Properties

Label 2160.3.c.m.1889.1
Level 21602160
Weight 33
Character 2160.1889
Analytic conductor 58.85658.856
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2160,3,Mod(1889,2160)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2160.1889");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 2160=24335 2160 = 2^{4} \cdot 3^{3} \cdot 5
Weight: k k == 3 3
Character orbit: [χ][\chi] == 2160.c (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: 58.855737101858.8557371018
Analytic rank: 00
Dimension: 44
Coefficient field: 4.0.31744.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+14x2+31 x^{4} + 14x^{2} + 31 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 270)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1889.1
Root 3.35300i3.35300i of defining polynomial
Character χ\chi == 2160.1889
Dual form 2160.3.c.m.1889.2

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+(1.585794.74186i)q50.813575iq7+15.3762iq11+5.89243iq1312.8995q171.24264q19+4.79899q23+(19.970615.0392i)q2542.6768iq294.21320q31+(3.857861.29016i)q3570.3144iq377.04300iq41+41.0496iq43+79.7990q47+48.3381q49+63.7279q53+(72.9117+24.3833i)q5536.6448iq5982.9411q61+(27.9411+9.34414i)q6589.0027iq6769.6982iq7189.6188iq73+12.5097q77134.095q79109.024q83+(20.4558+61.1677i)q85+137.514iq89+4.79394q91+(1.97056+5.89243i)q9590.6298iq97+O(q100)q+(1.58579 - 4.74186i) q^{5} -0.813575i q^{7} +15.3762i q^{11} +5.89243i q^{13} -12.8995 q^{17} -1.24264 q^{19} +4.79899 q^{23} +(-19.9706 - 15.0392i) q^{25} -42.6768i q^{29} -4.21320 q^{31} +(-3.85786 - 1.29016i) q^{35} -70.3144i q^{37} -7.04300i q^{41} +41.0496i q^{43} +79.7990 q^{47} +48.3381 q^{49} +63.7279 q^{53} +(72.9117 + 24.3833i) q^{55} -36.6448i q^{59} -82.9411 q^{61} +(27.9411 + 9.34414i) q^{65} -89.0027i q^{67} -69.6982i q^{71} -89.6188i q^{73} +12.5097 q^{77} -134.095 q^{79} -109.024 q^{83} +(-20.4558 + 61.1677i) q^{85} +137.514i q^{89} +4.79394 q^{91} +(-1.97056 + 5.89243i) q^{95} -90.6298i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+12q512q17+12q1960q2312q25+68q3172q35+240q47180q49+204q53+88q55196q6124q65312q77180q79108q83++60q95+O(q100) 4 q + 12 q^{5} - 12 q^{17} + 12 q^{19} - 60 q^{23} - 12 q^{25} + 68 q^{31} - 72 q^{35} + 240 q^{47} - 180 q^{49} + 204 q^{53} + 88 q^{55} - 196 q^{61} - 24 q^{65} - 312 q^{77} - 180 q^{79} - 108 q^{83}+ \cdots + 60 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2160Z)×\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times.

nn 271271 12971297 16211621 20812081
χ(n)\chi(n) 11 1-1 11 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 0 0
44 0 0
55 1.58579 4.74186i 0.317157 0.948373i
66 0 0
77 0.813575i 0.116225i −0.998310 0.0581125i 0.981492π-0.981492\pi
0.998310 0.0581125i 0.0185082π-0.0185082\pi
88 0 0
99 0 0
1010 0 0
1111 15.3762i 1.39783i 0.715203 + 0.698917i 0.246334π0.246334\pi
−0.715203 + 0.698917i 0.753666π0.753666\pi
1212 0 0
1313 5.89243i 0.453264i 0.973980 + 0.226632i 0.0727715π0.0727715\pi
−0.973980 + 0.226632i 0.927229π0.927229\pi
1414 0 0
1515 0 0
1616 0 0
1717 −12.8995 −0.758794 −0.379397 0.925234i 0.623869π-0.623869\pi
−0.379397 + 0.925234i 0.623869π0.623869\pi
1818 0 0
1919 −1.24264 −0.0654021 −0.0327011 0.999465i 0.510411π-0.510411\pi
−0.0327011 + 0.999465i 0.510411π0.510411\pi
2020 0 0
2121 0 0
2222 0 0
2323 4.79899 0.208652 0.104326 0.994543i 0.466732π-0.466732\pi
0.104326 + 0.994543i 0.466732π0.466732\pi
2424 0 0
2525 −19.9706 15.0392i −0.798823 0.601567i
2626 0 0
2727 0 0
2828 0 0
2929 42.6768i 1.47161i −0.677192 0.735807i 0.736803π-0.736803\pi
0.677192 0.735807i 0.263197π-0.263197\pi
3030 0 0
3131 −4.21320 −0.135910 −0.0679549 0.997688i 0.521647π-0.521647\pi
−0.0679549 + 0.997688i 0.521647π0.521647\pi
3232 0 0
3333 0 0
3434 0 0
3535 −3.85786 1.29016i −0.110225 0.0368616i
3636 0 0
3737 70.3144i 1.90039i −0.311657 0.950195i 0.600884π-0.600884\pi
0.311657 0.950195i 0.399116π-0.399116\pi
3838 0 0
3939 0 0
4040 0 0
4141 7.04300i 0.171781i −0.996305 0.0858903i 0.972627π-0.972627\pi
0.996305 0.0858903i 0.0273735π-0.0273735\pi
4242 0 0
4343 41.0496i 0.954643i 0.878729 + 0.477321i 0.158392π0.158392\pi
−0.878729 + 0.477321i 0.841608π0.841608\pi
4444 0 0
4545 0 0
4646 0 0
4747 79.7990 1.69785 0.848925 0.528513i 0.177250π-0.177250\pi
0.848925 + 0.528513i 0.177250π0.177250\pi
4848 0 0
4949 48.3381 0.986492
5050 0 0
5151 0 0
5252 0 0
5353 63.7279 1.20241 0.601207 0.799093i 0.294687π-0.294687\pi
