Properties

Label 2240.4.a.bi.1.1
Level 22402240
Weight 44
Character 2240.1
Self dual yes
Analytic conductor 132.164132.164
Analytic rank 11
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] = [2240,4,Mod(1,2240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2240.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 2240=2657 2240 = 2^{6} \cdot 5 \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 2240.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: 132.164278413132.164278413
Analytic rank: 11
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 70)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 2240.1

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+8.00000q3+5.00000q57.00000q7+37.0000q968.0000q1134.0000q13+40.0000q15+74.0000q17+128.000q1956.0000q2180.0000q23+25.0000q25+80.0000q27286.000q2924.0000q31544.000q3335.0000q35294.000q37272.000q39+66.0000q41+124.000q43+185.000q45+312.000q47+49.0000q49+592.000q51+34.0000q53340.000q55+1024.00q57168.000q59170.000q61259.000q63170.000q65564.000q67640.000q69+616.000q71+250.000q73+200.000q75+476.000q77944.000q79359.000q81672.000q83+370.000q852288.00q871430.00q89+238.000q91192.000q93+640.000q951270.00q972516.00q99+O(q100)q+8.00000 q^{3} +5.00000 q^{5} -7.00000 q^{7} +37.0000 q^{9} -68.0000 q^{11} -34.0000 q^{13} +40.0000 q^{15} +74.0000 q^{17} +128.000 q^{19} -56.0000 q^{21} -80.0000 q^{23} +25.0000 q^{25} +80.0000 q^{27} -286.000 q^{29} -24.0000 q^{31} -544.000 q^{33} -35.0000 q^{35} -294.000 q^{37} -272.000 q^{39} +66.0000 q^{41} +124.000 q^{43} +185.000 q^{45} +312.000 q^{47} +49.0000 q^{49} +592.000 q^{51} +34.0000 q^{53} -340.000 q^{55} +1024.00 q^{57} -168.000 q^{59} -170.000 q^{61} -259.000 q^{63} -170.000 q^{65} -564.000 q^{67} -640.000 q^{69} +616.000 q^{71} +250.000 q^{73} +200.000 q^{75} +476.000 q^{77} -944.000 q^{79} -359.000 q^{81} -672.000 q^{83} +370.000 q^{85} -2288.00 q^{87} -1430.00 q^{89} +238.000 q^{91} -192.000 q^{93} +640.000 q^{95} -1270.00 q^{97} -2516.00 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 8.00000 1.53960 0.769800 0.638285i 0.220356π-0.220356\pi
0.769800 + 0.638285i 0.220356π0.220356\pi
44 0 0
55 5.00000 0.447214
66 0 0
77 −7.00000 −0.377964
88 0 0
99 37.0000 1.37037
1010 0 0
1111 −68.0000 −1.86389 −0.931944 0.362602i 0.881889π-0.881889\pi
−0.931944 + 0.362602i 0.881889π0.881889\pi
1212 0 0
1313 −34.0000 −0.725377 −0.362689 0.931910i 0.618141π-0.618141\pi
−0.362689 + 0.931910i 0.618141π0.618141\pi
1414 0 0
1515 40.0000 0.688530
1616 0 0
1717 74.0000 1.05574 0.527872 0.849324i 0.322990π-0.322990\pi
0.527872 + 0.849324i 0.322990π0.322990\pi
1818 0 0
1919 128.000 1.54554 0.772769 0.634688i 0.218871π-0.218871\pi
0.772769 + 0.634688i 0.218871π0.218871\pi
2020 0 0
2121 −56.0000 −0.581914
2222 0 0
2323 −80.0000 −0.725268 −0.362634 0.931932i 0.618122π-0.618122\pi
−0.362634 + 0.931932i 0.618122π0.618122\pi
2424 0 0
2525 25.0000 0.200000
2626 0 0
2727 80.0000 0.570222
2828 0 0
2929 −286.000 −1.83134 −0.915670 0.401931i 0.868339π-0.868339\pi
−0.915670 + 0.401931i 0.868339π0.868339\pi
3030 0 0
3131 −24.0000 −0.139049 −0.0695246 0.997580i 0.522148π-0.522148\pi
−0.0695246 + 0.997580i 0.522148π0.522148\pi
3232 0 0
3333 −544.000 −2.86964
3434 0 0
3535 −35.0000 −0.169031
3636 0 0
3737 −294.000 −1.30631 −0.653153 0.757226i 0.726554π-0.726554\pi
−0.653153 + 0.757226i 0.726554π0.726554\pi
3838 0 0
3939 −272.000 −1.11679
4040 0 0
4141 66.0000 0.251402 0.125701 0.992068i 0.459882π-0.459882\pi
0.125701 + 0.992068i 0.459882π0.459882\pi
4242 0 0
4343 124.000 0.439763 0.219882 0.975527i 0.429433π-0.429433\pi
0.219882 + 0.975527i 0.429433π0.429433\pi
4444 0 0
4545 185.000 0.612848
4646 0 0
4747 312.000 0.968295 0.484148 0.874986i 0.339130π-0.339130\pi
0.484148 + 0.874986i 0.339130π0.339130\pi
4848 0 0
4949 49.0000 0.142857
5050 0 0
5151 592.000 1.62542
5252 0 0
5353 34.0000 0.0881181 0.0440590 0.999029i 0.485971π-0.485971\pi
0.0440590 + 0.999029i 0.485971π0.485971\pi
5454 0 0
5555 −340.000 −0.833556
5656 0 0
5757 1024.00 2.37951
5858 0 0
5959 −168.000 −0.370707 −0.185354 0.982672i 0.559343π-0.559343\pi
−0.185354 + 0.982672i 0.559343π0.559343\pi
6060 0 0
6161 −170.000 −0.356824 −0.178412 0.983956i 0.557096π-0.557096\pi
−0.178412 + 0.983956i 0.557096π0.557096\pi
6262 0 0
6363 −259.000 −0.517951
6464 0 0
6565 −170.000 −0.324399
6666 0 0
