Properties

Label 1280.4.d.m.641.1
Level 12801280
Weight 44
Character 1280.641
Analytic conductor 75.52275.522
Analytic rank 11
Dimension 22
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1280,4,Mod(641,1280)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1280, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1280.641"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 1280=285 1280 = 2^{8} \cdot 5
Weight: k k == 4 4
Character orbit: [χ][\chi] == 1280.d (of order 22, degree 11, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,0,0,0,0,0,32,0,22,0,0,0,0,0,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(15)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 75.522444807375.5224448073
Analytic rank: 11
Dimension: 22
Coefficient field: Q(i)\Q(i)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 641.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 1280.641
Dual form 1280.4.d.m.641.2

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q4.00000iq35.00000iq5+16.0000q7+11.0000q9+36.0000iq1142.0000iq1320.0000q15110.000q17+116.000iq1964.0000iq21+16.0000q2325.0000q25152.000iq27+198.000iq29240.000q31+144.000q3380.0000iq35+258.000iq37168.000q39442.000q41292.000iq4355.0000iq45392.000q4787.0000q49+440.000iq51142.000iq53+180.000q55+464.000q57348.000iq59570.000iq61+176.000q63210.000q65692.000iq6764.0000iq69+168.000q71+134.000q73+100.000iq75+576.000iq77784.000q79311.000q81564.000iq83+550.000iq85+792.000q871034.00q89672.000iq91+960.000iq93+580.000q95382.000q97+396.000iq99+O(q100)q-4.00000i q^{3} -5.00000i q^{5} +16.0000 q^{7} +11.0000 q^{9} +36.0000i q^{11} -42.0000i q^{13} -20.0000 q^{15} -110.000 q^{17} +116.000i q^{19} -64.0000i q^{21} +16.0000 q^{23} -25.0000 q^{25} -152.000i q^{27} +198.000i q^{29} -240.000 q^{31} +144.000 q^{33} -80.0000i q^{35} +258.000i q^{37} -168.000 q^{39} -442.000 q^{41} -292.000i q^{43} -55.0000i q^{45} -392.000 q^{47} -87.0000 q^{49} +440.000i q^{51} -142.000i q^{53} +180.000 q^{55} +464.000 q^{57} -348.000i q^{59} -570.000i q^{61} +176.000 q^{63} -210.000 q^{65} -692.000i q^{67} -64.0000i q^{69} +168.000 q^{71} +134.000 q^{73} +100.000i q^{75} +576.000i q^{77} -784.000 q^{79} -311.000 q^{81} -564.000i q^{83} +550.000i q^{85} +792.000 q^{87} -1034.00 q^{89} -672.000i q^{91} +960.000i q^{93} +580.000 q^{95} -382.000 q^{97} +396.000i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+32q7+22q940q15220q17+32q2350q25480q31+288q33336q39884q41784q47174q49+360q55+928q57+352q63420q65+764q97+O(q100) 2 q + 32 q^{7} + 22 q^{9} - 40 q^{15} - 220 q^{17} + 32 q^{23} - 50 q^{25} - 480 q^{31} + 288 q^{33} - 336 q^{39} - 884 q^{41} - 784 q^{47} - 174 q^{49} + 360 q^{55} + 928 q^{57} + 352 q^{63} - 420 q^{65}+ \cdots - 764 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1280Z)×\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times.

nn 257257 261261 511511
χ(n)\chi(n) 11 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 − 4.00000i − 0.769800i −0.922958 0.384900i 0.874236π-0.874236\pi
0.922958 0.384900i 0.125764π-0.125764\pi
44 0 0
55 − 5.00000i − 0.447214i
66 0 0
77 16.0000 0.863919 0.431959 0.901893i 0.357822π-0.357822\pi
0.431959 + 0.901893i 0.357822π0.357822\pi
88 0 0
99 11.0000 0.407407
1010 0 0
1111 36.0000i 0.986764i 0.869813 + 0.493382i 0.164240π0.164240\pi
−0.869813 + 0.493382i 0.835760π0.835760\pi
1212 0 0
1313 − 42.0000i − 0.896054i −0.894020 0.448027i 0.852127π-0.852127\pi
0.894020 0.448027i 0.147873π-0.147873\pi
1414 0 0
1515 −20.0000 −0.344265
1616 0 0
1717 −110.000 −1.56935 −0.784674 0.619909i 0.787170π-0.787170\pi
−0.784674 + 0.619909i 0.787170π0.787170\pi
1818 0 0
1919 116.000i 1.40064i 0.713827 + 0.700322i 0.246960π0.246960\pi
−0.713827 + 0.700322i 0.753040π0.753040\pi
2020 0 0
2121 − 64.0000i − 0.665045i
2222 0 0
2323 16.0000 0.145054 0.0725268 0.997366i 0.476894π-0.476894\pi
0.0725268 + 0.997366i 0.476894π0.476894\pi
2424 0 0
2525 −25.0000 −0.200000
2626 0 0
2727 − 152.000i − 1.08342i
2828 0 0
2929 198.000i 1.26785i 0.773394 + 0.633925i 0.218557π0.218557\pi
−0.773394 + 0.633925i 0.781443π0.781443\pi
3030 0 0
3131 −240.000 −1.39049 −0.695246 0.718772i 0.744705π-0.744705\pi
−0.695246 + 0.718772i 0.744705π0.744705\pi
3232 0 0
3333 144.000 0.759612
3434 0 0
3535 − 80.0000i − 0.386356i
3636 0 0
3737 258.000i 1.14635i 0.819433 + 0.573175i 0.194288π0.194288\pi
−0.819433 + 0.573175i 0.805712π0.805712\pi
3838 0 0
3939 −168.000 −0.689783
4040 0 0
4141 −442.000 −1.68363 −0.841815 0.539767i 0.818512π-0.818512\pi
−0.841815 + 0.539767i 0.818512π0.818512\pi
4242 0 0
4343 − 292.000i − 1.03557i −0.855510 0.517786i 0.826756π-0.826756\pi
0.855510 0.517786i 0.173244π-0.173244\pi
