Properties

Label 675.4.a.b.1.1
Level 675675
Weight 44
Character 675.1
Self dual yes
Analytic conductor 39.82639.826
Analytic rank 00
Dimension 11
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] = [675,4,Mod(1,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 675=3352 675 = 3^{3} \cdot 5^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 675.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1,-2,0,-4,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 39.826289253939.8262892539
Analytic rank: 00
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 135)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 675.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q2.00000q24.00000q4+24.0000q810.0000q11+80.0000q1316.0000q16+7.00000q17113.000q19+20.0000q2281.0000q23160.000q26+220.000q29189.000q31160.000q3214.0000q34170.000q37+226.000q38+130.000q4110.0000q43+40.0000q44+162.000q46+160.000q47343.000q49320.000q52+631.000q53440.000q58+560.000q59+229.000q61+378.000q62+448.000q64750.000q6728.0000q68890.000q71+890.000q73+340.000q74+452.000q7627.0000q79260.000q82+429.000q83+20.0000q86240.000q88+750.000q89+324.000q92320.000q94+1480.00q97+686.000q98+O(q100)q-2.00000 q^{2} -4.00000 q^{4} +24.0000 q^{8} -10.0000 q^{11} +80.0000 q^{13} -16.0000 q^{16} +7.00000 q^{17} -113.000 q^{19} +20.0000 q^{22} -81.0000 q^{23} -160.000 q^{26} +220.000 q^{29} -189.000 q^{31} -160.000 q^{32} -14.0000 q^{34} -170.000 q^{37} +226.000 q^{38} +130.000 q^{41} -10.0000 q^{43} +40.0000 q^{44} +162.000 q^{46} +160.000 q^{47} -343.000 q^{49} -320.000 q^{52} +631.000 q^{53} -440.000 q^{58} +560.000 q^{59} +229.000 q^{61} +378.000 q^{62} +448.000 q^{64} -750.000 q^{67} -28.0000 q^{68} -890.000 q^{71} +890.000 q^{73} +340.000 q^{74} +452.000 q^{76} -27.0000 q^{79} -260.000 q^{82} +429.000 q^{83} +20.0000 q^{86} -240.000 q^{88} +750.000 q^{89} +324.000 q^{92} -320.000 q^{94} +1480.00 q^{97} +686.000 q^{98} +O(q^{100})

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 −2.00000 −0.707107 −0.353553 0.935414i 0.615027π-0.615027\pi
−0.353553 + 0.935414i 0.615027π0.615027\pi
33 0 0
44 −4.00000 −0.500000
55 0 0
66 0 0
77 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
88 24.0000 1.06066
99 0 0
1010 0 0
1111 −10.0000 −0.274101 −0.137051 0.990564i 0.543762π-0.543762\pi
−0.137051 + 0.990564i 0.543762π0.543762\pi
1212 0 0
1313 80.0000 1.70677 0.853385 0.521281i 0.174546π-0.174546\pi
0.853385 + 0.521281i 0.174546π0.174546\pi
1414 0 0
1515 0 0
1616 −16.0000 −0.250000
1717 7.00000 0.0998676 0.0499338 0.998753i 0.484099π-0.484099\pi
0.0499338 + 0.998753i 0.484099π0.484099\pi
1818 0 0
1919 −113.000 −1.36442 −0.682210 0.731156i 0.738981π-0.738981\pi
−0.682210 + 0.731156i 0.738981π0.738981\pi
2020 0 0
2121 0 0
2222 20.0000 0.193819
2323 −81.0000 −0.734333 −0.367167 0.930155i 0.619672π-0.619672\pi
−0.367167 + 0.930155i 0.619672π0.619672\pi
2424 0 0
2525 0 0
2626 −160.000 −1.20687
2727 0 0
2828 0 0
2929 220.000 1.40872 0.704362 0.709841i 0.251233π-0.251233\pi
0.704362 + 0.709841i 0.251233π0.251233\pi
3030 0 0
3131 −189.000 −1.09501 −0.547506 0.836801i 0.684423π-0.684423\pi
−0.547506 + 0.836801i 0.684423π0.684423\pi
3232 −160.000 −0.883883
3333 0 0
3434 −14.0000 −0.0706171
3535 0 0
3636 0 0
3737 −170.000 −0.755347 −0.377673 0.925939i 0.623276π-0.623276\pi
−0.377673 + 0.925939i 0.623276π0.623276\pi
3838 226.000 0.964791
3939 0 0
4040 0 0
4141 130.000 0.495185 0.247593 0.968864i 0.420361π-0.420361\pi
0.247593 + 0.968864i 0.420361π0.420361\pi
4242 0 0
4343 −10.0000 −0.0354648 −0.0177324 0.999843i 0.505645π-0.505645\pi
−0.0177324 + 0.999843i 0.505645π0.505645\pi
4444 40.0000 0.137051
4545 0 0
4646 162.000 0.519252
4747 160.000 0.496562 0.248281 0.968688i 0.420134π-0.420134\pi
0.248281 + 0.968688i 0.420134π0.420134\pi
4848 0 0
4949 −343.000 −1.00000
5050 0 0
5151 0 0
5252 −320.000 −0.853385
5353 631.000 1.63537 0.817684 0.575667i 0.195258π-0.195258\pi
0.817684 + 0.575667i 0.195258π0.195258\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 −440.000 −0.996118
5959 560.000 1.23569 0.617846 0.786299i 0.288006π-0.288006\pi
0.617846 + 0.786299i 0.288006π0.288006\pi
6060 0 0
6161 229.000 0.480663 0.240332 0.970691i 0.422744π-0.422744\pi
0.240332 + 0.970691i 0.422744π0.422744\pi
6262 378.000 0.774291
6363 0 0
6464 448.000 0.875000
