Properties

Label 1156.1.o.a.191.1
Level 11561156
Weight 11
Character 1156.191
Analytic conductor 0.5770.577
Analytic rank 00
Dimension 3232
Projective image D68D_{68}
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(47,1156)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1156, base_ring=CyclotomicField(68))
 
chi = DirichletCharacter(H, H._module([34, 25]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1156.47");
 
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.o (of order 6868, degree 3232, 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: 3232
Coefficient field: Q(ζ68)\Q(\zeta_{68})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x32x30+x28x26+x24x22+x20x18+x16x14+x12++1 x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} + \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: D68D_{68}
Projective field: Galois closure of Q[x]/(x68)\mathbb{Q}[x]/(x^{68} - \cdots)

Embedding invariants

Embedding label 191.1
Root 0.361242+0.932472i-0.361242 + 0.932472i of defining polynomial
Character χ\chi == 1156.191
Dual form 1156.1.o.a.115.1

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+(0.6736960.739009i)q2+(0.0922684+0.995734i)q4+(0.273663+1.96183i)q5+(0.7980170.602635i)q8+(0.526432+0.850217i)q9+(1.265441.52391i)q10+(0.6344930.840204i)q13+(0.9829730.183750i)q16+(0.982973+0.183750i)q17+(0.9829730.183750i)q18+(1.97871+0.0914812i)q20+(2.81204+0.800095i)q25+(0.193463+1.03494i)q26+(0.292529+0.352279i)q29+(0.526432+0.850217i)q32+(0.5264320.850217i)q34+(0.7980170.602635i)q36+(0.806980+1.82764i)q37+(1.40065+1.40065i)q40+(0.241393+0.134455i)q41+(1.812040.800095i)q45+(0.895163+0.445738i)q49+(2.48574+1.53910i)q50+(0.8951630.554262i)q52+(0.9424851.52217i)q53+(0.06326190.453510i)q58+(0.555259+1.65667i)q61+(0.2736630.961826i)q64+(1.474701.47470i)q65+(0.273663+0.961826i)q68+(0.0922684+0.995734i)q72+(1.606171.10025i)q73+(1.894300.634905i)q74+(0.09148121.97871i)q80+(0.4457380.895163i)q81+(0.261989+0.0878098i)q82+(0.0914812+1.97871i)q85+(0.8119851.07524i)q89+(0.629488+1.87814i)q90+(1.497800.352279i)q97+(0.932472+0.361242i)q98+O(q100)q+(-0.673696 - 0.739009i) q^{2} +(-0.0922684 + 0.995734i) q^{4} +(0.273663 + 1.96183i) q^{5} +(0.798017 - 0.602635i) q^{8} +(-0.526432 + 0.850217i) q^{9} +(1.26544 - 1.52391i) q^{10} +(-0.634493 - 0.840204i) q^{13} +(-0.982973 - 0.183750i) q^{16} +(0.982973 + 0.183750i) q^{17} +(0.982973 - 0.183750i) q^{18} +(-1.97871 + 0.0914812i) q^{20} +(-2.81204 + 0.800095i) q^{25} +(-0.193463 + 1.03494i) q^{26} +(0.292529 + 0.352279i) q^{29} +(0.526432 + 0.850217i) q^{32} +(-0.526432 - 0.850217i) q^{34} +(-0.798017 - 0.602635i) q^{36} +(-0.806980 + 1.82764i) q^{37} +(1.40065 + 1.40065i) q^{40} +(-0.241393 + 0.134455i) q^{41} +(-1.81204 - 0.800095i) q^{45} +(-0.895163 + 0.445738i) q^{49} +(2.48574 + 1.53910i) q^{50} +(0.895163 - 0.554262i) q^{52} +(0.942485 - 1.52217i) q^{53} +(0.0632619 - 0.453510i) q^{58} +(-0.555259 + 1.65667i) q^{61} +(0.273663 - 0.961826i) q^{64} +(1.47470 - 1.47470i) q^{65} +(-0.273663 + 0.961826i) q^{68} +(0.0922684 + 0.995734i) q^{72} +(1.60617 - 1.10025i) q^{73} +(1.89430 - 0.634905i) q^{74} +(0.0914812 - 1.97871i) q^{80} +(-0.445738 - 0.895163i) q^{81} +(0.261989 + 0.0878098i) q^{82} +(-0.0914812 + 1.97871i) q^{85} +(0.811985 - 1.07524i) q^{89} +(0.629488 + 1.87814i) q^{90} +(1.49780 - 0.352279i) q^{97} +(0.932472 + 0.361242i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+2q4+2q52q102q16+2q17+2q182q2034q252q29+2q37+2q402q412q45+2q50+2q58+2q61+2q642q68+2q98+O(q100) 32 q + 2 q^{4} + 2 q^{5} - 2 q^{10} - 2 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{20} - 34 q^{25} - 2 q^{29} + 2 q^{37} + 2 q^{40} - 2 q^{41} - 2 q^{45} + 2 q^{50} + 2 q^{58} + 2 q^{61} + 2 q^{64} - 2 q^{68}+ \cdots - 2 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(2368)e\left(\frac{23}{68}\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 −0.673696 0.739009i −0.673696 0.739009i
33 0 0 −0.486604 0.873622i 0.661765π-0.661765\pi
0.486604 + 0.873622i 0.338235π0.338235\pi
44 −0.0922684 + 0.995734i −0.0922684 + 0.995734i
55 0.273663 + 1.96183i 0.273663 + 1.96183i 0.273663 + 0.961826i 0.411765π0.411765\pi
1.00000i 0.5π0.5\pi
66 0 0
77 0 0 −0.228951 0.973438i 0.573529π-0.573529\pi
0.228951 + 0.973438i 0.426471π0.426471\pi
88 0.798017 0.602635i 0.798017 0.602635i
