Properties

Label 3960.2.d.d.3169.4
Level 39603960
Weight 22
Character 3960.3169
Analytic conductor 31.62131.621
Analytic rank 00
Dimension 66
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3960,2,Mod(3169,3960)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3960, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3960.3169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 3960=2332511 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3960.d (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 31.620759200431.6207592004
Analytic rank: 00
Dimension: 66
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x62x5+2x4+2x3+4x24x+2 x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 24 2^{4}
Twist minimal: no (minimal twist has level 1320)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 3169.4
Root 1.451611.45161i1.45161 - 1.45161i of defining polynomial
Character χ\chi == 3960.3169
Dual form 3960.2.d.d.3169.3

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.311108+2.21432i)q51.52543iq71.00000q11+0.903212iq132.90321iq17+2.00000q19+8.85728iq23+(4.80642+1.37778i)q256.62222q2910.2351q31+(3.377780.474572i)q358.56199iq372.23506q4112.5763iq43+8.56199iq47+4.67307q49+3.18421iq53+(0.3111082.21432i)q55+12.0415q5913.6128q61+(2.00000+0.280996i)q65+14.3684iq676.91750q719.76049iq73+1.52543iq77+8.75557q79+7.09679iq83+(6.428640.903212i)q8514.9906q89+1.37778q91+(0.622216+4.42864i)q95+7.61285iq97+O(q100)q+(0.311108 + 2.21432i) q^{5} -1.52543i q^{7} -1.00000 q^{11} +0.903212i q^{13} -2.90321i q^{17} +2.00000 q^{19} +8.85728i q^{23} +(-4.80642 + 1.37778i) q^{25} -6.62222 q^{29} -10.2351 q^{31} +(3.37778 - 0.474572i) q^{35} -8.56199i q^{37} -2.23506 q^{41} -12.5763i q^{43} +8.56199i q^{47} +4.67307 q^{49} +3.18421i q^{53} +(-0.311108 - 2.21432i) q^{55} +12.0415 q^{59} -13.6128 q^{61} +(-2.00000 + 0.280996i) q^{65} +14.3684i q^{67} -6.91750 q^{71} -9.76049i q^{73} +1.52543i q^{77} +8.75557 q^{79} +7.09679i q^{83} +(6.42864 - 0.903212i) q^{85} -14.9906 q^{89} +1.37778 q^{91} +(0.622216 + 4.42864i) q^{95} +7.61285i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+2q56q11+12q192q2540q298q31+20q35+40q41+2q492q558q5928q6112q6516q71+52q79+12q8536q89+8q91++4q95+O(q100) 6 q + 2 q^{5} - 6 q^{11} + 12 q^{19} - 2 q^{25} - 40 q^{29} - 8 q^{31} + 20 q^{35} + 40 q^{41} + 2 q^{49} - 2 q^{55} - 8 q^{59} - 28 q^{61} - 12 q^{65} - 16 q^{71} + 52 q^{79} + 12 q^{85} - 36 q^{89} + 8 q^{91}+ \cdots + 4 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3960Z)×\left(\mathbb{Z}/3960\mathbb{Z}\right)^\times.

nn 991991 19811981 23772377 25212521 35213521
χ(n)\chi(n) 11 11 1-1 11 11

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 0 0
44 0 0
55 0.311108 + 2.21432i 0.139132 + 0.990274i
66 0 0
77 1.52543i 0.576557i −0.957547 0.288279i 0.906917π-0.906917\pi
0.957547 0.288279i 0.0930830π-0.0930830\pi
88 0 0
99 0 0
1010 0 0
1111 −1.00000 −0.301511
1212 0 0
1313 0.903212i 0.250506i 0.992125 + 0.125253i 0.0399742π0.0399742\pi
−0.992125 + 0.125253i 0.960026π0.960026\pi
1414 0 0
1515 0 0
1616 0 0
1717 2.90321i 0.704132i −0.935975 0.352066i 0.885479π-0.885479\pi
0.935975 0.352066i 0.114521π-0.114521\pi
1818 0 0
1919 2.00000 0.458831 0.229416 0.973329i 0.426318π-0.426318\pi
0.229416 + 0.973329i 0.426318π0.426318\pi
2020 0 0
2121 0 0
2222 0 0
2323 8.85728i 1.84687i 0.383754 + 0.923435i 0.374631π0.374631\pi
−0.383754 + 0.923435i 0.625369π0.625369\pi
2424 0 0
2525 −4.80642 + 1.37778i −0.961285 + 0.275557i
2626 0 0
2727 0 0
2828 0 0
2929 −6.62222 −1.22971 −0.614857 0.788638i 0.710786π-0.710786\pi
−0.614857 + 0.788638i 0.710786π0.710786\pi
3030 0 0
3131 −10.2351 −1.83827 −0.919136 0.393941i 0.871112π-0.871112\pi
−0.919136 + 0.393941i 0.871112π0.871112\pi
3232 0 0
3333 0 0
3434 0 0
3535 3.37778 0.474572i 0.570950 0.0802174i
3636 0 0
3737 8.56199i 1.40758i −0.710407 0.703791i 0.751489π-0.751489\pi
0.710407 0.703791i 0.248511π-0.248511\pi
3838 0 0
3939 0 0
4040 0 0
4141 −2.23506 −0.349058 −0.174529 0.984652i 0.555840π-0.555840\pi
−0.174529 + 0.984652i 0.555840π0.555840\pi
4242 0 0
4343 12.5763i 1.91787i −0.283634 0.958933i 0.591540π-0.591540\pi
0.283634 0.958933i 0.408460π-0.408460\pi
4444 0 0
4545 0 0
4646 0 0
4747 8.56199i 1.24889i 0.781067 + 0.624447i 0.214676π0.214676\pi
