Properties

Label 100.6.c.b.49.2
Level 100100
Weight 66
Character 100.49
Analytic conductor 16.03816.038
Analytic rank 00
Dimension 22
Inner twists 22

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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] = [100,6,Mod(49,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 6, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.49"); 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.c (of order 22, degree 11, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,0,0,0,0,0,0,198] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 16.038381981316.0383819813
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 4)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 49.2
Root 1.00000i1.00000i of defining polynomial
Character χ\chi == 100.49
Dual form 100.6.c.b.49.1

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) == q+12.0000iq388.0000iq7+99.0000q9+540.000q11+418.000iq13+594.000iq17836.000q19+1056.00q21+4104.00iq23+4104.00iq27+594.000q29+4256.00q31+6480.00iq33298.000iq375016.00q39+17226.0q41+12100.0iq431296.00iq47+9063.00q497128.00q5119494.0iq5310032.0iq57+7668.00q5934738.0q618712.00iq63+21812.0iq6749248.0q6946872.0q7167562.0iq7347520.0iq77+76912.0q7925191.0q8167716.0iq83+7128.00iq8729754.0q89+36784.0q91+51072.0iq93122398.iq97+53460.0q99+O(q100)q+12.0000i q^{3} -88.0000i q^{7} +99.0000 q^{9} +540.000 q^{11} +418.000i q^{13} +594.000i q^{17} -836.000 q^{19} +1056.00 q^{21} +4104.00i q^{23} +4104.00i q^{27} +594.000 q^{29} +4256.00 q^{31} +6480.00i q^{33} -298.000i q^{37} -5016.00 q^{39} +17226.0 q^{41} +12100.0i q^{43} -1296.00i q^{47} +9063.00 q^{49} -7128.00 q^{51} -19494.0i q^{53} -10032.0i q^{57} +7668.00 q^{59} -34738.0 q^{61} -8712.00i q^{63} +21812.0i q^{67} -49248.0 q^{69} -46872.0 q^{71} -67562.0i q^{73} -47520.0i q^{77} +76912.0 q^{79} -25191.0 q^{81} -67716.0i q^{83} +7128.00i q^{87} -29754.0 q^{89} +36784.0 q^{91} +51072.0i q^{93} -122398. i q^{97} +53460.0 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+198q9+1080q111672q19+2112q21+1188q29+8512q3110032q39+34452q41+18126q4914256q51+15336q5969476q6198496q6993744q71++106920q99+O(q100) 2 q + 198 q^{9} + 1080 q^{11} - 1672 q^{19} + 2112 q^{21} + 1188 q^{29} + 8512 q^{31} - 10032 q^{39} + 34452 q^{41} + 18126 q^{49} - 14256 q^{51} + 15336 q^{59} - 69476 q^{61} - 98496 q^{69} - 93744 q^{71}+ \cdots + 106920 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/100Z)×\left(\mathbb{Z}/100\mathbb{Z}\right)^\times.

nn 5151 7777
χ(n)\chi(n) 11 1-1

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 12.0000i 0.769800i 0.922958 + 0.384900i 0.125764π0.125764\pi
−0.922958 + 0.384900i 0.874236π0.874236\pi
44 0 0
55 0 0
66 0 0
77 − 88.0000i − 0.678793i −0.940643 0.339397i 0.889777π-0.889777\pi
0.940643 0.339397i 0.110223π-0.110223\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 418.000i 0.685990i 0.939337 + 0.342995i 0.111441π0.111441\pi
−0.939337 + 0.342995i 0.888559π0.888559\pi
1414 0 0
1515 0 0
1616 0 0
1717 594.000i 0.498499i 0.968439 + 0.249249i 0.0801839π0.0801839\pi
−0.968439 + 0.249249i 0.919816π0.919816\pi
1818 0 0
1919 −836.000 −0.531279 −0.265639 0.964072i 0.585583π-0.585583\pi
−0.265639 + 0.964072i 0.585583π0.585583\pi
2020 0 0
2121 1056.00 0.522535
2222 0 0
2323 4104.00i 1.61766i 0.588041 + 0.808831i 0.299899π0.299899\pi
−0.588041 + 0.808831i 0.700101π0.700101\pi
2424 0 0
2525 0 0
2626 0 0
2727 4104.00i 1.08342i
2828 0 0
2929 594.000 0.131157 0.0655785 0.997847i 0.479111π-0.479111\pi
0.0655785 + 0.997847i 0.479111π0.479111\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 6480.00i 1.03583i
3434 0 0
3535 0 0
3636 0 0
3737 − 298.000i − 0.0357859i −0.999840 0.0178930i 0.994304π-0.994304\pi
0.999840 0.0178930i 0.00569581π-0.00569581\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 12100.0i 0.997963i 0.866613 + 0.498981i 0.166292π0.166292\pi
−0.866613 + 0.498981i 0.833708π0.833708\pi
4444 0 0
4545 0 0
4646 0 0
