Properties

Label 2300.2.c.f.1749.1
Level 23002300
Weight 22
Character 2300.1749
Analytic conductor 18.36618.366
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] = [2300,2,Mod(1749,2300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2300, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2300.1749");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 2300=225223 2300 = 2^{2} \cdot 5^{2} \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2300.c (of order 22, degree 11, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 18.365592464918.3655924649
Analytic rank: 00
Dimension: 22
Coefficient field: Q(i)\Q(i)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2+1 x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 92)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1749.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 2300.1749
Dual form 2300.2.c.f.1749.2

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) == q1.00000iq3+2.00000iq7+2.00000q9+1.00000iq136.00000iq172.00000q19+2.00000q21+1.00000iq235.00000iq27+3.00000q29+5.00000q31+8.00000iq37+1.00000q39+3.00000q418.00000iq43+9.00000iq47+3.00000q496.00000q516.00000iq53+2.00000iq57+12.0000q59+14.0000q61+4.00000iq63+8.00000iq67+1.00000q6915.0000q71+7.00000iq73+10.0000q79+1.00000q816.00000iq833.00000iq872.00000q915.00000iq9310.0000iq97+O(q100)q-1.00000i q^{3} +2.00000i q^{7} +2.00000 q^{9} +1.00000i q^{13} -6.00000i q^{17} -2.00000 q^{19} +2.00000 q^{21} +1.00000i q^{23} -5.00000i q^{27} +3.00000 q^{29} +5.00000 q^{31} +8.00000i q^{37} +1.00000 q^{39} +3.00000 q^{41} -8.00000i q^{43} +9.00000i q^{47} +3.00000 q^{49} -6.00000 q^{51} -6.00000i q^{53} +2.00000i q^{57} +12.0000 q^{59} +14.0000 q^{61} +4.00000i q^{63} +8.00000i q^{67} +1.00000 q^{69} -15.0000 q^{71} +7.00000i q^{73} +10.0000 q^{79} +1.00000 q^{81} -6.00000i q^{83} -3.00000i q^{87} -2.00000 q^{91} -5.00000i q^{93} -10.0000i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+4q94q19+4q21+6q29+10q31+2q39+6q41+6q4912q51+24q59+28q61+2q6930q71+20q79+2q814q91+O(q100) 2 q + 4 q^{9} - 4 q^{19} + 4 q^{21} + 6 q^{29} + 10 q^{31} + 2 q^{39} + 6 q^{41} + 6 q^{49} - 12 q^{51} + 24 q^{59} + 28 q^{61} + 2 q^{69} - 30 q^{71} + 20 q^{79} + 2 q^{81} - 4 q^{91}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2300Z)×\left(\mathbb{Z}/2300\mathbb{Z}\right)^\times.

nn 277277 11511151 12011201
χ(n)\chi(n) 1-1 11 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 − 1.00000i − 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 2.00000i 0.755929i 0.925820 + 0.377964i 0.123376π0.123376\pi
−0.925820 + 0.377964i 0.876624π0.876624\pi
88 0 0
99 2.00000 0.666667
1010 0 0
1111 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1212 0 0
1313 1.00000i 0.277350i 0.990338 + 0.138675i 0.0442844π0.0442844\pi
−0.990338 + 0.138675i 0.955716π0.955716\pi
1414 0 0
1515 0 0
1616 0 0
1717 − 6.00000i − 1.45521i −0.685994 0.727607i 0.740633π-0.740633\pi
0.685994 0.727607i 0.259367π-0.259367\pi
1818 0 0
1919 −2.00000 −0.458831 −0.229416 0.973329i 0.573682π-0.573682\pi
−0.229416 + 0.973329i 0.573682π0.573682\pi
2020 0 0
2121 2.00000 0.436436
2222 0 0
2323 1.00000i 0.208514i
2424 0 0
2525 0 0
2626 0 0
2727 − 5.00000i − 0.962250i
2828 0 0
2929 3.00000 0.557086 0.278543 0.960424i 0.410149π-0.410149\pi
0.278543 + 0.960424i 0.410149π0.410149\pi
3030 0 0
3131 5.00000 0.898027 0.449013 0.893525i 0.351776π-0.351776\pi
0.449013 + 0.893525i 0.351776π0.351776\pi
3232 0 0
3333 0 0
3434 0 0
3535 0 0
3636 0 0
3737 8.00000i 1.31519i 0.753371 + 0.657596i 0.228427π0.228427\pi
−0.753371 + 0.657596i 0.771573π0.771573\pi
3838 0 0
3939 1.00000 0.160128
4040 0 0
4141 3.00000 0.468521 0.234261 0.972174i 0.424733π-0.424733\pi
0.234261 + 0.972174i 0.424733π0.424733\pi
4242 0 0
4343 − 8.00000i − 1.21999i −0.792406 0.609994i 0.791172π-0.791172\pi
0.792406 0.609994i 0.208828π-0.208828\pi
4444 0 0
4545 0 0
4646 0 0
4747 9.00000i 1.31278i 0.754420 + 0.656392i 0.227918π0.227918\pi
−0.754420 + 0.656392i 0.772082π0.772082\pi
4848 0 0
4949 3.00000 0.428571
5050 0 0
5151 −6.00000 −0.840168
5252 0 0
5353 − 6.00000i − 0.824163i −0.911147 0.412082i 0.864802π-0.864802\pi
0.911147 0.412082i 0.135198π-0.135198\pi
