Properties

Label 400.3.h.b.399.2
Level 400400
Weight 33
Character 400.399
Analytic conductor 10.89910.899
Analytic rank 00
Dimension 44
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [400,3,Mod(399,400)]
 
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([1, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.399");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 400=2452 400 = 2^{4} \cdot 5^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 400.h (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: 10.899210574410.8992105744
Analytic rank: 00
Dimension: 44
Coefficient field: Q(ζ12)\Q(\zeta_{12})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x2+1 x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 22 2^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 399.2
Root 0.8660250.500000i0.866025 - 0.500000i of defining polynomial
Character χ\chi == 400.399
Dual form 400.3.h.b.399.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q1.73205q3+3.46410q76.00000q9+12.1244iq1116.0000iq133.00000iq17+22.5167iq196.00000q2145.0333q23+25.9808q2712.0000q29+31.1769iq3121.0000iq33+50.0000iq37+27.7128iq3963.0000q4162.3538q4313.8564q4737.0000q49+5.19615iq5118.0000iq5339.0000iq57+55.4256iq59+26.0000q6120.7846q63+32.9090q67+78.0000q69+27.7128iq71+17.0000iq73+42.0000iq7786.6025iq79+9.00000q81+98.7269q83+20.7846q8799.0000q8955.4256iq9154.0000iq93134.000iq9772.7461iq99+O(q100)q-1.73205 q^{3} +3.46410 q^{7} -6.00000 q^{9} +12.1244i q^{11} -16.0000i q^{13} -3.00000i q^{17} +22.5167i q^{19} -6.00000 q^{21} -45.0333 q^{23} +25.9808 q^{27} -12.0000 q^{29} +31.1769i q^{31} -21.0000i q^{33} +50.0000i q^{37} +27.7128i q^{39} -63.0000 q^{41} -62.3538 q^{43} -13.8564 q^{47} -37.0000 q^{49} +5.19615i q^{51} -18.0000i q^{53} -39.0000i q^{57} +55.4256i q^{59} +26.0000 q^{61} -20.7846 q^{63} +32.9090 q^{67} +78.0000 q^{69} +27.7128i q^{71} +17.0000i q^{73} +42.0000i q^{77} -86.6025i q^{79} +9.00000 q^{81} +98.7269 q^{83} +20.7846 q^{87} -99.0000 q^{89} -55.4256i q^{91} -54.0000i q^{93} -134.000i q^{97} -72.7461i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q24q924q2148q29252q41148q49+104q61+312q69+36q81396q89+O(q100) 4 q - 24 q^{9} - 24 q^{21} - 48 q^{29} - 252 q^{41} - 148 q^{49} + 104 q^{61} + 312 q^{69} + 36 q^{81} - 396 q^{89}+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 1-1

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 −1.73205 −0.577350 −0.288675 0.957427i 0.593215π-0.593215\pi
−0.288675 + 0.957427i 0.593215π0.593215\pi
44 0 0
55 0 0
66 0 0
77 3.46410 0.494872 0.247436 0.968904i 0.420412π-0.420412\pi
0.247436 + 0.968904i 0.420412π0.420412\pi
88 0 0
99 −6.00000 −0.666667
1010 0 0
1111 12.1244i 1.10221i 0.834435 + 0.551107i 0.185794π0.185794\pi
−0.834435 + 0.551107i 0.814206π0.814206\pi
1212 0 0
1313 − 16.0000i − 1.23077i −0.788227 0.615385i 0.789001π-0.789001\pi
0.788227 0.615385i 0.210999π-0.210999\pi
1414 0 0
1515 0 0
1616 0 0
1717 − 3.00000i − 0.176471i −0.996100 0.0882353i 0.971877π-0.971877\pi
0.996100 0.0882353i 0.0281227π-0.0281227\pi
1818 0 0
1919 22.5167i 1.18509i 0.805538 + 0.592544i 0.201876π0.201876\pi
−0.805538 + 0.592544i 0.798124π0.798124\pi
2020 0 0
2121 −6.00000 −0.285714
2222 0 0
2323 −45.0333 −1.95797 −0.978985 0.203931i 0.934628π-0.934628\pi
−0.978985 + 0.203931i 0.934628π0.934628\pi
2424 0 0
2525 0 0
2626 0 0
2727 25.9808 0.962250
2828 0 0
2929 −12.0000 −0.413793 −0.206897 0.978363i 0.566336π-0.566336\pi
−0.206897 + 0.978363i 0.566336π0.566336\pi
3030 0 0
3131 31.1769i 1.00571i 0.864372 + 0.502853i 0.167716π0.167716\pi
−0.864372 + 0.502853i 0.832284π0.832284\pi
3232 0 0
3333 − 21.0000i − 0.636364i
3434 0 0
3535 0 0
3636 0 0
3737 50.0000i 1.35135i 0.737199 + 0.675676i 0.236148π0.236148\pi
−0.737199 + 0.675676i 0.763852π0.763852\pi
3838 0 0
3939 27.7128i 0.710585i
4040 0 0
4141 −63.0000 −1.53659 −0.768293 0.640099i 0.778893π-0.778893\pi
−0.768293 + 0.640099i 0.778893π0.778893\pi
4242 0 0
4343 −62.3538 −1.45009 −0.725045 0.688702i 0.758181π-0.758181\pi
−0.725045 + 0.688702i 0.758181π0.758181\pi
4444 0 0
4545 0 0
4646 0 0
4747 −13.8564 −0.294817 −0.147409 0.989076i 0.547093π-0.547093\pi
−0.147409 + 0.989076i 0.547093π0.547093\pi
4848 0 0
4949 −37.0000 −0.755102
5050 0 0
5151 5.19615i 0.101885i
5252 0 0
5353 − 18.0000i − 0.339623i −0.985477 0.169811i 0.945684π-0.945684\pi
0.985477 0.169811i 0.0543158π-0.0543158\pi
5454 0 0
5555 0 0
