Properties

Label 5850.2.a.cp.1.1
Level 58505850
Weight 22
Character 5850.1
Self dual yes
Analytic conductor 46.71246.712
Analytic rank 00
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] = [5850,2,Mod(1,5850)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5850, 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("5850.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 5850=2325213 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 5850.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,-3,0,3,0,0,-2,-3,0,0,-6,0,3,2,0,3,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 46.712485182446.7124851824
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.940.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x37x4 x^{3} - 7x - 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 130)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 2.895112.89511 of defining polynomial
Character χ\chi == 5850.1

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) == q1.00000q2+1.00000q44.38164q71.00000q82.00000q11+1.00000q13+4.38164q14+1.00000q165.86818q170.973070q19+2.00000q227.79021q231.00000q264.38164q280.973070q291.79021q311.00000q32+5.86818q340.591429q37+0.973070q384.81714q41+4.68532q432.00000q44+7.79021q460.381642q47+12.1988q49+1.00000q527.79021q53+4.38164q56+0.973070q58+0.973070q590.817143q61+1.79021q62+1.00000q64+1.79021q675.86818q68+3.92204q716.00000q73+0.591429q740.973070q76+8.76328q77+10.9731q79+4.81714q82+6.97307q834.68532q86+2.00000q880.973070q894.38164q917.79021q92+0.381642q9418.6074q9712.1988q98+O(q100)q-1.00000 q^{2} +1.00000 q^{4} -4.38164 q^{7} -1.00000 q^{8} -2.00000 q^{11} +1.00000 q^{13} +4.38164 q^{14} +1.00000 q^{16} -5.86818 q^{17} -0.973070 q^{19} +2.00000 q^{22} -7.79021 q^{23} -1.00000 q^{26} -4.38164 q^{28} -0.973070 q^{29} -1.79021 q^{31} -1.00000 q^{32} +5.86818 q^{34} -0.591429 q^{37} +0.973070 q^{38} -4.81714 q^{41} +4.68532 q^{43} -2.00000 q^{44} +7.79021 q^{46} -0.381642 q^{47} +12.1988 q^{49} +1.00000 q^{52} -7.79021 q^{53} +4.38164 q^{56} +0.973070 q^{58} +0.973070 q^{59} -0.817143 q^{61} +1.79021 q^{62} +1.00000 q^{64} +1.79021 q^{67} -5.86818 q^{68} +3.92204 q^{71} -6.00000 q^{73} +0.591429 q^{74} -0.973070 q^{76} +8.76328 q^{77} +10.9731 q^{79} +4.81714 q^{82} +6.97307 q^{83} -4.68532 q^{86} +2.00000 q^{88} -0.973070 q^{89} -4.38164 q^{91} -7.79021 q^{92} +0.381642 q^{94} -18.6074 q^{97} -12.1988 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q3q2+3q42q73q86q11+3q13+2q14+3q164q17+2q19+6q226q233q262q28+2q29+12q313q32+4q348q37+13q98+O(q100) 3 q - 3 q^{2} + 3 q^{4} - 2 q^{7} - 3 q^{8} - 6 q^{11} + 3 q^{13} + 2 q^{14} + 3 q^{16} - 4 q^{17} + 2 q^{19} + 6 q^{22} - 6 q^{23} - 3 q^{26} - 2 q^{28} + 2 q^{29} + 12 q^{31} - 3 q^{32} + 4 q^{34} - 8 q^{37}+ \cdots - 13 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 −1.00000 −0.707107
33 0 0
44 1.00000 0.500000
55 0 0
66 0 0
77 −4.38164 −1.65610 −0.828052 0.560651i 0.810551π-0.810551\pi
−0.828052 + 0.560651i 0.810551π0.810551\pi
88 −1.00000 −0.353553
99 0 0
1010 0 0
1111 −2.00000 −0.603023 −0.301511 0.953463i 0.597491π-0.597491\pi
−0.301511 + 0.953463i 0.597491π0.597491\pi
1212 0 0
1313 1.00000 0.277350
1414 4.38164 1.17104
1515 0 0
1616 1.00000 0.250000
1717 −5.86818 −1.42324 −0.711621 0.702564i 0.752039π-0.752039\pi
−0.711621 + 0.702564i 0.752039π0.752039\pi
1818 0 0
1919 −0.973070 −0.223238 −0.111619 0.993751i 0.535604π-0.535604\pi
−0.111619 + 0.993751i 0.535604π0.535604\pi
2020 0 0
2121 0 0
2222 2.00000 0.426401
2323 −7.79021 −1.62437 −0.812186 0.583399i 0.801722π-0.801722\pi
−0.812186 + 0.583399i 0.801722π0.801722\pi
2424 0 0
2525 0 0
2626 −1.00000 −0.196116
2727 0 0
2828 −4.38164 −0.828052
2929 −0.973070 −0.180695 −0.0903473 0.995910i 0.528798π-0.528798\pi
−0.0903473 + 0.995910i 0.528798π0.528798\pi
3030 0 0
3131 −1.79021 −0.321532 −0.160766 0.986993i 0.551396π-0.551396\pi
−0.160766 + 0.986993i 0.551396π0.551396\pi
3232 −1.00000 −0.176777
3333 0 0
3434 5.86818 1.00638
3535 0 0
3636 0 0
3737 −0.591429 −0.0972303 −0.0486151 0.998818i 0.515481π-0.515481\pi
−0.0486151 + 0.998818i 0.515481π0.515481\pi
3838 0.973070 0.157853
3939 0 0
4040 0 0
4141 −4.81714 −0.752311 −0.376156 0.926556i 0.622754π-0.622754\pi
−0.376156 + 0.926556i 0.622754π0.622754\pi
4242 0 0
4343 4.68532 0.714505 0.357252 0.934008i 0.383714π-0.383714\pi
0.357252 + 0.934008i 0.383714π0.383714\pi
4444 −2.00000 −0.301511
4545 0 0
4646 7.79021 1.14860
4747 −0.381642 −0.0556682 −0.0278341 0.999613i 0.508861π-0.508861\pi
−0.0278341 + 0.999613i 0.508861π0.508861\pi