0.601207 + 0.799093i 0.294687π0.294687\pi
5454 0 0
5555 72.9117 + 24.3833i 1.32567 + 0.443333i
5656 0 0
5757 0 0
5858 0 0
5959 36.6448i 0.621098i −0.950557 0.310549i 0.899487π-0.899487\pi
0.950557 0.310549i 0.100513π-0.100513\pi
6060 0 0
6161 −82.9411 −1.35969 −0.679845 0.733356i 0.737953π-0.737953\pi
−0.679845 + 0.733356i 0.737953π0.737953\pi
6262 0 0
6363 0 0
6464 0 0
6565 27.9411 + 9.34414i 0.429863 + 0.143756i
6666 0 0
6767 89.0027i 1.32840i −0.747556 0.664199i 0.768773π-0.768773\pi
0.747556 0.664199i 0.231227π-0.231227\pi
6868 0 0
6969 0 0
7070 0 0
7171 69.6982i 0.981665i −0.871254 0.490833i 0.836693π-0.836693\pi
0.871254 0.490833i 0.163307π-0.163307\pi
7272 0 0
7373 89.6188i 1.22766i −0.789440 0.613828i 0.789629π-0.789629\pi
0.789440 0.613828i 0.210371π-0.210371\pi
7474 0 0
7575 0 0
7676 0 0
7777 12.5097 0.162463
7878 0 0
7979 −134.095 −1.69741 −0.848705 0.528866i 0.822617π-0.822617\pi
−0.848705 + 0.528866i 0.822617π0.822617\pi
8080 0 0
8181 0 0
8282 0 0
8383 −109.024 −1.31355 −0.656773 0.754088i 0.728079π-0.728079\pi
−0.656773 + 0.754088i 0.728079π0.728079\pi
8484 0 0
8585 −20.4558 + 61.1677i −0.240657 + 0.719620i
8686 0 0
8787 0 0
8888 0 0
8989 137.514i 1.54510i 0.634953 + 0.772551i 0.281020π0.281020\pi
−0.634953 + 0.772551i 0.718980π0.718980\pi
9090 0 0
9191 4.79394 0.0526807
9292 0 0
9393 0 0
9494 0 0
9595 −1.97056 + 5.89243i −0.0207428 + 0.0620256i
9696 0 0
9797 90.6298i 0.934328i −0.884171 0.467164i 0.845276π-0.845276\pi
0.884171 0.467164i 0.154724π-0.154724\pi
9898 0 0
9999 0 0
100100 0 0
101101 49.7198i 0.492275i 0.969235 + 0.246138i 0.0791615π0.0791615\pi
−0.969235 + 0.246138i 0.920839π0.920839\pi
102102 0 0
103103 128.844i 1.25091i −0.780259 0.625456i 0.784913π-0.784913\pi
0.780259 0.625456i 0.215087π-0.215087\pi
104104 0 0
105105 0 0
106106 0 0
107107 −6.42641 −0.0600599 −0.0300299 0.999549i 0.509560π-0.509560\pi
−0.0300299 + 0.999549i 0.509560π0.509560\pi
108108 0 0
109109 108.279 0.993387 0.496694 0.867926i 0.334547π-0.334547\pi
0.496694 + 0.867926i 0.334547π0.334547\pi
110110 0 0
111111 0 0
112112 0 0
113113 −30.4264 −0.269260 −0.134630 0.990896i 0.542985π-0.542985\pi
−0.134630 + 0.990896i 0.542985π0.542985\pi
114114 0 0
115115 7.61017 22.7562i 0.0661754 0.197880i
116116 0 0
117117 0 0
118118 0 0
119119 10.4947i 0.0881909i
120120 0 0
121121 −115.426 −0.953937
122122 0 0
123123 0 0
124124 0 0
125125 −102.983 + 70.8488i −0.823862 + 0.566790i
126126 0 0
127127 133.725i 1.05296i −0.850189 0.526478i 0.823512π-0.823512\pi
0.850189 0.526478i 0.176488π-0.176488\pi
128128 0 0
129129 0 0
130130 0 0
131131 61.7838i 0.471632i 0.971798 + 0.235816i 0.0757763π0.0757763\pi
−0.971798 + 0.235816i 0.924224π0.924224\pi
132132 0 0
133133 1.01098i 0.00760137i
134134 0 0
135135 0 0
136136 0 0
137137 −163.919 −1.19649 −0.598244 0.801314i 0.704135π-0.704135\pi
−0.598244 + 0.801314i 0.704135π0.704135\pi
138138 0 0
139139 −182.250 −1.31115 −0.655575 0.755130i 0.727574π-0.727574\pi
−0.655575 + 0.755130i 0.727574π0.727574\pi
140140 0 0
141141 0 0
142142 0 0
143143 −90.6030 −0.633588
144144 0 0
145145 −202.368 67.6763i −1.39564 0.466733i
146146 0 0
147147 0 0
148148 0 0
149149 189.535i 1.27205i −0.771670 0.636023i 0.780578π-0.780578\pi
0.771670 0.636023i 0.219422π-0.219422\pi
150150 0 0
151151 113.338 0.750583 0.375292 0.926907i 0.377543π-0.377543\pi
0.375292 + 0.926907i 0.377543π0.377543\pi
152152 0 0
153153 0 0
154154 0 0
155155 −6.68124 + 19.9784i −0.0431048 + 0.128893i
156156 0 0
157157 113.189i 0.720946i −0.932770 0.360473i 0.882615π-0.882615\pi
0.932770 0.360473i 0.117385π-0.117385\pi
158158 0 0
159159 0 0
160160 0 0
161161 3.90434i 0.0242506i
162162 0 0
163163 152.414i 0.935053i −0.883979 0.467527i 0.845145π-0.845145\pi
0.883979 0.467527i 0.154855π-0.154855\pi
164164 0 0
165165 0 0
166166 0 0
167167 −105.853 −0.633849 −0.316925 0.948451i 0.602650π-0.602650\pi
−0.316925 + 0.948451i 0.602650π0.602650\pi
168168 0 0
169169 134.279 0.794552
170170 0 0
171171 0 0
172172 0 0
173173 110.012 0.635909 0.317954 0.948106i 0.397004π-0.397004\pi
0.317954 + 0.948106i 0.397004π0.397004\pi
174174 0 0
175175 −12.2355 + 16.2476i −0.0699171 + 0.0928432i
176176 0 0
177177 0 0
178178 0 0
179179 118.407i 0.661492i 0.943720 + 0.330746i 0.107300π0.107300\pi
−0.943720 + 0.330746i 0.892700π0.892700\pi
180180 0 0
181181 172.397 0.952469 0.476235 0.879318i 0.342001π-0.342001\pi
