Properties

Label 720.4.f.g.289.2
Level 720720
Weight 44
Character 720.289
Analytic conductor 42.48142.481
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [720,4,Mod(289,720)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(720, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.289");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 720=24325 720 = 2^{4} \cdot 3^{2} \cdot 5
Weight: k k == 4 4
Character orbit: [χ][\chi] == 720.f (of order 22, degree 11, not minimal)

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: no
Analytic conductor: 42.481375204142.4813752041
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
comment: defining polynomial
 
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: 1 1
Twist minimal: no (minimal twist has level 120)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 289.2
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 720.289
Dual form 720.4.f.g.289.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(10.0000+5.00000i)q510.0000iq746.0000q11+34.0000iq1366.0000iq17+104.000q19164.000iq23+(75.0000+100.000i)q25+224.000q29+72.0000q31+(50.0000100.000i)q3522.0000iq37194.000q41+108.000iq43480.000iq47+243.000q49+286.000iq53+(460.000230.000i)q55426.000q59+698.000q61+(170.000+340.000i)q65328.000iq67+188.000q71+740.000iq73+460.000iq77+1168.00q79412.000iq83+(330.000660.000i)q85+1206.00q89+340.000q91+(1040.00+520.000i)q951384.00iq97+O(q100)q+(10.0000 + 5.00000i) q^{5} -10.0000i q^{7} -46.0000 q^{11} +34.0000i q^{13} -66.0000i q^{17} +104.000 q^{19} -164.000i q^{23} +(75.0000 + 100.000i) q^{25} +224.000 q^{29} +72.0000 q^{31} +(50.0000 - 100.000i) q^{35} -22.0000i q^{37} -194.000 q^{41} +108.000i q^{43} -480.000i q^{47} +243.000 q^{49} +286.000i q^{53} +(-460.000 - 230.000i) q^{55} -426.000 q^{59} +698.000 q^{61} +(-170.000 + 340.000i) q^{65} -328.000i q^{67} +188.000 q^{71} +740.000i q^{73} +460.000i q^{77} +1168.00 q^{79} -412.000i q^{83} +(330.000 - 660.000i) q^{85} +1206.00 q^{89} +340.000 q^{91} +(1040.00 + 520.000i) q^{95} -1384.00i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+20q592q11+208q19+150q25+448q29+144q31+100q35388q41+486q49920q55852q59+1396q61340q65+376q71+2336q79+660q85++2080q95+O(q100) 2 q + 20 q^{5} - 92 q^{11} + 208 q^{19} + 150 q^{25} + 448 q^{29} + 144 q^{31} + 100 q^{35} - 388 q^{41} + 486 q^{49} - 920 q^{55} - 852 q^{59} + 1396 q^{61} - 340 q^{65} + 376 q^{71} + 2336 q^{79} + 660 q^{85}+ \cdots + 2080 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/720Z)×\left(\mathbb{Z}/720\mathbb{Z}\right)^\times.

nn 181181 271271 577577 641641
χ(n)\chi(n) 11 11 1-1 11

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 0 0
44 0 0
55 10.0000 + 5.00000i 0.894427 + 0.447214i
66 0 0
77 10.0000i 0.539949i −0.962867 0.269975i 0.912985π-0.912985\pi
0.962867 0.269975i 0.0870153π-0.0870153\pi
88 0 0
99 0 0
1010 0 0
1111 −46.0000 −1.26087 −0.630433 0.776244i 0.717123π-0.717123\pi
−0.630433 + 0.776244i 0.717123π0.717123\pi
1212 0 0
1313 34.0000i 0.725377i 0.931910 + 0.362689i 0.118141π0.118141\pi
−0.931910 + 0.362689i 0.881859π0.881859\pi
1414 0 0
1515 0 0
1616 0 0
1717 66.0000i 0.941609i −0.882238 0.470804i 0.843964π-0.843964\pi
0.882238 0.470804i 0.156036π-0.156036\pi
1818 0 0
1919 104.000 1.25575 0.627875 0.778314i 0.283925π-0.283925\pi
0.627875 + 0.778314i 0.283925π0.283925\pi
2020 0 0
2121 0 0
2222 0 0
2323 164.000i 1.48680i −0.668848 0.743399i 0.733212π-0.733212\pi
0.668848 0.743399i 0.266788π-0.266788\pi
2424 0 0
2525 75.0000 + 100.000i 0.600000 + 0.800000i
2626 0 0
2727 0 0
2828 0 0
2929 224.000 1.43434 0.717168 0.696900i 0.245438π-0.245438\pi
0.717168 + 0.696900i 0.245438π0.245438\pi
3030 0 0
3131 72.0000 0.417148 0.208574 0.978007i 0.433118π-0.433118\pi
0.208574 + 0.978007i 0.433118π0.433118\pi
3232 0 0
3333 0 0
3434 0 0
3535 50.0000 100.000i 0.241473 0.482945i
3636 0 0
3737 22.0000i 0.0977507i −0.998805 0.0488754i 0.984436π-0.984436\pi
0.998805 0.0488754i 0.0155637π-0.0155637\pi
3838 0 0
3939 0 0
4040 0 0
4141 −194.000 −0.738969 −0.369484 0.929237i 0.620466π-0.620466\pi
−0.369484 + 0.929237i 0.620466π0.620466\pi
4242 0 0
4343 108.000i 0.383020i 0.981491 + 0.191510i 0.0613384π0.0613384\pi
−0.981491 + 0.191510i 0.938662π0.938662\pi
4444 0 0
4545 0 0
4646 0 0
4747 480.000i 1.48969i −0.667240 0.744843i 0.732525π-0.732525\pi
0.667240 0.744843i 0.267475π-0.267475\pi
4848 0 0