4848 0 0
4949 12.1988 1.74268
5050 0 0
5151 0 0
5252 1.00000 0.138675
5353 −7.79021 −1.07007 −0.535034 0.844831i 0.679701π-0.679701\pi
−0.535034 + 0.844831i 0.679701π0.679701\pi
5454 0 0
5555 0 0
5656 4.38164 0.585522
5757 0 0
5858 0.973070 0.127770
5959 0.973070 0.126683 0.0633415 0.997992i 0.479824π-0.479824\pi
0.0633415 + 0.997992i 0.479824π0.479824\pi
6060 0 0
6161 −0.817143 −0.104624 −0.0523122 0.998631i 0.516659π-0.516659\pi
−0.0523122 + 0.998631i 0.516659π0.516659\pi
6262 1.79021 0.227357
6363 0 0
6464 1.00000 0.125000
6565 0 0
6666 0 0
6767 1.79021 0.218709 0.109355 0.994003i 0.465122π-0.465122\pi
0.109355 + 0.994003i 0.465122π0.465122\pi
6868 −5.86818 −0.711621
6969 0 0
7070 0 0
7171 3.92204 0.465460 0.232730 0.972541i 0.425234π-0.425234\pi
0.232730 + 0.972541i 0.425234π0.425234\pi
7272 0 0
7373 −6.00000 −0.702247 −0.351123 0.936329i 0.614200π-0.614200\pi
−0.351123 + 0.936329i 0.614200π0.614200\pi
7474 0.591429 0.0687522
7575 0 0
7676 −0.973070 −0.111619
7777 8.76328 0.998669
7878 0 0
7979 10.9731 1.23457 0.617283 0.786741i 0.288233π-0.288233\pi
0.617283 + 0.786741i 0.288233π0.288233\pi
8080 0 0
8181 0 0
8282 4.81714 0.531964
8383 6.97307 0.765394 0.382697 0.923874i 0.374995π-0.374995\pi
0.382697 + 0.923874i 0.374995π0.374995\pi
8484 0 0
8585 0 0
8686 −4.68532 −0.505231
8787 0 0
8888 2.00000 0.213201
8989 −0.973070 −0.103145 −0.0515726 0.998669i 0.516423π-0.516423\pi
−0.0515726 + 0.998669i 0.516423π0.516423\pi
9090 0 0
9191 −4.38164 −0.459321
9292 −7.79021 −0.812186
9393 0 0
9494 0.381642 0.0393633
9595 0 0
9696 0 0
9797 −18.6074 −1.88929 −0.944645 0.328093i 0.893594π-0.893594\pi
−0.944645 + 0.328093i 0.893594π0.893594\pi
9898 −12.1988 −1.23226
9999 0 0
100100 0 0
101101 −14.3437 −1.42725 −0.713626 0.700527i 0.752948π-0.752948\pi
−0.713626 + 0.700527i 0.752948π0.752948\pi
102102 0 0
103103 9.73635 0.959351 0.479676 0.877446i 0.340754π-0.340754\pi
0.479676 + 0.877446i 0.340754π0.340754\pi
104104 −1.00000 −0.0980581
105105 0 0
106106 7.79021 0.756652
107107 5.79021 0.559761 0.279881 0.960035i 0.409705π-0.409705\pi
0.279881 + 0.960035i 0.409705π0.409705\pi
108108 0 0
109109 −0.685320 −0.0656417 −0.0328209 0.999461i 0.510449π-0.510449\pi
−0.0328209 + 0.999461i 0.510449π0.510449\pi
110110 0 0
111111 0 0
112112 −4.38164 −0.414026
113113 −4.00000 −0.376288 −0.188144 0.982141i 0.560247π-0.560247\pi
−0.188144 + 0.982141i 0.560247π0.560247\pi
114114 0 0
115115 0 0
116116 −0.973070 −0.0903473
117117 0 0
118118 −0.973070 −0.0895784
119119 25.7122 2.35704
120120 0 0
121121 −7.00000 −0.636364
122122 0.817143 0.0739806
123123 0 0
124124 −1.79021 −0.160766
125125 0 0
126126 0 0
127127 11.7902 1.04621 0.523106 0.852268i 0.324773π-0.324773\pi
0.523106 + 0.852268i 0.324773π0.324773\pi
128128 −1.00000 −0.0883883
129129 0 0
130130 0 0
131131 16.9890 1.48434 0.742168 0.670214i 0.233798π-0.233798\pi
0.742168 + 0.670214i 0.233798π0.233798\pi
132132 0 0
133133 4.26365 0.369705
134134 −1.79021 −0.154651
135135 0 0
136136 5.86818 0.503192
137137 −4.20979 −0.359666 −0.179833 0.983697i 0.557556π-0.557556\pi
−0.179833 + 0.983697i 0.557556π0.557556\pi
138138 0 0
139139 −6.17185 −0.523490 −0.261745 0.965137i 0.584298π-0.584298\pi
−0.261745 + 0.965137i 0.584298π0.584298\pi
140140 0 0
141141 0 0
142142 −3.92204 −0.329130
143143 −2.00000 −0.167248
144144 0 0
145145 0 0
146146 6.00000 0.496564
147147 0 0
148148 −0.591429 −0.0486151
149149 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
150150 0 0
151151 15.5025 1.26157 0.630786 0.775957i 0.282732π-0.282732\pi
0.630786 + 0.775957i 0.282732π0.282732\pi
152152 0.973070 0.0789264
153153 0 0
154154 −8.76328 −0.706166
155155 0 0
156156 0 0
157157 8.97307 0.716129 0.358064 0.933697i 0.383437π-0.383437\pi
0.358064 + 0.933697i 0.383437π0.383437\pi
158158 −10.9731 −0.872971
159159 0 0
160160 0 0
161161 34.1339 2.69013
162162 0 0
163163 −12.6074 −0.987484 −0.493742 0.869608i 0.664371π-0.664371\pi
−0.493742 + 0.869608i 0.664371π0.664371\pi
164164 −4.81714 −0.376156
165165 0 0
166166 −6.97307 −0.541215
167167 −23.1609 −1.79224 −0.896120 0.443811i 0.853626π-0.853626\pi
−0.896120 + 0.443811i 0.853626π0.853626\pi
168168 0 0
169169 1.00000 0.0769231
170170 0 0
171171 0 0
172172 4.68532 0.357252
173173 19.7902 1.50462 0.752311 0.658808i 0.228939π-0.228939\pi
0.752311 + 0.658808i 0.228939π0.228939\pi
174174 0 0
175175 0 0
176176 −2.00000 −0.150756
177177 0 0
178178 0.973070 0.0729347
179179 −6.17185 −0.461306 −0.230653 0.973036i 0.574086π-0.574086\pi
−0.230653 + 0.973036i 0.574086π0.574086\pi
180180 0 0