4747 − 1296.00i − 0.0855777i −0.999084 0.0427888i 0.986376π-0.986376\pi
0.999084 0.0427888i 0.0136243π-0.0136243\pi
4848 0 0
4949 9063.00 0.539240
5050 0 0
5151 −7128.00 −0.383745
5252 0 0
5353 − 19494.0i − 0.953260i −0.879104 0.476630i 0.841858π-0.841858\pi
0.879104 0.476630i 0.158142π-0.158142\pi
5454 0 0
5555 0 0
5656 0 0
5757 − 10032.0i − 0.408978i
5858 0 0
5959 7668.00 0.286782 0.143391 0.989666i 0.454199π-0.454199\pi
0.143391 + 0.989666i 0.454199π0.454199\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 − 8712.00i − 0.276545i
6464 0 0
6565 0 0
6666 0 0
6767 21812.0i 0.593620i 0.954937 + 0.296810i 0.0959228π0.0959228\pi
−0.954937 + 0.296810i 0.904077π0.904077\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 − 67562.0i − 1.48387i −0.670473 0.741934i 0.733909π-0.733909\pi
0.670473 0.741934i 0.266091π-0.266091\pi
7474 0 0
7575 0 0
7676 0 0
7777 − 47520.0i − 0.913376i
7878 0 0
7979 76912.0 1.38652 0.693260 0.720687i 0.256174π-0.256174\pi
0.693260 + 0.720687i 0.256174π0.256174\pi
8080 0 0
8181 −25191.0 −0.426612
8282 0 0
8383 − 67716.0i − 1.07894i −0.842006 0.539468i 0.818625π-0.818625\pi
0.842006 0.539468i 0.181375π-0.181375\pi
8484 0 0
8585 0 0
8686 0 0
8787 7128.00i 0.100965i
8888 0 0
8989 −29754.0 −0.398172 −0.199086 0.979982i 0.563797π-0.563797\pi
−0.199086 + 0.979982i 0.563797π0.563797\pi
9090 0 0
9191 36784.0 0.465646
9292 0 0
9393 51072.0i 0.612316i
9494 0 0
9595 0 0
9696 0 0
9797 − 122398.i − 1.32082i −0.750903 0.660412i 0.770382π-0.770382\pi
0.750903 0.660412i 0.229618π-0.229618\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 27256.0i 0.253145i 0.991957 + 0.126572i 0.0403976π0.0403976\pi
−0.991957 + 0.126572i 0.959602π0.959602\pi
104104 0 0
105105 0 0
106106 0 0
107107 122364.i 1.03322i 0.856220 + 0.516612i 0.172807π0.172807\pi
−0.856220 + 0.516612i 0.827193π0.827193\pi
108108 0 0
109109 −99902.0 −0.805393 −0.402697 0.915334i 0.631927π-0.631927\pi
−0.402697 + 0.915334i 0.631927π0.631927\pi
110110 0 0
111111 3576.00 0.0275480
112112 0 0
113113 29646.0i 0.218409i 0.994019 + 0.109204i 0.0348303π0.0348303\pi
−0.994019 + 0.109204i 0.965170π0.965170\pi
114114 0 0
115115 0 0
116116 0 0
117117 41382.0i 0.279477i
118118 0 0
119119 52272.0 0.338378
120120 0 0
121121 130549. 0.810607
122122 0 0
123123 206712.i 1.23198i
124124 0 0
125125 0 0
126126 0 0
127127 336512.i 1.85136i 0.378305 + 0.925681i 0.376507π0.376507\pi
−0.378305 + 0.925681i 0.623493π0.623493\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 73568.0i 0.360628i
134134 0 0
135135 0 0
136136 0 0
137137 − 317142.i − 1.44362i −0.692092 0.721809i 0.743311π-0.743311\pi
0.692092 0.721809i 0.256689π-0.256689\pi
138138 0 0
139139 148324. 0.651140 0.325570 0.945518i 0.394444π-0.394444\pi
0.325570 + 0.945518i 0.394444π0.394444\pi
140140 0 0
141141 15552.0 0.0658777
142142 0 0
143143 225720.i 0.923060i
144144 0 0
145145 0 0
146146 0 0
147147 108756.i 0.415107i
148148 0 0
149149 −196614. −0.725519 −0.362759 0.931883i 0.618165π-0.618165\pi
−0.362759 + 0.931883i 0.618165π0.618165\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 58806.0i 0.203092i
154154 0 0
155155 0 0
156156 0 0
157157 120878.i 0.391380i 0.980666 + 0.195690i 0.0626946π0.0626946\pi
−0.980666 + 0.195690i 0.937305π0.937305\pi
158158 0 0
159159 233928. 0.733820
160160 0 0
161161 361152. 1.09806
162162 0 0
163163 111340.i 0.328233i 0.986441 + 0.164116i 0.0524773π0.0524773\pi
−0.986441 + 0.164116i 0.947523π0.947523\pi
164164 0 0
165165 0 0
166166 0 0
167167 − 491832.i − 1.36466i −0.731043 0.682332i 0.760966π-0.760966\pi
0.731043 0.682332i 0.239034π-0.239034\pi
168168 0 0
169169 196569. 0.529417
170170 0 0
171171 −82764.0 −0.216447
172172 0 0
173173 − 707454.i − 1.79714i −0.438826 0.898572i 0.644605π-0.644605\pi
0.438826 0.898572i 0.355395π-0.355395\pi
174174 0 0
175175 0 0
176176 0 0
177177 92016.0i 0.220765i
178178 0 0
179179 −493668. −1.15160 −0.575801 0.817590i 0.695310π-0.695310\pi
−0.575801 + 0.817590i 0.695310π0.695310\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.i − 0.920149i
