Properties

Label 352.2.g.b.175.2
Level 352352
Weight 22
Character 352.175
Analytic conductor 2.8112.811
Analytic rank 00
Dimension 88
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [352,2,Mod(175,352)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(352, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("352.175");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 352=2511 352 = 2^{5} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 352.g (of order 22, degree 11, not 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: 2.810734151152.81073415115
Analytic rank: 00
Dimension: 88
Coefficient field: 8.0.10070523904.6
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8+6x4+16 x^{8} + 6x^{4} + 16 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 26 2^{6}
Twist minimal: no (minimal twist has level 88)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 175.2
Root 1.16342+0.804019i-1.16342 + 0.804019i of defining polynomial
Character χ\chi == 352.175
Dual form 352.2.g.b.175.4

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) == q0.414214q32.64575iq5+3.29066q72.82843q9+(2.414212.27411i)q11+1.36303q13+1.09591iq155.49019iq17+2.27411iq191.36303q216.38741iq232.00000q25+2.41421q27+6.58132q291.09591iq31+(1.00000+0.941967i)q338.70626iq354.83756iq370.564588q39+10.0384iq41+6.43215iq43+7.48331iq45+3.82843q49+2.27411iq51+7.48331iq53+(6.01673+6.38741i)q550.941967iq573.24264q596.58132q619.30739q633.60625iq65+6.07107q67+2.64575iq69+6.38741iq710.941967iq73+0.828427q75+(7.944357.48331i)q77+9.30739q79+7.48528q81+4.54822iq8314.5257q852.72607q8710.6569q89+4.48528q91+0.453939iq93+6.01673q95+7.48528q97+(6.82843+6.43215i)q99+O(q100)q-0.414214 q^{3} -2.64575i q^{5} +3.29066 q^{7} -2.82843 q^{9} +(-2.41421 - 2.27411i) q^{11} +1.36303 q^{13} +1.09591i q^{15} -5.49019i q^{17} +2.27411i q^{19} -1.36303 q^{21} -6.38741i q^{23} -2.00000 q^{25} +2.41421 q^{27} +6.58132 q^{29} -1.09591i q^{31} +(1.00000 + 0.941967i) q^{33} -8.70626i q^{35} -4.83756i q^{37} -0.564588 q^{39} +10.0384i q^{41} +6.43215i q^{43} +7.48331i q^{45} +3.82843 q^{49} +2.27411i q^{51} +7.48331i q^{53} +(-6.01673 + 6.38741i) q^{55} -0.941967i q^{57} -3.24264 q^{59} -6.58132 q^{61} -9.30739 q^{63} -3.60625i q^{65} +6.07107 q^{67} +2.64575i q^{69} +6.38741i q^{71} -0.941967i q^{73} +0.828427 q^{75} +(-7.94435 - 7.48331i) q^{77} +9.30739 q^{79} +7.48528 q^{81} +4.54822i q^{83} -14.5257 q^{85} -2.72607 q^{87} -10.6569 q^{89} +4.48528 q^{91} +0.453939i q^{93} +6.01673 q^{95} +7.48528 q^{97} +(6.82843 + 6.43215i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+8q38q1116q25+8q27+8q33+8q49+8q598q6716q758q8140q8932q918q97+32q99+O(q100) 8 q + 8 q^{3} - 8 q^{11} - 16 q^{25} + 8 q^{27} + 8 q^{33} + 8 q^{49} + 8 q^{59} - 8 q^{67} - 16 q^{75} - 8 q^{81} - 40 q^{89} - 32 q^{91} - 8 q^{97} + 32 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/352Z)×\left(\mathbb{Z}/352\mathbb{Z}\right)^\times.

nn 133133 287287 321321
χ(n)\chi(n) 1-1 1-1 1-1

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 −0.414214 −0.239146 −0.119573 0.992825i 0.538153π-0.538153\pi
−0.119573 + 0.992825i 0.538153π0.538153\pi
44 0 0
55 2.64575i 1.18322i −0.806226 0.591608i 0.798493π-0.798493\pi
0.806226 0.591608i 0.201507π-0.201507\pi
66 0 0
77 3.29066 1.24375 0.621876 0.783116i 0.286371π-0.286371\pi
0.621876 + 0.783116i 0.286371π0.286371\pi
88 0 0
99 −2.82843 −0.942809
1010 0 0
1111 −2.41421 2.27411i −0.727913 0.685670i
1212 0 0
1313 1.36303 0.378038 0.189019 0.981973i 0.439469π-0.439469\pi
0.189019 + 0.981973i 0.439469π0.439469\pi
1414 0 0
1515 1.09591i 0.282962i
1616 0 0
1717 5.49019i 1.33157i −0.746146 0.665783i 0.768098π-0.768098\pi
0.746146 0.665783i 0.231902π-0.231902\pi
1818 0 0
1919 2.27411i 0.521716i 0.965377 + 0.260858i 0.0840055π0.0840055\pi
−0.965377 + 0.260858i 0.915994π0.915994\pi
2020 0 0
2121 −1.36303 −0.297439
2222 0 0
2323 6.38741i 1.33187i −0.746011 0.665933i 0.768033π-0.768033\pi
0.746011 0.665933i 0.231967π-0.231967\pi
2424 0 0
2525 −2.00000 −0.400000
2626 0 0
2727 2.41421 0.464616
2828 0 0
2929 6.58132 1.22212 0.611060 0.791584i 0.290743π-0.290743\pi
0.611060 + 0.791584i 0.290743π0.290743\pi
3030 0 0
3131 1.09591i 0.196831i −0.995145 0.0984153i 0.968623π-0.968623\pi
0.995145 0.0984153i 0.0313773π-0.0313773\pi
3232 0 0
3333 1.00000 + 0.941967i 0.174078 + 0.163975i
3434 0 0
3535 8.70626i 1.47163i
3636 0 0
3737 4.83756i 0.795291i −0.917539 0.397645i 0.869827π-0.869827\pi
0.917539 0.397645i 0.130173π-0.130173\pi
3838 0 0
3939 −0.564588 −0.0904064
4040 0 0
4141 10.0384i 1.56774i 0.620928 + 0.783868i 0.286756π0.286756\pi
−0.620928 + 0.783868i 0.713244π0.713244\pi
4242 0 0
4343 6.43215i 0.980894i 0.871471 + 0.490447i 0.163166π0.163166\pi
−0.871471 + 0.490447i 0.836834π0.836834\pi
4444 0 0
4545 7.48331i 1.11555i
4646 0 0
4747 0 0 1.00000 00
−1.00000 π\pi