5656 0 0
5757 − 39.0000i − 0.684211i
5858 0 0
5959 55.4256i 0.939417i 0.882821 + 0.469709i 0.155641π0.155641\pi
−0.882821 + 0.469709i 0.844359π0.844359\pi
6060 0 0
6161 26.0000 0.426230 0.213115 0.977027i 0.431639π-0.431639\pi
0.213115 + 0.977027i 0.431639π0.431639\pi
6262 0 0
6363 −20.7846 −0.329914
6464 0 0
6565 0 0
6666 0 0
6767 32.9090 0.491179 0.245589 0.969374i 0.421019π-0.421019\pi
0.245589 + 0.969374i 0.421019π0.421019\pi
6868 0 0
6969 78.0000 1.13043
7070 0 0
7171 27.7128i 0.390321i 0.980771 + 0.195161i 0.0625228π0.0625228\pi
−0.980771 + 0.195161i 0.937477π0.937477\pi
7272 0 0
7373 17.0000i 0.232877i 0.993198 + 0.116438i 0.0371477π0.0371477\pi
−0.993198 + 0.116438i 0.962852π0.962852\pi
7474 0 0
7575 0 0
7676 0 0
7777 42.0000i 0.545455i
7878 0 0
7979 − 86.6025i − 1.09623i −0.836401 0.548117i 0.815345π-0.815345\pi
0.836401 0.548117i 0.184655π-0.184655\pi
8080 0 0
8181 9.00000 0.111111
8282 0 0
8383 98.7269 1.18948 0.594740 0.803918i 0.297255π-0.297255\pi
0.594740 + 0.803918i 0.297255π0.297255\pi
8484 0 0
8585 0 0
8686 0 0
8787 20.7846 0.238904
8888 0 0
8989 −99.0000 −1.11236 −0.556180 0.831062i 0.687733π-0.687733\pi
−0.556180 + 0.831062i 0.687733π0.687733\pi
9090 0 0
9191 − 55.4256i − 0.609073i
9292 0 0
9393 − 54.0000i − 0.580645i
9494 0 0
9595 0 0
9696 0 0
9797 − 134.000i − 1.38144i −0.723121 0.690722i 0.757293π-0.757293\pi
0.723121 0.690722i 0.242707π-0.242707\pi
9898 0 0
9999 − 72.7461i − 0.734809i
100100 0 0
101101 150.000 1.48515 0.742574 0.669764i 0.233605π-0.233605\pi
0.742574 + 0.669764i 0.233605π0.233605\pi
102102 0 0
103103 110.851 1.07623 0.538113 0.842873i 0.319137π-0.319137\pi
0.538113 + 0.842873i 0.319137π0.319137\pi
104104 0 0
105105 0 0
106106 0 0
107107 −164.545 −1.53780 −0.768901 0.639368i 0.779196π-0.779196\pi
−0.768901 + 0.639368i 0.779196π0.779196\pi
108108 0 0
109109 74.0000 0.678899 0.339450 0.940624i 0.389759π-0.389759\pi
0.339450 + 0.940624i 0.389759π0.389759\pi
110110 0 0
111111 − 86.6025i − 0.780203i
112112 0 0
113113 201.000i 1.77876i 0.457168 + 0.889381i 0.348864π0.348864\pi
−0.457168 + 0.889381i 0.651136π0.651136\pi
114114 0 0
115115 0 0
116116 0 0
117117 96.0000i 0.820513i
118118 0 0
119119 − 10.3923i − 0.0873303i
120120 0 0
121121 −26.0000 −0.214876
122122 0 0
123123 109.119 0.887148
124124 0 0
125125 0 0
126126 0 0
127127 10.3923 0.0818292 0.0409146 0.999163i 0.486973π-0.486973\pi
0.0409146 + 0.999163i 0.486973π0.486973\pi
128128 0 0
129129 108.000 0.837209
130130 0 0
131131 6.92820i 0.0528870i 0.999650 + 0.0264435i 0.00841822π0.00841822\pi
−0.999650 + 0.0264435i 0.991582π0.991582\pi
132132 0 0
133133 78.0000i 0.586466i
134134 0 0
135135 0 0
136136 0 0
137137 − 207.000i − 1.51095i −0.655178 0.755474i 0.727406π-0.727406\pi
0.655178 0.755474i 0.272594π-0.272594\pi
138138 0 0
139139 − 178.401i − 1.28346i −0.766930 0.641731i 0.778217π-0.778217\pi
0.766930 0.641731i 0.221783π-0.221783\pi
140140 0 0
141141 24.0000 0.170213
142142 0 0
143143 193.990 1.35657
144144 0 0
145145 0 0
146146 0 0
147147 64.0859 0.435958
148148 0 0
149149 108.000 0.724832 0.362416 0.932016i 0.381952π-0.381952\pi
0.362416 + 0.932016i 0.381952π0.381952\pi
150150 0 0
151151 − 266.736i − 1.76646i −0.468938 0.883231i 0.655363π-0.655363\pi
0.468938 0.883231i 0.344637π-0.344637\pi
152152 0 0
153153 18.0000i 0.117647i
154154 0 0
155155 0 0
156156 0 0
157157 278.000i 1.77070i 0.464925 + 0.885350i 0.346081π0.346081\pi
−0.464925 + 0.885350i 0.653919π0.653919\pi
158158 0 0
159159 31.1769i 0.196081i
160160 0 0
161161 −156.000 −0.968944
162162 0 0
163163 −19.0526 −0.116887 −0.0584434 0.998291i 0.518614π-0.518614\pi
−0.0584434 + 0.998291i 0.518614π0.518614\pi
164164 0 0
165165 0 0
166166 0 0
167167 −263.272 −1.57648 −0.788239 0.615370i 0.789007π-0.789007\pi
−0.788239 + 0.615370i 0.789007π0.789007\pi
168168 0 0
169169 −87.0000 −0.514793
170170 0 0
171171 − 135.100i − 0.790058i
172172 0 0
173173 0 0 1.00000 00
−1.00000 π\pi
174174 0 0
175175 0 0
176176 0 0
177177 − 96.0000i − 0.542373i
178178 0 0
179179 − 12.1244i − 0.0677338i −0.999426 0.0338669i 0.989218π-0.989218\pi
0.999426 0.0338669i 0.0107822π-0.0107822\pi
180180 0 0
181181 166.000 0.917127 0.458564 0.888662i 0.348364π-0.348364\pi
0.458564 + 0.888662i 0.348364π0.348364\pi
182182 0 0
183183 −45.0333 −0.246084
184184 0 0
185185 0 0
186186 0 0
187187 36.3731 0.194508
188188 0 0
189189 90.0000 0.476190
190190 0 0
