Properties

Label 1156.1.l.a.339.1
Level 11561156
Weight 11
Character 1156.339
Analytic conductor 0.5770.577
Analytic rank 00
Dimension 1616
Projective image D34D_{34}
CM discriminant -4
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1156,1,Mod(67,1156)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1156, base_ring=CyclotomicField(34))
 
chi = DirichletCharacter(H, H._module([17, 23]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1156.67");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 1156=22172 1156 = 2^{2} \cdot 17^{2}
Weight: k k == 1 1
Character orbit: [χ][\chi] == 1156.l (of order 3434, degree 1616, 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: 0.5769191546040.576919154604
Analytic rank: 00
Dimension: 1616
Coefficient field: Q(ζ34)\Q(\zeta_{34})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16x15+x14x13+x12x11+x10x9+x8x7+x6x5++1 x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D34D_{34}
Projective field: Galois closure of Q[x]/(x34)\mathbb{Q}[x]/(x^{34} - \cdots)

Embedding invariants

Embedding label 339.1
Root 0.739009+0.673696i-0.739009 + 0.673696i of defining polynomial
Character χ\chi == 1156.339
Dual form 1156.1.l.a.815.1

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+(0.445738+0.895163i)q2+(0.6026350.798017i)q4+(0.0675278+0.361242i)q5+(0.9829730.183750i)q8+(0.739009+0.673696i)q9+(0.2932710.221468i)q10+(1.452850.271585i)q13+(0.273663+0.961826i)q16+(0.273663+0.961826i)q17+(0.2736630.961826i)q18+(0.3289720.163808i)q20+(0.806537+0.312454i)q25+(0.404479+1.42160i)q26+(1.07524+0.811985i)q29+(0.7390090.673696i)q32+(0.7390090.673696i)q34+(0.982973+0.183750i)q36+(0.942485+1.52217i)q37+0.367499iq40+(0.1327560.342683i)q41+(0.1934630.312454i)q45+(0.0922684+0.995734i)q49+(0.639202+0.582709i)q50+(1.092270.995734i)q52+(0.1363740.124322i)q53+(0.2475821.32445i)q58+(0.719401+0.0666624i)q61+(0.9324720.361242i)q64+0.543170iq65+(0.9324720.361242i)q68+(0.602635+0.798017i)q72+(1.295960.368731i)q73+(1.78269+0.165190i)q74+(0.3289720.163808i)q80+(0.09226840.995734i)q81+(0.365931+0.0339085i)q82+(0.3289720.163808i)q85+(0.876298+0.163808i)q89+(0.3659310.0339085i)q90+(1.075241.17948i)q97+(0.8502170.526432i)q98+O(q100)q+(-0.445738 + 0.895163i) q^{2} +(-0.602635 - 0.798017i) q^{4} +(-0.0675278 + 0.361242i) q^{5} +(0.982973 - 0.183750i) q^{8} +(-0.739009 + 0.673696i) q^{9} +(-0.293271 - 0.221468i) q^{10} +(1.45285 - 0.271585i) q^{13} +(-0.273663 + 0.961826i) q^{16} +(-0.273663 + 0.961826i) q^{17} +(-0.273663 - 0.961826i) q^{18} +(0.328972 - 0.163808i) q^{20} +(0.806537 + 0.312454i) q^{25} +(-0.404479 + 1.42160i) q^{26} +(-1.07524 + 0.811985i) q^{29} +(-0.739009 - 0.673696i) q^{32} +(-0.739009 - 0.673696i) q^{34} +(0.982973 + 0.183750i) q^{36} +(0.942485 + 1.52217i) q^{37} +0.367499i q^{40} +(-0.132756 - 0.342683i) q^{41} +(-0.193463 - 0.312454i) q^{45} +(-0.0922684 + 0.995734i) q^{49} +(-0.639202 + 0.582709i) q^{50} +(-1.09227 - 0.995734i) q^{52} +(0.136374 - 0.124322i) q^{53} +(-0.247582 - 1.32445i) q^{58} +(0.719401 + 0.0666624i) q^{61} +(0.932472 - 0.361242i) q^{64} +0.543170i q^{65} +(0.932472 - 0.361242i) q^{68} +(-0.602635 + 0.798017i) q^{72} +(-1.29596 - 0.368731i) q^{73} +(-1.78269 + 0.165190i) q^{74} +(-0.328972 - 0.163808i) q^{80} +(0.0922684 - 0.995734i) q^{81} +(0.365931 + 0.0339085i) q^{82} +(-0.328972 - 0.163808i) q^{85} +(0.876298 + 0.163808i) q^{89} +(0.365931 - 0.0339085i) q^{90} +(-1.07524 - 1.17948i) q^{97} +(-0.850217 - 0.526432i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+q2q417q5+q8+q9+2q13q16q17q18+16q252q26+q32+q34+q36+q49+q5015q522q53q64q68+q98+O(q100) 16 q + q^{2} - q^{4} - 17 q^{5} + q^{8} + q^{9} + 2 q^{13} - q^{16} - q^{17} - q^{18} + 16 q^{25} - 2 q^{26} + q^{32} + q^{34} + q^{36} + q^{49} + q^{50} - 15 q^{52} - 2 q^{53} - q^{64} - q^{68}+ \cdots - q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1156Z)×\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times.

