Properties

Label 1600.3.b.j.1151.1
Level 16001600
Weight 33
Character 1600.1151
Analytic conductor 43.59743.597
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] = [1600,3,Mod(1151,1600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1600.1151");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 1600=2652 1600 = 2^{6} \cdot 5^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 1600.b (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: 43.596842297643.5968422976
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ6)\Q(\zeta_{6})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x+1 x^{2} - x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 400)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1151.1
Root 0.500000+0.866025i0.500000 + 0.866025i of defining polynomial
Character χ\chi == 1600.1151
Dual form 1600.3.b.j.1151.2

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) == q1.73205iq3+3.46410iq7+6.00000q912.1244iq11+16.0000q13+3.00000q17+22.5167iq19+6.00000q21+45.0333iq2325.9808iq2712.0000q29+31.1769iq3121.0000q33+50.0000q3727.7128iq3963.0000q4162.3538iq4313.8564iq47+37.0000q495.19615iq51+18.0000q53+39.0000q57+55.4256iq5926.0000q61+20.7846iq6332.9090iq67+78.0000q69+27.7128iq71+17.0000q73+42.0000q77+86.6025iq79+9.00000q81+98.7269iq83+20.7846iq87+99.0000q89+55.4256iq91+54.0000q93+134.000q9772.7461iq99+O(q100)q-1.73205i q^{3} +3.46410i q^{7} +6.00000 q^{9} -12.1244i q^{11} +16.0000 q^{13} +3.00000 q^{17} +22.5167i q^{19} +6.00000 q^{21} +45.0333i q^{23} -25.9808i q^{27} -12.0000 q^{29} +31.1769i q^{31} -21.0000 q^{33} +50.0000 q^{37} -27.7128i q^{39} -63.0000 q^{41} -62.3538i q^{43} -13.8564i q^{47} +37.0000 q^{49} -5.19615i q^{51} +18.0000 q^{53} +39.0000 q^{57} +55.4256i q^{59} -26.0000 q^{61} +20.7846i q^{63} -32.9090i q^{67} +78.0000 q^{69} +27.7128i q^{71} +17.0000 q^{73} +42.0000 q^{77} +86.6025i q^{79} +9.00000 q^{81} +98.7269i q^{83} +20.7846i q^{87} +99.0000 q^{89} +55.4256i q^{91} +54.0000 q^{93} +134.000 q^{97} -72.7461i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+12q9+32q13+6q17+12q2124q2942q33+100q37126q41+74q49+36q53+78q5752q61+156q69+34q73+84q77+18q81+198q89++268q97+O(q100) 2 q + 12 q^{9} + 32 q^{13} + 6 q^{17} + 12 q^{21} - 24 q^{29} - 42 q^{33} + 100 q^{37} - 126 q^{41} + 74 q^{49} + 36 q^{53} + 78 q^{57} - 52 q^{61} + 156 q^{69} + 34 q^{73} + 84 q^{77} + 18 q^{81} + 198 q^{89}+ \cdots + 268 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1600Z)×\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times.

nn 577577 901901 11511151
χ(n)\chi(n) 11 11 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 − 1.73205i − 0.577350i −0.957427 0.288675i 0.906785π-0.906785\pi
0.957427 0.288675i 0.0932147π-0.0932147\pi
44 0 0
55 0 0
66 0 0
77 3.46410i 0.494872i 0.968904 + 0.247436i 0.0795879π0.0795879\pi
−0.968904 + 0.247436i 0.920412π0.920412\pi
88 0 0
99 6.00000 0.666667
1010 0 0
1111 − 12.1244i − 1.10221i −0.834435 0.551107i 0.814206π-0.814206\pi
0.834435 0.551107i 0.185794π-0.185794\pi
1212 0 0
1313 16.0000 1.23077 0.615385 0.788227i 0.289001π-0.289001\pi
0.615385 + 0.788227i 0.289001π0.289001\pi
1414 0 0
1515 0 0
1616 0 0
1717 3.00000 0.176471 0.0882353 0.996100i 0.471877π-0.471877\pi
0.0882353 + 0.996100i 0.471877π0.471877\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 45.0333i 1.95797i 0.203931 + 0.978985i 0.434628π0.434628\pi
−0.203931 + 0.978985i 0.565372π0.565372\pi
2424 0 0
2525 0 0
2626 0 0
2727 − 25.9808i − 0.962250i
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 −21.0000 −0.636364
3434 0 0
3535 0 0
3636 0 0
3737 50.0000 1.35135 0.675676 0.737199i 0.263852π-0.263852\pi
0.675676 + 0.737199i 0.263852π0.263852\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 − 62.3538i − 1.45009i −0.688702 0.725045i 0.741819π-0.741819\pi
