Properties

Label 720.3.j.e.559.4
Level 720720
Weight 33
Character 720.559
Analytic conductor 19.61919.619
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [720,3,Mod(559,720)]
 
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([1, 0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("720.559");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 720=24325 720 = 2^{4} \cdot 3^{2} \cdot 5
Weight: k k == 3 3
Character orbit: [χ][\chi] == 720.j (of order 22, degree 11, 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: 19.618579033919.6185790339
Analytic rank: 00
Dimension: 44
Coefficient field: Q(2,3)\Q(\sqrt{2}, \sqrt{-3})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+2x2+4 x^{4} + 2x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 273 2^{7}\cdot 3
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 559.4
Root 0.707107+1.22474i-0.707107 + 1.22474i of defining polynomial
Character χ\chi == 720.559
Dual form 720.3.j.e.559.2

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+(1.00000+4.89898i)q5+8.48528q713.8564iq119.79796iq1319.5959iq1713.8564iq19+25.4558q23+(23.0000+9.79796i)q25+22.0000q29+55.4256iq31+(8.48528+41.5692i)q3548.9898iq3722.0000q41+59.3970q438.48528q47+23.0000q49+29.3939iq53+(67.882313.8564i)q5513.8564iq59+46.0000q61+(48.00009.79796i)q65+59.3970q67+27.7128iq7178.3837iq73117.576iq77+76.3675q83+(96.000019.5959i)q85146.000q8983.1384iq91+(67.882313.8564i)q95+58.7878iq97+O(q100)q+(1.00000 + 4.89898i) q^{5} +8.48528 q^{7} -13.8564i q^{11} -9.79796i q^{13} -19.5959i q^{17} -13.8564i q^{19} +25.4558 q^{23} +(-23.0000 + 9.79796i) q^{25} +22.0000 q^{29} +55.4256i q^{31} +(8.48528 + 41.5692i) q^{35} -48.9898i q^{37} -22.0000 q^{41} +59.3970 q^{43} -8.48528 q^{47} +23.0000 q^{49} +29.3939i q^{53} +(67.8823 - 13.8564i) q^{55} -13.8564i q^{59} +46.0000 q^{61} +(48.0000 - 9.79796i) q^{65} +59.3970 q^{67} +27.7128i q^{71} -78.3837i q^{73} -117.576i q^{77} +76.3675 q^{83} +(96.0000 - 19.5959i) q^{85} -146.000 q^{89} -83.1384i q^{91} +(67.8823 - 13.8564i) q^{95} +58.7878i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+4q592q25+88q2988q41+92q49+184q61+192q65+384q85584q89+O(q100) 4 q + 4 q^{5} - 92 q^{25} + 88 q^{29} - 88 q^{41} + 92 q^{49} + 184 q^{61} + 192 q^{65} + 384 q^{85} - 584 q^{89}+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 1-1 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 1.00000 + 4.89898i 0.200000 + 0.979796i
66 0 0
77 8.48528 1.21218 0.606092 0.795395i 0.292737π-0.292737\pi
0.606092 + 0.795395i 0.292737π0.292737\pi
88 0 0
99 0 0
1010 0 0
1111 13.8564i 1.25967i −0.776728 0.629837i 0.783122π-0.783122\pi
0.776728 0.629837i 0.216878π-0.216878\pi
1212 0 0
1313 9.79796i 0.753689i −0.926277 0.376845i 0.877009π-0.877009\pi
0.926277 0.376845i 0.122991π-0.122991\pi
1414 0 0
1515 0 0
1616 0 0
1717 19.5959i 1.15270i −0.817203 0.576351i 0.804476π-0.804476\pi
0.817203 0.576351i 0.195524π-0.195524\pi
1818 0 0
1919 13.8564i 0.729285i −0.931148 0.364642i 0.881191π-0.881191\pi
0.931148 0.364642i 0.118809π-0.118809\pi
2020 0 0
2121 0 0
2222 0 0
2323 25.4558 1.10678 0.553388 0.832924i 0.313335π-0.313335\pi
0.553388 + 0.832924i 0.313335π0.313335\pi
2424 0 0
2525 −23.0000 + 9.79796i −0.920000 + 0.391918i
2626 0 0
2727 0 0
2828 0 0
2929 22.0000 0.758621 0.379310 0.925270i 0.376161π-0.376161\pi
0.379310 + 0.925270i 0.376161π0.376161\pi
3030 0 0
3131 55.4256i 1.78792i 0.448143 + 0.893962i 0.352085π0.352085\pi
−0.448143 + 0.893962i 0.647915π0.647915\pi
3232 0 0
3333 0 0
3434 0 0
3535 8.48528 + 41.5692i 0.242437 + 1.18769i
3636 0 0
3737 48.9898i 1.32405i −0.749482 0.662024i 0.769698π-0.769698\pi
0.749482 0.662024i 0.230302π-0.230302\pi
3838 0 0
3939 0 0
4040 0 0
4141 −22.0000 −0.536585 −0.268293 0.963337i 0.586459π-0.586459\pi
−0.268293 + 0.963337i 0.586459π0.586459\pi
4242 0 0
4343 59.3970 1.38132 0.690662 0.723177i 0.257319π-0.257319\pi
0.690662 + 0.723177i 0.257319π0.257319\pi
4444 0 0
4545 0 0
4646 0 0
4747 −8.48528 −0.180538 −0.0902690 0.995917i 0.528773π-0.528773\pi
−0.0902690 + 0.995917i 0.528773π0.528773\pi
4848 0 0
4949 23.0000 0.469388
5050 0 0
5151 0 0
5252 0 0
5353 29.3939i 0.554601i 0.960783 + 0.277301i 0.0894398π0.0894398\pi
−0.960783 + 0.277301i 0.910560π0.910560\pi
5454 0 0
5555 67.8823 13.8564i 1.23422 0.251935i
5656 0 0
5757 0 0
5858 0 0
5959 13.8564i 0.234854i −0.993081 0.117427i 0.962535π-0.962535\pi
0.993081 0.117427i 0.0374647π-0.0374647\pi
6060 0 0