nn 579579 581581
χ(n)\chi(n) 1-1 e(1334)e\left(\frac{13}{34}\right)

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 −0.445738 + 0.895163i −0.445738 + 0.895163i
33 0 0 −0.361242 0.932472i 0.617647π-0.617647\pi
0.361242 + 0.932472i 0.382353π0.382353\pi
44 −0.602635 0.798017i −0.602635 0.798017i
55 −0.0675278 + 0.361242i −0.0675278 + 0.361242i 0.932472 + 0.361242i 0.117647π0.117647\pi
−1.00000 π\pi
66 0 0
77 0 0 −0.673696 0.739009i 0.735294π-0.735294\pi
0.673696 + 0.739009i 0.264706π0.264706\pi
88 0.982973 0.183750i 0.982973 0.183750i
99 −0.739009 + 0.673696i −0.739009 + 0.673696i
1010 −0.293271 0.221468i −0.293271 0.221468i
1111 0 0 0.798017 0.602635i 0.205882π-0.205882\pi
−0.798017 + 0.602635i 0.794118π0.794118\pi
1212 0 0
1313 1.45285 0.271585i 1.45285 0.271585i 0.602635 0.798017i 0.294118π-0.294118\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
1414 0 0
1515 0 0
1616 −0.273663 + 0.961826i −0.273663 + 0.961826i
1717 −0.273663 + 0.961826i −0.273663 + 0.961826i
1818 −0.273663 0.961826i −0.273663 0.961826i
1919 0 0 −0.445738 0.895163i 0.647059π-0.647059\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
2020 0.328972 0.163808i 0.328972 0.163808i
2121 0 0
2222 0 0
2323 0 0 −0.673696 0.739009i 0.735294π-0.735294\pi
0.673696 + 0.739009i 0.264706π0.264706\pi
2424 0 0
2525 0.806537 + 0.312454i 0.806537 + 0.312454i
2626 −0.404479 + 1.42160i −0.404479 + 1.42160i
2727 0 0
2828 0 0
2929 −1.07524 + 0.811985i −1.07524 + 0.811985i −0.982973 0.183750i 0.941176π-0.941176\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
3030 0 0
3131 0 0 −0.183750 0.982973i 0.558824π-0.558824\pi
0.183750 + 0.982973i 0.441176π0.441176\pi
3232 −0.739009 0.673696i −0.739009 0.673696i
3333 0 0
3434 −0.739009 0.673696i −0.739009 0.673696i
3535 0 0
3636 0.982973 + 0.183750i 0.982973 + 0.183750i
3737 0.942485 + 1.52217i 0.942485 + 1.52217i 0.850217 + 0.526432i 0.176471π0.176471\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
3838 0 0
3939 0 0
4040 0.367499i 0.367499i
4141 −0.132756 0.342683i −0.132756 0.342683i 0.850217 0.526432i 0.176471π-0.176471\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
4242 0 0
4343 0 0 −0.273663 0.961826i 0.588235π-0.588235\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
4444 0 0
4545 −0.193463 0.312454i −0.193463 0.312454i
4646 0 0
4747 0 0 −0.739009 0.673696i 0.764706π-0.764706\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
4848 0 0
4949 −0.0922684 + 0.995734i −0.0922684 + 0.995734i
5050 −0.639202 + 0.582709i −0.639202 + 0.582709i
5151 0 0
5252 −1.09227 0.995734i −1.09227 0.995734i
5353 0.136374 0.124322i 0.136374 0.124322i −0.602635 0.798017i 0.705882π-0.705882\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 −0.247582 1.32445i −0.247582 1.32445i
5959 0 0 −0.0922684 0.995734i 0.529412π-0.529412\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
6060 0 0
6161 0.719401 + 0.0666624i 0.719401 + 0.0666624i 0.445738 0.895163i 0.352941π-0.352941\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
6262 0 0
6363 0 0
6464 0.932472 0.361242i 0.932472 0.361242i
6565 0.543170i 0.543170i
6666 0 0
6767 0 0 −0.445738 0.895163i 0.647059π-0.647059\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
6868 0.932472 0.361242i 0.932472 0.361242i
6969 0 0
7070 0 0
7171 0 0 −0.673696 0.739009i 0.735294π-0.735294\pi
0.673696 + 0.739009i 0.264706π0.264706\pi
7272 −0.602635 + 0.798017i −0.602635 + 0.798017i
7373 −1.29596 0.368731i −1.29596 0.368731i −0.445738 0.895163i 0.647059π-0.647059\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
7474 −1.78269 + 0.165190i −1.78269 + 0.165190i
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 0 0 0.895163 0.445738i 0.147059π-0.147059\pi
−0.895163 + 0.445738i 0.852941π0.852941\pi
8080 −0.328972 0.163808i −0.328972 0.163808i
8181 0.0922684 0.995734i 0.0922684 0.995734i
8282 0.365931 + 0.0339085i 0.365931 + 0.0339085i
8383 0 0 −0.932472 0.361242i 0.882353π-0.882353\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
8484 0 0
8585 −0.328972 0.163808i −0.328972 0.163808i
8686 0 0
8787 0 0
8888 0 0
8989 0.876298 + 0.163808i 0.876298 + 0.163808i 0.602635 0.798017i 0.294118π-0.294118\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
9090 0.365931 0.0339085i 0.365931 0.0339085i
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 −1.07524 1.17948i −1.07524 1.17948i −0.982973 0.183750i 0.941176π-0.941176\pi
−0.0922684 0.995734i 0.529412π-0.529412\pi
9898 −0.850217 0.526432i −0.850217 0.526432i
9999 0 0
100100 −0.236703 0.831926i −0.236703 0.831926i
101101 0.0505009 0.544991i 0.0505009 0.544991i −0.932472 0.361242i 0.882353π-0.882353\pi
0.982973 0.183750i 0.0588235π-0.0588235\pi
102102 0 0
103103 0 0 −0.0922684 0.995734i 0.529412π-0.529412\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
104104 1.37821 0.533922i 1.37821 0.533922i
105105 0 0
106106 0.0505009 + 0.177492i 0.0505009 + 0.177492i
107107 0 0 0.895163 0.445738i 0.147059π-0.147059\pi
−0.895163 + 0.445738i 0.852941π0.852941\pi
108108 0 0
109109 0.646741 1.66943i 0.646741 1.66943i −0.0922684 0.995734i 0.529412π-0.529412\pi
0.739009 0.673696i 0.235294π-0.235294\pi
110110 0 0
111111 0 0
112112 0 0