0.688702 0.725045i 0.258181π-0.258181\pi
4444 0 0
4545 0 0
4646 0 0
4747 − 13.8564i − 0.294817i −0.989076 0.147409i 0.952907π-0.952907\pi
0.989076 0.147409i 0.0470932π-0.0470932\pi
4848 0 0
4949 37.0000 0.755102
5050 0 0
5151 − 5.19615i − 0.101885i
5252 0 0
5353 18.0000 0.339623 0.169811 0.985477i 0.445684π-0.445684\pi
0.169811 + 0.985477i 0.445684π0.445684\pi
5454 0 0
5555 0 0
5656 0 0
5757 39.0000 0.684211
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 0.568361π-0.568361\pi
−0.213115 + 0.977027i 0.568361π0.568361\pi
6262 0 0
6363 20.7846i 0.329914i
6464 0 0
6565 0 0
6666 0 0
6767 − 32.9090i − 0.491179i −0.969374 0.245589i 0.921019π-0.921019\pi
0.969374 0.245589i 0.0789815π-0.0789815\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 17.0000 0.232877 0.116438 0.993198i 0.462852π-0.462852\pi
0.116438 + 0.993198i 0.462852π0.462852\pi
7474 0 0
7575 0 0
7676 0 0
7777 42.0000 0.545455
7878 0 0
7979 86.6025i 1.09623i 0.836401 + 0.548117i 0.184655π0.184655\pi
−0.836401 + 0.548117i 0.815345π0.815345\pi
8080 0 0
8181 9.00000 0.111111
8282 0 0
8383 98.7269i 1.18948i 0.803918 + 0.594740i 0.202745π0.202745\pi
−0.803918 + 0.594740i 0.797255π0.797255\pi
8484 0 0
8585 0 0
8686 0 0
8787 20.7846i 0.238904i
8888 0 0
8989 99.0000 1.11236 0.556180 0.831062i 0.312267π-0.312267\pi
0.556180 + 0.831062i 0.312267π0.312267\pi
9090 0 0
9191 55.4256i 0.609073i
9292 0 0
9393 54.0000 0.580645
9494 0 0
9595 0 0
9696 0 0
9797 134.000 1.38144 0.690722 0.723121i 0.257293π-0.257293\pi
0.690722 + 0.723121i 0.257293π0.257293\pi
9898 0 0
9999 − 72.7461i − 0.734809i
100100 0 0
101101 −150.000 −1.48515 −0.742574 0.669764i 0.766395π-0.766395\pi
−0.742574 + 0.669764i 0.766395π0.766395\pi
102102 0 0
103103 − 110.851i − 1.07623i −0.842873 0.538113i 0.819137π-0.819137\pi
0.842873 0.538113i 0.180863π-0.180863\pi
104104 0 0
105105 0 0
106106 0 0
107107 164.545i 1.53780i 0.639368 + 0.768901i 0.279196π0.279196\pi
−0.639368 + 0.768901i 0.720804π0.720804\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 201.000 1.77876 0.889381 0.457168i 0.151136π-0.151136\pi
0.889381 + 0.457168i 0.151136π0.151136\pi
114114 0 0
115115 0 0
116116 0 0
117117 96.0000 0.820513
118118 0 0
119119 10.3923i 0.0873303i
120120 0 0
121121 −26.0000 −0.214876
122122 0 0
123123 109.119i 0.887148i
124124 0 0
125125 0 0
126126 0 0
127127 10.3923i 0.0818292i 0.999163 + 0.0409146i 0.0130272π0.0130272\pi
−0.999163 + 0.0409146i 0.986973π0.986973\pi
128128 0 0
129129 −108.000 −0.837209
130130 0 0
131131 − 6.92820i − 0.0528870i −0.999650 0.0264435i 0.991582π-0.991582\pi
0.999650 0.0264435i 0.00841822π-0.00841822\pi
132132 0 0
133133 −78.0000 −0.586466
134134 0 0
135135 0 0
136136 0 0
137137 207.000 1.51095 0.755474 0.655178i 0.227406π-0.227406\pi
0.755474 + 0.655178i 0.227406π0.227406\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 − 193.990i − 1.35657i
144144 0 0
145145 0 0
146146 0 0
147147 − 64.0859i − 0.435958i
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 18.0000 0.117647
154154 0 0
155155 0 0
156156 0 0
157157 278.000 1.77070 0.885350 0.464925i 0.153919π-0.153919\pi
0.885350 + 0.464925i 0.153919π0.153919\pi
158158 0 0
159159 − 31.1769i − 0.196081i
160160 0 0
161161 −156.000 −0.968944
162162 0 0
163163 − 19.0526i − 0.116887i −0.998291 0.0584434i 0.981386π-0.981386\pi
0.998291 0.0584434i 0.0186137π-0.0186137\pi
164164 0 0
165165 0 0
166166 0 0
167167 − 263.272i − 1.57648i −0.615370 0.788239i 0.710993π-0.710993\pi
0.615370 0.788239i 0.289007π-0.289007\pi
168168 0 0
169169 87.0000 0.514793
170170 0 0
171171 135.100i 0.790058i
172172 0 0
173173 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
174174 0 0
175175 0 0
176176 0 0
177177 96.0000 0.542373
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 0.651636π-0.651636\pi
−0.458564 + 0.888662i 0.651636π0.651636\pi