4949 243.000 0.708455
5050 0 0
5151 0 0
5252 0 0
5353 286.000i 0.741229i 0.928787 + 0.370614i 0.120853π0.120853\pi
−0.928787 + 0.370614i 0.879147π0.879147\pi
5454 0 0
5555 −460.000 230.000i −1.12775 0.563876i
5656 0 0
5757 0 0
5858 0 0
5959 −426.000 −0.940008 −0.470004 0.882664i 0.655748π-0.655748\pi
−0.470004 + 0.882664i 0.655748π0.655748\pi
6060 0 0
6161 698.000 1.46508 0.732539 0.680725i 0.238335π-0.238335\pi
0.732539 + 0.680725i 0.238335π0.238335\pi
6262 0 0
6363 0 0
6464 0 0
6565 −170.000 + 340.000i −0.324399 + 0.648797i
6666 0 0
6767 328.000i 0.598083i −0.954240 0.299042i 0.903333π-0.903333\pi
0.954240 0.299042i 0.0966669π-0.0966669\pi
6868 0 0
6969 0 0
7070 0 0
7171 188.000 0.314246 0.157123 0.987579i 0.449778π-0.449778\pi
0.157123 + 0.987579i 0.449778π0.449778\pi
7272 0 0
7373 740.000i 1.18644i 0.805039 + 0.593222i 0.202144π0.202144\pi
−0.805039 + 0.593222i 0.797856π0.797856\pi
7474 0 0
7575 0 0
7676 0 0
7777 460.000i 0.680803i
7878 0 0
7979 1168.00 1.66342 0.831711 0.555209i 0.187362π-0.187362\pi
0.831711 + 0.555209i 0.187362π0.187362\pi
8080 0 0
8181 0 0
8282 0 0
8383 412.000i 0.544854i −0.962176 0.272427i 0.912174π-0.912174\pi
0.962176 0.272427i 0.0878263π-0.0878263\pi
8484 0 0
8585 330.000 660.000i 0.421100 0.842201i
8686 0 0
8787 0 0
8888 0 0
8989 1206.00 1.43636 0.718178 0.695859i 0.244976π-0.244976\pi
0.718178 + 0.695859i 0.244976π0.244976\pi
9090 0 0
9191 340.000 0.391667
9292 0 0
9393 0 0
9494 0 0
9595 1040.00 + 520.000i 1.12318 + 0.561588i
9696 0 0
9797 1384.00i 1.44870i −0.689432 0.724350i 0.742140π-0.742140\pi
0.689432 0.724350i 0.257860π-0.257860\pi
9898 0 0
9999 0 0
100100 0 0
101101 1128.00 1.11129 0.555645 0.831420i 0.312472π-0.312472\pi
0.555645 + 0.831420i 0.312472π0.312472\pi
102102 0 0
103103 758.000i 0.725126i −0.931959 0.362563i 0.881902π-0.881902\pi
0.931959 0.362563i 0.118098π-0.118098\pi
104104 0 0
105105 0 0
106106 0 0
107107 1324.00i 1.19622i 0.801413 + 0.598112i 0.204082π0.204082\pi
−0.801413 + 0.598112i 0.795918π0.795918\pi
108108 0 0
109109 −1602.00 −1.40774 −0.703871 0.710328i 0.748546π-0.748546\pi
−0.703871 + 0.710328i 0.748546π0.748546\pi
110110 0 0
111111 0 0
112112 0 0
113113 2074.00i 1.72660i −0.504693 0.863299i 0.668394π-0.668394\pi
0.504693 0.863299i 0.331606π-0.331606\pi
114114 0 0
115115 820.000 1640.00i 0.664916 1.32983i
116116 0 0
117117 0 0
118118 0 0
119119 −660.000 −0.508421
120120 0 0
121121 785.000 0.589782
122122 0 0
123123 0 0
124124 0 0
125125 250.000 + 1375.00i 0.178885 + 0.983870i
126126 0 0
127127 534.000i 0.373109i 0.982445 + 0.186554i 0.0597321π0.0597321\pi
−0.982445 + 0.186554i 0.940268π0.940268\pi
128128 0 0
129129 0 0
130130 0 0
131131 1806.00 1.20451 0.602256 0.798303i 0.294269π-0.294269\pi
0.602256 + 0.798303i 0.294269π0.294269\pi
132132 0 0
133133 1040.00i 0.678041i
134134 0 0
135135 0 0
136136 0 0
137137 1822.00i 1.13623i −0.822948 0.568117i 0.807672π-0.807672\pi
0.822948 0.568117i 0.192328π-0.192328\pi
138138 0 0
139139 532.000 0.324631 0.162315 0.986739i 0.448104π-0.448104\pi
0.162315 + 0.986739i 0.448104π0.448104\pi
140140 0 0
141141 0 0
142142 0 0
143143 1564.00i 0.914603i
144144 0 0
145145 2240.00 + 1120.00i 1.28291 + 0.641455i
146146 0 0
147147 0 0
148148 0 0
149149 −1284.00 −0.705969 −0.352984 0.935629i 0.614833π-0.614833\pi
−0.352984 + 0.935629i 0.614833π0.614833\pi
150150 0 0
151151 −184.000 −0.0991636 −0.0495818 0.998770i 0.515789π-0.515789\pi
−0.0495818 + 0.998770i 0.515789π0.515789\pi
152152 0 0
153153 0 0
154154 0 0
155155 720.000 + 360.000i 0.373108 + 0.186554i
156156 0 0
157157 3746.00i 1.90423i −0.305748 0.952113i 0.598906π-0.598906\pi
0.305748 0.952113i 0.401094π-0.401094\pi
158158 0 0
159159 0 0
160160 0 0
161161 −1640.00 −0.802796
162162 0 0
163163 1504.00i 0.722714i 0.932428 + 0.361357i 0.117686π0.117686\pi
−0.932428 + 0.361357i 0.882314π0.882314\pi
164164 0 0
165165 0 0
166166 0 0
167167 3012.00i 1.39566i 0.716262 + 0.697831i 0.245851π0.245851\pi
−0.716262 + 0.697831i 0.754149π0.754149\pi
168168 0 0
169169 1041.00 0.473828
170170 0 0
171171 0 0
172172 0 0
173173 438.000i 0.192489i −0.995358 0.0962443i 0.969317π-0.969317\pi
0.995358 0.0962443i 0.0306830π-0.0306830\pi
174174 0 0
175175 1000.00 750.000i 0.431959 0.323970i
176176 0 0
177177 0 0
178178 0 0
179179 1462.00 0.610475 0.305237 0.952276i 0.401264π-0.401264\pi
0.305237 + 0.952276i 0.401264π0.401264\pi
