Properties

Label 1440.2.m.c.719.5
Level 14401440
Weight 22
Character 1440.719
Analytic conductor 11.49811.498
Analytic rank 00
Dimension 1616
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1440,2,Mod(719,1440)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1440, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1440.719");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1440=25325 1440 = 2^{5} \cdot 3^{2} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1440.m (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: 11.498457891111.4984578911
Analytic rank: 00
Dimension: 1616
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x1617x12104x10+713x8+238x6+1004x4152x2+64 x^{16} - 17x^{12} - 104x^{10} + 713x^{8} + 238x^{6} + 1004x^{4} - 152x^{2} + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 220 2^{20}
Twist minimal: no (minimal twist has level 360)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 719.5
Root 0.877859+2.23141i-0.877859 + 2.23141i of defining polynomial
Character χ\chi == 1440.719
Dual form 1440.2.m.c.719.7

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.649011.51022i)q50.936426q7+2.20837iq11+3.33513q13+1.54417q17+3.12311q193.39228iq23+(0.438447+4.98074i)q258.44804q298.30571iq31+(1.54417+1.41421i)q35+7.60669q375.83095iq417.77769iq4310.7575iq476.12311q495.08842iq53+(3.335133.64162i)q5510.6937iq59+(5.499665.03680i)q65+12.1453iq6711.7460q715.59390iq732.06798iq771.02248iq79+14.0877q83+(2.546352.33205i)q85+13.0761iq893.12311q91+(5.150024.71659i)q952.18379iq97+O(q100)q+(-1.64901 - 1.51022i) q^{5} -0.936426 q^{7} +2.20837i q^{11} +3.33513 q^{13} +1.54417 q^{17} +3.12311 q^{19} -3.39228i q^{23} +(0.438447 + 4.98074i) q^{25} -8.44804 q^{29} -8.30571i q^{31} +(1.54417 + 1.41421i) q^{35} +7.60669 q^{37} -5.83095i q^{41} -7.77769i q^{43} -10.7575i q^{47} -6.12311 q^{49} -5.08842i q^{53} +(3.33513 - 3.64162i) q^{55} -10.6937i q^{59} +(-5.49966 - 5.03680i) q^{65} +12.1453i q^{67} -11.7460 q^{71} -5.59390i q^{73} -2.06798i q^{77} -1.02248i q^{79} +14.0877 q^{83} +(-2.54635 - 2.33205i) q^{85} +13.0761i q^{89} -3.12311 q^{91} +(-5.15002 - 4.71659i) q^{95} -2.18379i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q16q19+40q2532q49+16q91+O(q100) 16 q - 16 q^{19} + 40 q^{25} - 32 q^{49} + 16 q^{91}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1440Z)×\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times.

nn 577577 641641 901901 991991
χ(n)\chi(n) 1-1 1-1 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 0 0
44 0 0
55 −1.64901 1.51022i −0.737458 0.675393i
66 0 0
77 −0.936426 −0.353936 −0.176968 0.984217i 0.556629π-0.556629\pi
−0.176968 + 0.984217i 0.556629π0.556629\pi
88 0 0
99 0 0
1010 0 0
1111 2.20837i 0.665848i 0.942954 + 0.332924i 0.108035π0.108035\pi
−0.942954 + 0.332924i 0.891965π0.891965\pi
1212 0 0
1313 3.33513 0.924999 0.462500 0.886619i 0.346953π-0.346953\pi
0.462500 + 0.886619i 0.346953π0.346953\pi
1414 0 0
1515 0 0
1616 0 0
1717 1.54417 0.374517 0.187259 0.982311i 0.440040π-0.440040\pi
0.187259 + 0.982311i 0.440040π0.440040\pi
1818 0 0
1919 3.12311 0.716490 0.358245 0.933628i 0.383375π-0.383375\pi
0.358245 + 0.933628i 0.383375π0.383375\pi
2020 0 0
2121 0 0
2222 0 0
2323 3.39228i 0.707340i −0.935370 0.353670i 0.884934π-0.884934\pi
0.935370 0.353670i 0.115066π-0.115066\pi
2424 0 0
2525 0.438447 + 4.98074i 0.0876894 + 0.996148i
2626 0 0
2727 0 0
2828 0 0
2929 −8.44804 −1.56876 −0.784380 0.620280i 0.787019π-0.787019\pi
−0.784380 + 0.620280i 0.787019π0.787019\pi
3030 0 0
3131 8.30571i 1.49175i −0.666086 0.745875i 0.732032π-0.732032\pi
0.666086 0.745875i 0.267968π-0.267968\pi
3232 0 0
3333 0 0
3434 0 0
3535 1.54417 + 1.41421i 0.261013 + 0.239046i
3636 0 0
3737 7.60669 1.25053 0.625266 0.780412i 0.284990π-0.284990\pi
0.625266 + 0.780412i 0.284990π0.284990\pi
3838 0 0
3939 0 0
4040 0 0
4141 5.83095i 0.910642i −0.890327 0.455321i 0.849525π-0.849525\pi
0.890327 0.455321i 0.150475π-0.150475\pi
4242 0 0
4343 7.77769i 1.18609i −0.805171 0.593043i 0.797926π-0.797926\pi
0.805171 0.593043i 0.202074π-0.202074\pi
4444 0 0
4545 0 0
4646 0 0
4747 10.7575i 1.56914i −0.620040 0.784570i 0.712884π-0.712884\pi
0.620040 0.784570i 0.287116π-0.287116\pi
4848 0 0
4949 −6.12311 −0.874729
5050 0 0
5151 0 0
5252 0 0
5353 5.08842i 0.698949i −0.936946 0.349474i 0.886360π-0.886360\pi
0.936946 0.349474i 0.113640π-0.113640\pi
5454 0 0
5555 3.33513 3.64162i 0.449709 0.491035i
5656 0 0
5757 0 0
5858 0 0