113113 0 0 0.932472 0.361242i 0.117647π-0.117647\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
114114 0 0
115115 0 0
116116 1.29596 + 0.368731i 1.29596 + 0.368731i
117117 −0.890705 + 1.17948i −0.890705 + 1.17948i
118118 0 0
119119 0 0
120120 0 0
121121 0.273663 0.961826i 0.273663 0.961826i
122122 −0.380338 + 0.614268i −0.380338 + 0.614268i
123123 0 0
124124 0 0
125125 −0.360798 + 0.582709i −0.360798 + 0.582709i
126126 0 0
127127 0 0 −0.850217 0.526432i 0.823529π-0.823529\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
128128 −0.0922684 + 0.995734i −0.0922684 + 0.995734i
129129 0 0
130130 −0.486226 0.242112i −0.486226 0.242112i
131131 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 −0.0922684 + 0.995734i −0.0922684 + 0.995734i
137137 −1.18475 1.56886i −1.18475 1.56886i −0.739009 0.673696i 0.764706π-0.764706\pi
−0.445738 0.895163i 0.647059π-0.647059\pi
138138 0 0
139139 0 0 −0.895163 0.445738i 0.852941π-0.852941\pi
0.895163 + 0.445738i 0.147059π0.147059\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 −0.445738 0.895163i −0.445738 0.895163i
145145 −0.220714 0.443254i −0.220714 0.443254i
146146 0.907732 0.995734i 0.907732 0.995734i
147147 0 0
148148 0.646741 1.66943i 0.646741 1.66943i
149149 1.37821 + 0.533922i 1.37821 + 0.533922i 0.932472 0.361242i 0.117647π-0.117647\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
150150 0 0
151151 0 0 −0.602635 0.798017i 0.705882π-0.705882\pi
0.602635 + 0.798017i 0.294118π0.294118\pi
152152 0 0
153153 −0.445738 0.895163i −0.445738 0.895163i
154154 0 0
155155 0 0
156156 0 0
157157 −0.181395 1.95756i −0.181395 1.95756i −0.273663 0.961826i 0.588235π-0.588235\pi
0.0922684 0.995734i 0.470588π-0.470588\pi
158158 0 0
159159 0 0
160160 0.293271 0.221468i 0.293271 0.221468i
161161 0 0
162162 0.850217 + 0.526432i 0.850217 + 0.526432i
163163 0 0 0.526432 0.850217i 0.323529π-0.323529\pi
−0.526432 + 0.850217i 0.676471π0.676471\pi
164164 −0.193463 + 0.312454i −0.193463 + 0.312454i
165165 0 0
166166 0 0
167167 0 0 0.526432 0.850217i 0.323529π-0.323529\pi
−0.526432 + 0.850217i 0.676471π0.676471\pi
168168 0 0
169169 1.10455 0.427904i 1.10455 0.427904i
170170 0.293271 0.221468i 0.293271 0.221468i
171171 0 0
172172 0 0
173173 1.91545 + 0.544991i 1.91545 + 0.544991i 0.982973 + 0.183750i 0.0588235π0.0588235\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 −0.537235 + 0.711414i −0.537235 + 0.711414i
179179 0 0 1.00000 00
−1.00000 π\pi
180180 −0.132756 + 0.342683i −0.132756 + 0.342683i
181181 0.132756 + 0.710182i 0.132756 + 0.710182i 0.982973 + 0.183750i 0.0588235π0.0588235\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
182182 0 0
183183 0 0
184184 0 0
185185 −0.613514 + 0.237677i −0.613514 + 0.237677i
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 0 0 −0.850217 0.526432i 0.823529π-0.823529\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
192192 0 0
193193 0.719401 1.85699i 0.719401 1.85699i 0.273663 0.961826i 0.411765π-0.411765\pi
0.445738 0.895163i 0.352941π-0.352941\pi
194194 1.53511 0.436776i 1.53511 0.436776i
195195 0 0
196196 0.850217 0.526432i 0.850217 0.526432i
197197 −0.353470 + 1.89090i −0.353470 + 1.89090i 0.0922684 + 0.995734i 0.470588π0.470588\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
198198 0 0
199199 0 0 0.995734 0.0922684i 0.0294118π-0.0294118\pi
−0.995734 + 0.0922684i 0.970588π0.970588\pi
200200 0.850217 + 0.158933i 0.850217 + 0.158933i
201201 0 0
202202 0.465346 + 0.288130i 0.465346 + 0.288130i
203203 0 0
204204 0 0
205205 0.132756 0.0248164i 0.132756 0.0248164i
206206 0 0
207207 0 0
208208 −0.136374 + 1.47171i −0.136374 + 1.47171i
209209 0 0
210210 0 0
211211 0 0 0.995734 0.0922684i 0.0294118π-0.0294118\pi
−0.995734 + 0.0922684i 0.970588π0.970588\pi
212212 −0.181395 0.0339085i −0.181395 0.0339085i
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 1.20614 + 1.32307i 1.20614 + 1.32307i
219219 0 0
220220 0 0
221221 −0.136374 + 1.47171i −0.136374 + 1.47171i
222222 0 0
223223 0 0 0.850217 0.526432i 0.176471π-0.176471\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
224224 0 0
225225 −0.806537 + 0.312454i −0.806537 + 0.312454i
226226 0 0
227227 0 0 −0.961826 0.273663i 0.911765π-0.911765\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
228228 0 0
229229 1.25664 + 1.14558i 1.25664 + 1.14558i 0.982973 + 0.183750i 0.0588235π0.0588235\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
230230 0 0
231231 0 0
232232 −0.907732 + 0.995734i −0.907732 + 0.995734i
233233 −1.53511 1.15926i −1.53511 1.15926i −0.932472 0.361242i 0.882353π-0.882353\pi
−0.602635 0.798017i 0.705882π-0.705882\pi
234234 −0.658809 1.32307i −0.658809 1.32307i
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 0 0 0.739009 0.673696i 0.235294π-0.235294\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
240240 0 0
241241 −0.719401 + 0.0666624i −0.719401 + 0.0666624i −0.445738 0.895163i 0.647059π-0.647059\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
242242 0.739009 + 0.673696i 0.739009 + 0.673696i
243243 0 0
244244 −0.380338 0.614268i −0.380338 0.614268i
245245 −0.353470 0.100571i −0.353470 0.100571i
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 −0.360798 0.582709i −0.360798 0.582709i