−0.781067 + 0.624447i 0.785324π0.785324\pi
4848 0 0
4949 4.67307 0.667582
5050 0 0
5151 0 0
5252 0 0
5353 3.18421i 0.437385i 0.975794 + 0.218692i 0.0701791π0.0701791\pi
−0.975794 + 0.218692i 0.929821π0.929821\pi
5454 0 0
5555 −0.311108 2.21432i −0.0419498 0.298579i
5656 0 0
5757 0 0
5858 0 0
5959 12.0415 1.56767 0.783834 0.620970i 0.213261π-0.213261\pi
0.783834 + 0.620970i 0.213261π0.213261\pi
6060 0 0
6161 −13.6128 −1.74295 −0.871473 0.490443i 0.836835π-0.836835\pi
−0.871473 + 0.490443i 0.836835π0.836835\pi
6262 0 0
6363 0 0
6464 0 0
6565 −2.00000 + 0.280996i −0.248069 + 0.0348533i
6666 0 0
6767 14.3684i 1.75538i 0.479227 + 0.877691i 0.340917π0.340917\pi
−0.479227 + 0.877691i 0.659083π0.659083\pi
6868 0 0
6969 0 0
7070 0 0
7171 −6.91750 −0.820956 −0.410478 0.911870i 0.634638π-0.634638\pi
−0.410478 + 0.911870i 0.634638π0.634638\pi
7272 0 0
7373 9.76049i 1.14238i −0.820818 0.571190i 0.806482π-0.806482\pi
0.820818 0.571190i 0.193518π-0.193518\pi
7474 0 0
7575 0 0
7676 0 0
7777 1.52543i 0.173839i
7878 0 0
7979 8.75557 0.985078 0.492539 0.870290i 0.336069π-0.336069\pi
0.492539 + 0.870290i 0.336069π0.336069\pi
8080 0 0
8181 0 0
8282 0 0
8383 7.09679i 0.778974i 0.921032 + 0.389487i 0.127348π0.127348\pi
−0.921032 + 0.389487i 0.872652π0.872652\pi
8484 0 0
8585 6.42864 0.903212i 0.697284 0.0979671i
8686 0 0
8787 0 0
8888 0 0
8989 −14.9906 −1.58900 −0.794502 0.607262i 0.792268π-0.792268\pi
−0.794502 + 0.607262i 0.792268π0.792268\pi
9090 0 0
9191 1.37778 0.144431
9292 0 0
9393 0 0
9494 0 0
9595 0.622216 + 4.42864i 0.0638380 + 0.454369i
9696 0 0
9797 7.61285i 0.772968i 0.922296 + 0.386484i 0.126310π0.126310\pi
−0.922296 + 0.386484i 0.873690π0.873690\pi
9898 0 0
9999 0 0
100100 0 0
101101 −10.2351 −1.01843 −0.509213 0.860640i 0.670064π-0.670064\pi
−0.509213 + 0.860640i 0.670064π0.670064\pi
102102 0 0
103103 5.80642i 0.572124i 0.958211 + 0.286062i 0.0923463π0.0923463\pi
−0.958211 + 0.286062i 0.907654π0.907654\pi
104104 0 0
105105 0 0
106106 0 0
107107 7.00492i 0.677191i 0.940932 + 0.338596i 0.109952π0.109952\pi
−0.940932 + 0.338596i 0.890048π0.890048\pi
108108 0 0
109109 −9.61285 −0.920744 −0.460372 0.887726i 0.652284π-0.652284\pi
−0.460372 + 0.887726i 0.652284π0.652284\pi
110110 0 0
111111 0 0
112112 0 0
113113 11.4795i 1.07990i −0.841697 0.539950i 0.818443π-0.818443\pi
0.841697 0.539950i 0.181557π-0.181557\pi
114114 0 0
115115 −19.6128 + 2.75557i −1.82891 + 0.256958i
116116 0 0
117117 0 0
118118 0 0
119119 −4.42864 −0.405973
120120 0 0
121121 1.00000 0.0909091
122122 0 0
123123 0 0
124124 0 0
125125 −4.54617 10.2143i −0.406622 0.913597i
126126 0 0
127127 17.4336i 1.54698i −0.633809 0.773489i 0.718510π-0.718510\pi
0.633809 0.773489i 0.281490π-0.281490\pi
128128 0 0
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 3.05086i 0.264543i
134134 0 0
135135 0 0
136136 0 0
137137 4.69535i 0.401150i 0.979678 + 0.200575i 0.0642811π0.0642811\pi
−0.979678 + 0.200575i 0.935719π0.935719\pi
138138 0 0
139139 −14.4701 −1.22734 −0.613670 0.789563i 0.710307π-0.710307\pi
−0.613670 + 0.789563i 0.710307π0.710307\pi
140140 0 0
141141 0 0
142142 0 0
143143 0.903212i 0.0755304i
144144 0 0
145145 −2.06022 14.6637i −0.171092 1.21775i
146146 0 0
147147 0 0
148148 0 0
149149 −11.4795 −0.940437 −0.470218 0.882550i 0.655825π-0.655825\pi
−0.470218 + 0.882550i 0.655825π0.655825\pi
150150 0 0
151151 −3.24443 −0.264028 −0.132014 0.991248i 0.542144π-0.542144\pi
−0.132014 + 0.991248i 0.542144π0.542144\pi
152152 0 0
153153 0 0
154154 0 0
155155 −3.18421 22.6637i −0.255762 1.82039i
156156 0 0
157157 7.90813i 0.631138i −0.948903 0.315569i 0.897805π-0.897805\pi
0.948903 0.315569i 0.102195π-0.102195\pi
158158 0 0
159159 0 0
160160 0 0
161161 13.5111 1.06483
162162 0 0
163163 9.41927i 0.737774i 0.929474 + 0.368887i 0.120261π0.120261\pi
−0.929474 + 0.368887i 0.879739π0.879739\pi
164164 0 0
165165 0 0
166166 0 0
167167 17.3733i 1.34439i −0.740374 0.672195i 0.765352π-0.765352\pi
0.740374 0.672195i 0.234648π-0.234648\pi
168168 0 0
169169 12.1842 0.937247
170170 0 0
171171 0 0
172172 0 0
173173 13.5669i 1.03147i −0.856747 0.515737i 0.827518π-0.827518\pi
0.856747 0.515737i 0.172482π-0.172482\pi
174174 0 0
175175 2.10171 + 7.33185i 0.158874 + 0.554236i
176176 0 0
177177 0 0
178178 0 0
179179 −12.0000 −0.896922 −0.448461 0.893802i 0.648028π-0.648028\pi