6767 −564.000 −1.02841 −0.514206 0.857667i 0.671913π-0.671913\pi
−0.514206 + 0.857667i 0.671913π0.671913\pi
6868 0 0
6969 −640.000 −1.11662
7070 0 0
7171 616.000 1.02966 0.514829 0.857293i 0.327855π-0.327855\pi
0.514829 + 0.857293i 0.327855π0.327855\pi
7272 0 0
7373 250.000 0.400826 0.200413 0.979712i 0.435772π-0.435772\pi
0.200413 + 0.979712i 0.435772π0.435772\pi
7474 0 0
7575 200.000 0.307920
7676 0 0
7777 476.000 0.704484
7878 0 0
7979 −944.000 −1.34441 −0.672204 0.740366i 0.734652π-0.734652\pi
−0.672204 + 0.740366i 0.734652π0.734652\pi
8080 0 0
8181 −359.000 −0.492455
8282 0 0
8383 −672.000 −0.888694 −0.444347 0.895855i 0.646564π-0.646564\pi
−0.444347 + 0.895855i 0.646564π0.646564\pi
8484 0 0
8585 370.000 0.472143
8686 0 0
8787 −2288.00 −2.81953
8888 0 0
8989 −1430.00 −1.70314 −0.851571 0.524239i 0.824350π-0.824350\pi
−0.851571 + 0.524239i 0.824350π0.824350\pi
9090 0 0
9191 238.000 0.274167
9292 0 0
9393 −192.000 −0.214080
9494 0 0
9595 640.000 0.691185
9696 0 0
9797 −1270.00 −1.32937 −0.664685 0.747123i 0.731434π-0.731434\pi
−0.664685 + 0.747123i 0.731434π0.731434\pi
9898 0 0
9999 −2516.00 −2.55422
100100 0 0
101101 −930.000 −0.916222 −0.458111 0.888895i 0.651474π-0.651474\pi
−0.458111 + 0.888895i 0.651474π0.651474\pi
102102 0 0
103103 160.000 0.153061 0.0765304 0.997067i 0.475616π-0.475616\pi
0.0765304 + 0.997067i 0.475616π0.475616\pi
104104 0 0
105105 −280.000 −0.260240
106106 0 0
107107 −1404.00 −1.26850 −0.634251 0.773127i 0.718692π-0.718692\pi
−0.634251 + 0.773127i 0.718692π0.718692\pi
108108 0 0
109109 274.000 0.240775 0.120387 0.992727i 0.461586π-0.461586\pi
0.120387 + 0.992727i 0.461586π0.461586\pi
110110 0 0
111111 −2352.00 −2.01119
112112 0 0
113113 −798.000 −0.664332 −0.332166 0.943221i 0.607779π-0.607779\pi
−0.332166 + 0.943221i 0.607779π0.607779\pi
114114 0 0
115115 −400.000 −0.324349
116116 0 0
117117 −1258.00 −0.994035
118118 0 0
119119 −518.000 −0.399033
120120 0 0
121121 3293.00 2.47408
122122 0 0
123123 528.000 0.387058
124124 0 0
125125 125.000 0.0894427
126126 0 0
127127 −904.000 −0.631630 −0.315815 0.948821i 0.602278π-0.602278\pi
−0.315815 + 0.948821i 0.602278π0.602278\pi
128128 0 0
129129 992.000 0.677060
130130 0 0
131131 2080.00 1.38726 0.693628 0.720334i 0.256011π-0.256011\pi
0.693628 + 0.720334i 0.256011π0.256011\pi
132132 0 0
133133 −896.000 −0.584158
134134 0 0
135135 400.000 0.255011
136136 0 0
137137 2218.00 1.38319 0.691593 0.722287i 0.256909π-0.256909\pi
0.691593 + 0.722287i 0.256909π0.256909\pi
138138 0 0
139139 −2432.00 −1.48403 −0.742013 0.670386i 0.766129π-0.766129\pi
−0.742013 + 0.670386i 0.766129π0.766129\pi
140140 0 0
141141 2496.00 1.49079
142142 0 0
143143 2312.00 1.35202
144144 0 0
145145 −1430.00 −0.819000
146146 0 0
147147 392.000 0.219943
148148 0 0
149149 −1598.00 −0.878612 −0.439306 0.898337i 0.644776π-0.644776\pi
−0.439306 + 0.898337i 0.644776π0.644776\pi
150150 0 0
151151 −2672.00 −1.44003 −0.720014 0.693959i 0.755865π-0.755865\pi
−0.720014 + 0.693959i 0.755865π0.755865\pi
152152 0 0
153153 2738.00 1.44676
154154 0 0
155155 −120.000 −0.0621847
156156 0 0
157157 −1170.00 −0.594753 −0.297376 0.954760i 0.596112π-0.596112\pi
−0.297376 + 0.954760i 0.596112π0.596112\pi
158158 0 0
159159 272.000 0.135667
160160 0 0
161161 560.000 0.274125
162162 0 0
163163 −1580.00 −0.759234 −0.379617 0.925144i 0.623944π-0.623944\pi
−0.379617 + 0.925144i 0.623944π0.623944\pi
164164 0 0
165165 −2720.00 −1.28334
166166 0 0
167167 −704.000 −0.326211 −0.163105 0.986609i 0.552151π-0.552151\pi
−0.163105 + 0.986609i 0.552151π0.552151\pi
168168 0 0
169169 −1041.00 −0.473828
170170 0 0
171171 4736.00 2.11796
172172 0 0
173173 −18.0000 −0.00791049 −0.00395524 0.999992i 0.501259π-0.501259\pi
−0.00395524 + 0.999992i 0.501259π0.501259\pi
174174 0 0
175175 −175.000 −0.0755929
176176 0 0
177177 −1344.00 −0.570741
178178 0 0
179179 4268.00 1.78215 0.891076 0.453854i 0.149951π-0.149951\pi
0.891076 + 0.453854i 0.149951π0.149951\pi
180180 0 0
181181 −282.000 −0.115806 −0.0579030 0.998322i 0.518441π-0.518441\pi
−0.0579030 + 0.998322i 0.518441π0.518441\pi
182182 0 0
183183 −1360.00 −0.549367
184184 0 0
185185 −1470.00 −0.584198
186186 0 0
187187 −5032.00 −1.96779
188188 0 0
189189 −560.000 −0.215524
190190 0 0
191191 1424.00 0.539461 0.269730 0.962936i 0.413065π-0.413065\pi
0.269730 + 0.962936i 0.413065π0.413065\pi
192192 0 0