4444 0 0
4545 − 55.0000i − 0.182198i
4646 0 0
4747 −392.000 −1.21658 −0.608288 0.793716i 0.708143π-0.708143\pi
−0.608288 + 0.793716i 0.708143π0.708143\pi
4848 0 0
4949 −87.0000 −0.253644
5050 0 0
5151 440.000i 1.20808i
5252 0 0
5353 − 142.000i − 0.368023i −0.982924 0.184011i 0.941092π-0.941092\pi
0.982924 0.184011i 0.0589083π-0.0589083\pi
5454 0 0
5555 180.000 0.441294
5656 0 0
5757 464.000 1.07822
5858 0 0
5959 − 348.000i − 0.767894i −0.923355 0.383947i 0.874565π-0.874565\pi
0.923355 0.383947i 0.125435π-0.125435\pi
6060 0 0
6161 − 570.000i − 1.19641i −0.801343 0.598205i 0.795881π-0.795881\pi
0.801343 0.598205i 0.204119π-0.204119\pi
6262 0 0
6363 176.000 0.351967
6464 0 0
6565 −210.000 −0.400728
6666 0 0
6767 − 692.000i − 1.26181i −0.775860 0.630905i 0.782684π-0.782684\pi
0.775860 0.630905i 0.217316π-0.217316\pi
6868 0 0
6969 − 64.0000i − 0.111662i
7070 0 0
7171 168.000 0.280816 0.140408 0.990094i 0.455159π-0.455159\pi
0.140408 + 0.990094i 0.455159π0.455159\pi
7272 0 0
7373 134.000 0.214843 0.107421 0.994214i 0.465741π-0.465741\pi
0.107421 + 0.994214i 0.465741π0.465741\pi
7474 0 0
7575 100.000i 0.153960i
7676 0 0
7777 576.000i 0.852484i
7878 0 0
7979 −784.000 −1.11654 −0.558271 0.829658i 0.688535π-0.688535\pi
−0.558271 + 0.829658i 0.688535π0.688535\pi
8080 0 0
8181 −311.000 −0.426612
8282 0 0
8383 − 564.000i − 0.745868i −0.927858 0.372934i 0.878352π-0.878352\pi
0.927858 0.372934i 0.121648π-0.121648\pi
8484 0 0
8585 550.000i 0.701834i
8686 0 0
8787 792.000 0.975992
8888 0 0
8989 −1034.00 −1.23150 −0.615752 0.787940i 0.711148π-0.711148\pi
−0.615752 + 0.787940i 0.711148π0.711148\pi
9090 0 0
9191 − 672.000i − 0.774118i
9292 0 0
9393 960.000i 1.07040i
9494 0 0
9595 580.000 0.626387
9696 0 0
9797 −382.000 −0.399858 −0.199929 0.979810i 0.564071π-0.564071\pi
−0.199929 + 0.979810i 0.564071π0.564071\pi
9898 0 0
9999 396.000i 0.402015i
100100 0 0
101101 674.000i 0.664015i 0.943277 + 0.332007i 0.107726π0.107726\pi
−0.943277 + 0.332007i 0.892274π0.892274\pi
102102 0 0
103103 −992.000 −0.948977 −0.474489 0.880262i 0.657367π-0.657367\pi
−0.474489 + 0.880262i 0.657367π0.657367\pi
104104 0 0
105105 −320.000 −0.297417
106106 0 0
107107 − 500.000i − 0.451746i −0.974157 0.225873i 0.927477π-0.927477\pi
0.974157 0.225873i 0.0725234π-0.0725234\pi
108108 0 0
109109 1046.00i 0.919162i 0.888136 + 0.459581i 0.152000π0.152000\pi
−0.888136 + 0.459581i 0.848000π0.848000\pi
110110 0 0
111111 1032.00 0.882460
112112 0 0
113113 −558.000 −0.464533 −0.232266 0.972652i 0.574614π-0.574614\pi
−0.232266 + 0.972652i 0.574614π0.574614\pi
114114 0 0
115115 − 80.0000i − 0.0648699i
116116 0 0
117117 − 462.000i − 0.365059i
118118 0 0
119119 −1760.00 −1.35579
120120 0 0
121121 35.0000 0.0262960
122122 0 0
123123 1768.00i 1.29606i
124124 0 0
125125 125.000i 0.0894427i
126126 0 0
127127 328.000 0.229176 0.114588 0.993413i 0.463445π-0.463445\pi
0.114588 + 0.993413i 0.463445π0.463445\pi
128128 0 0
129129 −1168.00 −0.797183
130130 0 0
131131 212.000i 0.141393i 0.997498 + 0.0706967i 0.0225222π0.0225222\pi
−0.997498 + 0.0706967i 0.977478π0.977478\pi
132132 0 0
133133 1856.00i 1.21004i
134134 0 0
135135 −760.000 −0.484521
136136 0 0
137137 −1434.00 −0.894269 −0.447135 0.894467i 0.647556π-0.647556\pi
−0.447135 + 0.894467i 0.647556π0.647556\pi
138138 0 0
139139 2196.00i 1.34002i 0.742354 + 0.670008i 0.233709π0.233709\pi
−0.742354 + 0.670008i 0.766291π0.766291\pi
140140 0 0
141141 1568.00i 0.936521i
142142 0 0
143143 1512.00 0.884194
144144 0 0
145145 990.000 0.567000
146146 0 0
147147 348.000i 0.195255i
148148 0 0
149149 2418.00i 1.32946i 0.747081 + 0.664732i 0.231454π0.231454\pi
−0.747081 + 0.664732i 0.768546π0.768546\pi
150150 0 0
151151 3672.00 1.97896 0.989481 0.144666i 0.0462108π-0.0462108\pi
0.989481 + 0.144666i 0.0462108π0.0462108\pi
152152 0 0
153153 −1210.00 −0.639364
154154 0 0
155155 1200.00i 0.621847i
156156 0 0
157157 358.000i 0.181984i 0.995852 + 0.0909921i 0.0290038π0.0290038\pi
−0.995852 + 0.0909921i 0.970996π0.970996\pi
158158 0 0
159159 −568.000 −0.283304
160160 0 0
161161 256.000 0.125314
162162 0 0
163163 − 2564.00i − 1.23207i −0.787717 0.616037i 0.788737π-0.788737\pi
0.787717 0.616037i 0.211263π-0.211263\pi
164164 0 0
165165 − 720.000i − 0.339709i
166166 0 0
167167 −3056.00 −1.41605 −0.708025 0.706187i 0.750414π-0.750414\pi
−0.708025 + 0.706187i 0.750414π0.750414\pi
168168 0 0
169169 433.000 0.197087
170170 0 0
171171 1276.00i 0.570633i
172172 0 0
173173 − 234.000i − 0.102836i −0.998677 0.0514182i 0.983626π-0.983626\pi
0.998677 0.0514182i 0.0163741π-0.0163741\pi
174174 0 0
175175 −400.000 −0.172784
176176 0 0
177177 −1392.00 −0.591125