5454 0 0
5555 0 0
5656 0 0
5757 2.00000i 0.264906i
5858 0 0
5959 12.0000 1.56227 0.781133 0.624364i 0.214642π-0.214642\pi
0.781133 + 0.624364i 0.214642π0.214642\pi
6060 0 0
6161 14.0000 1.79252 0.896258 0.443533i 0.146275π-0.146275\pi
0.896258 + 0.443533i 0.146275π0.146275\pi
6262 0 0
6363 4.00000i 0.503953i
6464 0 0
6565 0 0
6666 0 0
6767 8.00000i 0.977356i 0.872464 + 0.488678i 0.162521π0.162521\pi
−0.872464 + 0.488678i 0.837479π0.837479\pi
6868 0 0
6969 1.00000 0.120386
7070 0 0
7171 −15.0000 −1.78017 −0.890086 0.455792i 0.849356π-0.849356\pi
−0.890086 + 0.455792i 0.849356π0.849356\pi
7272 0 0
7373 7.00000i 0.819288i 0.912245 + 0.409644i 0.134347π0.134347\pi
−0.912245 + 0.409644i 0.865653π0.865653\pi
7474 0 0
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 10.0000 1.12509 0.562544 0.826767i 0.309823π-0.309823\pi
0.562544 + 0.826767i 0.309823π0.309823\pi
8080 0 0
8181 1.00000 0.111111
8282 0 0
8383 − 6.00000i − 0.658586i −0.944228 0.329293i 0.893190π-0.893190\pi
0.944228 0.329293i 0.106810π-0.106810\pi
8484 0 0
8585 0 0
8686 0 0
8787 − 3.00000i − 0.321634i
8888 0 0
8989 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
9090 0 0
9191 −2.00000 −0.209657
9292 0 0
9393 − 5.00000i − 0.518476i
9494 0 0
9595 0 0
9696 0 0
9797 − 10.0000i − 1.01535i −0.861550 0.507673i 0.830506π-0.830506\pi
0.861550 0.507673i 0.169494π-0.169494\pi
9898 0 0
9999 0 0
100100 0 0
101101 6.00000 0.597022 0.298511 0.954406i 0.403510π-0.403510\pi
0.298511 + 0.954406i 0.403510π0.403510\pi
102102 0 0
103103 − 2.00000i − 0.197066i −0.995134 0.0985329i 0.968585π-0.968585\pi
0.995134 0.0985329i 0.0314150π-0.0314150\pi
104104 0 0
105105 0 0
106106 0 0
107107 − 6.00000i − 0.580042i −0.957020 0.290021i 0.906338π-0.906338\pi
0.957020 0.290021i 0.0936623π-0.0936623\pi
108108 0 0
109109 16.0000 1.53252 0.766261 0.642529i 0.222115π-0.222115\pi
0.766261 + 0.642529i 0.222115π0.222115\pi
110110 0 0
111111 8.00000 0.759326
112112 0 0
113113 − 18.0000i − 1.69330i −0.532152 0.846649i 0.678617π-0.678617\pi
0.532152 0.846649i 0.321383π-0.321383\pi
114114 0 0
115115 0 0
116116 0 0
117117 2.00000i 0.184900i
118118 0 0
119119 12.0000 1.10004
120120 0 0
121121 −11.0000 −1.00000
122122 0 0
123123 − 3.00000i − 0.270501i
124124 0 0
125125 0 0
126126 0 0
127127 11.0000i 0.976092i 0.872818 + 0.488046i 0.162290π0.162290\pi
−0.872818 + 0.488046i 0.837710π0.837710\pi
128128 0 0
129129 −8.00000 −0.704361
130130 0 0
131131 21.0000 1.83478 0.917389 0.397991i 0.130293π-0.130293\pi
0.917389 + 0.397991i 0.130293π0.130293\pi
132132 0 0
133133 − 4.00000i − 0.346844i
134134 0 0
135135 0 0
136136 0 0
137137 − 12.0000i − 1.02523i −0.858619 0.512615i 0.828677π-0.828677\pi
0.858619 0.512615i 0.171323π-0.171323\pi
138138 0 0
139139 −11.0000 −0.933008 −0.466504 0.884519i 0.654487π-0.654487\pi
−0.466504 + 0.884519i 0.654487π0.654487\pi
140140 0 0
141141 9.00000 0.757937
142142 0 0
143143 0 0
144144 0 0
145145 0 0
146146 0 0
147147 − 3.00000i − 0.247436i
148148 0 0
149149 −6.00000 −0.491539 −0.245770 0.969328i 0.579041π-0.579041\pi
−0.245770 + 0.969328i 0.579041π0.579041\pi
150150 0 0
151151 −7.00000 −0.569652 −0.284826 0.958579i 0.591936π-0.591936\pi
−0.284826 + 0.958579i 0.591936π0.591936\pi
152152 0 0
153153 − 12.0000i − 0.970143i
154154 0 0
155155 0 0
156156 0 0
157157 − 4.00000i − 0.319235i −0.987179 0.159617i 0.948974π-0.948974\pi
0.987179 0.159617i 0.0510260π-0.0510260\pi
158158 0 0
159159 −6.00000 −0.475831
160160 0 0
161161 −2.00000 −0.157622
162162 0 0
163163 1.00000i 0.0783260i 0.999233 + 0.0391630i 0.0124692π0.0124692\pi
−0.999233 + 0.0391630i 0.987531π0.987531\pi
164164 0 0
165165 0 0
166166 0 0
167167 12.0000i 0.928588i 0.885681 + 0.464294i 0.153692π0.153692\pi
−0.885681 + 0.464294i 0.846308π0.846308\pi
168168 0 0
169169 12.0000 0.923077
170170 0 0
171171 −4.00000 −0.305888
172172 0 0
173173 − 6.00000i − 0.456172i −0.973641 0.228086i 0.926753π-0.926753\pi
0.973641 0.228086i 0.0732467π-0.0732467\pi
174174 0 0
175175 0 0
176176 0 0
177177 − 12.0000i − 0.901975i
178178 0 0
179179 9.00000 0.672692 0.336346 0.941739i 0.390809π-0.390809\pi
0.336346 + 0.941739i 0.390809π0.390809\pi
180180 0 0
