Properties

Label 800.4.a.p.1.1
Level 800800
Weight 44
Character 800.1
Self dual yes
Analytic conductor 47.20247.202
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] = [800,4,Mod(1,800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("800.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 800=2552 800 = 2^{5} \cdot 5^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 800.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 47.201528004647.2015280046
Analytic rank: 00
Dimension: 22
Coefficient field: Q(10)\Q(\sqrt{10})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x210 x^{2} - 10 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 160)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 3.16228-3.16228 of defining polynomial
Character χ\chi == 800.1

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) == q6.32456q318.9737q7+13.0000q912.6491q1138.0000q1334.0000q17101.193q19+120.000q2182.2192q23+88.5438q27+270.000q29341.526q31+80.0000q33206.000q37+240.333q39270.000q41537.587q43+132.816q47+17.0000q49+215.035q51+258.000q53+640.000q5775.8947q59250.000q61246.658q63+815.868q67+520.000q69645.105q71+1078.00q73+240.000q77278.280q79911.000q81+1106.80q831707.63q87+890.000q89+720.999q91+2160.00q93+254.000q97164.438q99+O(q100)q-6.32456 q^{3} -18.9737 q^{7} +13.0000 q^{9} -12.6491 q^{11} -38.0000 q^{13} -34.0000 q^{17} -101.193 q^{19} +120.000 q^{21} -82.2192 q^{23} +88.5438 q^{27} +270.000 q^{29} -341.526 q^{31} +80.0000 q^{33} -206.000 q^{37} +240.333 q^{39} -270.000 q^{41} -537.587 q^{43} +132.816 q^{47} +17.0000 q^{49} +215.035 q^{51} +258.000 q^{53} +640.000 q^{57} -75.8947 q^{59} -250.000 q^{61} -246.658 q^{63} +815.868 q^{67} +520.000 q^{69} -645.105 q^{71} +1078.00 q^{73} +240.000 q^{77} -278.280 q^{79} -911.000 q^{81} +1106.80 q^{83} -1707.63 q^{87} +890.000 q^{89} +720.999 q^{91} +2160.00 q^{93} +254.000 q^{97} -164.438 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+26q976q1368q17+240q21+540q29+160q33412q37540q41+34q49+516q53+1280q57500q61+1040q69+2156q73+480q771822q81++508q97+O(q100) 2 q + 26 q^{9} - 76 q^{13} - 68 q^{17} + 240 q^{21} + 540 q^{29} + 160 q^{33} - 412 q^{37} - 540 q^{41} + 34 q^{49} + 516 q^{53} + 1280 q^{57} - 500 q^{61} + 1040 q^{69} + 2156 q^{73} + 480 q^{77} - 1822 q^{81}+ \cdots + 508 q^{97}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 −6.32456 −1.21716 −0.608581 0.793492i 0.708261π-0.708261\pi
−0.608581 + 0.793492i 0.708261π0.708261\pi
44 0 0
55 0 0
66 0 0
77 −18.9737 −1.02448 −0.512241 0.858842i 0.671184π-0.671184\pi
−0.512241 + 0.858842i 0.671184π0.671184\pi
88 0 0
99 13.0000 0.481481
1010 0 0
1111 −12.6491 −0.346714 −0.173357 0.984859i 0.555461π-0.555461\pi
−0.173357 + 0.984859i 0.555461π0.555461\pi
1212 0 0
1313 −38.0000 −0.810716 −0.405358 0.914158i 0.632853π-0.632853\pi
−0.405358 + 0.914158i 0.632853π0.632853\pi
1414 0 0
1515 0 0
1616 0 0
1717 −34.0000 −0.485071 −0.242536 0.970143i 0.577979π-0.577979\pi
−0.242536 + 0.970143i 0.577979π0.577979\pi
1818 0 0
1919 −101.193 −1.22185 −0.610927 0.791687i 0.709203π-0.709203\pi
−0.610927 + 0.791687i 0.709203π0.709203\pi
2020 0 0
2121 120.000 1.24696
2222 0 0
2323 −82.2192 −0.745387 −0.372693 0.927955i 0.621566π-0.621566\pi
−0.372693 + 0.927955i 0.621566π0.621566\pi
2424 0 0
2525 0 0
2626 0 0
2727 88.5438 0.631121
2828 0 0
2929 270.000 1.72889 0.864444 0.502729i 0.167671π-0.167671\pi
0.864444 + 0.502729i 0.167671π0.167671\pi
3030 0 0
3131 −341.526 −1.97871 −0.989353 0.145537i 0.953509π-0.953509\pi
−0.989353 + 0.145537i 0.953509π0.953509\pi
3232 0 0
3333 80.0000 0.422006
3434 0 0
3535 0 0
3636 0 0
3737 −206.000 −0.915302 −0.457651 0.889132i 0.651309π-0.651309\pi
−0.457651 + 0.889132i 0.651309π0.651309\pi
3838 0 0
3939 240.333 0.986772
4040 0 0
4141 −270.000 −1.02846 −0.514231 0.857652i 0.671922π-0.671922\pi
−0.514231 + 0.857652i 0.671922π0.671922\pi
4242 0 0
4343 −537.587 −1.90654 −0.953271 0.302117i 0.902307π-0.902307\pi
−0.953271 + 0.302117i 0.902307π0.902307\pi
4444 0 0
4545 0 0
4646 0 0
4747 132.816 0.412195 0.206097 0.978531i 0.433924π-0.433924\pi
0.206097 + 0.978531i 0.433924π0.433924\pi
4848 0 0
4949 17.0000 0.0495627
5050 0 0
5151 215.035 0.590410
5252 0 0
5353 258.000 0.668661 0.334330 0.942456i 0.391490π-0.391490\pi