182182 0 0
183183 45.0333i 0.246084i
184184 0 0
185185 0 0
186186 0 0
187187 − 36.3731i − 0.194508i
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 139.000 0.720207 0.360104 0.932912i 0.382741π-0.382741\pi
0.360104 + 0.932912i 0.382741π0.382741\pi
194194 0 0
195195 0 0
196196 0 0
197197 −126.000 −0.639594 −0.319797 0.947486i 0.603615π-0.603615\pi
−0.319797 + 0.947486i 0.603615π0.603615\pi
198198 0 0
199199 − 76.2102i − 0.382966i −0.981496 0.191483i 0.938670π-0.938670\pi
0.981496 0.191483i 0.0613297π-0.0613297\pi
200200 0 0
201201 −57.0000 −0.283582
202202 0 0
203203 − 41.5692i − 0.204774i
204204 0 0
205205 0 0
206206 0 0
207207 270.200i 1.30531i
208208 0 0
209209 273.000 1.30622
210210 0 0
211211 − 188.794i − 0.894756i −0.894345 0.447378i 0.852358π-0.852358\pi
0.894345 0.447378i 0.147642π-0.147642\pi
212212 0 0
213213 48.0000 0.225352
214214 0 0
215215 0 0
216216 0 0
217217 −108.000 −0.497696
218218 0 0
219219 − 29.4449i − 0.134451i
220220 0 0
221221 48.0000 0.217195
222222 0 0
223223 145.492i 0.652432i 0.945295 + 0.326216i 0.105774π0.105774\pi
−0.945295 + 0.326216i 0.894226π0.894226\pi
224224 0 0
225225 0 0
226226 0 0
227227 173.205i 0.763018i 0.924365 + 0.381509i 0.124595π0.124595\pi
−0.924365 + 0.381509i 0.875405π0.875405\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 −366.000 −1.57082 −0.785408 0.618979i 0.787547π-0.787547\pi
−0.785408 + 0.618979i 0.787547π0.787547\pi
234234 0 0
235235 0 0
236236 0 0
237237 150.000 0.632911
238238 0 0
239239 − 256.344i − 1.07257i −0.844038 0.536284i 0.819828π-0.819828\pi
0.844038 0.536284i 0.180172π-0.180172\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 − 249.415i − 1.02640i
244244 0 0
245245 0 0
246246 0 0
247247 360.267i 1.45857i
248248 0 0
249249 171.000 0.686747
250250 0 0
251251 − 168.009i − 0.669358i −0.942332 0.334679i 0.891372π-0.891372\pi
0.942332 0.334679i 0.108628π-0.108628\pi
252252 0 0
253253 546.000 2.15810
254254 0 0
255255 0 0
256256 0 0
257257 282.000 1.09728 0.548638 0.836060i 0.315146π-0.315146\pi
0.548638 + 0.836060i 0.315146π0.315146\pi
258258 0 0
259259 173.205i 0.668745i
260260 0 0
261261 −72.0000 −0.275862
262262 0 0
263263 169.741i 0.645403i 0.946501 + 0.322701i 0.104591π0.104591\pi
−0.946501 + 0.322701i 0.895409π0.895409\pi
264264 0 0
265265 0 0
266266 0 0
267267 − 171.473i − 0.642221i
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 96.0000 0.351648
274274 0 0
275275 0 0
276276 0 0
277277 76.0000 0.274368 0.137184 0.990546i 0.456195π-0.456195\pi
0.137184 + 0.990546i 0.456195π0.456195\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 − 316.965i − 1.12002i −0.828486 0.560009i 0.810798π-0.810798\pi
0.828486 0.560009i 0.189202π-0.189202\pi
284284 0 0
285285 0 0
286286 0 0
287287 − 218.238i − 0.760413i
288288 0 0
289289 −280.000 −0.968858
290290 0 0
291291 − 232.095i − 0.797577i
292292 0 0
293293 −426.000 −1.45392 −0.726962 0.686677i 0.759069π-0.759069\pi
−0.726962 + 0.686677i 0.759069π0.759069\pi
294294 0 0
295295 0 0
296296 0 0
297297 −315.000 −1.06061
298298 0 0
299299 720.533i 2.40981i
300300 0 0
301301 216.000 0.717608
302302 0 0
303303 259.808i 0.857451i
304304 0 0
305305 0 0
306306 0 0
307307 − 223.435i − 0.727800i −0.931438 0.363900i 0.881445π-0.881445\pi
0.931438 0.363900i 0.118555π-0.118555\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 −218.000 −0.696486 −0.348243 0.937404i 0.613222π-0.613222\pi
−0.348243 + 0.937404i 0.613222π0.613222\pi
314314 0 0
315315 0 0
316316 0 0
317317 12.0000 0.0378549 0.0189274 0.999821i 0.493975π-0.493975\pi
0.0189274 + 0.999821i 0.493975π0.493975\pi
318318 0 0
319319 145.492i 0.456089i
320320 0 0
321321 285.000 0.887850
322322 0 0
323323 67.5500i 0.209133i
324324 0 0
325325 0 0
326326 0 0
327327 − 128.172i − 0.391963i
328328 0 0
329329 48.0000 0.145897
330330 0 0
