Properties

Label 800.6.d.d.401.16
Level 800800
Weight 66
Character 800.401
Analytic conductor 128.307128.307
Analytic rank 00
Dimension 2020
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [800,6,Mod(401,800)]
 
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, 1, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("800.401");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 800=2552 800 = 2^{5} \cdot 5^{2}
Weight: k k == 6 6
Character orbit: [χ][\chi] == 800.d (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: 128.307055850128.307055850
Analytic rank: 00
Dimension: 2020
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20x19130x17+144x16+1560x1512320x1456128x13++11 ⁣ ⁣24 x^{20} - x^{19} - 130 x^{17} + 144 x^{16} + 1560 x^{15} - 12320 x^{14} - 56128 x^{13} + \cdots + 11\!\cdots\!24 Copy content Toggle raw display
Coefficient ring: Z[a1,,a19]\Z[a_1, \ldots, a_{19}]
Coefficient ring index: 2995431 2^{99}\cdot 5^{4}\cdot 31
Twist minimal: no (minimal twist has level 200)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 401.16
Root 4.123263.87282i4.12326 - 3.87282i of defining polynomial
Character χ\chi == 800.401
Dual form 800.6.d.d.401.5

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+18.2848iq3+2.25573q791.3327q9419.261iq11106.889iq13+849.098q17+335.414iq19+41.2454iq213541.78q23+2773.20iq275208.57iq295637.83q31+7666.09q3361.9860iq37+1954.44q39+16286.1q41+2417.19iq43+22781.9q4716801.9q49+15525.6iq51+13667.5iq536132.98q57+23407.1iq59+33444.7iq61206.022q63+66162.9iq6764760.7iq69+51421.4q71+21271.6q73945.738iq7738418.7q7972901.2q81+93166.7iq83+95237.5q8760678.0q89241.112iq91103086.iq93+157428.q97+38292.2iq99+O(q100)q+18.2848i q^{3} +2.25573 q^{7} -91.3327 q^{9} -419.261i q^{11} -106.889i q^{13} +849.098 q^{17} +335.414i q^{19} +41.2454i q^{21} -3541.78 q^{23} +2773.20i q^{27} -5208.57i q^{29} -5637.83 q^{31} +7666.09 q^{33} -61.9860i q^{37} +1954.44 q^{39} +16286.1 q^{41} +2417.19i q^{43} +22781.9 q^{47} -16801.9 q^{49} +15525.6i q^{51} +13667.5i q^{53} -6132.98 q^{57} +23407.1i q^{59} +33444.7i q^{61} -206.022 q^{63} +66162.9i q^{67} -64760.7i q^{69} +51421.4 q^{71} +21271.6 q^{73} -945.738i q^{77} -38418.7 q^{79} -72901.2 q^{81} +93166.7i q^{83} +95237.5 q^{87} -60678.0 q^{89} -241.112i q^{91} -103086. i q^{93} +157428. q^{97} +38292.2i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q+196q71620q9+7184q237160q312836q3322452q395804q4144180q47+62652q49+43696q57+1240q63+7724q71105136q73+7780q79+73688q97+O(q100) 20 q + 196 q^{7} - 1620 q^{9} + 7184 q^{23} - 7160 q^{31} - 2836 q^{33} - 22452 q^{39} - 5804 q^{41} - 44180 q^{47} + 62652 q^{49} + 43696 q^{57} + 1240 q^{63} + 7724 q^{71} - 105136 q^{73} + 7780 q^{79}+ \cdots - 73688 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/800Z)×\left(\mathbb{Z}/800\mathbb{Z}\right)^\times.

nn 101101 351351 577577
χ(n)\chi(n) 1-1 11 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 18.2848i 1.17297i 0.809961 + 0.586484i 0.199488π0.199488\pi
−0.809961 + 0.586484i 0.800512π0.800512\pi
44 0 0
55 0 0
66 0 0
77 2.25573 0.0173997 0.00869984 0.999962i 0.497231π-0.497231\pi
0.00869984 + 0.999962i 0.497231π0.497231\pi
88 0 0
99 −91.3327 −0.375855
1010 0 0
1111 − 419.261i − 1.04473i −0.852723 0.522363i 0.825050π-0.825050\pi
0.852723 0.522363i 0.174950π-0.174950\pi
1212 0 0
1313 − 106.889i − 0.175418i −0.996146 0.0877090i 0.972045π-0.972045\pi
0.996146 0.0877090i 0.0279546π-0.0279546\pi
1414 0 0
1515 0 0
1616 0 0
1717 849.098 0.712584 0.356292 0.934375i 0.384041π-0.384041\pi
0.356292 + 0.934375i 0.384041π0.384041\pi
1818 0 0
1919 335.414i 0.213156i 0.994304 + 0.106578i 0.0339894π0.0339894\pi
−0.994304 + 0.106578i 0.966011π0.966011\pi
2020 0 0
2121 41.2454i 0.0204093i
2222 0 0
2323 −3541.78 −1.39605 −0.698027 0.716071i 0.745938π-0.745938\pi
−0.698027 + 0.716071i 0.745938π0.745938\pi
2424 0 0
2525 0 0
2626 0 0
2727 2773.20i 0.732103i
2828 0 0
2929 − 5208.57i − 1.15007i −0.818129 0.575034i 0.804989π-0.804989\pi
0.818129 0.575034i 0.195011π-0.195011\pi
3030 0 0
3131 −5637.83 −1.05368 −0.526839 0.849965i 0.676623π-0.676623\pi
−0.526839 + 0.849965i 0.676623π0.676623\pi
3232 0 0
3333 7666.09 1.22543
3434 0 0
3535 0 0
3636 0 0
3737 − 61.9860i − 0.00744370i −0.999993 0.00372185i 0.998815π-0.998815\pi
0.999993 0.00372185i 0.00118470π-0.00118470\pi
3838 0 0
3939 1954.44 0.205760
4040 0 0
4141 16286.1 1.51306 0.756531 0.653958i 0.226893π-0.226893\pi
0.756531 + 0.653958i 0.226893π0.226893\pi
4242 0 0