−0.448461 + 0.893802i 0.648028π0.648028\pi
180180 0 0
181181 4.32693 0.321618 0.160809 0.986986i 0.448590π-0.448590\pi
0.160809 + 0.986986i 0.448590π0.448590\pi
182182 0 0
183183 0 0
184184 0 0
185185 18.9590 2.66370i 1.39389 0.195839i
186186 0 0
187187 2.90321i 0.212304i
188188 0 0
189189 0 0
190190 0 0
191191 8.00000 0.578860 0.289430 0.957199i 0.406534π-0.406534\pi
0.289430 + 0.957199i 0.406534π0.406534\pi
192192 0 0
193193 15.5669i 1.12053i 0.828313 + 0.560266i 0.189301π0.189301\pi
−0.828313 + 0.560266i 0.810699π0.810699\pi
194194 0 0
195195 0 0
196196 0 0
197197 14.3412i 1.02177i 0.859649 + 0.510885i 0.170682π0.170682\pi
−0.859649 + 0.510885i 0.829318π0.829318\pi
198198 0 0
199199 −1.24443 −0.0882154 −0.0441077 0.999027i 0.514044π-0.514044\pi
−0.0441077 + 0.999027i 0.514044π0.514044\pi
200200 0 0
201201 0 0
202202 0 0
203203 10.1017i 0.709001i
204204 0 0
205205 −0.695346 4.94914i −0.0485650 0.345663i
206206 0 0
207207 0 0
208208 0 0
209209 −2.00000 −0.138343
210210 0 0
211211 −24.9590 −1.71825 −0.859124 0.511768i 0.828991π-0.828991\pi
−0.859124 + 0.511768i 0.828991π0.828991\pi
212212 0 0
213213 0 0
214214 0 0
215215 27.8479 3.91258i 1.89921 0.266836i
216216 0 0
217217 15.6128i 1.05987i
218218 0 0
219219 0 0
220220 0 0
221221 2.62222 0.176389
222222 0 0
223223 1.53972i 0.103107i 0.998670 + 0.0515536i 0.0164173π0.0164173\pi
−0.998670 + 0.0515536i 0.983583π0.983583\pi
224224 0 0
225225 0 0
226226 0 0
227227 15.3002i 1.01551i 0.861501 + 0.507755i 0.169525π0.169525\pi
−0.861501 + 0.507755i 0.830475π0.830475\pi
228228 0 0
229229 −15.7146 −1.03845 −0.519224 0.854638i 0.673779π-0.673779\pi
−0.519224 + 0.854638i 0.673779π0.673779\pi
230230 0 0
231231 0 0
232232 0 0
233233 29.0049i 1.90018i −0.311983 0.950088i 0.600993π-0.600993\pi
0.311983 0.950088i 0.399007π-0.399007\pi
234234 0 0
235235 −18.9590 + 2.66370i −1.23675 + 0.173761i
236236 0 0
237237 0 0
238238 0 0
239239 −15.6128 −1.00991 −0.504956 0.863145i 0.668491π-0.668491\pi
−0.504956 + 0.863145i 0.668491π0.668491\pi
240240 0 0
241241 5.61285 0.361555 0.180778 0.983524i 0.442139π-0.442139\pi
0.180778 + 0.983524i 0.442139π0.442139\pi
242242 0 0
243243 0 0
244244 0 0
245245 1.45383 + 10.3477i 0.0928817 + 0.661089i
246246 0 0
247247 1.80642i 0.114940i
248248 0 0
249249 0 0
250250 0 0
251251 2.91750 0.184151 0.0920755 0.995752i 0.470650π-0.470650\pi
0.0920755 + 0.995752i 0.470650π0.470650\pi
252252 0 0
253253 8.85728i 0.556852i
254254 0 0
255255 0 0
256256 0 0
257257 11.0923i 0.691921i −0.938249 0.345961i 0.887553π-0.887553\pi
0.938249 0.345961i 0.112447π-0.112447\pi
258258 0 0
259259 −13.0607 −0.811552
260260 0 0
261261 0 0
262262 0 0
263263 5.46520i 0.336999i 0.985702 + 0.168499i 0.0538921π0.0538921\pi
−0.985702 + 0.168499i 0.946108π0.946108\pi
264264 0 0
265265 −7.05086 + 0.990632i −0.433131 + 0.0608540i
266266 0 0
267267 0 0
268268 0 0
269269 −10.8573 −0.661980 −0.330990 0.943634i 0.607383π-0.607383\pi
−0.330990 + 0.943634i 0.607383π0.607383\pi
270270 0 0
271271 −0.101710 −0.00617846 −0.00308923 0.999995i 0.500983π-0.500983\pi
−0.00308923 + 0.999995i 0.500983π0.500983\pi
272272 0 0
273273 0 0
274274 0 0
275275 4.80642 1.37778i 0.289838 0.0830835i
276276 0 0
277277 9.19850i 0.552684i 0.961059 + 0.276342i 0.0891223π0.0891223\pi
−0.961059 + 0.276342i 0.910878π0.910878\pi
278278 0 0
279279 0 0
280280 0 0
281281 1.11108 0.0662814 0.0331407 0.999451i 0.489449π-0.489449\pi
0.0331407 + 0.999451i 0.489449π0.489449\pi
282282 0 0
283283 15.7190i 0.934398i −0.884152 0.467199i 0.845263π-0.845263\pi
0.884152 0.467199i 0.154737π-0.154737\pi
284284 0 0
285285 0 0
286286 0 0
287287 3.40943i 0.201252i
288288 0 0
289289 8.57136 0.504198
290290 0 0
291291 0 0
292292 0 0
293293 6.43309i 0.375825i −0.982186 0.187912i 0.939828π-0.939828\pi
0.982186 0.187912i 0.0601721π-0.0601721\pi
294294 0 0
295295 3.74620 + 26.6637i 0.218112 + 1.55242i
296296 0 0
297297 0 0
298298 0 0
299299 −8.00000 −0.462652
300300 0 0
301301 −19.1842 −1.10576
302302 0 0
303303 0 0
304304 0 0
305305 −4.23506 30.1432i −0.242499 1.72599i
306306 0 0
307307 15.7190i 0.897131i 0.893750 + 0.448565i 0.148065π0.148065\pi
−0.893750 + 0.448565i 0.851935π0.851935\pi
308308 0 0
309309 0 0
310310 0 0
311311 −24.8988 −1.41188 −0.705940 0.708272i 0.749475π-0.749475\pi
