Properties

Label 800.6.d.c.401.19
Level 800800
Weight 66
Character 800.401
Analytic conductor 128.307128.307
Analytic rank 00
Dimension 2020
Inner twists 22

Related objects

Downloads

Learn more

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: x202x1917x18+78x17+253x16884x15+2396x14+19376x13++1099511627776 x^{20} - 2 x^{19} - 17 x^{18} + 78 x^{17} + 253 x^{16} - 884 x^{15} + 2396 x^{14} + 19376 x^{13} + \cdots + 1099511627776 Copy content Toggle raw display
Coefficient ring: Z[a1,,a19]\Z[a_1, \ldots, a_{19}]
Coefficient ring index: 29334512 2^{93}\cdot 3^{4}\cdot 5^{12}
Twist minimal: no (minimal twist has level 40)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 401.19
Root 3.90102+0.884346i-3.90102 + 0.884346i of defining polynomial
Character χ\chi == 800.401
Dual form 800.6.d.c.401.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+25.4343iq356.4938q7403.904q9+261.019iq11720.631iq13+1876.44q17+1992.33iq191436.88iq21+2570.29q234092.49iq27+1700.16iq29+7734.68q316638.83q3312228.1iq37+18328.8q39+14979.3q41+18113.9iq43+2141.03q4713615.4q49+47726.0iq511605.71iq5350673.5q572680.90iq59+44521.9iq61+22818.1q6312486.0iq67+65373.7iq698189.38q71+41082.7q7314746.0iq7746325.9q79+5940.95q81+61655.4iq8343242.3q87+53205.4q89+40711.2iq91+196726.iq93+39211.8q97105427.iq99+O(q100)q+25.4343i q^{3} -56.4938 q^{7} -403.904 q^{9} +261.019i q^{11} -720.631i q^{13} +1876.44 q^{17} +1992.33i q^{19} -1436.88i q^{21} +2570.29 q^{23} -4092.49i q^{27} +1700.16i q^{29} +7734.68 q^{31} -6638.83 q^{33} -12228.1i q^{37} +18328.8 q^{39} +14979.3 q^{41} +18113.9i q^{43} +2141.03 q^{47} -13615.4 q^{49} +47726.0i q^{51} -1605.71i q^{53} -50673.5 q^{57} -2680.90i q^{59} +44521.9i q^{61} +22818.1 q^{63} -12486.0i q^{67} +65373.7i q^{69} -8189.38 q^{71} +41082.7 q^{73} -14746.0i q^{77} -46325.9 q^{79} +5940.95 q^{81} +61655.4i q^{83} -43242.3 q^{87} +53205.4 q^{89} +40711.2i q^{91} +196726. i q^{93} +39211.8 q^{97} -105427. i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q196q71620q94676q237160q315672q33+44904q39+11608q41+44180q47+18756q495032q57+240620q63+200312q71+105136q73282080q79+147376q97+O(q100) 20 q - 196 q^{7} - 1620 q^{9} - 4676 q^{23} - 7160 q^{31} - 5672 q^{33} + 44904 q^{39} + 11608 q^{41} + 44180 q^{47} + 18756 q^{49} - 5032 q^{57} + 240620 q^{63} + 200312 q^{71} + 105136 q^{73} - 282080 q^{79}+ \cdots - 147376 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 25.4343i 1.63161i 0.578326 + 0.815806i 0.303706π0.303706\pi
−0.578326 + 0.815806i 0.696294π0.696294\pi
44 0 0
55 0 0
66 0 0
77 −56.4938 −0.435769 −0.217884 0.975975i 0.569916π-0.569916\pi
−0.217884 + 0.975975i 0.569916π0.569916\pi
88 0 0
99 −403.904 −1.66216
1010 0 0
1111 261.019i 0.650414i 0.945643 + 0.325207i 0.105434π0.105434\pi
−0.945643 + 0.325207i 0.894566π0.894566\pi
1212 0 0
1313 − 720.631i − 1.18265i −0.806435 0.591323i 0.798606π-0.798606\pi
0.806435 0.591323i 0.201394π-0.201394\pi
1414 0 0
1515 0 0
1616 0 0
1717 1876.44 1.57476 0.787378 0.616471i 0.211438π-0.211438\pi
0.787378 + 0.616471i 0.211438π0.211438\pi
1818 0 0
1919 1992.33i 1.26613i 0.774100 + 0.633063i 0.218203π0.218203\pi
−0.774100 + 0.633063i 0.781797π0.781797\pi
2020 0 0
2121 − 1436.88i − 0.711005i
2222 0 0
2323 2570.29 1.01313 0.506563 0.862203i 0.330916π-0.330916\pi
0.506563 + 0.862203i 0.330916π0.330916\pi
2424 0 0
2525 0 0
2626 0 0
2727 − 4092.49i − 1.08038i
2828 0 0
2929 1700.16i 0.375400i 0.982226 + 0.187700i 0.0601032π0.0601032\pi
−0.982226 + 0.187700i 0.939897π0.939897\pi
3030 0 0
3131 7734.68 1.44557 0.722783 0.691075i 0.242863π-0.242863\pi
0.722783 + 0.691075i 0.242863π0.242863\pi
3232 0 0
3333 −6638.83 −1.06122
3434 0 0
3535 0 0
3636 0 0
3737 − 12228.1i − 1.46844i −0.678913 0.734218i 0.737549π-0.737549\pi
0.678913 0.734218i 0.262451π-0.262451\pi
3838 0 0
3939 18328.8 1.92962
4040 0 0
4141 14979.3 1.39166 0.695830 0.718206i 0.255037π-0.255037\pi
0.695830 + 0.718206i 0.255037π0.255037\pi
4242 0 0
4343 18113.9i 1.49397i 0.664842 + 0.746984i 0.268499π0.268499\pi
−0.664842 + 0.746984i 0.731501π0.731501\pi
4444 0 0
4545 0 0
4646 0 0
4747 2141.03 0.141377 0.0706885 0.997498i 0.477480π-0.477480\pi
0.0706885 + 0.997498i 0.477480π0.477480\pi
4848 0 0
4949 −13615.4 −0.810106
5050 0 0
5151 47726.0i 2.56939i
5252 0 0
5353 − 1605.71i − 0.0785192i −0.999229 0.0392596i 0.987500π-0.987500\pi
0.999229 0.0392596i 0.0124999π-0.0124999\pi
5454 0 0
5555 0 0
5656 0 0