180180 0 0
181181 586.000 0.240647 0.120323 0.992735i 0.461607π-0.461607\pi
0.120323 + 0.992735i 0.461607π0.461607\pi
182182 0 0
183183 0 0
184184 0 0
185185 110.000 220.000i 0.0437155 0.0874309i
186186 0 0
187187 3036.00i 1.18724i
188188 0 0
189189 0 0
190190 0 0
191191 60.0000 0.0227301 0.0113650 0.999935i 0.496382π-0.496382\pi
0.0113650 + 0.999935i 0.496382π0.496382\pi
192192 0 0
193193 4676.00i 1.74397i 0.489534 + 0.871984i 0.337167π0.337167\pi
−0.489534 + 0.871984i 0.662833π0.662833\pi
194194 0 0
195195 0 0
196196 0 0
197197 2286.00i 0.826755i −0.910560 0.413378i 0.864349π-0.864349\pi
0.910560 0.413378i 0.135651π-0.135651\pi
198198 0 0
199199 −3536.00 −1.25960 −0.629800 0.776757i 0.716863π-0.716863\pi
−0.629800 + 0.776757i 0.716863π0.716863\pi
200200 0 0
201201 0 0
202202 0 0
203203 2240.00i 0.774469i
204204 0 0
205205 −1940.00 970.000i −0.660954 0.330477i
206206 0 0
207207 0 0
208208 0 0
209209 −4784.00 −1.58333
210210 0 0
211211 3500.00 1.14194 0.570971 0.820970i 0.306567π-0.306567\pi
0.570971 + 0.820970i 0.306567π0.306567\pi
212212 0 0
213213 0 0
214214 0 0
215215 −540.000 + 1080.00i −0.171292 + 0.342583i
216216 0 0
217217 720.000i 0.225239i
218218 0 0
219219 0 0
220220 0 0
221221 2244.00 0.683022
222222 0 0
223223 5874.00i 1.76391i 0.471333 + 0.881955i 0.343773π0.343773\pi
−0.471333 + 0.881955i 0.656227π0.656227\pi
224224 0 0
225225 0 0
226226 0 0
227227 124.000i 0.0362563i −0.999836 0.0181281i 0.994229π-0.994229\pi
0.999836 0.0181281i 0.00577068π-0.00577068\pi
228228 0 0
229229 1362.00 0.393028 0.196514 0.980501i 0.437038π-0.437038\pi
0.196514 + 0.980501i 0.437038π0.437038\pi
230230 0 0
231231 0 0
232232 0 0
233233 3870.00i 1.08812i −0.839046 0.544060i 0.816886π-0.816886\pi
0.839046 0.544060i 0.183114π-0.183114\pi
234234 0 0
235235 2400.00 4800.00i 0.666207 1.33241i
236236 0 0
237237 0 0
238238 0 0
239239 −6116.00 −1.65528 −0.827638 0.561262i 0.810316π-0.810316\pi
−0.827638 + 0.561262i 0.810316π0.810316\pi
240240 0 0
241241 −5962.00 −1.59355 −0.796776 0.604274i 0.793463π-0.793463\pi
−0.796776 + 0.604274i 0.793463π0.793463\pi
242242 0 0
243243 0 0
244244 0 0
245245 2430.00 + 1215.00i 0.633661 + 0.316831i
246246 0 0
247247 3536.00i 0.910892i
248248 0 0
249249 0 0
250250 0 0
251251 −1490.00 −0.374693 −0.187347 0.982294i 0.559989π-0.559989\pi
−0.187347 + 0.982294i 0.559989π0.559989\pi
252252 0 0
253253 7544.00i 1.87465i
254254 0 0
255255 0 0
256256 0 0
257257 5394.00i 1.30922i 0.755969 + 0.654608i 0.227166π0.227166\pi
−0.755969 + 0.654608i 0.772834π0.772834\pi
258258 0 0
259259 −220.000 −0.0527804
260260 0 0
261261 0 0
262262 0 0
263263 636.000i 0.149116i 0.997217 + 0.0745579i 0.0237546π0.0237546\pi
−0.997217 + 0.0745579i 0.976245π0.976245\pi
264264 0 0
265265 −1430.00 + 2860.00i −0.331488 + 0.662975i
266266 0 0
267267 0 0
268268 0 0
269269 −3360.00 −0.761572 −0.380786 0.924663i 0.624347π-0.624347\pi
−0.380786 + 0.924663i 0.624347π0.624347\pi
270270 0 0
271271 −5768.00 −1.29292 −0.646459 0.762948i 0.723751π-0.723751\pi
−0.646459 + 0.762948i 0.723751π0.723751\pi
272272 0 0
273273 0 0
274274 0 0
275275 −3450.00 4600.00i −0.756519 1.00869i
276276 0 0
277277 1398.00i 0.303241i −0.988439 0.151620i 0.951551π-0.951551\pi
0.988439 0.151620i 0.0484491π-0.0484491\pi
278278 0 0
279279 0 0
280280 0 0
281281 4194.00 0.890367 0.445183 0.895439i 0.353138π-0.353138\pi
0.445183 + 0.895439i 0.353138π0.353138\pi
282282 0 0
283283 8256.00i 1.73416i −0.498166 0.867082i 0.665993π-0.665993\pi
0.498166 0.867082i 0.334007π-0.334007\pi
284284 0 0
285285 0 0
286286 0 0
287287 1940.00i 0.399006i
288288 0 0
289289 557.000 0.113373
290290 0 0
291291 0 0
292292 0 0
293293 5534.00i 1.10341i 0.834039 + 0.551706i 0.186023π0.186023\pi
−0.834039 + 0.551706i 0.813977π0.813977\pi
294294 0 0
295295 −4260.00 2130.00i −0.840769 0.420384i
296296 0 0
297297 0 0
298298 0 0
299299 5576.00 1.07849
300300 0 0
301301 1080.00 0.206811
302302 0 0
303303 0 0
304304 0 0
305305 6980.00 + 3490.00i 1.31041 + 0.655203i
306306 0 0
307307 484.000i 0.0899783i 0.998987 + 0.0449892i 0.0143253π0.0143253\pi
−0.998987 + 0.0449892i 0.985675π0.985675\pi
308308 0 0
309309 0 0
310310 0 0
311311 −2724.00 −0.496668 −0.248334 0.968674i 0.579883π-0.579883\pi
−0.248334 + 0.968674i 0.579883π0.579883\pi
312312 0 0
313313 5308.00i 0.958549i −0.877665 0.479275i 0.840900π-0.840900\pi
0.877665 0.479275i 0.159100π-0.159100\pi