−0.705940 + 0.708272i 0.749475π0.749475\pi
312312 0 0
313313 17.1526i 0.969520i −0.874647 0.484760i 0.838907π-0.838907\pi
0.874647 0.484760i 0.161093π-0.161093\pi
314314 0 0
315315 0 0
316316 0 0
317317 12.3368i 0.692902i −0.938068 0.346451i 0.887387π-0.887387\pi
0.938068 0.346451i 0.112613π-0.112613\pi
318318 0 0
319319 6.62222 0.370773
320320 0 0
321321 0 0
322322 0 0
323323 5.80642i 0.323078i
324324 0 0
325325 −1.24443 4.34122i −0.0690286 0.240808i
326326 0 0
327327 0 0
328328 0 0
329329 13.0607 0.720060
330330 0 0
331331 −9.37778 −0.515450 −0.257725 0.966218i 0.582973π-0.582973\pi
−0.257725 + 0.966218i 0.582973π0.582973\pi
332332 0 0
333333 0 0
334334 0 0
335335 −31.8163 + 4.47013i −1.73831 + 0.244229i
336336 0 0
337337 18.0558i 0.983561i −0.870719 0.491780i 0.836346π-0.836346\pi
0.870719 0.491780i 0.163654π-0.163654\pi
338338 0 0
339339 0 0
340340 0 0
341341 10.2351 0.554260
342342 0 0
343343 17.8064i 0.961457i
344344 0 0
345345 0 0
346346 0 0
347347 16.5161i 0.886629i 0.896366 + 0.443314i 0.146197π0.146197\pi
−0.896366 + 0.443314i 0.853803π0.853803\pi
348348 0 0
349349 8.36842 0.447951 0.223976 0.974595i 0.428096π-0.428096\pi
0.223976 + 0.974595i 0.428096π0.428096\pi
350350 0 0
351351 0 0
352352 0 0
353353 11.7748i 0.626708i −0.949636 0.313354i 0.898547π-0.898547\pi
0.949636 0.313354i 0.101453π-0.101453\pi
354354 0 0
355355 −2.15209 15.3176i −0.114221 0.812972i
356356 0 0
357357 0 0
358358 0 0
359359 −12.2034 −0.644072 −0.322036 0.946727i 0.604367π-0.604367\pi
−0.322036 + 0.946727i 0.604367π0.604367\pi
360360 0 0
361361 −15.0000 −0.789474
362362 0 0
363363 0 0
364364 0 0
365365 21.6128 3.03657i 1.13127 0.158941i
366366 0 0
367367 18.6637i 0.974237i 0.873336 + 0.487119i 0.161952π0.161952\pi
−0.873336 + 0.487119i 0.838048π0.838048\pi
368368 0 0
369369 0 0
370370 0 0
371371 4.85728 0.252177
372372 0 0
373373 34.3225i 1.77715i 0.458731 + 0.888575i 0.348304π0.348304\pi
−0.458731 + 0.888575i 0.651696π0.651696\pi
374374 0 0
375375 0 0
376376 0 0
377377 5.98126i 0.308051i
378378 0 0
379379 11.7333 0.602699 0.301349 0.953514i 0.402563π-0.402563\pi
0.301349 + 0.953514i 0.402563π0.402563\pi
380380 0 0
381381 0 0
382382 0 0
383383 18.6637i 0.953671i −0.878993 0.476835i 0.841784π-0.841784\pi
0.878993 0.476835i 0.158216π-0.158216\pi
384384 0 0
385385 −3.37778 + 0.474572i −0.172148 + 0.0241865i
386386 0 0
387387 0 0
388388 0 0
389389 −15.1240 −0.766816 −0.383408 0.923579i 0.625250π-0.625250\pi
−0.383408 + 0.923579i 0.625250π0.625250\pi
390390 0 0
391391 25.7146 1.30044
392392 0 0
393393 0 0
394394 0 0
395395 2.72393 + 19.3876i 0.137056 + 0.975497i
396396 0 0
397397 34.1847i 1.71568i 0.513917 + 0.857840i 0.328194π0.328194\pi
−0.513917 + 0.857840i 0.671806π0.671806\pi
398398 0 0
399399 0 0
400400 0 0
401401 −17.0923 −0.853551 −0.426775 0.904358i 0.640351π-0.640351\pi
−0.426775 + 0.904358i 0.640351π0.640351\pi
402402 0 0
403403 9.24443i 0.460498i
404404 0 0
405405 0 0
406406 0 0
407407 8.56199i 0.424402i
408408 0 0
409409 27.1240 1.34119 0.670597 0.741822i 0.266038π-0.266038\pi
0.670597 + 0.741822i 0.266038π0.266038\pi
410410 0 0
411411 0 0
412412 0 0
413413 18.3684i 0.903851i
414414 0 0
415415 −15.7146 + 2.20787i −0.771397 + 0.108380i
416416 0 0
417417 0 0
418418 0 0
419419 14.4889 0.707827 0.353914 0.935278i 0.384851π-0.384851\pi
0.353914 + 0.935278i 0.384851π0.384851\pi
420420 0 0
421421 −7.67307 −0.373963 −0.186981 0.982363i 0.559870π-0.559870\pi
−0.186981 + 0.982363i 0.559870π0.559870\pi
422422 0 0
423423 0 0
424424 0 0
425425 4.00000 + 13.9541i 0.194029 + 0.676872i
426426 0 0
427427 20.7654i 1.00491i
428428 0 0
429429 0 0
430430 0 0
431431 8.38715 0.403995 0.201997 0.979386i 0.435257π-0.435257\pi
0.201997 + 0.979386i 0.435257π0.435257\pi
432432 0 0
433433 31.3461i 1.50640i 0.657792 + 0.753200i 0.271491π0.271491\pi
−0.657792 + 0.753200i 0.728509π0.728509\pi
434434 0 0
435435 0 0
436436 0 0
437437 17.7146i 0.847402i
438438 0 0
439439 37.5496 1.79214 0.896071 0.443910i 0.146409π-0.146409\pi
0.896071 + 0.443910i 0.146409π0.146409\pi
440440 0 0
441441 0 0
442442 0 0
443443 10.9304i 0.519319i 0.965700 + 0.259660i 0.0836104π0.0836104\pi
−0.965700 + 0.259660i 0.916390π0.916390\pi
444444 0 0
445445 −4.66370 33.1941i −0.221081 1.57355i
446446 0 0
447447 0 0
448448 0 0
