Properties

Label 2475.2.a.bc.1.2
Level 24752475
Weight 22
Character 2475.1
Self dual yes
Analytic conductor 19.76319.763
Analytic rank 11
Dimension 33
CM no
Inner twists 11

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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] = [2475,2,Mod(1,2475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2475, 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("2475.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 2475=325211 2475 = 3^{2} \cdot 5^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2475.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,1,0,1,0,0,-4,3,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 19.762974500319.7629745003
Analytic rank: 11
Dimension: 33
Coefficient field: 3.3.148.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x3x23x+1 x^{3} - x^{2} - 3x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 165)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 0.3111080.311108 of defining polynomial
Character χ\chi == 2475.1

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+0.311108q21.90321q4+0.903212q71.21432q81.00000q112.90321q13+0.280996q14+3.42864q16+2.28100q17+2.42864q190.311108q22+4.00000q230.903212q261.71900q287.05086q292.62222q31+3.49532q32+0.709636q345.80642q37+0.755569q38+10.6637q4110.7096q43+1.90321q44+1.24443q46+0.949145q476.18421q49+5.52543q52+0.815792q531.09679q562.19358q58+1.67307q597.24443q610.815792q625.76986q6412.8573q674.34122q689.28592q71+5.65878q731.80642q744.62222q760.903212q7716.5303q79+3.31756q82+7.76049q833.33185q86+1.21432q886.13335q892.62222q917.61285q92+0.295286q94+12.4701q971.92396q98+O(q100)q+0.311108 q^{2} -1.90321 q^{4} +0.903212 q^{7} -1.21432 q^{8} -1.00000 q^{11} -2.90321 q^{13} +0.280996 q^{14} +3.42864 q^{16} +2.28100 q^{17} +2.42864 q^{19} -0.311108 q^{22} +4.00000 q^{23} -0.903212 q^{26} -1.71900 q^{28} -7.05086 q^{29} -2.62222 q^{31} +3.49532 q^{32} +0.709636 q^{34} -5.80642 q^{37} +0.755569 q^{38} +10.6637 q^{41} -10.7096 q^{43} +1.90321 q^{44} +1.24443 q^{46} +0.949145 q^{47} -6.18421 q^{49} +5.52543 q^{52} +0.815792 q^{53} -1.09679 q^{56} -2.19358 q^{58} +1.67307 q^{59} -7.24443 q^{61} -0.815792 q^{62} -5.76986 q^{64} -12.8573 q^{67} -4.34122 q^{68} -9.28592 q^{71} +5.65878 q^{73} -1.80642 q^{74} -4.62222 q^{76} -0.903212 q^{77} -16.5303 q^{79} +3.31756 q^{82} +7.76049 q^{83} -3.33185 q^{86} +1.21432 q^{88} -6.13335 q^{89} -2.62222 q^{91} -7.61285 q^{92} +0.295286 q^{94} +12.4701 q^{97} -1.92396 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+q2+q44q7+3q83q112q136q143q166q19q22+12q23+4q2612q288q298q313q3218q344q37+2q38++21q98+O(q100) 3 q + q^{2} + q^{4} - 4 q^{7} + 3 q^{8} - 3 q^{11} - 2 q^{13} - 6 q^{14} - 3 q^{16} - 6 q^{19} - q^{22} + 12 q^{23} + 4 q^{26} - 12 q^{28} - 8 q^{29} - 8 q^{31} - 3 q^{32} - 18 q^{34} - 4 q^{37} + 2 q^{38}+ \cdots + 21 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 0.311108 0.219986 0.109993 0.993932i 0.464917π-0.464917\pi
0.109993 + 0.993932i 0.464917π0.464917\pi
33 0 0
44 −1.90321 −0.951606
55 0 0
66 0 0
77 0.903212 0.341382 0.170691 0.985325i 0.445400π-0.445400\pi
0.170691 + 0.985325i 0.445400π0.445400\pi
88 −1.21432 −0.429327
99 0 0
1010 0 0
1111 −1.00000 −0.301511
1212 0 0
1313 −2.90321 −0.805206 −0.402603 0.915375i 0.631894π-0.631894\pi
−0.402603 + 0.915375i 0.631894π0.631894\pi
1414 0.280996 0.0750994
1515 0 0
1616 3.42864 0.857160
1717 2.28100 0.553223 0.276611 0.960982i 0.410789π-0.410789\pi
0.276611 + 0.960982i 0.410789π0.410789\pi
1818 0 0
1919 2.42864 0.557168 0.278584 0.960412i 0.410135π-0.410135\pi
0.278584 + 0.960412i 0.410135π0.410135\pi
2020 0 0
2121 0 0
2222 −0.311108 −0.0663284
2323 4.00000 0.834058 0.417029 0.908893i 0.363071π-0.363071\pi
0.417029 + 0.908893i 0.363071π0.363071\pi
2424 0 0
2525 0 0
2626 −0.903212 −0.177134
2727 0 0
2828 −1.71900 −0.324861
2929 −7.05086 −1.30931 −0.654655 0.755927i 0.727186π-0.727186\pi
−0.654655 + 0.755927i 0.727186π0.727186\pi
3030 0 0
3131 −2.62222 −0.470964 −0.235482 0.971879i 0.575667π-0.575667\pi
−0.235482 + 0.971879i 0.575667π0.575667\pi
3232 3.49532 0.617890
3333 0 0
3434 0.709636 0.121702
3535 0 0
3636 0 0
3737 −5.80642 −0.954570 −0.477285 0.878749i 0.658379π-0.658379\pi
−0.477285 + 0.878749i 0.658379π0.658379\pi
3838 0.755569 0.122569
3939 0 0
4040 0 0
4141 10.6637 1.66539 0.832695 0.553731i 0.186797π-0.186797\pi
0.832695 + 0.553731i 0.186797π0.186797\pi
4242 0 0
4343 −10.7096 −1.63320 −0.816602 0.577201i 0.804145π-0.804145\pi
−0.816602 + 0.577201i 0.804145π0.804145\pi
