Properties

Label 784.6.a.i.1.1
Level 784784
Weight 66
Character 784.1
Self dual yes
Analytic conductor 125.741125.741
Analytic rank 11
Dimension 11
CM no
Inner twists 11

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,6,Mod(1,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 784=2472 784 = 2^{4} \cdot 7^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 784.a (trivial)

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: yes
Analytic conductor: 125.740914733125.740914733
Analytic rank: 11
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 14)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 784.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+10.0000q384.0000q5143.000q9+336.000q11584.000q13840.000q15+1458.00q17+470.000q19+4200.00q23+3931.00q253860.00q27+4866.00q297372.00q31+3360.00q33+14330.0q375840.00q396222.00q413704.00q43+12012.0q451812.00q47+14580.0q5137242.0q5328224.0q55+4700.00q57+34302.0q5924476.0q61+49056.0q65+17452.0q67+42000.0q6928224.0q713602.00q73+39310.0q7542872.0q793851.00q8135202.0q83122472.q85+48660.0q8726730.0q8973720.0q9339480.0q95+16978.0q9748048.0q99+O(q100)q+10.0000 q^{3} -84.0000 q^{5} -143.000 q^{9} +336.000 q^{11} -584.000 q^{13} -840.000 q^{15} +1458.00 q^{17} +470.000 q^{19} +4200.00 q^{23} +3931.00 q^{25} -3860.00 q^{27} +4866.00 q^{29} -7372.00 q^{31} +3360.00 q^{33} +14330.0 q^{37} -5840.00 q^{39} -6222.00 q^{41} -3704.00 q^{43} +12012.0 q^{45} -1812.00 q^{47} +14580.0 q^{51} -37242.0 q^{53} -28224.0 q^{55} +4700.00 q^{57} +34302.0 q^{59} -24476.0 q^{61} +49056.0 q^{65} +17452.0 q^{67} +42000.0 q^{69} -28224.0 q^{71} -3602.00 q^{73} +39310.0 q^{75} -42872.0 q^{79} -3851.00 q^{81} -35202.0 q^{83} -122472. q^{85} +48660.0 q^{87} -26730.0 q^{89} -73720.0 q^{93} -39480.0 q^{95} +16978.0 q^{97} -48048.0 q^{99} +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 0 0
33 10.0000 0.641500 0.320750 0.947164i 0.396065π-0.396065\pi
0.320750 + 0.947164i 0.396065π0.396065\pi
44 0 0
55 −84.0000 −1.50264 −0.751319 0.659939i 0.770582π-0.770582\pi
−0.751319 + 0.659939i 0.770582π0.770582\pi
66 0 0
77 0 0
88 0 0
99 −143.000 −0.588477
1010 0 0
1111 336.000 0.837255 0.418627 0.908158i 0.362511π-0.362511\pi
0.418627 + 0.908158i 0.362511π0.362511\pi
1212 0 0
1313 −584.000 −0.958417 −0.479208 0.877701i 0.659076π-0.659076\pi
−0.479208 + 0.877701i 0.659076π0.659076\pi
1414 0 0
1515 −840.000 −0.963943
1616 0 0
1717 1458.00 1.22359 0.611794 0.791017i 0.290448π-0.290448\pi
0.611794 + 0.791017i 0.290448π0.290448\pi
1818 0 0
1919 470.000 0.298685 0.149343 0.988786i 0.452284π-0.452284\pi
0.149343 + 0.988786i 0.452284π0.452284\pi
2020 0 0
2121 0 0
2222 0 0
2323 4200.00 1.65550 0.827751 0.561096i 0.189620π-0.189620\pi
0.827751 + 0.561096i 0.189620π0.189620\pi
2424 0 0
2525 3931.00 1.25792
2626 0 0
2727 −3860.00 −1.01901
2828 0 0
2929 4866.00 1.07443 0.537214 0.843446i 0.319477π-0.319477\pi
0.537214 + 0.843446i 0.319477π0.319477\pi
3030 0 0
3131 −7372.00 −1.37778 −0.688892 0.724864i 0.741903π-0.741903\pi
−0.688892 + 0.724864i 0.741903π0.741903\pi
3232 0 0
3333 3360.00 0.537099
3434 0 0
3535 0 0
3636 0 0
3737 14330.0 1.72085 0.860423 0.509581i 0.170200π-0.170200\pi
0.860423 + 0.509581i 0.170200π0.170200\pi
3838 0 0
3939 −5840.00 −0.614825
4040 0 0
4141 −6222.00 −0.578057 −0.289028 0.957321i 0.593332π-0.593332\pi
−0.289028 + 0.957321i 0.593332π0.593332\pi
4242 0 0
4343 −3704.00 −0.305492 −0.152746 0.988265i 0.548812π-0.548812\pi
−0.152746 + 0.988265i 0.548812π0.548812\pi
4444 0 0
4545 12012.0 0.884268
4646 0 0
4747 −1812.00 −0.119650 −0.0598251 0.998209i 0.519054π-0.519054\pi
−0.0598251 + 0.998209i 0.519054π0.519054\pi
4848 0 0
4949 0 0
5050 0 0
5151 14580.0 0.784932
5252 0 0
5353 −37242.0 −1.82114 −0.910570 0.413355i 0.864357π-0.864357\pi
−0.910570 + 0.413355i 0.864357π0.864357\pi
5454 0 0
5555 −28224.0 −1.25809
5656 0 0
5757 4700.00 0.191607
5858 0 0
5959 34302.0 1.28289 0.641445 0.767169i 0.278335π-0.278335\pi
0.641445 + 0.767169i 0.278335π0.278335\pi
6060 0 0
6161 −24476.0 −0.842201 −0.421101 0.907014i 0.638356π-0.638356\pi
−0.421101 + 0.907014i 0.638356π0.638356\pi
6262 0 0
6363 0 0
6464 0 0
6565 49056.0 1.44015
6666 0 0
6767 17452.0 0.474961 0.237481 0.971392i 0.423678π-0.423678\pi
0.237481 + 0.971392i 0.423678π0.423678\pi
6868 0 0
6969 42000.0 1.06201