0.334330 + 0.942456i 0.391490π0.391490\pi
5454 0 0
5555 0 0
5656 0 0
5757 640.000 1.48719
5858 0 0
5959 −75.8947 −0.167469 −0.0837343 0.996488i 0.526685π-0.526685\pi
−0.0837343 + 0.996488i 0.526685π0.526685\pi
6060 0 0
6161 −250.000 −0.524741 −0.262371 0.964967i 0.584504π-0.584504\pi
−0.262371 + 0.964967i 0.584504π0.584504\pi
6262 0 0
6363 −246.658 −0.493269
6464 0 0
6565 0 0
6666 0 0
6767 815.868 1.48767 0.743837 0.668362i 0.233004π-0.233004\pi
0.743837 + 0.668362i 0.233004π0.233004\pi
6868 0 0
6969 520.000 0.907256
7070 0 0
7171 −645.105 −1.07831 −0.539154 0.842207i 0.681256π-0.681256\pi
−0.539154 + 0.842207i 0.681256π0.681256\pi
7272 0 0
7373 1078.00 1.72836 0.864181 0.503182i 0.167837π-0.167837\pi
0.864181 + 0.503182i 0.167837π0.167837\pi
7474 0 0
7575 0 0
7676 0 0
7777 240.000 0.355202
7878 0 0
7979 −278.280 −0.396316 −0.198158 0.980170i 0.563496π-0.563496\pi
−0.198158 + 0.980170i 0.563496π0.563496\pi
8080 0 0
8181 −911.000 −1.24966
8282 0 0
8383 1106.80 1.46370 0.731848 0.681468i 0.238658π-0.238658\pi
0.731848 + 0.681468i 0.238658π0.238658\pi
8484 0 0
8585 0 0
8686 0 0
8787 −1707.63 −2.10434
8888 0 0
8989 890.000 1.06000 0.529999 0.847998i 0.322192π-0.322192\pi
0.529999 + 0.847998i 0.322192π0.322192\pi
9090 0 0
9191 720.999 0.830563
9292 0 0
9393 2160.00 2.40840
9494 0 0
9595 0 0
9696 0 0
9797 254.000 0.265874 0.132937 0.991124i 0.457559π-0.457559\pi
0.132937 + 0.991124i 0.457559π0.457559\pi
9898 0 0
9999 −164.438 −0.166936
100100 0 0
101101 598.000 0.589141 0.294570 0.955630i 0.404823π-0.404823\pi
0.294570 + 0.955630i 0.404823π0.404823\pi
102102 0 0
103103 499.640 0.477971 0.238985 0.971023i 0.423185π-0.423185\pi
0.238985 + 0.971023i 0.423185π0.423185\pi
104104 0 0
105105 0 0
106106 0 0
107107 −626.131 −0.565704 −0.282852 0.959164i 0.591281π-0.591281\pi
−0.282852 + 0.959164i 0.591281π0.591281\pi
108108 0 0
109109 854.000 0.750444 0.375222 0.926935i 0.377567π-0.377567\pi
0.375222 + 0.926935i 0.377567π0.377567\pi
110110 0 0
111111 1302.86 1.11407
112112 0 0
113113 −1698.00 −1.41358 −0.706789 0.707424i 0.749857π-0.749857\pi
−0.706789 + 0.707424i 0.749857π0.749857\pi
114114 0 0
115115 0 0
116116 0 0
117117 −494.000 −0.390345
118118 0 0
119119 645.105 0.496947
120120 0 0
121121 −1171.00 −0.879790
122122 0 0
123123 1707.63 1.25180
124124 0 0
125125 0 0
126126 0 0
127127 234.009 0.163503 0.0817516 0.996653i 0.473949π-0.473949\pi
0.0817516 + 0.996653i 0.473949π0.473949\pi
128128 0 0
129129 3400.00 2.32057
130130 0 0
131131 1732.93 1.15578 0.577888 0.816116i 0.303877π-0.303877\pi
0.577888 + 0.816116i 0.303877π0.303877\pi
132132 0 0
133133 1920.00 1.25177
134134 0 0
135135 0 0
136136 0 0
137137 −1546.00 −0.964115 −0.482057 0.876140i 0.660110π-0.660110\pi
−0.482057 + 0.876140i 0.660110π0.660110\pi
138138 0 0
139139 328.877 0.200683 0.100342 0.994953i 0.468006π-0.468006\pi
0.100342 + 0.994953i 0.468006π0.468006\pi
140140 0 0
141141 −840.000 −0.501708
142142 0 0
143143 480.666 0.281086
144144 0 0
145145 0 0
146146 0 0
147147 −107.517 −0.0603258
148148 0 0
149149 3246.00 1.78472 0.892358 0.451328i 0.149050π-0.149050\pi
0.892358 + 0.451328i 0.149050π0.149050\pi
150150 0 0
151151 −1505.24 −0.811225 −0.405613 0.914045i 0.632942π-0.632942\pi
−0.405613 + 0.914045i 0.632942π0.632942\pi
152152 0 0
153153 −442.000 −0.233553
154154 0 0
155155 0 0
156156 0 0
157157 1226.00 0.623219 0.311610 0.950210i 0.399132π-0.399132\pi
0.311610 + 0.950210i 0.399132π0.399132\pi
158158 0 0
159159 −1631.74 −0.813868
160160 0 0
161161 1560.00 0.763635
162162 0 0
163163 −1448.32 −0.695960 −0.347980 0.937502i 0.613132π-0.613132\pi
−0.347980 + 0.937502i 0.613132π0.613132\pi
164164 0 0
165165 0 0
166166 0 0
167167 2333.76 1.08139 0.540694 0.841219i 0.318162π-0.318162\pi
0.540694 + 0.841219i 0.318162π0.318162\pi
168168 0 0
169169 −753.000 −0.342740
170170 0 0
171171 −1315.51 −0.588300
172172 0 0
173173 3098.00 1.36148 0.680742 0.732524i 0.261658π-0.261658\pi
0.680742 + 0.732524i 0.261658π0.261658\pi
174174 0 0
175175 0 0
176176 0 0
177177 480.000 0.203836
178178 0 0
179179 2352.73 0.982411 0.491206 0.871044i 0.336556π-0.336556\pi
0.491206 + 0.871044i 0.336556π0.336556\pi
180180 0 0
181181 2182.00 0.896060 0.448030 0.894019i 0.352126π-0.352126\pi
0.448030 + 0.894019i 0.352126π0.352126\pi