449449 −11.2573 −0.531267 −0.265633 0.964074i 0.585581π-0.585581\pi
−0.265633 + 0.964074i 0.585581π0.585581\pi
450450 0 0
451451 2.23506 0.105245
452452 0 0
453453 0 0
454454 0 0
455455 0.428639 + 3.05086i 0.0200949 + 0.143026i
456456 0 0
457457 29.3733i 1.37403i −0.726645 0.687013i 0.758921π-0.758921\pi
0.726645 0.687013i 0.241079π-0.241079\pi
458458 0 0
459459 0 0
460460 0 0
461461 31.9496 1.48804 0.744021 0.668156i 0.232916π-0.232916\pi
0.744021 + 0.668156i 0.232916π0.232916\pi
462462 0 0
463463 34.4800i 1.60242i 0.598383 + 0.801210i 0.295810π0.295810\pi
−0.598383 + 0.801210i 0.704190π0.704190\pi
464464 0 0
465465 0 0
466466 0 0
467467 11.6128i 0.537379i 0.963227 + 0.268689i 0.0865905π0.0865905\pi
−0.963227 + 0.268689i 0.913410π0.913410\pi
468468 0 0
469469 21.9180 1.01208
470470 0 0
471471 0 0
472472 0 0
473473 12.5763i 0.578258i
474474 0 0
475475 −9.61285 + 2.75557i −0.441068 + 0.126434i
476476 0 0
477477 0 0
478478 0 0
479479 −41.0607 −1.87611 −0.938056 0.346485i 0.887375π-0.887375\pi
−0.938056 + 0.346485i 0.887375π0.887375\pi
480480 0 0
481481 7.73329 0.352608
482482 0 0
483483 0 0
484484 0 0
485485 −16.8573 + 2.36842i −0.765450 + 0.107544i
486486 0 0
487487 4.47013i 0.202561i −0.994858 0.101280i 0.967706π-0.967706\pi
0.994858 0.101280i 0.0322939π-0.0322939\pi
488488 0 0
489489 0 0
490490 0 0
491491 21.5941 0.974529 0.487264 0.873255i 0.337995π-0.337995\pi
0.487264 + 0.873255i 0.337995π0.337995\pi
492492 0 0
493493 19.2257i 0.865882i
494494 0 0
495495 0 0
496496 0 0
497497 10.5521i 0.473329i
498498 0 0
499499 26.8385 1.20146 0.600729 0.799453i 0.294877π-0.294877\pi
0.600729 + 0.799453i 0.294877π0.294877\pi
500500 0 0
501501 0 0
502502 0 0
503503 17.7605i 0.791901i 0.918272 + 0.395951i 0.129585π0.129585\pi
−0.918272 + 0.395951i 0.870415π0.870415\pi
504504 0 0
505505 −3.18421 22.6637i −0.141695 1.00852i
506506 0 0
507507 0 0
508508 0 0
509509 18.0830 0.801514 0.400757 0.916184i 0.368747π-0.368747\pi
0.400757 + 0.916184i 0.368747π0.368747\pi
510510 0 0
511511 −14.8889 −0.658647
512512 0 0
513513 0 0
514514 0 0
515515 −12.8573 + 1.80642i −0.566559 + 0.0796005i
516516 0 0
517517 8.56199i 0.376556i
518518 0 0
519519 0 0
520520 0 0
521521 −2.40006 −0.105149 −0.0525743 0.998617i 0.516743π-0.516743\pi
−0.0525743 + 0.998617i 0.516743π0.516743\pi
522522 0 0
523523 19.7101i 0.861863i −0.902385 0.430932i 0.858185π-0.858185\pi
0.902385 0.430932i 0.141815π-0.141815\pi
524524 0 0
525525 0 0
526526 0 0
527527 29.7146i 1.29439i
528528 0 0
529529 −55.4514 −2.41093
530530 0 0
531531 0 0
532532 0 0
533533 2.01874i 0.0874412i
534534 0 0
535535 −15.5111 + 2.17929i −0.670605 + 0.0942188i
536536 0 0
537537 0 0
538538 0 0
539539 −4.67307 −0.201283
540540 0 0
541541 −2.59057 −0.111377 −0.0556887 0.998448i 0.517735π-0.517735\pi
−0.0556887 + 0.998448i 0.517735π0.517735\pi
542542 0 0
543543 0 0
544544 0 0
545545 −2.99063 21.2859i −0.128105 0.911789i
546546 0 0
547547 24.2810i 1.03818i 0.854719 + 0.519090i 0.173729π0.173729\pi
−0.854719 + 0.519090i 0.826271π0.826271\pi
548548 0 0
549549 0 0
550550 0 0
551551 −13.2444 −0.564232
552552 0 0
553553 13.3560i 0.567954i
554554 0 0
555555 0 0
556556 0 0
557557 45.1798i 1.91433i 0.289546 + 0.957164i 0.406496π0.406496\pi
−0.289546 + 0.957164i 0.593504π0.593504\pi
558558 0 0
559559 11.3590 0.480437
560560 0 0
561561 0 0
562562 0 0
563563 2.97634i 0.125438i −0.998031 0.0627189i 0.980023π-0.980023\pi
0.998031 0.0627189i 0.0199772π-0.0199772\pi
564564 0 0
565565 25.4193 3.57136i 1.06940 0.150248i
566566 0 0
567567 0 0
568568 0 0
569569 39.1753 1.64231 0.821157 0.570702i 0.193329π-0.193329\pi
0.821157 + 0.570702i 0.193329π0.193329\pi
570570 0 0
571571 −11.1240 −0.465524 −0.232762 0.972534i 0.574776π-0.574776\pi
−0.232762 + 0.972534i 0.574776π0.574776\pi
572572 0 0
573573 0 0
574574 0 0
575575 −12.2034 42.5718i −0.508918 1.77537i
576576 0 0
577577 6.19358i 0.257842i 0.991655 + 0.128921i 0.0411514π0.0411514\pi
−0.991655 + 0.128921i 0.958849π0.958849\pi
578578 0 0
579579 0 0
580580 0 0
581581 10.8256 0.449123
582582 0 0
583583 3.18421i 0.131876i
584584 0 0
585585 0 0
586586 0 0
587587 7.22570i 0.298236i −0.988819 0.149118i 0.952357π-0.952357\pi
0.988819 0.149118i 0.0476435π-0.0476435\pi
588588 0 0
589589 −20.4701 −0.843457
590590 0 0
591591 0 0
592592 0 0