331331 465.922i 1.40762i 0.710389 + 0.703809i 0.248519π0.248519\pi
−0.710389 + 0.703809i 0.751481π0.751481\pi
332332 0 0
333333 300.000 0.900901
334334 0 0
335335 0 0
336336 0 0
337337 −67.0000 −0.198813 −0.0994065 0.995047i 0.531694π-0.531694\pi
−0.0994065 + 0.995047i 0.531694π0.531694\pi
338338 0 0
339339 − 348.142i − 1.02697i
340340 0 0
341341 378.000 1.10850
342342 0 0
343343 297.913i 0.868550i
344344 0 0
345345 0 0
346346 0 0
347347 192.258i 0.554057i 0.960862 + 0.277028i 0.0893496π0.0893496\pi
−0.960862 + 0.277028i 0.910650π0.910650\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 114.000 0.322946 0.161473 0.986877i 0.448376π-0.448376\pi
0.161473 + 0.986877i 0.448376π0.448376\pi
354354 0 0
355355 0 0
356356 0 0
357357 18.0000 0.0504202
358358 0 0
359359 − 370.659i − 1.03248i −0.856445 0.516238i 0.827332π-0.827332\pi
0.856445 0.516238i 0.172668π-0.172668\pi
360360 0 0
361361 −146.000 −0.404432
362362 0 0
363363 45.0333i 0.124059i
364364 0 0
365365 0 0
366366 0 0
367367 117.779i 0.320925i 0.987042 + 0.160462i 0.0512986π0.0512986\pi
−0.987042 + 0.160462i 0.948701π0.948701\pi
368368 0 0
369369 −378.000 −1.02439
370370 0 0
371371 62.3538i 0.168070i
372372 0 0
373373 −274.000 −0.734584 −0.367292 0.930106i 0.619715π-0.619715\pi
−0.367292 + 0.930106i 0.619715π0.619715\pi
374374 0 0
375375 0 0
376376 0 0
377377 −192.000 −0.509284
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 − 460.726i − 1.20294i −0.798896 0.601469i 0.794582π-0.794582\pi
0.798896 0.601469i 0.205418π-0.205418\pi
384384 0 0
385385 0 0
386386 0 0
387387 − 374.123i − 0.966726i
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 −12.0000 −0.0305344
394394 0 0
395395 0 0
396396 0 0
397397 −532.000 −1.34005 −0.670025 0.742338i 0.733717π-0.733717\pi
−0.670025 + 0.742338i 0.733717π0.733717\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 498.831i 1.23779i
404404 0 0
405405 0 0
406406 0 0
407407 − 606.218i − 1.48948i
408408 0 0
409409 25.0000 0.0611247 0.0305623 0.999533i 0.490270π-0.490270\pi
0.0305623 + 0.999533i 0.490270π0.490270\pi
410410 0 0
411411 − 358.535i − 0.872347i
412412 0 0
413413 −192.000 −0.464891
414414 0 0
415415 0 0
416416 0 0
417417 −309.000 −0.741007
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 0.652440π-0.652440\pi
−0.460808 + 0.887500i 0.652440π0.652440\pi
422422 0 0
423423 − 83.1384i − 0.196545i
424424 0 0
425425 0 0
426426 0 0
427427 − 90.0666i − 0.210929i
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 307.000 0.709007 0.354503 0.935055i 0.384650π-0.384650\pi
0.354503 + 0.935055i 0.384650π0.384650\pi
434434 0 0
435435 0 0
436436 0 0
437437 −1014.00 −2.32037
438438 0 0
439439 561.184i 1.27832i 0.769072 + 0.639162i 0.220719π0.220719\pi
−0.769072 + 0.639162i 0.779281π0.779281\pi
440440 0 0
441441 222.000 0.503401
442442 0 0
443443 479.778i 1.08302i 0.840694 + 0.541510i 0.182147π0.182147\pi
−0.840694 + 0.541510i 0.817853π0.817853\pi
444444 0 0
445445 0 0
446446 0 0
447447 − 187.061i − 0.418482i
448448 0 0
449449 −39.0000 −0.0868597 −0.0434298 0.999056i 0.513828π-0.513828\pi
−0.0434298 + 0.999056i 0.513828π0.513828\pi
450450 0 0
451451 763.834i 1.69365i
452452 0 0
453453 −462.000 −1.01987
454454 0 0
455455 0 0
456456 0 0
457457 −349.000 −0.763676 −0.381838 0.924229i 0.624709π-0.624709\pi
−0.381838 + 0.924229i 0.624709π0.624709\pi
458458 0 0
459459 − 77.9423i − 0.169809i
460460 0 0
461461 372.000 0.806941 0.403471 0.914993i 0.367804π-0.367804\pi
0.403471 + 0.914993i 0.367804π0.367804\pi
462462 0 0
463463 − 422.620i − 0.912787i −0.889778 0.456394i 0.849141π-0.849141\pi
0.889778 0.456394i 0.150859π-0.150859\pi
464464 0 0
465465 0 0
466466 0 0
467467 713.605i 1.52806i 0.645180 + 0.764031i 0.276783π0.276783\pi
−0.645180 + 0.764031i 0.723217π0.723217\pi
468468 0 0
469469 114.000 0.243070
470470 0 0