4444 1.90321 0.286920
4545 0 0
4646 1.24443 0.183481
4747 0.949145 0.138447 0.0692235 0.997601i 0.477948π-0.477948\pi
0.0692235 + 0.997601i 0.477948π0.477948\pi
4848 0 0
4949 −6.18421 −0.883458
5050 0 0
5151 0 0
5252 5.52543 0.766239
5353 0.815792 0.112058 0.0560288 0.998429i 0.482156π-0.482156\pi
0.0560288 + 0.998429i 0.482156π0.482156\pi
5454 0 0
5555 0 0
5656 −1.09679 −0.146564
5757 0 0
5858 −2.19358 −0.288031
5959 1.67307 0.217815 0.108908 0.994052i 0.465265π-0.465265\pi
0.108908 + 0.994052i 0.465265π0.465265\pi
6060 0 0
6161 −7.24443 −0.927554 −0.463777 0.885952i 0.653506π-0.653506\pi
−0.463777 + 0.885952i 0.653506π0.653506\pi
6262 −0.815792 −0.103606
6363 0 0
6464 −5.76986 −0.721232
6565 0 0
6666 0 0
6767 −12.8573 −1.57077 −0.785383 0.619010i 0.787534π-0.787534\pi
−0.785383 + 0.619010i 0.787534π0.787534\pi
6868 −4.34122 −0.526450
6969 0 0
7070 0 0
7171 −9.28592 −1.10204 −0.551018 0.834493i 0.685760π-0.685760\pi
−0.551018 + 0.834493i 0.685760π0.685760\pi
7272 0 0
7373 5.65878 0.662310 0.331155 0.943576i 0.392562π-0.392562\pi
0.331155 + 0.943576i 0.392562π0.392562\pi
7474 −1.80642 −0.209993
7575 0 0
7676 −4.62222 −0.530204
7777 −0.903212 −0.102931
7878 0 0
7979 −16.5303 −1.85981 −0.929905 0.367800i 0.880111π-0.880111\pi
−0.929905 + 0.367800i 0.880111π0.880111\pi
8080 0 0
8181 0 0
8282 3.31756 0.366363
8383 7.76049 0.851825 0.425912 0.904764i 0.359953π-0.359953\pi
0.425912 + 0.904764i 0.359953π0.359953\pi
8484 0 0
8585 0 0
8686 −3.33185 −0.359283
8787 0 0
8888 1.21432 0.129447
8989 −6.13335 −0.650134 −0.325067 0.945691i 0.605387π-0.605387\pi
−0.325067 + 0.945691i 0.605387π0.605387\pi
9090 0 0
9191 −2.62222 −0.274883
9292 −7.61285 −0.793694
9393 0 0
9494 0.295286 0.0304565
9595 0 0
9696 0 0
9797 12.4701 1.26615 0.633075 0.774091i 0.281793π-0.281793\pi
0.633075 + 0.774091i 0.281793π0.281793\pi
9898 −1.92396 −0.194349
9999 0 0
100100 0 0
101101 −16.1748 −1.60946 −0.804728 0.593643i 0.797689π-0.797689\pi
−0.804728 + 0.593643i 0.797689π0.797689\pi
102102 0 0
103103 17.1526 1.69009 0.845046 0.534693i 0.179573π-0.179573\pi
0.845046 + 0.534693i 0.179573π0.179573\pi
104104 3.52543 0.345697
105105 0 0
106106 0.253799 0.0246512
107107 −13.5669 −1.31156 −0.655782 0.754951i 0.727661π-0.727661\pi
−0.655782 + 0.754951i 0.727661π0.727661\pi
108108 0 0
109109 −10.0000 −0.957826 −0.478913 0.877862i 0.658969π-0.658969\pi
−0.478913 + 0.877862i 0.658969π0.658969\pi
110110 0 0
111111 0 0
112112 3.09679 0.292619
113113 14.2351 1.33912 0.669561 0.742757i 0.266482π-0.266482\pi
0.669561 + 0.742757i 0.266482π0.266482\pi
114114 0 0
115115 0 0
116116 13.4193 1.24595
117117 0 0
118118 0.520505 0.0479164
119119 2.06022 0.188860
120120 0 0
121121 1.00000 0.0909091
122122 −2.25380 −0.204049
123123 0 0
124124 4.99063 0.448172
125125 0 0
126126 0 0
127127 −11.0049 −0.976529 −0.488264 0.872696i 0.662370π-0.662370\pi
−0.488264 + 0.872696i 0.662370π0.662370\pi
128128 −8.78568 −0.776552
129129 0 0
130130 0 0
131131 −1.24443 −0.108726 −0.0543632 0.998521i 0.517313π-0.517313\pi
−0.0543632 + 0.998521i 0.517313π0.517313\pi
132132 0 0
133133 2.19358 0.190207
134134 −4.00000 −0.345547
135135 0 0
136136 −2.76986 −0.237513
137137 −4.42864 −0.378364 −0.189182 0.981942i 0.560584π-0.560584\pi
−0.189182 + 0.981942i 0.560584π0.560584\pi
138138 0 0
139139 0.917502 0.0778215 0.0389108 0.999243i 0.487611π-0.487611\pi
0.0389108 + 0.999243i 0.487611π0.487611\pi
140140 0 0
141141 0 0
142142 −2.88892 −0.242433
143143 2.90321 0.242779
144144 0 0
145145 0 0
146146 1.76049 0.145699
147147 0 0
148148 11.0509 0.908375
149149 −2.19358 −0.179705 −0.0898524 0.995955i 0.528640π-0.528640\pi
−0.0898524 + 0.995955i 0.528640π0.528640\pi
150150 0 0
151151 −10.4286 −0.848671 −0.424335 0.905505i 0.639492π-0.639492\pi
−0.424335 + 0.905505i 0.639492π0.639492\pi
152152 −2.94914 −0.239207
153153 0 0
154154 −0.280996 −0.0226433
155155 0 0
156156 0 0
157157 −5.80642 −0.463403 −0.231702 0.972787i 0.574429π-0.574429\pi
−0.231702 + 0.972787i 0.574429π0.574429\pi
158158 −5.14272 −0.409133
159159 0 0
160160 0 0
161161 3.61285 0.284732
162162 0 0
163163 −11.0509 −0.865570 −0.432785 0.901497i 0.642469π-0.642469\pi
−0.432785 + 0.901497i 0.642469π0.642469\pi
164164 −20.2953 −1.58480
165165 0 0
166166 2.41435 0.187390
167167 13.9541 1.07980 0.539899 0.841730i 0.318462π-0.318462\pi
0.539899 + 0.841730i 0.318462π0.318462\pi
168168 0 0
169169 −4.57136 −0.351643
170170 0 0
171171 0 0
172172 20.3827 1.55417
173173 −18.8430 −1.43261 −0.716303 0.697789i 0.754167π-0.754167\pi
−0.716303 + 0.697789i 0.754167π0.754167\pi