191191 301.377i 1.57789i 0.614464 + 0.788945i 0.289372π0.289372\pi
−0.614464 + 0.788945i 0.710628π0.710628\pi
192192 0 0
193193 139.000i 0.720207i 0.932912 + 0.360104i 0.117259π0.117259\pi
−0.932912 + 0.360104i 0.882741π0.882741\pi
194194 0 0
195195 0 0
196196 0 0
197197 − 126.000i − 0.639594i −0.947486 0.319797i 0.896385π-0.896385\pi
0.947486 0.319797i 0.103615π-0.103615\pi
198198 0 0
199199 76.2102i 0.382966i 0.981496 + 0.191483i 0.0613297π0.0613297\pi
−0.981496 + 0.191483i 0.938670π0.938670\pi
200200 0 0
201201 −57.0000 −0.283582
202202 0 0
203203 −41.5692 −0.204774
204204 0 0
205205 0 0
206206 0 0
207207 270.200 1.30531
208208 0 0
209209 −273.000 −1.30622
210210 0 0
211211 188.794i 0.894756i 0.894345 + 0.447378i 0.147642π0.147642\pi
−0.894345 + 0.447378i 0.852358π0.852358\pi
212212 0 0
213213 − 48.0000i − 0.225352i
214214 0 0
215215 0 0
216216 0 0
217217 108.000i 0.497696i
218218 0 0
219219 − 29.4449i − 0.134451i
220220 0 0
221221 −48.0000 −0.217195
222222 0 0
223223 −145.492 −0.652432 −0.326216 0.945295i 0.605774π-0.605774\pi
−0.326216 + 0.945295i 0.605774π0.605774\pi
224224 0 0
225225 0 0
226226 0 0
227227 −173.205 −0.763018 −0.381509 0.924365i 0.624595π-0.624595\pi
−0.381509 + 0.924365i 0.624595π0.624595\pi
228228 0 0
229229 140.000 0.611354 0.305677 0.952135i 0.401117π-0.401117\pi
0.305677 + 0.952135i 0.401117π0.401117\pi
230230 0 0
231231 − 72.7461i − 0.314918i
232232 0 0
233233 − 366.000i − 1.57082i −0.618979 0.785408i 0.712453π-0.712453\pi
0.618979 0.785408i 0.287547π-0.287547\pi
234234 0 0
235235 0 0
236236 0 0
237237 150.000i 0.632911i
238238 0 0
239239 256.344i 1.07257i 0.844038 + 0.536284i 0.180172π0.180172\pi
−0.844038 + 0.536284i 0.819828π0.819828\pi
240240 0 0
241241 73.0000 0.302905 0.151452 0.988465i 0.451605π-0.451605\pi
0.151452 + 0.988465i 0.451605π0.451605\pi
242242 0 0
243243 −249.415 −1.02640
244244 0 0
245245 0 0
246246 0 0
247247 360.267 1.45857
248248 0 0
249249 −171.000 −0.686747
250250 0 0
251251 168.009i 0.669358i 0.942332 + 0.334679i 0.108628π0.108628\pi
−0.942332 + 0.334679i 0.891372π0.891372\pi
252252 0 0
253253 − 546.000i − 2.15810i
254254 0 0
255255 0 0
256256 0 0
257257 − 282.000i − 1.09728i −0.836060 0.548638i 0.815146π-0.815146\pi
0.836060 0.548638i 0.184854π-0.184854\pi
258258 0 0
259259 173.205i 0.668745i
260260 0 0
261261 72.0000 0.275862
262262 0 0
263263 −169.741 −0.645403 −0.322701 0.946501i 0.604591π-0.604591\pi
−0.322701 + 0.946501i 0.604591π0.604591\pi
264264 0 0
265265 0 0
266266 0 0
267267 171.473 0.642221
268268 0 0
269269 −288.000 −1.07063 −0.535316 0.844652i 0.679807π-0.679807\pi
−0.535316 + 0.844652i 0.679807π0.679807\pi
270270 0 0
271271 169.741i 0.626350i 0.949695 + 0.313175i 0.101393π0.101393\pi
−0.949695 + 0.313175i 0.898607π0.898607\pi
272272 0 0
273273 96.0000i 0.351648i
274274 0 0
275275 0 0
276276 0 0
277277 76.0000i 0.274368i 0.990546 + 0.137184i 0.0438052π0.0438052\pi
−0.990546 + 0.137184i 0.956195π0.956195\pi
278278 0 0
279279 − 187.061i − 0.670471i
280280 0 0
281281 −354.000 −1.25979 −0.629893 0.776682i 0.716901π-0.716901\pi
−0.629893 + 0.776682i 0.716901π0.716901\pi
282282 0 0
283283 −316.965 −1.12002 −0.560009 0.828486i 0.689202π-0.689202\pi
−0.560009 + 0.828486i 0.689202π0.689202\pi
284284 0 0
285285 0 0
286286 0 0
287287 −218.238 −0.760413
288288 0 0
289289 280.000 0.968858
290290 0 0
291291 232.095i 0.797577i
292292 0 0
293293 426.000i 1.45392i 0.686677 + 0.726962i 0.259069π0.259069\pi
−0.686677 + 0.726962i 0.740931π0.740931\pi
294294 0 0
295295 0 0
296296 0 0
297297 315.000i 1.06061i
298298 0 0
299299 720.533i 2.40981i
300300 0 0
301301 −216.000 −0.717608
302302 0 0
303303 −259.808 −0.857451
304304 0 0
305305 0 0
306306 0 0
307307 223.435 0.727800 0.363900 0.931438i 0.381445π-0.381445\pi
0.363900 + 0.931438i 0.381445π0.381445\pi
308308 0 0
309309 −192.000 −0.621359
310310 0 0
311311 433.013i 1.39232i 0.717885 + 0.696162i 0.245110π0.245110\pi
−0.717885 + 0.696162i 0.754890π0.754890\pi
312312 0 0
313313 − 218.000i − 0.696486i −0.937404 0.348243i 0.886778π-0.886778\pi
0.937404 0.348243i 0.113222π-0.113222\pi
314314 0 0
315315 0 0
316316 0 0
317317 12.0000i 0.0378549i 0.999821 + 0.0189274i 0.00602515π0.00602515\pi
−0.999821 + 0.0189274i 0.993975π0.993975\pi
318318 0 0
319319 − 145.492i − 0.456089i
320320 0 0
321321 285.000 0.887850
322322 0 0
323323 67.5500 0.209133
324324 0 0
325325 0 0
326326 0 0
327327 −128.172 −0.391963
328328 0 0