7070 0 0
7171 −28224.0 −0.664466 −0.332233 0.943197i 0.607802π-0.607802\pi
−0.332233 + 0.943197i 0.607802π0.607802\pi
7272 0 0
7373 −3602.00 −0.0791109 −0.0395555 0.999217i 0.512594π-0.512594\pi
−0.0395555 + 0.999217i 0.512594π0.512594\pi
7474 0 0
7575 39310.0 0.806956
7676 0 0
7777 0 0
7878 0 0
7979 −42872.0 −0.772869 −0.386435 0.922317i 0.626294π-0.626294\pi
−0.386435 + 0.922317i 0.626294π0.626294\pi
8080 0 0
8181 −3851.00 −0.0652170
8282 0 0
8383 −35202.0 −0.560883 −0.280441 0.959871i 0.590481π-0.590481\pi
−0.280441 + 0.959871i 0.590481π0.590481\pi
8484 0 0
8585 −122472. −1.83861
8686 0 0
8787 48660.0 0.689246
8888 0 0
8989 −26730.0 −0.357704 −0.178852 0.983876i 0.557238π-0.557238\pi
−0.178852 + 0.983876i 0.557238π0.557238\pi
9090 0 0
9191 0 0
9292 0 0
9393 −73720.0 −0.883849
9494 0 0
9595 −39480.0 −0.448816
9696 0 0
9797 16978.0 0.183213 0.0916067 0.995795i 0.470800π-0.470800\pi
0.0916067 + 0.995795i 0.470800π0.470800\pi
9898 0 0
9999 −48048.0 −0.492705
100100 0 0
101101 −99204.0 −0.967667 −0.483833 0.875160i 0.660756π-0.660756\pi
−0.483833 + 0.875160i 0.660756π0.660756\pi
102102 0 0
103103 −131644. −1.22267 −0.611333 0.791373i 0.709366π-0.709366\pi
−0.611333 + 0.791373i 0.709366π0.709366\pi
104104 0 0
105105 0 0
106106 0 0
107107 −48852.0 −0.412499 −0.206250 0.978499i 0.566126π-0.566126\pi
−0.206250 + 0.978499i 0.566126π0.566126\pi
108108 0 0
109109 −56374.0 −0.454478 −0.227239 0.973839i 0.572970π-0.572970\pi
−0.227239 + 0.973839i 0.572970π0.572970\pi
110110 0 0
111111 143300. 1.10392
112112 0 0
113113 8742.00 0.0644043 0.0322021 0.999481i 0.489748π-0.489748\pi
0.0322021 + 0.999481i 0.489748π0.489748\pi
114114 0 0
115115 −352800. −2.48762
116116 0 0
117117 83512.0 0.564007
118118 0 0
119119 0 0
120120 0 0
121121 −48155.0 −0.299005
122122 0 0
123123 −62220.0 −0.370823
124124 0 0
125125 −67704.0 −0.387560
126126 0 0
127127 −315992. −1.73847 −0.869234 0.494401i 0.835388π-0.835388\pi
−0.869234 + 0.494401i 0.835388π0.835388\pi
128128 0 0
129129 −37040.0 −0.195973
130130 0 0
131131 −24666.0 −0.125580 −0.0627900 0.998027i 0.520000π-0.520000\pi
−0.0627900 + 0.998027i 0.520000π0.520000\pi
132132 0 0
133133 0 0
134134 0 0
135135 324240. 1.53120
136136 0 0
137137 303234. 1.38031 0.690155 0.723662i 0.257542π-0.257542\pi
0.690155 + 0.723662i 0.257542π0.257542\pi
138138 0 0
139139 250586. 1.10007 0.550034 0.835142i 0.314615π-0.314615\pi
0.550034 + 0.835142i 0.314615π0.314615\pi
140140 0 0
141141 −18120.0 −0.0767557
142142 0 0
143143 −196224. −0.802439
144144 0 0
145145 −408744. −1.61448
146146 0 0
147147 0 0
148148 0 0
149149 −60594.0 −0.223596 −0.111798 0.993731i 0.535661π-0.535661\pi
−0.111798 + 0.993731i 0.535661π0.535661\pi
150150 0 0
151151 −124448. −0.444166 −0.222083 0.975028i 0.571286π-0.571286\pi
−0.222083 + 0.975028i 0.571286π0.571286\pi
152152 0 0
153153 −208494. −0.720054
154154 0 0
155155 619248. 2.07031
156156 0 0
157157 −76040.0 −0.246203 −0.123101 0.992394i 0.539284π-0.539284\pi
−0.123101 + 0.992394i 0.539284π0.539284\pi
158158 0 0
159159 −372420. −1.16826
160160 0 0
161161 0 0
162162 0 0
163163 −124256. −0.366310 −0.183155 0.983084i 0.558631π-0.558631\pi
−0.183155 + 0.983084i 0.558631π0.558631\pi
164164 0 0
165165 −282240. −0.807065
166166 0 0
167167 −72420.0 −0.200940 −0.100470 0.994940i 0.532035π-0.532035\pi
−0.100470 + 0.994940i 0.532035π0.532035\pi
168168 0 0
169169 −30237.0 −0.0814370
170170 0 0
171171 −67210.0 −0.175770
172172 0 0
173173 441552. 1.12167 0.560837 0.827926i 0.310479π-0.310479\pi
0.560837 + 0.827926i 0.310479π0.310479\pi
174174 0 0
175175 0 0
176176 0 0
177177 343020. 0.822974
178178 0 0
179179 10692.0 0.0249417 0.0124709 0.999922i 0.496030π-0.496030\pi
0.0124709 + 0.999922i 0.496030π0.496030\pi
180180 0 0
181181 546064. 1.23893 0.619465 0.785024i 0.287349π-0.287349\pi
0.619465 + 0.785024i 0.287349π0.287349\pi
182182 0 0
183183 −244760. −0.540272
184184 0 0
185185 −1.20372e6 −2.58581
186186 0 0
187187 489888. 1.02445
188188 0 0
189189 0 0
190190 0 0
191191 575976. 1.14241 0.571204 0.820808i 0.306477π-0.306477\pi
0.571204 + 0.820808i 0.306477π0.306477\pi
192192 0 0
193193 −413938. −0.799912 −0.399956 0.916534i 0.630975π-0.630975\pi
−0.399956 + 0.916534i 0.630975π0.630975\pi
194194 0 0
195195 490560. 0.923859
196196 0 0