6161 46.0000 0.754098 0.377049 0.926193i 0.376939π-0.376939\pi
0.377049 + 0.926193i 0.376939π0.376939\pi
6262 0 0
6363 0 0
6464 0 0
6565 48.0000 9.79796i 0.738462 0.150738i
6666 0 0
6767 59.3970 0.886522 0.443261 0.896393i 0.353822π-0.353822\pi
0.443261 + 0.896393i 0.353822π0.353822\pi
6868 0 0
6969 0 0
7070 0 0
7171 27.7128i 0.390321i 0.980771 + 0.195161i 0.0625228π0.0625228\pi
−0.980771 + 0.195161i 0.937477π0.937477\pi
7272 0 0
7373 78.3837i 1.07375i −0.843662 0.536874i 0.819605π-0.819605\pi
0.843662 0.536874i 0.180395π-0.180395\pi
7474 0 0
7575 0 0
7676 0 0
7777 117.576i 1.52695i
7878 0 0
7979 0 0 1.00000 00
−1.00000 π\pi
8080 0 0
8181 0 0
8282 0 0
8383 76.3675 0.920091 0.460045 0.887895i 0.347833π-0.347833\pi
0.460045 + 0.887895i 0.347833π0.347833\pi
8484 0 0
8585 96.0000 19.5959i 1.12941 0.230540i
8686 0 0
8787 0 0
8888 0 0
8989 −146.000 −1.64045 −0.820225 0.572041i 0.806152π-0.806152\pi
−0.820225 + 0.572041i 0.806152π0.806152\pi
9090 0 0
9191 83.1384i 0.913609i
9292 0 0
9393 0 0
9494 0 0
9595 67.8823 13.8564i 0.714550 0.145857i
9696 0 0
9797 58.7878i 0.606059i 0.952981 + 0.303030i 0.0979981π0.0979981\pi
−0.952981 + 0.303030i 0.902002π0.902002\pi
9898 0 0
9999 0 0
100100 0 0
101101 70.0000 0.693069 0.346535 0.938037i 0.387358π-0.387358\pi
0.346535 + 0.938037i 0.387358π0.387358\pi
102102 0 0
103103 −25.4558 −0.247144 −0.123572 0.992336i 0.539435π-0.539435\pi
−0.123572 + 0.992336i 0.539435π0.539435\pi
104104 0 0
105105 0 0
106106 0 0
107107 42.4264 0.396508 0.198254 0.980151i 0.436473π-0.436473\pi
0.198254 + 0.980151i 0.436473π0.436473\pi
108108 0 0
109109 −146.000 −1.33945 −0.669725 0.742609i 0.733588π-0.733588\pi
−0.669725 + 0.742609i 0.733588π0.733588\pi
110110 0 0
111111 0 0
112112 0 0
113113 39.1918i 0.346830i 0.984849 + 0.173415i 0.0554803π0.0554803\pi
−0.984849 + 0.173415i 0.944520π0.944520\pi
114114 0 0
115115 25.4558 + 124.708i 0.221355 + 1.08441i
116116 0 0
117117 0 0
118118 0 0
119119 166.277i 1.39728i
120120 0 0
121121 −71.0000 −0.586777
122122 0 0
123123 0 0
124124 0 0
125125 −71.0000 102.879i −0.568000 0.823029i
126126 0 0
127127 110.309 0.868572 0.434286 0.900775i 0.357001π-0.357001\pi
0.434286 + 0.900775i 0.357001π0.357001\pi
128128 0 0
129129 0 0
130130 0 0
131131 180.133i 1.37506i 0.726154 + 0.687532i 0.241306π0.241306\pi
−0.726154 + 0.687532i 0.758694π0.758694\pi
132132 0 0
133133 117.576i 0.884026i
134134 0 0
135135 0 0
136136 0 0
137137 215.555i 1.57339i 0.617339 + 0.786697i 0.288211π0.288211\pi
−0.617339 + 0.786697i 0.711789π0.711789\pi
138138 0 0
139139 13.8564i 0.0996864i 0.998757 + 0.0498432i 0.0158722π0.0158722\pi
−0.998757 + 0.0498432i 0.984128π0.984128\pi
140140 0 0
141141 0 0
142142 0 0
143143 −135.765 −0.949402
144144 0 0
145145 22.0000 + 107.778i 0.151724 + 0.743293i
146146 0 0
147147 0 0
148148 0 0
149149 2.00000 0.0134228 0.00671141 0.999977i 0.497864π-0.497864\pi
0.00671141 + 0.999977i 0.497864π0.497864\pi
150150 0 0
151151 27.7128i 0.183529i −0.995781 0.0917643i 0.970749π-0.970749\pi
0.995781 0.0917643i 0.0292506π-0.0292506\pi
152152 0 0
153153 0 0
154154 0 0
155155 −271.529 + 55.4256i −1.75180 + 0.357585i
156156 0 0
157157 68.5857i 0.436852i −0.975854 0.218426i 0.929908π-0.929908\pi
0.975854 0.218426i 0.0700922π-0.0700922\pi
158158 0 0
159159 0 0
160160 0 0
161161 216.000 1.34161
162162 0 0
163163 −110.309 −0.676740 −0.338370 0.941013i 0.609876π-0.609876\pi
−0.338370 + 0.941013i 0.609876π0.609876\pi
164164 0 0
165165 0 0
166166 0 0
167167 93.3381 0.558911 0.279455 0.960159i 0.409846π-0.409846\pi
0.279455 + 0.960159i 0.409846π0.409846\pi
168168 0 0
169169 73.0000 0.431953
170170 0 0
171171 0 0
172172 0 0
173173 48.9898i 0.283178i −0.989926 0.141589i 0.954779π-0.954779\pi
0.989926 0.141589i 0.0452211π-0.0452211\pi
174174 0 0
175175 −195.161 + 83.1384i −1.11521 + 0.475077i
176176 0 0
177177 0 0
178178 0 0
179179 263.272i 1.47079i −0.677638 0.735396i 0.736996π-0.736996\pi
0.677638 0.735396i 0.263004π-0.263004\pi
180180 0 0
181181 26.0000 0.143646 0.0718232 0.997417i 0.477118π-0.477118\pi
0.0718232 + 0.997417i 0.477118π0.477118\pi
182182 0 0
183183 0 0
184184 0 0
185185 240.000 48.9898i 1.29730 0.264810i
186186 0 0
187187 −271.529 −1.45203
188188 0 0
189189 0 0
190190 0 0
191191 110.851i 0.580373i 0.956970 + 0.290187i 0.0937174π0.0937174\pi
−0.956970 + 0.290187i 0.906283π0.906283\pi
192192 0 0
193193 333.131i 1.72607i 0.505148 + 0.863033i 0.331438π0.331438\pi
−0.505148 + 0.863033i 0.668562π0.668562\pi