4848 0 0
4949 3.82843 0.546918
5050 0 0
5151 2.27411i 0.318439i
5252 0 0
5353 7.48331i 1.02791i 0.857816 + 0.513956i 0.171821π0.171821\pi
−0.857816 + 0.513956i 0.828179π0.828179\pi
5454 0 0
5555 −6.01673 + 6.38741i −0.811295 + 0.861278i
5656 0 0
5757 0.941967i 0.124767i
5858 0 0
5959 −3.24264 −0.422156 −0.211078 0.977469i 0.567697π-0.567697\pi
−0.211078 + 0.977469i 0.567697π0.567697\pi
6060 0 0
6161 −6.58132 −0.842651 −0.421326 0.906909i 0.638435π-0.638435\pi
−0.421326 + 0.906909i 0.638435π0.638435\pi
6262 0 0
6363 −9.30739 −1.17262
6464 0 0
6565 3.60625i 0.447300i
6666 0 0
6767 6.07107 0.741699 0.370849 0.928693i 0.379067π-0.379067\pi
0.370849 + 0.928693i 0.379067π0.379067\pi
6868 0 0
6969 2.64575i 0.318511i
7070 0 0
7171 6.38741i 0.758046i 0.925387 + 0.379023i 0.123740π0.123740\pi
−0.925387 + 0.379023i 0.876260π0.876260\pi
7272 0 0
7373 0.941967i 0.110249i −0.998479 0.0551244i 0.982444π-0.982444\pi
0.998479 0.0551244i 0.0175556π-0.0175556\pi
7474 0 0
7575 0.828427 0.0956585
7676 0 0
7777 −7.94435 7.48331i −0.905343 0.852803i
7878 0 0
7979 9.30739 1.04716 0.523581 0.851976i 0.324596π-0.324596\pi
0.523581 + 0.851976i 0.324596π0.324596\pi
8080 0 0
8181 7.48528 0.831698
8282 0 0
8383 4.54822i 0.499232i 0.968345 + 0.249616i 0.0803044π0.0803044\pi
−0.968345 + 0.249616i 0.919696π0.919696\pi
8484 0 0
8585 −14.5257 −1.57553
8686 0 0
8787 −2.72607 −0.292265
8888 0 0
8989 −10.6569 −1.12962 −0.564812 0.825220i 0.691051π-0.691051\pi
−0.564812 + 0.825220i 0.691051π0.691051\pi
9090 0 0
9191 4.48528 0.470185
9292 0 0
9393 0.453939i 0.0470713i
9494 0 0
9595 6.01673 0.617303
9696 0 0
9797 7.48528 0.760015 0.380008 0.924983i 0.375921π-0.375921\pi
0.380008 + 0.924983i 0.375921π0.375921\pi
9898 0 0
9999 6.82843 + 6.43215i 0.686283 + 0.646456i
100100 0 0
101101 17.2517 1.71661 0.858306 0.513138i 0.171517π-0.171517\pi
0.858306 + 0.513138i 0.171517π0.171517\pi
102102 0 0
103103 18.0663i 1.78013i 0.455836 + 0.890064i 0.349340π0.349340\pi
−0.455836 + 0.890064i 0.650660π0.650660\pi
104104 0 0
105105 3.60625i 0.351934i
106106 0 0
107107 8.70626i 0.841666i 0.907138 + 0.420833i 0.138262π0.138262\pi
−0.907138 + 0.420833i 0.861738π0.861738\pi
108108 0 0
109109 −2.72607 −0.261110 −0.130555 0.991441i 0.541676π-0.541676\pi
−0.130555 + 0.991441i 0.541676π0.541676\pi
110110 0 0
111111 2.00378i 0.190191i
112112 0 0
113113 6.17157 0.580573 0.290286 0.956940i 0.406249π-0.406249\pi
0.290286 + 0.956940i 0.406249π0.406249\pi
114114 0 0
115115 −16.8995 −1.57589
116116 0 0
117117 −3.85525 −0.356418
118118 0 0
119119 18.0663i 1.65614i
120120 0 0
121121 0.656854 + 10.9804i 0.0597140 + 0.998216i
122122 0 0
123123 4.15804i 0.374918i
124124 0 0
125125 7.93725i 0.709930i
126126 0 0
127127 0.564588 0.0500990 0.0250495 0.999686i 0.492026π-0.492026\pi
0.0250495 + 0.999686i 0.492026π0.492026\pi
128128 0 0
129129 2.66428i 0.234577i
130130 0 0
131131 6.82233i 0.596070i −0.954555 0.298035i 0.903669π-0.903669\pi
0.954555 0.298035i 0.0963311π-0.0963311\pi
132132 0 0
133133 7.48331i 0.648886i
134134 0 0
135135 6.38741i 0.549741i
136136 0 0
137137 −8.65685 −0.739605 −0.369802 0.929110i 0.620575π-0.620575\pi
−0.369802 + 0.929110i 0.620575π0.620575\pi
138138 0 0
139139 19.6866i 1.66980i −0.550403 0.834899i 0.685526π-0.685526\pi
0.550403 0.834899i 0.314474π-0.314474\pi
140140 0 0
141141 0 0
142142 0 0
143143 −3.29066 3.09969i −0.275179 0.259209i
144144 0 0
145145 17.4125i 1.44603i
146146 0 0
147147 −1.58579 −0.130793
148148 0 0
149149 21.1070 1.72915 0.864576 0.502503i 0.167587π-0.167587\pi
0.864576 + 0.502503i 0.167587π0.167587\pi
150150 0 0
151151 −13.1626 −1.07116 −0.535580 0.844485i 0.679907π-0.679907\pi
−0.535580 + 0.844485i 0.679907π0.679907\pi
152152 0 0
153153 15.5286i 1.25541i
154154 0 0
155155 −2.89949 −0.232893
156156 0 0
157157 0.453939i 0.0362283i −0.999836 0.0181141i 0.994234π-0.994234\pi
0.999836 0.0181141i 0.00576623π-0.00576623\pi
158158 0 0
159159 3.09969i 0.245821i
160160 0 0
161161 21.0188i 1.65651i
162162 0 0
163163 12.8284 1.00480 0.502400 0.864635i 0.332451π-0.332451\pi
0.502400 + 0.864635i 0.332451π0.332451\pi
164164 0 0
165165 2.49221 2.64575i 0.194018 0.205971i
166166 0 0
167167 21.9054 1.69509 0.847546 0.530721i 0.178079π-0.178079\pi
0.847546 + 0.530721i 0.178079π0.178079\pi
168168 0 0
169169 −11.1421 −0.857087
170170 0 0
171171 6.43215i 0.491879i
172172 0 0
173173 −5.45214 −0.414519 −0.207259 0.978286i 0.566454π-0.566454\pi
−0.207259 + 0.978286i 0.566454π0.566454\pi
174174 0 0
175175 −6.58132 −0.497501
176176 0 0
177177 1.34315 0.100957
178178 0 0
179179 −9.72792 −0.727099 −0.363550 0.931575i 0.618435π-0.618435\pi
−0.363550 + 0.931575i 0.618435π0.618435\pi
180180 0 0
181181 2.64575i 0.196657i 0.995154 + 0.0983286i 0.0313496π0.0313496\pi
−0.995154 + 0.0983286i 0.968650π0.968650\pi
182182 0 0
183183 2.72607 0.201517
184184 0 0
