Properties

Label 400.4.c.i.49.1
Level 400400
Weight 44
Character 400.49
Analytic conductor 23.60123.601
Analytic rank 00
Dimension 22
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [400,4,Mod(49,400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(400, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.49");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 400=2452 400 = 2^{4} \cdot 5^{2}
Weight: k k == 4 4
Character orbit: [χ][\chi] == 400.c (of order 22, degree 11, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 23.600764002323.6007640023
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
comment: defining polynomial
 
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,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 8)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 49.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 400.49
Dual form 400.4.c.i.49.2

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) == q4.00000iq324.0000iq7+11.0000q9+44.0000q1122.0000iq13+50.0000iq17+44.0000q1996.0000q2156.0000iq23152.000iq27198.000q29+160.000q31176.000iq33162.000iq3788.0000q39198.000q41+52.0000iq43528.000iq47233.000q49+200.000q51+242.000iq53176.000iq57668.000q59+550.000q61264.000iq63188.000iq67224.000q69728.000q71154.000iq731056.00iq77656.000q79311.000q81+236.000iq83+792.000iq87714.000q89528.000q91640.000iq93478.000iq97+484.000q99+O(q100)q-4.00000i q^{3} -24.0000i q^{7} +11.0000 q^{9} +44.0000 q^{11} -22.0000i q^{13} +50.0000i q^{17} +44.0000 q^{19} -96.0000 q^{21} -56.0000i q^{23} -152.000i q^{27} -198.000 q^{29} +160.000 q^{31} -176.000i q^{33} -162.000i q^{37} -88.0000 q^{39} -198.000 q^{41} +52.0000i q^{43} -528.000i q^{47} -233.000 q^{49} +200.000 q^{51} +242.000i q^{53} -176.000i q^{57} -668.000 q^{59} +550.000 q^{61} -264.000i q^{63} -188.000i q^{67} -224.000 q^{69} -728.000 q^{71} -154.000i q^{73} -1056.00i q^{77} -656.000 q^{79} -311.000 q^{81} +236.000i q^{83} +792.000i q^{87} -714.000 q^{89} -528.000 q^{91} -640.000i q^{93} -478.000i q^{97} +484.000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+22q9+88q11+88q19192q21396q29+320q31176q39396q41466q49+400q511336q59+1100q61448q691456q711312q79622q81++968q99+O(q100) 2 q + 22 q^{9} + 88 q^{11} + 88 q^{19} - 192 q^{21} - 396 q^{29} + 320 q^{31} - 176 q^{39} - 396 q^{41} - 466 q^{49} + 400 q^{51} - 1336 q^{59} + 1100 q^{61} - 448 q^{69} - 1456 q^{71} - 1312 q^{79} - 622 q^{81}+ \cdots + 968 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/400Z)×\left(\mathbb{Z}/400\mathbb{Z}\right)^\times.

nn 101101 177177 351351
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 0 0
66 0 0
77 − 24.0000i − 1.29588i −0.761692 0.647939i 0.775631π-0.775631\pi
0.761692 0.647939i 0.224369π-0.224369\pi
88 0 0
99 11.0000 0.407407
1010 0 0
1111 44.0000 1.20605 0.603023 0.797724i 0.293963π-0.293963\pi
0.603023 + 0.797724i 0.293963π0.293963\pi
1212 0 0
1313 − 22.0000i − 0.469362i −0.972072 0.234681i 0.924595π-0.924595\pi
0.972072 0.234681i 0.0754045π-0.0754045\pi
1414 0 0
1515 0 0
1616 0 0
1717 50.0000i 0.713340i 0.934230 + 0.356670i 0.116088π0.116088\pi
−0.934230 + 0.356670i 0.883912π0.883912\pi
1818 0 0
1919 44.0000 0.531279 0.265639 0.964072i 0.414417π-0.414417\pi
0.265639 + 0.964072i 0.414417π0.414417\pi
2020 0 0
2121 −96.0000 −0.997567
2222 0 0
2323 − 56.0000i − 0.507687i −0.967245 0.253844i 0.918305π-0.918305\pi
0.967245 0.253844i 0.0816949π-0.0816949\pi
2424 0 0
2525 0 0
2626 0 0
2727 − 152.000i − 1.08342i
2828 0 0
2929 −198.000 −1.26785 −0.633925 0.773394i 0.718557π-0.718557\pi
−0.633925 + 0.773394i 0.718557π0.718557\pi
3030 0 0
3131 160.000 0.926995 0.463498 0.886098i 0.346594π-0.346594\pi
0.463498 + 0.886098i 0.346594π0.346594\pi
3232 0 0
3333 − 176.000i − 0.928414i
3434 0 0
3535 0 0
3636 0 0
3737 − 162.000i − 0.719801i −0.932991 0.359900i 0.882811π-0.882811\pi
0.932991 0.359900i 0.117189π-0.117189\pi
3838 0 0
3939 −88.0000 −0.361315
4040 0 0
4141 −198.000 −0.754205 −0.377102 0.926172i 0.623080π-0.623080\pi
−0.377102 + 0.926172i 0.623080π0.623080\pi
4242 0 0
4343 52.0000i 0.184417i 0.995740 + 0.0922084i 0.0293926π0.0293926\pi
−0.995740 + 0.0922084i 0.970607π0.970607\pi
4444 0 0
4545 0 0
4646 0 0
4747 − 528.000i − 1.63865i −0.573327 0.819327i 0.694347π-0.694347\pi
0.573327 0.819327i 0.305653π-0.305653\pi
4848 0 0
4949 −233.000 −0.679300
5050 0 0
5151 200.000 0.549129
5252 0 0
5353 242.000i 0.627194i 0.949556 + 0.313597i 0.101534π0.101534\pi
−0.949556 + 0.313597i 0.898466π0.898466\pi
5454 0 0
5555 0 0