0.476235 + 0.879318i 0.342001π0.342001\pi
182182 0 0
183183 0 0
184184 0 0
185185 −333.421 111.504i −1.80228 0.602722i
186186 0 0
187187 198.345i 1.06067i
188188 0 0
189189 0 0
190190 0 0
191191 289.393i 1.51515i 0.652749 + 0.757574i 0.273616π0.273616\pi
−0.652749 + 0.757574i 0.726384π0.726384\pi
192192 0 0
193193 127.833i 0.662347i −0.943570 0.331173i 0.892555π-0.892555\pi
0.943570 0.331173i 0.107445π-0.107445\pi
194194 0 0
195195 0 0
196196 0 0
197197 280.414 1.42342 0.711711 0.702472i 0.247920π-0.247920\pi
0.711711 + 0.702472i 0.247920π0.247920\pi
198198 0 0
199199 −156.426 −0.786062 −0.393031 0.919525i 0.628574π-0.628574\pi
−0.393031 + 0.919525i 0.628574π0.628574\pi
200200 0 0
201201 0 0
202202 0 0
203203 −34.7208 −0.171038
204204 0 0
205205 −33.3970 11.1687i −0.162912 0.0544815i
206206 0 0
207207 0 0
208208 0 0
209209 19.1070i 0.0914213i
210210 0 0
211211 −22.5076 −0.106671 −0.0533355 0.998577i 0.516985π-0.516985\pi
−0.0533355 + 0.998577i 0.516985π0.516985\pi
212212 0 0
213213 0 0
214214 0 0
215215 194.652 + 65.0959i 0.905357 + 0.302772i
216216 0 0
217217 3.42776i 0.0157961i
218218 0 0
219219 0 0
220220 0 0
221221 76.0094i 0.343934i
222222 0 0
223223 354.826i 1.59115i −0.605856 0.795575i 0.707169π-0.707169\pi
0.605856 0.795575i 0.292831π-0.292831\pi
224224 0 0
225225 0 0
226226 0 0
227227 415.098 1.82862 0.914312 0.405011i 0.132732π-0.132732\pi
0.914312 + 0.405011i 0.132732π0.132732\pi
228228 0 0
229229 −220.220 −0.961661 −0.480830 0.876814i 0.659665π-0.659665\pi
−0.480830 + 0.876814i 0.659665π0.659665\pi
230230 0 0
231231 0 0
232232 0 0
233233 10.0345 0.0430665 0.0215332 0.999768i 0.493145π-0.493145\pi
0.0215332 + 0.999768i 0.493145π0.493145\pi
234234 0 0
235235 126.544 378.396i 0.538486 1.61020i
236236 0 0
237237 0 0
238238 0 0
239239 114.363i 0.478507i −0.970957 0.239253i 0.923097π-0.923097\pi
0.970957 0.239253i 0.0769027π-0.0769027\pi
240240 0 0
241241 −63.7208 −0.264402 −0.132201 0.991223i 0.542204π-0.542204\pi
−0.132201 + 0.991223i 0.542204π0.542204\pi
242242 0 0
243243 0 0
244244 0 0
245245 76.6539 229.213i 0.312873 0.935562i
246246 0 0
247247 7.32218i 0.0296444i
248248 0 0
249249 0 0
250250 0 0
251251 229.631i 0.914866i −0.889244 0.457433i 0.848769π-0.848769\pi
0.889244 0.457433i 0.151231π-0.151231\pi
252252 0 0
253253 73.7901i 0.291660i
254254 0 0
255255 0 0
256256 0 0
257257 388.227 1.51061 0.755306 0.655372i 0.227488π-0.227488\pi
0.755306 + 0.655372i 0.227488π0.227488\pi
258258 0 0
259259 −57.2061 −0.220873
260260 0 0
261261 0 0
262262 0 0
263263 −226.877 −0.862651 −0.431325 0.902196i 0.641954π-0.641954\pi
−0.431325 + 0.902196i 0.641954π0.641954\pi
264264 0 0
265265 101.059 302.189i 0.381354 1.14034i
266266 0 0
267267 0 0
268268 0 0
269269 226.772i 0.843019i 0.906824 + 0.421509i 0.138500π0.138500\pi
−0.906824 + 0.421509i 0.861500π0.861500\pi
270270 0 0
271271 −322.889 −1.19147 −0.595737 0.803180i 0.703140π-0.703140\pi
−0.595737 + 0.803180i 0.703140π0.703140\pi
272272 0 0
273273 0 0
274274 0 0
275275 231.245 307.071i 0.840890 1.11662i
276276 0 0
277277 200.564i 0.724058i 0.932167 + 0.362029i 0.117916π0.117916\pi
−0.932167 + 0.362029i 0.882084π0.882084\pi
278278 0 0
279279 0 0
280280 0 0
281281 128.030i 0.455624i 0.973705 + 0.227812i 0.0731572π0.0731572\pi
−0.973705 + 0.227812i 0.926843π0.926843\pi
282282 0 0
283283 420.235i 1.48493i 0.669885 + 0.742465i 0.266344π0.266344\pi
−0.669885 + 0.742465i 0.733656π0.733656\pi
284284 0 0
285285 0 0
286286 0 0
287287 −5.73001 −0.0199652
288288 0 0
289289 −122.603 −0.424232
290290 0 0
291291 0 0
292292 0 0
293293 137.434 0.469056 0.234528 0.972109i 0.424645π-0.424645\pi
0.234528 + 0.972109i 0.424645π0.424645\pi
294294 0 0
295295 −173.765 58.1108i −0.589032 0.196986i
296296 0 0
297297 0 0
298298 0 0
299299 28.2777i 0.0945744i
300300 0 0
301301 33.3970 0.110953
302302 0 0
303303 0 0
304304 0 0
305305 −131.527 + 393.296i −0.431236 + 1.28949i
306306 0 0
307307 117.849i 0.383872i 0.981407 + 0.191936i 0.0614766π0.0614766\pi
−0.981407 + 0.191936i 0.938523π0.938523\pi
308308 0 0
309309 0 0
310310 0 0
311311 499.326i 1.60555i −0.596283 0.802774i 0.703356π-0.703356\pi
0.596283 0.802774i 0.296644π-0.296644\pi
312312 0 0
313313 491.806i 1.57127i −0.618693 0.785633i 0.712338π-0.712338\pi
0.618693 0.785633i 0.287662π-0.287662\pi
314314 0 0
315315 0 0
316316 0 0
317317 −241.399 −0.761511 −0.380756 0.924676i 0.624336π-0.624336\pi