181181 −16.0000 −1.18927 −0.594635 0.803996i 0.702704π-0.702704\pi
−0.594635 + 0.803996i 0.702704π0.702704\pi
182182 0 0
183183 − 14.0000i − 1.03491i
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 10.0000 0.727393
190190 0 0
191191 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
192192 0 0
193193 7.00000i 0.503871i 0.967744 + 0.251936i 0.0810671π0.0810671\pi
−0.967744 + 0.251936i 0.918933π0.918933\pi
194194 0 0
195195 0 0
196196 0 0
197197 − 15.0000i − 1.06871i −0.845262 0.534353i 0.820555π-0.820555\pi
0.845262 0.534353i 0.179445π-0.179445\pi
198198 0 0
199199 4.00000 0.283552 0.141776 0.989899i 0.454719π-0.454719\pi
0.141776 + 0.989899i 0.454719π0.454719\pi
200200 0 0
201201 8.00000 0.564276
202202 0 0
203203 6.00000i 0.421117i
204204 0 0
205205 0 0
206206 0 0
207207 2.00000i 0.139010i
208208 0 0
209209 0 0
210210 0 0
211211 −16.0000 −1.10149 −0.550743 0.834675i 0.685655π-0.685655\pi
−0.550743 + 0.834675i 0.685655π0.685655\pi
212212 0 0
213213 15.0000i 1.02778i
214214 0 0
215215 0 0
216216 0 0
217217 10.0000i 0.678844i
218218 0 0
219219 7.00000 0.473016
220220 0 0
221221 6.00000 0.403604
222222 0 0
223223 − 8.00000i − 0.535720i −0.963458 0.267860i 0.913684π-0.913684\pi
0.963458 0.267860i 0.0863164π-0.0863164\pi
224224 0 0
225225 0 0
226226 0 0
227227 18.0000i 1.19470i 0.801980 + 0.597351i 0.203780π0.203780\pi
−0.801980 + 0.597351i 0.796220π0.796220\pi
228228 0 0
229229 4.00000 0.264327 0.132164 0.991228i 0.457808π-0.457808\pi
0.132164 + 0.991228i 0.457808π0.457808\pi
230230 0 0
231231 0 0
232232 0 0
233233 9.00000i 0.589610i 0.955557 + 0.294805i 0.0952546π0.0952546\pi
−0.955557 + 0.294805i 0.904745π0.904745\pi
234234 0 0
235235 0 0
236236 0 0
237237 − 10.0000i − 0.649570i
238238 0 0
239239 −21.0000 −1.35838 −0.679189 0.733964i 0.737668π-0.737668\pi
−0.679189 + 0.733964i 0.737668π0.737668\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 − 16.0000i − 1.02640i
244244 0 0
245245 0 0
246246 0 0
247247 − 2.00000i − 0.127257i
248248 0 0
249249 −6.00000 −0.380235
250250 0 0
251251 −18.0000 −1.13615 −0.568075 0.822977i 0.692312π-0.692312\pi
−0.568075 + 0.822977i 0.692312π0.692312\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0 0
257257 27.0000i 1.68421i 0.539311 + 0.842107i 0.318685π0.318685\pi
−0.539311 + 0.842107i 0.681315π0.681315\pi
258258 0 0
259259 −16.0000 −0.994192
260260 0 0
261261 6.00000 0.371391
262262 0 0
263263 6.00000i 0.369976i 0.982741 + 0.184988i 0.0592246π0.0592246\pi
−0.982741 + 0.184988i 0.940775π0.940775\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 0 0
269269 15.0000 0.914566 0.457283 0.889321i 0.348823π-0.348823\pi
0.457283 + 0.889321i 0.348823π0.348823\pi
270270 0 0
271271 8.00000 0.485965 0.242983 0.970031i 0.421874π-0.421874\pi
0.242983 + 0.970031i 0.421874π0.421874\pi
272272 0 0
273273 2.00000i 0.121046i
274274 0 0
275275 0 0
276276 0 0
277277 − 19.0000i − 1.14160i −0.821089 0.570800i 0.806633π-0.806633\pi
0.821089 0.570800i 0.193367π-0.193367\pi
278278 0 0
279279 10.0000 0.598684
280280 0 0
281281 30.0000 1.78965 0.894825 0.446417i 0.147300π-0.147300\pi
0.894825 + 0.446417i 0.147300π0.147300\pi
282282 0 0
283283 4.00000i 0.237775i 0.992908 + 0.118888i 0.0379328π0.0379328\pi
−0.992908 + 0.118888i 0.962067π0.962067\pi
284284 0 0
285285 0 0
286286 0 0
287287 6.00000i 0.354169i
288288 0 0
289289 −19.0000 −1.11765
290290 0 0
291291 −10.0000 −0.586210
292292 0 0
293293 − 12.0000i − 0.701047i −0.936554 0.350524i 0.886004π-0.886004\pi
0.936554 0.350524i 0.113996π-0.113996\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 −1.00000 −0.0578315
300300 0 0
301301 16.0000 0.922225
302302 0 0
303303 − 6.00000i − 0.344691i
304304 0 0
305305 0 0
306306 0 0
307307 20.0000i 1.14146i 0.821138 + 0.570730i 0.193340π0.193340\pi
−0.821138 + 0.570730i 0.806660π0.806660\pi
308308 0 0
309309 −2.00000 −0.113776
310310 0 0
311311 −15.0000 −0.850572 −0.425286 0.905059i 0.639826π-0.639826\pi
−0.425286 + 0.905059i 0.639826π0.639826\pi
312312 0 0
313313 4.00000i 0.226093i 0.993590 + 0.113047i 0.0360610π0.0360610\pi
−0.993590 + 0.113047i 0.963939π0.963939\pi
314314 0 0
315315 0 0
316316 0 0
317317 − 18.0000i − 1.01098i −0.862832 0.505490i 0.831312π-0.831312\pi