184184 0 0
185185 0 0
186186 0 0
187187 320760.i 0.670774i
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 − 7106.00i − 0.0137319i −0.999976 0.00686597i 0.997814π-0.997814\pi
0.999976 0.00686597i 0.00218552π-0.00218552\pi
194194 0 0
195195 0 0
196196 0 0
197197 − 530442.i − 0.973806i −0.873456 0.486903i 0.838127π-0.838127\pi
0.873456 0.486903i 0.161873π-0.161873\pi
198198 0 0
199199 −56168.0 −0.100544 −0.0502720 0.998736i 0.516009π-0.516009\pi
−0.0502720 + 0.998736i 0.516009π0.516009\pi
200200 0 0
201201 −261744. −0.456969
202202 0 0
203203 − 52272.0i − 0.0890285i
204204 0 0
205205 0 0
206206 0 0
207207 406296.i 0.659047i
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.i − 0.849465i
214214 0 0
215215 0 0
216216 0 0
217217 − 374528.i − 0.539927i
218218 0 0
219219 810744. 1.14228
220220 0 0
221221 −248292. −0.341965
222222 0 0
223223 − 779360.i − 1.04948i −0.851261 0.524742i 0.824162π-0.824162\pi
0.851261 0.524742i 0.175838π-0.175838\pi
224224 0 0
225225 0 0
226226 0 0
227227 − 744876.i − 0.959443i −0.877421 0.479722i 0.840738π-0.840738\pi
0.877421 0.479722i 0.159262π-0.159262\pi
228228 0 0
229229 272746. 0.343692 0.171846 0.985124i 0.445027π-0.445027\pi
0.171846 + 0.985124i 0.445027π0.445027\pi
230230 0 0
231231 570240. 0.703117
232232 0 0
233233 153846.i 0.185651i 0.995682 + 0.0928253i 0.0295898π0.0295898\pi
−0.995682 + 0.0928253i 0.970410π0.970410\pi
234234 0 0
235235 0 0
236236 0 0
237237 922944.i 1.06734i
238238 0 0
239239 −1.15474e6 −1.30764 −0.653820 0.756650i 0.726834π-0.726834\pi
−0.653820 + 0.756650i 0.726834π0.726834\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.i 0.755017i
244244 0 0
245245 0 0
246246 0 0
247247 − 349448.i − 0.364452i
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 2.21616e6i 2.17671i
254254 0 0
255255 0 0
256256 0 0
257257 132354.i 0.124998i 0.998045 + 0.0624992i 0.0199071π0.0199071\pi
−0.998045 + 0.0624992i 0.980093π0.980093\pi
258258 0 0
259259 −26224.0 −0.0242912
260260 0 0
261261 58806.0 0.0534343
262262 0 0
263263 − 943272.i − 0.840906i −0.907314 0.420453i 0.861871π-0.861871\pi
0.907314 0.420453i 0.138129π-0.138129\pi
264264 0 0
265265 0 0
266266 0 0
267267 − 357048.i − 0.306513i
268268 0 0
269269 −967518. −0.815227 −0.407613 0.913155i 0.633639π-0.633639\pi
−0.407613 + 0.913155i 0.633639π0.633639\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.i 0.358454i
274274 0 0
275275 0 0
276276 0 0
277277 2.22273e6i 1.74055i 0.492566 + 0.870275i 0.336059π0.336059\pi
−0.492566 + 0.870275i 0.663941π0.663941\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 1.55228e6i 1.15213i 0.817403 + 0.576067i 0.195413π0.195413\pi
−0.817403 + 0.576067i 0.804587π0.804587\pi
284284 0 0
285285 0 0
286286 0 0
287287 − 1.51589e6i − 1.08633i
288288 0 0
289289 1.06702e6 0.751499
290290 0 0
291291 1.46878e6 1.01677
292292 0 0
293293 1.07217e6i 0.729616i 0.931083 + 0.364808i 0.118865π0.118865\pi
−0.931083 + 0.364808i 0.881135π0.881135\pi
294294 0 0
295295 0 0
296296 0 0
297297 2.21616e6i 1.45784i
298298 0 0
299299 −1.71547e6 −1.10970
300300 0 0
301301 1.06480e6 0.677410
302302 0 0
303303 135432.i 0.0847451i
304304 0 0
305305 0 0
306306 0 0
307307 1.58589e6i 0.960346i 0.877174 + 0.480173i 0.159426π0.159426\pi
−0.877174 + 0.480173i 0.840574π0.840574\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.i − 0.337435i −0.985664 0.168717i 0.946038π-0.946038\pi
0.985664 0.168717i 0.0539625π-0.0539625\pi
314314 0 0
315315 0 0
316316 0 0
317317 − 2.48287e6i − 1.38773i −0.720105 0.693865i 0.755906π-0.755906\pi
0.720105 0.693865i 0.244094π-0.244094\pi
318318 0 0
319319 320760. 0.176483
320320 0 0
321321 −1.46837e6 −0.795376
322322 0 0
323323 − 496584.i − 0.264842i
324324 0 0
325325 0 0
326326 0 0
327327 − 1.19882e6i − 0.619992i
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 − 29502.0i − 0.0145794i
334334 0 0
335335 0 0
336336 0 0
337337 639122.i 0.306555i 0.988183 + 0.153278i 0.0489829π0.0489829\pi