251251 0 0 1.00000 00
−1.00000 π\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 −0.850217 0.526432i −0.850217 0.526432i
257257 −0.658809 0.600584i −0.658809 0.600584i 0.273663 0.961826i 0.411765π-0.411765\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
258258 0 0
259259 0 0
260260 0.433459 0.327333i 0.433459 0.327333i
261261 0.247582 1.32445i 0.247582 1.32445i
262262 0 0
263263 0 0 0.273663 0.961826i 0.411765π-0.411765\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
264264 0 0
265265 0.0357011 + 0.0576592i 0.0357011 + 0.0576592i
266266 0 0
267267 0 0
268268 0 0
269269 1.72198 0.857445i 1.72198 0.857445i 0.739009 0.673696i 0.235294π-0.235294\pi
0.982973 0.183750i 0.0588235π-0.0588235\pi
270270 0 0
271271 0 0 −0.273663 0.961826i 0.588235π-0.588235\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
272272 −0.850217 0.526432i −0.850217 0.526432i
273273 0 0
274274 1.93247 0.361242i 1.93247 0.361242i
275275 0 0
276276 0 0
277277 −1.04837 + 1.69318i −1.04837 + 1.69318i −0.445738 + 0.895163i 0.647059π0.647059\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
278278 0 0
279279 0 0
280280 0 0
281281 1.18475 0.221468i 1.18475 0.221468i 0.445738 0.895163i 0.352941π-0.352941\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
282282 0 0
283283 0 0 −0.995734 0.0922684i 0.970588π-0.970588\pi
0.995734 + 0.0922684i 0.0294118π0.0294118\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 1.00000 1.00000
289289 −0.850217 0.526432i −0.850217 0.526432i
290290 0.495165 0.495165
291291 0 0
292292 0.486734 + 1.25640i 0.486734 + 1.25640i
293293 −0.537235 0.711414i −0.537235 0.711414i 0.445738 0.895163i 0.352941π-0.352941\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
294294 0 0
295295 0 0
296296 1.20614 + 1.32307i 1.20614 + 1.32307i
297297 0 0
298298 −1.09227 + 0.995734i −1.09227 + 0.995734i
299299 0 0
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 −0.0726608 + 0.255376i −0.0726608 + 0.255376i
306306 1.00000 1.00000
307307 0 0 −0.273663 0.961826i 0.588235π-0.588235\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
308308 0 0
309309 0 0
310310 0 0
311311 0 0 −0.183750 0.982973i 0.558824π-0.558824\pi
0.183750 + 0.982973i 0.441176π0.441176\pi
312312 0 0
313313 −1.01267 1.63552i −1.01267 1.63552i −0.739009 0.673696i 0.764706π-0.764706\pi
−0.273663 0.961826i 0.588235π-0.588235\pi
314314 1.83319 + 0.710182i 1.83319 + 0.710182i
315315 0 0
316316 0 0
317317 0.353470 1.89090i 0.353470 1.89090i −0.0922684 0.995734i 0.529412π-0.529412\pi
0.445738 0.895163i 0.352941π-0.352941\pi
318318 0 0
319319 0 0
320320 0.0675278 + 0.361242i 0.0675278 + 0.361242i
321321 0 0
322322 0 0
323323 0 0
324324 −0.850217 + 0.526432i −0.850217 + 0.526432i
325325 1.25664 + 0.234906i 1.25664 + 0.234906i
326326 0 0
327327 0 0
328328 −0.193463 0.312454i −0.193463 0.312454i
329329 0 0
330330 0 0
331331 0 0 −0.602635 0.798017i 0.705882π-0.705882\pi
0.602635 + 0.798017i 0.294118π0.294118\pi
332332 0 0
333333 −1.72198 0.489946i −1.72198 0.489946i
334334 0 0
335335 0 0
336336 0 0
337337 −1.04837 + 0.0971461i −1.04837 + 0.0971461i −0.602635 0.798017i 0.705882π-0.705882\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
338338 −0.109295 + 1.17948i −0.109295 + 1.17948i
339339 0 0
340340 0.0675278 + 0.361242i 0.0675278 + 0.361242i
341341 0 0
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 −1.34164 + 1.47171i −1.34164 + 1.47171i
347347 0 0 −0.183750 0.982973i 0.558824π-0.558824\pi
0.183750 + 0.982973i 0.441176π0.441176\pi
348348 0 0
349349 −1.25664 1.14558i −1.25664 1.14558i −0.982973 0.183750i 0.941176π-0.941176\pi
−0.273663 0.961826i 0.588235π-0.588235\pi
350350 0 0
351351 0 0
352352 0 0
353353 −0.510366 + 0.197717i −0.510366 + 0.197717i −0.602635 0.798017i 0.705882π-0.705882\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
354354 0 0
355355 0 0
356356 −0.397365 0.798017i −0.397365 0.798017i
357357 0 0
358358 0 0
359359 0 0 −0.0922684 0.995734i 0.529412π-0.529412\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
360360 −0.247582 0.271585i −0.247582 0.271585i
361361 −0.602635 + 0.798017i −0.602635 + 0.798017i
362362 −0.694903 0.197717i −0.694903 0.197717i
363363 0 0
364364 0 0
365365 0.220714 0.443254i 0.220714 0.443254i
366366 0 0
367367 0 0 0.995734 0.0922684i 0.0294118π-0.0294118\pi
−0.995734 + 0.0922684i 0.970588π0.970588\pi
368368 0 0
369369 0.328972 + 0.163808i 0.328972 + 0.163808i
370370 0.0607073 0.655137i 0.0607073 0.655137i
371371 0 0
372372 0 0
373373 −1.67148 + 0.312454i −1.67148 + 0.312454i −0.932472 0.361242i 0.882353π-0.882353\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
374374 0 0
375375 0 0
376376 0 0
377377 −1.34164 + 1.47171i −1.34164 + 1.47171i
378378 0 0
379379 0 0 0.995734 0.0922684i 0.0294118π-0.0294118\pi
−0.995734 + 0.0922684i 0.970588π0.970588\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 0.932472 0.361242i 0.117647π-0.117647\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
384384 0 0
385385 0 0
386386 1.34164 + 1.47171i 1.34164 + 1.47171i
387387 0 0
388388 −0.293271 + 1.56886i −0.293271 + 1.56886i
389389 0.0505009 + 0.177492i 0.0505009 + 0.177492i 0.982973 0.183750i 0.0588235π-0.0588235\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