99 −0.526432 + 0.850217i −0.526432 + 0.850217i
1010 1.26544 1.52391i 1.26544 1.52391i
1111 0 0 0.769334 0.638847i 0.220588π-0.220588\pi
−0.769334 + 0.638847i 0.779412π0.779412\pi
1212 0 0
1313 −0.634493 0.840204i −0.634493 0.840204i 0.361242 0.932472i 0.382353π-0.382353\pi
−0.995734 + 0.0922684i 0.970588π0.970588\pi
1414 0 0
1515 0 0
1616 −0.982973 0.183750i −0.982973 0.183750i
1717 0.982973 + 0.183750i 0.982973 + 0.183750i
1818 0.982973 0.183750i 0.982973 0.183750i
1919 0 0 0.673696 0.739009i 0.264706π-0.264706\pi
−0.673696 + 0.739009i 0.735294π0.735294\pi
2020 −1.97871 + 0.0914812i −1.97871 + 0.0914812i
2121 0 0
2222 0 0
2323 0 0 −0.228951 0.973438i 0.573529π-0.573529\pi
0.228951 + 0.973438i 0.426471π0.426471\pi
2424 0 0
2525 −2.81204 + 0.800095i −2.81204 + 0.800095i
2626 −0.193463 + 1.03494i −0.193463 + 1.03494i
2727 0 0
2828 0 0
2929 0.292529 + 0.352279i 0.292529 + 0.352279i 0.895163 0.445738i 0.147059π-0.147059\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
3030 0 0
3131 0 0 −0.990410 0.138156i 0.955882π-0.955882\pi
0.990410 + 0.138156i 0.0441176π0.0441176\pi
3232 0.526432 + 0.850217i 0.526432 + 0.850217i
3333 0 0
3434 −0.526432 0.850217i −0.526432 0.850217i
3535 0 0
3636 −0.798017 0.602635i −0.798017 0.602635i
3737 −0.806980 + 1.82764i −0.806980 + 1.82764i −0.361242 + 0.932472i 0.617647π0.617647\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
3838 0 0
3939 0 0
4040 1.40065 + 1.40065i 1.40065 + 1.40065i
4141 −0.241393 + 0.134455i −0.241393 + 0.134455i −0.602635 0.798017i 0.705882π-0.705882\pi
0.361242 + 0.932472i 0.382353π0.382353\pi
4242 0 0
4343 0 0 −0.183750 0.982973i 0.558824π-0.558824\pi
0.183750 + 0.982973i 0.441176π0.441176\pi
4444 0 0
4545 −1.81204 0.800095i −1.81204 0.800095i
4646 0 0
4747 0 0 0.850217 0.526432i 0.176471π-0.176471\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
4848 0 0
4949 −0.895163 + 0.445738i −0.895163 + 0.445738i
5050 2.48574 + 1.53910i 2.48574 + 1.53910i
5151 0 0
5252 0.895163 0.554262i 0.895163 0.554262i
5353 0.942485 1.52217i 0.942485 1.52217i 0.0922684 0.995734i 0.470588π-0.470588\pi
0.850217 0.526432i 0.176471π-0.176471\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 0.0632619 0.453510i 0.0632619 0.453510i
5959 0 0 −0.895163 0.445738i 0.852941π-0.852941\pi
0.895163 + 0.445738i 0.147059π0.147059\pi
6060 0 0
6161 −0.555259 + 1.65667i −0.555259 + 1.65667i 0.183750 + 0.982973i 0.441176π0.441176\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
6262 0 0
6363 0 0
6464 0.273663 0.961826i 0.273663 0.961826i
6565 1.47470 1.47470i 1.47470 1.47470i
6666 0 0
6767 0 0 −0.739009 0.673696i 0.764706π-0.764706\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
6868 −0.273663 + 0.961826i −0.273663 + 0.961826i
6969 0 0
7070 0 0
7171 0 0 0.973438 0.228951i 0.0735294π-0.0735294\pi
−0.973438 + 0.228951i 0.926471π0.926471\pi
7272 0.0922684 + 0.995734i 0.0922684 + 0.995734i
7373 1.60617 1.10025i 1.60617 1.10025i 0.673696 0.739009i 0.264706π-0.264706\pi
0.932472 0.361242i 0.117647π-0.117647\pi
7474 1.89430 0.634905i 1.89430 0.634905i
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 0 0 −0.0461835 0.998933i 0.514706π-0.514706\pi
0.0461835 + 0.998933i 0.485294π0.485294\pi
8080 0.0914812 1.97871i 0.0914812 1.97871i
8181 −0.445738 0.895163i −0.445738 0.895163i
8282 0.261989 + 0.0878098i 0.261989 + 0.0878098i
8383 0 0 0.961826 0.273663i 0.0882353π-0.0882353\pi
−0.961826 + 0.273663i 0.911765π0.911765\pi
8484 0 0
8585 −0.0914812 + 1.97871i −0.0914812 + 1.97871i
8686 0 0
8787 0 0
8888 0 0
8989 0.811985 1.07524i 0.811985 1.07524i −0.183750 0.982973i 0.558824π-0.558824\pi
0.995734 0.0922684i 0.0294118π-0.0294118\pi
9090 0.629488 + 1.87814i 0.629488 + 1.87814i
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 1.49780 0.352279i 1.49780 0.352279i 0.602635 0.798017i 0.294118π-0.294118\pi
0.895163 + 0.445738i 0.147059π0.147059\pi
9898 0.932472 + 0.361242i 0.932472 + 0.361242i
9999 0 0
100100 −0.537220 2.87387i −0.537220 2.87387i
101101 0.163808 + 0.328972i 0.163808 + 0.328972i 0.961826 0.273663i 0.0882353π-0.0882353\pi
−0.798017 + 0.602635i 0.794118π0.794118\pi
102102 0 0
103103 0 0 0.445738 0.895163i 0.352941π-0.352941\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
104104 −1.01267 0.288130i −1.01267 0.288130i
105105 0 0
106106 −1.75984 + 0.328972i −1.75984 + 0.328972i