593593 21.5955i 0.886821i 0.896319 + 0.443410i 0.146232π0.146232\pi
−0.896319 + 0.443410i 0.853768π0.853768\pi
594594 0 0
595595 −1.37778 9.80642i −0.0564837 0.402024i
596596 0 0
597597 0 0
598598 0 0
599599 38.4514 1.57108 0.785541 0.618810i 0.212385π-0.212385\pi
0.785541 + 0.618810i 0.212385π0.212385\pi
600600 0 0
601601 22.5906 0.921489 0.460744 0.887533i 0.347583π-0.347583\pi
0.460744 + 0.887533i 0.347583π0.347583\pi
602602 0 0
603603 0 0
604604 0 0
605605 0.311108 + 2.21432i 0.0126483 + 0.0900249i
606606 0 0
607607 22.9733i 0.932457i 0.884664 + 0.466228i 0.154387π0.154387\pi
−0.884664 + 0.466228i 0.845613π0.845613\pi
608608 0 0
609609 0 0
610610 0 0
611611 −7.73329 −0.312856
612612 0 0
613613 23.5383i 0.950704i −0.879796 0.475352i 0.842321π-0.842321\pi
0.879796 0.475352i 0.157679π-0.157679\pi
614614 0 0
615615 0 0
616616 0 0
617617 22.8256i 0.918926i 0.888197 + 0.459463i 0.151958π0.151958\pi
−0.888197 + 0.459463i 0.848042π0.848042\pi
618618 0 0
619619 25.3778 1.02002 0.510010 0.860169i 0.329642π-0.329642\pi
0.510010 + 0.860169i 0.329642π0.329642\pi
620620 0 0
621621 0 0
622622 0 0
623623 22.8671i 0.916152i
624624 0 0
625625 21.2034 13.2444i 0.848137 0.529777i
626626 0 0
627627 0 0
628628 0 0
629629 −24.8573 −0.991125
630630 0 0
631631 28.6735 1.14148 0.570738 0.821132i 0.306657π-0.306657\pi
0.570738 + 0.821132i 0.306657π0.306657\pi
632632 0 0
633633 0 0
634634 0 0
635635 38.6035 5.42372i 1.53193 0.215234i
636636 0 0
637637 4.22077i 0.167233i
638638 0 0
639639 0 0
640640 0 0
641641 18.6035 0.734793 0.367397 0.930064i 0.380249π-0.380249\pi
0.367397 + 0.930064i 0.380249π0.380249\pi
642642 0 0
643643 27.9081i 1.10059i −0.834971 0.550295i 0.814515π-0.814515\pi
0.834971 0.550295i 0.185485π-0.185485\pi
644644 0 0
645645 0 0
646646 0 0
647647 20.5620i 0.808375i 0.914676 + 0.404188i 0.132446π0.132446\pi
−0.914676 + 0.404188i 0.867554π0.867554\pi
648648 0 0
649649 −12.0415 −0.472670
650650 0 0
651651 0 0
652652 0 0
653653 10.7685i 0.421403i −0.977550 0.210702i 0.932425π-0.932425\pi
0.977550 0.210702i 0.0675748π-0.0675748\pi
654654 0 0
655655 −0.387152 2.75557i −0.0151273 0.107669i
656656 0 0
657657 0 0
658658 0 0
659659 −8.20342 −0.319560 −0.159780 0.987153i 0.551078π-0.551078\pi
−0.159780 + 0.987153i 0.551078π0.551078\pi
660660 0 0
661661 16.1017 0.626284 0.313142 0.949706i 0.398618π-0.398618\pi
0.313142 + 0.949706i 0.398618π0.398618\pi
662662 0 0
663663 0 0
664664 0 0
665665 6.75557 0.949145i 0.261970 0.0368063i
666666 0 0
667667 58.6548i 2.27112i
668668 0 0
669669 0 0
670670 0 0
671671 13.6128 0.525518
672672 0 0
673673 10.8845i 0.419566i −0.977748 0.209783i 0.932724π-0.932724\pi
0.977748 0.209783i 0.0672757π-0.0672757\pi
674674 0 0
675675 0 0
676676 0 0
677677 2.60793i 0.100231i −0.998743 0.0501154i 0.984041π-0.984041\pi
0.998743 0.0501154i 0.0159589π-0.0159589\pi
678678 0 0
679679 11.6128 0.445660
680680 0 0
681681 0 0
682682 0 0
683683 9.60300i 0.367449i 0.982978 + 0.183724i 0.0588154π0.0588154\pi
−0.982978 + 0.183724i 0.941185π0.941185\pi
684684 0 0
685685 −10.3970 + 1.46076i −0.397249 + 0.0558127i
686686 0 0
687687 0 0
688688 0 0
689689 −2.87601 −0.109567
690690 0 0
691691 26.6351 1.01325 0.506624 0.862167i 0.330893π-0.330893\pi
0.506624 + 0.862167i 0.330893π0.330893\pi
692692 0 0
693693 0 0
694694 0 0
695695 −4.50177 32.0415i −0.170762 1.21540i
696696 0 0
697697 6.48886i 0.245783i
698698 0 0
699699 0 0
700700 0 0
701701 2.62222 0.0990397 0.0495199 0.998773i 0.484231π-0.484231\pi
0.0495199 + 0.998773i 0.484231π0.484231\pi
702702 0 0
703703 17.1240i 0.645843i
704704 0 0
705705 0 0
706706 0 0
707707 15.6128i 0.587182i
708708 0 0
709709 −29.1842 −1.09604 −0.548018 0.836467i 0.684617π-0.684617\pi
−0.548018 + 0.836467i 0.684617π0.684617\pi
710710 0 0
711711 0 0
712712 0 0
713713 90.6548i 3.39505i
714714 0 0
715715 2.00000 0.280996i 0.0747958 0.0105087i
716716 0 0
717717 0 0
718718 0 0
719719 40.9403 1.52681 0.763407 0.645918i 0.223525π-0.223525\pi
0.763407 + 0.645918i 0.223525π0.223525\pi
720720 0 0
721721 8.85728 0.329862
722722 0 0
723723 0 0
724724 0 0
725725 31.8292 9.12399i 1.18211 0.338856i
726726 0 0
727727 11.2257i 0.416338i −0.978093 0.208169i 0.933250π-0.933250\pi
0.978093 0.208169i 0.0667504π-0.0667504\pi
728728 0 0
729729 0 0
730730 0 0
731731 −36.5116 −1.35043
732732 0 0
