Properties

Label 2385.1.ca.a.694.2
Level 23852385
Weight 11
Character 2385.694
Analytic conductor 1.1901.190
Analytic rank 00
Dimension 4848
Projective image D52D_{52}
CM discriminant -15
Inner twists 88

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2385,1,Mod(19,2385)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2385, base_ring=CyclotomicField(52))
 
chi = DirichletCharacter(H, H._module([0, 26, 37]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2385.19");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 2385=32553 2385 = 3^{2} \cdot 5 \cdot 53
Weight: k k == 1 1
Character orbit: [χ][\chi] == 2385.ca (of order 5252, degree 2424, 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: 1.190270055131.19027005513
Analytic rank: 00
Dimension: 4848
Relative dimension: 22 over Q(ζ52)\Q(\zeta_{52})
Coefficient field: Q(ζ104)\Q(\zeta_{104})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x48x44+x40x36+x32x28+x24x20+x16x12+x8x4+1 x^{48} - x^{44} + x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 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
Projective image: D52D_{52}
Projective field: Galois closure of Q[x]/(x52)\mathbb{Q}[x]/(x^{52} - \cdots)

Embedding invariants

Embedding label 694.2
Root 0.787183+0.616719i0.787183 + 0.616719i of defining polynomial
Character χ\chi == 2385.694
Dual form 2385.1.ca.a.244.2

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) == q+(0.556340+1.78536i)q2+(2.05501+1.41847i)q4+(0.9981760.0603785i)q5+(2.203701.72649i)q8+(0.663123+1.74851i)q10+(0.9709422.56016i)q16+(0.0989396+0.814841i)q17+(0.186505+1.01773i)q19+(1.96561+1.53996i)q20+(1.37312+1.37312i)q23+(0.9927090.120537i)q25+(0.509195+0.307819i)q31+(2.31661+0.140129i)q32+(1.50983+0.276686i)q34+(1.71325+0.899182i)q38+(2.303931.59029i)q40+(3.215431.68759i)q46+(1.30452+1.47250i)q47+(0.5680650.822984i)q49+(0.767485+1.70528i)q50+(0.7871830.616719i)q53+(0.9709421.23932i)q61+(0.8328540.737844i)q62+(0.383375+1.55542i)q64+(0.9525061.81485i)q68+(1.826891.82689i)q76+(0.5939211.90596i)q79+(0.8145922.61412i)q80+(1.16387+1.16387i)q83+(0.0495602+0.819328i)q85+(0.8740434.76950i)q92+(1.90318+3.14825i)q94+(0.247614+1.00461i)q95+(1.153281.47206i)q98+O(q100)q+(0.556340 + 1.78536i) q^{2} +(-2.05501 + 1.41847i) q^{4} +(0.998176 - 0.0603785i) q^{5} +(-2.20370 - 1.72649i) q^{8} +(0.663123 + 1.74851i) q^{10} +(0.970942 - 2.56016i) q^{16} +(-0.0989396 + 0.814841i) q^{17} +(0.186505 + 1.01773i) q^{19} +(-1.96561 + 1.53996i) q^{20} +(-1.37312 + 1.37312i) q^{23} +(0.992709 - 0.120537i) q^{25} +(-0.509195 + 0.307819i) q^{31} +(2.31661 + 0.140129i) q^{32} +(-1.50983 + 0.276686i) q^{34} +(-1.71325 + 0.899182i) q^{38} +(-2.30393 - 1.59029i) q^{40} +(-3.21543 - 1.68759i) q^{46} +(1.30452 + 1.47250i) q^{47} +(-0.568065 - 0.822984i) q^{49} +(0.767485 + 1.70528i) q^{50} +(0.787183 - 0.616719i) q^{53} +(0.970942 - 1.23932i) q^{61} +(-0.832854 - 0.737844i) q^{62} +(0.383375 + 1.55542i) q^{64} +(-0.952506 - 1.81485i) q^{68} +(-1.82689 - 1.82689i) q^{76} +(0.593921 - 1.90596i) q^{79} +(0.814592 - 2.61412i) q^{80} +(1.16387 + 1.16387i) q^{83} +(-0.0495602 + 0.819328i) q^{85} +(0.874043 - 4.76950i) q^{92} +(-1.90318 + 3.14825i) q^{94} +(0.247614 + 1.00461i) q^{95} +(1.15328 - 1.47206i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q+4q164q194q31+4q49+4q61+4q76+4q794q85+O(q100) 48 q + 4 q^{16} - 4 q^{19} - 4 q^{31} + 4 q^{49} + 4 q^{61} + 4 q^{76} + 4 q^{79} - 4 q^{85}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2385Z)×\left(\mathbb{Z}/2385\mathbb{Z}\right)^\times.