193193 −1870.00 −0.697438 −0.348719 0.937227i 0.613383π-0.613383\pi
−0.348719 + 0.937227i 0.613383π0.613383\pi
194194 0 0
195195 −1360.00 −0.499444
196196 0 0
197197 3618.00 1.30849 0.654243 0.756284i 0.272987π-0.272987\pi
0.654243 + 0.756284i 0.272987π0.272987\pi
198198 0 0
199199 2736.00 0.974623 0.487311 0.873228i 0.337978π-0.337978\pi
0.487311 + 0.873228i 0.337978π0.337978\pi
200200 0 0
201201 −4512.00 −1.58334
202202 0 0
203203 2002.00 0.692182
204204 0 0
205205 330.000 0.112430
206206 0 0
207207 −2960.00 −0.993885
208208 0 0
209209 −8704.00 −2.88071
210210 0 0
211211 348.000 0.113542 0.0567709 0.998387i 0.481920π-0.481920\pi
0.0567709 + 0.998387i 0.481920π0.481920\pi
212212 0 0
213213 4928.00 1.58526
214214 0 0
215215 620.000 0.196668
216216 0 0
217217 168.000 0.0525557
218218 0 0
219219 2000.00 0.617112
220220 0 0
221221 −2516.00 −0.765812
222222 0 0
223223 5888.00 1.76811 0.884057 0.467378i 0.154801π-0.154801\pi
0.884057 + 0.467378i 0.154801π0.154801\pi
224224 0 0
225225 925.000 0.274074
226226 0 0
227227 4304.00 1.25844 0.629221 0.777226i 0.283374π-0.283374\pi
0.629221 + 0.777226i 0.283374π0.283374\pi
228228 0 0
229229 −3674.00 −1.06020 −0.530098 0.847937i 0.677845π-0.677845\pi
−0.530098 + 0.847937i 0.677845π0.677845\pi
230230 0 0
231231 3808.00 1.08462
232232 0 0
233233 −838.000 −0.235619 −0.117809 0.993036i 0.537587π-0.537587\pi
−0.117809 + 0.993036i 0.537587π0.537587\pi
234234 0 0
235235 1560.00 0.433035
236236 0 0
237237 −7552.00 −2.06985
238238 0 0
239239 5832.00 1.57841 0.789207 0.614128i 0.210492π-0.210492\pi
0.789207 + 0.614128i 0.210492π0.210492\pi
240240 0 0
241241 1690.00 0.451711 0.225856 0.974161i 0.427482π-0.427482\pi
0.225856 + 0.974161i 0.427482π0.427482\pi
242242 0 0
243243 −5032.00 −1.32841
244244 0 0
245245 245.000 0.0638877
246246 0 0
247247 −4352.00 −1.12110
248248 0 0
249249 −5376.00 −1.36823
250250 0 0
251251 −5760.00 −1.44848 −0.724239 0.689549i 0.757809π-0.757809\pi
−0.724239 + 0.689549i 0.757809π0.757809\pi
252252 0 0
253253 5440.00 1.35182
254254 0 0
255255 2960.00 0.726911
256256 0 0
257257 −350.000 −0.0849510 −0.0424755 0.999098i 0.513524π-0.513524\pi
−0.0424755 + 0.999098i 0.513524π0.513524\pi
258258 0 0
259259 2058.00 0.493737
260260 0 0
261261 −10582.0 −2.50961
262262 0 0
263263 −2968.00 −0.695873 −0.347937 0.937518i 0.613118π-0.613118\pi
−0.347937 + 0.937518i 0.613118π0.613118\pi
264264 0 0
265265 170.000 0.0394076
266266 0 0
267267 −11440.0 −2.62216
268268 0 0
269269 4494.00 1.01860 0.509301 0.860588i 0.329904π-0.329904\pi
0.509301 + 0.860588i 0.329904π0.329904\pi
270270 0 0
271271 1312.00 0.294090 0.147045 0.989130i 0.453024π-0.453024\pi
0.147045 + 0.989130i 0.453024π0.453024\pi
272272 0 0
273273 1904.00 0.422107
274274 0 0
275275 −1700.00 −0.372778
276276 0 0
277277 5234.00 1.13531 0.567654 0.823267i 0.307851π-0.307851\pi
0.567654 + 0.823267i 0.307851π0.307851\pi
278278 0 0
279279 −888.000 −0.190549
280280 0 0
281281 −5718.00 −1.21390 −0.606952 0.794738i 0.707608π-0.707608\pi
−0.606952 + 0.794738i 0.707608π0.707608\pi
282282 0 0
283283 3752.00 0.788103 0.394052 0.919088i 0.371073π-0.371073\pi
0.394052 + 0.919088i 0.371073π0.371073\pi
284284 0 0
285285 5120.00 1.06415
286286 0 0
287287 −462.000 −0.0950209
288288 0 0
289289 563.000 0.114594
290290 0 0
291291 −10160.0 −2.04670
292292 0 0
293293 −7698.00 −1.53489 −0.767444 0.641116i 0.778472π-0.778472\pi
−0.767444 + 0.641116i 0.778472π0.778472\pi
294294 0 0
295295 −840.000 −0.165785
296296 0 0
297297 −5440.00 −1.06283
298298 0 0
299299 2720.00 0.526093
300300 0 0
301301 −868.000 −0.166215
302302 0 0
303303 −7440.00 −1.41062
304304 0 0
305305 −850.000 −0.159577
306306 0 0
307307 1456.00 0.270679 0.135339 0.990799i 0.456788π-0.456788\pi
0.135339 + 0.990799i 0.456788π0.456788\pi
308308 0 0
309309 1280.00 0.235653
310310 0 0
311311 9592.00 1.74891 0.874457 0.485103i 0.161218π-0.161218\pi
0.874457 + 0.485103i 0.161218π0.161218\pi
312312 0 0
313313 3570.00 0.644691 0.322346 0.946622i 0.395529π-0.395529\pi
0.322346 + 0.946622i 0.395529π0.395529\pi
314314 0 0
315315 −1295.00 −0.231635
316316 0 0
317317 3866.00 0.684972 0.342486 0.939523i 0.388731π-0.388731\pi
0.342486 + 0.939523i 0.388731π0.388731\pi
318318 0 0
319319 19448.0 3.41341
320320 0 0
321321 −11232.0 −1.95299
322322 0 0
323323 9472.00 1.63169
324324 0 0
325325 −850.000 −0.145075
326326 0 0
