Properties

Label 560.6.a.s.1.1
Level 560560
Weight 66
Character 560.1
Self dual yes
Analytic conductor 89.81589.815
Analytic rank 11
Dimension 33
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [560,6,Mod(1,560)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(560, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("560.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 560=2457 560 = 2^{4} \cdot 5 \cdot 7
Weight: k k == 6 6
Character orbit: [χ][\chi] == 560.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: 89.814939095389.8149390953
Analytic rank: 11
Dimension: 33
Coefficient field: Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3463x1890 x^{3} - 463x - 1890 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 22 2^{2}
Twist minimal: no (minimal twist has level 280)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 19.0769-19.0769 of defining polynomial
Character χ\chi == 560.1

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) == q21.0769q325.0000q549.0000q7+201.235q9+286.081q11751.545q13+526.922q15845.554q17+1518.68q19+1032.77q212468.45q23+625.000q25+880.283q27+895.029q29+9826.32q316029.69q33+1225.00q352697.90q37+15840.2q39+5770.13q413203.78q435030.87q45+21898.9q47+2401.00q49+17821.6q51+18207.6q537152.02q5532009.1q57+5021.37q59+22688.3q619860.50q63+18788.6q6515653.8q67+52027.2q69+21027.2q7152797.0q7313173.0q7514018.0q7780685.6q7967453.6q81+64197.4q83+21138.9q8518864.4q8772078.1q89+36825.7q91207108.q9337967.1q95+42008.8q97+57569.4q99+O(q100)q-21.0769 q^{3} -25.0000 q^{5} -49.0000 q^{7} +201.235 q^{9} +286.081 q^{11} -751.545 q^{13} +526.922 q^{15} -845.554 q^{17} +1518.68 q^{19} +1032.77 q^{21} -2468.45 q^{23} +625.000 q^{25} +880.283 q^{27} +895.029 q^{29} +9826.32 q^{31} -6029.69 q^{33} +1225.00 q^{35} -2697.90 q^{37} +15840.2 q^{39} +5770.13 q^{41} -3203.78 q^{43} -5030.87 q^{45} +21898.9 q^{47} +2401.00 q^{49} +17821.6 q^{51} +18207.6 q^{53} -7152.02 q^{55} -32009.1 q^{57} +5021.37 q^{59} +22688.3 q^{61} -9860.50 q^{63} +18788.6 q^{65} -15653.8 q^{67} +52027.2 q^{69} +21027.2 q^{71} -52797.0 q^{73} -13173.0 q^{75} -14018.0 q^{77} -80685.6 q^{79} -67453.6 q^{81} +64197.4 q^{83} +21138.9 q^{85} -18864.4 q^{87} -72078.1 q^{89} +36825.7 q^{91} -207108. q^{93} -37967.1 q^{95} +42008.8 q^{97} +57569.4 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q6q375q5147q7+209q9+578q11+80q13+150q151244q17944q19+294q211096q23+1875q25+3006q27+1868q29+6620q31+2662q33++156568q99+O(q100) 3 q - 6 q^{3} - 75 q^{5} - 147 q^{7} + 209 q^{9} + 578 q^{11} + 80 q^{13} + 150 q^{15} - 1244 q^{17} - 944 q^{19} + 294 q^{21} - 1096 q^{23} + 1875 q^{25} + 3006 q^{27} + 1868 q^{29} + 6620 q^{31} + 2662 q^{33}+ \cdots + 156568 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 −21.0769 −1.35208 −0.676041 0.736864i 0.736306π-0.736306\pi
−0.676041 + 0.736864i 0.736306π0.736306\pi
44 0 0
55 −25.0000 −0.447214
66 0 0
77 −49.0000 −0.377964
88 0 0
99 201.235 0.828126
1010 0 0
1111 286.081 0.712865 0.356432 0.934321i 0.383993π-0.383993\pi
0.356432 + 0.934321i 0.383993π0.383993\pi
1212 0 0
1313 −751.545 −1.23338 −0.616690 0.787206i 0.711527π-0.711527\pi
−0.616690 + 0.787206i 0.711527π0.711527\pi
1414 0 0
1515 526.922 0.604670
1616 0 0
1717 −845.554 −0.709609 −0.354805 0.934940i 0.615453π-0.615453\pi
−0.354805 + 0.934940i 0.615453π0.615453\pi
1818 0 0
1919 1518.68 0.965124 0.482562 0.875862i 0.339706π-0.339706\pi
0.482562 + 0.875862i 0.339706π0.339706\pi
2020 0 0
2121 1032.77 0.511039
2222 0 0
2323 −2468.45 −0.972982 −0.486491 0.873685i 0.661723π-0.661723\pi
−0.486491 + 0.873685i 0.661723π0.661723\pi
2424 0 0
2525 625.000 0.200000
2626 0 0
2727 880.283 0.232387
2828 0 0
2929 895.029 0.197625 0.0988125 0.995106i 0.468496π-0.468496\pi
0.0988125 + 0.995106i 0.468496π0.468496\pi
3030 0 0
3131 9826.32 1.83648 0.918241 0.396023i 0.129610π-0.129610\pi
0.918241 + 0.396023i 0.129610π0.129610\pi
3232 0 0
3333 −6029.69 −0.963852
3434 0 0
3535 1225.00 0.169031
3636 0 0
3737 −2697.90 −0.323982 −0.161991 0.986792i 0.551792π-0.551792\pi
−0.161991 + 0.986792i 0.551792π0.551792\pi
3838 0 0
3939 15840.2 1.66763
4040 0 0
4141 5770.13 0.536075 0.268038 0.963408i 0.413625π-0.413625\pi
0.268038 + 0.963408i 0.413625π0.413625\pi
4242 0 0
4343 −3203.78 −0.264236 −0.132118 0.991234i 0.542178π-0.542178\pi
−0.132118 + 0.991234i 0.542178π0.542178\pi
4444 0 0
4545 −5030.87 −0.370349
4646 0 0
4747 21898.9 1.44603 0.723016 0.690831i 0.242755π-0.242755\pi