6565 0 0
6666 0 0
6767 −750.000 −1.36757 −0.683784 0.729684i 0.739667π-0.739667\pi
−0.683784 + 0.729684i 0.739667π0.739667\pi
6868 −28.0000 −0.0499338
6969 0 0
7070 0 0
7171 −890.000 −1.48766 −0.743828 0.668371i 0.766992π-0.766992\pi
−0.743828 + 0.668371i 0.766992π0.766992\pi
7272 0 0
7373 890.000 1.42694 0.713470 0.700686i 0.247122π-0.247122\pi
0.713470 + 0.700686i 0.247122π0.247122\pi
7474 340.000 0.534111
7575 0 0
7676 452.000 0.682210
7777 0 0
7878 0 0
7979 −27.0000 −0.0384524 −0.0192262 0.999815i 0.506120π-0.506120\pi
−0.0192262 + 0.999815i 0.506120π0.506120\pi
8080 0 0
8181 0 0
8282 −260.000 −0.350149
8383 429.000 0.567336 0.283668 0.958923i 0.408449π-0.408449\pi
0.283668 + 0.958923i 0.408449π0.408449\pi
8484 0 0
8585 0 0
8686 20.0000 0.0250774
8787 0 0
8888 −240.000 −0.290728
8989 750.000 0.893257 0.446628 0.894720i 0.352625π-0.352625\pi
0.446628 + 0.894720i 0.352625π0.352625\pi
9090 0 0
9191 0 0
9292 324.000 0.367167
9393 0 0
9494 −320.000 −0.351122
9595 0 0
9696 0 0
9797 1480.00 1.54919 0.774594 0.632459i 0.217954π-0.217954\pi
0.774594 + 0.632459i 0.217954π0.217954\pi
9898 686.000 0.707107
9999 0 0
100100 0 0
101101 1500.00 1.47778 0.738889 0.673827i 0.235351π-0.235351\pi
0.738889 + 0.673827i 0.235351π0.235351\pi
102102 0 0
103103 460.000 0.440050 0.220025 0.975494i 0.429386π-0.429386\pi
0.220025 + 0.975494i 0.429386π0.429386\pi
104104 1920.00 1.81030
105105 0 0
106106 −1262.00 −1.15638
107107 −420.000 −0.379467 −0.189733 0.981836i 0.560762π-0.560762\pi
−0.189733 + 0.981836i 0.560762π0.560762\pi
108108 0 0
109109 −607.000 −0.533395 −0.266698 0.963780i 0.585932π-0.585932\pi
−0.266698 + 0.963780i 0.585932π0.585932\pi
110110 0 0
111111 0 0
112112 0 0
113113 2170.00 1.80652 0.903259 0.429097i 0.141168π-0.141168\pi
0.903259 + 0.429097i 0.141168π0.141168\pi
114114 0 0
115115 0 0
116116 −880.000 −0.704362
117117 0 0
118118 −1120.00 −0.873766
119119 0 0
120120 0 0
121121 −1231.00 −0.924869
122122 −458.000 −0.339880
123123 0 0
124124 756.000 0.547506
125125 0 0
126126 0 0
127127 1610.00 1.12492 0.562458 0.826826i 0.309856π-0.309856\pi
0.562458 + 0.826826i 0.309856π0.309856\pi
128128 384.000 0.265165
129129 0 0
130130 0 0
131131 −2370.00 −1.58067 −0.790335 0.612674i 0.790094π-0.790094\pi
−0.790335 + 0.612674i 0.790094π0.790094\pi
132132 0 0
133133 0 0
134134 1500.00 0.967017
135135 0 0
136136 168.000 0.105926
137137 1797.00 1.12064 0.560321 0.828275i 0.310678π-0.310678\pi
0.560321 + 0.828275i 0.310678π0.310678\pi
138138 0 0
139139 −124.000 −0.0756658 −0.0378329 0.999284i 0.512045π-0.512045\pi
−0.0378329 + 0.999284i 0.512045π0.512045\pi
140140 0 0
141141 0 0
142142 1780.00 1.05193
143143 −800.000 −0.467828
144144 0 0
145145 0 0
146146 −1780.00 −1.00900
147147 0 0
148148 680.000 0.377673
149149 70.0000 0.0384874 0.0192437 0.999815i 0.493874π-0.493874\pi
0.0192437 + 0.999815i 0.493874π0.493874\pi
150150 0 0
151151 2248.00 1.21152 0.605760 0.795647i 0.292869π-0.292869\pi
0.605760 + 0.795647i 0.292869π0.292869\pi
152152 −2712.00 −1.44719
153153 0 0
154154 0 0
155155 0 0
156156 0 0
157157 −1010.00 −0.513419 −0.256709 0.966489i 0.582638π-0.582638\pi
−0.256709 + 0.966489i 0.582638π0.582638\pi
158158 54.0000 0.0271899
159159 0 0
160160 0 0
161161 0 0
162162 0 0
163163 −590.000 −0.283511 −0.141756 0.989902i 0.545275π-0.545275\pi
−0.141756 + 0.989902i 0.545275π0.545275\pi
164164 −520.000 −0.247593
165165 0 0
166166 −858.000 −0.401167
167167 2403.00 1.11347 0.556736 0.830690i 0.312054π-0.312054\pi
0.556736 + 0.830690i 0.312054π0.312054\pi
168168 0 0
169169 4203.00 1.91306
170170 0 0
171171 0 0
172172 40.0000 0.0177324
173173 801.000 0.352017 0.176008 0.984389i 0.443681π-0.443681\pi
0.176008 + 0.984389i 0.443681π0.443681\pi
174174 0 0
175175 0 0
176176 160.000 0.0685253
177177 0 0
178178 −1500.00 −0.631628
179179 2360.00 0.985445 0.492723 0.870186i 0.336002π-0.336002\pi
0.492723 + 0.870186i 0.336002π0.336002\pi
180180 0 0
181181 1241.00 0.509629 0.254814 0.966990i 0.417986π-0.417986\pi
0.254814 + 0.966990i 0.417986π0.417986\pi
182182 0 0
183183 0 0
184184 −1944.00 −0.778878
185185 0 0
186186 0 0
187187 −70.0000 −0.0273738
188188 −640.000 −0.248281
189189 0 0
190190 0 0
191191 4990.00 1.89039 0.945193 0.326512i 0.105873π-0.105873\pi
0.945193 + 0.326512i 0.105873π0.105873\pi
192192 0 0