197197 −494946. −0.908641 −0.454320 0.890838i 0.650118π-0.650118\pi
−0.454320 + 0.890838i 0.650118π0.650118\pi
198198 0 0
199199 520364. 0.931482 0.465741 0.884921i 0.345788π-0.345788\pi
0.465741 + 0.884921i 0.345788π0.345788\pi
200200 0 0
201201 174520. 0.304688
202202 0 0
203203 0 0
204204 0 0
205205 522648. 0.868610
206206 0 0
207207 −600600. −0.974225
208208 0 0
209209 157920. 0.250076
210210 0 0
211211 −183284. −0.283412 −0.141706 0.989909i 0.545259π-0.545259\pi
−0.141706 + 0.989909i 0.545259π0.545259\pi
212212 0 0
213213 −282240. −0.426255
214214 0 0
215215 311136. 0.459044
216216 0 0
217217 0 0
218218 0 0
219219 −36020.0 −0.0507497
220220 0 0
221221 −851472. −1.17271
222222 0 0
223223 −1.27746e6 −1.72023 −0.860115 0.510100i 0.829608π-0.829608\pi
−0.860115 + 0.510100i 0.829608π0.829608\pi
224224 0 0
225225 −562133. −0.740257
226226 0 0
227227 −1.28764e6 −1.65856 −0.829279 0.558835i 0.811248π-0.811248\pi
−0.829279 + 0.558835i 0.811248π0.811248\pi
228228 0 0
229229 −350936. −0.442221 −0.221110 0.975249i 0.570968π-0.570968\pi
−0.221110 + 0.975249i 0.570968π0.570968\pi
230230 0 0
231231 0 0
232232 0 0
233233 836154. 1.00901 0.504506 0.863408i 0.331675π-0.331675\pi
0.504506 + 0.863408i 0.331675π0.331675\pi
234234 0 0
235235 152208. 0.179791
236236 0 0
237237 −428720. −0.495796
238238 0 0
239239 −774336. −0.876869 −0.438434 0.898763i 0.644467π-0.644467\pi
−0.438434 + 0.898763i 0.644467π0.644467\pi
240240 0 0
241241 1.15285e6 1.27859 0.639293 0.768963i 0.279227π-0.279227\pi
0.639293 + 0.768963i 0.279227π0.279227\pi
242242 0 0
243243 899470. 0.977172
244244 0 0
245245 0 0
246246 0 0
247247 −274480. −0.286265
248248 0 0
249249 −352020. −0.359806
250250 0 0
251251 1.35801e6 1.36056 0.680282 0.732951i 0.261858π-0.261858\pi
0.680282 + 0.732951i 0.261858π0.261858\pi
252252 0 0
253253 1.41120e6 1.38608
254254 0 0
255255 −1.22472e6 −1.17947
256256 0 0
257257 317742. 0.300083 0.150042 0.988680i 0.452059π-0.452059\pi
0.150042 + 0.988680i 0.452059π0.452059\pi
258258 0 0
259259 0 0
260260 0 0
261261 −695838. −0.632276
262262 0 0
263263 −1.05101e6 −0.936951 −0.468475 0.883477i 0.655196π-0.655196\pi
−0.468475 + 0.883477i 0.655196π0.655196\pi
264264 0 0
265265 3.12833e6 2.73651
266266 0 0
267267 −267300. −0.229467
268268 0 0
269269 −1.18958e6 −1.00234 −0.501169 0.865349i 0.667097π-0.667097\pi
−0.501169 + 0.865349i 0.667097π0.667097\pi
270270 0 0
271271 −1.43008e6 −1.18287 −0.591435 0.806353i 0.701438π-0.701438\pi
−0.591435 + 0.806353i 0.701438π0.701438\pi
272272 0 0
273273 0 0
274274 0 0
275275 1.32082e6 1.05320
276276 0 0
277277 63302.0 0.0495699 0.0247849 0.999693i 0.492110π-0.492110\pi
0.0247849 + 0.999693i 0.492110π0.492110\pi
278278 0 0
279279 1.05420e6 0.810795
280280 0 0
281281 −496614. −0.375192 −0.187596 0.982246i 0.560070π-0.560070\pi
−0.187596 + 0.982246i 0.560070π0.560070\pi
282282 0 0
283283 −1.15842e6 −0.859803 −0.429902 0.902876i 0.641452π-0.641452\pi
−0.429902 + 0.902876i 0.641452π0.641452\pi
284284 0 0
285285 −394800. −0.287915
286286 0 0
287287 0 0
288288 0 0
289289 705907. 0.497168
290290 0 0
291291 169780. 0.117531
292292 0 0
293293 −1.43886e6 −0.979151 −0.489575 0.871961i 0.662848π-0.662848\pi
−0.489575 + 0.871961i 0.662848π0.662848\pi
294294 0 0
295295 −2.88137e6 −1.92772
296296 0 0
297297 −1.29696e6 −0.853170
298298 0 0
299299 −2.45280e6 −1.58666
300300 0 0
301301 0 0
302302 0 0
303303 −992040. −0.620758
304304 0 0
305305 2.05598e6 1.26552
306306 0 0
307307 −989098. −0.598954 −0.299477 0.954104i 0.596812π-0.596812\pi
−0.299477 + 0.954104i 0.596812π0.596812\pi
308308 0 0
309309 −1.31644e6 −0.784341
310310 0 0
311311 −2.22050e6 −1.30182 −0.650909 0.759155i 0.725612π-0.725612\pi
−0.650909 + 0.759155i 0.725612π0.725612\pi
312312 0 0
313313 −2.33008e6 −1.34434 −0.672171 0.740396i 0.734638π-0.734638\pi
−0.672171 + 0.740396i 0.734638π0.734638\pi
314314 0 0
315315 0 0
316316 0 0
317317 427542. 0.238963 0.119481 0.992836i 0.461877π-0.461877\pi
0.119481 + 0.992836i 0.461877π0.461877\pi
318318 0 0
319319 1.63498e6 0.899569
320320 0 0
321321 −488520. −0.264618
322322 0 0
323323 685260. 0.365468
324324 0 0
325325 −2.29570e6 −1.20561
326326 0 0
327327 −563740. −0.291548
328328 0 0
329329 0 0
330330 0 0
331331 396616. 0.198976 0.0994879 0.995039i 0.468280π-0.468280\pi
0.0994879 + 0.995039i 0.468280π0.468280\pi
332332 0 0