5757 −50673.5 −2.06583
5858 0 0
5959 − 2680.90i − 0.100265i −0.998743 0.0501327i 0.984036π-0.984036\pi
0.998743 0.0501327i 0.0159644π-0.0159644\pi
6060 0 0
6161 44521.9i 1.53197i 0.642860 + 0.765984i 0.277748π0.277748\pi
−0.642860 + 0.765984i 0.722252π0.722252\pi
6262 0 0
6363 22818.1 0.724316
6464 0 0
6565 0 0
6666 0 0
6767 − 12486.0i − 0.339809i −0.985461 0.169905i 0.945654π-0.945654\pi
0.985461 0.169905i 0.0543460π-0.0543460\pi
6868 0 0
6969 65373.7i 1.65303i
7070 0 0
7171 −8189.38 −0.192799 −0.0963996 0.995343i 0.530733π-0.530733\pi
−0.0963996 + 0.995343i 0.530733π0.530733\pi
7272 0 0
7373 41082.7 0.902302 0.451151 0.892448i 0.351014π-0.351014\pi
0.451151 + 0.892448i 0.351014π0.351014\pi
7474 0 0
7575 0 0
7676 0 0
7777 − 14746.0i − 0.283430i
7878 0 0
7979 −46325.9 −0.835134 −0.417567 0.908646i 0.637117π-0.637117\pi
−0.417567 + 0.908646i 0.637117π0.637117\pi
8080 0 0
8181 5940.95 0.100611
8282 0 0
8383 61655.4i 0.982372i 0.871055 + 0.491186i 0.163436π0.163436\pi
−0.871055 + 0.491186i 0.836564π0.836564\pi
8484 0 0
8585 0 0
8686 0 0
8787 −43242.3 −0.612507
8888 0 0
8989 53205.4 0.712001 0.356000 0.934486i 0.384140π-0.384140\pi
0.356000 + 0.934486i 0.384140π0.384140\pi
9090 0 0
9191 40711.2i 0.515360i
9292 0 0
9393 196726.i 2.35860i
9494 0 0
9595 0 0
9696 0 0
9797 39211.8 0.423143 0.211571 0.977363i 0.432142π-0.432142\pi
0.211571 + 0.977363i 0.432142π0.432142\pi
9898 0 0
9999 − 105427.i − 1.08109i
100100 0 0
101101 − 41893.0i − 0.408637i −0.978904 0.204319i 0.934502π-0.934502\pi
0.978904 0.204319i 0.0654979π-0.0654979\pi
102102 0 0
103103 −118358. −1.09927 −0.549635 0.835405i 0.685233π-0.685233\pi
−0.549635 + 0.835405i 0.685233π0.685233\pi
104104 0 0
105105 0 0
106106 0 0
107107 − 147978.i − 1.24951i −0.780822 0.624754i 0.785199π-0.785199\pi
0.780822 0.624754i 0.214801π-0.214801\pi
108108 0 0
109109 126538.i 1.02013i 0.860135 + 0.510066i 0.170379π0.170379\pi
−0.860135 + 0.510066i 0.829621π0.829621\pi
110110 0 0
111111 311014. 2.39592
112112 0 0
113113 221898. 1.63478 0.817388 0.576088i 0.195421π-0.195421\pi
0.817388 + 0.576088i 0.195421π0.195421\pi
114114 0 0
115115 0 0
116116 0 0
117117 291066.i 1.96574i
118118 0 0
119119 −106007. −0.686229
120120 0 0
121121 92920.2 0.576961
122122 0 0
123123 380989.i 2.27065i
124124 0 0
125125 0 0
126126 0 0
127127 237825. 1.30842 0.654212 0.756312i 0.273001π-0.273001\pi
0.654212 + 0.756312i 0.273001π0.273001\pi
128128 0 0
129129 −460715. −2.43758
130130 0 0
131131 − 151213.i − 0.769856i −0.922947 0.384928i 0.874226π-0.874226\pi
0.922947 0.384928i 0.125774π-0.125774\pi
132132 0 0
133133 − 112554.i − 0.551738i
134134 0 0
135135 0 0
136136 0 0
137137 −163216. −0.742954 −0.371477 0.928442i 0.621148π-0.621148\pi
−0.371477 + 0.928442i 0.621148π0.621148\pi
138138 0 0
139139 7490.33i 0.0328824i 0.999865 + 0.0164412i 0.00523364π0.00523364\pi
−0.999865 + 0.0164412i 0.994766π0.994766\pi
140140 0 0
141141 54455.7i 0.230672i
142142 0 0
143143 188098. 0.769209
144144 0 0
145145 0 0
146146 0 0
147147 − 346300.i − 1.32178i
148148 0 0
149149 35543.3i 0.131157i 0.997847 + 0.0655786i 0.0208893π0.0208893\pi
−0.997847 + 0.0655786i 0.979111π0.979111\pi
150150 0 0
151151 −549802. −1.96229 −0.981147 0.193263i 0.938093π-0.938093\pi
−0.981147 + 0.193263i 0.938093π0.938093\pi
152152 0 0
153153 −757903. −2.61749
154154 0 0
155155 0 0
156156 0 0
157157 252420.i 0.817287i 0.912694 + 0.408643i 0.133998π0.133998\pi
−0.912694 + 0.408643i 0.866002π0.866002\pi
158158 0 0
159159 40840.0 0.128113
160160 0 0
161161 −145206. −0.441488
162162 0 0
163163 − 383218.i − 1.12974i −0.825182 0.564868i 0.808927π-0.808927\pi
0.825182 0.564868i 0.191073π-0.191073\pi
164164 0 0
165165 0 0
166166 0 0
167167 108418. 0.300821 0.150411 0.988624i 0.451940π-0.451940\pi
0.150411 + 0.988624i 0.451940π0.451940\pi
168168 0 0
169169 −148016. −0.398650
170170 0 0
171171 − 804710.i − 2.10450i
172172 0 0
173173 − 305932.i − 0.777157i −0.921416 0.388579i 0.872966π-0.872966\pi
0.921416 0.388579i 0.127034π-0.127034\pi
174174 0 0
175175 0 0
176176 0 0
177177 68186.9 0.163594
178178 0 0
179179 209868.i 0.489568i 0.969578 + 0.244784i 0.0787170π0.0787170\pi
−0.969578 + 0.244784i 0.921283π0.921283\pi
180180 0 0
181181 212990.i 0.483239i 0.970371 + 0.241620i 0.0776786π0.0776786\pi
−0.970371 + 0.241620i 0.922321π0.922321\pi
182182 0 0
183183 −1.13239e6 −2.49958
184184 0 0
185185 0 0
186186 0 0
187187 489787.i 1.02424i
188188 0 0
189189 231201.i 0.470798i