178178 0 0
179179 − 524.000i − 0.218802i −0.993998 0.109401i 0.965107π-0.965107\pi
0.993998 0.109401i 0.0348933π-0.0348933\pi
180180 0 0
181181 1138.00i 0.467331i 0.972317 + 0.233665i 0.0750720π0.0750720\pi
−0.972317 + 0.233665i 0.924928π0.924928\pi
182182 0 0
183183 −2280.00 −0.920997
184184 0 0
185185 1290.00 0.512663
186186 0 0
187187 − 3960.00i − 1.54858i
188188 0 0
189189 − 2432.00i − 0.935989i
190190 0 0
191191 −1520.00 −0.575829 −0.287915 0.957656i 0.592962π-0.592962\pi
−0.287915 + 0.957656i 0.592962π0.592962\pi
192192 0 0
193193 −2142.00 −0.798884 −0.399442 0.916759i 0.630796π-0.630796\pi
−0.399442 + 0.916759i 0.630796π0.630796\pi
194194 0 0
195195 840.000i 0.308480i
196196 0 0
197197 2306.00i 0.833988i 0.908909 + 0.416994i 0.136916π0.136916\pi
−0.908909 + 0.416994i 0.863084π0.863084\pi
198198 0 0
199199 3288.00 1.17126 0.585628 0.810580i 0.300848π-0.300848\pi
0.585628 + 0.810580i 0.300848π0.300848\pi
200200 0 0
201201 −2768.00 −0.971342
202202 0 0
203203 3168.00i 1.09532i
204204 0 0
205205 2210.00i 0.752942i
206206 0 0
207207 176.000 0.0590959
208208 0 0
209209 −4176.00 −1.38211
210210 0 0
211211 3876.00i 1.26462i 0.774715 + 0.632310i 0.217893π0.217893\pi
−0.774715 + 0.632310i 0.782107π0.782107\pi
212212 0 0
213213 − 672.000i − 0.216172i
214214 0 0
215215 −1460.00 −0.463122
216216 0 0
217217 −3840.00 −1.20127
218218 0 0
219219 − 536.000i − 0.165386i
220220 0 0
221221 4620.00i 1.40622i
222222 0 0
223223 5688.00 1.70806 0.854028 0.520226i 0.174152π-0.174152\pi
0.854028 + 0.520226i 0.174152π0.174152\pi
224224 0 0
225225 −275.000 −0.0814815
226226 0 0
227227 2796.00i 0.817520i 0.912642 + 0.408760i 0.134039π0.134039\pi
−0.912642 + 0.408760i 0.865961π0.865961\pi
228228 0 0
229229 − 4446.00i − 1.28297i −0.767136 0.641485i 0.778319π-0.778319\pi
0.767136 0.641485i 0.221681π-0.221681\pi
230230 0 0
231231 2304.00 0.656243
232232 0 0
233233 −2522.00 −0.709106 −0.354553 0.935036i 0.615367π-0.615367\pi
−0.354553 + 0.935036i 0.615367π0.615367\pi
234234 0 0
235235 1960.00i 0.544069i
236236 0 0
237237 3136.00i 0.859515i
238238 0 0
239239 −816.000 −0.220848 −0.110424 0.993885i 0.535221π-0.535221\pi
−0.110424 + 0.993885i 0.535221π0.535221\pi
240240 0 0
241241 −5422.00 −1.44922 −0.724609 0.689160i 0.757980π-0.757980\pi
−0.724609 + 0.689160i 0.757980π0.757980\pi
242242 0 0
243243 − 2860.00i − 0.755017i
244244 0 0
245245 435.000i 0.113433i
246246 0 0
247247 4872.00 1.25505
248248 0 0
249249 −2256.00 −0.574169
250250 0 0
251251 − 5900.00i − 1.48368i −0.670575 0.741842i 0.733952π-0.733952\pi
0.670575 0.741842i 0.266048π-0.266048\pi
252252 0 0
253253 576.000i 0.143134i
254254 0 0
255255 2200.00 0.540272
256256 0 0
257257 5250.00 1.27426 0.637132 0.770754i 0.280120π-0.280120\pi
0.637132 + 0.770754i 0.280120π0.280120\pi
258258 0 0
259259 4128.00i 0.990353i
260260 0 0
261261 2178.00i 0.516532i
262262 0 0
263263 6240.00 1.46302 0.731511 0.681829i 0.238815π-0.238815\pi
0.731511 + 0.681829i 0.238815π0.238815\pi
264264 0 0
265265 −710.000 −0.164585
266266 0 0
267267 4136.00i 0.948012i
268268 0 0
269269 − 714.000i − 0.161834i −0.996721 0.0809170i 0.974215π-0.974215\pi
0.996721 0.0809170i 0.0257849π-0.0257849\pi
270270 0 0
271271 −2144.00 −0.480586 −0.240293 0.970700i 0.577243π-0.577243\pi
−0.240293 + 0.970700i 0.577243π0.577243\pi
272272 0 0
273273 −2688.00 −0.595916
274274 0 0
275275 − 900.000i − 0.197353i
276276 0 0
277277 4466.00i 0.968722i 0.874868 + 0.484361i 0.160948π0.160948\pi
−0.874868 + 0.484361i 0.839052π0.839052\pi
278278 0 0
279279 −2640.00 −0.566497
280280 0 0
281281 5302.00 1.12559 0.562795 0.826596i 0.309726π-0.309726\pi
0.562795 + 0.826596i 0.309726π0.309726\pi
282282 0 0
283283 − 6932.00i − 1.45606i −0.685546 0.728029i 0.740436π-0.740436\pi
0.685546 0.728029i 0.259564π-0.259564\pi
284284 0 0
285285 − 2320.00i − 0.482193i
286286 0 0
287287 −7072.00 −1.45452
288288 0 0
289289 7187.00 1.46285
290290 0 0
291291 1528.00i 0.307811i
292292 0 0
293293 4034.00i 0.804330i 0.915567 + 0.402165i 0.131742π0.131742\pi
−0.915567 + 0.402165i 0.868258π0.868258\pi
294294 0 0
295295 −1740.00 −0.343413
296296 0 0
297297 5472.00 1.06908
298298 0 0
299299 − 672.000i − 0.129976i
300300 0 0
301301 − 4672.00i − 0.894650i
302302 0 0
303303 2696.00 0.511159
304304 0 0
305305 −2850.00 −0.535051
306306 0 0
307307 3836.00i 0.713134i 0.934270 + 0.356567i 0.116053π0.116053\pi
−0.934270 + 0.356567i 0.883947π0.883947\pi
308308 0 0
309309 3968.00i 0.730523i
310310 0 0
311311 664.000 0.121067 0.0605337 0.998166i 0.480720π-0.480720\pi
0.0605337 + 0.998166i 0.480720π0.480720\pi
312312 0 0
313313 −2986.00 −0.539229 −0.269615 0.962968i 0.586896π-0.586896\pi