329329 −48.0000 −0.145897
330330 0 0
331331 − 465.922i − 1.40762i −0.710389 0.703809i 0.751481π-0.751481\pi
0.710389 0.703809i 0.248519π-0.248519\pi
332332 0 0
333333 − 300.000i − 0.900901i
334334 0 0
335335 0 0
336336 0 0
337337 67.0000i 0.198813i 0.995047 + 0.0994065i 0.0316944π0.0316944\pi
−0.995047 + 0.0994065i 0.968306π0.968306\pi
338338 0 0
339339 − 348.142i − 1.02697i
340340 0 0
341341 −378.000 −1.10850
342342 0 0
343343 −297.913 −0.868550
344344 0 0
345345 0 0
346346 0 0
347347 −192.258 −0.554057 −0.277028 0.960862i 0.589350π-0.589350\pi
−0.277028 + 0.960862i 0.589350π0.589350\pi
348348 0 0
349349 −254.000 −0.727794 −0.363897 0.931439i 0.618554π-0.618554\pi
−0.363897 + 0.931439i 0.618554π0.618554\pi
350350 0 0
351351 − 415.692i − 1.18431i
352352 0 0
353353 114.000i 0.322946i 0.986877 + 0.161473i 0.0516245π0.0516245\pi
−0.986877 + 0.161473i 0.948376π0.948376\pi
354354 0 0
355355 0 0
356356 0 0
357357 18.0000i 0.0504202i
358358 0 0
359359 370.659i 1.03248i 0.856445 + 0.516238i 0.172668π0.172668\pi
−0.856445 + 0.516238i 0.827332π0.827332\pi
360360 0 0
361361 −146.000 −0.404432
362362 0 0
363363 45.0333 0.124059
364364 0 0
365365 0 0
366366 0 0
367367 117.779 0.320925 0.160462 0.987042i 0.448701π-0.448701\pi
0.160462 + 0.987042i 0.448701π0.448701\pi
368368 0 0
369369 378.000 1.02439
370370 0 0
371371 − 62.3538i − 0.168070i
372372 0 0
373373 274.000i 0.734584i 0.930106 + 0.367292i 0.119715π0.119715\pi
−0.930106 + 0.367292i 0.880285π0.880285\pi
374374 0 0
375375 0 0
376376 0 0
377377 192.000i 0.509284i
378378 0 0
379379 − 299.645i − 0.790619i −0.918548 0.395310i 0.870637π-0.870637\pi
0.918548 0.395310i 0.129363π-0.129363\pi
380380 0 0
381381 −18.0000 −0.0472441
382382 0 0
383383 460.726 1.20294 0.601469 0.798896i 0.294582π-0.294582\pi
0.601469 + 0.798896i 0.294582π0.294582\pi
384384 0 0
385385 0 0
386386 0 0
387387 374.123 0.966726
388388 0 0
389389 510.000 1.31105 0.655527 0.755172i 0.272447π-0.272447\pi
0.655527 + 0.755172i 0.272447π0.272447\pi
390390 0 0
391391 135.100i 0.345524i
392392 0 0
393393 − 12.0000i − 0.0305344i
394394 0 0
395395 0 0
396396 0 0
397397 − 532.000i − 1.34005i −0.742338 0.670025i 0.766283π-0.766283\pi
0.742338 0.670025i 0.233717π-0.233717\pi
398398 0 0
399399 − 135.100i − 0.338596i
400400 0 0
401401 477.000 1.18953 0.594763 0.803901i 0.297246π-0.297246\pi
0.594763 + 0.803901i 0.297246π0.297246\pi
402402 0 0
403403 498.831 1.23779
404404 0 0
405405 0 0
406406 0 0
407407 −606.218 −1.48948
408408 0 0
409409 −25.0000 −0.0611247 −0.0305623 0.999533i 0.509730π-0.509730\pi
−0.0305623 + 0.999533i 0.509730π0.509730\pi
410410 0 0
411411 358.535i 0.872347i
412412 0 0
413413 192.000i 0.464891i
414414 0 0
415415 0 0
416416 0 0
417417 309.000i 0.741007i
418418 0 0
419419 57.1577i 0.136415i 0.997671 + 0.0682073i 0.0217279π0.0217279\pi
−0.997671 + 0.0682073i 0.978272π0.978272\pi
420420 0 0
421421 388.000 0.921615 0.460808 0.887500i 0.347560π-0.347560\pi
0.460808 + 0.887500i 0.347560π0.347560\pi
422422 0 0
423423 83.1384 0.196545
424424 0 0
425425 0 0
426426 0 0
427427 90.0666 0.210929
428428 0 0
429429 −336.000 −0.783217
430430 0 0
431431 − 245.951i − 0.570652i −0.958430 0.285326i 0.907898π-0.907898\pi
0.958430 0.285326i 0.0921019π-0.0921019\pi
432432 0 0
433433 307.000i 0.709007i 0.935055 + 0.354503i 0.115350π0.115350\pi
−0.935055 + 0.354503i 0.884650π0.884650\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 1014.00i − 2.32037i
438438 0 0
439439 − 561.184i − 1.27832i −0.769072 0.639162i 0.779281π-0.779281\pi
0.769072 0.639162i 0.220719π-0.220719\pi
440440 0 0
441441 222.000 0.503401
442442 0 0
443443 479.778 1.08302 0.541510 0.840694i 0.317853π-0.317853\pi
0.541510 + 0.840694i 0.317853π0.317853\pi
444444 0 0
445445 0 0
446446 0 0
447447 −187.061 −0.418482
448448 0 0
449449 39.0000 0.0868597 0.0434298 0.999056i 0.486172π-0.486172\pi
0.0434298 + 0.999056i 0.486172π0.486172\pi
450450 0 0
451451 − 763.834i − 1.69365i
452452 0 0
453453 462.000i 1.01987i
454454 0 0
455455 0 0
456456 0 0
457457 349.000i 0.763676i 0.924229 + 0.381838i 0.124709π0.124709\pi
−0.924229 + 0.381838i 0.875291π0.875291\pi
458458 0 0
459459 − 77.9423i − 0.169809i
460460 0 0
461461 −372.000 −0.806941 −0.403471 0.914993i 0.632196π-0.632196\pi
−0.403471 + 0.914993i 0.632196π0.632196\pi
462462 0 0
463463 422.620 0.912787 0.456394 0.889778i 0.349141π-0.349141\pi
0.456394 + 0.889778i 0.349141π0.349141\pi