733733 7.74176i 0.285948i −0.989726 0.142974i 0.954333π-0.954333\pi
0.989726 0.142974i 0.0456666π-0.0456666\pi
734734 0 0
735735 0 0
736736 0 0
737737 14.3684i 0.529267i
738738 0 0
739739 24.1017 0.886596 0.443298 0.896374i 0.353808π-0.353808\pi
0.443298 + 0.896374i 0.353808π0.353808\pi
740740 0 0
741741 0 0
742742 0 0
743743 8.22077i 0.301591i 0.988565 + 0.150795i 0.0481835π0.0481835\pi
−0.988565 + 0.150795i 0.951817π0.951817\pi
744744 0 0
745745 −3.57136 25.4193i −0.130845 0.931290i
746746 0 0
747747 0 0
748748 0 0
749749 10.6855 0.390440
750750 0 0
751751 11.8163 0.431182 0.215591 0.976484i 0.430832π-0.430832\pi
0.215591 + 0.976484i 0.430832π0.430832\pi
752752 0 0
753753 0 0
754754 0 0
755755 −1.00937 7.18421i −0.0367347 0.261460i
756756 0 0
757757 10.6637i 0.387579i −0.981043 0.193789i 0.937922π-0.937922\pi
0.981043 0.193789i 0.0620779π-0.0620779\pi
758758 0 0
759759 0 0
760760 0 0
761761 42.7052 1.54806 0.774031 0.633148i 0.218237π-0.218237\pi
0.774031 + 0.633148i 0.218237π0.218237\pi
762762 0 0
763763 14.6637i 0.530862i
764764 0 0
765765 0 0
766766 0 0
767767 10.8760i 0.392710i
768768 0 0
769769 −7.63158 −0.275202 −0.137601 0.990488i 0.543939π-0.543939\pi
−0.137601 + 0.990488i 0.543939π0.543939\pi
770770 0 0
771771 0 0
772772 0 0
773773 8.52051i 0.306461i −0.988190 0.153231i 0.951032π-0.951032\pi
0.988190 0.153231i 0.0489677π-0.0489677\pi
774774 0 0
775775 49.1941 14.1017i 1.76710 0.506548i
776776 0 0
777777 0 0
778778 0 0
779779 −4.47013 −0.160159
780780 0 0
781781 6.91750 0.247528
782782 0 0
783783 0 0
784784 0 0
785785 17.5111 2.46028i 0.624999 0.0878112i
786786 0 0
787787 41.3131i 1.47265i 0.676626 + 0.736327i 0.263441π0.263441\pi
−0.676626 + 0.736327i 0.736559π0.736559\pi
788788 0 0
789789 0 0
790790 0 0
791791 −17.5111 −0.622624
792792 0 0
793793 12.2953i 0.436618i
794794 0 0
795795 0 0
796796 0 0
797797 48.7239i 1.72589i 0.505298 + 0.862945i 0.331383π0.331383\pi
−0.505298 + 0.862945i 0.668617π0.668617\pi
798798 0 0
799799 24.8573 0.879387
800800 0 0
801801 0 0
802802 0 0
803803 9.76049i 0.344440i
804804 0 0
805805 4.20342 + 29.9180i 0.148151 + 1.05447i
806806 0 0
807807 0 0
808808 0 0
809809 −52.4197 −1.84298 −0.921490 0.388402i 0.873027π-0.873027\pi
−0.921490 + 0.388402i 0.873027π0.873027\pi
810810 0 0
811811 −22.8573 −0.802628 −0.401314 0.915941i 0.631446π-0.631446\pi
−0.401314 + 0.915941i 0.631446π0.631446\pi
812812 0 0
813813 0 0
814814 0 0
815815 −20.8573 + 2.93041i −0.730599 + 0.102648i
816816 0 0
817817 25.1526i 0.879977i
818818 0 0
819819 0 0
820820 0 0
821821 −52.5402 −1.83367 −0.916833 0.399272i 0.869263π-0.869263\pi
−0.916833 + 0.399272i 0.869263π0.869263\pi
822822 0 0
823823 24.8859i 0.867467i 0.901041 + 0.433733i 0.142804π0.142804\pi
−0.901041 + 0.433733i 0.857196π0.857196\pi
824824 0 0
825825 0 0
826826 0 0
827827 8.60793i 0.299327i −0.988737 0.149663i 0.952181π-0.952181\pi
0.988737 0.149663i 0.0478190π-0.0478190\pi
828828 0 0
829829 −6.16193 −0.214013 −0.107006 0.994258i 0.534127π-0.534127\pi
−0.107006 + 0.994258i 0.534127π0.534127\pi
830830 0 0
831831 0 0
832832 0 0
833833 13.5669i 0.470066i
834834 0 0
835835 38.4701 5.40498i 1.33131 0.187047i
836836 0 0
837837 0 0
838838 0 0
839839 −46.4929 −1.60511 −0.802556 0.596577i 0.796527π-0.796527\pi
−0.802556 + 0.596577i 0.796527π0.796527\pi
840840 0 0
841841 14.8537 0.512198
842842 0 0
843843 0 0
844844 0 0
845845 3.79060 + 26.9797i 0.130401 + 0.928131i
846846 0 0
847847 1.52543i 0.0524143i
848848 0 0
849849 0 0
850850 0 0
851851 75.8360 2.59962
852852 0 0
853853 0.699791i 0.0239604i −0.999928 0.0119802i 0.996186π-0.996186\pi
0.999928 0.0119802i 0.00381351π-0.00381351\pi
854854 0 0
855855 0 0
856856 0 0
857857 16.0558i 0.548455i 0.961665 + 0.274227i 0.0884221π0.0884221\pi
−0.961665 + 0.274227i 0.911578π0.911578\pi
858858 0 0
859859 −1.11108 −0.0379095 −0.0189547 0.999820i 0.506034π-0.506034\pi
−0.0189547 + 0.999820i 0.506034π0.506034\pi
860860 0 0
861861 0 0
862862 0 0
863863 43.0134i 1.46419i 0.681201 + 0.732096i 0.261458π0.261458\pi
−0.681201 + 0.732096i 0.738542π0.738542\pi
864864 0 0
865865 30.0415 4.22077i 1.02144 0.143511i
866866 0 0
867867 0 0
868868 0 0
869869 −8.75557 −0.297012
870870 0 0
871871 −12.9777 −0.439733
872872 0 0
873873 0 0
874874 0 0
875875 −15.5812 + 6.93485i −0.526741 + 0.234441i
876876 0 0
