Properties

Label 4608.2.k.n.1153.1
Level 46084608
Weight 22
Character 4608.1153
Analytic conductor 36.79536.795
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] = [4608,2,Mod(1153,4608)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4608, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4608.1153");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 4608=2932 4608 = 2^{9} \cdot 3^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4608.k (of order 44, degree 22, 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: 36.795065251436.7950652514
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,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 1153.1
Root 1.00000i-1.00000i of defining polynomial
Character χ\chi == 4608.1153
Dual form 4608.2.k.n.3457.1

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+(1.000001.00000i)q54.00000iq7+(4.00000+4.00000i)q11+(3.00000+3.00000i)q13+6.00000q17+(4.000004.00000i)q19+8.00000iq23+3.00000iq25+(3.00000+3.00000i)q29+4.00000q31+(4.000004.00000i)q35+(1.000001.00000i)q372.00000iq41+(4.00000+4.00000i)q43+8.00000q479.00000q49+(7.00000+7.00000i)q53+8.00000iq55+(3.000003.00000i)q61+6.00000q65+(8.00000+8.00000i)q67+10.0000iq73+(16.0000+16.0000i)q7712.0000q79+(4.00000+4.00000i)q83+(6.000006.00000i)q8516.0000iq89+(12.000012.0000i)q918.00000q95+8.00000q97+O(q100)q+(1.00000 - 1.00000i) q^{5} -4.00000i q^{7} +(-4.00000 + 4.00000i) q^{11} +(3.00000 + 3.00000i) q^{13} +6.00000 q^{17} +(-4.00000 - 4.00000i) q^{19} +8.00000i q^{23} +3.00000i q^{25} +(3.00000 + 3.00000i) q^{29} +4.00000 q^{31} +(-4.00000 - 4.00000i) q^{35} +(1.00000 - 1.00000i) q^{37} -2.00000i q^{41} +(-4.00000 + 4.00000i) q^{43} +8.00000 q^{47} -9.00000 q^{49} +(-7.00000 + 7.00000i) q^{53} +8.00000i q^{55} +(-3.00000 - 3.00000i) q^{61} +6.00000 q^{65} +(8.00000 + 8.00000i) q^{67} +10.0000i q^{73} +(16.0000 + 16.0000i) q^{77} -12.0000 q^{79} +(4.00000 + 4.00000i) q^{83} +(6.00000 - 6.00000i) q^{85} -16.0000i q^{89} +(12.0000 - 12.0000i) q^{91} -8.00000 q^{95} +8.00000 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q58q11+6q13+12q178q19+6q29+8q318q35+2q378q43+16q4718q4914q536q61+12q65+16q67+32q7724q79++16q97+O(q100) 2 q + 2 q^{5} - 8 q^{11} + 6 q^{13} + 12 q^{17} - 8 q^{19} + 6 q^{29} + 8 q^{31} - 8 q^{35} + 2 q^{37} - 8 q^{43} + 16 q^{47} - 18 q^{49} - 14 q^{53} - 6 q^{61} + 12 q^{65} + 16 q^{67} + 32 q^{77} - 24 q^{79}+ \cdots + 16 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/4608Z)×\left(\mathbb{Z}/4608\mathbb{Z}\right)^\times.

nn 20532053 35833583 40974097
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 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 1.00000i 0.447214 0.447214i −0.447214 0.894427i 0.647584π-0.647584\pi
0.894427 + 0.447214i 0.147584π0.147584\pi
66 0 0
77 4.00000i 1.51186i −0.654654 0.755929i 0.727186π-0.727186\pi
0.654654 0.755929i 0.272814π-0.272814\pi
88 0 0
99 0 0
1010 0 0
1111 −4.00000 + 4.00000i −1.20605 + 1.20605i −0.233748 + 0.972297i 0.575099π0.575099\pi
−0.972297 + 0.233748i 0.924901π0.924901\pi
1212 0 0
1313 3.00000 + 3.00000i 0.832050 + 0.832050i 0.987797 0.155747i 0.0497784π-0.0497784\pi
−0.155747 + 0.987797i 0.549778π0.549778\pi
1414 0 0
1515 0 0
1616 0 0
1717 6.00000 1.45521 0.727607 0.685994i 0.240633π-0.240633\pi
0.727607 + 0.685994i 0.240633π0.240633\pi
1818 0 0
1919 −4.00000 4.00000i −0.917663 0.917663i 0.0791961 0.996859i 0.474765π-0.474765\pi
−0.996859 + 0.0791961i 0.974765π0.974765\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 3.00000i 0.600000i
2626 0 0
2727 0 0
2828 0 0
2929 3.00000 + 3.00000i 0.557086 + 0.557086i 0.928477 0.371391i 0.121119π-0.121119\pi
−0.371391 + 0.928477i 0.621119π0.621119\pi
3030 0 0
3131 4.00000 0.718421 0.359211 0.933257i 0.383046π-0.383046\pi
0.359211 + 0.933257i 0.383046π0.383046\pi
3232 0 0
3333 0 0
3434 0 0
3535 −4.00000 4.00000i −0.676123 0.676123i
3636 0 0
3737 1.00000 1.00000i 0.164399 0.164399i −0.620113 0.784512i 0.712913π-0.712913\pi
0.784512 + 0.620113i 0.212913π0.212913\pi
3838 0 0
3939 0 0
4040 0 0
4141 2.00000i 0.312348i −0.987730 0.156174i 0.950084π-0.950084\pi
0.987730 0.156174i 0.0499160π-0.0499160\pi
4242 0 0
4343 −4.00000 + 4.00000i −0.609994 + 0.609994i −0.942944 0.332950i 0.891956π-0.891956\pi
0.332950 + 0.942944i 0.391956π0.391956\pi
4444 0 0
4545 0 0
4646 0 0
4747 8.00000 1.16692 0.583460 0.812142i 0.301699π-0.301699\pi
0.583460 + 0.812142i 0.301699π0.301699\pi
4848 0 0
4949 −9.00000 −1.28571
5050 0 0
5151 0 0
5252 0 0
5353 −7.00000 + 7.00000i −0.961524 + 0.961524i −0.999287 0.0377628i 0.987977π-0.987977\pi