5656 0 0
5757 − 176.000i − 0.408978i
5858 0 0
5959 −668.000 −1.47400 −0.737002 0.675891i 0.763759π-0.763759\pi
−0.737002 + 0.675891i 0.763759π0.763759\pi
6060 0 0
6161 550.000 1.15443 0.577215 0.816592i 0.304139π-0.304139\pi
0.577215 + 0.816592i 0.304139π0.304139\pi
6262 0 0
6363 − 264.000i − 0.527950i
6464 0 0
6565 0 0
6666 0 0
6767 − 188.000i − 0.342804i −0.985201 0.171402i 0.945170π-0.945170\pi
0.985201 0.171402i 0.0548297π-0.0548297\pi
6868 0 0
6969 −224.000 −0.390818
7070 0 0
7171 −728.000 −1.21687 −0.608435 0.793604i 0.708202π-0.708202\pi
−0.608435 + 0.793604i 0.708202π0.708202\pi
7272 0 0
7373 − 154.000i − 0.246909i −0.992350 0.123454i 0.960603π-0.960603\pi
0.992350 0.123454i 0.0393973π-0.0393973\pi
7474 0 0
7575 0 0
7676 0 0
7777 − 1056.00i − 1.56289i
7878 0 0
7979 −656.000 −0.934250 −0.467125 0.884191i 0.654710π-0.654710\pi
−0.467125 + 0.884191i 0.654710π0.654710\pi
8080 0 0
8181 −311.000 −0.426612
8282 0 0
8383 236.000i 0.312101i 0.987749 + 0.156050i 0.0498762π0.0498762\pi
−0.987749 + 0.156050i 0.950124π0.950124\pi
8484 0 0
8585 0 0
8686 0 0
8787 792.000i 0.975992i
8888 0 0
8989 −714.000 −0.850380 −0.425190 0.905104i 0.639793π-0.639793\pi
−0.425190 + 0.905104i 0.639793π0.639793\pi
9090 0 0
9191 −528.000 −0.608236
9292 0 0
9393 − 640.000i − 0.713601i
9494 0 0
9595 0 0
9696 0 0
9797 − 478.000i − 0.500346i −0.968201 0.250173i 0.919513π-0.919513\pi
0.968201 0.250173i 0.0804875π-0.0804875\pi
9898 0 0
9999 484.000 0.491352
100100 0 0
101101 1566.00 1.54280 0.771400 0.636350i 0.219557π-0.219557\pi
0.771400 + 0.636350i 0.219557π0.219557\pi
102102 0 0
103103 − 968.000i − 0.926018i −0.886354 0.463009i 0.846770π-0.846770\pi
0.886354 0.463009i 0.153230π-0.153230\pi
104104 0 0
105105 0 0
106106 0 0
107107 780.000i 0.704724i 0.935864 + 0.352362i 0.114621π0.114621\pi
−0.935864 + 0.352362i 0.885379π0.885379\pi
108108 0 0
109109 1994.00 1.75221 0.876103 0.482123i 0.160134π-0.160134\pi
0.876103 + 0.482123i 0.160134π0.160134\pi
110110 0 0
111111 −648.000 −0.554103
112112 0 0
113113 942.000i 0.784212i 0.919920 + 0.392106i 0.128253π0.128253\pi
−0.919920 + 0.392106i 0.871747π0.871747\pi
114114 0 0
115115 0 0
116116 0 0
117117 − 242.000i − 0.191221i
118118 0 0
119119 1200.00 0.924402
120120 0 0
121121 605.000 0.454545
122122 0 0
123123 792.000i 0.580587i
124124 0 0
125125 0 0
126126 0 0
127127 − 1408.00i − 0.983778i −0.870658 0.491889i 0.836307π-0.836307\pi
0.870658 0.491889i 0.163693π-0.163693\pi
128128 0 0
129129 208.000 0.141964
130130 0 0
131131 2692.00 1.79543 0.897714 0.440578i 0.145227π-0.145227\pi
0.897714 + 0.440578i 0.145227π0.145227\pi
132132 0 0
133133 − 1056.00i − 0.688472i
134134 0 0
135135 0 0
136136 0 0
137137 1626.00i 1.01400i 0.861945 + 0.507002i 0.169246π0.169246\pi
−0.861945 + 0.507002i 0.830754π0.830754\pi
138138 0 0
139139 −684.000 −0.417382 −0.208691 0.977982i 0.566920π-0.566920\pi
−0.208691 + 0.977982i 0.566920π0.566920\pi
140140 0 0
141141 −2112.00 −1.26144
142142 0 0
143143 − 968.000i − 0.566072i
144144 0 0
145145 0 0
146146 0 0
147147 932.000i 0.522926i
148148 0 0
149149 −302.000 −0.166046 −0.0830228 0.996548i 0.526457π-0.526457\pi
−0.0830228 + 0.996548i 0.526457π0.526457\pi
150150 0 0
151151 −1352.00 −0.728637 −0.364319 0.931274i 0.618698π-0.618698\pi
−0.364319 + 0.931274i 0.618698π0.618698\pi
152152 0 0
153153 550.000i 0.290620i
154154 0 0
155155 0 0
156156 0 0
157157 3142.00i 1.59719i 0.601868 + 0.798595i 0.294423π0.294423\pi
−0.601868 + 0.798595i 0.705577π0.705577\pi
158158 0 0
159159 968.000 0.482814
160160 0 0
161161 −1344.00 −0.657901
162162 0 0
163163 3036.00i 1.45888i 0.684043 + 0.729441i 0.260220π0.260220\pi
−0.684043 + 0.729441i 0.739780π0.739780\pi
164164 0 0
165165 0 0
166166 0 0
167167 264.000i 0.122329i 0.998128 + 0.0611645i 0.0194814π0.0194814\pi
−0.998128 + 0.0611645i 0.980519π0.980519\pi
168168 0 0
169169 1713.00 0.779700
170170 0 0
171171 484.000 0.216447
172172 0 0
173173 2826.00i 1.24195i 0.783832 + 0.620973i 0.213263π0.213263\pi
−0.783832 + 0.620973i 0.786737π0.786737\pi
174174 0 0
175175 0 0
176176 0 0
177177 2672.00i 1.13469i
178178 0 0
179179 3084.00 1.28776 0.643880 0.765127i 0.277324π-0.277324\pi
0.643880 + 0.765127i 0.277324π0.277324\pi
180180 0 0
181181 −2418.00 −0.992975 −0.496488 0.868044i 0.665377π-0.665377\pi
−0.496488 + 0.868044i 0.665377π0.665377\pi
182182 0 0
183183 − 2200.00i − 0.888681i
184184 0 0
185185 0 0
186186 0 0
187187 2200.00i 0.860320i
188188 0 0
189189 −3648.00 −1.40398
190190 0 0
191191 960.000 0.363681 0.181841 0.983328i 0.441794π-0.441794\pi
