 0
392392 0 0
393393 −20.9375 −1.05616
394394 0 0
395395 28.7509 1.44661
396396 0 0
397397 9.53339 0.478467 0.239234 0.970962i 0.423104π-0.423104\pi
0.239234 + 0.970962i 0.423104π0.423104\pi
398398 0 0
399399 −16.4254 −0.822299
400400 0 0
401401 −3.05120 −0.152370 −0.0761848 0.997094i 0.524274π-0.524274\pi
−0.0761848 + 0.997094i 0.524274π0.524274\pi
402402 0 0
403403 −4.69882 −0.234065
404404 0 0
405405 −40.4819 −2.01156
406406 0 0
407407 4.76529 0.236206
408408 0 0
409409 39.7028 1.96318 0.981589 0.191003i 0.0611742π-0.0611742\pi
0.981589 + 0.191003i 0.0611742π0.0611742\pi
410410 0 0
411411 −9.21092 −0.454341
412412 0 0
413413 −27.8779 −1.37178
414414 0 0
415415 20.2294 0.993022
416416 0 0
417417 −1.26714 −0.0620523
418418 0 0
419419 30.8981 1.50947 0.754736 0.656028i 0.227765π-0.227765\pi
0.754736 + 0.656028i 0.227765π0.227765\pi
420420 0 0
421421 −2.14868 −0.104720 −0.0523602 0.998628i 0.516674π-0.516674\pi
−0.0523602 + 0.998628i 0.516674π0.516674\pi
422422 0 0
423423 6.06477 0.294879
424424 0 0
425425 −58.9756 −2.86074
426426 0 0
427427 11.6003 0.561376
428428 0 0
429429 −7.89315 −0.381085
430430 0 0
431431 25.1005 1.20905 0.604524 0.796587i 0.293363π-0.293363\pi
0.604524 + 0.796587i 0.293363π0.293363\pi
432432 0 0
433433 −5.95292 −0.286079 −0.143040 0.989717i 0.545688π-0.545688\pi
−0.143040 + 0.989717i 0.545688π0.545688\pi
434434 0 0
435435 42.5782 2.04147
436436 0 0
437437 0 0
438438 0 0
439439 −24.1766 −1.15389 −0.576943 0.816784i 0.695755π-0.695755\pi
−0.576943 + 0.816784i 0.695755π0.695755\pi
440440 0 0
441441 −8.49998 −0.404761
442442 0 0
443443 −6.51214 −0.309401 −0.154701 0.987961i 0.549441π-0.549441\pi
−0.154701 + 0.987961i 0.549441π0.549441\pi
444444 0 0
445445 65.4278 3.10158
446446 0 0
447447 6.63406 0.313780
448448 0 0
449449 29.7300 1.40304 0.701522 0.712647i 0.252504π-0.252504\pi
0.701522 + 0.712647i 0.252504π0.252504\pi
450450 0 0
451451 −13.6480 −0.642659
452452 0 0
453453 52.7459 2.47822
454454 0 0
455455 10.7445 0.503712
456456 0 0
457457 −4.37251 −0.204538 −0.102269 0.994757i 0.532610π-0.532610\pi
−0.102269 + 0.994757i 0.532610π0.532610\pi
458458 0 0
459459 −4.31282 −0.201305
460460 0 0
461461 7.86593 0.366353 0.183177 0.983080i 0.441362π-0.441362\pi
0.183177 + 0.983080i 0.441362π0.441362\pi
462462 0 0
463463 21.9472 1.01997 0.509987 0.860182i 0.329650π-0.329650\pi
0.509987 + 0.860182i 0.329650π0.329650\pi
464464 0 0
465465 33.5077 1.55388
466466 0 0
467467 −29.6404 −1.37159 −0.685797 0.727793i 0.740546π-0.740546\pi
−0.685797 + 0.727793i 0.740546π0.740546\pi
468468 0 0
469469 17.1819 0.793387
470470 0 0
471471 29.6775 1.36747
472472 0 0
473473 4.00684 0.184235
474474 0 0
475475 41.1518 1.88818
476476 0 0
477477 23.3838 1.07067