464464 0 0
465465 0 0
466466 0 0
467467 −713.605 −1.52806 −0.764031 0.645180i 0.776783π-0.776783\pi
−0.764031 + 0.645180i 0.776783π0.776783\pi
468468 0 0
469469 114.000 0.243070
470470 0 0
471471 − 481.510i − 1.02231i
472472 0 0
473473 − 756.000i − 1.59831i
474474 0 0
475475 0 0
476476 0 0
477477 108.000i 0.226415i
478478 0 0
479479 − 758.638i − 1.58380i −0.610653 0.791898i 0.709093π-0.709093\pi
0.610653 0.791898i 0.290907π-0.290907\pi
480480 0 0
481481 800.000 1.66320
482482 0 0
483483 270.200 0.559420
484484 0 0
485485 0 0
486486 0 0
487487 523.079 1.07408 0.537042 0.843555i 0.319541π-0.319541\pi
0.537042 + 0.843555i 0.319541π0.319541\pi
488488 0 0
489489 33.0000 0.0674847
490490 0 0
491491 478.046i 0.973617i 0.873509 + 0.486809i 0.161839π0.161839\pi
−0.873509 + 0.486809i 0.838161π0.838161\pi
492492 0 0
493493 36.0000i 0.0730223i
494494 0 0
495495 0 0
496496 0 0
497497 96.0000i 0.193159i
498498 0 0
499499 62.3538i 0.124958i 0.998046 + 0.0624788i 0.0199006π0.0199006\pi
−0.998046 + 0.0624788i 0.980099π0.980099\pi
500500 0 0
501501 456.000 0.910180
502502 0 0
503503 561.184 1.11567 0.557837 0.829950i 0.311631π-0.311631\pi
0.557837 + 0.829950i 0.311631π0.311631\pi
504504 0 0
505505 0 0
506506 0 0
507507 150.688 0.297216
508508 0 0
509509 −390.000 −0.766208 −0.383104 0.923705i 0.625145π-0.625145\pi
−0.383104 + 0.923705i 0.625145π0.625145\pi
510510 0 0
511511 58.8897i 0.115244i
512512 0 0
513513 585.000i 1.14035i
514514 0 0
515515 0 0
516516 0 0
517517 − 168.000i − 0.324952i
518518 0 0
519519 0 0
520520 0 0
521521 −183.000 −0.351248 −0.175624 0.984457i 0.556194π-0.556194\pi
−0.175624 + 0.984457i 0.556194π0.556194\pi
522522 0 0
523523 185.329 0.354358 0.177179 0.984179i 0.443303π-0.443303\pi
0.177179 + 0.984179i 0.443303π0.443303\pi
524524 0 0
525525 0 0
526526 0 0
527527 93.5307 0.177478
528528 0 0
529529 1499.00 2.83365
530530 0 0
531531 − 332.554i − 0.626278i
532532 0 0
533533 1008.00i 1.89118i
534534 0 0
535535 0 0
536536 0 0
537537 21.0000i 0.0391061i
538538 0 0
539539 − 448.601i − 0.832284i
540540 0 0
541541 −968.000 −1.78928 −0.894640 0.446789i 0.852568π-0.852568\pi
−0.894640 + 0.446789i 0.852568π0.852568\pi
542542 0 0
543543 −287.520 −0.529504
544544 0 0
545545 0 0
546546 0 0
547547 −510.955 −0.934104 −0.467052 0.884230i 0.654684π-0.654684\pi
−0.467052 + 0.884230i 0.654684π0.654684\pi
548548 0 0
549549 −156.000 −0.284153
550550 0 0
551551 − 270.200i − 0.490381i
552552 0 0
553553 − 300.000i − 0.542495i
554554 0 0
555555 0 0
556556 0 0
557557 − 552.000i − 0.991023i −0.868601 0.495512i 0.834981π-0.834981\pi
0.868601 0.495512i 0.165019π-0.165019\pi
558558 0 0
559559 997.661i 1.78472i
560560 0 0
561561 −63.0000 −0.112299
562562 0 0
563563 −401.836 −0.713740 −0.356870 0.934154i 0.616156π-0.616156\pi
−0.356870 + 0.934154i 0.616156π0.616156\pi
564564 0 0
565565 0 0
566566 0 0
567567 31.1769 0.0549857
568568 0 0
569569 −117.000 −0.205624 −0.102812 0.994701i 0.532784π-0.532784\pi
−0.102812 + 0.994701i 0.532784π0.532784\pi
570570 0 0
571571 − 297.913i − 0.521739i −0.965374 0.260869i 0.915991π-0.915991\pi
0.965374 0.260869i 0.0840092π-0.0840092\pi
572572 0 0
573573 − 522.000i − 0.910995i
574574 0 0
575575 0 0
576576 0 0
577577 491.000i 0.850953i 0.904969 + 0.425477i 0.139894π0.139894\pi
−0.904969 + 0.425477i 0.860106π0.860106\pi
578578 0 0
579579 − 240.755i − 0.415812i
580580 0 0
581581 342.000 0.588640
582582 0 0
583583 218.238 0.374337
584584 0 0
585585 0 0
586586 0 0
587587 −244.219 −0.416046 −0.208023 0.978124i 0.566703π-0.566703\pi
−0.208023 + 0.978124i 0.566703π0.566703\pi
588588 0 0
589589 −702.000 −1.19185
590590 0 0
591591 218.238i 0.369270i
592592 0 0
593593 57.0000i 0.0961214i 0.998844 + 0.0480607i 0.0153041π0.0153041\pi
−0.998844 + 0.0480607i 0.984696π0.984696\pi
594594 0 0
595595 0 0
596596 0 0
597597 − 132.000i − 0.221106i
598598 0 0
599599 633.931i 1.05831i 0.848524 + 0.529157i 0.177492π0.177492\pi
−0.848524 + 0.529157i 0.822508π0.822508\pi
600600 0 0
601601 263.000 0.437604 0.218802 0.975769i 0.429785π-0.429785\pi
0.218802 + 0.975769i 0.429785π0.429785\pi
602602 0 0
603603 −197.454 −0.327452
604604 0 0
605605 0 0
606606 0 0
607607 −484.974 −0.798969 −0.399485 0.916740i 0.630811π-0.630811\pi
−0.399485 + 0.916740i 0.630811π0.630811\pi
608608 0 0
609609 72.0000 0.118227
610610 0 0
611611 221.703i 0.362852i
612612 0 0
613613 − 194.000i − 0.316476i −0.987401 0.158238i 0.949419π-0.949419\pi