0.723016 + 0.690831i 0.242755π0.242755\pi
4848 0 0
4949 2401.00 0.142857
5050 0 0
5151 17821.6 0.959450
5252 0 0
5353 18207.6 0.890353 0.445177 0.895443i 0.353141π-0.353141\pi
0.445177 + 0.895443i 0.353141π0.353141\pi
5454 0 0
5555 −7152.02 −0.318803
5656 0 0
5757 −32009.1 −1.30493
5858 0 0
5959 5021.37 0.187798 0.0938992 0.995582i 0.470067π-0.470067\pi
0.0938992 + 0.995582i 0.470067π0.470067\pi
6060 0 0
6161 22688.3 0.780689 0.390345 0.920669i 0.372356π-0.372356\pi
0.390345 + 0.920669i 0.372356π0.372356\pi
6262 0 0
6363 −9860.50 −0.313002
6464 0 0
6565 18788.6 0.551584
6666 0 0
6767 −15653.8 −0.426024 −0.213012 0.977050i 0.568327π-0.568327\pi
−0.213012 + 0.977050i 0.568327π0.568327\pi
6868 0 0
6969 52027.2 1.31555
7070 0 0
7171 21027.2 0.495035 0.247518 0.968883i 0.420385π-0.420385\pi
0.247518 + 0.968883i 0.420385π0.420385\pi
7272 0 0
7373 −52797.0 −1.15958 −0.579792 0.814764i 0.696866π-0.696866\pi
−0.579792 + 0.814764i 0.696866π0.696866\pi
7474 0 0
7575 −13173.0 −0.270416
7676 0 0
7777 −14018.0 −0.269438
7878 0 0
7979 −80685.6 −1.45455 −0.727275 0.686347i 0.759213π-0.759213\pi
−0.727275 + 0.686347i 0.759213π0.759213\pi
8080 0 0
8181 −67453.6 −1.14233
8282 0 0
8383 64197.4 1.02287 0.511437 0.859321i 0.329113π-0.329113\pi
0.511437 + 0.859321i 0.329113π0.329113\pi
8484 0 0
8585 21138.9 0.317347
8686 0 0
8787 −18864.4 −0.267205
8888 0 0
8989 −72078.1 −0.964558 −0.482279 0.876018i 0.660191π-0.660191\pi
−0.482279 + 0.876018i 0.660191π0.660191\pi
9090 0 0
9191 36825.7 0.466173
9292 0 0
9393 −207108. −2.48307
9494 0 0
9595 −37967.1 −0.431617
9696 0 0
9797 42008.8 0.453326 0.226663 0.973973i 0.427218π-0.427218\pi
0.226663 + 0.973973i 0.427218π0.427218\pi
9898 0 0
9999 57569.4 0.590342
100100 0 0
101101 46466.6 0.453249 0.226625 0.973982i 0.427231π-0.427231\pi
0.226625 + 0.973982i 0.427231π0.427231\pi
102102 0 0
103103 127580. 1.18493 0.592463 0.805598i 0.298156π-0.298156\pi
0.592463 + 0.805598i 0.298156π0.298156\pi
104104 0 0
105105 −25819.2 −0.228544
106106 0 0
107107 −81394.7 −0.687285 −0.343642 0.939101i 0.611661π-0.611661\pi
−0.343642 + 0.939101i 0.611661π0.611661\pi
108108 0 0
109109 43842.4 0.353450 0.176725 0.984260i 0.443450π-0.443450\pi
0.176725 + 0.984260i 0.443450π0.443450\pi
110110 0 0
111111 56863.3 0.438051
112112 0 0
113113 −182786. −1.34663 −0.673313 0.739358i 0.735129π-0.735129\pi
−0.673313 + 0.739358i 0.735129π0.735129\pi
114114 0 0
115115 61711.3 0.435131
116116 0 0
117117 −151237. −1.02139
118118 0 0
119119 41432.2 0.268207
120120 0 0
121121 −79208.7 −0.491824
122122 0 0
123123 −121616. −0.724818
124124 0 0
125125 −15625.0 −0.0894427
126126 0 0
127127 79395.4 0.436804 0.218402 0.975859i 0.429916π-0.429916\pi
0.218402 + 0.975859i 0.429916π0.429916\pi
128128 0 0
129129 67525.7 0.357268
130130 0 0
131131 146610. 0.746422 0.373211 0.927747i 0.378257π-0.378257\pi
0.373211 + 0.927747i 0.378257π0.378257\pi
132132 0 0
133133 −74415.5 −0.364783
134134 0 0
135135 −22007.1 −0.103927
136136 0 0
137137 −292940. −1.33345 −0.666726 0.745303i 0.732305π-0.732305\pi
−0.666726 + 0.745303i 0.732305π0.732305\pi
138138 0 0
139139 −227589. −0.999110 −0.499555 0.866282i 0.666503π-0.666503\pi
−0.499555 + 0.866282i 0.666503π0.666503\pi
140140 0 0
141141 −461561. −1.95515
142142 0 0
143143 −215003. −0.879233
144144 0 0
145145 −22375.7 −0.0883806
146146 0 0
147147 −50605.6 −0.193155
148148 0 0
149149 −210681. −0.777426 −0.388713 0.921359i 0.627080π-0.627080\pi
−0.388713 + 0.921359i 0.627080π0.627080\pi
150150 0 0
151151 −530330. −1.89279 −0.946397 0.323004i 0.895307π-0.895307\pi
−0.946397 + 0.323004i 0.895307π0.895307\pi
152152 0 0
153153 −170155. −0.587646
154154 0 0
155155 −245658. −0.821299
156156 0 0
157157 467511. 1.51371 0.756855 0.653582i 0.226735π-0.226735\pi
0.756855 + 0.653582i 0.226735π0.226735\pi
158158 0 0
159159 −383759. −1.20383
160160 0 0
161161 120954. 0.367753
162162 0 0
163163 346889. 1.02264 0.511319 0.859391i 0.329157π-0.329157\pi
0.511319 + 0.859391i 0.329157π0.329157\pi
164164 0 0
165165 150742. 0.431048
166166 0 0
167167 −483668. −1.34201 −0.671006 0.741452i 0.734137π-0.734137\pi
−0.671006 + 0.741452i 0.734137π0.734137\pi
168168 0 0
169169 193527. 0.521224
170170 0 0
171171 305612. 0.799245
172172 0 0
173173 −417227. −1.05988 −0.529940 0.848035i 0.677786π-0.677786\pi
−0.529940 + 0.848035i 0.677786π0.677786\pi
174174 0 0
175175 −30625.0 −0.0755929
176176 0 0
177177 −105835. −0.253919