185185 −12.7990 −0.941000
186186 0 0
187187 −12.4853 + 13.2545i −0.913014 + 0.969264i
188188 0 0
189189 7.94435 0.577866
190190 0 0
191191 16.9704i 1.22794i −0.789331 0.613968i 0.789572π-0.789572\pi
0.789331 0.613968i 0.210428π-0.210428\pi
192192 0 0
193193 12.8643i 0.925993i 0.886360 + 0.462996i 0.153226π0.153226\pi
−0.886360 + 0.462996i 0.846774π0.846774\pi
194194 0 0
195195 1.49376i 0.106970i
196196 0 0
197197 −10.4366 −0.743574 −0.371787 0.928318i 0.621255π-0.621255\pi
−0.371787 + 0.928318i 0.621255π0.621255\pi
198198 0 0
199199 21.1660i 1.50042i −0.661200 0.750209i 0.729953π-0.729953\pi
0.661200 0.750209i 0.270047π-0.270047\pi
200200 0 0
201201 −2.51472 −0.177375
202202 0 0
203203 21.6569 1.52001
204204 0 0
205205 26.5591 1.85497
206206 0 0
207207 18.0663i 1.25570i
208208 0 0
209209 5.17157 5.49019i 0.357725 0.379764i
210210 0 0
211211 9.09644i 0.626225i 0.949716 + 0.313112i 0.101372π0.101372\pi
−0.949716 + 0.313112i 0.898628π0.898628\pi
212212 0 0
213213 2.64575i 0.181284i
214214 0 0
215215 17.0179 1.16061
216216 0 0
217217 3.60625i 0.244808i
218218 0 0
219219 0.390175i 0.0263656i
220220 0 0
221221 7.48331i 0.503382i
222222 0 0
223223 4.19560i 0.280958i 0.990084 + 0.140479i 0.0448642π0.0448642\pi
−0.990084 + 0.140479i 0.955136π0.955136\pi
224224 0 0
225225 5.65685 0.377124
226226 0 0
227227 13.2545i 0.879731i −0.898064 0.439865i 0.855026π-0.855026\pi
0.898064 0.439865i 0.144974π-0.144974\pi
228228 0 0
229229 10.1291i 0.669348i −0.942334 0.334674i 0.891374π-0.891374\pi
0.942334 0.334674i 0.108626π-0.108626\pi
230230 0 0
231231 3.29066 + 3.09969i 0.216509 + 0.203945i
232232 0 0
233233 8.31609i 0.544805i −0.962183 0.272402i 0.912182π-0.912182\pi
0.962183 0.272402i 0.0878182π-0.0878182\pi
234234 0 0
235235 0 0
236236 0 0
237237 −3.85525 −0.250425
238238 0 0
239239 −5.45214 −0.352670 −0.176335 0.984330i 0.556424π-0.556424\pi
−0.176335 + 0.984330i 0.556424π0.556424\pi
240240 0 0
241241 4.54822i 0.292977i 0.989212 + 0.146488i 0.0467971π0.0467971\pi
−0.989212 + 0.146488i 0.953203π0.953203\pi
242242 0 0
243243 −10.3431 −0.663513
244244 0 0
245245 10.1291i 0.647122i
246246 0 0
247247 3.09969i 0.197229i
248248 0 0
249249 1.88393i 0.119389i
250250 0 0
251251 −18.4142 −1.16229 −0.581147 0.813798i 0.697396π-0.697396\pi
−0.581147 + 0.813798i 0.697396π0.697396\pi
252252 0 0
253253 −14.5257 + 15.4206i −0.913221 + 0.969483i
254254 0 0
255255 6.01673 0.376782
256256 0 0
257257 6.48528 0.404541 0.202270 0.979330i 0.435168π-0.435168\pi
0.202270 + 0.979330i 0.435168π0.435168\pi
258258 0 0
259259 15.9188i 0.989144i
260260 0 0
261261 −18.6148 −1.15223
262262 0 0
263263 −19.1794 −1.18265 −0.591325 0.806433i 0.701395π-0.701395\pi
−0.591325 + 0.806433i 0.701395π0.701395\pi
264264 0 0
265265 19.7990 1.21624
266266 0 0
267267 4.41421 0.270145
268268 0 0
269269 13.6827i 0.834249i −0.908849 0.417124i 0.863038π-0.863038\pi
0.908849 0.417124i 0.136962π-0.136962\pi
270270 0 0
271271 12.5980 0.765277 0.382638 0.923898i 0.375016π-0.375016\pi
0.382638 + 0.923898i 0.375016π0.375016\pi
272272 0 0
273273 −1.85786 −0.112443
274274 0 0
275275 4.82843 + 4.54822i 0.291165 + 0.274268i
276276 0 0
277277 3.85525 0.231639 0.115820 0.993270i 0.463051π-0.463051\pi
0.115820 + 0.993270i 0.463051π0.463051\pi
278278 0 0
279279 3.09969i 0.185574i
280280 0 0
281281 6.43215i 0.383710i 0.981423 + 0.191855i 0.0614503π0.0614503\pi
−0.981423 + 0.191855i 0.938550π0.938550\pi
282282 0 0
283283 1.88393i 0.111988i 0.998431 + 0.0559941i 0.0178328π0.0178328\pi
−0.998431 + 0.0559941i 0.982167π0.982167\pi
284284 0 0
285285 −2.49221 −0.147626
286286 0 0
287287 33.0329i 1.94987i
288288 0 0
289289 −13.1421 −0.773067
290290 0 0
291291 −3.10051 −0.181755
292292 0 0
293293 −14.5257 −0.848598 −0.424299 0.905522i 0.639480π-0.639480\pi
−0.424299 + 0.905522i 0.639480π0.639480\pi
294294 0 0
295295 8.57922i 0.499502i
296296 0 0
297297 −5.82843 5.49019i −0.338200 0.318573i
298298 0 0
299299 8.70626i 0.503496i
300300 0 0
301301 21.1660i 1.21999i
302302 0 0
303303 −7.14590 −0.410521
304304 0 0
305305 17.4125i 0.997038i
306306 0 0
307307 22.3509i 1.27563i 0.770188 + 0.637817i 0.220162π0.220162\pi
−0.770188 + 0.637817i 0.779838π0.779838\pi
308308 0 0
309309 7.48331i 0.425711i
310310 0 0
311311 14.9666i 0.848680i 0.905503 + 0.424340i 0.139494π0.139494\pi
−0.905503 + 0.424340i 0.860506π0.860506\pi
312312 0 0
313313 7.82843 0.442489 0.221244 0.975218i 0.428988π-0.428988\pi
0.221244 + 0.975218i 0.428988π0.428988\pi
314314 0 0
315315 24.6250i 1.38746i
316316 0 0
317317 15.4206i 0.866105i 0.901369 + 0.433053i 0.142564π0.142564\pi
−0.901369 + 0.433053i 0.857436π0.857436\pi
318318 0 0
319319 −15.8887 14.9666i −0.889596 0.837970i
320320 0 0
321321 3.60625i 0.201281i
322322 0 0
323323 12.4853 0.694700
324324 0 0
325325 −2.72607 −0.151215
326326 0 0
327327 1.12918 0.0624435
328328 0 0
329329 0 0
330330 0 0