0.987401 0.158238i 0.0505814π-0.0505814\pi
614614 0 0
615615 0 0
616616 0 0
617617 726.000i 1.17666i 0.808620 + 0.588331i 0.200215π0.200215\pi
−0.808620 + 0.588331i 0.799785π0.799785\pi
618618 0 0
619619 − 408.764i − 0.660362i −0.943918 0.330181i 0.892890π-0.892890\pi
0.943918 0.330181i 0.107110π-0.107110\pi
620620 0 0
621621 −1170.00 −1.88406
622622 0 0
623623 −342.946 −0.550475
624624 0 0
625625 0 0
626626 0 0
627627 472.850 0.754147
628628 0 0
629629 150.000 0.238474
630630 0 0
631631 502.295i 0.796030i 0.917379 + 0.398015i 0.130301π0.130301\pi
−0.917379 + 0.398015i 0.869699π0.869699\pi
632632 0 0
633633 − 327.000i − 0.516588i
634634 0 0
635635 0 0
636636 0 0
637637 592.000i 0.929356i
638638 0 0
639639 − 166.277i − 0.260214i
640640 0 0
641641 −174.000 −0.271451 −0.135725 0.990746i 0.543337π-0.543337\pi
−0.135725 + 0.990746i 0.543337π0.543337\pi
642642 0 0
643643 −976.877 −1.51925 −0.759624 0.650362i 0.774617π-0.774617\pi
−0.759624 + 0.650362i 0.774617π0.774617\pi
644644 0 0
645645 0 0
646646 0 0
647647 921.451 1.42419 0.712095 0.702083i 0.247746π-0.247746\pi
0.712095 + 0.702083i 0.247746π0.247746\pi
648648 0 0
649649 −672.000 −1.03544
650650 0 0
651651 − 187.061i − 0.287345i
652652 0 0
653653 − 222.000i − 0.339969i −0.985447 0.169985i 0.945628π-0.945628\pi
0.985447 0.169985i 0.0543718π-0.0543718\pi
654654 0 0
655655 0 0
656656 0 0
657657 − 102.000i − 0.155251i
658658 0 0
659659 857.365i 1.30101i 0.759502 + 0.650505i 0.225443π0.225443\pi
−0.759502 + 0.650505i 0.774557π0.774557\pi
660660 0 0
661661 −268.000 −0.405446 −0.202723 0.979236i 0.564979π-0.564979\pi
−0.202723 + 0.979236i 0.564979π0.564979\pi
662662 0 0
663663 83.1384 0.125397
664664 0 0
665665 0 0
666666 0 0
667667 540.400 0.810195
668668 0 0
669669 252.000 0.376682
670670 0 0
671671 315.233i 0.469796i
672672 0 0
673673 550.000i 0.817236i 0.912705 + 0.408618i 0.133989π0.133989\pi
−0.912705 + 0.408618i 0.866011π0.866011\pi
674674 0 0
675675 0 0
676676 0 0
677677 − 600.000i − 0.886263i −0.896457 0.443131i 0.853867π-0.853867\pi
0.896457 0.443131i 0.146133π-0.146133\pi
678678 0 0
679679 − 464.190i − 0.683637i
680680 0 0
681681 300.000 0.440529
682682 0 0
683683 −729.193 −1.06763 −0.533817 0.845600i 0.679243π-0.679243\pi
−0.533817 + 0.845600i 0.679243π0.679243\pi
684684 0 0
685685 0 0
686686 0 0
687687 −242.487 −0.352965
688688 0 0
689689 −288.000 −0.417997
690690 0 0
691691 1231.49i 1.78218i 0.453824 + 0.891091i 0.350059π0.350059\pi
−0.453824 + 0.891091i 0.649941π0.649941\pi
692692 0 0
693693 − 252.000i − 0.363636i
694694 0 0
695695 0 0
696696 0 0
697697 189.000i 0.271162i
698698 0 0
699699 633.931i 0.906911i
700700 0 0
701701 1008.00 1.43795 0.718973 0.695038i 0.244613π-0.244613\pi
0.718973 + 0.695038i 0.244613π0.244613\pi
702702 0 0
703703 −1125.83 −1.60147
704704 0 0
705705 0 0
706706 0 0
707707 519.615 0.734958
708708 0 0
709709 −388.000 −0.547250 −0.273625 0.961837i 0.588223π-0.588223\pi
−0.273625 + 0.961837i 0.588223π0.588223\pi
710710 0 0
711711 519.615i 0.730823i
712712 0 0
713713 − 1404.00i − 1.96914i
714714 0 0
715715 0 0
716716 0 0
717717 − 444.000i − 0.619247i
718718 0 0
719719 973.413i 1.35384i 0.736056 + 0.676921i 0.236686π0.236686\pi
−0.736056 + 0.676921i 0.763314π0.763314\pi
720720 0 0
721721 384.000 0.532594
722722 0 0
723723 −126.440 −0.174882
724724 0 0
725725 0 0
726726 0 0
727727 −187.061 −0.257306 −0.128653 0.991690i 0.541065π-0.541065\pi
−0.128653 + 0.991690i 0.541065π0.541065\pi
728728 0 0
729729 351.000 0.481481
730730 0 0
731731 187.061i 0.255898i
732732 0 0
733733 − 976.000i − 1.33151i −0.746168 0.665757i 0.768109π-0.768109\pi
0.746168 0.665757i 0.231891π-0.231891\pi
734734 0 0
735735 0 0
736736 0 0
737737 399.000i 0.541384i
738738 0 0
739739 270.200i 0.365629i 0.983147 + 0.182815i 0.0585208π0.0585208\pi
−0.983147 + 0.182815i 0.941479π0.941479\pi
740740 0 0
741741 −624.000 −0.842105
742742 0 0
743743 38.1051 0.0512855 0.0256427 0.999671i 0.491837π-0.491837\pi
0.0256427 + 0.999671i 0.491837π0.491837\pi
744744 0 0
745745 0 0
746746 0 0
747747 −592.361 −0.792987
748748 0 0
749749 −570.000 −0.761015
750750 0 0
751751 − 921.451i − 1.22697i −0.789708 0.613483i 0.789768π-0.789768\pi
0.789708 0.613483i 0.210232π-0.210232\pi
752752 0 0
753753 − 291.000i − 0.386454i
754754 0 0
755755 0 0
756756 0 0
757757 − 392.000i − 0.517834i −0.965900 0.258917i 0.916634π-0.916634\pi