178178 0 0
179179 −553314. −1.29074 −0.645371 0.763869i 0.723297π-0.723297\pi
−0.645371 + 0.763869i 0.723297π0.723297\pi
180180 0 0
181181 188698. 0.428125 0.214062 0.976820i 0.431330π-0.431330\pi
0.214062 + 0.976820i 0.431330π0.431330\pi
182182 0 0
183183 −478199. −1.05556
184184 0 0
185185 67447.5 0.144889
186186 0 0
187187 −241897. −0.505855
188188 0 0
189189 −43133.8 −0.0878342
190190 0 0
191191 −273571. −0.542608 −0.271304 0.962494i 0.587455π-0.587455\pi
−0.271304 + 0.962494i 0.587455π0.587455\pi
192192 0 0
193193 312739. 0.604350 0.302175 0.953252i 0.402287π-0.402287\pi
0.302175 + 0.953252i 0.402287π0.402287\pi
194194 0 0
195195 −396005. −0.745787
196196 0 0
197197 125978. 0.231274 0.115637 0.993292i 0.463109π-0.463109\pi
0.115637 + 0.993292i 0.463109π0.463109\pi
198198 0 0
199199 −701921. −1.25648 −0.628240 0.778019i 0.716225π-0.716225\pi
−0.628240 + 0.778019i 0.716225π0.716225\pi
200200 0 0
201201 329934. 0.576019
202202 0 0
203203 −43856.4 −0.0746953
204204 0 0
205205 −144253. −0.239740
206206 0 0
207207 −496738. −0.805752
208208 0 0
209209 434466. 0.688003
210210 0 0
211211 1.01585e6 1.57081 0.785403 0.618985i 0.212456π-0.212456\pi
0.785403 + 0.618985i 0.212456π0.212456\pi
212212 0 0
213213 −443188. −0.669328
214214 0 0
215215 80094.5 0.118170
216216 0 0
217217 −481490. −0.694125
218218 0 0
219219 1.11280e6 1.56785
220220 0 0
221221 635472. 0.875217
222222 0 0
223223 −1.02507e6 −1.38035 −0.690177 0.723641i 0.742467π-0.742467\pi
−0.690177 + 0.723641i 0.742467π0.742467\pi
224224 0 0
225225 125772. 0.165625
226226 0 0
227227 501667. 0.646177 0.323088 0.946369i 0.395279π-0.395279\pi
0.323088 + 0.946369i 0.395279π0.395279\pi
228228 0 0
229229 1.09069e6 1.37440 0.687200 0.726468i 0.258840π-0.258840\pi
0.687200 + 0.726468i 0.258840π0.258840\pi
230230 0 0
231231 295455. 0.364302
232232 0 0
233233 −115383. −0.139237 −0.0696183 0.997574i 0.522178π-0.522178\pi
−0.0696183 + 0.997574i 0.522178π0.522178\pi
234234 0 0
235235 −547473. −0.646685
236236 0 0
237237 1.70060e6 1.96667
238238 0 0
239239 755233. 0.855236 0.427618 0.903960i 0.359353π-0.359353\pi
0.427618 + 0.903960i 0.359353π0.359353\pi
240240 0 0
241241 −1.19575e6 −1.32616 −0.663082 0.748547i 0.730752π-0.730752\pi
−0.663082 + 0.748547i 0.730752π0.730752\pi
242242 0 0
243243 1.20780e6 1.31214
244244 0 0
245245 −60025.0 −0.0638877
246246 0 0
247247 −1.14136e6 −1.19036
248248 0 0
249249 −1.35308e6 −1.38301
250250 0 0
251251 −1.43265e6 −1.43535 −0.717673 0.696381i 0.754793π-0.754793\pi
−0.717673 + 0.696381i 0.754793π0.754793\pi
252252 0 0
253253 −706177. −0.693605
254254 0 0
255255 −445541. −0.429079
256256 0 0
257257 978660. 0.924270 0.462135 0.886810i 0.347084π-0.347084\pi
0.462135 + 0.886810i 0.347084π0.347084\pi
258258 0 0
259259 132197. 0.122454
260260 0 0
261261 180111. 0.163659
262262 0 0
263263 −662781. −0.590854 −0.295427 0.955365i 0.595462π-0.595462\pi
−0.295427 + 0.955365i 0.595462π0.595462\pi
264264 0 0
265265 −455189. −0.398178
266266 0 0
267267 1.51918e6 1.30416
268268 0 0
269269 −522166. −0.439975 −0.219988 0.975503i 0.570602π-0.570602\pi
−0.219988 + 0.975503i 0.570602π0.570602\pi
270270 0 0
271271 999234. 0.826502 0.413251 0.910617i 0.364393π-0.364393\pi
0.413251 + 0.910617i 0.364393π0.364393\pi
272272 0 0
273273 −776171. −0.630305
274274 0 0
275275 178801. 0.142573
276276 0 0
277277 1.41873e6 1.11097 0.555484 0.831527i 0.312533π-0.312533\pi
0.555484 + 0.831527i 0.312533π0.312533\pi
278278 0 0
279279 1.97740e6 1.52084
280280 0 0
281281 1.42688e6 1.07800 0.539002 0.842305i 0.318802π-0.318802\pi
0.539002 + 0.842305i 0.318802π0.318802\pi
282282 0 0
283283 −2.54018e6 −1.88538 −0.942689 0.333674i 0.891712π-0.891712\pi
−0.942689 + 0.333674i 0.891712π0.891712\pi
284284 0 0
285285 800228. 0.583581
286286 0 0
287287 −282736. −0.202617
288288 0 0
289289 −704895. −0.496455
290290 0 0
291291 −885413. −0.612934
292292 0 0
293293 −2.55139e6 −1.73623 −0.868117 0.496359i 0.834670π-0.834670\pi
−0.868117 + 0.496359i 0.834670π0.834670\pi
294294 0 0
295295 −125534. −0.0839860
296296 0 0
297297 251832. 0.165661
298298 0 0
299299 1.85515e6 1.20006
300300 0 0
301301 156985. 0.0998717
302302 0 0
303303 −979370. −0.612830
304304 0 0
305305 −567209. −0.349135
306306 0 0
307307 1.82818e6 1.10707 0.553534 0.832827i 0.313279π-0.313279\pi
0.553534 + 0.832827i 0.313279π0.313279\pi
308308 0 0
309309 −2.68900e6 −1.60212
310310 0 0
311311 2.15857e6 1.26551 0.632754 0.774353i 0.281925π-0.281925\pi