190190 0 0
191191 177246. 0.351555 0.175777 0.984430i 0.443756π-0.443756\pi
0.175777 + 0.984430i 0.443756π0.443756\pi
192192 0 0
193193 −758117. −1.46502 −0.732509 0.680758i 0.761651π-0.761651\pi
−0.732509 + 0.680758i 0.761651π0.761651\pi
194194 0 0
195195 0 0
196196 0 0
197197 353509.i 0.648985i 0.945888 + 0.324492i 0.105193π0.105193\pi
−0.945888 + 0.324492i 0.894807π0.894807\pi
198198 0 0
199199 −233027. −0.417132 −0.208566 0.978008i 0.566880π-0.566880\pi
−0.208566 + 0.978008i 0.566880π0.566880\pi
200200 0 0
201201 317572. 0.554437
202202 0 0
203203 − 96048.4i − 0.163587i
204204 0 0
205205 0 0
206206 0 0
207207 −1.03815e6 −1.68397
208208 0 0
209209 −520035. −0.823507
210210 0 0
211211 401222.i 0.620410i 0.950670 + 0.310205i 0.100398π0.100398\pi
−0.950670 + 0.310205i 0.899602π0.899602\pi
212212 0 0
213213 − 208291.i − 0.314573i
214214 0 0
215215 0 0
216216 0 0
217217 −436961. −0.629932
218218 0 0
219219 1.04491e6i 1.47221i
220220 0 0
221221 − 1.35222e6i − 1.86238i
222222 0 0
223223 −475659. −0.640521 −0.320260 0.947330i 0.603770π-0.603770\pi
−0.320260 + 0.947330i 0.603770π0.603770\pi
224224 0 0
225225 0 0
226226 0 0
227227 − 28559.0i − 0.0367856i −0.999831 0.0183928i 0.994145π-0.994145\pi
0.999831 0.0183928i 0.00585494π-0.00585494\pi
228228 0 0
229229 969736.i 1.22198i 0.791638 + 0.610991i 0.209229π0.209229\pi
−0.791638 + 0.610991i 0.790771π0.790771\pi
230230 0 0
231231 375053. 0.462448
232232 0 0
233233 16005.7 0.0193146 0.00965728 0.999953i 0.496926π-0.496926\pi
0.00965728 + 0.999953i 0.496926π0.496926\pi
234234 0 0
235235 0 0
236236 0 0
237237 − 1.17827e6i − 1.36261i
238238 0 0
239239 −1.26598e6 −1.43361 −0.716807 0.697272i 0.754397π-0.754397\pi
−0.716807 + 0.697272i 0.754397π0.754397\pi
240240 0 0
241241 414590. 0.459807 0.229904 0.973213i 0.426159π-0.426159\pi
0.229904 + 0.973213i 0.426159π0.426159\pi
242242 0 0
243243 − 843371.i − 0.916227i
244244 0 0
245245 0 0
246246 0 0
247247 1.43573e6 1.49738
248248 0 0
249249 −1.56816e6 −1.60285
250250 0 0
251251 − 184150.i − 0.184496i −0.995736 0.0922479i 0.970595π-0.970595\pi
0.995736 0.0922479i 0.0294052π-0.0294052\pi
252252 0 0
253253 670895.i 0.658951i
254254 0 0
255255 0 0
256256 0 0
257257 846268. 0.799236 0.399618 0.916682i 0.369143π-0.369143\pi
0.399618 + 0.916682i 0.369143π0.369143\pi
258258 0 0
259259 690813.i 0.639899i
260260 0 0
261261 − 686701.i − 0.623974i
262262 0 0
263263 −1.53385e6 −1.36740 −0.683698 0.729765i 0.739629π-0.739629\pi
−0.683698 + 0.729765i 0.739629π0.739629\pi
264264 0 0
265265 0 0
266266 0 0
267267 1.35324e6i 1.16171i
268268 0 0
269269 646714.i 0.544918i 0.962167 + 0.272459i 0.0878370π0.0878370\pi
−0.962167 + 0.272459i 0.912163π0.912163\pi
270270 0 0
271271 1.58318e6 1.30950 0.654752 0.755844i 0.272773π-0.272773\pi
0.654752 + 0.755844i 0.272773π0.272773\pi
272272 0 0
273273 −1.03546e6 −0.840867
274274 0 0
275275 0 0
276276 0 0
277277 − 1.62475e6i − 1.27229i −0.771568 0.636147i 0.780527π-0.780527\pi
0.771568 0.636147i 0.219473π-0.219473\pi
278278 0 0
279279 −3.12407e6 −2.40276
280280 0 0
281281 −1.48375e6 −1.12097 −0.560487 0.828163i 0.689386π-0.689386\pi
−0.560487 + 0.828163i 0.689386π0.689386\pi
282282 0 0
283283 1.18244e6i 0.877634i 0.898577 + 0.438817i 0.144602π0.144602\pi
−0.898577 + 0.438817i 0.855398π0.855398\pi
284284 0 0
285285 0 0
286286 0 0
287287 −846241. −0.606442
288288 0 0
289289 2.10118e6 1.47985
290290 0 0
291291 997325.i 0.690405i
292292 0 0
293293 887981.i 0.604275i 0.953264 + 0.302137i 0.0977002π0.0977002\pi
−0.953264 + 0.302137i 0.902300π0.902300\pi
294294 0 0
295295 0 0
296296 0 0
297297 1.06822e6 0.702697
298298 0 0
299299 − 1.85223e6i − 1.19817i
300300 0 0
301301 − 1.02332e6i − 0.651024i
302302 0 0
303303 1.06552e6 0.666738
304304 0 0
305305 0 0
306306 0 0
307307 1.47690e6i 0.894346i 0.894447 + 0.447173i 0.147569π0.147569\pi
−0.894447 + 0.447173i 0.852431π0.852431\pi
308308 0 0
309309 − 3.01035e6i − 1.79358i
310310 0 0
311311 −364521. −0.213708 −0.106854 0.994275i 0.534078π-0.534078\pi
−0.106854 + 0.994275i 0.534078π0.534078\pi
312312 0 0
313313 −324246. −0.187074 −0.0935371 0.995616i 0.529817π-0.529817\pi
−0.0935371 + 0.995616i 0.529817π0.529817\pi
314314 0 0
315315 0 0
316316 0 0
317317 1.55670e6i 0.870074i 0.900413 + 0.435037i 0.143265π0.143265\pi
−0.900413 + 0.435037i 0.856735π0.856735\pi
318318 0 0
319319 −443773. −0.244165
320320 0 0
321321 3.76373e6 2.03871
322322 0 0