4343 2417.19i 0.199361i 0.995020 + 0.0996803i 0.0317820π0.0317820\pi
−0.995020 + 0.0996803i 0.968218π0.968218\pi
4444 0 0
4545 0 0
4646 0 0
4747 22781.9 1.50434 0.752170 0.658970i 0.229007π-0.229007\pi
0.752170 + 0.658970i 0.229007π0.229007\pi
4848 0 0
4949 −16801.9 −0.999697
5050 0 0
5151 15525.6i 0.835838i
5252 0 0
5353 13667.5i 0.668344i 0.942512 + 0.334172i 0.108457π0.108457\pi
−0.942512 + 0.334172i 0.891543π0.891543\pi
5454 0 0
5555 0 0
5656 0 0
5757 −6132.98 −0.250025
5858 0 0
5959 23407.1i 0.875423i 0.899116 + 0.437711i 0.144211π0.144211\pi
−0.899116 + 0.437711i 0.855789π0.855789\pi
6060 0 0
6161 33444.7i 1.15081i 0.817869 + 0.575405i 0.195155π0.195155\pi
−0.817869 + 0.575405i 0.804845π0.804845\pi
6262 0 0
6363 −206.022 −0.00653975
6464 0 0
6565 0 0
6666 0 0
6767 66162.9i 1.80064i 0.435226 + 0.900321i 0.356668π0.356668\pi
−0.435226 + 0.900321i 0.643332π0.643332\pi
6868 0 0
6969 − 64760.7i − 1.63753i
7070 0 0
7171 51421.4 1.21059 0.605296 0.796001i 0.293055π-0.293055\pi
0.605296 + 0.796001i 0.293055π0.293055\pi
7272 0 0
7373 21271.6 0.467189 0.233595 0.972334i 0.424951π-0.424951\pi
0.233595 + 0.972334i 0.424951π0.424951\pi
7474 0 0
7575 0 0
7676 0 0
7777 − 945.738i − 0.0181779i
7878 0 0
7979 −38418.7 −0.692589 −0.346294 0.938126i 0.612560π-0.612560\pi
−0.346294 + 0.938126i 0.612560π0.612560\pi
8080 0 0
8181 −72901.2 −1.23459
8282 0 0
8383 93166.7i 1.48445i 0.670151 + 0.742225i 0.266229π0.266229\pi
−0.670151 + 0.742225i 0.733771π0.733771\pi
8484 0 0
8585 0 0
8686 0 0
8787 95237.5 1.34899
8888 0 0
8989 −60678.0 −0.812000 −0.406000 0.913873i 0.633077π-0.633077\pi
−0.406000 + 0.913873i 0.633077π0.633077\pi
9090 0 0
9191 − 241.112i − 0.00305222i
9292 0 0
9393 − 103086.i − 1.23593i
9494 0 0
9595 0 0
9696 0 0
9797 157428. 1.69884 0.849418 0.527721i 0.176953π-0.176953\pi
0.849418 + 0.527721i 0.176953π0.176953\pi
9898 0 0
9999 38292.2i 0.392665i
100100 0 0
101101 124508.i 1.21449i 0.794516 + 0.607243i 0.207725π0.207725\pi
−0.794516 + 0.607243i 0.792275π0.792275\pi
102102 0 0
103103 10346.4 0.0960938 0.0480469 0.998845i 0.484700π-0.484700\pi
0.0480469 + 0.998845i 0.484700π0.484700\pi
104104 0 0
105105 0 0
106106 0 0
107107 70765.9i 0.597537i 0.954326 + 0.298769i 0.0965758π0.0965758\pi
−0.954326 + 0.298769i 0.903424π0.903424\pi
108108 0 0
109109 − 128453.i − 1.03557i −0.855511 0.517784i 0.826757π-0.826757\pi
0.855511 0.517784i 0.173243π-0.173243\pi
110110 0 0
111111 1133.40 0.00873123
112112 0 0
113113 −115196. −0.848672 −0.424336 0.905505i 0.639492π-0.639492\pi
−0.424336 + 0.905505i 0.639492π0.639492\pi
114114 0 0
115115 0 0
116116 0 0
117117 9762.45i 0.0659317i
118118 0 0
119119 1915.33 0.0123987
120120 0 0
121121 −14728.7 −0.0914537
122122 0 0
123123 297787.i 1.77477i
124124 0 0
125125 0 0
126126 0 0
127127 −146026. −0.803378 −0.401689 0.915776i 0.631577π-0.631577\pi
−0.401689 + 0.915776i 0.631577π0.631577\pi
128128 0 0
129129 −44197.7 −0.233844
130130 0 0
131131 − 12998.0i − 0.0661757i −0.999452 0.0330878i 0.989466π-0.989466\pi
0.999452 0.0330878i 0.0105341π-0.0105341\pi
132132 0 0
133133 756.603i 0.00370885i
134134 0 0
135135 0 0
136136 0 0
137137 189204. 0.861249 0.430624 0.902531i 0.358293π-0.358293\pi
0.430624 + 0.902531i 0.358293π0.358293\pi
138138 0 0
139139 44334.4i 0.194627i 0.995254 + 0.0973136i 0.0310250π0.0310250\pi
−0.995254 + 0.0973136i 0.968975π0.968975\pi
140140 0 0
141141 416562.i 1.76454i
142142 0 0
143143 −44814.3 −0.183264
144144 0 0
145145 0 0
146146 0 0
147147 − 307219.i − 1.17261i
148148 0 0
149149 352240.i 1.29979i 0.760024 + 0.649895i 0.225187π0.225187\pi
−0.760024 + 0.649895i 0.774813π0.774813\pi
150150 0 0
151151 −446273. −1.59279 −0.796395 0.604776i 0.793262π-0.793262\pi
−0.796395 + 0.604776i 0.793262π0.793262\pi
152152 0 0
153153 −77550.5 −0.267828
154154 0 0
155155 0 0
156156 0 0
157157 − 383316.i − 1.24110i −0.784165 0.620552i 0.786909π-0.786909\pi
0.784165 0.620552i 0.213091π-0.213091\pi
158158 0 0
159159 −249907. −0.783946
160160 0 0
161161 −7989.29 −0.0242909
162162 0 0
163163 405200.i 1.19454i 0.802040 + 0.597270i 0.203748π0.203748\pi
−0.802040 + 0.597270i 0.796252π0.796252\pi
164164 0 0
165165 0 0
166166 0 0
167167 193042. 0.535625 0.267812 0.963471i 0.413699π-0.413699\pi
0.267812 + 0.963471i 0.413699π0.413699\pi
168168 0 0
169169 359868. 0.969229
170170 0 0
171171 − 30634.3i − 0.0801157i
172172 0 0
173173 − 599397.i − 1.52265i −0.648372 0.761323i 0.724550π-0.724550\pi
0.648372 0.761323i 0.275450π-0.275450\pi
174174 0 0