−0.988183 + 0.153278i 0.951017π0.951017\pi
338338 0 0
339339 −355752. −0.168131
340340 0 0
341341 2.29824e6 1.07031
342342 0 0
343343 − 2.27656e6i − 1.04483i
344344 0 0
345345 0 0
346346 0 0
347347 − 2.90466e6i − 1.29501i −0.762063 0.647503i 0.775813π-0.775813\pi
0.762063 0.647503i 0.224187π-0.224187\pi
348348 0 0
349349 3.99157e6 1.75420 0.877102 0.480304i 0.159474π-0.159474\pi
0.877102 + 0.480304i 0.159474π0.159474\pi
350350 0 0
351351 −1.71547e6 −0.743217
352352 0 0
353353 − 1.42922e6i − 0.610466i −0.952278 0.305233i 0.901266π-0.901266\pi
0.952278 0.305233i 0.0987344π-0.0987344\pi
354354 0 0
355355 0 0
356356 0 0
357357 627264.i 0.260483i
358358 0 0
359359 −1.16186e6 −0.475794 −0.237897 0.971290i 0.576458π-0.576458\pi
−0.237897 + 0.971290i 0.576458π0.576458\pi
360360 0 0
361361 −1.77720e6 −0.717743
362362 0 0
363363 1.56659e6i 0.624005i
364364 0 0
365365 0 0
366366 0 0
367367 − 1.08923e6i − 0.422139i −0.977471 0.211069i 0.932305π-0.932305\pi
0.977471 0.211069i 0.0676946π-0.0676946\pi
368368 0 0
369369 1.70537e6 0.652009
370370 0 0
371371 −1.71547e6 −0.647066
372372 0 0
373373 − 3.50577e6i − 1.30470i −0.757918 0.652350i 0.773783π-0.773783\pi
0.757918 0.652350i 0.226217π-0.226217\pi
374374 0 0
375375 0 0
376376 0 0
377377 248292.i 0.0899724i
378378 0 0
379379 −4.04385e6 −1.44610 −0.723048 0.690798i 0.757260π-0.757260\pi
−0.723048 + 0.690798i 0.757260π0.757260\pi
380380 0 0
381381 −4.03814e6 −1.42518
382382 0 0
383383 − 5.18746e6i − 1.80700i −0.428591 0.903499i 0.640990π-0.640990\pi
0.428591 0.903499i 0.359010π-0.359010\pi
384384 0 0
385385 0 0
386386 0 0
387387 1.19790e6i 0.406577i
388388 0 0
389389 950346. 0.318425 0.159213 0.987244i 0.449104π-0.449104\pi
0.159213 + 0.987244i 0.449104π0.449104\pi
390390 0 0
391391 −2.43778e6 −0.806403
392392 0 0
393393 1.21176e6i 0.395763i
394394 0 0
395395 0 0
396396 0 0
397397 − 520738.i − 0.165822i −0.996557 0.0829112i 0.973578π-0.973578\pi
0.996557 0.0829112i 0.0264218π-0.0264218\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 1.77901e6i 0.545651i
404404 0 0
405405 0 0
406406 0 0
407407 − 160920.i − 0.0481531i
408408 0 0
409409 −2.64051e6 −0.780511 −0.390255 0.920707i 0.627613π-0.627613\pi
−0.390255 + 0.920707i 0.627613π0.627613\pi
410410 0 0
411411 3.80570e6 1.11130
412412 0 0
413413 − 674784.i − 0.194666i
414414 0 0
415415 0 0
416416 0 0
417417 1.77989e6i 0.501248i
418418 0 0
419419 4.98020e6 1.38584 0.692918 0.721016i 0.256325π-0.256325\pi
0.692918 + 0.721016i 0.256325π0.256325\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.i − 0.0348650i
424424 0 0
425425 0 0
426426 0 0
427427 3.05694e6i 0.811368i
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 66958.0i 0.0171626i 0.999963 + 0.00858129i 0.00273154π0.00273154\pi
−0.999963 + 0.00858129i 0.997268π0.997268\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 3.43094e6i − 0.859429i
438438 0 0
439439 6.50135e6 1.61006 0.805031 0.593233i 0.202149π-0.202149\pi
0.805031 + 0.593233i 0.202149π0.202149\pi
440440 0 0
441441 897237. 0.219690
442442 0 0
443443 4.60760e6i 1.11549i 0.830012 + 0.557745i 0.188333π0.188333\pi
−0.830012 + 0.557745i 0.811667π0.811667\pi
444444 0 0
445445 0 0
446446 0 0
447447 − 2.35937e6i − 0.558505i
448448 0 0
449449 −3.77671e6 −0.884092 −0.442046 0.896992i 0.645747π-0.645747\pi
−0.442046 + 0.896992i 0.645747π0.645747\pi
450450 0 0
451451 9.30204e6 2.15346
452452 0 0
453453 892320.i 0.204303i
454454 0 0
455455 0 0
456456 0 0
457457 − 3.18069e6i − 0.712412i −0.934407 0.356206i 0.884070π-0.884070\pi
0.934407 0.356206i 0.115930π-0.115930\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 4.35122e6i 0.943318i 0.881781 + 0.471659i 0.156345π0.156345\pi
−0.881781 + 0.471659i 0.843655π0.843655\pi
464464 0 0
465465 0 0
466466 0 0
467467 7.07994e6i 1.50223i 0.660170 + 0.751117i 0.270484π0.270484\pi
−0.660170 + 0.751117i 0.729516π0.729516\pi
468468 0 0
469469 1.91946e6 0.402945
470470 0 0
471471 −1.45054e6 −0.301284
472472 0 0
473473 6.53400e6i 1.34285i