5959 10.6937i 1.39219i −0.717947 0.696097i 0.754918π-0.754918\pi
0.717947 0.696097i 0.245082π-0.245082\pi
6060 0 0
6161 0 0 1.00000 00
−1.00000 π\pi
6262 0 0
6363 0 0
6464 0 0
6565 −5.49966 5.03680i −0.682148 0.624738i
6666 0 0
6767 12.1453i 1.48378i 0.670521 + 0.741890i 0.266071π0.266071\pi
−0.670521 + 0.741890i 0.733929π0.733929\pi
6868 0 0
6969 0 0
7070 0 0
7171 −11.7460 −1.39400 −0.697000 0.717071i 0.745482π-0.745482\pi
−0.697000 + 0.717071i 0.745482π0.745482\pi
7272 0 0
7373 5.59390i 0.654716i −0.944900 0.327358i 0.893842π-0.893842\pi
0.944900 0.327358i 0.106158π-0.106158\pi
7474 0 0
7575 0 0
7676 0 0
7777 2.06798i 0.235668i
7878 0 0
7979 1.02248i 0.115038i −0.998344 0.0575190i 0.981681π-0.981681\pi
0.998344 0.0575190i 0.0183190π-0.0183190\pi
8080 0 0
8181 0 0
8282 0 0
8383 14.0877 1.54632 0.773161 0.634210i 0.218675π-0.218675\pi
0.773161 + 0.634210i 0.218675π0.218675\pi
8484 0 0
8585 −2.54635 2.33205i −0.276191 0.252946i
8686 0 0
8787 0 0
8888 0 0
8989 13.0761i 1.38607i 0.720906 + 0.693033i 0.243726π0.243726\pi
−0.720906 + 0.693033i 0.756274π0.756274\pi
9090 0 0
9191 −3.12311 −0.327390
9292 0 0
9393 0 0
9494 0 0
9595 −5.15002 4.71659i −0.528381 0.483912i
9696 0 0
9797 2.18379i 0.221730i −0.993835 0.110865i 0.964638π-0.964638\pi
0.993835 0.110865i 0.0353622π-0.0353622\pi
9898 0 0
9999 0 0
100100 0 0
101101 −3.29801 −0.328165 −0.164082 0.986447i 0.552466π-0.552466\pi
−0.164082 + 0.986447i 0.552466π0.552466\pi
102102 0 0
103103 18.0227 1.77583 0.887913 0.460012i 0.152155π-0.152155\pi
0.887913 + 0.460012i 0.152155π0.152155\pi
104104 0 0
105105 0 0
106106 0 0
107107 −10.9993 −1.06334 −0.531672 0.846950i 0.678436π-0.678436\pi
−0.531672 + 0.846950i 0.678436π0.678436\pi
108108 0 0
109109 11.9473i 1.14435i −0.820133 0.572173i 0.806100π-0.806100\pi
0.820133 0.572173i 0.193900π-0.193900\pi
110110 0 0
111111 0 0
112112 0 0
113113 12.5435 1.17999 0.589996 0.807406i 0.299129π-0.299129\pi
0.589996 + 0.807406i 0.299129π0.299129\pi
114114 0 0
115115 −5.12311 + 5.59390i −0.477732 + 0.521634i
116116 0 0
117117 0 0
118118 0 0
119119 −1.44600 −0.132555
120120 0 0
121121 6.12311 0.556646
122122 0 0
123123 0 0
124124 0 0
125125 6.79903 8.87543i 0.608124 0.793842i
126126 0 0
127127 −4.68213 −0.415472 −0.207736 0.978185i 0.566609π-0.566609\pi
−0.207736 + 0.978185i 0.566609π0.566609\pi
128128 0 0
129129 0 0
130130 0 0
131131 0.620058i 0.0541747i 0.999633 + 0.0270874i 0.00862323π0.00862323\pi
−0.999633 + 0.0270874i 0.991377π0.991377\pi
132132 0 0
133133 −2.92456 −0.253591
134134 0 0
135135 0 0
136136 0 0
137137 1.54417 0.131928 0.0659638 0.997822i 0.478988π-0.478988\pi
0.0659638 + 0.997822i 0.478988π0.478988\pi
138138 0 0
139139 12.0000 1.01783 0.508913 0.860818i 0.330047π-0.330047\pi
0.508913 + 0.860818i 0.330047π0.330047\pi
140140 0 0
141141 0 0
142142 0 0
143143 7.36520i 0.615909i
144144 0 0
145145 13.9309 + 12.7584i 1.15690 + 1.05953i
146146 0 0
147147 0 0
148148 0 0
149149 −1.85201 −0.151722 −0.0758612 0.997118i 0.524171π-0.524171\pi
−0.0758612 + 0.997118i 0.524171π0.524171\pi
150150 0 0
151151 17.6339i 1.43503i 0.696545 + 0.717513i 0.254720π0.254720\pi
−0.696545 + 0.717513i 0.745280π0.745280\pi
152152 0 0
153153 0 0
154154 0 0
155155 −12.5435 + 13.6962i −1.00752 + 1.10010i
156156 0 0
157157 −2.80928 −0.224205 −0.112102 0.993697i 0.535758π-0.535758\pi
−0.112102 + 0.993697i 0.535758π0.535758\pi
158158 0 0
159159 0 0
160160 0 0
161161 3.17662i 0.250353i
162162 0 0
163163 15.5554i 1.21839i −0.793020 0.609195i 0.791492π-0.791492\pi
0.793020 0.609195i 0.208508π-0.208508\pi
164164 0 0
165165 0 0
166166 0 0
167167 9.43318i 0.729961i 0.931015 + 0.364981i 0.118924π0.118924\pi
−0.931015 + 0.364981i 0.881076π0.881076\pi
168168 0 0
169169 −1.87689 −0.144376
170170 0 0
171171 0 0
172172 0 0
173173 1.69614i 0.128955i 0.997919 + 0.0644776i 0.0205381π0.0205381\pi
−0.997919 + 0.0644776i 0.979462π0.979462\pi
174174 0 0
175175 −0.410574 4.66410i −0.0310364 0.352572i
176176 0 0
177177 0 0
178178 0 0
179179 8.21342i 0.613900i −0.951726 0.306950i 0.900692π-0.900692\pi
0.951726 0.306950i 0.0993084π-0.0993084\pi
180180 0 0
181181 4.66410i 0.346680i −0.984862 0.173340i 0.944544π-0.944544\pi
0.984862 0.173340i 0.0554559π-0.0554559\pi
182182 0 0
183183 0 0
184184 0 0
185185 −12.5435 11.4878i −0.922215 0.844600i
186186 0 0
187187 3.41011i 0.249372i
188188 0 0
189189 0 0
190190 0 0
191191 13.1921 0.954544 0.477272 0.878756i 0.341626π-0.341626\pi
0.477272 + 0.878756i 0.341626π0.341626\pi
