Properties

Label 100.6.a.b.1.1
Level 100100
Weight 66
Character 100.1
Self dual yes
Analytic conductor 16.03816.038
Analytic rank 00
Dimension 11
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [100,6,Mod(1,100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(100, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("100.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 100=2252 100 = 2^{2} \cdot 5^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 100.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: 16.038381981316.0383819813
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 4)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 100.1

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+12.0000q3+88.0000q799.0000q9+540.000q11+418.000q13594.000q17+836.000q19+1056.00q21+4104.00q234104.00q27594.000q29+4256.00q31+6480.00q33+298.000q37+5016.00q39+17226.0q41+12100.0q43+1296.00q479063.00q497128.00q5119494.0q53+10032.0q577668.00q5934738.0q618712.00q6321812.0q67+49248.0q6946872.0q7167562.0q73+47520.0q7776912.0q7925191.0q8167716.0q837128.00q87+29754.0q89+36784.0q91+51072.0q93+122398.q9753460.0q99+O(q100)q+12.0000 q^{3} +88.0000 q^{7} -99.0000 q^{9} +540.000 q^{11} +418.000 q^{13} -594.000 q^{17} +836.000 q^{19} +1056.00 q^{21} +4104.00 q^{23} -4104.00 q^{27} -594.000 q^{29} +4256.00 q^{31} +6480.00 q^{33} +298.000 q^{37} +5016.00 q^{39} +17226.0 q^{41} +12100.0 q^{43} +1296.00 q^{47} -9063.00 q^{49} -7128.00 q^{51} -19494.0 q^{53} +10032.0 q^{57} -7668.00 q^{59} -34738.0 q^{61} -8712.00 q^{63} -21812.0 q^{67} +49248.0 q^{69} -46872.0 q^{71} -67562.0 q^{73} +47520.0 q^{77} -76912.0 q^{79} -25191.0 q^{81} -67716.0 q^{83} -7128.00 q^{87} +29754.0 q^{89} +36784.0 q^{91} +51072.0 q^{93} +122398. q^{97} -53460.0 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 12.0000 0.769800 0.384900 0.922958i 0.374236π-0.374236\pi
0.384900 + 0.922958i 0.374236π0.374236\pi
44 0 0
55 0 0
66 0 0
77 88.0000 0.678793 0.339397 0.940643i 0.389777π-0.389777\pi
0.339397 + 0.940643i 0.389777π0.389777\pi
88 0 0
99 −99.0000 −0.407407
1010 0 0
1111 540.000 1.34559 0.672794 0.739830i 0.265094π-0.265094\pi
0.672794 + 0.739830i 0.265094π0.265094\pi
1212 0 0
1313 418.000 0.685990 0.342995 0.939337i 0.388559π-0.388559\pi
0.342995 + 0.939337i 0.388559π0.388559\pi
1414 0 0
1515 0 0
1616 0 0
1717 −594.000 −0.498499 −0.249249 0.968439i 0.580184π-0.580184\pi
−0.249249 + 0.968439i 0.580184π0.580184\pi
1818 0 0
1919 836.000 0.531279 0.265639 0.964072i 0.414417π-0.414417\pi
0.265639 + 0.964072i 0.414417π0.414417\pi
2020 0 0
2121 1056.00 0.522535
2222 0 0
2323 4104.00 1.61766 0.808831 0.588041i 0.200101π-0.200101\pi
0.808831 + 0.588041i 0.200101π0.200101\pi
2424 0 0
2525 0 0
2626 0 0
2727 −4104.00 −1.08342
2828 0 0
2929 −594.000 −0.131157 −0.0655785 0.997847i 0.520889π-0.520889\pi
−0.0655785 + 0.997847i 0.520889π0.520889\pi
3030 0 0
3131 4256.00 0.795422 0.397711 0.917511i 0.369805π-0.369805\pi
0.397711 + 0.917511i 0.369805π0.369805\pi
3232 0 0
3333 6480.00 1.03583
3434 0 0
3535 0 0
3636 0 0
3737 298.000 0.0357859 0.0178930 0.999840i 0.494304π-0.494304\pi
0.0178930 + 0.999840i 0.494304π0.494304\pi
3838 0 0
3939 5016.00 0.528075
4040 0 0
4141 17226.0 1.60039 0.800193 0.599742i 0.204730π-0.204730\pi
0.800193 + 0.599742i 0.204730π0.204730\pi
4242 0 0
4343 12100.0 0.997963 0.498981 0.866613i 0.333708π-0.333708\pi
0.498981 + 0.866613i 0.333708π0.333708\pi
4444 0 0
4545 0 0
4646 0 0
4747 1296.00 0.0855777 0.0427888 0.999084i 0.486376π-0.486376\pi
0.0427888 + 0.999084i 0.486376π0.486376\pi
4848 0 0
4949 −9063.00 −0.539240
5050 0 0
5151 −7128.00 −0.383745
5252 0 0
5353 −19494.0 −0.953260 −0.476630 0.879104i 0.658142π-0.658142\pi
−0.476630 + 0.879104i 0.658142π0.658142\pi
5454 0 0
5555 0 0
5656 0 0
5757 10032.0 0.408978
5858 0 0
5959 −7668.00 −0.286782 −0.143391 0.989666i 0.545801π-0.545801\pi
−0.143391 + 0.989666i 0.545801π0.545801\pi
6060 0 0
6161 −34738.0 −1.19531 −0.597655 0.801754i 0.703901π-0.703901\pi
−0.597655 + 0.801754i 0.703901π0.703901\pi
6262 0 0
6363 −8712.00 −0.276545
6464 0 0
6565 0 0
6666 0 0
6767 −21812.0 −0.593620 −0.296810 0.954937i 0.595923π-0.595923\pi
−0.296810 + 0.954937i 0.595923π0.595923\pi
6868 0 0
6969 49248.0 1.24528
7070 0 0
7171 −46872.0 −1.10349 −0.551744 0.834014i 0.686037π-0.686037\pi
−0.551744 + 0.834014i 0.686037π0.686037\pi
7272 0 0
