Properties

Label 5040.2.t.h.1009.2
Level 50405040
Weight 22
Character 5040.1009
Analytic conductor 40.24540.245
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] = [5040,2,Mod(1009,5040)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5040, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("5040.1009");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 5040=243257 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 5040.t (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: 40.244602618740.2446026187
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,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1009.2
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 5040.1009
Dual form 5040.2.t.h.1009.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.00000+2.00000i)q5+1.00000iq7+2.00000q116.00000iq134.00000iq176.00000q19+8.00000iq23+(3.000004.00000i)q25+6.00000q29+2.00000q31+(2.000001.00000i)q35+4.00000iq372.00000q41+4.00000iq43+8.00000iq471.00000q49+6.00000iq53+(2.00000+4.00000i)q55+8.00000q5910.0000q61+(12.0000+6.00000i)q658.00000iq676.00000q71+14.0000iq73+2.00000iq7712.0000q79+8.00000iq83+(8.00000+4.00000i)q8510.0000q89+6.00000q91+(6.0000012.0000i)q9510.0000iq97+O(q100)q+(-1.00000 + 2.00000i) q^{5} +1.00000i q^{7} +2.00000 q^{11} -6.00000i q^{13} -4.00000i q^{17} -6.00000 q^{19} +8.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} +6.00000 q^{29} +2.00000 q^{31} +(-2.00000 - 1.00000i) q^{35} +4.00000i q^{37} -2.00000 q^{41} +4.00000i q^{43} +8.00000i q^{47} -1.00000 q^{49} +6.00000i q^{53} +(-2.00000 + 4.00000i) q^{55} +8.00000 q^{59} -10.0000 q^{61} +(12.0000 + 6.00000i) q^{65} -8.00000i q^{67} -6.00000 q^{71} +14.0000i q^{73} +2.00000i q^{77} -12.0000 q^{79} +8.00000i q^{83} +(8.00000 + 4.00000i) q^{85} -10.0000 q^{89} +6.00000 q^{91} +(6.00000 - 12.0000i) q^{95} -10.0000i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q5+4q1112q196q25+12q29+4q314q354q412q494q55+16q5920q61+24q6512q7124q79+16q8520q89+12q91++12q95+O(q100) 2 q - 2 q^{5} + 4 q^{11} - 12 q^{19} - 6 q^{25} + 12 q^{29} + 4 q^{31} - 4 q^{35} - 4 q^{41} - 2 q^{49} - 4 q^{55} + 16 q^{59} - 20 q^{61} + 24 q^{65} - 12 q^{71} - 24 q^{79} + 16 q^{85} - 20 q^{89} + 12 q^{91}+ \cdots + 12 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/5040Z)×\left(\mathbb{Z}/5040\mathbb{Z}\right)^\times.

nn 20172017 28012801 31513151 36013601 37813781
χ(n)\chi(n) 1-1 11 11 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 0 0
44 0 0
55 −1.00000 + 2.00000i −0.447214 + 0.894427i
66 0 0
77 1.00000i 0.377964i
88 0 0
99 0 0
1010 0 0
1111 2.00000 0.603023 0.301511 0.953463i 0.402509π-0.402509\pi
0.301511 + 0.953463i 0.402509π0.402509\pi
1212 0 0
1313 6.00000i 1.66410i −0.554700 0.832050i 0.687167π-0.687167\pi
0.554700 0.832050i 0.312833π-0.312833\pi
1414 0 0
1515 0 0
1616 0 0
1717 4.00000i 0.970143i −0.874475 0.485071i 0.838794π-0.838794\pi
0.874475 0.485071i 0.161206π-0.161206\pi
1818 0 0
1919 −6.00000 −1.37649 −0.688247 0.725476i 0.741620π-0.741620\pi
−0.688247 + 0.725476i 0.741620π0.741620\pi
2020 0 0
2121 0 0
2222 0 0
2323 8.00000i 1.66812i 0.551677 + 0.834058i 0.313988π0.313988\pi
−0.551677 + 0.834058i 0.686012π0.686012\pi
2424 0 0
2525 −3.00000 4.00000i −0.600000 0.800000i
2626 0 0
2727 0 0
2828 0 0
2929 6.00000 1.11417 0.557086 0.830455i 0.311919π-0.311919\pi
0.557086 + 0.830455i 0.311919π0.311919\pi
3030 0 0
3131 2.00000 0.359211 0.179605 0.983739i 0.442518π-0.442518\pi
0.179605 + 0.983739i 0.442518π0.442518\pi
3232 0 0
3333 0 0
3434 0 0
3535 −2.00000 1.00000i −0.338062 0.169031i
3636 0 0
3737 4.00000i 0.657596i 0.944400 + 0.328798i 0.106644π0.106644\pi
−0.944400 + 0.328798i 0.893356π0.893356\pi
3838 0 0
3939 0 0
4040 0 0
4141 −2.00000 −0.312348 −0.156174 0.987730i 0.549916π-0.549916\pi
−0.156174 + 0.987730i 0.549916π0.549916\pi
4242 0 0
4343 4.00000i 0.609994i 0.952353 + 0.304997i 0.0986555π0.0986555\pi
−0.952353 + 0.304997i 0.901344π0.901344\pi
4444 0 0
4545 0 0
4646 0 0
4747 8.00000i 1.16692i 0.812142 + 0.583460i 0.198301π0.198301\pi
−0.812142 + 0.583460i 0.801699π0.801699\pi
4848 0 0
4949 −1.00000 −0.142857
5050 0 0
5151 0 0
5252 0 0
5353 6.00000i 0.824163i 0.911147 + 0.412082i 0.135198π0.135198\pi
−0.911147 + 0.412082i 0.864802π0.864802\pi
5454 0 0
5555 −2.00000 + 4.00000i −0.269680 + 0.539360i