−0.269615 + 0.962968i 0.586896π0.586896\pi
314314 0 0
315315 − 880.000i − 0.157404i
316316 0 0
317317 2726.00i 0.482989i 0.970402 + 0.241494i 0.0776375π0.0776375\pi
−0.970402 + 0.241494i 0.922362π0.922362\pi
318318 0 0
319319 −7128.00 −1.25107
320320 0 0
321321 −2000.00 −0.347754
322322 0 0
323323 − 12760.0i − 2.19810i
324324 0 0
325325 1050.00i 0.179211i
326326 0 0
327327 4184.00 0.707571
328328 0 0
329329 −6272.00 −1.05102
330330 0 0
331331 − 9212.00i − 1.52972i −0.644197 0.764860i 0.722808π-0.722808\pi
0.644197 0.764860i 0.277192π-0.277192\pi
332332 0 0
333333 2838.00i 0.467031i
334334 0 0
335335 −3460.00 −0.564298
336336 0 0
337337 −3278.00 −0.529864 −0.264932 0.964267i 0.585349π-0.585349\pi
−0.264932 + 0.964267i 0.585349π0.585349\pi
338338 0 0
339339 2232.00i 0.357598i
340340 0 0
341341 − 8640.00i − 1.37209i
342342 0 0
343343 −6880.00 −1.08305
344344 0 0
345345 −320.000 −0.0499369
346346 0 0
347347 4956.00i 0.766721i 0.923599 + 0.383360i 0.125233π0.125233\pi
−0.923599 + 0.383360i 0.874767π0.874767\pi
348348 0 0
349349 4678.00i 0.717500i 0.933434 + 0.358750i 0.116797π0.116797\pi
−0.933434 + 0.358750i 0.883203π0.883203\pi
350350 0 0
351351 −6384.00 −0.970805
352352 0 0
353353 1890.00 0.284970 0.142485 0.989797i 0.454491π-0.454491\pi
0.142485 + 0.989797i 0.454491π0.454491\pi
354354 0 0
355355 − 840.000i − 0.125585i
356356 0 0
357357 7040.00i 1.04369i
358358 0 0
359359 −6472.00 −0.951474 −0.475737 0.879588i 0.657819π-0.657819\pi
−0.475737 + 0.879588i 0.657819π0.657819\pi
360360 0 0
361361 −6597.00 −0.961802
362362 0 0
363363 − 140.000i − 0.0202427i
364364 0 0
365365 − 670.000i − 0.0960806i
366366 0 0
367367 −1960.00 −0.278777 −0.139389 0.990238i 0.544514π-0.544514\pi
−0.139389 + 0.990238i 0.544514π0.544514\pi
368368 0 0
369369 −4862.00 −0.685923
370370 0 0
371371 − 2272.00i − 0.317942i
372372 0 0
373373 − 8750.00i − 1.21463i −0.794460 0.607316i 0.792246π-0.792246\pi
0.794460 0.607316i 0.207754π-0.207754\pi
374374 0 0
375375 500.000 0.0688530
376376 0 0
377377 8316.00 1.13606
378378 0 0
379379 − 380.000i − 0.0515021i −0.999668 0.0257510i 0.991802π-0.991802\pi
0.999668 0.0257510i 0.00819772π-0.00819772\pi
380380 0 0
381381 − 1312.00i − 0.176419i
382382 0 0
383383 9688.00 1.29252 0.646258 0.763119i 0.276333π-0.276333\pi
0.646258 + 0.763119i 0.276333π0.276333\pi
384384 0 0
385385 2880.00 0.381243
386386 0 0
387387 − 3212.00i − 0.421900i
388388 0 0
389389 − 3870.00i − 0.504413i −0.967673 0.252207i 0.918844π-0.918844\pi
0.967673 0.252207i 0.0811563π-0.0811563\pi
390390 0 0
391391 −1760.00 −0.227639
392392 0 0
393393 848.000 0.108845
394394 0 0
395395 3920.00i 0.499333i
396396 0 0
397397 1622.00i 0.205053i 0.994730 + 0.102526i 0.0326926π0.0326926\pi
−0.994730 + 0.102526i 0.967307π0.967307\pi
398398 0 0
399399 7424.00 0.931491
400400 0 0
401401 9906.00 1.23362 0.616811 0.787112i 0.288424π-0.288424\pi
0.616811 + 0.787112i 0.288424π0.288424\pi
402402 0 0
403403 10080.0i 1.24596i
404404 0 0
405405 1555.00i 0.190787i
406406 0 0
407407 −9288.00 −1.13118
408408 0 0
409409 4214.00 0.509459 0.254730 0.967012i 0.418014π-0.418014\pi
0.254730 + 0.967012i 0.418014π0.418014\pi
410410 0 0
411411 5736.00i 0.688409i
412412 0 0
413413 − 5568.00i − 0.663398i
414414 0 0
415415 −2820.00 −0.333562
416416 0 0
417417 8784.00 1.03155
418418 0 0
419419 7012.00i 0.817562i 0.912632 + 0.408781i 0.134046π0.134046\pi
−0.912632 + 0.408781i 0.865954π0.865954\pi
420420 0 0
421421 1602.00i 0.185455i 0.995692 + 0.0927277i 0.0295586π0.0295586\pi
−0.995692 + 0.0927277i 0.970441π0.970441\pi
422422 0 0
423423 −4312.00 −0.495642
424424 0 0
425425 2750.00 0.313870
426426 0 0
427427 − 9120.00i − 1.03360i
428428 0 0
429429 − 6048.00i − 0.680653i
430430 0 0
431431 3584.00 0.400546 0.200273 0.979740i 0.435817π-0.435817\pi
0.200273 + 0.979740i 0.435817π0.435817\pi
432432 0 0
433433 −3470.00 −0.385121 −0.192561 0.981285i 0.561679π-0.561679\pi
−0.192561 + 0.981285i 0.561679π0.561679\pi
434434 0 0
435435 − 3960.00i − 0.436477i
436436 0 0
437437 1856.00i 0.203168i
438438 0 0
439439 −3416.00 −0.371382 −0.185691 0.982608i 0.559452π-0.559452\pi
−0.185691 + 0.982608i 0.559452π0.559452\pi
440440 0 0
441441 −957.000 −0.103337
442442 0 0
443443 9708.00i 1.04118i 0.853808 + 0.520588i 0.174287π0.174287\pi
−0.853808 + 0.520588i 0.825713π0.825713\pi
444444 0 0
445445 5170.00i 0.550745i
446446 0 0
447447 9672.00 1.02342
448448 0 0
449449 −10366.0 −1.08954 −0.544768 0.838587i 0.683382π-0.683382\pi
−0.544768 + 0.838587i 0.683382π0.683382\pi
450450 0 0
451451 − 15912.0i − 1.66135i
452452 0 0
453453 − 14688.0i − 1.52340i
454454 0 0
455455 −3360.00 −0.346196
456456 0 0