192192 0 0
193193 23.3331i 1.67955i −0.542934 0.839775i 0.682687π-0.682687\pi
0.542934 0.839775i 0.317313π-0.317313\pi
194194 0 0
195195 0 0
196196 0 0
197197 4.92539i 0.350920i −0.984487 0.175460i 0.943859π-0.943859\pi
0.984487 0.175460i 0.0561412π-0.0561412\pi
198198 0 0
199199 17.6339i 1.25003i 0.780611 + 0.625017i 0.214908π0.214908\pi
−0.780611 + 0.625017i 0.785092π0.785092\pi
200200 0 0
201201 0 0
202202 0 0
203203 7.91096 0.555241
204204 0 0
205205 −8.80604 + 9.61528i −0.615041 + 0.671560i
206206 0 0
207207 0 0
208208 0 0
209209 6.89697i 0.477073i
210210 0 0
211211 −4.00000 −0.275371 −0.137686 0.990476i 0.543966π-0.543966\pi
−0.137686 + 0.990476i 0.543966π0.543966\pi
212212 0 0
213213 0 0
214214 0 0
215215 −11.7460 + 12.8255i −0.801074 + 0.874689i
216216 0 0
217217 7.77769i 0.527984i
218218 0 0
219219 0 0
220220 0 0
221221 5.15002 0.346428
222222 0 0
223223 −21.9989 −1.47316 −0.736578 0.676352i 0.763560π-0.763560\pi
−0.736578 + 0.676352i 0.763560π0.763560\pi
224224 0 0
225225 0 0
226226 0 0
227227 −3.08835 −0.204981 −0.102490 0.994734i 0.532681π-0.532681\pi
−0.102490 + 0.994734i 0.532681π0.532681\pi
228228 0 0
229229 2.61914i 0.173077i −0.996248 0.0865387i 0.972419π-0.972419\pi
0.996248 0.0865387i 0.0275806π-0.0275806\pi
230230 0 0
231231 0 0
232232 0 0
233233 20.4544 1.34002 0.670008 0.742354i 0.266291π-0.266291\pi
0.670008 + 0.742354i 0.266291π0.266291\pi
234234 0 0
235235 −16.2462 + 17.7392i −1.05979 + 1.15718i
236236 0 0
237237 0 0
238238 0 0
239239 23.4921 1.51958 0.759789 0.650170i 0.225302π-0.225302\pi
0.759789 + 0.650170i 0.225302π0.225302\pi
240240 0 0
241241 −4.00000 −0.257663 −0.128831 0.991667i 0.541123π-0.541123\pi
−0.128831 + 0.991667i 0.541123π0.541123\pi
242242 0 0
243243 0 0
244244 0 0
245245 10.0970 + 9.24726i 0.645076 + 0.590786i
246246 0 0
247247 10.4160 0.662752
248248 0 0
249249 0 0
250250 0 0
251251 3.44849i 0.217666i 0.994060 + 0.108833i 0.0347114π0.0347114\pi
−0.994060 + 0.108833i 0.965289π0.965289\pi
252252 0 0
253253 7.49141 0.470981
254254 0 0
255255 0 0
256256 0 0
257257 −15.6318 −0.975087 −0.487543 0.873099i 0.662107π-0.662107\pi
−0.487543 + 0.873099i 0.662107π0.662107\pi
258258 0 0
259259 −7.12311 −0.442608
260260 0 0
261261 0 0
262262 0 0
263263 14.7304i 0.908316i 0.890921 + 0.454158i 0.150060π0.150060\pi
−0.890921 + 0.454158i 0.849940π0.849940\pi
264264 0 0
265265 −7.68466 + 8.39084i −0.472065 + 0.515445i
266266 0 0
267267 0 0
268268 0 0
269269 15.0441 0.917253 0.458626 0.888629i 0.348342π-0.348342\pi
0.458626 + 0.888629i 0.348342π0.348342\pi
270270 0 0
271271 10.3507i 0.628758i −0.949297 0.314379i 0.898204π-0.898204\pi
0.949297 0.314379i 0.101796π-0.101796\pi
272272 0 0
273273 0 0
274274 0 0
275275 −10.9993 + 0.968253i −0.663283 + 0.0583879i
276276 0 0
277277 −23.3459 −1.40272 −0.701360 0.712807i 0.747424π-0.747424\pi
−0.701360 + 0.712807i 0.747424π0.747424\pi
278278 0 0
279279 0 0
280280 0 0
281281 3.00252i 0.179116i −0.995982 0.0895578i 0.971455π-0.971455\pi
0.995982 0.0895578i 0.0285454π-0.0285454\pi
282282 0 0
283283 23.3331i 1.38701i −0.720453 0.693503i 0.756066π-0.756066\pi
0.720453 0.693503i 0.243934π-0.243934\pi
284284 0 0
285285 0 0
286286 0 0
287287 5.46026i 0.322309i
288288 0 0
289289 −14.6155 −0.859737
290290 0 0
291291 0 0
292292 0 0
293293 29.8326i 1.74284i 0.490536 + 0.871421i 0.336801π0.336801\pi
−0.490536 + 0.871421i 0.663199π0.663199\pi
294294 0 0
295295 −16.1498 + 17.6339i −0.940278 + 1.02669i
296296 0 0
297297 0 0
298298 0 0
299299 11.3137i 0.654289i
300300 0 0
301301 7.28323i 0.419799i
302302 0 0
303303 0 0
304304 0 0
305305 0 0
306306 0 0
307307 4.36758i 0.249271i −0.992203 0.124636i 0.960224π-0.960224\pi
0.992203 0.124636i 0.0397762π-0.0397762\pi
308308 0 0
309309 0 0
310310 0 0
311311 10.3000 0.584062 0.292031 0.956409i 0.405669π-0.405669\pi
0.292031 + 0.956409i 0.405669π0.405669\pi
312312 0 0
313313 32.0682i 1.81260i −0.422631 0.906302i 0.638893π-0.638893\pi
0.422631 0.906302i 0.361107π-0.361107\pi
314314 0 0
315315 0 0
316316 0 0
317317 24.5354i 1.37805i 0.724739 + 0.689023i 0.241960π0.241960\pi
−0.724739 + 0.689023i 0.758040π0.758040\pi
318318 0 0
319319 18.6564i 1.04456i
320320 0 0
321321 0 0
322322 0 0
323323 4.82262 0.268338
324324 0 0
325325 1.46228 + 16.6114i 0.0811127 + 0.921436i
326326 0 0
327327 0 0
328328 0 0
329329 10.0736i 0.555375i
330330 0 0
331331 1.36932 0.0752645 0.0376322 0.999292i 0.488018π-0.488018\pi
0.0376322 + 0.999292i 0.488018π0.488018\pi