314314 0 0
315315 0 0
316316 0 0
317317 4218.00i 0.747339i −0.927562 0.373670i 0.878099π-0.878099\pi
0.927562 0.373670i 0.121901π-0.121901\pi
318318 0 0
319319 −10304.0 −1.80851
320320 0 0
321321 0 0
322322 0 0
323323 6864.00i 1.18242i
324324 0 0
325325 −3400.00 + 2550.00i −0.580302 + 0.435226i
326326 0 0
327327 0 0
328328 0 0
329329 −4800.00 −0.804354
330330 0 0
331331 4640.00 0.770506 0.385253 0.922811i 0.374114π-0.374114\pi
0.385253 + 0.922811i 0.374114π0.374114\pi
332332 0 0
333333 0 0
334334 0 0
335335 1640.00 3280.00i 0.267471 0.534942i
336336 0 0
337337 8156.00i 1.31835i −0.751987 0.659177i 0.770905π-0.770905\pi
0.751987 0.659177i 0.229095π-0.229095\pi
338338 0 0
339339 0 0
340340 0 0
341341 −3312.00 −0.525967
342342 0 0
343343 5860.00i 0.922479i
344344 0 0
345345 0 0
346346 0 0
347347 4124.00i 0.638006i 0.947754 + 0.319003i 0.103348π0.103348\pi
−0.947754 + 0.319003i 0.896652π0.896652\pi
348348 0 0
349349 −3650.00 −0.559828 −0.279914 0.960025i 0.590306π-0.590306\pi
−0.279914 + 0.960025i 0.590306π0.590306\pi
350350 0 0
351351 0 0
352352 0 0
353353 6834.00i 1.03042i 0.857065 + 0.515208i 0.172285π0.172285\pi
−0.857065 + 0.515208i 0.827715π0.827715\pi
354354 0 0
355355 1880.00 + 940.000i 0.281071 + 0.140535i
356356 0 0
357357 0 0
358358 0 0
359359 −3904.00 −0.573942 −0.286971 0.957939i 0.592648π-0.592648\pi
−0.286971 + 0.957939i 0.592648π0.592648\pi
360360 0 0
361361 3957.00 0.576906
362362 0 0
363363 0 0
364364 0 0
365365 −3700.00 + 7400.00i −0.530594 + 1.06119i
366366 0 0
367367 13174.0i 1.87378i 0.349624 + 0.936890i 0.386309π0.386309\pi
−0.349624 + 0.936890i 0.613691π0.613691\pi
368368 0 0
369369 0 0
370370 0 0
371371 2860.00 0.400226
372372 0 0
373373 1090.00i 0.151308i 0.997134 + 0.0756542i 0.0241045π0.0241045\pi
−0.997134 + 0.0756542i 0.975895π0.975895\pi
374374 0 0
375375 0 0
376376 0 0
377377 7616.00i 1.04043i
378378 0 0
379379 −9220.00 −1.24960 −0.624802 0.780784i 0.714820π-0.714820\pi
−0.624802 + 0.780784i 0.714820π0.714820\pi
380380 0 0
381381 0 0
382382 0 0
383383 3960.00i 0.528320i 0.964479 + 0.264160i 0.0850947π0.0850947\pi
−0.964479 + 0.264160i 0.914905π0.914905\pi
384384 0 0
385385 −2300.00 + 4600.00i −0.304465 + 0.608929i
386386 0 0
387387 0 0
388388 0 0
389389 −1788.00 −0.233047 −0.116523 0.993188i 0.537175π-0.537175\pi
−0.116523 + 0.993188i 0.537175π0.537175\pi
390390 0 0
391391 −10824.0 −1.39998
392392 0 0
393393 0 0
394394 0 0
395395 11680.0 + 5840.00i 1.48781 + 0.743905i
396396 0 0
397397 9642.00i 1.21894i 0.792810 + 0.609469i 0.208617π0.208617\pi
−0.792810 + 0.609469i 0.791383π0.791383\pi
398398 0 0
399399 0 0
400400 0 0
401401 410.000 0.0510584 0.0255292 0.999674i 0.491873π-0.491873\pi
0.0255292 + 0.999674i 0.491873π0.491873\pi
402402 0 0
403403 2448.00i 0.302589i
404404 0 0
405405 0 0
406406 0 0
407407 1012.00i 0.123251i
408408 0 0
409409 −13766.0 −1.66427 −0.832133 0.554576i 0.812880π-0.812880\pi
−0.832133 + 0.554576i 0.812880π0.812880\pi
410410 0 0
411411 0 0
412412 0 0
413413 4260.00i 0.507557i
414414 0 0
415415 2060.00 4120.00i 0.243666 0.487332i
416416 0 0
417417 0 0
418418 0 0
419419 −16998.0 −1.98188 −0.990939 0.134315i 0.957117π-0.957117\pi
−0.990939 + 0.134315i 0.957117π0.957117\pi
420420 0 0
421421 −2450.00 −0.283624 −0.141812 0.989894i 0.545293π-0.545293\pi
−0.141812 + 0.989894i 0.545293π0.545293\pi
422422 0 0
423423 0 0
424424 0 0
425425 6600.00 4950.00i 0.753287 0.564965i
426426 0 0
427427 6980.00i 0.791068i
428428 0 0
429429 0 0
430430 0 0
431431 −9248.00 −1.03355 −0.516776 0.856121i 0.672868π-0.672868\pi
−0.516776 + 0.856121i 0.672868π0.672868\pi
432432 0 0
433433 5028.00i 0.558038i 0.960286 + 0.279019i 0.0900092π0.0900092\pi
−0.960286 + 0.279019i 0.909991π0.909991\pi
434434 0 0
435435 0 0
436436 0 0
437437 17056.0i 1.86705i
438438 0 0
439439 3120.00 0.339202 0.169601 0.985513i 0.445752π-0.445752\pi
0.169601 + 0.985513i 0.445752π0.445752\pi
440440 0 0
441441 0 0
442442 0 0
443443 8220.00i 0.881589i 0.897608 + 0.440795i 0.145303π0.145303\pi
−0.897608 + 0.440795i 0.854697π0.854697\pi
444444 0 0
445445 12060.0 + 6030.00i 1.28472 + 0.642358i
446446 0 0
447447 0 0
448448 0 0
449449 −5826.00 −0.612352 −0.306176 0.951975i 0.599050π-0.599050\pi
−0.306176 + 0.951975i 0.599050π0.599050\pi
450450 0 0
451451 8924.00 0.931740
452452 0 0
453453 0 0
454454 0 0
455455 3400.00 + 1700.00i 0.350317 + 0.175159i
456456 0 0