457457 16742.0 1.71369 0.856847 0.515572i 0.172420π-0.172420\pi
0.856847 + 0.515572i 0.172420π0.172420\pi
458458 0 0
459459 16720.0i 1.70027i
460460 0 0
461461 − 1258.00i − 0.127095i −0.997979 0.0635476i 0.979759π-0.979759\pi
0.997979 0.0635476i 0.0202415π-0.0202415\pi
462462 0 0
463463 −13528.0 −1.35788 −0.678941 0.734193i 0.737561π-0.737561\pi
−0.678941 + 0.734193i 0.737561π0.737561\pi
464464 0 0
465465 4800.00 0.478698
466466 0 0
467467 − 6916.00i − 0.685298i −0.939463 0.342649i 0.888676π-0.888676\pi
0.939463 0.342649i 0.111324π-0.111324\pi
468468 0 0
469469 − 11072.0i − 1.09010i
470470 0 0
471471 1432.00 0.140091
472472 0 0
473473 10512.0 1.02187
474474 0 0
475475 − 2900.00i − 0.280129i
476476 0 0
477477 − 1562.00i − 0.149935i
478478 0 0
479479 −1728.00 −0.164832 −0.0824158 0.996598i 0.526264π-0.526264\pi
−0.0824158 + 0.996598i 0.526264π0.526264\pi
480480 0 0
481481 10836.0 1.02719
482482 0 0
483483 − 1024.00i − 0.0964671i
484484 0 0
485485 1910.00i 0.178822i
486486 0 0
487487 16656.0 1.54981 0.774903 0.632080i 0.217799π-0.217799\pi
0.774903 + 0.632080i 0.217799π0.217799\pi
488488 0 0
489489 −10256.0 −0.948451
490490 0 0
491491 − 1084.00i − 0.0996339i −0.998758 0.0498169i 0.984136π-0.984136\pi
0.998758 0.0498169i 0.0158638π-0.0158638\pi
492492 0 0
493493 − 21780.0i − 1.98970i
494494 0 0
495495 1980.00 0.179787
496496 0 0
497497 2688.00 0.242602
498498 0 0
499499 − 5804.00i − 0.520687i −0.965516 0.260343i 0.916164π-0.916164\pi
0.965516 0.260343i 0.0838358π-0.0838358\pi
500500 0 0
501501 12224.0i 1.09008i
502502 0 0
503503 10512.0 0.931823 0.465911 0.884831i 0.345727π-0.345727\pi
0.465911 + 0.884831i 0.345727π0.345727\pi
504504 0 0
505505 3370.00 0.296956
506506 0 0
507507 − 1732.00i − 0.151718i
508508 0 0
509509 − 4314.00i − 0.375667i −0.982201 0.187834i 0.939853π-0.939853\pi
0.982201 0.187834i 0.0601466π-0.0601466\pi
510510 0 0
511511 2144.00 0.185607
512512 0 0
513513 17632.0 1.51749
514514 0 0
515515 4960.00i 0.424396i
516516 0 0
517517 − 14112.0i − 1.20047i
518518 0 0
519519 −936.000 −0.0791635
520520 0 0
521521 1190.00 0.100067 0.0500334 0.998748i 0.484067π-0.484067\pi
0.0500334 + 0.998748i 0.484067π0.484067\pi
522522 0 0
523523 − 3780.00i − 0.316038i −0.987436 0.158019i 0.949489π-0.949489\pi
0.987436 0.158019i 0.0505107π-0.0505107\pi
524524 0 0
525525 1600.00i 0.133009i
526526 0 0
527527 26400.0 2.18217
528528 0 0
529529 −11911.0 −0.978959
530530 0 0
531531 − 3828.00i − 0.312846i
532532 0 0
533533 18564.0i 1.50862i
534534 0 0
535535 −2500.00 −0.202027
536536 0 0
537537 −2096.00 −0.168434
538538 0 0
539539 − 3132.00i − 0.250287i
540540 0 0
541541 − 11002.0i − 0.874331i −0.899381 0.437165i 0.855982π-0.855982\pi
0.899381 0.437165i 0.144018π-0.144018\pi
542542 0 0
543543 4552.00 0.359751
544544 0 0
545545 5230.00 0.411062
546546 0 0
547547 − 5908.00i − 0.461806i −0.972977 0.230903i 0.925832π-0.925832\pi
0.972977 0.230903i 0.0741680π-0.0741680\pi
548548 0 0
549549 − 6270.00i − 0.487426i
550550 0 0
551551 −22968.0 −1.77581
552552 0 0
553553 −12544.0 −0.964602
554554 0 0
555555 − 5160.00i − 0.394648i
556556 0 0
557557 14806.0i 1.12630i 0.826354 + 0.563151i 0.190411π0.190411\pi
−0.826354 + 0.563151i 0.809589π0.809589\pi
558558 0 0
559559 −12264.0 −0.927928
560560 0 0
561561 −15840.0 −1.19210
562562 0 0
563563 684.000i 0.0512028i 0.999672 + 0.0256014i 0.00815007π0.00815007\pi
−0.999672 + 0.0256014i 0.991850π0.991850\pi
564564 0 0
565565 2790.00i 0.207745i
566566 0 0
567567 −4976.00 −0.368558
568568 0 0
569569 2582.00 0.190234 0.0951169 0.995466i 0.469677π-0.469677\pi
0.0951169 + 0.995466i 0.469677π0.469677\pi
570570 0 0
571571 − 2540.00i − 0.186157i −0.995659 0.0930785i 0.970329π-0.970329\pi
0.995659 0.0930785i 0.0296708π-0.0296708\pi
572572 0 0
573573 6080.00i 0.443273i
574574 0 0
575575 −400.000 −0.0290107
576576 0 0
577577 22786.0 1.64401 0.822005 0.569480i 0.192856π-0.192856\pi
0.822005 + 0.569480i 0.192856π0.192856\pi
578578 0 0
579579 8568.00i 0.614981i
580580 0 0
581581 − 9024.00i − 0.644369i
582582 0 0
583583 5112.00 0.363152
584584 0 0
585585 −2310.00 −0.163259
586586 0 0
587587 7884.00i 0.554357i 0.960818 + 0.277178i 0.0893993π0.0893993\pi
−0.960818 + 0.277178i 0.910601π0.910601\pi
588588 0 0
589589 − 27840.0i − 1.94758i
590590 0 0
591591 9224.00 0.642005
592592 0 0
593593 −21902.0 −1.51671 −0.758354 0.651843i 0.773996π-0.773996\pi
−0.758354 + 0.651843i 0.773996π0.773996\pi
594594 0 0
595595 8800.00i 0.606327i
596596 0 0
597597 − 13152.0i − 0.901634i
598598 0 0
599599 15080.0 1.02863 0.514317 0.857600i 0.328045π-0.328045\pi
0.514317 + 0.857600i 0.328045π0.328045\pi
600600 0 0
601601 19702.0 1.33721 0.668603 0.743619i 0.266892π-0.266892\pi