0.862832 0.505490i 0.168688π-0.168688\pi
318318 0 0
319319 0 0
320320 0 0
321321 −6.00000 −0.334887
322322 0 0
323323 12.0000i 0.667698i
324324 0 0
325325 0 0
326326 0 0
327327 − 16.0000i − 0.884802i
328328 0 0
329329 −18.0000 −0.992372
330330 0 0
331331 −25.0000 −1.37412 −0.687062 0.726599i 0.741100π-0.741100\pi
−0.687062 + 0.726599i 0.741100π0.741100\pi
332332 0 0
333333 16.0000i 0.876795i
334334 0 0
335335 0 0
336336 0 0
337337 8.00000i 0.435788i 0.975972 + 0.217894i 0.0699187π0.0699187\pi
−0.975972 + 0.217894i 0.930081π0.930081\pi
338338 0 0
339339 −18.0000 −0.977626
340340 0 0
341341 0 0
342342 0 0
343343 20.0000i 1.07990i
344344 0 0
345345 0 0
346346 0 0
347347 − 12.0000i − 0.644194i −0.946707 0.322097i 0.895612π-0.895612\pi
0.946707 0.322097i 0.104388π-0.104388\pi
348348 0 0
349349 −29.0000 −1.55233 −0.776167 0.630527i 0.782839π-0.782839\pi
−0.776167 + 0.630527i 0.782839π0.782839\pi
350350 0 0
351351 5.00000 0.266880
352352 0 0
353353 27.0000i 1.43706i 0.695493 + 0.718532i 0.255186π0.255186\pi
−0.695493 + 0.718532i 0.744814π0.744814\pi
354354 0 0
355355 0 0
356356 0 0
357357 − 12.0000i − 0.635107i
358358 0 0
359359 30.0000 1.58334 0.791670 0.610949i 0.209212π-0.209212\pi
0.791670 + 0.610949i 0.209212π0.209212\pi
360360 0 0
361361 −15.0000 −0.789474
362362 0 0
363363 11.0000i 0.577350i
364364 0 0
365365 0 0
366366 0 0
367367 26.0000i 1.35719i 0.734513 + 0.678594i 0.237411π0.237411\pi
−0.734513 + 0.678594i 0.762589π0.762589\pi
368368 0 0
369369 6.00000 0.312348
370370 0 0
371371 12.0000 0.623009
372372 0 0
373373 − 20.0000i − 1.03556i −0.855514 0.517780i 0.826758π-0.826758\pi
0.855514 0.517780i 0.173242π-0.173242\pi
374374 0 0
375375 0 0
376376 0 0
377377 3.00000i 0.154508i
378378 0 0
379379 28.0000 1.43826 0.719132 0.694874i 0.244540π-0.244540\pi
0.719132 + 0.694874i 0.244540π0.244540\pi
380380 0 0
381381 11.0000 0.563547
382382 0 0
383383 36.0000i 1.83951i 0.392488 + 0.919757i 0.371614π0.371614\pi
−0.392488 + 0.919757i 0.628386π0.628386\pi
384384 0 0
385385 0 0
386386 0 0
387387 − 16.0000i − 0.813326i
388388 0 0
389389 36.0000 1.82527 0.912636 0.408773i 0.134043π-0.134043\pi
0.912636 + 0.408773i 0.134043π0.134043\pi
390390 0 0
391391 6.00000 0.303433
392392 0 0
393393 − 21.0000i − 1.05931i
394394 0 0
395395 0 0
396396 0 0
397397 11.0000i 0.552074i 0.961147 + 0.276037i 0.0890213π0.0890213\pi
−0.961147 + 0.276037i 0.910979π0.910979\pi
398398 0 0
399399 −4.00000 −0.200250
400400 0 0
401401 24.0000 1.19850 0.599251 0.800561i 0.295465π-0.295465\pi
0.599251 + 0.800561i 0.295465π0.295465\pi
402402 0 0
403403 5.00000i 0.249068i
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 −17.0000 −0.840596 −0.420298 0.907386i 0.638074π-0.638074\pi
−0.420298 + 0.907386i 0.638074π0.638074\pi
410410 0 0
411411 −12.0000 −0.591916
412412 0 0
413413 24.0000i 1.18096i
414414 0 0
415415 0 0
416416 0 0
417417 11.0000i 0.538672i
418418 0 0
419419 −36.0000 −1.75872 −0.879358 0.476162i 0.842028π-0.842028\pi
−0.879358 + 0.476162i 0.842028π0.842028\pi
420420 0 0
421421 2.00000 0.0974740 0.0487370 0.998812i 0.484480π-0.484480\pi
0.0487370 + 0.998812i 0.484480π0.484480\pi
422422 0 0
423423 18.0000i 0.875190i
424424 0 0
425425 0 0
426426 0 0
427427 28.0000i 1.35501i
428428 0 0
429429 0 0
430430 0 0
431431 12.0000 0.578020 0.289010 0.957326i 0.406674π-0.406674\pi
0.289010 + 0.957326i 0.406674π0.406674\pi
432432 0 0
433433 16.0000i 0.768911i 0.923144 + 0.384455i 0.125611π0.125611\pi
−0.923144 + 0.384455i 0.874389π0.874389\pi
434434 0 0
435435 0 0
436436 0 0
437437 − 2.00000i − 0.0956730i
438438 0 0
439439 −35.0000 −1.67046 −0.835229 0.549902i 0.814665π-0.814665\pi
−0.835229 + 0.549902i 0.814665π0.814665\pi
440440 0 0
441441 6.00000 0.285714
442442 0 0
443443 − 21.0000i − 0.997740i −0.866677 0.498870i 0.833748π-0.833748\pi
0.866677 0.498870i 0.166252π-0.166252\pi
444444 0 0
445445 0 0
446446 0 0
447447 6.00000i 0.283790i
448448 0 0
449449 −6.00000 −0.283158 −0.141579 0.989927i 0.545218π-0.545218\pi
−0.141579 + 0.989927i 0.545218π0.545218\pi
450450 0 0
451451 0 0
452452 0 0
453453 7.00000i 0.328889i
454454 0 0
455455 0 0
456456 0 0
457457 − 10.0000i − 0.467780i −0.972263 0.233890i 0.924854π-0.924854\pi