−0.380756 + 0.924676i 0.624336π0.624336\pi
318318 0 0
319319 656.205 2.05707
320320 0 0
321321 0 0
322322 0 0
323323 16.0294 0.0496267
324324 0 0
325325 88.6173 117.675i 0.272669 0.362078i
326326 0 0
327327 0 0
328328 0 0
329329 64.9225i 0.197333i
330330 0 0
331331 87.8091 0.265284 0.132642 0.991164i 0.457654π-0.457654\pi
0.132642 + 0.991164i 0.457654π0.457654\pi
332332 0 0
333333 0 0
334334 0 0
335335 −422.039 141.139i −1.25982 0.421311i
336336 0 0
337337 452.138i 1.34166i −0.741613 0.670828i 0.765939π-0.765939\pi
0.741613 0.670828i 0.234061π-0.234061\pi
338338 0 0
339339 0 0
340340 0 0
341341 64.7829i 0.189979i
342342 0 0
343343 79.1919i 0.230880i
344344 0 0
345345 0 0
346346 0 0
347347 −189.411 −0.545854 −0.272927 0.962035i 0.587992π-0.587992\pi
−0.272927 + 0.962035i 0.587992π0.587992\pi
348348 0 0
349349 −155.794 −0.446401 −0.223200 0.974773i 0.571650π-0.571650\pi
−0.223200 + 0.974773i 0.571650π0.571650\pi
350350 0 0
351351 0 0
352352 0 0
353353 263.387 0.746138 0.373069 0.927804i 0.378305π-0.378305\pi
0.373069 + 0.927804i 0.378305π0.378305\pi
354354 0 0
355355 −330.500 110.527i −0.930985 0.311342i
356356 0 0
357357 0 0
358358 0 0
359359 79.6346i 0.221823i 0.993830 + 0.110912i 0.0353771π0.0353771\pi
−0.993830 + 0.110912i 0.964623π0.964623\pi
360360 0 0
361361 −359.456 −0.995723
362362 0 0
363363 0 0
364364 0 0
365365 −424.960 142.116i −1.16428 0.389360i
366366 0 0
367367 475.953i 1.29688i 0.761268 + 0.648438i 0.224577π0.224577\pi
−0.761268 + 0.648438i 0.775423π0.775423\pi
368368 0 0
369369 0 0
370370 0 0
371371 51.8475i 0.139751i
372372 0 0
373373 61.7838i 0.165640i −0.996565 0.0828201i 0.973607π-0.973607\pi
0.996565 0.0828201i 0.0263927π-0.0263927\pi
374374 0 0
375375 0 0
376376 0 0
377377 251.470 0.667030
378378 0 0
379379 142.345 0.375581 0.187791 0.982209i 0.439867π-0.439867\pi
0.187791 + 0.982209i 0.439867π0.439867\pi
380380 0 0
381381 0 0
382382 0 0
383383 −357.520 −0.933472 −0.466736 0.884397i 0.654570π-0.654570\pi
−0.466736 + 0.884397i 0.654570π0.654570\pi
384384 0 0
385385 19.8377 59.3192i 0.0515264 0.154076i
386386 0 0
387387 0 0
388388 0 0
389389 411.079i 1.05676i 0.849009 + 0.528379i 0.177200π0.177200\pi
−0.849009 + 0.528379i 0.822800π0.822800\pi
390390 0 0
391391 −61.9045 −0.158324
392392 0 0
393393 0 0
394394 0 0
395395 −212.647 + 635.863i −0.538346 + 1.60978i
396396 0 0
397397 457.462i 1.15230i 0.817345 + 0.576149i 0.195445π0.195445\pi
−0.817345 + 0.576149i 0.804555π0.804555\pi
398398 0 0
399399 0 0
400400 0 0
401401 467.283i 1.16529i −0.812725 0.582647i 0.802017π-0.802017\pi
0.812725 0.582647i 0.197983π-0.197983\pi
402402 0 0
403403 24.8260i 0.0616030i
404404 0 0
405405 0 0
406406 0 0
407407 1081.17 2.65643
408408 0 0
409409 −448.574 −1.09676 −0.548378 0.836230i 0.684755π-0.684755\pi
−0.548378 + 0.836230i 0.684755π0.684755\pi
410410 0 0
411411 0 0
412412 0 0
413413 −29.8133 −0.0721871
414414 0 0
415415 −172.889 + 516.979i −0.416601 + 1.24573i
416416 0 0
417417 0 0
418418 0 0
419419 360.834i 0.861180i −0.902548 0.430590i 0.858306π-0.858306\pi
0.902548 0.430590i 0.141694π-0.141694\pi
420420 0 0
421421 357.059 0.848121 0.424060 0.905634i 0.360604π-0.360604\pi
0.424060 + 0.905634i 0.360604π0.360604\pi
422422 0 0
423423 0 0
424424 0 0
425425 257.610 + 193.998i 0.606142 + 0.456465i
426426 0 0
427427 67.4789i 0.158030i
428428 0 0
429429 0 0
430430 0 0
431431 655.947i 1.52192i 0.648800 + 0.760959i 0.275271π0.275271\pi
−0.648800 + 0.760959i 0.724729π0.724729\pi
432432 0 0
433433 164.372i 0.379612i −0.981822 0.189806i 0.939214π-0.939214\pi
0.981822 0.189806i 0.0607859π-0.0607859\pi
434434 0 0
435435 0 0
436436 0 0
437437 −5.96342 −0.0136463
438438 0 0
439439 132.286 0.301336 0.150668 0.988584i 0.451858π-0.451858\pi
0.150668 + 0.988584i 0.451858π0.451858\pi
440440 0 0
441441 0 0
442442 0 0
443443 −455.485 −1.02818 −0.514092 0.857735i 0.671871π-0.671871\pi
−0.514092 + 0.857735i 0.671871π0.671871\pi
444444 0 0
445445 652.073 + 218.068i 1.46533 + 0.490040i
446446 0 0
447447 0 0
448448 0 0
449449 415.749i 0.925944i −0.886373 0.462972i 0.846783π-0.846783\pi
0.886373 0.462972i 0.153217π-0.153217\pi
450450 0 0
451451 108.294 0.240121
452452 0 0
453453 0 0
454454 0 0
455455 7.60216 22.7322i 0.0167081 0.0499609i
456456 0 0
457457 303.643i 0.664426i −0.943204 0.332213i 0.892205π-0.892205\pi
0.943204 0.332213i 0.107795π-0.107795\pi
458458 0 0
459459 0 0
460460 0 0