nn 14321432 14861486 18561856
χ(n)\chi(n) 1-1 e(4752)e\left(\frac{47}{52}\right) 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 0.556340 + 1.78536i 0.556340 + 1.78536i 0.616719 + 0.787183i 0.288462π0.288462\pi
−0.0603785 + 0.998176i 0.519231π0.519231\pi
33 0 0
44 −2.05501 + 1.41847i −2.05501 + 1.41847i
55 0.998176 0.0603785i 0.998176 0.0603785i
66 0 0
77 0 0 0.464723 0.885456i 0.346154π-0.346154\pi
−0.464723 + 0.885456i 0.653846π0.653846\pi
88 −2.20370 1.72649i −2.20370 1.72649i
99 0 0
1010 0.663123 + 1.74851i 0.663123 + 1.74851i
1111 0 0 0.970942 0.239316i 0.0769231π-0.0769231\pi
−0.970942 + 0.239316i 0.923077π0.923077\pi
1212 0 0
1313 0 0 0.568065 0.822984i 0.307692π-0.307692\pi
−0.568065 + 0.822984i 0.692308π0.692308\pi
1414 0 0
1515 0 0
1616 0.970942 2.56016i 0.970942 2.56016i
1717 −0.0989396 + 0.814841i −0.0989396 + 0.814841i 0.855781 + 0.517338i 0.173077π0.173077\pi
−0.954721 + 0.297503i 0.903846π0.903846\pi
1818 0 0
1919 0.186505 + 1.01773i 0.186505 + 1.01773i 0.935016 + 0.354605i 0.115385π0.115385\pi
−0.748511 + 0.663123i 0.769231π0.769231\pi
2020 −1.96561 + 1.53996i −1.96561 + 1.53996i
2121 0 0
2222 0 0
2323 −1.37312 + 1.37312i −1.37312 + 1.37312i −0.517338 + 0.855781i 0.673077π0.673077\pi
−0.855781 + 0.517338i 0.826923π0.826923\pi
2424 0 0
2525 0.992709 0.120537i 0.992709 0.120537i
2626 0 0
2727 0 0
2828 0 0
2929 0 0 −0.970942 0.239316i 0.923077π-0.923077\pi
0.970942 + 0.239316i 0.0769231π0.0769231\pi
3030 0 0
3131 −0.509195 + 0.307819i −0.509195 + 0.307819i −0.748511 0.663123i 0.769231π-0.769231\pi
0.239316 + 0.970942i 0.423077π0.423077\pi
3232 2.31661 + 0.140129i 2.31661 + 0.140129i
3333 0 0
3434 −1.50983 + 0.276686i −1.50983 + 0.276686i
3535 0 0
3636 0 0
3737 0 0 −0.935016 0.354605i 0.884615π-0.884615\pi
0.935016 + 0.354605i 0.115385π0.115385\pi
3838 −1.71325 + 0.899182i −1.71325 + 0.899182i
3939 0 0
4040 −2.30393 1.59029i −2.30393 1.59029i
4141 0 0 −0.855781 0.517338i 0.826923π-0.826923\pi
0.855781 + 0.517338i 0.173077π0.173077\pi
4242 0 0
4343 0 0 0.935016 0.354605i 0.115385π-0.115385\pi
−0.935016 + 0.354605i 0.884615π0.884615\pi
4444 0 0
4545 0 0
4646 −3.21543 1.68759i −3.21543 1.68759i
4747 1.30452 + 1.47250i 1.30452 + 1.47250i 0.787183 + 0.616719i 0.211538π0.211538\pi
0.517338 + 0.855781i 0.326923π0.326923\pi
4848 0 0
4949 −0.568065 0.822984i −0.568065 0.822984i
5050 0.767485 + 1.70528i 0.767485 + 1.70528i
5151 0 0
5252 0 0
5353 0.787183 0.616719i 0.787183 0.616719i
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0 0
5959 0 0 0.748511 0.663123i 0.230769π-0.230769\pi
−0.748511 + 0.663123i 0.769231π0.769231\pi
6060 0 0
6161 0.970942 1.23932i 0.970942 1.23932i 1.00000i 0.5π-0.5\pi
0.970942 0.239316i 0.0769231π-0.0769231\pi
6262 −0.832854 0.737844i −0.832854 0.737844i
6363 0 0
6464 0.383375 + 1.55542i 0.383375 + 1.55542i
6565 0 0
6666 0 0
6767 0 0 0.180255 0.983620i 0.442308π-0.442308\pi
−0.180255 + 0.983620i 0.557692π0.557692\pi
6868 −0.952506 1.81485i −0.952506 1.81485i
6969 0 0
7070 0 0
7171 0 0 −0.911900 0.410413i 0.865385π-0.865385\pi
0.911900 + 0.410413i 0.134615π0.134615\pi
7272 0 0
7373 0 0 −0.616719 0.787183i 0.711538π-0.711538\pi
0.616719 + 0.787183i 0.288462π0.288462\pi
7474 0 0
7575 0 0
7676 −1.82689 1.82689i −1.82689 1.82689i
7777 0 0
7878 0 0
7979 0.593921 1.90596i 0.593921 1.90596i 0.239316 0.970942i 0.423077π-0.423077\pi
0.354605 0.935016i 0.384615π-0.384615\pi
8080 0.814592 2.61412i 0.814592 2.61412i
8181 0 0
8282 0 0
8383 1.16387 + 1.16387i 1.16387 + 1.16387i 0.983620 + 0.180255i 0.0576923π0.0576923\pi
0.180255 + 0.983620i 0.442308π0.442308\pi
8484 0 0
8585 −0.0495602 + 0.819328i −0.0495602 + 0.819328i
8686 0 0
8787 0 0
8888 0 0
8989 0 0 −0.992709 0.120537i 0.961538π-0.961538\pi
0.992709 + 0.120537i 0.0384615π0.0384615\pi
9090 0 0
9191 0 0
9292 0.874043 4.76950i 0.874043 4.76950i
9393 0 0
9494 −1.90318 + 3.14825i −1.90318 + 3.14825i
9595 0.247614 + 1.00461i 0.247614 + 1.00461i
9696 0 0
9797 0 0 −0.748511 0.663123i 0.769231π-0.769231\pi
0.748511 + 0.663123i 0.230769π0.230769\pi
9898 1.15328 1.47206i 1.15328 1.47206i
9999 0 0
100100 −1.86905 + 1.65583i −1.86905 + 1.65583i
101101 0 0 −0.0603785 0.998176i 0.519231π-0.519231\pi
0.0603785 + 0.998176i 0.480769π0.480769\pi
102102 0 0
103103 0 0 0.911900 0.410413i 0.134615π-0.134615\pi
−0.911900 + 0.410413i 0.865385π0.865385\pi
104104 0 0
105105 0 0
106106 1.53901 + 1.06230i 1.53901 + 1.06230i
107107 1.41421i 1.41421i −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 0.707107i 0.250000π-0.250000\pi
108108 0 0
109109 −0.506219 1.12477i −0.506219 1.12477i −0.970942 0.239316i 0.923077π-0.923077\pi
0.464723 0.885456i 0.346154π-0.346154\pi
110110 0 0
111111 0 0
112112 0 0
113113 −1.76768 0.927751i −1.76768 0.927751i −0.911900 0.410413i 0.865385π-0.865385\pi
−0.855781 0.517338i 0.826923π-0.826923\pi
114114 0 0
115115 −1.28771 + 1.45352i −1.28771 + 1.45352i
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 0.885456 0.464723i 0.885456 0.464723i