5656 0 0
5757 0 0
5858 0 0
5959 8.00000 1.04151 0.520756 0.853706i 0.325650π-0.325650\pi
0.520756 + 0.853706i 0.325650π0.325650\pi
6060 0 0
6161 −10.0000 −1.28037 −0.640184 0.768221i 0.721142π-0.721142\pi
−0.640184 + 0.768221i 0.721142π0.721142\pi
6262 0 0
6363 0 0
6464 0 0
6565 12.0000 + 6.00000i 1.48842 + 0.744208i
6666 0 0
6767 8.00000i 0.977356i −0.872464 0.488678i 0.837479π-0.837479\pi
0.872464 0.488678i 0.162521π-0.162521\pi
6868 0 0
6969 0 0
7070 0 0
7171 −6.00000 −0.712069 −0.356034 0.934473i 0.615871π-0.615871\pi
−0.356034 + 0.934473i 0.615871π0.615871\pi
7272 0 0
7373 14.0000i 1.63858i 0.573382 + 0.819288i 0.305631π0.305631\pi
−0.573382 + 0.819288i 0.694369π0.694369\pi
7474 0 0
7575 0 0
7676 0 0
7777 2.00000i 0.227921i
7878 0 0
7979 −12.0000 −1.35011 −0.675053 0.737769i 0.735879π-0.735879\pi
−0.675053 + 0.737769i 0.735879π0.735879\pi
8080 0 0
8181 0 0
8282 0 0
8383 8.00000i 0.878114i 0.898459 + 0.439057i 0.144687π0.144687\pi
−0.898459 + 0.439057i 0.855313π0.855313\pi
8484 0 0
8585 8.00000 + 4.00000i 0.867722 + 0.433861i
8686 0 0
8787 0 0
8888 0 0
8989 −10.0000 −1.06000 −0.529999 0.847998i 0.677808π-0.677808\pi
−0.529999 + 0.847998i 0.677808π0.677808\pi
9090 0 0
9191 6.00000 0.628971
9292 0 0
9393 0 0
9494 0 0
9595 6.00000 12.0000i 0.615587 1.23117i
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 −10.0000 −0.995037 −0.497519 0.867453i 0.665755π-0.665755\pi
−0.497519 + 0.867453i 0.665755π0.665755\pi
102102 0 0
103103 8.00000i 0.788263i 0.919054 + 0.394132i 0.128955π0.128955\pi
−0.919054 + 0.394132i 0.871045π0.871045\pi
104104 0 0
105105 0 0
106106 0 0
107107 12.0000i 1.16008i 0.814587 + 0.580042i 0.196964π0.196964\pi
−0.814587 + 0.580042i 0.803036π0.803036\pi
108108 0 0
109109 14.0000 1.34096 0.670478 0.741929i 0.266089π-0.266089\pi
0.670478 + 0.741929i 0.266089π0.266089\pi
110110 0 0
111111 0 0
112112 0 0
113113 6.00000i 0.564433i 0.959351 + 0.282216i 0.0910696π0.0910696\pi
−0.959351 + 0.282216i 0.908930π0.908930\pi
114114 0 0
115115 −16.0000 8.00000i −1.49201 0.746004i
116116 0 0
117117 0 0
118118 0 0
119119 4.00000 0.366679
120120 0 0
121121 −7.00000 −0.636364
122122 0 0
123123 0 0
124124 0 0
125125 11.0000 2.00000i 0.983870 0.178885i
126126 0 0
127127 4.00000i 0.354943i −0.984126 0.177471i 0.943208π-0.943208\pi
0.984126 0.177471i 0.0567917π-0.0567917\pi
128128 0 0
129129 0 0
130130 0 0
131131 −12.0000 −1.04844 −0.524222 0.851581i 0.675644π-0.675644\pi
−0.524222 + 0.851581i 0.675644π0.675644\pi
132132 0 0
133133 6.00000i 0.520266i
134134 0 0
135135 0 0
136136 0 0
137137 6.00000i 0.512615i 0.966595 + 0.256307i 0.0825059π0.0825059\pi
−0.966595 + 0.256307i 0.917494π0.917494\pi
138138 0 0
139139 −14.0000 −1.18746 −0.593732 0.804663i 0.702346π-0.702346\pi
−0.593732 + 0.804663i 0.702346π0.702346\pi
140140 0 0
141141 0 0
142142 0 0
143143 12.0000i 1.00349i
144144 0 0
145145 −6.00000 + 12.0000i −0.498273 + 0.996546i
146146 0 0
147147 0 0
148148 0 0
149149 10.0000 0.819232 0.409616 0.912258i 0.365663π-0.365663\pi
0.409616 + 0.912258i 0.365663π0.365663\pi
150150 0 0
151151 8.00000 0.651031 0.325515 0.945537i 0.394462π-0.394462\pi
0.325515 + 0.945537i 0.394462π0.394462\pi
152152 0 0
153153 0 0
154154 0 0
155155 −2.00000 + 4.00000i −0.160644 + 0.321288i
156156 0 0
157157 22.0000i 1.75579i −0.478852 0.877896i 0.658947π-0.658947\pi
0.478852 0.877896i 0.341053π-0.341053\pi
158158 0 0
159159 0 0
160160 0 0
161161 −8.00000 −0.630488
162162 0 0
163163 4.00000i 0.313304i −0.987654 0.156652i 0.949930π-0.949930\pi
0.987654 0.156652i 0.0500701π-0.0500701\pi
164164 0 0
165165 0 0
166166 0 0
167167 12.0000i 0.928588i −0.885681 0.464294i 0.846308π-0.846308\pi
0.885681 0.464294i 0.153692π-0.153692\pi
168168 0 0
169169 −23.0000 −1.76923
170170 0 0
171171 0 0
172172 0 0
173173 8.00000i 0.608229i 0.952636 + 0.304114i 0.0983605π0.0983605\pi
−0.952636 + 0.304114i 0.901639π0.901639\pi
174174 0 0
175175 4.00000 3.00000i 0.302372 0.226779i
176176 0 0
177177 0 0
178178 0 0
179179 −10.0000 −0.747435 −0.373718 0.927543i 0.621917π-0.621917\pi
−0.373718 + 0.927543i 0.621917π0.621917\pi
180180 0 0
181181 2.00000 0.148659 0.0743294 0.997234i 0.476318π-0.476318\pi
0.0743294 + 0.997234i 0.476318π0.476318\pi
182182 0 0
183183 0 0
184184 0 0
185185 −8.00000 4.00000i −0.588172 0.294086i
186186 0 0