461461 428.790i 0.930130i 0.885277 + 0.465065i 0.153969π0.153969\pi
−0.885277 + 0.465065i 0.846031π0.846031\pi
462462 0 0
463463 814.484i 1.75914i −0.475765 0.879572i 0.657829π-0.657829\pi
0.475765 0.879572i 0.342171π-0.342171\pi
464464 0 0
465465 0 0
466466 0 0
467467 607.118 1.30004 0.650019 0.759918i 0.274761π-0.274761\pi
0.650019 + 0.759918i 0.274761π0.274761\pi
468468 0 0
469469 −72.4104 −0.154393
470470 0 0
471471 0 0
472472 0 0
473473 −631.186 −1.33443
474474 0 0
475475 24.8162 + 18.6883i 0.0522447 + 0.0393438i
476476 0 0
477477 0 0
478478 0 0
479479 343.889i 0.717931i 0.933351 + 0.358965i 0.116870π0.116870\pi
−0.933351 + 0.358965i 0.883130π0.883130\pi
480480 0 0
481481 414.323 0.861378
482482 0 0
483483 0 0
484484 0 0
485485 −429.754 143.720i −0.886092 0.296329i
486486 0 0
487487 300.759i 0.617576i 0.951131 + 0.308788i 0.0999233π0.0999233\pi
−0.951131 + 0.308788i 0.900077π0.900077\pi
488488 0 0
489489 0 0
490490 0 0
491491 173.914i 0.354203i 0.984193 + 0.177101i 0.0566720π0.0566720\pi
−0.984193 + 0.177101i 0.943328π0.943328\pi
492492 0 0
493493 550.509i 1.11665i
494494 0 0
495495 0 0
496496 0 0
497497 −56.7048 −0.114094
498498 0 0
499499 761.610 1.52627 0.763136 0.646237i 0.223658π-0.223658\pi
0.763136 + 0.646237i 0.223658π0.223658\pi
500500 0 0
501501 0 0
502502 0 0
503503 280.632 0.557917 0.278959 0.960303i 0.410011π-0.410011\pi
0.278959 + 0.960303i 0.410011π0.410011\pi
504504 0 0
505505 235.765 + 78.8450i 0.466860 + 0.156129i
506506 0 0
507507 0 0
508508 0 0
509509 633.176i 1.24396i −0.783032 0.621981i 0.786328π-0.786328\pi
0.783032 0.621981i 0.213672π-0.213672\pi
510510 0 0
511511 −72.9117 −0.142684
512512 0 0
513513 0 0
514514 0 0
515515 −610.960 204.319i −1.18633 0.396736i
516516 0 0
517517 1227.00i 2.37331i
518518 0 0
519519 0 0
520520 0 0
521521 92.3966i 0.177345i 0.996061 + 0.0886723i 0.0282624π0.0282624\pi
−0.996061 + 0.0886723i 0.971738π0.971738\pi
522522 0 0
523523 818.552i 1.56511i 0.622582 + 0.782554i 0.286084π0.286084\pi
−0.622582 + 0.782554i 0.713916π0.713916\pi
524524 0 0
525525 0 0
526526 0 0
527527 54.3482 0.103128
528528 0 0
529529 −505.970 −0.956464
530530 0 0
531531 0 0
532532 0 0
533533 41.5004 0.0778620
534534 0 0
535535 −10.1909 + 30.4732i −0.0190484 + 0.0569592i
536536 0 0
537537 0 0
538538 0 0
539539 743.254i 1.37895i
540540 0 0
541541 −376.985 −0.696830 −0.348415 0.937340i 0.613280π-0.613280\pi
−0.348415 + 0.937340i 0.613280π0.613280\pi
542542 0 0
543543 0 0
544544 0 0
545545 171.708 513.445i 0.315060 0.942102i
546546 0 0
547547 337.346i 0.616721i −0.951270 0.308360i 0.900220π-0.900220\pi
0.951270 0.308360i 0.0997803π-0.0997803\pi
548548 0 0
549549 0 0
550550 0 0
551551 53.0319i 0.0962467i
552552 0 0
553553 109.097i 0.197282i
554554 0 0
555555 0 0
556556 0 0
557557 303.338 0.544593 0.272296 0.962213i 0.412217π-0.412217\pi
0.272296 + 0.962213i 0.412217π0.412217\pi
558558 0 0
559559 −241.882 −0.432705
560560 0 0
561561 0 0
562562 0 0
563563 −234.093 −0.415796 −0.207898 0.978150i 0.566662π-0.566662\pi
−0.207898 + 0.978150i 0.566662π0.566662\pi
564564 0 0
565565 −48.2498 + 144.278i −0.0853978 + 0.255359i
566566 0 0
567567 0 0
568568 0 0
569569 66.5257i 0.116917i −0.998290 0.0584584i 0.981381π-0.981381\pi
0.998290 0.0584584i 0.0186185π-0.0186185\pi
570570 0 0
571571 −1115.54 −1.95365 −0.976826 0.214035i 0.931339π-0.931339\pi
−0.976826 + 0.214035i 0.931339π0.931339\pi
572572 0 0
573573 0 0
574574 0 0
575575 −95.8385 72.1728i −0.166676 0.125518i
576576 0 0
577577 957.356i 1.65920i −0.558361 0.829598i 0.688570π-0.688570\pi
0.558361 0.829598i 0.311430π-0.311430\pi
578578 0 0
579579 0 0
580580 0 0
581581 88.6996i 0.152667i
582582 0 0
583583 979.891i 1.68077i
584584 0 0
585585 0 0
586586 0 0
587587 79.8974 0.136111 0.0680557 0.997682i 0.478320π-0.478320\pi
0.0680557 + 0.997682i 0.478320π0.478320\pi
588588 0 0
589589 5.23550 0.00888879
590590 0 0
591591 0 0
592592 0 0
593593 −213.831 −0.360593 −0.180296 0.983612i 0.557706π-0.557706\pi
−0.180296 + 0.983612i 0.557706π0.557706\pi
594594 0 0
595595 49.7645 + 16.6424i 0.0836378 + 0.0279704i
596596 0 0
597597 0 0
598598 0 0
599599 915.493i 1.52837i −0.644998 0.764184i 0.723142π-0.723142\pi
0.644998 0.764184i 0.276858π-0.276858\pi
600600 0 0
601601 479.426 0.797714 0.398857 0.917013i 0.369407π-0.369407\pi
0.398857 + 0.917013i 0.369407π0.369407\pi
602602 0 0
603603 0 0
604604 0 0