457457 16896.0i 1.72946i −0.502240 0.864728i 0.667491π-0.667491\pi
0.502240 0.864728i 0.332509π-0.332509\pi
458458 0 0
459459 0 0
460460 0 0
461461 996.000 0.100625 0.0503127 0.998734i 0.483978π-0.483978\pi
0.0503127 + 0.998734i 0.483978π0.483978\pi
462462 0 0
463463 10046.0i 1.00837i 0.863594 + 0.504187i 0.168208π0.168208\pi
−0.863594 + 0.504187i 0.831792π0.831792\pi
464464 0 0
465465 0 0
466466 0 0
467467 8388.00i 0.831157i −0.909557 0.415579i 0.863579π-0.863579\pi
0.909557 0.415579i 0.136421π-0.136421\pi
468468 0 0
469469 −3280.00 −0.322935
470470 0 0
471471 0 0
472472 0 0
473473 4968.00i 0.482936i
474474 0 0
475475 7800.00 + 10400.0i 0.753450 + 1.00460i
476476 0 0
477477 0 0
478478 0 0
479479 −11396.0 −1.08705 −0.543525 0.839393i 0.682911π-0.682911\pi
−0.543525 + 0.839393i 0.682911π0.682911\pi
480480 0 0
481481 748.000 0.0709062
482482 0 0
483483 0 0
484484 0 0
485485 6920.00 13840.0i 0.647878 1.29576i
486486 0 0
487487 6454.00i 0.600531i −0.953856 0.300266i 0.902925π-0.902925\pi
0.953856 0.300266i 0.0970753π-0.0970753\pi
488488 0 0
489489 0 0
490490 0 0
491491 18638.0 1.71308 0.856539 0.516083i 0.172610π-0.172610\pi
0.856539 + 0.516083i 0.172610π0.172610\pi
492492 0 0
493493 14784.0i 1.35058i
494494 0 0
495495 0 0
496496 0 0
497497 1880.00i 0.169677i
498498 0 0
499499 17768.0 1.59400 0.796999 0.603981i 0.206420π-0.206420\pi
0.796999 + 0.603981i 0.206420π0.206420\pi
500500 0 0
501501 0 0
502502 0 0
503503 7952.00i 0.704895i 0.935832 + 0.352447i 0.114650π0.114650\pi
−0.935832 + 0.352447i 0.885350π0.885350\pi
504504 0 0
505505 11280.0 + 5640.00i 0.993967 + 0.496984i
506506 0 0
507507 0 0
508508 0 0
509509 −12896.0 −1.12300 −0.561498 0.827478i 0.689775π-0.689775\pi
−0.561498 + 0.827478i 0.689775π0.689775\pi
510510 0 0
511511 7400.00 0.640620
512512 0 0
513513 0 0
514514 0 0
515515 3790.00 7580.00i 0.324286 0.648572i
516516 0 0
517517 22080.0i 1.87829i
518518 0 0
519519 0 0
520520 0 0
521521 2714.00 0.228220 0.114110 0.993468i 0.463598π-0.463598\pi
0.114110 + 0.993468i 0.463598π0.463598\pi
522522 0 0
523523 13792.0i 1.15312i −0.817055 0.576560i 0.804395π-0.804395\pi
0.817055 0.576560i 0.195605π-0.195605\pi
524524 0 0
525525 0 0
526526 0 0
527527 4752.00i 0.392790i
528528 0 0
529529 −14729.0 −1.21057
530530 0 0
531531 0 0
532532 0 0
533533 6596.00i 0.536031i
534534 0 0
535535 −6620.00 + 13240.0i −0.534967 + 1.06993i
536536 0 0
537537 0 0
538538 0 0
539539 −11178.0 −0.893266
540540 0 0
541541 6802.00 0.540556 0.270278 0.962782i 0.412884π-0.412884\pi
0.270278 + 0.962782i 0.412884π0.412884\pi
542542 0 0
543543 0 0
544544 0 0
545545 −16020.0 8010.00i −1.25912 0.629561i
546546 0 0
547547 18188.0i 1.42169i 0.703350 + 0.710843i 0.251687π0.251687\pi
−0.703350 + 0.710843i 0.748313π0.748313\pi
548548 0 0
549549 0 0
550550 0 0
551551 23296.0 1.80117
552552 0 0
553553 11680.0i 0.898163i
554554 0 0
555555 0 0
556556 0 0
557557 21462.0i 1.63263i −0.577608 0.816314i 0.696014π-0.696014\pi
0.577608 0.816314i 0.303986π-0.303986\pi
558558 0 0
559559 −3672.00 −0.277834
560560 0 0
561561 0 0
562562 0 0
563563 17244.0i 1.29085i 0.763824 + 0.645424i 0.223319π0.223319\pi
−0.763824 + 0.645424i 0.776681π0.776681\pi
564564 0 0
565565 10370.0 20740.0i 0.772158 1.54432i
566566 0 0
567567 0 0
568568 0 0
569569 8790.00 0.647620 0.323810 0.946122i 0.395036π-0.395036\pi
0.323810 + 0.946122i 0.395036π0.395036\pi
570570 0 0
571571 5984.00 0.438568 0.219284 0.975661i 0.429628π-0.429628\pi
0.219284 + 0.975661i 0.429628π0.429628\pi
572572 0 0
573573 0 0
574574 0 0
575575 16400.0 12300.0i 1.18944 0.892079i
576576 0 0
577577 9344.00i 0.674170i −0.941474 0.337085i 0.890559π-0.890559\pi
0.941474 0.337085i 0.109441π-0.109441\pi
578578 0 0
579579 0 0
580580 0 0
581581 −4120.00 −0.294193
582582 0 0
583583 13156.0i 0.934590i
584584 0 0
585585 0 0
586586 0 0
587587 6932.00i 0.487418i −0.969848 0.243709i 0.921636π-0.921636\pi
0.969848 0.243709i 0.0783642π-0.0783642\pi
588588 0 0
589589 7488.00 0.523833
590590 0 0
591591 0 0
592592 0 0
593593 9382.00i 0.649701i 0.945765 + 0.324850i 0.105314π0.105314\pi
−0.945765 + 0.324850i 0.894686π0.894686\pi
594594 0 0
595595 −6600.00 3300.00i −0.454746 0.227373i
596596 0 0
597597 0 0
598598 0 0
599599 −4096.00 −0.279396 −0.139698 0.990194i 0.544613π-0.544613\pi
−0.139698 + 0.990194i 0.544613π0.544613\pi
600600 0 0
601601 22962.0 1.55847 0.779234 0.626733i 0.215608π-0.215608\pi