174174 0 0
175175 0 0
176176 −3.42864 −0.258443
177177 0 0
178178 −1.90813 −0.143021
179179 −4.85728 −0.363050 −0.181525 0.983386i 0.558103π-0.558103\pi
−0.181525 + 0.983386i 0.558103π0.558103\pi
180180 0 0
181181 −16.7971 −1.24852 −0.624258 0.781219i 0.714598π-0.714598\pi
−0.624258 + 0.781219i 0.714598π0.714598\pi
182182 −0.815792 −0.0604705
183183 0 0
184184 −4.85728 −0.358083
185185 0 0
186186 0 0
187187 −2.28100 −0.166803
188188 −1.80642 −0.131747
189189 0 0
190190 0 0
191191 −16.8573 −1.21975 −0.609875 0.792498i 0.708780π-0.708780\pi
−0.609875 + 0.792498i 0.708780π0.708780\pi
192192 0 0
193193 24.6178 1.77203 0.886013 0.463661i 0.153464π-0.153464\pi
0.886013 + 0.463661i 0.153464π0.153464\pi
194194 3.87955 0.278536
195195 0 0
196196 11.7699 0.840704
197197 14.8716 1.05956 0.529778 0.848137i 0.322275π-0.322275\pi
0.529778 + 0.848137i 0.322275π0.322275\pi
198198 0 0
199199 −11.2257 −0.795768 −0.397884 0.917436i 0.630255π-0.630255\pi
−0.397884 + 0.917436i 0.630255π0.630255\pi
200200 0 0
201201 0 0
202202 −5.03212 −0.354059
203203 −6.36842 −0.446975
204204 0 0
205205 0 0
206206 5.33630 0.371797
207207 0 0
208208 −9.95407 −0.690190
209209 −2.42864 −0.167993
210210 0 0
211211 −11.9398 −0.821968 −0.410984 0.911643i 0.634815π-0.634815\pi
−0.410984 + 0.911643i 0.634815π0.634815\pi
212212 −1.55262 −0.106635
213213 0 0
214214 −4.22077 −0.288526
215215 0 0
216216 0 0
217217 −2.36842 −0.160779
218218 −3.11108 −0.210709
219219 0 0
220220 0 0
221221 −6.62222 −0.445458
222222 0 0
223223 −21.8064 −1.46027 −0.730133 0.683305i 0.760542π-0.760542\pi
−0.730133 + 0.683305i 0.760542π0.760542\pi
224224 3.15701 0.210937
225225 0 0
226226 4.42864 0.294589
227227 3.19850 0.212292 0.106146 0.994351i 0.466149π-0.466149\pi
0.106146 + 0.994351i 0.466149π0.466149\pi
228228 0 0
229229 7.12399 0.470766 0.235383 0.971903i 0.424366π-0.424366\pi
0.235383 + 0.971903i 0.424366π0.424366\pi
230230 0 0
231231 0 0
232232 8.56199 0.562122
233233 −19.5254 −1.27915 −0.639577 0.768727i 0.720890π-0.720890\pi
−0.639577 + 0.768727i 0.720890π0.720890\pi
234234 0 0
235235 0 0
236236 −3.18421 −0.207274
237237 0 0
238238 0.640951 0.0415467
239239 21.9813 1.42185 0.710925 0.703268i 0.248277π-0.248277\pi
0.710925 + 0.703268i 0.248277π0.248277\pi
240240 0 0
241241 5.34614 0.344375 0.172188 0.985064i 0.444916π-0.444916\pi
0.172188 + 0.985064i 0.444916π0.444916\pi
242242 0.311108 0.0199988
243243 0 0
244244 13.7877 0.882666
245245 0 0
246246 0 0
247247 −7.05086 −0.448635
248248 3.18421 0.202197
249249 0 0
250250 0 0
251251 23.7748 1.50065 0.750325 0.661069i 0.229897π-0.229897\pi
0.750325 + 0.661069i 0.229897π0.229897\pi
252252 0 0
253253 −4.00000 −0.251478
254254 −3.42372 −0.214823
255255 0 0
256256 8.80642 0.550401
257257 −8.13335 −0.507345 −0.253672 0.967290i 0.581638π-0.581638\pi
−0.253672 + 0.967290i 0.581638π0.581638\pi
258258 0 0
259259 −5.24443 −0.325873
260260 0 0
261261 0 0
262262 −0.387152 −0.0239183
263263 22.9032 1.41227 0.706136 0.708076i 0.250437π-0.250437\pi
0.706136 + 0.708076i 0.250437π0.250437\pi
264264 0 0
265265 0 0
266266 0.682439 0.0418430
267267 0 0
268268 24.4701 1.49475
269269 −11.8350 −0.721593 −0.360796 0.932645i 0.617495π-0.617495\pi
−0.360796 + 0.932645i 0.617495π0.617495\pi
270270 0 0
271271 14.8988 0.905036 0.452518 0.891755i 0.350526π-0.350526\pi
0.452518 + 0.891755i 0.350526π0.350526\pi
272272 7.82071 0.474200
273273 0 0
274274 −1.37778 −0.0832350
275275 0 0
276276 0 0
277277 27.6686 1.66245 0.831223 0.555939i 0.187641π-0.187641\pi
0.831223 + 0.555939i 0.187641π0.187641\pi
278278 0.285442 0.0171197
279279 0 0
280280 0 0
281281 −9.80642 −0.585002 −0.292501 0.956265i 0.594488π-0.594488\pi
−0.292501 + 0.956265i 0.594488π0.594488\pi
282282 0 0
283283 19.0049 1.12973 0.564863 0.825185i 0.308929π-0.308929\pi
0.564863 + 0.825185i 0.308929π0.308929\pi
284284 17.6731 1.04870
285285 0 0
286286 0.903212 0.0534080
287287 9.63158 0.568534
288288 0 0
289289 −11.7971 −0.693944
290290 0 0
291291 0 0
292292 −10.7699 −0.630258
293293 −30.7511 −1.79650 −0.898250 0.439485i 0.855161π-0.855161\pi
−0.898250 + 0.439485i 0.855161π0.855161\pi
294294 0 0
295295 0 0
296296 7.05086 0.409823
297297 0 0
298298 −0.682439 −0.0395326
299299 −11.6128 −0.671588
300300 0 0
301301 −9.67307 −0.557547
302302 −3.24443 −0.186696
303303 0 0
304304 8.32693 0.477582
305305 0 0
306306 0 0
307307 13.4938 0.770131 0.385065 0.922889i 0.374179π-0.374179\pi
0.385065 + 0.922889i 0.374179π0.374179\pi
308308 1.71900 0.0979493
309309 0 0
310310 0 0