187187 8.00000i 0.585018i
188188 0 0
189189 0 0
190190 0 0
191191 −18.0000 −1.30243 −0.651217 0.758891i 0.725741π-0.725741\pi
−0.651217 + 0.758891i 0.725741π0.725741\pi
192192 0 0
193193 8.00000i 0.575853i 0.957653 + 0.287926i 0.0929658π0.0929658\pi
−0.957653 + 0.287926i 0.907034π0.907034\pi
194194 0 0
195195 0 0
196196 0 0
197197 2.00000i 0.142494i −0.997459 0.0712470i 0.977302π-0.977302\pi
0.997459 0.0712470i 0.0226979π-0.0226979\pi
198198 0 0
199199 6.00000 0.425329 0.212664 0.977125i 0.431786π-0.431786\pi
0.212664 + 0.977125i 0.431786π0.431786\pi
200200 0 0
201201 0 0
202202 0 0
203203 6.00000i 0.421117i
204204 0 0
205205 2.00000 4.00000i 0.139686 0.279372i
206206 0 0
207207 0 0
208208 0 0
209209 −12.0000 −0.830057
210210 0 0
211211 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
212212 0 0
213213 0 0
214214 0 0
215215 −8.00000 4.00000i −0.545595 0.272798i
216216 0 0
217217 2.00000i 0.135769i
218218 0 0
219219 0 0
220220 0 0
221221 −24.0000 −1.61441
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 8.00000i 0.530979i −0.964114 0.265489i 0.914466π-0.914466\pi
0.964114 0.265489i 0.0855335π-0.0855335\pi
228228 0 0
229229 −14.0000 −0.925146 −0.462573 0.886581i 0.653074π-0.653074\pi
−0.462573 + 0.886581i 0.653074π0.653074\pi
230230 0 0
231231 0 0
232232 0 0
233233 10.0000i 0.655122i −0.944830 0.327561i 0.893773π-0.893773\pi
0.944830 0.327561i 0.106227π-0.106227\pi
234234 0 0
235235 −16.0000 8.00000i −1.04372 0.521862i
236236 0 0
237237 0 0
238238 0 0
239239 −26.0000 −1.68180 −0.840900 0.541190i 0.817974π-0.817974\pi
−0.840900 + 0.541190i 0.817974π0.817974\pi
240240 0 0
241241 −26.0000 −1.67481 −0.837404 0.546585i 0.815928π-0.815928\pi
−0.837404 + 0.546585i 0.815928π0.815928\pi
242242 0 0
243243 0 0
244244 0 0
245245 1.00000 2.00000i 0.0638877 0.127775i
246246 0 0
247247 36.0000i 2.29063i
248248 0 0
249249 0 0
250250 0 0
251251 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
252252 0 0
253253 16.0000i 1.00591i
254254 0 0
255255 0 0
256256 0 0
257257 0 0 1.00000 00
−1.00000 π\pi
258258 0 0
259259 −4.00000 −0.248548
260260 0 0
261261 0 0
262262 0 0
263263 16.0000i 0.986602i −0.869859 0.493301i 0.835790π-0.835790\pi
0.869859 0.493301i 0.164210π-0.164210\pi
264264 0 0
265265 −12.0000 6.00000i −0.737154 0.368577i
266266 0 0
267267 0 0
268268 0 0
269269 18.0000 1.09748 0.548740 0.835993i 0.315108π-0.315108\pi
0.548740 + 0.835993i 0.315108π0.315108\pi
270270 0 0
271271 −10.0000 −0.607457 −0.303728 0.952759i 0.598232π-0.598232\pi
−0.303728 + 0.952759i 0.598232π0.598232\pi
272272 0 0
273273 0 0
274274 0 0
275275 −6.00000 8.00000i −0.361814 0.482418i
276276 0 0
277277 28.0000i 1.68236i 0.540758 + 0.841178i 0.318138π0.318138\pi
−0.540758 + 0.841178i 0.681862π0.681862\pi
278278 0 0
279279 0 0
280280 0 0
281281 −30.0000 −1.78965 −0.894825 0.446417i 0.852700π-0.852700\pi
−0.894825 + 0.446417i 0.852700π0.852700\pi
282282 0 0
283283 20.0000i 1.18888i 0.804141 + 0.594438i 0.202626π0.202626\pi
−0.804141 + 0.594438i 0.797374π0.797374\pi
284284 0 0
285285 0 0
286286 0 0
287287 2.00000i 0.118056i
288288 0 0
289289 1.00000 0.0588235
290290 0 0
291291 0 0
292292 0 0
293293 0 0 1.00000 00
−1.00000 π\pi
294294 0 0
295295 −8.00000 + 16.0000i −0.465778 + 0.931556i
296296 0 0
297297 0 0
298298 0 0
299299 48.0000 2.77591
300300 0 0
301301 −4.00000 −0.230556
302302 0 0
303303 0 0
304304 0 0
305305 10.0000 20.0000i 0.572598 1.14520i
306306 0 0
307307 12.0000i 0.684876i 0.939540 + 0.342438i 0.111253π0.111253\pi
−0.939540 + 0.342438i 0.888747π0.888747\pi
308308 0 0
309309 0 0
310310 0 0
311311 24.0000 1.36092 0.680458 0.732787i 0.261781π-0.261781\pi
0.680458 + 0.732787i 0.261781π0.261781\pi
312312 0 0
313313 2.00000i 0.113047i 0.998401 + 0.0565233i 0.0180015π0.0180015\pi
−0.998401 + 0.0565233i 0.981998π0.981998\pi
314314 0 0
315315 0 0
316316 0 0
317317 2.00000i 0.112331i 0.998421 + 0.0561656i 0.0178875π0.0178875\pi
−0.998421 + 0.0561656i 0.982113π0.982113\pi
318318 0 0
319319 12.0000 0.671871
320320 0 0
321321 0 0
322322 0 0
323323 24.0000i 1.33540i
324324 0 0
325325 −24.0000 + 18.0000i −1.33128 + 0.998460i
326326 0 0
327327 0 0
328328 0 0
329329 −8.00000 −0.441054
330330 0 0
331331 8.00000 0.439720 0.219860 0.975531i 0.429440π-0.429440\pi
0.219860 + 0.975531i 0.429440π0.429440\pi
332332 0 0
333333 0 0
334334 0 0