323323 3.73849e6i 1.99384i
324324 0 0
325325 0 0
326326 0 0
327327 −3.21842e6 −1.66446
328328 0 0
329329 −120955. −0.0616077
330330 0 0
331331 558769.i 0.280325i 0.990128 + 0.140163i 0.0447626π0.0447626\pi
−0.990128 + 0.140163i 0.955237π0.955237\pi
332332 0 0
333333 4.93899e6i 2.44077i
334334 0 0
335335 0 0
336336 0 0
337337 −2.18320e6 −1.04717 −0.523587 0.851972i 0.675407π-0.675407\pi
−0.523587 + 0.851972i 0.675407π0.675407\pi
338338 0 0
339339 5.64384e6i 2.66732i
340340 0 0
341341 2.01890e6i 0.940216i
342342 0 0
343343 1.71868e6 0.788787
344344 0 0
345345 0 0
346346 0 0
347347 2.53924e6i 1.13209i 0.824375 + 0.566043i 0.191527π0.191527\pi
−0.824375 + 0.566043i 0.808473π0.808473\pi
348348 0 0
349349 2.58452e6i 1.13584i 0.823085 + 0.567918i 0.192251π0.192251\pi
−0.823085 + 0.567918i 0.807749π0.807749\pi
350350 0 0
351351 −2.94918e6 −1.27771
352352 0 0
353353 −284338. −0.121450 −0.0607250 0.998155i 0.519341π-0.519341\pi
−0.0607250 + 0.998155i 0.519341π0.519341\pi
354354 0 0
355355 0 0
356356 0 0
357357 − 2.69623e6i − 1.11966i
358358 0 0
359359 1.97109e6 0.807179 0.403590 0.914940i 0.367762π-0.367762\pi
0.403590 + 0.914940i 0.367762π0.367762\pi
360360 0 0
361361 −1.49328e6 −0.603077
362362 0 0
363363 2.36336e6i 0.941377i
364364 0 0
365365 0 0
366366 0 0
367367 1.04179e6 0.403754 0.201877 0.979411i 0.435296π-0.435296\pi
0.201877 + 0.979411i 0.435296π0.435296\pi
368368 0 0
369369 −6.05022e6 −2.31316
370370 0 0
371371 90712.4i 0.0342162i
372372 0 0
373373 1.58767e6i 0.590866i 0.955363 + 0.295433i 0.0954639π0.0954639\pi
−0.955363 + 0.295433i 0.904536π0.904536\pi
374374 0 0
375375 0 0
376376 0 0
377377 1.22519e6 0.443965
378378 0 0
379379 − 995922.i − 0.356145i −0.984017 0.178073i 0.943014π-0.943014\pi
0.984017 0.178073i 0.0569862π-0.0569862\pi
380380 0 0
381381 6.04892e6i 2.13484i
382382 0 0
383383 1.53418e6 0.534415 0.267208 0.963639i 0.413899π-0.413899\pi
0.267208 + 0.963639i 0.413899π0.413899\pi
384384 0 0
385385 0 0
386386 0 0
387387 − 7.31629e6i − 2.48321i
388388 0 0
389389 − 4.70941e6i − 1.57795i −0.614428 0.788973i 0.710613π-0.710613\pi
0.614428 0.788973i 0.289387π-0.289387\pi
390390 0 0
391391 4.82301e6 1.59542
392392 0 0
393393 3.84599e6 1.25611
394394 0 0
395395 0 0
396396 0 0
397397 − 485420.i − 0.154576i −0.997009 0.0772879i 0.975374π-0.975374\pi
0.997009 0.0772879i 0.0246261π-0.0246261\pi
398398 0 0
399399 2.86274e6 0.900223
400400 0 0
401401 1.73402e6 0.538508 0.269254 0.963069i 0.413223π-0.413223\pi
0.269254 + 0.963069i 0.413223π0.413223\pi
402402 0 0
403403 − 5.57385e6i − 1.70959i
404404 0 0
405405 0 0
406406 0 0
407407 3.19177e6 0.955092
408408 0 0
409409 −853587. −0.252313 −0.126156 0.992010i 0.540264π-0.540264\pi
−0.126156 + 0.992010i 0.540264π0.540264\pi
410410 0 0
411411 − 4.15129e6i − 1.21221i
412412 0 0
413413 151454.i 0.0436925i
414414 0 0
415415 0 0
416416 0 0
417417 −190511. −0.0536514
418418 0 0
419419 3.86903e6i 1.07663i 0.842743 + 0.538316i 0.180939π0.180939\pi
−0.842743 + 0.538316i 0.819061π0.819061\pi
420420 0 0
421421 1.15014e6i 0.316260i 0.987418 + 0.158130i 0.0505464π0.0505464\pi
−0.987418 + 0.158130i 0.949454π0.949454\pi
422422 0 0
423423 −864773. −0.234991
424424 0 0
425425 0 0
426426 0 0
427427 − 2.51522e6i − 0.667583i
428428 0 0
429429 4.78415e6i 1.25505i
430430 0 0
431431 3.09078e6 0.801448 0.400724 0.916199i 0.368759π-0.368759\pi
0.400724 + 0.916199i 0.368759π0.368759\pi
432432 0 0
433433 −2.47892e6 −0.635394 −0.317697 0.948192i 0.602910π-0.602910\pi
−0.317697 + 0.948192i 0.602910π0.602910\pi
434434 0 0
435435 0 0
436436 0 0
437437 5.12087e6i 1.28275i
438438 0 0
439439 −997159. −0.246947 −0.123473 0.992348i 0.539403π-0.539403\pi
−0.123473 + 0.992348i 0.539403π0.539403\pi
440440 0 0
441441 5.49934e6 1.34652
442442 0 0
443443 2.10966e6i 0.510744i 0.966843 + 0.255372i 0.0821980π0.0821980\pi
−0.966843 + 0.255372i 0.917802π0.917802\pi
444444 0 0
445445 0 0
446446 0 0
447447 −904020. −0.213998
448448 0 0
449449 6.24963e6 1.46298 0.731490 0.681852i 0.238825π-0.238825\pi
0.731490 + 0.681852i 0.238825π0.238825\pi
450450 0 0
451451 3.90989e6i 0.905156i
452452 0 0
453453 − 1.39838e7i − 3.20170i
454454 0 0
455455 0 0
456456 0 0
457457 −1.87669e6 −0.420340 −0.210170 0.977665i 0.567402π-0.567402\pi
−0.210170 + 0.977665i 0.567402π0.567402\pi
458458 0 0
459459 − 7.67933e6i − 1.70134i
460460 0 0
461461 − 8.54777e6i − 1.87327i −0.350307 0.936635i 0.613923π-0.613923\pi