0.0377628 + 0.999287i 0.487977π0.487977\pi
5454 0 0
5555 8.00000i 1.07872i
5656 0 0
5757 0 0
5858 0 0
5959 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
6060 0 0
6161 −3.00000 3.00000i −0.384111 0.384111i 0.488470 0.872581i 0.337555π-0.337555\pi
−0.872581 + 0.488470i 0.837555π0.837555\pi
6262 0 0
6363 0 0
6464 0 0
6565 6.00000 0.744208
6666 0 0
6767 8.00000 + 8.00000i 0.977356 + 0.977356i 0.999749 0.0223937i 0.00712872π-0.00712872\pi
−0.0223937 + 0.999749i 0.507129π0.507129\pi
6868 0 0
6969 0 0
7070 0 0
7171 0 0 1.00000 00
−1.00000 π\pi
7272 0 0
7373 10.0000i 1.17041i 0.810885 + 0.585206i 0.198986π0.198986\pi
−0.810885 + 0.585206i 0.801014π0.801014\pi
7474 0 0
7575 0 0
7676 0 0
7777 16.0000 + 16.0000i 1.82337 + 1.82337i
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 4.00000 + 4.00000i 0.439057 + 0.439057i 0.891695 0.452638i 0.149517π-0.149517\pi
−0.452638 + 0.891695i 0.649517π0.649517\pi
8484 0 0
8585 6.00000 6.00000i 0.650791 0.650791i
8686 0 0
8787 0 0
8888 0 0
8989 16.0000i 1.69600i −0.529999 0.847998i 0.677808π-0.677808\pi
0.529999 0.847998i 0.322192π-0.322192\pi
9090 0 0
9191 12.0000 12.0000i 1.25794 1.25794i
9292 0 0
9393 0 0
9494 0 0
9595 −8.00000 −0.820783
9696 0 0
9797 8.00000 0.812277 0.406138 0.913812i 0.366875π-0.366875\pi
0.406138 + 0.913812i 0.366875π0.366875\pi
9898 0 0
9999 0 0
100100 0 0
101101 −7.00000 + 7.00000i −0.696526 + 0.696526i −0.963660 0.267133i 0.913924π-0.913924\pi
0.267133 + 0.963660i 0.413924π0.413924\pi
102102 0 0
103103 4.00000i 0.394132i 0.980390 + 0.197066i 0.0631413π0.0631413\pi
−0.980390 + 0.197066i 0.936859π0.936859\pi
104104 0 0
105105 0 0
106106 0 0
107107 8.00000 8.00000i 0.773389 0.773389i −0.205308 0.978697i 0.565820π-0.565820\pi
0.978697 + 0.205308i 0.0658197π0.0658197\pi
108108 0 0
109109 5.00000 + 5.00000i 0.478913 + 0.478913i 0.904784 0.425871i 0.140032π-0.140032\pi
−0.425871 + 0.904784i 0.640032π0.640032\pi
110110 0 0
111111 0 0
112112 0 0
113113 16.0000 1.50515 0.752577 0.658505i 0.228811π-0.228811\pi
0.752577 + 0.658505i 0.228811π0.228811\pi
114114 0 0
115115 8.00000 + 8.00000i 0.746004 + 0.746004i
116116 0 0
117117 0 0
118118 0 0
119119 24.0000i 2.20008i
120120 0 0
121121 21.0000i 1.90909i
122122 0 0
123123 0 0
124124 0 0
125125 8.00000 + 8.00000i 0.715542 + 0.715542i
126126 0 0
127127 4.00000 0.354943 0.177471 0.984126i 0.443208π-0.443208\pi
0.177471 + 0.984126i 0.443208π0.443208\pi
128128 0 0
129129 0 0
130130 0 0
131131 8.00000 + 8.00000i 0.698963 + 0.698963i 0.964187 0.265224i 0.0854458π-0.0854458\pi
−0.265224 + 0.964187i 0.585446π0.585446\pi
132132 0 0
133133 −16.0000 + 16.0000i −1.38738 + 1.38738i
134134 0 0
135135 0 0
136136 0 0
137137 2.00000i 0.170872i 0.996344 + 0.0854358i 0.0272282π0.0272282\pi
−0.996344 + 0.0854358i 0.972772π0.972772\pi
138138 0 0
139139 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
140140 0 0
141141 0 0
142142 0 0
143143 −24.0000 −2.00698
144144 0 0
145145 6.00000 0.498273
146146 0 0
147147 0 0
148148 0 0
149149 1.00000 1.00000i 0.0819232 0.0819232i −0.664958 0.746881i 0.731550π-0.731550\pi
0.746881 + 0.664958i 0.231550π0.231550\pi
150150 0 0
151151 4.00000i 0.325515i −0.986666 0.162758i 0.947961π-0.947961\pi
0.986666 0.162758i 0.0520389π-0.0520389\pi
152152 0 0
153153 0 0
154154 0 0
155155 4.00000 4.00000i 0.321288 0.321288i
156156 0 0
157157 −3.00000 3.00000i −0.239426 0.239426i 0.577186 0.816612i 0.304151π-0.304151\pi
−0.816612 + 0.577186i 0.804151π0.804151\pi
158158 0 0
159159 0 0
160160 0 0
161161 32.0000 2.52195
162162 0 0
163163 −12.0000 12.0000i −0.939913 0.939913i 0.0583818 0.998294i 0.481406π-0.481406\pi
−0.998294 + 0.0583818i 0.981406π0.981406\pi
164164 0 0
165165 0 0
166166 0 0
167167 8.00000i 0.619059i −0.950890 0.309529i 0.899829π-0.899829\pi
0.950890 0.309529i 0.100171π-0.100171\pi
168168 0 0
169169 5.00000i 0.384615i
170170 0 0
171171 0 0
172172 0 0
173173 11.0000 + 11.0000i 0.836315 + 0.836315i 0.988372 0.152057i 0.0485898π-0.0485898\pi
−0.152057 + 0.988372i 0.548590π0.548590\pi
174174 0 0
175175 12.0000 0.907115
176176 0 0
177177 0 0
178178 0 0
179179 −8.00000 8.00000i −0.597948 0.597948i 0.341818 0.939766i 0.388957π-0.388957\pi
−0.939766 + 0.341818i 0.888957π0.888957\pi
180180 0 0
181181 9.00000 9.00000i 0.668965 0.668965i −0.288512 0.957476i 0.593160π-0.593160\pi
0.957476 + 0.288512i 0.0931604π0.0931604\pi
182182 0 0
183183 0 0
184184 0 0
185185 2.00000i 0.147043i
186186 0 0
187187 −24.0000 + 24.0000i −1.75505 + 1.75505i
188188 0 0
189189 0 0
190190 0 0
191191 24.0000 1.73658 0.868290 0.496058i 0.165220π-0.165220\pi