331331 18.0711 0.993276 0.496638 0.867958i 0.334568π-0.334568\pi
0.496638 + 0.867958i 0.334568π0.334568\pi
332332 0 0
333333 13.6827i 0.749807i
334334 0 0
335335 16.0625i 0.877590i
336336 0 0
337337 19.1348i 1.04234i 0.853453 + 0.521171i 0.174504π0.174504\pi
−0.853453 + 0.521171i 0.825496π0.825496\pi
338338 0 0
339339 −2.55635 −0.138842
340340 0 0
341341 −2.49221 + 2.64575i −0.134961 + 0.143275i
342342 0 0
343343 −10.4366 −0.563521
344344 0 0
345345 7.00000 0.376867
346346 0 0
347347 4.15804i 0.223215i 0.993752 + 0.111608i 0.0356000π0.0356000\pi
−0.993752 + 0.111608i 0.964400π0.964400\pi
348348 0 0
349349 14.5257 0.777541 0.388771 0.921335i 0.372900π-0.372900\pi
0.388771 + 0.921335i 0.372900π0.372900\pi
350350 0 0
351351 3.29066 0.175642
352352 0 0
353353 1.82843 0.0973174 0.0486587 0.998815i 0.484505π-0.484505\pi
0.0486587 + 0.998815i 0.484505π0.484505\pi
354354 0 0
355355 16.8995 0.896932
356356 0 0
357357 7.48331i 0.396059i
358358 0 0
359359 −3.29066 −0.173674 −0.0868371 0.996223i 0.527676π-0.527676\pi
−0.0868371 + 0.996223i 0.527676π0.527676\pi
360360 0 0
361361 13.8284 0.727812
362362 0 0
363363 −0.272078 4.54822i −0.0142804 0.238720i
364364 0 0
365365 −2.49221 −0.130448
366366 0 0
367367 22.2619i 1.16206i −0.813881 0.581031i 0.802649π-0.802649\pi
0.813881 0.581031i 0.197351π-0.197351\pi
368368 0 0
369369 28.3929i 1.47808i
370370 0 0
371371 24.6250i 1.27847i
372372 0 0
373373 −0.233860 −0.0121088 −0.00605440 0.999982i 0.501927π-0.501927\pi
−0.00605440 + 0.999982i 0.501927π0.501927\pi
374374 0 0
375375 3.28772i 0.169777i
376376 0 0
377377 8.97056 0.462007
378378 0 0
379379 16.0711 0.825515 0.412758 0.910841i 0.364566π-0.364566\pi
0.412758 + 0.910841i 0.364566π0.364566\pi
380380 0 0
381381 −0.233860 −0.0119810
382382 0 0
383383 7.29529i 0.372772i 0.982477 + 0.186386i 0.0596775π0.0596775\pi
−0.982477 + 0.186386i 0.940323π0.940323\pi
384384 0 0
385385 −19.7990 + 21.0188i −1.00905 + 1.07122i
386386 0 0
387387 18.1929i 0.924796i
388388 0 0
389389 32.5790i 1.65182i 0.563801 + 0.825911i 0.309339π0.309339\pi
−0.563801 + 0.825911i 0.690661π0.690661\pi
390390 0 0
391391 −35.0681 −1.77347
392392 0 0
393393 2.82590i 0.142548i
394394 0 0
395395 24.6250i 1.23902i
396396 0 0
397397 22.4499i 1.12673i −0.826208 0.563365i 0.809506π-0.809506\pi
0.826208 0.563365i 0.190494π-0.190494\pi
398398 0 0
399399 3.09969i 0.155179i
400400 0 0
401401 −4.82843 −0.241120 −0.120560 0.992706i 0.538469π-0.538469\pi
−0.120560 + 0.992706i 0.538469π0.538469\pi
402402 0 0
403403 1.49376i 0.0744094i
404404 0 0
405405 19.8042i 0.984078i
406406 0 0
407407 −11.0011 + 11.6789i −0.545307 + 0.578902i
408408 0 0
409409 1.88393i 0.0931545i 0.998915 + 0.0465773i 0.0148314π0.0148314\pi
−0.998915 + 0.0465773i 0.985169π0.985169\pi
410410 0 0
411411 3.58579 0.176874
412412 0 0
413413 −10.6704 −0.525057
414414 0 0
415415 12.0335 0.590699
416416 0 0
417417 8.15447i 0.399326i
418418 0 0
419419 −16.1421 −0.788595 −0.394297 0.918983i 0.629012π-0.629012\pi
−0.394297 + 0.918983i 0.629012π0.629012\pi
420420 0 0
421421 7.48331i 0.364714i 0.983232 + 0.182357i 0.0583727π0.0583727\pi
−0.983232 + 0.182357i 0.941627π0.941627\pi
422422 0 0
423423 0 0
424424 0 0
425425 10.9804i 0.532626i
426426 0 0
427427 −21.6569 −1.04805
428428 0 0
429429 1.36303 + 1.28393i 0.0658079 + 0.0619889i
430430 0 0
431431 −2.16148 −0.104115 −0.0520575 0.998644i 0.516578π-0.516578\pi
−0.0520575 + 0.998644i 0.516578π0.516578\pi
432432 0 0
433433 −17.3431 −0.833458 −0.416729 0.909031i 0.636824π-0.636824\pi
−0.416729 + 0.909031i 0.636824π0.636824\pi
434434 0 0
435435 7.21250i 0.345813i
436436 0 0
437437 14.5257 0.694857
438438 0 0
439439 34.5035 1.64676 0.823380 0.567490i 0.192085π-0.192085\pi
0.823380 + 0.567490i 0.192085π0.192085\pi
440440 0 0
441441 −10.8284 −0.515639
442442 0 0
443443 −26.4142 −1.25498 −0.627489 0.778626i 0.715917π-0.715917\pi
−0.627489 + 0.778626i 0.715917π0.715917\pi
444444 0 0
445445 28.1954i 1.33659i
446446 0 0
447447 −8.74280 −0.413520
448448 0 0
449449 15.9706 0.753697 0.376849 0.926275i 0.377008π-0.377008\pi
0.376849 + 0.926275i 0.377008π0.377008\pi
450450 0 0
451451 22.8284 24.2349i 1.07495 1.14117i
452452 0 0
453453 5.45214 0.256164
454454 0 0
455455 11.8669i 0.556331i
456456 0 0
457457 22.7411i 1.06378i −0.846812 0.531892i 0.821481π-0.821481\pi
0.846812 0.531892i 0.178519π-0.178519\pi
458458 0 0
459459 13.2545i 0.618666i
460460 0 0
461461 3.85525 0.179557 0.0897783 0.995962i 0.471384π-0.471384\pi
0.0897783 + 0.995962i 0.471384π0.471384\pi
462462 0 0
463463 22.2619i 1.03460i 0.855804 + 0.517300i 0.173063π0.173063\pi
−0.855804 + 0.517300i 0.826937π0.826937\pi
464464 0 0
465465 1.20101 0.0556955
466466 0 0
467467 −36.0711 −1.66917 −0.834585 0.550879i 0.814292π-0.814292\pi
−0.834585 + 0.550879i 0.814292π0.814292\pi
468468 0 0
469469 19.9778 0.922489
470470 0 0