107107 0 0 0.998933 0.0461835i 0.0147059π-0.0147059\pi
−0.998933 + 0.0461835i 0.985294π0.985294\pi
108108 0 0
109109 −0.0449462 + 0.0806938i −0.0449462 + 0.0806938i −0.895163 0.445738i 0.852941π-0.852941\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
110110 0 0
111111 0 0
112112 0 0
113113 1.23549 0.688163i 1.23549 0.688163i 0.273663 0.961826i 0.411765π-0.411765\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
114114 0 0
115115 0 0
116116 −0.377767 + 0.258777i −0.377767 + 0.258777i
117117 1.04837 0.0971461i 1.04837 0.0971461i
118118 0 0
119119 0 0
120120 0 0
121121 0.183750 0.982973i 0.183750 0.982973i
122122 1.59837 0.705749i 1.59837 0.705749i
123123 0 0
124124 0 0
125125 −1.53910 3.48574i −1.53910 3.48574i
126126 0 0
127127 0 0 0.361242 0.932472i 0.382353π-0.382353\pi
−0.361242 + 0.932472i 0.617647π0.617647\pi
128128 −0.895163 + 0.445738i −0.895163 + 0.445738i
129129 0 0
130130 −2.08331 0.0963172i −2.08331 0.0963172i
131131 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 0.895163 0.445738i 0.895163 0.445738i
137137 −0.147263 + 1.58923i −0.147263 + 1.58923i 0.526432 + 0.850217i 0.323529π0.323529\pi
−0.673696 + 0.739009i 0.735294π0.735294\pi
138138 0 0
139139 0 0 0.0461835 0.998933i 0.485294π-0.485294\pi
−0.0461835 + 0.998933i 0.514706π0.514706\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 0.673696 0.739009i 0.673696 0.739009i
145145 −0.611055 + 0.670296i −0.611055 + 0.670296i
146146 −1.89516 0.445738i −1.89516 0.445738i
147147 0 0
148148 −1.74538 0.972171i −1.74538 0.972171i
149149 0.465346 + 1.63552i 0.465346 + 1.63552i 0.739009 + 0.673696i 0.235294π0.235294\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
150150 0 0
151151 0 0 −0.995734 0.0922684i 0.970588π-0.970588\pi
0.995734 + 0.0922684i 0.0294118π0.0294118\pi
152152 0 0
153153 −0.673696 + 0.739009i −0.673696 + 0.739009i
154154 0 0
155155 0 0
156156 0 0
157157 −0.537235 + 1.07891i −0.537235 + 1.07891i 0.445738 + 0.895163i 0.352941π0.352941\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
158158 0 0
159159 0 0
160160 −1.52391 + 1.26544i −1.52391 + 1.26544i
161161 0 0
162162 −0.361242 + 0.932472i −0.361242 + 0.932472i
163163 0 0 −0.403921 0.914794i 0.632353π-0.632353\pi
0.403921 + 0.914794i 0.367647π0.367647\pi
164164 −0.111609 0.252769i −0.111609 0.252769i
165165 0 0
166166 0 0
167167 0 0 0.914794 0.403921i 0.132353π-0.132353\pi
−0.914794 + 0.403921i 0.867647π0.867647\pi
168168 0 0
169169 −0.0296988 + 0.104380i −0.0296988 + 0.104380i
170170 1.52391 1.26544i 1.52391 1.26544i
171171 0 0
172172 0 0
173173 0.524354 0.359191i 0.524354 0.359191i −0.273663 0.961826i 0.588235π-0.588235\pi
0.798017 + 0.602635i 0.205882π0.205882\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 −1.34164 + 0.124322i −1.34164 + 0.124322i
179179 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
180180 0.963876 1.73049i 0.963876 1.73049i
181181 −0.134455 + 0.963876i −0.134455 + 0.963876i 0.798017 + 0.602635i 0.205882π0.205882\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
182182 0 0
183183 0 0
184184 0 0
185185 −3.80634 1.08300i −3.80634 1.08300i
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 0 0 −0.932472 0.361242i 0.882353π-0.882353\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
192192 0 0
193193 0.922758 1.65667i 0.922758 1.65667i 0.183750 0.982973i 0.441176π-0.441176\pi
0.739009 0.673696i 0.235294π-0.235294\pi
194194 −1.26940 0.869557i −1.26940 0.869557i
195195 0 0
196196 −0.361242 0.932472i −0.361242 0.932472i
197197 1.11943 0.156154i 1.11943 0.156154i 0.445738 0.895163i 0.352941π-0.352941\pi
0.673696 + 0.739009i 0.264706π0.264706\pi
198198 0 0
199199 0 0 −0.317791 0.948161i 0.602941π-0.602941\pi
0.317791 + 0.948161i 0.397059π0.397059\pi
200200 −1.76189 + 2.33312i −1.76189 + 2.33312i
201201 0 0
202202 0.132756 0.342683i 0.132756 0.342683i
203203 0 0
204204 0 0
205205 −0.329838 0.436776i −0.329838 0.436776i
206206 0 0
207207 0 0
208208 0.469302 + 0.942485i 0.469302 + 0.942485i
209209 0 0
210210 0 0
211211 0 0 0.948161 0.317791i 0.102941π-0.102941\pi
−0.948161 + 0.317791i 0.897059π0.897059\pi
212212 1.42871 + 1.07891i 1.42871 + 1.07891i
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 0.0899135 0.0211475i 0.0899135 0.0211475i
219219 0 0
220220 0 0
221221 −0.469302 0.942485i −0.469302 0.942485i
222222 0 0
223223 0 0 −0.361242 0.932472i 0.617647π-0.617647\pi