175175 0 0
176176 0 0
177177 −427994. −1.02684
178178 0 0
179179 421278.i 0.982736i 0.870952 + 0.491368i 0.163503π0.163503\pi
−0.870952 + 0.491368i 0.836497π0.836497\pi
180180 0 0
181181 183362.i 0.416018i 0.978127 + 0.208009i 0.0666983π0.0666983\pi
−0.978127 + 0.208009i 0.933302π0.933302\pi
182182 0 0
183183 −611529. −1.34986
184184 0 0
185185 0 0
186186 0 0
187187 − 355994.i − 0.744455i
188188 0 0
189189 6255.58i 0.0127384i
190190 0 0
191191 −982533. −1.94878 −0.974392 0.224856i 0.927809π-0.927809\pi
−0.974392 + 0.224856i 0.927809π0.927809\pi
192192 0 0
193193 −164978. −0.318810 −0.159405 0.987213i 0.550958π-0.550958\pi
−0.159405 + 0.987213i 0.550958π0.550958\pi
194194 0 0
195195 0 0
196196 0 0
197197 − 506605.i − 0.930044i −0.885299 0.465022i 0.846046π-0.846046\pi
0.885299 0.465022i 0.153954π-0.153954\pi
198198 0 0
199199 −475645. −0.851433 −0.425716 0.904857i 0.639978π-0.639978\pi
−0.425716 + 0.904857i 0.639978π0.639978\pi
200200 0 0
201201 −1.20977e6 −2.11210
202202 0 0
203203 − 11749.1i − 0.0200108i
204204 0 0
205205 0 0
206206 0 0
207207 323481. 0.524714
208208 0 0
209209 140626. 0.222690
210210 0 0
211211 260466.i 0.402759i 0.979513 + 0.201379i 0.0645424π0.0645424\pi
−0.979513 + 0.201379i 0.935458π0.935458\pi
212212 0 0
213213 940228.i 1.41999i
214214 0 0
215215 0 0
216216 0 0
217217 −12717.4 −0.0183337
218218 0 0
219219 388946.i 0.547998i
220220 0 0
221221 − 90759.2i − 0.125000i
222222 0 0
223223 −624180. −0.840519 −0.420260 0.907404i 0.638061π-0.638061\pi
−0.420260 + 0.907404i 0.638061π0.638061\pi
224224 0 0
225225 0 0
226226 0 0
227227 − 656014.i − 0.844984i −0.906367 0.422492i 0.861155π-0.861155\pi
0.906367 0.422492i 0.138845π-0.138845\pi
228228 0 0
229229 807777.i 1.01790i 0.860798 + 0.508948i 0.169965π0.169965\pi
−0.860798 + 0.508948i 0.830035π0.830035\pi
230230 0 0
231231 17292.6 0.0213221
232232 0 0
233233 −1.30452e6 −1.57421 −0.787103 0.616822i 0.788420π-0.788420\pi
−0.787103 + 0.616822i 0.788420π0.788420\pi
234234 0 0
235235 0 0
236236 0 0
237237 − 702478.i − 0.812385i
238238 0 0
239239 1.21861e6 1.37997 0.689985 0.723824i 0.257617π-0.257617\pi
0.689985 + 0.723824i 0.257617π0.257617\pi
240240 0 0
241241 −983578. −1.09085 −0.545426 0.838159i 0.683632π-0.683632\pi
−0.545426 + 0.838159i 0.683632π0.683632\pi
242242 0 0
243243 − 659093.i − 0.716030i
244244 0 0
245245 0 0
246246 0 0
247247 35852.1 0.0373914
248248 0 0
249249 −1.70353e6 −1.74121
250250 0 0
251251 1.60324e6i 1.60625i 0.595809 + 0.803126i 0.296832π0.296832\pi
−0.595809 + 0.803126i 0.703168π0.703168\pi
252252 0 0
253253 1.48493e6i 1.45849i
254254 0 0
255255 0 0
256256 0 0
257257 1.07709e6 1.01723 0.508617 0.860993i 0.330157π-0.330157\pi
0.508617 + 0.860993i 0.330157π0.330157\pi
258258 0 0
259259 − 139.823i 0 0.000129518i
260260 0 0
261261 475713.i 0.432259i
262262 0 0
263263 812889. 0.724673 0.362336 0.932047i 0.381979π-0.381979\pi
0.362336 + 0.932047i 0.381979π0.381979\pi
264264 0 0
265265 0 0
266266 0 0
267267 − 1.10948e6i − 0.952451i
268268 0 0
269269 − 113957.i − 0.0960201i −0.998847 0.0480101i 0.984712π-0.984712\pi
0.998847 0.0480101i 0.0152880π-0.0152880\pi
270270 0 0
271271 −372728. −0.308297 −0.154148 0.988048i 0.549263π-0.549263\pi
−0.154148 + 0.988048i 0.549263π0.549263\pi
272272 0 0
273273 4408.68 0.00358015
274274 0 0
275275 0 0
276276 0 0
277277 − 914263.i − 0.715932i −0.933735 0.357966i 0.883470π-0.883470\pi
0.933735 0.357966i 0.116530π-0.116530\pi
278278 0 0
279279 514918. 0.396030
280280 0 0
281281 −511184. −0.386199 −0.193100 0.981179i 0.561854π-0.561854\pi
−0.193100 + 0.981179i 0.561854π0.561854\pi
282282 0 0
283283 − 533078.i − 0.395662i −0.980236 0.197831i 0.936610π-0.936610\pi
0.980236 0.197831i 0.0633897π-0.0633897\pi
284284 0 0
285285 0 0
286286 0 0
287287 36736.9 0.0263268
288288 0 0
289289 −698889. −0.492225
290290 0 0
291291 2.87853e6i 1.99268i
292292 0 0
293293 2.54648e6i 1.73289i 0.499273 + 0.866445i 0.333600π0.333600\pi
−0.499273 + 0.866445i 0.666400π0.666400\pi
294294 0 0
295295 0 0
296296 0 0
297297 1.16269e6 0.764847
298298 0 0
299299 378577.i 0.244893i
300300 0 0
301301 5452.51i 0.00346881i
302302 0 0
303303 −2.27659e6 −1.42455
304304 0 0
305305 0 0
306306 0 0
307307 740673.i 0.448518i 0.974530 + 0.224259i 0.0719962π0.0719962\pi
−0.974530 + 0.224259i 0.928004π0.928004\pi
308308 0 0
309309 189181.i 0.112715i
310310 0 0
311311 −1.08876e6 −0.638310 −0.319155 0.947702i 0.603399π-0.603399\pi
−0.319155 + 0.947702i 0.603399π0.603399\pi
312312 0 0