311311 17.5526 0.995318 0.497659 0.867373i 0.334193π-0.334193\pi
0.497659 + 0.867373i 0.334193π0.334193\pi
312312 0 0
313313 −14.3970 −0.813766 −0.406883 0.913480i 0.633384π-0.633384\pi
−0.406883 + 0.913480i 0.633384π0.633384\pi
314314 −1.80642 −0.101942
315315 0 0
316316 31.4608 1.76981
317317 29.4608 1.65468 0.827341 0.561701i 0.189853π-0.189853\pi
0.827341 + 0.561701i 0.189853π0.189853\pi
318318 0 0
319319 7.05086 0.394772
320320 0 0
321321 0 0
322322 1.12399 0.0626372
323323 5.53972 0.308238
324324 0 0
325325 0 0
326326 −3.43801 −0.190414
327327 0 0
328328 −12.9491 −0.714997
329329 0.857279 0.0472633
330330 0 0
331331 −2.62222 −0.144130 −0.0720650 0.997400i 0.522959π-0.522959\pi
−0.0720650 + 0.997400i 0.522959π0.522959\pi
332332 −14.7699 −0.810601
333333 0 0
334334 4.34122 0.237541
335335 0 0
336336 0 0
337337 5.00492 0.272635 0.136318 0.990665i 0.456473π-0.456473\pi
0.136318 + 0.990665i 0.456473π0.456473\pi
338338 −1.42219 −0.0773567
339339 0 0
340340 0 0
341341 2.62222 0.142001
342342 0 0
343343 −11.9081 −0.642979
344344 13.0049 0.701178
345345 0 0
346346 −5.86220 −0.315154
347347 −22.8113 −1.22458 −0.612289 0.790634i 0.709751π-0.709751\pi
−0.612289 + 0.790634i 0.709751π0.709751\pi
348348 0 0
349349 21.2257 1.13619 0.568093 0.822965i 0.307681π-0.307681\pi
0.568093 + 0.822965i 0.307681π0.307681\pi
350350 0 0
351351 0 0
352352 −3.49532 −0.186301
353353 7.18421 0.382377 0.191188 0.981553i 0.438766π-0.438766\pi
0.191188 + 0.981553i 0.438766π0.438766\pi
354354 0 0
355355 0 0
356356 11.6731 0.618672
357357 0 0
358358 −1.51114 −0.0798661
359359 14.1017 0.744260 0.372130 0.928181i 0.378628π-0.378628\pi
0.372130 + 0.928181i 0.378628π0.378628\pi
360360 0 0
361361 −13.1017 −0.689564
362362 −5.22570 −0.274656
363363 0 0
364364 4.99063 0.261580
365365 0 0
366366 0 0
367367 3.90813 0.204003 0.102001 0.994784i 0.467475π-0.467475\pi
0.102001 + 0.994784i 0.467475π0.467475\pi
368368 13.7146 0.714921
369369 0 0
370370 0 0
371371 0.736833 0.0382545
372372 0 0
373373 −12.9763 −0.671890 −0.335945 0.941882i 0.609056π-0.609056\pi
−0.335945 + 0.941882i 0.609056π0.609056\pi
374374 −0.709636 −0.0366944
375375 0 0
376376 −1.15257 −0.0594390
377377 20.4701 1.05427
378378 0 0
379379 36.0830 1.85346 0.926729 0.375731i 0.122608π-0.122608\pi
0.926729 + 0.375731i 0.122608π0.122608\pi
380380 0 0
381381 0 0
382382 −5.24443 −0.268328
383383 20.2953 1.03704 0.518520 0.855065i 0.326483π-0.326483\pi
0.518520 + 0.855065i 0.326483π0.326483\pi
384384 0 0
385385 0 0
386386 7.65878 0.389822
387387 0 0
388388 −23.7333 −1.20488
389389 −30.4701 −1.54490 −0.772448 0.635078i 0.780968π-0.780968\pi
−0.772448 + 0.635078i 0.780968π0.780968\pi
390390 0 0
391391 9.12399 0.461420
392392 7.50961 0.379292
393393 0 0
394394 4.62666 0.233088
395395 0 0
396396 0 0
397397 −4.97773 −0.249825 −0.124912 0.992168i 0.539865π-0.539865\pi
−0.124912 + 0.992168i 0.539865π0.539865\pi
398398 −3.49240 −0.175058
399399 0 0
400400 0 0
401401 1.86665 0.0932159 0.0466079 0.998913i 0.485159π-0.485159\pi
0.0466079 + 0.998913i 0.485159π0.485159\pi
402402 0 0
403403 7.61285 0.379223
404404 30.7841 1.53157
405405 0 0
406406 −1.98126 −0.0983285
407407 5.80642 0.287814
408408 0 0
409409 −3.63158 −0.179570 −0.0897851 0.995961i 0.528618π-0.528618\pi
−0.0897851 + 0.995961i 0.528618π0.528618\pi
410410 0 0
411411 0 0
412412 −32.6450 −1.60830
413413 1.51114 0.0743582
414414 0 0
415415 0 0
416416 −10.1476 −0.497529
417417 0 0
418418 −0.755569 −0.0369561
419419 −4.85728 −0.237294 −0.118647 0.992937i 0.537856π-0.537856\pi
−0.118647 + 0.992937i 0.537856π0.537856\pi
420420 0 0
421421 22.6321 1.10302 0.551510 0.834169i 0.314052π-0.314052\pi
0.551510 + 0.834169i 0.314052π0.314052\pi
422422 −3.71456 −0.180822
423423 0 0
424424 −0.990632 −0.0481093
425425 0 0
426426 0 0
427427 −6.54326 −0.316650
428428 25.8207 1.24809
429429 0 0
430430 0 0
431431 −1.24443 −0.0599421 −0.0299711 0.999551i 0.509542π-0.509542\pi
−0.0299711 + 0.999551i 0.509542π0.509542\pi
432432 0 0
433433 16.0000 0.768911 0.384455 0.923144i 0.374389π-0.374389\pi
0.384455 + 0.923144i 0.374389π0.374389\pi
434434 −0.736833 −0.0353691
435435 0 0
436436 19.0321 0.911473
437437 9.71456 0.464710
438438 0 0
439439 −2.42864 −0.115913 −0.0579563 0.998319i 0.518458π-0.518458\pi
−0.0579563 + 0.998319i 0.518458π0.518458\pi
440440 0 0
441441 0 0
442442 −2.06022 −0.0979948
443443 31.0509 1.47527 0.737635 0.675199i 0.235942π-0.235942\pi
0.737635 + 0.675199i 0.235942π0.235942\pi
444444 0 0
445445 0 0
446446 −6.78415 −0.321239
447447 0 0
448448 −5.21141 −0.246216