182182 0 0
183183 1581.14 0.638695
184184 0 0
185185 0 0
186186 0 0
187187 430.070 0.168181
188188 0 0
189189 −1680.00 −0.646572
190190 0 0
191191 3023.14 1.14527 0.572635 0.819810i 0.305921π-0.305921\pi
0.572635 + 0.819810i 0.305921π0.305921\pi
192192 0 0
193193 −1298.00 −0.484104 −0.242052 0.970263i 0.577820π-0.577820\pi
−0.242052 + 0.970263i 0.577820π0.577820\pi
194194 0 0
195195 0 0
196196 0 0
197197 −2846.00 −1.02928 −0.514642 0.857405i 0.672075π-0.672075\pi
−0.514642 + 0.857405i 0.672075π0.672075\pi
198198 0 0
199199 3592.35 1.27967 0.639836 0.768511i 0.279002π-0.279002\pi
0.639836 + 0.768511i 0.279002π0.279002\pi
200200 0 0
201201 −5160.00 −1.81074
202202 0 0
203203 −5122.89 −1.77121
204204 0 0
205205 0 0
206206 0 0
207207 −1068.85 −0.358890
208208 0 0
209209 1280.00 0.423634
210210 0 0
211211 −4186.86 −1.36604 −0.683021 0.730398i 0.739334π-0.739334\pi
−0.683021 + 0.730398i 0.739334π0.739334\pi
212212 0 0
213213 4080.00 1.31247
214214 0 0
215215 0 0
216216 0 0
217217 6480.00 2.02715
218218 0 0
219219 −6817.87 −2.10369
220220 0 0
221221 1292.00 0.393255
222222 0 0
223223 −4762.39 −1.43010 −0.715052 0.699071i 0.753597π-0.753597\pi
−0.715052 + 0.699071i 0.753597π0.753597\pi
224224 0 0
225225 0 0
226226 0 0
227227 −1663.36 −0.486348 −0.243174 0.969983i 0.578189π-0.578189\pi
−0.243174 + 0.969983i 0.578189π0.578189\pi
228228 0 0
229229 −1050.00 −0.302995 −0.151498 0.988458i 0.548410π-0.548410\pi
−0.151498 + 0.988458i 0.548410π0.548410\pi
230230 0 0
231231 −1517.89 −0.432338
232232 0 0
233233 −2778.00 −0.781085 −0.390543 0.920585i 0.627713π-0.627713\pi
−0.390543 + 0.920585i 0.627713π0.627713\pi
234234 0 0
235235 0 0
236236 0 0
237237 1760.00 0.482381
238238 0 0
239239 −2555.12 −0.691536 −0.345768 0.938320i 0.612382π-0.612382\pi
−0.345768 + 0.938320i 0.612382π0.612382\pi
240240 0 0
241241 −5350.00 −1.42997 −0.714987 0.699138i 0.753567π-0.753567\pi
−0.714987 + 0.699138i 0.753567π0.753567\pi
242242 0 0
243243 3370.99 0.889913
244244 0 0
245245 0 0
246246 0 0
247247 3845.33 0.990577
248248 0 0
249249 −7000.00 −1.78155
250250 0 0
251251 −5881.84 −1.47912 −0.739558 0.673093i 0.764966π-0.764966\pi
−0.739558 + 0.673093i 0.764966π0.764966\pi
252252 0 0
253253 1040.00 0.258436
254254 0 0
255255 0 0
256256 0 0
257257 −1074.00 −0.260678 −0.130339 0.991469i 0.541607π-0.541607\pi
−0.130339 + 0.991469i 0.541607π0.541607\pi
258258 0 0
259259 3908.58 0.937711
260260 0 0
261261 3510.00 0.832427
262262 0 0
263263 1486.27 0.348469 0.174235 0.984704i 0.444255π-0.444255\pi
0.174235 + 0.984704i 0.444255π0.444255\pi
264264 0 0
265265 0 0
266266 0 0
267267 −5628.85 −1.29019
268268 0 0
269269 406.000 0.0920233 0.0460116 0.998941i 0.485349π-0.485349\pi
0.0460116 + 0.998941i 0.485349π0.485349\pi
270270 0 0
271271 392.122 0.0878957 0.0439479 0.999034i 0.486006π-0.486006\pi
0.0439479 + 0.999034i 0.486006π0.486006\pi
272272 0 0
273273 −4560.00 −1.01093
274274 0 0
275275 0 0
276276 0 0
277277 −5934.00 −1.28715 −0.643573 0.765385i 0.722549π-0.722549\pi
−0.643573 + 0.765385i 0.722549π0.722549\pi
278278 0 0
279279 −4439.84 −0.952710
280280 0 0
281281 −1870.00 −0.396992 −0.198496 0.980102i 0.563606π-0.563606\pi
−0.198496 + 0.980102i 0.563606π0.563606\pi
282282 0 0
283283 −4888.88 −1.02690 −0.513452 0.858118i 0.671634π-0.671634\pi
−0.513452 + 0.858118i 0.671634π0.671634\pi
284284 0 0
285285 0 0
286286 0 0
287287 5122.89 1.05364
288288 0 0
289289 −3757.00 −0.764706
290290 0 0
291291 −1606.44 −0.323612
292292 0 0
293293 −5198.00 −1.03642 −0.518209 0.855254i 0.673401π-0.673401\pi
−0.518209 + 0.855254i 0.673401π0.673401\pi
294294 0 0
295295 0 0
296296 0 0
297297 −1120.00 −0.218818
298298 0 0
299299 3124.33 0.604297
300300 0 0
301301 10200.0 1.95322
302302 0 0
303303 −3782.08 −0.717079
304304 0 0
305305 0 0
306306 0 0
307307 3750.46 0.697232 0.348616 0.937266i 0.386652π-0.386652\pi
0.348616 + 0.937266i 0.386652π0.386652\pi
308308 0 0
309309 −3160.00 −0.581767
310310 0 0
311311 6261.31 1.14163 0.570814 0.821079i 0.306628π-0.306628\pi
0.570814 + 0.821079i 0.306628π0.306628\pi
312312 0 0
313313 −2218.00 −0.400539 −0.200270 0.979741i 0.564182π-0.564182\pi
−0.200270 + 0.979741i 0.564182π0.564182\pi
314314 0 0
315315 0 0
316316 0 0
317317 −4134.00 −0.732456 −0.366228 0.930525i 0.619351π-0.619351\pi