333333 −2.04919e6 −1.01268
334334 0 0
335335 −1.46597e6 −0.713695
336336 0 0
337337 −3.21819e6 −1.54361 −0.771805 0.635860i 0.780646π-0.780646\pi
−0.771805 + 0.635860i 0.780646π0.780646\pi
338338 0 0
339339 87420.0 0.0413154
340340 0 0
341341 −2.47699e6 −1.15356
342342 0 0
343343 0 0
344344 0 0
345345 −3.52800e6 −1.59581
346346 0 0
347347 −2.78018e6 −1.23951 −0.619755 0.784796i 0.712768π-0.712768\pi
−0.619755 + 0.784796i 0.712768π0.712768\pi
348348 0 0
349349 338800. 0.148895 0.0744475 0.997225i 0.476281π-0.476281\pi
0.0744475 + 0.997225i 0.476281π0.476281\pi
350350 0 0
351351 2.25424e6 0.976635
352352 0 0
353353 362046. 0.154642 0.0773209 0.997006i 0.475363π-0.475363\pi
0.0773209 + 0.997006i 0.475363π0.475363\pi
354354 0 0
355355 2.37082e6 0.998451
356356 0 0
357357 0 0
358358 0 0
359359 −876528. −0.358946 −0.179473 0.983763i 0.557439π-0.557439\pi
−0.179473 + 0.983763i 0.557439π0.557439\pi
360360 0 0
361361 −2.25520e6 −0.910787
362362 0 0
363363 −481550. −0.191812
364364 0 0
365365 302568. 0.118875
366366 0 0
367367 2.98062e6 1.15516 0.577578 0.816335i 0.303998π-0.303998\pi
0.577578 + 0.816335i 0.303998π0.303998\pi
368368 0 0
369369 889746. 0.340173
370370 0 0
371371 0 0
372372 0 0
373373 3.91441e6 1.45678 0.728391 0.685162i 0.240268π-0.240268\pi
0.728391 + 0.685162i 0.240268π0.240268\pi
374374 0 0
375375 −677040. −0.248620
376376 0 0
377377 −2.84174e6 −1.02975
378378 0 0
379379 −3.60661e6 −1.28974 −0.644868 0.764294i 0.723088π-0.723088\pi
−0.644868 + 0.764294i 0.723088π0.723088\pi
380380 0 0
381381 −3.15992e6 −1.11523
382382 0 0
383383 −2.66644e6 −0.928826 −0.464413 0.885619i 0.653735π-0.653735\pi
−0.464413 + 0.885619i 0.653735π0.653735\pi
384384 0 0
385385 0 0
386386 0 0
387387 529672. 0.179775
388388 0 0
389389 −213366. −0.0714910 −0.0357455 0.999361i 0.511381π-0.511381\pi
−0.0357455 + 0.999361i 0.511381π0.511381\pi
390390 0 0
391391 6.12360e6 2.02565
392392 0 0
393393 −246660. −0.0805596
394394 0 0
395395 3.60125e6 1.16134
396396 0 0
397397 4.09408e6 1.30371 0.651854 0.758345i 0.273992π-0.273992\pi
0.651854 + 0.758345i 0.273992π0.273992\pi
398398 0 0
399399 0 0
400400 0 0
401401 942366. 0.292657 0.146328 0.989236i 0.453254π-0.453254\pi
0.146328 + 0.989236i 0.453254π0.453254\pi
402402 0 0
403403 4.30525e6 1.32049
404404 0 0
405405 323484. 0.0979976
406406 0 0
407407 4.81488e6 1.44079
408408 0 0
409409 4.84561e6 1.43232 0.716160 0.697936i 0.245898π-0.245898\pi
0.716160 + 0.697936i 0.245898π0.245898\pi
410410 0 0
411411 3.03234e6 0.885469
412412 0 0
413413 0 0
414414 0 0
415415 2.95697e6 0.842804
416416 0 0
417417 2.50586e6 0.705694
418418 0 0
419419 −1.73485e6 −0.482754 −0.241377 0.970431i 0.577599π-0.577599\pi
−0.241377 + 0.970431i 0.577599π0.577599\pi
420420 0 0
421421 −1.65145e6 −0.454109 −0.227055 0.973882i 0.572910π-0.572910\pi
−0.227055 + 0.973882i 0.572910π0.572910\pi
422422 0 0
423423 259116. 0.0704115
424424 0 0
425425 5.73140e6 1.53918
426426 0 0
427427 0 0
428428 0 0
429429 −1.96224e6 −0.514765
430430 0 0
431431 −4.14360e6 −1.07445 −0.537223 0.843440i 0.680527π-0.680527\pi
−0.537223 + 0.843440i 0.680527π0.680527\pi
432432 0 0
433433 3.03966e6 0.779121 0.389561 0.921001i 0.372627π-0.372627\pi
0.389561 + 0.921001i 0.372627π0.372627\pi
434434 0 0
435435 −4.08744e6 −1.03569
436436 0 0
437437 1.97400e6 0.494474
438438 0 0
439439 2.54271e6 0.629703 0.314852 0.949141i 0.398045π-0.398045\pi
0.314852 + 0.949141i 0.398045π0.398045\pi
440440 0 0
441441 0 0
442442 0 0
443443 2.43210e6 0.588806 0.294403 0.955681i 0.404879π-0.404879\pi
0.294403 + 0.955681i 0.404879π0.404879\pi
444444 0 0
445445 2.24532e6 0.537500
446446 0 0
447447 −605940. −0.143437
448448 0 0
449449 1.82853e6 0.428042 0.214021 0.976829i 0.431344π-0.431344\pi
0.214021 + 0.976829i 0.431344π0.431344\pi
450450 0 0
451451 −2.09059e6 −0.483981
452452 0 0
453453 −1.24448e6 −0.284933
454454 0 0
455455 0 0
456456 0 0
457457 1.58063e6 0.354030 0.177015 0.984208i 0.443356π-0.443356\pi
0.177015 + 0.984208i 0.443356π0.443356\pi
458458 0 0
459459 −5.62788e6 −1.24685
460460 0 0
461461 −5.09604e6 −1.11681 −0.558407 0.829567i 0.688587π-0.688587\pi
−0.558407 + 0.829567i 0.688587π0.688587\pi
462462 0 0
463463 7.02338e6 1.52263 0.761313 0.648384i 0.224555π-0.224555\pi
0.761313 + 0.648384i 0.224555π0.224555\pi
464464 0 0