474474 0 0
475475 0 0
476476 0 0
477477 − 1.92991e6i − 0.388365i
478478 0 0
479479 −3.22186e6 −0.641604 −0.320802 0.947146i 0.603952π-0.603952\pi
−0.320802 + 0.947146i 0.603952π0.603952\pi
480480 0 0
481481 124564. 0.0245488
482482 0 0
483483 4.33382e6i 0.845286i
484484 0 0
485485 0 0
486486 0 0
487487 2.29710e6i 0.438891i 0.975625 + 0.219446i 0.0704248π0.0704248\pi
−0.975625 + 0.219446i 0.929575π0.929575\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.i 0.0653816i
494494 0 0
495495 0 0
496496 0 0
497497 4.12474e6i 0.749040i
498498 0 0
499499 4.13628e6 0.743634 0.371817 0.928306i 0.378735π-0.378735\pi
0.371817 + 0.928306i 0.378735π0.378735\pi
500500 0 0
501501 5.90198e6 1.05052
502502 0 0
503503 − 8.33263e6i − 1.46846i −0.678901 0.734230i 0.737543π-0.737543\pi
0.678901 0.734230i 0.262457π-0.262457\pi
504504 0 0
505505 0 0
506506 0 0
507507 2.35883e6i 0.407546i
508508 0 0
509509 −4.34101e6 −0.742670 −0.371335 0.928499i 0.621100π-0.621100\pi
−0.371335 + 0.928499i 0.621100π0.621100\pi
510510 0 0
511511 −5.94546e6 −1.00724
512512 0 0
513513 − 3.43094e6i − 0.575599i
514514 0 0
515515 0 0
516516 0 0
517517 − 699840.i − 0.115152i
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 7.72196e6i 1.23445i 0.786787 + 0.617224i 0.211743π0.211743\pi
−0.786787 + 0.617224i 0.788257π0.788257\pi
524524 0 0
525525 0 0
526526 0 0
527527 2.52806e6i 0.396517i
528528 0 0
529529 −1.04065e7 −1.61683
530530 0 0
531531 759132. 0.116837
532532 0 0
533533 7.20047e6i 1.09785i
534534 0 0
535535 0 0
536536 0 0
537537 − 5.92402e6i − 0.886504i
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 − 6.71340e6i − 0.977109i
544544 0 0
545545 0 0
546546 0 0
547547 2.15772e6i 0.308337i 0.988045 + 0.154169i 0.0492699π0.0492699\pi
−0.988045 + 0.154169i 0.950730π0.950730\pi
548548 0 0
549549 −3.43906e6 −0.486978
550550 0 0
551551 −496584. −0.0696809
552552 0 0
553553 − 6.76826e6i − 0.941161i
554554 0 0
555555 0 0
556556 0 0
557557 − 2.67597e6i − 0.365463i −0.983163 0.182731i 0.941506π-0.941506\pi
0.983163 0.182731i 0.0584939π-0.0584939\pi
558558 0 0
559559 −5.05780e6 −0.684592
560560 0 0
561561 −3.84912e6 −0.516362
562562 0 0
563563 3.55331e6i 0.472457i 0.971698 + 0.236228i 0.0759113π0.0759113\pi
−0.971698 + 0.236228i 0.924089π0.924089\pi
564564 0 0
565565 0 0
566566 0 0
567567 2.21681e6i 0.289581i
568568 0 0
569569 1.29225e7 1.67327 0.836633 0.547764i 0.184521π-0.184521\pi
0.836633 + 0.547764i 0.184521π0.184521\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 − 8.68838e6i − 1.10548i
574574 0 0
575575 0 0
576576 0 0
577577 − 1.58241e7i − 1.97869i −0.145579 0.989347i 0.546505π-0.546505\pi
0.145579 0.989347i 0.453495π-0.453495\pi
578578 0 0
579579 85272.0 0.0105709
580580 0 0
581581 −5.95901e6 −0.732375
582582 0 0
583583 − 1.05268e7i − 1.28269i
584584 0 0
585585 0 0
586586 0 0
587587 4.60220e6i 0.551278i 0.961261 + 0.275639i 0.0888894π0.0888894\pi
−0.961261 + 0.275639i 0.911111π0.911111\pi
588588 0 0
589589 −3.55802e6 −0.422590
590590 0 0
591591 6.36530e6 0.749636
592592 0 0
593593 − 8.61122e6i − 1.00561i −0.864401 0.502803i 0.832302π-0.832302\pi
0.864401 0.502803i 0.167698π-0.167698\pi
594594 0 0
595595 0 0
596596 0 0
597597 − 674016.i − 0.0773988i
598598 0 0
599599 7.98228e6 0.908992 0.454496 0.890749i 0.349819π-0.349819\pi
0.454496 + 0.890749i 0.349819π0.349819\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 2.15939e6i 0.241845i
604604 0 0
605605 0 0
606606 0 0
607607 − 9.95843e6i − 1.09703i −0.836140 0.548516i 0.815193π-0.815193\pi
0.836140 0.548516i 0.184807π-0.184807\pi
608608 0 0
609609 627264. 0.0685342
610610 0 0
611611 541728. 0.0587054
612612 0 0
613613 − 4.19586e6i − 0.450993i −0.974244 0.225497i 0.927600π-0.927600\pi
0.974244 0.225497i 0.0724005π-0.0724005\pi
614614 0 0
615615 0 0
616616 0 0
617617 9.12551e6i 0.965038i 0.875885 + 0.482519i 0.160278π0.160278\pi
−0.875885 + 0.482519i 0.839722π0.839722\pi
618618 0 0
619619 −6.45734e6 −0.677372 −0.338686 0.940900i 0.609982π-0.609982\pi