194194 0 0
195195 0 0
196196 0 0
197197 107.778i 0.547094i 0.961859 + 0.273547i 0.0881969π0.0881969\pi
−0.961859 + 0.273547i 0.911803π0.911803\pi
198198 0 0
199199 249.415i 1.25334i −0.779283 0.626672i 0.784417π-0.784417\pi
0.779283 0.626672i 0.215583π-0.215583\pi
200200 0 0
201201 0 0
202202 0 0
203203 186.676 0.919587
204204 0 0
205205 −22.0000 107.778i −0.107317 0.525744i
206206 0 0
207207 0 0
208208 0 0
209209 −192.000 −0.918660
210210 0 0
211211 96.9948i 0.459691i 0.973227 + 0.229846i 0.0738221π0.0738221\pi
−0.973227 + 0.229846i 0.926178π0.926178\pi
212212 0 0
213213 0 0
214214 0 0
215215 59.3970 + 290.985i 0.276265 + 1.35342i
216216 0 0
217217 470.302i 2.16729i
218218 0 0
219219 0 0
220220 0 0
221221 −192.000 −0.868778
222222 0 0
223223 −229.103 −1.02737 −0.513683 0.857980i 0.671719π-0.671719\pi
−0.513683 + 0.857980i 0.671719π0.671719\pi
224224 0 0
225225 0 0
226226 0 0
227227 −296.985 −1.30830 −0.654152 0.756363i 0.726974π-0.726974\pi
−0.654152 + 0.756363i 0.726974π0.726974\pi
228228 0 0
229229 −70.0000 −0.305677 −0.152838 0.988251i 0.548841π-0.548841\pi
−0.152838 + 0.988251i 0.548841π0.548841\pi
230230 0 0
231231 0 0
232232 0 0
233233 156.767i 0.672821i 0.941715 + 0.336411i 0.109213π0.109213\pi
−0.941715 + 0.336411i 0.890787π0.890787\pi
234234 0 0
235235 −8.48528 41.5692i −0.0361076 0.176890i
236236 0 0
237237 0 0
238238 0 0
239239 332.554i 1.39144i −0.718314 0.695719i 0.755086π-0.755086\pi
0.718314 0.695719i 0.244914π-0.244914\pi
240240 0 0
241241 −122.000 −0.506224 −0.253112 0.967437i 0.581454π-0.581454\pi
−0.253112 + 0.967437i 0.581454π0.581454\pi
242242 0 0
243243 0 0
244244 0 0
245245 23.0000 + 112.677i 0.0938776 + 0.459904i
246246 0 0
247247 −135.765 −0.549654
248248 0 0
249249 0 0
250250 0 0
251251 290.985i 1.15930i −0.814865 0.579650i 0.803189π-0.803189\pi
0.814865 0.579650i 0.196811π-0.196811\pi
252252 0 0
253253 352.727i 1.39418i
254254 0 0
255255 0 0
256256 0 0
257257 78.3837i 0.304995i −0.988304 0.152497i 0.951268π-0.951268\pi
0.988304 0.152497i 0.0487316π-0.0487316\pi
258258 0 0
259259 415.692i 1.60499i
260260 0 0
261261 0 0
262262 0 0
263263 −347.897 −1.32280 −0.661400 0.750033i 0.730038π-0.730038\pi
−0.661400 + 0.750033i 0.730038π0.730038\pi
264264 0 0
265265 −144.000 + 29.3939i −0.543396 + 0.110920i
266266 0 0
267267 0 0
268268 0 0
269269 −142.000 −0.527881 −0.263941 0.964539i 0.585022π-0.585022\pi
−0.263941 + 0.964539i 0.585022π0.585022\pi
270270 0 0
271271 332.554i 1.22714i 0.789642 + 0.613568i 0.210266π0.210266\pi
−0.789642 + 0.613568i 0.789734π0.789734\pi
272272 0 0
273273 0 0
274274 0 0
275275 135.765 + 318.697i 0.493689 + 1.15890i
276276 0 0
277277 88.1816i 0.318345i −0.987251 0.159173i 0.949117π-0.949117\pi
0.987251 0.159173i 0.0508826π-0.0508826\pi
278278 0 0
279279 0 0
280280 0 0
281281 −406.000 −1.44484 −0.722420 0.691455i 0.756970π-0.756970\pi
−0.722420 + 0.691455i 0.756970π0.756970\pi
282282 0 0
283283 93.3381 0.329817 0.164908 0.986309i 0.447267π-0.447267\pi
0.164908 + 0.986309i 0.447267π0.447267\pi
284284 0 0
285285 0 0
286286 0 0
287287 −186.676 −0.650440
288288 0 0
289289 −95.0000 −0.328720
290290 0 0
291291 0 0
292292 0 0
293293 303.737i 1.03664i −0.855186 0.518322i 0.826557π-0.826557\pi
0.855186 0.518322i 0.173443π-0.173443\pi
294294 0 0
295295 67.8823 13.8564i 0.230109 0.0469709i
296296 0 0
297297 0 0
298298 0 0
299299 249.415i 0.834165i
300300 0 0
301301 504.000 1.67442
302302 0 0
303303 0 0
304304 0 0
305305 46.0000 + 225.353i 0.150820 + 0.738862i
306306 0 0
307307 −280.014 −0.912099 −0.456049 0.889955i 0.650736π-0.650736\pi
−0.456049 + 0.889955i 0.650736π0.650736\pi
308308 0 0
309309 0 0
310310 0 0
311311 138.564i 0.445544i 0.974871 + 0.222772i 0.0715105π0.0715105\pi
−0.974871 + 0.222772i 0.928490π0.928490\pi
312312 0 0
313313 607.473i 1.94081i 0.241484 + 0.970405i 0.422366π0.422366\pi
−0.241484 + 0.970405i 0.577634π0.577634\pi
314314 0 0
315315 0 0
316316 0 0
317317 68.5857i 0.216359i −0.994131 0.108179i 0.965498π-0.965498\pi
0.994131 0.108179i 0.0345021π-0.0345021\pi
318318 0 0
319319 304.841i 0.955614i
320320 0 0
321321 0 0
322322 0 0
323323 −271.529 −0.840647
324324 0 0
325325 96.0000 + 225.353i 0.295385 + 0.693394i
326326 0 0
327327 0 0
328328 0 0
329329 −72.0000 −0.218845
330330 0 0
331331 180.133i 0.544209i 0.962268 + 0.272105i 0.0877197π0.0877197\pi
−0.962268 + 0.272105i 0.912280π0.912280\pi
332332 0 0
333333 0 0
334334 0 0
335335 59.3970 + 290.985i 0.177304 + 0.868611i