313313 1.08277e6 0.624705 0.312353 0.949966i 0.398883π-0.398883\pi
0.312353 + 0.949966i 0.398883π0.398883\pi
314314 0 0
315315 0 0
316316 0 0
317317 2.93243e6i 1.63900i 0.573078 + 0.819501i 0.305749π0.305749\pi
−0.573078 + 0.819501i 0.694251π0.694251\pi
318318 0 0
319319 −2.18375e6 −1.20151
320320 0 0
321321 −1.29394e6 −0.700892
322322 0 0
323323 284800.i 0.151892i
324324 0 0
325325 0 0
326326 0 0
327327 2.34874e6 1.21469
328328 0 0
329329 51389.8 0.0261750
330330 0 0
331331 357214.i 0.179209i 0.995977 + 0.0896043i 0.0285602π0.0285602\pi
−0.995977 + 0.0896043i 0.971440π0.971440\pi
332332 0 0
333333 5661.34i 0.00279775i
334334 0 0
335335 0 0
336336 0 0
337337 1.45195e6 0.696429 0.348215 0.937415i 0.386788π-0.386788\pi
0.348215 + 0.937415i 0.386788π0.386788\pi
338338 0 0
339339 − 2.10633e6i − 0.995465i
340340 0 0
341341 2.36372e6i 1.10081i
342342 0 0
343343 −75812.5 −0.0347941
344344 0 0
345345 0 0
346346 0 0
347347 393735.i 0.175541i 0.996141 + 0.0877707i 0.0279743π0.0279743\pi
−0.996141 + 0.0877707i 0.972026π0.972026\pi
348348 0 0
349349 1.73875e6i 0.764140i 0.924133 + 0.382070i 0.124789π0.124789\pi
−0.924133 + 0.382070i 0.875211π0.875211\pi
350350 0 0
351351 296424. 0.128424
352352 0 0
353353 −2.05124e6 −0.876154 −0.438077 0.898937i 0.644340π-0.644340\pi
−0.438077 + 0.898937i 0.644340π0.644340\pi
354354 0 0
355355 0 0
356356 0 0
357357 35021.4i 0.0145433i
358358 0 0
359359 −3.56728e6 −1.46084 −0.730418 0.683000i 0.760675π-0.760675\pi
−0.730418 + 0.683000i 0.760675π0.760675\pi
360360 0 0
361361 2.36360e6 0.954564
362362 0 0
363363 − 269311.i − 0.107272i
364364 0 0
365365 0 0
366366 0 0
367367 3.72721e6 1.44450 0.722251 0.691631i 0.243107π-0.243107\pi
0.722251 + 0.691631i 0.243107π0.243107\pi
368368 0 0
369369 −1.48745e6 −0.568691
370370 0 0
371371 30830.2i 0.0116290i
372372 0 0
373373 1.71134e6i 0.636891i 0.947941 + 0.318446i 0.103161π0.103161\pi
−0.947941 + 0.318446i 0.896839π0.896839\pi
374374 0 0
375375 0 0
376376 0 0
377377 −556738. −0.201743
378378 0 0
379379 − 3.60174e6i − 1.28799i −0.765028 0.643997i 0.777275π-0.777275\pi
0.765028 0.643997i 0.222725π-0.222725\pi
380380 0 0
381381 − 2.67005e6i − 0.942337i
382382 0 0
383383 3.80875e6 1.32674 0.663369 0.748293i 0.269126π-0.269126\pi
0.663369 + 0.748293i 0.269126π0.269126\pi
384384 0 0
385385 0 0
386386 0 0
387387 − 220768.i − 0.0749306i
388388 0 0
389389 431800.i 0.144680i 0.997380 + 0.0723401i 0.0230467π0.0230467\pi
−0.997380 + 0.0723401i 0.976953π0.976953\pi
390390 0 0
391391 −3.00732e6 −0.994805
392392 0 0
393393 237665. 0.0776220
394394 0 0
395395 0 0
396396 0 0
397397 2.28465e6i 0.727518i 0.931493 + 0.363759i 0.118507π0.118507\pi
−0.931493 + 0.363759i 0.881493π0.881493\pi
398398 0 0
399399 −13834.3 −0.00435036
400400 0 0
401401 1.63473e6 0.507674 0.253837 0.967247i 0.418307π-0.418307\pi
0.253837 + 0.967247i 0.418307π0.418307\pi
402402 0 0
403403 602621.i 0.184834i
404404 0 0
405405 0 0
406406 0 0
407407 −25988.3 −0.00777663
408408 0 0
409409 5.21834e6 1.54250 0.771248 0.636534i 0.219633π-0.219633\pi
0.771248 + 0.636534i 0.219633π0.219633\pi
410410 0 0
411411 3.45955e6i 1.01022i
412412 0 0
413413 52800.0i 0.0152321i
414414 0 0
415415 0 0
416416 0 0
417417 −810644. −0.228292
418418 0 0
419419 666477.i 0.185460i 0.995691 + 0.0927299i 0.0295593π0.0295593\pi
−0.995691 + 0.0927299i 0.970441π0.970441\pi
420420 0 0
421421 6.82007e6i 1.87536i 0.347504 + 0.937678i 0.387029π0.387029\pi
−0.347504 + 0.937678i 0.612971π0.612971\pi
422422 0 0
423423 −2.08073e6 −0.565413
424424 0 0
425425 0 0
426426 0 0
427427 75442.2i 0.0200237i
428428 0 0
429429 − 819419.i − 0.214963i
430430 0 0
431431 1.38707e6 0.359671 0.179836 0.983697i 0.442443π-0.442443\pi
0.179836 + 0.983697i 0.442443π0.442443\pi
432432 0 0
433433 1.33169e6 0.341336 0.170668 0.985329i 0.445407π-0.445407\pi
0.170668 + 0.985329i 0.445407π0.445407\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 1.18797e6i − 0.297577i
438438 0 0
439439 2.78241e6 0.689064 0.344532 0.938775i 0.388038π-0.388038\pi
0.344532 + 0.938775i 0.388038π0.388038\pi
440440 0 0
441441 1.53456e6 0.375741
442442 0 0
443443 4.63595e6i 1.12235i 0.827696 + 0.561177i 0.189651π0.189651\pi
−0.827696 + 0.561177i 0.810349π0.810349\pi
444444 0 0
445445 0 0
446446 0 0
447447 −6.44063e6 −1.52461
448448 0 0
449449 1.18197e6 0.276688 0.138344 0.990384i 0.455822π-0.455822\pi
0.138344 + 0.990384i 0.455822π0.455822\pi
450450 0 0
451451 − 6.82811e6i − 1.58074i
452452 0 0
453453 − 8.16001e6i − 1.86829i
454454 0 0