0.668603 + 0.743619i 0.266892π0.266892\pi
602602 0 0
603603 − 7612.00i − 0.514071i
604604 0 0
605605 − 175.000i − 0.0117599i
606606 0 0
607607 −7320.00 −0.489472 −0.244736 0.969590i 0.578701π-0.578701\pi
−0.244736 + 0.969590i 0.578701π0.578701\pi
608608 0 0
609609 12672.0 0.843178
610610 0 0
611611 16464.0i 1.09012i
612612 0 0
613613 − 24350.0i − 1.60438i −0.597066 0.802192i 0.703667π-0.703667\pi
0.597066 0.802192i 0.296333π-0.296333\pi
614614 0 0
615615 8840.00 0.579615
616616 0 0
617617 −19546.0 −1.27535 −0.637676 0.770305i 0.720104π-0.720104\pi
−0.637676 + 0.770305i 0.720104π0.720104\pi
618618 0 0
619619 3476.00i 0.225706i 0.993612 + 0.112853i 0.0359990π0.0359990\pi
−0.993612 + 0.112853i 0.964001π0.964001\pi
620620 0 0
621621 − 2432.00i − 0.157154i
622622 0 0
623623 −16544.0 −1.06392
624624 0 0
625625 625.000 0.0400000
626626 0 0
627627 16704.0i 1.06394i
628628 0 0
629629 − 28380.0i − 1.79902i
630630 0 0
631631 21880.0 1.38039 0.690197 0.723621i 0.257524π-0.257524\pi
0.690197 + 0.723621i 0.257524π0.257524\pi
632632 0 0
633633 15504.0 0.973505
634634 0 0
635635 − 1640.00i − 0.102490i
636636 0 0
637637 3654.00i 0.227279i
638638 0 0
639639 1848.00 0.114406
640640 0 0
641641 20994.0 1.29362 0.646812 0.762649i 0.276102π-0.276102\pi
0.646812 + 0.762649i 0.276102π0.276102\pi
642642 0 0
643643 18204.0i 1.11648i 0.829680 + 0.558239i 0.188523π0.188523\pi
−0.829680 + 0.558239i 0.811477π0.811477\pi
644644 0 0
645645 5840.00i 0.356511i
646646 0 0
647647 −2064.00 −0.125416 −0.0627080 0.998032i 0.519974π-0.519974\pi
−0.0627080 + 0.998032i 0.519974π0.519974\pi
648648 0 0
649649 12528.0 0.757730
650650 0 0
651651 15360.0i 0.924740i
652652 0 0
653653 9942.00i 0.595805i 0.954596 + 0.297902i 0.0962870π0.0962870\pi
−0.954596 + 0.297902i 0.903713π0.903713\pi
654654 0 0
655655 1060.00 0.0632330
656656 0 0
657657 1474.00 0.0875285
658658 0 0
659659 − 24236.0i − 1.43263i −0.697779 0.716313i 0.745828π-0.745828\pi
0.697779 0.716313i 0.254172π-0.254172\pi
660660 0 0
661661 − 17614.0i − 1.03647i −0.855239 0.518234i 0.826590π-0.826590\pi
0.855239 0.518234i 0.173410π-0.173410\pi
662662 0 0
663663 18480.0 1.08251
664664 0 0
665665 9280.00 0.541147
666666 0 0
667667 3168.00i 0.183906i
668668 0 0
669669 − 22752.0i − 1.31486i
670670 0 0
671671 20520.0 1.18057
672672 0 0
673673 13058.0 0.747918 0.373959 0.927445i 0.378000π-0.378000\pi
0.373959 + 0.927445i 0.378000π0.378000\pi
674674 0 0
675675 3800.00i 0.216685i
676676 0 0
677677 33186.0i 1.88396i 0.335668 + 0.941980i 0.391038π0.391038\pi
−0.335668 + 0.941980i 0.608962π0.608962\pi
678678 0 0
679679 −6112.00 −0.345445
680680 0 0
681681 11184.0 0.629327
682682 0 0
683683 − 31716.0i − 1.77684i −0.459035 0.888418i 0.651805π-0.651805\pi
0.459035 0.888418i 0.348195π-0.348195\pi
684684 0 0
685685 7170.00i 0.399929i
686686 0 0
687687 −17784.0 −0.987630
688688 0 0
689689 −5964.00 −0.329768
690690 0 0
691691 2084.00i 0.114731i 0.998353 + 0.0573655i 0.0182700π0.0182700\pi
−0.998353 + 0.0573655i 0.981730π0.981730\pi
692692 0 0
693693 6336.00i 0.347308i
694694 0 0
695695 10980.0 0.599274
696696 0 0
697697 48620.0 2.64220
698698 0 0
699699 10088.0i 0.545870i
700700 0 0
701701 − 7418.00i − 0.399678i −0.979829 0.199839i 0.935958π-0.935958\pi
0.979829 0.199839i 0.0640418π-0.0640418\pi
702702 0 0
703703 −29928.0 −1.60563
704704 0 0
705705 7840.00 0.418825
706706 0 0
707707 10784.0i 0.573655i
708708 0 0
709709 18242.0i 0.966280i 0.875543 + 0.483140i 0.160504π0.160504\pi
−0.875543 + 0.483140i 0.839496π0.839496\pi
710710 0 0
711711 −8624.00 −0.454888
712712 0 0
713713 −3840.00 −0.201696
714714 0 0
715715 − 7560.00i − 0.395424i
716716 0 0
717717 3264.00i 0.170009i
718718 0 0
719719 −3024.00 −0.156851 −0.0784257 0.996920i 0.524989π-0.524989\pi
−0.0784257 + 0.996920i 0.524989π0.524989\pi
720720 0 0
721721 −15872.0 −0.819839
722722 0 0
723723 21688.0i 1.11561i
724724 0 0
725725 − 4950.00i − 0.253570i
726726 0 0
727727 −26176.0 −1.33537 −0.667685 0.744444i 0.732715π-0.732715\pi
−0.667685 + 0.744444i 0.732715π0.732715\pi
728728 0 0
729729 −19837.0 −1.00782
730730 0 0
731731 32120.0i 1.62517i
732732 0 0
733733 − 17818.0i − 0.897848i −0.893570 0.448924i 0.851807π-0.851807\pi
0.893570 0.448924i 0.148193π-0.148193\pi
734734 0 0
735735 1740.00 0.0873209
736736 0 0
737737 24912.0 1.24511
738738 0 0
739739 22052.0i 1.09769i 0.835923 + 0.548847i 0.184933π0.184933\pi
−0.835923 + 0.548847i 0.815067π0.815067\pi
740740 0 0
741741 − 19488.0i − 0.966140i
742742 0 0
743743 15840.0 0.782117 0.391059 0.920366i 0.372109π-0.372109\pi
0.391059 + 0.920366i 0.372109π0.372109\pi
744744 0 0
745745 12090.0 0.594555
746746 0 0