−0.366228 + 0.930525i 0.619351π0.619351\pi
318318 0 0
319319 −3415.26 −0.599429
320320 0 0
321321 3960.00 0.688553
322322 0 0
323323 3440.56 0.592687
324324 0 0
325325 0 0
326326 0 0
327327 −5401.17 −0.913411
328328 0 0
329329 −2520.00 −0.422286
330330 0 0
331331 11953.4 1.98495 0.992476 0.122443i 0.0390729π-0.0390729\pi
0.992476 + 0.122443i 0.0390729π0.0390729\pi
332332 0 0
333333 −2678.00 −0.440701
334334 0 0
335335 0 0
336336 0 0
337337 8014.00 1.29540 0.647701 0.761895i 0.275731π-0.275731\pi
0.647701 + 0.761895i 0.275731π0.275731\pi
338338 0 0
339339 10739.1 1.72055
340340 0 0
341341 4320.00 0.686044
342342 0 0
343343 6185.42 0.973706
344344 0 0
345345 0 0
346346 0 0
347347 4484.11 0.693716 0.346858 0.937918i 0.387248π-0.387248\pi
0.346858 + 0.937918i 0.387248π0.387248\pi
348348 0 0
349349 910.000 0.139574 0.0697868 0.997562i 0.477768π-0.477768\pi
0.0697868 + 0.997562i 0.477768π0.477768\pi
350350 0 0
351351 −3364.66 −0.511659
352352 0 0
353353 −12962.0 −1.95438 −0.977192 0.212357i 0.931886π-0.931886\pi
−0.977192 + 0.212357i 0.931886π0.931886\pi
354354 0 0
355355 0 0
356356 0 0
357357 −4080.00 −0.604864
358358 0 0
359359 12193.7 1.79265 0.896325 0.443398i 0.146227π-0.146227\pi
0.896325 + 0.443398i 0.146227π0.146227\pi
360360 0 0
361361 3381.00 0.492929
362362 0 0
363363 7406.05 1.07085
364364 0 0
365365 0 0
366366 0 0
367367 −3434.23 −0.488462 −0.244231 0.969717i 0.578536π-0.578536\pi
−0.244231 + 0.969717i 0.578536π0.578536\pi
368368 0 0
369369 −3510.00 −0.495185
370370 0 0
371371 −4895.21 −0.685031
372372 0 0
373373 −4622.00 −0.641603 −0.320802 0.947146i 0.603952π-0.603952\pi
−0.320802 + 0.947146i 0.603952π0.603952\pi
374374 0 0
375375 0 0
376376 0 0
377377 −10260.0 −1.40164
378378 0 0
379379 −8449.61 −1.14519 −0.572595 0.819838i 0.694063π-0.694063\pi
−0.572595 + 0.819838i 0.694063π0.694063\pi
380380 0 0
381381 −1480.00 −0.199010
382382 0 0
383383 1815.15 0.242166 0.121083 0.992642i 0.461363π-0.461363\pi
0.121083 + 0.992642i 0.461363π0.461363\pi
384384 0 0
385385 0 0
386386 0 0
387387 −6988.63 −0.917964
388388 0 0
389389 −11106.0 −1.44755 −0.723774 0.690037i 0.757594π-0.757594\pi
−0.723774 + 0.690037i 0.757594π0.757594\pi
390390 0 0
391391 2795.45 0.361566
392392 0 0
393393 −10960.0 −1.40677
394394 0 0
395395 0 0
396396 0 0
397397 5754.00 0.727418 0.363709 0.931513i 0.381510π-0.381510\pi
0.363709 + 0.931513i 0.381510π0.381510\pi
398398 0 0
399399 −12143.1 −1.52360
400400 0 0
401401 −1118.00 −0.139228 −0.0696138 0.997574i 0.522177π-0.522177\pi
−0.0696138 + 0.997574i 0.522177π0.522177\pi
402402 0 0
403403 12978.0 1.60417
404404 0 0
405405 0 0
406406 0 0
407407 2605.72 0.317348
408408 0 0
409409 −11374.0 −1.37508 −0.687540 0.726146i 0.741310π-0.741310\pi
−0.687540 + 0.726146i 0.741310π0.741310\pi
410410 0 0
411411 9777.76 1.17348
412412 0 0
413413 1440.00 0.171568
414414 0 0
415415 0 0
416416 0 0
417417 −2080.00 −0.244264
418418 0 0
419419 −12674.4 −1.47777 −0.738885 0.673832i 0.764647π-0.764647\pi
−0.738885 + 0.673832i 0.764647π0.764647\pi
420420 0 0
421421 1150.00 0.133130 0.0665648 0.997782i 0.478796π-0.478796\pi
0.0665648 + 0.997782i 0.478796π0.478796\pi
422422 0 0
423423 1726.60 0.198464
424424 0 0
425425 0 0
426426 0 0
427427 4743.42 0.537588
428428 0 0
429429 −3040.00 −0.342127
430430 0 0
431431 1353.45 0.151261 0.0756307 0.997136i 0.475903π-0.475903\pi
0.0756307 + 0.997136i 0.475903π0.475903\pi
432432 0 0
433433 7918.00 0.878787 0.439394 0.898295i 0.355193π-0.355193\pi
0.439394 + 0.898295i 0.355193π0.355193\pi
434434 0 0
435435 0 0
436436 0 0
437437 8320.00 0.910754
438438 0 0
439439 14217.6 1.54572 0.772858 0.634579i 0.218827π-0.218827\pi
0.772858 + 0.634579i 0.218827π0.218827\pi
440440 0 0
441441 221.000 0.0238635
442442 0 0
443443 −10581.0 −1.13480 −0.567401 0.823441i 0.692051π-0.692051\pi
−0.567401 + 0.823441i 0.692051π0.692051\pi
444444 0 0
445445 0 0
446446 0 0
447447 −20529.5 −2.17229
448448 0 0
449449 4474.00 0.470247 0.235124 0.971965i 0.424450π-0.424450\pi
0.235124 + 0.971965i 0.424450π0.424450\pi
450450 0 0
451451 3415.26 0.356582
452452 0 0
453453 9520.00 0.987392
454454 0 0
455455 0 0
456456 0 0
457457 −4154.00 −0.425199 −0.212599 0.977139i 0.568193π-0.568193\pi
−0.212599 + 0.977139i 0.568193π0.568193\pi