0.965900 0.258917i 0.0833655π-0.0833655\pi
758758 0 0
759759 945.700i 1.24598i
760760 0 0
761761 −1335.00 −1.75427 −0.877135 0.480243i 0.840548π-0.840548\pi
−0.877135 + 0.480243i 0.840548π0.840548\pi
762762 0 0
763763 256.344 0.335968
764764 0 0
765765 0 0
766766 0 0
767767 886.810 1.15621
768768 0 0
769769 −509.000 −0.661899 −0.330949 0.943649i 0.607369π-0.607369\pi
−0.330949 + 0.943649i 0.607369π0.607369\pi
770770 0 0
771771 488.438i 0.633513i
772772 0 0
773773 684.000i 0.884864i 0.896802 + 0.442432i 0.145884π0.145884\pi
−0.896802 + 0.442432i 0.854116π0.854116\pi
774774 0 0
775775 0 0
776776 0 0
777777 − 300.000i − 0.386100i
778778 0 0
779779 − 1418.55i − 1.82099i
780780 0 0
781781 −336.000 −0.430218
782782 0 0
783783 −311.769 −0.398173
784784 0 0
785785 0 0
786786 0 0
787787 6.92820 0.00880331 0.00440165 0.999990i 0.498599π-0.498599\pi
0.00440165 + 0.999990i 0.498599π0.498599\pi
788788 0 0
789789 294.000 0.372624
790790 0 0
791791 696.284i 0.880258i
792792 0 0
793793 − 416.000i − 0.524590i
794794 0 0
795795 0 0
796796 0 0
797797 1374.00i 1.72396i 0.506938 + 0.861982i 0.330777π0.330777\pi
−0.506938 + 0.861982i 0.669223π0.669223\pi
798798 0 0
799799 41.5692i 0.0520266i
800800 0 0
801801 594.000 0.741573
802802 0 0
803803 −206.114 −0.256680
804804 0 0
805805 0 0
806806 0 0
807807 498.831 0.618130
808808 0 0
809809 −546.000 −0.674907 −0.337454 0.941342i 0.609566π-0.609566\pi
−0.337454 + 0.941342i 0.609566π0.609566\pi
810810 0 0
811811 1309.43i 1.61459i 0.590150 + 0.807294i 0.299069π0.299069\pi
−0.590150 + 0.807294i 0.700931π0.700931\pi
812812 0 0
813813 − 294.000i − 0.361624i
814814 0 0
815815 0 0
816816 0 0
817817 − 1404.00i − 1.71848i
818818 0 0
819819 332.554i 0.406049i
820820 0 0
821821 1038.00 1.26431 0.632156 0.774841i 0.282170π-0.282170\pi
0.632156 + 0.774841i 0.282170π0.282170\pi
822822 0 0
823823 −381.051 −0.463003 −0.231501 0.972835i 0.574364π-0.574364\pi
−0.231501 + 0.972835i 0.574364π0.574364\pi
824824 0 0
825825 0 0
826826 0 0
827827 102.191 0.123568 0.0617842 0.998090i 0.480321π-0.480321\pi
0.0617842 + 0.998090i 0.480321π0.480321\pi
828828 0 0
829829 104.000 0.125452 0.0627262 0.998031i 0.480021π-0.480021\pi
0.0627262 + 0.998031i 0.480021π0.480021\pi
830830 0 0
831831 − 131.636i − 0.158407i
832832 0 0
833833 111.000i 0.133253i
834834 0 0
835835 0 0
836836 0 0
837837 810.000i 0.967742i
838838 0 0
839839 − 1053.09i − 1.25517i −0.778548 0.627585i 0.784044π-0.784044\pi
0.778548 0.627585i 0.215956π-0.215956\pi
840840 0 0
841841 −697.000 −0.828775
842842 0 0
843843 613.146 0.727338
844844 0 0
845845 0 0
846846 0 0
847847 −90.0666 −0.106336
848848 0 0
849849 549.000 0.646643
850850 0 0
851851 − 2251.67i − 2.64591i
852852 0 0
853853 1234.00i 1.44666i 0.690503 + 0.723329i 0.257389π0.257389\pi
−0.690503 + 0.723329i 0.742611π0.742611\pi
854854 0 0
855855 0 0
856856 0 0
857857 1185.00i 1.38273i 0.722505 + 0.691365i 0.242990π0.242990\pi
−0.722505 + 0.691365i 0.757010π0.757010\pi
858858 0 0
859859 1692.21i 1.96998i 0.172609 + 0.984990i 0.444780π0.444780\pi
−0.172609 + 0.984990i 0.555220π0.555220\pi
860860 0 0
861861 378.000 0.439024
862862 0 0
863863 −893.738 −1.03562 −0.517809 0.855496i 0.673252π-0.673252\pi
−0.517809 + 0.855496i 0.673252π0.673252\pi
864864 0 0
865865 0 0
866866 0 0
867867 −484.974 −0.559371
868868 0 0
869869 1050.00 1.20829
870870 0 0
871871 − 526.543i − 0.604527i
872872 0 0
873873 804.000i 0.920962i
874874 0 0
875875 0 0
876876 0 0
877877 20.0000i 0.0228050i 0.999935 + 0.0114025i 0.00362961π0.00362961\pi
−0.999935 + 0.0114025i 0.996370π0.996370\pi
878878 0 0
879879 − 737.854i − 0.839424i
880880 0 0
881881 −330.000 −0.374574 −0.187287 0.982305i 0.559969π-0.559969\pi
−0.187287 + 0.982305i 0.559969π0.559969\pi
882882 0 0
883883 95.2628 0.107885 0.0539427 0.998544i 0.482821π-0.482821\pi
0.0539427 + 0.998544i 0.482821π0.482821\pi
884884 0 0
885885 0 0
886886 0 0
887887 −1212.44 −1.36689 −0.683447 0.730000i 0.739520π-0.739520\pi
−0.683447 + 0.730000i 0.739520π0.739520\pi
888888 0 0
889889 36.0000 0.0404949
890890 0 0
891891 109.119i 0.122468i
892892 0 0
893893 − 312.000i − 0.349384i
894894 0 0
895895 0 0
896896 0 0
897897 − 1248.00i − 1.39130i
898898 0 0
899899 − 374.123i − 0.416155i
900900 0 0
901901 −54.0000 −0.0599334
902902 0 0
903903 374.123 0.414311
904904 0 0
905905 0 0
906906 0 0
907907 297.913 0.328459 0.164230 0.986422i 0.447486π-0.447486\pi
0.164230 + 0.986422i 0.447486π0.447486\pi