327327 2192.00 0.370697
328328 0 0
329329 −2184.00 −0.365981
330330 0 0
331331 2940.00 0.488209 0.244104 0.969749i 0.421506π-0.421506\pi
0.244104 + 0.969749i 0.421506π0.421506\pi
332332 0 0
333333 −10878.0 −1.79012
334334 0 0
335335 −2820.00 −0.459920
336336 0 0
337337 −414.000 −0.0669199 −0.0334600 0.999440i 0.510653π-0.510653\pi
−0.0334600 + 0.999440i 0.510653π0.510653\pi
338338 0 0
339339 −6384.00 −1.02281
340340 0 0
341341 1632.00 0.259172
342342 0 0
343343 −343.000 −0.0539949
344344 0 0
345345 −3200.00 −0.499369
346346 0 0
347347 5068.00 0.784048 0.392024 0.919955i 0.371775π-0.371775\pi
0.392024 + 0.919955i 0.371775π0.371775\pi
348348 0 0
349349 −2882.00 −0.442034 −0.221017 0.975270i 0.570938π-0.570938\pi
−0.221017 + 0.975270i 0.570938π0.570938\pi
350350 0 0
351351 −2720.00 −0.413626
352352 0 0
353353 −6350.00 −0.957440 −0.478720 0.877968i 0.658899π-0.658899\pi
−0.478720 + 0.877968i 0.658899π0.658899\pi
354354 0 0
355355 3080.00 0.460477
356356 0 0
357357 −4144.00 −0.614352
358358 0 0
359359 4656.00 0.684497 0.342248 0.939610i 0.388812π-0.388812\pi
0.342248 + 0.939610i 0.388812π0.388812\pi
360360 0 0
361361 9525.00 1.38869
362362 0 0
363363 26344.0 3.80909
364364 0 0
365365 1250.00 0.179255
366366 0 0
367367 −8336.00 −1.18566 −0.592828 0.805329i 0.701989π-0.701989\pi
−0.592828 + 0.805329i 0.701989π0.701989\pi
368368 0 0
369369 2442.00 0.344513
370370 0 0
371371 −238.000 −0.0333055
372372 0 0
373373 −4862.00 −0.674919 −0.337460 0.941340i 0.609568π-0.609568\pi
−0.337460 + 0.941340i 0.609568π0.609568\pi
374374 0 0
375375 1000.00 0.137706
376376 0 0
377377 9724.00 1.32841
378378 0 0
379379 3932.00 0.532911 0.266456 0.963847i 0.414147π-0.414147\pi
0.266456 + 0.963847i 0.414147π0.414147\pi
380380 0 0
381381 −7232.00 −0.972458
382382 0 0
383383 −8120.00 −1.08332 −0.541661 0.840597i 0.682204π-0.682204\pi
−0.541661 + 0.840597i 0.682204π0.682204\pi
384384 0 0
385385 2380.00 0.315055
386386 0 0
387387 4588.00 0.602639
388388 0 0
389389 4346.00 0.566455 0.283227 0.959053i 0.408595π-0.408595\pi
0.283227 + 0.959053i 0.408595π0.408595\pi
390390 0 0
391391 −5920.00 −0.765696
392392 0 0
393393 16640.0 2.13582
394394 0 0
395395 −4720.00 −0.601238
396396 0 0
397397 4494.00 0.568129 0.284065 0.958805i 0.408317π-0.408317\pi
0.284065 + 0.958805i 0.408317π0.408317\pi
398398 0 0
399399 −7168.00 −0.899371
400400 0 0
401401 2578.00 0.321045 0.160523 0.987032i 0.448682π-0.448682\pi
0.160523 + 0.987032i 0.448682π0.448682\pi
402402 0 0
403403 816.000 0.100863
404404 0 0
405405 −1795.00 −0.220233
406406 0 0
407407 19992.0 2.43481
408408 0 0
409409 3730.00 0.450945 0.225473 0.974249i 0.427607π-0.427607\pi
0.225473 + 0.974249i 0.427607π0.427607\pi
410410 0 0
411411 17744.0 2.12955
412412 0 0
413413 1176.00 0.140114
414414 0 0
415415 −3360.00 −0.397436
416416 0 0
417417 −19456.0 −2.28481
418418 0 0
419419 2872.00 0.334860 0.167430 0.985884i 0.446453π-0.446453\pi
0.167430 + 0.985884i 0.446453π0.446453\pi
420420 0 0
421421 2210.00 0.255840 0.127920 0.991784i 0.459170π-0.459170\pi
0.127920 + 0.991784i 0.459170π0.459170\pi
422422 0 0
423423 11544.0 1.32692
424424 0 0
425425 1850.00 0.211149
426426 0 0
427427 1190.00 0.134867
428428 0 0
429429 18496.0 2.08157
430430 0 0
431431 −456.000 −0.0509623 −0.0254811 0.999675i 0.508112π-0.508112\pi
−0.0254811 + 0.999675i 0.508112π0.508112\pi
432432 0 0
433433 −5318.00 −0.590223 −0.295112 0.955463i 0.595357π-0.595357\pi
−0.295112 + 0.955463i 0.595357π0.595357\pi
434434 0 0
435435 −11440.0 −1.26093
436436 0 0
437437 −10240.0 −1.12093
438438 0 0
439439 16264.0 1.76820 0.884098 0.467301i 0.154774π-0.154774\pi
0.884098 + 0.467301i 0.154774π0.154774\pi
440440 0 0
441441 1813.00 0.195767
442442 0 0
443443 −4812.00 −0.516084 −0.258042 0.966134i 0.583077π-0.583077\pi
−0.258042 + 0.966134i 0.583077π0.583077\pi
444444 0 0
445445 −7150.00 −0.761669
446446 0 0
447447 −12784.0 −1.35271
448448 0 0
449449 −2590.00 −0.272226 −0.136113 0.990693i 0.543461π-0.543461\pi
−0.136113 + 0.990693i 0.543461π0.543461\pi
450450 0 0
451451 −4488.00 −0.468585
452452 0 0
453453 −21376.0 −2.21707
454454 0 0
455455 1190.00 0.122611
456456 0 0
457457 −14294.0 −1.46312 −0.731559 0.681778i 0.761207π-0.761207\pi
−0.731559 + 0.681778i 0.761207π0.761207\pi
458458 0 0
459459 5920.00 0.602009
460460 0 0
461461 −8258.00 −0.834302 −0.417151 0.908837i 0.636971π-0.636971\pi