605605 −183.042 + 547.336i −0.302548 + 0.904688i
606606 0 0
607607 219.893i 0.362261i −0.983459 0.181131i 0.942024π-0.942024\pi
0.983459 0.181131i 0.0579757π-0.0579757\pi
608608 0 0
609609 0 0
610610 0 0
611611 470.210i 0.769575i
612612 0 0
613613 862.066i 1.40631i 0.711038 + 0.703154i 0.248225π0.248225\pi
−0.711038 + 0.703154i 0.751775π0.751775\pi
614614 0 0
615615 0 0
616616 0 0
617617 695.423 1.12710 0.563552 0.826080i 0.309434π-0.309434\pi
0.563552 + 0.826080i 0.309434π0.309434\pi
618618 0 0
619619 512.073 0.827259 0.413629 0.910445i 0.364261π-0.364261\pi
0.413629 + 0.910445i 0.364261π0.364261\pi
620620 0 0
621621 0 0
622622 0 0
623623 111.878 0.179580
624624 0 0
625625 172.647 + 600.681i 0.276235 + 0.961090i
626626 0 0
627627 0 0
628628 0 0
629629 907.020i 1.44200i
630630 0 0
631631 643.375 1.01961 0.509806 0.860290i 0.329717π-0.329717\pi
0.509806 + 0.860290i 0.329717π0.329717\pi
632632 0 0
633633 0 0
634634 0 0
635635 −634.108 212.060i −0.998595 0.333953i
636636 0 0
637637 284.829i 0.447141i
638638 0 0
639639 0 0
640640 0 0
641641 196.925i 0.307215i 0.988132 + 0.153608i 0.0490892π0.0490892\pi
−0.988132 + 0.153608i 0.950911π0.950911\pi
642642 0 0
643643 236.954i 0.368513i 0.982878 + 0.184256i 0.0589877π0.0589877\pi
−0.982878 + 0.184256i 0.941012π0.941012\pi
644644 0 0
645645 0 0
646646 0 0
647647 −17.3818 −0.0268653 −0.0134326 0.999910i 0.504276π-0.504276\pi
−0.0134326 + 0.999910i 0.504276π0.504276\pi
648648 0 0
649649 563.456 0.868191
650650 0 0
651651 0 0
652652 0 0
653653 −785.704 −1.20322 −0.601611 0.798789i 0.705474π-0.705474\pi
−0.601611 + 0.798789i 0.705474π0.705474\pi
654654 0 0
655655 292.971 + 97.9760i 0.447283 + 0.149582i
656656 0 0
657657 0 0
658658 0 0
659659 498.767i 0.756855i −0.925631 0.378427i 0.876465π-0.876465\pi
0.925631 0.378427i 0.123535π-0.123535\pi
660660 0 0
661661 303.133 0.458597 0.229299 0.973356i 0.426357π-0.426357\pi
0.229299 + 0.973356i 0.426357π0.426357\pi
662662 0 0
663663 0 0
664664 0 0
665665 4.79394 + 1.60320i 0.00720893 + 0.00241083i
666666 0 0
667667 204.805i 0.307055i
668668 0 0
669669 0 0
670670 0 0
671671 1275.32i 1.90062i
672672 0 0
673673 463.133i 0.688163i 0.938940 + 0.344081i 0.111810π0.111810\pi
−0.938940 + 0.344081i 0.888190π0.888190\pi
674674 0 0
675675 0 0
676676 0 0
677677 311.064 0.459474 0.229737 0.973253i 0.426213π-0.426213\pi
0.229737 + 0.973253i 0.426213π0.426213\pi
678678 0 0
679679 −73.7342 −0.108592
680680 0 0
681681 0 0
682682 0 0
683683 −232.009 −0.339691 −0.169846 0.985471i 0.554327π-0.554327\pi
−0.169846 + 0.985471i 0.554327π0.554327\pi
684684 0 0
685685 −259.940 + 777.281i −0.379475 + 1.13472i
686686 0 0
687687 0 0
688688 0 0
689689 375.513i 0.545011i
690690 0 0
691691 552.904 0.800150 0.400075 0.916482i 0.368984π-0.368984\pi
0.400075 + 0.916482i 0.368984π0.368984\pi
692692 0 0
693693 0 0
694694 0 0
695695 −289.009 + 864.204i −0.415841 + 1.24346i
696696 0 0
697697 90.8512i 0.130346i
698698 0 0
699699 0 0
700700 0 0
701701 250.274i 0.357024i 0.983938 + 0.178512i 0.0571284π0.0571284\pi
−0.983938 + 0.178512i 0.942872π0.942872\pi
702702 0 0
703703 87.3755i 0.124290i
704704 0 0
705705 0 0
706706 0 0
707707 40.4508 0.0572147
708708 0 0
709709 1170.57 1.65102 0.825510 0.564388i 0.190888π-0.190888\pi
0.825510 + 0.564388i 0.190888π0.190888\pi
710710 0 0
711711 0 0
712712 0 0
713713 −20.2191 −0.0283578
714714 0 0
715715 −143.677 + 429.627i −0.200947 + 0.600877i
716716 0 0
717717 0 0
718718 0 0
719719 168.127i 0.233834i 0.993142 + 0.116917i 0.0373012π0.0373012\pi
−0.993142 + 0.116917i 0.962699π0.962699\pi
720720 0 0
721721 −104.824 −0.145387
722722 0 0
723723 0 0
724724 0 0
725725 −641.823 + 852.279i −0.885274 + 1.17556i
726726 0 0
727727 382.835i 0.526595i −0.964715 0.263298i 0.915190π-0.915190\pi
0.964715 0.263298i 0.0848101π-0.0848101\pi
728728 0 0
729729 0 0
730730 0 0
731731 529.520i 0.724377i
732732 0 0
733733 1403.08i 1.91416i 0.289819 + 0.957082i 0.406405π0.406405\pi
−0.289819 + 0.957082i 0.593595π0.593595\pi
734734 0 0
735735 0 0
736736 0 0
737737 1368.52 1.85688
738738 0 0
739739 −899.125 −1.21668 −0.608339 0.793677i 0.708164π-0.708164\pi
−0.608339 + 0.793677i 0.708164π0.708164\pi
740740 0 0
741741 0 0
742742 0 0
743743 316.587 0.426093 0.213046 0.977042i 0.431661π-0.431661\pi
0.213046 + 0.977042i 0.431661π0.431661\pi
744744 0 0
745745 −898.749 300.562i −1.20637 0.403439i
746746 0 0
747747 0 0
748748 0 0