0.181841 + 0.983328i 0.441794π0.441794\pi
192192 0 0
193193 − 2882.00i − 1.07488i −0.843304 0.537438i 0.819392π-0.819392\pi
0.843304 0.537438i 0.180608π-0.180608\pi
194194 0 0
195195 0 0
196196 0 0
197197 1086.00i 0.392763i 0.980528 + 0.196381i 0.0629191π0.0629191\pi
−0.980528 + 0.196381i 0.937081π0.937081\pi
198198 0 0
199199 88.0000 0.0313475 0.0156738 0.999877i 0.495011π-0.495011\pi
0.0156738 + 0.999877i 0.495011π0.495011\pi
200200 0 0
201201 −752.000 −0.263890
202202 0 0
203203 4752.00i 1.64298i
204204 0 0
205205 0 0
206206 0 0
207207 − 616.000i − 0.206836i
208208 0 0
209209 1936.00 0.640746
210210 0 0
211211 3476.00 1.13411 0.567056 0.823679i 0.308082π-0.308082\pi
0.567056 + 0.823679i 0.308082π0.308082\pi
212212 0 0
213213 2912.00i 0.936746i
214214 0 0
215215 0 0
216216 0 0
217217 − 3840.00i − 1.20127i
218218 0 0
219219 −616.000 −0.190070
220220 0 0
221221 1100.00 0.334815
222222 0 0
223223 928.000i 0.278670i 0.990245 + 0.139335i 0.0444965π0.0444965\pi
−0.990245 + 0.139335i 0.955503π0.955503\pi
224224 0 0
225225 0 0
226226 0 0
227227 − 156.000i − 0.0456127i −0.999740 0.0228064i 0.992740π-0.992740\pi
0.999740 0.0228064i 0.00726012π-0.00726012\pi
228228 0 0
229229 1634.00 0.471519 0.235759 0.971811i 0.424242π-0.424242\pi
0.235759 + 0.971811i 0.424242π0.424242\pi
230230 0 0
231231 −4224.00 −1.20311
232232 0 0
233233 902.000i 0.253614i 0.991927 + 0.126807i 0.0404728π0.0404728\pi
−0.991927 + 0.126807i 0.959527π0.959527\pi
234234 0 0
235235 0 0
236236 0 0
237237 2624.00i 0.719186i
238238 0 0
239239 1616.00 0.437365 0.218683 0.975796i 0.429824π-0.429824\pi
0.218683 + 0.975796i 0.429824π0.429824\pi
240240 0 0
241241 4818.00 1.28778 0.643889 0.765119i 0.277320π-0.277320\pi
0.643889 + 0.765119i 0.277320π0.277320\pi
242242 0 0
243243 − 2860.00i − 0.755017i
244244 0 0
245245 0 0
246246 0 0
247247 − 968.000i − 0.249362i
248248 0 0
249249 944.000 0.240255
250250 0 0
251251 2140.00 0.538150 0.269075 0.963119i 0.413282π-0.413282\pi
0.269075 + 0.963119i 0.413282π0.413282\pi
252252 0 0
253253 − 2464.00i − 0.612294i
254254 0 0
255255 0 0
256256 0 0
257257 770.000i 0.186892i 0.995624 + 0.0934461i 0.0297883π0.0297883\pi
−0.995624 + 0.0934461i 0.970212π0.970212\pi
258258 0 0
259259 −3888.00 −0.932774
260260 0 0
261261 −2178.00 −0.516532
262262 0 0
263263 − 7400.00i − 1.73499i −0.497442 0.867497i 0.665727π-0.665727\pi
0.497442 0.867497i 0.334273π-0.334273\pi
264264 0 0
265265 0 0
266266 0 0
267267 2856.00i 0.654623i
268268 0 0
269269 2794.00 0.633283 0.316642 0.948545i 0.397445π-0.397445\pi
0.316642 + 0.948545i 0.397445π0.397445\pi
270270 0 0
271271 −8624.00 −1.93310 −0.966551 0.256474i 0.917439π-0.917439\pi
−0.966551 + 0.256474i 0.917439π0.917439\pi
272272 0 0
273273 2112.00i 0.468220i
274274 0 0
275275 0 0
276276 0 0
277277 − 1874.00i − 0.406490i −0.979128 0.203245i 0.934851π-0.934851\pi
0.979128 0.203245i 0.0651488π-0.0651488\pi
278278 0 0
279279 1760.00 0.377665
280280 0 0
281281 3338.00 0.708642 0.354321 0.935124i 0.384712π-0.384712\pi
0.354321 + 0.935124i 0.384712π0.384712\pi
282282 0 0
283283 7172.00i 1.50647i 0.657751 + 0.753235i 0.271508π0.271508\pi
−0.657751 + 0.753235i 0.728492π0.728492\pi
284284 0 0
285285 0 0
286286 0 0
287287 4752.00i 0.977358i
288288 0 0
289289 2413.00 0.491146
290290 0 0
291291 −1912.00 −0.385166
292292 0 0
293293 − 5214.00i − 1.03961i −0.854286 0.519804i 0.826005π-0.826005\pi
0.854286 0.519804i 0.173995π-0.173995\pi
294294 0 0
295295 0 0
296296 0 0
297297 − 6688.00i − 1.30666i
298298 0 0
299299 −1232.00 −0.238289
300300 0 0
301301 1248.00 0.238982
302302 0 0
303303 − 6264.00i − 1.18765i
304304 0 0
305305 0 0
306306 0 0
307307 − 396.000i − 0.0736186i −0.999322 0.0368093i 0.988281π-0.988281\pi
0.999322 0.0368093i 0.0117194π-0.0117194\pi
308308 0 0
309309 −3872.00 −0.712849
310310 0 0
311311 4056.00 0.739533 0.369766 0.929125i 0.379438π-0.379438\pi
0.369766 + 0.929125i 0.379438π0.379438\pi
312312 0 0
313313 − 2154.00i − 0.388982i −0.980904 0.194491i 0.937695π-0.937695\pi
0.980904 0.194491i 0.0623055π-0.0623055\pi
314314 0 0
315315 0 0
316316 0 0
317317 − 7386.00i − 1.30864i −0.756217 0.654320i 0.772955π-0.772955\pi
0.756217 0.654320i 0.227045π-0.227045\pi
318318 0 0
319319 −8712.00 −1.52909
320320 0 0
321321 3120.00 0.542497
322322 0 0
323323 2200.00i 0.378982i
324324 0 0
325325 0 0
326326 0 0
327327 − 7976.00i − 1.34885i
328328 0 0
329329 −12672.0 −2.12350
330330 0 0
331331 1132.00 0.187977 0.0939884 0.995573i 0.470038π-0.470038\pi