332332 0 0
333333 0 0
334334 0 0
335335 18.3421 20.0276i 1.00213 1.09423i
336336 0 0
337337 29.8844i 1.62791i 0.580929 + 0.813954i 0.302690π0.302690\pi
−0.580929 + 0.813954i 0.697310π0.697310\pi
338338 0 0
339339 0 0
340340 0 0
341341 18.3421 0.993279
342342 0 0
343343 12.2888 0.663534
344344 0 0
345345 0 0
346346 0 0
347347 14.0877 0.756265 0.378133 0.925751i 0.376566π-0.376566\pi
0.378133 + 0.925751i 0.376566π0.376566\pi
348348 0 0
349349 33.2228i 1.77838i 0.457540 + 0.889189i 0.348731π0.348731\pi
−0.457540 + 0.889189i 0.651269π0.651269\pi
350350 0 0
351351 0 0
352352 0 0
353353 −7.72087 −0.410940 −0.205470 0.978663i 0.565872π-0.565872\pi
−0.205470 + 0.978663i 0.565872π0.565872\pi
354354 0 0
355355 19.3693 + 17.7392i 1.02802 + 0.941497i
356356 0 0
357357 0 0
358358 0 0
359359 −1.44600 −0.0763172 −0.0381586 0.999272i 0.512149π-0.512149\pi
−0.0381586 + 0.999272i 0.512149π0.512149\pi
360360 0 0
361361 −9.24621 −0.486643
362362 0 0
363363 0 0
364364 0 0
365365 −8.44804 + 9.22437i −0.442190 + 0.482826i
366366 0 0
367367 −32.4149 −1.69204 −0.846022 0.533148i 0.821009π-0.821009\pi
−0.846022 + 0.533148i 0.821009π0.821009\pi
368368 0 0
369369 0 0
370370 0 0
371371 4.76493i 0.247383i
372372 0 0
373373 9.47954 0.490832 0.245416 0.969418i 0.421075π-0.421075\pi
0.245416 + 0.969418i 0.421075π0.421075\pi
374374 0 0
375375 0 0
376376 0 0
377377 −28.1753 −1.45110
378378 0 0
379379 16.4924 0.847159 0.423579 0.905859i 0.360773π-0.360773\pi
0.423579 + 0.905859i 0.360773π0.360773\pi
380380 0 0
381381 0 0
382382 0 0
383383 10.0138i 0.511682i −0.966719 0.255841i 0.917648π-0.917648\pi
0.966719 0.255841i 0.0823524π-0.0823524\pi
384384 0 0
385385 −3.12311 + 3.41011i −0.159168 + 0.173795i
386386 0 0
387387 0 0
388388 0 0
389389 −9.89404 −0.501648 −0.250824 0.968033i 0.580702π-0.580702\pi
−0.250824 + 0.968033i 0.580702π0.580702\pi
390390 0 0
391391 5.23827i 0.264911i
392392 0 0
393393 0 0
394394 0 0
395395 −1.54417 + 1.68608i −0.0776958 + 0.0848357i
396396 0 0
397397 −10.3007 −0.516977 −0.258488 0.966014i 0.583224π-0.583224\pi
−0.258488 + 0.966014i 0.583224π0.583224\pi
398398 0 0
399399 0 0
400400 0 0
401401 0.522293i 0.0260821i −0.999915 0.0130410i 0.995849π-0.995849\pi
0.999915 0.0130410i 0.00415121π-0.00415121\pi
402402 0 0
403403 27.7006i 1.37987i
404404 0 0
405405 0 0
406406 0 0
407407 16.7984i 0.832665i
408408 0 0
409409 3.12311 0.154428 0.0772138 0.997015i 0.475398π-0.475398\pi
0.0772138 + 0.997015i 0.475398π0.475398\pi
410410 0 0
411411 0 0
412412 0 0
413413 10.0138i 0.492748i
414414 0 0
415415 −23.2306 21.2755i −1.14035 1.04437i
416416 0 0
417417 0 0
418418 0 0
419419 32.4291i 1.58427i 0.610348 + 0.792134i 0.291030π0.291030\pi
−0.610348 + 0.792134i 0.708970π0.708970\pi
420420 0 0
421421 30.6037i 1.49153i 0.666207 + 0.745767i 0.267917π0.267917\pi
−0.666207 + 0.745767i 0.732083π0.732083\pi
422422 0 0
423423 0 0
424424 0 0
425425 0.677039 + 7.69113i 0.0328412 + 0.373074i
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 1.44600 0.0696516 0.0348258 0.999393i 0.488912π-0.488912\pi
0.0348258 + 0.999393i 0.488912π0.488912\pi
432432 0 0
433433 15.5554i 0.747544i −0.927521 0.373772i 0.878064π-0.878064\pi
0.927521 0.373772i 0.121936π-0.121936\pi
434434 0 0
435435 0 0
436436 0 0
437437 10.5945i 0.506802i
438438 0 0
439439 26.9621i 1.28683i 0.765517 + 0.643415i 0.222483π0.222483\pi
−0.765517 + 0.643415i 0.777517π0.777517\pi
440440 0 0
441441 0 0
442442 0 0
443443 25.0870 1.19192 0.595959 0.803015i 0.296772π-0.296772\pi
0.595959 + 0.803015i 0.296772π0.296772\pi
444444 0 0
445445 19.7479 21.5626i 0.936139 1.02217i
446446 0 0
447447 0 0
448448 0 0
449449 9.89949i 0.467186i −0.972334 0.233593i 0.924952π-0.924952\pi
0.972334 0.233593i 0.0750483π-0.0750483\pi
450450 0 0
451451 12.8769 0.606349
452452 0 0
453453 0 0
454454 0 0
455455 5.15002 + 4.71659i 0.241437 + 0.221117i
456456 0 0
457457 13.3716i 0.625496i 0.949836 + 0.312748i 0.101250π0.101250\pi
−0.949836 + 0.312748i 0.898750π0.898750\pi
458458 0 0
459459 0 0
460460 0 0
461461 −1.85201 −0.0862567 −0.0431283 0.999070i 0.513732π-0.513732\pi
−0.0431283 + 0.999070i 0.513732π0.513732\pi
462462 0 0
463463 −13.2252 −0.614629 −0.307315 0.951608i 0.599430π-0.599430\pi
−0.307315 + 0.951608i 0.599430π0.599430\pi
464464 0 0
465465 0 0
466466 0 0
467467 −18.9103 −0.875063 −0.437532 0.899203i 0.644147π-0.644147\pi
−0.437532 + 0.899203i 0.644147π0.644147\pi
468468 0 0
469469 11.3732i 0.525163i
470470 0 0