465465 6.19248e6 1.32810
466466 0 0
467467 −4.24845e6 −0.901443 −0.450722 0.892665i 0.648833π-0.648833\pi
−0.450722 + 0.892665i 0.648833π0.648833\pi
468468 0 0
469469 0 0
470470 0 0
471471 −760400. −0.157939
472472 0 0
473473 −1.24454e6 −0.255775
474474 0 0
475475 1.84757e6 0.375722
476476 0 0
477477 5.32561e6 1.07170
478478 0 0
479479 559284. 0.111377 0.0556883 0.998448i 0.482265π-0.482265\pi
0.0556883 + 0.998448i 0.482265π0.482265\pi
480480 0 0
481481 −8.36872e6 −1.64929
482482 0 0
483483 0 0
484484 0 0
485485 −1.42615e6 −0.275303
486486 0 0
487487 1.32057e6 0.252312 0.126156 0.992010i 0.459736π-0.459736\pi
0.126156 + 0.992010i 0.459736π0.459736\pi
488488 0 0
489489 −1.24256e6 −0.234988
490490 0 0
491491 −6.27193e6 −1.17408 −0.587040 0.809558i 0.699707π-0.699707\pi
−0.587040 + 0.809558i 0.699707π0.699707\pi
492492 0 0
493493 7.09463e6 1.31466
494494 0 0
495495 4.03603e6 0.740358
496496 0 0
497497 0 0
498498 0 0
499499 3.93785e6 0.707959 0.353979 0.935253i 0.384828π-0.384828\pi
0.353979 + 0.935253i 0.384828π0.384828\pi
500500 0 0
501501 −724200. −0.128903
502502 0 0
503503 −7.59830e6 −1.33905 −0.669525 0.742790i 0.733502π-0.733502\pi
−0.669525 + 0.742790i 0.733502π0.733502\pi
504504 0 0
505505 8.33314e6 1.45405
506506 0 0
507507 −302370. −0.0522419
508508 0 0
509509 7.82664e6 1.33900 0.669501 0.742812i 0.266508π-0.266508\pi
0.669501 + 0.742812i 0.266508π0.266508\pi
510510 0 0
511511 0 0
512512 0 0
513513 −1.81420e6 −0.304363
514514 0 0
515515 1.10581e7 1.83722
516516 0 0
517517 −608832. −0.100178
518518 0 0
519519 4.41552e6 0.719554
520520 0 0
521521 −8.94454e6 −1.44366 −0.721828 0.692072i 0.756698π-0.756698\pi
−0.721828 + 0.692072i 0.756698π0.756698\pi
522522 0 0
523523 4.07481e6 0.651407 0.325704 0.945472i 0.394399π-0.394399\pi
0.325704 + 0.945472i 0.394399π0.394399\pi
524524 0 0
525525 0 0
526526 0 0
527527 −1.07484e7 −1.68584
528528 0 0
529529 1.12037e7 1.74069
530530 0 0
531531 −4.90519e6 −0.754952
532532 0 0
533533 3.63365e6 0.554019
534534 0 0
535535 4.10357e6 0.619837
536536 0 0
537537 106920. 0.0160001
538538 0 0
539539 0 0
540540 0 0
541541 −1.18676e7 −1.74329 −0.871644 0.490140i 0.836946π-0.836946\pi
−0.871644 + 0.490140i 0.836946π0.836946\pi
542542 0 0
543543 5.46064e6 0.794775
544544 0 0
545545 4.73542e6 0.682915
546546 0 0
547547 5.37801e6 0.768516 0.384258 0.923226i 0.374457π-0.374457\pi
0.384258 + 0.923226i 0.374457π0.374457\pi
548548 0 0
549549 3.50007e6 0.495616
550550 0 0
551551 2.28702e6 0.320916
552552 0 0
553553 0 0
554554 0 0
555555 −1.20372e7 −1.65880
556556 0 0
557557 −5.64878e6 −0.771466 −0.385733 0.922611i 0.626051π-0.626051\pi
−0.385733 + 0.922611i 0.626051π0.626051\pi
558558 0 0
559559 2.16314e6 0.292789
560560 0 0
561561 4.89888e6 0.657188
562562 0 0
563563 4.56407e6 0.606850 0.303425 0.952855i 0.401870π-0.401870\pi
0.303425 + 0.952855i 0.401870π0.401870\pi
564564 0 0
565565 −734328. −0.0967763
566566 0 0
567567 0 0
568568 0 0
569569 8.00165e6 1.03609 0.518047 0.855352i 0.326659π-0.326659\pi
0.518047 + 0.855352i 0.326659π0.326659\pi
570570 0 0
571571 1.37164e7 1.76055 0.880275 0.474464i 0.157358π-0.157358\pi
0.880275 + 0.474464i 0.157358π0.157358\pi
572572 0 0
573573 5.75976e6 0.732855
574574 0 0
575575 1.65102e7 2.08249
576576 0 0
577577 −6.09797e6 −0.762510 −0.381255 0.924470i 0.624508π-0.624508\pi
−0.381255 + 0.924470i 0.624508π0.624508\pi
578578 0 0
579579 −4.13938e6 −0.513144
580580 0 0
581581 0 0
582582 0 0
583583 −1.25133e7 −1.52476
584584 0 0
585585 −7.01501e6 −0.847498
586586 0 0
587587 −8.08462e6 −0.968422 −0.484211 0.874951i 0.660893π-0.660893\pi
−0.484211 + 0.874951i 0.660893π0.660893\pi
588588 0 0
589589 −3.46484e6 −0.411524
590590 0 0
591591 −4.94946e6 −0.582893
592592 0 0
593593 −1.41575e6 −0.165330 −0.0826649 0.996577i 0.526343π-0.526343\pi
−0.0826649 + 0.996577i 0.526343π0.526343\pi
594594 0 0
595595 0 0
596596 0 0
597597 5.20364e6 0.597546
598598 0 0
599599 −8.75460e6 −0.996941 −0.498470 0.866907i 0.666105π-0.666105\pi
−0.498470 + 0.866907i 0.666105π0.666105\pi
600600 0 0
601601 −8.70276e6 −0.982813 −0.491407 0.870930i 0.663517π-0.663517\pi
−0.491407 + 0.870930i 0.663517π0.663517\pi
602602 0 0
603603 −2.49564e6 −0.279504
604604 0 0
605605 4.04502e6 0.449296
606606 0 0
607607 −1.69578e7 −1.86809 −0.934045 0.357157i 0.883746π-0.883746\pi