471471 − 481.510i − 1.02231i
472472 0 0
473473 −756.000 −1.59831
474474 0 0
475475 0 0
476476 0 0
477477 108.000 0.226415
478478 0 0
479479 758.638i 1.58380i 0.610653 + 0.791898i 0.290907π0.290907\pi
−0.610653 + 0.791898i 0.709093π0.709093\pi
480480 0 0
481481 800.000 1.66320
482482 0 0
483483 270.200i 0.559420i
484484 0 0
485485 0 0
486486 0 0
487487 523.079i 1.07408i 0.843555 + 0.537042i 0.180459π0.180459\pi
−0.843555 + 0.537042i 0.819541π0.819541\pi
488488 0 0
489489 −33.0000 −0.0674847
490490 0 0
491491 − 478.046i − 0.973617i −0.873509 0.486809i 0.838161π-0.838161\pi
0.873509 0.486809i 0.161839π-0.161839\pi
492492 0 0
493493 −36.0000 −0.0730223
494494 0 0
495495 0 0
496496 0 0
497497 −96.0000 −0.193159
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 − 561.184i − 1.11567i −0.829950 0.557837i 0.811631π-0.811631\pi
0.829950 0.557837i 0.188369π-0.188369\pi
504504 0 0
505505 0 0
506506 0 0
507507 − 150.688i − 0.297216i
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 585.000 1.14035
514514 0 0
515515 0 0
516516 0 0
517517 −168.000 −0.324952
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 185.329i 0.354358i 0.984179 + 0.177179i 0.0566972π0.0566972\pi
−0.984179 + 0.177179i 0.943303π0.943303\pi
524524 0 0
525525 0 0
526526 0 0
527527 93.5307i 0.177478i
528528 0 0
529529 −1499.00 −2.83365
530530 0 0
531531 332.554i 0.626278i
532532 0 0
533533 −1008.00 −1.89118
534534 0 0
535535 0 0
536536 0 0
537537 −21.0000 −0.0391061
538538 0 0
539539 − 448.601i − 0.832284i
540540 0 0
541541 968.000 1.78928 0.894640 0.446789i 0.147432π-0.147432\pi
0.894640 + 0.446789i 0.147432π0.147432\pi
542542 0 0
543543 287.520i 0.529504i
544544 0 0
545545 0 0
546546 0 0
547547 510.955i 0.934104i 0.884230 + 0.467052i 0.154684π0.154684\pi
−0.884230 + 0.467052i 0.845316π0.845316\pi
548548 0 0
549549 −156.000 −0.284153
550550 0 0
551551 − 270.200i − 0.490381i
552552 0 0
553553 −300.000 −0.542495
554554 0 0
555555 0 0
556556 0 0
557557 −552.000 −0.991023 −0.495512 0.868601i 0.665019π-0.665019\pi
−0.495512 + 0.868601i 0.665019π0.665019\pi
558558 0 0
559559 − 997.661i − 1.78472i
560560 0 0
561561 −63.0000 −0.112299
562562 0 0
563563 − 401.836i − 0.713740i −0.934154 0.356870i 0.883844π-0.883844\pi
0.934154 0.356870i 0.116156π-0.116156\pi
564564 0 0
565565 0 0
566566 0 0
567567 31.1769i 0.0549857i
568568 0 0
569569 117.000 0.205624 0.102812 0.994701i 0.467216π-0.467216\pi
0.102812 + 0.994701i 0.467216π0.467216\pi
570570 0 0
571571 297.913i 0.521739i 0.965374 + 0.260869i 0.0840092π0.0840092\pi
−0.965374 + 0.260869i 0.915991π0.915991\pi
572572 0 0
573573 522.000 0.910995
574574 0 0
575575 0 0
576576 0 0
577577 −491.000 −0.850953 −0.425477 0.904969i 0.639894π-0.639894\pi
−0.425477 + 0.904969i 0.639894π0.639894\pi
578578 0 0
579579 − 240.755i − 0.415812i
580580 0 0
581581 −342.000 −0.588640
582582 0 0
583583 − 218.238i − 0.374337i
584584 0 0
585585 0 0
586586 0 0
587587 244.219i 0.416046i 0.978124 + 0.208023i 0.0667029π0.0667029\pi
−0.978124 + 0.208023i 0.933297π0.933297\pi
588588 0 0
589589 −702.000 −1.19185
590590 0 0
591591 218.238i 0.369270i
592592 0 0
593593 57.0000 0.0961214 0.0480607 0.998844i 0.484696π-0.484696\pi
0.0480607 + 0.998844i 0.484696π0.484696\pi
594594 0 0
595595 0 0
596596 0 0
597597 −132.000 −0.221106
598598 0 0
599599 − 633.931i − 1.05831i −0.848524 0.529157i 0.822508π-0.822508\pi
0.848524 0.529157i 0.177492π-0.177492\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 − 197.454i − 0.327452i
604604 0 0
605605 0 0
606606 0 0
607607 − 484.974i − 0.798969i −0.916740 0.399485i 0.869189π-0.869189\pi
0.916740 0.399485i 0.130811π-0.130811\pi
608608 0 0
609609 −72.0000 −0.118227
610610 0 0
611611 − 221.703i − 0.362852i
612612 0 0
613613 194.000 0.316476 0.158238 0.987401i 0.449419π-0.449419\pi
0.158238 + 0.987401i 0.449419π0.449419\pi