0.972263 0.233890i 0.0751456π-0.0751456\pi
458458 0 0
459459 −30.0000 −1.40028
460460 0 0
461461 −27.0000 −1.25752 −0.628758 0.777601i 0.716436π-0.716436\pi
−0.628758 + 0.777601i 0.716436π0.716436\pi
462462 0 0
463463 16.0000i 0.743583i 0.928316 + 0.371792i 0.121256π0.121256\pi
−0.928316 + 0.371792i 0.878744π0.878744\pi
464464 0 0
465465 0 0
466466 0 0
467467 − 30.0000i − 1.38823i −0.719862 0.694117i 0.755795π-0.755795\pi
0.719862 0.694117i 0.244205π-0.244205\pi
468468 0 0
469469 −16.0000 −0.738811
470470 0 0
471471 −4.00000 −0.184310
472472 0 0
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 − 12.0000i − 0.549442i
478478 0 0
479479 −42.0000 −1.91903 −0.959514 0.281659i 0.909115π-0.909115\pi
−0.959514 + 0.281659i 0.909115π0.909115\pi
480480 0 0
481481 −8.00000 −0.364769
482482 0 0
483483 2.00000i 0.0910032i
484484 0 0
485485 0 0
486486 0 0
487487 23.0000i 1.04223i 0.853487 + 0.521115i 0.174484π0.174484\pi
−0.853487 + 0.521115i 0.825516π0.825516\pi
488488 0 0
489489 1.00000 0.0452216
490490 0 0
491491 3.00000 0.135388 0.0676941 0.997706i 0.478436π-0.478436\pi
0.0676941 + 0.997706i 0.478436π0.478436\pi
492492 0 0
493493 − 18.0000i − 0.810679i
494494 0 0
495495 0 0
496496 0 0
497497 − 30.0000i − 1.34568i
498498 0 0
499499 −5.00000 −0.223831 −0.111915 0.993718i 0.535699π-0.535699\pi
−0.111915 + 0.993718i 0.535699π0.535699\pi
500500 0 0
501501 12.0000 0.536120
502502 0 0
503503 − 6.00000i − 0.267527i −0.991013 0.133763i 0.957294π-0.957294\pi
0.991013 0.133763i 0.0427062π-0.0427062\pi
504504 0 0
505505 0 0
506506 0 0
507507 − 12.0000i − 0.532939i
508508 0 0
509509 3.00000 0.132973 0.0664863 0.997787i 0.478821π-0.478821\pi
0.0664863 + 0.997787i 0.478821π0.478821\pi
510510 0 0
511511 −14.0000 −0.619324
512512 0 0
513513 10.0000i 0.441511i
514514 0 0
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 −6.00000 −0.263371
520520 0 0
521521 −24.0000 −1.05146 −0.525730 0.850652i 0.676208π-0.676208\pi
−0.525730 + 0.850652i 0.676208π0.676208\pi
522522 0 0
523523 − 38.0000i − 1.66162i −0.556553 0.830812i 0.687876π-0.687876\pi
0.556553 0.830812i 0.312124π-0.312124\pi
524524 0 0
525525 0 0
526526 0 0
527527 − 30.0000i − 1.30682i
528528 0 0
529529 −1.00000 −0.0434783
530530 0 0
531531 24.0000 1.04151
532532 0 0
533533 3.00000i 0.129944i
534534 0 0
535535 0 0
536536 0 0
537537 − 9.00000i − 0.388379i
538538 0 0
539539 0 0
540540 0 0
541541 −7.00000 −0.300954 −0.150477 0.988614i 0.548081π-0.548081\pi
−0.150477 + 0.988614i 0.548081π0.548081\pi
542542 0 0
543543 16.0000i 0.686626i
544544 0 0
545545 0 0
546546 0 0
547547 − 1.00000i − 0.0427569i −0.999771 0.0213785i 0.993195π-0.993195\pi
0.999771 0.0213785i 0.00680549π-0.00680549\pi
548548 0 0
549549 28.0000 1.19501
550550 0 0
551551 −6.00000 −0.255609
552552 0 0
553553 20.0000i 0.850487i
554554 0 0
555555 0 0
556556 0 0
557557 24.0000i 1.01691i 0.861088 + 0.508456i 0.169784π0.169784\pi
−0.861088 + 0.508456i 0.830216π0.830216\pi
558558 0 0
559559 8.00000 0.338364
560560 0 0
561561 0 0
562562 0 0
563563 12.0000i 0.505740i 0.967500 + 0.252870i 0.0813744π0.0813744\pi
−0.967500 + 0.252870i 0.918626π0.918626\pi
564564 0 0
565565 0 0
566566 0 0
567567 2.00000i 0.0839921i
568568 0 0
569569 −24.0000 −1.00613 −0.503066 0.864248i 0.667795π-0.667795\pi
−0.503066 + 0.864248i 0.667795π0.667795\pi
570570 0 0
571571 −34.0000 −1.42286 −0.711428 0.702759i 0.751951π-0.751951\pi
−0.711428 + 0.702759i 0.751951π0.751951\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 0 0
577577 − 7.00000i − 0.291414i −0.989328 0.145707i 0.953454π-0.953454\pi
0.989328 0.145707i 0.0465456π-0.0465456\pi
578578 0 0
579579 7.00000 0.290910
580580 0 0
581581 12.0000 0.497844
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 21.0000i 0.866763i 0.901211 + 0.433381i 0.142680π0.142680\pi
−0.901211 + 0.433381i 0.857320π0.857320\pi
588588 0 0
589589 −10.0000 −0.412043
590590 0 0
591591 −15.0000 −0.617018
592592 0 0
593593 42.0000i 1.72473i 0.506284 + 0.862367i 0.331019π0.331019\pi
−0.506284 + 0.862367i 0.668981π0.668981\pi
594594 0 0
595595 0 0
596596 0 0
597597 − 4.00000i − 0.163709i
598598 0 0
599599 −24.0000 −0.980613 −0.490307 0.871550i 0.663115π-0.663115\pi