335335 16.0000 + 8.00000i 0.874173 + 0.437087i
336336 0 0
337337 8.00000i 0.435788i −0.975972 0.217894i 0.930081π-0.930081\pi
0.975972 0.217894i 0.0699187π-0.0699187\pi
338338 0 0
339339 0 0
340340 0 0
341341 4.00000 0.216612
342342 0 0
343343 1.00000i 0.0539949i
344344 0 0
345345 0 0
346346 0 0
347347 36.0000i 1.93258i 0.257454 + 0.966291i 0.417117π0.417117\pi
−0.257454 + 0.966291i 0.582883π0.582883\pi
348348 0 0
349349 26.0000 1.39175 0.695874 0.718164i 0.255017π-0.255017\pi
0.695874 + 0.718164i 0.255017π0.255017\pi
350350 0 0
351351 0 0
352352 0 0
353353 20.0000i 1.06449i 0.846590 + 0.532246i 0.178652π0.178652\pi
−0.846590 + 0.532246i 0.821348π0.821348\pi
354354 0 0
355355 6.00000 12.0000i 0.318447 0.636894i
356356 0 0
357357 0 0
358358 0 0
359359 −6.00000 −0.316668 −0.158334 0.987386i 0.550612π-0.550612\pi
−0.158334 + 0.987386i 0.550612π0.550612\pi
360360 0 0
361361 17.0000 0.894737
362362 0 0
363363 0 0
364364 0 0
365365 −28.0000 14.0000i −1.46559 0.732793i
366366 0 0
367367 32.0000i 1.67039i 0.549957 + 0.835193i 0.314644π0.314644\pi
−0.549957 + 0.835193i 0.685356π0.685356\pi
368368 0 0
369369 0 0
370370 0 0
371371 −6.00000 −0.311504
372372 0 0
373373 24.0000i 1.24267i 0.783544 + 0.621336i 0.213410π0.213410\pi
−0.783544 + 0.621336i 0.786590π0.786590\pi
374374 0 0
375375 0 0
376376 0 0
377377 36.0000i 1.85409i
378378 0 0
379379 20.0000 1.02733 0.513665 0.857991i 0.328287π-0.328287\pi
0.513665 + 0.857991i 0.328287π0.328287\pi
380380 0 0
381381 0 0
382382 0 0
383383 20.0000i 1.02195i −0.859595 0.510976i 0.829284π-0.829284\pi
0.859595 0.510976i 0.170716π-0.170716\pi
384384 0 0
385385 −4.00000 2.00000i −0.203859 0.101929i
386386 0 0
387387 0 0
388388 0 0
389389 2.00000 0.101404 0.0507020 0.998714i 0.483854π-0.483854\pi
0.0507020 + 0.998714i 0.483854π0.483854\pi
390390 0 0
391391 32.0000 1.61831
392392 0 0
393393 0 0
394394 0 0
395395 12.0000 24.0000i 0.603786 1.20757i
396396 0 0
397397 2.00000i 0.100377i −0.998740 0.0501886i 0.984018π-0.984018\pi
0.998740 0.0501886i 0.0159822π-0.0159822\pi
398398 0 0
399399 0 0
400400 0 0
401401 14.0000 0.699127 0.349563 0.936913i 0.386330π-0.386330\pi
0.349563 + 0.936913i 0.386330π0.386330\pi
402402 0 0
403403 12.0000i 0.597763i
404404 0 0
405405 0 0
406406 0 0
407407 8.00000i 0.396545i
408408 0 0
409409 −26.0000 −1.28562 −0.642809 0.766027i 0.722231π-0.722231\pi
−0.642809 + 0.766027i 0.722231π0.722231\pi
410410 0 0
411411 0 0
412412 0 0
413413 8.00000i 0.393654i
414414 0 0
415415 −16.0000 8.00000i −0.785409 0.392705i
416416 0 0
417417 0 0
418418 0 0
419419 −20.0000 −0.977064 −0.488532 0.872546i 0.662467π-0.662467\pi
−0.488532 + 0.872546i 0.662467π0.662467\pi
420420 0 0
421421 34.0000 1.65706 0.828529 0.559946i 0.189178π-0.189178\pi
0.828529 + 0.559946i 0.189178π0.189178\pi
422422 0 0
423423 0 0
424424 0 0
425425 −16.0000 + 12.0000i −0.776114 + 0.582086i
426426 0 0
427427 10.0000i 0.483934i
428428 0 0
429429 0 0
430430 0 0
431431 2.00000 0.0963366 0.0481683 0.998839i 0.484662π-0.484662\pi
0.0481683 + 0.998839i 0.484662π0.484662\pi
432432 0 0
433433 26.0000i 1.24948i 0.780833 + 0.624740i 0.214795π0.214795\pi
−0.780833 + 0.624740i 0.785205π0.785205\pi
434434 0 0
435435 0 0
436436 0 0
437437 48.0000i 2.29615i
438438 0 0
439439 −18.0000 −0.859093 −0.429547 0.903045i 0.641327π-0.641327\pi
−0.429547 + 0.903045i 0.641327π0.641327\pi
440440 0 0
441441 0 0
442442 0 0
443443 12.0000i 0.570137i 0.958507 + 0.285069i 0.0920164π0.0920164\pi
−0.958507 + 0.285069i 0.907984π0.907984\pi
444444 0 0
445445 10.0000 20.0000i 0.474045 0.948091i
446446 0 0
447447 0 0
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 −4.00000 −0.188353
452452 0 0
453453 0 0
454454 0 0
455455 −6.00000 + 12.0000i −0.281284 + 0.562569i
456456 0 0
457457 28.0000i 1.30978i 0.755722 + 0.654892i 0.227286π0.227286\pi
−0.755722 + 0.654892i 0.772714π0.772714\pi
458458 0 0
459459 0 0
460460 0 0
461461 18.0000 0.838344 0.419172 0.907907i 0.362320π-0.362320\pi
0.419172 + 0.907907i 0.362320π0.362320\pi
462462 0 0
463463 36.0000i 1.67306i 0.547920 + 0.836531i 0.315420π0.315420\pi
−0.547920 + 0.836531i 0.684580π0.684580\pi
464464 0 0
465465 0 0
466466 0 0
467467 24.0000i 1.11059i −0.831654 0.555294i 0.812606π-0.812606\pi
0.831654 0.555294i 0.187394π-0.187394\pi
468468 0 0
469469 8.00000 0.369406