181181 −19.3706 −1.43981 −0.719904 0.694074i 0.755814π-0.755814\pi
−0.719904 + 0.694074i 0.755814π0.755814\pi
182182 4.38164 0.324789
183183 0 0
184184 7.79021 0.574302
185185 0 0
186186 0 0
187187 11.7364 0.858247
188188 −0.381642 −0.0278341
189189 0 0
190190 0 0
191191 3.73635 0.270353 0.135177 0.990822i 0.456840π-0.456840\pi
0.135177 + 0.990822i 0.456840π0.456840\pi
192192 0 0
193193 15.3706 1.10640 0.553201 0.833048i 0.313406π-0.313406\pi
0.553201 + 0.833048i 0.313406π0.313406\pi
194194 18.6074 1.33593
195195 0 0
196196 12.1988 0.871342
197197 −26.9890 −1.92289 −0.961443 0.275004i 0.911321π-0.911321\pi
−0.961443 + 0.275004i 0.911321π0.911321\pi
198198 0 0
199199 23.3168 1.65288 0.826441 0.563023i 0.190362π-0.190362\pi
0.826441 + 0.563023i 0.190362π0.190362\pi
200200 0 0
201201 0 0
202202 14.3437 1.00922
203203 4.26365 0.299249
204204 0 0
205205 0 0
206206 −9.73635 −0.678364
207207 0 0
208208 1.00000 0.0693375
209209 1.94614 0.134617
210210 0 0
211211 15.3547 1.05706 0.528531 0.848914i 0.322743π-0.322743\pi
0.528531 + 0.848914i 0.322743π0.322743\pi
212212 −7.79021 −0.535034
213213 0 0
214214 −5.79021 −0.395811
215215 0 0
216216 0 0
217217 7.84407 0.532490
218218 0.685320 0.0464157
219219 0 0
220220 0 0
221221 −5.86818 −0.394736
222222 0 0
223223 24.8331 1.66295 0.831473 0.555566i 0.187498π-0.187498\pi
0.831473 + 0.555566i 0.187498π0.187498\pi
224224 4.38164 0.292761
225225 0 0
226226 4.00000 0.266076
227227 21.5266 1.42877 0.714384 0.699754i 0.246707π-0.246707\pi
0.714384 + 0.699754i 0.246707π0.246707\pi
228228 0 0
229229 −2.63146 −0.173892 −0.0869459 0.996213i 0.527711π-0.527711\pi
−0.0869459 + 0.996213i 0.527711π0.527711\pi
230230 0 0
231231 0 0
232232 0.973070 0.0638852
233233 29.0290 1.90175 0.950877 0.309568i 0.100184π-0.100184\pi
0.950877 + 0.309568i 0.100184π0.100184\pi
234234 0 0
235235 0 0
236236 0.973070 0.0633415
237237 0 0
238238 −25.7122 −1.66668
239239 −2.13182 −0.137896 −0.0689481 0.997620i 0.521964π-0.521964\pi
−0.0689481 + 0.997620i 0.521964π0.521964\pi
240240 0 0
241241 22.4996 1.44933 0.724665 0.689102i 0.241995π-0.241995\pi
0.724665 + 0.689102i 0.241995π0.241995\pi
242242 7.00000 0.449977
243243 0 0
244244 −0.817143 −0.0523122
245245 0 0
246246 0 0
247247 −0.973070 −0.0619150
248248 1.79021 0.113679
249249 0 0
250250 0 0
251251 0.419574 0.0264833 0.0132416 0.999912i 0.495785π-0.495785\pi
0.0132416 + 0.999912i 0.495785π0.495785\pi
252252 0 0
253253 15.5804 0.979533
254254 −11.7902 −0.739784
255255 0 0
256256 1.00000 0.0625000
257257 −19.6584 −1.22626 −0.613128 0.789983i 0.710089π-0.710089\pi
−0.613128 + 0.789983i 0.710089π0.710089\pi
258258 0 0
259259 2.59143 0.161024
260260 0 0
261261 0 0
262262 −16.9890 −1.04958
263263 10.7633 0.663692 0.331846 0.943333i 0.392328π-0.392328\pi
0.331846 + 0.943333i 0.392328π0.392328\pi
264264 0 0
265265 0 0
266266 −4.26365 −0.261421
267267 0 0
268268 1.79021 0.109355
269269 14.7633 0.900133 0.450067 0.892995i 0.351400π-0.351400\pi
0.450067 + 0.892995i 0.351400π0.351400\pi
270270 0 0
271271 −27.2388 −1.65464 −0.827320 0.561731i 0.810136π-0.810136\pi
−0.827320 + 0.561731i 0.810136π0.810136\pi
272272 −5.86818 −0.355810
273273 0 0
274274 4.20979 0.254323
275275 0 0
276276 0 0
277277 −2.87100 −0.172502 −0.0862509 0.996273i 0.527489π-0.527489\pi
−0.0862509 + 0.996273i 0.527489π0.527489\pi
278278 6.17185 0.370163
279279 0 0
280280 0 0
281281 −5.39264 −0.321698 −0.160849 0.986979i 0.551423π-0.551423\pi
−0.160849 + 0.986979i 0.551423π0.551423\pi
282282 0 0
283283 −24.9511 −1.48319 −0.741593 0.670850i 0.765930π-0.765930\pi
−0.741593 + 0.670850i 0.765930π0.765930\pi
284284 3.92204 0.232730
285285 0 0
286286 2.00000 0.118262
287287 21.1070 1.24591
288288 0 0
289289 17.4355 1.02562
290290 0 0
291291 0 0
292292 −6.00000 −0.351123
293293 −24.9351 −1.45673 −0.728363 0.685191i 0.759719π-0.759719\pi
−0.728363 + 0.685191i 0.759719π0.759719\pi
294294 0 0
295295 0 0
296296 0.591429 0.0343761
297297 0 0
298298 0 0
299299 −7.79021 −0.450520
300300 0 0
301301 −20.5294 −1.18329
302302 −15.5025 −0.892066
303303 0 0
304304 −0.973070 −0.0558094
305305 0 0
306306 0 0
307307 −14.8171 −0.845659 −0.422829 0.906209i 0.638963π-0.638963\pi
−0.422829 + 0.906209i 0.638963π0.638963\pi
308308 8.76328 0.499334
309309 0 0
310310 0 0
311311 −12.8710 −0.729848 −0.364924 0.931037i 0.618905π-0.618905\pi
−0.364924 + 0.931037i 0.618905π0.618905\pi
312312 0 0
313313 19.9220 1.12606 0.563030 0.826436i 0.309636π-0.309636\pi
0.563030 + 0.826436i 0.309636π0.309636\pi
314314 −8.97307 −0.506380
315315 0 0
316316 10.9731 0.617283