455455 0 0
456456 0 0
457457 1.55240e6 0.347708 0.173854 0.984771i 0.444378π-0.444378\pi
0.173854 + 0.984771i 0.444378π0.444378\pi
458458 0 0
459459 2.35472e6i 0.521684i
460460 0 0
461461 − 7.43437e6i − 1.62926i −0.579978 0.814632i 0.696939π-0.696939\pi
0.579978 0.814632i 0.303061π-0.303061\pi
462462 0 0
463463 −20179.5 −0.00437480 −0.00218740 0.999998i 0.500696π-0.500696\pi
−0.00218740 + 0.999998i 0.500696π0.500696\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 3.58698e6i − 0.761092i −0.924762 0.380546i 0.875736π-0.875736\pi
0.924762 0.380546i 0.124264π-0.124264\pi
468468 0 0
469469 149245.i 0.0313306i
470470 0 0
471471 7.00885e6 1.45578
472472 0 0
473473 1.01343e6 0.208277
474474 0 0
475475 0 0
476476 0 0
477477 − 1.24829e6i − 0.251200i
478478 0 0
479479 −183482. −0.0365388 −0.0182694 0.999833i 0.505816π-0.505816\pi
−0.0182694 + 0.999833i 0.505816π0.505816\pi
480480 0 0
481481 −6625.61 −0.00130576
482482 0 0
483483 − 146082.i − 0.0284925i
484484 0 0
485485 0 0
486486 0 0
487487 −6.68968e6 −1.27815 −0.639077 0.769143i 0.720683π-0.720683\pi
−0.639077 + 0.769143i 0.720683π0.720683\pi
488488 0 0
489489 −7.40899e6 −1.40116
490490 0 0
491491 − 9.90038e6i − 1.85331i −0.375913 0.926655i 0.622671π-0.622671\pi
0.375913 0.926655i 0.377329π-0.377329\pi
492492 0 0
493493 − 4.42259e6i − 0.819520i
494494 0 0
495495 0 0
496496 0 0
497497 115993. 0.0210639
498498 0 0
499499 5.95907e6i 1.07134i 0.844428 + 0.535670i 0.179941π0.179941\pi
−0.844428 + 0.535670i 0.820059π0.820059\pi
500500 0 0
501501 3.52973e6i 0.628271i
502502 0 0
503503 3.69353e6 0.650910 0.325455 0.945557i 0.394482π-0.394482\pi
0.325455 + 0.945557i 0.394482π0.394482\pi
504504 0 0
505505 0 0
506506 0 0
507507 6.58010e6i 1.13687i
508508 0 0
509509 − 7.94222e6i − 1.35877i −0.733780 0.679387i 0.762246π-0.762246\pi
0.733780 0.679387i 0.237754π-0.237754\pi
510510 0 0
511511 47982.9 0.00812894
512512 0 0
513513 −930172. −0.156052
514514 0 0
515515 0 0
516516 0 0
517517 − 9.55157e6i − 1.57162i
518518 0 0
519519 1.09598e7 1.78602
520520 0 0
521521 −1.06312e7 −1.71588 −0.857940 0.513749i 0.828256π-0.828256\pi
−0.857940 + 0.513749i 0.828256π0.828256\pi
522522 0 0
523523 − 3.13913e6i − 0.501828i −0.968009 0.250914i 0.919269π-0.919269\pi
0.968009 0.250914i 0.0807312π-0.0807312\pi
524524 0 0
525525 0 0
526526 0 0
527527 −4.78708e6 −0.750834
528528 0 0
529529 6.10788e6 0.948967
530530 0 0
531531 − 2.13783e6i − 0.329032i
532532 0 0
533533 − 1.74080e6i − 0.265418i
534534 0 0
535535 0 0
536536 0 0
537537 −7.70298e6 −1.15272
538538 0 0
539539 7.04438e6i 1.04441i
540540 0 0
541541 − 1.20044e7i − 1.76339i −0.471821 0.881694i 0.656403π-0.656403\pi
0.471821 0.881694i 0.343597π-0.343597\pi
542542 0 0
543543 −3.35273e6 −0.487976
544544 0 0
545545 0 0
546546 0 0
547547 9.93035e6i 1.41905i 0.704682 + 0.709523i 0.251090π0.251090\pi
−0.704682 + 0.709523i 0.748910π0.748910\pi
548548 0 0
549549 − 3.05460e6i − 0.432537i
550550 0 0
551551 1.74703e6 0.245144
552552 0 0
553553 −86662.2 −0.0120508
554554 0 0
555555 0 0
556556 0 0
557557 8.72764e6i 1.19195i 0.803002 + 0.595976i 0.203235π0.203235\pi
−0.803002 + 0.595976i 0.796765π0.796765\pi
558558 0 0
559559 258370. 0.0349714
560560 0 0
561561 6.50926e6 0.873222
562562 0 0
563563 − 2.13884e6i − 0.284386i −0.989839 0.142193i 0.954585π-0.954585\pi
0.989839 0.142193i 0.0454154π-0.0454154\pi
564564 0 0
565565 0 0
566566 0 0
567567 −164445. −0.0214814
568568 0 0
569569 2.98366e6 0.386339 0.193169 0.981165i 0.438123π-0.438123\pi
0.193169 + 0.981165i 0.438123π0.438123\pi
570570 0 0
571571 − 8.50264e6i − 1.09135i −0.837997 0.545674i 0.816274π-0.816274\pi
0.837997 0.545674i 0.183726π-0.183726\pi
572572 0 0
573573 − 1.79654e7i − 2.28586i
574574 0 0
575575 0 0
576576 0 0
577577 −1.55926e7 −1.94975 −0.974874 0.222756i 0.928495π-0.928495\pi
−0.974874 + 0.222756i 0.928495π0.928495\pi
578578 0 0
579579 − 3.01658e6i − 0.373954i
580580 0 0
581581 210159.i 0.0258289i
582582 0 0
583583 5.73025e6 0.698236
584584 0 0
585585 0 0
586586 0 0
587587 − 1.01432e7i − 1.21501i −0.794314 0.607507i 0.792170π-0.792170\pi
0.794314 0.607507i 0.207830π-0.207830\pi
588588 0 0
589589 − 1.89101e6i − 0.224598i
590590 0 0
591591 9.26315e6 1.09091
592592 0 0
593593 1.44098e7 1.68276 0.841381 0.540442i 0.181743π-0.181743\pi
0.841381 + 0.540442i 0.181743π0.181743\pi
594594 0 0
595595 0 0
596596 0 0
597597 − 8.69706e6i − 0.998704i
598598 0 0
599599 3.13415e6 0.356905 0.178452 0.983949i 0.442891π-0.442891\pi