470470 0 0
471471 0 0
472472 0 0
473473 8.00000i 0.367840i
474474 0 0
475475 18.0000 + 24.0000i 0.825897 + 1.10120i
476476 0 0
477477 0 0
478478 0 0
479479 −8.00000 −0.365529 −0.182765 0.983157i 0.558505π-0.558505\pi
−0.182765 + 0.983157i 0.558505π0.558505\pi
480480 0 0
481481 24.0000 1.09431
482482 0 0
483483 0 0
484484 0 0
485485 20.0000 + 10.0000i 0.908153 + 0.454077i
486486 0 0
487487 12.0000i 0.543772i −0.962329 0.271886i 0.912353π-0.912353\pi
0.962329 0.271886i 0.0876473π-0.0876473\pi
488488 0 0
489489 0 0
490490 0 0
491491 −30.0000 −1.35388 −0.676941 0.736038i 0.736695π-0.736695\pi
−0.676941 + 0.736038i 0.736695π0.736695\pi
492492 0 0
493493 24.0000i 1.08091i
494494 0 0
495495 0 0
496496 0 0
497497 6.00000i 0.269137i
498498 0 0
499499 −12.0000 −0.537194 −0.268597 0.963253i 0.586560π-0.586560\pi
−0.268597 + 0.963253i 0.586560π0.586560\pi
500500 0 0
501501 0 0
502502 0 0
503503 12.0000i 0.535054i 0.963550 + 0.267527i 0.0862064π0.0862064\pi
−0.963550 + 0.267527i 0.913794π0.913794\pi
504504 0 0
505505 10.0000 20.0000i 0.444994 0.889988i
506506 0 0
507507 0 0
508508 0 0
509509 30.0000 1.32973 0.664863 0.746965i 0.268490π-0.268490\pi
0.664863 + 0.746965i 0.268490π0.268490\pi
510510 0 0
511511 −14.0000 −0.619324
512512 0 0
513513 0 0
514514 0 0
515515 −16.0000 8.00000i −0.705044 0.352522i
516516 0 0
517517 16.0000i 0.703679i
518518 0 0
519519 0 0
520520 0 0
521521 26.0000 1.13908 0.569540 0.821963i 0.307121π-0.307121\pi
0.569540 + 0.821963i 0.307121π0.307121\pi
522522 0 0
523523 28.0000i 1.22435i −0.790721 0.612177i 0.790294π-0.790294\pi
0.790721 0.612177i 0.209706π-0.209706\pi
524524 0 0
525525 0 0
526526 0 0
527527 8.00000i 0.348485i
528528 0 0
529529 −41.0000 −1.78261
530530 0 0
531531 0 0
532532 0 0
533533 12.0000i 0.519778i
534534 0 0
535535 −24.0000 12.0000i −1.03761 0.518805i
536536 0 0
537537 0 0
538538 0 0
539539 −2.00000 −0.0861461
540540 0 0
541541 22.0000 0.945854 0.472927 0.881102i 0.343197π-0.343197\pi
0.472927 + 0.881102i 0.343197π0.343197\pi
542542 0 0
543543 0 0
544544 0 0
545545 −14.0000 + 28.0000i −0.599694 + 1.19939i
546546 0 0
547547 40.0000i 1.71028i −0.518400 0.855138i 0.673472π-0.673472\pi
0.518400 0.855138i 0.326528π-0.326528\pi
548548 0 0
549549 0 0
550550 0 0
551551 −36.0000 −1.53365
552552 0 0
553553 12.0000i 0.510292i
554554 0 0
555555 0 0
556556 0 0
557557 42.0000i 1.77960i 0.456354 + 0.889799i 0.349155π0.349155\pi
−0.456354 + 0.889799i 0.650845π0.650845\pi
558558 0 0
559559 24.0000 1.01509
560560 0 0
561561 0 0
562562 0 0
563563 4.00000i 0.168580i 0.996441 + 0.0842900i 0.0268622π0.0268622\pi
−0.996441 + 0.0842900i 0.973138π0.973138\pi
564564 0 0
565565 −12.0000 6.00000i −0.504844 0.252422i
566566 0 0
567567 0 0
568568 0 0
569569 −46.0000 −1.92842 −0.964210 0.265139i 0.914582π-0.914582\pi
−0.964210 + 0.265139i 0.914582π0.914582\pi
570570 0 0
571571 −4.00000 −0.167395 −0.0836974 0.996491i 0.526673π-0.526673\pi
−0.0836974 + 0.996491i 0.526673π0.526673\pi
572572 0 0
573573 0 0
574574 0 0
575575 32.0000 24.0000i 1.33449 1.00087i
576576 0 0
577577 26.0000i 1.08239i −0.840896 0.541197i 0.817971π-0.817971\pi
0.840896 0.541197i 0.182029π-0.182029\pi
578578 0 0
579579 0 0
580580 0 0
581581 −8.00000 −0.331896
582582 0 0
583583 12.0000i 0.496989i
584584 0 0
585585 0 0
586586 0 0
587587 12.0000i 0.495293i −0.968850 0.247647i 0.920343π-0.920343\pi
0.968850 0.247647i 0.0796572π-0.0796572\pi
588588 0 0
589589 −12.0000 −0.494451
590590 0 0
591591 0 0
592592 0 0
593593 12.0000i 0.492781i 0.969171 + 0.246390i 0.0792446π0.0792446\pi
−0.969171 + 0.246390i 0.920755π0.920755\pi
594594 0 0
595595 −4.00000 + 8.00000i −0.163984 + 0.327968i
596596 0 0
597597 0 0
598598 0 0
599599 −30.0000 −1.22577 −0.612883 0.790173i 0.709990π-0.709990\pi
−0.612883 + 0.790173i 0.709990π0.709990\pi
600600 0 0
601601 38.0000 1.55005 0.775026 0.631929i 0.217737π-0.217737\pi
0.775026 + 0.631929i 0.217737π0.217737\pi
602602 0 0
603603 0 0
604604 0 0
605605 7.00000 14.0000i 0.284590 0.569181i
606606 0 0
607607 8.00000i 0.324710i −0.986732 0.162355i 0.948091π-0.948091\pi
0.986732 0.162355i 0.0519090π-0.0519090\pi
608608 0 0
609609 0 0
610610 0 0
611611 48.0000 1.94187
612612 0 0
613613 28.0000i 1.13091i −0.824779 0.565455i 0.808701π-0.808701\pi
0.824779 0.565455i 0.191299π-0.191299\pi
614614 0 0
615615 0 0