193193 2260.00 0.842893 0.421447 0.906853i 0.361523π-0.361523\pi
0.421447 + 0.906853i 0.361523π0.361523\pi
194194 −2960.00 −1.09544
195195 0 0
196196 1372.00 0.500000
197197 −2247.00 −0.812650 −0.406325 0.913729i 0.633190π-0.633190\pi
−0.406325 + 0.913729i 0.633190π0.633190\pi
198198 0 0
199199 4564.00 1.62580 0.812898 0.582406i 0.197889π-0.197889\pi
0.812898 + 0.582406i 0.197889π0.197889\pi
200200 0 0
201201 0 0
202202 −3000.00 −1.04495
203203 0 0
204204 0 0
205205 0 0
206206 −920.000 −0.311162
207207 0 0
208208 −1280.00 −0.426692
209209 1130.00 0.373989
210210 0 0
211211 4949.00 1.61471 0.807354 0.590068i 0.200899π-0.200899\pi
0.807354 + 0.590068i 0.200899π0.200899\pi
212212 −2524.00 −0.817684
213213 0 0
214214 840.000 0.268323
215215 0 0
216216 0 0
217217 0 0
218218 1214.00 0.377167
219219 0 0
220220 0 0
221221 560.000 0.170451
222222 0 0
223223 −3890.00 −1.16813 −0.584067 0.811706i 0.698539π-0.698539\pi
−0.584067 + 0.811706i 0.698539π0.698539\pi
224224 0 0
225225 0 0
226226 −4340.00 −1.27740
227227 2453.00 0.717231 0.358615 0.933485i 0.383249π-0.383249\pi
0.358615 + 0.933485i 0.383249π0.383249\pi
228228 0 0
229229 −6213.00 −1.79287 −0.896434 0.443178i 0.853851π-0.853851\pi
−0.896434 + 0.443178i 0.853851π0.853851\pi
230230 0 0
231231 0 0
232232 5280.00 1.49418
233233 −3450.00 −0.970030 −0.485015 0.874506i 0.661186π-0.661186\pi
−0.485015 + 0.874506i 0.661186π0.661186\pi
234234 0 0
235235 0 0
236236 −2240.00 −0.617846
237237 0 0
238238 0 0
239239 −6490.00 −1.75650 −0.878249 0.478203i 0.841288π-0.841288\pi
−0.878249 + 0.478203i 0.841288π0.841288\pi
240240 0 0
241241 −3401.00 −0.909036 −0.454518 0.890738i 0.650188π-0.650188\pi
−0.454518 + 0.890738i 0.650188π0.650188\pi
242242 2462.00 0.653981
243243 0 0
244244 −916.000 −0.240332
245245 0 0
246246 0 0
247247 −9040.00 −2.32875
248248 −4536.00 −1.16144
249249 0 0
250250 0 0
251251 4980.00 1.25233 0.626165 0.779691i 0.284624π-0.284624\pi
0.626165 + 0.779691i 0.284624π0.284624\pi
252252 0 0
253253 810.000 0.201282
254254 −3220.00 −0.795436
255255 0 0
256256 −4352.00 −1.06250
257257 3357.00 0.814801 0.407401 0.913250i 0.366435π-0.366435\pi
0.407401 + 0.913250i 0.366435π0.366435\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 4740.00 1.11770
263263 −4540.00 −1.06444 −0.532221 0.846605i 0.678643π-0.678643\pi
−0.532221 + 0.846605i 0.678643π0.678643\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 3000.00 0.683784
269269 −8410.00 −1.90620 −0.953098 0.302662i 0.902125π-0.902125\pi
−0.953098 + 0.302662i 0.902125π0.902125\pi
270270 0 0
271271 259.000 0.0580558 0.0290279 0.999579i 0.490759π-0.490759\pi
0.0290279 + 0.999579i 0.490759π0.490759\pi
272272 −112.000 −0.0249669
273273 0 0
274274 −3594.00 −0.792414
275275 0 0
276276 0 0
277277 4170.00 0.904516 0.452258 0.891887i 0.350619π-0.350619\pi
0.452258 + 0.891887i 0.350619π0.350619\pi
278278 248.000 0.0535038
279279 0 0
280280 0 0
281281 1740.00 0.369394 0.184697 0.982796i 0.440870π-0.440870\pi
0.184697 + 0.982796i 0.440870π0.440870\pi
282282 0 0
283283 5070.00 1.06495 0.532474 0.846446i 0.321262π-0.321262\pi
0.532474 + 0.846446i 0.321262π0.321262\pi
284284 3560.00 0.743828
285285 0 0
286286 1600.00 0.330804
287287 0 0
288288 0 0
289289 −4864.00 −0.990026
290290 0 0
291291 0 0
292292 −3560.00 −0.713470
293293 −159.000 −0.0317027 −0.0158513 0.999874i 0.505046π-0.505046\pi
−0.0158513 + 0.999874i 0.505046π0.505046\pi
294294 0 0
295295 0 0
296296 −4080.00 −0.801166
297297 0 0
298298 −140.000 −0.0272147
299299 −6480.00 −1.25334
300300 0 0
301301 0 0
302302 −4496.00 −0.856675
303303 0 0
304304 1808.00 0.341105
305305 0 0
306306 0 0
307307 −6490.00 −1.20653 −0.603264 0.797542i 0.706133π-0.706133\pi
−0.603264 + 0.797542i 0.706133π0.706133\pi
308308 0 0
309309 0 0
310310 0 0
311311 8220.00 1.49876 0.749379 0.662142i 0.230352π-0.230352\pi
0.749379 + 0.662142i 0.230352π0.230352\pi
312312 0 0
313313 4660.00 0.841530 0.420765 0.907170i 0.361762π-0.361762\pi
0.420765 + 0.907170i 0.361762π0.361762\pi
314314 2020.00 0.363042
315315 0 0
316316 108.000 0.0192262
317317 −6817.00 −1.20783 −0.603913 0.797050i 0.706393π-0.706393\pi
−0.603913 + 0.797050i 0.706393π0.706393\pi
318318 0 0
319319 −2200.00 −0.386133
320320 0 0
321321 0 0
322322 0 0
323323 −791.000 −0.136261
324324 0 0
325325 0 0
326326 1180.00 0.200473