478478 0 0
479479 38.7485 1.77046 0.885232 0.465150i 0.153999π-0.153999\pi
0.885232 + 0.465150i 0.153999π0.153999\pi
480480 0 0
481481 2.63883 0.120320
482482 0 0
483483 0 0
484484 0 0
485485 34.9831 1.58850
486486 0 0
487487 −15.6777 −0.710426 −0.355213 0.934785i 0.615592π-0.615592\pi
−0.355213 + 0.934785i 0.615592π0.615592\pi
488488 0 0
489489 15.0437 0.680300
490490 0 0
491491 16.8561 0.760705 0.380352 0.924842i 0.375803π-0.375803\pi
0.380352 + 0.924842i 0.375803π0.375803\pi
492492 0 0
493493 22.4204 1.00976
494494 0 0
495495 26.3659 1.18506
496496 0 0
497497 27.2119 1.22062
498498 0 0
499499 16.9853 0.760368 0.380184 0.924911i 0.375861π-0.375861\pi
0.380184 + 0.924911i 0.375861π0.375861\pi
500500 0 0
501501 −49.1138 −2.19424
502502 0 0
503503 5.66325 0.252512 0.126256 0.991998i 0.459704π-0.459704\pi
0.126256 + 0.991998i 0.459704π0.459704\pi
504504 0 0
505505 63.4609 2.82397
506506 0 0
507507 26.5121 1.17745
508508 0 0
509509 10.4262 0.462131 0.231066 0.972938i 0.425779π-0.425779\pi
0.231066 + 0.972938i 0.425779π0.425779\pi
510510 0 0
511511 −9.57376 −0.423518
512512 0 0
513513 3.00939 0.132868
514514 0 0
515515 −40.0049 −1.76283
516516 0 0
517517 5.61952 0.247146
518518 0 0
519519 −3.79664 −0.166654
520520 0 0
521521 27.8011 1.21799 0.608995 0.793174i 0.291573π-0.291573\pi
0.608995 + 0.793174i 0.291573π0.291573\pi
522522 0 0
523523 −21.1154 −0.923312 −0.461656 0.887059i 0.652745π-0.652745\pi
−0.461656 + 0.887059i 0.652745π0.652745\pi
524524 0 0
525525 −53.5123 −2.33547
526526 0 0
527527 17.6441 0.768589
528528 0 0
529529 0 0
530530 0 0
531531 −37.8824 −1.64396
532532 0 0
533533 −7.55773 −0.327361
534534 0 0
535535 −8.58162 −0.371016
536536 0 0
537537 21.0743 0.909423
538538 0 0
539539 −7.87594 −0.339241
540540 0 0
541541 −31.1340 −1.33856 −0.669278 0.743012i 0.733396π-0.733396\pi
−0.669278 + 0.743012i 0.733396π0.733396\pi
542542 0 0
543543 −10.1350 −0.434933
544544 0 0
545545 45.3297 1.94171
546546 0 0
547547 −23.8705 −1.02063 −0.510313 0.859988i 0.670471π-0.670471\pi
−0.510313 + 0.859988i 0.670471π0.670471\pi
548548 0 0
549549 15.7632 0.672758
550550 0 0
551551 −15.6444 −0.666474
552552 0 0
553553 13.7369 0.584151
554554 0 0
555555 −18.8177 −0.798767
556556 0 0
557557 46.8977 1.98712 0.993560 0.113305i 0.0361439π-0.0361439\pi
0.993560 + 0.113305i 0.0361439π0.0361439\pi
558558 0 0
559559 2.21883 0.0938465
560560 0 0
561561 29.6389 1.25135
562562 0 0
563563 −6.76143 −0.284960 −0.142480 0.989798i 0.545508π-0.545508\pi
−0.142480 + 0.989798i 0.545508π0.545508\pi
564564 0 0
565565 47.2913 1.98956
566566 0 0
567567 −19.3419 −0.812281
568568 0 0
569569 2.06692 0.0866497 0.0433248 0.999061i 0.486205π-0.486205\pi
0.0433248 + 0.999061i 0.486205π0.486205\pi