122122 2.75280 + 1.04400i 2.75280 + 1.04400i
123123 0 0
124124 0.609768 1.35485i 0.609768 1.35485i
125125 0.983620 0.180255i 0.983620 0.180255i
126126 0 0
127127 0 0 −0.998176 0.0603785i 0.980769π-0.980769\pi
0.998176 + 0.0603785i 0.0192308π0.0192308\pi
128128 −0.577549 + 0.349141i −0.577549 + 0.349141i
129129 0 0
130130 0 0
131131 0 0 −0.120537 0.992709i 0.538462π-0.538462\pi
0.120537 + 0.992709i 0.461538π0.461538\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 1.62485 1.62485i 1.62485 1.62485i
137137 0.587763 + 0.972278i 0.587763 + 0.972278i 0.998176 + 0.0603785i 0.0192308π0.0192308\pi
−0.410413 + 0.911900i 0.634615π0.634615\pi
138138 0 0
139139 1.50308 1.17759i 1.50308 1.17759i 0.568065 0.822984i 0.307692π-0.307692\pi
0.935016 0.354605i 0.115385π-0.115385\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 0 0
145145 0 0
146146 0 0
147147 0 0
148148 0 0
149149 0 0 −0.354605 0.935016i 0.615385π-0.615385\pi
0.354605 + 0.935016i 0.384615π0.384615\pi
150150 0 0
151151 1.34731 + 1.05555i 1.34731 + 1.05555i 0.992709 + 0.120537i 0.0384615π0.0384615\pi
0.354605 + 0.935016i 0.384615π0.384615\pi
152152 1.34610 2.56477i 1.34610 2.56477i
153153 0 0
154154 0 0
155155 −0.489680 + 0.338002i −0.489680 + 0.338002i
156156 0 0
157157 0 0 −0.297503 0.954721i 0.596154π-0.596154\pi
0.297503 + 0.954721i 0.403846π0.403846\pi
158158 3.73324 3.73324
159159 0 0
160160 2.32085 2.32085
161161 0 0
162162 0 0
163163 0 0 0.822984 0.568065i 0.192308π-0.192308\pi
−0.822984 + 0.568065i 0.807692π0.807692\pi
164164 0 0
165165 0 0
166166 −1.43042 + 2.72545i −1.43042 + 2.72545i
167167 −1.39403 1.09215i −1.39403 1.09215i −0.983620 0.180255i 0.942308π-0.942308\pi
−0.410413 0.911900i 0.634615π-0.634615\pi
168168 0 0
169169 −0.354605 0.935016i −0.354605 0.935016i
170170 −1.49037 + 0.367342i −1.49037 + 0.367342i
171171 0 0
172172 0 0
173173 −0.237125 0.0434547i −0.237125 0.0434547i 0.0603785 0.998176i 0.480769π-0.480769\pi
−0.297503 + 0.954721i 0.596154π0.596154\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 0 0 0.787183 0.616719i 0.211538π-0.211538\pi
−0.787183 + 0.616719i 0.788462π0.788462\pi
180180 0 0
181181 −1.01773 1.68353i −1.01773 1.68353i −0.663123 0.748511i 0.730769π-0.730769\pi
−0.354605 0.935016i 0.615385π-0.615385\pi
182182 0 0
183183 0 0
184184 5.39663 0.655269i 5.39663 0.655269i
185185 0 0
186186 0 0
187187 0 0
188188 −4.76950 1.17558i −4.76950 1.17558i
189189 0 0
190190 −1.65583 + 1.00099i −1.65583 + 1.00099i
191191 0 0 −0.998176 0.0603785i 0.980769π-0.980769\pi
0.998176 + 0.0603785i 0.0192308π0.0192308\pi
192192 0 0
193193 0 0 0.983620 0.180255i 0.0576923π-0.0576923\pi
−0.983620 + 0.180255i 0.942308π0.942308\pi
194194 0 0
195195 0 0
196196 2.33476 + 0.885456i 2.33476 + 0.885456i
197197 −1.61489 + 0.847562i −1.61489 + 0.847562i −0.616719 + 0.787183i 0.711538π0.711538\pi
−0.998176 + 0.0603785i 0.980769π0.980769\pi
198198 0 0
199199 −1.09148 0.753393i −1.09148 0.753393i −0.120537 0.992709i 0.538462π-0.538462\pi
−0.970942 + 0.239316i 0.923077π0.923077\pi
200200 −2.39574 1.44828i −2.39574 1.44828i
201201 0 0
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 1.13613i 1.13613i 0.822984 + 0.568065i 0.192308π0.192308\pi
−0.822984 + 0.568065i 0.807692π0.807692\pi
212212 −0.742872 + 2.38396i −0.742872 + 2.38396i
213213 0 0
214214 2.52488 0.786784i 2.52488 0.786784i
215215 0 0
216216 0 0
217217 0 0
218218 1.72649 1.52954i 1.72649 1.52954i
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 0 0 −0.239316 0.970942i 0.576923π-0.576923\pi
0.239316 + 0.970942i 0.423077π0.423077\pi
224224 0 0
225225 0 0
226226 0.672936 3.67209i 0.672936 3.67209i
227227 −0.0561186 0.106925i −0.0561186 0.106925i 0.855781 0.517338i 0.173077π-0.173077\pi
−0.911900 + 0.410413i 0.865385π0.865385\pi
228228 0 0
229229 1.63397 + 0.198399i 1.63397 + 0.198399i 0.885456 0.464723i 0.153846π-0.153846\pi
0.748511 + 0.663123i 0.230769π0.230769\pi
230230 −3.31146 1.49037i −3.31146 1.49037i
231231 0 0
232232 0 0
233233 −0.119877 + 1.98180i −0.119877 + 1.98180i 0.0603785 + 0.998176i 0.480769π0.480769\pi
−0.180255 + 0.983620i 0.557692π0.557692\pi
234234 0 0
235235 1.39105 + 1.39105i 1.39105 + 1.39105i
236236 0 0
237237 0 0
238238 0 0
239239 0 0 0.297503 0.954721i 0.403846π-0.403846\pi
−0.297503 + 0.954721i 0.596154π0.596154\pi
240240 0 0
241241 −0.475142 + 1.92773i −0.475142 + 1.92773i −0.120537 + 0.992709i 0.538462π0.538462\pi
−0.354605 + 0.935016i 0.615385π0.615385\pi
242242 1.32231 + 1.32231i 1.32231 + 1.32231i
243243 0 0
244244 −0.237362 + 3.92406i −0.237362 + 3.92406i
245245 −0.616719 0.787183i −0.616719 0.787183i
246246 0 0
247247 0 0
248248 1.65356 + 0.200779i 1.65356 + 0.200779i
249249 0 0
250250 0.869047 + 1.65583i 0.869047 + 1.65583i
251251 0 0 0.180255 0.983620i 0.442308π-0.442308\pi
−0.180255 + 0.983620i 0.557692π0.557692\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0.254432 + 0.225408i 0.254432 + 0.225408i
257257 1.09215 1.39403i 1.09215 1.39403i 0.180255 0.983620i 0.442308π-0.442308\pi