−0.338686 + 0.940900i 0.609982π0.609982\pi
620620 0 0
621621 −1.68428e7 −1.75261
622622 0 0
623623 2.61835e6i 0.270276i
624624 0 0
625625 0 0
626626 0 0
627627 − 5.41728e6i − 0.550316i
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 − 4.07035e6i − 0.403759i
634634 0 0
635635 0 0
636636 0 0
637637 3.78833e6i 0.369913i
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.i − 0.0466009i −0.999729 0.0233004i 0.992583π-0.992583\pi
0.999729 0.0233004i 0.00741743π-0.00741743\pi
644644 0 0
645645 0 0
646646 0 0
647647 2.48119e6i 0.233023i 0.993189 + 0.116512i 0.0371713π0.0371713\pi
−0.993189 + 0.116512i 0.962829π0.962829\pi
648648 0 0
649649 4.14072e6 0.385891
650650 0 0
651651 4.49434e6 0.415636
652652 0 0
653653 5.29130e6i 0.485601i 0.970076 + 0.242800i 0.0780660π0.0780660\pi
−0.970076 + 0.242800i 0.921934π0.921934\pi
654654 0 0
655655 0 0
656656 0 0
657657 − 6.68864e6i − 0.604539i
658658 0 0
659659 −4.72468e6 −0.423798 −0.211899 0.977292i 0.567965π-0.567965\pi
−0.211899 + 0.977292i 0.567965π0.567965\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 − 2.97950e6i − 0.263245i
664664 0 0
665665 0 0
666666 0 0
667667 2.43778e6i 0.212168i
668668 0 0
669669 9.35232e6 0.807893
670670 0 0
671671 −1.87585e7 −1.60839
672672 0 0
673673 9.40925e6i 0.800787i 0.916343 + 0.400394i 0.131127π0.131127\pi
−0.916343 + 0.400394i 0.868873π0.868873\pi
674674 0 0
675675 0 0
676676 0 0
677677 1.50086e7i 1.25854i 0.777185 + 0.629272i 0.216647π0.216647\pi
−0.777185 + 0.629272i 0.783353π0.783353\pi
678678 0 0
679679 −1.07710e7 −0.896567
680680 0 0
681681 8.93851e6 0.738580
682682 0 0
683683 1.29707e7i 1.06393i 0.846768 + 0.531963i 0.178545π0.178545\pi
−0.846768 + 0.531963i 0.821455π0.821455\pi
684684 0 0
685685 0 0
686686 0 0
687687 3.27295e6i 0.264574i
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 − 4.70448e6i − 0.372116i
694694 0 0
695695 0 0
696696 0 0
697697 1.02322e7i 0.797791i
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.i 0.0190123i
704704 0 0
705705 0 0
706706 0 0
707707 − 993168.i − 0.0747264i
708708 0 0
709709 −1.51311e7 −1.13046 −0.565231 0.824933i 0.691213π-0.691213\pi
−0.565231 + 0.824933i 0.691213π0.691213\pi
710710 0 0
711711 7.61429e6 0.564879
712712 0 0
713713 1.74666e7i 1.28672i
714714 0 0
715715 0 0
716716 0 0
717717 − 1.38568e7i − 1.00662i
718718 0 0
719719 1.50323e7 1.08443 0.542217 0.840238i 0.317585π-0.317585\pi
0.542217 + 0.840238i 0.317585π0.317585\pi
720720 0 0
721721 2.39853e6 0.171833
722722 0 0
723723 7.88489e6i 0.560983i
724724 0 0
725725 0 0
726726 0 0
727727 − 7.41230e6i − 0.520136i −0.965590 0.260068i 0.916255π-0.916255\pi
0.965590 0.260068i 0.0837449π-0.0837449\pi
728728 0 0
729729 −1.44612e7 −1.00782
730730 0 0
731731 −7.18740e6 −0.497483
732732 0 0
733733 2.77928e6i 0.191061i 0.995426 + 0.0955306i 0.0304548π0.0304548\pi
−0.995426 + 0.0955306i 0.969545π0.969545\pi
734734 0 0
735735 0 0
736736 0 0
737737 1.17785e7i 0.798768i
738738 0 0
739739 1.21046e7 0.815342 0.407671 0.913129i 0.366341π-0.366341\pi
0.407671 + 0.913129i 0.366341π0.366341\pi
740740 0 0
741741 4.19338e6 0.280555
742742 0 0
743743 − 4.46926e6i − 0.297005i −0.988912 0.148502i 0.952555π-0.952555\pi
0.988912 0.148502i 0.0474452π-0.0474452\pi
744744 0 0
745745 0 0
746746 0 0
747747 − 6.70388e6i − 0.439567i
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 1.61028e7i 1.03494i
754754 0 0
755755 0 0
756756 0 0
757757 9.60868e6i 0.609430i 0.952444 + 0.304715i 0.0985612π0.0985612\pi
−0.952444 + 0.304715i 0.901439π0.901439\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 8.79138e6i 0.546696i
764764 0 0
765765 0 0
766766 0 0
767767 3.20522e6i 0.196730i
768768 0 0
769769 2.15923e7 1.31669 0.658345 0.752716i 0.271257π-0.271257\pi
0.658345 + 0.752716i 0.271257π0.271257\pi
770770 0 0
771771 −1.58825e6 −0.0962238
772772 0 0
773773 1.48400e7i 0.893276i 0.894715 + 0.446638i 0.147379π0.147379\pi
−0.894715 + 0.446638i 0.852621π0.852621\pi
774774 0 0
775775 0 0
776776 0 0
777777 − 314688.i − 0.0186994i