−0.417151 + 0.908837i 0.636971π0.636971\pi
462462 0 0
463463 −7344.00 −0.737159 −0.368580 0.929596i 0.620156π-0.620156\pi
−0.368580 + 0.929596i 0.620156π0.620156\pi
464464 0 0
465465 −960.000 −0.0957396
466466 0 0
467467 −6288.00 −0.623071 −0.311535 0.950235i 0.600843π-0.600843\pi
−0.311535 + 0.950235i 0.600843π0.600843\pi
468468 0 0
469469 3948.00 0.388703
470470 0 0
471471 −9360.00 −0.915682
472472 0 0
473473 −8432.00 −0.819670
474474 0 0
475475 3200.00 0.309108
476476 0 0
477477 1258.00 0.120754
478478 0 0
479479 392.000 0.0373924 0.0186962 0.999825i 0.494048π-0.494048\pi
0.0186962 + 0.999825i 0.494048π0.494048\pi
480480 0 0
481481 9996.00 0.947564
482482 0 0
483483 4480.00 0.422044
484484 0 0
485485 −6350.00 −0.594513
486486 0 0
487487 −512.000 −0.0476405 −0.0238203 0.999716i 0.507583π-0.507583\pi
−0.0238203 + 0.999716i 0.507583π0.507583\pi
488488 0 0
489489 −12640.0 −1.16892
490490 0 0
491491 −13308.0 −1.22318 −0.611590 0.791175i 0.709470π-0.709470\pi
−0.611590 + 0.791175i 0.709470π0.709470\pi
492492 0 0
493493 −21164.0 −1.93343
494494 0 0
495495 −12580.0 −1.14228
496496 0 0
497497 −4312.00 −0.389174
498498 0 0
499499 6252.00 0.560878 0.280439 0.959872i 0.409520π-0.409520\pi
0.280439 + 0.959872i 0.409520π0.409520\pi
500500 0 0
501501 −5632.00 −0.502234
502502 0 0
503503 12568.0 1.11407 0.557037 0.830488i 0.311938π-0.311938\pi
0.557037 + 0.830488i 0.311938π0.311938\pi
504504 0 0
505505 −4650.00 −0.409747
506506 0 0
507507 −8328.00 −0.729506
508508 0 0
509509 5502.00 0.479120 0.239560 0.970882i 0.422997π-0.422997\pi
0.239560 + 0.970882i 0.422997π0.422997\pi
510510 0 0
511511 −1750.00 −0.151498
512512 0 0
513513 10240.0 0.881300
514514 0 0
515515 800.000 0.0684509
516516 0 0
517517 −21216.0 −1.80479
518518 0 0
519519 −144.000 −0.0121790
520520 0 0
521521 −19086.0 −1.60494 −0.802469 0.596694i 0.796481π-0.796481\pi
−0.802469 + 0.596694i 0.796481π0.796481\pi
522522 0 0
523523 16184.0 1.35311 0.676555 0.736392i 0.263472π-0.263472\pi
0.676555 + 0.736392i 0.263472π0.263472\pi
524524 0 0
525525 −1400.00 −0.116383
526526 0 0
527527 −1776.00 −0.146800
528528 0 0
529529 −5767.00 −0.473987
530530 0 0
531531 −6216.00 −0.508006
532532 0 0
533533 −2244.00 −0.182361
534534 0 0
535535 −7020.00 −0.567292
536536 0 0
537537 34144.0 2.74380
538538 0 0
539539 −3332.00 −0.266270
540540 0 0
541541 16042.0 1.27486 0.637430 0.770508i 0.279997π-0.279997\pi
0.637430 + 0.770508i 0.279997π0.279997\pi
542542 0 0
543543 −2256.00 −0.178295
544544 0 0
545545 1370.00 0.107678
546546 0 0
547547 6180.00 0.483067 0.241534 0.970392i 0.422350π-0.422350\pi
0.241534 + 0.970392i 0.422350π0.422350\pi
548548 0 0
549549 −6290.00 −0.488981
550550 0 0
551551 −36608.0 −2.83041
552552 0 0
553553 6608.00 0.508139
554554 0 0
555555 −11760.0 −0.899431
556556 0 0
557557 −9078.00 −0.690569 −0.345285 0.938498i 0.612218π-0.612218\pi
−0.345285 + 0.938498i 0.612218π0.612218\pi
558558 0 0
559559 −4216.00 −0.318994
560560 0 0
561561 −40256.0 −3.02961
562562 0 0
563563 −9464.00 −0.708455 −0.354227 0.935159i 0.615256π-0.615256\pi
−0.354227 + 0.935159i 0.615256π0.615256\pi
564564 0 0
565565 −3990.00 −0.297098
566566 0 0
567567 2513.00 0.186131
568568 0 0
569569 15722.0 1.15835 0.579174 0.815204i 0.303375π-0.303375\pi
0.579174 + 0.815204i 0.303375π0.303375\pi
570570 0 0
571571 17084.0 1.25209 0.626045 0.779787i 0.284673π-0.284673\pi
0.626045 + 0.779787i 0.284673π0.284673\pi
572572 0 0
573573 11392.0 0.830554
574574 0 0
575575 −2000.00 −0.145054
576576 0 0
577577 −16526.0 −1.19235 −0.596175 0.802854i 0.703314π-0.703314\pi
−0.596175 + 0.802854i 0.703314π0.703314\pi
578578 0 0
579579 −14960.0 −1.07378
580580 0 0
581581 4704.00 0.335895
582582 0 0
583583 −2312.00 −0.164242
584584 0 0
585585 −6290.00 −0.444546
586586 0 0
587587 −2832.00 −0.199130 −0.0995649 0.995031i 0.531745π-0.531745\pi
−0.0995649 + 0.995031i 0.531745π0.531745\pi
588588 0 0
589589 −3072.00 −0.214906
590590 0 0
591591 28944.0 2.01455
592592 0 0
593593 9666.00 0.669368 0.334684 0.942330i 0.391370π-0.391370\pi
0.334684 + 0.942330i 0.391370π0.391370\pi
594594 0 0
595595 −2590.00 −0.178453
596596 0 0
597597 21888.0 1.50053
598598 0 0
599599 4536.00 0.309409 0.154704 0.987961i 0.450557π-0.450557\pi
0.154704 + 0.987961i 0.450557π0.450557\pi
600600 0 0
601601 −15542.0 −1.05486 −0.527430 0.849598i 0.676844π-0.676844\pi