0.779234 + 0.626733i 0.215608π0.215608\pi
602602 0 0
603603 0 0
604604 0 0
605605 7850.00 + 3925.00i 0.527517 + 0.263759i
606606 0 0
607607 3490.00i 0.233369i 0.993169 + 0.116684i 0.0372266π0.0372266\pi
−0.993169 + 0.116684i 0.962773π0.962773\pi
608608 0 0
609609 0 0
610610 0 0
611611 16320.0 1.08058
612612 0 0
613613 6386.00i 0.420764i −0.977619 0.210382i 0.932529π-0.932529\pi
0.977619 0.210382i 0.0674707π-0.0674707\pi
614614 0 0
615615 0 0
616616 0 0
617617 19534.0i 1.27457i 0.770629 + 0.637285i 0.219942π0.219942\pi
−0.770629 + 0.637285i 0.780058π0.780058\pi
618618 0 0
619619 8764.00 0.569071 0.284535 0.958666i 0.408161π-0.408161\pi
0.284535 + 0.958666i 0.408161π0.408161\pi
620620 0 0
621621 0 0
622622 0 0
623623 12060.0i 0.775560i
624624 0 0
625625 −4375.00 + 15000.0i −0.280000 + 0.960000i
626626 0 0
627627 0 0
628628 0 0
629629 −1452.00 −0.0920430
630630 0 0
631631 −7856.00 −0.495630 −0.247815 0.968807i 0.579712π-0.579712\pi
−0.247815 + 0.968807i 0.579712π0.579712\pi
632632 0 0
633633 0 0
634634 0 0
635635 −2670.00 + 5340.00i −0.166859 + 0.333719i
636636 0 0
637637 8262.00i 0.513897i
638638 0 0
639639 0 0
640640 0 0
641641 22974.0 1.41563 0.707815 0.706398i 0.249681π-0.249681\pi
0.707815 + 0.706398i 0.249681π0.249681\pi
642642 0 0
643643 6216.00i 0.381237i −0.981664 0.190618i 0.938951π-0.938951\pi
0.981664 0.190618i 0.0610493π-0.0610493\pi
644644 0 0
645645 0 0
646646 0 0
647647 13384.0i 0.813260i 0.913593 + 0.406630i 0.133296π0.133296\pi
−0.913593 + 0.406630i 0.866704π0.866704\pi
648648 0 0
649649 19596.0 1.18522
650650 0 0
651651 0 0
652652 0 0
653653 12882.0i 0.771993i 0.922500 + 0.385997i 0.126142π0.126142\pi
−0.922500 + 0.385997i 0.873858π0.873858\pi
654654 0 0
655655 18060.0 + 9030.00i 1.07735 + 0.538674i
656656 0 0
657657 0 0
658658 0 0
659659 2082.00 0.123070 0.0615351 0.998105i 0.480400π-0.480400\pi
0.0615351 + 0.998105i 0.480400π0.480400\pi
660660 0 0
661661 −9430.00 −0.554893 −0.277447 0.960741i 0.589488π-0.589488\pi
−0.277447 + 0.960741i 0.589488π0.589488\pi
662662 0 0
663663 0 0
664664 0 0
665665 5200.00 10400.0i 0.303229 0.606458i
666666 0 0
667667 36736.0i 2.13257i
668668 0 0
669669 0 0
670670 0 0
671671 −32108.0 −1.84727
672672 0 0
673673 3268.00i 0.187180i −0.995611 0.0935900i 0.970166π-0.970166\pi
0.995611 0.0935900i 0.0298343π-0.0298343\pi
674674 0 0
675675 0 0
676676 0 0
677677 15606.0i 0.885949i 0.896534 + 0.442974i 0.146077π0.146077\pi
−0.896534 + 0.442974i 0.853923π0.853923\pi
678678 0 0
679679 −13840.0 −0.782225
680680 0 0
681681 0 0
682682 0 0
683683 428.000i 0.0239780i −0.999928 0.0119890i 0.996184π-0.996184\pi
0.999928 0.0119890i 0.00381631π-0.00381631\pi
684684 0 0
685685 9110.00 18220.0i 0.508139 1.01628i
686686 0 0
687687 0 0
688688 0 0
689689 −9724.00 −0.537670
690690 0 0
691691 6384.00 0.351460 0.175730 0.984438i 0.443771π-0.443771\pi
0.175730 + 0.984438i 0.443771π0.443771\pi
692692 0 0
693693 0 0
694694 0 0
695695 5320.00 + 2660.00i 0.290358 + 0.145179i
696696 0 0
697697 12804.0i 0.695819i
698698 0 0
699699 0 0
700700 0 0
701701 12224.0 0.658622 0.329311 0.944221i 0.393184π-0.393184\pi
0.329311 + 0.944221i 0.393184π0.393184\pi
702702 0 0
703703 2288.00i 0.122750i
704704 0 0
705705 0 0
706706 0 0
707707 11280.0i 0.600040i
708708 0 0
709709 −19510.0 −1.03345 −0.516723 0.856153i 0.672848π-0.672848\pi
−0.516723 + 0.856153i 0.672848π0.672848\pi
710710 0 0
711711 0 0
712712 0 0
713713 11808.0i 0.620215i
714714 0 0
715715 7820.00 15640.0i 0.409023 0.818046i
716716 0 0
717717 0 0
718718 0 0
719719 3368.00 0.174694 0.0873472 0.996178i 0.472161π-0.472161\pi
0.0873472 + 0.996178i 0.472161π0.472161\pi
720720 0 0
721721 −7580.00 −0.391531
722722 0 0
723723 0 0
724724 0 0
725725 16800.0 + 22400.0i 0.860602 + 1.14747i
726726 0 0
727727 22134.0i 1.12917i −0.825376 0.564584i 0.809037π-0.809037\pi
0.825376 0.564584i 0.190963π-0.190963\pi
728728 0 0
729729 0 0
730730 0 0
731731 7128.00 0.360655
732732 0 0
733733 32298.0i 1.62750i −0.581219 0.813748i 0.697424π-0.697424\pi
0.581219 0.813748i 0.302576π-0.302576\pi
734734 0 0
735735 0 0
736736 0 0
737737 15088.0i 0.754103i
738738 0 0
739739 25104.0 1.24962 0.624808 0.780779i 0.285177π-0.285177\pi
0.624808 + 0.780779i 0.285177π0.285177\pi
740740 0 0
741741 0 0
742742 0 0
743743 27696.0i 1.36752i 0.729707 + 0.683760i 0.239657π0.239657\pi
−0.729707 + 0.683760i 0.760343π0.760343\pi