336336 0 0
337337 470.302i 1.39555i −0.716315 0.697777i 0.754172π-0.754172\pi
0.716315 0.697777i 0.245828π-0.245828\pi
338338 0 0
339339 0 0
340340 0 0
341341 768.000 2.25220
342342 0 0
343343 −220.617 −0.643199
344344 0 0
345345 0 0
346346 0 0
347347 619.426 1.78509 0.892544 0.450960i 0.148918π-0.148918\pi
0.892544 + 0.450960i 0.148918π0.148918\pi
348348 0 0
349349 −214.000 −0.613181 −0.306590 0.951842i 0.599188π-0.599188\pi
−0.306590 + 0.951842i 0.599188π0.599188\pi
350350 0 0
351351 0 0
352352 0 0
353353 352.727i 0.999225i 0.866249 + 0.499613i 0.166524π0.166524\pi
−0.866249 + 0.499613i 0.833476π0.833476\pi
354354 0 0
355355 −135.765 + 27.7128i −0.382435 + 0.0780643i
356356 0 0
357357 0 0
358358 0 0
359359 27.7128i 0.0771945i −0.999255 0.0385972i 0.987711π-0.987711\pi
0.999255 0.0385972i 0.0122889π-0.0122889\pi
360360 0 0
361361 169.000 0.468144
362362 0 0
363363 0 0
364364 0 0
365365 384.000 78.3837i 1.05205 0.214750i
366366 0 0
367367 246.073 0.670499 0.335250 0.942129i 0.391179π-0.391179\pi
0.335250 + 0.942129i 0.391179π0.391179\pi
368368 0 0
369369 0 0
370370 0 0
371371 249.415i 0.672278i
372372 0 0
373373 382.120i 1.02445i 0.858851 + 0.512226i 0.171179π0.171179\pi
−0.858851 + 0.512226i 0.828821π0.828821\pi
374374 0 0
375375 0 0
376376 0 0
377377 215.555i 0.571764i
378378 0 0
379379 290.985i 0.767769i 0.923381 + 0.383885i 0.125414π0.125414\pi
−0.923381 + 0.383885i 0.874586π0.874586\pi
380380 0 0
381381 0 0
382382 0 0
383383 568.514 1.48437 0.742185 0.670195i 0.233789π-0.233789\pi
0.742185 + 0.670195i 0.233789π0.233789\pi
384384 0 0
385385 576.000 117.576i 1.49610 0.305391i
386386 0 0
387387 0 0
388388 0 0
389389 −670.000 −1.72237 −0.861183 0.508296i 0.830276π-0.830276\pi
−0.861183 + 0.508296i 0.830276π0.830276\pi
390390 0 0
391391 498.831i 1.27578i
392392 0 0
393393 0 0
394394 0 0
395395 0 0
396396 0 0
397397 362.524i 0.913160i −0.889682 0.456580i 0.849074π-0.849074\pi
0.889682 0.456580i 0.150926π-0.150926\pi
398398 0 0
399399 0 0
400400 0 0
401401 −2.00000 −0.00498753 −0.00249377 0.999997i 0.500794π-0.500794\pi
−0.00249377 + 0.999997i 0.500794π0.500794\pi
402402 0 0
403403 543.058 1.34754
404404 0 0
405405 0 0
406406 0 0
407407 −678.823 −1.66787
408408 0 0
409409 −650.000 −1.58924 −0.794621 0.607106i 0.792330π-0.792330\pi
−0.794621 + 0.607106i 0.792330π0.792330\pi
410410 0 0
411411 0 0
412412 0 0
413413 117.576i 0.284686i
414414 0 0
415415 76.3675 + 374.123i 0.184018 + 0.901501i
416416 0 0
417417 0 0
418418 0 0
419419 540.400i 1.28974i −0.764293 0.644869i 0.776912π-0.776912\pi
0.764293 0.644869i 0.223088π-0.223088\pi
420420 0 0
421421 −482.000 −1.14489 −0.572447 0.819942i 0.694006π-0.694006\pi
−0.572447 + 0.819942i 0.694006π0.694006\pi
422422 0 0
423423 0 0
424424 0 0
425425 192.000 + 450.706i 0.451765 + 1.06048i
426426 0 0
427427 390.323 0.914105
428428 0 0
429429 0 0
430430 0 0
431431 221.703i 0.514391i 0.966359 + 0.257195i 0.0827984π0.0827984\pi
−0.966359 + 0.257195i 0.917202π0.917202\pi
432432 0 0
433433 568.282i 1.31243i −0.754575 0.656214i 0.772157π-0.772157\pi
0.754575 0.656214i 0.227843π-0.227843\pi
434434 0 0
435435 0 0
436436 0 0
437437 352.727i 0.807155i
438438 0 0
439439 526.543i 1.19942i 0.800219 + 0.599708i 0.204717π0.204717\pi
−0.800219 + 0.599708i 0.795283π0.795283\pi
440440 0 0
441441 0 0
442442 0 0
443443 −432.749 −0.976861 −0.488430 0.872603i 0.662430π-0.662430\pi
−0.488430 + 0.872603i 0.662430π0.662430\pi
444444 0 0
445445 −146.000 715.251i −0.328090 1.60731i
446446 0 0
447447 0 0
448448 0 0
449449 26.0000 0.0579065 0.0289532 0.999581i 0.490783π-0.490783\pi
0.0289532 + 0.999581i 0.490783π0.490783\pi
450450 0 0
451451 304.841i 0.675922i
452452 0 0
453453 0 0
454454 0 0
455455 407.294 83.1384i 0.895151 0.182722i
456456 0 0
457457 137.171i 0.300156i 0.988674 + 0.150078i 0.0479525π0.0479525\pi
−0.988674 + 0.150078i 0.952047π0.952047\pi
458458 0 0
459459 0 0
460460 0 0
461461 502.000 1.08894 0.544469 0.838781i 0.316731π-0.316731\pi
0.544469 + 0.838781i 0.316731π0.316731\pi
462462 0 0
463463 823.072 1.77769 0.888847 0.458204i 0.151507π-0.151507\pi
0.888847 + 0.458204i 0.151507π0.151507\pi
464464 0 0
465465 0 0
466466 0 0
467467 178.191 0.381565 0.190783 0.981632i 0.438897π-0.438897\pi
0.190783 + 0.981632i 0.438897π0.438897\pi
468468 0 0
469469 504.000 1.07463
470470 0 0
471471 0 0
472472 0 0
473473 823.029i 1.74002i
474474 0 0
475475 135.765 + 318.697i 0.285820 + 0.670942i