614614 0 0
615615 0 0
616616 0 0
617617 −726.000 −1.17666 −0.588331 0.808620i 0.700215π-0.700215\pi
−0.588331 + 0.808620i 0.700215π0.700215\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 342.946i 0.550475i
624624 0 0
625625 0 0
626626 0 0
627627 − 472.850i − 0.754147i
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 −327.000 −0.516588
634634 0 0
635635 0 0
636636 0 0
637637 592.000 0.929356
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 − 976.877i − 1.51925i −0.650362 0.759624i 0.725383π-0.725383\pi
0.650362 0.759624i 0.274617π-0.274617\pi
644644 0 0
645645 0 0
646646 0 0
647647 921.451i 1.42419i 0.702083 + 0.712095i 0.252254π0.252254\pi
−0.702083 + 0.712095i 0.747746π0.747746\pi
648648 0 0
649649 672.000 1.03544
650650 0 0
651651 187.061i 0.287345i
652652 0 0
653653 222.000 0.339969 0.169985 0.985447i 0.445628π-0.445628\pi
0.169985 + 0.985447i 0.445628π0.445628\pi
654654 0 0
655655 0 0
656656 0 0
657657 102.000 0.155251
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 0.435021π-0.435021\pi
0.202723 + 0.979236i 0.435021π0.435021\pi
662662 0 0
663663 − 83.1384i − 0.125397i
664664 0 0
665665 0 0
666666 0 0
667667 − 540.400i − 0.810195i
668668 0 0
669669 252.000 0.376682
670670 0 0
671671 315.233i 0.469796i
672672 0 0
673673 550.000 0.817236 0.408618 0.912705i 0.366011π-0.366011\pi
0.408618 + 0.912705i 0.366011π0.366011\pi
674674 0 0
675675 0 0
676676 0 0
677677 −600.000 −0.886263 −0.443131 0.896457i 0.646133π-0.646133\pi
−0.443131 + 0.896457i 0.646133π0.646133\pi
678678 0 0
679679 464.190i 0.683637i
680680 0 0
681681 300.000 0.440529
682682 0 0
683683 − 729.193i − 1.06763i −0.845600 0.533817i 0.820757π-0.820757\pi
0.845600 0.533817i 0.179243π-0.179243\pi
684684 0 0
685685 0 0
686686 0 0
687687 − 242.487i − 0.352965i
688688 0 0
689689 288.000 0.417997
690690 0 0
691691 − 1231.49i − 1.78218i −0.453824 0.891091i 0.649941π-0.649941\pi
0.453824 0.891091i 0.350059π-0.350059\pi
692692 0 0
693693 252.000 0.363636
694694 0 0
695695 0 0
696696 0 0
697697 −189.000 −0.271162
698698 0 0
699699 633.931i 0.906911i
700700 0 0
701701 −1008.00 −1.43795 −0.718973 0.695038i 0.755387π-0.755387\pi
−0.718973 + 0.695038i 0.755387π0.755387\pi
702702 0 0
703703 1125.83i 1.60147i
704704 0 0
705705 0 0
706706 0 0
707707 − 519.615i − 0.734958i
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 −1404.00 −1.96914
714714 0 0
715715 0 0
716716 0 0
717717 −444.000 −0.619247
718718 0 0
719719 − 973.413i − 1.35384i −0.736056 0.676921i 0.763314π-0.763314\pi
0.736056 0.676921i 0.236686π-0.236686\pi
720720 0 0
721721 384.000 0.532594
722722 0 0
723723 − 126.440i − 0.174882i
724724 0 0
725725 0 0
726726 0 0
727727 − 187.061i − 0.257306i −0.991690 0.128653i 0.958935π-0.958935\pi
0.991690 0.128653i 0.0410653π-0.0410653\pi
728728 0 0
729729 −351.000 −0.481481
730730 0 0
731731 − 187.061i − 0.255898i
732732 0 0
733733 976.000 1.33151 0.665757 0.746168i 0.268109π-0.268109\pi
0.665757 + 0.746168i 0.268109π0.268109\pi
734734 0 0
735735 0 0
736736 0 0
737737 −399.000 −0.541384
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 − 38.1051i − 0.0512855i −0.999671 0.0256427i 0.991837π-0.991837\pi
0.999671 0.0256427i 0.00816323π-0.00816323\pi
744744 0 0
745745 0 0
746746 0 0
747747 592.361i 0.792987i
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 −291.000 −0.386454
754754 0 0
755755 0 0
756756 0 0
757757 −392.000 −0.517834 −0.258917 0.965900i 0.583366π-0.583366\pi
−0.258917 + 0.965900i 0.583366π0.583366\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 256.344i 0.335968i
764764 0 0
765765 0 0
766766 0 0
767767 886.810i 1.15621i
768768 0 0
769769 509.000 0.661899 0.330949 0.943649i 0.392631π-0.392631\pi
0.330949 + 0.943649i 0.392631π0.392631\pi
770770 0 0
771771 − 488.438i − 0.633513i
772772 0 0