0.0939884 + 0.995573i 0.470038π0.470038\pi
332332 0 0
333333 − 1782.00i − 0.293252i
334334 0 0
335335 0 0
336336 0 0
337337 − 3342.00i − 0.540209i −0.962831 0.270104i 0.912942π-0.912942\pi
0.962831 0.270104i 0.0870582π-0.0870582\pi
338338 0 0
339339 3768.00 0.603686
340340 0 0
341341 7040.00 1.11800
342342 0 0
343343 − 2640.00i − 0.415588i
344344 0 0
345345 0 0
346346 0 0
347347 − 2244.00i − 0.347159i −0.984820 0.173580i 0.944467π-0.944467\pi
0.984820 0.173580i 0.0555334π-0.0555334\pi
348348 0 0
349349 6522.00 1.00033 0.500164 0.865931i 0.333273π-0.333273\pi
0.500164 + 0.865931i 0.333273π0.333273\pi
350350 0 0
351351 −3344.00 −0.508517
352352 0 0
353353 11230.0i 1.69324i 0.532200 + 0.846618i 0.321365π0.321365\pi
−0.532200 + 0.846618i 0.678635π0.678635\pi
354354 0 0
355355 0 0
356356 0 0
357357 − 4800.00i − 0.711605i
358358 0 0
359359 1848.00 0.271682 0.135841 0.990731i 0.456626π-0.456626\pi
0.135841 + 0.990731i 0.456626π0.456626\pi
360360 0 0
361361 −4923.00 −0.717743
362362 0 0
363363 − 2420.00i − 0.349909i
364364 0 0
365365 0 0
366366 0 0
367367 − 7120.00i − 1.01270i −0.862328 0.506350i 0.830994π-0.830994\pi
0.862328 0.506350i 0.169006π-0.169006\pi
368368 0 0
369369 −2178.00 −0.307269
370370 0 0
371371 5808.00 0.812766
372372 0 0
373373 − 6350.00i − 0.881476i −0.897636 0.440738i 0.854717π-0.854717\pi
0.897636 0.440738i 0.145283π-0.145283\pi
374374 0 0
375375 0 0
376376 0 0
377377 4356.00i 0.595081i
378378 0 0
379379 −7900.00 −1.07070 −0.535351 0.844630i 0.679821π-0.679821\pi
−0.535351 + 0.844630i 0.679821π0.679821\pi
380380 0 0
381381 −5632.00 −0.757313
382382 0 0
383383 10368.0i 1.38324i 0.722263 + 0.691619i 0.243102π0.243102\pi
−0.722263 + 0.691619i 0.756898π0.756898\pi
384384 0 0
385385 0 0
386386 0 0
387387 572.000i 0.0751328i
388388 0 0
389389 −8830.00 −1.15090 −0.575448 0.817838i 0.695172π-0.695172\pi
−0.575448 + 0.817838i 0.695172π0.695172\pi
390390 0 0
391391 2800.00 0.362154
392392 0 0
393393 − 10768.0i − 1.38212i
394394 0 0
395395 0 0
396396 0 0
397397 9878.00i 1.24877i 0.781116 + 0.624386i 0.214651π0.214651\pi
−0.781116 + 0.624386i 0.785349π0.785349\pi
398398 0 0
399399 −4224.00 −0.529986
400400 0 0
401401 −13134.0 −1.63561 −0.817806 0.575494i 0.804810π-0.804810\pi
−0.817806 + 0.575494i 0.804810π0.804810\pi
402402 0 0
403403 − 3520.00i − 0.435096i
404404 0 0
405405 0 0
406406 0 0
407407 − 7128.00i − 0.868113i
408408 0 0
409409 −906.000 −0.109533 −0.0547663 0.998499i 0.517441π-0.517441\pi
−0.0547663 + 0.998499i 0.517441π0.517441\pi
410410 0 0
411411 6504.00 0.780581
412412 0 0
413413 16032.0i 1.91013i
414414 0 0
415415 0 0
416416 0 0
417417 2736.00i 0.321301i
418418 0 0
419419 −5412.00 −0.631011 −0.315505 0.948924i 0.602174π-0.602174\pi
−0.315505 + 0.948924i 0.602174π0.602174\pi
420420 0 0
421421 −4642.00 −0.537381 −0.268690 0.963227i 0.586591π-0.586591\pi
−0.268690 + 0.963227i 0.586591π0.586591\pi
422422 0 0
423423 − 5808.00i − 0.667600i
424424 0 0
425425 0 0
426426 0 0
427427 − 13200.0i − 1.49600i
428428 0 0
429429 −3872.00 −0.435762
430430 0 0
431431 −656.000 −0.0733142 −0.0366571 0.999328i 0.511671π-0.511671\pi
−0.0366571 + 0.999328i 0.511671π0.511671\pi
432432 0 0
433433 − 9490.00i − 1.05326i −0.850096 0.526629i 0.823456π-0.823456\pi
0.850096 0.526629i 0.176544π-0.176544\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 2464.00i − 0.269723i
438438 0 0
439439 5544.00 0.602735 0.301368 0.953508i 0.402557π-0.402557\pi
0.301368 + 0.953508i 0.402557π0.402557\pi
440440 0 0
441441 −2563.00 −0.276752
442442 0 0
443443 7652.00i 0.820672i 0.911935 + 0.410336i 0.134588π0.134588\pi
−0.911935 + 0.410336i 0.865412π0.865412\pi
444444 0 0
445445 0 0
446446 0 0
447447 1208.00i 0.127822i
448448 0 0
449449 446.000 0.0468776 0.0234388 0.999725i 0.492539π-0.492539\pi
0.0234388 + 0.999725i 0.492539π0.492539\pi
450450 0 0
451451 −8712.00 −0.909605
452452 0 0
453453 5408.00i 0.560905i
454454 0 0
455455 0 0
456456 0 0
457457 1562.00i 0.159885i 0.996799 + 0.0799423i 0.0254736π0.0254736\pi
−0.996799 + 0.0799423i 0.974526π0.974526\pi
458458 0 0
459459 7600.00 0.772849
460460 0 0
461461 10582.0 1.06910 0.534548 0.845138i 0.320482π-0.320482\pi
0.534548 + 0.845138i 0.320482π0.320482\pi
462462 0 0
463463 − 10768.0i − 1.08085i −0.841394 0.540423i 0.818264π-0.818264\pi
0.841394 0.540423i 0.181736π-0.181736\pi
464464 0 0
465465 0 0
466466 0 0
467467 9876.00i 0.978601i 0.872115 + 0.489301i 0.162748π0.162748\pi
−0.872115 + 0.489301i 0.837252π0.837252\pi
468468 0 0
469469 −4512.00 −0.444232
470470 0 0
471471 12568.0 1.22952