0.911900 0.410413i 0.134615π-0.134615\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 0.230158 0.0717201i 0.230158 0.0717201i −0.180255 0.983620i 0.557692π-0.557692\pi
0.410413 + 0.911900i 0.365385π0.365385\pi
264264 0 0
265265 0.748511 0.663123i 0.748511 0.663123i
266266 0 0
267267 0 0
268268 0 0
269269 0 0 −0.568065 0.822984i 0.692308π-0.692308\pi
0.568065 + 0.822984i 0.307692π0.307692\pi
270270 0 0
271271 −0.616337 0.695701i −0.616337 0.695701i 0.354605 0.935016i 0.384615π-0.384615\pi
−0.970942 + 0.239316i 0.923077π0.923077\pi
272272 1.99006 + 1.04446i 1.99006 + 1.04446i
273273 0 0
274274 −1.40887 + 1.59029i −1.40887 + 1.59029i
275275 0 0
276276 0 0
277277 0 0 −0.855781 0.517338i 0.826923π-0.826923\pi
0.855781 + 0.517338i 0.173077π0.173077\pi
278278 2.93864 + 2.02840i 2.93864 + 2.02840i
279279 0 0
280280 0 0
281281 0 0 −0.935016 0.354605i 0.884615π-0.884615\pi
0.935016 + 0.354605i 0.115385π0.115385\pi
282282 0 0
283283 0 0 0.410413 0.911900i 0.365385π-0.365385\pi
−0.410413 + 0.911900i 0.634615π0.634615\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0 0
289289 0.316765 + 0.0780756i 0.316765 + 0.0780756i
290290 0 0
291291 0 0
292292 0 0
293293 −0.357882 + 0.0434547i −0.357882 + 0.0434547i −0.297503 0.954721i 0.596154π-0.596154\pi
−0.0603785 + 0.998176i 0.519231π0.519231\pi
294294 0 0
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 0 0
301301 0 0
302302 −1.13498 + 2.99269i −1.13498 + 2.99269i
303303 0 0
304304 2.78663 + 0.510670i 2.78663 + 0.510670i
305305 0.894342 1.29568i 0.894342 1.29568i
306306 0 0
307307 0 0 0.970942 0.239316i 0.0769231π-0.0769231\pi
−0.970942 + 0.239316i 0.923077π0.923077\pi
308308 0 0
309309 0 0
310310 −0.875884 0.686211i −0.875884 0.686211i
311311 0 0 0.464723 0.885456i 0.346154π-0.346154\pi
−0.464723 + 0.885456i 0.653846π0.653846\pi
312312 0 0
313313 0 0 0.998176 0.0603785i 0.0192308π-0.0192308\pi
−0.998176 + 0.0603785i 0.980769π0.980769\pi
314314 0 0
315315 0 0
316316 1.48303 + 4.75922i 1.48303 + 4.75922i
317317 1.23344 1.23344 0.616719 0.787183i 0.288462π-0.288462\pi
0.616719 + 0.787183i 0.288462π0.288462\pi
318318 0 0
319319 0 0
320320 0.476590 + 1.52943i 0.476590 + 1.52943i
321321 0 0
322322 0 0
323323 −0.847739 + 0.0512787i −0.847739 + 0.0512787i
324324 0 0
325325 0 0
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 −1.12785 + 1.63397i −1.12785 + 1.63397i −0.464723 + 0.885456i 0.653846π0.653846\pi
−0.663123 + 0.748511i 0.730769π0.730769\pi
332332 −4.04269 0.740851i −4.04269 0.740851i
333333 0 0
334334 1.17433 3.09646i 1.17433 3.09646i
335335 0 0
336336 0 0
337337 0 0 −0.180255 0.983620i 0.557692π-0.557692\pi
0.180255 + 0.983620i 0.442308π0.442308\pi
338338 1.47206 1.15328i 1.47206 1.15328i
339339 0 0
340340 −1.06035 1.75403i −1.06035 1.75403i
341341 0 0
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 −0.0543397 0.447528i −0.0543397 0.447528i
347347 0.350034 + 0.0862757i 0.350034 + 0.0862757i 0.410413 0.911900i 0.365385π-0.365385\pi
−0.0603785 + 0.998176i 0.519231π0.519231\pi
348348 0 0
349349 −0.103342 + 0.0624722i −0.103342 + 0.0624722i −0.568065 0.822984i 0.692308π-0.692308\pi
0.464723 + 0.885456i 0.346154π0.346154\pi
350350 0 0
351351 0 0
352352 0 0
353353 −0.291069 + 0.646728i −0.291069 + 0.646728i −0.998176 0.0603785i 0.980769π-0.980769\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 0 0 −0.855781 0.517338i 0.826923π-0.826923\pi
0.855781 + 0.517338i 0.173077π0.173077\pi
360360 0 0
361361 −0.0659688 + 0.0250187i −0.0659688 + 0.0250187i
362362 2.43950 2.75362i 2.43950 2.75362i
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 0 0 −0.568065 0.822984i 0.692308π-0.692308\pi
0.568065 + 0.822984i 0.307692π0.307692\pi
368368 2.18219 + 4.84863i 2.18219 + 4.84863i
369369 0 0
370370 0 0
371371 0 0
372372 0 0
373373 0 0 0.954721 0.297503i 0.0961538π-0.0961538\pi
−0.954721 + 0.297503i 0.903846π0.903846\pi
374374 0 0
375375 0 0
376376 −0.332519 5.49720i −0.332519 5.49720i
377377 0 0
378378 0 0
379379 −0.872172 + 1.11325i −0.872172 + 1.11325i 0.120537 + 0.992709i 0.461538π0.461538\pi
−0.992709 + 0.120537i 0.961538π0.961538\pi
380380 −1.93386 1.71325i −1.93386 1.71325i
381381 0 0
382382 0 0
383383 −0.247614 + 0.409604i −0.247614 + 0.409604i −0.954721 0.297503i 0.903846π-0.903846\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
384384 0 0
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 0 0 −0.911900 0.410413i 0.865385π-0.865385\pi
0.911900 + 0.410413i 0.134615π0.134615\pi
390390 0 0
391391 −0.983018 1.25473i −0.983018 1.25473i
392392 −0.169028 + 2.79437i −0.169028 + 2.79437i
393393 0 0
394394 −2.41163 2.41163i −2.41163 2.41163i
395395 0.477758 1.93834i 0.477758 1.93834i
396396 0 0
397397 0 0 0.297503 0.954721i 0.403846π-0.403846\pi
−0.297503 + 0.954721i 0.596154π0.596154\pi
398398 0.737844 2.36782i 0.737844 2.36782i
399399 0 0
400400 0.655269 2.65853i 0.655269 2.65853i
401401 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
402402 0 0