0.178452 + 0.983949i 0.442891π0.442891\pi
600600 0 0
601601 1.57244e7 1.77578 0.887889 0.460058i 0.152171π-0.152171\pi
0.887889 + 0.460058i 0.152171π0.152171\pi
602602 0 0
603603 − 6.04283e6i − 0.676780i
604604 0 0
605605 0 0
606606 0 0
607607 1.03887e7 1.14443 0.572217 0.820102i 0.306083π-0.306083\pi
0.572217 + 0.820102i 0.306083π0.306083\pi
608608 0 0
609609 214830. 0.0234721
610610 0 0
611611 − 2.43513e6i − 0.263888i
612612 0 0
613613 1.46355e7i 1.57310i 0.617525 + 0.786551i 0.288135π0.288135\pi
−0.617525 + 0.786551i 0.711865π0.711865\pi
614614 0 0
615615 0 0
616616 0 0
617617 −6.06227e6 −0.641095 −0.320547 0.947233i 0.603867π-0.603867\pi
−0.320547 + 0.947233i 0.603867π0.603867\pi
618618 0 0
619619 888836.i 0.0932384i 0.998913 + 0.0466192i 0.0148447π0.0148447\pi
−0.998913 + 0.0466192i 0.985155π0.985155\pi
620620 0 0
621621 − 9.82207e6i − 1.02205i
622622 0 0
623623 −136873. −0.0141285
624624 0 0
625625 0 0
626626 0 0
627627 2.57132e6i 0.261208i
628628 0 0
629629 − 52632.2i − 0.00530426i
630630 0 0
631631 −5.86047e6 −0.585948 −0.292974 0.956120i 0.594645π-0.594645\pi
−0.292974 + 0.956120i 0.594645π0.594645\pi
632632 0 0
633633 −4.76256e6 −0.472423
634634 0 0
635635 0 0
636636 0 0
637637 1.79594e6i 0.175365i
638638 0 0
639639 −4.69645e6 −0.455007
640640 0 0
641641 6.88679e6 0.662021 0.331011 0.943627i 0.392610π-0.392610\pi
0.331011 + 0.943627i 0.392610π0.392610\pi
642642 0 0
643643 7.66403e6i 0.731021i 0.930807 + 0.365510i 0.119106π0.119106\pi
−0.930807 + 0.365510i 0.880894π0.880894\pi
644644 0 0
645645 0 0
646646 0 0
647647 −3.93185e6 −0.369263 −0.184631 0.982808i 0.559109π-0.559109\pi
−0.184631 + 0.982808i 0.559109π0.559109\pi
648648 0 0
649649 9.81369e6 0.914577
650650 0 0
651651 − 232535.i − 0.0215048i
652652 0 0
653653 − 5.55582e6i − 0.509876i −0.966957 0.254938i 0.917945π-0.917945\pi
0.966957 0.254938i 0.0820551π-0.0820551\pi
654654 0 0
655655 0 0
656656 0 0
657657 −1.94279e6 −0.175595
658658 0 0
659659 2.17299e6i 0.194914i 0.995240 + 0.0974572i 0.0310709π0.0310709\pi
−0.995240 + 0.0974572i 0.968929π0.968929\pi
660660 0 0
661661 6.93458e6i 0.617329i 0.951171 + 0.308665i 0.0998821π0.0998821\pi
−0.951171 + 0.308665i 0.900118π0.900118\pi
662662 0 0
663663 1.65951e6 0.146621
664664 0 0
665665 0 0
666666 0 0
667667 1.84476e7i 1.60556i
668668 0 0
669669 − 1.14130e7i − 0.985902i
670670 0 0
671671 1.40221e7 1.20228
672672 0 0
673673 7.72402e6 0.657364 0.328682 0.944441i 0.393396π-0.393396\pi
0.328682 + 0.944441i 0.393396π0.393396\pi
674674 0 0
675675 0 0
676676 0 0
677677 1.38586e7i 1.16211i 0.813865 + 0.581054i 0.197360π0.197360\pi
−0.813865 + 0.581054i 0.802640π0.802640\pi
678678 0 0
679679 355113. 0.0295592
680680 0 0
681681 1.19951e7 0.991139
682682 0 0
683683 − 778871.i − 0.0638872i −0.999490 0.0319436i 0.989830π-0.989830\pi
0.999490 0.0319436i 0.0101697π-0.0101697\pi
684684 0 0
685685 0 0
686686 0 0
687687 −1.47700e7 −1.19396
688688 0 0
689689 1.46090e6 0.117239
690690 0 0
691691 − 6.98899e6i − 0.556826i −0.960461 0.278413i 0.910192π-0.910192\pi
0.960461 0.278413i 0.0898084π-0.0898084\pi
692692 0 0
693693 86376.8i 0.00683225i
694694 0 0
695695 0 0
696696 0 0
697697 1.38285e7 1.07818
698698 0 0
699699 − 2.38529e7i − 1.84649i
700700 0 0
701701 − 4.14587e6i − 0.318655i −0.987226 0.159328i 0.949067π-0.949067\pi
0.987226 0.159328i 0.0509326π-0.0509326\pi
702702 0 0
703703 20791.0 0.00158667
704704 0 0
705705 0 0
706706 0 0
707707 280855.i 0.0211317i
708708 0 0
709709 1.52511e7i 1.13943i 0.821843 + 0.569714i 0.192946π0.192946\pi
−0.821843 + 0.569714i 0.807054π0.807054\pi
710710 0 0
711711 3.50889e6 0.260313
712712 0 0
713713 1.99680e7 1.47099
714714 0 0
715715 0 0
716716 0 0
717717 2.22820e7i 1.61866i
718718 0 0
719719 1.60151e6 0.115534 0.0577668 0.998330i 0.481602π-0.481602\pi
0.0577668 + 0.998330i 0.481602π0.481602\pi
720720 0 0
721721 23338.6 0.00167200
722722 0 0
723723 − 1.79845e7i − 1.27954i
724724 0 0
725725 0 0
726726 0 0
727727 6.15453e6 0.431876 0.215938 0.976407i 0.430719π-0.430719\pi
0.215938 + 0.976407i 0.430719π0.430719\pi
728728 0 0
729729 −5.66362e6 −0.394708
730730 0 0
731731 2.05243e6i 0.142061i
732732 0 0
733733 − 7.15476e6i − 0.491853i −0.969289 0.245926i 0.920908π-0.920908\pi
0.969289 0.245926i 0.0790921π-0.0790921\pi
734734 0 0
735735 0 0
736736 0 0
737737 2.77395e7 1.88118
738738 0 0
739739 − 2.74026e7i − 1.84578i −0.385063 0.922890i 0.625820π-0.625820\pi
0.385063 0.922890i 0.374180π-0.374180\pi
740740 0 0
741741 655547.i 0.0438589i
742742 0 0