472472 0 0
473473 2288.00i 0.222415i
474474 0 0
475475 0 0
476476 0 0
477477 2662.00i 0.255523i
478478 0 0
479479 −352.000 −0.0335768 −0.0167884 0.999859i 0.505344π-0.505344\pi
−0.0167884 + 0.999859i 0.505344π0.505344\pi
480480 0 0
481481 −3564.00 −0.337847
482482 0 0
483483 5376.00i 0.506452i
484484 0 0
485485 0 0
486486 0 0
487487 15176.0i 1.41209i 0.708165 + 0.706047i 0.249523π0.249523\pi
−0.708165 + 0.706047i 0.750477π0.750477\pi
488488 0 0
489489 12144.0 1.12305
490490 0 0
491491 8844.00 0.812880 0.406440 0.913677i 0.366770π-0.366770\pi
0.406440 + 0.913677i 0.366770π0.366770\pi
492492 0 0
493493 − 9900.00i − 0.904409i
494494 0 0
495495 0 0
496496 0 0
497497 17472.0i 1.57691i
498498 0 0
499499 19404.0 1.74077 0.870383 0.492375i 0.163871π-0.163871\pi
0.870383 + 0.492375i 0.163871π0.163871\pi
500500 0 0
501501 1056.00 0.0941689
502502 0 0
503503 16488.0i 1.46156i 0.682614 + 0.730779i 0.260843π0.260843\pi
−0.682614 + 0.730779i 0.739157π0.739157\pi
504504 0 0
505505 0 0
506506 0 0
507507 − 6852.00i − 0.600213i
508508 0 0
509509 12954.0 1.12805 0.564024 0.825759i 0.309253π-0.309253\pi
0.564024 + 0.825759i 0.309253π0.309253\pi
510510 0 0
511511 −3696.00 −0.319964
512512 0 0
513513 − 6688.00i − 0.575599i
514514 0 0
515515 0 0
516516 0 0
517517 − 23232.0i − 1.97629i
518518 0 0
519519 11304.0 0.956051
520520 0 0
521521 10970.0 0.922465 0.461233 0.887279i 0.347407π-0.347407\pi
0.461233 + 0.887279i 0.347407π0.347407\pi
522522 0 0
523523 − 16940.0i − 1.41632i −0.706053 0.708159i 0.749526π-0.749526\pi
0.706053 0.708159i 0.250474π-0.250474\pi
524524 0 0
525525 0 0
526526 0 0
527527 8000.00i 0.661263i
528528 0 0
529529 9031.00 0.742254
530530 0 0
531531 −7348.00 −0.600520
532532 0 0
533533 4356.00i 0.353995i
534534 0 0
535535 0 0
536536 0 0
537537 − 12336.0i − 0.991318i
538538 0 0
539539 −10252.0 −0.819267
540540 0 0
541541 198.000 0.0157351 0.00786755 0.999969i 0.497496π-0.497496\pi
0.00786755 + 0.999969i 0.497496π0.497496\pi
542542 0 0
543543 9672.00i 0.764393i
544544 0 0
545545 0 0
546546 0 0
547547 15268.0i 1.19344i 0.802449 + 0.596721i 0.203530π0.203530\pi
−0.802449 + 0.596721i 0.796470π0.796470\pi
548548 0 0
549549 6050.00 0.470324
550550 0 0
551551 −8712.00 −0.673582
552552 0 0
553553 15744.0i 1.21067i
554554 0 0
555555 0 0
556556 0 0
557557 20854.0i 1.58638i 0.608976 + 0.793189i 0.291581π0.291581\pi
−0.608976 + 0.793189i 0.708419π0.708419\pi
558558 0 0
559559 1144.00 0.0865582
560560 0 0
561561 8800.00 0.662275
562562 0 0
563563 − 19316.0i − 1.44595i −0.690872 0.722977i 0.742773π-0.742773\pi
0.690872 0.722977i 0.257227π-0.257227\pi
564564 0 0
565565 0 0
566566 0 0
567567 7464.00i 0.552837i
568568 0 0
569569 −7018.00 −0.517065 −0.258532 0.966003i 0.583239π-0.583239\pi
−0.258532 + 0.966003i 0.583239π0.583239\pi
570570 0 0
571571 −24420.0 −1.78975 −0.894873 0.446320i 0.852734π-0.852734\pi
−0.894873 + 0.446320i 0.852734π0.852734\pi
572572 0 0
573573 − 3840.00i − 0.279962i
574574 0 0
575575 0 0
576576 0 0
577577 23234.0i 1.67633i 0.545415 + 0.838166i 0.316372π0.316372\pi
−0.545415 + 0.838166i 0.683628π0.683628\pi
578578 0 0
579579 −11528.0 −0.827439
580580 0 0
581581 5664.00 0.404445
582582 0 0
583583 10648.0i 0.756424i
584584 0 0
585585 0 0
586586 0 0
587587 10604.0i 0.745611i 0.927909 + 0.372806i 0.121604π0.121604\pi
−0.927909 + 0.372806i 0.878396π0.878396\pi
588588 0 0
589589 7040.00 0.492493
590590 0 0
591591 4344.00 0.302349
592592 0 0
593593 13838.0i 0.958277i 0.877739 + 0.479139i 0.159051π0.159051\pi
−0.877739 + 0.479139i 0.840949π0.840949\pi
594594 0 0
595595 0 0
596596 0 0
597597 − 352.000i − 0.0241313i
598598 0 0
599599 −3960.00 −0.270119 −0.135059 0.990837i 0.543123π-0.543123\pi
−0.135059 + 0.990837i 0.543123π0.543123\pi
600600 0 0
601601 −5942.00 −0.403293 −0.201647 0.979458i 0.564629π-0.564629\pi
−0.201647 + 0.979458i 0.564629π0.564629\pi
602602 0 0
603603 − 2068.00i − 0.139661i
604604 0 0
605605 0 0
606606 0 0
607607 3040.00i 0.203278i 0.994821 + 0.101639i 0.0324087π0.0324087\pi
−0.994821 + 0.101639i 0.967591π0.967591\pi
608608 0 0
609609 19008.0 1.26477
610610 0 0
611611 −11616.0 −0.769121
612612 0 0
613613 2530.00i 0.166698i 0.996520 + 0.0833489i 0.0265616π0.0265616\pi
−0.996520 + 0.0833489i 0.973438π0.973438\pi
614614 0 0
615615 0 0
616616 0 0
617617 − 19206.0i − 1.25317i −0.779354 0.626584i 0.784453π-0.784453\pi
0.779354 0.626584i 0.215547π-0.215547\pi
618618 0 0
619619 10996.0 0.714001 0.357000 0.934104i 0.383799π-0.383799\pi
0.357000 + 0.934104i 0.383799π0.383799\pi