0.632754 + 0.774353i 0.281925π0.281925\pi
312312 0 0
313313 151212. 0.0872421 0.0436210 0.999048i 0.486111π-0.486111\pi
0.0436210 + 0.999048i 0.486111π0.486111\pi
314314 0 0
315315 246512. 0.139979
316316 0 0
317317 2.59481e6 1.45030 0.725148 0.688593i 0.241771π-0.241771\pi
0.725148 + 0.688593i 0.241771π0.241771\pi
318318 0 0
319319 256051. 0.140880
320320 0 0
321321 1.71555e6 0.929265
322322 0 0
323323 −1.28413e6 −0.684861
324324 0 0
325325 −469716. −0.246676
326326 0 0
327327 −924060. −0.477893
328328 0 0
329329 −1.07305e6 −0.546549
330330 0 0
331331 351723. 0.176453 0.0882267 0.996100i 0.471880π-0.471880\pi
0.0882267 + 0.996100i 0.471880π0.471880\pi
332332 0 0
333333 −542911. −0.268298
334334 0 0
335335 391346. 0.190524
336336 0 0
337337 666107. 0.319499 0.159749 0.987158i 0.448931π-0.448931\pi
0.159749 + 0.987158i 0.448931π0.448931\pi
338338 0 0
339339 3.85256e6 1.82075
340340 0 0
341341 2.81112e6 1.30916
342342 0 0
343343 −117649. −0.0539949
344344 0 0
345345 −1.30068e6 −0.588333
346346 0 0
347347 −428588. −0.191080 −0.0955402 0.995426i 0.530458π-0.530458\pi
−0.0955402 + 0.995426i 0.530458π0.530458\pi
348348 0 0
349349 233734. 0.102721 0.0513603 0.998680i 0.483644π-0.483644\pi
0.0513603 + 0.998680i 0.483644π0.483644\pi
350350 0 0
351351 −661572. −0.286622
352352 0 0
353353 730202. 0.311893 0.155947 0.987765i 0.450157π-0.450157\pi
0.155947 + 0.987765i 0.450157π0.450157\pi
354354 0 0
355355 −525681. −0.221386
356356 0 0
357357 −873260. −0.362638
358358 0 0
359359 1.27637e6 0.522684 0.261342 0.965246i 0.415835π-0.415835\pi
0.261342 + 0.965246i 0.415835π0.415835\pi
360360 0 0
361361 −169699. −0.0685350
362362 0 0
363363 1.66947e6 0.664986
364364 0 0
365365 1.31993e6 0.518582
366366 0 0
367367 −4.92829e6 −1.90999 −0.954995 0.296623i 0.904139π-0.904139\pi
−0.954995 + 0.296623i 0.904139π0.904139\pi
368368 0 0
369369 1.16115e6 0.443938
370370 0 0
371371 −892171. −0.336522
372372 0 0
373373 −2.33084e6 −0.867444 −0.433722 0.901047i 0.642800π-0.642800\pi
−0.433722 + 0.901047i 0.642800π0.642800\pi
374374 0 0
375375 329326. 0.120934
376376 0 0
377377 −672655. −0.243747
378378 0 0
379379 −96821.4 −0.0346237 −0.0173119 0.999850i 0.505511π-0.505511\pi
−0.0173119 + 0.999850i 0.505511π0.505511\pi
380380 0 0
381381 −1.67341e6 −0.590594
382382 0 0
383383 −1.02936e6 −0.358566 −0.179283 0.983798i 0.557378π-0.557378\pi
−0.179283 + 0.983798i 0.557378π0.557378\pi
384384 0 0
385385 350449. 0.120496
386386 0 0
387387 −644711. −0.218820
388388 0 0
389389 −1.81126e6 −0.606885 −0.303443 0.952850i 0.598136π-0.598136\pi
−0.303443 + 0.952850i 0.598136π0.598136\pi
390390 0 0
391391 2.08721e6 0.690437
392392 0 0
393393 −3.09007e6 −1.00922
394394 0 0
395395 2.01714e6 0.650494
396396 0 0
397397 1.80750e6 0.575576 0.287788 0.957694i 0.407080π-0.407080\pi
0.287788 + 0.957694i 0.407080π0.407080\pi
398398 0 0
399399 1.56845e6 0.493216
400400 0 0
401401 −3.13485e6 −0.973545 −0.486773 0.873529i 0.661826π-0.661826\pi
−0.486773 + 0.873529i 0.661826π0.661826\pi
402402 0 0
403403 −7.38492e6 −2.26508
404404 0 0
405405 1.68634e6 0.510867
406406 0 0
407407 −771817. −0.230956
408408 0 0
409409 −6.02204e6 −1.78006 −0.890031 0.455900i 0.849317π-0.849317\pi
−0.890031 + 0.455900i 0.849317π0.849317\pi
410410 0 0
411411 6.17426e6 1.80294
412412 0 0
413413 −246047. −0.0709811
414414 0 0
415415 −1.60494e6 −0.457443
416416 0 0
417417 4.79686e6 1.35088
418418 0 0
419419 6.77548e6 1.88541 0.942704 0.333631i 0.108274π-0.108274\pi
0.942704 + 0.333631i 0.108274π0.108274\pi
420420 0 0
421421 765395. 0.210465 0.105233 0.994448i 0.466441π-0.466441\pi
0.105233 + 0.994448i 0.466441π0.466441\pi
422422 0 0
423423 4.40682e6 1.19750
424424 0 0
425425 −528471. −0.141922
426426 0 0
427427 −1.11173e6 −0.295073
428428 0 0
429429 4.53158e6 1.18879
430430 0 0
431431 3.94945e6 1.02410 0.512052 0.858955i 0.328886π-0.328886\pi
0.512052 + 0.858955i 0.328886π0.328886\pi
432432 0 0
433433 −4.14225e6 −1.06174 −0.530868 0.847454i 0.678134π-0.678134\pi
−0.530868 + 0.847454i 0.678134π0.678134\pi
434434 0 0
435435 471610. 0.119498
436436 0 0
437437 −3.74880e6 −0.939049
438438 0 0
439439 6.06844e6 1.50285 0.751425 0.659818i 0.229367π-0.229367\pi
0.751425 + 0.659818i 0.229367π0.229367\pi
440440 0 0
441441 483164. 0.118304
442442 0 0
443443 1.61019e6 0.389823 0.194912 0.980821i 0.437558π-0.437558\pi
0.194912 + 0.980821i 0.437558π0.437558\pi
444444 0 0
445445 1.80195e6 0.431363