471471 0.188028i 0.00866386i
472472 0 0
473473 14.6274 15.5286i 0.672569 0.714005i
474474 0 0
475475 4.54822i 0.208687i
476476 0 0
477477 21.1660i 0.969125i
478478 0 0
479479 27.3576 1.25000 0.625000 0.780625i 0.285099π-0.285099\pi
0.625000 + 0.780625i 0.285099π0.285099\pi
480480 0 0
481481 6.59377i 0.300650i
482482 0 0
483483 8.70626i 0.396149i
484484 0 0
485485 19.8042i 0.899262i
486486 0 0
487487 26.6455i 1.20742i −0.797202 0.603712i 0.793688π-0.793688\pi
0.797202 0.603712i 0.206312π-0.206312\pi
488488 0 0
489489 −5.31371 −0.240294
490490 0 0
491491 25.7286i 1.16112i 0.814219 + 0.580558i 0.197166π0.197166\pi
−0.814219 + 0.580558i 0.802834π0.802834\pi
492492 0 0
493493 36.1326i 1.62733i
494494 0 0
495495 17.0179 18.0663i 0.764897 0.812021i
496496 0 0
497497 21.0188i 0.942821i
498498 0 0
499499 −18.4853 −0.827515 −0.413757 0.910387i 0.635784π-0.635784\pi
−0.413757 + 0.910387i 0.635784π0.635784\pi
500500 0 0
501501 −9.07353 −0.405375
502502 0 0
503503 3.85525 0.171897 0.0859484 0.996300i 0.472608π-0.472608\pi
0.0859484 + 0.996300i 0.472608π0.472608\pi
504504 0 0
505505 45.6438i 2.03112i
506506 0 0
507507 4.61522 0.204969
508508 0 0
509509 35.6787i 1.58143i −0.612184 0.790715i 0.709709π-0.709709\pi
0.612184 0.790715i 0.290291π-0.290291\pi
510510 0 0
511511 3.09969i 0.137122i
512512 0 0
513513 5.49019i 0.242398i
514514 0 0
515515 47.7990 2.10628
516516 0 0
517517 0 0
518518 0 0
519519 2.25835 0.0991306
520520 0 0
521521 −20.1127 −0.881153 −0.440577 0.897715i 0.645226π-0.645226\pi
−0.440577 + 0.897715i 0.645226π0.645226\pi
522522 0 0
523523 17.0223i 0.744335i 0.928166 + 0.372168i 0.121385π0.121385\pi
−0.928166 + 0.372168i 0.878615π0.878615\pi
524524 0 0
525525 2.72607 0.118975
526526 0 0
527527 −6.01673 −0.262093
528528 0 0
529529 −17.7990 −0.773869
530530 0 0
531531 9.17157 0.398012
532532 0 0
533533 13.6827i 0.592663i
534534 0 0
535535 23.0346 0.995873
536536 0 0
537537 4.02944 0.173883
538538 0 0
539539 −9.24264 8.70626i −0.398109 0.375005i
540540 0 0
541541 −17.2517 −0.741710 −0.370855 0.928691i 0.620935π-0.620935\pi
−0.370855 + 0.928691i 0.620935π0.620935\pi
542542 0 0
543543 1.09591i 0.0470298i
544544 0 0
545545 7.21250i 0.308950i
546546 0 0
547547 41.2572i 1.76403i −0.471221 0.882015i 0.656187π-0.656187\pi
0.471221 0.882015i 0.343813π-0.343813\pi
548548 0 0
549549 18.6148 0.794459
550550 0 0
551551 14.9666i 0.637600i
552552 0 0
553553 30.6274 1.30241
554554 0 0
555555 5.30152 0.225037
556556 0 0
557557 −23.8331 −1.00984 −0.504919 0.863167i 0.668478π-0.668478\pi
−0.504919 + 0.863167i 0.668478π0.668478\pi
558558 0 0
559559 8.76725i 0.370815i
560560 0 0
561561 5.17157 5.49019i 0.218344 0.231796i
562562 0 0
563563 11.7607i 0.495655i 0.968804 + 0.247828i 0.0797167π0.0797167\pi
−0.968804 + 0.247828i 0.920283π0.920283\pi
564564 0 0
565565 16.3284i 0.686943i
566566 0 0
567567 24.6315 1.03443
568568 0 0
569569 2.66428i 0.111693i 0.998439 + 0.0558463i 0.0177857π0.0177857\pi
−0.998439 + 0.0558463i 0.982214π0.982214\pi
570570 0 0
571571 21.9607i 0.919028i 0.888170 + 0.459514i 0.151976π0.151976\pi
−0.888170 + 0.459514i 0.848024π0.848024\pi
572572 0 0
573573 7.02938i 0.293656i
574574 0 0
575575 12.7748i 0.532747i
576576 0 0
577577 −31.6274 −1.31667 −0.658333 0.752727i 0.728738π-0.728738\pi
−0.658333 + 0.752727i 0.728738π0.728738\pi
578578 0 0
579579 5.32857i 0.221448i
580580 0 0
581581 14.9666i 0.620920i
582582 0 0
583583 17.0179 18.0663i 0.704808 0.748231i
584584 0 0
585585 10.2000i 0.421719i
586586 0 0
587587 30.2843 1.24997 0.624983 0.780639i 0.285106π-0.285106\pi
0.624983 + 0.780639i 0.285106π0.285106\pi
588588 0 0
589589 2.49221 0.102690
590590 0 0
591591 4.32296 0.177823
592592 0 0
593593 1.88393i 0.0773639i 0.999252 + 0.0386819i 0.0123159π0.0123159\pi
−0.999252 + 0.0386819i 0.987684π0.987684\pi
594594 0 0
595595 −47.7990 −1.95957
596596 0 0
597597 8.76725i 0.358820i
598598 0 0
599599 0 0 1.00000 00
−1.00000 π\pi
600600 0 0
601601 32.7795i 1.33710i −0.743666 0.668552i 0.766915π-0.766915\pi
0.743666 0.668552i 0.233085π-0.233085\pi
602602 0 0
603603 −17.1716 −0.699281
604604 0 0
605605 29.0513 1.73787i 1.18110 0.0706546i
606606 0 0
607607 −29.0513 −1.17916 −0.589579 0.807711i 0.700706π-0.700706\pi
−0.589579 + 0.807711i 0.700706π0.700706\pi
608608 0 0
609609 −8.97056 −0.363506
610610 0 0
611611 0 0
612612 0 0
613613 26.7930 1.08216 0.541079 0.840972i 0.318016π-0.318016\pi
0.541079 + 0.840972i 0.318016π0.318016\pi
614614 0 0
615615 −11.0011 −0.443609
616616 0 0
617617 33.1127 1.33307 0.666534 0.745475i 0.267777π-0.267777\pi
0.666534 + 0.745475i 0.267777π0.267777\pi
618618 0 0
619619 −31.5269 −1.26717 −0.633587 0.773672i 0.718418π-0.718418\pi
−0.633587 + 0.773672i 0.718418π0.718418\pi
620620 0 0
621621 15.4206i 0.618806i
622622 0 0
623623 −35.0681 −1.40497
624624 0 0
625625 −31.0000 −1.24000
626626 0 0