0.350307 0.936635i 0.386077π-0.386077\pi
462462 0 0
463463 −7.55869e6 −1.63868 −0.819340 0.573308i 0.805660π-0.805660\pi
−0.819340 + 0.573308i 0.805660π0.805660\pi
464464 0 0
465465 0 0
466466 0 0
467467 3.29127e6i 0.698346i 0.937058 + 0.349173i 0.113538π0.113538\pi
−0.937058 + 0.349173i 0.886462π0.886462\pi
468468 0 0
469469 705380.i 0.148078i
470470 0 0
471471 −6.42013e6 −1.33349
472472 0 0
473473 −4.72807e6 −0.971698
474474 0 0
475475 0 0
476476 0 0
477477 648551.i 0.130511i
478478 0 0
479479 −4.95610e6 −0.986965 −0.493482 0.869756i 0.664276π-0.664276\pi
−0.493482 + 0.869756i 0.664276π0.664276\pi
480480 0 0
481481 −8.81196e6 −1.73664
482482 0 0
483483 − 3.69321e6i − 0.720338i
484484 0 0
485485 0 0
486486 0 0
487487 −7.56942e6 −1.44624 −0.723120 0.690723i 0.757293π-0.757293\pi
−0.723120 + 0.690723i 0.757293π0.757293\pi
488488 0 0
489489 9.74688e6 1.84329
490490 0 0
491491 − 1.25015e6i − 0.234023i −0.993131 0.117012i 0.962668π-0.962668\pi
0.993131 0.117012i 0.0373315π-0.0373315\pi
492492 0 0
493493 3.19025e6i 0.591163i
494494 0 0
495495 0 0
496496 0 0
497497 462649. 0.0840158
498498 0 0
499499 − 5.59295e6i − 1.00552i −0.864427 0.502758i 0.832319π-0.832319\pi
0.864427 0.502758i 0.167681π-0.167681\pi
500500 0 0
501501 2.75753e6i 0.490824i
502502 0 0
503503 9.76813e6 1.72144 0.860719 0.509080i 0.170014π-0.170014\pi
0.860719 + 0.509080i 0.170014π0.170014\pi
504504 0 0
505505 0 0
506506 0 0
507507 − 3.76469e6i − 0.650443i
508508 0 0
509509 9.05091e6i 1.54845i 0.632909 + 0.774226i 0.281861π0.281861\pi
−0.632909 + 0.774226i 0.718139π0.718139\pi
510510 0 0
511511 −2.32092e6 −0.393195
512512 0 0
513513 8.15359e6 1.36790
514514 0 0
515515 0 0
516516 0 0
517517 558850.i 0.0919536i
518518 0 0
519519 7.78116e6 1.26802
520520 0 0
521521 −7.68287e6 −1.24002 −0.620011 0.784593i 0.712872π-0.712872\pi
−0.620011 + 0.784593i 0.712872π0.712872\pi
522522 0 0
523523 − 8.45353e6i − 1.35140i −0.737177 0.675700i 0.763841π-0.763841\pi
0.737177 0.675700i 0.236159π-0.236159\pi
524524 0 0
525525 0 0
526526 0 0
527527 1.45137e7 2.27641
528528 0 0
529529 170070. 0.0264234
530530 0 0
531531 1.08283e6i 0.166657i
532532 0 0
533533 − 1.07946e7i − 1.64584i
534534 0 0
535535 0 0
536536 0 0
537537 −5.33784e6 −0.798785
538538 0 0
539539 − 3.55389e6i − 0.526904i
540540 0 0
541541 − 4.67406e6i − 0.686596i −0.939227 0.343298i 0.888456π-0.888456\pi
0.939227 0.343298i 0.111544π-0.111544\pi
542542 0 0
543543 −5.41725e6 −0.788459
544544 0 0
545545 0 0
546546 0 0
547547 − 1.86478e6i − 0.266477i −0.991084 0.133238i 0.957462π-0.957462\pi
0.991084 0.133238i 0.0425376π-0.0425376\pi
548548 0 0
549549 − 1.79826e7i − 2.54637i
550550 0 0
551551 −3.38727e6 −0.475304
552552 0 0
553553 2.61713e6 0.363925
554554 0 0
555555 0 0
556556 0 0
557557 9.40472e6i 1.28442i 0.766528 + 0.642211i 0.221983π0.221983\pi
−0.766528 + 0.642211i 0.778017π0.778017\pi
558558 0 0
559559 1.30535e7 1.76683
560560 0 0
561561 −1.24574e7 −1.67117
562562 0 0
563563 − 849619.i − 0.112967i −0.998404 0.0564837i 0.982011π-0.982011\pi
0.998404 0.0564837i 0.0179889π-0.0179889\pi
564564 0 0
565565 0 0
566566 0 0
567567 −335627. −0.0438429
568568 0 0
569569 −5.41948e6 −0.701741 −0.350870 0.936424i 0.614114π-0.614114\pi
−0.350870 + 0.936424i 0.614114π0.614114\pi
570570 0 0
571571 − 331372.i − 0.0425329i −0.999774 0.0212664i 0.993230π-0.993230\pi
0.999774 0.0212664i 0.00676983π-0.00676983\pi
572572 0 0
573573 4.50813e6i 0.573601i
574574 0 0
575575 0 0
576576 0 0
577577 1.51001e7 1.88817 0.944086 0.329701i 0.106948π-0.106948\pi
0.944086 + 0.329701i 0.106948π0.106948\pi
578578 0 0
579579 − 1.92822e7i − 2.39034i
580580 0 0
581581 − 3.48315e6i − 0.428087i
582582 0 0
583583 419119. 0.0510700
584584 0 0
585585 0 0
586586 0 0
587587 1.51509e7i 1.81486i 0.420199 + 0.907432i 0.361960π0.361960\pi
−0.420199 + 0.907432i 0.638040π0.638040\pi
588588 0 0
589589 1.54100e7i 1.83027i
590590 0 0
591591 −8.99125e6 −1.05889
592592 0 0
593593 1.46568e7 1.71160 0.855800 0.517307i 0.173066π-0.173066\pi
0.855800 + 0.517307i 0.173066π0.173066\pi
594594 0 0
595595 0 0
596596 0 0
597597 − 5.92688e6i − 0.680597i
598598 0 0
599599 5.14552e6 0.585952 0.292976 0.956120i 0.405354π-0.405354\pi
0.292976 + 0.956120i 0.405354π0.405354\pi
600600 0 0
601601 9.03954e6 1.02085 0.510423 0.859923i 0.329489π-0.329489\pi
0.510423 + 0.859923i 0.329489π0.329489\pi
602602 0 0
603603 5.04314e6i 0.564817i
604604 0 0
605605 0 0
606606 0 0