446446 0 0
447447 4.44049e6 1.05114
448448 0 0
449449 740602. 0.173368 0.0866841 0.996236i 0.472373π-0.472373\pi
0.0866841 + 0.996236i 0.472373π0.472373\pi
450450 0 0
451451 1.65072e6 0.382149
452452 0 0
453453 1.11777e7 2.55921
454454 0 0
455455 −920643. −0.208479
456456 0 0
457457 −44871.6 −0.0100504 −0.00502518 0.999987i 0.501600π-0.501600\pi
−0.00502518 + 0.999987i 0.501600π0.501600\pi
458458 0 0
459459 −744327. −0.164904
460460 0 0
461461 −6.14817e6 −1.34739 −0.673695 0.739009i 0.735294π-0.735294\pi
−0.673695 + 0.739009i 0.735294π0.735294\pi
462462 0 0
463463 5.91399e6 1.28212 0.641059 0.767492i 0.278496π-0.278496\pi
0.641059 + 0.767492i 0.278496π0.278496\pi
464464 0 0
465465 5.17770e6 1.11046
466466 0 0
467467 −4.46680e6 −0.947772 −0.473886 0.880586i 0.657149π-0.657149\pi
−0.473886 + 0.880586i 0.657149π0.657149\pi
468468 0 0
469469 767038. 0.161022
470470 0 0
471471 −9.85368e6 −2.04666
472472 0 0
473473 −916540. −0.188364
474474 0 0
475475 949177. 0.193025
476476 0 0
477477 3.66399e6 0.737325
478478 0 0
479479 3.58911e6 0.714740 0.357370 0.933963i 0.383674π-0.383674\pi
0.357370 + 0.933963i 0.383674π0.383674\pi
480480 0 0
481481 2.02759e6 0.399593
482482 0 0
483483 −2.54933e6 −0.497232
484484 0 0
485485 −1.05022e6 −0.202734
486486 0 0
487487 −3.77868e6 −0.721968 −0.360984 0.932572i 0.617559π-0.617559\pi
−0.360984 + 0.932572i 0.617559π0.617559\pi
488488 0 0
489489 −7.31134e6 −1.38269
490490 0 0
491491 −1.51375e6 −0.283369 −0.141684 0.989912i 0.545252π-0.545252\pi
−0.141684 + 0.989912i 0.545252π0.545252\pi
492492 0 0
493493 −756796. −0.140237
494494 0 0
495495 −1.43924e6 −0.264009
496496 0 0
497497 −1.03033e6 −0.187106
498498 0 0
499499 −2.20454e6 −0.396338 −0.198169 0.980168i 0.563500π-0.563500\pi
−0.198169 + 0.980168i 0.563500π0.563500\pi
500500 0 0
501501 1.01942e7 1.81451
502502 0 0
503503 9.13351e6 1.60960 0.804799 0.593547i 0.202273π-0.202273\pi
0.804799 + 0.593547i 0.202273π0.202273\pi
504504 0 0
505505 −1.16166e6 −0.202699
506506 0 0
507507 −4.07894e6 −0.704738
508508 0 0
509509 5.86974e6 1.00421 0.502105 0.864807i 0.332559π-0.332559\pi
0.502105 + 0.864807i 0.332559π0.332559\pi
510510 0 0
511511 2.58705e6 0.438282
512512 0 0
513513 1.33687e6 0.224283
514514 0 0
515515 −3.18951e6 −0.529915
516516 0 0
517517 6.26486e6 1.03083
518518 0 0
519519 8.79383e6 1.43305
520520 0 0
521521 −4.28621e6 −0.691797 −0.345899 0.938272i 0.612426π-0.612426\pi
−0.345899 + 0.938272i 0.612426π0.612426\pi
522522 0 0
523523 412959. 0.0660165 0.0330082 0.999455i 0.489491π-0.489491\pi
0.0330082 + 0.999455i 0.489491π0.489491\pi
524524 0 0
525525 645479. 0.102208
526526 0 0
527527 −8.30869e6 −1.30318
528528 0 0
529529 −343091. −0.0533053
530530 0 0
531531 1.01047e6 0.155521
532532 0 0
533533 −4.33651e6 −0.661184
534534 0 0
535535 2.03487e6 0.307363
536536 0 0
537537 1.16621e7 1.74519
538538 0 0
539539 686880. 0.101838
540540 0 0
541541 5.93333e6 0.871576 0.435788 0.900049i 0.356470π-0.356470\pi
0.435788 + 0.900049i 0.356470π0.356470\pi
542542 0 0
543543 −3.97716e6 −0.578860
544544 0 0
545545 −1.09606e6 −0.158068
546546 0 0
547547 −3.77825e6 −0.539912 −0.269956 0.962873i 0.587009π-0.587009\pi
−0.269956 + 0.962873i 0.587009π0.587009\pi
548548 0 0
549549 4.56568e6 0.646509
550550 0 0
551551 1.35927e6 0.190733
552552 0 0
553553 3.95360e6 0.549768
554554 0 0
555555 −1.42158e6 −0.195902
556556 0 0
557557 2.28752e6 0.312412 0.156206 0.987724i 0.450074π-0.450074\pi
0.156206 + 0.987724i 0.450074π0.450074\pi
558558 0 0
559559 2.40778e6 0.325903
560560 0 0
561561 5.09843e6 0.683958
562562 0 0
563563 393869. 0.0523698 0.0261849 0.999657i 0.491664π-0.491664\pi
0.0261849 + 0.999657i 0.491664π0.491664\pi
564564 0 0
565565 4.56965e6 0.602229
566566 0 0
567567 3.30523e6 0.431761
568568 0 0
569569 1.15221e7 1.49194 0.745972 0.665977i 0.231985π-0.231985\pi
0.745972 + 0.665977i 0.231985π0.231985\pi
570570 0 0
571571 −8.55465e6 −1.09802 −0.549012 0.835814i 0.684996π-0.684996\pi
−0.549012 + 0.835814i 0.684996π0.684996\pi
572572 0 0
573573 5.76602e6 0.733651
574574 0 0
575575 −1.54278e6 −0.194596
576576 0 0
577577 −2.89933e6 −0.362542 −0.181271 0.983433i 0.558021π-0.558021\pi
−0.181271 + 0.983433i 0.558021π0.558021\pi
578578 0 0
579579 −6.59156e6 −0.817131
580580 0 0
581581 −3.14567e6 −0.386610
582582 0 0
583583 5.20884e6 0.634701
584584 0 0
585585 3.78092e6 0.456781
586586 0 0
587587 1.03041e7 1.23428 0.617140 0.786854i 0.288291π-0.288291\pi