327327 0 0
328328 3120.00 0.525223
329329 0 0
330330 0 0
331331 192.000 0.0318830 0.0159415 0.999873i 0.494925π-0.494925\pi
0.0159415 + 0.999873i 0.494925π0.494925\pi
332332 −1716.00 −0.283668
333333 0 0
334334 −4806.00 −0.787343
335335 0 0
336336 0 0
337337 −4840.00 −0.782349 −0.391174 0.920317i 0.627931π-0.627931\pi
−0.391174 + 0.920317i 0.627931π0.627931\pi
338338 −8406.00 −1.35274
339339 0 0
340340 0 0
341341 1890.00 0.300144
342342 0 0
343343 0 0
344344 −240.000 −0.0376161
345345 0 0
346346 −1602.00 −0.248913
347347 −860.000 −0.133047 −0.0665234 0.997785i 0.521191π-0.521191\pi
−0.0665234 + 0.997785i 0.521191π0.521191\pi
348348 0 0
349349 5377.00 0.824711 0.412356 0.911023i 0.364706π-0.364706\pi
0.412356 + 0.911023i 0.364706π0.364706\pi
350350 0 0
351351 0 0
352352 1600.00 0.242274
353353 −8010.00 −1.20773 −0.603866 0.797086i 0.706374π-0.706374\pi
−0.603866 + 0.797086i 0.706374π0.706374\pi
354354 0 0
355355 0 0
356356 −3000.00 −0.446628
357357 0 0
358358 −4720.00 −0.696815
359359 −12930.0 −1.90089 −0.950445 0.310894i 0.899372π-0.899372\pi
−0.950445 + 0.310894i 0.899372π0.899372\pi
360360 0 0
361361 5910.00 0.861642
362362 −2482.00 −0.360362
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 6000.00 0.853399 0.426700 0.904393i 0.359676π-0.359676\pi
0.426700 + 0.904393i 0.359676π0.359676\pi
368368 1296.00 0.183583
369369 0 0
370370 0 0
371371 0 0
372372 0 0
373373 140.000 0.0194341 0.00971706 0.999953i 0.496907π-0.496907\pi
0.00971706 + 0.999953i 0.496907π0.496907\pi
374374 140.000 0.0193562
375375 0 0
376376 3840.00 0.526683
377377 17600.0 2.40437
378378 0 0
379379 6217.00 0.842601 0.421301 0.906921i 0.361574π-0.361574\pi
0.421301 + 0.906921i 0.361574π0.361574\pi
380380 0 0
381381 0 0
382382 −9980.00 −1.33670
383383 4551.00 0.607168 0.303584 0.952805i 0.401817π-0.401817\pi
0.303584 + 0.952805i 0.401817π0.401817\pi
384384 0 0
385385 0 0
386386 −4520.00 −0.596015
387387 0 0
388388 −5920.00 −0.774594
389389 2310.00 0.301084 0.150542 0.988604i 0.451898π-0.451898\pi
0.150542 + 0.988604i 0.451898π0.451898\pi
390390 0 0
391391 −567.000 −0.0733361
392392 −8232.00 −1.06066
393393 0 0
394394 4494.00 0.574631
395395 0 0
396396 0 0
397397 2900.00 0.366617 0.183308 0.983055i 0.441319π-0.441319\pi
0.183308 + 0.983055i 0.441319π0.441319\pi
398398 −9128.00 −1.14961
399399 0 0
400400 0 0
401401 −2250.00 −0.280199 −0.140099 0.990137i 0.544742π-0.544742\pi
−0.140099 + 0.990137i 0.544742π0.544742\pi
402402 0 0
403403 −15120.0 −1.86894
404404 −6000.00 −0.738889
405405 0 0
406406 0 0
407407 1700.00 0.207041
408408 0 0
409409 −11263.0 −1.36166 −0.680831 0.732441i 0.738381π-0.738381\pi
−0.680831 + 0.732441i 0.738381π0.738381\pi
410410 0 0
411411 0 0
412412 −1840.00 −0.220025
413413 0 0
414414 0 0
415415 0 0
416416 −12800.0 −1.50859
417417 0 0
418418 −2260.00 −0.264450
419419 6910.00 0.805670 0.402835 0.915273i 0.368025π-0.368025\pi
0.402835 + 0.915273i 0.368025π0.368025\pi
420420 0 0
421421 −5249.00 −0.607650 −0.303825 0.952728i 0.598264π-0.598264\pi
−0.303825 + 0.952728i 0.598264π0.598264\pi
422422 −9898.00 −1.14177
423423 0 0
424424 15144.0 1.73457
425425 0 0
426426 0 0
427427 0 0
428428 1680.00 0.189733
429429 0 0
430430 0 0
431431 11880.0 1.32770 0.663851 0.747865i 0.268921π-0.268921\pi
0.663851 + 0.747865i 0.268921π0.268921\pi
432432 0 0
433433 4280.00 0.475020 0.237510 0.971385i 0.423669π-0.423669\pi
0.237510 + 0.971385i 0.423669π0.423669\pi
434434 0 0
435435 0 0
436436 2428.00 0.266698
437437 9153.00 1.00194
438438 0 0
439439 6463.00 0.702647 0.351324 0.936254i 0.385732π-0.385732\pi
0.351324 + 0.936254i 0.385732π0.385732\pi
440440 0 0
441441 0 0
442442 −1120.00 −0.120527
443443 11721.0 1.25707 0.628534 0.777782i 0.283655π-0.283655\pi
0.628534 + 0.777782i 0.283655π0.283655\pi
444444 0 0
445445 0 0
446446 7780.00 0.825995
447447 0 0
448448 0 0
449449 2180.00 0.229133 0.114566 0.993416i 0.463452π-0.463452\pi
0.114566 + 0.993416i 0.463452π0.463452\pi
450450 0 0
451451 −1300.00 −0.135731
452452 −8680.00 −0.903259
453453 0 0
454454 −4906.00 −0.507159
455455 0 0
456456 0 0
457457 17840.0 1.82608 0.913042 0.407866i 0.133727π-0.133727\pi
0.913042 + 0.407866i 0.133727π0.133727\pi
458458 12426.0 1.26775
459459 0 0
460460 0 0
461461 2250.00 0.227317 0.113658 0.993520i 0.463743π-0.463743\pi