607607 1.25949e7 1.38747 0.693733 0.720232i 0.255965π-0.255965\pi
0.693733 + 0.720232i 0.255965π0.255965\pi
608608 0 0
609609 2.44292e6 0.266911
610610 0 0
611611 − 1.54290e6i − 0.167199i
612612 0 0
613613 − 8.66424e6i − 0.931278i −0.884975 0.465639i 0.845825π-0.845825\pi
0.884975 0.465639i 0.154175π-0.154175\pi
614614 0 0
615615 0 0
616616 0 0
617617 −6.86089e6 −0.725551 −0.362775 0.931877i 0.618171π-0.618171\pi
−0.362775 + 0.931877i 0.618171π0.618171\pi
618618 0 0
619619 3.44552e6i 0.361434i 0.983535 + 0.180717i 0.0578417π0.0578417\pi
−0.983535 + 0.180717i 0.942158π0.942158\pi
620620 0 0
621621 − 1.05189e7i − 1.09457i
622622 0 0
623623 −3.00578e6 −0.310268
624624 0 0
625625 0 0
626626 0 0
627627 − 1.32267e7i − 1.34364i
628628 0 0
629629 − 2.29454e7i − 2.31243i
630630 0 0
631631 7.79725e6 0.779593 0.389797 0.920901i 0.372545π-0.372545\pi
0.389797 + 0.920901i 0.372545π0.372545\pi
632632 0 0
633633 −1.02048e7 −1.01227
634634 0 0
635635 0 0
636636 0 0
637637 9.81171e6i 0.958068i
638638 0 0
639639 3.30773e6 0.320463
640640 0 0
641641 7.82134e6 0.751859 0.375929 0.926648i 0.377324π-0.377324\pi
0.375929 + 0.926648i 0.377324π0.377324\pi
642642 0 0
643643 − 1.35325e7i − 1.29078i −0.763854 0.645389i 0.776695π-0.776695\pi
0.763854 0.645389i 0.223305π-0.223305\pi
644644 0 0
645645 0 0
646646 0 0
647647 −1.34237e6 −0.126070 −0.0630352 0.998011i 0.520078π-0.520078\pi
−0.0630352 + 0.998011i 0.520078π0.520078\pi
648648 0 0
649649 699766. 0.0652140
650650 0 0
651651 − 1.11138e7i − 1.02780i
652652 0 0
653653 − 5.36490e6i − 0.492355i −0.969225 0.246178i 0.920825π-0.920825\pi
0.969225 0.246178i 0.0791747π-0.0791747\pi
654654 0 0
655655 0 0
656656 0 0
657657 −1.65935e7 −1.49977
658658 0 0
659659 8.49067e6i 0.761603i 0.924657 + 0.380801i 0.124352π0.124352\pi
−0.924657 + 0.380801i 0.875648π0.875648\pi
660660 0 0
661661 9.80254e6i 0.872640i 0.899792 + 0.436320i 0.143718π0.143718\pi
−0.899792 + 0.436320i 0.856282π0.856282\pi
662662 0 0
663663 3.43929e7 3.03868
664664 0 0
665665 0 0
666666 0 0
667667 4.36990e6i 0.380327i
668668 0 0
669669 − 1.20981e7i − 1.04508i
670670 0 0
671671 −1.16211e7 −0.996413
672672 0 0
673673 −7.99241e6 −0.680205 −0.340103 0.940388i 0.610462π-0.610462\pi
−0.340103 + 0.940388i 0.610462π0.610462\pi
674674 0 0
675675 0 0
676676 0 0
677677 − 8.50891e6i − 0.713514i −0.934197 0.356757i 0.883882π-0.883882\pi
0.934197 0.356757i 0.116118π-0.116118\pi
678678 0 0
679679 −2.21522e6 −0.184392
680680 0 0
681681 726378. 0.0600198
682682 0 0
683683 1.39302e7i 1.14263i 0.820732 + 0.571314i 0.193566π0.193566\pi
−0.820732 + 0.571314i 0.806434π0.806434\pi
684684 0 0
685685 0 0
686686 0 0
687687 −2.46646e7 −1.99380
688688 0 0
689689 −1.15712e6 −0.0928604
690690 0 0
691691 1.79579e6i 0.143074i 0.997438 + 0.0715371i 0.0227904π0.0227904\pi
−0.997438 + 0.0715371i 0.977210π0.977210\pi
692692 0 0
693693 5.95595e6i 0.471106i
694694 0 0
695695 0 0
696696 0 0
697697 2.81079e7 2.19152
698698 0 0
699699 407094.i 0.0315139i
700700 0 0
701701 1.76628e7i 1.35758i 0.734334 + 0.678789i 0.237495π0.237495\pi
−0.734334 + 0.678789i 0.762505π0.762505\pi
702702 0 0
703703 2.43624e7 1.85923
704704 0 0
705705 0 0
706706 0 0
707707 2.36670e6i 0.178071i
708708 0 0
709709 1.67397e7i 1.25064i 0.780369 + 0.625319i 0.215031π0.215031\pi
−0.780369 + 0.625319i 0.784969π0.784969\pi
710710 0 0
711711 1.87112e7 1.38812
712712 0 0
713713 1.98804e7 1.46454
714714 0 0
715715 0 0
716716 0 0
717717 − 3.21993e7i − 2.33910i
718718 0 0
719719 1.41699e7 1.02222 0.511111 0.859515i 0.329234π-0.329234\pi
0.511111 + 0.859515i 0.329234π0.329234\pi
720720 0 0
721721 6.68649e6 0.479027
722722 0 0
723723 1.05448e7i 0.750227i
724724 0 0
725725 0 0
726726 0 0
727727 3.78412e6 0.265539 0.132770 0.991147i 0.457613π-0.457613\pi
0.132770 + 0.991147i 0.457613π0.457613\pi
728728 0 0
729729 2.28942e7 1.59554
730730 0 0
731731 3.39897e7i 2.35263i
732732 0 0
733733 2.58722e7i 1.77858i 0.457345 + 0.889290i 0.348801π0.348801\pi
−0.457345 + 0.889290i 0.651199π0.651199\pi
734734 0 0
735735 0 0
736736 0 0
737737 3.25907e6 0.221017
738738 0 0
739739 5.89215e6i 0.396883i 0.980113 + 0.198441i 0.0635880π0.0635880\pi
−0.980113 + 0.198441i 0.936412π0.936412\pi
740740 0 0
741741 3.65169e7i 2.44314i
742742 0 0
743743 −2.47551e7 −1.64510 −0.822551 0.568692i 0.807450π-0.807450\pi
−0.822551 + 0.568692i 0.807450π0.807450\pi
744744 0 0
745745 0 0
746746 0 0
747747 − 2.49029e7i − 1.63286i
748748 0 0
749749 8.35986e6i 0.544496i