390390 0 0
391391 0 0
392392 0.0922684 + 0.995734i 0.0922684 + 0.995734i
393393 0 0
394394 −1.53511 1.15926i −1.53511 1.15926i
395395 0 0
396396 0 0
397397 0.328972 + 1.75984i 0.328972 + 1.75984i 0.602635 + 0.798017i 0.294118π0.294118\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
398398 0 0
399399 0 0
400400 −0.521245 + 0.690241i −0.521245 + 0.690241i
401401 −1.78269 + 0.887674i −1.78269 + 0.887674i −0.850217 + 0.526432i 0.823529π0.823529\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
402402 0 0
403403 0 0
404404 −0.465346 + 0.288130i −0.465346 + 0.288130i
405405 0.353470 + 0.100571i 0.353470 + 0.100571i
406406 0 0
407407 0 0
408408 0 0
409409 1.73901 0.673696i 1.73901 0.673696i 0.739009 0.673696i 0.235294π-0.235294\pi
1.00000 00
410410 −0.0369597 + 0.129900i −0.0369597 + 0.129900i
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 −1.25664 0.778076i −1.25664 0.778076i
417417 0 0
418418 0 0
419419 0 0 −0.895163 0.445738i 0.852941π-0.852941\pi
0.895163 + 0.445738i 0.147059π0.147059\pi
420420 0 0
421421 0.0505009 + 0.544991i 0.0505009 + 0.544991i 0.982973 + 0.183750i 0.0588235π0.0588235\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
422422 0 0
423423 0 0
424424 0.111208 0.147263i 0.111208 0.147263i
425425 −0.521245 + 0.690241i −0.521245 + 0.690241i
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 0 0 0.961826 0.273663i 0.0882353π-0.0882353\pi
−0.961826 + 0.273663i 0.911765π0.911765\pi
432432 0 0
433433 0.876298 + 1.75984i 0.876298 + 1.75984i 0.602635 + 0.798017i 0.294118π0.294118\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
434434 0 0
435435 0 0
436436 −1.72198 + 0.489946i −1.72198 + 0.489946i
437437 0 0
438438 0 0
439439 0 0 −0.895163 0.445738i 0.852941π-0.852941\pi
0.895163 + 0.445738i 0.147059π0.147059\pi
440440 0 0
441441 −0.602635 0.798017i −0.602635 0.798017i
442442 −1.25664 0.778076i −1.25664 0.778076i
443443 0 0 0.602635 0.798017i 0.294118π-0.294118\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
444444 0 0
445445 −0.118349 + 0.305494i −0.118349 + 0.305494i
446446 0 0
447447 0 0
448448 0 0
449449 −1.58923 + 1.20013i −1.58923 + 1.20013i −0.739009 + 0.673696i 0.764706π0.764706\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
450450 0.0798070 0.861255i 0.0798070 0.861255i
451451 0 0
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 −0.149783 + 0.526432i −0.149783 + 0.526432i 0.850217 + 0.526432i 0.176471π0.176471\pi
−1.00000 π\pi
458458 −1.58561 + 0.614268i −1.58561 + 0.614268i
459459 0 0
460460 0 0
461461 0.726337 0.961826i 0.726337 0.961826i −0.273663 0.961826i 0.588235π-0.588235\pi
1.00000 00
462462 0 0
463463 0 0 0.850217 0.526432i 0.176471π-0.176471\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
464464 −0.486734 1.25640i −0.486734 1.25640i
465465 0 0
466466 1.72198 0.857445i 1.72198 0.857445i
467467 0 0 0.602635 0.798017i 0.294118π-0.294118\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
468468 1.47802 1.47802
469469 0 0
470470 0 0
471471 0 0
472472 0 0
473473 0 0
474474 0 0
475475 0 0
476476 0 0
477477 −0.0170269 + 0.183750i −0.0170269 + 0.183750i
478478 0 0
479479 0 0 0.183750 0.982973i 0.441176π-0.441176\pi
−0.183750 + 0.982973i 0.558824π0.558824\pi
480480 0 0
481481 1.78269 + 1.95552i 1.78269 + 1.95552i
482482 0.260991 0.673696i 0.260991 0.673696i
483483 0 0
484484 −0.932472 + 0.361242i −0.932472 + 0.361242i
485485 0.498687 0.308774i 0.498687 0.308774i
486486 0 0
487487 0 0 −0.798017 0.602635i 0.794118π-0.794118\pi
0.798017 + 0.602635i 0.205882π0.205882\pi
488488 0.719401 0.0666624i 0.719401 0.0666624i
489489 0 0
490490 0.247582 0.271585i 0.247582 0.271585i
491491 0 0 −0.850217 0.526432i 0.823529π-0.823529\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
492492 0 0
493493 −0.486734 1.25640i −0.486734 1.25640i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 0 0 0.895163 0.445738i 0.147059π-0.147059\pi
−0.895163 + 0.445738i 0.852941π0.852941\pi
500500 0.682442 0.0632375i 0.682442 0.0632375i
501501 0 0
502502 0 0
503503 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
504504 0 0
505505 0.193463 + 0.0550451i 0.193463 + 0.0550451i
506506 0 0
507507 0 0
508508 0 0
509509 0.0822551 0.165190i 0.0822551 0.165190i −0.850217 0.526432i 0.823529π-0.823529\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
510510 0 0
511511 0 0
512512 0.850217 0.526432i 0.850217 0.526432i
513513 0 0
514514 0.831277 0.322039i 0.831277 0.322039i
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0.0998072 + 0.533922i 0.0998072 + 0.533922i
521521 0 0 −0.739009 0.673696i 0.764706π-0.764706\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
522522 1.07524 + 0.811985i 1.07524 + 0.811985i
523523 0 0 −0.445738 0.895163i 0.647059π-0.647059\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 −0.0922684 + 0.995734i −0.0922684 + 0.995734i
530530 −0.0675278 + 0.00625737i −0.0675278 + 0.00625737i
531531 0 0
532532 0 0
533533 −0.285942 0.461813i −0.285942 0.461813i
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 1.92365i 1.92365i
539539 0 0
540540 0 0
541541 −0.380338 0.614268i −0.380338 0.614268i 0.602635 0.798017i 0.294118π-0.294118\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