570570 0 0
571571 17.8482 0.746924 0.373462 0.927645i 0.378171π-0.378171\pi
0.373462 + 0.927645i 0.378171π0.378171\pi
572572 0 0
573573 8.51969 0.355915
574574 0 0
575575 0 0
576576 0 0
577577 −14.8779 −0.619376 −0.309688 0.950838i 0.600225π-0.600225\pi
−0.309688 + 0.950838i 0.600225π0.600225\pi
578578 0 0
579579 −36.3160 −1.50924
580580 0 0
581581 9.66540 0.400988
582582 0 0
583583 21.6671 0.897359
584584 0 0
585585 14.6004 0.603652
586586 0 0
587587 −29.5524 −1.21976 −0.609879 0.792495i 0.708782π-0.708782\pi
−0.609879 + 0.792495i 0.708782π0.708782\pi
588588 0 0
589589 −12.3117 −0.507293
590590 0 0
591591 18.5286 0.762163
592592 0 0
593593 24.1392 0.991276 0.495638 0.868529i 0.334934π-0.334934\pi
0.495638 + 0.868529i 0.334934π0.334934\pi
594594 0 0
595595 −40.3459 −1.65402
596596 0 0
597597 −57.3460 −2.34701
598598 0 0
599599 12.0404 0.491959 0.245980 0.969275i 0.420890π-0.420890\pi
0.245980 + 0.969275i 0.420890π0.420890\pi
600600 0 0
601601 32.6696 1.33262 0.666310 0.745675i 0.267873π-0.267873\pi
0.666310 + 0.745675i 0.267873π0.267873\pi
602602 0 0
603603 23.3480 0.950803
604604 0 0
605605 −20.3585 −0.827692
606606 0 0
607607 −4.09287 −0.166124 −0.0830622 0.996544i 0.526470π-0.526470\pi
−0.0830622 + 0.996544i 0.526470π0.526470\pi
608608 0 0
609609 20.3434 0.824357
610610 0 0
611611 3.11187 0.125893
612612 0 0
613613 29.7094 1.19995 0.599975 0.800019i 0.295177π-0.295177\pi
0.599975 + 0.800019i 0.295177π0.295177\pi
614614 0 0
615615 53.8948 2.17325
616616 0 0
617617 −20.8936 −0.841146 −0.420573 0.907259i 0.638171π-0.638171\pi
−0.420573 + 0.907259i 0.638171π0.638171\pi
618618 0 0
619619 −36.3294 −1.46020 −0.730102 0.683339i 0.760527π-0.760527\pi
−0.730102 + 0.683339i 0.760527π0.760527\pi
620620 0 0
621621 0 0
622622 0 0
623623 31.2607 1.25244
624624 0 0
625625 51.1745 2.04698
626626 0 0
627627 −20.6813 −0.825933
628628 0 0
629629 −9.90883 −0.395091
630630 0 0
631631 −1.77569 −0.0706890 −0.0353445 0.999375i 0.511253π-0.511253\pi
−0.0353445 + 0.999375i 0.511253π0.511253\pi
632632 0 0
633633 −0.239099 −0.00950333
634634 0 0
635635 −33.5077 −1.32971
636636 0 0
637637 −4.36139 −0.172805
638638 0 0
639639 36.9773 1.46280
640640 0 0
641641 33.0344 1.30478 0.652389 0.757884i 0.273767π-0.273767\pi
0.652389 + 0.757884i 0.273767π0.273767\pi
642642 0 0
643643 43.0895 1.69928 0.849642 0.527360i 0.176818π-0.176818\pi
0.849642 + 0.527360i 0.176818π0.176818\pi
644644 0 0
645645 −15.8227 −0.623017
646646 0 0
647647 0.0891034 0.00350302 0.00175151 0.999998i 0.499442π-0.499442\pi
0.00175151 + 0.999998i 0.499442π0.499442\pi
648648 0 0
649649 −35.1013 −1.37785
650650 0 0
651651 16.0096 0.627466
652652 0 0
653653 −9.03587 −0.353601 −0.176801 0.984247i 0.556575π-0.556575\pi