7373 −67562.0 −1.48387 −0.741934 0.670473i 0.766091π-0.766091\pi
−0.741934 + 0.670473i 0.766091π0.766091\pi
7474 0 0
7575 0 0
7676 0 0
7777 47520.0 0.913376
7878 0 0
7979 −76912.0 −1.38652 −0.693260 0.720687i 0.743826π-0.743826\pi
−0.693260 + 0.720687i 0.743826π0.743826\pi
8080 0 0
8181 −25191.0 −0.426612
8282 0 0
8383 −67716.0 −1.07894 −0.539468 0.842006i 0.681375π-0.681375\pi
−0.539468 + 0.842006i 0.681375π0.681375\pi
8484 0 0
8585 0 0
8686 0 0
8787 −7128.00 −0.100965
8888 0 0
8989 29754.0 0.398172 0.199086 0.979982i 0.436203π-0.436203\pi
0.199086 + 0.979982i 0.436203π0.436203\pi
9090 0 0
9191 36784.0 0.465646
9292 0 0
9393 51072.0 0.612316
9494 0 0
9595 0 0
9696 0 0
9797 122398. 1.32082 0.660412 0.750903i 0.270382π-0.270382\pi
0.660412 + 0.750903i 0.270382π0.270382\pi
9898 0 0
9999 −53460.0 −0.548202
100100 0 0
101101 11286.0 0.110087 0.0550436 0.998484i 0.482470π-0.482470\pi
0.0550436 + 0.998484i 0.482470π0.482470\pi
102102 0 0
103103 27256.0 0.253145 0.126572 0.991957i 0.459602π-0.459602\pi
0.126572 + 0.991957i 0.459602π0.459602\pi
104104 0 0
105105 0 0
106106 0 0
107107 −122364. −1.03322 −0.516612 0.856220i 0.672807π-0.672807\pi
−0.516612 + 0.856220i 0.672807π0.672807\pi
108108 0 0
109109 99902.0 0.805393 0.402697 0.915334i 0.368073π-0.368073\pi
0.402697 + 0.915334i 0.368073π0.368073\pi
110110 0 0
111111 3576.00 0.0275480
112112 0 0
113113 29646.0 0.218409 0.109204 0.994019i 0.465170π-0.465170\pi
0.109204 + 0.994019i 0.465170π0.465170\pi
114114 0 0
115115 0 0
116116 0 0
117117 −41382.0 −0.279477
118118 0 0
119119 −52272.0 −0.338378
120120 0 0
121121 130549. 0.810607
122122 0 0
123123 206712. 1.23198
124124 0 0
125125 0 0
126126 0 0
127127 −336512. −1.85136 −0.925681 0.378305i 0.876507π-0.876507\pi
−0.925681 + 0.378305i 0.876507π0.876507\pi
128128 0 0
129129 145200. 0.768232
130130 0 0
131131 100980. 0.514111 0.257056 0.966397i 0.417248π-0.417248\pi
0.257056 + 0.966397i 0.417248π0.417248\pi
132132 0 0
133133 73568.0 0.360628
134134 0 0
135135 0 0
136136 0 0
137137 317142. 1.44362 0.721809 0.692092i 0.243311π-0.243311\pi
0.721809 + 0.692092i 0.243311π0.243311\pi
138138 0 0
139139 −148324. −0.651140 −0.325570 0.945518i 0.605556π-0.605556\pi
−0.325570 + 0.945518i 0.605556π0.605556\pi
140140 0 0
141141 15552.0 0.0658777
142142 0 0
143143 225720. 0.923060
144144 0 0
145145 0 0
146146 0 0
147147 −108756. −0.415107
148148 0 0
149149 196614. 0.725519 0.362759 0.931883i 0.381835π-0.381835\pi
0.362759 + 0.931883i 0.381835π0.381835\pi
150150 0 0
151151 74360.0 0.265398 0.132699 0.991156i 0.457636π-0.457636\pi
0.132699 + 0.991156i 0.457636π0.457636\pi
152152 0 0
153153 58806.0 0.203092
154154 0 0
155155 0 0
156156 0 0
157157 −120878. −0.391380 −0.195690 0.980666i 0.562695π-0.562695\pi
−0.195690 + 0.980666i 0.562695π0.562695\pi
158158 0 0
159159 −233928. −0.733820
160160 0 0
161161 361152. 1.09806
162162 0 0
163163 111340. 0.328233 0.164116 0.986441i 0.447523π-0.447523\pi
0.164116 + 0.986441i 0.447523π0.447523\pi
164164 0 0
165165 0 0
166166 0 0
167167 491832. 1.36466 0.682332 0.731043i 0.260966π-0.260966\pi
0.682332 + 0.731043i 0.260966π0.260966\pi
168168 0 0
169169 −196569. −0.529417
170170 0 0
171171 −82764.0 −0.216447
172172 0 0
173173 −707454. −1.79714 −0.898572 0.438826i 0.855395π-0.855395\pi
−0.898572 + 0.438826i 0.855395π0.855395\pi
174174 0 0
175175 0 0
176176 0 0
177177 −92016.0 −0.220765
178178 0 0
179179 493668. 1.15160 0.575801 0.817590i 0.304690π-0.304690\pi
0.575801 + 0.817590i 0.304690π0.304690\pi
180180 0 0
181181 −559450. −1.26930 −0.634651 0.772799i 0.718856π-0.718856\pi
−0.634651 + 0.772799i 0.718856π0.718856\pi
182182 0 0
183183 −416856. −0.920149
184184 0 0
185185 0 0
186186 0 0
187187 −320760. −0.670774
188188 0 0
189189 −361152. −0.735420
190190 0 0
191191 −724032. −1.43607 −0.718033 0.696009i 0.754957π-0.754957\pi
−0.718033 + 0.696009i 0.754957π0.754957\pi
192192 0 0
193193 −7106.00 −0.0137319 −0.00686597 0.999976i 0.502186π-0.502186\pi
−0.00686597 + 0.999976i 0.502186π0.502186\pi
194194 0 0
195195 0 0
196196 0 0
197197 530442. 0.973806 0.486903 0.873456i 0.338127π-0.338127\pi
0.486903 + 0.873456i 0.338127π0.338127\pi
198198 0 0
199199 56168.0 0.100544 0.0502720 0.998736i 0.483991π-0.483991\pi
0.0502720 + 0.998736i 0.483991π0.483991\pi
200200 0 0
201201 −261744. −0.456969
202202 0 0
203203 −52272.0 −0.0890285
204204 0 0
205205 0 0
206206 0 0
207207 −406296. −0.659047