471471 0 0
472472 0 0
473473 17.1760 0.789754
474474 0 0
475475 1.36932 + 15.5554i 0.0628286 + 0.713730i
476476 0 0
477477 0 0
478478 0 0
479479 14.6381 0.668830 0.334415 0.942426i 0.391461π-0.391461\pi
0.334415 + 0.942426i 0.391461π0.391461\pi
480480 0 0
481481 25.3693 1.15674
482482 0 0
483483 0 0
484484 0 0
485485 −3.29801 + 3.60109i −0.149755 + 0.163517i
486486 0 0
487487 29.4903 1.33633 0.668167 0.744011i 0.267079π-0.267079\pi
0.668167 + 0.744011i 0.267079π0.267079\pi
488488 0 0
489489 0 0
490490 0 0
491491 16.3505i 0.737888i 0.929452 + 0.368944i 0.120281π0.120281\pi
−0.929452 + 0.368944i 0.879719π0.879719\pi
492492 0 0
493493 −13.0452 −0.587528
494494 0 0
495495 0 0
496496 0 0
497497 10.9993 0.493387
498498 0 0
499499 −16.8769 −0.755514 −0.377757 0.925905i 0.623304π-0.623304\pi
−0.377757 + 0.925905i 0.623304π0.623304\pi
500500 0 0
501501 0 0
502502 0 0
503503 16.0547i 0.715844i 0.933751 + 0.357922i 0.116515π0.116515\pi
−0.933751 + 0.357922i 0.883485π0.883485\pi
504504 0 0
505505 5.43845 + 4.98074i 0.242008 + 0.221640i
506506 0 0
507507 0 0
508508 0 0
509509 −3.29801 −0.146182 −0.0730909 0.997325i 0.523286π-0.523286\pi
−0.0730909 + 0.997325i 0.523286π0.523286\pi
510510 0 0
511511 5.23827i 0.231728i
512512 0 0
513513 0 0
514514 0 0
515515 −29.7195 27.2183i −1.30960 1.19938i
516516 0 0
517517 23.7565 1.04481
518518 0 0
519519 0 0
520520 0 0
521521 2.65433i 0.116288i −0.998308 0.0581441i 0.981482π-0.981482\pi
0.998308 0.0581441i 0.0185183π-0.0185183\pi
522522 0 0
523523 4.36758i 0.190981i 0.995430 + 0.0954905i 0.0304420π0.0304420\pi
−0.995430 + 0.0954905i 0.969558π0.969558\pi
524524 0 0
525525 0 0
526526 0 0
527527 12.8255i 0.558686i
528528 0 0
529529 11.4924 0.499671
530530 0 0
531531 0 0
532532 0 0
533533 19.4470i 0.842343i
534534 0 0
535535 18.1379 + 16.6114i 0.784172 + 0.718174i
536536 0 0
537537 0 0
538538 0 0
539539 13.5221i 0.582437i
540540 0 0
541541 9.90237i 0.425736i −0.977081 0.212868i 0.931720π-0.931720\pi
0.977081 0.212868i 0.0682804π-0.0682804\pi
542542 0 0
543543 0 0
544544 0 0
545545 −18.0431 + 19.7012i −0.772883 + 0.843908i
546546 0 0
547547 16.5129i 0.706039i −0.935616 0.353019i 0.885155π-0.885155\pi
0.935616 0.353019i 0.114845π-0.114845\pi
548548 0 0
549549 0 0
550550 0 0
551551 −26.3841 −1.12400
552552 0 0
553553 0.957477i 0.0407161i
554554 0 0
555555 0 0
556556 0 0
557557 32.6443i 1.38318i −0.722289 0.691591i 0.756910π-0.756910\pi
0.722289 0.691591i 0.243090π-0.243090\pi
558558 0 0
559559 25.9396i 1.09713i
560560 0 0
561561 0 0
562562 0 0
563563 −14.0877 −0.593724 −0.296862 0.954920i 0.595940π-0.595940\pi
−0.296862 + 0.954920i 0.595940π0.595940\pi
564564 0 0
565565 −20.6843 18.9435i −0.870195 0.796958i
566566 0 0
567567 0 0
568568 0 0
569569 30.0467i 1.25962i −0.776748 0.629811i 0.783132π-0.783132\pi
0.776748 0.629811i 0.216868π-0.216868\pi
570570 0 0
571571 −33.8617 −1.41707 −0.708535 0.705676i 0.750644π-0.750644\pi
−0.708535 + 0.705676i 0.750644π0.750644\pi
572572 0 0
573573 0 0
574574 0 0
575575 16.8961 1.48734i 0.704615 0.0620262i
576576 0 0
577577 7.77769i 0.323789i −0.986808 0.161895i 0.948240π-0.948240\pi
0.986808 0.161895i 0.0517605π-0.0517605\pi
578578 0 0
579579 0 0
580580 0 0
581581 −13.1921 −0.547299
582582 0 0
583583 11.2371 0.465394
584584 0 0
585585 0 0
586586 0 0
587587 10.9993 0.453990 0.226995 0.973896i 0.427110π-0.427110\pi
0.226995 + 0.973896i 0.427110π0.427110\pi
588588 0 0
589589 25.9396i 1.06882i
590590 0 0
591591 0 0
592592 0 0
593593 43.8071 1.79894 0.899472 0.436978i 0.143951π-0.143951\pi
0.899472 + 0.436978i 0.143951π0.143951\pi
594594 0 0
595595 2.38447 + 2.18379i 0.0977538 + 0.0895267i
596596 0 0
597597 0 0
598598 0 0
599599 −45.5382 −1.86064 −0.930320 0.366749i 0.880471π-0.880471\pi
−0.930320 + 0.366749i 0.880471π0.880471\pi
600600 0 0
601601 −23.3693 −0.953254 −0.476627 0.879106i 0.658141π-0.658141\pi
−0.476627 + 0.879106i 0.658141π0.658141\pi
602602 0 0
603603 0 0
604604 0 0
605605 −10.0970 9.24726i −0.410503 0.375955i
606606 0 0
607607 9.71010 0.394121 0.197060 0.980391i 0.436860π-0.436860\pi
0.197060 + 0.980391i 0.436860π0.436860\pi
608608 0 0
609609 0 0
610610 0 0
611611 35.8776i 1.45145i
612612 0 0
613613 23.8718 0.964172 0.482086 0.876124i 0.339879π-0.339879\pi
0.482086 + 0.876124i 0.339879π0.339879\pi
614614 0 0
615615 0 0
616616 0 0
617617 15.6318 0.629314 0.314657 0.949205i 0.398111π-0.398111\pi
0.314657 + 0.949205i 0.398111π0.398111\pi
618618 0 0