−0.176801 + 0.984247i 0.556575π0.556575\pi
654654 0 0
655655 35.8860 1.40218
656656 0 0
657657 −13.0095 −0.507548
658658 0 0
659659 7.78944 0.303433 0.151717 0.988424i 0.451520π-0.451520\pi
0.151717 + 0.988424i 0.451520π0.451520\pi
660660 0 0
661661 27.8692 1.08399 0.541993 0.840383i 0.317670π-0.317670\pi
0.541993 + 0.840383i 0.317670π0.317670\pi
662662 0 0
663663 16.4128 0.637422
664664 0 0
665665 28.1524 1.09170
666666 0 0
667667 0 0
668668 0 0
669669 14.5321 0.561845
670670 0 0
671671 14.6059 0.563856
672672 0 0
673673 0.885122 0.0341189 0.0170595 0.999854i 0.494570π-0.494570\pi
0.0170595 + 0.999854i 0.494570π0.494570\pi
674674 0 0
675675 9.80428 0.377367
676676 0 0
677677 −45.3102 −1.74141 −0.870707 0.491802i 0.836338π-0.836338\pi
−0.870707 + 0.491802i 0.836338π0.836338\pi
678678 0 0
679679 16.7146 0.641446
680680 0 0
681681 −58.2105 −2.23063
682682 0 0
683683 51.8395 1.98358 0.991791 0.127866i 0.0408128π-0.0408128\pi
0.991791 + 0.127866i 0.0408128π0.0408128\pi
684684 0 0
685685 15.7871 0.603195
686686 0 0
687687 33.1931 1.26640
688688 0 0
689689 11.9984 0.457102
690690 0 0
691691 −31.3012 −1.19075 −0.595377 0.803447i 0.702997π-0.702997\pi
−0.595377 + 0.803447i 0.702997π0.702997\pi
692692 0 0
693693 12.5974 0.478534
694694 0 0
695695 2.17183 0.0823821
696696 0 0
697697 28.3793 1.07494
698698 0 0
699699 −11.5370 −0.436368
700700 0 0
701701 −12.3084 −0.464881 −0.232440 0.972611i 0.574671π-0.574671\pi
−0.232440 + 0.972611i 0.574671π0.574671\pi
702702 0 0
703703 6.91416 0.260772
704704 0 0
705705 −22.1910 −0.835762
706706 0 0
707707 30.3210 1.14034
708708 0 0
709709 19.3568 0.726959 0.363480 0.931602i 0.381589π-0.381589\pi
0.363480 + 0.931602i 0.381589π0.381589\pi
710710 0 0
711711 18.6666 0.700052
712712 0 0
713713 0 0
714714 0 0
715715 13.5285 0.505937
716716 0 0
717717 25.3243 0.945752
718718 0 0
719719 −0.616416 −0.0229885 −0.0114942 0.999934i 0.503659π-0.503659\pi
−0.0114942 + 0.999934i 0.503659π0.503659\pi
720720 0 0
721721 −19.1139 −0.711840
722722 0 0
723723 −31.7873 −1.18218
724724 0 0
725725 −50.9679 −1.89290
726726 0 0
727727 −45.3126 −1.68055 −0.840275 0.542160i 0.817607π-0.817607\pi
−0.840275 + 0.542160i 0.817607π0.817607\pi
728728 0 0
729729 −20.2484 −0.749940
730730 0 0
731731 −8.33173 −0.308160
732732 0 0
733733 −17.3915 −0.642370 −0.321185 0.947017i 0.604081π-0.604081\pi
−0.321185 + 0.947017i 0.604081π0.604081\pi
734734 0 0
735735 31.1014 1.14719
736736 0 0
737737 21.6339 0.796893
738738 0 0
739739 −33.9686 −1.24956 −0.624778 0.780803i 0.714810π-0.714810\pi
−0.624778 + 0.780803i 0.714810π0.714810\pi
740740 0 0
741741 −11.4525 −0.420718
742742 0 0
743743 −25.9127 −0.950643 −0.475321 0.879812i 0.657668π-0.657668\pi