−0.490307 + 0.871550i 0.663115π0.663115\pi
600600 0 0
601601 −19.0000 −0.775026 −0.387513 0.921864i 0.626666π-0.626666\pi
−0.387513 + 0.921864i 0.626666π0.626666\pi
602602 0 0
603603 16.0000i 0.651570i
604604 0 0
605605 0 0
606606 0 0
607607 8.00000i 0.324710i 0.986732 + 0.162355i 0.0519090π0.0519090\pi
−0.986732 + 0.162355i 0.948091π0.948091\pi
608608 0 0
609609 6.00000 0.243132
610610 0 0
611611 −9.00000 −0.364101
612612 0 0
613613 − 26.0000i − 1.05013i −0.851062 0.525065i 0.824041π-0.824041\pi
0.851062 0.525065i 0.175959π-0.175959\pi
614614 0 0
615615 0 0
616616 0 0
617617 − 18.0000i − 0.724653i −0.932051 0.362326i 0.881983π-0.881983\pi
0.932051 0.362326i 0.118017π-0.118017\pi
618618 0 0
619619 −20.0000 −0.803868 −0.401934 0.915669i 0.631662π-0.631662\pi
−0.401934 + 0.915669i 0.631662π0.631662\pi
620620 0 0
621621 5.00000 0.200643
622622 0 0
623623 0 0
624624 0 0
625625 0 0
626626 0 0
627627 0 0
628628 0 0
629629 48.0000 1.91389
630630 0 0
631631 −40.0000 −1.59237 −0.796187 0.605050i 0.793153π-0.793153\pi
−0.796187 + 0.605050i 0.793153π0.793153\pi
632632 0 0
633633 16.0000i 0.635943i
634634 0 0
635635 0 0
636636 0 0
637637 3.00000i 0.118864i
638638 0 0
639639 −30.0000 −1.18678
640640 0 0
641641 24.0000 0.947943 0.473972 0.880540i 0.342820π-0.342820\pi
0.473972 + 0.880540i 0.342820π0.342820\pi
642642 0 0
643643 4.00000i 0.157745i 0.996885 + 0.0788723i 0.0251319π0.0251319\pi
−0.996885 + 0.0788723i 0.974868π0.974868\pi
644644 0 0
645645 0 0
646646 0 0
647647 33.0000i 1.29736i 0.761060 + 0.648682i 0.224679π0.224679\pi
−0.761060 + 0.648682i 0.775321π0.775321\pi
648648 0 0
649649 0 0
650650 0 0
651651 10.0000 0.391931
652652 0 0
653653 − 27.0000i − 1.05659i −0.849060 0.528296i 0.822831π-0.822831\pi
0.849060 0.528296i 0.177169π-0.177169\pi
654654 0 0
655655 0 0
656656 0 0
657657 14.0000i 0.546192i
658658 0 0
659659 −6.00000 −0.233727 −0.116863 0.993148i 0.537284π-0.537284\pi
−0.116863 + 0.993148i 0.537284π0.537284\pi
660660 0 0
661661 14.0000 0.544537 0.272268 0.962221i 0.412226π-0.412226\pi
0.272268 + 0.962221i 0.412226π0.412226\pi
662662 0 0
663663 − 6.00000i − 0.233021i
664664 0 0
665665 0 0
666666 0 0
667667 3.00000i 0.116160i
668668 0 0
669669 −8.00000 −0.309298
670670 0 0
671671 0 0
672672 0 0
673673 13.0000i 0.501113i 0.968102 + 0.250557i 0.0806136π0.0806136\pi
−0.968102 + 0.250557i 0.919386π0.919386\pi
674674 0 0
675675 0 0
676676 0 0
677677 18.0000i 0.691796i 0.938272 + 0.345898i 0.112426π0.112426\pi
−0.938272 + 0.345898i 0.887574π0.887574\pi
678678 0 0
679679 20.0000 0.767530
680680 0 0
681681 18.0000 0.689761
682682 0 0
683683 − 39.0000i − 1.49229i −0.665782 0.746147i 0.731902π-0.731902\pi
0.665782 0.746147i 0.268098π-0.268098\pi
684684 0 0
685685 0 0
686686 0 0
687687 − 4.00000i − 0.152610i
688688 0 0
689689 6.00000 0.228582
690690 0 0
691691 −28.0000 −1.06517 −0.532585 0.846376i 0.678779π-0.678779\pi
−0.532585 + 0.846376i 0.678779π0.678779\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 − 18.0000i − 0.681799i
698698 0 0
699699 9.00000 0.340411
700700 0 0
701701 30.0000 1.13308 0.566542 0.824033i 0.308281π-0.308281\pi
0.566542 + 0.824033i 0.308281π0.308281\pi
702702 0 0
703703 − 16.0000i − 0.603451i
704704 0 0
705705 0 0
706706 0 0
707707 12.0000i 0.451306i
708708 0 0
709709 −38.0000 −1.42712 −0.713560 0.700594i 0.752918π-0.752918\pi
−0.713560 + 0.700594i 0.752918π0.752918\pi
710710 0 0
711711 20.0000 0.750059
712712 0 0
713713 5.00000i 0.187251i
714714 0 0
715715 0 0
716716 0 0
717717 21.0000i 0.784259i
718718 0 0
719719 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
720720 0 0
721721 4.00000 0.148968
722722 0 0
723723 4.00000i 0.148762i
724724 0 0
725725 0 0
726726 0 0
727727 − 28.0000i − 1.03846i −0.854634 0.519231i 0.826218π-0.826218\pi
0.854634 0.519231i 0.173782π-0.173782\pi
728728 0 0
729729 −13.0000 −0.481481
730730 0 0
731731 −48.0000 −1.77534
732732 0 0
733733 22.0000i 0.812589i 0.913742 + 0.406294i 0.133179π0.133179\pi
−0.913742 + 0.406294i 0.866821π0.866821\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 25.0000 0.919640 0.459820 0.888012i 0.347914π-0.347914\pi
0.459820 + 0.888012i 0.347914π0.347914\pi
740740 0 0
741741 −2.00000 −0.0734718