627627 −2.14214 + 2.27411i −0.0855487 + 0.0908192i
628628 0 0
629629 −26.5591 −1.05898
630630 0 0
631631 11.6789i 0.464930i 0.972605 + 0.232465i 0.0746791π0.0746791\pi
−0.972605 + 0.232465i 0.925321π0.925321\pi
632632 0 0
633633 3.76787i 0.149759i
634634 0 0
635635 1.49376i 0.0592780i
636636 0 0
637637 5.21828 0.206756
638638 0 0
639639 18.0663i 0.714693i
640640 0 0
641641 −17.8284 −0.704181 −0.352090 0.935966i 0.614529π-0.614529\pi
−0.352090 + 0.935966i 0.614529π0.614529\pi
642642 0 0
643643 −0.615224 −0.0242621 −0.0121310 0.999926i 0.503862π-0.503862\pi
−0.0121310 + 0.999926i 0.503862π0.503862\pi
644644 0 0
645645 −7.04903 −0.277555
646646 0 0
647647 23.5459i 0.925683i −0.886441 0.462841i 0.846830π-0.846830\pi
0.886441 0.462841i 0.153170π-0.153170\pi
648648 0 0
649649 7.82843 + 7.37412i 0.307293 + 0.289459i
650650 0 0
651651 1.49376i 0.0585450i
652652 0 0
653653 36.5866i 1.43174i 0.698232 + 0.715872i 0.253970π0.253970\pi
−0.698232 + 0.715872i 0.746030π0.746030\pi
654654 0 0
655655 −18.0502 −0.705279
656656 0 0
657657 2.66428i 0.103944i
658658 0 0
659659 10.9804i 0.427735i −0.976863 0.213867i 0.931394π-0.931394\pi
0.976863 0.213867i 0.0686060π-0.0686060\pi
660660 0 0
661661 12.3209i 0.479227i 0.970868 + 0.239613i 0.0770207π0.0770207\pi
−0.970868 + 0.239613i 0.922979π0.922979\pi
662662 0 0
663663 3.09969i 0.120382i
664664 0 0
665665 19.7990 0.767772
666666 0 0
667667 42.0375i 1.62770i
668668 0 0
669669 1.73787i 0.0671901i
670670 0 0
671671 15.8887 + 14.9666i 0.613376 + 0.577780i
672672 0 0
673673 38.2697i 1.47519i 0.675245 + 0.737594i 0.264038π0.264038\pi
−0.675245 + 0.737594i 0.735962π0.735962\pi
674674 0 0
675675 −4.82843 −0.185846
676676 0 0
677677 2.49221 0.0957834 0.0478917 0.998853i 0.484750π-0.484750\pi
0.0478917 + 0.998853i 0.484750π0.484750\pi
678678 0 0
679679 24.6315 0.945270
680680 0 0
681681 5.49019i 0.210384i
682682 0 0
683683 36.4264 1.39382 0.696909 0.717160i 0.254558π-0.254558\pi
0.696909 + 0.717160i 0.254558π0.254558\pi
684684 0 0
685685 22.9039i 0.875112i
686686 0 0
687687 4.19560i 0.160072i
688688 0 0
689689 10.2000i 0.388590i
690690 0 0
691691 8.75736 0.333146 0.166573 0.986029i 0.446730π-0.446730\pi
0.166573 + 0.986029i 0.446730π0.446730\pi
692692 0 0
693693 22.4700 + 21.1660i 0.853565 + 0.804030i
694694 0 0
695695 −52.0859 −1.97573
696696 0 0
697697 55.1127 2.08754
698698 0 0
699699 3.44464i 0.130288i
700700 0 0
701701 −26.0914 −0.985459 −0.492729 0.870183i 0.664001π-0.664001\pi
−0.492729 + 0.870183i 0.664001π0.664001\pi
702702 0 0
703703 11.0011 0.414916
704704 0 0
705705 0 0
706706 0 0
707707 56.7696 2.13504
708708 0 0
709709 46.2617i 1.73739i −0.495343 0.868697i 0.664958π-0.664958\pi
0.495343 0.868697i 0.335042π-0.335042\pi
710710 0 0
711711 −26.3253 −0.987274
712712 0 0
713713 −7.00000 −0.262152
714714 0 0
715715 −8.20101 + 8.70626i −0.306700 + 0.325596i
716716 0 0
717717 2.25835 0.0843396
718718 0 0
719719 5.10347i 0.190327i 0.995462 + 0.0951637i 0.0303375π0.0303375\pi
−0.995462 + 0.0951637i 0.969663π0.969663\pi
720720 0 0
721721 59.4501i 2.21404i
722722 0 0
723723 1.88393i 0.0700643i
724724 0 0
725725 −13.1626 −0.488848
726726 0 0
727727 8.57922i 0.318186i −0.987264 0.159093i 0.949143π-0.949143\pi
0.987264 0.159093i 0.0508569π-0.0508569\pi
728728 0 0
729729 −18.1716 −0.673021
730730 0 0
731731 35.3137 1.30612
732732 0 0
733733 −27.4544 −1.01405 −0.507026 0.861931i 0.669255π-0.669255\pi
−0.507026 + 0.861931i 0.669255π0.669255\pi
734734 0 0
735735 4.19560i 0.154757i
736736 0 0
737737 −14.6569 13.8063i −0.539892 0.508561i
738738 0 0
739739 47.6894i 1.75428i 0.480234 + 0.877141i 0.340552π0.340552\pi
−0.480234 + 0.877141i 0.659448π0.659448\pi
740740 0 0
741741 1.28393i 0.0471665i
742742 0 0
743743 −25.1961 −0.924355 −0.462177 0.886788i 0.652932π-0.652932\pi
−0.462177 + 0.886788i 0.652932π0.652932\pi
744744 0 0
745745 55.8438i 2.04596i
746746 0 0
747747 12.8643i 0.470680i
748748 0 0
749749 28.6493i 1.04682i
750750 0 0
751751 7.29529i 0.266209i 0.991102 + 0.133104i 0.0424946π0.0424946\pi
−0.991102 + 0.133104i 0.957505π0.957505\pi
752752 0 0
753753 7.62742 0.277959
754754 0 0
755755 34.8250i 1.26741i
756756 0 0
757757 28.6493i 1.04128i 0.853777 + 0.520639i 0.174306π0.174306\pi
−0.853777 + 0.520639i 0.825694π0.825694\pi
758758 0 0
759759 6.01673 6.38741i 0.218393 0.231848i
760760 0 0
761761 7.37412i 0.267312i 0.991028 + 0.133656i 0.0426717π0.0426717\pi
−0.991028 + 0.133656i 0.957328π0.957328\pi
762762 0 0
763763 −8.97056 −0.324756
764764 0 0
765765 41.0848 1.48542
766766 0 0
767767 −4.41983 −0.159591
768768 0 0
769769 2.82590i 0.101905i −0.998701 0.0509523i 0.983774π-0.983774\pi
0.998701 0.0509523i 0.0162256π-0.0162256\pi
770770 0 0
771771 −2.68629 −0.0967444
772772 0 0
773773 8.76725i 0.315336i −0.987492 0.157668i 0.949602π-0.949602\pi
0.987492 0.157668i 0.0503976π-0.0503976\pi
774774 0 0