0.868290 + 0.496058i 0.165220π0.165220\pi
192192 0 0
193193 8.00000 0.575853 0.287926 0.957653i 0.407034π-0.407034\pi
0.287926 + 0.957653i 0.407034π0.407034\pi
194194 0 0
195195 0 0
196196 0 0
197197 −1.00000 + 1.00000i −0.0712470 + 0.0712470i −0.741832 0.670585i 0.766043π-0.766043\pi
0.670585 + 0.741832i 0.266043π0.266043\pi
198198 0 0
199199 4.00000i 0.283552i −0.989899 0.141776i 0.954719π-0.954719\pi
0.989899 0.141776i 0.0452813π-0.0452813\pi
200200 0 0
201201 0 0
202202 0 0
203203 12.0000 12.0000i 0.842235 0.842235i
204204 0 0
205205 −2.00000 2.00000i −0.139686 0.139686i
206206 0 0
207207 0 0
208208 0 0
209209 32.0000 2.21349
210210 0 0
211211 −16.0000 16.0000i −1.10149 1.10149i −0.994232 0.107254i 0.965794π-0.965794\pi
−0.107254 0.994232i 0.534206π-0.534206\pi
212212 0 0
213213 0 0
214214 0 0
215215 8.00000i 0.545595i
216216 0 0
217217 16.0000i 1.08615i
218218 0 0
219219 0 0
220220 0 0
221221 18.0000 + 18.0000i 1.21081 + 1.21081i
222222 0 0
223223 −12.0000 −0.803579 −0.401790 0.915732i 0.631612π-0.631612\pi
−0.401790 + 0.915732i 0.631612π0.631612\pi
224224 0 0
225225 0 0
226226 0 0
227227 12.0000 + 12.0000i 0.796468 + 0.796468i 0.982537 0.186069i 0.0595747π-0.0595747\pi
−0.186069 + 0.982537i 0.559575π0.559575\pi
228228 0 0
229229 −7.00000 + 7.00000i −0.462573 + 0.462573i −0.899498 0.436925i 0.856068π-0.856068\pi
0.436925 + 0.899498i 0.356068π0.356068\pi
230230 0 0
231231 0 0
232232 0 0
233233 16.0000i 1.04819i −0.851658 0.524097i 0.824403π-0.824403\pi
0.851658 0.524097i 0.175597π-0.175597\pi
234234 0 0
235235 8.00000 8.00000i 0.521862 0.521862i
236236 0 0
237237 0 0
238238 0 0
239239 8.00000 0.517477 0.258738 0.965947i 0.416693π-0.416693\pi
0.258738 + 0.965947i 0.416693π0.416693\pi
240240 0 0
241241 −24.0000 −1.54598 −0.772988 0.634421i 0.781239π-0.781239\pi
−0.772988 + 0.634421i 0.781239π0.781239\pi
242242 0 0
243243 0 0
244244 0 0
245245 −9.00000 + 9.00000i −0.574989 + 0.574989i
246246 0 0
247247 24.0000i 1.52708i
248248 0 0
249249 0 0
250250 0 0
251251 −4.00000 + 4.00000i −0.252478 + 0.252478i −0.821986 0.569508i 0.807134π-0.807134\pi
0.569508 + 0.821986i 0.307134π0.307134\pi
252252 0 0
253253 −32.0000 32.0000i −2.01182 2.01182i
254254 0 0
255255 0 0
256256 0 0
257257 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
258258 0 0
259259 −4.00000 4.00000i −0.248548 0.248548i
260260 0 0
261261 0 0
262262 0 0
263263 16.0000i 0.986602i 0.869859 + 0.493301i 0.164210π0.164210\pi
−0.869859 + 0.493301i 0.835790π0.835790\pi
264264 0 0
265265 14.0000i 0.860013i
266266 0 0
267267 0 0
268268 0 0
269269 3.00000 + 3.00000i 0.182913 + 0.182913i 0.792624 0.609711i 0.208714π-0.208714\pi
−0.609711 + 0.792624i 0.708714π0.708714\pi
270270 0 0
271271 28.0000 1.70088 0.850439 0.526073i 0.176336π-0.176336\pi
0.850439 + 0.526073i 0.176336π0.176336\pi
272272 0 0
273273 0 0
274274 0 0
275275 −12.0000 12.0000i −0.723627 0.723627i
276276 0 0
277277 15.0000 15.0000i 0.901263 0.901263i −0.0942828 0.995545i 0.530056π-0.530056\pi
0.995545 + 0.0942828i 0.0300558π0.0300558\pi
278278 0 0
279279 0 0
280280 0 0
281281 0 0 1.00000 00
−1.00000 π\pi
282282 0 0
283283 8.00000 8.00000i 0.475551 0.475551i −0.428155 0.903705i 0.640836π-0.640836\pi
0.903705 + 0.428155i 0.140836π0.140836\pi
284284 0 0
285285 0 0
286286 0 0
287287 −8.00000 −0.472225
288288 0 0
289289 19.0000 1.11765
290290 0 0
291291 0 0
292292 0 0
293293 −1.00000 + 1.00000i −0.0584206 + 0.0584206i −0.735714 0.677293i 0.763153π-0.763153\pi
0.677293 + 0.735714i 0.263153π0.263153\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 −24.0000 + 24.0000i −1.38796 + 1.38796i
300300 0 0
301301 16.0000 + 16.0000i 0.922225 + 0.922225i
302302 0 0
303303 0 0
304304 0 0
305305 −6.00000 −0.343559
306306 0 0
307307 24.0000 + 24.0000i 1.36975 + 1.36975i 0.860787 + 0.508965i 0.169972π0.169972\pi
0.508965 + 0.860787i 0.330028π0.330028\pi
308308 0 0
309309 0 0
310310 0 0
311311 16.0000i 0.907277i 0.891186 + 0.453638i 0.149874π0.149874\pi
−0.891186 + 0.453638i 0.850126π0.850126\pi
312312 0 0
313313 8.00000i 0.452187i −0.974106 0.226093i 0.927405π-0.927405\pi
0.974106 0.226093i 0.0725954π-0.0725954\pi
314314 0 0
315315 0 0
316316 0 0
317317 19.0000 + 19.0000i 1.06715 + 1.06715i 0.997577 + 0.0695692i 0.0221625π0.0221625\pi
0.0695692 + 0.997577i 0.477838π0.477838\pi
318318 0 0
319319 −24.0000 −1.34374
320320 0 0
321321 0 0
322322 0 0
323323 −24.0000 24.0000i −1.33540 1.33540i
324324 0 0
325325 −9.00000 + 9.00000i −0.499230 + 0.499230i
326326 0 0
327327 0 0
328328 0 0
329329 32.0000i 1.76422i