616616 0 0
617617 26.0000i 1.04672i 0.852111 + 0.523360i 0.175322π0.175322\pi
−0.852111 + 0.523360i 0.824678π0.824678\pi
618618 0 0
619619 −22.0000 −0.884255 −0.442127 0.896952i 0.645776π-0.645776\pi
−0.442127 + 0.896952i 0.645776π0.645776\pi
620620 0 0
621621 0 0
622622 0 0
623623 10.0000i 0.400642i
624624 0 0
625625 −7.00000 + 24.0000i −0.280000 + 0.960000i
626626 0 0
627627 0 0
628628 0 0
629629 16.0000 0.637962
630630 0 0
631631 4.00000 0.159237 0.0796187 0.996825i 0.474630π-0.474630\pi
0.0796187 + 0.996825i 0.474630π0.474630\pi
632632 0 0
633633 0 0
634634 0 0
635635 8.00000 + 4.00000i 0.317470 + 0.158735i
636636 0 0
637637 6.00000i 0.237729i
638638 0 0
639639 0 0
640640 0 0
641641 −14.0000 −0.552967 −0.276483 0.961019i 0.589169π-0.589169\pi
−0.276483 + 0.961019i 0.589169π0.589169\pi
642642 0 0
643643 12.0000i 0.473234i 0.971603 + 0.236617i 0.0760386π0.0760386\pi
−0.971603 + 0.236617i 0.923961π0.923961\pi
644644 0 0
645645 0 0
646646 0 0
647647 36.0000i 1.41531i 0.706560 + 0.707653i 0.250246π0.250246\pi
−0.706560 + 0.707653i 0.749754π0.749754\pi
648648 0 0
649649 16.0000 0.628055
650650 0 0
651651 0 0
652652 0 0
653653 34.0000i 1.33052i 0.746611 + 0.665261i 0.231680π0.231680\pi
−0.746611 + 0.665261i 0.768320π0.768320\pi
654654 0 0
655655 12.0000 24.0000i 0.468879 0.937758i
656656 0 0
657657 0 0
658658 0 0
659659 26.0000 1.01282 0.506408 0.862294i 0.330973π-0.330973\pi
0.506408 + 0.862294i 0.330973π0.330973\pi
660660 0 0
661661 38.0000 1.47803 0.739014 0.673690i 0.235292π-0.235292\pi
0.739014 + 0.673690i 0.235292π0.235292\pi
662662 0 0
663663 0 0
664664 0 0
665665 12.0000 + 6.00000i 0.465340 + 0.232670i
666666 0 0
667667 48.0000i 1.85857i
668668 0 0
669669 0 0
670670 0 0
671671 −20.0000 −0.772091
672672 0 0
673673 12.0000i 0.462566i −0.972887 0.231283i 0.925708π-0.925708\pi
0.972887 0.231283i 0.0742923π-0.0742923\pi
674674 0 0
675675 0 0
676676 0 0
677677 40.0000i 1.53732i −0.639655 0.768662i 0.720923π-0.720923\pi
0.639655 0.768662i 0.279077π-0.279077\pi
678678 0 0
679679 10.0000 0.383765
680680 0 0
681681 0 0
682682 0 0
683683 4.00000i 0.153056i −0.997067 0.0765279i 0.975617π-0.975617\pi
0.997067 0.0765279i 0.0243834π-0.0243834\pi
684684 0 0
685685 −12.0000 6.00000i −0.458496 0.229248i
686686 0 0
687687 0 0
688688 0 0
689689 36.0000 1.37149
690690 0 0
691691 2.00000 0.0760836 0.0380418 0.999276i 0.487888π-0.487888\pi
0.0380418 + 0.999276i 0.487888π0.487888\pi
692692 0 0
693693 0 0
694694 0 0
695695 14.0000 28.0000i 0.531050 1.06210i
696696 0 0
697697 8.00000i 0.303022i
698698 0 0
699699 0 0
700700 0 0
701701 34.0000 1.28416 0.642081 0.766637i 0.278071π-0.278071\pi
0.642081 + 0.766637i 0.278071π0.278071\pi
702702 0 0
703703 24.0000i 0.905177i
704704 0 0
705705 0 0
706706 0 0
707707 10.0000i 0.376089i
708708 0 0
709709 6.00000 0.225335 0.112667 0.993633i 0.464061π-0.464061\pi
0.112667 + 0.993633i 0.464061π0.464061\pi
710710 0 0
711711 0 0
712712 0 0
713713 16.0000i 0.599205i
714714 0 0
715715 24.0000 + 12.0000i 0.897549 + 0.448775i
716716 0 0
717717 0 0
718718 0 0
719719 4.00000 0.149175 0.0745874 0.997214i 0.476236π-0.476236\pi
0.0745874 + 0.997214i 0.476236π0.476236\pi
720720 0 0
721721 −8.00000 −0.297936
722722 0 0
723723 0 0
724724 0 0
725725 −18.0000 24.0000i −0.668503 0.891338i
726726 0 0
727727 24.0000i 0.890111i −0.895503 0.445055i 0.853184π-0.853184\pi
0.895503 0.445055i 0.146816π-0.146816\pi
728728 0 0
729729 0 0
730730 0 0
731731 16.0000 0.591781
732732 0 0
733733 14.0000i 0.517102i −0.965998 0.258551i 0.916755π-0.916755\pi
0.965998 0.258551i 0.0832450π-0.0832450\pi
734734 0 0
735735 0 0
736736 0 0
737737 16.0000i 0.589368i
738738 0 0
739739 −44.0000 −1.61857 −0.809283 0.587419i 0.800144π-0.800144\pi
−0.809283 + 0.587419i 0.800144π0.800144\pi
740740 0 0
741741 0 0
742742 0 0
743743 48.0000i 1.76095i 0.474093 + 0.880475i 0.342776π0.342776\pi
−0.474093 + 0.880475i 0.657224π0.657224\pi
744744 0 0
745745 −10.0000 + 20.0000i −0.366372 + 0.732743i
746746 0 0
747747 0 0
748748 0 0
749749 −12.0000 −0.438470
750750 0 0
751751 −20.0000 −0.729810 −0.364905 0.931045i 0.618899π-0.618899\pi
−0.364905 + 0.931045i 0.618899π0.618899\pi
752752 0 0
753753 0 0
754754 0 0
755755 −8.00000 + 16.0000i −0.291150 + 0.582300i
756756 0 0
757757 32.0000i 1.16306i −0.813525 0.581530i 0.802454π-0.802454\pi