458458 0 0
459459 −3010.49 −0.306138
460460 0 0
461461 −11282.0 −1.13982 −0.569908 0.821709i 0.693021π-0.693021\pi
−0.569908 + 0.821709i 0.693021π0.693021\pi
462462 0 0
463463 5458.09 0.547860 0.273930 0.961750i 0.411676π-0.411676\pi
0.273930 + 0.961750i 0.411676π0.411676\pi
464464 0 0
465465 0 0
466466 0 0
467467 3775.76 0.374136 0.187068 0.982347i 0.440102π-0.440102\pi
0.187068 + 0.982347i 0.440102π0.440102\pi
468468 0 0
469469 −15480.0 −1.52409
470470 0 0
471471 −7753.90 −0.758559
472472 0 0
473473 6800.00 0.661024
474474 0 0
475475 0 0
476476 0 0
477477 3354.00 0.321948
478478 0 0
479479 8930.27 0.851847 0.425923 0.904759i 0.359949π-0.359949\pi
0.425923 + 0.904759i 0.359949π0.359949\pi
480480 0 0
481481 7828.00 0.742050
482482 0 0
483483 −9866.31 −0.929467
484484 0 0
485485 0 0
486486 0 0
487487 −2422.30 −0.225390 −0.112695 0.993630i 0.535948π-0.535948\pi
−0.112695 + 0.993630i 0.535948π0.535948\pi
488488 0 0
489489 9160.00 0.847095
490490 0 0
491491 8993.52 0.826623 0.413311 0.910590i 0.364372π-0.364372\pi
0.413311 + 0.910590i 0.364372π0.364372\pi
492492 0 0
493493 −9180.00 −0.838634
494494 0 0
495495 0 0
496496 0 0
497497 12240.0 1.10471
498498 0 0
499499 3541.75 0.317737 0.158868 0.987300i 0.449215π-0.449215\pi
0.158868 + 0.987300i 0.449215π0.449215\pi
500500 0 0
501501 −14760.0 −1.31622
502502 0 0
503503 −2384.36 −0.211358 −0.105679 0.994400i 0.533702π-0.533702\pi
−0.105679 + 0.994400i 0.533702π0.533702\pi
504504 0 0
505505 0 0
506506 0 0
507507 4762.39 0.417170
508508 0 0
509509 2350.00 0.204640 0.102320 0.994752i 0.467373π-0.467373\pi
0.102320 + 0.994752i 0.467373π0.467373\pi
510510 0 0
511511 −20453.6 −1.77067
512512 0 0
513513 −8960.00 −0.771138
514514 0 0
515515 0 0
516516 0 0
517517 −1680.00 −0.142914
518518 0 0
519519 −19593.5 −1.65714
520520 0 0
521521 858.000 0.0721491 0.0360745 0.999349i 0.488515π-0.488515\pi
0.0360745 + 0.999349i 0.488515π0.488515\pi
522522 0 0
523523 −5799.62 −0.484894 −0.242447 0.970165i 0.577950π-0.577950\pi
−0.242447 + 0.970165i 0.577950π0.577950\pi
524524 0 0
525525 0 0
526526 0 0
527527 11611.9 0.959813
528528 0 0
529529 −5407.00 −0.444399
530530 0 0
531531 −986.631 −0.0806330
532532 0 0
533533 10260.0 0.833790
534534 0 0
535535 0 0
536536 0 0
537537 −14880.0 −1.19575
538538 0 0
539539 −215.035 −0.0171841
540540 0 0
541541 20478.0 1.62739 0.813695 0.581292i 0.197453π-0.197453\pi
0.813695 + 0.581292i 0.197453π0.197453\pi
542542 0 0
543543 −13800.2 −1.09065
544544 0 0
545545 0 0
546546 0 0
547547 10429.2 0.815210 0.407605 0.913158i 0.366364π-0.366364\pi
0.407605 + 0.913158i 0.366364π0.366364\pi
548548 0 0
549549 −3250.00 −0.252653
550550 0 0
551551 −27322.1 −2.11245
552552 0 0
553553 5280.00 0.406019
554554 0 0
555555 0 0
556556 0 0
557557 13194.0 1.00368 0.501838 0.864962i 0.332657π-0.332657\pi
0.501838 + 0.864962i 0.332657π0.332657\pi
558558 0 0
559559 20428.3 1.54566
560560 0 0
561561 −2720.00 −0.204703
562562 0 0
563563 −9771.44 −0.731469 −0.365734 0.930719i 0.619182π-0.619182\pi
−0.365734 + 0.930719i 0.619182π0.619182\pi
564564 0 0
565565 0 0
566566 0 0
567567 17285.0 1.28025
568568 0 0
569569 4594.00 0.338472 0.169236 0.985576i 0.445870π-0.445870\pi
0.169236 + 0.985576i 0.445870π0.445870\pi
570570 0 0
571571 −4389.24 −0.321688 −0.160844 0.986980i 0.551422π-0.551422\pi
−0.160844 + 0.986980i 0.551422π0.551422\pi
572572 0 0
573573 −19120.0 −1.39398
574574 0 0
575575 0 0
576576 0 0
577577 14926.0 1.07691 0.538455 0.842654i 0.319008π-0.319008\pi
0.538455 + 0.842654i 0.319008π0.319008\pi
578578 0 0
579579 8209.27 0.589233
580580 0 0
581581 −21000.0 −1.49953
582582 0 0
583583 −3263.47 −0.231834
584584 0 0
585585 0 0
586586 0 0
587587 8101.76 0.569668 0.284834 0.958577i 0.408061π-0.408061\pi
0.284834 + 0.958577i 0.408061π0.408061\pi
588588 0 0
589589 34560.0 2.41769
590590 0 0
591591 17999.7 1.25281
592592 0 0
593593 26958.0 1.86683 0.933417 0.358794i 0.116812π-0.116812\pi
0.933417 + 0.358794i 0.116812π0.116812\pi
594594 0 0
595595 0 0
596596 0 0
597597 −22720.0 −1.55757
598598 0 0
599599 −6349.85 −0.433135 −0.216568 0.976268i 0.569486π-0.569486\pi
−0.216568 + 0.976268i 0.569486π0.569486\pi
600600 0 0
601601 21970.0 1.49114 0.745570 0.666427i 0.232177π-0.232177\pi