403403 0 0
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 0 0
409409 −0.902438 1.71945i −0.902438 1.71945i −0.663123 0.748511i 0.730769π-0.730769\pi
−0.239316 0.970942i 0.576923π-0.576923\pi
410410 0 0
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 1.23202 + 1.09148i 1.23202 + 1.09148i
416416 0 0
417417 0 0
418418 0 0
419419 0 0 −0.0603785 0.998176i 0.519231π-0.519231\pi
0.0603785 + 0.998176i 0.480769π0.480769\pi
420420 0 0
421421 1.74122 0.783659i 1.74122 0.783659i 0.748511 0.663123i 0.230769π-0.230769\pi
0.992709 0.120537i 0.0384615π-0.0384615\pi
422422 −2.02840 + 0.632075i −2.02840 + 0.632075i
423423 0 0
424424 −2.79948 −2.79948
425425 0.820826i 0.820826i
426426 0 0
427427 0 0
428428 2.00602 + 2.90622i 2.00602 + 2.90622i
429429 0 0
430430 0 0
431431 0 0 −0.885456 0.464723i 0.846154π-0.846154\pi
0.885456 + 0.464723i 0.153846π0.153846\pi
432432 0 0
433433 0 0 0.663123 0.748511i 0.269231π-0.269231\pi
−0.663123 + 0.748511i 0.730769π0.730769\pi
434434 0 0
435435 0 0
436436 2.63574 + 1.59336i 2.63574 + 1.59336i
437437 −1.65356 1.14137i −1.65356 1.14137i
438438 0 0
439439 −1.56806 + 0.822984i −1.56806 + 0.822984i −0.568065 + 0.822984i 0.692308π0.692308\pi
−1.00000 π\pi
440440 0 0
441441 0 0
442442 0 0
443443 −0.697593 + 0.127839i −0.697593 + 0.127839i −0.517338 0.855781i 0.673077π-0.673077\pi
−0.180255 + 0.983620i 0.557692π0.557692\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 0 0 −0.120537 0.992709i 0.538462π-0.538462\pi
0.120537 + 0.992709i 0.461538π0.461538\pi
450450 0 0
451451 0 0
452452 4.94859 0.600867i 4.94859 0.600867i
453453 0 0
454454 0.159679 0.159679i 0.159679 0.159679i
455455 0 0
456456 0 0
457457 0 0 0.787183 0.616719i 0.211538π-0.211538\pi
−0.787183 + 0.616719i 0.788462π0.788462\pi
458458 0.554827 + 3.02759i 0.554827 + 3.02759i
459459 0 0
460460 0.584473 4.81357i 0.584473 4.81357i
461461 0 0 0.354605 0.935016i 0.384615π-0.384615\pi
−0.354605 + 0.935016i 0.615385π0.615385\pi
462462 0 0
463463 0 0 −0.983620 0.180255i 0.942308π-0.942308\pi
0.983620 + 0.180255i 0.0576923π0.0576923\pi
464464 0 0
465465 0 0
466466 −3.60491 + 0.888530i −3.60491 + 0.888530i
467467 −0.677097 1.78536i −0.677097 1.78536i −0.616719 0.787183i 0.711538π-0.711538\pi
−0.0603785 0.998176i 0.519231π-0.519231\pi
468468 0 0
469469 0 0
470470 −1.70962 + 3.25742i −1.70962 + 3.25742i
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 0.307819 + 0.987826i 0.307819 + 0.987826i
476476 0 0
477477 0 0
478478 0 0
479479 0 0 −0.297503 0.954721i 0.596154π-0.596154\pi
0.297503 + 0.954721i 0.403846π0.403846\pi
480480 0 0
481481 0 0
482482 −3.70602 + 0.224173i −3.70602 + 0.224173i
483483 0 0
484484 −1.16042 + 2.21100i −1.16042 + 2.21100i
485485 0 0
486486 0 0
487487 0 0 −0.354605 0.935016i 0.615385π-0.615385\pi
0.354605 + 0.935016i 0.384615π0.384615\pi
488488 −4.27934 + 1.05476i −4.27934 + 1.05476i
489489 0 0
490490 1.06230 1.53901i 1.06230 1.53901i
491491 0 0 −0.983620 0.180255i 0.942308π-0.942308\pi
0.983620 + 0.180255i 0.0576923π0.0576923\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 0.293668 + 1.60250i 0.293668 + 1.60250i
497497 0 0
498498 0 0
499499 0.186505 + 0.308518i 0.186505 + 0.308518i 0.935016 0.354605i 0.115385π-0.115385\pi
−0.748511 + 0.663123i 0.769231π0.769231\pi
500500 −1.76566 + 1.76566i −1.76566 + 1.76566i
501501 0 0
502502 0 0
503503 0.677097 + 0.210992i 0.677097 + 0.210992i 0.616719 0.787183i 0.288462π-0.288462\pi
0.0603785 + 0.998176i 0.480769π0.480769\pi
504504 0 0
505505 0 0
506506 0 0
507507 0 0
508508 0 0
509509 0 0 −0.998176 0.0603785i 0.980769π-0.980769\pi
0.998176 + 0.0603785i 0.0192308π0.0192308\pi
510510 0 0
511511 0 0
512512 −0.537862 + 1.19508i −0.537862 + 1.19508i
513513 0 0
514514 3.09646 + 1.17433i 3.09646 + 1.17433i
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 0 0 0.663123 0.748511i 0.269231π-0.269231\pi
−0.663123 + 0.748511i 0.730769π0.730769\pi
522522 0 0
523523 0 0 −0.885456 0.464723i 0.846154π-0.846154\pi
0.885456 + 0.464723i 0.153846π0.153846\pi
524524 0 0
525525 0 0
526526 0.256092 + 0.371013i 0.256092 + 0.371013i
527527 −0.200444 0.445368i −0.200444 0.445368i
528528 0 0
529529 2.77091i 2.77091i
530530 1.60034 + 0.967439i 1.60034 + 0.967439i
531531 0 0
532532 0 0
533533 0 0
534534 0 0
535535 −0.0853881 1.41163i −0.0853881 1.41163i
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0 0
541541 0.423807 + 1.71945i 0.423807 + 1.71945i 0.663123 + 0.748511i 0.269231π0.269231\pi
−0.239316 + 0.970942i 0.576923π0.576923\pi
542542 0.899182 1.48743i 0.899182 1.48743i
543543 0 0
544544 −0.343388 + 1.87381i −0.343388 + 1.87381i
545545 −0.573207 1.09215i −0.573207 1.09215i
546546 0 0
547547 0 0 −0.992709 0.120537i 0.961538π-0.961538\pi
0.992709 + 0.120537i 0.0384615π0.0384615\pi
548548 −2.58700 1.16432i −2.58700 1.16432i
549549 0 0
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 −1.41847 + 4.55203i −1.41847 + 4.55203i
557557 −0.489680 + 1.57144i −0.489680 + 1.57144i 0.297503 + 0.954721i 0.403846π0.403846\pi