208208 0 0
209209 451440. 0.714882
210210 0 0
211211 −339196. −0.524499 −0.262249 0.965000i 0.584464π-0.584464\pi
−0.262249 + 0.965000i 0.584464π0.584464\pi
212212 0 0
213213 −562464. −0.849465
214214 0 0
215215 0 0
216216 0 0
217217 374528. 0.539927
218218 0 0
219219 −810744. −1.14228
220220 0 0
221221 −248292. −0.341965
222222 0 0
223223 −779360. −1.04948 −0.524742 0.851261i 0.675838π-0.675838\pi
−0.524742 + 0.851261i 0.675838π0.675838\pi
224224 0 0
225225 0 0
226226 0 0
227227 744876. 0.959443 0.479722 0.877421i 0.340738π-0.340738\pi
0.479722 + 0.877421i 0.340738π0.340738\pi
228228 0 0
229229 −272746. −0.343692 −0.171846 0.985124i 0.554973π-0.554973\pi
−0.171846 + 0.985124i 0.554973π0.554973\pi
230230 0 0
231231 570240. 0.703117
232232 0 0
233233 153846. 0.185651 0.0928253 0.995682i 0.470410π-0.470410\pi
0.0928253 + 0.995682i 0.470410π0.470410\pi
234234 0 0
235235 0 0
236236 0 0
237237 −922944. −1.06734
238238 0 0
239239 1.15474e6 1.30764 0.653820 0.756650i 0.273166π-0.273166\pi
0.653820 + 0.756650i 0.273166π0.273166\pi
240240 0 0
241241 657074. 0.728738 0.364369 0.931255i 0.381285π-0.381285\pi
0.364369 + 0.931255i 0.381285π0.381285\pi
242242 0 0
243243 694980. 0.755017
244244 0 0
245245 0 0
246246 0 0
247247 349448. 0.364452
248248 0 0
249249 −812592. −0.830566
250250 0 0
251251 1.34190e6 1.34442 0.672211 0.740359i 0.265345π-0.265345\pi
0.672211 + 0.740359i 0.265345π0.265345\pi
252252 0 0
253253 2.21616e6 2.17671
254254 0 0
255255 0 0
256256 0 0
257257 −132354. −0.124998 −0.0624992 0.998045i 0.519907π-0.519907\pi
−0.0624992 + 0.998045i 0.519907π0.519907\pi
258258 0 0
259259 26224.0 0.0242912
260260 0 0
261261 58806.0 0.0534343
262262 0 0
263263 −943272. −0.840906 −0.420453 0.907314i 0.638129π-0.638129\pi
−0.420453 + 0.907314i 0.638129π0.638129\pi
264264 0 0
265265 0 0
266266 0 0
267267 357048. 0.306513
268268 0 0
269269 967518. 0.815227 0.407613 0.913155i 0.366361π-0.366361\pi
0.407613 + 0.913155i 0.366361π0.366361\pi
270270 0 0
271271 −518320. −0.428721 −0.214360 0.976755i 0.568767π-0.568767\pi
−0.214360 + 0.976755i 0.568767π0.568767\pi
272272 0 0
273273 441408. 0.358454
274274 0 0
275275 0 0
276276 0 0
277277 −2.22273e6 −1.74055 −0.870275 0.492566i 0.836059π-0.836059\pi
−0.870275 + 0.492566i 0.836059π0.836059\pi
278278 0 0
279279 −421344. −0.324061
280280 0 0
281281 −196614. −0.148542 −0.0742709 0.997238i 0.523663π-0.523663\pi
−0.0742709 + 0.997238i 0.523663π0.523663\pi
282282 0 0
283283 1.55228e6 1.15213 0.576067 0.817403i 0.304587π-0.304587\pi
0.576067 + 0.817403i 0.304587π0.304587\pi
284284 0 0
285285 0 0
286286 0 0
287287 1.51589e6 1.08633
288288 0 0
289289 −1.06702e6 −0.751499
290290 0 0
291291 1.46878e6 1.01677
292292 0 0
293293 1.07217e6 0.729616 0.364808 0.931083i 0.381135π-0.381135\pi
0.364808 + 0.931083i 0.381135π0.381135\pi
294294 0 0
295295 0 0
296296 0 0
297297 −2.21616e6 −1.45784
298298 0 0
299299 1.71547e6 1.10970
300300 0 0
301301 1.06480e6 0.677410
302302 0 0
303303 135432. 0.0847451
304304 0 0
305305 0 0
306306 0 0
307307 −1.58589e6 −0.960346 −0.480173 0.877174i 0.659426π-0.659426\pi
−0.480173 + 0.877174i 0.659426π0.659426\pi
308308 0 0
309309 327072. 0.194871
310310 0 0
311311 −730728. −0.428405 −0.214203 0.976789i 0.568715π-0.568715\pi
−0.214203 + 0.976789i 0.568715π0.568715\pi
312312 0 0
313313 −584858. −0.337435 −0.168717 0.985664i 0.553962π-0.553962\pi
−0.168717 + 0.985664i 0.553962π0.553962\pi
314314 0 0
315315 0 0
316316 0 0
317317 2.48287e6 1.38773 0.693865 0.720105i 0.255906π-0.255906\pi
0.693865 + 0.720105i 0.255906π0.255906\pi
318318 0 0
319319 −320760. −0.176483
320320 0 0
321321 −1.46837e6 −0.795376
322322 0 0
323323 −496584. −0.264842
324324 0 0
325325 0 0
326326 0 0
327327 1.19882e6 0.619992
328328 0 0
329329 114048. 0.0580895
330330 0 0
331331 377948. 0.189610 0.0948052 0.995496i 0.469777π-0.469777\pi
0.0948052 + 0.995496i 0.469777π0.469777\pi
332332 0 0
333333 −29502.0 −0.0145794
334334 0 0
335335 0 0
336336 0 0
337337 −639122. −0.306555 −0.153278 0.988183i 0.548983π-0.548983\pi
−0.153278 + 0.988183i 0.548983π0.548983\pi
338338 0 0
339339 355752. 0.168131
340340 0 0
341341 2.29824e6 1.07031
342342 0 0
343343 −2.27656e6 −1.04483
344344 0 0
345345 0 0
346346 0 0
347347 2.90466e6 1.29501 0.647503 0.762063i 0.275813π-0.275813\pi
0.647503 + 0.762063i 0.275813π0.275813\pi
348348 0 0