317317 3.94614 0.221637 0.110819 0.993841i 0.464653π-0.464653\pi
0.110819 + 0.993841i 0.464653π0.464653\pi
318318 0 0
319319 1.94614 0.108963
320320 0 0
321321 0 0
322322 −34.1339 −1.90221
323323 5.71015 0.317721
324324 0 0
325325 0 0
326326 12.6074 0.698257
327327 0 0
328328 4.81714 0.265982
329329 1.67222 0.0921923
330330 0 0
331331 21.4245 1.17760 0.588798 0.808280i 0.299601π-0.299601\pi
0.588798 + 0.808280i 0.299601π0.299601\pi
332332 6.97307 0.382697
333333 0 0
334334 23.1609 1.26731
335335 0 0
336336 0 0
337337 −11.2388 −0.612217 −0.306109 0.951997i 0.599027π-0.599027\pi
−0.306109 + 0.951997i 0.599027π0.599027\pi
338338 −1.00000 −0.0543928
339339 0 0
340340 0 0
341341 3.58043 0.193891
342342 0 0
343343 −22.7792 −1.22996
344344 −4.68532 −0.252616
345345 0 0
346346 −19.7902 −1.06393
347347 16.9490 0.909868 0.454934 0.890525i 0.349663π-0.349663\pi
0.454934 + 0.890525i 0.349663π0.349663\pi
348348 0 0
349349 −10.2119 −0.546630 −0.273315 0.961925i 0.588120π-0.588120\pi
−0.273315 + 0.961925i 0.588120π0.588120\pi
350350 0 0
351351 0 0
352352 2.00000 0.106600
353353 14.9511 0.795765 0.397882 0.917436i 0.369745π-0.369745\pi
0.397882 + 0.917436i 0.369745π0.369745\pi
354354 0 0
355355 0 0
356356 −0.973070 −0.0515726
357357 0 0
358358 6.17185 0.326193
359359 −11.8441 −0.625106 −0.312553 0.949900i 0.601184π-0.601184\pi
−0.312553 + 0.949900i 0.601184π0.601184\pi
360360 0 0
361361 −18.0531 −0.950165
362362 19.3706 1.01810
363363 0 0
364364 −4.38164 −0.229660
365365 0 0
366366 0 0
367367 16.0539 0.838005 0.419002 0.907985i 0.362380π-0.362380\pi
0.419002 + 0.907985i 0.362380π0.362380\pi
368368 −7.79021 −0.406093
369369 0 0
370370 0 0
371371 34.1339 1.77214
372372 0 0
373373 −6.87100 −0.355767 −0.177883 0.984052i 0.556925π-0.556925\pi
−0.177883 + 0.984052i 0.556925π0.556925\pi
374374 −11.7364 −0.606872
375375 0 0
376376 0.381642 0.0196817
377377 −0.973070 −0.0501157
378378 0 0
379379 1.84407 0.0947236 0.0473618 0.998878i 0.484919π-0.484919\pi
0.0473618 + 0.998878i 0.484919π0.484919\pi
380380 0 0
381381 0 0
382382 −3.73635 −0.191168
383383 9.25264 0.472788 0.236394 0.971657i 0.424034π-0.424034\pi
0.236394 + 0.971657i 0.424034π0.424034\pi
384384 0 0
385385 0 0
386386 −15.3706 −0.782345
387387 0 0
388388 −18.6074 −0.944645
389389 21.2686 1.07836 0.539180 0.842191i 0.318734π-0.318734\pi
0.539180 + 0.842191i 0.318734π0.318734\pi
390390 0 0
391391 45.7143 2.31187
392392 −12.1988 −0.616132
393393 0 0
394394 26.9890 1.35969
395395 0 0
396396 0 0
397397 −33.4727 −1.67995 −0.839974 0.542627i 0.817430π-0.817430\pi
−0.839974 + 0.542627i 0.817430π0.817430\pi
398398 −23.3168 −1.16876
399399 0 0
400400 0 0
401401 −17.7364 −0.885711 −0.442856 0.896593i 0.646035π-0.646035\pi
−0.442856 + 0.896593i 0.646035π0.646035\pi
402402 0 0
403403 −1.79021 −0.0891769
404404 −14.3437 −0.713626
405405 0 0
406406 −4.26365 −0.211601
407407 1.18286 0.0586321
408408 0 0
409409 7.68249 0.379875 0.189937 0.981796i 0.439171π-0.439171\pi
0.189937 + 0.981796i 0.439171π0.439171\pi
410410 0 0
411411 0 0
412412 9.73635 0.479676
413413 −4.26365 −0.209800
414414 0 0
415415 0 0
416416 −1.00000 −0.0490290
417417 0 0
418418 −1.94614 −0.0951889
419419 −11.8061 −0.576768 −0.288384 0.957515i 0.593118π-0.593118\pi
−0.288384 + 0.957515i 0.593118π0.593118\pi
420420 0 0
421421 −26.3678 −1.28509 −0.642544 0.766249i 0.722121π-0.722121\pi
−0.642544 + 0.766249i 0.722121π0.722121\pi
422422 −15.3547 −0.747456
423423 0 0
424424 7.79021 0.378326
425425 0 0
426426 0 0
427427 3.58043 0.173269
428428 5.79021 0.279881
429429 0 0
430430 0 0
431431 −1.71225 −0.0824761 −0.0412381 0.999149i 0.513130π-0.513130\pi
−0.0412381 + 0.999149i 0.513130π0.513130\pi
432432 0 0
433433 −11.9220 −0.572936 −0.286468 0.958090i 0.592481π-0.592481\pi
−0.286468 + 0.958090i 0.592481π0.592481\pi
434434 −7.84407 −0.376528
435435 0 0
436436 −0.685320 −0.0328209
437437 7.58043 0.362621
438438 0 0
439439 −12.3437 −0.589133 −0.294567 0.955631i 0.595175π-0.595175\pi
−0.294567 + 0.955631i 0.595175π0.595175\pi
440440 0 0
441441 0 0
442442 5.86818 0.279121
443443 28.1580 1.33783 0.668914 0.743340i 0.266759π-0.266759\pi
0.668914 + 0.743340i 0.266759π0.266759\pi
444444 0 0
445445 0 0
446446 −24.8331 −1.17588
447447 0 0
448448 −4.38164 −0.207013
449449 29.0531 1.37110 0.685551 0.728025i 0.259561π-0.259561\pi
0.685551 + 0.728025i 0.259561π0.259561\pi
450450 0 0
451451 9.63429 0.453661
452452 −4.00000 −0.188144
453453 0 0
454454 −21.5266 −1.01029
455455 0 0
456456 0 0
457457 −11.5266 −0.539190 −0.269595 0.962974i 0.586890π-0.586890\pi
−0.269595 + 0.962974i 0.586890π0.586890\pi