0.745570 + 0.666427i 0.232177π0.232177\pi
602602 0 0
603603 10606.3 0.716287
604604 0 0
605605 0 0
606606 0 0
607607 3876.95 0.259243 0.129622 0.991564i 0.458624π-0.458624\pi
0.129622 + 0.991564i 0.458624π0.458624\pi
608608 0 0
609609 32400.0 2.15585
610610 0 0
611611 −5047.00 −0.334173
612612 0 0
613613 −2878.00 −0.189627 −0.0948135 0.995495i 0.530225π-0.530225\pi
−0.0948135 + 0.995495i 0.530225π0.530225\pi
614614 0 0
615615 0 0
616616 0 0
617617 −27354.0 −1.78481 −0.892407 0.451231i 0.850985π-0.850985\pi
−0.892407 + 0.451231i 0.850985π0.850985\pi
618618 0 0
619619 −12547.9 −0.814771 −0.407386 0.913256i 0.633559π-0.633559\pi
−0.407386 + 0.913256i 0.633559π0.633559\pi
620620 0 0
621621 −7280.00 −0.470429
622622 0 0
623623 −16886.6 −1.08595
624624 0 0
625625 0 0
626626 0 0
627627 −8095.43 −0.515631
628628 0 0
629629 7004.00 0.443987
630630 0 0
631631 30876.5 1.94798 0.973988 0.226598i 0.0727605π-0.0727605\pi
0.973988 + 0.226598i 0.0727605π0.0727605\pi
632632 0 0
633633 26480.0 1.66269
634634 0 0
635635 0 0
636636 0 0
637637 −646.000 −0.0401812
638638 0 0
639639 −8386.36 −0.519185
640640 0 0
641641 −9430.00 −0.581065 −0.290532 0.956865i 0.593832π-0.593832\pi
−0.290532 + 0.956865i 0.593832π0.593832\pi
642642 0 0
643643 −9847.33 −0.603952 −0.301976 0.953316i 0.597646π-0.597646\pi
−0.301976 + 0.953316i 0.597646π0.597646\pi
644644 0 0
645645 0 0
646646 0 0
647647 −30048.0 −1.82582 −0.912911 0.408158i 0.866171π-0.866171\pi
−0.912911 + 0.408158i 0.866171π0.866171\pi
648648 0 0
649649 960.000 0.0580636
650650 0 0
651651 −40983.1 −2.46737
652652 0 0
653653 −18742.0 −1.12317 −0.561586 0.827418i 0.689809π-0.689809\pi
−0.561586 + 0.827418i 0.689809π0.689809\pi
654654 0 0
655655 0 0
656656 0 0
657657 14014.0 0.832174
658658 0 0
659659 8323.11 0.491992 0.245996 0.969271i 0.420885π-0.420885\pi
0.245996 + 0.969271i 0.420885π0.420885\pi
660660 0 0
661661 7630.00 0.448975 0.224488 0.974477i 0.427929π-0.427929\pi
0.224488 + 0.974477i 0.427929π0.427929\pi
662662 0 0
663663 −8171.33 −0.478655
664664 0 0
665665 0 0
666666 0 0
667667 −22199.2 −1.28869
668668 0 0
669669 30120.0 1.74067
670670 0 0
671671 3162.28 0.181935
672672 0 0
673673 10878.0 0.623055 0.311528 0.950237i 0.399159π-0.399159\pi
0.311528 + 0.950237i 0.399159π0.399159\pi
674674 0 0
675675 0 0
676676 0 0
677677 −126.000 −0.00715299 −0.00357649 0.999994i 0.501138π-0.501138\pi
−0.00357649 + 0.999994i 0.501138π0.501138\pi
678678 0 0
679679 −4819.31 −0.272383
680680 0 0
681681 10520.0 0.591964
682682 0 0
683683 16412.2 0.919467 0.459734 0.888057i 0.347945π-0.347945\pi
0.459734 + 0.888057i 0.347945π0.347945\pi
684684 0 0
685685 0 0
686686 0 0
687687 6640.78 0.368794
688688 0 0
689689 −9804.00 −0.542094
690690 0 0
691691 13193.0 0.726319 0.363159 0.931727i 0.381698π-0.381698\pi
0.363159 + 0.931727i 0.381698π0.381698\pi
692692 0 0
693693 3120.00 0.171023
694694 0 0
695695 0 0
696696 0 0
697697 9180.00 0.498877
698698 0 0
699699 17569.6 0.950707
700700 0 0
701701 −22010.0 −1.18589 −0.592943 0.805244i 0.702034π-0.702034\pi
−0.592943 + 0.805244i 0.702034π0.702034\pi
702702 0 0
703703 20845.7 1.11837
704704 0 0
705705 0 0
706706 0 0
707707 −11346.3 −0.603564
708708 0 0
709709 550.000 0.0291335 0.0145668 0.999894i 0.495363π-0.495363\pi
0.0145668 + 0.999894i 0.495363π0.495363\pi
710710 0 0
711711 −3617.65 −0.190819
712712 0 0
713713 28080.0 1.47490
714714 0 0
715715 0 0
716716 0 0
717717 16160.0 0.841710
718718 0 0
719719 −17936.4 −0.930343 −0.465171 0.885221i 0.654007π-0.654007\pi
−0.465171 + 0.885221i 0.654007π0.654007\pi
720720 0 0
721721 −9480.00 −0.489672
722722 0 0
723723 33836.4 1.74051
724724 0 0
725725 0 0
726726 0 0
727727 16728.4 0.853403 0.426701 0.904393i 0.359676π-0.359676\pi
0.426701 + 0.904393i 0.359676π0.359676\pi
728728 0 0
729729 3277.00 0.166489
730730 0 0
731731 18278.0 0.924808
732732 0 0
733733 −2422.00 −0.122044 −0.0610222 0.998136i 0.519436π-0.519436\pi
−0.0610222 + 0.998136i 0.519436π0.519436\pi
734734 0 0
735735 0 0
736736 0 0
737737 −10320.0 −0.515797
738738 0 0
739739 −19555.5 −0.973426 −0.486713 0.873562i 0.661804π-0.661804\pi
−0.486713 + 0.873562i 0.661804π0.661804\pi
740740 0 0
741741 −24320.0 −1.20569
742742 0 0
743743 31059.9 1.53362 0.766808 0.641876i 0.221844π-0.221844\pi