349349 −3.99157e6 −1.75420 −0.877102 0.480304i 0.840526π-0.840526\pi
−0.877102 + 0.480304i 0.840526π0.840526\pi
350350 0 0
351351 −1.71547e6 −0.743217
352352 0 0
353353 −1.42922e6 −0.610466 −0.305233 0.952278i 0.598734π-0.598734\pi
−0.305233 + 0.952278i 0.598734π0.598734\pi
354354 0 0
355355 0 0
356356 0 0
357357 −627264. −0.260483
358358 0 0
359359 1.16186e6 0.475794 0.237897 0.971290i 0.423542π-0.423542\pi
0.237897 + 0.971290i 0.423542π0.423542\pi
360360 0 0
361361 −1.77720e6 −0.717743
362362 0 0
363363 1.56659e6 0.624005
364364 0 0
365365 0 0
366366 0 0
367367 1.08923e6 0.422139 0.211069 0.977471i 0.432305π-0.432305\pi
0.211069 + 0.977471i 0.432305π0.432305\pi
368368 0 0
369369 −1.70537e6 −0.652009
370370 0 0
371371 −1.71547e6 −0.647066
372372 0 0
373373 −3.50577e6 −1.30470 −0.652350 0.757918i 0.726217π-0.726217\pi
−0.652350 + 0.757918i 0.726217π0.726217\pi
374374 0 0
375375 0 0
376376 0 0
377377 −248292. −0.0899724
378378 0 0
379379 4.04385e6 1.44610 0.723048 0.690798i 0.242740π-0.242740\pi
0.723048 + 0.690798i 0.242740π0.242740\pi
380380 0 0
381381 −4.03814e6 −1.42518
382382 0 0
383383 −5.18746e6 −1.80700 −0.903499 0.428591i 0.859010π-0.859010\pi
−0.903499 + 0.428591i 0.859010π0.859010\pi
384384 0 0
385385 0 0
386386 0 0
387387 −1.19790e6 −0.406577
388388 0 0
389389 −950346. −0.318425 −0.159213 0.987244i 0.550896π-0.550896\pi
−0.159213 + 0.987244i 0.550896π0.550896\pi
390390 0 0
391391 −2.43778e6 −0.806403
392392 0 0
393393 1.21176e6 0.395763
394394 0 0
395395 0 0
396396 0 0
397397 520738. 0.165822 0.0829112 0.996557i 0.473578π-0.473578\pi
0.0829112 + 0.996557i 0.473578π0.473578\pi
398398 0 0
399399 882816. 0.277612
400400 0 0
401401 764370. 0.237379 0.118690 0.992931i 0.462131π-0.462131\pi
0.118690 + 0.992931i 0.462131π0.462131\pi
402402 0 0
403403 1.77901e6 0.545651
404404 0 0
405405 0 0
406406 0 0
407407 160920. 0.0481531
408408 0 0
409409 2.64051e6 0.780511 0.390255 0.920707i 0.372387π-0.372387\pi
0.390255 + 0.920707i 0.372387π0.372387\pi
410410 0 0
411411 3.80570e6 1.11130
412412 0 0
413413 −674784. −0.194666
414414 0 0
415415 0 0
416416 0 0
417417 −1.77989e6 −0.501248
418418 0 0
419419 −4.98020e6 −1.38584 −0.692918 0.721016i 0.743675π-0.743675\pi
−0.692918 + 0.721016i 0.743675π0.743675\pi
420420 0 0
421421 −237994. −0.0654426 −0.0327213 0.999465i 0.510417π-0.510417\pi
−0.0327213 + 0.999465i 0.510417π0.510417\pi
422422 0 0
423423 −128304. −0.0348650
424424 0 0
425425 0 0
426426 0 0
427427 −3.05694e6 −0.811368
428428 0 0
429429 2.70864e6 0.710572
430430 0 0
431431 −3.88238e6 −1.00671 −0.503356 0.864079i 0.667902π-0.667902\pi
−0.503356 + 0.864079i 0.667902π0.667902\pi
432432 0 0
433433 66958.0 0.0171626 0.00858129 0.999963i 0.497268π-0.497268\pi
0.00858129 + 0.999963i 0.497268π0.497268\pi
434434 0 0
435435 0 0
436436 0 0
437437 3.43094e6 0.859429
438438 0 0
439439 −6.50135e6 −1.61006 −0.805031 0.593233i 0.797851π-0.797851\pi
−0.805031 + 0.593233i 0.797851π0.797851\pi
440440 0 0
441441 897237. 0.219690
442442 0 0
443443 4.60760e6 1.11549 0.557745 0.830012i 0.311667π-0.311667\pi
0.557745 + 0.830012i 0.311667π0.311667\pi
444444 0 0
445445 0 0
446446 0 0
447447 2.35937e6 0.558505
448448 0 0
449449 3.77671e6 0.884092 0.442046 0.896992i 0.354253π-0.354253\pi
0.442046 + 0.896992i 0.354253π0.354253\pi
450450 0 0
451451 9.30204e6 2.15346
452452 0 0
453453 892320. 0.204303
454454 0 0
455455 0 0
456456 0 0
457457 3.18069e6 0.712412 0.356206 0.934407i 0.384070π-0.384070\pi
0.356206 + 0.934407i 0.384070π0.384070\pi
458458 0 0
459459 2.43778e6 0.540085
460460 0 0
461461 6.68547e6 1.46514 0.732571 0.680691i 0.238320π-0.238320\pi
0.732571 + 0.680691i 0.238320π0.238320\pi
462462 0 0
463463 4.35122e6 0.943318 0.471659 0.881781i 0.343655π-0.343655\pi
0.471659 + 0.881781i 0.343655π0.343655\pi
464464 0 0
465465 0 0
466466 0 0
467467 −7.07994e6 −1.50223 −0.751117 0.660170i 0.770484π-0.770484\pi
−0.751117 + 0.660170i 0.770484π0.770484\pi
468468 0 0
469469 −1.91946e6 −0.402945
470470 0 0
471471 −1.45054e6 −0.301284
472472 0 0
473473 6.53400e6 1.34285
474474 0 0
475475 0 0
476476 0 0
477477 1.92991e6 0.388365
478478 0 0
479479 3.22186e6 0.641604 0.320802 0.947146i 0.396048π-0.396048\pi
0.320802 + 0.947146i 0.396048π0.396048\pi
480480 0 0
481481 124564. 0.0245488
482482 0 0
483483 4.33382e6 0.845286
484484 0 0
485485 0 0
486486 0 0
487487 −2.29710e6 −0.438891 −0.219446 0.975625i 0.570425π-0.570425\pi