620620 0 0
621621 −8512.00 −0.550040
622622 0 0
623623 17136.0i 1.10199i
624624 0 0
625625 0 0
626626 0 0
627627 − 7744.00i − 0.493247i
628628 0 0
629629 8100.00 0.513463
630630 0 0
631631 6680.00 0.421437 0.210718 0.977547i 0.432420π-0.432420\pi
0.210718 + 0.977547i 0.432420π0.432420\pi
632632 0 0
633633 − 13904.0i − 0.873040i
634634 0 0
635635 0 0
636636 0 0
637637 5126.00i 0.318838i
638638 0 0
639639 −8008.00 −0.495761
640640 0 0
641641 6274.00 0.386596 0.193298 0.981140i 0.438082π-0.438082\pi
0.193298 + 0.981140i 0.438082π0.438082\pi
642642 0 0
643643 9084.00i 0.557135i 0.960417 + 0.278568i 0.0898596π0.0898596\pi
−0.960417 + 0.278568i 0.910140π0.910140\pi
644644 0 0
645645 0 0
646646 0 0
647647 23656.0i 1.43742i 0.695308 + 0.718712i 0.255268π0.255268\pi
−0.695308 + 0.718712i 0.744732π0.744732\pi
648648 0 0
649649 −29392.0 −1.77771
650650 0 0
651651 −15360.0 −0.924740
652652 0 0
653653 6762.00i 0.405234i 0.979258 + 0.202617i 0.0649446π0.0649446\pi
−0.979258 + 0.202617i 0.935055π0.935055\pi
654654 0 0
655655 0 0
656656 0 0
657657 − 1694.00i − 0.100592i
658658 0 0
659659 15276.0 0.902987 0.451494 0.892274i 0.350891π-0.350891\pi
0.451494 + 0.892274i 0.350891π0.350891\pi
660660 0 0
661661 11054.0 0.650455 0.325228 0.945636i 0.394559π-0.394559\pi
0.325228 + 0.945636i 0.394559π0.394559\pi
662662 0 0
663663 − 4400.00i − 0.257740i
664664 0 0
665665 0 0
666666 0 0
667667 11088.0i 0.643672i
668668 0 0
669669 3712.00 0.214520
670670 0 0
671671 24200.0 1.39230
672672 0 0
673673 21278.0i 1.21873i 0.792889 + 0.609366i 0.208576π0.208576\pi
−0.792889 + 0.609366i 0.791424π0.791424\pi
674674 0 0
675675 0 0
676676 0 0
677677 8926.00i 0.506727i 0.967371 + 0.253363i 0.0815368π0.0815368\pi
−0.967371 + 0.253363i 0.918463π0.918463\pi
678678 0 0
679679 −11472.0 −0.648387
680680 0 0
681681 −624.000 −0.0351127
682682 0 0
683683 8116.00i 0.454685i 0.973815 + 0.227343i 0.0730037π0.0730037\pi
−0.973815 + 0.227343i 0.926996π0.926996\pi
684684 0 0
685685 0 0
686686 0 0
687687 − 6536.00i − 0.362975i
688688 0 0
689689 5324.00 0.294381
690690 0 0
691691 11764.0 0.647646 0.323823 0.946118i 0.395032π-0.395032\pi
0.323823 + 0.946118i 0.395032π0.395032\pi
692692 0 0
693693 − 11616.0i − 0.636732i
694694 0 0
695695 0 0
696696 0 0
697697 − 9900.00i − 0.538005i
698698 0 0
699699 3608.00 0.195232
700700 0 0
701701 −4698.00 −0.253126 −0.126563 0.991959i 0.540395π-0.540395\pi
−0.126563 + 0.991959i 0.540395π0.540395\pi
702702 0 0
703703 − 7128.00i − 0.382415i
704704 0 0
705705 0 0
706706 0 0
707707 − 37584.0i − 1.99928i
708708 0 0
709709 −24638.0 −1.30508 −0.652538 0.757756i 0.726296π-0.726296\pi
−0.652538 + 0.757756i 0.726296π0.726296\pi
710710 0 0
711711 −7216.00 −0.380620
712712 0 0
713713 − 8960.00i − 0.470624i
714714 0 0
715715 0 0
716716 0 0
717717 − 6464.00i − 0.336684i
718718 0 0
719719 16624.0 0.862268 0.431134 0.902288i 0.358114π-0.358114\pi
0.431134 + 0.902288i 0.358114π0.358114\pi
720720 0 0
721721 −23232.0 −1.20001
722722 0 0
723723 − 19272.0i − 0.991332i
724724 0 0
725725 0 0
726726 0 0
727727 − 30216.0i − 1.54147i −0.637155 0.770735i 0.719889π-0.719889\pi
0.637155 0.770735i 0.280111π-0.280111\pi
728728 0 0
729729 −19837.0 −1.00782
730730 0 0
731731 −2600.00 −0.131552
732732 0 0
733733 3322.00i 0.167395i 0.996491 + 0.0836977i 0.0266730π0.0266730\pi
−0.996491 + 0.0836977i 0.973327π0.973327\pi
734734 0 0
735735 0 0
736736 0 0
737737 − 8272.00i − 0.413437i
738738 0 0
739739 −14692.0 −0.731331 −0.365666 0.930746i 0.619159π-0.619159\pi
−0.365666 + 0.930746i 0.619159π0.619159\pi
740740 0 0
741741 −3872.00 −0.191959
742742 0 0
743743 28600.0i 1.41216i 0.708134 + 0.706078i 0.249537π0.249537\pi
−0.708134 + 0.706078i 0.750463π0.750463\pi
744744 0 0
745745 0 0
746746 0 0
747747 2596.00i 0.127152i
748748 0 0
749749 18720.0 0.913236
750750 0 0
751751 29616.0 1.43902 0.719509 0.694483i 0.244367π-0.244367\pi
0.719509 + 0.694483i 0.244367π0.244367\pi
752752 0 0
753753 − 8560.00i − 0.414268i
754754 0 0
755755 0 0
756756 0 0
757757 2894.00i 0.138949i 0.997584 + 0.0694744i 0.0221322π0.0221322\pi
−0.997584 + 0.0694744i 0.977868π0.977868\pi
758758 0 0
759759 −9856.00 −0.471344
760760 0 0
761761 14762.0 0.703183 0.351591 0.936154i 0.385641π-0.385641\pi
0.351591 + 0.936154i 0.385641π0.385641\pi
762762 0 0
763763 − 47856.0i − 2.27065i
764764 0 0
765765 0 0
766766 0 0
767767 14696.0i 0.691841i
768768 0 0
769769 7678.00 0.360047 0.180023 0.983662i 0.442383π-0.442383\pi
0.180023 + 0.983662i 0.442383π0.442383\pi
770770 0 0
771771 3080.00 0.143870