0.617140 + 0.786854i 0.288291π0.288291\pi
588588 0 0
589589 1.49231e7 1.77243
590590 0 0
591591 −2.65521e6 −0.312702
592592 0 0
593593 −6.25856e6 −0.730866 −0.365433 0.930838i 0.619079π-0.619079\pi
−0.365433 + 0.930838i 0.619079π0.619079\pi
594594 0 0
595595 −1.03580e6 −0.119946
596596 0 0
597597 1.47943e7 1.69887
598598 0 0
599599 −5.46416e6 −0.622238 −0.311119 0.950371i 0.600704π-0.600704\pi
−0.311119 + 0.950371i 0.600704π0.600704\pi
600600 0 0
601601 −8.28445e6 −0.935572 −0.467786 0.883842i 0.654948π-0.654948\pi
−0.467786 + 0.883842i 0.654948π0.654948\pi
602602 0 0
603603 −3.15010e6 −0.352802
604604 0 0
605605 1.98022e6 0.219950
606606 0 0
607607 3.06212e6 0.337326 0.168663 0.985674i 0.446055π-0.446055\pi
0.168663 + 0.985674i 0.446055π0.446055\pi
608608 0 0
609609 924356. 0.100994
610610 0 0
611611 −1.64580e7 −1.78351
612612 0 0
613613 −1.19291e7 −1.28220 −0.641100 0.767457i 0.721522π-0.721522\pi
−0.641100 + 0.767457i 0.721522π0.721522\pi
614614 0 0
615615 3.04041e6 0.324148
616616 0 0
617617 −4.51435e6 −0.477400 −0.238700 0.971093i 0.576721π-0.576721\pi
−0.238700 + 0.971093i 0.576721π0.576721\pi
618618 0 0
619619 −1.41481e7 −1.48412 −0.742062 0.670331i 0.766152π-0.766152\pi
−0.742062 + 0.670331i 0.766152π0.766152\pi
620620 0 0
621621 −2.17293e6 −0.226109
622622 0 0
623623 3.53183e6 0.364569
624624 0 0
625625 390625. 0.0400000
626626 0 0
627627 −9.15719e6 −0.930237
628628 0 0
629629 2.28122e6 0.229901
630630 0 0
631631 −3.95815e6 −0.395748 −0.197874 0.980227i 0.563404π-0.563404\pi
−0.197874 + 0.980227i 0.563404π0.563404\pi
632632 0 0
633633 −2.14109e7 −2.12386
634634 0 0
635635 −1.98489e6 −0.195345
636636 0 0
637637 −1.80446e6 −0.176197
638638 0 0
639639 4.23141e6 0.409952
640640 0 0
641641 −1.87473e7 −1.80217 −0.901083 0.433647i 0.857226π-0.857226\pi
−0.901083 + 0.433647i 0.857226π0.857226\pi
642642 0 0
643643 −3.25738e6 −0.310700 −0.155350 0.987860i 0.549650π-0.549650\pi
−0.155350 + 0.987860i 0.549650π0.549650\pi
644644 0 0
645645 −1.68814e6 −0.159775
646646 0 0
647647 5.76628e6 0.541546 0.270773 0.962643i 0.412721π-0.412721\pi
0.270773 + 0.962643i 0.412721π0.412721\pi
648648 0 0
649649 1.43652e6 0.133875
650650 0 0
651651 1.01483e7 0.938514
652652 0 0
653653 −9.30278e6 −0.853748 −0.426874 0.904311i 0.640385π-0.640385\pi
−0.426874 + 0.904311i 0.640385π0.640385\pi
654654 0 0
655655 −3.66524e6 −0.333810
656656 0 0
657657 −1.06246e7 −0.960282
658658 0 0
659659 1.05250e7 0.944081 0.472040 0.881577i 0.343518π-0.343518\pi
0.472040 + 0.881577i 0.343518π0.343518\pi
660660 0 0
661661 −1.73879e7 −1.54790 −0.773950 0.633246i 0.781722π-0.781722\pi
−0.773950 + 0.633246i 0.781722π0.781722\pi
662662 0 0
663663 −1.33938e7 −1.18337
664664 0 0
665665 1.86039e6 0.163136
666666 0 0
667667 −2.20934e6 −0.192286
668668 0 0
669669 2.16052e7 1.86635
670670 0 0
671671 6.49070e6 0.556526
672672 0 0
673673 −1.08486e7 −0.923282 −0.461641 0.887067i 0.652739π-0.652739\pi
−0.461641 + 0.887067i 0.652739π0.652739\pi
674674 0 0
675675 550177. 0.0464775
676676 0 0
677677 −1.83721e7 −1.54059 −0.770294 0.637689i 0.779890π-0.779890\pi
−0.770294 + 0.637689i 0.779890π0.779890\pi
678678 0 0
679679 −2.05843e6 −0.171341
680680 0 0
681681 −1.05736e7 −0.873684
682682 0 0
683683 −6.45618e6 −0.529571 −0.264785 0.964307i 0.585301π-0.585301\pi
−0.264785 + 0.964307i 0.585301π0.585301\pi
684684 0 0
685685 7.32350e6 0.596338
686686 0 0
687687 −2.29884e7 −1.85830
688688 0 0
689689 −1.36838e7 −1.09814
690690 0 0
691691 −1.09563e7 −0.872913 −0.436456 0.899725i 0.643767π-0.643767\pi
−0.436456 + 0.899725i 0.643767π0.643767\pi
692692 0 0
693693 −2.82090e6 −0.223128
694694 0 0
695695 5.68971e6 0.446816
696696 0 0
697697 −4.87896e6 −0.380404
698698 0 0
699699 2.43192e6 0.188259
700700 0 0
701701 −2.50941e7 −1.92875 −0.964375 0.264538i 0.914781π-0.914781\pi
−0.964375 + 0.264538i 0.914781π0.914781\pi
702702 0 0
703703 −4.09725e6 −0.312683
704704 0 0
705705 1.15390e7 0.874371
706706 0 0
707707 −2.27686e6 −0.171312
708708 0 0
709709 −1.52164e7 −1.13683 −0.568416 0.822741i 0.692444π-0.692444\pi
−0.568416 + 0.822741i 0.692444π0.692444\pi
710710 0 0
711711 −1.62367e7 −1.20455
712712 0 0
713713 −2.42558e7 −1.78686
714714 0 0
715715 5.37507e6 0.393205
716716 0 0
717717 −1.59179e7 −1.15635
718718 0 0
719719 2.44444e7 1.76342 0.881712 0.471788i 0.156391π-0.156391\pi
0.881712 + 0.471788i 0.156391π0.156391\pi
720720 0 0
721721 −6.25144e6 −0.447860
722722 0 0
723723 2.52026e7 1.79308