773773 −684.000 −0.884864 −0.442432 0.896802i 0.645884π-0.645884\pi
−0.442432 + 0.896802i 0.645884π0.645884\pi
774774 0 0
775775 0 0
776776 0 0
777777 300.000 0.386100
778778 0 0
779779 − 1418.55i − 1.82099i
780780 0 0
781781 336.000 0.430218
782782 0 0
783783 311.769i 0.398173i
784784 0 0
785785 0 0
786786 0 0
787787 − 6.92820i − 0.00880331i −0.999990 0.00440165i 0.998599π-0.998599\pi
0.999990 0.00440165i 0.00140109π-0.00140109\pi
788788 0 0
789789 294.000 0.372624
790790 0 0
791791 696.284i 0.880258i
792792 0 0
793793 −416.000 −0.524590
794794 0 0
795795 0 0
796796 0 0
797797 1374.00 1.72396 0.861982 0.506938i 0.169223π-0.169223\pi
0.861982 + 0.506938i 0.169223π0.169223\pi
798798 0 0
799799 − 41.5692i − 0.0520266i
800800 0 0
801801 594.000 0.741573
802802 0 0
803803 − 206.114i − 0.256680i
804804 0 0
805805 0 0
806806 0 0
807807 498.831i 0.618130i
808808 0 0
809809 546.000 0.674907 0.337454 0.941342i 0.390434π-0.390434\pi
0.337454 + 0.941342i 0.390434π0.390434\pi
810810 0 0
811811 − 1309.43i − 1.61459i −0.590150 0.807294i 0.700931π-0.700931\pi
0.590150 0.807294i 0.299069π-0.299069\pi
812812 0 0
813813 294.000 0.361624
814814 0 0
815815 0 0
816816 0 0
817817 1404.00 1.71848
818818 0 0
819819 332.554i 0.406049i
820820 0 0
821821 −1038.00 −1.26431 −0.632156 0.774841i 0.717830π-0.717830\pi
−0.632156 + 0.774841i 0.717830π0.717830\pi
822822 0 0
823823 381.051i 0.463003i 0.972835 + 0.231501i 0.0743638π0.0743638\pi
−0.972835 + 0.231501i 0.925636π0.925636\pi
824824 0 0
825825 0 0
826826 0 0
827827 − 102.191i − 0.123568i −0.998090 0.0617842i 0.980321π-0.980321\pi
0.998090 0.0617842i 0.0196790π-0.0196790\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 111.000 0.133253
834834 0 0
835835 0 0
836836 0 0
837837 810.000 0.967742
838838 0 0
839839 1053.09i 1.25517i 0.778548 + 0.627585i 0.215956π0.215956\pi
−0.778548 + 0.627585i 0.784044π0.784044\pi
840840 0 0
841841 −697.000 −0.828775
842842 0 0
843843 613.146i 0.727338i
844844 0 0
845845 0 0
846846 0 0
847847 − 90.0666i − 0.106336i
848848 0 0
849849 −549.000 −0.646643
850850 0 0
851851 2251.67i 2.64591i
852852 0 0
853853 −1234.00 −1.44666 −0.723329 0.690503i 0.757389π-0.757389\pi
−0.723329 + 0.690503i 0.757389π0.757389\pi
854854 0 0
855855 0 0
856856 0 0
857857 −1185.00 −1.38273 −0.691365 0.722505i 0.742990π-0.742990\pi
−0.691365 + 0.722505i 0.742990π0.742990\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 893.738i 1.03562i 0.855496 + 0.517809i 0.173252π0.173252\pi
−0.855496 + 0.517809i 0.826748π0.826748\pi
864864 0 0
865865 0 0
866866 0 0
867867 484.974i 0.559371i
868868 0 0
869869 1050.00 1.20829
870870 0 0
871871 − 526.543i − 0.604527i
872872 0 0
873873 804.000 0.920962
874874 0 0
875875 0 0
876876 0 0
877877 20.0000 0.0228050 0.0114025 0.999935i 0.496370π-0.496370\pi
0.0114025 + 0.999935i 0.496370π0.496370\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 95.2628i 0.107885i 0.998544 + 0.0539427i 0.0171788π0.0171788\pi
−0.998544 + 0.0539427i 0.982821π0.982821\pi
884884 0 0
885885 0 0
886886 0 0
887887 − 1212.44i − 1.36689i −0.730000 0.683447i 0.760480π-0.760480\pi
0.730000 0.683447i 0.239520π-0.239520\pi
888888 0 0
889889 −36.0000 −0.0404949
890890 0 0
891891 − 109.119i − 0.122468i
892892 0 0
893893 312.000 0.349384
894894 0 0
895895 0 0
896896 0 0
897897 1248.00 1.39130
898898 0 0
899899 − 374.123i − 0.416155i
900900 0 0
901901 54.0000 0.0599334
902902 0 0
903903 − 374.123i − 0.414311i
904904 0 0
905905 0 0
906906 0 0
907907 − 297.913i − 0.328459i −0.986422 0.164230i 0.947486π-0.947486\pi
0.986422 0.164230i 0.0525138π-0.0525138\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 1197.00 1.31106
914914 0 0
915915 0 0
916916 0 0
917917 24.0000 0.0261723
918918 0 0
919919 758.638i 0.825504i 0.910843 + 0.412752i 0.135432π0.135432\pi
−0.910843 + 0.412752i 0.864568π0.864568\pi