476476 0 0
477477 0 0
478478 0 0
479479 775.959i 1.61996i −0.586460 0.809978i 0.699479π-0.699479\pi
0.586460 0.809978i 0.300521π-0.300521\pi
480480 0 0
481481 −480.000 −0.997921
482482 0 0
483483 0 0
484484 0 0
485485 −288.000 + 58.7878i −0.593814 + 0.121212i
486486 0 0
487487 347.897 0.714367 0.357183 0.934034i 0.383737π-0.383737\pi
0.357183 + 0.934034i 0.383737π0.383737\pi
488488 0 0
489489 0 0
490490 0 0
491491 928.379i 1.89079i 0.325923 + 0.945396i 0.394325π0.394325\pi
−0.325923 + 0.945396i 0.605675π0.605675\pi
492492 0 0
493493 431.110i 0.874463i
494494 0 0
495495 0 0
496496 0 0
497497 235.151i 0.473141i
498498 0 0
499499 512.687i 1.02743i −0.857961 0.513714i 0.828269π-0.828269\pi
0.857961 0.513714i 0.171731π-0.171731\pi
500500 0 0
501501 0 0
502502 0 0
503503 704.278 1.40016 0.700078 0.714066i 0.253149π-0.253149\pi
0.700078 + 0.714066i 0.253149π0.253149\pi
504504 0 0
505505 70.0000 + 342.929i 0.138614 + 0.679066i
506506 0 0
507507 0 0
508508 0 0
509509 −170.000 −0.333988 −0.166994 0.985958i 0.553406π-0.553406\pi
−0.166994 + 0.985958i 0.553406π0.553406\pi
510510 0 0
511511 665.108i 1.30158i
512512 0 0
513513 0 0
514514 0 0
515515 −25.4558 124.708i −0.0494288 0.242151i
516516 0 0
517517 117.576i 0.227419i
518518 0 0
519519 0 0
520520 0 0
521521 −722.000 −1.38580 −0.692898 0.721035i 0.743667π-0.743667\pi
−0.692898 + 0.721035i 0.743667π0.743667\pi
522522 0 0
523523 −246.073 −0.470503 −0.235252 0.971935i 0.575591π-0.575591\pi
−0.235252 + 0.971935i 0.575591π0.575591\pi
524524 0 0
525525 0 0
526526 0 0
527527 1086.12 2.06094
528528 0 0
529529 119.000 0.224953
530530 0 0
531531 0 0
532532 0 0
533533 215.555i 0.404419i
534534 0 0
535535 42.4264 + 207.846i 0.0793017 + 0.388497i
536536 0 0
537537 0 0
538538 0 0
539539 318.697i 0.591275i
540540 0 0
541541 362.000 0.669131 0.334566 0.942372i 0.391410π-0.391410\pi
0.334566 + 0.942372i 0.391410π0.391410\pi
542542 0 0
543543 0 0
544544 0 0
545545 −146.000 715.251i −0.267890 1.31239i
546546 0 0
547547 −42.4264 −0.0775620 −0.0387810 0.999248i 0.512347π-0.512347\pi
−0.0387810 + 0.999248i 0.512347π0.512347\pi
548548 0 0
549549 0 0
550550 0 0
551551 304.841i 0.553250i
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 0 0
557557 656.463i 1.17857i 0.807925 + 0.589285i 0.200590π0.200590\pi
−0.807925 + 0.589285i 0.799410π0.799410\pi
558558 0 0
559559 581.969i 1.04109i
560560 0 0
561561 0 0
562562 0 0
563563 517.602 0.919364 0.459682 0.888083i 0.347963π-0.347963\pi
0.459682 + 0.888083i 0.347963π0.347963\pi
564564 0 0
565565 −192.000 + 39.1918i −0.339823 + 0.0693661i
566566 0 0
567567 0 0
568568 0 0
569569 842.000 1.47979 0.739895 0.672723i 0.234875π-0.234875\pi
0.739895 + 0.672723i 0.234875π0.234875\pi
570570 0 0
571571 401.836i 0.703740i 0.936049 + 0.351870i 0.114454π0.114454\pi
−0.936049 + 0.351870i 0.885546π0.885546\pi
572572 0 0
573573 0 0
574574 0 0
575575 −585.484 + 249.415i −1.01823 + 0.433766i
576576 0 0
577577 39.1918i 0.0679235i −0.999423 0.0339617i 0.989188π-0.989188\pi
0.999423 0.0339617i 0.0108124π-0.0108124\pi
578578 0 0
579579 0 0
580580 0 0
581581 648.000 1.11532
582582 0 0
583583 407.294 0.698617
584584 0 0
585585 0 0
586586 0 0
587587 −59.3970 −0.101187 −0.0505937 0.998719i 0.516111π-0.516111\pi
−0.0505937 + 0.998719i 0.516111π0.516111\pi
588588 0 0
589589 768.000 1.30390
590590 0 0
591591 0 0
592592 0 0
593593 509.494i 0.859180i −0.903024 0.429590i 0.858658π-0.858658\pi
0.903024 0.429590i 0.141342π-0.141342\pi
594594 0 0
595595 814.587 166.277i 1.36905 0.279457i
596596 0 0
597597 0 0
598598 0 0
599599 859.097i 1.43422i 0.696961 + 0.717110i 0.254535π0.254535\pi
−0.696961 + 0.717110i 0.745465π0.745465\pi
600600 0 0
601601 598.000 0.995008 0.497504 0.867462i 0.334250π-0.334250\pi
0.497504 + 0.867462i 0.334250π0.334250\pi
602602 0 0
603603 0 0
604604 0 0
605605 −71.0000 347.828i −0.117355 0.574922i
606606 0 0
607607 −127.279 −0.209686 −0.104843 0.994489i 0.533434π-0.533434\pi
−0.104843 + 0.994489i 0.533434π0.533434\pi
608608 0 0
609609 0 0
610610 0 0
611611 83.1384i 0.136069i
612612 0 0
613613 205.757i 0.335656i 0.985816 + 0.167828i 0.0536753π0.0536753\pi
−0.985816 + 0.167828i 0.946325π0.946325\pi
614614 0 0
615615 0 0
616616 0 0
617617 431.110i 0.698720i 0.936989 + 0.349360i 0.113601π0.113601\pi
−0.936989 + 0.349360i 0.886399π0.886399\pi
618618 0 0
619619 41.5692i 0.0671554i −0.999436 0.0335777i 0.989310π-0.989310\pi
0.999436 0.0335777i 0.0106901π-0.0106901\pi
620620 0 0