−0.787183 + 0.616719i 0.788462π0.788462\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 0 0
563563 0.295181 + 0.376771i 0.295181 + 0.376771i 0.911900 0.410413i 0.134615π-0.134615\pi
−0.616719 + 0.787183i 0.711538π0.711538\pi
564564 0 0
565565 −1.82047 0.819328i −1.82047 0.819328i
566566 0 0
567567 0 0
568568 0 0
569569 0 0 0.180255 0.983620i 0.442308π-0.442308\pi
−0.180255 + 0.983620i 0.557692π0.557692\pi
570570 0 0
571571 −0.424644 + 0.702447i −0.424644 + 0.702447i −0.992709 0.120537i 0.961538π-0.961538\pi
0.568065 + 0.822984i 0.307692π0.307692\pi
572572 0 0
573573 0 0
574574 0 0
575575 −1.19760 + 1.52862i −1.19760 + 1.52862i
576576 0 0
577577 0 0 0.748511 0.663123i 0.230769π-0.230769\pi
−0.748511 + 0.663123i 0.769231π0.769231\pi
578578 0.0368363 + 0.608976i 0.0368363 + 0.608976i
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 −0.276686 0.614771i −0.276686 0.614771i
587587 −0.894342 1.29568i −0.894342 1.29568i −0.954721 0.297503i 0.903846π-0.903846\pi
0.0603785 0.998176i 0.480769π-0.480769\pi
588588 0 0
589589 −0.408244 0.460812i −0.408244 0.460812i
590590 0 0
591591 0 0
592592 0 0
593593 1.32231 0.501487i 1.32231 0.501487i 0.410413 0.911900i 0.365385π-0.365385\pi
0.911900 + 0.410413i 0.134615π0.134615\pi
594594 0 0
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 0 0 −0.935016 0.354605i 0.884615π-0.884615\pi
0.935016 + 0.354605i 0.115385π0.115385\pi
600600 0 0
601601 −0.0495602 + 0.110118i −0.0495602 + 0.110118i −0.935016 0.354605i 0.884615π-0.884615\pi
0.885456 + 0.464723i 0.153846π0.153846\pi
602602 0 0
603603 0 0
604604 −4.26601 0.258046i −4.26601 0.258046i
605605 0.855781 0.517338i 0.855781 0.517338i
606606 0 0
607607 0 0 −0.970942 0.239316i 0.923077π-0.923077\pi
0.970942 + 0.239316i 0.0769231π0.0769231\pi
608608 0.289448 + 2.38382i 0.289448 + 2.38382i
609609 0 0
610610 2.81081 + 0.875884i 2.81081 + 0.875884i
611611 0 0
612612 0 0
613613 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
614614 0 0
615615 0 0
616616 0 0
617617 −0.269846 1.47250i −0.269846 1.47250i −0.787183 0.616719i 0.788462π-0.788462\pi
0.517338 0.855781i 0.326923π-0.326923\pi
618618 0 0
619619 −0.0576926 + 0.475142i −0.0576926 + 0.475142i 0.935016 + 0.354605i 0.115385π0.115385\pi
−0.992709 + 0.120537i 0.961538π0.961538\pi
620620 0.526852 1.38919i 0.526852 1.38919i
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 0.970942 0.239316i 0.970942 0.239316i
626626 0 0
627627 0 0
628628 0 0
629629 0 0
630630 0 0
631631 −0.120537 + 0.00729113i −0.120537 + 0.00729113i −0.120537 0.992709i 0.538462π-0.538462\pi
1.00000i 0.5π0.5\pi
632632 −4.59945 + 3.17477i −4.59945 + 3.17477i
633633 0 0
634634 0.686211 + 2.20213i 0.686211 + 2.20213i
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 −0.555415 + 0.383375i −0.555415 + 0.383375i
641641 0 0 0.998176 0.0603785i 0.0192308π-0.0192308\pi
−0.998176 + 0.0603785i 0.980769π0.980769\pi
642642 0 0
643643 0 0 0.464723 0.885456i 0.346154π-0.346154\pi
−0.464723 + 0.885456i 0.653846π0.653846\pi
644644 0 0
645645 0 0
646646 −0.563182 1.48499i −0.563182 1.48499i
647647 1.93834 0.477758i 1.93834 0.477758i 0.954721 0.297503i 0.0961538π-0.0961538\pi
0.983620 0.180255i 0.0576923π-0.0576923\pi
648648 0 0
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 0.189769 1.56289i 0.189769 1.56289i −0.517338 0.855781i 0.673077π-0.673077\pi
0.707107 0.707107i 0.250000π-0.250000\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
660660 0 0
661661 −0.239316 + 0.0290582i −0.239316 + 0.0290582i −0.239316 0.970942i 0.576923π-0.576923\pi
1.00000i 0.5π0.5\pi
662662 −3.54468 1.10457i −3.54468 1.10457i
663663 0 0
664664 −0.555415 4.57426i −0.555415 4.57426i
665665 0 0
666666 0 0
667667 0 0
668668 4.41394 + 0.266994i 4.41394 + 0.266994i
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 0 0 −0.935016 0.354605i 0.884615π-0.884615\pi
0.935016 + 0.354605i 0.115385π0.115385\pi
674674 0 0
675675 0 0
676676 2.05501 + 1.41847i 2.05501 + 1.41847i
677677 −0.409604 0.247614i −0.409604 0.247614i 0.297503 0.954721i 0.403846π-0.403846\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
678678 0 0
679679 0 0
680680 1.52378 1.71999i 1.52378 1.71999i
681681 0 0
682682 0 0
683683 −1.20940 1.36513i −1.20940 1.36513i −0.911900 0.410413i 0.865385π-0.865385\pi
−0.297503 0.954721i 0.596154π-0.596154\pi
684684 0 0
685685 0.645395 + 0.935016i 0.645395 + 0.935016i
686686 0 0
687687 0 0
688688 0 0
689689 0 0
690690 0 0
691691 1.50308 0.468379i 1.50308 0.468379i 0.568065 0.822984i 0.307692π-0.307692\pi
0.935016 + 0.354605i 0.115385π0.115385\pi
692692 0.548932 0.247054i 0.548932 0.247054i
693693 0 0
694694 0.0407051 + 0.672936i 0.0407051 + 0.672936i
695695 1.42924 1.26619i 1.42924 1.26619i
696696 0 0
697697 0 0
698698 −0.169028 0.149746i −0.169028 0.149746i
699699 0 0
700700 0 0
701701 0 0 0.517338 0.855781i 0.326923π-0.326923\pi
−0.517338 + 0.855781i 0.673077π0.673077\pi
702702 0 0
703703 0 0
704704 0 0
705705 0 0