−0.527430 + 0.849598i 0.676844π0.676844\pi
602602 0 0
603603 −20868.0 −1.40930
604604 0 0
605605 16465.0 1.10644
606606 0 0
607607 −23648.0 −1.58129 −0.790645 0.612275i 0.790254π-0.790254\pi
−0.790645 + 0.612275i 0.790254π0.790254\pi
608608 0 0
609609 16016.0 1.06568
610610 0 0
611611 −10608.0 −0.702379
612612 0 0
613613 906.000 0.0596949 0.0298475 0.999554i 0.490498π-0.490498\pi
0.0298475 + 0.999554i 0.490498π0.490498\pi
614614 0 0
615615 2640.00 0.173098
616616 0 0
617617 26666.0 1.73992 0.869962 0.493119i 0.164143π-0.164143\pi
0.869962 + 0.493119i 0.164143π0.164143\pi
618618 0 0
619619 3352.00 0.217655 0.108827 0.994061i 0.465290π-0.465290\pi
0.108827 + 0.994061i 0.465290π0.465290\pi
620620 0 0
621621 −6400.00 −0.413564
622622 0 0
623623 10010.0 0.643727
624624 0 0
625625 625.000 0.0400000
626626 0 0
627627 −69632.0 −4.43514
628628 0 0
629629 −21756.0 −1.37912
630630 0 0
631631 2792.00 0.176145 0.0880727 0.996114i 0.471929π-0.471929\pi
0.0880727 + 0.996114i 0.471929π0.471929\pi
632632 0 0
633633 2784.00 0.174809
634634 0 0
635635 −4520.00 −0.282474
636636 0 0
637637 −1666.00 −0.103625
638638 0 0
639639 22792.0 1.41101
640640 0 0
641641 19330.0 1.19109 0.595545 0.803322i 0.296936π-0.296936\pi
0.595545 + 0.803322i 0.296936π0.296936\pi
642642 0 0
643643 15160.0 0.929785 0.464893 0.885367i 0.346093π-0.346093\pi
0.464893 + 0.885367i 0.346093π0.346093\pi
644644 0 0
645645 4960.00 0.302790
646646 0 0
647647 −23472.0 −1.42624 −0.713122 0.701040i 0.752719π-0.752719\pi
−0.713122 + 0.701040i 0.752719π0.752719\pi
648648 0 0
649649 11424.0 0.690957
650650 0 0
651651 1344.00 0.0809148
652652 0 0
653653 −542.000 −0.0324810 −0.0162405 0.999868i 0.505170π-0.505170\pi
−0.0162405 + 0.999868i 0.505170π0.505170\pi
654654 0 0
655655 10400.0 0.620399
656656 0 0
657657 9250.00 0.549280
658658 0 0
659659 19764.0 1.16828 0.584140 0.811653i 0.301432π-0.301432\pi
0.584140 + 0.811653i 0.301432π0.301432\pi
660660 0 0
661661 −4130.00 −0.243023 −0.121512 0.992590i 0.538774π-0.538774\pi
−0.121512 + 0.992590i 0.538774π0.538774\pi
662662 0 0
663663 −20128.0 −1.17904
664664 0 0
665665 −4480.00 −0.261244
666666 0 0
667667 22880.0 1.32821
668668 0 0
669669 47104.0 2.72219
670670 0 0
671671 11560.0 0.665080
672672 0 0
673673 −24366.0 −1.39560 −0.697801 0.716292i 0.745838π-0.745838\pi
−0.697801 + 0.716292i 0.745838π0.745838\pi
674674 0 0
675675 2000.00 0.114044
676676 0 0
677677 16790.0 0.953164 0.476582 0.879130i 0.341876π-0.341876\pi
0.476582 + 0.879130i 0.341876π0.341876\pi
678678 0 0
679679 8890.00 0.502455
680680 0 0
681681 34432.0 1.93750
682682 0 0
683683 7764.00 0.434965 0.217483 0.976064i 0.430215π-0.430215\pi
0.217483 + 0.976064i 0.430215π0.430215\pi
684684 0 0
685685 11090.0 0.618580
686686 0 0
687687 −29392.0 −1.63228
688688 0 0
689689 −1156.00 −0.0639189
690690 0 0
691691 2064.00 0.113630 0.0568149 0.998385i 0.481905π-0.481905\pi
0.0568149 + 0.998385i 0.481905π0.481905\pi
692692 0 0
693693 17612.0 0.965403
694694 0 0
695695 −12160.0 −0.663676
696696 0 0
697697 4884.00 0.265416
698698 0 0
699699 −6704.00 −0.362759
700700 0 0
701701 −1230.00 −0.0662717 −0.0331358 0.999451i 0.510549π-0.510549\pi
−0.0331358 + 0.999451i 0.510549π0.510549\pi
702702 0 0
703703 −37632.0 −2.01894
704704 0 0
705705 12480.0 0.666701
706706 0 0
707707 6510.00 0.346300
708708 0 0
709709 −5158.00 −0.273220 −0.136610 0.990625i 0.543621π-0.543621\pi
−0.136610 + 0.990625i 0.543621π0.543621\pi
710710 0 0
711711 −34928.0 −1.84234
712712 0 0
713713 1920.00 0.100848
714714 0 0
715715 11560.0 0.604643
716716 0 0
717717 46656.0 2.43013
718718 0 0
719719 −23800.0 −1.23448 −0.617239 0.786775i 0.711749π-0.711749\pi
−0.617239 + 0.786775i 0.711749π0.711749\pi
720720 0 0
721721 −1120.00 −0.0578516
722722 0 0
723723 13520.0 0.695455
724724 0 0
725725 −7150.00 −0.366268
726726 0 0
727727 −12832.0 −0.654625 −0.327313 0.944916i 0.606143π-0.606143\pi
−0.327313 + 0.944916i 0.606143π0.606143\pi
728728 0 0
729729 −30563.0 −1.55276
730730 0 0
731731 9176.00 0.464277
732732 0 0
733733 −15370.0 −0.774494 −0.387247 0.921976i 0.626574π-0.626574\pi
−0.387247 + 0.921976i 0.626574π0.626574\pi
734734 0 0
735735 1960.00 0.0983615
736736 0 0
737737 38352.0 1.91684
738738 0 0
739739 −16940.0 −0.843231 −0.421616 0.906775i 0.638537π-0.638537\pi
−0.421616 + 0.906775i 0.638537π0.638537\pi
740740 0 0
741741 −34816.0 −1.72604
742742 0 0