743743 1.20016e7 0.797569 0.398785 0.917045i 0.369432π-0.369432\pi
0.398785 + 0.917045i 0.369432π0.369432\pi
744744 0 0
745745 0 0
746746 0 0
747747 − 8.50916e6i − 0.557937i
748748 0 0
749749 159629.i 0.0103970i
750750 0 0
751751 −3.38961e6 −0.219305 −0.109653 0.993970i 0.534974π-0.534974\pi
−0.109653 + 0.993970i 0.534974π0.534974\pi
752752 0 0
753753 −2.93148e7 −1.88408
754754 0 0
755755 0 0
756756 0 0
757757 3.47336e6i 0.220298i 0.993915 + 0.110149i 0.0351328π0.0351328\pi
−0.993915 + 0.110149i 0.964867π0.964867\pi
758758 0 0
759759 −2.71516e7 −1.71077
760760 0 0
761761 −1.16257e6 −0.0727710 −0.0363855 0.999338i 0.511584π-0.511584\pi
−0.0363855 + 0.999338i 0.511584π0.511584\pi
762762 0 0
763763 − 289755.i − 0.0180186i
764764 0 0
765765 0 0
766766 0 0
767767 2.50196e6 0.153565
768768 0 0
769769 −1.71387e7 −1.04511 −0.522556 0.852605i 0.675021π-0.675021\pi
−0.522556 + 0.852605i 0.675021π0.675021\pi
770770 0 0
771771 1.96944e7i 1.19318i
772772 0 0
773773 3.17392e7i 1.91050i 0.295800 + 0.955250i 0.404414π0.404414\pi
−0.295800 + 0.955250i 0.595586π0.595586\pi
774774 0 0
775775 0 0
776776 0 0
777777 2556.64 0.000151921 0
778778 0 0
779779 5.46258e6i 0.322518i
780780 0 0
781781 − 2.15590e7i − 1.26474i
782782 0 0
783783 1.44444e7 0.841968
784784 0 0
785785 0 0
786786 0 0
787787 − 2.67032e6i − 0.153683i −0.997043 0.0768416i 0.975516π-0.975516\pi
0.997043 0.0768416i 0.0244836π-0.0244836\pi
788788 0 0
789789 1.48635e7i 0.850018i
790790 0 0
791791 −259850. −0.0147666
792792 0 0
793793 3.57487e6 0.201873
794794 0 0
795795 0 0
796796 0 0
797797 3.37393e7i 1.88144i 0.339188 + 0.940719i 0.389848π0.389848\pi
−0.339188 + 0.940719i 0.610152π0.610152\pi
798798 0 0
799799 1.93441e7 1.07197
800800 0 0
801801 5.54189e6 0.305194
802802 0 0
803803 − 8.91835e6i − 0.488085i
804804 0 0
805805 0 0
806806 0 0
807807 2.08369e6 0.112629
808808 0 0
809809 1.25443e6 0.0673870 0.0336935 0.999432i 0.489273π-0.489273\pi
0.0336935 + 0.999432i 0.489273π0.489273\pi
810810 0 0
811811 1.12827e7i 0.602365i 0.953567 + 0.301182i 0.0973813π0.0973813\pi
−0.953567 + 0.301182i 0.902619π0.902619\pi
812812 0 0
813813 − 6.81525e6i − 0.361622i
814814 0 0
815815 0 0
816816 0 0
817817 −810760. −0.0424949
818818 0 0
819819 22021.4i 0.00114719i
820820 0 0
821821 1.21845e7i 0.630886i 0.948945 + 0.315443i 0.102153π0.102153\pi
−0.948945 + 0.315443i 0.897847π0.897847\pi
822822 0 0
823823 2.12650e7 1.09437 0.547187 0.837010i 0.315698π-0.315698\pi
0.547187 + 0.837010i 0.315698π0.315698\pi
824824 0 0
825825 0 0
826826 0 0
827827 6.06316e6i 0.308273i 0.988050 + 0.154136i 0.0492596π0.0492596\pi
−0.988050 + 0.154136i 0.950740π0.950740\pi
828828 0 0
829829 − 727353.i − 0.0367586i −0.999831 0.0183793i 0.994149π-0.994149\pi
0.999831 0.0183793i 0.00585064π-0.00585064\pi
830830 0 0
831831 1.67171e7 0.839765
832832 0 0
833833 −1.42665e7 −0.712368
834834 0 0
835835 0 0
836836 0 0
837837 − 1.56348e7i − 0.771401i
838838 0 0
839839 1.36723e7 0.670560 0.335280 0.942118i 0.391169π-0.391169\pi
0.335280 + 0.942118i 0.391169π0.391169\pi
840840 0 0
841841 −6.61809e6 −0.322658
842842 0 0
843843 − 9.34688e6i − 0.452999i
844844 0 0
845845 0 0
846846 0 0
847847 −33223.9 −0.00159126
848848 0 0
849849 9.74720e6 0.464099
850850 0 0
851851 219541.i 0.0103918i
852852 0 0
853853 3.66971e7i 1.72687i 0.504462 + 0.863434i 0.331691π0.331691\pi
−0.504462 + 0.863434i 0.668309π0.668309\pi
854854 0 0
855855 0 0
856856 0 0
857857 −1.73498e7 −0.806941 −0.403470 0.914993i 0.632196π-0.632196\pi
−0.403470 + 0.914993i 0.632196π0.632196\pi
858858 0 0
859859 − 1.90085e7i − 0.878954i −0.898254 0.439477i 0.855164π-0.855164\pi
0.898254 0.439477i 0.144836π-0.144836\pi
860860 0 0
861861 671726.i 0.0308805i
862862 0 0
863863 −3.46920e7 −1.58563 −0.792816 0.609460i 0.791386π-0.791386\pi
−0.792816 + 0.609460i 0.791386π0.791386\pi
864864 0 0
865865 0 0
866866 0 0
867867 − 1.27790e7i − 0.577364i
868868 0 0
869869 1.61075e7i 0.723566i
870870 0 0
871871 7.07207e6 0.315865
872872 0 0
873873 −1.43783e7 −0.638515
874874 0 0
875875 0 0
876876 0 0
877877 − 3.99003e7i − 1.75177i −0.482520 0.875885i 0.660279π-0.660279\pi
0.482520 0.875885i 0.339721π-0.339721\pi
878878 0 0
879879 −4.65618e7 −2.03262
880880 0 0
881881 −3.50875e7 −1.52304 −0.761522 0.648139i 0.775548π-0.775548\pi
−0.761522 + 0.648139i 0.775548π0.775548\pi
882882 0 0
883883 1.47881e7i 0.638279i 0.947708 + 0.319139i 0.103394π0.103394\pi
−0.947708 + 0.319139i 0.896606π0.896606\pi
884884 0 0
885885 0 0
886886 0 0