0.113658 + 0.993520i 0.463743π0.463743\pi
462462 0 0
463463 −1230.00 −0.123462 −0.0617310 0.998093i 0.519662π-0.519662\pi
−0.0617310 + 0.998093i 0.519662π0.519662\pi
464464 −3520.00 −0.352181
465465 0 0
466466 6900.00 0.685915
467467 5813.00 0.576003 0.288002 0.957630i 0.407009π-0.407009\pi
0.288002 + 0.957630i 0.407009π0.407009\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 13440.0 1.31065
473473 100.000 0.00972094
474474 0 0
475475 0 0
476476 0 0
477477 0 0
478478 12980.0 1.24203
479479 6750.00 0.643873 0.321937 0.946761i 0.395666π-0.395666\pi
0.321937 + 0.946761i 0.395666π0.395666\pi
480480 0 0
481481 −13600.0 −1.28920
482482 6802.00 0.642785
483483 0 0
484484 4924.00 0.462434
485485 0 0
486486 0 0
487487 6610.00 0.615047 0.307523 0.951541i 0.400500π-0.400500\pi
0.307523 + 0.951541i 0.400500π0.400500\pi
488488 5496.00 0.509820
489489 0 0
490490 0 0
491491 4990.00 0.458647 0.229323 0.973350i 0.426349π-0.426349\pi
0.229323 + 0.973350i 0.426349π0.426349\pi
492492 0 0
493493 1540.00 0.140686
494494 18080.0 1.64668
495495 0 0
496496 3024.00 0.273753
497497 0 0
498498 0 0
499499 1483.00 0.133042 0.0665212 0.997785i 0.478810π-0.478810\pi
0.0665212 + 0.997785i 0.478810π0.478810\pi
500500 0 0
501501 0 0
502502 −9960.00 −0.885531
503503 −11641.0 −1.03190 −0.515951 0.856618i 0.672561π-0.672561\pi
−0.515951 + 0.856618i 0.672561π0.672561\pi
504504 0 0
505505 0 0
506506 −1620.00 −0.142328
507507 0 0
508508 −6440.00 −0.562458
509509 −2620.00 −0.228152 −0.114076 0.993472i 0.536391π-0.536391\pi
−0.114076 + 0.993472i 0.536391π0.536391\pi
510510 0 0
511511 0 0
512512 5632.00 0.486136
513513 0 0
514514 −6714.00 −0.576151
515515 0 0
516516 0 0
517517 −1600.00 −0.136108
518518 0 0
519519 0 0
520520 0 0
521521 13690.0 1.15119 0.575595 0.817735i 0.304771π-0.304771\pi
0.575595 + 0.817735i 0.304771π0.304771\pi
522522 0 0
523523 10220.0 0.854473 0.427237 0.904140i 0.359487π-0.359487\pi
0.427237 + 0.904140i 0.359487π0.359487\pi
524524 9480.00 0.790335
525525 0 0
526526 9080.00 0.752675
527527 −1323.00 −0.109356
528528 0 0
529529 −5606.00 −0.460754
530530 0 0
531531 0 0
532532 0 0
533533 10400.0 0.845167
534534 0 0
535535 0 0
536536 −18000.0 −1.45053
537537 0 0
538538 16820.0 1.34788
539539 3430.00 0.274101
540540 0 0
541541 −2778.00 −0.220768 −0.110384 0.993889i 0.535208π-0.535208\pi
−0.110384 + 0.993889i 0.535208π0.535208\pi
542542 −518.000 −0.0410517
543543 0 0
544544 −1120.00 −0.0882713
545545 0 0
546546 0 0
547547 12830.0 1.00287 0.501436 0.865195i 0.332805π-0.332805\pi
0.501436 + 0.865195i 0.332805π0.332805\pi
548548 −7188.00 −0.560321
549549 0 0
550550 0 0
551551 −24860.0 −1.92209
552552 0 0
553553 0 0
554554 −8340.00 −0.639590
555555 0 0
556556 496.000 0.0378329
557557 −4950.00 −0.376550 −0.188275 0.982116i 0.560290π-0.560290\pi
−0.188275 + 0.982116i 0.560290π0.560290\pi
558558 0 0
559559 −800.000 −0.0605302
560560 0 0
561561 0 0
562562 −3480.00 −0.261201
563563 6540.00 0.489570 0.244785 0.969577i 0.421283π-0.421283\pi
0.244785 + 0.969577i 0.421283π0.421283\pi
564564 0 0
565565 0 0
566566 −10140.0 −0.753032
567567 0 0
568568 −21360.0 −1.57790
569569 15240.0 1.12284 0.561418 0.827532i 0.310256π-0.310256\pi
0.561418 + 0.827532i 0.310256π0.310256\pi
570570 0 0
571571 −5281.00 −0.387045 −0.193523 0.981096i 0.561991π-0.561991\pi
−0.193523 + 0.981096i 0.561991π0.561991\pi
572572 3200.00 0.233914
573573 0 0
574574 0 0
575575 0 0
576576 0 0
577577 10510.0 0.758296 0.379148 0.925336i 0.376217π-0.376217\pi
0.379148 + 0.925336i 0.376217π0.376217\pi
578578 9728.00 0.700054
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 −6310.00 −0.448256
584584 21360.0 1.51350
585585 0 0
586586 318.000 0.0224172
587587 4107.00 0.288780 0.144390 0.989521i 0.453878π-0.453878\pi
0.144390 + 0.989521i 0.453878π0.453878\pi
588588 0 0
589589 21357.0 1.49406
590590 0 0
591591 0 0
592592 2720.00 0.188837
593593 26129.0 1.80943 0.904713 0.426022i 0.140085π-0.140085\pi
0.904713 + 0.426022i 0.140085π0.140085\pi
594594 0 0
595595 0 0
596596 −280.000 −0.0192437
597597 0 0
598598 12960.0 0.886244
599599 4360.00 0.297404 0.148702 0.988882i 0.452491π-0.452491\pi
0.148702 + 0.988882i 0.452491π0.452491\pi
600600 0 0
601601 −16639.0 −1.12932 −0.564658 0.825325i 0.690992π-0.690992\pi
−0.564658 + 0.825325i 0.690992π0.690992\pi
602602 0 0
603603 0 0