330330 0 0
331331 16.0000 16.0000i 0.879440 0.879440i −0.114037 0.993477i 0.536378π-0.536378\pi
0.993477 + 0.114037i 0.0363782π0.0363782\pi
332332 0 0
333333 0 0
334334 0 0
335335 16.0000 0.874173
336336 0 0
337337 −30.0000 −1.63420 −0.817102 0.576493i 0.804421π-0.804421\pi
−0.817102 + 0.576493i 0.804421π0.804421\pi
338338 0 0
339339 0 0
340340 0 0
341341 −16.0000 + 16.0000i −0.866449 + 0.866449i
342342 0 0
343343 8.00000i 0.431959i
344344 0 0
345345 0 0
346346 0 0
347347 −20.0000 + 20.0000i −1.07366 + 1.07366i −0.0765939 + 0.997062i 0.524404π0.524404\pi
−0.997062 + 0.0765939i 0.975596π0.975596\pi
348348 0 0
349349 11.0000 + 11.0000i 0.588817 + 0.588817i 0.937311 0.348494i 0.113307π-0.113307\pi
−0.348494 + 0.937311i 0.613307π0.613307\pi
350350 0 0
351351 0 0
352352 0 0
353353 16.0000 0.851594 0.425797 0.904819i 0.359994π-0.359994\pi
0.425797 + 0.904819i 0.359994π0.359994\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 16.0000i 0.844448i 0.906492 + 0.422224i 0.138750π0.138750\pi
−0.906492 + 0.422224i 0.861250π0.861250\pi
360360 0 0
361361 13.0000i 0.684211i
362362 0 0
363363 0 0
364364 0 0
365365 10.0000 + 10.0000i 0.523424 + 0.523424i
366366 0 0
367367 −20.0000 −1.04399 −0.521996 0.852948i 0.674812π-0.674812\pi
−0.521996 + 0.852948i 0.674812π0.674812\pi
368368 0 0
369369 0 0
370370 0 0
371371 28.0000 + 28.0000i 1.45369 + 1.45369i
372372 0 0
373373 −15.0000 + 15.0000i −0.776671 + 0.776671i −0.979263 0.202593i 0.935063π-0.935063\pi
0.202593 + 0.979263i 0.435063π0.435063\pi
374374 0 0
375375 0 0
376376 0 0
377377 18.0000i 0.927047i
378378 0 0
379379 −12.0000 + 12.0000i −0.616399 + 0.616399i −0.944606 0.328207i 0.893556π-0.893556\pi
0.328207 + 0.944606i 0.393556π0.393556\pi
380380 0 0
381381 0 0
382382 0 0
383383 −24.0000 −1.22634 −0.613171 0.789950i 0.710106π-0.710106\pi
−0.613171 + 0.789950i 0.710106π0.710106\pi
384384 0 0
385385 32.0000 1.63087
386386 0 0
387387 0 0
388388 0 0
389389 −25.0000 + 25.0000i −1.26755 + 1.26755i −0.320201 + 0.947350i 0.603750π0.603750\pi
−0.947350 + 0.320201i 0.896250π0.896250\pi
390390 0 0
391391 48.0000i 2.42746i
392392 0 0
393393 0 0
394394 0 0
395395 −12.0000 + 12.0000i −0.603786 + 0.603786i
396396 0 0
397397 27.0000 + 27.0000i 1.35509 + 1.35509i 0.879862 + 0.475229i 0.157635π0.157635\pi
0.475229 + 0.879862i 0.342365π0.342365\pi
398398 0 0
399399 0 0
400400 0 0
401401 −6.00000 −0.299626 −0.149813 0.988714i 0.547867π-0.547867\pi
−0.149813 + 0.988714i 0.547867π0.547867\pi
402402 0 0
403403 12.0000 + 12.0000i 0.597763 + 0.597763i
404404 0 0
405405 0 0
406406 0 0
407407 8.00000i 0.396545i
408408 0 0
409409 8.00000i 0.395575i −0.980245 0.197787i 0.936624π-0.936624\pi
0.980245 0.197787i 0.0633755π-0.0633755\pi
410410 0 0
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 8.00000 0.392705
416416 0 0
417417 0 0
418418 0 0
419419 −12.0000 12.0000i −0.586238 0.586238i 0.350372 0.936611i 0.386055π-0.386055\pi
−0.936611 + 0.350372i 0.886055π0.886055\pi
420420 0 0
421421 9.00000 9.00000i 0.438633 0.438633i −0.452919 0.891552i 0.649617π-0.649617\pi
0.891552 + 0.452919i 0.149617π0.149617\pi
422422 0 0
423423 0 0
424424 0 0
425425 18.0000i 0.873128i
426426 0 0
427427 −12.0000 + 12.0000i −0.580721 + 0.580721i
428428 0 0
429429 0 0
430430 0 0
431431 8.00000 0.385346 0.192673 0.981263i 0.438284π-0.438284\pi
0.192673 + 0.981263i 0.438284π0.438284\pi
432432 0 0
433433 8.00000 0.384455 0.192228 0.981350i 0.438429π-0.438429\pi
0.192228 + 0.981350i 0.438429π0.438429\pi
434434 0 0
435435 0 0
436436 0 0
437437 32.0000 32.0000i 1.53077 1.53077i
438438 0 0
439439 20.0000i 0.954548i 0.878755 + 0.477274i 0.158375π0.158375\pi
−0.878755 + 0.477274i 0.841625π0.841625\pi
440440 0 0
441441 0 0
442442 0 0
443443 12.0000 12.0000i 0.570137 0.570137i −0.362029 0.932167i 0.617916π-0.617916\pi
0.932167 + 0.362029i 0.117916π0.117916\pi
444444 0 0
445445 −16.0000 16.0000i −0.758473 0.758473i
446446 0 0
447447 0 0
448448 0 0
449449 10.0000 0.471929 0.235965 0.971762i 0.424175π-0.424175\pi
0.235965 + 0.971762i 0.424175π0.424175\pi
450450 0 0
451451 8.00000 + 8.00000i 0.376705 + 0.376705i
452452 0 0
453453 0 0
454454 0 0
455455 24.0000i 1.12514i
456456 0 0
457457 8.00000i 0.374224i 0.982339 + 0.187112i 0.0599128π0.0599128\pi
−0.982339 + 0.187112i 0.940087π0.940087\pi
458458 0 0
459459 0 0
460460 0 0
461461 −19.0000 19.0000i −0.884918 0.884918i 0.109111 0.994030i 0.465200π-0.465200\pi
−0.994030 + 0.109111i 0.965200π0.965200\pi
462462 0 0
463463 −4.00000 −0.185896 −0.0929479 0.995671i 0.529629π-0.529629\pi
−0.0929479 + 0.995671i 0.529629π0.529629\pi