706706 −1.31658 0.159861i −1.31658 0.159861i
707707 0 0
708708 0 0
709709 −0.872172 1.11325i −0.872172 1.11325i −0.992709 0.120537i 0.961538π-0.961538\pi
0.120537 0.992709i 0.461538π-0.461538\pi
710710 0 0
711711 0 0
712712 0 0
713713 0.276513 1.12186i 0.276513 1.12186i
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
720720 0 0
721721 0 0
722722 −0.0813684 0.103859i −0.0813684 0.103859i
723723 0 0
724724 4.47947 + 2.01605i 4.47947 + 2.01605i
725725 0 0
726726 0 0
727727 0 0 −0.464723 0.885456i 0.653846π-0.653846\pi
0.464723 + 0.885456i 0.346154π0.346154\pi
728728 0 0
729729 0 0
730730 0 0
731731 0 0
732732 0 0
733733 0 0 −0.748511 0.663123i 0.769231π-0.769231\pi
0.748511 + 0.663123i 0.230769π0.230769\pi
734734 0 0
735735 0 0
736736 −3.37340 + 2.98857i −3.37340 + 2.98857i
737737 0 0
738738 0 0
739739 −1.12477 + 0.506219i −1.12477 + 0.506219i −0.885456 0.464723i 0.846154π-0.846154\pi
−0.239316 + 0.970942i 0.576923π0.576923\pi
740740 0 0
741741 0 0
742742 0 0
743743 0.120757i 0.120757i 0.998176 + 0.0603785i 0.0192308π0.0192308\pi
−0.998176 + 0.0603785i 0.980769π0.980769\pi
744744 0 0
745745 0 0
746746 0 0
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 −0.159861 + 0.180446i −0.159861 + 0.180446i −0.822984 0.568065i 0.807692π-0.807692\pi
0.663123 + 0.748511i 0.269231π0.269231\pi
752752 5.03645 1.91008i 5.03645 1.91008i
753753 0 0
754754 0 0
755755 1.40859 + 0.972278i 1.40859 + 0.972278i
756756 0 0
757757 0 0 0.885456 0.464723i 0.153846π-0.153846\pi
−0.885456 + 0.464723i 0.846154π0.846154\pi
758758 −2.47277 0.937797i −2.47277 0.937797i
759759 0 0
760760 1.18878 2.64137i 1.18878 2.64137i
761761 0 0 0.983620 0.180255i 0.0576923π-0.0576923\pi
−0.983620 + 0.180255i 0.942308π0.942308\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 −0.869047 0.214201i −0.869047 0.214201i
767767 0 0
768768 0 0
769769 1.63406 + 0.509195i 1.63406 + 0.509195i 0.970942 0.239316i 0.0769231π-0.0769231\pi
0.663123 + 0.748511i 0.269231π0.269231\pi
770770 0 0
771771 0 0
772772 0 0
773773 −0.366901 0.606928i −0.366901 0.606928i 0.616719 0.787183i 0.288462π-0.288462\pi
−0.983620 + 0.180255i 0.942308π0.942308\pi
774774 0 0
775775 −0.468379 + 0.366951i −0.468379 + 0.366951i
776776 0 0
777777 0 0
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 1.69325 2.45310i 1.69325 2.45310i
783783 0 0
784784 −2.65853 + 0.655269i −2.65853 + 0.655269i
785785 0 0
786786 0 0
787787 0 0 −0.787183 0.616719i 0.788462π-0.788462\pi
0.787183 + 0.616719i 0.211538π0.211538\pi
788788 2.11638 4.03243i 2.11638 4.03243i
789789 0 0
790790 3.72643 0.225408i 3.72643 0.225408i
791791 0 0
792792 0 0
793793 0 0
794794 0 0
795795 0 0
796796 3.31166 3.31166
797797 0.590668 + 1.89552i 0.590668 + 1.89552i 0.410413 + 0.911900i 0.365385π0.365385\pi
0.180255 + 0.983620i 0.442308π0.442308\pi
798798 0 0
799799 −1.32892 + 0.917289i −1.32892 + 0.917289i
800800 2.31661 0.140129i 2.31661 0.140129i
801801 0 0
802802 0 0
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 0 0 −0.983620 0.180255i 0.942308π-0.942308\pi
0.983620 + 0.180255i 0.0576923π0.0576923\pi
810810 0 0
811811 −0.627974 + 1.65583i −0.627974 + 1.65583i 0.120537 + 0.992709i 0.461538π0.461538\pi
−0.748511 + 0.663123i 0.769231π0.769231\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 0 0
818818 2.56778 2.56778i 2.56778 2.56778i
819819 0 0
820820 0 0
821821 0 0 −0.954721 0.297503i 0.903846π-0.903846\pi
0.954721 + 0.297503i 0.0961538π0.0961538\pi
822822 0 0
823823 0 0 −0.120537 0.992709i 0.538462π-0.538462\pi
0.120537 + 0.992709i 0.461538π0.461538\pi
824824 0 0
825825 0 0
826826 0 0
827827 1.49429 + 0.0903879i 1.49429 + 0.0903879i 0.787183 0.616719i 0.211538π-0.211538\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
828828 0 0
829829 1.79393 0.328749i 1.79393 0.328749i 0.822984 0.568065i 0.192308π-0.192308\pi
0.970942 + 0.239316i 0.0769231π0.0769231\pi
830830 −1.26326 + 2.80684i −1.26326 + 2.80684i
831831 0 0
832832 0 0
833833 0.726805 0.381457i 0.726805 0.381457i
834834 0 0
835835 −1.45743 1.00599i −1.45743 1.00599i
836836 0 0
837837 0 0
838838 0 0
839839 0 0 0.663123 0.748511i 0.269231π-0.269231\pi
−0.663123 + 0.748511i 0.730769π0.730769\pi
840840 0 0
841841 0.885456 + 0.464723i 0.885456 + 0.464723i
842842 2.36782 + 2.67272i 2.36782 + 2.67272i
843843 0 0
844844 −1.61157 2.33476i −1.61157 2.33476i
845845 −0.410413 0.911900i −0.410413 0.911900i
846846 0 0
847847 0 0
848848 −0.814592 2.61412i −0.814592 2.61412i
849849 0 0
850850 −1.46547 + 0.456658i −1.46547 + 0.456658i
851851 0 0
852852 0 0
853853 0 0 −0.0603785 0.998176i 0.519231π-0.519231\pi
0.0603785 + 0.998176i 0.480769π0.480769\pi
854854 0 0
855855 0 0
856856 −2.44163 + 3.11651i −2.44163 + 3.11651i
857857 1.36513 + 1.20940i 1.36513 + 1.20940i 0.954721 + 0.297503i 0.0961538π0.0961538\pi
0.410413 + 0.911900i 0.365385π0.365385\pi
858858 0 0
859859 −0.317391 1.28771i −0.317391 1.28771i −0.885456 0.464723i 0.846154π-0.846154\pi
0.568065 0.822984i 0.307692π-0.307692\pi
860860 0 0