747747 − 6204.00i − 0.303872i
748748 0 0
749749 − 8000.00i − 0.390272i
750750 0 0
751751 −21024.0 −1.02154 −0.510770 0.859717i 0.670640π-0.670640\pi
−0.510770 + 0.859717i 0.670640π0.670640\pi
752752 0 0
753753 −23600.0 −1.14214
754754 0 0
755755 − 18360.0i − 0.885018i
756756 0 0
757757 38034.0i 1.82612i 0.407831 + 0.913058i 0.366285π0.366285\pi
−0.407831 + 0.913058i 0.633715π0.633715\pi
758758 0 0
759759 2304.00 0.110184
760760 0 0
761761 −37802.0 −1.80069 −0.900343 0.435182i 0.856684π-0.856684\pi
−0.900343 + 0.435182i 0.856684π0.856684\pi
762762 0 0
763763 16736.0i 0.794081i
764764 0 0
765765 6050.00i 0.285932i
766766 0 0
767767 −14616.0 −0.688075
768768 0 0
769769 15042.0 0.705369 0.352684 0.935742i 0.385269π-0.385269\pi
0.352684 + 0.935742i 0.385269π0.385269\pi
770770 0 0
771771 − 21000.0i − 0.980929i
772772 0 0
773773 − 5950.00i − 0.276852i −0.990373 0.138426i 0.955796π-0.955796\pi
0.990373 0.138426i 0.0442043π-0.0442043\pi
774774 0 0
775775 6000.00 0.278099
776776 0 0
777777 16512.0 0.762374
778778 0 0
779779 − 51272.0i − 2.35816i
780780 0 0
781781 6048.00i 0.277099i
782782 0 0
783783 30096.0 1.37362
784784 0 0
785785 1790.00 0.0813858
786786 0 0
787787 − 23364.0i − 1.05824i −0.848546 0.529121i 0.822522π-0.822522\pi
0.848546 0.529121i 0.177478π-0.177478\pi
788788 0 0
789789 − 24960.0i − 1.12624i
790790 0 0
791791 −8928.00 −0.401319
792792 0 0
793793 −23940.0 −1.07205
794794 0 0
795795 2840.00i 0.126697i
796796 0 0
797797 19846.0i 0.882034i 0.897499 + 0.441017i 0.145382π0.145382\pi
−0.897499 + 0.441017i 0.854618π0.854618\pi
798798 0 0
799799 43120.0 1.90923
800800 0 0
801801 −11374.0 −0.501724
802802 0 0
803803 4824.00i 0.211999i
804804 0 0
805805 − 1280.00i − 0.0560423i
806806 0 0
807807 −2856.00 −0.124580
808808 0 0
809809 −24762.0 −1.07613 −0.538063 0.842905i 0.680844π-0.680844\pi
−0.538063 + 0.842905i 0.680844π0.680844\pi
810810 0 0
811811 16644.0i 0.720653i 0.932826 + 0.360327i 0.117335π0.117335\pi
−0.932826 + 0.360327i 0.882665π0.882665\pi
812812 0 0
813813 8576.00i 0.369955i
814814 0 0
815815 −12820.0 −0.551000
816816 0 0
817817 33872.0 1.45047
818818 0 0
819819 − 7392.00i − 0.315381i
820820 0 0
821821 − 3182.00i − 0.135265i −0.997710 0.0676325i 0.978455π-0.978455\pi
0.997710 0.0676325i 0.0215445π-0.0215445\pi
822822 0 0
823823 −7504.00 −0.317829 −0.158914 0.987292i 0.550799π-0.550799\pi
−0.158914 + 0.987292i 0.550799π0.550799\pi
824824 0 0
825825 −3600.00 −0.151922
826826 0 0
827827 12604.0i 0.529969i 0.964253 + 0.264984i 0.0853668π0.0853668\pi
−0.964253 + 0.264984i 0.914633π0.914633\pi
828828 0 0
829829 12230.0i 0.512383i 0.966626 + 0.256191i 0.0824678π0.0824678\pi
−0.966626 + 0.256191i 0.917532π0.917532\pi
830830 0 0
831831 17864.0 0.745722
832832 0 0
833833 9570.00 0.398056
834834 0 0
835835 15280.0i 0.633277i
836836 0 0
837837 36480.0i 1.50649i
838838 0 0
839839 9656.00 0.397333 0.198666 0.980067i 0.436339π-0.436339\pi
0.198666 + 0.980067i 0.436339π0.436339\pi
840840 0 0
841841 −14815.0 −0.607446
842842 0 0
843843 − 21208.0i − 0.866480i
844844 0 0
845845 − 2165.00i − 0.0881400i
846846 0 0
847847 560.000 0.0227176
848848 0 0
849849 −27728.0 −1.12087
850850 0 0
851851 4128.00i 0.166282i
852852 0 0
853853 − 5806.00i − 0.233052i −0.993188 0.116526i 0.962824π-0.962824\pi
0.993188 0.116526i 0.0371759π-0.0371759\pi
854854 0 0
855855 6380.00 0.255195
856856 0 0
857857 39094.0 1.55826 0.779128 0.626865i 0.215662π-0.215662\pi
0.779128 + 0.626865i 0.215662π0.215662\pi
858858 0 0
859859 − 18876.0i − 0.749756i −0.927074 0.374878i 0.877685π-0.877685\pi
0.927074 0.374878i 0.122315π-0.122315\pi
860860 0 0
861861 28288.0i 1.11969i
862862 0 0
863863 −32296.0 −1.27389 −0.636946 0.770909i 0.719803π-0.719803\pi
−0.636946 + 0.770909i 0.719803π0.719803\pi
864864 0 0
865865 −1170.00 −0.0459898
866866 0 0
867867 − 28748.0i − 1.12611i
868868 0 0
869869 − 28224.0i − 1.10176i
870870 0 0
871871 −29064.0 −1.13065
872872 0 0
873873 −4202.00 −0.162905
874874 0 0
875875 2000.00i 0.0772712i
876876 0 0
877877 − 9578.00i − 0.368787i −0.982853 0.184393i 0.940968π-0.940968\pi
0.982853 0.184393i 0.0590321π-0.0590321\pi
878878 0 0
879879 16136.0 0.619174
880880 0 0
881881 −41710.0 −1.59506 −0.797529 0.603281i 0.793860π-0.793860\pi
−0.797529 + 0.603281i 0.793860π0.793860\pi
882882 0 0
883883 − 2260.00i − 0.0861326i −0.999072 0.0430663i 0.986287π-0.986287\pi
0.999072 0.0430663i 0.0137127π-0.0137127\pi
884884 0 0
885885 6960.00i 0.264359i
886886 0 0
887887 −33696.0 −1.27554 −0.637768 0.770228i 0.720142π-0.720142\pi
−0.637768 + 0.770228i 0.720142π0.720142\pi
888888 0 0
889889 5248.00 0.197989
890890 0 0
891891 − 11196.0i − 0.420965i
892892 0 0