458458 2.63146 0.122960
459459 0 0
460460 0 0
461461 −28.4217 −1.32373 −0.661865 0.749623i 0.730235π-0.730235\pi
−0.661865 + 0.749623i 0.730235π0.730235\pi
462462 0 0
463463 −27.4727 −1.27677 −0.638383 0.769719i 0.720396π-0.720396\pi
−0.638383 + 0.769719i 0.720396π0.720396\pi
464464 −0.973070 −0.0451737
465465 0 0
466466 −29.0290 −1.34474
467467 18.2098 0.842648 0.421324 0.906910i 0.361565π-0.361565\pi
0.421324 + 0.906910i 0.361565π0.361565\pi
468468 0 0
469469 −7.84407 −0.362206
470470 0 0
471471 0 0
472472 −0.973070 −0.0447892
473473 −9.37064 −0.430862
474474 0 0
475475 0 0
476476 25.7122 1.17852
477477 0 0
478478 2.13182 0.0975073
479479 33.6045 1.53543 0.767715 0.640791i 0.221394π-0.221394\pi
0.767715 + 0.640791i 0.221394π0.221394\pi
480480 0 0
481481 −0.591429 −0.0269668
482482 −22.4996 −1.02483
483483 0 0
484484 −7.00000 −0.318182
485485 0 0
486486 0 0
487487 8.00000 0.362515 0.181257 0.983436i 0.441983π-0.441983\pi
0.181257 + 0.983436i 0.441983π0.441983\pi
488488 0.817143 0.0369903
489489 0 0
490490 0 0
491491 19.8061 0.893839 0.446919 0.894574i 0.352521π-0.352521\pi
0.446919 + 0.894574i 0.352521π0.352521\pi
492492 0 0
493493 5.71015 0.257172
494494 0.973070 0.0437805
495495 0 0
496496 −1.79021 −0.0803829
497497 −17.1850 −0.770851
498498 0 0
499499 9.12900 0.408670 0.204335 0.978901i 0.434497π-0.434497\pi
0.204335 + 0.978901i 0.434497π0.434497\pi
500500 0 0
501501 0 0
502502 −0.419574 −0.0187265
503503 −10.6074 −0.472959 −0.236479 0.971637i 0.575994π-0.575994\pi
−0.236479 + 0.971637i 0.575994π0.575994\pi
504504 0 0
505505 0 0
506506 −15.5804 −0.692634
507507 0 0
508508 11.7902 0.523106
509509 5.63429 0.249735 0.124868 0.992173i 0.460149π-0.460149\pi
0.124868 + 0.992173i 0.460149π0.460149\pi
510510 0 0
511511 26.2899 1.16299
512512 −1.00000 −0.0441942
513513 0 0
514514 19.6584 0.867094
515515 0 0
516516 0 0
517517 0.763283 0.0335692
518518 −2.59143 −0.113861
519519 0 0
520520 0 0
521521 22.8012 0.998939 0.499470 0.866331i 0.333528π-0.333528\pi
0.499470 + 0.866331i 0.333528π0.333528\pi
522522 0 0
523523 23.6286 1.03321 0.516604 0.856224i 0.327196π-0.327196\pi
0.516604 + 0.856224i 0.327196π0.327196\pi
524524 16.9890 0.742168
525525 0 0
526526 −10.7633 −0.469301
527527 10.5053 0.457617
528528 0 0
529529 37.6874 1.63858
530530 0 0
531531 0 0
532532 4.26365 0.184853
533533 −4.81714 −0.208654
534534 0 0
535535 0 0
536536 −1.79021 −0.0773254
537537 0 0
538538 −14.7633 −0.636490
539539 −24.3976 −1.05088
540540 0 0
541541 11.3147 0.486456 0.243228 0.969969i 0.421794π-0.421794\pi
0.243228 + 0.969969i 0.421794π0.421794\pi
542542 27.2388 1.17001
543543 0 0
544544 5.86818 0.251596
545545 0 0
546546 0 0
547547 16.8412 0.720080 0.360040 0.932937i 0.382763π-0.382763\pi
0.360040 + 0.932937i 0.382763π0.382763\pi
548548 −4.20979 −0.179833
549549 0 0
550550 0 0
551551 0.946866 0.0403379
552552 0 0
553553 −48.0801 −2.04457
554554 2.87100 0.121977
555555 0 0
556556 −6.17185 −0.261745
557557 35.7523 1.51487 0.757436 0.652909i 0.226452π-0.226452\pi
0.757436 + 0.652909i 0.226452π0.226452\pi
558558 0 0
559559 4.68532 0.198168
560560 0 0
561561 0 0
562562 5.39264 0.227475
563563 13.3685 0.563417 0.281708 0.959500i 0.409099π-0.409099\pi
0.281708 + 0.959500i 0.409099π0.409099\pi
564564 0 0
565565 0 0
566566 24.9511 1.04877
567567 0 0
568568 −3.92204 −0.164565
569569 29.9621 1.25608 0.628038 0.778183i 0.283858π-0.283858\pi
0.628038 + 0.778183i 0.283858π0.283858\pi
570570 0 0
571571 30.5156 1.27704 0.638518 0.769607i 0.279548π-0.279548\pi
0.638518 + 0.769607i 0.279548π0.279548\pi
572572 −2.00000 −0.0836242
573573 0 0
574574 −21.1070 −0.880989
575575 0 0
576576 0 0
577577 33.1609 1.38050 0.690252 0.723569i 0.257500π-0.257500\pi
0.690252 + 0.723569i 0.257500π0.257500\pi
578578 −17.4355 −0.725221
579579 0 0
580580 0 0
581581 −30.5535 −1.26757
582582 0 0
583583 15.5804 0.645275
584584 6.00000 0.248282
585585 0 0
586586 24.9351 1.03006
587587 −14.1339 −0.583369 −0.291685 0.956515i 0.594216π-0.594216\pi
−0.291685 + 0.956515i 0.594216π0.594216\pi
588588 0 0
589589 1.74200 0.0717780
590590 0 0
591591 0 0
592592 −0.591429 −0.0243076
593593 9.39264 0.385710 0.192855 0.981227i 0.438225π-0.438225\pi
0.192855 + 0.981227i 0.438225π0.438225\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 7.79021 0.318566
599599 −45.5584 −1.86147 −0.930733 0.365699i 0.880830π-0.880830\pi
−0.930733 + 0.365699i 0.880830π0.880830\pi
600600 0 0
601601 26.7254 1.09015 0.545075 0.838387i 0.316501π-0.316501\pi
0.545075 + 0.838387i 0.316501π0.316501\pi
602602 20.5294 0.836716