0.766808 + 0.641876i 0.221844π0.221844\pi
744744 0 0
745745 0 0
746746 0 0
747747 14388.4 0.704743
748748 0 0
749749 11880.0 0.579554
750750 0 0
751751 12155.8 0.590641 0.295320 0.955398i 0.404574π-0.404574\pi
0.295320 + 0.955398i 0.404574π0.404574\pi
752752 0 0
753753 37200.0 1.80032
754754 0 0
755755 0 0
756756 0 0
757757 19346.0 0.928854 0.464427 0.885611i 0.346260π-0.346260\pi
0.464427 + 0.885611i 0.346260π0.346260\pi
758758 0 0
759759 −6577.54 −0.314558
760760 0 0
761761 −33078.0 −1.57566 −0.787830 0.615893i 0.788795π-0.788795\pi
−0.787830 + 0.615893i 0.788795π0.788795\pi
762762 0 0
763763 −16203.5 −0.768816
764764 0 0
765765 0 0
766766 0 0
767767 2884.00 0.135769
768768 0 0
769769 32530.0 1.52544 0.762719 0.646730i 0.223864π-0.223864\pi
0.762719 + 0.646730i 0.223864π0.223864\pi
770770 0 0
771771 6792.57 0.317287
772772 0 0
773773 12002.0 0.558450 0.279225 0.960226i 0.409922π-0.409922\pi
0.279225 + 0.960226i 0.409922π0.409922\pi
774774 0 0
775775 0 0
776776 0 0
777777 −24720.0 −1.14134
778778 0 0
779779 27322.1 1.25663
780780 0 0
781781 8160.00 0.373864
782782 0 0
783783 23906.8 1.09114
784784 0 0
785785 0 0
786786 0 0
787787 −19954.0 −0.903789 −0.451895 0.892071i 0.649252π-0.649252\pi
−0.451895 + 0.892071i 0.649252π0.649252\pi
788788 0 0
789789 −9400.00 −0.424143
790790 0 0
791791 32217.3 1.44819
792792 0 0
793793 9500.00 0.425416
794794 0 0
795795 0 0
796796 0 0
797797 32666.0 1.45181 0.725903 0.687797i 0.241422π-0.241422\pi
0.725903 + 0.687797i 0.241422π0.241422\pi
798798 0 0
799799 −4515.73 −0.199944
800800 0 0
801801 11570.0 0.510369
802802 0 0
803803 −13635.7 −0.599246
804804 0 0
805805 0 0
806806 0 0
807807 −2567.77 −0.112007
808808 0 0
809809 −23110.0 −1.00433 −0.502166 0.864771i 0.667463π-0.667463\pi
−0.502166 + 0.864771i 0.667463π0.667463\pi
810810 0 0
811811 −35632.5 −1.54282 −0.771411 0.636338i 0.780448π-0.780448\pi
−0.771411 + 0.636338i 0.780448π0.780448\pi
812812 0 0
813813 −2480.00 −0.106983
814814 0 0
815815 0 0
816816 0 0
817817 54400.0 2.32952
818818 0 0
819819 9372.99 0.399901
820820 0 0
821821 −8850.00 −0.376208 −0.188104 0.982149i 0.560234π-0.560234\pi
−0.188104 + 0.982149i 0.560234π0.560234\pi
822822 0 0
823823 −13895.0 −0.588519 −0.294259 0.955726i 0.595073π-0.595073\pi
−0.294259 + 0.955726i 0.595073π0.595073\pi
824824 0 0
825825 0 0
826826 0 0
827827 −35841.3 −1.50704 −0.753520 0.657425i 0.771646π-0.771646\pi
−0.753520 + 0.657425i 0.771646π0.771646\pi
828828 0 0
829829 −23034.0 −0.965023 −0.482511 0.875890i 0.660275π-0.660275\pi
−0.482511 + 0.875890i 0.660275π0.660275\pi
830830 0 0
831831 37529.9 1.56666
832832 0 0
833833 −578.000 −0.0240414
834834 0 0
835835 0 0
836836 0 0
837837 −30240.0 −1.24880
838838 0 0
839839 36960.7 1.52089 0.760444 0.649403i 0.224981π-0.224981\pi
0.760444 + 0.649403i 0.224981π0.224981\pi
840840 0 0
841841 48511.0 1.98905
842842 0 0
843843 11826.9 0.483204
844844 0 0
845845 0 0
846846 0 0
847847 22218.2 0.901328
848848 0 0
849849 30920.0 1.24991
850850 0 0
851851 16937.2 0.682254
852852 0 0
853853 19122.0 0.767555 0.383778 0.923425i 0.374623π-0.374623\pi
0.383778 + 0.923425i 0.374623π0.374623\pi
854854 0 0
855855 0 0
856856 0 0
857857 −17786.0 −0.708936 −0.354468 0.935068i 0.615338π-0.615338\pi
−0.354468 + 0.935068i 0.615338π0.615338\pi
858858 0 0
859859 28713.5 1.14050 0.570251 0.821470i 0.306846π-0.306846\pi
0.570251 + 0.821470i 0.306846π0.306846\pi
860860 0 0
861861 −32400.0 −1.28245
862862 0 0
863863 23748.7 0.936750 0.468375 0.883530i 0.344840π-0.344840\pi
0.468375 + 0.883530i 0.344840π0.344840\pi
864864 0 0
865865 0 0
866866 0 0
867867 23761.4 0.930770
868868 0 0
869869 3520.00 0.137408
870870 0 0
871871 −31003.0 −1.20608
872872 0 0
873873 3302.00 0.128013
874874 0 0
875875 0 0
876876 0 0
877877 7706.00 0.296708 0.148354 0.988934i 0.452602π-0.452602\pi
0.148354 + 0.988934i 0.452602π0.452602\pi
878878 0 0
879879 32875.0 1.26149
880880 0 0
881881 10410.0 0.398095 0.199048 0.979990i 0.436215π-0.436215\pi
0.199048 + 0.979990i 0.436215π0.436215\pi
882882 0 0
883883 −26822.4 −1.02225 −0.511125 0.859506i 0.670771π-0.670771\pi
−0.511125 + 0.859506i 0.670771π0.670771\pi
884884 0 0
885885 0 0
886886 0 0
887887 21130.3 0.799873 0.399937 0.916543i 0.369032π-0.369032\pi
0.399937 + 0.916543i 0.369032π0.369032\pi