0.813525 0.581530i 0.197546π-0.197546\pi
758758 0 0
759759 0 0
760760 0 0
761761 6.00000 0.217500 0.108750 0.994069i 0.465315π-0.465315\pi
0.108750 + 0.994069i 0.465315π0.465315\pi
762762 0 0
763763 14.0000i 0.506834i
764764 0 0
765765 0 0
766766 0 0
767767 48.0000i 1.73318i
768768 0 0
769769 −30.0000 −1.08183 −0.540914 0.841078i 0.681921π-0.681921\pi
−0.540914 + 0.841078i 0.681921π0.681921\pi
770770 0 0
771771 0 0
772772 0 0
773773 0 0 1.00000 00
−1.00000 π\pi
774774 0 0
775775 −6.00000 8.00000i −0.215526 0.287368i
776776 0 0
777777 0 0
778778 0 0
779779 12.0000 0.429945
780780 0 0
781781 −12.0000 −0.429394
782782 0 0
783783 0 0
784784 0 0
785785 44.0000 + 22.0000i 1.57043 + 0.785214i
786786 0 0
787787 28.0000i 0.998092i −0.866575 0.499046i 0.833684π-0.833684\pi
0.866575 0.499046i 0.166316π-0.166316\pi
788788 0 0
789789 0 0
790790 0 0
791791 −6.00000 −0.213335
792792 0 0
793793 60.0000i 2.13066i
794794 0 0
795795 0 0
796796 0 0
797797 8.00000i 0.283375i 0.989911 + 0.141687i 0.0452527π0.0452527\pi
−0.989911 + 0.141687i 0.954747π0.954747\pi
798798 0 0
799799 32.0000 1.13208
800800 0 0
801801 0 0
802802 0 0
803803 28.0000i 0.988099i
804804 0 0
805805 8.00000 16.0000i 0.281963 0.563926i
806806 0 0
807807 0 0
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 14.0000 0.491606 0.245803 0.969320i 0.420948π-0.420948\pi
0.245803 + 0.969320i 0.420948π0.420948\pi
812812 0 0
813813 0 0
814814 0 0
815815 8.00000 + 4.00000i 0.280228 + 0.140114i
816816 0 0
817817 24.0000i 0.839654i
818818 0 0
819819 0 0
820820 0 0
821821 −22.0000 −0.767805 −0.383903 0.923374i 0.625420π-0.625420\pi
−0.383903 + 0.923374i 0.625420π0.625420\pi
822822 0 0
823823 12.0000i 0.418294i 0.977884 + 0.209147i 0.0670687π0.0670687\pi
−0.977884 + 0.209147i 0.932931π0.932931\pi
824824 0 0
825825 0 0
826826 0 0
827827 20.0000i 0.695468i −0.937593 0.347734i 0.886951π-0.886951\pi
0.937593 0.347734i 0.113049π-0.113049\pi
828828 0 0
829829 −18.0000 −0.625166 −0.312583 0.949890i 0.601194π-0.601194\pi
−0.312583 + 0.949890i 0.601194π0.601194\pi
830830 0 0
831831 0 0
832832 0 0
833833 4.00000i 0.138592i
834834 0 0
835835 24.0000 + 12.0000i 0.830554 + 0.415277i
836836 0 0
837837 0 0
838838 0 0
839839 20.0000 0.690477 0.345238 0.938515i 0.387798π-0.387798\pi
0.345238 + 0.938515i 0.387798π0.387798\pi
840840 0 0
841841 7.00000 0.241379
842842 0 0
843843 0 0
844844 0 0
845845 23.0000 46.0000i 0.791224 1.58245i
846846 0 0
847847 7.00000i 0.240523i
848848 0 0
849849 0 0
850850 0 0
851851 −32.0000 −1.09695
852852 0 0
853853 38.0000i 1.30110i −0.759465 0.650548i 0.774539π-0.774539\pi
0.759465 0.650548i 0.225461π-0.225461\pi
854854 0 0
855855 0 0
856856 0 0
857857 24.0000i 0.819824i −0.912125 0.409912i 0.865559π-0.865559\pi
0.912125 0.409912i 0.134441π-0.134441\pi
858858 0 0
859859 −10.0000 −0.341196 −0.170598 0.985341i 0.554570π-0.554570\pi
−0.170598 + 0.985341i 0.554570π0.554570\pi
860860 0 0
861861 0 0
862862 0 0
863863 48.0000i 1.63394i 0.576681 + 0.816970i 0.304348π0.304348\pi
−0.576681 + 0.816970i 0.695652π0.695652\pi
864864 0 0
865865 −16.0000 8.00000i −0.544016 0.272008i
866866 0 0
867867 0 0
868868 0 0
869869 −24.0000 −0.814144
870870 0 0
871871 −48.0000 −1.62642
872872 0 0
873873 0 0
874874 0 0
875875 2.00000 + 11.0000i 0.0676123 + 0.371868i
876876 0 0
877877 28.0000i 0.945493i −0.881199 0.472746i 0.843263π-0.843263\pi
0.881199 0.472746i 0.156737π-0.156737\pi
878878 0 0
879879 0 0
880880 0 0
881881 −30.0000 −1.01073 −0.505363 0.862907i 0.668641π-0.668641\pi
−0.505363 + 0.862907i 0.668641π0.668641\pi
882882 0 0
883883 24.0000i 0.807664i 0.914833 + 0.403832i 0.132322π0.132322\pi
−0.914833 + 0.403832i 0.867678π0.867678\pi
884884 0 0
885885 0 0
886886 0 0
887887 0 0 1.00000 00
−1.00000 π\pi
888888 0 0
889889 4.00000 0.134156
890890 0 0
891891 0 0
892892 0 0
893893 48.0000i 1.60626i
894894 0 0
895895 10.0000 20.0000i 0.334263 0.668526i
896896 0 0
897897 0 0
898898 0 0
899899 12.0000 0.400222
900900 0 0
901901 24.0000 0.799556
902902 0 0
903903 0 0
904904 0 0
905905 −2.00000 + 4.00000i −0.0664822 + 0.132964i
906906 0 0
907907 24.0000i 0.796907i −0.917189 0.398453i 0.869547π-0.869547\pi
0.917189 0.398453i 0.130453π-0.130453\pi
908908 0 0
909909 0 0
910910 0 0
911911 6.00000 0.198789 0.0993944 0.995048i 0.468309π-0.468309\pi