542542 0 0
543543 0 0
544544 0.850217 0.526432i 0.850217 0.526432i
545545 0.559395 + 0.346363i 0.559395 + 0.346363i
546546 0 0
547547 0 0 −0.183750 0.982973i 0.558824π-0.558824\pi
0.183750 + 0.982973i 0.441176π0.441176\pi
548548 −0.538007 + 1.89090i −0.538007 + 1.89090i
549549 −0.576554 + 0.435393i −0.576554 + 0.435393i
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 −1.04837 1.69318i −1.04837 1.69318i
555555 0 0
556556 0 0
557557 −0.397365 + 0.798017i −0.397365 + 0.798017i 0.602635 + 0.798017i 0.294118π0.294118\pi
−1.00000 π\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 −0.329838 + 1.15926i −0.329838 + 1.15926i
563563 0 0 0.982973 0.183750i 0.0588235π-0.0588235\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
564564 0 0
565565 0 0
566566 0 0
567567 0 0
568568 0 0
569569 1.47802 1.34739i 1.47802 1.34739i 0.739009 0.673696i 0.235294π-0.235294\pi
0.739009 0.673696i 0.235294π-0.235294\pi
570570 0 0
571571 0 0 −0.673696 0.739009i 0.735294π-0.735294\pi
0.673696 + 0.739009i 0.264706π0.264706\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 −0.445738 + 0.895163i −0.445738 + 0.895163i
577577 1.70043 1.70043 0.850217 0.526432i 0.176471π-0.176471\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
578578 0.850217 0.526432i 0.850217 0.526432i
579579 0 0
580580 −0.220714 + 0.443254i −0.220714 + 0.443254i
581581 0 0
582582 0 0
583583 0 0
584584 −1.34164 0.124322i −1.34164 0.124322i
585585 −0.365931 0.401408i −0.365931 0.401408i
586586 0.876298 0.163808i 0.876298 0.163808i
587587 0 0 0.739009 0.673696i 0.235294π-0.235294\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
588588 0 0
589589 0 0
590590 0 0
591591 0 0
592592 −1.72198 + 0.489946i −1.72198 + 0.489946i
593593 1.93247 0.361242i 1.93247 0.361242i 0.932472 0.361242i 0.117647π-0.117647\pi
1.00000 00
594594 0 0
595595 0 0
596596 −0.404479 1.42160i −0.404479 1.42160i
597597 0 0
598598 0 0
599599 0 0 0.445738 0.895163i 0.352941π-0.352941\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
600600 0 0
601601 −0.907732 0.995734i −0.907732 0.995734i 0.0922684 0.995734i 0.470588π-0.470588\pi
−1.00000 π\pi
602602 0 0
603603 0 0
604604 0 0
605605 0.328972 + 0.163808i 0.328972 + 0.163808i
606606 0 0
607607 0 0 0.798017 0.602635i 0.205882π-0.205882\pi
−0.798017 + 0.602635i 0.794118π0.794118\pi
608608 0 0
609609 0 0
610610 −0.196216 0.178874i −0.196216 0.178874i
611611 0 0
612612 −0.445738 + 0.895163i −0.445738 + 0.895163i
613613 1.02474 0.634493i 1.02474 0.634493i 0.0922684 0.995734i 0.470588π-0.470588\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
614614 0 0
615615 0 0
616616 0 0
617617 −0.709310 1.14558i −0.709310 1.14558i −0.982973 0.183750i 0.941176π-0.941176\pi
0.273663 0.961826i 0.411765π-0.411765\pi
618618 0 0
619619 0 0 −0.361242 0.932472i 0.617647π-0.617647\pi
0.361242 + 0.932472i 0.382353π0.382353\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 0.453067 + 0.413025i 0.453067 + 0.413025i
626626 1.91545 0.177492i 1.91545 0.177492i
627627 0 0
628628 −1.45285 + 1.32445i −1.45285 + 1.32445i
629629 −1.72198 + 0.489946i −1.72198 + 0.489946i
630630 0 0
631631 0 0 0.739009 0.673696i 0.235294π-0.235294\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
632632 0 0
633633 0 0
634634 1.53511 + 1.15926i 1.53511 + 1.15926i
635635 0 0
636636 0 0
637637 0.136374 + 1.47171i 0.136374 + 1.47171i
638638 0 0
639639 0 0
640640 −0.353470 0.100571i −0.353470 0.100571i
641641 1.04837 + 0.0971461i 1.04837 + 0.0971461i 0.602635 0.798017i 0.294118π-0.294118\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
642642 0 0
643643 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 0.445738 0.895163i 0.352941π-0.352941\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
648648 −0.0922684 0.995734i −0.0922684 0.995734i
649649 0 0
650650 −0.770410 + 1.02019i −0.770410 + 1.02019i
651651 0 0
652652 0 0
653653 1.05286i 1.05286i 0.850217 + 0.526432i 0.176471π0.176471\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
654654 0 0
655655 0 0
656656 0.365931 0.0339085i 0.365931 0.0339085i
657657 1.20614 0.600584i 1.20614 0.600584i
658658 0 0
659659 0 0 0.0922684 0.995734i 0.470588π-0.470588\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
660660 0 0
661661 1.86494 + 0.722483i 1.86494 + 0.722483i 0.932472 + 0.361242i 0.117647π0.117647\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 1.20614 1.32307i 1.20614 1.32307i
667667 0 0
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 −1.53511 + 0.436776i −1.53511 + 0.436776i −0.932472 0.361242i 0.882353π-0.882353\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
674674 0.380338 0.981767i 0.380338 0.981767i
675675 0 0
676676 −1.00711 0.623578i −1.00711 0.623578i
677677 0.293271 1.56886i 0.293271 1.56886i −0.445738 0.895163i 0.647059π-0.647059\pi
0.739009 0.673696i 0.235294π-0.235294\pi
678678 0 0
679679 0 0
680680 −0.353470 0.100571i −0.353470 0.100571i
681681 0 0
682682 0 0
683683 0 0 −0.798017 0.602635i 0.794118π-0.794118\pi
0.798017 + 0.602635i 0.205882π0.205882\pi
684684 0 0
685685 0.646741 0.322039i 0.646741 0.322039i
686686 0 0
687687 0 0
688688 0 0
689689 0.164368 0.217658i 0.164368 0.217658i
690690 0 0