724724 0 0
725725 559393. 0.0395250
726726 0 0
727727 −2.58767e7 −1.81582 −0.907912 0.419161i 0.862324π-0.862324\pi
−0.907912 + 0.419161i 0.862324π0.862324\pi
728728 0 0
729729 −9.06548e6 −0.631789
730730 0 0
731731 2.70897e6 0.187504
732732 0 0
733733 2.63428e7 1.81093 0.905467 0.424416i 0.139521π-0.139521\pi
0.905467 + 0.424416i 0.139521π0.139521\pi
734734 0 0
735735 1.26514e6 0.0863814
736736 0 0
737737 −4.47827e6 −0.303697
738738 0 0
739739 −1.67769e7 −1.13006 −0.565029 0.825071i 0.691135π-0.691135\pi
−0.565029 + 0.825071i 0.691135π0.691135\pi
740740 0 0
741741 2.40563e7 1.60947
742742 0 0
743743 9.59030e6 0.637324 0.318662 0.947868i 0.396767π-0.396767\pi
0.318662 + 0.947868i 0.396767π0.396767\pi
744744 0 0
745745 5.26701e6 0.347675
746746 0 0
747747 1.29187e7 0.847069
748748 0 0
749749 3.98834e6 0.259769
750750 0 0
751751 −1.08659e7 −0.703020 −0.351510 0.936184i 0.614332π-0.614332\pi
−0.351510 + 0.936184i 0.614332π0.614332\pi
752752 0 0
753753 3.01958e7 1.94070
754754 0 0
755755 1.32582e7 0.846484
756756 0 0
757757 −1.88916e7 −1.19820 −0.599098 0.800676i 0.704474π-0.704474\pi
−0.599098 + 0.800676i 0.704474π0.704474\pi
758758 0 0
759759 1.48840e7 0.937811
760760 0 0
761761 −2.38282e7 −1.49152 −0.745761 0.666214i 0.767914π-0.767914\pi
−0.745761 + 0.666214i 0.767914π0.767914\pi
762762 0 0
763763 −2.14828e6 −0.133592
764764 0 0
765765 4.25387e6 0.262803
766766 0 0
767767 −3.77378e6 −0.231627
768768 0 0
769769 −1.44907e7 −0.883638 −0.441819 0.897104i 0.645667π-0.645667\pi
−0.441819 + 0.897104i 0.645667π0.645667\pi
770770 0 0
771771 −2.06271e7 −1.24969
772772 0 0
773773 3.26526e7 1.96548 0.982739 0.184995i 0.0592269π-0.0592269\pi
0.982739 + 0.184995i 0.0592269π0.0592269\pi
774774 0 0
775775 6.14145e6 0.367296
776776 0 0
777777 −2.78630e6 −0.165568
778778 0 0
779779 8.76300e6 0.517379
780780 0 0
781781 6.01549e6 0.352893
782782 0 0
783783 787878. 0.0459256
784784 0 0
785785 −1.16878e7 −0.676952
786786 0 0
787787 3.95371e6 0.227545 0.113773 0.993507i 0.463706π-0.463706\pi
0.113773 + 0.993507i 0.463706π0.463706\pi
788788 0 0
789789 1.39693e7 0.798884
790790 0 0
791791 8.95651e6 0.508976
792792 0 0
793793 −1.70513e7 −0.962886
794794 0 0
795795 9.59397e6 0.538369
796796 0 0
797797 2.69614e7 1.50348 0.751738 0.659462i 0.229216π-0.229216\pi
0.751738 + 0.659462i 0.229216π0.229216\pi
798798 0 0
799799 −1.85167e7 −1.02612
800800 0 0
801801 −1.45046e7 −0.798776
802802 0 0
803803 −1.51042e7 −0.826627
804804 0 0
805805 −3.02385e6 −0.164464
806806 0 0
807807 1.10056e7 0.594883
808808 0 0
809809 4.71873e6 0.253486 0.126743 0.991936i 0.459548π-0.459548\pi
0.126743 + 0.991936i 0.459548π0.459548\pi
810810 0 0
811811 1.31852e7 0.703938 0.351969 0.936012i 0.385512π-0.385512\pi
0.351969 + 0.936012i 0.385512π0.385512\pi
812812 0 0
813813 −2.10607e7 −1.11750
814814 0 0
815815 −8.67223e6 −0.457338
816816 0 0
817817 −4.86553e6 −0.255020
818818 0 0
819819 7.41061e6 0.386050
820820 0 0
821821 5.15697e6 0.267015 0.133508 0.991048i 0.457376π-0.457376\pi
0.133508 + 0.991048i 0.457376π0.457376\pi
822822 0 0
823823 −2.37615e7 −1.22286 −0.611428 0.791300i 0.709404π-0.709404\pi
−0.611428 + 0.791300i 0.709404π0.709404\pi
824824 0 0
825825 −3.76856e6 −0.192770
826826 0 0
827827 5.40811e6 0.274968 0.137484 0.990504i 0.456098π-0.456098\pi
0.137484 + 0.990504i 0.456098π0.456098\pi
828828 0 0
829829 −8.68373e6 −0.438854 −0.219427 0.975629i 0.570419π-0.570419\pi
−0.219427 + 0.975629i 0.570419π0.570419\pi
830830 0 0
831831 −2.99025e7 −1.50212
832832 0 0
833833 −2.03018e6 −0.101373
834834 0 0
835835 1.20917e7 0.600166
836836 0 0
837837 8.64994e6 0.426775
838838 0 0
839839 −8.19162e6 −0.401759 −0.200879 0.979616i 0.564380π-0.564380\pi
−0.200879 + 0.979616i 0.564380π0.564380\pi
840840 0 0
841841 −1.97101e7 −0.960944
842842 0 0
843843 −3.00741e7 −1.45755
844844 0 0
845845 −4.83817e6 −0.233098
846846 0 0
847847 3.88123e6 0.185892
848848 0 0
849849 5.35390e7 2.54919
850850 0 0
851851 6.65963e6 0.315229
852852 0 0
853853 −1.03765e7 −0.488292 −0.244146 0.969738i 0.578508π-0.578508\pi
−0.244146 + 0.969738i 0.578508π0.578508\pi
854854 0 0
855855 −7.64029e6 −0.357433
856856 0 0
857857 −2.83309e7 −1.31768 −0.658838 0.752285i 0.728952π-0.728952\pi
−0.658838 + 0.752285i 0.728952π0.728952\pi
858858 0 0
859859 −7.91250e6 −0.365874 −0.182937 0.983125i 0.558560π-0.558560\pi
−0.182937 + 0.983125i 0.558560π0.558560\pi
860860 0 0
861861 5.95920e6 0.273955