877877 8.03704i 0.271392i −0.990751 0.135696i 0.956673π-0.956673\pi
0.990751 0.135696i 0.0433270π-0.0433270\pi
878878 0 0
879879 0 0
880880 0 0
881881 17.9367 0.604303 0.302152 0.953260i 0.402295π-0.402295\pi
0.302152 + 0.953260i 0.402295π0.402295\pi
882882 0 0
883883 3.22570i 0.108553i 0.998526 + 0.0542766i 0.0172853π0.0172853\pi
−0.998526 + 0.0542766i 0.982715π0.982715\pi
884884 0 0
885885 0 0
886886 0 0
887887 1.43662i 0.0482371i −0.999709 0.0241186i 0.992322π-0.992322\pi
0.999709 0.0241186i 0.00767792π-0.00767792\pi
888888 0 0
889889 −26.5936 −0.891922
890890 0 0
891891 0 0
892892 0 0
893893 17.1240i 0.573032i
894894 0 0
895895 −3.73329 26.5718i −0.124790 0.888199i
896896 0 0
897897 0 0
898898 0 0
899899 67.7788 2.26055
900900 0 0
901901 9.24443 0.307977
902902 0 0
903903 0 0
904904 0 0
905905 1.34614 + 9.58120i 0.0447473 + 0.318490i
906906 0 0
907907 19.4380i 0.645428i 0.946496 + 0.322714i 0.104595π0.104595\pi
−0.946496 + 0.322714i 0.895405π0.895405\pi
908908 0 0
909909 0 0
910910 0 0
911911 −16.6735 −0.552419 −0.276210 0.961097i 0.589078π-0.589078\pi
−0.276210 + 0.961097i 0.589078π0.589078\pi
912912 0 0
913913 7.09679i 0.234869i
914914 0 0
915915 0 0
916916 0 0
917917 1.89829i 0.0626871i
918918 0 0
919919 31.4479 1.03737 0.518684 0.854966i 0.326422π-0.326422\pi
0.518684 + 0.854966i 0.326422π0.326422\pi
920920 0 0
921921 0 0
922922 0 0
923923 6.24797i 0.205654i
924924 0 0
925925 11.7966 + 41.1526i 0.387869 + 1.35309i
926926 0 0
927927 0 0
928928 0 0
929929 −44.3881 −1.45633 −0.728163 0.685404i 0.759626π-0.759626\pi
−0.728163 + 0.685404i 0.759626π0.759626\pi
930930 0 0
931931 9.34614 0.306307
932932 0 0
933933 0 0
934934 0 0
935935 −6.42864 + 0.903212i −0.210239 + 0.0295382i
936936 0 0
937937 21.6686i 0.707883i 0.935268 + 0.353942i 0.115159π0.115159\pi
−0.935268 + 0.353942i 0.884841π0.884841\pi
938938 0 0
939939 0 0
940940 0 0
941941 −15.4795 −0.504617 −0.252309 0.967647i 0.581190π-0.581190\pi
−0.252309 + 0.967647i 0.581190π0.581190\pi
942942 0 0
943943 19.7966i 0.644665i
944944 0 0
945945 0 0
946946 0 0
947947 50.0098i 1.62510i −0.582890 0.812551i 0.698078π-0.698078\pi
0.582890 0.812551i 0.301922π-0.301922\pi
948948 0 0
949949 8.81579 0.286173
950950 0 0
951951 0 0
952952 0 0
953953 10.9032i 0.353190i −0.984284 0.176595i 0.943492π-0.943492\pi
0.984284 0.176595i 0.0565082π-0.0565082\pi
954954 0 0
955955 2.48886 + 17.7146i 0.0805377 + 0.573230i
956956 0 0
957957 0 0
958958 0 0
959959 7.16241 0.231286
960960 0 0
961961 73.7565 2.37924
962962 0 0
963963 0 0
964964 0 0
965965 −34.4701 + 4.84299i −1.10963 + 0.155901i
966966 0 0
967967 43.6815i 1.40470i −0.711830 0.702352i 0.752133π-0.752133\pi
0.711830 0.702352i 0.247867π-0.247867\pi
968968 0 0
969969 0 0
970970 0 0
971971 2.55215 0.0819023 0.0409512 0.999161i 0.486961π-0.486961\pi
0.0409512 + 0.999161i 0.486961π0.486961\pi
972972 0 0
973973 22.0731i 0.707632i
974974 0 0
975975 0 0
976976 0 0
977977 6.40990i 0.205071i −0.994729 0.102535i 0.967304π-0.967304\pi
0.994729 0.102535i 0.0326955π-0.0326955\pi
978978 0 0
979979 14.9906 0.479103
980980 0 0
981981 0 0
982982 0 0
983983 40.1748i 1.28138i −0.767800 0.640689i 0.778649π-0.778649\pi
0.767800 0.640689i 0.221351π-0.221351\pi
984984 0 0
985985 −31.7560 + 4.46167i −1.01183 + 0.142160i
986986 0 0
987987 0 0
988988 0 0
989989 111.392 3.54205
990990 0 0
991991 18.2351 0.579256 0.289628 0.957139i 0.406468π-0.406468\pi
0.289628 + 0.957139i 0.406468π0.406468\pi
992992 0 0
993993 0 0
994994 0 0
995995 −0.387152 2.75557i −0.0122736 0.0873574i
996996 0 0
997997 4.16638i 0.131951i 0.997821 + 0.0659753i 0.0210158π0.0210158\pi
−0.997821 + 0.0659753i 0.978984π0.978984\pi
998998 0 0
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 3960.2.d.d.3169.4 6
3.2 odd 2 1320.2.d.b.529.5 yes 6
5.4 even 2 inner 3960.2.d.d.3169.3 6
12.11 even 2 2640.2.d.f.529.2 6
15.2 even 4 6600.2.a.bu.1.3 3
15.8 even 4 6600.2.a.bq.1.1 3
15.14 odd 2 1320.2.d.b.529.2 6
60.59 even 2 2640.2.d.f.529.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1320.2.d.b.529.2 6 15.14 odd 2
1320.2.d.b.529.5 yes 6 3.2 odd 2
2640.2.d.f.529.2 6 12.11 even 2
2640.2.d.f.529.5 6 60.59 even 2
3960.2.d.d.3169.3 6 5.4 even 2 inner
3960.2.d.d.3169.4 6 1.1 even 1 trivial
6600.2.a.bq.1.1 3 15.8 even 4
6600.2.a.bu.1.3 3 15.2 even 4