0.361242 + 0.932472i 0.382353π0.382353\pi
224224 0 0
225225 0.800095 2.81204i 0.800095 2.81204i
226226 −1.34090 0.449425i −1.34090 0.449425i
227227 0 0 −0.565136 0.824997i 0.691176π-0.691176\pi
0.565136 + 0.824997i 0.308824π0.308824\pi
228228 0 0
229229 −0.981767 1.58561i −0.981767 1.58561i −0.798017 0.602635i 0.794118π-0.794118\pi
−0.183750 0.982973i 0.558824π-0.558824\pi
230230 0 0
231231 0 0
232232 0.445738 + 0.104837i 0.445738 + 0.104837i
233233 0.869557 + 0.722071i 0.869557 + 0.722071i 0.961826 0.273663i 0.0882353π-0.0882353\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
234234 −0.778076 0.709310i −0.778076 0.709310i
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 0 0 −0.850217 0.526432i 0.823529π-0.823529\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
240240 0 0
241241 −0.309277 0.922758i −0.309277 0.922758i −0.982973 0.183750i 0.941176π-0.941176\pi
0.673696 0.739009i 0.264706π-0.264706\pi
242242 −0.850217 + 0.526432i −0.850217 + 0.526432i
243243 0 0
244244 −1.59837 0.705749i −1.59837 0.705749i
245245 −1.11943 1.63417i −1.11943 1.63417i
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 −1.53910 + 3.48574i −1.53910 + 3.48574i
251251 0 0 1.00000 00
−1.00000 π\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0.932472 + 0.361242i 0.932472 + 0.361242i
257257 0.778076 + 1.25664i 0.778076 + 1.25664i 0.961826 + 0.273663i 0.0882353π0.0882353\pi
−0.183750 + 0.982973i 0.558824π0.558824\pi
258258 0 0
259259 0 0
260260 1.33234 + 1.60447i 1.33234 + 1.60447i
261261 −0.453510 + 0.0632619i −0.453510 + 0.0632619i
262262 0 0
263263 0 0 0.183750 0.982973i 0.441176π-0.441176\pi
−0.183750 + 0.982973i 0.558824π0.558824\pi
264264 0 0
265265 3.24415 + 1.43243i 3.24415 + 1.43243i
266266 0 0
267267 0 0
268268 0 0
269269 1.64823 0.0762025i 1.64823 0.0762025i 0.798017 0.602635i 0.205882π-0.205882\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
270270 0 0
271271 0 0 0.982973 0.183750i 0.0588235π-0.0588235\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
272272 −0.932472 0.361242i −0.932472 0.361242i
273273 0 0
274274 1.27366 0.961826i 1.27366 0.961826i
275275 0 0
276276 0 0
277277 −0.581427 + 0.256725i −0.581427 + 0.256725i −0.673696 0.739009i 0.735294π-0.735294\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
278278 0 0
279279 0 0
280280 0 0
281281 1.58923 1.20013i 1.58923 1.20013i 0.739009 0.673696i 0.235294π-0.235294\pi
0.850217 0.526432i 0.176471π-0.176471\pi
282282 0 0
283283 0 0 0.317791 0.948161i 0.397059π-0.397059\pi
−0.317791 + 0.948161i 0.602941π0.602941\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 −1.00000 −1.00000
289289 0.932472 + 0.361242i 0.932472 + 0.361242i
290290 0.907020 0.907020
291291 0 0
292292 0.947359 + 1.70083i 0.947359 + 1.70083i
293293 −0.136374 + 1.47171i −0.136374 + 1.47171i 0.602635 + 0.798017i 0.294118π0.294118\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
294294 0 0
295295 0 0
296296 0.457413 + 1.94480i 0.457413 + 1.94480i
297297 0 0
298298 0.895163 1.44574i 0.895163 1.44574i
299299 0 0
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 −3.40205 0.635953i −3.40205 0.635953i
306306 1.00000 1.00000
307307 0 0 0.982973 0.183750i 0.0588235π-0.0588235\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
308308 0 0
309309 0 0
310310 0 0
311311 0 0 −0.990410 0.138156i 0.955882π-0.955882\pi
0.990410 + 0.138156i 0.0441176π0.0441176\pi
312312 0 0
313313 −1.50941 0.666468i −1.50941 0.666468i −0.526432 0.850217i 0.676471π-0.676471\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
314314 1.15926 0.329838i 1.15926 0.329838i
315315 0 0
316316 0 0
317317 1.63417 0.227957i 1.63417 0.227957i 0.739009 0.673696i 0.235294π-0.235294\pi
0.895163 + 0.445738i 0.147059π0.147059\pi
318318 0 0
319319 0 0
320320 1.96183 + 0.273663i 1.96183 + 0.273663i
321321 0 0
322322 0 0
323323 0 0
324324 0.932472 0.361242i 0.932472 0.361242i
325325 2.45646 + 1.85503i 2.45646 + 1.85503i
326326 0 0
327327 0 0
328328 −0.111609 + 0.252769i −0.111609 + 0.252769i
329329 0 0
330330 0 0
331331 0 0 −0.995734 0.0922684i 0.970588π-0.970588\pi
0.995734 + 0.0922684i 0.0294118π0.0294118\pi
332332 0 0
333333 −1.12907 1.64823i −1.12907 1.64823i
334334 0 0
335335 0 0
336336 0 0
337337 −0.581427 1.73474i −0.581427 1.73474i −0.673696 0.739009i 0.735294π-0.735294\pi
0.0922684 0.995734i 0.470588π-0.470588\pi