464464 0 0
465465 0 0
466466 0 0
467467 4.00000 + 4.00000i 0.185098 + 0.185098i 0.793573 0.608475i 0.208218π-0.208218\pi
−0.608475 + 0.793573i 0.708218π0.708218\pi
468468 0 0
469469 32.0000 32.0000i 1.47762 1.47762i
470470 0 0
471471 0 0
472472 0 0
473473 32.0000i 1.47136i
474474 0 0
475475 12.0000 12.0000i 0.550598 0.550598i
476476 0 0
477477 0 0
478478 0 0
479479 16.0000 0.731059 0.365529 0.930800i 0.380888π-0.380888\pi
0.365529 + 0.930800i 0.380888π0.380888\pi
480480 0 0
481481 6.00000 0.273576
482482 0 0
483483 0 0
484484 0 0
485485 8.00000 8.00000i 0.363261 0.363261i
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 8.00000 8.00000i 0.361035 0.361035i −0.503159 0.864194i 0.667829π-0.667829\pi
0.864194 + 0.503159i 0.167829π0.167829\pi
492492 0 0
493493 18.0000 + 18.0000i 0.810679 + 0.810679i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 −8.00000 8.00000i −0.358129 0.358129i 0.504994 0.863123i 0.331495π-0.331495\pi
−0.863123 + 0.504994i 0.831495π0.831495\pi
500500 0 0
501501 0 0
502502 0 0
503503 16.0000i 0.713405i 0.934218 + 0.356702i 0.116099π0.116099\pi
−0.934218 + 0.356702i 0.883901π0.883901\pi
504504 0 0
505505 14.0000i 0.622992i
506506 0 0
507507 0 0
508508 0 0
509509 −11.0000 11.0000i −0.487566 0.487566i 0.419971 0.907537i 0.362040π-0.362040\pi
−0.907537 + 0.419971i 0.862040π0.862040\pi
510510 0 0
511511 40.0000 1.76950
512512 0 0
513513 0 0
514514 0 0
515515 4.00000 + 4.00000i 0.176261 + 0.176261i
516516 0 0
517517 −32.0000 + 32.0000i −1.40736 + 1.40736i
518518 0 0
519519 0 0
520520 0 0
521521 30.0000i 1.31432i 0.753749 + 0.657162i 0.228243π0.228243\pi
−0.753749 + 0.657162i 0.771757π0.771757\pi
522522 0 0
523523 −12.0000 + 12.0000i −0.524723 + 0.524723i −0.918994 0.394271i 0.870997π-0.870997\pi
0.394271 + 0.918994i 0.370997π0.370997\pi
524524 0 0
525525 0 0
526526 0 0
527527 24.0000 1.04546
528528 0 0
529529 −41.0000 −1.78261
530530 0 0
531531 0 0
532532 0 0
533533 6.00000 6.00000i 0.259889 0.259889i
534534 0 0
535535 16.0000i 0.691740i
536536 0 0
537537 0 0
538538 0 0
539539 36.0000 36.0000i 1.55063 1.55063i
540540 0 0
541541 3.00000 + 3.00000i 0.128980 + 0.128980i 0.768650 0.639670i 0.220929π-0.220929\pi
−0.639670 + 0.768650i 0.720929π0.720929\pi
542542 0 0
543543 0 0
544544 0 0
545545 10.0000 0.428353
546546 0 0
547547 −12.0000 12.0000i −0.513083 0.513083i 0.402387 0.915470i 0.368181π-0.368181\pi
−0.915470 + 0.402387i 0.868181π0.868181\pi
548548 0 0
549549 0 0
550550 0 0
551551 24.0000i 1.02243i
552552 0 0
553553 48.0000i 2.04117i
554554 0 0
555555 0 0
556556 0 0
557557 11.0000 + 11.0000i 0.466085 + 0.466085i 0.900644 0.434559i 0.143096π-0.143096\pi
−0.434559 + 0.900644i 0.643096π0.643096\pi
558558 0 0
559559 −24.0000 −1.01509
560560 0 0
561561 0 0
562562 0 0
563563 −20.0000 20.0000i −0.842900 0.842900i 0.146336 0.989235i 0.453252π-0.453252\pi
−0.989235 + 0.146336i 0.953252π0.953252\pi
564564 0 0
565565 16.0000 16.0000i 0.673125 0.673125i
566566 0 0
567567 0 0
568568 0 0
569569 18.0000i 0.754599i 0.926091 + 0.377300i 0.123147π0.123147\pi
−0.926091 + 0.377300i 0.876853π0.876853\pi
570570 0 0
571571 24.0000 24.0000i 1.00437 1.00437i 0.00437833 0.999990i 0.498606π-0.498606\pi
0.999990 0.00437833i 0.00139367π-0.00139367\pi
572572 0 0
573573 0 0
574574 0 0
575575 −24.0000 −1.00087
576576 0 0
577577 −18.0000 −0.749350 −0.374675 0.927156i 0.622246π-0.622246\pi
−0.374675 + 0.927156i 0.622246π0.622246\pi
578578 0 0
579579 0 0
580580 0 0
581581 16.0000 16.0000i 0.663792 0.663792i
582582 0 0
583583 56.0000i 2.31928i
584584 0 0
585585 0 0
586586 0 0
587587 16.0000 16.0000i 0.660391 0.660391i −0.295081 0.955472i 0.595347π-0.595347\pi
0.955472 + 0.295081i 0.0953468π0.0953468\pi
588588 0 0
589589 −16.0000 16.0000i −0.659269 0.659269i
590590 0 0
591591 0 0
592592 0 0
593593 −16.0000 −0.657041 −0.328521 0.944497i 0.606550π-0.606550\pi
−0.328521 + 0.944497i 0.606550π0.606550\pi
594594 0 0
595595 −24.0000 24.0000i −0.983904 0.983904i
596596 0 0
597597 0 0
598598 0 0
599599 40.0000i 1.63436i −0.576386 0.817178i 0.695537π-0.695537\pi
0.576386 0.817178i 0.304463π-0.304463\pi
600600 0 0
601601 38.0000i 1.55005i −0.631929 0.775026i 0.717737π-0.717737\pi
0.631929 0.775026i 0.282263π-0.282263\pi
602602 0 0
603603 0 0
604604 0 0
605605 −21.0000 21.0000i −0.853771 0.853771i
606606 0 0
607607 −12.0000 −0.487065 −0.243532 0.969893i 0.578306π-0.578306\pi
−0.243532 + 0.969893i 0.578306π0.578306\pi
608608 0 0
609609 0 0
610610 0 0
611611 24.0000 + 24.0000i 0.970936 + 0.970936i
612612 0 0