908908 0 0
909909 −900.000 −0.990099
910910 0 0
911911 − 48.4974i − 0.0532354i −0.999646 0.0266177i 0.991526π-0.991526\pi
0.999646 0.0266177i 0.00847367π-0.00847367\pi
912912 0 0
913913 1197.00i 1.31106i
914914 0 0
915915 0 0
916916 0 0
917917 24.0000i 0.0261723i
918918 0 0
919919 − 758.638i − 0.825504i −0.910843 0.412752i 0.864568π-0.864568\pi
0.910843 0.412752i 0.135432π-0.135432\pi
920920 0 0
921921 −387.000 −0.420195
922922 0 0
923923 443.405 0.480395
924924 0 0
925925 0 0
926926 0 0
927927 −665.108 −0.717484
928928 0 0
929929 258.000 0.277718 0.138859 0.990312i 0.455657π-0.455657\pi
0.138859 + 0.990312i 0.455657π0.455657\pi
930930 0 0
931931 − 833.116i − 0.894862i
932932 0 0
933933 − 750.000i − 0.803859i
934934 0 0
935935 0 0
936936 0 0
937937 − 481.000i − 0.513340i −0.966499 0.256670i 0.917375π-0.917375\pi
0.966499 0.256670i 0.0826254π-0.0826254\pi
938938 0 0
939939 377.587i 0.402116i
940940 0 0
941941 −24.0000 −0.0255048 −0.0127524 0.999919i 0.504059π-0.504059\pi
−0.0127524 + 0.999919i 0.504059π0.504059\pi
942942 0 0
943943 2837.10 3.00859
944944 0 0
945945 0 0
946946 0 0
947947 665.108 0.702331 0.351166 0.936313i 0.385785π-0.385785\pi
0.351166 + 0.936313i 0.385785π0.385785\pi
948948 0 0
949949 272.000 0.286617
950950 0 0
951951 − 20.7846i − 0.0218555i
952952 0 0
953953 291.000i 0.305352i 0.988276 + 0.152676i 0.0487890π0.0487890\pi
−0.988276 + 0.152676i 0.951211π0.951211\pi
954954 0 0
955955 0 0
956956 0 0
957957 252.000i 0.263323i
958958 0 0
959959 − 717.069i − 0.747726i
960960 0 0
961961 −11.0000 −0.0114464
962962 0 0
963963 987.269 1.02520
964964 0 0
965965 0 0
966966 0 0
967967 −1094.66 −1.13201 −0.566006 0.824401i 0.691512π-0.691512\pi
−0.566006 + 0.824401i 0.691512π0.691512\pi
968968 0 0
969969 −117.000 −0.120743
970970 0 0
971971 − 611.414i − 0.629674i −0.949146 0.314837i 0.898050π-0.898050\pi
0.949146 0.314837i 0.101950π-0.101950\pi
972972 0 0
973973 − 618.000i − 0.635149i
974974 0 0
975975 0 0
976976 0 0
977977 − 231.000i − 0.236438i −0.992988 0.118219i 0.962282π-0.962282\pi
0.992988 0.118219i 0.0377185π-0.0377185\pi
978978 0 0
979979 − 1200.31i − 1.22606i
980980 0 0
981981 −444.000 −0.452599
982982 0 0
983983 −162.813 −0.165628 −0.0828142 0.996565i 0.526391π-0.526391\pi
−0.0828142 + 0.996565i 0.526391π0.526391\pi
984984 0 0
985985 0 0
986986 0 0
987987 83.1384 0.0842335
988988 0 0
989989 2808.00 2.83923
990990 0 0
991991 723.997i 0.730572i 0.930895 + 0.365286i 0.119029π0.119029\pi
−0.930895 + 0.365286i 0.880971π0.880971\pi
992992 0 0
993993 807.000i 0.812689i
994994 0 0
995995 0 0
996996 0 0
997997 1100.00i 1.10331i 0.834072 + 0.551655i 0.186003π0.186003\pi
−0.834072 + 0.551655i 0.813997π0.813997\pi
998998 0 0
999999 1299.04i 1.30034i
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 400.3.h.b.399.2 4
3.2 odd 2 3600.3.j.f.1999.3 4
4.3 odd 2 inner 400.3.h.b.399.3 4
5.2 odd 4 400.3.b.e.351.2 yes 2
5.3 odd 4 400.3.b.f.351.1 yes 2
5.4 even 2 inner 400.3.h.b.399.4 4
8.3 odd 2 1600.3.h.h.1599.2 4
8.5 even 2 1600.3.h.h.1599.3 4
12.11 even 2 3600.3.j.f.1999.2 4
15.2 even 4 3600.3.e.j.3151.2 2
15.8 even 4 3600.3.e.u.3151.1 2
15.14 odd 2 3600.3.j.f.1999.1 4
20.3 even 4 400.3.b.f.351.2 yes 2
20.7 even 4 400.3.b.e.351.1 2
20.19 odd 2 inner 400.3.h.b.399.1 4
40.3 even 4 1600.3.b.i.1151.1 2
40.13 odd 4 1600.3.b.i.1151.2 2
40.19 odd 2 1600.3.h.h.1599.4 4
40.27 even 4 1600.3.b.j.1151.2 2
40.29 even 2 1600.3.h.h.1599.1 4
40.37 odd 4 1600.3.b.j.1151.1 2
60.23 odd 4 3600.3.e.u.3151.2 2
60.47 odd 4 3600.3.e.j.3151.1 2
60.59 even 2 3600.3.j.f.1999.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
400.3.b.e.351.1 2 20.7 even 4
400.3.b.e.351.2 yes 2 5.2 odd 4
400.3.b.f.351.1 yes 2 5.3 odd 4
400.3.b.f.351.2 yes 2 20.3 even 4
400.3.h.b.399.1 4 20.19 odd 2 inner
400.3.h.b.399.2 4 1.1 even 1 trivial
400.3.h.b.399.3 4 4.3 odd 2 inner
400.3.h.b.399.4 4 5.4 even 2 inner
1600.3.b.i.1151.1 2 40.3 even 4
1600.3.b.i.1151.2 2 40.13 odd 4
1600.3.b.j.1151.1 2 40.37 odd 4
1600.3.b.j.1151.2 2 40.27 even 4
1600.3.h.h.1599.1 4 40.29 even 2
1600.3.h.h.1599.2 4 8.3 odd 2
1600.3.h.h.1599.3 4 8.5 even 2
1600.3.h.h.1599.4 4 40.19 odd 2
3600.3.e.j.3151.1 2 60.47 odd 4
3600.3.e.j.3151.2 2 15.2 even 4
3600.3.e.u.3151.1 2 15.8 even 4
3600.3.e.u.3151.2 2 60.23 odd 4
3600.3.j.f.1999.1 4 15.14 odd 2
3600.3.j.f.1999.2 4 12.11 even 2
3600.3.j.f.1999.3 4 3.2 odd 2
3600.3.j.f.1999.4 4 60.59 even 2