888888 0 0
889889 −4440.00 −0.167506
890890 0 0
891891 11523.3 0.433273
892892 0 0
893893 −13440.0 −0.503642
894894 0 0
895895 0 0
896896 0 0
897897 −19760.0 −0.735526
898898 0 0
899899 −92212.0 −3.42096
900900 0 0
901901 −8772.00 −0.324348
902902 0 0
903903 −64510.5 −2.37738
904904 0 0
905905 0 0
906906 0 0
907907 −19220.3 −0.703639 −0.351819 0.936068i 0.614437π-0.614437\pi
−0.351819 + 0.936068i 0.614437π0.614437\pi
908908 0 0
909909 7774.00 0.283660
910910 0 0
911911 −39402.0 −1.43298 −0.716491 0.697597i 0.754253π-0.754253\pi
−0.716491 + 0.697597i 0.754253π0.754253\pi
912912 0 0
913913 −14000.0 −0.507483
914914 0 0
915915 0 0
916916 0 0
917917 −32880.0 −1.18407
918918 0 0
919919 −42931.1 −1.54099 −0.770493 0.637449i 0.779990π-0.779990\pi
−0.770493 + 0.637449i 0.779990π0.779990\pi
920920 0 0
921921 −23720.0 −0.848643
922922 0 0
923923 24514.0 0.874201
924924 0 0
925925 0 0
926926 0 0
927927 6495.32 0.230134
928928 0 0
929929 34746.0 1.22710 0.613552 0.789654i 0.289740π-0.289740\pi
0.613552 + 0.789654i 0.289740π0.289740\pi
930930 0 0
931931 −1720.28 −0.0605584
932932 0 0
933933 −39600.0 −1.38955
934934 0 0
935935 0 0
936936 0 0
937937 −21594.0 −0.752876 −0.376438 0.926442i 0.622851π-0.622851\pi
−0.376438 + 0.926442i 0.622851π0.622851\pi
938938 0 0
939939 14027.9 0.487521
940940 0 0
941941 −20018.0 −0.693484 −0.346742 0.937961i 0.612712π-0.612712\pi
−0.346742 + 0.937961i 0.612712π0.612712\pi
942942 0 0
943943 22199.2 0.766601
944944 0 0
945945 0 0
946946 0 0
947947 46150.3 1.58361 0.791807 0.610771i 0.209141π-0.209141\pi
0.791807 + 0.610771i 0.209141π0.209141\pi
948948 0 0
949949 −40964.0 −1.40121
950950 0 0
951951 26145.7 0.891517
952952 0 0
953953 342.000 0.0116248 0.00581242 0.999983i 0.498150π-0.498150\pi
0.00581242 + 0.999983i 0.498150π0.498150\pi
954954 0 0
955955 0 0
956956 0 0
957957 21600.0 0.729602
958958 0 0
959959 29333.3 0.987718
960960 0 0
961961 86849.0 2.91528
962962 0 0
963963 −8139.70 −0.272376
964964 0 0
965965 0 0
966966 0 0
967967 −51728.5 −1.72025 −0.860123 0.510087i 0.829613π-0.829613\pi
−0.860123 + 0.510087i 0.829613π0.829613\pi
968968 0 0
969969 −21760.0 −0.721395
970970 0 0
971971 3099.03 0.102423 0.0512115 0.998688i 0.483692π-0.483692\pi
0.0512115 + 0.998688i 0.483692π0.483692\pi
972972 0 0
973973 −6240.00 −0.205596
974974 0 0
975975 0 0
976976 0 0
977977 −26226.0 −0.858796 −0.429398 0.903115i 0.641274π-0.641274\pi
−0.429398 + 0.903115i 0.641274π0.641274\pi
978978 0 0
979979 −11257.7 −0.367516
980980 0 0
981981 11102.0 0.361325
982982 0 0
983983 11049.0 0.358503 0.179251 0.983803i 0.442632π-0.442632\pi
0.179251 + 0.983803i 0.442632π0.442632\pi
984984 0 0
985985 0 0
986986 0 0
987987 15937.9 0.513990
988988 0 0
989989 44200.0 1.42111
990990 0 0
991991 −45928.9 −1.47223 −0.736115 0.676856i 0.763342π-0.763342\pi
−0.736115 + 0.676856i 0.763342π0.763342\pi
992992 0 0
993993 −75600.0 −2.41601
994994 0 0
995995 0 0
996996 0 0
997997 31026.0 0.985560 0.492780 0.870154i 0.335981π-0.335981\pi
0.492780 + 0.870154i 0.335981π0.335981\pi
998998 0 0
999999 −18240.0 −0.577666
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 800.4.a.p.1.1 2
4.3 odd 2 inner 800.4.a.p.1.2 2
5.2 odd 4 800.4.c.j.449.3 4
5.3 odd 4 800.4.c.j.449.1 4
5.4 even 2 160.4.a.f.1.2 yes 2
8.3 odd 2 1600.4.a.ch.1.1 2
8.5 even 2 1600.4.a.ch.1.2 2
15.14 odd 2 1440.4.a.v.1.2 2
20.3 even 4 800.4.c.j.449.4 4
20.7 even 4 800.4.c.j.449.2 4
20.19 odd 2 160.4.a.f.1.1 2
40.19 odd 2 320.4.a.p.1.2 2
40.29 even 2 320.4.a.p.1.1 2
60.59 even 2 1440.4.a.v.1.1 2
80.19 odd 4 1280.4.d.u.641.1 4
80.29 even 4 1280.4.d.u.641.3 4
80.59 odd 4 1280.4.d.u.641.4 4
80.69 even 4 1280.4.d.u.641.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
160.4.a.f.1.1 2 20.19 odd 2
160.4.a.f.1.2 yes 2 5.4 even 2
320.4.a.p.1.1 2 40.29 even 2
320.4.a.p.1.2 2 40.19 odd 2
800.4.a.p.1.1 2 1.1 even 1 trivial
800.4.a.p.1.2 2 4.3 odd 2 inner
800.4.c.j.449.1 4 5.3 odd 4
800.4.c.j.449.2 4 20.7 even 4
800.4.c.j.449.3 4 5.2 odd 4
800.4.c.j.449.4 4 20.3 even 4
1280.4.d.u.641.1 4 80.19 odd 4
1280.4.d.u.641.2 4 80.69 even 4
1280.4.d.u.641.3 4 80.29 even 4
1280.4.d.u.641.4 4 80.59 odd 4
1440.4.a.v.1.1 2 60.59 even 2
1440.4.a.v.1.2 2 15.14 odd 2
1600.4.a.ch.1.1 2 8.3 odd 2
1600.4.a.ch.1.2 2 8.5 even 2