749749 5.22837i 0.00698046i
750750 0 0
751751 286.433 0.381402 0.190701 0.981648i 0.438924π-0.438924\pi
0.190701 + 0.981648i 0.438924π0.438924\pi
752752 0 0
753753 0 0
754754 0 0
755755 179.730 537.434i 0.238053 0.711833i
756756 0 0
757757 783.221i 1.03464i 0.855793 + 0.517319i 0.173070π0.173070\pi
−0.855793 + 0.517319i 0.826930π0.826930\pi
758758 0 0
759759 0 0
760760 0 0
761761 1031.91i 1.35599i −0.735064 0.677997i 0.762848π-0.762848\pi
0.735064 0.677997i 0.237152π-0.237152\pi
762762 0 0
763763 88.0933i 0.115456i
764764 0 0
765765 0 0
766766 0 0
767767 215.927 0.281521
768768 0 0
769769 −831.250 −1.08095 −0.540475 0.841360i 0.681755π-0.681755\pi
−0.540475 + 0.841360i 0.681755π0.681755\pi
770770 0 0
771771 0 0
772772 0 0
773773 −395.360 −0.511462 −0.255731 0.966748i 0.582316π-0.582316\pi
−0.255731 + 0.966748i 0.582316π0.582316\pi
774774 0 0
775775 84.1400 + 63.3631i 0.108568 + 0.0817588i
776776 0 0
777777 0 0
778778 0 0
779779 8.75192i 0.0112348i
780780 0 0
781781 1071.69 1.37220
782782 0 0
783783 0 0
784784 0 0
785785 −536.725 179.493i −0.683726 0.228653i
786786 0 0
787787 573.929i 0.729262i 0.931152 + 0.364631i 0.118805π0.118805\pi
−0.931152 + 0.364631i 0.881195π0.881195\pi
788788 0 0
789789 0 0
790790 0 0
791791 24.7542i 0.0312948i
792792 0 0
793793 488.725i 0.616299i
794794 0 0
795795 0 0
796796 0 0
797797 1408.39 1.76712 0.883560 0.468319i 0.155140π-0.155140\pi
0.883560 + 0.468319i 0.155140π0.155140\pi
798798 0 0
799799 −1029.37 −1.28832
800800 0 0
801801 0 0
802802 0 0
803803 1377.99 1.71606
804804 0 0
805805 −18.5139 6.19145i −0.0229986 0.00769124i
806806 0 0
807807 0 0
808808 0 0
809809 105.645i 0.130587i −0.997866 0.0652936i 0.979202π-0.979202\pi
0.997866 0.0652936i 0.0207984π-0.0207984\pi
810810 0 0
811811 1090.81 1.34502 0.672508 0.740090i 0.265217π-0.265217\pi
0.672508 + 0.740090i 0.265217π0.265217\pi
812812 0 0
813813 0 0
814814 0 0
815815 −722.725 241.696i −0.886779 0.296559i
816816 0 0
817817 51.0099i 0.0624357i
818818 0 0
819819 0 0
820820 0 0
821821 851.302i 1.03691i −0.855105 0.518454i 0.826508π-0.826508\pi
0.855105 0.518454i 0.173492π-0.173492\pi
822822 0 0
823823 1120.12i 1.36103i 0.732736 + 0.680513i 0.238243π0.238243\pi
−0.732736 + 0.680513i 0.761757π0.761757\pi
824824 0 0
825825 0 0
826826 0 0
827827 1214.63 1.46871 0.734357 0.678763i 0.237484π-0.237484\pi
0.734357 + 0.678763i 0.237484π0.237484\pi
828828 0 0
829829 1495.22 1.80364 0.901821 0.432111i 0.142231π-0.142231\pi
0.901821 + 0.432111i 0.142231π0.142231\pi
830830 0 0
831831 0 0
832832 0 0
833833 −623.537 −0.748544
834834 0 0
835835 −167.860 + 501.940i −0.201030 + 0.601125i
836836 0 0
837837 0 0
838838 0 0
839839 463.865i 0.552879i 0.961031 + 0.276439i 0.0891545π0.0891545\pi
−0.961031 + 0.276439i 0.910846π0.910846\pi
840840 0 0
841841 −980.308 −1.16565
842842 0 0
843843 0 0
844844 0 0
845845 212.938 636.734i 0.251998 0.753531i
846846 0 0
847847 93.9081i 0.110871i
848848 0 0
849849 0 0
850850 0 0
851851 337.438i 0.396519i
852852 0 0
853853 495.850i 0.581301i 0.956829 + 0.290651i 0.0938717π0.0938717\pi
−0.956829 + 0.290651i 0.906128π0.906128\pi
854854 0 0
855855 0 0
856856 0 0
857857 1704.43 1.98884 0.994418 0.105511i 0.0336478π-0.0336478\pi
0.994418 + 0.105511i 0.0336478π0.0336478\pi
858858 0 0
859859 207.523 0.241586 0.120793 0.992678i 0.461456π-0.461456\pi
0.120793 + 0.992678i 0.461456π0.461456\pi
860860 0 0
861861 0 0
862862 0 0
863863 −117.426 −0.136068 −0.0680338 0.997683i 0.521673π-0.521673\pi
−0.0680338 + 0.997683i 0.521673π0.521673\pi
864864 0 0
865865 174.456 521.663i 0.201683 0.603079i
866866 0 0
867867 0 0
868868 0 0
869869 2061.87i 2.37270i
870870 0 0
871871 524.442 0.602115
872872 0 0
873873 0 0
874874 0 0
875875 57.6408 + 83.7842i 0.0658752 + 0.0957534i
876876 0 0
877877 908.637i 1.03607i −0.855358 0.518037i 0.826663π-0.826663\pi
0.855358 0.518037i 0.173337π-0.173337\pi
878878 0 0
879879 0 0
880880 0 0
881881 1226.54i 1.39221i 0.717941 + 0.696104i 0.245085π0.245085\pi
−0.717941 + 0.696104i 0.754915π0.754915\pi
882882 0 0
883883 760.022i 0.860728i −0.902656 0.430364i 0.858385π-0.858385\pi
0.902656 0.430364i 0.141615π-0.141615\pi
884884 0 0
885885 0 0
886886 0 0
887887 597.542 0.673667 0.336833 0.941564i 0.390644π-0.390644\pi
0.336833 + 0.941564i 0.390644π0.390644\pi
888888 0 0
889889 −108.796 −0.122380
890890 0 0
891891 0 0
892892 0 0
893893 −99.1615 −0.111043
894894 0 0