338338 0.0971461 0.0483730i 0.0971461 0.0483730i
339339 0 0
340340 −1.96183 0.273663i −1.96183 0.273663i
341341 0 0
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 −0.618701 0.145517i −0.618701 0.145517i
347347 0 0 0.138156 0.990410i 0.455882π-0.455882\pi
−0.138156 + 0.990410i 0.544118π0.544118\pi
348348 0 0
349349 0.380338 + 0.614268i 0.380338 + 0.614268i 0.982973 0.183750i 0.0588235π-0.0588235\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
350350 0 0
351351 0 0
352352 0 0
353353 −0.538007 + 1.89090i −0.538007 + 1.89090i −0.0922684 + 0.995734i 0.529412π0.529412\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
354354 0 0
355355 0 0
356356 0.995734 + 0.907732i 0.995734 + 0.907732i
357357 0 0
358358 0 0
359359 0 0 −0.895163 0.445738i 0.852941π-0.852941\pi
0.895163 + 0.445738i 0.147059π0.147059\pi
360360 −1.92821 + 0.453510i −1.92821 + 0.453510i
361361 −0.0922684 0.995734i −0.0922684 0.995734i
362362 0.802895 0.549996i 0.802895 0.549996i
363363 0 0
364364 0 0
365365 2.59805 + 2.84992i 2.59805 + 2.84992i
366366 0 0
367367 0 0 0.948161 0.317791i 0.102941π-0.102941\pi
−0.948161 + 0.317791i 0.897059π0.897059\pi
368368 0 0
369369 0.0127611 0.276018i 0.0127611 0.276018i
370370 1.76397 + 3.54253i 1.76397 + 3.54253i
371371 0 0
372372 0 0
373373 −0.435393 0.576554i −0.435393 0.576554i 0.526432 0.850217i 0.323529π-0.323529\pi
−0.961826 + 0.273663i 0.911765π0.911765\pi
374374 0 0
375375 0 0
376376 0 0
377377 0.110379 0.469302i 0.110379 0.469302i
378378 0 0
379379 0 0 −0.317791 0.948161i 0.602941π-0.602941\pi
0.317791 + 0.948161i 0.397059π0.397059\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 −0.961826 0.273663i 0.911765π-0.911765\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
384384 0 0
385385 0 0
386386 −1.84595 + 0.434164i −1.84595 + 0.434164i
387387 0 0
388388 0.212577 + 1.52391i 0.212577 + 1.52391i
389389 −0.163808 0.876298i −0.163808 0.876298i −0.961826 0.273663i 0.911765π-0.911765\pi
0.798017 0.602635i 0.205882π-0.205882\pi
390390 0 0
391391 0 0
392392 −0.445738 + 0.895163i −0.445738 + 0.895163i
393393 0 0
394394 −0.869557 0.722071i −0.869557 0.722071i
395395 0 0
396396 0 0
397397 −0.0127611 + 0.0914812i −0.0127611 + 0.0914812i −0.995734 0.0922684i 0.970588π-0.970588\pi
0.982973 + 0.183750i 0.0588235π0.0588235\pi
398398 0 0
399399 0 0
400400 2.91118 0.269761i 2.91118 0.269761i
401401 −0.0293534 0.634905i −0.0293534 0.634905i −0.961826 0.273663i 0.911765π-0.911765\pi
0.932472 0.361242i 0.117647π-0.117647\pi
402402 0 0
403403 0 0
404404 −0.342683 + 0.132756i −0.342683 + 0.132756i
405405 1.63417 1.11943i 1.63417 1.11943i
406406 0 0
407407 0 0
408408 0 0
409409 −0.149783 + 0.526432i −0.149783 + 0.526432i 0.850217 + 0.526432i 0.176471π0.176471\pi
−1.00000 π\pi
410410 −0.100571 + 0.538007i −0.100571 + 0.538007i
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0.380338 0.981767i 0.380338 0.981767i
417417 0 0
418418 0 0
419419 0 0 −0.998933 0.0461835i 0.985294π-0.985294\pi
0.998933 + 0.0461835i 0.0147059π0.0147059\pi
420420 0 0
421421 0.163808 0.328972i 0.163808 0.328972i −0.798017 0.602635i 0.794118π-0.794118\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
422422 0 0
423423 0 0
424424 −0.165190 1.78269i −0.165190 1.78269i
425425 −2.91118 + 0.269761i −2.91118 + 0.269761i
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 0 0 −0.824997 0.565136i 0.808824π-0.808824\pi
0.824997 + 0.565136i 0.191176π0.191176\pi
432432 0 0
433433 −0.811985 + 0.890705i −0.811985 + 0.890705i −0.995734 0.0922684i 0.970588π-0.970588\pi
0.183750 + 0.982973i 0.441176π0.441176\pi
434434 0 0
435435 0 0
436436 −0.0762025 0.0521999i −0.0762025 0.0521999i
437437 0 0
438438 0 0
439439 0 0 0.0461835 0.998933i 0.485294π-0.485294\pi
−0.0461835 + 0.998933i 0.514706π0.514706\pi
440440 0 0
441441 0.0922684 0.995734i 0.0922684 0.995734i
442442 −0.380338 + 0.981767i −0.380338 + 0.981767i
443443 0 0 −0.0922684 0.995734i 0.529412π-0.529412\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
444444 0 0
445445 2.33165 + 1.29872i 2.33165 + 1.29872i
446446 0 0
447447 0 0
448448 0 0
449449 −1.45890 + 1.21146i −1.45890 + 1.21146i −0.526432 + 0.850217i 0.676471π0.676471\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
450450 −2.61715 + 1.30318i −2.61715 + 1.30318i
451451 0 0
452452 0.571231 + 1.29371i 0.571231 + 1.29371i