619619 −18.7386 −0.753169 −0.376585 0.926382i 0.622902π-0.622902\pi
−0.376585 + 0.926382i 0.622902π0.622902\pi
620620 0 0
621621 0 0
622622 0 0
623623 12.2448i 0.490578i
624624 0 0
625625 −24.6155 + 4.36758i −0.984621 + 0.174703i
626626 0 0
627627 0 0
628628 0 0
629629 11.7460 0.468346
630630 0 0
631631 17.6339i 0.701995i 0.936376 + 0.350997i 0.114157π0.114157\pi
−0.936376 + 0.350997i 0.885843π0.885843\pi
632632 0 0
633633 0 0
634634 0 0
635635 7.72087 + 7.07107i 0.306393 + 0.280607i
636636 0 0
637637 −20.4214 −0.809124
638638 0 0
639639 0 0
640640 0 0
641641 7.07107i 0.279290i −0.990202 0.139645i 0.955404π-0.955404\pi
0.990202 0.139645i 0.0445962π-0.0445962\pi
642642 0 0
643643 8.73516i 0.344481i 0.985055 + 0.172241i 0.0551007π0.0551007\pi
−0.985055 + 0.172241i 0.944899π0.944899\pi
644644 0 0
645645 0 0
646646 0 0
647647 1.32431i 0.0520639i 0.999661 + 0.0260319i 0.00828716π0.00828716\pi
−0.999661 + 0.0260319i 0.991713π0.991713\pi
648648 0 0
649649 23.6155 0.926991
650650 0 0
651651 0 0
652652 0 0
653653 15.8459i 0.620098i −0.950721 0.310049i 0.899654π-0.899654\pi
0.950721 0.310049i 0.100346π-0.100346\pi
654654 0 0
655655 0.936426 1.02248i 0.0365892 0.0399516i
656656 0 0
657657 0 0
658658 0 0
659659 33.3211i 1.29800i 0.760786 + 0.649002i 0.224813π0.224813\pi
−0.760786 + 0.649002i 0.775187π0.775187\pi
660660 0 0
661661 44.5960i 1.73458i −0.497800 0.867292i 0.665859π-0.665859\pi
0.497800 0.867292i 0.334141π-0.334141\pi
662662 0 0
663663 0 0
664664 0 0
665665 4.82262 + 4.41674i 0.187013 + 0.171274i
666666 0 0
667667 28.6581i 1.10965i
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 0 0 1.00000 00
−1.00000 π\pi
674674 0 0
675675 0 0
676676 0 0
677677 5.25145i 0.201830i −0.994895 0.100915i 0.967823π-0.967823\pi
0.994895 0.100915i 0.0321770π-0.0321770\pi
678678 0 0
679679 2.04496i 0.0784783i
680680 0 0
681681 0 0
682682 0 0
683683 20.2644 0.775394 0.387697 0.921787i 0.373271π-0.373271\pi
0.387697 + 0.921787i 0.373271π0.373271\pi
684684 0 0
685685 −2.54635 2.33205i −0.0972911 0.0891030i
686686 0 0
687687 0 0
688688 0 0
689689 16.9706i 0.646527i
690690 0 0
691691 23.1231 0.879644 0.439822 0.898085i 0.355041π-0.355041\pi
0.439822 + 0.898085i 0.355041π0.355041\pi
692692 0 0
693693 0 0
694694 0 0
695695 −19.7881 18.1227i −0.750605 0.687433i
696696 0 0
697697 9.00400i 0.341051i
698698 0 0
699699 0 0
700700 0 0
701701 −20.1941 −0.762720 −0.381360 0.924427i 0.624544π-0.624544\pi
−0.381360 + 0.924427i 0.624544π0.624544\pi
702702 0 0
703703 23.7565 0.895993
704704 0 0
705705 0 0
706706 0 0
707707 3.08835 0.116149
708708 0 0
709709 30.6037i 1.14935i 0.818383 + 0.574673i 0.194871π0.194871\pi
−0.818383 + 0.574673i 0.805129π0.805129\pi
710710 0 0
711711 0 0
712712 0 0
713713 −28.1753 −1.05517
714714 0 0
715715 11.1231 12.1453i 0.415981 0.454207i
716716 0 0
717717 0 0
718718 0 0
719719 −32.3461 −1.20631 −0.603154 0.797625i 0.706089π-0.706089\pi
−0.603154 + 0.797625i 0.706089π0.706089\pi
720720 0 0
721721 −16.8769 −0.628528
722722 0 0
723723 0 0
724724 0 0
725725 −3.70402 42.0775i −0.137564 1.56272i
726726 0 0
727727 9.47954 0.351577 0.175788 0.984428i 0.443753π-0.443753\pi
0.175788 + 0.984428i 0.443753π0.443753\pi
728728 0 0
729729 0 0
730730 0 0
731731 12.0101i 0.444210i
732732 0 0
733733 19.6002 0.723951 0.361975 0.932188i 0.382102π-0.382102\pi
0.361975 + 0.932188i 0.382102π0.382102\pi
734734 0 0
735735 0 0
736736 0 0
737737 −26.8212 −0.987973
738738 0 0
739739 −35.6155 −1.31014 −0.655069 0.755569i 0.727361π-0.727361\pi
−0.655069 + 0.755569i 0.727361π0.727361\pi
740740 0 0
741741 0 0
742742 0 0
743743 10.0138i 0.367371i −0.982985 0.183686i 0.941197π-0.941197\pi
0.982985 0.183686i 0.0588028π-0.0588028\pi
744744 0 0
745745 3.05398 + 2.79695i 0.111889 + 0.102472i
746746 0 0
747747 0 0
748748 0 0
749749 10.3000 0.376355
750750 0 0
751751 41.5286i 1.51540i −0.652604 0.757699i 0.726323π-0.726323\pi
0.652604 0.757699i 0.273677π-0.273677\pi
752752 0 0
753753 0 0
754754 0 0
755755 26.6311 29.0784i 0.969207 1.05827i
756756 0 0
757757 3.33513 0.121217 0.0606087 0.998162i 0.480696π-0.480696\pi
0.0606087 + 0.998162i 0.480696π0.480696\pi
758758 0 0
759759 0 0
760760 0 0
761761 49.3019i 1.78719i 0.448870 + 0.893597i 0.351827π0.351827\pi
−0.448870 + 0.893597i 0.648173π0.648173\pi
762762 0 0
763763 11.1878i 0.405025i
764764 0 0
765765 0 0
766766 0 0
767767 35.6647i 1.28778i
768768 0 0
769769 25.6155 0.923720 0.461860 0.886953i 0.347182π-0.347182\pi
0.461860 + 0.886953i 0.347182π0.347182\pi