920920 0 0
921921 −387.000 −0.420195
922922 0 0
923923 443.405i 0.480395i
924924 0 0
925925 0 0
926926 0 0
927927 − 665.108i − 0.717484i
928928 0 0
929929 −258.000 −0.277718 −0.138859 0.990312i 0.544343π-0.544343\pi
−0.138859 + 0.990312i 0.544343π0.544343\pi
930930 0 0
931931 833.116i 0.894862i
932932 0 0
933933 750.000 0.803859
934934 0 0
935935 0 0
936936 0 0
937937 481.000 0.513340 0.256670 0.966499i 0.417375π-0.417375\pi
0.256670 + 0.966499i 0.417375π0.417375\pi
938938 0 0
939939 377.587i 0.402116i
940940 0 0
941941 24.0000 0.0255048 0.0127524 0.999919i 0.495941π-0.495941\pi
0.0127524 + 0.999919i 0.495941π0.495941\pi
942942 0 0
943943 − 2837.10i − 3.00859i
944944 0 0
945945 0 0
946946 0 0
947947 − 665.108i − 0.702331i −0.936313 0.351166i 0.885785π-0.885785\pi
0.936313 0.351166i 0.114215π-0.114215\pi
948948 0 0
949949 272.000 0.286617
950950 0 0
951951 − 20.7846i − 0.0218555i
952952 0 0
953953 291.000 0.305352 0.152676 0.988276i 0.451211π-0.451211\pi
0.152676 + 0.988276i 0.451211π0.451211\pi
954954 0 0
955955 0 0
956956 0 0
957957 252.000 0.263323
958958 0 0
959959 717.069i 0.747726i
960960 0 0
961961 −11.0000 −0.0114464
962962 0 0
963963 987.269i 1.02520i
964964 0 0
965965 0 0
966966 0 0
967967 − 1094.66i − 1.13201i −0.824401 0.566006i 0.808488π-0.808488\pi
0.824401 0.566006i 0.191512π-0.191512\pi
968968 0 0
969969 117.000 0.120743
970970 0 0
971971 611.414i 0.629674i 0.949146 + 0.314837i 0.101950π0.101950\pi
−0.949146 + 0.314837i 0.898050π0.898050\pi
972972 0 0
973973 618.000 0.635149
974974 0 0
975975 0 0
976976 0 0
977977 231.000 0.236438 0.118219 0.992988i 0.462282π-0.462282\pi
0.118219 + 0.992988i 0.462282π0.462282\pi
978978 0 0
979979 − 1200.31i − 1.22606i
980980 0 0
981981 444.000 0.452599
982982 0 0
983983 162.813i 0.165628i 0.996565 + 0.0828142i 0.0263908π0.0263908\pi
−0.996565 + 0.0828142i 0.973609π0.973609\pi
984984 0 0
985985 0 0
986986 0 0
987987 − 83.1384i − 0.0842335i
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 807.000 0.812689
994994 0 0
995995 0 0
996996 0 0
997997 1100.00 1.10331 0.551655 0.834072i 0.313997π-0.313997\pi
0.551655 + 0.834072i 0.313997π0.313997\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 1600.3.b.j.1151.1 2
4.3 odd 2 inner 1600.3.b.j.1151.2 2
5.2 odd 4 1600.3.h.h.1599.1 4
5.3 odd 4 1600.3.h.h.1599.3 4
5.4 even 2 1600.3.b.i.1151.2 2
8.3 odd 2 400.3.b.e.351.1 2
8.5 even 2 400.3.b.e.351.2 yes 2
20.3 even 4 1600.3.h.h.1599.2 4
20.7 even 4 1600.3.h.h.1599.4 4
20.19 odd 2 1600.3.b.i.1151.1 2
24.5 odd 2 3600.3.e.j.3151.2 2
24.11 even 2 3600.3.e.j.3151.1 2
40.3 even 4 400.3.h.b.399.3 4
40.13 odd 4 400.3.h.b.399.2 4
40.19 odd 2 400.3.b.f.351.2 yes 2
40.27 even 4 400.3.h.b.399.1 4
40.29 even 2 400.3.b.f.351.1 yes 2
40.37 odd 4 400.3.h.b.399.4 4
120.29 odd 2 3600.3.e.u.3151.1 2
120.53 even 4 3600.3.j.f.1999.3 4
120.59 even 2 3600.3.e.u.3151.2 2
120.77 even 4 3600.3.j.f.1999.1 4
120.83 odd 4 3600.3.j.f.1999.2 4
120.107 odd 4 3600.3.j.f.1999.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
400.3.b.e.351.1 2 8.3 odd 2
400.3.b.e.351.2 yes 2 8.5 even 2
400.3.b.f.351.1 yes 2 40.29 even 2
400.3.b.f.351.2 yes 2 40.19 odd 2
400.3.h.b.399.1 4 40.27 even 4
400.3.h.b.399.2 4 40.13 odd 4
400.3.h.b.399.3 4 40.3 even 4
400.3.h.b.399.4 4 40.37 odd 4
1600.3.b.i.1151.1 2 20.19 odd 2
1600.3.b.i.1151.2 2 5.4 even 2
1600.3.b.j.1151.1 2 1.1 even 1 trivial
1600.3.b.j.1151.2 2 4.3 odd 2 inner
1600.3.h.h.1599.1 4 5.2 odd 4
1600.3.h.h.1599.2 4 20.3 even 4
1600.3.h.h.1599.3 4 5.3 odd 4
1600.3.h.h.1599.4 4 20.7 even 4
3600.3.e.j.3151.1 2 24.11 even 2
3600.3.e.j.3151.2 2 24.5 odd 2
3600.3.e.u.3151.1 2 120.29 odd 2
3600.3.e.u.3151.2 2 120.59 even 2
3600.3.j.f.1999.1 4 120.77 even 4
3600.3.j.f.1999.2 4 120.83 odd 4
3600.3.j.f.1999.3 4 120.53 even 4
3600.3.j.f.1999.4 4 120.107 odd 4