775775 2.19181i 0.0787322i
776776 0 0
777777 6.59377i 0.236550i
778778 0 0
779779 −22.8284 −0.817913
780780 0 0
781781 14.5257 15.4206i 0.519769 0.551791i
782782 0 0
783783 15.8887 0.567816
784784 0 0
785785 −1.20101 −0.0428659
786786 0 0
787787 32.9411i 1.17422i 0.809506 + 0.587112i 0.199735π0.199735\pi
−0.809506 + 0.587112i 0.800265π0.800265\pi
788788 0 0
789789 7.94435 0.282826
790790 0 0
791791 20.3085 0.722088
792792 0 0
793793 −8.97056 −0.318554
794794 0 0
795795 −8.20101 −0.290860
796796 0 0
797797 44.0699i 1.56104i 0.625133 + 0.780518i 0.285045π0.285045\pi
−0.625133 + 0.780518i 0.714955π0.714955\pi
798798 0 0
799799 0 0
800800 0 0
801801 30.1421 1.06502
802802 0 0
803803 −2.14214 + 2.27411i −0.0755943 + 0.0802516i
804804 0 0
805805 −55.6105 −1.96001
806806 0 0
807807 5.66756i 0.199507i
808808 0 0
809809 0.941967i 0.0331178i −0.999863 0.0165589i 0.994729π-0.994729\pi
0.999863 0.0165589i 0.00527110π-0.00527110\pi
810810 0 0
811811 5.65180i 0.198462i −0.995064 0.0992308i 0.968362π-0.968362\pi
0.995064 0.0992308i 0.0316382π-0.0316382\pi
812812 0 0
813813 −5.21828 −0.183013
814814 0 0
815815 33.9408i 1.18890i
816816 0 0
817817 −14.6274 −0.511749
818818 0 0
819819 −12.6863 −0.443295
820820 0 0
821821 −21.3408 −0.744800 −0.372400 0.928072i 0.621465π-0.621465\pi
−0.372400 + 0.928072i 0.621465π0.621465\pi
822822 0 0
823823 35.9446i 1.25295i 0.779441 + 0.626475i 0.215503π0.215503\pi
−0.779441 + 0.626475i 0.784497π0.784497\pi
824824 0 0
825825 −2.00000 1.88393i −0.0696311 0.0655902i
826826 0 0
827827 50.7438i 1.76454i 0.470748 + 0.882268i 0.343984π0.343984\pi
−0.470748 + 0.882268i 0.656016π0.656016\pi
828828 0 0
829829 41.8781i 1.45449i −0.686380 0.727243i 0.740801π-0.740801\pi
0.686380 0.727243i 0.259199π-0.259199\pi
830830 0 0
831831 −1.59689 −0.0553957
832832 0 0
833833 21.0188i 0.728257i
834834 0 0
835835 57.9563i 2.00566i
836836 0 0
837837 2.64575i 0.0914505i
838838 0 0
839839 54.3870i 1.87765i 0.344398 + 0.938824i 0.388083π0.388083\pi
−0.344398 + 0.938824i 0.611917π0.611917\pi
840840 0 0
841841 14.3137 0.493576
842842 0 0
843843 2.66428i 0.0917628i
844844 0 0
845845 29.4793i 1.01412i
846846 0 0
847847 2.16148 + 36.1326i 0.0742694 + 1.24153i
848848 0 0
849849 0.780351i 0.0267816i
850850 0 0
851851 −30.8995 −1.05922
852852 0 0
853853 −58.1027 −1.98940 −0.994699 0.102833i 0.967209π-0.967209\pi
−0.994699 + 0.102833i 0.967209π0.967209\pi
854854 0 0
855855 −17.0179 −0.581999
856856 0 0
857857 21.9607i 0.750165i 0.926992 + 0.375082i 0.122386π0.122386\pi
−0.926992 + 0.375082i 0.877614π0.877614\pi
858858 0 0
859859 49.2426 1.68014 0.840069 0.542480i 0.182515π-0.182515\pi
0.840069 + 0.542480i 0.182515π0.182515\pi
860860 0 0
861861 13.6827i 0.466305i
862862 0 0
863863 14.9666i 0.509470i 0.967011 + 0.254735i 0.0819882π0.0819882\pi
−0.967011 + 0.254735i 0.918012π0.918012\pi
864864 0 0
865865 14.4250i 0.490465i
866866 0 0
867867 5.44365 0.184876
868868 0 0
869869 −22.4700 21.1660i −0.762243 0.718008i
870870 0 0
871871 8.27508 0.280390
872872 0 0
873873 −21.1716 −0.716549
874874 0 0
875875 26.1188i 0.882976i
876876 0 0
877877 29.2852 0.988891 0.494445 0.869209i 0.335371π-0.335371\pi
0.494445 + 0.869209i 0.335371π0.335371\pi
878878 0 0
879879 6.01673 0.202939
880880 0 0
881881 6.51472 0.219486 0.109743 0.993960i 0.464997π-0.464997\pi
0.109743 + 0.993960i 0.464997π0.464997\pi
882882 0 0
883883 4.34315 0.146158 0.0730792 0.997326i 0.476717π-0.476717\pi
0.0730792 + 0.997326i 0.476717π0.476717\pi
884884 0 0
885885 3.55363i 0.119454i
886886 0 0
887887 −46.5369 −1.56256 −0.781279 0.624183i 0.785432π-0.785432\pi
−0.781279 + 0.624183i 0.785432π0.785432\pi
888888 0 0
889889 1.85786 0.0623108
890890 0 0
891891 −18.0711 17.0223i −0.605404 0.570270i
892892 0 0
893893 0 0
894894 0 0
895895 25.7377i 0.860315i
896896 0 0
897897 3.60625i 0.120409i
898898 0 0
899899 7.21250i 0.240550i
900900 0 0
901901 41.0848 1.36873
902902 0 0
903903 8.76725i 0.291756i
904904 0 0
905905 7.00000 0.232688
906906 0 0
907907 33.5147 1.11284 0.556419 0.830902i 0.312175π-0.312175\pi
0.556419 + 0.830902i 0.312175π0.312175\pi
908908 0 0
909909 −48.7953 −1.61844
910910 0 0
911911 44.8999i 1.48760i −0.668402 0.743800i 0.733022π-0.733022\pi
0.668402 0.743800i 0.266978π-0.266978\pi
912912 0 0
913913 10.3431 10.9804i 0.342308 0.363397i
914914 0 0
915915 7.21250i 0.238438i
916916 0 0
917917 22.4499i 0.741362i
918918 0 0
919919 23.5992 0.778465 0.389233 0.921139i 0.372740π-0.372740\pi
0.389233 + 0.921139i 0.372740π0.372740\pi
920920 0 0
921921 9.25805i 0.305063i
922922 0 0
923923 8.70626i 0.286570i
924924 0 0
925925 9.67513i 0.318116i
926926 0 0
927927 51.0993i 1.67832i
928928 0 0
929929 34.4853 1.13143 0.565713 0.824602i 0.308601π-0.308601\pi
0.565713 + 0.824602i 0.308601π0.308601\pi
930930 0 0
931931 8.70626i 0.285336i
932932 0 0
933933 6.19938i 0.202959i
934934 0 0