770770 0 0
771771 0 0
772772 0 0
773773 2.27678i 0.0818901i 0.999161 + 0.0409450i 0.0130369π0.0130369\pi
−0.999161 + 0.0409450i 0.986963π0.986963\pi
774774 0 0
775775 41.3686 3.64162i 1.48600 0.130811i
776776 0 0
777777 0 0
778778 0 0
779779 18.2107i 0.652465i
780780 0 0
781781 25.9396i 0.928192i
782782 0 0
783783 0 0
784784 0 0
785785 4.63252 + 4.24264i 0.165342 + 0.151426i
786786 0 0
787787 19.9230i 0.710177i 0.934833 + 0.355088i 0.115549π0.115549\pi
−0.934833 + 0.355088i 0.884451π0.884451\pi
788788 0 0
789789 0 0
790790 0 0
791791 −11.7460 −0.417641
792792 0 0
793793 0 0
794794 0 0
795795 0 0
796796 0 0
797797 15.6829i 0.555516i 0.960651 + 0.277758i 0.0895913π0.0895913\pi
−0.960651 + 0.277758i 0.910409π0.910409\pi
798798 0 0
799799 16.6114i 0.587670i
800800 0 0
801801 0 0
802802 0 0
803803 12.3534 0.435942
804804 0 0
805805 4.79741 5.23827i 0.169087 0.184625i
806806 0 0
807807 0 0
808808 0 0
809809 20.6695i 0.726700i −0.931653 0.363350i 0.881633π-0.881633\pi
0.931653 0.363350i 0.118367π-0.118367\pi
810810 0 0
811811 49.4773 1.73738 0.868691 0.495354i 0.164962π-0.164962\pi
0.868691 + 0.495354i 0.164962π0.164962\pi
812812 0 0
813813 0 0
814814 0 0
815815 −23.4921 + 25.6509i −0.822892 + 0.898513i
816816 0 0
817817 24.2905i 0.849818i
818818 0 0
819819 0 0
820820 0 0
821821 −12.1521 −0.424110 −0.212055 0.977258i 0.568016π-0.568016\pi
−0.212055 + 0.977258i 0.568016π0.568016\pi
822822 0 0
823823 28.6692 0.999345 0.499673 0.866214i 0.333454π-0.333454\pi
0.499673 + 0.866214i 0.333454π0.333454\pi
824824 0 0
825825 0 0
826826 0 0
827827 −39.1746 −1.36224 −0.681118 0.732174i 0.738506π-0.738506\pi
−0.681118 + 0.732174i 0.738506π0.738506\pi
828828 0 0
829829 4.66410i 0.161991i −0.996714 0.0809954i 0.974190π-0.974190\pi
0.996714 0.0809954i 0.0258099π-0.0258099\pi
830830 0 0
831831 0 0
832832 0 0
833833 −9.45514 −0.327601
834834 0 0
835835 14.2462 15.5554i 0.493010 0.538316i
836836 0 0
837837 0 0
838838 0 0
839839 −24.9381 −0.860959 −0.430479 0.902600i 0.641656π-0.641656\pi
−0.430479 + 0.902600i 0.641656π0.641656\pi
840840 0 0
841841 42.3693 1.46101
842842 0 0
843843 0 0
844844 0 0
845845 3.09501 + 2.83453i 0.106472 + 0.0975108i
846846 0 0
847847 −5.73384 −0.197017
848848 0 0
849849 0 0
850850 0 0
851851 25.8040i 0.884551i
852852 0 0
853853 −45.5249 −1.55874 −0.779371 0.626563i 0.784461π-0.784461\pi
−0.779371 + 0.626563i 0.784461π0.784461\pi
854854 0 0
855855 0 0
856856 0 0
857857 40.7188 1.39093 0.695464 0.718561i 0.255199π-0.255199\pi
0.695464 + 0.718561i 0.255199π0.255199\pi
858858 0 0
859859 33.7538 1.15166 0.575832 0.817568i 0.304678π-0.304678\pi
0.575832 + 0.817568i 0.304678π0.304678\pi
860860 0 0
861861 0 0
862862 0 0
863863 45.6786i 1.55492i −0.628935 0.777458i 0.716509π-0.716509\pi
0.628935 0.777458i 0.283491π-0.283491\pi
864864 0 0
865865 2.56155 2.79695i 0.0870954 0.0950991i
866866 0 0
867867 0 0
868868 0 0
869869 2.25801 0.0765978
870870 0 0
871871 40.5061i 1.37250i
872872 0 0
873873 0 0
874874 0 0
875875 −6.36679 + 8.31118i −0.215237 + 0.280969i
876876 0 0
877877 46.5766 1.57278 0.786389 0.617731i 0.211948π-0.211948\pi
0.786389 + 0.617731i 0.211948π0.211948\pi
878878 0 0
879879 0 0
880880 0 0
881881 5.83095i 0.196450i 0.995164 + 0.0982249i 0.0313164π0.0313164\pi
−0.995164 + 0.0982249i 0.968684π0.968684\pi
882882 0 0
883883 0 0 1.00000 00
−1.00000 π\pi
884884 0 0
885885 0 0
886886 0 0
887887 16.2177i 0.544538i −0.962221 0.272269i 0.912226π-0.912226\pi
0.962221 0.272269i 0.0877741π-0.0877741\pi
888888 0 0
889889 4.38447 0.147050
890890 0 0
891891 0 0
892892 0 0
893893 33.5968i 1.12427i
894894 0 0
895895 −12.4041 + 13.5440i −0.414623 + 0.452725i
896896 0 0
897897 0 0
898898 0 0
899899 70.1670i 2.34020i
900900 0 0
901901 7.85741i 0.261768i
902902 0 0
903903 0 0
904904 0 0
905905 −7.04383 + 7.69113i −0.234145 + 0.255662i
906906 0 0
907907 16.5129i 0.548300i 0.961687 + 0.274150i 0.0883965π0.0883965\pi
−0.961687 + 0.274150i 0.911603π0.911603\pi
908908 0 0
909909 0 0
910910 0 0
911911 36.6842 1.21540 0.607700 0.794167i 0.292092π-0.292092\pi
0.607700 + 0.794167i 0.292092π0.292092\pi
912912 0 0
913913 31.1107i 1.02962i
914914 0 0
915915 0 0
916916 0 0
917917 0.580639i 0.0191744i
918918 0 0
919919 30.1554i 0.994735i −0.867540 0.497368i 0.834300π-0.834300\pi
0.867540 0.497368i 0.165700π-0.165700\pi
920920 0 0
921921 0 0
922922 0 0
923923 −39.1746 −1.28945
924924 0 0
925925 3.33513 + 37.8869i 0.109658 + 1.24571i
926926 0 0
927927 0 0