−0.934045 + 0.357157i 0.883746π0.883746\pi
608608 0 0
609609 0 0
610610 0 0
611611 1.05821e6 0.114675
612612 0 0
613613 1.76743e7 1.89973 0.949866 0.312658i 0.101220π-0.101220\pi
0.949866 + 0.312658i 0.101220π0.101220\pi
614614 0 0
615615 5.22648e6 0.557213
616616 0 0
617617 −9.70636e6 −1.02646 −0.513232 0.858250i 0.671552π-0.671552\pi
−0.513232 + 0.858250i 0.671552π0.671552\pi
618618 0 0
619619 1.48739e7 1.56027 0.780133 0.625613i 0.215151π-0.215151\pi
0.780133 + 0.625613i 0.215151π0.215151\pi
620620 0 0
621621 −1.62120e7 −1.68697
622622 0 0
623623 0 0
624624 0 0
625625 −6.59724e6 −0.675557
626626 0 0
627627 1.57920e6 0.160424
628628 0 0
629629 2.08931e7 2.10561
630630 0 0
631631 −1.26353e7 −1.26331 −0.631656 0.775248i 0.717625π-0.717625\pi
−0.631656 + 0.775248i 0.717625π0.717625\pi
632632 0 0
633633 −1.83284e6 −0.181809
634634 0 0
635635 2.65433e7 2.61229
636636 0 0
637637 0 0
638638 0 0
639639 4.03603e6 0.391023
640640 0 0
641641 6.23398e6 0.599267 0.299634 0.954054i 0.403136π-0.403136\pi
0.299634 + 0.954054i 0.403136π0.403136\pi
642642 0 0
643643 1.06874e7 1.01940 0.509701 0.860352i 0.329756π-0.329756\pi
0.509701 + 0.860352i 0.329756π0.329756\pi
644644 0 0
645645 3.11136e6 0.294477
646646 0 0
647647 1.83258e7 1.72109 0.860544 0.509376i 0.170124π-0.170124\pi
0.860544 + 0.509376i 0.170124π0.170124\pi
648648 0 0
649649 1.15255e7 1.07411
650650 0 0
651651 0 0
652652 0 0
653653 −7.28857e6 −0.668897 −0.334448 0.942414i 0.608550π-0.608550\pi
−0.334448 + 0.942414i 0.608550π0.608550\pi
654654 0 0
655655 2.07194e6 0.188701
656656 0 0
657657 515086. 0.0465550
658658 0 0
659659 −4.54337e6 −0.407534 −0.203767 0.979019i 0.565319π-0.565319\pi
−0.203767 + 0.979019i 0.565319π0.565319\pi
660660 0 0
661661 2.10021e7 1.86964 0.934821 0.355120i 0.115560π-0.115560\pi
0.934821 + 0.355120i 0.115560π0.115560\pi
662662 0 0
663663 −8.51472e6 −0.752292
664664 0 0
665665 0 0
666666 0 0
667667 2.04372e7 1.77872
668668 0 0
669669 −1.27746e7 −1.10353
670670 0 0
671671 −8.22394e6 −0.705137
672672 0 0
673673 3.46923e6 0.295253 0.147627 0.989043i 0.452837π-0.452837\pi
0.147627 + 0.989043i 0.452837π0.452837\pi
674674 0 0
675675 −1.51737e7 −1.28183
676676 0 0
677677 1.80916e7 1.51707 0.758536 0.651631i 0.225915π-0.225915\pi
0.758536 + 0.651631i 0.225915π0.225915\pi
678678 0 0
679679 0 0
680680 0 0
681681 −1.28764e7 −1.06397
682682 0 0
683683 −4.67752e6 −0.383675 −0.191838 0.981427i 0.561445π-0.561445\pi
−0.191838 + 0.981427i 0.561445π0.561445\pi
684684 0 0
685685 −2.54717e7 −2.07411
686686 0 0
687687 −3.50936e6 −0.283685
688688 0 0
689689 2.17493e7 1.74541
690690 0 0
691691 1.68960e7 1.34614 0.673069 0.739579i 0.264976π-0.264976\pi
0.673069 + 0.739579i 0.264976π0.264976\pi
692692 0 0
693693 0 0
694694 0 0
695695 −2.10492e7 −1.65300
696696 0 0
697697 −9.07168e6 −0.707303
698698 0 0
699699 8.36154e6 0.647282
700700 0 0
701701 2.40964e6 0.185207 0.0926035 0.995703i 0.470481π-0.470481\pi
0.0926035 + 0.995703i 0.470481π0.470481\pi
702702 0 0
703703 6.73510e6 0.513991
704704 0 0
705705 1.52208e6 0.115336
706706 0 0
707707 0 0
708708 0 0
709709 −5.77010e6 −0.431090 −0.215545 0.976494i 0.569153π-0.569153\pi
−0.215545 + 0.976494i 0.569153π0.569153\pi
710710 0 0
711711 6.13070e6 0.454816
712712 0 0
713713 −3.09624e7 −2.28092
714714 0 0
715715 1.64828e7 1.20578
716716 0 0
717717 −7.74336e6 −0.562512
718718 0 0
719719 −1.43716e7 −1.03677 −0.518385 0.855147i 0.673467π-0.673467\pi
−0.518385 + 0.855147i 0.673467π0.673467\pi
720720 0 0
721721 0 0
722722 0 0
723723 1.15285e7 0.820214
724724 0 0
725725 1.91282e7 1.35154
726726 0 0
727727 −1.40705e7 −0.987353 −0.493676 0.869646i 0.664347π-0.664347\pi
−0.493676 + 0.869646i 0.664347π0.664347\pi
728728 0 0
729729 9.93049e6 0.692073
730730 0 0
731731 −5.40043e6 −0.373796
732732 0 0
733733 3.75000e6 0.257793 0.128897 0.991658i 0.458856π-0.458856\pi
0.128897 + 0.991658i 0.458856π0.458856\pi
734734 0 0
735735 0 0
736736 0 0
737737 5.86387e6 0.397664
738738 0 0
739739 −2.61318e7 −1.76019 −0.880093 0.474802i 0.842520π-0.842520\pi
−0.880093 + 0.474802i 0.842520π0.842520\pi
740740 0 0
741741 −2.74480e6 −0.183639
742742 0 0
743743 159072. 0.0105711 0.00528557 0.999986i 0.498318π-0.498318\pi
0.00528557 + 0.999986i 0.498318π0.498318\pi
744744 0 0
745745 5.08990e6 0.335984
746746 0 0
747747 5.03389e6 0.330067