778778 0 0
779779 −1.44009e7 −0.850251
780780 0 0
781781 −2.53109e7 −1.48484
782782 0 0
783783 2.43778e6i 0.142098i
784784 0 0
785785 0 0
786786 0 0
787787 − 2.48785e7i − 1.43182i −0.698194 0.715909i 0.746013π-0.746013\pi
0.698194 0.715909i 0.253987π-0.253987\pi
788788 0 0
789789 1.13193e7 0.647330
790790 0 0
791791 2.60885e6 0.148254
792792 0 0
793793 − 1.45205e7i − 0.819970i
794794 0 0
795795 0 0
796796 0 0
797797 3.16080e7i 1.76259i 0.472568 + 0.881294i 0.343327π0.343327\pi
−0.472568 + 0.881294i 0.656673π0.656673\pi
798798 0 0
799799 769824. 0.0426604
800800 0 0
801801 −2.94565e6 −0.162218
802802 0 0
803803 − 3.64835e7i − 1.99668i
804804 0 0
805805 0 0
806806 0 0
807807 − 1.16102e7i − 0.627562i
808808 0 0
809809 3.10009e6 0.166534 0.0832669 0.996527i 0.473465π-0.473465\pi
0.0832669 + 0.996527i 0.473465π0.473465\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 − 6.21984e6i − 0.330030i
814814 0 0
815815 0 0
816816 0 0
817817 − 1.01156e7i − 0.530196i
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 − 1.53118e7i − 0.787999i −0.919111 0.394000i 0.871091π-0.871091\pi
0.919111 0.394000i 0.128909π-0.128909\pi
824824 0 0
825825 0 0
826826 0 0
827827 9.59310e6i 0.487748i 0.969807 + 0.243874i 0.0784183π0.0784183\pi
−0.969807 + 0.243874i 0.921582π0.921582\pi
828828 0 0
829829 −2.52209e7 −1.27460 −0.637302 0.770615i 0.719949π-0.719949\pi
−0.637302 + 0.770615i 0.719949π0.719949\pi
830830 0 0
831831 −2.66727e7 −1.33988
832832 0 0
833833 5.38342e6i 0.268810i
834834 0 0
835835 0 0
836836 0 0
837837 1.74666e7i 0.861778i
838838 0 0
839839 1.77623e7 0.871154 0.435577 0.900151i 0.356544π-0.356544\pi
0.435577 + 0.900151i 0.356544π0.356544\pi
840840 0 0
841841 −2.01583e7 −0.982798
842842 0 0
843843 − 2.35937e6i − 0.114348i
844844 0 0
845845 0 0
846846 0 0
847847 − 1.14883e7i − 0.550234i
848848 0 0
849849 −1.86273e7 −0.886913
850850 0 0
851851 1.22299e6 0.0578895
852852 0 0
853853 486970.i 0.0229155i 0.999934 + 0.0114578i 0.00364720π0.00364720\pi
−0.999934 + 0.0114578i 0.996353π0.996353\pi
854854 0 0
855855 0 0
856856 0 0
857857 − 1.92634e6i − 0.0895945i −0.998996 0.0447972i 0.985736π-0.985736\pi
0.998996 0.0447972i 0.0142642π-0.0142642\pi
858858 0 0
859859 −2.23538e7 −1.03364 −0.516820 0.856094i 0.672884π-0.672884\pi
−0.516820 + 0.856094i 0.672884π0.672884\pi
860860 0 0
861861 1.81907e7 0.836258
862862 0 0
863863 − 1.85838e7i − 0.849390i −0.905337 0.424695i 0.860381π-0.860381\pi
0.905337 0.424695i 0.139619π-0.139619\pi
864864 0 0
865865 0 0
866866 0 0
867867 1.28043e7i 0.578504i
868868 0 0
869869 4.15325e7 1.86569
870870 0 0
871871 −9.11742e6 −0.407217
872872 0 0
873873 − 1.21174e7i − 0.538114i
874874 0 0
875875 0 0
876876 0 0
877877 − 2.91048e7i − 1.27781i −0.769286 0.638905i 0.779388π-0.779388\pi
0.769286 0.638905i 0.220612π-0.220612\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 − 1.59995e7i − 0.690566i −0.938499 0.345283i 0.887783π-0.887783\pi
0.938499 0.345283i 0.112217π-0.112217\pi
884884 0 0
885885 0 0
886886 0 0
887887 − 3.45874e7i − 1.47608i −0.674758 0.738039i 0.735752π-0.735752\pi
0.674758 0.738039i 0.264248π-0.264248\pi
888888 0 0
889889 2.96131e7 1.25669
890890 0 0
891891 −1.36031e7 −0.574044
892892 0 0
893893 1.08346e6i 0.0454656i
894894 0 0
895895 0 0
896896 0 0
897897 − 2.05857e7i − 0.854248i
898898 0 0
899899 2.52806e6 0.104325
900900 0 0
901901 1.15794e7 0.475199
902902 0 0
903903 1.27776e7i 0.521471i
904904 0 0
905905 0 0
906906 0 0
907907 1.74396e7i 0.703914i 0.936016 + 0.351957i 0.114484π0.114484\pi
−0.936016 + 0.351957i 0.885516π0.885516\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 − 3.65666e7i − 1.45180i
914914 0 0
915915 0 0
916916 0 0
917917 − 8.88624e6i − 0.348975i
918918 0 0
919919 1.76411e7 0.689028 0.344514 0.938781i 0.388044π-0.388044\pi
0.344514 + 0.938781i 0.388044π0.388044\pi
920920 0 0
921921 −1.90307e7 −0.739275
922922 0 0
923923 − 1.95925e7i − 0.756982i
924924 0 0
925925 0 0
926926 0 0
927927 2.69834e6i 0.103133i