750750 0 0
751751 −1.98371e6 −0.128345 −0.0641724 0.997939i 0.520441π-0.520441\pi
−0.0641724 + 0.997939i 0.520441π0.520441\pi
752752 0 0
753753 4.68372e6 0.301026
754754 0 0
755755 0 0
756756 0 0
757757 1.85647e7i 1.17746i 0.808328 + 0.588732i 0.200373π0.200373\pi
−0.808328 + 0.588732i 0.799627π0.799627\pi
758758 0 0
759759 −1.70638e7 −1.07515
760760 0 0
761761 −5.16348e6 −0.323207 −0.161603 0.986856i 0.551667π-0.551667\pi
−0.161603 + 0.986856i 0.551667π0.551667\pi
762762 0 0
763763 − 7.14864e6i − 0.444542i
764764 0 0
765765 0 0
766766 0 0
767767 −1.93194e6 −0.118578
768768 0 0
769769 3.01408e7 1.83797 0.918985 0.394293i 0.129011π-0.129011\pi
0.918985 + 0.394293i 0.129011π0.129011\pi
770770 0 0
771771 2.15242e7i 1.30404i
772772 0 0
773773 − 1.51718e7i − 0.913246i −0.889660 0.456623i 0.849059π-0.849059\pi
0.889660 0.456623i 0.150941π-0.150941\pi
774774 0 0
775775 0 0
776776 0 0
777777 −1.75704e7 −1.04407
778778 0 0
779779 2.98438e7i 1.76202i
780780 0 0
781781 − 2.13758e6i − 0.125399i
782782 0 0
783783 6.95788e6 0.405576
784784 0 0
785785 0 0
786786 0 0
787787 1.46106e7i 0.840874i 0.907322 + 0.420437i 0.138123π0.138123\pi
−0.907322 + 0.420437i 0.861877π0.861877\pi
788788 0 0
789789 − 3.90125e7i − 2.23106i
790790 0 0
791791 −1.25359e7 −0.712384
792792 0 0
793793 3.20839e7 1.81177
794794 0 0
795795 0 0
796796 0 0
797797 4.81785e6i 0.268663i 0.990936 + 0.134331i 0.0428887π0.0428887\pi
−0.990936 + 0.134331i 0.957111π0.957111\pi
798798 0 0
799799 4.01753e6 0.222634
800800 0 0
801801 −2.14899e7 −1.18346
802802 0 0
803803 1.07234e7i 0.586870i
804804 0 0
805805 0 0
806806 0 0
807807 −1.64487e7 −0.889095
808808 0 0
809809 −267715. −0.0143814 −0.00719072 0.999974i 0.502289π-0.502289\pi
−0.00719072 + 0.999974i 0.502289π0.502289\pi
810810 0 0
811811 − 1.10232e7i − 0.588514i −0.955726 0.294257i 0.904928π-0.904928\pi
0.955726 0.294257i 0.0950722π-0.0950722\pi
812812 0 0
813813 4.02671e7i 2.13660i
814814 0 0
815815 0 0
816816 0 0
817817 −3.60889e7 −1.89155
818818 0 0
819819 − 1.64434e7i − 0.856609i
820820 0 0
821821 − 7.52183e6i − 0.389462i −0.980857 0.194731i 0.937617π-0.937617\pi
0.980857 0.194731i 0.0623834π-0.0623834\pi
822822 0 0
823823 −2.86933e7 −1.47666 −0.738331 0.674439i 0.764386π-0.764386\pi
−0.738331 + 0.674439i 0.764386π0.764386\pi
824824 0 0
825825 0 0
826826 0 0
827827 − 1.90830e7i − 0.970248i −0.874445 0.485124i 0.838774π-0.838774\pi
0.874445 0.485124i 0.161226π-0.161226\pi
828828 0 0
829829 2.31916e7i 1.17205i 0.810295 + 0.586023i 0.199307π0.199307\pi
−0.810295 + 0.586023i 0.800693π0.800693\pi
830830 0 0
831831 4.13245e7 2.07589
832832 0 0
833833 −2.55486e7 −1.27572
834834 0 0
835835 0 0
836836 0 0
837837 − 3.16541e7i − 1.56177i
838838 0 0
839839 887580. 0.0435314 0.0217657 0.999763i 0.493071π-0.493071\pi
0.0217657 + 0.999763i 0.493071π0.493071\pi
840840 0 0
841841 1.76206e7 0.859075
842842 0 0
843843 − 3.77382e7i − 1.82899i
844844 0 0
845845 0 0
846846 0 0
847847 −5.24942e6 −0.251422
848848 0 0
849849 −3.00746e7 −1.43196
850850 0 0
851851 − 3.14299e7i − 1.48771i
852852 0 0
853853 − 1.39449e7i − 0.656208i −0.944642 0.328104i 0.893590π-0.893590\pi
0.944642 0.328104i 0.106410π-0.106410\pi
854854 0 0
855855 0 0
856856 0 0
857857 3.58423e7 1.66703 0.833516 0.552495i 0.186324π-0.186324\pi
0.833516 + 0.552495i 0.186324π0.186324\pi
858858 0 0
859859 767053.i 0.0354685i 0.999843 + 0.0177342i 0.00564528π0.00564528\pi
−0.999843 + 0.0177342i 0.994355π0.994355\pi
860860 0 0
861861 − 2.15236e7i − 0.989478i
862862 0 0
863863 −2.90420e7 −1.32739 −0.663697 0.748002i 0.731013π-0.731013\pi
−0.663697 + 0.748002i 0.731013π0.731013\pi
864864 0 0
865865 0 0
866866 0 0
867867 5.34421e7i 2.41455i
868868 0 0
869869 − 1.20919e7i − 0.543183i
870870 0 0
871871 −8.99778e6 −0.401874
872872 0 0
873873 −1.58378e7 −0.703330
874874 0 0
875875 0 0
876876 0 0
877877 − 9.62715e6i − 0.422667i −0.977414 0.211334i 0.932219π-0.932219\pi
0.977414 0.211334i 0.0677807π-0.0677807\pi
878878 0 0
879879 −2.25852e7 −0.985942
880880 0 0
881881 3.88627e7 1.68691 0.843457 0.537196i 0.180517π-0.180517\pi
0.843457 + 0.537196i 0.180517π0.180517\pi
882882 0 0
883883 − 4.29023e6i − 0.185173i −0.995705 0.0925867i 0.970486π-0.970486\pi
0.995705 0.0925867i 0.0295135π-0.0295135\pi
884884 0 0
885885 0 0
886886 0 0
887887 −1.30883e7 −0.558564 −0.279282 0.960209i 0.590096π-0.590096\pi
−0.279282 + 0.960209i 0.590096π0.590096\pi
888888 0 0