613613 7.00000 7.00000i 0.282727 0.282727i −0.551468 0.834196i 0.685932π-0.685932\pi
0.834196 + 0.551468i 0.185932π0.185932\pi
614614 0 0
615615 0 0
616616 0 0
617617 32.0000i 1.28827i −0.764911 0.644136i 0.777217π-0.777217\pi
0.764911 0.644136i 0.222783π-0.222783\pi
618618 0 0
619619 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
620620 0 0
621621 0 0
622622 0 0
623623 −64.0000 −2.56411
624624 0 0
625625 1.00000 0.0400000
626626 0 0
627627 0 0
628628 0 0
629629 6.00000 6.00000i 0.239236 0.239236i
630630 0 0
631631 20.0000i 0.796187i −0.917345 0.398094i 0.869672π-0.869672\pi
0.917345 0.398094i 0.130328π-0.130328\pi
632632 0 0
633633 0 0
634634 0 0
635635 4.00000 4.00000i 0.158735 0.158735i
636636 0 0
637637 −27.0000 27.0000i −1.06978 1.06978i
638638 0 0
639639 0 0
640640 0 0
641641 −22.0000 −0.868948 −0.434474 0.900684i 0.643066π-0.643066\pi
−0.434474 + 0.900684i 0.643066π0.643066\pi
642642 0 0
643643 12.0000 + 12.0000i 0.473234 + 0.473234i 0.902959 0.429726i 0.141390π-0.141390\pi
−0.429726 + 0.902959i 0.641390π0.641390\pi
644644 0 0
645645 0 0
646646 0 0
647647 24.0000i 0.943537i −0.881722 0.471769i 0.843616π-0.843616\pi
0.881722 0.471769i 0.156384π-0.156384\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 −19.0000 19.0000i −0.743527 0.743527i 0.229728 0.973255i 0.426216π-0.426216\pi
−0.973255 + 0.229728i 0.926216π0.926216\pi
654654 0 0
655655 16.0000 0.625172
656656 0 0
657657 0 0
658658 0 0
659659 8.00000 + 8.00000i 0.311636 + 0.311636i 0.845543 0.533907i 0.179277π-0.179277\pi
−0.533907 + 0.845543i 0.679277π0.679277\pi
660660 0 0
661661 7.00000 7.00000i 0.272268 0.272268i −0.557744 0.830013i 0.688333π-0.688333\pi
0.830013 + 0.557744i 0.188333π0.188333\pi
662662 0 0
663663 0 0
664664 0 0
665665 32.0000i 1.24091i
666666 0 0
667667 −24.0000 + 24.0000i −0.929284 + 0.929284i
668668 0 0
669669 0 0
670670 0 0
671671 24.0000 0.926510
672672 0 0
673673 −8.00000 −0.308377 −0.154189 0.988041i 0.549276π-0.549276\pi
−0.154189 + 0.988041i 0.549276π0.549276\pi
674674 0 0
675675 0 0
676676 0 0
677677 −9.00000 + 9.00000i −0.345898 + 0.345898i −0.858579 0.512681i 0.828652π-0.828652\pi
0.512681 + 0.858579i 0.328652π0.328652\pi
678678 0 0
679679 32.0000i 1.22805i
680680 0 0
681681 0 0
682682 0 0
683683 12.0000 12.0000i 0.459167 0.459167i −0.439215 0.898382i 0.644743π-0.644743\pi
0.898382 + 0.439215i 0.144743π0.144743\pi
684684 0 0
685685 2.00000 + 2.00000i 0.0764161 + 0.0764161i
686686 0 0
687687 0 0
688688 0 0
689689 −42.0000 −1.60007
690690 0 0
691691 −36.0000 36.0000i −1.36950 1.36950i −0.861145 0.508360i 0.830252π-0.830252\pi
−0.508360 0.861145i 0.669748π-0.669748\pi
692692 0 0
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 12.0000i 0.454532i
698698 0 0
699699 0 0
700700 0 0
701701 −11.0000 11.0000i −0.415464 0.415464i 0.468173 0.883637i 0.344913π-0.344913\pi
−0.883637 + 0.468173i 0.844913π0.844913\pi
702702 0 0
703703 −8.00000 −0.301726
704704 0 0
705705 0 0
706706 0 0
707707 28.0000 + 28.0000i 1.05305 + 1.05305i
708708 0 0
709709 −33.0000 + 33.0000i −1.23934 + 1.23934i −0.279070 + 0.960271i 0.590026π0.590026\pi
−0.960271 + 0.279070i 0.909974π0.909974\pi
710710 0 0
711711 0 0
712712 0 0
713713 32.0000i 1.19841i
714714 0 0
715715 −24.0000 + 24.0000i −0.897549 + 0.897549i
716716 0 0
717717 0 0
718718 0 0
719719 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
720720 0 0
721721 16.0000 0.595871
722722 0 0
723723 0 0
724724 0 0
725725 −9.00000 + 9.00000i −0.334252 + 0.334252i
726726 0 0
727727 52.0000i 1.92857i 0.264861 + 0.964287i 0.414674π0.414674\pi
−0.264861 + 0.964287i 0.585326π0.585326\pi
728728 0 0
729729 0 0
730730 0 0
731731 −24.0000 + 24.0000i −0.887672 + 0.887672i
732732 0 0
733733 37.0000 + 37.0000i 1.36663 + 1.36663i 0.865201 + 0.501425i 0.167191π0.167191\pi
0.501425 + 0.865201i 0.332809π0.332809\pi
734734 0 0
735735 0 0
736736 0 0
737737 −64.0000 −2.35747
738738 0 0
739739 24.0000 + 24.0000i 0.882854 + 0.882854i 0.993824 0.110970i 0.0353956π-0.0353956\pi
−0.110970 + 0.993824i 0.535396π0.535396\pi
740740 0 0
741741 0 0
742742 0 0
743743 24.0000i 0.880475i 0.897881 + 0.440237i 0.145106π0.145106\pi
−0.897881 + 0.440237i 0.854894π0.854894\pi
744744 0 0
745745 2.00000i 0.0732743i
746746 0 0
747747 0 0
748748 0 0
749749 −32.0000 32.0000i −1.16925 1.16925i
750750 0 0
751751 28.0000 1.02173 0.510867 0.859660i 0.329324π-0.329324\pi
0.510867 + 0.859660i 0.329324π0.329324\pi
752752 0 0
753753 0 0
754754 0 0
755755 −4.00000 4.00000i −0.145575 0.145575i
756756 0 0
757757 −7.00000 + 7.00000i −0.254419 + 0.254419i −0.822780 0.568360i 0.807578π-0.807578\pi