−0.219446 + 0.975625i 0.570425π0.570425\pi
488488 0 0
489489 1.33608e6 0.252674
490490 0 0
491491 2.82150e6 0.528173 0.264087 0.964499i 0.414930π-0.414930\pi
0.264087 + 0.964499i 0.414930π0.414930\pi
492492 0 0
493493 352836. 0.0653816
494494 0 0
495495 0 0
496496 0 0
497497 −4.12474e6 −0.749040
498498 0 0
499499 −4.13628e6 −0.743634 −0.371817 0.928306i 0.621265π-0.621265\pi
−0.371817 + 0.928306i 0.621265π0.621265\pi
500500 0 0
501501 5.90198e6 1.05052
502502 0 0
503503 −8.33263e6 −1.46846 −0.734230 0.678901i 0.762457π-0.762457\pi
−0.734230 + 0.678901i 0.762457π0.762457\pi
504504 0 0
505505 0 0
506506 0 0
507507 −2.35883e6 −0.407546
508508 0 0
509509 4.34101e6 0.742670 0.371335 0.928499i 0.378900π-0.378900\pi
0.371335 + 0.928499i 0.378900π0.378900\pi
510510 0 0
511511 −5.94546e6 −1.00724
512512 0 0
513513 −3.43094e6 −0.575599
514514 0 0
515515 0 0
516516 0 0
517517 699840. 0.115152
518518 0 0
519519 −8.48945e6 −1.38344
520520 0 0
521521 −6.74185e6 −1.08814 −0.544070 0.839040i 0.683117π-0.683117\pi
−0.544070 + 0.839040i 0.683117π0.683117\pi
522522 0 0
523523 7.72196e6 1.23445 0.617224 0.786787i 0.288257π-0.288257\pi
0.617224 + 0.786787i 0.288257π0.288257\pi
524524 0 0
525525 0 0
526526 0 0
527527 −2.52806e6 −0.396517
528528 0 0
529529 1.04065e7 1.61683
530530 0 0
531531 759132. 0.116837
532532 0 0
533533 7.20047e6 1.09785
534534 0 0
535535 0 0
536536 0 0
537537 5.92402e6 0.886504
538538 0 0
539539 −4.89402e6 −0.725594
540540 0 0
541541 −682066. −0.100192 −0.0500960 0.998744i 0.515953π-0.515953\pi
−0.0500960 + 0.998744i 0.515953π0.515953\pi
542542 0 0
543543 −6.71340e6 −0.977109
544544 0 0
545545 0 0
546546 0 0
547547 −2.15772e6 −0.308337 −0.154169 0.988045i 0.549270π-0.549270\pi
−0.154169 + 0.988045i 0.549270π0.549270\pi
548548 0 0
549549 3.43906e6 0.486978
550550 0 0
551551 −496584. −0.0696809
552552 0 0
553553 −6.76826e6 −0.941161
554554 0 0
555555 0 0
556556 0 0
557557 2.67597e6 0.365463 0.182731 0.983163i 0.441506π-0.441506\pi
0.182731 + 0.983163i 0.441506π0.441506\pi
558558 0 0
559559 5.05780e6 0.684592
560560 0 0
561561 −3.84912e6 −0.516362
562562 0 0
563563 3.55331e6 0.472457 0.236228 0.971698i 0.424089π-0.424089\pi
0.236228 + 0.971698i 0.424089π0.424089\pi
564564 0 0
565565 0 0
566566 0 0
567567 −2.21681e6 −0.289581
568568 0 0
569569 −1.29225e7 −1.67327 −0.836633 0.547764i 0.815479π-0.815479\pi
−0.836633 + 0.547764i 0.815479π0.815479\pi
570570 0 0
571571 −6.08357e6 −0.780851 −0.390426 0.920634i 0.627672π-0.627672\pi
−0.390426 + 0.920634i 0.627672π0.627672\pi
572572 0 0
573573 −8.68838e6 −1.10548
574574 0 0
575575 0 0
576576 0 0
577577 1.58241e7 1.97869 0.989347 0.145579i 0.0465047π-0.0465047\pi
0.989347 + 0.145579i 0.0465047π0.0465047\pi
578578 0 0
579579 −85272.0 −0.0105709
580580 0 0
581581 −5.95901e6 −0.732375
582582 0 0
583583 −1.05268e7 −1.28269
584584 0 0
585585 0 0
586586 0 0
587587 −4.60220e6 −0.551278 −0.275639 0.961261i 0.588889π-0.588889\pi
−0.275639 + 0.961261i 0.588889π0.588889\pi
588588 0 0
589589 3.55802e6 0.422590
590590 0 0
591591 6.36530e6 0.749636
592592 0 0
593593 −8.61122e6 −1.00561 −0.502803 0.864401i 0.667698π-0.667698\pi
−0.502803 + 0.864401i 0.667698π0.667698\pi
594594 0 0
595595 0 0
596596 0 0
597597 674016. 0.0773988
598598 0 0
599599 −7.98228e6 −0.908992 −0.454496 0.890749i 0.650181π-0.650181\pi
−0.454496 + 0.890749i 0.650181π0.650181\pi
600600 0 0
601601 1.01740e7 1.14896 0.574481 0.818518i 0.305204π-0.305204\pi
0.574481 + 0.818518i 0.305204π0.305204\pi
602602 0 0
603603 2.15939e6 0.241845
604604 0 0
605605 0 0
606606 0 0
607607 9.95843e6 1.09703 0.548516 0.836140i 0.315193π-0.315193\pi
0.548516 + 0.836140i 0.315193π0.315193\pi
608608 0 0
609609 −627264. −0.0685342
610610 0 0
611611 541728. 0.0587054
612612 0 0
613613 −4.19586e6 −0.450993 −0.225497 0.974244i 0.572400π-0.572400\pi
−0.225497 + 0.974244i 0.572400π0.572400\pi
614614 0 0
615615 0 0
616616 0 0
617617 −9.12551e6 −0.965038 −0.482519 0.875885i 0.660278π-0.660278\pi
−0.482519 + 0.875885i 0.660278π0.660278\pi
618618 0 0
619619 6.45734e6 0.677372 0.338686 0.940900i 0.390018π-0.390018\pi
0.338686 + 0.940900i 0.390018π0.390018\pi
620620 0 0
621621 −1.68428e7 −1.75261
622622 0 0
623623 2.61835e6 0.270276
624624 0 0
625625 0 0
626626 0 0
627627 5.41728e6 0.550316
628628 0 0
629629 −177012. −0.0178392
630630 0 0
631631 −1.40514e7 −1.40490 −0.702450 0.711733i 0.747910π-0.747910\pi