744744 0 0
745745 −12840.0 6420.00i −0.631438 0.315719i
746746 0 0
747747 0 0
748748 0 0
749749 13240.0 0.645900
750750 0 0
751751 2176.00 0.105730 0.0528651 0.998602i 0.483165π-0.483165\pi
0.0528651 + 0.998602i 0.483165π0.483165\pi
752752 0 0
753753 0 0
754754 0 0
755755 −1840.00 920.000i −0.0886946 0.0443473i
756756 0 0
757757 25514.0i 1.22500i 0.790472 + 0.612498i 0.209835π0.209835\pi
−0.790472 + 0.612498i 0.790165π0.790165\pi
758758 0 0
759759 0 0
760760 0 0
761761 −18238.0 −0.868761 −0.434380 0.900730i 0.643033π-0.643033\pi
−0.434380 + 0.900730i 0.643033π0.643033\pi
762762 0 0
763763 16020.0i 0.760109i
764764 0 0
765765 0 0
766766 0 0
767767 14484.0i 0.681860i
768768 0 0
769769 14462.0 0.678170 0.339085 0.940756i 0.389882π-0.389882\pi
0.339085 + 0.940756i 0.389882π0.389882\pi
770770 0 0
771771 0 0
772772 0 0
773773 34034.0i 1.58359i 0.610785 + 0.791797i 0.290854π0.290854\pi
−0.610785 + 0.791797i 0.709146π0.709146\pi
774774 0 0
775775 5400.00 + 7200.00i 0.250289 + 0.333718i
776776 0 0
777777 0 0
778778 0 0
779779 −20176.0 −0.927959
780780 0 0
781781 −8648.00 −0.396222
782782 0 0
783783 0 0
784784 0 0
785785 18730.0 37460.0i 0.851595 1.70319i
786786 0 0
787787 22064.0i 0.999360i −0.866210 0.499680i 0.833451π-0.833451\pi
0.866210 0.499680i 0.166549π-0.166549\pi
788788 0 0
789789 0 0
790790 0 0
791791 −20740.0 −0.932275
792792 0 0
793793 23732.0i 1.06273i
794794 0 0
795795 0 0
796796 0 0
797797 23334.0i 1.03705i 0.855061 + 0.518527i 0.173520π0.173520\pi
−0.855061 + 0.518527i 0.826480π0.826480\pi
798798 0 0
799799 −31680.0 −1.40270
800800 0 0
801801 0 0
802802 0 0
803803 34040.0i 1.49595i
804804 0 0
805805 −16400.0 8200.00i −0.718042 0.359021i
806806 0 0
807807 0 0
808808 0 0
809809 −7566.00 −0.328809 −0.164404 0.986393i 0.552570π-0.552570\pi
−0.164404 + 0.986393i 0.552570π0.552570\pi
810810 0 0
811811 −5964.00 −0.258230 −0.129115 0.991630i 0.541214π-0.541214\pi
−0.129115 + 0.991630i 0.541214π0.541214\pi
812812 0 0
813813 0 0
814814 0 0
815815 −7520.00 + 15040.0i −0.323207 + 0.646415i
816816 0 0
817817 11232.0i 0.480977i
818818 0 0
819819 0 0
820820 0 0
821821 11880.0 0.505012 0.252506 0.967595i 0.418745π-0.418745\pi
0.252506 + 0.967595i 0.418745π0.418745\pi
822822 0 0
823823 1762.00i 0.0746287i −0.999304 0.0373144i 0.988120π-0.988120\pi
0.999304 0.0373144i 0.0118803π-0.0118803\pi
824824 0 0
825825 0 0
826826 0 0
827827 14124.0i 0.593881i −0.954896 0.296941i 0.904034π-0.904034\pi
0.954896 0.296941i 0.0959663π-0.0959663\pi
828828 0 0
829829 21350.0 0.894471 0.447235 0.894416i 0.352409π-0.352409\pi
0.447235 + 0.894416i 0.352409π0.352409\pi
830830 0 0
831831 0 0
832832 0 0
833833 16038.0i 0.667087i
834834 0 0
835835 −15060.0 + 30120.0i −0.624159 + 1.24832i
836836 0 0
837837 0 0
838838 0 0
839839 26136.0 1.07546 0.537732 0.843116i 0.319281π-0.319281\pi
0.537732 + 0.843116i 0.319281π0.319281\pi
840840 0 0
841841 25787.0 1.05732
842842 0 0
843843 0 0
844844 0 0
845845 10410.0 + 5205.00i 0.423805 + 0.211902i
846846 0 0
847847 7850.00i 0.318452i
848848 0 0
849849 0 0
850850 0 0
851851 −3608.00 −0.145336
852852 0 0
853853 7030.00i 0.282184i 0.989997 + 0.141092i 0.0450613π0.0450613\pi
−0.989997 + 0.141092i 0.954939π0.954939\pi
854854 0 0
855855 0 0
856856 0 0
857857 9574.00i 0.381612i 0.981628 + 0.190806i 0.0611102π0.0611102\pi
−0.981628 + 0.190806i 0.938890π0.938890\pi
858858 0 0
859859 −43748.0 −1.73767 −0.868837 0.495098i 0.835132π-0.835132\pi
−0.868837 + 0.495098i 0.835132π0.835132\pi
860860 0 0
861861 0 0
862862 0 0
863863 41436.0i 1.63441i −0.576345 0.817206i 0.695522π-0.695522\pi
0.576345 0.817206i 0.304478π-0.304478\pi
864864 0 0
865865 2190.00 4380.00i 0.0860835 0.172167i
866866 0 0
867867 0 0
868868 0 0
869869 −53728.0 −2.09735
870870 0 0
871871 11152.0 0.433836
872872 0 0
873873 0 0
874874 0 0
875875 13750.0 2500.00i 0.531240 0.0965891i
876876 0 0
877877 4606.00i 0.177347i 0.996061 + 0.0886736i 0.0282628π0.0282628\pi
−0.996061 + 0.0886736i 0.971737π0.971737\pi
878878 0 0
879879 0 0
880880 0 0
881881 4610.00 0.176294 0.0881469 0.996107i 0.471906π-0.471906\pi
0.0881469 + 0.996107i 0.471906π0.471906\pi
882882 0 0
883883 23512.0i 0.896084i 0.894013 + 0.448042i 0.147878π0.147878\pi
−0.894013 + 0.448042i 0.852122π0.852122\pi
884884 0 0
885885 0 0
886886 0 0
887887 30396.0i 1.15062i −0.817936 0.575309i 0.804882π-0.804882\pi