862862 0 0
863863 3.56407e7 1.62899 0.814495 0.580170i 0.197014π-0.197014\pi
0.814495 + 0.580170i 0.197014π0.197014\pi
864864 0 0
865865 1.04307e7 0.473993
866866 0 0
867867 1.48570e7 0.671248
868868 0 0
869869 −2.30826e7 −1.03690
870870 0 0
871871 1.17646e7 0.525449
872872 0 0
873873 8.45362e6 0.375411
874874 0 0
875875 765625. 0.0338062
876876 0 0
877877 2.22712e6 0.0977789 0.0488895 0.998804i 0.484432π-0.484432\pi
0.0488895 + 0.998804i 0.484432π0.484432\pi
878878 0 0
879879 5.37754e7 2.34753
880880 0 0
881881 2.71435e7 1.17822 0.589110 0.808053i 0.299479π-0.299479\pi
0.589110 + 0.808053i 0.299479π0.299479\pi
882882 0 0
883883 −8.65272e6 −0.373466 −0.186733 0.982411i 0.559790π-0.559790\pi
−0.186733 + 0.982411i 0.559790π0.559790\pi
884884 0 0
885885 2.64587e6 0.113556
886886 0 0
887887 −2.48135e7 −1.05896 −0.529480 0.848323i 0.677613π-0.677613\pi
−0.529480 + 0.848323i 0.677613π0.677613\pi
888888 0 0
889889 −3.89038e6 −0.165096
890890 0 0
891891 −1.92972e7 −0.814329
892892 0 0
893893 3.32575e7 1.39560
894894 0 0
895895 1.38329e7 0.577237
896896 0 0
897897 −3.91008e7 −1.62257
898898 0 0
899899 8.79484e6 0.362935
900900 0 0
901901 −1.53955e7 −0.631803
902902 0 0
903903 −3.30876e6 −0.135035
904904 0 0
905905 −4.71744e6 −0.191463
906906 0 0
907907 3.85211e7 1.55482 0.777411 0.628993i 0.216533π-0.216533\pi
0.777411 + 0.628993i 0.216533π0.216533\pi
908908 0 0
909909 9.35068e6 0.375348
910910 0 0
911911 1.96525e7 0.784554 0.392277 0.919847i 0.371687π-0.371687\pi
0.392277 + 0.919847i 0.371687π0.371687\pi
912912 0 0
913913 1.83657e7 0.729171
914914 0 0
915915 1.19550e7 0.472059
916916 0 0
917917 −7.18387e6 −0.282121
918918 0 0
919919 2.65362e7 1.03646 0.518228 0.855243i 0.326592π-0.326592\pi
0.518228 + 0.855243i 0.326592π0.326592\pi
920920 0 0
921921 −3.85324e7 −1.49685
922922 0 0
923923 −1.58029e7 −0.610566
924924 0 0
925925 −1.68619e6 −0.0647965
926926 0 0
927927 2.56736e7 0.981268
928928 0 0
929929 −6.33956e6 −0.241002 −0.120501 0.992713i 0.538450π-0.538450\pi
−0.120501 + 0.992713i 0.538450π0.538450\pi
930930 0 0
931931 3.64636e6 0.137875
932932 0 0
933933 −4.54959e7 −1.71107
934934 0 0
935935 6.04742e6 0.226225
936936 0 0
937937 2.07109e7 0.770639 0.385320 0.922783i 0.374091π-0.374091\pi
0.385320 + 0.922783i 0.374091π0.374091\pi
938938 0 0
939939 −3.18708e6 −0.117958
940940 0 0
941941 4.32264e7 1.59138 0.795692 0.605702i 0.207108π-0.207108\pi
0.795692 + 0.605702i 0.207108π0.207108\pi
942942 0 0
943943 −1.42433e7 −0.521592
944944 0 0
945945 1.07835e6 0.0392807
946946 0 0
947947 3.25763e6 0.118039 0.0590197 0.998257i 0.481203π-0.481203\pi
0.0590197 + 0.998257i 0.481203π0.481203\pi
948948 0 0
949949 3.96793e7 1.43021
950950 0 0
951951 −5.46904e7 −1.96092
952952 0 0
953953 −1.58737e7 −0.566168 −0.283084 0.959095i 0.591358π-0.591358\pi
−0.283084 + 0.959095i 0.591358π0.591358\pi
954954 0 0
955955 6.83927e6 0.242662
956956 0 0
957957 −5.39675e6 −0.190481
958958 0 0
959959 1.43541e7 0.503998
960960 0 0
961961 6.79274e7 2.37266
962962 0 0
963963 −1.63794e7 −0.569158
964964 0 0
965965 −7.81847e6 −0.270274
966966 0 0
967967 −3.78998e7 −1.30338 −0.651690 0.758486i 0.725940π-0.725940\pi
−0.651690 + 0.758486i 0.725940π0.725940\pi
968968 0 0
969969 2.70654e7 0.925988
970970 0 0
971971 4.44989e7 1.51461 0.757306 0.653061i 0.226515π-0.226515\pi
0.757306 + 0.653061i 0.226515π0.226515\pi
972972 0 0
973973 1.11518e7 0.377628
974974 0 0
975975 9.90014e6 0.333526
976976 0 0
977977 3.58249e7 1.20074 0.600369 0.799723i 0.295020π-0.295020\pi
0.600369 + 0.799723i 0.295020π0.295020\pi
978978 0 0
979979 −2.06202e7 −0.687599
980980 0 0
981981 8.82261e6 0.292701
982982 0 0
983983 −2.97430e7 −0.981749 −0.490874 0.871230i 0.663323π-0.663323\pi
−0.490874 + 0.871230i 0.663323π0.663323\pi
984984 0 0
985985 −3.14944e6 −0.103429
986986 0 0
987987 2.26165e7 0.738979
988988 0 0
989989 7.90837e6 0.257097
990990 0 0
991991 −4.84017e7 −1.56558 −0.782792 0.622284i 0.786205π-0.786205\pi
−0.782792 + 0.622284i 0.786205π0.786205\pi
992992 0 0
993993 −7.41321e6 −0.238580
994994 0 0
995995 1.75480e7 0.561915
996996 0 0
997997 −2.75881e7 −0.878991 −0.439495 0.898245i 0.644843π-0.644843\pi
−0.439495 + 0.898245i 0.644843π0.644843\pi
998998 0 0
999999 −2.37491e6 −0.0752894
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 560.6.a.s.1.1 3
4.3 odd 2 280.6.a.e.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.6.a.e.1.3 3 4.3 odd 2
560.6.a.s.1.1 3 1.1 even 1 trivial