604604 −8992.00 −0.605760
605605 0 0
606606 0 0
607607 −490.000 −0.0327652 −0.0163826 0.999866i 0.505215π-0.505215\pi
−0.0163826 + 0.999866i 0.505215π0.505215\pi
608608 18080.0 1.20599
609609 0 0
610610 0 0
611611 12800.0 0.847516
612612 0 0
613613 −18400.0 −1.21235 −0.606174 0.795332i 0.707296π-0.707296\pi
−0.606174 + 0.795332i 0.707296π0.707296\pi
614614 12980.0 0.853144
615615 0 0
616616 0 0
617617 7827.00 0.510702 0.255351 0.966848i 0.417809π-0.417809\pi
0.255351 + 0.966848i 0.417809π0.417809\pi
618618 0 0
619619 −19756.0 −1.28281 −0.641406 0.767202i 0.721649π-0.721649\pi
−0.641406 + 0.767202i 0.721649π0.721649\pi
620620 0 0
621621 0 0
622622 −16440.0 −1.05978
623623 0 0
624624 0 0
625625 0 0
626626 −9320.00 −0.595051
627627 0 0
628628 4040.00 0.256709
629629 −1190.00 −0.0754347
630630 0 0
631631 9829.00 0.620105 0.310053 0.950719i 0.399653π-0.399653\pi
0.310053 + 0.950719i 0.399653π0.399653\pi
632632 −648.000 −0.0407849
633633 0 0
634634 13634.0 0.854062
635635 0 0
636636 0 0
637637 −27440.0 −1.70677
638638 4400.00 0.273037
639639 0 0
640640 0 0
641641 6000.00 0.369713 0.184856 0.982766i 0.440818π-0.440818\pi
0.184856 + 0.982766i 0.440818π0.440818\pi
642642 0 0
643643 −8280.00 −0.507825 −0.253912 0.967227i 0.581717π-0.581717\pi
−0.253912 + 0.967227i 0.581717π0.581717\pi
644644 0 0
645645 0 0
646646 1582.00 0.0963513
647647 −16637.0 −1.01092 −0.505462 0.862849i 0.668678π-0.668678\pi
−0.505462 + 0.862849i 0.668678π0.668678\pi
648648 0 0
649649 −5600.00 −0.338705
650650 0 0
651651 0 0
652652 2360.00 0.141756
653653 19751.0 1.18364 0.591820 0.806070i 0.298410π-0.298410\pi
0.591820 + 0.806070i 0.298410π0.298410\pi
654654 0 0
655655 0 0
656656 −2080.00 −0.123796
657657 0 0
658658 0 0
659659 −14260.0 −0.842930 −0.421465 0.906845i 0.638484π-0.638484\pi
−0.421465 + 0.906845i 0.638484π0.638484\pi
660660 0 0
661661 22318.0 1.31327 0.656634 0.754210i 0.271980π-0.271980\pi
0.656634 + 0.754210i 0.271980π0.271980\pi
662662 −384.000 −0.0225447
663663 0 0
664664 10296.0 0.601750
665665 0 0
666666 0 0
667667 −17820.0 −1.03447
668668 −9612.00 −0.556736
669669 0 0
670670 0 0
671671 −2290.00 −0.131750
672672 0 0
673673 −20040.0 −1.14782 −0.573912 0.818917i 0.694575π-0.694575\pi
−0.573912 + 0.818917i 0.694575π0.694575\pi
674674 9680.00 0.553204
675675 0 0
676676 −16812.0 −0.956532
677677 −2310.00 −0.131138 −0.0655691 0.997848i 0.520886π-0.520886\pi
−0.0655691 + 0.997848i 0.520886π0.520886\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 −3780.00 −0.212234
683683 −26739.0 −1.49801 −0.749004 0.662566i 0.769468π-0.769468\pi
−0.749004 + 0.662566i 0.769468π0.769468\pi
684684 0 0
685685 0 0
686686 0 0
687687 0 0
688688 160.000 0.00886620
689689 50480.0 2.79120
690690 0 0
691691 5101.00 0.280827 0.140413 0.990093i 0.455157π-0.455157\pi
0.140413 + 0.990093i 0.455157π0.455157\pi
692692 −3204.00 −0.176008
693693 0 0
694694 1720.00 0.0940783
695695 0 0
696696 0 0
697697 910.000 0.0494530
698698 −10754.0 −0.583159
699699 0 0
700700 0 0
701701 −26030.0 −1.40248 −0.701241 0.712925i 0.747370π-0.747370\pi
−0.701241 + 0.712925i 0.747370π0.747370\pi
702702 0 0
703703 19210.0 1.03061
704704 −4480.00 −0.239839
705705 0 0
706706 16020.0 0.853995
707707 0 0
708708 0 0
709709 −3854.00 −0.204147 −0.102073 0.994777i 0.532548π-0.532548\pi
−0.102073 + 0.994777i 0.532548π0.532548\pi
710710 0 0
711711 0 0
712712 18000.0 0.947442
713713 15309.0 0.804105
714714 0 0
715715 0 0
716716 −9440.00 −0.492723
717717 0 0
718718 25860.0 1.34413
719719 870.000 0.0451259 0.0225630 0.999745i 0.492817π-0.492817\pi
0.0225630 + 0.999745i 0.492817π0.492817\pi
720720 0 0
721721 0 0
722722 −11820.0 −0.609273
723723 0 0
724724 −4964.00 −0.254814
725725 0 0
726726 0 0
727727 −35780.0 −1.82532 −0.912659 0.408721i 0.865975π-0.865975\pi
−0.912659 + 0.408721i 0.865975π0.865975\pi
728728 0 0
729729 0 0
730730 0 0
731731 −70.0000 −0.00354178
732732 0 0
733733 3400.00 0.171326 0.0856629 0.996324i 0.472699π-0.472699\pi
0.0856629 + 0.996324i 0.472699π0.472699\pi
734734 −12000.0 −0.603444
735735 0 0
736736 12960.0 0.649065
737737 7500.00 0.374852
738738 0 0
739739 −683.000 −0.0339981 −0.0169990 0.999856i 0.505411π-0.505411\pi
−0.0169990 + 0.999856i 0.505411π0.505411\pi
740740 0 0
741741 0 0
742742 0 0
743743 −13400.0 −0.661640 −0.330820 0.943694i 0.607325π-0.607325\pi