0.817936 0.575309i 0.195118π-0.195118\pi
888888 0 0
889889 5340.00 0.201460
890890 0 0
891891 0 0
892892 0 0
893893 49920.0i 1.87067i
894894 0 0
895895 14620.0 + 7310.00i 0.546025 + 0.273013i
896896 0 0
897897 0 0
898898 0 0
899899 16128.0 0.598330
900900 0 0
901901 18876.0 0.697948
902902 0 0
903903 0 0
904904 0 0
905905 5860.00 + 2930.00i 0.215241 + 0.107620i
906906 0 0
907907 3452.00i 0.126375i −0.998002 0.0631873i 0.979873π-0.979873\pi
0.998002 0.0631873i 0.0201266π-0.0201266\pi
908908 0 0
909909 0 0
910910 0 0
911911 14256.0 0.518466 0.259233 0.965815i 0.416530π-0.416530\pi
0.259233 + 0.965815i 0.416530π0.416530\pi
912912 0 0
913913 18952.0i 0.686988i
914914 0 0
915915 0 0
916916 0 0
917917 18060.0i 0.650375i
918918 0 0
919919 8064.00 0.289452 0.144726 0.989472i 0.453770π-0.453770\pi
0.144726 + 0.989472i 0.453770π0.453770\pi
920920 0 0
921921 0 0
922922 0 0
923923 6392.00i 0.227947i
924924 0 0
925925 2200.00 1650.00i 0.0782006 0.0586504i
926926 0 0
927927 0 0
928928 0 0
929929 −40930.0 −1.44550 −0.722750 0.691109i 0.757122π-0.757122\pi
−0.722750 + 0.691109i 0.757122π0.757122\pi
930930 0 0
931931 25272.0 0.889642
932932 0 0
933933 0 0
934934 0 0
935935 −15180.0 + 30360.0i −0.530951 + 1.06190i
936936 0 0
937937 9016.00i 0.314344i 0.987571 + 0.157172i 0.0502376π0.0502376\pi
−0.987571 + 0.157172i 0.949762π0.949762\pi
938938 0 0
939939 0 0
940940 0 0
941941 10444.0 0.361812 0.180906 0.983500i 0.442097π-0.442097\pi
0.180906 + 0.983500i 0.442097π0.442097\pi
942942 0 0
943943 31816.0i 1.09870i
944944 0 0
945945 0 0
946946 0 0
947947 21516.0i 0.738306i 0.929369 + 0.369153i 0.120352π0.120352\pi
−0.929369 + 0.369153i 0.879648π0.879648\pi
948948 0 0
949949 −25160.0 −0.860620
950950 0 0
951951 0 0
952952 0 0
953953 28098.0i 0.955072i −0.878612 0.477536i 0.841530π-0.841530\pi
0.878612 0.477536i 0.158470π-0.158470\pi
954954 0 0
955955 600.000 + 300.000i 0.0203304 + 0.0101652i
956956 0 0
957957 0 0
958958 0 0
959959 −18220.0 −0.613508
960960 0 0
961961 −24607.0 −0.825988
962962 0 0
963963 0 0
964964 0 0
965965 −23380.0 + 46760.0i −0.779926 + 1.55985i
966966 0 0
967967 14558.0i 0.484130i 0.970260 + 0.242065i 0.0778247π0.0778247\pi
−0.970260 + 0.242065i 0.922175π0.922175\pi
968968 0 0
969969 0 0
970970 0 0
971971 24846.0 0.821160 0.410580 0.911825i 0.365326π-0.365326\pi
0.410580 + 0.911825i 0.365326π0.365326\pi
972972 0 0
973973 5320.00i 0.175284i
974974 0 0
975975 0 0
976976 0 0
977977 12950.0i 0.424061i 0.977263 + 0.212030i 0.0680076π0.0680076\pi
−0.977263 + 0.212030i 0.931992π0.931992\pi
978978 0 0
979979 −55476.0 −1.81105
980980 0 0
981981 0 0
982982 0 0
983983 26728.0i 0.867234i 0.901097 + 0.433617i 0.142763π0.142763\pi
−0.901097 + 0.433617i 0.857237π0.857237\pi
984984 0 0
985985 11430.0 22860.0i 0.369736 0.739472i
986986 0 0
987987 0 0
988988 0 0
989989 17712.0 0.569473
990990 0 0
991991 −3880.00 −0.124372 −0.0621858 0.998065i 0.519807π-0.519807\pi
−0.0621858 + 0.998065i 0.519807π0.519807\pi
992992 0 0
993993 0 0
994994 0 0
995995 −35360.0 17680.0i −1.12662 0.563310i
996996 0 0
997997 18582.0i 0.590269i 0.955456 + 0.295134i 0.0953644π0.0953644\pi
−0.955456 + 0.295134i 0.904636π0.904636\pi
998998 0 0
999999 0 0
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 720.4.f.g.289.2 2
3.2 odd 2 240.4.f.b.49.2 2
4.3 odd 2 360.4.f.c.289.2 2
5.4 even 2 inner 720.4.f.g.289.1 2
12.11 even 2 120.4.f.a.49.1 2
15.2 even 4 1200.4.a.bh.1.1 1
15.8 even 4 1200.4.a.f.1.1 1
15.14 odd 2 240.4.f.b.49.1 2
20.3 even 4 1800.4.a.y.1.1 1
20.7 even 4 1800.4.a.j.1.1 1
20.19 odd 2 360.4.f.c.289.1 2
24.5 odd 2 960.4.f.g.769.1 2
24.11 even 2 960.4.f.l.769.2 2
60.23 odd 4 600.4.a.o.1.1 1
60.47 odd 4 600.4.a.b.1.1 1
60.59 even 2 120.4.f.a.49.2 yes 2
120.29 odd 2 960.4.f.g.769.2 2
120.59 even 2 960.4.f.l.769.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
120.4.f.a.49.1 2 12.11 even 2
120.4.f.a.49.2 yes 2 60.59 even 2
240.4.f.b.49.1 2 15.14 odd 2
240.4.f.b.49.2 2 3.2 odd 2
360.4.f.c.289.1 2 20.19 odd 2
360.4.f.c.289.2 2 4.3 odd 2
600.4.a.b.1.1 1 60.47 odd 4
600.4.a.o.1.1 1 60.23 odd 4
720.4.f.g.289.1 2 5.4 even 2 inner
720.4.f.g.289.2 2 1.1 even 1 trivial
960.4.f.g.769.1 2 24.5 odd 2
960.4.f.g.769.2 2 120.29 odd 2
960.4.f.l.769.1 2 120.59 even 2
960.4.f.l.769.2 2 24.11 even 2
1200.4.a.f.1.1 1 15.8 even 4
1200.4.a.bh.1.1 1 15.2 even 4
1800.4.a.j.1.1 1 20.7 even 4
1800.4.a.y.1.1 1 20.3 even 4