−0.702450 + 0.711733i 0.747910π0.747910\pi
632632 0 0
633633 −4.07035e6 −0.403759
634634 0 0
635635 0 0
636636 0 0
637637 −3.78833e6 −0.369913
638638 0 0
639639 4.64033e6 0.449569
640640 0 0
641641 8.47168e6 0.814375 0.407188 0.913345i 0.366510π-0.366510\pi
0.407188 + 0.913345i 0.366510π0.366510\pi
642642 0 0
643643 −488564. −0.0466009 −0.0233004 0.999729i 0.507417π-0.507417\pi
−0.0233004 + 0.999729i 0.507417π0.507417\pi
644644 0 0
645645 0 0
646646 0 0
647647 −2.48119e6 −0.233023 −0.116512 0.993189i 0.537171π-0.537171\pi
−0.116512 + 0.993189i 0.537171π0.537171\pi
648648 0 0
649649 −4.14072e6 −0.385891
650650 0 0
651651 4.49434e6 0.415636
652652 0 0
653653 5.29130e6 0.485601 0.242800 0.970076i 0.421934π-0.421934\pi
0.242800 + 0.970076i 0.421934π0.421934\pi
654654 0 0
655655 0 0
656656 0 0
657657 6.68864e6 0.604539
658658 0 0
659659 4.72468e6 0.423798 0.211899 0.977292i 0.432035π-0.432035\pi
0.211899 + 0.977292i 0.432035π0.432035\pi
660660 0 0
661661 −6.17420e6 −0.549639 −0.274819 0.961496i 0.588618π-0.588618\pi
−0.274819 + 0.961496i 0.588618π0.588618\pi
662662 0 0
663663 −2.97950e6 −0.263245
664664 0 0
665665 0 0
666666 0 0
667667 −2.43778e6 −0.212168
668668 0 0
669669 −9.35232e6 −0.807893
670670 0 0
671671 −1.87585e7 −1.60839
672672 0 0
673673 9.40925e6 0.800787 0.400394 0.916343i 0.368873π-0.368873\pi
0.400394 + 0.916343i 0.368873π0.368873\pi
674674 0 0
675675 0 0
676676 0 0
677677 −1.50086e7 −1.25854 −0.629272 0.777185i 0.716647π-0.716647\pi
−0.629272 + 0.777185i 0.716647π0.716647\pi
678678 0 0
679679 1.07710e7 0.896567
680680 0 0
681681 8.93851e6 0.738580
682682 0 0
683683 1.29707e7 1.06393 0.531963 0.846768i 0.321455π-0.321455\pi
0.531963 + 0.846768i 0.321455π0.321455\pi
684684 0 0
685685 0 0
686686 0 0
687687 −3.27295e6 −0.264574
688688 0 0
689689 −8.14849e6 −0.653927
690690 0 0
691691 2.26556e7 1.80501 0.902506 0.430677i 0.141725π-0.141725\pi
0.902506 + 0.430677i 0.141725π0.141725\pi
692692 0 0
693693 −4.70448e6 −0.372116
694694 0 0
695695 0 0
696696 0 0
697697 −1.02322e7 −0.797791
698698 0 0
699699 1.84615e6 0.142914
700700 0 0
701701 1.90169e7 1.46166 0.730828 0.682562i 0.239134π-0.239134\pi
0.730828 + 0.682562i 0.239134π0.239134\pi
702702 0 0
703703 249128. 0.0190123
704704 0 0
705705 0 0
706706 0 0
707707 993168. 0.0747264
708708 0 0
709709 1.51311e7 1.13046 0.565231 0.824933i 0.308787π-0.308787\pi
0.565231 + 0.824933i 0.308787π0.308787\pi
710710 0 0
711711 7.61429e6 0.564879
712712 0 0
713713 1.74666e7 1.28672
714714 0 0
715715 0 0
716716 0 0
717717 1.38568e7 1.00662
718718 0 0
719719 −1.50323e7 −1.08443 −0.542217 0.840238i 0.682415π-0.682415\pi
−0.542217 + 0.840238i 0.682415π0.682415\pi
720720 0 0
721721 2.39853e6 0.171833
722722 0 0
723723 7.88489e6 0.560983
724724 0 0
725725 0 0
726726 0 0
727727 7.41230e6 0.520136 0.260068 0.965590i 0.416255π-0.416255\pi
0.260068 + 0.965590i 0.416255π0.416255\pi
728728 0 0
729729 1.44612e7 1.00782
730730 0 0
731731 −7.18740e6 −0.497483
732732 0 0
733733 2.77928e6 0.191061 0.0955306 0.995426i 0.469545π-0.469545\pi
0.0955306 + 0.995426i 0.469545π0.469545\pi
734734 0 0
735735 0 0
736736 0 0
737737 −1.17785e7 −0.798768
738738 0 0
739739 −1.21046e7 −0.815342 −0.407671 0.913129i 0.633659π-0.633659\pi
−0.407671 + 0.913129i 0.633659π0.633659\pi
740740 0 0
741741 4.19338e6 0.280555
742742 0 0
743743 −4.46926e6 −0.297005 −0.148502 0.988912i 0.547445π-0.547445\pi
−0.148502 + 0.988912i 0.547445π0.547445\pi
744744 0 0
745745 0 0
746746 0 0
747747 6.70388e6 0.439567
748748 0 0
749749 −1.07680e7 −0.701345
750750 0 0
751751 2.88463e7 1.86634 0.933168 0.359442i 0.117033π-0.117033\pi
0.933168 + 0.359442i 0.117033π0.117033\pi
752752 0 0
753753 1.61028e7 1.03494
754754 0 0
755755 0 0
756756 0 0
757757 −9.60868e6 −0.609430 −0.304715 0.952444i 0.598561π-0.598561\pi
−0.304715 + 0.952444i 0.598561π0.598561\pi
758758 0 0
759759 2.65939e7 1.67563
760760 0 0
761761 4.54588e6 0.284549 0.142274 0.989827i 0.454558π-0.454558\pi
0.142274 + 0.989827i 0.454558π0.454558\pi
762762 0 0
763763 8.79138e6 0.546696
764764 0 0
765765 0 0
766766 0 0
767767 −3.20522e6 −0.196730
768768 0 0
769769 −2.15923e7 −1.31669 −0.658345 0.752716i 0.728743π-0.728743\pi
−0.658345 + 0.752716i 0.728743π0.728743\pi
770770 0 0
771771 −1.58825e6 −0.0962238
772772 0 0
773773 1.48400e7 0.893276 0.446638 0.894715i 0.352621π-0.352621\pi
0.446638 + 0.894715i 0.352621π0.352621\pi