928928 0 0
929929 3.00252i 0.0985096i 0.998786 + 0.0492548i 0.0156846π0.0156846\pi
−0.998786 + 0.0492548i 0.984315π0.984315\pi
930930 0 0
931931 −19.1231 −0.626734
932932 0 0
933933 0 0
934934 0 0
935935 5.15002 5.62329i 0.168424 0.183901i
936936 0 0
937937 0 0 1.00000 00
−1.00000 π\pi
938938 0 0
939939 0 0
940940 0 0
941941 3.29801 0.107512 0.0537561 0.998554i 0.482881π-0.482881\pi
0.0537561 + 0.998554i 0.482881π0.482881\pi
942942 0 0
943943 −19.7802 −0.644133
944944 0 0
945945 0 0
946946 0 0
947947 32.9979 1.07229 0.536144 0.844126i 0.319880π-0.319880\pi
0.536144 + 0.844126i 0.319880π0.319880\pi
948948 0 0
949949 18.6564i 0.605612i
950950 0 0
951951 0 0
952952 0 0
953953 −12.5435 −0.406323 −0.203162 0.979145i 0.565122π-0.565122\pi
−0.203162 + 0.979145i 0.565122π0.565122\pi
954954 0 0
955955 −21.7538 19.9230i −0.703936 0.644692i
956956 0 0
957957 0 0
958958 0 0
959959 −1.44600 −0.0466939
960960 0 0
961961 −37.9848 −1.22532
962962 0 0
963963 0 0
964964 0 0
965965 −35.2381 + 38.4764i −1.13436 + 1.23860i
966966 0 0
967967 −15.0981 −0.485522 −0.242761 0.970086i 0.578053π-0.578053\pi
−0.242761 + 0.970086i 0.578053π0.578053\pi
968968 0 0
969969 0 0
970970 0 0
971971 19.8753i 0.637829i 0.947783 + 0.318915i 0.103318π0.103318\pi
−0.947783 + 0.318915i 0.896682π0.896682\pi
972972 0 0
973973 −11.2371 −0.360245
974974 0 0
975975 0 0
976976 0 0
977977 37.6305 1.20390 0.601952 0.798532i 0.294390π-0.294390\pi
0.601952 + 0.798532i 0.294390π0.294390\pi
978978 0 0
979979 −28.8769 −0.922910
980980 0 0
981981 0 0
982982 0 0
983983 53.0438i 1.69183i 0.533315 + 0.845917i 0.320946π0.320946\pi
−0.533315 + 0.845917i 0.679054π0.679054\pi
984984 0 0
985985 −7.43845 + 8.12201i −0.237009 + 0.258789i
986986 0 0
987987 0 0
988988 0 0
989989 −26.3841 −0.838966
990990 0 0
991991 17.6339i 0.560159i −0.959977 0.280080i 0.909639π-0.909639\pi
0.959977 0.280080i 0.0903609π-0.0903609\pi
992992 0 0
993993 0 0
994994 0 0
995995 26.6311 29.0784i 0.844264 0.921848i
996996 0 0
997997 25.5141 0.808039 0.404019 0.914750i 0.367613π-0.367613\pi
0.404019 + 0.914750i 0.367613π0.367613\pi
998998 0 0
999999 0 0
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 1440.2.m.c.719.5 16
3.2 odd 2 inner 1440.2.m.c.719.11 16
4.3 odd 2 360.2.m.c.179.13 yes 16
5.2 odd 4 7200.2.b.i.4751.8 16
5.3 odd 4 7200.2.b.i.4751.11 16
5.4 even 2 inner 1440.2.m.c.719.8 16
8.3 odd 2 inner 1440.2.m.c.719.12 16
8.5 even 2 360.2.m.c.179.16 yes 16
12.11 even 2 360.2.m.c.179.4 yes 16
15.2 even 4 7200.2.b.i.4751.5 16
15.8 even 4 7200.2.b.i.4751.10 16
15.14 odd 2 inner 1440.2.m.c.719.10 16
20.3 even 4 1800.2.b.g.251.5 16
20.7 even 4 1800.2.b.g.251.12 16
20.19 odd 2 360.2.m.c.179.3 yes 16
24.5 odd 2 360.2.m.c.179.1 16
24.11 even 2 inner 1440.2.m.c.719.6 16
40.3 even 4 7200.2.b.i.4751.7 16
40.13 odd 4 1800.2.b.g.251.10 16
40.19 odd 2 inner 1440.2.m.c.719.9 16
40.27 even 4 7200.2.b.i.4751.12 16
40.29 even 2 360.2.m.c.179.2 yes 16
40.37 odd 4 1800.2.b.g.251.7 16
60.23 odd 4 1800.2.b.g.251.11 16
60.47 odd 4 1800.2.b.g.251.6 16
60.59 even 2 360.2.m.c.179.14 yes 16
120.29 odd 2 360.2.m.c.179.15 yes 16
120.53 even 4 1800.2.b.g.251.8 16
120.59 even 2 inner 1440.2.m.c.719.7 16
120.77 even 4 1800.2.b.g.251.9 16
120.83 odd 4 7200.2.b.i.4751.6 16
120.107 odd 4 7200.2.b.i.4751.9 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.m.c.179.1 16 24.5 odd 2
360.2.m.c.179.2 yes 16 40.29 even 2
360.2.m.c.179.3 yes 16 20.19 odd 2
360.2.m.c.179.4 yes 16 12.11 even 2
360.2.m.c.179.13 yes 16 4.3 odd 2
360.2.m.c.179.14 yes 16 60.59 even 2
360.2.m.c.179.15 yes 16 120.29 odd 2
360.2.m.c.179.16 yes 16 8.5 even 2
1440.2.m.c.719.5 16 1.1 even 1 trivial
1440.2.m.c.719.6 16 24.11 even 2 inner
1440.2.m.c.719.7 16 120.59 even 2 inner
1440.2.m.c.719.8 16 5.4 even 2 inner
1440.2.m.c.719.9 16 40.19 odd 2 inner
1440.2.m.c.719.10 16 15.14 odd 2 inner
1440.2.m.c.719.11 16 3.2 odd 2 inner
1440.2.m.c.719.12 16 8.3 odd 2 inner
1800.2.b.g.251.5 16 20.3 even 4
1800.2.b.g.251.6 16 60.47 odd 4
1800.2.b.g.251.7 16 40.37 odd 4
1800.2.b.g.251.8 16 120.53 even 4
1800.2.b.g.251.9 16 120.77 even 4
1800.2.b.g.251.10 16 40.13 odd 4
1800.2.b.g.251.11 16 60.23 odd 4
1800.2.b.g.251.12 16 20.7 even 4
7200.2.b.i.4751.5 16 15.2 even 4
7200.2.b.i.4751.6 16 120.83 odd 4
7200.2.b.i.4751.7 16 40.3 even 4
7200.2.b.i.4751.8 16 5.2 odd 4
7200.2.b.i.4751.9 16 120.107 odd 4
7200.2.b.i.4751.10 16 15.8 even 4
7200.2.b.i.4751.11 16 5.3 odd 4
7200.2.b.i.4751.12 16 40.27 even 4