743743 39792.0 1.96477 0.982387 0.186858i 0.0598305π-0.0598305\pi
0.982387 + 0.186858i 0.0598305π0.0598305\pi
744744 0 0
745745 −7990.00 −0.392927
746746 0 0
747747 −24864.0 −1.21784
748748 0 0
749749 9828.00 0.479449
750750 0 0
751751 −776.000 −0.0377052 −0.0188526 0.999822i 0.506001π-0.506001\pi
−0.0188526 + 0.999822i 0.506001π0.506001\pi
752752 0 0
753753 −46080.0 −2.23008
754754 0 0
755755 −13360.0 −0.644000
756756 0 0
757757 17882.0 0.858563 0.429282 0.903171i 0.358767π-0.358767\pi
0.429282 + 0.903171i 0.358767π0.358767\pi
758758 0 0
759759 43520.0 2.08126
760760 0 0
761761 6946.00 0.330870 0.165435 0.986221i 0.447097π-0.447097\pi
0.165435 + 0.986221i 0.447097π0.447097\pi
762762 0 0
763763 −1918.00 −0.0910043
764764 0 0
765765 13690.0 0.647010
766766 0 0
767767 5712.00 0.268903
768768 0 0
769769 35002.0 1.64136 0.820679 0.571389i 0.193595π-0.193595\pi
0.820679 + 0.571389i 0.193595π0.193595\pi
770770 0 0
771771 −2800.00 −0.130791
772772 0 0
773773 14414.0 0.670680 0.335340 0.942097i 0.391149π-0.391149\pi
0.335340 + 0.942097i 0.391149π0.391149\pi
774774 0 0
775775 −600.000 −0.0278099
776776 0 0
777777 16464.0 0.760158
778778 0 0
779779 8448.00 0.388551
780780 0 0
781781 −41888.0 −1.91917
782782 0 0
783783 −22880.0 −1.04427
784784 0 0
785785 −5850.00 −0.265981
786786 0 0
787787 7312.00 0.331188 0.165594 0.986194i 0.447046π-0.447046\pi
0.165594 + 0.986194i 0.447046π0.447046\pi
788788 0 0
789789 −23744.0 −1.07137
790790 0 0
791791 5586.00 0.251094
792792 0 0
793793 5780.00 0.258832
794794 0 0
795795 1360.00 0.0606720
796796 0 0
797797 −4290.00 −0.190664 −0.0953322 0.995446i 0.530391π-0.530391\pi
−0.0953322 + 0.995446i 0.530391π0.530391\pi
798798 0 0
799799 23088.0 1.02227
800800 0 0
801801 −52910.0 −2.33394
802802 0 0
803803 −17000.0 −0.747095
804804 0 0
805805 2800.00 0.122593
806806 0 0
807807 35952.0 1.56824
808808 0 0
809809 −28246.0 −1.22754 −0.613768 0.789487i 0.710347π-0.710347\pi
−0.613768 + 0.789487i 0.710347π0.710347\pi
810810 0 0
811811 15656.0 0.677875 0.338937 0.940809i 0.389933π-0.389933\pi
0.338937 + 0.940809i 0.389933π0.389933\pi
812812 0 0
813813 10496.0 0.452781
814814 0 0
815815 −7900.00 −0.339540
816816 0 0
817817 15872.0 0.679671
818818 0 0
819819 8806.00 0.375710
820820 0 0
821821 27506.0 1.16926 0.584632 0.811298i 0.301239π-0.301239\pi
0.584632 + 0.811298i 0.301239π0.301239\pi
822822 0 0
823823 36552.0 1.54814 0.774072 0.633097i 0.218217π-0.218217\pi
0.774072 + 0.633097i 0.218217π0.218217\pi
824824 0 0
825825 −13600.0 −0.573929
826826 0 0
827827 −18892.0 −0.794364 −0.397182 0.917740i 0.630012π-0.630012\pi
−0.397182 + 0.917740i 0.630012π0.630012\pi
828828 0 0
829829 19446.0 0.814701 0.407351 0.913272i 0.366453π-0.366453\pi
0.407351 + 0.913272i 0.366453π0.366453\pi
830830 0 0
831831 41872.0 1.74792
832832 0 0
833833 3626.00 0.150820
834834 0 0
835835 −3520.00 −0.145886
836836 0 0
837837 −1920.00 −0.0792890
838838 0 0
839839 12416.0 0.510903 0.255452 0.966822i 0.417776π-0.417776\pi
0.255452 + 0.966822i 0.417776π0.417776\pi
840840 0 0
841841 57407.0 2.35381
842842 0 0
843843 −45744.0 −1.86893
844844 0 0
845845 −5205.00 −0.211902
846846 0 0
847847 −23051.0 −0.935114
848848 0 0
849849 30016.0 1.21336
850850 0 0
851851 23520.0 0.947421
852852 0 0
853853 −19210.0 −0.771088 −0.385544 0.922689i 0.625986π-0.625986\pi
−0.385544 + 0.922689i 0.625986π0.625986\pi
854854 0 0
855855 23680.0 0.947180
856856 0 0
857857 530.000 0.0211254 0.0105627 0.999944i 0.496638π-0.496638\pi
0.0105627 + 0.999944i 0.496638π0.496638\pi
858858 0 0
859859 2624.00 0.104226 0.0521128 0.998641i 0.483404π-0.483404\pi
0.0521128 + 0.998641i 0.483404π0.483404\pi
860860 0 0
861861 −3696.00 −0.146294
862862 0 0
863863 37136.0 1.46480 0.732401 0.680874i 0.238400π-0.238400\pi
0.732401 + 0.680874i 0.238400π0.238400\pi
864864 0 0
865865 −90.0000 −0.00353768
866866 0 0
867867 4504.00 0.176429
868868 0 0
869869 64192.0 2.50583
870870 0 0
871871 19176.0 0.745986
872872 0 0
873873 −46990.0 −1.82173
874874 0 0
875875 −875.000 −0.0338062
876876 0 0
877877 −44606.0 −1.71749 −0.858744 0.512404i 0.828755π-0.828755\pi
−0.858744 + 0.512404i 0.828755π0.828755\pi
878878 0 0
879879 −61584.0 −2.36311
880880 0 0
881881 −41806.0 −1.59873 −0.799364 0.600847i 0.794830π-0.794830\pi
−0.799364 + 0.600847i 0.794830π0.794830\pi
882882 0 0
883883 −8324.00 −0.317242 −0.158621 0.987340i 0.550705π-0.550705\pi