603603 0 0
604604 15.5025 0.630786
605605 0 0
606606 0 0
607607 −30.0801 −1.22091 −0.610456 0.792050i 0.709014π-0.709014\pi
−0.610456 + 0.792050i 0.709014π0.709014\pi
608608 0.973070 0.0394632
609609 0 0
610610 0 0
611611 −0.381642 −0.0154396
612612 0 0
613613 −17.2686 −0.697471 −0.348735 0.937221i 0.613389π-0.613389\pi
−0.348735 + 0.937221i 0.613389π0.613389\pi
614614 14.8171 0.597971
615615 0 0
616616 −8.76328 −0.353083
617617 14.3437 0.577456 0.288728 0.957411i 0.406768π-0.406768\pi
0.288728 + 0.957411i 0.406768π0.406768\pi
618618 0 0
619619 −38.4514 −1.54549 −0.772747 0.634715i 0.781118π-0.781118\pi
−0.772747 + 0.634715i 0.781118π0.781118\pi
620620 0 0
621621 0 0
622622 12.8710 0.516080
623623 4.26365 0.170819
624624 0 0
625625 0 0
626626 −19.9220 −0.796245
627627 0 0
628628 8.97307 0.358064
629629 3.47061 0.138382
630630 0 0
631631 −8.18568 −0.325867 −0.162933 0.986637i 0.552096π-0.552096\pi
−0.162933 + 0.986637i 0.552096π0.552096\pi
632632 −10.9731 −0.436485
633633 0 0
634634 −3.94614 −0.156721
635635 0 0
636636 0 0
637637 12.1988 0.483333
638638 −1.94614 −0.0770485
639639 0 0
640640 0 0
641641 12.3657 0.488416 0.244208 0.969723i 0.421472π-0.421472\pi
0.244208 + 0.969723i 0.421472π0.421472\pi
642642 0 0
643643 −46.8972 −1.84945 −0.924723 0.380642i 0.875703π-0.875703\pi
−0.924723 + 0.380642i 0.875703π0.875703\pi
644644 34.1339 1.34506
645645 0 0
646646 −5.71015 −0.224663
647647 26.1878 1.02955 0.514774 0.857326i 0.327876π-0.327876\pi
0.514774 + 0.857326i 0.327876π0.327876\pi
648648 0 0
649649 −1.94614 −0.0763927
650650 0 0
651651 0 0
652652 −12.6074 −0.493742
653653 10.7633 0.421200 0.210600 0.977572i 0.432458π-0.432458\pi
0.210600 + 0.977572i 0.432458π0.432458\pi
654654 0 0
655655 0 0
656656 −4.81714 −0.188078
657657 0 0
658658 −1.67222 −0.0651898
659659 −31.4727 −1.22600 −0.613001 0.790082i 0.710038π-0.710038\pi
−0.613001 + 0.790082i 0.710038π0.710038\pi
660660 0 0
661661 25.2147 0.980739 0.490369 0.871515i 0.336862π-0.336862\pi
0.490369 + 0.871515i 0.336862π0.336862\pi
662662 −21.4245 −0.832687
663663 0 0
664664 −6.97307 −0.270608
665665 0 0
666666 0 0
667667 7.58043 0.293515
668668 −23.1609 −0.896120
669669 0 0
670670 0 0
671671 1.63429 0.0630909
672672 0 0
673673 23.2388 0.895791 0.447895 0.894086i 0.352174π-0.352174\pi
0.447895 + 0.894086i 0.352174π0.352174\pi
674674 11.2388 0.432903
675675 0 0
676676 1.00000 0.0384615
677677 47.2629 1.81646 0.908231 0.418470i 0.137433π-0.137433\pi
0.908231 + 0.418470i 0.137433π0.137433\pi
678678 0 0
679679 81.5308 3.12886
680680 0 0
681681 0 0
682682 −3.58043 −0.137102
683683 6.97307 0.266817 0.133409 0.991061i 0.457408π-0.457408\pi
0.133409 + 0.991061i 0.457408π0.457408\pi
684684 0 0
685685 0 0
686686 22.7792 0.869714
687687 0 0
688688 4.68532 0.178626
689689 −7.79021 −0.296783
690690 0 0
691691 −32.2899 −1.22836 −0.614182 0.789164i 0.710514π-0.710514\pi
−0.614182 + 0.789164i 0.710514π0.710514\pi
692692 19.7902 0.752311
693693 0 0
694694 −16.9490 −0.643374
695695 0 0
696696 0 0
697697 28.2678 1.07072
698698 10.2119 0.386526
699699 0 0
700700 0 0
701701 0.521643 0.0197022 0.00985109 0.999951i 0.496864π-0.496864\pi
0.00985109 + 0.999951i 0.496864π0.496864\pi
702702 0 0
703703 0.575502 0.0217055
704704 −2.00000 −0.0753778
705705 0 0
706706 −14.9511 −0.562691
707707 62.8490 2.36368
708708 0 0
709709 −33.2147 −1.24740 −0.623702 0.781662i 0.714372π-0.714372\pi
−0.623702 + 0.781662i 0.714372π0.714372\pi
710710 0 0
711711 0 0
712712 0.973070 0.0364674
713713 13.9461 0.522287
714714 0 0
715715 0 0
716716 −6.17185 −0.230653
717717 0 0
718718 11.8441 0.442017
719719 4.26365 0.159007 0.0795036 0.996835i 0.474666π-0.474666\pi
0.0795036 + 0.996835i 0.474666π0.474666\pi
720720 0 0
721721 −42.6612 −1.58879
722722 18.0531 0.671868
723723 0 0
724724 −19.3706 −0.719904
725725 0 0
726726 0 0
727727 47.5266 1.76266 0.881331 0.472499i 0.156648π-0.156648\pi
0.881331 + 0.472499i 0.156648π0.156648\pi
728728 4.38164 0.162394
729729 0 0
730730 0 0
731731 −27.4943 −1.01691
732732 0 0
733733 44.8593 1.65692 0.828458 0.560052i 0.189219π-0.189219\pi
0.828458 + 0.560052i 0.189219π0.189219\pi
734734 −16.0539 −0.592559
735735 0 0
736736 7.79021 0.287151
737737 −3.58043 −0.131887
738738 0 0
739739 −18.4514 −0.678747 −0.339373 0.940652i 0.610215π-0.610215\pi
−0.339373 + 0.940652i 0.610215π0.610215\pi
740740 0 0
741741 0 0
742742 −34.1339 −1.25310
743743 14.2201 0.521684 0.260842 0.965382i 0.416000π-0.416000\pi
0.260842 + 0.965382i 0.416000π0.416000\pi
744744 0 0
745745 0 0
746746 6.87100 0.251565
747747 0 0