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 0.361242 1.93247i 0.361242 1.93247i 1.00000i 0.5π-0.5\pi
0.361242 0.932472i 0.382353π-0.382353\pi
458458 −0.510366 + 1.79375i −0.510366 + 1.79375i
459459 0 0
460460 0 0
461461 −1.98297 + 0.183750i −1.98297 + 0.183750i −0.982973 + 0.183750i 0.941176π0.941176\pi
−1.00000 π\pi
462462 0 0
463463 0 0 0.932472 0.361242i 0.117647π-0.117647\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
464464 −0.222817 0.400033i −0.222817 0.400033i
465465 0 0
466466 −0.0521999 1.12907i −0.0521999 1.12907i
467467 0 0 0.995734 0.0922684i 0.0294118π-0.0294118\pi
−0.995734 + 0.0922684i 0.970588π0.970588\pi
468468 1.05286i 1.05286i
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 0.798017 + 1.60263i 0.798017 + 1.60263i
478478 0 0
479479 0 0 −0.138156 0.990410i 0.544118π-0.544118\pi
0.138156 + 0.990410i 0.455882π0.455882\pi
480480 0 0
481481 2.04761 0.481593i 2.04761 0.481593i
482482 −0.473568 + 0.850217i −0.473568 + 0.850217i
483483 0 0
484484 0.961826 + 0.273663i 0.961826 + 0.273663i
485485 1.10100 + 2.84201i 1.10100 + 2.84201i
486486 0 0
487487 0 0 0.638847 0.769334i 0.279412π-0.279412\pi
−0.638847 + 0.769334i 0.720588π0.720588\pi
488488 0.555259 + 1.65667i 0.555259 + 1.65667i
489489 0 0
490490 −0.453510 + 1.92821i −0.453510 + 1.92821i
491491 0 0 0.361242 0.932472i 0.382353π-0.382353\pi
−0.361242 + 0.932472i 0.617647π0.617647\pi
492492 0 0
493493 0.222817 + 0.400033i 0.222817 + 0.400033i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 0 0 −0.0461835 0.998933i 0.514706π-0.514706\pi
0.0461835 + 0.998933i 0.485294π0.485294\pi
500500 3.61288 1.21092i 3.61288 1.21092i
501501 0 0
502502 0 0
503503 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
504504 0 0
505505 −0.600557 + 0.411391i −0.600557 + 0.411391i
506506 0 0
507507 0 0
508508 0 0
509509 −0.658809 + 0.600584i −0.658809 + 0.600584i −0.932472 0.361242i 0.882353π-0.882353\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
510510 0 0
511511 0 0
512512 −0.361242 0.932472i −0.361242 0.932472i
513513 0 0
514514 0.404479 1.42160i 0.404479 1.42160i
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 0.288130 2.06554i 0.288130 2.06554i
521521 −1.37665 0.323785i −1.37665 0.323785i −0.526432 0.850217i 0.676471π-0.676471\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
522522 0.352279 + 0.292529i 0.352279 + 0.292529i
523523 0 0 −0.739009 0.673696i 0.764706π-0.764706\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 −0.895163 + 0.445738i −0.895163 + 0.445738i
530530 −1.12699 3.36248i −1.12699 3.36248i
531531 0 0
532532 0 0
533533 0.266132 + 0.117509i 0.266132 + 0.117509i
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 −1.16672 1.16672i −1.16672 1.16672i
539539 0 0
540540 0 0
541541 −0.393100 + 0.890286i −0.393100 + 0.890286i 0.602635 + 0.798017i 0.294118π0.294118\pi
−0.995734 + 0.0922684i 0.970588π0.970588\pi
542542 0 0
543543 0 0
544544 0.361242 + 0.932472i 0.361242 + 0.932472i
545545 −0.170607 0.0660936i −0.170607 0.0660936i
546546 0 0
547547 0 0 −0.990410 0.138156i 0.955882π-0.955882\pi
0.990410 + 0.138156i 0.0441176π0.0441176\pi
548548 −1.56886 0.293271i −1.56886 0.293271i
549549 −1.11622 1.34421i −1.11622 1.34421i
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 0.581427 + 0.256725i 0.581427 + 0.256725i
555555 0 0
556556 0 0
557557 0.995734 0.907732i 0.995734 0.907732i 1.00000i 0.5π-0.5\pi
0.995734 + 0.0922684i 0.0294118π0.0294118\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 −1.95756 0.365931i −1.95756 0.365931i
563563 0 0 0.798017 0.602635i 0.205882π-0.205882\pi
−0.798017 + 0.602635i 0.794118π0.794118\pi
564564 0 0
565565 1.68816 + 2.23549i 1.68816 + 2.23549i
566566 0 0
567567 0 0
568568 0 0
569569 0 0 −0.850217 0.526432i 0.823529π-0.823529\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
570570 0 0
571571 0 0 −0.228951 0.973438i 0.573529π-0.573529\pi
0.228951 + 0.973438i 0.426471π0.426471\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 0.673696 + 0.739009i 0.673696 + 0.739009i
577577 −0.722483 −0.722483 −0.361242 0.932472i 0.617647π-0.617647\pi
−0.361242 + 0.932472i 0.617647π0.617647\pi
578578 −0.361242 0.932472i −0.361242 0.932472i
579579 0 0
580580 −0.611055 0.670296i −0.611055 0.670296i
581581 0 0
582582 0 0
583583 0 0
584584 0.618701 1.84595i 0.618701 1.84595i
585585 0.477485 + 2.03014i 0.477485 + 2.03014i