−0.158621 + 0.987340i 0.550705π0.550705\pi
884884 0 0
885885 −6720.00 −0.255243
886886 0 0
887887 −6592.00 −0.249535 −0.124768 0.992186i 0.539819π-0.539819\pi
−0.124768 + 0.992186i 0.539819π0.539819\pi
888888 0 0
889889 6328.00 0.238734
890890 0 0
891891 24412.0 0.917882
892892 0 0
893893 39936.0 1.49654
894894 0 0
895895 21340.0 0.797003
896896 0 0
897897 21760.0 0.809972
898898 0 0
899899 6864.00 0.254647
900900 0 0
901901 2516.00 0.0930301
902902 0 0
903903 −6944.00 −0.255905
904904 0 0
905905 −1410.00 −0.0517900
906906 0 0
907907 −43948.0 −1.60890 −0.804448 0.594023i 0.797539π-0.797539\pi
−0.804448 + 0.594023i 0.797539π0.797539\pi
908908 0 0
909909 −34410.0 −1.25556
910910 0 0
911911 14936.0 0.543196 0.271598 0.962411i 0.412448π-0.412448\pi
0.271598 + 0.962411i 0.412448π0.412448\pi
912912 0 0
913913 45696.0 1.65643
914914 0 0
915915 −6800.00 −0.245684
916916 0 0
917917 −14560.0 −0.524333
918918 0 0
919919 8104.00 0.290888 0.145444 0.989366i 0.453539π-0.453539\pi
0.145444 + 0.989366i 0.453539π0.453539\pi
920920 0 0
921921 11648.0 0.416737
922922 0 0
923923 −20944.0 −0.746891
924924 0 0
925925 −7350.00 −0.261261
926926 0 0
927927 5920.00 0.209750
928928 0 0
929929 −43622.0 −1.54057 −0.770286 0.637699i 0.779887π-0.779887\pi
−0.770286 + 0.637699i 0.779887π0.779887\pi
930930 0 0
931931 6272.00 0.220791
932932 0 0
933933 76736.0 2.69263
934934 0 0
935935 −25160.0 −0.880021
936936 0 0
937937 −30278.0 −1.05564 −0.527822 0.849355i 0.676991π-0.676991\pi
−0.527822 + 0.849355i 0.676991π0.676991\pi
938938 0 0
939939 28560.0 0.992567
940940 0 0
941941 −45594.0 −1.57951 −0.789757 0.613420i 0.789793π-0.789793\pi
−0.789757 + 0.613420i 0.789793π0.789793\pi
942942 0 0
943943 −5280.00 −0.182333
944944 0 0
945945 −2800.00 −0.0963852
946946 0 0
947947 −5836.00 −0.200258 −0.100129 0.994974i 0.531926π-0.531926\pi
−0.100129 + 0.994974i 0.531926π0.531926\pi
948948 0 0
949949 −8500.00 −0.290750
950950 0 0
951951 30928.0 1.05458
952952 0 0
953953 7274.00 0.247249 0.123624 0.992329i 0.460548π-0.460548\pi
0.123624 + 0.992329i 0.460548π0.460548\pi
954954 0 0
955955 7120.00 0.241254
956956 0 0
957957 155584. 5.25529
958958 0 0
959959 −15526.0 −0.522795
960960 0 0
961961 −29215.0 −0.980665
962962 0 0
963963 −51948.0 −1.73832
964964 0 0
965965 −9350.00 −0.311904
966966 0 0
967967 −2432.00 −0.0808768 −0.0404384 0.999182i 0.512875π-0.512875\pi
−0.0404384 + 0.999182i 0.512875π0.512875\pi
968968 0 0
969969 75776.0 2.51215
970970 0 0
971971 7496.00 0.247743 0.123871 0.992298i 0.460469π-0.460469\pi
0.123871 + 0.992298i 0.460469π0.460469\pi
972972 0 0
973973 17024.0 0.560909
974974 0 0
975975 −6800.00 −0.223358
976976 0 0
977977 −56574.0 −1.85257 −0.926286 0.376822i 0.877017π-0.877017\pi
−0.926286 + 0.376822i 0.877017π0.877017\pi
978978 0 0
979979 97240.0 3.17447
980980 0 0
981981 10138.0 0.329950
982982 0 0
983983 −25776.0 −0.836345 −0.418172 0.908368i 0.637329π-0.637329\pi
−0.418172 + 0.908368i 0.637329π0.637329\pi
984984 0 0
985985 18090.0 0.585173
986986 0 0
987987 −17472.0 −0.563465
988988 0 0
989989 −9920.00 −0.318946
990990 0 0
991991 −60080.0 −1.92584 −0.962918 0.269793i 0.913045π-0.913045\pi
−0.962918 + 0.269793i 0.913045π0.913045\pi
992992 0 0
993993 23520.0 0.751646
994994 0 0
995995 13680.0 0.435864
996996 0 0
997997 −49906.0 −1.58529 −0.792647 0.609680i 0.791298π-0.791298\pi
−0.792647 + 0.609680i 0.791298π0.791298\pi
998998 0 0
999999 −23520.0 −0.744885
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 2240.4.a.bi.1.1 1
4.3 odd 2 2240.4.a.d.1.1 1
8.3 odd 2 560.4.a.q.1.1 1
8.5 even 2 70.4.a.a.1.1 1
24.5 odd 2 630.4.a.s.1.1 1
40.13 odd 4 350.4.c.n.99.2 2
40.29 even 2 350.4.a.v.1.1 1
40.37 odd 4 350.4.c.n.99.1 2
56.5 odd 6 490.4.e.j.361.1 2
56.13 odd 2 490.4.a.g.1.1 1
56.37 even 6 490.4.e.r.361.1 2
56.45 odd 6 490.4.e.j.471.1 2
56.53 even 6 490.4.e.r.471.1 2
280.69 odd 2 2450.4.a.x.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.4.a.a.1.1 1 8.5 even 2
350.4.a.v.1.1 1 40.29 even 2
350.4.c.n.99.1 2 40.37 odd 4
350.4.c.n.99.2 2 40.13 odd 4
490.4.a.g.1.1 1 56.13 odd 2
490.4.e.j.361.1 2 56.5 odd 6
490.4.e.j.471.1 2 56.45 odd 6
490.4.e.r.361.1 2 56.37 even 6
490.4.e.r.471.1 2 56.53 even 6
560.4.a.q.1.1 1 8.3 odd 2
630.4.a.s.1.1 1 24.5 odd 2
2240.4.a.d.1.1 1 4.3 odd 2
2240.4.a.bi.1.1 1 1.1 even 1 trivial
2450.4.a.x.1.1 1 280.69 odd 2