748748 0 0
749749 0 0
750750 0 0
751751 2.65311e7 1.71654 0.858272 0.513196i 0.171539π-0.171539\pi
0.858272 + 0.513196i 0.171539π0.171539\pi
752752 0 0
753753 1.35801e7 0.872802
754754 0 0
755755 1.04536e7 0.667421
756756 0 0
757757 −1.52032e7 −0.964260 −0.482130 0.876100i 0.660137π-0.660137\pi
−0.482130 + 0.876100i 0.660137π0.660137\pi
758758 0 0
759759 1.41120e7 0.889169
760760 0 0
761761 −4.71380e6 −0.295059 −0.147530 0.989058i 0.547132π-0.547132\pi
−0.147530 + 0.989058i 0.547132π0.547132\pi
762762 0 0
763763 0 0
764764 0 0
765765 1.75135e7 1.08198
766766 0 0
767767 −2.00324e7 −1.22954
768768 0 0
769769 1.58977e6 0.0969434 0.0484717 0.998825i 0.484565π-0.484565\pi
0.0484717 + 0.998825i 0.484565π0.484565\pi
770770 0 0
771771 3.17742e6 0.192504
772772 0 0
773773 9.69095e6 0.583334 0.291667 0.956520i 0.405790π-0.405790\pi
0.291667 + 0.956520i 0.405790π0.405790\pi
774774 0 0
775775 −2.89793e7 −1.73314
776776 0 0
777777 0 0
778778 0 0
779779 −2.92434e6 −0.172657
780780 0 0
781781 −9.48326e6 −0.556327
782782 0 0
783783 −1.87828e7 −1.09485
784784 0 0
785785 6.38736e6 0.369954
786786 0 0
787787 −1.57170e6 −0.0904549 −0.0452275 0.998977i 0.514401π-0.514401\pi
−0.0452275 + 0.998977i 0.514401π0.514401\pi
788788 0 0
789789 −1.05101e7 −0.601054
790790 0 0
791791 0 0
792792 0 0
793793 1.42940e7 0.807180
794794 0 0
795795 3.12833e7 1.75547
796796 0 0
797797 2.25298e6 0.125635 0.0628175 0.998025i 0.479991π-0.479991\pi
0.0628175 + 0.998025i 0.479991π0.479991\pi
798798 0 0
799799 −2.64190e6 −0.146403
800800 0 0
801801 3.82239e6 0.210501
802802 0 0
803803 −1.21027e6 −0.0662360
804804 0 0
805805 0 0
806806 0 0
807807 −1.18958e7 −0.643000
808808 0 0
809809 −2.37938e7 −1.27818 −0.639090 0.769132i 0.720689π-0.720689\pi
−0.639090 + 0.769132i 0.720689π0.720689\pi
810810 0 0
811811 5.32300e6 0.284187 0.142093 0.989853i 0.454617π-0.454617\pi
0.142093 + 0.989853i 0.454617π0.454617\pi
812812 0 0
813813 −1.43008e7 −0.758812
814814 0 0
815815 1.04375e7 0.550431
816816 0 0
817817 −1.74088e6 −0.0912460
818818 0 0
819819 0 0
820820 0 0
821821 1.48802e7 0.770464 0.385232 0.922820i 0.374121π-0.374121\pi
0.385232 + 0.922820i 0.374121π0.374121\pi
822822 0 0
823823 −2.00601e7 −1.03236 −0.516182 0.856479i 0.672647π-0.672647\pi
−0.516182 + 0.856479i 0.672647π0.672647\pi
824824 0 0
825825 1.32082e7 0.675628
826826 0 0
827827 −1.21539e7 −0.617949 −0.308975 0.951070i 0.599986π-0.599986\pi
−0.308975 + 0.951070i 0.599986π0.599986\pi
828828 0 0
829829 −3.21197e7 −1.62325 −0.811625 0.584179i 0.801417π-0.801417\pi
−0.811625 + 0.584179i 0.801417π0.801417\pi
830830 0 0
831831 633020. 0.0317991
832832 0 0
833833 0 0
834834 0 0
835835 6.08328e6 0.301941
836836 0 0
837837 2.84559e7 1.40397
838838 0 0
839839 −1.01320e6 −0.0496922 −0.0248461 0.999691i 0.507910π-0.507910\pi
−0.0248461 + 0.999691i 0.507910π0.507910\pi
840840 0 0
841841 3.16681e6 0.154394
842842 0 0
843843 −4.96614e6 −0.240686
844844 0 0
845845 2.53991e6 0.122370
846846 0 0
847847 0 0
848848 0 0
849849 −1.15842e7 −0.551564
850850 0 0
851851 6.01860e7 2.84886
852852 0 0
853853 −234824. −0.0110502 −0.00552510 0.999985i 0.501759π-0.501759\pi
−0.00552510 + 0.999985i 0.501759π0.501759\pi
854854 0 0
855855 5.64564e6 0.264118
856856 0 0
857857 −2.83802e7 −1.31997 −0.659985 0.751279i 0.729437π-0.729437\pi
−0.659985 + 0.751279i 0.729437π0.729437\pi
858858 0 0
859859 4.00081e7 1.84997 0.924986 0.380001i 0.124076π-0.124076\pi
0.924986 + 0.380001i 0.124076π0.124076\pi
860860 0 0
861861 0 0
862862 0 0
863863 2.08030e7 0.950823 0.475411 0.879764i 0.342299π-0.342299\pi
0.475411 + 0.879764i 0.342299π0.342299\pi
864864 0 0
865865 −3.70904e7 −1.68547
866866 0 0
867867 7.05907e6 0.318933
868868 0 0
869869 −1.44050e7 −0.647088
870870 0 0
871871 −1.01920e7 −0.455211
872872 0 0
873873 −2.42785e6 −0.107817
874874 0 0
875875 0 0
876876 0 0
877877 3.03559e7 1.33273 0.666367 0.745624i 0.267848π-0.267848\pi
0.666367 + 0.745624i 0.267848π0.267848\pi
878878 0 0
879879 −1.43886e7 −0.628125
880880 0 0
881881 2.58936e7 1.12396 0.561981 0.827150i 0.310039π-0.310039\pi
0.561981 + 0.827150i 0.310039π0.310039\pi
882882 0 0
883883 1.88813e7 0.814950 0.407475 0.913216i 0.366409π-0.366409\pi
0.407475 + 0.913216i 0.366409π0.366409\pi
884884 0 0
885885 −2.88137e7 −1.23663
886886 0 0