742742 0 0
743743 − 6.00000i − 0.220119i −0.993925 0.110059i 0.964896π-0.964896\pi
0.993925 0.110059i 0.0351041π-0.0351041\pi
744744 0 0
745745 0 0
746746 0 0
747747 − 12.0000i − 0.439057i
748748 0 0
749749 12.0000 0.438470
750750 0 0
751751 −4.00000 −0.145962 −0.0729810 0.997333i 0.523251π-0.523251\pi
−0.0729810 + 0.997333i 0.523251π0.523251\pi
752752 0 0
753753 18.0000i 0.655956i
754754 0 0
755755 0 0
756756 0 0
757757 20.0000i 0.726912i 0.931611 + 0.363456i 0.118403π0.118403\pi
−0.931611 + 0.363456i 0.881597π0.881597\pi
758758 0 0
759759 0 0
760760 0 0
761761 −15.0000 −0.543750 −0.271875 0.962333i 0.587644π-0.587644\pi
−0.271875 + 0.962333i 0.587644π0.587644\pi
762762 0 0
763763 32.0000i 1.15848i
764764 0 0
765765 0 0
766766 0 0
767767 12.0000i 0.433295i
768768 0 0
769769 28.0000 1.00971 0.504853 0.863205i 0.331547π-0.331547\pi
0.504853 + 0.863205i 0.331547π0.331547\pi
770770 0 0
771771 27.0000 0.972381
772772 0 0
773773 − 24.0000i − 0.863220i −0.902060 0.431610i 0.857946π-0.857946\pi
0.902060 0.431610i 0.142054π-0.142054\pi
774774 0 0
775775 0 0
776776 0 0
777777 16.0000i 0.573997i
778778 0 0
779779 −6.00000 −0.214972
780780 0 0
781781 0 0
782782 0 0
783783 − 15.0000i − 0.536056i
784784 0 0
785785 0 0
786786 0 0
787787 − 40.0000i − 1.42585i −0.701242 0.712923i 0.747371π-0.747371\pi
0.701242 0.712923i 0.252629π-0.252629\pi
788788 0 0
789789 6.00000 0.213606
790790 0 0
791791 36.0000 1.28001
792792 0 0
793793 14.0000i 0.497155i
794794 0 0
795795 0 0
796796 0 0
797797 − 30.0000i − 1.06265i −0.847167 0.531327i 0.821693π-0.821693\pi
0.847167 0.531327i 0.178307π-0.178307\pi
798798 0 0
799799 54.0000 1.91038
800800 0 0
801801 0 0
802802 0 0
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 − 15.0000i − 0.528025i
808808 0 0
809809 30.0000 1.05474 0.527372 0.849635i 0.323177π-0.323177\pi
0.527372 + 0.849635i 0.323177π0.323177\pi
810810 0 0
811811 −7.00000 −0.245803 −0.122902 0.992419i 0.539220π-0.539220\pi
−0.122902 + 0.992419i 0.539220π0.539220\pi
812812 0 0
813813 − 8.00000i − 0.280572i
814814 0 0
815815 0 0
816816 0 0
817817 16.0000i 0.559769i
818818 0 0
819819 −4.00000 −0.139771
820820 0 0
821821 −6.00000 −0.209401 −0.104701 0.994504i 0.533388π-0.533388\pi
−0.104701 + 0.994504i 0.533388π0.533388\pi
822822 0 0
823823 − 41.0000i − 1.42917i −0.699549 0.714585i 0.746616π-0.746616\pi
0.699549 0.714585i 0.253384π-0.253384\pi
824824 0 0
825825 0 0
826826 0 0
827827 − 36.0000i − 1.25184i −0.779886 0.625921i 0.784723π-0.784723\pi
0.779886 0.625921i 0.215277π-0.215277\pi
828828 0 0
829829 −38.0000 −1.31979 −0.659897 0.751356i 0.729400π-0.729400\pi
−0.659897 + 0.751356i 0.729400π0.729400\pi
830830 0 0
831831 −19.0000 −0.659103
832832 0 0
833833 − 18.0000i − 0.623663i
834834 0 0
835835 0 0
836836 0 0
837837 − 25.0000i − 0.864126i
838838 0 0
839839 −18.0000 −0.621429 −0.310715 0.950503i 0.600568π-0.600568\pi
−0.310715 + 0.950503i 0.600568π0.600568\pi
840840 0 0
841841 −20.0000 −0.689655
842842 0 0
843843 − 30.0000i − 1.03325i
844844 0 0
845845 0 0
846846 0 0
847847 − 22.0000i − 0.755929i
848848 0 0
849849 4.00000 0.137280
850850 0 0
851851 −8.00000 −0.274236
852852 0 0
853853 − 2.00000i − 0.0684787i −0.999414 0.0342393i 0.989099π-0.989099\pi
0.999414 0.0342393i 0.0109009π-0.0109009\pi
854854 0 0
855855 0 0
856856 0 0
857857 − 33.0000i − 1.12726i −0.826028 0.563629i 0.809405π-0.809405\pi
0.826028 0.563629i 0.190595π-0.190595\pi
858858 0 0
859859 19.0000 0.648272 0.324136 0.946011i 0.394927π-0.394927\pi
0.324136 + 0.946011i 0.394927π0.394927\pi
860860 0 0
861861 6.00000 0.204479
862862 0 0
863863 9.00000i 0.306364i 0.988198 + 0.153182i 0.0489520π0.0489520\pi
−0.988198 + 0.153182i 0.951048π0.951048\pi
864864 0 0
865865 0 0
866866 0 0
867867 19.0000i 0.645274i
868868 0 0
869869 0 0
870870 0 0
871871 −8.00000 −0.271070
872872 0 0
873873 − 20.0000i − 0.676897i
874874 0 0
875875 0 0
876876 0 0
877877 50.0000i 1.68838i 0.536044 + 0.844190i 0.319918π0.319918\pi
−0.536044 + 0.844190i 0.680082π0.680082\pi
878878 0 0
879879 −12.0000 −0.404750
880880 0 0
881881 30.0000 1.01073 0.505363 0.862907i 0.331359π-0.331359\pi
0.505363 + 0.862907i 0.331359π0.331359\pi
882882 0 0