748748 11.7364 0.429124
749749 −25.3706 −0.927023
750750 0 0
751751 −28.7951 −1.05075 −0.525375 0.850871i 0.676075π-0.676075\pi
−0.525375 + 0.850871i 0.676075π0.676075\pi
752752 −0.381642 −0.0139170
753753 0 0
754754 0.973070 0.0354371
755755 0 0
756756 0 0
757757 13.7364 0.499256 0.249628 0.968342i 0.419692π-0.419692\pi
0.249628 + 0.968342i 0.419692π0.419692\pi
758758 −1.84407 −0.0669797
759759 0 0
760760 0 0
761761 −5.39264 −0.195483 −0.0977416 0.995212i 0.531162π-0.531162\pi
−0.0977416 + 0.995212i 0.531162π0.531162\pi
762762 0 0
763763 3.00282 0.108710
764764 3.73635 0.135177
765765 0 0
766766 −9.25264 −0.334312
767767 0.973070 0.0351355
768768 0 0
769769 −2.34371 −0.0845163 −0.0422582 0.999107i 0.513455π-0.513455\pi
−0.0422582 + 0.999107i 0.513455π0.513455\pi
770770 0 0
771771 0 0
772772 15.3706 0.553201
773773 29.3547 1.05582 0.527908 0.849302i 0.322977π-0.322977\pi
0.527908 + 0.849302i 0.322977π0.322977\pi
774774 0 0
775775 0 0
776776 18.6074 0.667965
777777 0 0
778778 −21.2686 −0.762515
779779 4.68742 0.167944
780780 0 0
781781 −7.84407 −0.280683
782782 −45.7143 −1.63474
783783 0 0
784784 12.1988 0.435671
785785 0 0
786786 0 0
787787 34.6336 1.23455 0.617277 0.786746i 0.288236π-0.288236\pi
0.617277 + 0.786746i 0.288236π0.288236\pi
788788 −26.9890 −0.961443
789789 0 0
790790 0 0
791791 17.5266 0.623173
792792 0 0
793793 −0.817143 −0.0290176
794794 33.4727 1.18790
795795 0 0
796796 23.3168 0.826441
797797 −27.8221 −0.985508 −0.492754 0.870169i 0.664010π-0.664010\pi
−0.492754 + 0.870169i 0.664010π0.664010\pi
798798 0 0
799799 2.23954 0.0792293
800800 0 0
801801 0 0
802802 17.7364 0.626292
803803 12.0000 0.423471
804804 0 0
805805 0 0
806806 1.79021 0.0630576
807807 0 0
808808 14.3437 0.504610
809809 23.1768 0.814852 0.407426 0.913238i 0.366426π-0.366426\pi
0.407426 + 0.913238i 0.366426π0.366426\pi
810810 0 0
811811 36.0857 1.26714 0.633570 0.773685i 0.281589π-0.281589\pi
0.633570 + 0.773685i 0.281589π0.281589\pi
812812 4.26365 0.149625
813813 0 0
814814 −1.18286 −0.0414591
815815 0 0
816816 0 0
817817 −4.55915 −0.159504
818818 −7.68249 −0.268612
819819 0 0
820820 0 0
821821 −38.3196 −1.33736 −0.668682 0.743549i 0.733141π-0.733141\pi
−0.668682 + 0.743549i 0.733141π0.733141\pi
822822 0 0
823823 53.3486 1.85962 0.929808 0.368044i 0.119973π-0.119973\pi
0.929808 + 0.368044i 0.119973π0.119973\pi
824824 −9.73635 −0.339182
825825 0 0
826826 4.26365 0.148351
827827 −14.5053 −0.504398 −0.252199 0.967675i 0.581154π-0.581154\pi
−0.252199 + 0.967675i 0.581154π0.581154\pi
828828 0 0
829829 −13.3926 −0.465146 −0.232573 0.972579i 0.574714π-0.574714\pi
−0.232573 + 0.972579i 0.574714π0.574714\pi
830830 0 0
831831 0 0
832832 1.00000 0.0346688
833833 −71.5846 −2.48026
834834 0 0
835835 0 0
836836 1.94614 0.0673087
837837 0 0
838838 11.8061 0.407836
839839 −2.52164 −0.0870568 −0.0435284 0.999052i 0.513860π-0.513860\pi
−0.0435284 + 0.999052i 0.513860π0.513860\pi
840840 0 0
841841 −28.0531 −0.967349
842842 26.3678 0.908695
843843 0 0
844844 15.3547 0.528531
845845 0 0
846846 0 0
847847 30.6715 1.05388
848848 −7.79021 −0.267517
849849 0 0
850850 0 0
851851 4.60736 0.157938
852852 0 0
853853 36.4078 1.24658 0.623290 0.781990i 0.285795π-0.285795\pi
0.623290 + 0.781990i 0.285795π0.285795\pi
854854 −3.58043 −0.122520
855855 0 0
856856 −5.79021 −0.197905
857857 −21.4188 −0.731654 −0.365827 0.930683i 0.619214π-0.619214\pi
−0.365827 + 0.930683i 0.619214π0.619214\pi
858858 0 0
859859 −41.9461 −1.43118 −0.715592 0.698519i 0.753843π-0.753843\pi
−0.715592 + 0.698519i 0.753843π0.753843\pi
860860 0 0
861861 0 0
862862 1.71225 0.0583194
863863 −38.3278 −1.30469 −0.652346 0.757921i 0.726215π-0.726215\pi
−0.652346 + 0.757921i 0.726215π0.726215\pi
864864 0 0
865865 0 0
866866 11.9220 0.405127
867867 0 0
868868 7.84407 0.266245
869869 −21.9461 −0.744472
870870 0 0
871871 1.79021 0.0606591
872872 0.685320 0.0232078
873873 0 0
874874 −7.58043 −0.256412
875875 0 0
876876 0 0
877877 −43.3327 −1.46324 −0.731621 0.681712i 0.761236π-0.761236\pi
−0.731621 + 0.681712i 0.761236π0.761236\pi
878878 12.3437 0.416580
879879 0 0
880880 0 0
881881 −1.09107 −0.0367590 −0.0183795 0.999831i 0.505851π-0.505851\pi
−0.0183795 + 0.999831i 0.505851π0.505851\pi
882882 0 0
883883 28.3735 0.954843 0.477422 0.878674i 0.341571π-0.341571\pi
0.477422 + 0.878674i 0.341571π0.341571\pi
884884 −5.86818 −0.197368
885885 0 0
886886 −28.1580 −0.945987
887887 −4.50529 −0.151273 −0.0756364 0.997135i 0.524099π-0.524099\pi
−0.0756364 + 0.997135i 0.524099π0.524099\pi
888888 0 0
889889 −51.6605 −1.73264
890890 0 0