887887 −2.34431e7 −1.00048 −0.500238 0.865888i 0.666754π-0.666754\pi
−0.500238 + 0.865888i 0.666754π0.666754\pi
888888 0 0
889889 0 0
890890 0 0
891891 −1.29394e6 −0.0546033
892892 0 0
893893 −851640. −0.0357378
894894 0 0
895895 −898128. −0.0374784
896896 0 0
897897 −2.45280e7 −1.01784
898898 0 0
899899 −3.58722e7 −1.48033
900900 0 0
901901 −5.42988e7 −2.22833
902902 0 0
903903 0 0
904904 0 0
905905 −4.58694e7 −1.86166
906906 0 0
907907 5.60873e6 0.226384 0.113192 0.993573i 0.463892π-0.463892\pi
0.113192 + 0.993573i 0.463892π0.463892\pi
908908 0 0
909909 1.41862e7 0.569450
910910 0 0
911911 −2.16215e7 −0.863156 −0.431578 0.902076i 0.642043π-0.642043\pi
−0.431578 + 0.902076i 0.642043π0.642043\pi
912912 0 0
913913 −1.18279e7 −0.469602
914914 0 0
915915 2.05598e7 0.811834
916916 0 0
917917 0 0
918918 0 0
919919 −4.51695e7 −1.76424 −0.882119 0.471028i 0.843883π-0.843883\pi
−0.882119 + 0.471028i 0.843883π0.843883\pi
920920 0 0
921921 −9.89098e6 −0.384229
922922 0 0
923923 1.64828e7 0.636835
924924 0 0
925925 5.63312e7 2.16469
926926 0 0
927927 1.88251e7 0.719512
928928 0 0
929929 2.28729e7 0.869524 0.434762 0.900545i 0.356832π-0.356832\pi
0.434762 + 0.900545i 0.356832π0.356832\pi
930930 0 0
931931 0 0
932932 0 0
933933 −2.22050e7 −0.835117
934934 0 0
935935 −4.11506e7 −1.53938
936936 0 0
937937 1.79616e7 0.668336 0.334168 0.942514i 0.391545π-0.391545\pi
0.334168 + 0.942514i 0.391545π0.391545\pi
938938 0 0
939939 −2.33008e7 −0.862395
940940 0 0
941941 1.79697e7 0.661558 0.330779 0.943708i 0.392689π-0.392689\pi
0.330779 + 0.943708i 0.392689π0.392689\pi
942942 0 0
943943 −2.61324e7 −0.956974
944944 0 0
945945 0 0
946946 0 0
947947 −4.32115e7 −1.56576 −0.782879 0.622174i 0.786250π-0.786250\pi
−0.782879 + 0.622174i 0.786250π0.786250\pi
948948 0 0
949949 2.10357e6 0.0758213
950950 0 0
951951 4.27542e6 0.153295
952952 0 0
953953 −7.50965e6 −0.267848 −0.133924 0.990992i 0.542758π-0.542758\pi
−0.133924 + 0.990992i 0.542758π0.542758\pi
954954 0 0
955955 −4.83820e7 −1.71662
956956 0 0
957957 1.63498e7 0.577074
958958 0 0
959959 0 0
960960 0 0
961961 2.57172e7 0.898288
962962 0 0
963963 6.98584e6 0.242746
964964 0 0
965965 3.47708e7 1.20198
966966 0 0
967967 1.69305e7 0.582242 0.291121 0.956686i 0.405972π-0.405972\pi
0.291121 + 0.956686i 0.405972π0.405972\pi
968968 0 0
969969 6.85260e6 0.234448
970970 0 0
971971 2.86144e7 0.973949 0.486974 0.873416i 0.338101π-0.338101\pi
0.486974 + 0.873416i 0.338101π0.338101\pi
972972 0 0
973973 0 0
974974 0 0
975975 −2.29570e7 −0.773400
976976 0 0
977977 3.69445e7 1.23826 0.619132 0.785287i 0.287485π-0.287485\pi
0.619132 + 0.785287i 0.287485π0.287485\pi
978978 0 0
979979 −8.98128e6 −0.299489
980980 0 0
981981 8.06148e6 0.267450
982982 0 0
983983 −3.88787e7 −1.28330 −0.641650 0.766998i 0.721750π-0.721750\pi
−0.641650 + 0.766998i 0.721750π0.721750\pi
984984 0 0
985985 4.15755e7 1.36536
986986 0 0
987987 0 0
988988 0 0
989989 −1.55568e7 −0.505743
990990 0 0
991991 −2.49212e7 −0.806092 −0.403046 0.915180i 0.632049π-0.632049\pi
−0.403046 + 0.915180i 0.632049π0.632049\pi
992992 0 0
993993 3.96616e6 0.127643
994994 0 0
995995 −4.37106e7 −1.39968
996996 0 0
997997 −1.01956e7 −0.324845 −0.162422 0.986721i 0.551931π-0.551931\pi
−0.162422 + 0.986721i 0.551931π0.551931\pi
998998 0 0
999999 −5.53138e7 −1.75356
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 784.6.a.i.1.1 1
4.3 odd 2 98.6.a.a.1.1 1
7.6 odd 2 112.6.a.c.1.1 1
12.11 even 2 882.6.a.x.1.1 1
21.20 even 2 1008.6.a.b.1.1 1
28.3 even 6 98.6.c.c.79.1 2
28.11 odd 6 98.6.c.d.79.1 2
28.19 even 6 98.6.c.c.67.1 2
28.23 odd 6 98.6.c.d.67.1 2
28.27 even 2 14.6.a.a.1.1 1
56.13 odd 2 448.6.a.l.1.1 1
56.27 even 2 448.6.a.e.1.1 1
84.83 odd 2 126.6.a.f.1.1 1
140.27 odd 4 350.6.c.d.99.1 2
140.83 odd 4 350.6.c.d.99.2 2
140.139 even 2 350.6.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.6.a.a.1.1 1 28.27 even 2
98.6.a.a.1.1 1 4.3 odd 2
98.6.c.c.67.1 2 28.19 even 6
98.6.c.c.79.1 2 28.3 even 6
98.6.c.d.67.1 2 28.23 odd 6
98.6.c.d.79.1 2 28.11 odd 6
112.6.a.c.1.1 1 7.6 odd 2
126.6.a.f.1.1 1 84.83 odd 2
350.6.a.i.1.1 1 140.139 even 2
350.6.c.d.99.1 2 140.27 odd 4
350.6.c.d.99.2 2 140.83 odd 4
448.6.a.e.1.1 1 56.27 even 2
448.6.a.l.1.1 1 56.13 odd 2
784.6.a.i.1.1 1 1.1 even 1 trivial
882.6.a.x.1.1 1 12.11 even 2
1008.6.a.b.1.1 1 21.20 even 2