586586 1.17948 0.890705i 1.17948 0.890705i
587587 0 0 0.526432 0.850217i 0.323529π-0.323529\pi
−0.526432 + 0.850217i 0.676471π0.676471\pi
588588 0 0
589589 0 0
590590 0 0
591591 0 0
592592 1.12907 1.64823i 1.12907 1.64823i
593593 1.27366 0.961826i 1.27366 0.961826i 0.273663 0.961826i 0.411765π-0.411765\pi
1.00000 00
594594 0 0
595595 0 0
596596 −1.67148 + 0.312454i −1.67148 + 0.312454i
597597 0 0
598598 0 0
599599 0 0 0.739009 0.673696i 0.235294π-0.235294\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
600600 0 0
601601 0.445738 + 1.89516i 0.445738 + 1.89516i 0.445738 + 0.895163i 0.352941π0.352941\pi
1.00000i 0.500000π0.500000\pi
602602 0 0
603603 0 0
604604 0 0
605605 1.97871 + 0.0914812i 1.97871 + 0.0914812i
606606 0 0
607607 0 0 −0.638847 0.769334i 0.720588π-0.720588\pi
0.638847 + 0.769334i 0.279412π0.279412\pi
608608 0 0
609609 0 0
610610 1.82197 + 2.94258i 1.82197 + 2.94258i
611611 0 0
612612 −0.673696 0.739009i −0.673696 0.739009i
613613 0.172075 0.0666624i 0.172075 0.0666624i −0.273663 0.961826i 0.588235π-0.588235\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
614614 0 0
615615 0 0
616616 0 0
617617 0.786384 1.78099i 0.786384 1.78099i 0.183750 0.982973i 0.441176π-0.441176\pi
0.602635 0.798017i 0.294118π-0.294118\pi
618618 0 0
619619 0 0 0.873622 0.486604i 0.161765π-0.161765\pi
−0.873622 + 0.486604i 0.838235π0.838235\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 3.93148 2.43427i 3.93148 2.43427i
626626 0.524354 + 1.56446i 0.524354 + 1.56446i
627627 0 0
628628 −1.02474 0.634493i −1.02474 0.634493i
629629 −1.12907 + 1.64823i −1.12907 + 1.64823i
630630 0 0
631631 0 0 0.526432 0.850217i 0.323529π-0.323529\pi
−0.526432 + 0.850217i 0.676471π0.676471\pi
632632 0 0
633633 0 0
634634 −1.26940 1.05409i −1.26940 1.05409i
635635 0 0
636636 0 0
637637 0.942485 + 0.469302i 0.942485 + 0.469302i
638638 0 0
639639 0 0
640640 −1.11943 1.63417i −1.11943 1.63417i
641641 −1.73474 0.581427i −1.73474 0.581427i −0.739009 0.673696i 0.764706π-0.764706\pi
−0.995734 + 0.0922684i 0.970588π0.970588\pi
642642 0 0
643643 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 0.739009 0.673696i 0.235294π-0.235294\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
648648 −0.895163 0.445738i −0.895163 0.445738i
649649 0 0
650650 −0.284021 3.06508i −0.284021 3.06508i
651651 0 0
652652 0 0
653653 0.571231 + 0.571231i 0.571231 + 0.571231i 0.932472 0.361242i 0.117647π-0.117647\pi
−0.361242 + 0.932472i 0.617647π0.617647\pi
654654 0 0
655655 0 0
656656 0.261989 0.0878098i 0.261989 0.0878098i
657657 0.0899135 + 1.94480i 0.0899135 + 1.94480i
658658 0 0
659659 0 0 −0.445738 0.895163i 0.647059π-0.647059\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
660660 0 0
661661 0 0 −0.273663 0.961826i 0.588235π-0.588235\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 −0.457413 + 1.94480i −0.457413 + 1.94480i
667667 0 0
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 −1.05409 0.722071i −1.05409 0.722071i −0.0922684 0.995734i 0.529412π-0.529412\pi
−0.961826 + 0.273663i 0.911765π0.911765\pi
674674 −0.890286 + 1.59837i −0.890286 + 1.59837i
675675 0 0
676676 −0.101195 0.0392031i −0.101195 0.0392031i
677677 −0.176521 1.26544i −0.176521 1.26544i −0.850217 0.526432i 0.823529π-0.823529\pi
0.673696 0.739009i 0.264706π-0.264706\pi
678678 0 0
679679 0 0
680680 1.11943 + 1.63417i 1.11943 + 1.63417i
681681 0 0
682682 0 0
683683 0 0 −0.769334 0.638847i 0.779412π-0.779412\pi
0.769334 + 0.638847i 0.220588π0.220588\pi
684684 0 0
685685 −3.15808 + 0.146007i −3.15808 + 0.146007i
686686 0 0
687687 0 0
688688 0 0
689689 −1.87693 + 0.173923i −1.87693 + 0.173923i
690690 0 0
691691 0 0 0.873622 0.486604i 0.161765π-0.161765\pi
−0.873622 + 0.486604i 0.838235π0.838235\pi
692692 0.309277 + 0.555259i 0.309277 + 0.555259i
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 −0.261989 + 0.0878098i −0.261989 + 0.0878098i
698698 0.197717 0.694903i 0.197717 0.694903i
699699 0 0
700700 0 0
701701 −0.312454 0.193463i −0.312454 0.193463i 0.361242 0.932472i 0.382353π-0.382353\pi
−0.673696 + 0.739009i 0.735294π0.735294\pi
702702 0 0
703703 0 0
704704 0 0
705705 0 0
706706 1.75984 0.876298i 1.75984 0.876298i
707707 0 0
708708 0 0
709709 0.571231 0.571231i 0.571231 0.571231i −0.361242 0.932472i 0.617647π-0.617647\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