883883 52.0000i 1.74994i 0.484178 + 0.874970i 0.339119π0.339119\pi
−0.484178 + 0.874970i 0.660881π0.660881\pi
884884 0 0
885885 0 0
886886 0 0
887887 − 51.0000i − 1.71241i −0.516634 0.856206i 0.672815π-0.672815\pi
0.516634 0.856206i 0.327185π-0.327185\pi
888888 0 0
889889 −22.0000 −0.737856
890890 0 0
891891 0 0
892892 0 0
893893 − 18.0000i − 0.602347i
894894 0 0
895895 0 0
896896 0 0
897897 1.00000i 0.0333890i
898898 0 0
899899 15.0000 0.500278
900900 0 0
901901 −36.0000 −1.19933
902902 0 0
903903 − 16.0000i − 0.532447i
904904 0 0
905905 0 0
906906 0 0
907907 50.0000i 1.66022i 0.557598 + 0.830111i 0.311723π0.311723\pi
−0.557598 + 0.830111i 0.688277π0.688277\pi
908908 0 0
909909 12.0000 0.398015
910910 0 0
911911 18.0000 0.596367 0.298183 0.954509i 0.403619π-0.403619\pi
0.298183 + 0.954509i 0.403619π0.403619\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 0 0
917917 42.0000i 1.38696i
918918 0 0
919919 −38.0000 −1.25350 −0.626752 0.779219i 0.715616π-0.715616\pi
−0.626752 + 0.779219i 0.715616π0.715616\pi
920920 0 0
921921 20.0000 0.659022
922922 0 0
923923 − 15.0000i − 0.493731i
924924 0 0
925925 0 0
926926 0 0
927927 − 4.00000i − 0.131377i
928928 0 0
929929 −15.0000 −0.492134 −0.246067 0.969253i 0.579138π-0.579138\pi
−0.246067 + 0.969253i 0.579138π0.579138\pi
930930 0 0
931931 −6.00000 −0.196642
932932 0 0
933933 15.0000i 0.491078i
934934 0 0
935935 0 0
936936 0 0
937937 − 28.0000i − 0.914720i −0.889282 0.457360i 0.848795π-0.848795\pi
0.889282 0.457360i 0.151205π-0.151205\pi
938938 0 0
939939 4.00000 0.130535
940940 0 0
941941 30.0000 0.977972 0.488986 0.872292i 0.337367π-0.337367\pi
0.488986 + 0.872292i 0.337367π0.337367\pi
942942 0 0
943943 3.00000i 0.0976934i
944944 0 0
945945 0 0
946946 0 0
947947 − 3.00000i − 0.0974869i −0.998811 0.0487435i 0.984478π-0.984478\pi
0.998811 0.0487435i 0.0155217π-0.0155217\pi
948948 0 0
949949 −7.00000 −0.227230
950950 0 0
951951 −18.0000 −0.583690
952952 0 0
953953 6.00000i 0.194359i 0.995267 + 0.0971795i 0.0309821π0.0309821\pi
−0.995267 + 0.0971795i 0.969018π0.969018\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 24.0000 0.775000
960960 0 0
961961 −6.00000 −0.193548
962962 0 0
963963 − 12.0000i − 0.386695i
964964 0 0
965965 0 0
966966 0 0
967967 47.0000i 1.51142i 0.654907 + 0.755709i 0.272708π0.272708\pi
−0.654907 + 0.755709i 0.727292π0.727292\pi
968968 0 0
969969 12.0000 0.385496
970970 0 0
971971 18.0000 0.577647 0.288824 0.957382i 0.406736π-0.406736\pi
0.288824 + 0.957382i 0.406736π0.406736\pi
972972 0 0
973973 − 22.0000i − 0.705288i
974974 0 0
975975 0 0
976976 0 0
977977 48.0000i 1.53566i 0.640656 + 0.767828i 0.278662π0.278662\pi
−0.640656 + 0.767828i 0.721338π0.721338\pi
978978 0 0
979979 0 0
980980 0 0
981981 32.0000 1.02168
982982 0 0
983983 18.0000i 0.574111i 0.957914 + 0.287055i 0.0926764π0.0926764\pi
−0.957914 + 0.287055i 0.907324π0.907324\pi
984984 0 0
985985 0 0
986986 0 0
987987 18.0000i 0.572946i
988988 0 0
989989 8.00000 0.254385
990990 0 0
991991 −16.0000 −0.508257 −0.254128 0.967170i 0.581789π-0.581789\pi
−0.254128 + 0.967170i 0.581789π0.581789\pi
992992 0 0
993993 25.0000i 0.793351i
994994 0 0
995995 0 0
996996 0 0
997997 62.0000i 1.96356i 0.190022 + 0.981780i 0.439144π0.439144\pi
−0.190022 + 0.981780i 0.560856π0.560856\pi
998998 0 0
999999 40.0000 1.26554
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 2300.2.c.f.1749.1 2
5.2 odd 4 2300.2.a.c.1.1 1
5.3 odd 4 92.2.a.b.1.1 1
5.4 even 2 inner 2300.2.c.f.1749.2 2
15.8 even 4 828.2.a.b.1.1 1
20.3 even 4 368.2.a.b.1.1 1
20.7 even 4 9200.2.a.ba.1.1 1
35.13 even 4 4508.2.a.a.1.1 1
40.3 even 4 1472.2.a.j.1.1 1
40.13 odd 4 1472.2.a.c.1.1 1
60.23 odd 4 3312.2.a.g.1.1 1
115.68 even 4 2116.2.a.d.1.1 1
460.183 odd 4 8464.2.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
92.2.a.b.1.1 1 5.3 odd 4
368.2.a.b.1.1 1 20.3 even 4
828.2.a.b.1.1 1 15.8 even 4
1472.2.a.c.1.1 1 40.13 odd 4
1472.2.a.j.1.1 1 40.3 even 4
2116.2.a.d.1.1 1 115.68 even 4
2300.2.a.c.1.1 1 5.2 odd 4
2300.2.c.f.1749.1 2 1.1 even 1 trivial
2300.2.c.f.1749.2 2 5.4 even 2 inner
3312.2.a.g.1.1 1 60.23 odd 4
4508.2.a.a.1.1 1 35.13 even 4
8464.2.a.f.1.1 1 460.183 odd 4
9200.2.a.ba.1.1 1 20.7 even 4