−0.330820 + 0.943694i 0.607325π0.607325\pi
744744 0 0
745745 0 0
746746 −280.000 −0.0137420
747747 0 0
748748 280.000 0.0136869
749749 0 0
750750 0 0
751751 −23219.0 −1.12819 −0.564097 0.825709i 0.690776π-0.690776\pi
−0.564097 + 0.825709i 0.690776π0.690776\pi
752752 −2560.00 −0.124140
753753 0 0
754754 −35200.0 −1.70014
755755 0 0
756756 0 0
757757 −19630.0 −0.942489 −0.471245 0.882003i 0.656195π-0.656195\pi
−0.471245 + 0.882003i 0.656195π0.656195\pi
758758 −12434.0 −0.595809
759759 0 0
760760 0 0
761761 −2940.00 −0.140046 −0.0700229 0.997545i 0.522307π-0.522307\pi
−0.0700229 + 0.997545i 0.522307π0.522307\pi
762762 0 0
763763 0 0
764764 −19960.0 −0.945193
765765 0 0
766766 −9102.00 −0.429332
767767 44800.0 2.10904
768768 0 0
769769 −13987.0 −0.655896 −0.327948 0.944696i 0.606357π-0.606357\pi
−0.327948 + 0.944696i 0.606357π0.606357\pi
770770 0 0
771771 0 0
772772 −9040.00 −0.421447
773773 19839.0 0.923104 0.461552 0.887113i 0.347293π-0.347293\pi
0.461552 + 0.887113i 0.347293π0.347293\pi
774774 0 0
775775 0 0
776776 35520.0 1.64316
777777 0 0
778778 −4620.00 −0.212898
779779 −14690.0 −0.675640
780780 0 0
781781 8900.00 0.407768
782782 1134.00 0.0518565
783783 0 0
784784 5488.00 0.250000
785785 0 0
786786 0 0
787787 38390.0 1.73883 0.869413 0.494086i 0.164497π-0.164497\pi
0.869413 + 0.494086i 0.164497π0.164497\pi
788788 8988.00 0.406325
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 18320.0 0.820381
794794 −5800.00 −0.259237
795795 0 0
796796 −18256.0 −0.812898
797797 −28027.0 −1.24563 −0.622815 0.782369i 0.714011π-0.714011\pi
−0.622815 + 0.782369i 0.714011π0.714011\pi
798798 0 0
799799 1120.00 0.0495904
800800 0 0
801801 0 0
802802 4500.00 0.198130
803803 −8900.00 −0.391126
804804 0 0
805805 0 0
806806 30240.0 1.32154
807807 0 0
808808 36000.0 1.56742
809809 −8630.00 −0.375049 −0.187525 0.982260i 0.560046π-0.560046\pi
−0.187525 + 0.982260i 0.560046π0.560046\pi
810810 0 0
811811 −1932.00 −0.0836519 −0.0418260 0.999125i 0.513317π-0.513317\pi
−0.0418260 + 0.999125i 0.513317π0.513317\pi
812812 0 0
813813 0 0
814814 −3400.00 −0.146400
815815 0 0
816816 0 0
817817 1130.00 0.0483889
818818 22526.0 0.962840
819819 0 0
820820 0 0
821821 18090.0 0.768996 0.384498 0.923126i 0.374375π-0.374375\pi
0.384498 + 0.923126i 0.374375π0.374375\pi
822822 0 0
823823 −12890.0 −0.545950 −0.272975 0.962021i 0.588008π-0.588008\pi
−0.272975 + 0.962021i 0.588008π0.588008\pi
824824 11040.0 0.466743
825825 0 0
826826 0 0
827827 14887.0 0.625963 0.312982 0.949759i 0.398672π-0.398672\pi
0.312982 + 0.949759i 0.398672π0.398672\pi
828828 0 0
829829 12666.0 0.530649 0.265325 0.964159i 0.414521π-0.414521\pi
0.265325 + 0.964159i 0.414521π0.414521\pi
830830 0 0
831831 0 0
832832 35840.0 1.49342
833833 −2401.00 −0.0998676
834834 0 0
835835 0 0
836836 −4520.00 −0.186995
837837 0 0
838838 −13820.0 −0.569694
839839 −43820.0 −1.80314 −0.901570 0.432633i 0.857584π-0.857584\pi
−0.901570 + 0.432633i 0.857584π0.857584\pi
840840 0 0
841841 24011.0 0.984501
842842 10498.0 0.429673
843843 0 0
844844 −19796.0 −0.807354
845845 0 0
846846 0 0
847847 0 0
848848 −10096.0 −0.408842
849849 0 0
850850 0 0
851851 13770.0 0.554676
852852 0 0
853853 −19320.0 −0.775503 −0.387752 0.921764i 0.626748π-0.626748\pi
−0.387752 + 0.921764i 0.626748π0.626748\pi
854854 0 0
855855 0 0
856856 −10080.0 −0.402485
857857 −3653.00 −0.145606 −0.0728029 0.997346i 0.523194π-0.523194\pi
−0.0728029 + 0.997346i 0.523194π0.523194\pi
858858 0 0
859859 24373.0 0.968098 0.484049 0.875041i 0.339166π-0.339166\pi
0.484049 + 0.875041i 0.339166π0.339166\pi
860860 0 0
861861 0 0
862862 −23760.0 −0.938827
863863 −17629.0 −0.695363 −0.347681 0.937613i 0.613031π-0.613031\pi
−0.347681 + 0.937613i 0.613031π0.613031\pi
864864 0 0
865865 0 0
866866 −8560.00 −0.335890
867867 0 0
868868 0 0
869869 270.000 0.0105398
870870 0 0
871871 −60000.0 −2.33412
872872 −14568.0 −0.565751
873873 0 0
874874 −18306.0 −0.708478
875875 0 0
876876 0 0
877877 21210.0 0.816660 0.408330 0.912834i 0.366111π-0.366111\pi
0.408330 + 0.912834i 0.366111π0.366111\pi
878878 −12926.0 −0.496847
879879 0 0
880880 0 0
881881 −39340.0 −1.50442 −0.752212 0.658921i 0.771013π-0.771013\pi
−0.752212 + 0.658921i 0.771013π0.771013\pi
882882 0 0
883883 4240.00 0.161594 0.0807969 0.996731i 0.474253π-0.474253\pi