449449 37.3590 1.76308 0.881541 0.472107i 0.156506π-0.156506\pi
0.881541 + 0.472107i 0.156506π0.156506\pi
450450 0 0
451451 −10.6637 −0.502134
452452 −27.0923 −1.27432
453453 0 0
454454 0.995078 0.0467013
455455 0 0
456456 0 0
457457 −8.73822 −0.408757 −0.204378 0.978892i 0.565517π-0.565517\pi
−0.204378 + 0.978892i 0.565517π0.565517\pi
458458 2.21633 0.103562
459459 0 0
460460 0 0
461461 −31.7877 −1.48050 −0.740250 0.672332i 0.765293π-0.765293\pi
−0.740250 + 0.672332i 0.765293π0.765293\pi
462462 0 0
463463 −12.0919 −0.561957 −0.280978 0.959714i 0.590659π-0.590659\pi
−0.280978 + 0.959714i 0.590659π0.590659\pi
464464 −24.1748 −1.12229
465465 0 0
466466 −6.07451 −0.281396
467467 −15.3461 −0.710135 −0.355067 0.934841i 0.615542π-0.615542\pi
−0.355067 + 0.934841i 0.615542π0.615542\pi
468468 0 0
469469 −11.6128 −0.536231
470470 0 0
471471 0 0
472472 −2.03164 −0.0935139
473473 10.7096 0.492430
474474 0 0
475475 0 0
476476 −3.92104 −0.179721
477477 0 0
478478 6.83854 0.312788
479479 −5.89829 −0.269500 −0.134750 0.990880i 0.543023π-0.543023\pi
−0.134750 + 0.990880i 0.543023π0.543023\pi
480480 0 0
481481 16.8573 0.768626
482482 1.66323 0.0757579
483483 0 0
484484 −1.90321 −0.0865096
485485 0 0
486486 0 0
487487 −31.3461 −1.42043 −0.710215 0.703985i 0.751402π-0.751402\pi
−0.710215 + 0.703985i 0.751402π0.751402\pi
488488 8.79706 0.398224
489489 0 0
490490 0 0
491491 8.00000 0.361035 0.180517 0.983572i 0.442223π-0.442223\pi
0.180517 + 0.983572i 0.442223π0.442223\pi
492492 0 0
493493 −16.0830 −0.724341
494494 −2.19358 −0.0986937
495495 0 0
496496 −8.99063 −0.403691
497497 −8.38715 −0.376215
498498 0 0
499499 15.1427 0.677881 0.338941 0.940808i 0.389931π-0.389931\pi
0.338941 + 0.940808i 0.389931π0.389931\pi
500500 0 0
501501 0 0
502502 7.39652 0.330123
503503 26.0370 1.16093 0.580467 0.814284i 0.302870π-0.302870\pi
0.580467 + 0.814284i 0.302870π0.302870\pi
504504 0 0
505505 0 0
506506 −1.24443 −0.0553217
507507 0 0
508508 20.9447 0.929271
509509 24.5718 1.08913 0.544564 0.838719i 0.316695π-0.316695\pi
0.544564 + 0.838719i 0.316695π0.316695\pi
510510 0 0
511511 5.11108 0.226101
512512 20.3111 0.897633
513513 0 0
514514 −2.53035 −0.111609
515515 0 0
516516 0 0
517517 −0.949145 −0.0417433
518518 −1.63158 −0.0716877
519519 0 0
520520 0 0
521521 4.88892 0.214188 0.107094 0.994249i 0.465845π-0.465845\pi
0.107094 + 0.994249i 0.465845π0.465845\pi
522522 0 0
523523 4.22077 0.184562 0.0922808 0.995733i 0.470584π-0.470584\pi
0.0922808 + 0.995733i 0.470584π0.470584\pi
524524 2.36842 0.103465
525525 0 0
526526 7.12537 0.310681
527527 −5.98126 −0.260548
528528 0 0
529529 −7.00000 −0.304348
530530 0 0
531531 0 0
532532 −4.17484 −0.181002
533533 −30.9590 −1.34098
534534 0 0
535535 0 0
536536 15.6128 0.674372
537537 0 0
538538 −3.68196 −0.158741
539539 6.18421 0.266373
540540 0 0
541541 −13.6128 −0.585262 −0.292631 0.956225i 0.594531π-0.594531\pi
−0.292631 + 0.956225i 0.594531π0.594531\pi
542542 4.63512 0.199096
543543 0 0
544544 7.97280 0.341831
545545 0 0
546546 0 0
547547 7.48394 0.319990 0.159995 0.987118i 0.448852π-0.448852\pi
0.159995 + 0.987118i 0.448852π0.448852\pi
548548 8.42864 0.360054
549549 0 0
550550 0 0
551551 −17.1240 −0.729506
552552 0 0
553553 −14.9304 −0.634906
554554 8.60793 0.365716
555555 0 0
556556 −1.74620 −0.0740554
557557 −32.2908 −1.36821 −0.684103 0.729385i 0.739806π-0.739806\pi
−0.684103 + 0.729385i 0.739806π0.739806\pi
558558 0 0
559559 31.0923 1.31507
560560 0 0
561561 0 0
562562 −3.05086 −0.128693
563563 −7.49378 −0.315825 −0.157913 0.987453i 0.550476π-0.550476\pi
−0.157913 + 0.987453i 0.550476π0.550476\pi
564564 0 0
565565 0 0
566566 5.91258 0.248524
567567 0 0
568568 11.2761 0.473134
569569 12.9491 0.542856 0.271428 0.962459i 0.412504π-0.412504\pi
0.271428 + 0.962459i 0.412504π0.412504\pi
570570 0 0
571571 −15.2859 −0.639696 −0.319848 0.947469i 0.603632π-0.603632\pi
−0.319848 + 0.947469i 0.603632π0.603632\pi
572572 −5.52543 −0.231030
573573 0 0
574574 2.99646 0.125070
575575 0 0
576576 0 0
577577 28.4415 1.18404 0.592019 0.805924i 0.298331π-0.298331\pi
0.592019 + 0.805924i 0.298331π0.298331\pi
578578 −3.67016 −0.152658
579579 0 0
580580 0 0
581581 7.00937 0.290798
582582 0 0
583583 −0.815792 −0.0337866
584584 −6.87157 −0.284348
585585 0 0
586586 −9.56691 −0.395206
587587 8.47013 0.349600 0.174800 0.984604i 0.444072π-0.444072\pi
0.174800 + 0.984604i 0.444072π0.444072\pi
588588 0 0
589589 −6.36842 −0.262406
590590 0 0
591591 0 0
592592 −19.9081 −0.818219
593593 −26.5763 −1.09136 −0.545679 0.837995i 0.683728π-0.683728\pi