691691 0 0 −0.361242 0.932472i 0.617647π-0.617647\pi
0.361242 + 0.932472i 0.382353π0.382353\pi
692692 −0.719401 1.85699i −0.719401 1.85699i
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 0.365931 0.0339085i 0.365931 0.0339085i
698698 1.58561 0.614268i 1.58561 0.614268i
699699 0 0
700700 0 0
701701 0.404479 0.368731i 0.404479 0.368731i −0.445738 0.895163i 0.647059π-0.647059\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
702702 0 0
703703 0 0
704704 0 0
705705 0 0
706706 0.0505009 0.544991i 0.0505009 0.544991i
707707 0 0
708708 0 0
709709 1.05286i 1.05286i −0.850217 0.526432i 0.823529π-0.823529\pi
0.850217 0.526432i 0.176471π-0.176471\pi
710710 0 0
711711 0 0
712712 0.891477 0.891477
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 0.361242 0.932472i 0.382353π-0.382353\pi
−0.361242 + 0.932472i 0.617647π0.617647\pi
720720 0.353470 0.100571i 0.353470 0.100571i
721721 0 0
722722 −0.445738 0.895163i −0.445738 0.895163i
723723 0 0
724724 0.486734 0.533922i 0.486734 0.533922i
725725 −1.12093 + 0.318932i −1.12093 + 0.318932i
726726 0 0
727727 0 0 −0.932472 0.361242i 0.882353π-0.882353\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
728728 0 0
729729 0.602635 + 0.798017i 0.602635 + 0.798017i
730730 0.298404 + 0.395150i 0.298404 + 0.395150i
731731 0 0
732732 0 0
733733 −1.96595 −1.96595 −0.982973 0.183750i 0.941176π-0.941176\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 −0.293271 + 0.221468i −0.293271 + 0.221468i
739739 0 0 0.0922684 0.995734i 0.470588π-0.470588\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
740740 0.559395 + 0.346363i 0.559395 + 0.346363i
741741 0 0
742742 0 0
743743 0 0 0.673696 0.739009i 0.264706π-0.264706\pi
−0.673696 + 0.739009i 0.735294π0.735294\pi
744744 0 0
745745 −0.285942 + 0.461813i −0.285942 + 0.461813i
746746 0.465346 1.63552i 0.465346 1.63552i
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 0 0 −0.961826 0.273663i 0.911765π-0.911765\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
752752 0 0
753753 0 0
754754 −0.719401 1.85699i −0.719401 1.85699i
755755 0 0
756756 0 0
757757 1.20527 1.20527 0.602635 0.798017i 0.294118π-0.294118\pi
0.602635 + 0.798017i 0.294118π0.294118\pi
758758 0 0
759759 0 0
760760 0 0
761761 −0.538007 1.89090i −0.538007 1.89090i −0.445738 0.895163i 0.647059π-0.647059\pi
−0.0922684 0.995734i 0.529412π-0.529412\pi
762762 0 0
763763 0 0
764764 0 0
765765 0.353470 0.100571i 0.353470 0.100571i
766766 0 0
767767 0 0
768768 0 0
769769 0.757949 + 0.469302i 0.757949 + 0.469302i 0.850217 0.526432i 0.176471π-0.176471\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
770770 0 0
771771 0 0
772772 −1.91545 + 0.544991i −1.91545 + 0.544991i
773773 1.83319 0.710182i 1.83319 0.710182i 0.850217 0.526432i 0.176471π-0.176471\pi
0.982973 0.183750i 0.0588235π-0.0588235\pi
774774 0 0
775775 0 0
776776 −1.27366 0.961826i −1.27366 0.961826i
777777 0 0
778778 −0.181395 0.0339085i −0.181395 0.0339085i
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −0.932472 0.361242i −0.932472 0.361242i
785785 0.719401 + 0.0666624i 0.719401 + 0.0666624i
786786 0 0
787787 0 0 −0.895163 0.445738i 0.852941π-0.852941\pi
0.895163 + 0.445738i 0.147059π0.147059\pi
788788 1.72198 0.857445i 1.72198 0.857445i
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 1.06329 0.0985281i 1.06329 0.0985281i
794794 −1.72198 0.489946i −1.72198 0.489946i
795795 0 0
796796 0 0
797797 0.0170269 + 0.183750i 0.0170269 + 0.183750i 1.00000 00
−0.982973 + 0.183750i 0.941176π0.941176\pi
798798 0 0
799799 0 0
800800 −0.385539 0.774267i −0.385539 0.774267i
801801 −0.757949 + 0.469302i −0.757949 + 0.469302i
802802 1.99147i 1.99147i
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 −0.0505009 0.544991i −0.0505009 0.544991i
809809 0.353470 + 1.89090i 0.353470 + 1.89090i 0.445738 + 0.895163i 0.352941π0.352941\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
810810 −0.247582 + 0.271585i −0.247582 + 0.271585i
811811 0 0 −0.798017 0.602635i 0.794118π-0.794118\pi
0.798017 + 0.602635i 0.205882π0.205882\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 0 0
818818 −0.172075 + 1.85699i −0.172075 + 1.85699i
819819 0 0
820820 −0.0998072 0.0909863i −0.0998072 0.0909863i
821821 −0.694903 + 0.197717i −0.694903 + 0.197717i −0.602635 0.798017i 0.705882π-0.705882\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
822822 0 0
823823 0 0 −0.961826 0.273663i 0.911765π-0.911765\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
828828 0 0
829829 1.47802 1.47802 0.739009 0.673696i 0.235294π-0.235294\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
830830 0 0
831831 0 0
832832 1.25664 0.778076i 1.25664 0.778076i
833833 −0.932472 0.361242i −0.932472 0.361242i
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 0 0 0.183750 0.982973i 0.441176π-0.441176\pi
−0.183750 + 0.982973i 0.558824π0.558824\pi
840840 0 0
841841 0.223162 0.784333i 0.223162 0.784333i
842842 −0.510366 0.197717i −0.510366 0.197717i
843843 0 0
844844 0 0
845845 0.0799891 + 0.427904i 0.0799891 + 0.427904i
846846 0 0
847847 0 0
848848 0.0822551 + 0.165190i 0.0822551 + 0.165190i
849849 0 0
850850 −0.385539 0.774267i −0.385539 0.774267i
851851 0 0
852852 0 0