−0.475321 + 0.879812i 0.657668π0.657668\pi
744744 0 0
745745 −11.3705 −0.416582
746746 0 0
747747 13.1340 0.480548
748748 0 0
749749 −4.10021 −0.149818
750750 0 0
751751 −21.5515 −0.786427 −0.393213 0.919447i 0.628637π-0.628637\pi
−0.393213 + 0.919447i 0.628637π0.628637\pi
752752 0 0
753753 8.17831 0.298034
754754 0 0
755755 −90.4041 −3.29014
756756 0 0
757757 −30.5862 −1.11167 −0.555837 0.831292i 0.687602π-0.687602\pi
−0.555837 + 0.831292i 0.687602π0.687602\pi
758758 0 0
759759 0 0
760760 0 0
761761 22.0332 0.798702 0.399351 0.916798i 0.369235π-0.369235\pi
0.399351 + 0.916798i 0.369235π0.369235\pi
762762 0 0
763763 21.6581 0.784074
764764 0 0
765765 −54.8247 −1.98219
766766 0 0
767767 −19.4377 −0.701855
768768 0 0
769769 −42.3961 −1.52884 −0.764421 0.644717i 0.776975π-0.776975\pi
−0.764421 + 0.644717i 0.776975π0.776975\pi
770770 0 0
771771 20.8853 0.752164
772772 0 0
773773 −10.2548 −0.368838 −0.184419 0.982848i 0.559040π-0.559040\pi
−0.184419 + 0.982848i 0.559040π0.559040\pi
774774 0 0
775775 −40.1101 −1.44080
776776 0 0
777777 −8.99091 −0.322547
778778 0 0
779779 −19.8025 −0.709497
780780 0 0
781781 34.2626 1.22601
782782 0 0
783783 −3.72723 −0.133200
784784 0 0
785785 −50.8659 −1.81548
786786 0 0
787787 48.6462 1.73405 0.867025 0.498265i 0.166030π-0.166030\pi
0.867025 + 0.498265i 0.166030π0.166030\pi
788788 0 0
789789 40.6129 1.44586
790790 0 0
791791 22.5953 0.803396
792792 0 0
793793 8.08820 0.287220
794794 0 0
795795 −85.5615 −3.03455
796796 0 0
797797 −46.1175 −1.63356 −0.816782 0.576946i 0.804244π-0.804244\pi
−0.816782 + 0.576946i 0.804244π0.804244\pi
798798 0 0
799799 −11.6851 −0.413390
800800 0 0
801801 42.4792 1.50093
802802 0 0
803803 −12.0544 −0.425390
804804 0 0
805805 0 0
806806 0 0
807807 10.1720 0.358070
808808 0 0
809809 33.9809 1.19470 0.597352 0.801979i 0.296220π-0.296220\pi
0.597352 + 0.801979i 0.296220π0.296220\pi
810810 0 0
811811 −5.04290 −0.177080 −0.0885400 0.996073i 0.528220π-0.528220\pi
−0.0885400 + 0.996073i 0.528220π0.528220\pi
812812 0 0
813813 −32.3885 −1.13592
814814 0 0
815815 −25.7842 −0.903182
816816 0 0
817817 5.81369 0.203395
818818 0 0
819819 6.97592 0.243759
820820 0 0
821821 2.44191 0.0852231 0.0426116 0.999092i 0.486432π-0.486432\pi
0.0426116 + 0.999092i 0.486432π0.486432\pi
822822 0 0
823823 2.84938 0.0993232 0.0496616 0.998766i 0.484186π-0.484186\pi
0.0496616 + 0.998766i 0.484186π0.484186\pi
824824 0 0
825825 −67.3777 −2.34579
826826 0 0
827827 3.88626 0.135139 0.0675693 0.997715i 0.478476π-0.478476\pi
0.0675693 + 0.997715i 0.478476π0.478476\pi
828828 0 0
829829 20.3631 0.707239 0.353620 0.935389i 0.384951π-0.384951\pi
0.353620 + 0.935389i 0.384951π0.384951\pi
830830 0 0