895895 561.470 + 187.768i 0.627341 + 0.209797i
896896 0 0
897897 0 0
898898 0 0
899899 179.806i 0.200007i
900900 0 0
901901 −822.058 −0.912384
902902 0 0
903903 0 0
904904 0 0
905905 273.385 817.483i 0.302083 0.903296i
906906 0 0
907907 1708.26i 1.88341i 0.336435 + 0.941707i 0.390779π0.390779\pi
−0.336435 + 0.941707i 0.609221π0.609221\pi
908908 0 0
909909 0 0
910910 0 0
911911 1432.15i 1.57206i 0.618187 + 0.786031i 0.287868π0.287868\pi
−0.618187 + 0.786031i 0.712132π0.712132\pi
912912 0 0
913913 1676.38i 1.83612i
914914 0 0
915915 0 0
916916 0 0
917917 50.2658 0.0548155
918918 0 0
919919 244.398 0.265939 0.132969 0.991120i 0.457549π-0.457549\pi
0.132969 + 0.991120i 0.457549π0.457549\pi
920920 0 0
921921 0 0
922922 0 0
923923 410.692 0.444954
924924 0 0
925925 −1057.47 + 1404.22i −1.14321 + 1.51807i
926926 0 0
927927 0 0
928928 0 0
929929 376.003i 0.404740i 0.979309 + 0.202370i 0.0648643π0.0648643\pi
−0.979309 + 0.202370i 0.935136π0.935136\pi
930930 0 0
931931 −60.0669 −0.0645187
932932 0 0
933933 0 0
934934 0 0
935935 −940.524 314.532i −1.00591 0.336398i
936936 0 0
937937 412.076i 0.439782i 0.975524 + 0.219891i 0.0705701π0.0705701\pi
−0.975524 + 0.219891i 0.929430π0.929430\pi
938938 0 0
939939 0 0
940940 0 0
941941 334.579i 0.355556i −0.984071 0.177778i 0.943109π-0.943109\pi
0.984071 0.177778i 0.0568910π-0.0568910\pi
942942 0 0
943943 33.7993i 0.0358423i
944944 0 0
945945 0 0
946946 0 0
947947 −611.132 −0.645335 −0.322667 0.946512i 0.604580π-0.604580\pi
−0.322667 + 0.946512i 0.604580π0.604580\pi
948948 0 0
949949 528.073 0.556452
950950 0 0
951951 0 0
952952 0 0
953953 −1445.17 −1.51644 −0.758221 0.651997i 0.773931π-0.773931\pi
−0.758221 + 0.651997i 0.773931π0.773931\pi
954954 0 0
955955 1372.26 + 458.916i 1.43693 + 0.480540i
956956 0 0
957957 0 0
958958 0 0
959959 133.360i 0.139062i
960960 0 0
961961 −943.249 −0.981529
962962 0 0
963963 0 0
964964 0 0
965965 −606.167 202.716i −0.628152 0.210068i
966966 0 0
967967 1183.07i 1.22344i 0.791073 + 0.611721i 0.209523π0.209523\pi
−0.791073 + 0.611721i 0.790477π0.790477\pi
968968 0 0
969969 0 0
970970 0 0
971971 1444.94i 1.48810i 0.668124 + 0.744050i 0.267097π0.267097\pi
−0.668124 + 0.744050i 0.732903π0.732903\pi
972972 0 0
973973 148.274i 0.152388i
974974 0 0
975975 0 0
976976 0 0
977977 −1246.51 −1.27586 −0.637929 0.770095i 0.720209π-0.720209\pi
−0.637929 + 0.770095i 0.720209π0.720209\pi
978978 0 0
979979 −2114.44 −2.15979
980980 0 0
981981 0 0
982982 0 0
983983 −144.005 −0.146495 −0.0732477 0.997314i 0.523336π-0.523336\pi
−0.0732477 + 0.997314i 0.523336π0.523336\pi
984984 0 0
985985 444.677 1329.69i 0.451449 1.34994i
986986 0 0
987987 0 0
988988 0 0
989989 196.997i 0.199188i
990990 0 0
991991 −725.742 −0.732333 −0.366167 0.930549i 0.619330π-0.619330\pi
−0.366167 + 0.930549i 0.619330π0.619330\pi
992992 0 0
993993 0 0
994994 0 0
995995 −248.059 + 741.753i −0.249305 + 0.745480i
996996 0 0
997997 881.323i 0.883975i 0.897021 + 0.441987i 0.145726π0.145726\pi
−0.897021 + 0.441987i 0.854274π0.854274\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 2160.3.c.m.1889.1 4
3.2 odd 2 2160.3.c.g.1889.4 4
4.3 odd 2 270.3.b.d.269.1 yes 4
5.4 even 2 2160.3.c.g.1889.3 4
12.11 even 2 270.3.b.a.269.4 yes 4
15.14 odd 2 inner 2160.3.c.m.1889.2 4
20.3 even 4 1350.3.d.o.701.7 8
20.7 even 4 1350.3.d.o.701.2 8
20.19 odd 2 270.3.b.a.269.3 4
36.7 odd 6 810.3.j.a.539.4 8
36.11 even 6 810.3.j.f.539.1 8
36.23 even 6 810.3.j.f.269.2 8
36.31 odd 6 810.3.j.a.269.3 8
60.23 odd 4 1350.3.d.o.701.3 8
60.47 odd 4 1350.3.d.o.701.6 8
60.59 even 2 270.3.b.d.269.2 yes 4
180.59 even 6 810.3.j.a.269.4 8
180.79 odd 6 810.3.j.f.539.2 8
180.119 even 6 810.3.j.a.539.3 8
180.139 odd 6 810.3.j.f.269.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.3.b.a.269.3 4 20.19 odd 2
270.3.b.a.269.4 yes 4 12.11 even 2
270.3.b.d.269.1 yes 4 4.3 odd 2
270.3.b.d.269.2 yes 4 60.59 even 2
810.3.j.a.269.3 8 36.31 odd 6
810.3.j.a.269.4 8 180.59 even 6
810.3.j.a.539.3 8 180.119 even 6
810.3.j.a.539.4 8 36.7 odd 6
810.3.j.f.269.1 8 180.139 odd 6
810.3.j.f.269.2 8 36.23 even 6
810.3.j.f.539.1 8 36.11 even 6
810.3.j.f.539.2 8 180.79 odd 6
1350.3.d.o.701.2 8 20.7 even 4
1350.3.d.o.701.3 8 60.23 odd 4
1350.3.d.o.701.6 8 60.47 odd 4
1350.3.d.o.701.7 8 20.3 even 4
2160.3.c.g.1889.3 4 5.4 even 2
2160.3.c.g.1889.4 4 3.2 odd 2
2160.3.c.m.1889.1 4 1.1 even 1 trivial
2160.3.c.m.1889.2 4 15.14 odd 2 inner