928928 0 0
929929 −3.96785e7 −1.50840 −0.754199 0.656646i 0.771975π-0.771975\pi
−0.754199 + 0.656646i 0.771975π0.771975\pi
930930 0 0
931931 −7.57667e6 −0.286486
932932 0 0
933933 − 8.76874e6i − 0.329787i
934934 0 0
935935 0 0
936936 0 0
937937 3.93413e7i 1.46386i 0.681380 + 0.731930i 0.261380π0.261380\pi
−0.681380 + 0.731930i 0.738620π0.738620\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 7.06955e7i 2.58888i
944944 0 0
945945 0 0
946946 0 0
947947 − 3.79025e7i − 1.37339i −0.726947 0.686693i 0.759062π-0.759062\pi
0.726947 0.686693i 0.240938π-0.240938\pi
948948 0 0
949949 2.82409e7 1.01792
950950 0 0
951951 2.97944e7 1.06828
952952 0 0
953953 2.66462e7i 0.950394i 0.879879 + 0.475197i 0.157623π0.157623\pi
−0.879879 + 0.475197i 0.842377π0.842377\pi
954954 0 0
955955 0 0
956956 0 0
957957 3.84912e6i 0.135857i
958958 0 0
959959 −2.79085e7 −0.979918
960960 0 0
961961 −1.05156e7 −0.367304
962962 0 0
963963 1.21140e7i 0.420943i
964964 0 0
965965 0 0
966966 0 0
967967 4.09790e7i 1.40927i 0.709568 + 0.704637i 0.248890π0.248890\pi
−0.709568 + 0.704637i 0.751110π0.751110\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 − 1.30525e7i − 0.441990i
974974 0 0
975975 0 0
976976 0 0
977977 2.53555e7i 0.849839i 0.905231 + 0.424919i 0.139698π0.139698\pi
−0.905231 + 0.424919i 0.860302π0.860302\pi
978978 0 0
979979 −1.60672e7 −0.535775
980980 0 0
981981 −9.89030e6 −0.328123
982982 0 0
983983 − 1.19139e7i − 0.393252i −0.980479 0.196626i 0.937002π-0.937002\pi
0.980479 0.196626i 0.0629984π-0.0629984\pi
984984 0 0
985985 0 0
986986 0 0
987987 − 1.36858e6i − 0.0447173i
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 4.53538e6i 0.145962i
994994 0 0
995995 0 0
996996 0 0
997997 − 1.73001e7i − 0.551201i −0.961272 0.275601i 0.911123π-0.911123\pi
0.961272 0.275601i 0.0888767π-0.0888767\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.c.b.49.2 2
3.2 odd 2 900.6.d.a.649.1 2
4.3 odd 2 400.6.c.f.49.1 2
5.2 odd 4 100.6.a.b.1.1 1
5.3 odd 4 4.6.a.a.1.1 1
5.4 even 2 inner 100.6.c.b.49.1 2
15.2 even 4 900.6.a.h.1.1 1
15.8 even 4 36.6.a.a.1.1 1
15.14 odd 2 900.6.d.a.649.2 2
20.3 even 4 16.6.a.b.1.1 1
20.7 even 4 400.6.a.d.1.1 1
20.19 odd 2 400.6.c.f.49.2 2
35.3 even 12 196.6.e.d.177.1 2
35.13 even 4 196.6.a.e.1.1 1
35.18 odd 12 196.6.e.g.177.1 2
35.23 odd 12 196.6.e.g.165.1 2
35.33 even 12 196.6.e.d.165.1 2
40.3 even 4 64.6.a.b.1.1 1
40.13 odd 4 64.6.a.f.1.1 1
45.13 odd 12 324.6.e.a.217.1 2
45.23 even 12 324.6.e.d.217.1 2
45.38 even 12 324.6.e.d.109.1 2
45.43 odd 12 324.6.e.a.109.1 2
55.43 even 4 484.6.a.a.1.1 1
60.23 odd 4 144.6.a.c.1.1 1
65.8 even 4 676.6.d.a.337.2 2
65.18 even 4 676.6.d.a.337.1 2
65.38 odd 4 676.6.a.a.1.1 1
80.3 even 4 256.6.b.c.129.2 2
80.13 odd 4 256.6.b.g.129.1 2
80.43 even 4 256.6.b.c.129.1 2
80.53 odd 4 256.6.b.g.129.2 2
120.53 even 4 576.6.a.bc.1.1 1
120.83 odd 4 576.6.a.bd.1.1 1
140.83 odd 4 784.6.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4.6.a.a.1.1 1 5.3 odd 4
16.6.a.b.1.1 1 20.3 even 4
36.6.a.a.1.1 1 15.8 even 4
64.6.a.b.1.1 1 40.3 even 4
64.6.a.f.1.1 1 40.13 odd 4
100.6.a.b.1.1 1 5.2 odd 4
100.6.c.b.49.1 2 5.4 even 2 inner
100.6.c.b.49.2 2 1.1 even 1 trivial
144.6.a.c.1.1 1 60.23 odd 4
196.6.a.e.1.1 1 35.13 even 4
196.6.e.d.165.1 2 35.33 even 12
196.6.e.d.177.1 2 35.3 even 12
196.6.e.g.165.1 2 35.23 odd 12
196.6.e.g.177.1 2 35.18 odd 12
256.6.b.c.129.1 2 80.43 even 4
256.6.b.c.129.2 2 80.3 even 4
256.6.b.g.129.1 2 80.13 odd 4
256.6.b.g.129.2 2 80.53 odd 4
324.6.e.a.109.1 2 45.43 odd 12
324.6.e.a.217.1 2 45.13 odd 12
324.6.e.d.109.1 2 45.38 even 12
324.6.e.d.217.1 2 45.23 even 12
400.6.a.d.1.1 1 20.7 even 4
400.6.c.f.49.1 2 4.3 odd 2
400.6.c.f.49.2 2 20.19 odd 2
484.6.a.a.1.1 1 55.43 even 4
576.6.a.bc.1.1 1 120.53 even 4
576.6.a.bd.1.1 1 120.83 odd 4
676.6.a.a.1.1 1 65.38 odd 4
676.6.d.a.337.1 2 65.18 even 4
676.6.d.a.337.2 2 65.8 even 4
784.6.a.d.1.1 1 140.83 odd 4
900.6.a.h.1.1 1 15.2 even 4
900.6.d.a.649.1 2 3.2 odd 2
900.6.d.a.649.2 2 15.14 odd 2