0.568360 + 0.822780i 0.307578π0.307578\pi
758758 0 0
759759 0 0
760760 0 0
761761 18.0000i 0.652499i −0.945284 0.326250i 0.894215π-0.894215\pi
0.945284 0.326250i 0.105785π-0.105785\pi
762762 0 0
763763 20.0000 20.0000i 0.724049 0.724049i
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 40.0000 1.44244 0.721218 0.692708i 0.243582π-0.243582\pi
0.721218 + 0.692708i 0.243582π0.243582\pi
770770 0 0
771771 0 0
772772 0 0
773773 9.00000 9.00000i 0.323708 0.323708i −0.526480 0.850188i 0.676489π-0.676489\pi
0.850188 + 0.526480i 0.176489π0.176489\pi
774774 0 0
775775 12.0000i 0.431053i
776776 0 0
777777 0 0
778778 0 0
779779 −8.00000 + 8.00000i −0.286630 + 0.286630i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 0 0
785785 −6.00000 −0.214149
786786 0 0
787787 12.0000 + 12.0000i 0.427754 + 0.427754i 0.887863 0.460109i 0.152190π-0.152190\pi
−0.460109 + 0.887863i 0.652190π0.652190\pi
788788 0 0
789789 0 0
790790 0 0
791791 64.0000i 2.27558i
792792 0 0
793793 18.0000i 0.639199i
794794 0 0
795795 0 0
796796 0 0
797797 −5.00000 5.00000i −0.177109 0.177109i 0.612985 0.790094i 0.289968π-0.289968\pi
−0.790094 + 0.612985i 0.789968π0.789968\pi
798798 0 0
799799 48.0000 1.69812
800800 0 0
801801 0 0
802802 0 0
803803 −40.0000 40.0000i −1.41157 1.41157i
804804 0 0
805805 32.0000 32.0000i 1.12785 1.12785i
806806 0 0
807807 0 0
808808 0 0
809809 2.00000i 0.0703163i 0.999382 + 0.0351581i 0.0111935π0.0111935\pi
−0.999382 + 0.0351581i 0.988807π0.988807\pi
810810 0 0
811811 4.00000 4.00000i 0.140459 0.140459i −0.633381 0.773840i 0.718333π-0.718333\pi
0.773840 + 0.633381i 0.218333π0.218333\pi
812812 0 0
813813 0 0
814814 0 0
815815 −24.0000 −0.840683
816816 0 0
817817 32.0000 1.11954
818818 0 0
819819 0 0
820820 0 0
821821 −39.0000 + 39.0000i −1.36111 + 1.36111i −0.488603 + 0.872506i 0.662493π0.662493\pi
−0.872506 + 0.488603i 0.837507π0.837507\pi
822822 0 0
823823 44.0000i 1.53374i 0.641800 + 0.766872i 0.278188π0.278188\pi
−0.641800 + 0.766872i 0.721812π0.721812\pi
824824 0 0
825825 0 0
826826 0 0
827827 −32.0000 + 32.0000i −1.11275 + 1.11275i −0.119972 + 0.992777i 0.538280π0.538280\pi
−0.992777 + 0.119972i 0.961720π0.961720\pi
828828 0 0
829829 −29.0000 29.0000i −1.00721 1.00721i −0.999974 0.00723783i 0.997696π-0.997696\pi
−0.00723783 0.999974i 0.502304π-0.502304\pi
830830 0 0
831831 0 0
832832 0 0
833833 −54.0000 −1.87099
834834 0 0
835835 −8.00000 8.00000i −0.276851 0.276851i
836836 0 0
837837 0 0
838838 0 0
839839 48.0000i 1.65714i 0.559883 + 0.828572i 0.310846π0.310846\pi
−0.559883 + 0.828572i 0.689154π0.689154\pi
840840 0 0
841841 11.0000i 0.379310i
842842 0 0
843843 0 0
844844 0 0
845845 5.00000 + 5.00000i 0.172005 + 0.172005i
846846 0 0
847847 −84.0000 −2.88627
848848 0 0
849849 0 0
850850 0 0
851851 8.00000 + 8.00000i 0.274236 + 0.274236i
852852 0 0
853853 1.00000 1.00000i 0.0342393 0.0342393i −0.689780 0.724019i 0.742293π-0.742293\pi
0.724019 + 0.689780i 0.242293π0.242293\pi
854854 0 0
855855 0 0
856856 0 0
857857 18.0000i 0.614868i 0.951569 + 0.307434i 0.0994704π0.0994704\pi
−0.951569 + 0.307434i 0.900530π0.900530\pi
858858 0 0
859859 −12.0000 + 12.0000i −0.409435 + 0.409435i −0.881541 0.472107i 0.843494π-0.843494\pi
0.472107 + 0.881541i 0.343494π0.343494\pi
860860 0 0
861861 0 0
862862 0 0
863863 24.0000 0.816970 0.408485 0.912765i 0.366057π-0.366057\pi
0.408485 + 0.912765i 0.366057π0.366057\pi
864864 0 0
865865 22.0000 0.748022
866866 0 0
867867 0 0
868868 0 0
869869 48.0000 48.0000i 1.62829 1.62829i
870870 0 0
871871 48.0000i 1.62642i
872872 0 0
873873 0 0
874874 0 0
875875 32.0000 32.0000i 1.08180 1.08180i
876876 0 0
877877 −5.00000 5.00000i −0.168838 0.168838i 0.617630 0.786468i 0.288093π-0.288093\pi
−0.786468 + 0.617630i 0.788093π0.788093\pi
878878 0 0
879879 0 0
880880 0 0
881881 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
882882 0 0
883883 4.00000 + 4.00000i 0.134611 + 0.134611i 0.771202 0.636591i 0.219656π-0.219656\pi
−0.636591 + 0.771202i 0.719656π0.719656\pi
884884 0 0
885885 0 0
886886 0 0
887887 48.0000i 1.61168i 0.592132 + 0.805841i 0.298286π0.298286\pi
−0.592132 + 0.805841i 0.701714π0.701714\pi
888888 0 0
889889 16.0000i 0.536623i
890890 0 0
891891 0 0
892892 0 0
893893 −32.0000 32.0000i −1.07084 1.07084i
894894 0 0
895895 −16.0000 −0.534821
896896 0 0
897897 0 0
898898 0 0
899899 12.0000 + 12.0000i 0.400222 + 0.400222i
900900 0 0
901901 −42.0000 + 42.0000i −1.39922 + 1.39922i
902902 0 0
903903 0 0
904904 0 0
905905 18.0000i 0.598340i
906906 0 0
907907 28.0000 28.0000i 0.929725 0.929725i −0.0679631 0.997688i 0.521650π-0.521650\pi