831831 72.0751 2.50026
832832 0 0
833833 16.3771 0.567432
834834 0 0
835835 84.1789 2.91313
836836 0 0
837837 −2.93321 −0.101387
838838 0 0
839839 −7.05733 −0.243646 −0.121823 0.992552i 0.538874π-0.538874\pi
−0.121823 + 0.992552i 0.538874π0.538874\pi
840840 0 0
841841 −9.62388 −0.331858
842842 0 0
843843 21.9933 0.757490
844844 0 0
845845 −45.4406 −1.56321
846846 0 0
847847 −9.72710 −0.334227
848848 0 0
849849 −35.0145 −1.20169
850850 0 0
851851 0 0
852852 0 0
853853 −22.4781 −0.769635 −0.384818 0.922993i 0.625736π-0.625736\pi
−0.384818 + 0.922993i 0.625736π0.625736\pi
854854 0 0
855855 38.2554 1.30831
856856 0 0
857857 6.43977 0.219978 0.109989 0.993933i 0.464918π-0.464918\pi
0.109989 + 0.993933i 0.464918π0.464918\pi
858858 0 0
859859 −37.7008 −1.28633 −0.643167 0.765726i 0.722380π-0.722380\pi
−0.643167 + 0.765726i 0.722380π0.722380\pi
860860 0 0
861861 25.7504 0.877571
862862 0 0
863863 −34.5566 −1.17632 −0.588159 0.808745i 0.700147π-0.700147\pi
−0.588159 + 0.808745i 0.700147π0.700147\pi
864864 0 0
865865 6.50727 0.221254
866866 0 0
867867 −21.2449 −0.721513
868868 0 0
869869 17.2962 0.586733
870870 0 0
871871 11.9800 0.405926
872872 0 0
873873 22.7129 0.768715
874874 0 0
875875 52.1118 1.76170
876876 0 0
877877 −7.17164 −0.242169 −0.121085 0.992642i 0.538637π-0.538637\pi
−0.121085 + 0.992642i 0.538637π0.538637\pi
878878 0 0
879879 37.5062 1.26505
880880 0 0
881881 −8.08174 −0.272281 −0.136140 0.990690i 0.543470π-0.543470\pi
−0.136140 + 0.990690i 0.543470π0.543470\pi
882882 0 0
883883 41.0042 1.37990 0.689950 0.723857i 0.257633π-0.257633\pi
0.689950 + 0.723857i 0.257633π0.257633\pi
884884 0 0
885885 138.612 4.65939
886886 0 0
887887 37.8321 1.27028 0.635138 0.772398i 0.280943π-0.280943\pi
0.635138 + 0.772398i 0.280943π0.280943\pi
888888 0 0
889889 −16.0096 −0.536945
890890 0 0
891891 −24.3534 −0.815871
892892 0 0
893893 8.15361 0.272850
894894 0 0
895895 −36.1204 −1.20737
896896 0 0
897897 0 0
898898 0 0
899899 15.2484 0.508562
900900 0 0
901901 −45.0541 −1.50097
902902 0 0
903903 −7.55991 −0.251578
904904 0 0
905905 17.3709 0.577427
906906 0 0
907907 −15.9611 −0.529978 −0.264989 0.964251i 0.585368π-0.585368\pi
−0.264989 + 0.964251i 0.585368π0.585368\pi
908908 0 0
909909 41.2022 1.36659
910910 0 0
911911 37.5172 1.24300 0.621501 0.783414i 0.286523π-0.286523\pi
0.621501 + 0.783414i 0.286523π0.286523\pi
912912 0 0
913913 12.1698 0.402760
914914 0 0
915915 −57.6776 −1.90676
916916 0 0
917917 17.1460 0.566210
918918 0 0
919919 26.7175 0.881330 0.440665 0.897672i 0.354743π-0.354743\pi
0.440665 + 0.897672i 0.354743π0.354743\pi
920920 0 0
921921 78.2979 2.58000
922922 0 0
923923 18.9733 0.624513
924924 0 0
925925 22.5256 0.740638
926926 0 0
927927 −25.9733 −0.853076