0.0807969 + 0.996731i 0.474253π0.474253\pi
884884 −2240.00 −0.0852255
885885 0 0
886886 −23442.0 −0.888882
887887 −15933.0 −0.603132 −0.301566 0.953445i 0.597509π-0.597509\pi
−0.301566 + 0.953445i 0.597509π0.597509\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 15560.0 0.584067
893893 −18080.0 −0.677519
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 −4360.00 −0.162021
899899 −41580.0 −1.54257
900900 0 0
901901 4417.00 0.163320
902902 2600.00 0.0959762
903903 0 0
904904 52080.0 1.91610
905905 0 0
906906 0 0
907907 6780.00 0.248210 0.124105 0.992269i 0.460394π-0.460394\pi
0.124105 + 0.992269i 0.460394π0.460394\pi
908908 −9812.00 −0.358615
909909 0 0
910910 0 0
911911 24740.0 0.899751 0.449875 0.893091i 0.351468π-0.351468\pi
0.449875 + 0.893091i 0.351468π0.351468\pi
912912 0 0
913913 −4290.00 −0.155507
914914 −35680.0 −1.29124
915915 0 0
916916 24852.0 0.896434
917917 0 0
918918 0 0
919919 −48344.0 −1.73528 −0.867640 0.497194i 0.834364π-0.834364\pi
−0.867640 + 0.497194i 0.834364π0.834364\pi
920920 0 0
921921 0 0
922922 −4500.00 −0.160737
923923 −71200.0 −2.53909
924924 0 0
925925 0 0
926926 2460.00 0.0873009
927927 0 0
928928 −35200.0 −1.24515
929929 29650.0 1.04713 0.523566 0.851985i 0.324601π-0.324601\pi
0.523566 + 0.851985i 0.324601π0.324601\pi
930930 0 0
931931 38759.0 1.36442
932932 13800.0 0.485015
933933 0 0
934934 −11626.0 −0.407296
935935 0 0
936936 0 0
937937 −10260.0 −0.357716 −0.178858 0.983875i 0.557240π-0.557240\pi
−0.178858 + 0.983875i 0.557240π0.557240\pi
938938 0 0
939939 0 0
940940 0 0
941941 16270.0 0.563642 0.281821 0.959467i 0.409062π-0.409062\pi
0.281821 + 0.959467i 0.409062π0.409062\pi
942942 0 0
943943 −10530.0 −0.363631
944944 −8960.00 −0.308923
945945 0 0
946946 −200.000 −0.00687374
947947 −23103.0 −0.792763 −0.396382 0.918086i 0.629734π-0.629734\pi
−0.396382 + 0.918086i 0.629734π0.629734\pi
948948 0 0
949949 71200.0 2.43546
950950 0 0
951951 0 0
952952 0 0
953953 −32090.0 −1.09076 −0.545381 0.838188i 0.683615π-0.683615\pi
−0.545381 + 0.838188i 0.683615π0.683615\pi
954954 0 0
955955 0 0
956956 25960.0 0.878249
957957 0 0
958958 −13500.0 −0.455287
959959 0 0
960960 0 0
961961 5930.00 0.199053
962962 27200.0 0.911604
963963 0 0
964964 13604.0 0.454518
965965 0 0
966966 0 0
967967 42010.0 1.39705 0.698527 0.715584i 0.253839π-0.253839\pi
0.698527 + 0.715584i 0.253839π0.253839\pi
968968 −29544.0 −0.980971
969969 0 0
970970 0 0
971971 −17490.0 −0.578044 −0.289022 0.957322i 0.593330π-0.593330\pi
−0.289022 + 0.957322i 0.593330π0.593330\pi
972972 0 0
973973 0 0
974974 −13220.0 −0.434904
975975 0 0
976976 −3664.00 −0.120166
977977 −22130.0 −0.724669 −0.362334 0.932048i 0.618020π-0.618020\pi
−0.362334 + 0.932048i 0.618020π0.618020\pi
978978 0 0
979979 −7500.00 −0.244843
980980 0 0
981981 0 0
982982 −9980.00 −0.324312
983983 40959.0 1.32898 0.664491 0.747296i 0.268648π-0.268648\pi
0.664491 + 0.747296i 0.268648π0.268648\pi
984984 0 0
985985 0 0
986986 −3080.00 −0.0994799
987987 0 0
988988 36160.0 1.16438
989989 810.000 0.0260430
990990 0 0
991991 61169.0 1.96074 0.980372 0.197157i 0.0631707π-0.0631707\pi
0.980372 + 0.197157i 0.0631707π0.0631707\pi
992992 30240.0 0.967864
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 −26190.0 −0.831941 −0.415971 0.909378i 0.636558π-0.636558\pi
−0.415971 + 0.909378i 0.636558π0.636558\pi
998998 −2966.00 −0.0940752
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 675.4.a.b.1.1 1
3.2 odd 2 675.4.a.i.1.1 1
5.2 odd 4 675.4.b.c.649.1 2
5.3 odd 4 675.4.b.c.649.2 2
5.4 even 2 135.4.a.d.1.1 yes 1
15.2 even 4 675.4.b.d.649.2 2
15.8 even 4 675.4.b.d.649.1 2
15.14 odd 2 135.4.a.a.1.1 1
20.19 odd 2 2160.4.a.d.1.1 1
45.4 even 6 405.4.e.e.136.1 2
45.14 odd 6 405.4.e.j.136.1 2
45.29 odd 6 405.4.e.j.271.1 2
45.34 even 6 405.4.e.e.271.1 2
60.59 even 2 2160.4.a.n.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
135.4.a.a.1.1 1 15.14 odd 2
135.4.a.d.1.1 yes 1 5.4 even 2
405.4.e.e.136.1 2 45.4 even 6
405.4.e.e.271.1 2 45.34 even 6
405.4.e.j.136.1 2 45.14 odd 6
405.4.e.j.271.1 2 45.29 odd 6
675.4.a.b.1.1 1 1.1 even 1 trivial
675.4.a.i.1.1 1 3.2 odd 2
675.4.b.c.649.1 2 5.2 odd 4
675.4.b.c.649.2 2 5.3 odd 4
675.4.b.d.649.1 2 15.8 even 4
675.4.b.d.649.2 2 15.2 even 4
2160.4.a.d.1.1 1 20.19 odd 2
2160.4.a.n.1.1 1 60.59 even 2