−0.545679 + 0.837995i 0.683728π0.683728\pi
594594 0 0
595595 0 0
596596 4.17484 0.171008
597597 0 0
598598 −3.61285 −0.147740
599599 8.77430 0.358508 0.179254 0.983803i 0.442632π-0.442632\pi
0.179254 + 0.983803i 0.442632π0.442632\pi
600600 0 0
601601 −41.8163 −1.70572 −0.852861 0.522139i 0.825134π-0.825134\pi
−0.852861 + 0.522139i 0.825134π0.825134\pi
602602 −3.00937 −0.122653
603603 0 0
604604 19.8479 0.807600
605605 0 0
606606 0 0
607607 29.9353 1.21504 0.607519 0.794305i 0.292165π-0.292165\pi
0.607519 + 0.794305i 0.292165π0.292165\pi
608608 8.48886 0.344269
609609 0 0
610610 0 0
611611 −2.75557 −0.111478
612612 0 0
613613 26.1289 1.05534 0.527668 0.849450i 0.323066π-0.323066\pi
0.527668 + 0.849450i 0.323066π0.323066\pi
614614 4.19802 0.169418
615615 0 0
616616 1.09679 0.0441909
617617 3.66323 0.147476 0.0737380 0.997278i 0.476507π-0.476507\pi
0.0737380 + 0.997278i 0.476507π0.476507\pi
618618 0 0
619619 43.2958 1.74020 0.870102 0.492872i 0.164053π-0.164053\pi
0.870102 + 0.492872i 0.164053π0.164053\pi
620620 0 0
621621 0 0
622622 5.46076 0.218956
623623 −5.53972 −0.221944
624624 0 0
625625 0 0
626626 −4.47902 −0.179018
627627 0 0
628628 11.0509 0.440977
629629 −13.2444 −0.528090
630630 0 0
631631 8.97773 0.357398 0.178699 0.983904i 0.442811π-0.442811\pi
0.178699 + 0.983904i 0.442811π0.442811\pi
632632 20.0731 0.798466
633633 0 0
634634 9.16547 0.364007
635635 0 0
636636 0 0
637637 17.9541 0.711366
638638 2.19358 0.0868445
639639 0 0
640640 0 0
641641 −9.21279 −0.363883 −0.181942 0.983309i 0.558238π-0.558238\pi
−0.181942 + 0.983309i 0.558238π0.558238\pi
642642 0 0
643643 −16.3783 −0.645896 −0.322948 0.946417i 0.604674π-0.604674\pi
−0.322948 + 0.946417i 0.604674π0.604674\pi
644644 −6.87601 −0.270953
645645 0 0
646646 1.72345 0.0678082
647647 −9.80642 −0.385530 −0.192765 0.981245i 0.561746π-0.561746\pi
−0.192765 + 0.981245i 0.561746π0.561746\pi
648648 0 0
649649 −1.67307 −0.0656738
650650 0 0
651651 0 0
652652 21.0321 0.823681
653653 −33.0736 −1.29427 −0.647135 0.762375i 0.724033π-0.724033\pi
−0.647135 + 0.762375i 0.724033π0.724033\pi
654654 0 0
655655 0 0
656656 36.5620 1.42751
657657 0 0
658658 0.266706 0.0103973
659659 −34.1017 −1.32841 −0.664207 0.747549i 0.731231π-0.731231\pi
−0.664207 + 0.747549i 0.731231π0.731231\pi
660660 0 0
661661 −5.40943 −0.210402 −0.105201 0.994451i 0.533549π-0.533549\pi
−0.105201 + 0.994451i 0.533549π0.533549\pi
662662 −0.815792 −0.0317066
663663 0 0
664664 −9.42372 −0.365711
665665 0 0
666666 0 0
667667 −28.2034 −1.09204
668668 −26.5575 −1.02754
669669 0 0
670670 0 0
671671 7.24443 0.279668
672672 0 0
673673 24.1476 0.930823 0.465412 0.885094i 0.345906π-0.345906\pi
0.465412 + 0.885094i 0.345906π0.345906\pi
674674 1.55707 0.0599761
675675 0 0
676676 8.70027 0.334626
677677 −26.2810 −1.01006 −0.505030 0.863102i 0.668519π-0.668519\pi
−0.505030 + 0.863102i 0.668519π0.668519\pi
678678 0 0
679679 11.2632 0.432241
680680 0 0
681681 0 0
682682 0.815792 0.0312383
683683 −15.3176 −0.586110 −0.293055 0.956096i 0.594672π-0.594672\pi
−0.293055 + 0.956096i 0.594672π0.594672\pi
684684 0 0
685685 0 0
686686 −3.70471 −0.141447
687687 0 0
688688 −36.7195 −1.39992
689689 −2.36842 −0.0902295
690690 0 0
691691 15.0223 0.571474 0.285737 0.958308i 0.407762π-0.407762\pi
0.285737 + 0.958308i 0.407762π0.407762\pi
692692 35.8622 1.36328
693693 0 0
694694 −7.09679 −0.269390
695695 0 0
696696 0 0
697697 24.3239 0.921332
698698 6.60348 0.249945
699699 0 0
700700 0 0
701701 19.9081 0.751920 0.375960 0.926636i 0.377313π-0.377313\pi
0.375960 + 0.926636i 0.377313π0.377313\pi
702702 0 0
703703 −14.1017 −0.531856
704704 5.76986 0.217460
705705 0 0
706706 2.23506 0.0841177
707707 −14.6093 −0.549440
708708 0 0
709709 −13.5081 −0.507306 −0.253653 0.967295i 0.581632π-0.581632\pi
−0.253653 + 0.967295i 0.581632π0.581632\pi
710710 0 0
711711 0 0
712712 7.44785 0.279120
713713 −10.4889 −0.392811
714714 0 0
715715 0 0
716716 9.24443 0.345481
717717 0 0
718718 4.38715 0.163727
719719 16.0830 0.599794 0.299897 0.953972i 0.403048π-0.403048\pi
0.299897 + 0.953972i 0.403048π0.403048\pi
720720 0 0
721721 15.4924 0.576967
722722 −4.07604 −0.151695
723723 0 0
724724 31.9684 1.18809
725725 0 0
726726 0 0
727727 −23.6128 −0.875752 −0.437876 0.899035i 0.644269π-0.644269\pi
−0.437876 + 0.899035i 0.644269π0.644269\pi
728728 3.18421 0.118015
729729 0 0
730730 0 0
731731 −24.4286 −0.903526
732732 0 0
733733 30.0459 1.10977 0.554886 0.831926i 0.312762π-0.312762\pi
0.554886 + 0.831926i 0.312762π0.312762\pi
734734 1.21585 0.0448779
735735 0 0
736736 13.9813 0.515356