774774 0 0
775775 0 0
776776 0 0
777777 314688. 0.0186994
778778 0 0
779779 1.44009e7 0.850251
780780 0 0
781781 −2.53109e7 −1.48484
782782 0 0
783783 2.43778e6 0.142098
784784 0 0
785785 0 0
786786 0 0
787787 2.48785e7 1.43182 0.715909 0.698194i 0.246013π-0.246013\pi
0.715909 + 0.698194i 0.246013π0.246013\pi
788788 0 0
789789 −1.13193e7 −0.647330
790790 0 0
791791 2.60885e6 0.148254
792792 0 0
793793 −1.45205e7 −0.819970
794794 0 0
795795 0 0
796796 0 0
797797 −3.16080e7 −1.76259 −0.881294 0.472568i 0.843327π-0.843327\pi
−0.881294 + 0.472568i 0.843327π0.843327\pi
798798 0 0
799799 −769824. −0.0426604
800800 0 0
801801 −2.94565e6 −0.162218
802802 0 0
803803 −3.64835e7 −1.99668
804804 0 0
805805 0 0
806806 0 0
807807 1.16102e7 0.627562
808808 0 0
809809 −3.10009e6 −0.166534 −0.0832669 0.996527i 0.526535π-0.526535\pi
−0.0832669 + 0.996527i 0.526535π0.526535\pi
810810 0 0
811811 1.87180e6 0.0999328 0.0499664 0.998751i 0.484089π-0.484089\pi
0.0499664 + 0.998751i 0.484089π0.484089\pi
812812 0 0
813813 −6.21984e6 −0.330030
814814 0 0
815815 0 0
816816 0 0
817817 1.01156e7 0.530196
818818 0 0
819819 −3.64162e6 −0.189707
820820 0 0
821821 −2.00184e7 −1.03650 −0.518252 0.855228i 0.673417π-0.673417\pi
−0.518252 + 0.855228i 0.673417π0.673417\pi
822822 0 0
823823 −1.53118e7 −0.787999 −0.394000 0.919111i 0.628909π-0.628909\pi
−0.394000 + 0.919111i 0.628909π0.628909\pi
824824 0 0
825825 0 0
826826 0 0
827827 −9.59310e6 −0.487748 −0.243874 0.969807i 0.578418π-0.578418\pi
−0.243874 + 0.969807i 0.578418π0.578418\pi
828828 0 0
829829 2.52209e7 1.27460 0.637302 0.770615i 0.280051π-0.280051\pi
0.637302 + 0.770615i 0.280051π0.280051\pi
830830 0 0
831831 −2.66727e7 −1.33988
832832 0 0
833833 5.38342e6 0.268810
834834 0 0
835835 0 0
836836 0 0
837837 −1.74666e7 −0.861778
838838 0 0
839839 −1.77623e7 −0.871154 −0.435577 0.900151i 0.643456π-0.643456\pi
−0.435577 + 0.900151i 0.643456π0.643456\pi
840840 0 0
841841 −2.01583e7 −0.982798
842842 0 0
843843 −2.35937e6 −0.114348
844844 0 0
845845 0 0
846846 0 0
847847 1.14883e7 0.550234
848848 0 0
849849 1.86273e7 0.886913
850850 0 0
851851 1.22299e6 0.0578895
852852 0 0
853853 486970. 0.0229155 0.0114578 0.999934i 0.496353π-0.496353\pi
0.0114578 + 0.999934i 0.496353π0.496353\pi
854854 0 0
855855 0 0
856856 0 0
857857 1.92634e6 0.0895945 0.0447972 0.998996i 0.485736π-0.485736\pi
0.0447972 + 0.998996i 0.485736π0.485736\pi
858858 0 0
859859 2.23538e7 1.03364 0.516820 0.856094i 0.327116π-0.327116\pi
0.516820 + 0.856094i 0.327116π0.327116\pi
860860 0 0
861861 1.81907e7 0.836258
862862 0 0
863863 −1.85838e7 −0.849390 −0.424695 0.905337i 0.639619π-0.639619\pi
−0.424695 + 0.905337i 0.639619π0.639619\pi
864864 0 0
865865 0 0
866866 0 0
867867 −1.28043e7 −0.578504
868868 0 0
869869 −4.15325e7 −1.86569
870870 0 0
871871 −9.11742e6 −0.407217
872872 0 0
873873 −1.21174e7 −0.538114
874874 0 0
875875 0 0
876876 0 0
877877 2.91048e7 1.27781 0.638905 0.769286i 0.279388π-0.279388\pi
0.638905 + 0.769286i 0.279388π0.279388\pi
878878 0 0
879879 1.28660e7 0.561659
880880 0 0
881881 −3.14696e6 −0.136600 −0.0683001 0.997665i 0.521758π-0.521758\pi
−0.0683001 + 0.997665i 0.521758π0.521758\pi
882882 0 0
883883 −1.59995e7 −0.690566 −0.345283 0.938499i 0.612217π-0.612217\pi
−0.345283 + 0.938499i 0.612217π0.612217\pi
884884 0 0
885885 0 0
886886 0 0
887887 3.45874e7 1.47608 0.738039 0.674758i 0.235752π-0.235752\pi
0.738039 + 0.674758i 0.235752π0.235752\pi
888888 0 0
889889 −2.96131e7 −1.25669
890890 0 0
891891 −1.36031e7 −0.574044
892892 0 0
893893 1.08346e6 0.0454656
894894 0 0
895895 0 0
896896 0 0
897897 2.05857e7 0.854248
898898 0 0
899899 −2.52806e6 −0.104325
900900 0 0
901901 1.15794e7 0.475199
902902 0 0
903903 1.27776e7 0.521471
904904 0 0
905905 0 0
906906 0 0
907907 −1.74396e7 −0.703914 −0.351957 0.936016i 0.614484π-0.614484\pi
−0.351957 + 0.936016i 0.614484π0.614484\pi
908908 0 0
909909 −1.11731e6 −0.0448503
910910 0 0
911911 −2.59589e6 −0.103631 −0.0518155 0.998657i 0.516501π-0.516501\pi
−0.0518155 + 0.998657i 0.516501π0.516501\pi
912912 0 0
913913 −3.65666e7 −1.45180
914914 0 0
915915 0 0
916916 0 0
917917 8.88624e6 0.348975
918918 0 0
919919 −1.76411e7 −0.689028 −0.344514 0.938781i 0.611956π-0.611956\pi
−0.344514 + 0.938781i 0.611956π0.611956\pi
920920 0 0
921921 −1.90307e7 −0.739275
922922 0 0
923923 −1.95925e7 −0.756982
924924 0 0
925925 0 0