853853 1.01267 0.288130i 1.01267 0.288130i 0.273663 0.961826i 0.411765π-0.411765\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
854854 0 0
855855 0 0
856856 0 0
857857 −0.840204 0.634493i −0.840204 0.634493i 0.0922684 0.995734i 0.470588π-0.470588\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
858858 0 0
859859 0 0 0.982973 0.183750i 0.0588235π-0.0588235\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 −0.602635 0.798017i 0.705882π-0.705882\pi
0.602635 + 0.798017i 0.294118π0.294118\pi
864864 0 0
865865 −0.326219 + 0.655137i −0.326219 + 0.655137i
866866 −1.96595 −1.96595
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0.328972 1.75984i 0.328972 1.75984i
873873 1.58923 + 0.147263i 1.58923 + 0.147263i
874874 0 0
875875 0 0
876876 0 0
877877 1.07524 + 0.811985i 1.07524 + 0.811985i 0.982973 0.183750i 0.0588235π-0.0588235\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
878878 0 0
879879 0 0
880880 0 0
881881 −1.53511 + 0.436776i −1.53511 + 0.436776i −0.932472 0.361242i 0.882353π-0.882353\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
882882 0.982973 0.183750i 0.982973 0.183750i
883883 0 0 0.273663 0.961826i 0.411765π-0.411765\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
884884 1.25664 0.778076i 1.25664 0.778076i
885885 0 0
886886 0 0
887887 0 0 0.895163 0.445738i 0.147059π-0.147059\pi
−0.895163 + 0.445738i 0.852941π0.852941\pi
888888 0 0
889889 0 0
890890 −0.220714 0.242112i −0.220714 0.242112i
891891 0 0
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 −0.365931 1.95756i −0.365931 1.95756i
899899 0 0
900900 0.735391 + 0.455335i 0.735391 + 0.455335i
901901 0.0822551 + 0.165190i 0.0822551 + 0.165190i
902902 0 0
903903 0 0
904904 0 0
905905 −0.265512 −0.265512
906906 0 0
907907 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
908908 0 0
909909 0.329838 + 0.436776i 0.329838 + 0.436776i
910910 0 0
911911 0 0 −0.961826 0.273663i 0.911765π-0.911765\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
912912 0 0
913913 0 0
914914 −0.404479 0.368731i −0.404479 0.368731i
915915 0 0
916916 0.156896 1.69318i 0.156896 1.69318i
917917 0 0
918918 0 0
919919 0 0 −0.739009 0.673696i 0.764706π-0.764706\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
920920 0 0
921921 0 0
922922 0.537235 + 1.07891i 0.537235 + 1.07891i
923923 0 0
924924 0 0
925925 0.284542 + 1.52217i 0.284542 + 1.52217i
926926 0 0
927927 0 0
928928 1.34164 + 0.124322i 1.34164 + 0.124322i
929929 1.53511 + 0.436776i 1.53511 + 0.436776i 0.932472 0.361242i 0.117647π-0.117647\pi
0.602635 + 0.798017i 0.294118π0.294118\pi
930930 0 0
931931 0 0
932932 1.92365i 1.92365i
933933 0 0
934934 0 0
935935 0 0
936936 −0.658809 + 1.32307i −0.658809 + 1.32307i
937937 −0.111208 1.20013i −0.111208 1.20013i −0.850217 0.526432i 0.823529π-0.823529\pi
0.739009 0.673696i 0.235294π-0.235294\pi
938938 0 0
939939 0 0
940940 0 0
941941 1.58923 0.147263i 1.58923 0.147263i 0.739009 0.673696i 0.235294π-0.235294\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 −0.895163 0.445738i 0.852941π-0.852941\pi
0.895163 + 0.445738i 0.147059π0.147059\pi
948948 0 0
949949 −1.98297 0.183750i −1.98297 0.183750i
950950 0 0
951951 0 0
952952 0 0
953953 0.876298 + 0.163808i 0.876298 + 0.163808i 0.602635 0.798017i 0.294118π-0.294118\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
954954 −0.156896 0.0971461i −0.156896 0.0971461i
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −0.932472 + 0.361242i −0.932472 + 0.361242i
962962 −2.54512 + 0.724149i −2.54512 + 0.724149i
963963 0 0
964964 0.486734 + 0.533922i 0.486734 + 0.533922i
965965 0.622242 + 0.385276i 0.622242 + 0.385276i
966966 0 0
967967 0 0 −0.273663 0.961826i 0.588235π-0.588235\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
968968 0.0922684 0.995734i 0.0922684 0.995734i
969969 0 0
970970 0.0541192 + 0.584039i 0.0541192 + 0.584039i
971971 0 0 0.932472 0.361242i 0.117647π-0.117647\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 −0.260991 + 0.673696i −0.260991 + 0.673696i
977977 −1.70043 −1.70043 −0.850217 0.526432i 0.823529π-0.823529\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
978978 0 0
979979 0 0
980980 0.132756 + 0.342683i 0.132756 + 0.342683i
981981 0.646741 + 1.66943i 0.646741 + 1.66943i
982982 0 0
983983 0 0 −0.961826 0.273663i 0.911765π-0.911765\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
984984 0 0
985985 −0.659202 0.255376i −0.659202 0.255376i
986986 1.34164 + 0.124322i 1.34164 + 0.124322i
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 0.673696 0.739009i 0.264706π-0.264706\pi
−0.673696 + 0.739009i 0.735294π0.735294\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 −1.78269 0.887674i −1.78269 0.887674i −0.932472 0.361242i 0.882353π-0.882353\pi
−0.850217 0.526432i 0.823529π-0.823529\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 1156.1.l.a.339.1 16
4.3 odd 2 CM 1156.1.l.a.339.1 16
289.237 even 34 inner 1156.1.l.a.815.1 yes 16
1156.815 odd 34 inner 1156.1.l.a.815.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1156.1.l.a.339.1 16 1.1 even 1 trivial
1156.1.l.a.339.1 16 4.3 odd 2 CM
1156.1.l.a.815.1 yes 16 289.237 even 34 inner
1156.1.l.a.815.1 yes 16 1156.815 odd 34 inner