737737 12.8573 0.473604
738738 0 0
739739 −24.4099 −0.897933 −0.448966 0.893549i 0.648208π-0.648208\pi
−0.448966 + 0.893549i 0.648208π0.648208\pi
740740 0 0
741741 0 0
742742 0.229234 0.00841546
743743 −33.1798 −1.21725 −0.608624 0.793459i 0.708278π-0.708278\pi
−0.608624 + 0.793459i 0.708278π0.708278\pi
744744 0 0
745745 0 0
746746 −4.03704 −0.147807
747747 0 0
748748 4.34122 0.158731
749749 −12.2538 −0.447744
750750 0 0
751751 −22.5718 −0.823658 −0.411829 0.911261i 0.635110π-0.635110\pi
−0.411829 + 0.911261i 0.635110π0.635110\pi
752752 3.25428 0.118671
753753 0 0
754754 6.36842 0.231924
755755 0 0
756756 0 0
757757 4.94914 0.179880 0.0899399 0.995947i 0.471333π-0.471333\pi
0.0899399 + 0.995947i 0.471333π0.471333\pi
758758 11.2257 0.407736
759759 0 0
760760 0 0
761761 −14.6637 −0.531559 −0.265779 0.964034i 0.585629π-0.585629\pi
−0.265779 + 0.964034i 0.585629π0.585629\pi
762762 0 0
763763 −9.03212 −0.326985
764764 32.0830 1.16072
765765 0 0
766766 6.31402 0.228135
767767 −4.85728 −0.175386
768768 0 0
769769 −44.5718 −1.60730 −0.803651 0.595101i 0.797112π-0.797112\pi
−0.803651 + 0.595101i 0.797112π0.797112\pi
770770 0 0
771771 0 0
772772 −46.8528 −1.68627
773773 −17.3145 −0.622759 −0.311380 0.950286i 0.600791π-0.600791\pi
−0.311380 + 0.950286i 0.600791π0.600791\pi
774774 0 0
775775 0 0
776776 −15.1427 −0.543592
777777 0 0
778778 −9.47949 −0.339856
779779 25.8983 0.927903
780780 0 0
781781 9.28592 0.332276
782782 2.83854 0.101506
783783 0 0
784784 −21.2034 −0.757265
785785 0 0
786786 0 0
787787 36.5161 1.30166 0.650828 0.759225i 0.274422π-0.274422\pi
0.650828 + 0.759225i 0.274422π0.274422\pi
788788 −28.3037 −1.00828
789789 0 0
790790 0 0
791791 12.8573 0.457152
792792 0 0
793793 21.0321 0.746872
794794 −1.54861 −0.0549581
795795 0 0
796796 21.3649 0.757258
797797 14.3180 0.507171 0.253585 0.967313i 0.418390π-0.418390\pi
0.253585 + 0.967313i 0.418390π0.418390\pi
798798 0 0
799799 2.16500 0.0765921
800800 0 0
801801 0 0
802802 0.580728 0.0205062
803803 −5.65878 −0.199694
804804 0 0
805805 0 0
806806 2.36842 0.0834239
807807 0 0
808808 19.6414 0.690983
809809 −32.0544 −1.12697 −0.563486 0.826125i 0.690540π-0.690540\pi
−0.563486 + 0.826125i 0.690540π0.690540\pi
810810 0 0
811811 −8.44738 −0.296627 −0.148314 0.988940i 0.547385π-0.547385\pi
−0.148314 + 0.988940i 0.547385π0.547385\pi
812812 12.1204 0.425344
813813 0 0
814814 1.80642 0.0633151
815815 0 0
816816 0 0
817817 −26.0098 −0.909969
818818 −1.12981 −0.0395030
819819 0 0
820820 0 0
821821 −17.2159 −0.600837 −0.300419 0.953807i 0.597126π-0.597126\pi
−0.300419 + 0.953807i 0.597126π0.597126\pi
822822 0 0
823823 12.7654 0.444974 0.222487 0.974936i 0.428582π-0.428582\pi
0.222487 + 0.974936i 0.428582π0.428582\pi
824824 −20.8287 −0.725602
825825 0 0
826826 0.470127 0.0163578
827827 −8.70964 −0.302864 −0.151432 0.988468i 0.548388π-0.548388\pi
−0.151432 + 0.988468i 0.548388π0.548388\pi
828828 0 0
829829 −8.32693 −0.289206 −0.144603 0.989490i 0.546191π-0.546191\pi
−0.144603 + 0.989490i 0.546191π0.546191\pi
830830 0 0
831831 0 0
832832 16.7511 0.580741
833833 −14.1062 −0.488749
834834 0 0
835835 0 0
836836 4.62222 0.159863
837837 0 0
838838 −1.51114 −0.0522014
839839 −12.8988 −0.445315 −0.222657 0.974897i 0.571473π-0.571473\pi
−0.222657 + 0.974897i 0.571473π0.571473\pi
840840 0 0
841841 20.7146 0.714295
842842 7.04101 0.242649
843843 0 0
844844 22.7239 0.782190
845845 0 0
846846 0 0
847847 0.903212 0.0310347
848848 2.79706 0.0960513
849849 0 0
850850 0 0
851851 −23.2257 −0.796167
852852 0 0
853853 −19.6686 −0.673441 −0.336720 0.941605i 0.609318π-0.609318\pi
−0.336720 + 0.941605i 0.609318π0.609318\pi
854854 −2.03566 −0.0696588
855855 0 0
856856 16.4746 0.563089
857857 −31.8207 −1.08697 −0.543487 0.839417i 0.682896π-0.682896\pi
−0.543487 + 0.839417i 0.682896π0.682896\pi
858858 0 0
859859 27.8292 0.949519 0.474760 0.880116i 0.342535π-0.342535\pi
0.474760 + 0.880116i 0.342535π0.342535\pi
860860 0 0
861861 0 0
862862 −0.387152 −0.0131865
863863 4.82870 0.164371 0.0821854 0.996617i 0.473810π-0.473810\pi
0.0821854 + 0.996617i 0.473810π0.473810\pi
864864 0 0
865865 0 0
866866 4.97773 0.169150
867867 0 0
868868 4.50760 0.152998
869869 16.5303 0.560754
870870 0 0
871871 37.3274 1.26479
872872 12.1432 0.411221
873873 0 0
874874 3.02227 0.102230
875875 0 0
876876 0 0
877877 21.9826 0.742301 0.371151 0.928573i 0.378963π-0.378963\pi
0.371151 + 0.928573i 0.378963π0.378963\pi
878878 −0.755569 −0.0254992
879879 0 0
880880 0 0
881881 12.1017 0.407717 0.203858 0.979000i 0.434652π-0.434652\pi