893893 − 45472.0i − 1.70399i
894894 0 0
895895 −2620.00 −0.0978513
896896 0 0
897897 −2688.00 −0.100055
898898 0 0
899899 − 47520.0i − 1.76294i
900900 0 0
901901 15620.0i 0.577556i
902902 0 0
903903 −18688.0 −0.688702
904904 0 0
905905 5690.00 0.208997
906906 0 0
907907 7756.00i 0.283940i 0.989871 + 0.141970i 0.0453437π0.0453437\pi
−0.989871 + 0.141970i 0.954656π0.954656\pi
908908 0 0
909909 7414.00i 0.270525i
910910 0 0
911911 5312.00 0.193188 0.0965941 0.995324i 0.469205π-0.469205\pi
0.0965941 + 0.995324i 0.469205π0.469205\pi
912912 0 0
913913 20304.0 0.735996
914914 0 0
915915 11400.0i 0.411882i
916916 0 0
917917 3392.00i 0.122152i
918918 0 0
919919 −23576.0 −0.846246 −0.423123 0.906072i 0.639066π-0.639066\pi
−0.423123 + 0.906072i 0.639066π0.639066\pi
920920 0 0
921921 15344.0 0.548971
922922 0 0
923923 − 7056.00i − 0.251626i
924924 0 0
925925 − 6450.00i − 0.229270i
926926 0 0
927927 −10912.0 −0.386620
928928 0 0
929929 −19038.0 −0.672354 −0.336177 0.941799i 0.609134π-0.609134\pi
−0.336177 + 0.941799i 0.609134π0.609134\pi
930930 0 0
931931 − 10092.0i − 0.355265i
932932 0 0
933933 − 2656.00i − 0.0931978i
934934 0 0
935935 −19800.0 −0.692545
936936 0 0
937937 −20570.0 −0.717175 −0.358587 0.933496i 0.616741π-0.616741\pi
−0.358587 + 0.933496i 0.616741π0.616741\pi
938938 0 0
939939 11944.0i 0.415099i
940940 0 0
941941 − 21386.0i − 0.740875i −0.928857 0.370438i 0.879208π-0.879208\pi
0.928857 0.370438i 0.120792π-0.120792\pi
942942 0 0
943943 −7072.00 −0.244216
944944 0 0
945945 −12160.0 −0.418587
946946 0 0
947947 − 38020.0i − 1.30463i −0.757948 0.652315i 0.773798π-0.773798\pi
0.757948 0.652315i 0.226202π-0.226202\pi
948948 0 0
949949 − 5628.00i − 0.192511i
950950 0 0
951951 10904.0 0.371805
952952 0 0
953953 −20202.0 −0.686681 −0.343340 0.939211i 0.611558π-0.611558\pi
−0.343340 + 0.939211i 0.611558π0.611558\pi
954954 0 0
955955 7600.00i 0.257519i
956956 0 0
957957 28512.0i 0.963074i
958958 0 0
959959 −22944.0 −0.772576
960960 0 0
961961 27809.0 0.933470
962962 0 0
963963 − 5500.00i − 0.184045i
964964 0 0
965965 10710.0i 0.357272i
966966 0 0
967967 29840.0 0.992337 0.496168 0.868226i 0.334740π-0.334740\pi
0.496168 + 0.868226i 0.334740π0.334740\pi
968968 0 0
969969 −51040.0 −1.69210
970970 0 0
971971 − 12476.0i − 0.412332i −0.978517 0.206166i 0.933901π-0.933901\pi
0.978517 0.206166i 0.0660986π-0.0660986\pi
972972 0 0
973973 35136.0i 1.15767i
974974 0 0
975975 4200.00 0.137957
976976 0 0
977977 −36974.0 −1.21075 −0.605375 0.795940i 0.706977π-0.706977\pi
−0.605375 + 0.795940i 0.706977π0.706977\pi
978978 0 0
979979 − 37224.0i − 1.21520i
980980 0 0
981981 11506.0i 0.374473i
982982 0 0
983983 −16368.0 −0.531087 −0.265543 0.964099i 0.585551π-0.585551\pi
−0.265543 + 0.964099i 0.585551π0.585551\pi
984984 0 0
985985 11530.0 0.372971
986986 0 0
987987 25088.0i 0.809078i
988988 0 0
989989 − 4672.00i − 0.150213i
990990 0 0
991991 49552.0 1.58837 0.794183 0.607678i 0.207899π-0.207899\pi
0.794183 + 0.607678i 0.207899π0.207899\pi
992992 0 0
993993 −36848.0 −1.17758
994994 0 0
995995 − 16440.0i − 0.523802i
996996 0 0
997997 − 24414.0i − 0.775526i −0.921759 0.387763i 0.873248π-0.873248\pi
0.921759 0.387763i 0.126752π-0.126752\pi
998998 0 0
999999 39216.0 1.24198
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 1280.4.d.m.641.1 2
4.3 odd 2 1280.4.d.d.641.2 2
8.3 odd 2 1280.4.d.d.641.1 2
8.5 even 2 inner 1280.4.d.m.641.2 2
16.3 odd 4 320.4.a.e.1.1 1
16.5 even 4 80.4.a.b.1.1 1
16.11 odd 4 40.4.a.b.1.1 1
16.13 even 4 320.4.a.j.1.1 1
48.5 odd 4 720.4.a.d.1.1 1
48.11 even 4 360.4.a.f.1.1 1
80.19 odd 4 1600.4.a.bk.1.1 1
80.27 even 4 200.4.c.f.49.1 2
80.29 even 4 1600.4.a.q.1.1 1
80.37 odd 4 400.4.c.h.49.2 2
80.43 even 4 200.4.c.f.49.2 2
80.53 odd 4 400.4.c.h.49.1 2
80.59 odd 4 200.4.a.d.1.1 1
80.69 even 4 400.4.a.p.1.1 1
112.27 even 4 1960.4.a.e.1.1 1
240.59 even 4 1800.4.a.h.1.1 1
240.107 odd 4 1800.4.f.d.649.2 2
240.203 odd 4 1800.4.f.d.649.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.4.a.b.1.1 1 16.11 odd 4
80.4.a.b.1.1 1 16.5 even 4
200.4.a.d.1.1 1 80.59 odd 4
200.4.c.f.49.1 2 80.27 even 4
200.4.c.f.49.2 2 80.43 even 4
320.4.a.e.1.1 1 16.3 odd 4
320.4.a.j.1.1 1 16.13 even 4
360.4.a.f.1.1 1 48.11 even 4
400.4.a.p.1.1 1 80.69 even 4
400.4.c.h.49.1 2 80.53 odd 4
400.4.c.h.49.2 2 80.37 odd 4
720.4.a.d.1.1 1 48.5 odd 4
1280.4.d.d.641.1 2 8.3 odd 2
1280.4.d.d.641.2 2 4.3 odd 2
1280.4.d.m.641.1 2 1.1 even 1 trivial
1280.4.d.m.641.2 2 8.5 even 2 inner
1600.4.a.q.1.1 1 80.29 even 4
1600.4.a.bk.1.1 1 80.19 odd 4
1800.4.a.h.1.1 1 240.59 even 4
1800.4.f.d.649.1 2 240.203 odd 4
1800.4.f.d.649.2 2 240.107 odd 4
1960.4.a.e.1.1 1 112.27 even 4