772772 0 0
773773 − 27390.0i − 1.27445i −0.770678 0.637225i 0.780082π-0.780082\pi
0.770678 0.637225i 0.219918π-0.219918\pi
774774 0 0
775775 0 0
776776 0 0
777777 15552.0i 0.718050i
778778 0 0
779779 −8712.00 −0.400693
780780 0 0
781781 −32032.0 −1.46760
782782 0 0
783783 30096.0i 1.37362i
784784 0 0
785785 0 0
786786 0 0
787787 − 19756.0i − 0.894823i −0.894328 0.447411i 0.852346π-0.852346\pi
0.894328 0.447411i 0.147654π-0.147654\pi
788788 0 0
789789 −29600.0 −1.33560
790790 0 0
791791 22608.0 1.01624
792792 0 0
793793 − 12100.0i − 0.541846i
794794 0 0
795795 0 0
796796 0 0
797797 38854.0i 1.72682i 0.504499 + 0.863412i 0.331677π0.331677\pi
−0.504499 + 0.863412i 0.668323π0.668323\pi
798798 0 0
799799 26400.0 1.16892
800800 0 0
801801 −7854.00 −0.346451
802802 0 0
803803 − 6776.00i − 0.297783i
804804 0 0
805805 0 0
806806 0 0
807807 − 11176.0i − 0.487502i
808808 0 0
809809 14278.0 0.620504 0.310252 0.950654i 0.399587π-0.399587\pi
0.310252 + 0.950654i 0.399587π0.399587\pi
810810 0 0
811811 716.000 0.0310014 0.0155007 0.999880i 0.495066π-0.495066\pi
0.0155007 + 0.999880i 0.495066π0.495066\pi
812812 0 0
813813 34496.0i 1.48810i
814814 0 0
815815 0 0
816816 0 0
817817 2288.00i 0.0979767i
818818 0 0
819819 −5808.00 −0.247800
820820 0 0
821821 −23538.0 −1.00059 −0.500293 0.865856i 0.666775π-0.666775\pi
−0.500293 + 0.865856i 0.666775π0.666775\pi
822822 0 0
823823 − 6616.00i − 0.280218i −0.990136 0.140109i 0.955255π-0.955255\pi
0.990136 0.140109i 0.0447453π-0.0447453\pi
824824 0 0
825825 0 0
826826 0 0
827827 − 27236.0i − 1.14521i −0.819831 0.572605i 0.805933π-0.805933\pi
0.819831 0.572605i 0.194067π-0.194067\pi
828828 0 0
829829 −12070.0 −0.505680 −0.252840 0.967508i 0.581365π-0.581365\pi
−0.252840 + 0.967508i 0.581365π0.581365\pi
830830 0 0
831831 −7496.00 −0.312916
832832 0 0
833833 − 11650.0i − 0.484572i
834834 0 0
835835 0 0
836836 0 0
837837 − 24320.0i − 1.00433i
838838 0 0
839839 −42024.0 −1.72924 −0.864618 0.502429i 0.832440π-0.832440\pi
−0.864618 + 0.502429i 0.832440π0.832440\pi
840840 0 0
841841 14815.0 0.607446
842842 0 0
843843 − 13352.0i − 0.545513i
844844 0 0
845845 0 0
846846 0 0
847847 − 14520.0i − 0.589036i
848848 0 0
849849 28688.0 1.15968
850850 0 0
851851 −9072.00 −0.365434
852852 0 0
853853 − 2414.00i − 0.0968978i −0.998826 0.0484489i 0.984572π-0.984572\pi
0.998826 0.0484489i 0.0154278π-0.0154278\pi
854854 0 0
855855 0 0
856856 0 0
857857 − 37686.0i − 1.50213i −0.660226 0.751067i 0.729539π-0.729539\pi
0.660226 0.751067i 0.270461π-0.270461\pi
858858 0 0
859859 40644.0 1.61438 0.807192 0.590289i 0.200986π-0.200986\pi
0.807192 + 0.590289i 0.200986π0.200986\pi
860860 0 0
861861 19008.0 0.752370
862862 0 0
863863 − 18656.0i − 0.735872i −0.929851 0.367936i 0.880065π-0.880065\pi
0.929851 0.367936i 0.119935π-0.119935\pi
864864 0 0
865865 0 0
866866 0 0
867867 − 9652.00i − 0.378084i
868868 0 0
869869 −28864.0 −1.12675
870870 0 0
871871 −4136.00 −0.160899
872872 0 0
873873 − 5258.00i − 0.203845i
874874 0 0
875875 0 0
876876 0 0
877877 − 13002.0i − 0.500623i −0.968165 0.250311i 0.919467π-0.919467\pi
0.968165 0.250311i 0.0805330π-0.0805330\pi
878878 0 0
879879 −20856.0 −0.800291
880880 0 0
881881 49490.0 1.89258 0.946289 0.323323i 0.104800π-0.104800\pi
0.946289 + 0.323323i 0.104800π0.104800\pi
882882 0 0
883883 1100.00i 0.0419229i 0.999780 + 0.0209615i 0.00667273π0.00667273\pi
−0.999780 + 0.0209615i 0.993327π0.993327\pi
884884 0 0
885885 0 0
886886 0 0
887887 14104.0i 0.533896i 0.963711 + 0.266948i 0.0860152π0.0860152\pi
−0.963711 + 0.266948i 0.913985π0.913985\pi
888888 0 0
889889 −33792.0 −1.27486
890890 0 0
891891 −13684.0 −0.514513
892892 0 0
893893 − 23232.0i − 0.870581i
894894 0 0
895895 0 0
896896 0 0
897897 4928.00i 0.183435i
898898 0 0
899899 −31680.0 −1.17529
900900 0 0
901901 −12100.0 −0.447402
902902 0 0
903903 − 4992.00i − 0.183968i
904904 0 0
905905 0 0
906906 0 0
907907 12716.0i 0.465521i 0.972534 + 0.232761i 0.0747759π0.0747759\pi
−0.972534 + 0.232761i 0.925224π0.925224\pi
908908 0 0
909909 17226.0 0.628548
910910 0 0
911911 39632.0 1.44135 0.720673 0.693275i 0.243833π-0.243833\pi
0.720673 + 0.693275i 0.243833π0.243833\pi
912912 0 0
913913 10384.0i 0.376408i
914914 0 0
915915 0 0
916916 0 0
917917 − 64608.0i − 2.32666i
918918 0 0
919919 5704.00 0.204742 0.102371 0.994746i 0.467357π-0.467357\pi
0.102371 + 0.994746i 0.467357π0.467357\pi
920920 0 0
921921 −1584.00 −0.0566716
922922 0 0
923923 16016.0i 0.571152i
924924 0 0
925925 0 0
926926 0 0
927927 − 10648.0i − 0.377267i