0.203858 + 0.979000i 0.434652π0.434652\pi
882882 0 0
883883 8.73683 0.294018 0.147009 0.989135i 0.453035π-0.453035\pi
0.147009 + 0.989135i 0.453035π0.453035\pi
884884 12.6035 0.423901
885885 0 0
886886 9.66016 0.324540
887887 19.8524 0.666577 0.333288 0.942825i 0.391842π-0.391842\pi
0.333288 + 0.942825i 0.391842π0.391842\pi
888888 0 0
889889 −9.93978 −0.333369
890890 0 0
891891 0 0
892892 41.5022 1.38960
893893 2.30513 0.0771383
894894 0 0
895895 0 0
896896 −7.93533 −0.265101
897897 0 0
898898 11.6227 0.387854
899899 18.4889 0.616638
900900 0 0
901901 1.86082 0.0619928
902902 −3.31756 −0.110463
903903 0 0
904904 −17.2859 −0.574921
905905 0 0
906906 0 0
907907 32.8287 1.09006 0.545030 0.838417i 0.316518π-0.316518\pi
0.545030 + 0.838417i 0.316518π0.316518\pi
908908 −6.08742 −0.202018
909909 0 0
910910 0 0
911911 16.3497 0.541689 0.270845 0.962623i 0.412697π-0.412697\pi
0.270845 + 0.962623i 0.412697π0.412697\pi
912912 0 0
913913 −7.76049 −0.256835
914914 −2.71853 −0.0899209
915915 0 0
916916 −13.5585 −0.447984
917917 −1.12399 −0.0371173
918918 0 0
919919 20.0228 0.660490 0.330245 0.943895i 0.392869π-0.392869\pi
0.330245 + 0.943895i 0.392869π0.392869\pi
920920 0 0
921921 0 0
922922 −9.88940 −0.325690
923923 26.9590 0.887366
924924 0 0
925925 0 0
926926 −3.76187 −0.123623
927927 0 0
928928 −24.6450 −0.809011
929929 43.5308 1.42820 0.714100 0.700044i 0.246836π-0.246836\pi
0.714100 + 0.700044i 0.246836π0.246836\pi
930930 0 0
931931 −15.0192 −0.492235
932932 37.1610 1.21725
933933 0 0
934934 −4.77430 −0.156220
935935 0 0
936936 0 0
937937 −43.4563 −1.41966 −0.709828 0.704375i 0.751227π-0.751227\pi
−0.709828 + 0.704375i 0.751227π0.751227\pi
938938 −3.61285 −0.117964
939939 0 0
940940 0 0
941941 23.7244 0.773393 0.386697 0.922207i 0.373616π-0.373616\pi
0.386697 + 0.922207i 0.373616π0.373616\pi
942942 0 0
943943 42.6548 1.38903
944944 5.73636 0.186703
945945 0 0
946946 3.33185 0.108328
947947 11.7047 0.380352 0.190176 0.981750i 0.439094π-0.439094\pi
0.190176 + 0.981750i 0.439094π0.439094\pi
948948 0 0
949949 −16.4286 −0.533296
950950 0 0
951951 0 0
952952 −2.50177 −0.0810828
953953 46.1258 1.49416 0.747081 0.664733i 0.231455π-0.231455\pi
0.747081 + 0.664733i 0.231455π0.231455\pi
954954 0 0
955955 0 0
956956 −41.8350 −1.35304
957957 0 0
958958 −1.83500 −0.0592863
959959 −4.00000 −0.129167
960960 0 0
961961 −24.1240 −0.778193
962962 5.24443 0.169087
963963 0 0
964964 −10.1748 −0.327710
965965 0 0
966966 0 0
967967 −17.0495 −0.548274 −0.274137 0.961691i 0.588392π-0.588392\pi
−0.274137 + 0.961691i 0.588392π0.588392\pi
968968 −1.21432 −0.0390297
969969 0 0
970970 0 0
971971 58.1847 1.86724 0.933618 0.358271i 0.116634π-0.116634\pi
0.933618 + 0.358271i 0.116634π0.116634\pi
972972 0 0
973973 0.828699 0.0265669
974974 −9.75203 −0.312475
975975 0 0
976976 −24.8385 −0.795062
977977 −51.7373 −1.65522 −0.827612 0.561301i 0.810301π-0.810301\pi
−0.827612 + 0.561301i 0.810301π0.810301\pi
978978 0 0
979979 6.13335 0.196023
980980 0 0
981981 0 0
982982 2.48886 0.0794228
983983 −26.3970 −0.841933 −0.420967 0.907076i 0.638309π-0.638309\pi
−0.420967 + 0.907076i 0.638309π0.638309\pi
984984 0 0
985985 0 0
986986 −5.00354 −0.159345
987987 0 0
988988 13.4193 0.426924
989989 −42.8385 −1.36219
990990 0 0
991991 −23.0923 −0.733552 −0.366776 0.930309i 0.619539π-0.619539\pi
−0.366776 + 0.930309i 0.619539π0.619539\pi
992992 −9.16547 −0.291004
993993 0 0
994994 −2.60931 −0.0827622
995995 0 0
996996 0 0
997997 −12.9131 −0.408961 −0.204480 0.978871i 0.565550π-0.565550\pi
−0.204480 + 0.978871i 0.565550π0.565550\pi
998998 4.71102 0.149125
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 2475.2.a.bc.1.2 3
3.2 odd 2 825.2.a.j.1.2 3
5.2 odd 4 495.2.c.e.199.4 6
5.3 odd 4 495.2.c.e.199.3 6
5.4 even 2 2475.2.a.ba.1.2 3
15.2 even 4 165.2.c.b.34.3 6
15.8 even 4 165.2.c.b.34.4 yes 6
15.14 odd 2 825.2.a.l.1.2 3
33.32 even 2 9075.2.a.ch.1.2 3
60.23 odd 4 2640.2.d.h.529.5 6
60.47 odd 4 2640.2.d.h.529.2 6
165.32 odd 4 1815.2.c.e.364.4 6
165.98 odd 4 1815.2.c.e.364.3 6
165.164 even 2 9075.2.a.cg.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.c.b.34.3 6 15.2 even 4
165.2.c.b.34.4 yes 6 15.8 even 4
495.2.c.e.199.3 6 5.3 odd 4
495.2.c.e.199.4 6 5.2 odd 4
825.2.a.j.1.2 3 3.2 odd 2
825.2.a.l.1.2 3 15.14 odd 2
1815.2.c.e.364.3 6 165.98 odd 4
1815.2.c.e.364.4 6 165.32 odd 4
2475.2.a.ba.1.2 3 5.4 even 2
2475.2.a.bc.1.2 3 1.1 even 1 trivial
2640.2.d.h.529.2 6 60.47 odd 4
2640.2.d.h.529.5 6 60.23 odd 4
9075.2.a.cg.1.2 3 165.164 even 2
9075.2.a.ch.1.2 3 33.32 even 2