0.997688 + 0.0679631i 0.0216500π0.0216500\pi
908908 0 0
909909 0 0
910910 0 0
911911 40.0000 1.32526 0.662630 0.748947i 0.269440π-0.269440\pi
0.662630 + 0.748947i 0.269440π0.269440\pi
912912 0 0
913913 −32.0000 −1.05905
914914 0 0
915915 0 0
916916 0 0
917917 32.0000 32.0000i 1.05673 1.05673i
918918 0 0
919919 20.0000i 0.659739i −0.944027 0.329870i 0.892995π-0.892995\pi
0.944027 0.329870i 0.107005π-0.107005\pi
920920 0 0
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 3.00000 + 3.00000i 0.0986394 + 0.0986394i
926926 0 0
927927 0 0
928928 0 0
929929 −42.0000 −1.37798 −0.688988 0.724773i 0.741945π-0.741945\pi
−0.688988 + 0.724773i 0.741945π0.741945\pi
930930 0 0
931931 36.0000 + 36.0000i 1.17985 + 1.17985i
932932 0 0
933933 0 0
934934 0 0
935935 48.0000i 1.56977i
936936 0 0
937937 26.0000i 0.849383i −0.905338 0.424691i 0.860383π-0.860383\pi
0.905338 0.424691i 0.139617π-0.139617\pi
938938 0 0
939939 0 0
940940 0 0
941941 −35.0000 35.0000i −1.14097 1.14097i −0.988274 0.152694i 0.951205π-0.951205\pi
−0.152694 0.988274i 0.548795π-0.548795\pi
942942 0 0
943943 16.0000 0.521032
944944 0 0
945945 0 0
946946 0 0
947947 −40.0000 40.0000i −1.29983 1.29983i −0.928505 0.371321i 0.878905π-0.878905\pi
−0.371321 0.928505i 0.621095π-0.621095\pi
948948 0 0
949949 −30.0000 + 30.0000i −0.973841 + 0.973841i
950950 0 0
951951 0 0
952952 0 0
953953 18.0000i 0.583077i 0.956559 + 0.291539i 0.0941672π0.0941672\pi
−0.956559 + 0.291539i 0.905833π0.905833\pi
954954 0 0
955955 24.0000 24.0000i 0.776622 0.776622i
956956 0 0
957957 0 0
958958 0 0
959959 8.00000 0.258333
960960 0 0
961961 −15.0000 −0.483871
962962 0 0
963963 0 0
964964 0 0
965965 8.00000 8.00000i 0.257529 0.257529i
966966 0 0
967967 20.0000i 0.643157i −0.946883 0.321578i 0.895787π-0.895787\pi
0.946883 0.321578i 0.104213π-0.104213\pi
968968 0 0
969969 0 0
970970 0 0
971971 −28.0000 + 28.0000i −0.898563 + 0.898563i −0.995309 0.0967463i 0.969156π-0.969156\pi
0.0967463 + 0.995309i 0.469156π0.469156\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 −38.0000 −1.21573 −0.607864 0.794041i 0.707973π-0.707973\pi
−0.607864 + 0.794041i 0.707973π0.707973\pi
978978 0 0
979979 64.0000 + 64.0000i 2.04545 + 2.04545i
980980 0 0
981981 0 0
982982 0 0
983983 32.0000i 1.02064i 0.859984 + 0.510321i 0.170473π0.170473\pi
−0.859984 + 0.510321i 0.829527π0.829527\pi
984984 0 0
985985 2.00000i 0.0637253i
986986 0 0
987987 0 0
988988 0 0
989989 −32.0000 32.0000i −1.01754 1.01754i
990990 0 0
991991 −44.0000 −1.39771 −0.698853 0.715265i 0.746306π-0.746306\pi
−0.698853 + 0.715265i 0.746306π0.746306\pi
992992 0 0
993993 0 0
994994 0 0
995995 −4.00000 4.00000i −0.126809 0.126809i
996996 0 0
997997 33.0000 33.0000i 1.04512 1.04512i 0.0461877 0.998933i 0.485293π-0.485293\pi
0.998933 0.0461877i 0.0147072π-0.0147072\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 4608.2.k.n.1153.1 yes 2
3.2 odd 2 4608.2.k.l.1153.1 yes 2
4.3 odd 2 4608.2.k.u.1153.1 yes 2
8.3 odd 2 4608.2.k.d.1153.1 2
8.5 even 2 4608.2.k.k.1153.1 yes 2
12.11 even 2 4608.2.k.e.1153.1 yes 2
16.3 odd 4 4608.2.k.d.3457.1 yes 2
16.5 even 4 inner 4608.2.k.n.3457.1 yes 2
16.11 odd 4 4608.2.k.u.3457.1 yes 2
16.13 even 4 4608.2.k.k.3457.1 yes 2
24.5 odd 2 4608.2.k.m.1153.1 yes 2
24.11 even 2 4608.2.k.t.1153.1 yes 2
32.5 even 8 9216.2.a.t.1.2 2
32.11 odd 8 9216.2.a.a.1.1 2
32.21 even 8 9216.2.a.t.1.1 2
32.27 odd 8 9216.2.a.a.1.2 2
48.5 odd 4 4608.2.k.l.3457.1 yes 2
48.11 even 4 4608.2.k.e.3457.1 yes 2
48.29 odd 4 4608.2.k.m.3457.1 yes 2
48.35 even 4 4608.2.k.t.3457.1 yes 2
96.5 odd 8 9216.2.a.v.1.1 2
96.11 even 8 9216.2.a.c.1.2 2
96.53 odd 8 9216.2.a.v.1.2 2
96.59 even 8 9216.2.a.c.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4608.2.k.d.1153.1 2 8.3 odd 2
4608.2.k.d.3457.1 yes 2 16.3 odd 4
4608.2.k.e.1153.1 yes 2 12.11 even 2
4608.2.k.e.3457.1 yes 2 48.11 even 4
4608.2.k.k.1153.1 yes 2 8.5 even 2
4608.2.k.k.3457.1 yes 2 16.13 even 4
4608.2.k.l.1153.1 yes 2 3.2 odd 2
4608.2.k.l.3457.1 yes 2 48.5 odd 4
4608.2.k.m.1153.1 yes 2 24.5 odd 2
4608.2.k.m.3457.1 yes 2 48.29 odd 4
4608.2.k.n.1153.1 yes 2 1.1 even 1 trivial
4608.2.k.n.3457.1 yes 2 16.5 even 4 inner
4608.2.k.t.1153.1 yes 2 24.11 even 2
4608.2.k.t.3457.1 yes 2 48.35 even 4
4608.2.k.u.1153.1 yes 2 4.3 odd 2
4608.2.k.u.3457.1 yes 2 16.11 odd 4
9216.2.a.a.1.1 2 32.11 odd 8
9216.2.a.a.1.2 2 32.27 odd 8
9216.2.a.c.1.1 2 96.59 even 8
9216.2.a.c.1.2 2 96.11 even 8
9216.2.a.t.1.1 2 32.21 even 8
9216.2.a.t.1.2 2 32.5 even 8
9216.2.a.v.1.1 2 96.5 odd 8
9216.2.a.v.1.2 2 96.53 odd 8