928928 0 0
929929 −8162.00 −0.288252 −0.144126 0.989559i 0.546037π-0.546037\pi
−0.144126 + 0.989559i 0.546037π0.546037\pi
930930 0 0
931931 −10252.0 −0.360898
932932 0 0
933933 − 16224.0i − 0.569293i
934934 0 0
935935 0 0
936936 0 0
937937 − 55110.0i − 1.92141i −0.277564 0.960707i 0.589527π-0.589527\pi
0.277564 0.960707i 0.410473π-0.410473\pi
938938 0 0
939939 −8616.00 −0.299438
940940 0 0
941941 16374.0 0.567245 0.283622 0.958936i 0.408464π-0.408464\pi
0.283622 + 0.958936i 0.408464π0.408464\pi
942942 0 0
943943 11088.0i 0.382900i
944944 0 0
945945 0 0
946946 0 0
947947 − 8460.00i − 0.290299i −0.989410 0.145149i 0.953634π-0.953634\pi
0.989410 0.145149i 0.0463663π-0.0463663\pi
948948 0 0
949949 −3388.00 −0.115889
950950 0 0
951951 −29544.0 −1.00739
952952 0 0
953953 20502.0i 0.696878i 0.937331 + 0.348439i 0.113288π0.113288\pi
−0.937331 + 0.348439i 0.886712π0.886712\pi
954954 0 0
955955 0 0
956956 0 0
957957 34848.0i 1.17709i
958958 0 0
959959 39024.0 1.31403
960960 0 0
961961 −4191.00 −0.140680
962962 0 0
963963 8580.00i 0.287110i
964964 0 0
965965 0 0
966966 0 0
967967 36520.0i 1.21448i 0.794518 + 0.607241i 0.207724π0.207724\pi
−0.794518 + 0.607241i 0.792276π0.792276\pi
968968 0 0
969969 8800.00 0.291741
970970 0 0
971971 −20244.0 −0.669064 −0.334532 0.942384i 0.608578π-0.608578\pi
−0.334532 + 0.942384i 0.608578π0.608578\pi
972972 0 0
973973 16416.0i 0.540876i
974974 0 0
975975 0 0
976976 0 0
977977 50034.0i 1.63841i 0.573499 + 0.819206i 0.305586π0.305586\pi
−0.573499 + 0.819206i 0.694414π0.694414\pi
978978 0 0
979979 −31416.0 −1.02560
980980 0 0
981981 21934.0 0.713862
982982 0 0
983983 37128.0i 1.20468i 0.798240 + 0.602339i 0.205765π0.205765\pi
−0.798240 + 0.602339i 0.794235π0.794235\pi
984984 0 0
985985 0 0
986986 0 0
987987 50688.0i 1.63467i
988988 0 0
989989 2912.00 0.0936261
990990 0 0
991991 −27808.0 −0.891373 −0.445686 0.895189i 0.647040π-0.647040\pi
−0.445686 + 0.895189i 0.647040π0.647040\pi
992992 0 0
993993 − 4528.00i − 0.144705i
994994 0 0
995995 0 0
996996 0 0
997997 − 28514.0i − 0.905765i −0.891570 0.452882i 0.850396π-0.850396\pi
0.891570 0.452882i 0.149604π-0.149604\pi
998998 0 0
999999 −24624.0 −0.779849
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 400.4.c.i.49.1 2
4.3 odd 2 200.4.c.e.49.2 2
5.2 odd 4 400.4.a.g.1.1 1
5.3 odd 4 16.4.a.a.1.1 1
5.4 even 2 inner 400.4.c.i.49.2 2
12.11 even 2 1800.4.f.u.649.2 2
15.8 even 4 144.4.a.e.1.1 1
20.3 even 4 8.4.a.a.1.1 1
20.7 even 4 200.4.a.g.1.1 1
20.19 odd 2 200.4.c.e.49.1 2
35.13 even 4 784.4.a.e.1.1 1
40.3 even 4 64.4.a.d.1.1 1
40.13 odd 4 64.4.a.b.1.1 1
40.27 even 4 1600.4.a.o.1.1 1
40.37 odd 4 1600.4.a.bm.1.1 1
55.43 even 4 1936.4.a.l.1.1 1
60.23 odd 4 72.4.a.c.1.1 1
60.47 odd 4 1800.4.a.d.1.1 1
60.59 even 2 1800.4.f.u.649.1 2
80.3 even 4 256.4.b.a.129.1 2
80.13 odd 4 256.4.b.g.129.2 2
80.43 even 4 256.4.b.a.129.2 2
80.53 odd 4 256.4.b.g.129.1 2
120.53 even 4 576.4.a.j.1.1 1
120.83 odd 4 576.4.a.k.1.1 1
140.3 odd 12 392.4.i.b.177.1 2
140.23 even 12 392.4.i.g.361.1 2
140.83 odd 4 392.4.a.e.1.1 1
140.103 odd 12 392.4.i.b.361.1 2
140.123 even 12 392.4.i.g.177.1 2
180.23 odd 12 648.4.i.e.217.1 2
180.43 even 12 648.4.i.h.433.1 2
180.83 odd 12 648.4.i.e.433.1 2
180.103 even 12 648.4.i.h.217.1 2
220.43 odd 4 968.4.a.a.1.1 1
260.103 even 4 1352.4.a.a.1.1 1
340.203 even 4 2312.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.4.a.a.1.1 1 20.3 even 4
16.4.a.a.1.1 1 5.3 odd 4
64.4.a.b.1.1 1 40.13 odd 4
64.4.a.d.1.1 1 40.3 even 4
72.4.a.c.1.1 1 60.23 odd 4
144.4.a.e.1.1 1 15.8 even 4
200.4.a.g.1.1 1 20.7 even 4
200.4.c.e.49.1 2 20.19 odd 2
200.4.c.e.49.2 2 4.3 odd 2
256.4.b.a.129.1 2 80.3 even 4
256.4.b.a.129.2 2 80.43 even 4
256.4.b.g.129.1 2 80.53 odd 4
256.4.b.g.129.2 2 80.13 odd 4
392.4.a.e.1.1 1 140.83 odd 4
392.4.i.b.177.1 2 140.3 odd 12
392.4.i.b.361.1 2 140.103 odd 12
392.4.i.g.177.1 2 140.123 even 12
392.4.i.g.361.1 2 140.23 even 12
400.4.a.g.1.1 1 5.2 odd 4
400.4.c.i.49.1 2 1.1 even 1 trivial
400.4.c.i.49.2 2 5.4 even 2 inner
576.4.a.j.1.1 1 120.53 even 4
576.4.a.k.1.1 1 120.83 odd 4
648.4.i.e.217.1 2 180.23 odd 12
648.4.i.e.433.1 2 180.83 odd 12
648.4.i.h.217.1 2 180.103 even 12
648.4.i.h.433.1 2 180.43 even 12
784.4.a.e.1.1 1 35.13 even 4
968.4.a.a.1.1 1 220.43 odd 4
1352.4.a.a.1.1 1 260.103 even 4
1600.4.a.o.1.1 1 40.27 even 4
1600.4.a.bm.1.1 1 40.37 odd 4
1800.4.a.d.1.1 1 60.47 odd 4
1800.4.f.u.649.1 2 60.59 even 2
1800.4.f.u.649.2 2 12.11 even 2
1936.4.a.l.1.1 1 55.43 even 4
2312.4.a.a.1.1 1 340.203 even 4