928928 0 0
929929 −43.8177 −1.43761 −0.718805 0.695211i 0.755311π-0.755311\pi
−0.718805 + 0.695211i 0.755311π0.755311\pi
930930 0 0
931931 −11.4275 −0.374523
932932 0 0
933933 −47.3251 −1.54936
934934 0 0
935935 −50.7997 −1.66133
936936 0 0
937937 34.4360 1.12498 0.562488 0.826805i 0.309844π-0.309844\pi
0.562488 + 0.826805i 0.309844π0.309844\pi
938938 0 0
939939 −22.9787 −0.749883
940940 0 0
941941 −35.8492 −1.16865 −0.584326 0.811519i 0.698641π-0.698641\pi
−0.584326 + 0.811519i 0.698641π0.698641\pi
942942 0 0
943943 0 0
944944 0 0
945945 6.70722 0.218186
946946 0 0
947947 −0.975923 −0.0317132 −0.0158566 0.999874i 0.505048π-0.505048\pi
−0.0158566 + 0.999874i 0.505048π0.505048\pi
948948 0 0
949949 −6.67524 −0.216688
950950 0 0
951951 43.5903 1.41351
952952 0 0
953953 −16.6476 −0.539267 −0.269634 0.962963i 0.586903π-0.586903\pi
−0.269634 + 0.962963i 0.586903π0.586903\pi
954954 0 0
955955 −14.6024 −0.472522
956956 0 0
957957 25.6145 0.827999
958958 0 0
959959 7.54292 0.243574
960960 0 0
961961 −19.0000 −0.612903
962962 0 0
963963 −5.57164 −0.179544
964964 0 0
965965 62.2440 2.00370
966966 0 0
967967 −52.3940 −1.68488 −0.842439 0.538792i 0.818881π-0.818881\pi
−0.842439 + 0.538792i 0.818881π0.818881\pi
968968 0 0
969969 43.0043 1.38150
970970 0 0
971971 −51.8696 −1.66457 −0.832287 0.554344i 0.812969π-0.812969\pi
−0.832287 + 0.554344i 0.812969π0.812969\pi
972972 0 0
973973 1.03768 0.0332664
974974 0 0
975975 −37.3111 −1.19491
976976 0 0
977977 −18.1728 −0.581399 −0.290699 0.956814i 0.593888π-0.593888\pi
−0.290699 + 0.956814i 0.593888π0.593888\pi
978978 0 0
979979 39.3606 1.25797
980980 0 0
981981 29.4304 0.939641
982982 0 0
983983 23.6079 0.752975 0.376488 0.926422i 0.377132π-0.377132\pi
0.376488 + 0.926422i 0.377132π0.377132\pi
984984 0 0
985985 −31.7571 −1.01187
986986 0 0
987987 −10.6026 −0.337486
988988 0 0
989989 0 0
990990 0 0
991991 −3.77401 −0.119885 −0.0599427 0.998202i 0.519092π-0.519092\pi
−0.0599427 + 0.998202i 0.519092π0.519092\pi
992992 0 0
993993 −60.6694 −1.92529
994994 0 0
995995 98.2884 3.11595
996996 0 0
997997 −14.6939 −0.465361 −0.232681 0.972553i 0.574750π-0.574750\pi
−0.232681 + 0.972553i 0.574750π0.574750\pi
998998 0 0
999999 1.64727 0.0521175
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 8464.2.a.cb.1.4 8
4.3 odd 2 1058.2.a.n.1.6 yes 8
12.11 even 2 9522.2.a.ce.1.1 8
23.22 odd 2 inner 8464.2.a.cb.1.3 8
92.91 even 2 1058.2.a.n.1.5 8
276.275 odd 2 9522.2.a.ce.1.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1058.2.a.n.1.5 8 92.91 even 2
1058.2.a.n.1.6 yes 8 4.3 odd 2
8464.2.a.cb.1.3 8 23.22 odd 2 inner
8464.2.a.cb.1.4 8 1.1 even 1 trivial
9522.2.a.ce.1.1 8 12.11 even 2
9522.2.a.ce.1.8 8 276.275 odd 2