926926 0 0
927927 −2.69834e6 −0.103133
928928 0 0
929929 3.96785e7 1.50840 0.754199 0.656646i 0.228025π-0.228025\pi
0.754199 + 0.656646i 0.228025π0.228025\pi
930930 0 0
931931 −7.57667e6 −0.286486
932932 0 0
933933 −8.76874e6 −0.329787
934934 0 0
935935 0 0
936936 0 0
937937 −3.93413e7 −1.46386 −0.731930 0.681380i 0.761380π-0.761380\pi
−0.731930 + 0.681380i 0.761380π0.761380\pi
938938 0 0
939939 −7.01830e6 −0.259757
940940 0 0
941941 4.62506e7 1.70272 0.851361 0.524581i 0.175778π-0.175778\pi
0.851361 + 0.524581i 0.175778π0.175778\pi
942942 0 0
943943 7.06955e7 2.58888
944944 0 0
945945 0 0
946946 0 0
947947 3.79025e7 1.37339 0.686693 0.726947i 0.259062π-0.259062\pi
0.686693 + 0.726947i 0.259062π0.259062\pi
948948 0 0
949949 −2.82409e7 −1.01792
950950 0 0
951951 2.97944e7 1.06828
952952 0 0
953953 2.66462e7 0.950394 0.475197 0.879879i 0.342377π-0.342377\pi
0.475197 + 0.879879i 0.342377π0.342377\pi
954954 0 0
955955 0 0
956956 0 0
957957 −3.84912e6 −0.135857
958958 0 0
959959 2.79085e7 0.979918
960960 0 0
961961 −1.05156e7 −0.367304
962962 0 0
963963 1.21140e7 0.420943
964964 0 0
965965 0 0
966966 0 0
967967 −4.09790e7 −1.40927 −0.704637 0.709568i 0.748890π-0.748890\pi
−0.704637 + 0.709568i 0.748890π0.748890\pi
968968 0 0
969969 −5.95901e6 −0.203875
970970 0 0
971971 −2.72034e7 −0.925922 −0.462961 0.886379i 0.653213π-0.653213\pi
−0.462961 + 0.886379i 0.653213π0.653213\pi
972972 0 0
973973 −1.30525e7 −0.441990
974974 0 0
975975 0 0
976976 0 0
977977 −2.53555e7 −0.849839 −0.424919 0.905231i 0.639698π-0.639698\pi
−0.424919 + 0.905231i 0.639698π0.639698\pi
978978 0 0
979979 1.60672e7 0.535775
980980 0 0
981981 −9.89030e6 −0.328123
982982 0 0
983983 −1.19139e7 −0.393252 −0.196626 0.980479i 0.562998π-0.562998\pi
−0.196626 + 0.980479i 0.562998π0.562998\pi
984984 0 0
985985 0 0
986986 0 0
987987 1.36858e6 0.0447173
988988 0 0
989989 4.96584e7 1.61437
990990 0 0
991991 2.91931e7 0.944268 0.472134 0.881527i 0.343484π-0.343484\pi
0.472134 + 0.881527i 0.343484π0.343484\pi
992992 0 0
993993 4.53538e6 0.145962
994994 0 0
995995 0 0
996996 0 0
997997 1.73001e7 0.551201 0.275601 0.961272i 0.411123π-0.411123\pi
0.275601 + 0.961272i 0.411123π0.411123\pi
998998 0 0
999999 −1.22299e6 −0.0387713
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 100.6.a.b.1.1 1
3.2 odd 2 900.6.a.h.1.1 1
4.3 odd 2 400.6.a.d.1.1 1
5.2 odd 4 100.6.c.b.49.1 2
5.3 odd 4 100.6.c.b.49.2 2
5.4 even 2 4.6.a.a.1.1 1
15.2 even 4 900.6.d.a.649.2 2
15.8 even 4 900.6.d.a.649.1 2
15.14 odd 2 36.6.a.a.1.1 1
20.3 even 4 400.6.c.f.49.1 2
20.7 even 4 400.6.c.f.49.2 2
20.19 odd 2 16.6.a.b.1.1 1
35.4 even 6 196.6.e.g.177.1 2
35.9 even 6 196.6.e.g.165.1 2
35.19 odd 6 196.6.e.d.165.1 2
35.24 odd 6 196.6.e.d.177.1 2
35.34 odd 2 196.6.a.e.1.1 1
40.19 odd 2 64.6.a.b.1.1 1
40.29 even 2 64.6.a.f.1.1 1
45.4 even 6 324.6.e.a.217.1 2
45.14 odd 6 324.6.e.d.217.1 2
45.29 odd 6 324.6.e.d.109.1 2
45.34 even 6 324.6.e.a.109.1 2
55.54 odd 2 484.6.a.a.1.1 1
60.59 even 2 144.6.a.c.1.1 1
65.34 odd 4 676.6.d.a.337.2 2
65.44 odd 4 676.6.d.a.337.1 2
65.64 even 2 676.6.a.a.1.1 1
80.19 odd 4 256.6.b.c.129.2 2
80.29 even 4 256.6.b.g.129.1 2
80.59 odd 4 256.6.b.c.129.1 2
80.69 even 4 256.6.b.g.129.2 2
120.29 odd 2 576.6.a.bc.1.1 1
120.59 even 2 576.6.a.bd.1.1 1
140.139 even 2 784.6.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4.6.a.a.1.1 1 5.4 even 2
16.6.a.b.1.1 1 20.19 odd 2
36.6.a.a.1.1 1 15.14 odd 2
64.6.a.b.1.1 1 40.19 odd 2
64.6.a.f.1.1 1 40.29 even 2
100.6.a.b.1.1 1 1.1 even 1 trivial
100.6.c.b.49.1 2 5.2 odd 4
100.6.c.b.49.2 2 5.3 odd 4
144.6.a.c.1.1 1 60.59 even 2
196.6.a.e.1.1 1 35.34 odd 2
196.6.e.d.165.1 2 35.19 odd 6
196.6.e.d.177.1 2 35.24 odd 6
196.6.e.g.165.1 2 35.9 even 6
196.6.e.g.177.1 2 35.4 even 6
256.6.b.c.129.1 2 80.59 odd 4
256.6.b.c.129.2 2 80.19 odd 4
256.6.b.g.129.1 2 80.29 even 4
256.6.b.g.129.2 2 80.69 even 4
324.6.e.a.109.1 2 45.34 even 6
324.6.e.a.217.1 2 45.4 even 6
324.6.e.d.109.1 2 45.29 odd 6
324.6.e.d.217.1 2 45.14 odd 6
400.6.a.d.1.1 1 4.3 odd 2
400.6.c.f.49.1 2 20.3 even 4
400.6.c.f.49.2 2 20.7 even 4
484.6.a.a.1.1 1 55.54 odd 2
576.6.a.bc.1.1 1 120.29 odd 2
576.6.a.bd.1.1 1 120.59 even 2
676.6.a.a.1.1 1 65.64 even 2
676.6.d.a.337.1 2 65.44 odd 4
676.6.d.a.337.2 2 65.34 odd 4
784.6.a.d.1.1 1 140.139 even 2
900.6.a.h.1.1 1 3.2 odd 2
900.6.d.a.649.1 2 15.8 even 4
900.6.d.a.649.2 2 15.2 even 4