0.0993944 + 0.995048i 0.468309π0.468309\pi
912912 0 0
913913 16.0000i 0.529523i
914914 0 0
915915 0 0
916916 0 0
917917 12.0000i 0.396275i
918918 0 0
919919 60.0000 1.97922 0.989609 0.143787i 0.0459280π-0.0459280\pi
0.989609 + 0.143787i 0.0459280π0.0459280\pi
920920 0 0
921921 0 0
922922 0 0
923923 36.0000i 1.18495i
924924 0 0
925925 16.0000 12.0000i 0.526077 0.394558i
926926 0 0
927927 0 0
928928 0 0
929929 −30.0000 −0.984268 −0.492134 0.870519i 0.663783π-0.663783\pi
−0.492134 + 0.870519i 0.663783π0.663783\pi
930930 0 0
931931 6.00000 0.196642
932932 0 0
933933 0 0
934934 0 0
935935 16.0000 + 8.00000i 0.523256 + 0.261628i
936936 0 0
937937 26.0000i 0.849383i 0.905338 + 0.424691i 0.139617π0.139617\pi
−0.905338 + 0.424691i 0.860383π0.860383\pi
938938 0 0
939939 0 0
940940 0 0
941941 10.0000 0.325991 0.162995 0.986627i 0.447884π-0.447884\pi
0.162995 + 0.986627i 0.447884π0.447884\pi
942942 0 0
943943 16.0000i 0.521032i
944944 0 0
945945 0 0
946946 0 0
947947 12.0000i 0.389948i −0.980808 0.194974i 0.937538π-0.937538\pi
0.980808 0.194974i 0.0624622π-0.0624622\pi
948948 0 0
949949 84.0000 2.72676
950950 0 0
951951 0 0
952952 0 0
953953 10.0000i 0.323932i −0.986796 0.161966i 0.948217π-0.948217\pi
0.986796 0.161966i 0.0517835π-0.0517835\pi
954954 0 0
955955 18.0000 36.0000i 0.582466 1.16493i
956956 0 0
957957 0 0
958958 0 0
959959 −6.00000 −0.193750
960960 0 0
961961 −27.0000 −0.870968
962962 0 0
963963 0 0
964964 0 0
965965 −16.0000 8.00000i −0.515058 0.257529i
966966 0 0
967967 56.0000i 1.80084i −0.435023 0.900419i 0.643260π-0.643260\pi
0.435023 0.900419i 0.356740π-0.356740\pi
968968 0 0
969969 0 0
970970 0 0
971971 −24.0000 −0.770197 −0.385098 0.922876i 0.625832π-0.625832\pi
−0.385098 + 0.922876i 0.625832π0.625832\pi
972972 0 0
973973 14.0000i 0.448819i
974974 0 0
975975 0 0
976976 0 0
977977 18.0000i 0.575871i 0.957650 + 0.287936i 0.0929689π0.0929689\pi
−0.957650 + 0.287936i 0.907031π0.907031\pi
978978 0 0
979979 −20.0000 −0.639203
980980 0 0
981981 0 0
982982 0 0
983983 16.0000i 0.510321i 0.966899 + 0.255160i 0.0821283π0.0821283\pi
−0.966899 + 0.255160i 0.917872π0.917872\pi
984984 0 0
985985 4.00000 + 2.00000i 0.127451 + 0.0637253i
986986 0 0
987987 0 0
988988 0 0
989989 −32.0000 −1.01754
990990 0 0
991991 −4.00000 −0.127064 −0.0635321 0.997980i 0.520237π-0.520237\pi
−0.0635321 + 0.997980i 0.520237π0.520237\pi
992992 0 0
993993 0 0
994994 0 0
995995 −6.00000 + 12.0000i −0.190213 + 0.380426i
996996 0 0
997997 42.0000i 1.33015i −0.746775 0.665077i 0.768399π-0.768399\pi
0.746775 0.665077i 0.231601π-0.231601\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 5040.2.t.h.1009.2 2
3.2 odd 2 1680.2.t.e.1009.2 2
4.3 odd 2 630.2.g.c.379.1 2
5.4 even 2 inner 5040.2.t.h.1009.1 2
12.11 even 2 210.2.g.b.169.2 yes 2
15.2 even 4 8400.2.a.bp.1.1 1
15.8 even 4 8400.2.a.w.1.1 1
15.14 odd 2 1680.2.t.e.1009.1 2
20.3 even 4 3150.2.a.d.1.1 1
20.7 even 4 3150.2.a.bk.1.1 1
20.19 odd 2 630.2.g.c.379.2 2
60.23 odd 4 1050.2.a.p.1.1 1
60.47 odd 4 1050.2.a.d.1.1 1
60.59 even 2 210.2.g.b.169.1 2
84.11 even 6 1470.2.n.b.79.1 4
84.23 even 6 1470.2.n.b.949.2 4
84.47 odd 6 1470.2.n.f.949.2 4
84.59 odd 6 1470.2.n.f.79.1 4
84.83 odd 2 1470.2.g.b.589.2 2
420.59 odd 6 1470.2.n.f.79.2 4
420.83 even 4 7350.2.a.bz.1.1 1
420.167 even 4 7350.2.a.bk.1.1 1
420.179 even 6 1470.2.n.b.79.2 4
420.299 odd 6 1470.2.n.f.949.1 4
420.359 even 6 1470.2.n.b.949.1 4
420.419 odd 2 1470.2.g.b.589.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.g.b.169.1 2 60.59 even 2
210.2.g.b.169.2 yes 2 12.11 even 2
630.2.g.c.379.1 2 4.3 odd 2
630.2.g.c.379.2 2 20.19 odd 2
1050.2.a.d.1.1 1 60.47 odd 4
1050.2.a.p.1.1 1 60.23 odd 4
1470.2.g.b.589.1 2 420.419 odd 2
1470.2.g.b.589.2 2 84.83 odd 2
1470.2.n.b.79.1 4 84.11 even 6
1470.2.n.b.79.2 4 420.179 even 6
1470.2.n.b.949.1 4 420.359 even 6
1470.2.n.b.949.2 4 84.23 even 6
1470.2.n.f.79.1 4 84.59 odd 6
1470.2.n.f.79.2 4 420.59 odd 6
1470.2.n.f.949.1 4 420.299 odd 6
1470.2.n.f.949.2 4 84.47 odd 6
1680.2.t.e.1009.1 2 15.14 odd 2
1680.2.t.e.1009.2 2 3.2 odd 2
3150.2.a.d.1.1 1 20.3 even 4
3150.2.a.bk.1.1 1 20.7 even 4
5040.2.t.h.1009.1 2 5.4 even 2 inner
5040.2.t.h.1009.2 2 1.1 even 1 trivial
7350.2.a.bk.1.1 1 420.167 even 4
7350.2.a.bz.1.1 1 420.83 even 4
8400.2.a.w.1.1 1 15.8 even 4
8400.2.a.bp.1.1 1 15.2 even 4