935935 35.0681 + 33.0329i 1.14685 + 1.08029i
936936 0 0
937937 21.7991i 0.712146i −0.934458 0.356073i 0.884115π-0.884115\pi
0.934458 0.356073i 0.115885π-0.115885\pi
938938 0 0
939939 −3.24264 −0.105820
940940 0 0
941941 14.7595 0.481147 0.240573 0.970631i 0.422665π-0.422665\pi
0.240573 + 0.970631i 0.422665π0.422665\pi
942942 0 0
943943 64.1194 2.08801
944944 0 0
945945 21.0188i 0.683741i
946946 0 0
947947 −24.4142 −0.793355 −0.396678 0.917958i 0.629837π-0.629837\pi
−0.396678 + 0.917958i 0.629837π0.629837\pi
948948 0 0
949949 1.28393i 0.0416783i
950950 0 0
951951 6.38741i 0.207126i
952952 0 0
953953 36.5474i 1.18389i 0.805980 + 0.591943i 0.201639π0.201639\pi
−0.805980 + 0.591943i 0.798361π0.798361\pi
954954 0 0
955955 −44.8995 −1.45291
956956 0 0
957957 6.58132 + 6.19938i 0.212744 + 0.200398i
958958 0 0
959959 −28.4867 −0.919885
960960 0 0
961961 29.7990 0.961258
962962 0 0
963963 24.6250i 0.793530i
964964 0 0
965965 34.0358 1.09565
966966 0 0
967967 −3.85525 −0.123976 −0.0619882 0.998077i 0.519744π-0.519744\pi
−0.0619882 + 0.998077i 0.519744π0.519744\pi
968968 0 0
969969 −5.17157 −0.166135
970970 0 0
971971 −32.8406 −1.05391 −0.526953 0.849895i 0.676666π-0.676666\pi
−0.526953 + 0.849895i 0.676666π0.676666\pi
972972 0 0
973973 64.7820i 2.07681i
974974 0 0
975975 1.12918 0.0361625
976976 0 0
977977 −45.6274 −1.45975 −0.729875 0.683580i 0.760422π-0.760422\pi
−0.729875 + 0.683580i 0.760422π0.760422\pi
978978 0 0
979979 25.7279 + 24.2349i 0.822268 + 0.774549i
980980 0 0
981981 7.71049 0.246177
982982 0 0
983983 17.8783i 0.570229i −0.958493 0.285114i 0.907968π-0.907968\pi
0.958493 0.285114i 0.0920316π-0.0920316\pi
984984 0 0
985985 27.6125i 0.879809i
986986 0 0
987987 0 0
988988 0 0
989989 41.0848 1.30642
990990 0 0
991991 29.9333i 0.950861i −0.879753 0.475431i 0.842292π-0.842292\pi
0.879753 0.475431i 0.157708π-0.157708\pi
992992 0 0
993993 −7.48528 −0.237538
994994 0 0
995995 −56.0000 −1.77532
996996 0 0
997997 55.6105 1.76120 0.880600 0.473860i 0.157140π-0.157140\pi
0.880600 + 0.473860i 0.157140π0.157140\pi
998998 0 0
999999 11.6789i 0.369504i
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 352.2.g.b.175.2 8
3.2 odd 2 3168.2.h.g.2287.8 8
4.3 odd 2 88.2.g.b.43.8 yes 8
8.3 odd 2 inner 352.2.g.b.175.3 8
8.5 even 2 88.2.g.b.43.2 yes 8
11.10 odd 2 inner 352.2.g.b.175.1 8
12.11 even 2 792.2.h.g.307.1 8
16.3 odd 4 2816.2.e.o.2815.10 16
16.5 even 4 2816.2.e.o.2815.11 16
16.11 odd 4 2816.2.e.o.2815.8 16
16.13 even 4 2816.2.e.o.2815.5 16
24.5 odd 2 792.2.h.g.307.7 8
24.11 even 2 3168.2.h.g.2287.1 8
33.32 even 2 3168.2.h.g.2287.5 8
44.3 odd 10 968.2.k.g.475.7 32
44.7 even 10 968.2.k.g.699.5 32
44.15 odd 10 968.2.k.g.699.4 32
44.19 even 10 968.2.k.g.475.2 32
44.27 odd 10 968.2.k.g.723.1 32
44.31 odd 10 968.2.k.g.403.3 32
44.35 even 10 968.2.k.g.403.6 32
44.39 even 10 968.2.k.g.723.8 32
44.43 even 2 88.2.g.b.43.1 8
88.5 even 10 968.2.k.g.723.6 32
88.13 odd 10 968.2.k.g.403.1 32
88.21 odd 2 88.2.g.b.43.7 yes 8
88.29 odd 10 968.2.k.g.699.7 32
88.37 even 10 968.2.k.g.699.2 32
88.43 even 2 inner 352.2.g.b.175.4 8
88.53 even 10 968.2.k.g.403.8 32
88.61 odd 10 968.2.k.g.723.3 32
88.69 even 10 968.2.k.g.475.5 32
88.85 odd 10 968.2.k.g.475.4 32
132.131 odd 2 792.2.h.g.307.8 8
176.21 odd 4 2816.2.e.o.2815.12 16
176.43 even 4 2816.2.e.o.2815.7 16
176.109 odd 4 2816.2.e.o.2815.6 16
176.131 even 4 2816.2.e.o.2815.9 16
264.131 odd 2 3168.2.h.g.2287.4 8
264.197 even 2 792.2.h.g.307.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
88.2.g.b.43.1 8 44.43 even 2
88.2.g.b.43.2 yes 8 8.5 even 2
88.2.g.b.43.7 yes 8 88.21 odd 2
88.2.g.b.43.8 yes 8 4.3 odd 2
352.2.g.b.175.1 8 11.10 odd 2 inner
352.2.g.b.175.2 8 1.1 even 1 trivial
352.2.g.b.175.3 8 8.3 odd 2 inner
352.2.g.b.175.4 8 88.43 even 2 inner
792.2.h.g.307.1 8 12.11 even 2
792.2.h.g.307.2 8 264.197 even 2
792.2.h.g.307.7 8 24.5 odd 2
792.2.h.g.307.8 8 132.131 odd 2
968.2.k.g.403.1 32 88.13 odd 10
968.2.k.g.403.3 32 44.31 odd 10
968.2.k.g.403.6 32 44.35 even 10
968.2.k.g.403.8 32 88.53 even 10
968.2.k.g.475.2 32 44.19 even 10
968.2.k.g.475.4 32 88.85 odd 10
968.2.k.g.475.5 32 88.69 even 10
968.2.k.g.475.7 32 44.3 odd 10
968.2.k.g.699.2 32 88.37 even 10
968.2.k.g.699.4 32 44.15 odd 10
968.2.k.g.699.5 32 44.7 even 10
968.2.k.g.699.7 32 88.29 odd 10
968.2.k.g.723.1 32 44.27 odd 10
968.2.k.g.723.3 32 88.61 odd 10
968.2.k.g.723.6 32 88.5 even 10
968.2.k.g.723.8 32 44.39 even 10
2816.2.e.o.2815.5 16 16.13 even 4
2816.2.e.o.2815.6 16 176.109 odd 4
2816.2.e.o.2815.7 16 176.43 even 4
2816.2.e.o.2815.8 16 16.11 odd 4
2816.2.e.o.2815.9 16 176.131 even 4
2816.2.e.o.2815.10 16 16.3 odd 4
2816.2.e.o.2815.11 16 16.5 even 4
2816.2.e.o.2815.12 16 176.21 odd 4
3168.2.h.g.2287.1 8 24.11 even 2
3168.2.h.g.2287.4 8 264.131 odd 2
3168.2.h.g.2287.5 8 33.32 even 2
3168.2.h.g.2287.8 8 3.2 odd 2