621621 0 0
622622 0 0
623623 −1238.85 −1.98853
624624 0 0
625625 433.000 450.706i 0.692800 0.721130i
626626 0 0
627627 0 0
628628 0 0
629629 −960.000 −1.52623
630630 0 0
631631 969.948i 1.53716i 0.639753 + 0.768580i 0.279037π0.279037\pi
−0.639753 + 0.768580i 0.720963π0.720963\pi
632632 0 0
633633 0 0
634634 0 0
635635 110.309 + 540.400i 0.173714 + 0.851023i
636636 0 0
637637 225.353i 0.353772i
638638 0 0
639639 0 0
640640 0 0
641641 −166.000 −0.258970 −0.129485 0.991581i 0.541332π-0.541332\pi
−0.129485 + 0.991581i 0.541332π0.541332\pi
642642 0 0
643643 −144.250 −0.224339 −0.112169 0.993689i 0.535780π-0.535780\pi
−0.112169 + 0.993689i 0.535780π0.535780\pi
644644 0 0
645645 0 0
646646 0 0
647647 −687.308 −1.06230 −0.531150 0.847278i 0.678240π-0.678240\pi
−0.531150 + 0.847278i 0.678240π0.678240\pi
648648 0 0
649649 −192.000 −0.295840
650650 0 0
651651 0 0
652652 0 0
653653 29.3939i 0.0450136i −0.999747 0.0225068i 0.992835π-0.992835\pi
0.999747 0.0225068i 0.00716474π-0.00716474\pi
654654 0 0
655655 −882.469 + 180.133i −1.34728 + 0.275013i
656656 0 0
657657 0 0
658658 0 0
659659 623.538i 0.946189i 0.881012 + 0.473094i 0.156863π0.156863\pi
−0.881012 + 0.473094i 0.843137π0.843137\pi
660660 0 0
661661 −98.0000 −0.148260 −0.0741301 0.997249i 0.523618π-0.523618\pi
−0.0741301 + 0.997249i 0.523618π0.523618\pi
662662 0 0
663663 0 0
664664 0 0
665665 576.000 117.576i 0.866165 0.176805i
666666 0 0
667667 560.029 0.839623
668668 0 0
669669 0 0
670670 0 0
671671 637.395i 0.949918i
672672 0 0
673673 489.898i 0.727932i −0.931412 0.363966i 0.881423π-0.881423\pi
0.931412 0.363966i 0.118577π-0.118577\pi
674674 0 0
675675 0 0
676676 0 0
677677 146.969i 0.217089i 0.994092 + 0.108545i 0.0346190π0.0346190\pi
−0.994092 + 0.108545i 0.965381π0.965381\pi
678678 0 0
679679 498.831i 0.734655i
680680 0 0
681681 0 0
682682 0 0
683683 −398.808 −0.583907 −0.291953 0.956433i 0.594305π-0.594305\pi
−0.291953 + 0.956433i 0.594305π0.594305\pi
684684 0 0
685685 −1056.00 + 215.555i −1.54161 + 0.314679i
686686 0 0
687687 0 0
688688 0 0
689689 288.000 0.417997
690690 0 0
691691 789.815i 1.14300i −0.820601 0.571502i 0.806361π-0.806361\pi
0.820601 0.571502i 0.193639π-0.193639\pi
692692 0 0
693693 0 0
694694 0 0
695695 −67.8823 + 13.8564i −0.0976723 + 0.0199373i
696696 0 0
697697 431.110i 0.618523i
698698 0 0
699699 0 0
700700 0 0
701701 −718.000 −1.02425 −0.512126 0.858911i 0.671142π-0.671142\pi
−0.512126 + 0.858911i 0.671142π0.671142\pi
702702 0 0
703703 −678.823 −0.965608
704704 0 0
705705 0 0
706706 0 0
707707 593.970 0.840127
708708 0 0
709709 −838.000 −1.18195 −0.590973 0.806691i 0.701256π-0.701256\pi
−0.590973 + 0.806691i 0.701256π0.701256\pi
710710 0 0
711711 0 0
712712 0 0
713713 1410.91i 1.97883i
714714 0 0
715715 −135.765 665.108i −0.189880 0.930220i
716716 0 0
717717 0 0
718718 0 0
719719 221.703i 0.308348i −0.988044 0.154174i 0.950728π-0.950728\pi
0.988044 0.154174i 0.0492717π-0.0492717\pi
720720 0 0
721721 −216.000 −0.299584
722722 0 0
723723 0 0
724724 0 0
725725 −506.000 + 215.555i −0.697931 + 0.297317i
726726 0 0
727727 347.897 0.478537 0.239269 0.970953i 0.423092π-0.423092\pi
0.239269 + 0.970953i 0.423092π0.423092\pi
728728 0 0
729729 0 0
730730 0 0
731731 1163.94i 1.59225i
732732 0 0
733733 676.059i 0.922318i 0.887317 + 0.461159i 0.152566π0.152566\pi
−0.887317 + 0.461159i 0.847434π0.847434\pi
734734 0 0
735735 0 0
736736 0 0
737737 823.029i 1.11673i
738738 0 0
739739 235.559i 0.318754i −0.987218 0.159377i 0.949052π-0.949052\pi
0.987218 0.159377i 0.0509485π-0.0509485\pi
740740 0 0
741741 0 0
742742 0 0
743743 1349.16 1.81583 0.907914 0.419157i 0.137674π-0.137674\pi
0.907914 + 0.419157i 0.137674π0.137674\pi
744744 0 0
745745 2.00000 + 9.79796i 0.00268456 + 0.0131516i
746746 0 0
747747 0 0
748748 0 0
749749 360.000 0.480641
750750 0 0
751751 1163.94i 1.54985i 0.632053 + 0.774926i 0.282213π0.282213\pi
−0.632053 + 0.774926i 0.717787π0.717787\pi
752752 0 0
753753 0 0
754754 0 0
755755 135.765 27.7128i 0.179821 0.0367057i
756756 0 0
757757 1205.15i 1.59201i 0.605292 + 0.796003i 0.293056π0.293056\pi
−0.605292 + 0.796003i 0.706944π0.706944\pi
758758 0 0
759759 0 0
760760 0 0
761761 −530.000 −0.696452 −0.348226 0.937411i 0.613216π-0.613216\pi
−0.348226 + 0.937411i 0.613216π0.613216\pi
762762 0 0
763763 −1238.85 −1.62366
764764 0 0
765765 0 0
766766 0 0
767767 −135.765 −0.177007
768768 0 0
769769 386.000 0.501951 0.250975 0.967993i 0.419249π-0.419249\pi