891891 0 0
892892 24.8331 0.831473
893893 0.371364 0.0124272
894894 0 0
895895 0 0
896896 4.38164 0.146380
897897 0 0
898898 −29.0531 −0.969516
899899 1.74200 0.0580991
900900 0 0
901901 45.7143 1.52297
902902 −9.63429 −0.320787
903903 0 0
904904 4.00000 0.133038
905905 0 0
906906 0 0
907907 −48.0503 −1.59548 −0.797742 0.602999i 0.793972π-0.793972\pi
−0.797742 + 0.602999i 0.793972π0.793972\pi
908908 21.5266 0.714384
909909 0 0
910910 0 0
911911 −12.5755 −0.416645 −0.208322 0.978060i 0.566800π-0.566800\pi
−0.208322 + 0.978060i 0.566800π0.566800\pi
912912 0 0
913913 −13.9461 −0.461550
914914 11.5266 0.381265
915915 0 0
916916 −2.63146 −0.0869459
917917 −74.4397 −2.45822
918918 0 0
919919 23.6881 0.781400 0.390700 0.920518i 0.372233π-0.372233\pi
0.390700 + 0.920518i 0.372233π0.372233\pi
920920 0 0
921921 0 0
922922 28.4217 0.936018
923923 3.92204 0.129095
924924 0 0
925925 0 0
926926 27.4727 0.902809
927927 0 0
928928 0.973070 0.0319426
929929 −45.0850 −1.47919 −0.739595 0.673052i 0.764983π-0.764983\pi
−0.739595 + 0.673052i 0.764983π0.764983\pi
930930 0 0
931931 −11.8703 −0.389033
932932 29.0290 0.950877
933933 0 0
934934 −18.2098 −0.595842
935935 0 0
936936 0 0
937937 28.7951 0.940696 0.470348 0.882481i 0.344128π-0.344128\pi
0.470348 + 0.882481i 0.344128π0.344128\pi
938938 7.84407 0.256118
939939 0 0
940940 0 0
941941 2.84690 0.0928062 0.0464031 0.998923i 0.485224π-0.485224\pi
0.0464031 + 0.998923i 0.485224π0.485224\pi
942942 0 0
943943 37.5266 1.22203
944944 0.973070 0.0316707
945945 0 0
946946 9.37064 0.304666
947947 −11.3168 −0.367746 −0.183873 0.982950i 0.558864π-0.558864\pi
−0.183873 + 0.982950i 0.558864π0.558864\pi
948948 0 0
949949 −6.00000 −0.194768
950950 0 0
951951 0 0
952952 −25.7122 −0.833339
953953 28.4535 0.921700 0.460850 0.887478i 0.347545π-0.347545\pi
0.460850 + 0.887478i 0.347545π0.347545\pi
954954 0 0
955955 0 0
956956 −2.13182 −0.0689481
957957 0 0
958958 −33.6045 −1.08571
959959 18.4458 0.595645
960960 0 0
961961 −27.7951 −0.896617
962962 0.591429 0.0190684
963963 0 0
964964 22.4996 0.724665
965965 0 0
966966 0 0
967967 −1.48863 −0.0478713 −0.0239356 0.999714i 0.507620π-0.507620\pi
−0.0239356 + 0.999714i 0.507620π0.507620\pi
968968 7.00000 0.224989
969969 0 0
970970 0 0
971971 −49.6446 −1.59317 −0.796585 0.604527i 0.793362π-0.793362\pi
−0.796585 + 0.604527i 0.793362π0.793362\pi
972972 0 0
973973 27.0429 0.866954
974974 −8.00000 −0.256337
975975 0 0
976976 −0.817143 −0.0261561
977977 39.6066 1.26713 0.633564 0.773690i 0.281591π-0.281591\pi
0.633564 + 0.773690i 0.281591π0.281591\pi
978978 0 0
979979 1.94614 0.0621989
980980 0 0
981981 0 0
982982 −19.8061 −0.632039
983983 0.725351 0.0231351 0.0115676 0.999933i 0.496318π-0.496318\pi
0.0115676 + 0.999933i 0.496318π0.496318\pi
984984 0 0
985985 0 0
986986 −5.71015 −0.181848
987987 0 0
988988 −0.973070 −0.0309575
989989 −36.4996 −1.16062
990990 0 0
991991 −35.5046 −1.12784 −0.563920 0.825830i 0.690707π-0.690707\pi
−0.563920 + 0.825830i 0.690707π0.690707\pi
992992 1.79021 0.0568393
993993 0 0
994994 17.1850 0.545074
995995 0 0
996996 0 0
997997 10.4196 0.329991 0.164996 0.986294i 0.447239π-0.447239\pi
0.164996 + 0.986294i 0.447239π0.447239\pi
998998 −9.12900 −0.288973
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 5850.2.a.cp.1.1 3
3.2 odd 2 650.2.a.o.1.1 3
5.2 odd 4 1170.2.e.f.469.1 6
5.3 odd 4 1170.2.e.f.469.4 6
5.4 even 2 5850.2.a.cs.1.3 3
12.11 even 2 5200.2.a.cf.1.3 3
15.2 even 4 130.2.b.a.79.6 yes 6
15.8 even 4 130.2.b.a.79.1 6
15.14 odd 2 650.2.a.n.1.3 3
39.38 odd 2 8450.2.a.bs.1.1 3
60.23 odd 4 1040.2.d.b.209.6 6
60.47 odd 4 1040.2.d.b.209.1 6
60.59 even 2 5200.2.a.ce.1.1 3
195.8 odd 4 1690.2.c.d.1689.1 6
195.38 even 4 1690.2.b.a.339.4 6
195.47 odd 4 1690.2.c.a.1689.6 6
195.77 even 4 1690.2.b.a.339.3 6
195.83 odd 4 1690.2.c.a.1689.1 6
195.122 odd 4 1690.2.c.d.1689.6 6
195.194 odd 2 8450.2.a.cc.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.2.b.a.79.1 6 15.8 even 4
130.2.b.a.79.6 yes 6 15.2 even 4
650.2.a.n.1.3 3 15.14 odd 2
650.2.a.o.1.1 3 3.2 odd 2
1040.2.d.b.209.1 6 60.47 odd 4
1040.2.d.b.209.6 6 60.23 odd 4
1170.2.e.f.469.1 6 5.2 odd 4
1170.2.e.f.469.4 6 5.3 odd 4
1690.2.b.a.339.3 6 195.77 even 4
1690.2.b.a.339.4 6 195.38 even 4
1690.2.c.a.1689.1 6 195.83 odd 4
1690.2.c.a.1689.6 6 195.47 odd 4
1690.2.c.d.1689.1 6 195.8 odd 4
1690.2.c.d.1689.6 6 195.122 odd 4
5200.2.a.ce.1.1 3 60.59 even 2
5200.2.a.cf.1.3 3 12.11 even 2
5850.2.a.cp.1.1 3 1.1 even 1 trivial
5850.2.a.cs.1.3 3 5.4 even 2
8450.2.a.bs.1.1 3 39.38 odd 2
8450.2.a.cc.1.3 3 195.194 odd 2