887887 1.17291e7 0.500560 0.250280 0.968173i 0.419477π-0.419477\pi
0.250280 + 0.968173i 0.419477π0.419477\pi
888888 0 0
889889 −329394. −0.0139785
890890 0 0
891891 3.05646e7i 1.28981i
892892 0 0
893893 7.64139e6i 0.320659i
894894 0 0
895895 0 0
896896 0 0
897897 −6.92219e6 −0.287252
898898 0 0
899899 2.93651e7i 1.21180i
900900 0 0
901901 1.16051e7i 0.476251i
902902 0 0
903903 −99697.9 −0.00406880
904904 0 0
905905 0 0
906906 0 0
907907 − 1.36136e7i − 0.549483i −0.961518 0.274742i 0.911408π-0.911408\pi
0.961518 0.274742i 0.0885923π-0.0885923\pi
908908 0 0
909909 − 1.13716e7i − 0.456470i
910910 0 0
911911 −1.26888e7 −0.506551 −0.253276 0.967394i 0.581508π-0.581508\pi
−0.253276 + 0.967394i 0.581508π0.581508\pi
912912 0 0
913913 3.90611e7 1.55084
914914 0 0
915915 0 0
916916 0 0
917917 − 29319.9i − 0.00115144i
918918 0 0
919919 4.25253e7 1.66096 0.830479 0.557050i 0.188067π-0.188067\pi
0.830479 + 0.557050i 0.188067π0.188067\pi
920920 0 0
921921 −1.35430e7 −0.526098
922922 0 0
923923 − 5.49637e6i − 0.212360i
924924 0 0
925925 0 0
926926 0 0
927927 −944963. −0.0361173
928928 0 0
929929 4.25450e6 0.161737 0.0808686 0.996725i 0.474231π-0.474231\pi
0.0808686 + 0.996725i 0.474231π0.474231\pi
930930 0 0
931931 − 5.63560e6i − 0.213092i
932932 0 0
933933 − 1.99078e7i − 0.748718i
934934 0 0
935935 0 0
936936 0 0
937937 1.07844e7 0.401279 0.200640 0.979665i 0.435698π-0.435698\pi
0.200640 + 0.979665i 0.435698π0.435698\pi
938938 0 0
939939 1.97982e7i 0.732760i
940940 0 0
941941 − 112960.i − 0.00415862i −0.999998 0.00207931i 0.999338π-0.999338\pi
0.999998 0.00207931i 0.000661865π-0.000661865\pi
942942 0 0
943943 −5.76817e7 −2.11232
944944 0 0
945945 0 0
946946 0 0
947947 − 1.62952e7i − 0.590454i −0.955427 0.295227i 0.904605π-0.904605\pi
0.955427 0.295227i 0.0953953π-0.0953953\pi
948948 0 0
949949 − 2.27370e6i − 0.0819534i
950950 0 0
951951 −5.36188e7 −1.92250
952952 0 0
953953 −1.07203e7 −0.382363 −0.191181 0.981555i 0.561232π-0.561232\pi
−0.191181 + 0.981555i 0.561232π0.561232\pi
954954 0 0
955955 0 0
956956 0 0
957957 − 3.99294e7i − 1.40933i
958958 0 0
959959 426792. 0.0149855
960960 0 0
961961 3.15601e6 0.110238
962962 0 0
963963 − 6.46324e6i − 0.224587i
964964 0 0
965965 0 0
966966 0 0
967967 3.92793e7 1.35082 0.675411 0.737442i 0.263966π-0.263966\pi
0.675411 + 0.737442i 0.263966π0.263966\pi
968968 0 0
969969 −5.20750e6 −0.178164
970970 0 0
971971 − 2.76288e7i − 0.940405i −0.882559 0.470202i 0.844181π-0.844181\pi
0.882559 0.470202i 0.155819π-0.155819\pi
972972 0 0
973973 100006.i 0.00338645i
974974 0 0
975975 0 0
976976 0 0
977977 −2.56548e7 −0.859868 −0.429934 0.902860i 0.641463π-0.641463\pi
−0.429934 + 0.902860i 0.641463π0.641463\pi
978978 0 0
979979 2.54399e7i 0.848318i
980980 0 0
981981 1.17320e7i 0.389223i
982982 0 0
983983 5.21860e6 0.172254 0.0861271 0.996284i 0.472551π-0.472551\pi
0.0861271 + 0.996284i 0.472551π0.472551\pi
984984 0 0
985985 0 0
986986 0 0
987987 939650.i 0.0307025i
988988 0 0
989989 − 8.56115e6i − 0.278318i
990990 0 0
991991 −4.76772e7 −1.54215 −0.771075 0.636744i 0.780281π-0.780281\pi
−0.771075 + 0.636744i 0.780281π0.780281\pi
992992 0 0
993993 −6.53158e6 −0.210206
994994 0 0
995995 0 0
996996 0 0
997997 − 2.96368e7i − 0.944263i −0.881528 0.472132i 0.843485π-0.843485\pi
0.881528 0.472132i 0.156515π-0.156515\pi
998998 0 0
999999 171900. 0.00544955
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 800.6.d.d.401.16 20
4.3 odd 2 200.6.d.c.101.5 20
5.2 odd 4 800.6.f.d.49.32 40
5.3 odd 4 800.6.f.d.49.9 40
5.4 even 2 800.6.d.b.401.5 20
8.3 odd 2 200.6.d.c.101.6 yes 20
8.5 even 2 inner 800.6.d.d.401.5 20
20.3 even 4 200.6.f.d.149.12 40
20.7 even 4 200.6.f.d.149.29 40
20.19 odd 2 200.6.d.d.101.16 yes 20
40.3 even 4 200.6.f.d.149.30 40
40.13 odd 4 800.6.f.d.49.31 40
40.19 odd 2 200.6.d.d.101.15 yes 20
40.27 even 4 200.6.f.d.149.11 40
40.29 even 2 800.6.d.b.401.16 20
40.37 odd 4 800.6.f.d.49.10 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
200.6.d.c.101.5 20 4.3 odd 2
200.6.d.c.101.6 yes 20 8.3 odd 2
200.6.d.d.101.15 yes 20 40.19 odd 2
200.6.d.d.101.16 yes 20 20.19 odd 2
200.6.f.d.149.11 40 40.27 even 4
200.6.f.d.149.12 40 20.3 even 4
200.6.f.d.149.29 40 20.7 even 4
200.6.f.d.149.30 40 40.3 even 4
800.6.d.b.401.5 20 5.4 even 2
800.6.d.b.401.16 20 40.29 even 2
800.6.d.d.401.5 20 8.5 even 2 inner
800.6.d.d.401.16 20 1.1 even 1 trivial
800.6.f.d.49.9 40 5.3 odd 4
800.6.f.d.49.10 40 40.37 odd 4
800.6.f.d.49.31 40 40.13 odd 4
800.6.f.d.49.32 40 5.2 odd 4