0.250975 + 0.967993i 0.419249π0.419249\pi
770770 0 0
771771 0 0
772772 0 0
773773 695.655i 0.899942i 0.893043 + 0.449971i 0.148566π0.148566\pi
−0.893043 + 0.449971i 0.851434π0.851434\pi
774774 0 0
775775 −543.058 1274.79i −0.700720 1.64489i
776776 0 0
777777 0 0
778778 0 0
779779 304.841i 0.391323i
780780 0 0
781781 384.000 0.491677
782782 0 0
783783 0 0
784784 0 0
785785 336.000 68.5857i 0.428025 0.0873703i
786786 0 0
787787 −1298.25 −1.64962 −0.824808 0.565413i 0.808717π-0.808717\pi
−0.824808 + 0.565413i 0.808717π0.808717\pi
788788 0 0
789789 0 0
790790 0 0
791791 332.554i 0.420422i
792792 0 0
793793 450.706i 0.568356i
794794 0 0
795795 0 0
796796 0 0
797797 1361.92i 1.70880i −0.519613 0.854402i 0.673924π-0.673924\pi
0.519613 0.854402i 0.326076π-0.326076\pi
798798 0 0
799799 166.277i 0.208106i
800800 0 0
801801 0 0
802802 0 0
803803 −1086.12 −1.35257
804804 0 0
805805 216.000 + 1058.18i 0.268323 + 1.31451i
806806 0 0
807807 0 0
808808 0 0
809809 1006.00 1.24351 0.621755 0.783212i 0.286420π-0.286420\pi
0.621755 + 0.783212i 0.286420π0.286420\pi
810810 0 0
811811 651.251i 0.803022i −0.915854 0.401511i 0.868485π-0.868485\pi
0.915854 0.401511i 0.131515π-0.131515\pi
812812 0 0
813813 0 0
814814 0 0
815815 −110.309 540.400i −0.135348 0.663067i
816816 0 0
817817 823.029i 1.00738i
818818 0 0
819819 0 0
820820 0 0
821821 482.000 0.587089 0.293544 0.955945i 0.405165π-0.405165\pi
0.293544 + 0.955945i 0.405165π0.405165\pi
822822 0 0
823823 −636.396 −0.773264 −0.386632 0.922234i 0.626362π-0.626362\pi
−0.386632 + 0.922234i 0.626362π0.626362\pi
824824 0 0
825825 0 0
826826 0 0
827827 −398.808 −0.482235 −0.241117 0.970496i 0.577514π-0.577514\pi
−0.241117 + 0.970496i 0.577514π0.577514\pi
828828 0 0
829829 −1106.00 −1.33414 −0.667069 0.744996i 0.732451π-0.732451\pi
−0.667069 + 0.744996i 0.732451π0.732451\pi
830830 0 0
831831 0 0
832832 0 0
833833 450.706i 0.541064i
834834 0 0
835835 93.3381 + 457.261i 0.111782 + 0.547618i
836836 0 0
837837 0 0
838838 0 0
839839 360.267i 0.429400i −0.976680 0.214700i 0.931123π-0.931123\pi
0.976680 0.214700i 0.0688774π-0.0688774\pi
840840 0 0
841841 −357.000 −0.424495
842842 0 0
843843 0 0
844844 0 0
845845 73.0000 + 357.626i 0.0863905 + 0.423225i
846846 0 0
847847 −602.455 −0.711281
848848 0 0
849849 0 0
850850 0 0
851851 1247.08i 1.46542i
852852 0 0
853853 676.059i 0.792566i 0.918128 + 0.396283i 0.129700π0.129700\pi
−0.918128 + 0.396283i 0.870300π0.870300\pi
854854 0 0
855855 0 0
856856 0 0
857857 1077.78i 1.25761i 0.777561 + 0.628807i 0.216457π0.216457\pi
−0.777561 + 0.628807i 0.783543π0.783543\pi
858858 0 0
859859 568.113i 0.661365i 0.943742 + 0.330683i 0.107279π0.107279\pi
−0.943742 + 0.330683i 0.892721π0.892721\pi
860860 0 0
861861 0 0
862862 0 0
863863 195.161 0.226143 0.113072 0.993587i 0.463931π-0.463931\pi
0.113072 + 0.993587i 0.463931π0.463931\pi
864864 0 0
865865 240.000 48.9898i 0.277457 0.0566356i
866866 0 0
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 581.969i 0.668162i
872872 0 0
873873 0 0
874874 0 0
875875 −602.455 872.954i −0.688520 0.997661i
876876 0 0
877877 244.949i 0.279303i 0.990201 + 0.139652i 0.0445983π0.0445983\pi
−0.990201 + 0.139652i 0.955402π0.955402\pi
878878 0 0
879879 0 0
880880 0 0
881881 −550.000 −0.624291 −0.312145 0.950034i 0.601048π-0.601048\pi
−0.312145 + 0.950034i 0.601048π0.601048\pi
882882 0 0
883883 636.396 0.720720 0.360360 0.932813i 0.382654π-0.382654\pi
0.360360 + 0.932813i 0.382654π0.382654\pi
884884 0 0
885885 0 0
886886 0 0
887887 −1230.37 −1.38711 −0.693555 0.720404i 0.743956π-0.743956\pi
−0.693555 + 0.720404i 0.743956π0.743956\pi
888888 0 0
889889 936.000 1.05287
890890 0 0
891891 0 0
892892 0 0
893893 117.576i 0.131664i
894894 0 0
895895 1289.76 263.272i 1.44108 0.294158i
896896 0 0
897897 0 0
898898 0 0
899899 1219.36i 1.35636i
900900 0 0
901901 576.000 0.639290
902902 0 0
903903 0 0
904904 0 0
905905 26.0000 + 127.373i 0.0287293 + 0.140744i
906906 0 0
907907 −585.484 −0.645518 −0.322759 0.946481i 0.604610π-0.604610\pi
−0.322759 + 0.946481i 0.604610π0.604610\pi
908908 0 0
909909 0 0
910910 0 0
911911 886.810i 0.973447i 0.873556 + 0.486723i 0.161808π0.161808\pi
−0.873556 + 0.486723i 0.838192π0.838192\pi
912912 0 0
913913 1058.18i 1.15901i
914914 0 0
915915 0 0
916916 0 0
917917 1528.48i 1.66683i
918918 0 0
919919 193.990i 0.211088i −0.994415 0.105544i 0.966342π-0.966342\pi
0.994415 0.105544i 0.0336584π-0.0336584\pi
920920 0 0
921921 0 0