861861 0 0
862862 0 0
863863 −0.795403 1.51551i −0.795403 1.51551i −0.855781 0.517338i 0.826923π-0.826923\pi
0.0603785 0.998176i 0.480769π-0.480769\pi
864864 0 0
865865 −0.239316 0.0290582i −0.239316 0.0290582i
866866 0 0
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 −0.826353 + 3.35265i −0.826353 + 3.35265i
873873 0 0
874874 1.11781 3.58718i 1.11781 3.58718i
875875 0 0
876876 0 0
877877 0 0 0.239316 0.970942i 0.423077π-0.423077\pi
−0.239316 + 0.970942i 0.576923π0.576923\pi
878878 −2.34170 2.34170i −2.34170 2.34170i
879879 0 0
880880 0 0
881881 0 0 −0.616719 0.787183i 0.711538π-0.711538\pi
0.616719 + 0.787183i 0.288462π0.288462\pi
882882 0 0
883883 0 0 −0.911900 0.410413i 0.865385π-0.865385\pi
0.911900 + 0.410413i 0.134615π0.134615\pi
884884 0 0
885885 0 0
886886 −0.616337 1.17433i −0.616337 1.17433i
887887 0.239062 1.30452i 0.239062 1.30452i −0.616719 0.787183i 0.711538π-0.711538\pi
0.855781 0.517338i 0.173077π-0.173077\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 −1.25530 + 1.60228i −1.25530 + 1.60228i
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 0 0
901901 0.424644 + 0.702447i 0.424644 + 0.702447i
902902 0 0
903903 0 0
904904 2.29369 + 5.09637i 2.29369 + 5.09637i
905905 −1.11752 1.61901i −1.11752 1.61901i
906906 0 0
907907 0 0 −0.663123 0.748511i 0.730769π-0.730769\pi
0.663123 + 0.748511i 0.269231π0.269231\pi
908908 0.266994 + 0.140129i 0.266994 + 0.140129i
909909 0 0
910910 0 0
911911 0 0 0.935016 0.354605i 0.115385π-0.115385\pi
−0.935016 + 0.354605i 0.884615π0.884615\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 −3.63924 + 1.91002i −3.63924 + 1.91002i
917917 0 0
918918 0 0
919919 −0.646140 + 1.43566i −0.646140 + 1.43566i 0.239316 + 0.970942i 0.423077π0.423077\pi
−0.885456 + 0.464723i 0.846154π0.846154\pi
920920 5.34722 0.979914i 5.34722 0.979914i
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 0 0 0.992709 0.120537i 0.0384615π-0.0384615\pi
−0.992709 + 0.120537i 0.961538π0.961538\pi
930930 0 0
931931 0.731626 0.731626i 0.731626 0.731626i
932932 −2.56477 4.24265i −2.56477 4.24265i
933933 0 0
934934 2.81081 2.20213i 2.81081 2.20213i
935935 0 0
936936 0 0
937937 0 0 0.120537 0.992709i 0.461538π-0.461538\pi
−0.120537 + 0.992709i 0.538462π0.538462\pi
938938 0 0
939939 0 0
940940 −4.83178 0.885456i −4.83178 0.885456i
941941 0 0 0.568065 0.822984i 0.307692π-0.307692\pi
−0.568065 + 0.822984i 0.692308π0.692308\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0.573207 1.09215i 0.573207 1.09215i −0.410413 0.911900i 0.634615π-0.634615\pi
0.983620 0.180255i 0.0576923π-0.0576923\pi
948948 0 0
949949 0 0
950950 −1.59237 + 1.09914i −1.59237 + 1.09914i
951951 0 0
952952 0 0
953953 −1.03468 −1.03468 −0.517338 0.855781i 0.673077π-0.673077\pi
−0.517338 + 0.855781i 0.673077π0.673077\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −0.300196 + 0.571976i −0.300196 + 0.571976i
962962 0 0
963963 0 0
964964 −1.75800 4.63547i −1.75800 4.63547i
965965 0 0
966966 0 0
967967 0 0 0.568065 0.822984i 0.307692π-0.307692\pi
−0.568065 + 0.822984i 0.692308π0.692308\pi
968968 −2.75362 0.504620i −2.75362 0.504620i
969969 0 0
970970 0 0
971971 0 0 0.120537 0.992709i 0.461538π-0.461538\pi
−0.120537 + 0.992709i 0.538462π0.538462\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 −2.23012 3.68907i −2.23012 3.68907i
977977 −0.937797 + 0.937797i −0.937797 + 0.937797i −0.998176 0.0603785i 0.980769π-0.980769\pi
0.0603785 + 0.998176i 0.480769π0.480769\pi
978978 0 0
979979 0 0
980980 2.38396 + 0.742872i 2.38396 + 0.742872i
981981 0 0
982982 0 0
983983 −1.85396 0.456959i −1.85396 0.456959i −0.855781 0.517338i 0.826923π-0.826923\pi
−0.998176 + 0.0603785i 0.980769π0.980769\pi
984984 0 0
985985 −1.56077 + 0.943521i −1.56077 + 0.943521i
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 −0.447528 0.169725i −0.447528 0.169725i 0.120537 0.992709i 0.461538π-0.461538\pi
−0.568065 + 0.822984i 0.692308π0.692308\pi
992992 −1.22274 + 0.641745i −1.22274 + 0.641745i
993993 0 0
994994 0 0
995995 −1.13498 0.686117i −1.13498 0.686117i
996996 0 0
997997 0 0 0.935016 0.354605i 0.115385π-0.115385\pi
−0.935016 + 0.354605i 0.884615π0.884615\pi
998998 −0.447054 + 0.504620i −0.447054 + 0.504620i
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 2385.1.ca.a.694.2 yes 48
3.2 odd 2 inner 2385.1.ca.a.694.1 yes 48
5.4 even 2 inner 2385.1.ca.a.694.1 yes 48
15.14 odd 2 CM 2385.1.ca.a.694.2 yes 48
53.32 odd 52 inner 2385.1.ca.a.244.1 48
159.32 even 52 inner 2385.1.ca.a.244.2 yes 48
265.244 odd 52 inner 2385.1.ca.a.244.2 yes 48
795.509 even 52 inner 2385.1.ca.a.244.1 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2385.1.ca.a.244.1 48 53.32 odd 52 inner
2385.1.ca.a.244.1 48 795.509 even 52 inner
2385.1.ca.a.244.2 yes 48 159.32 even 52 inner
2385.1.ca.a.244.2 yes 48 265.244 odd 52 inner
2385.1.ca.a.694.1 yes 48 3.2 odd 2 inner
2385.1.ca.a.694.1 yes 48 5.4 even 2 inner
2385.1.ca.a.694.2 yes 48 1.1 even 1 trivial
2385.1.ca.a.694.2 yes 48 15.14 odd 2 CM