889889 −1.34356e7 −0.570170
890890 0 0
891891 1.55070e6i 0.0654386i
892892 0 0
893893 4.26564e6i 0.179001i
894894 0 0
895895 0 0
896896 0 0
897897 4.71103e7 1.95495
898898 0 0
899899 1.31502e7i 0.542665i
900900 0 0
901901 − 3.01301e6i − 0.123649i
902902 0 0
903903 2.60276e7 1.06222
904904 0 0
905905 0 0
906906 0 0
907907 2.36895e7i 0.956175i 0.878312 + 0.478087i 0.158670π0.158670\pi
−0.878312 + 0.478087i 0.841330π0.841330\pi
908908 0 0
909909 1.69208e7i 0.679220i
910910 0 0
911911 −1.27323e7 −0.508289 −0.254144 0.967166i 0.581794π-0.581794\pi
−0.254144 + 0.967166i 0.581794π0.581794\pi
912912 0 0
913913 −1.60932e7 −0.638948
914914 0 0
915915 0 0
916916 0 0
917917 8.54258e6i 0.335479i
918918 0 0
919919 −3.36064e7 −1.31260 −0.656302 0.754499i 0.727880π-0.727880\pi
−0.656302 + 0.754499i 0.727880π0.727880\pi
920920 0 0
921921 −3.75640e7 −1.45923
922922 0 0
923923 5.90152e6i 0.228013i
924924 0 0
925925 0 0
926926 0 0
927927 4.78053e7 1.82716
928928 0 0
929929 2.44326e7 0.928816 0.464408 0.885621i 0.346267π-0.346267\pi
0.464408 + 0.885621i 0.346267π0.346267\pi
930930 0 0
931931 − 2.71265e7i − 1.02570i
932932 0 0
933933 − 9.27134e6i − 0.348689i
934934 0 0
935935 0 0
936936 0 0
937937 2.46226e7 0.916188 0.458094 0.888904i 0.348532π-0.348532\pi
0.458094 + 0.888904i 0.348532π0.348532\pi
938938 0 0
939939 − 8.24698e6i − 0.305233i
940940 0 0
941941 − 3.64578e7i − 1.34220i −0.741368 0.671098i 0.765823π-0.765823\pi
0.741368 0.671098i 0.234177π-0.234177\pi
942942 0 0
943943 3.85013e7 1.40993
944944 0 0
945945 0 0
946946 0 0
947947 − 1.49302e7i − 0.540992i −0.962721 0.270496i 0.912812π-0.912812\pi
0.962721 0.270496i 0.0871876π-0.0871876\pi
948948 0 0
949949 − 2.96055e7i − 1.06710i
950950 0 0
951951 −3.95935e7 −1.41962
952952 0 0
953953 −2.82853e7 −1.00885 −0.504426 0.863455i 0.668296π-0.668296\pi
−0.504426 + 0.863455i 0.668296π0.668296\pi
954954 0 0
955955 0 0
956956 0 0
957957 − 1.12871e7i − 0.398383i
958958 0 0
959959 9.22071e6 0.323756
960960 0 0
961961 3.11960e7 1.08966
962962 0 0
963963 5.97691e7i 2.07688i
964964 0 0
965965 0 0
966966 0 0
967967 3.47503e7 1.19507 0.597533 0.801844i 0.296148π-0.296148\pi
0.597533 + 0.801844i 0.296148π0.296148\pi
968968 0 0
969969 −9.50860e7 −3.25317
970970 0 0
971971 4.65499e7i 1.58442i 0.610247 + 0.792211i 0.291070π0.291070\pi
−0.610247 + 0.792211i 0.708930π0.708930\pi
972972 0 0
973973 − 423158.i − 0.0143291i
974974 0 0
975975 0 0
976976 0 0
977977 −4.15712e7 −1.39334 −0.696668 0.717394i 0.745335π-0.745335\pi
−0.696668 + 0.717394i 0.745335π0.745335\pi
978978 0 0
979979 1.38876e7i 0.463096i
980980 0 0
981981 − 5.11094e7i − 1.69562i
982982 0 0
983983 −2.55186e7 −0.842313 −0.421157 0.906988i 0.638376π-0.638376\pi
−0.421157 + 0.906988i 0.638376π0.638376\pi
984984 0 0
985985 0 0
986986 0 0
987987 − 3.07641e6i − 0.100520i
988988 0 0
989989 4.65581e7i 1.51358i
990990 0 0
991991 3.10296e7 1.00367 0.501836 0.864963i 0.332658π-0.332658\pi
0.501836 + 0.864963i 0.332658π0.332658\pi
992992 0 0
993993 −1.42119e7 −0.457382
994994 0 0
995995 0 0
996996 0 0
997997 1.66036e7i 0.529011i 0.964384 + 0.264505i 0.0852087π0.0852087\pi
−0.964384 + 0.264505i 0.914791π0.914791\pi
998998 0 0
999999 −5.00435e7 −1.58648
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.c.401.19 20
4.3 odd 2 200.6.d.b.101.18 20
5.2 odd 4 800.6.f.b.49.19 20
5.3 odd 4 800.6.f.c.49.2 20
5.4 even 2 160.6.d.a.81.2 20
8.3 odd 2 200.6.d.b.101.17 20
8.5 even 2 inner 800.6.d.c.401.2 20
20.3 even 4 200.6.f.b.149.13 20
20.7 even 4 200.6.f.c.149.8 20
20.19 odd 2 40.6.d.a.21.3 20
40.3 even 4 200.6.f.c.149.7 20
40.13 odd 4 800.6.f.b.49.20 20
40.19 odd 2 40.6.d.a.21.4 yes 20
40.27 even 4 200.6.f.b.149.14 20
40.29 even 2 160.6.d.a.81.19 20
40.37 odd 4 800.6.f.c.49.1 20
60.59 even 2 360.6.k.b.181.18 20
120.59 even 2 360.6.k.b.181.17 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.6.d.a.21.3 20 20.19 odd 2
40.6.d.a.21.4 yes 20 40.19 odd 2
160.6.d.a.81.2 20 5.4 even 2
160.6.d.a.81.19 20 40.29 even 2
200.6.d.b.101.17 20 8.3 odd 2
200.6.d.b.101.18 20 4.3 odd 2
200.6.f.b.149.13 20 20.3 even 4
200.6.f.b.149.14 20 40.27 even 4
200.6.f.c.149.7 20 40.3 even 4
200.6.f.c.149.8 20 20.7 even 4
360.6.k.b.181.17 20 120.59 even 2
360.6.k.b.181.18 20 60.59 even 2
800.6.d.c.401.2 20 8.5 even 2 inner
800.6.d.c.401.19 20 1.1 even 1 trivial
800.6.f.b.49.19 20 5.2 odd 4
800.6.f.b.49.20 20 40.13 odd 4
800.6.f.c.49.1 20 40.37 odd 4
800.6.f.c.49.2 20 5.3 odd 4