922922 0 0
923923 271.529 0.294181
924924 0 0
925925 480.000 + 1126.77i 0.518919 + 1.21812i
926926 0 0
927927 0 0
928928 0 0
929929 −1318.00 −1.41873 −0.709365 0.704841i 0.751018π-0.751018\pi
−0.709365 + 0.704841i 0.751018π0.751018\pi
930930 0 0
931931 318.697i 0.342317i
932932 0 0
933933 0 0
934934 0 0
935935 −271.529 1330.22i −0.290405 1.42269i
936936 0 0
937937 548.686i 0.585577i −0.956177 0.292789i 0.905417π-0.905417\pi
0.956177 0.292789i 0.0945832π-0.0945832\pi
938938 0 0
939939 0 0
940940 0 0
941941 1654.00 1.75770 0.878852 0.477094i 0.158310π-0.158310\pi
0.878852 + 0.477094i 0.158310π0.158310\pi
942942 0 0
943943 −560.029 −0.593880
944944 0 0
945945 0 0
946946 0 0
947947 −1417.04 −1.49635 −0.748174 0.663502i 0.769069π-0.769069\pi
−0.748174 + 0.663502i 0.769069π0.769069\pi
948948 0 0
949949 −768.000 −0.809273
950950 0 0
951951 0 0
952952 0 0
953953 137.171i 0.143936i 0.997407 + 0.0719682i 0.0229280π0.0229280\pi
−0.997407 + 0.0719682i 0.977072π0.977072\pi
954954 0 0
955955 −543.058 + 110.851i −0.568647 + 0.116075i
956956 0 0
957957 0 0
958958 0 0
959959 1829.05i 1.90724i
960960 0 0
961961 −2111.00 −2.19667
962962 0 0
963963 0 0
964964 0 0
965965 −1632.00 + 333.131i −1.69119 + 0.345213i
966966 0 0
967967 −1450.98 −1.50050 −0.750250 0.661154i 0.770067π-0.770067\pi
−0.750250 + 0.661154i 0.770067π0.770067\pi
968968 0 0
969969 0 0
970970 0 0
971971 817.528i 0.841944i 0.907074 + 0.420972i 0.138311π0.138311\pi
−0.907074 + 0.420972i 0.861689π0.861689\pi
972972 0 0
973973 117.576i 0.120838i
974974 0 0
975975 0 0
976976 0 0
977977 1704.84i 1.74498i −0.488633 0.872490i 0.662504π-0.662504\pi
0.488633 0.872490i 0.337496π-0.337496\pi
978978 0 0
979979 2023.04i 2.06643i
980980 0 0
981981 0 0
982982 0 0
983983 738.219 0.750986 0.375493 0.926825i 0.377473π-0.377473\pi
0.375493 + 0.926825i 0.377473π0.377473\pi
984984 0 0
985985 −528.000 + 107.778i −0.536041 + 0.109419i
986986 0 0
987987 0 0
988988 0 0
989989 1512.00 1.52882
990990 0 0
991991 775.959i 0.783006i −0.920177 0.391503i 0.871955π-0.871955\pi
0.920177 0.391503i 0.128045π-0.128045\pi
992992 0 0
993993 0 0
994994 0 0
995995 1221.88 249.415i 1.22802 0.250669i
996996 0 0
997997 1420.70i 1.42498i 0.701683 + 0.712489i 0.252432π0.252432\pi
−0.701683 + 0.712489i 0.747568π0.747568\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 720.3.j.e.559.4 4
3.2 odd 2 80.3.h.b.79.3 yes 4
4.3 odd 2 inner 720.3.j.e.559.3 4
5.2 odd 4 3600.3.e.bd.3151.3 4
5.3 odd 4 3600.3.e.bd.3151.1 4
5.4 even 2 inner 720.3.j.e.559.1 4
12.11 even 2 80.3.h.b.79.1 4
15.2 even 4 400.3.b.h.351.2 4
15.8 even 4 400.3.b.h.351.4 4
15.14 odd 2 80.3.h.b.79.2 yes 4
20.3 even 4 3600.3.e.bd.3151.4 4
20.7 even 4 3600.3.e.bd.3151.2 4
20.19 odd 2 inner 720.3.j.e.559.2 4
24.5 odd 2 320.3.h.e.319.2 4
24.11 even 2 320.3.h.e.319.4 4
48.5 odd 4 1280.3.e.j.639.3 8
48.11 even 4 1280.3.e.j.639.7 8
48.29 odd 4 1280.3.e.j.639.6 8
48.35 even 4 1280.3.e.j.639.2 8
60.23 odd 4 400.3.b.h.351.1 4
60.47 odd 4 400.3.b.h.351.3 4
60.59 even 2 80.3.h.b.79.4 yes 4
120.29 odd 2 320.3.h.e.319.3 4
120.53 even 4 1600.3.b.t.1151.1 4
120.59 even 2 320.3.h.e.319.1 4
120.77 even 4 1600.3.b.t.1151.3 4
120.83 odd 4 1600.3.b.t.1151.4 4
120.107 odd 4 1600.3.b.t.1151.2 4
240.29 odd 4 1280.3.e.j.639.4 8
240.59 even 4 1280.3.e.j.639.1 8
240.149 odd 4 1280.3.e.j.639.5 8
240.179 even 4 1280.3.e.j.639.8 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
80.3.h.b.79.1 4 12.11 even 2
80.3.h.b.79.2 yes 4 15.14 odd 2
80.3.h.b.79.3 yes 4 3.2 odd 2
80.3.h.b.79.4 yes 4 60.59 even 2
320.3.h.e.319.1 4 120.59 even 2
320.3.h.e.319.2 4 24.5 odd 2
320.3.h.e.319.3 4 120.29 odd 2
320.3.h.e.319.4 4 24.11 even 2
400.3.b.h.351.1 4 60.23 odd 4
400.3.b.h.351.2 4 15.2 even 4
400.3.b.h.351.3 4 60.47 odd 4
400.3.b.h.351.4 4 15.8 even 4
720.3.j.e.559.1 4 5.4 even 2 inner
720.3.j.e.559.2 4 20.19 odd 2 inner
720.3.j.e.559.3 4 4.3 odd 2 inner
720.3.j.e.559.4 4 1.1 even 1 trivial
1280.3.e.j.639.1 8 240.59 even 4
1280.3.e.j.639.2 8 48.35 even 4
1280.3.e.j.639.3 8 48.5 odd 4
1280.3.e.j.639.4 8 240.29 odd 4
1280.3.e.j.639.5 8 240.149 odd 4
1280.3.e.j.639.6 8 48.29 odd 4
1280.3.e.j.639.7 8 48.11 even 4
1280.3.e.j.639.8 8 240.179 even 4
1600.3.b.t.1151.1 4 120.53 even 4
1600.3.b.t.1151.2 4 120.107 odd 4
1600.3.b.t.1151.3 4 120.77 even 4
1600.3.b.t.1151.4 4 120.83 odd 4
3600.3.e.bd.3151.1 4 5.3 odd 4
3600.3.e.bd.3151.2 4 20.7 even 4
3600.3.e.bd.3151.3 4 5.2 odd 4
3600.3.e.bd.3151.4 4 20.3 even 4