710710 0 0
711711 0 0
712712 1.34739i 1.34739i
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 −0.873622 0.486604i 0.838235π-0.838235\pi
0.873622 + 0.486604i 0.161765π0.161765\pi
720720 1.63417 + 1.11943i 1.63417 + 1.11943i
721721 0 0
722722 −0.673696 + 0.739009i −0.673696 + 0.739009i
723723 0 0
724724 −0.947359 0.222817i −0.947359 0.222817i
725725 −1.10446 0.756572i −1.10446 0.756572i
726726 0 0
727727 0 0 −0.273663 0.961826i 0.588235π-0.588235\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
728728 0 0
729729 0.995734 + 0.0922684i 0.995734 + 0.0922684i
730730 0.355825 3.83996i 0.355825 3.83996i
731731 0 0
732732 0 0
733733 1.59603i 1.59603i −0.602635 0.798017i 0.705882π-0.705882\pi
0.602635 0.798017i 0.294118π-0.294118\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 −0.212577 + 0.176521i −0.212577 + 0.176521i
739739 0 0 0.895163 0.445738i 0.147059π-0.147059\pi
−0.895163 + 0.445738i 0.852941π0.852941\pi
740740 1.42958 3.69018i 1.42958 3.69018i
741741 0 0
742742 0 0
743743 0 0 0.228951 0.973438i 0.426471π-0.426471\pi
−0.228951 + 0.973438i 0.573529π0.573529\pi
744744 0 0
745745 −3.08126 + 1.36051i −3.08126 + 1.36051i
746746 −0.132756 + 0.710182i −0.132756 + 0.710182i
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 0 0 0.824997 0.565136i 0.191176π-0.191176\pi
−0.824997 + 0.565136i 0.808824π0.808824\pi
752752 0 0
753753 0 0
754754 −0.421180 + 0.234596i −0.421180 + 0.234596i
755755 0 0
756756 0 0
757757 0.184537i 0.184537i 0.995734 + 0.0922684i 0.0294118π0.0294118\pi
−0.995734 + 0.0922684i 0.970588π0.970588\pi
758758 0 0
759759 0 0
760760 0 0
761761 −1.56886 + 0.293271i −1.56886 + 0.293271i −0.895163 0.445738i 0.852941π-0.852941\pi
−0.673696 + 0.739009i 0.735294π0.735294\pi
762762 0 0
763763 0 0
764764 0 0
765765 −1.63417 1.11943i −1.63417 1.11943i
766766 0 0
767767 0 0
768768 0 0
769769 1.25640 + 0.486734i 1.25640 + 0.486734i 0.895163 0.445738i 0.147059π-0.147059\pi
0.361242 + 0.932472i 0.382353π0.382353\pi
770770 0 0
771771 0 0
772772 1.56446 + 1.07168i 1.56446 + 1.07168i
773773 −1.15926 0.329838i −1.15926 0.329838i −0.361242 0.932472i 0.617647π-0.617647\pi
−0.798017 + 0.602635i 0.794118π0.794118\pi
774774 0 0
775775 0 0
776776 0.982973 1.18375i 0.982973 1.18375i
777777 0 0
778778 −0.537235 + 0.711414i −0.537235 + 0.711414i
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 0.961826 0.273663i 0.961826 0.273663i
785785 −2.26366 0.758702i −2.26366 0.758702i
786786 0 0
787787 0 0 0.0461835 0.998933i 0.485294π-0.485294\pi
−0.0461835 + 0.998933i 0.514706π0.514706\pi
788788 0.0521999 + 1.12907i 0.0521999 + 1.12907i
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 1.74425 0.584613i 1.74425 0.584613i
794794 0.0762025 0.0521999i 0.0762025 0.0521999i
795795 0 0
796796 0 0
797797 −1.60263 0.798017i −1.60263 0.798017i −0.602635 0.798017i 0.705882π-0.705882\pi
−1.00000 π\pi
798798 0 0
799799 0 0
800800 −2.16060 1.96965i −2.16060 1.96965i
801801 0.486734 + 1.25640i 0.486734 + 1.25640i
802802 −0.449425 + 0.449425i −0.449425 + 0.449425i
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0.328972 + 0.163808i 0.328972 + 0.163808i
809809 0.156154 1.11943i 0.156154 1.11943i −0.739009 0.673696i 0.764706π-0.764706\pi
0.895163 0.445738i 0.147059π-0.147059\pi
810810 −1.92821 0.453510i −1.92821 0.453510i
811811 0 0 −0.769334 0.638847i 0.779412π-0.779412\pi
0.769334 + 0.638847i 0.220588π0.220588\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 0 0
818818 0.489946 0.243964i 0.489946 0.243964i
819819 0 0
820820 0.465346 0.288130i 0.465346 0.288130i
821821 0.987432 1.44147i 0.987432 1.44147i 0.0922684 0.995734i 0.470588π-0.470588\pi
0.895163 0.445738i 0.147059π-0.147059\pi
822822 0 0
823823 0 0 −0.565136 0.824997i 0.691176π-0.691176\pi
0.565136 + 0.824997i 0.308824π0.308824\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
828828 0 0
829829 −1.70043 −1.70043 −0.850217 0.526432i 0.823529π-0.823529\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
830830 0 0
831831 0 0
832832 −0.981767 + 0.380338i −0.981767 + 0.380338i
833833 −0.961826 + 0.273663i −0.961826 + 0.273663i
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 0 0 0.990410 0.138156i 0.0441176π-0.0441176\pi
−0.990410 + 0.138156i 0.955882π0.955882\pi
840840 0 0
841841 0.145222 0.776870i 0.145222 0.776870i
842842 −0.353470 + 0.100571i −0.353470 + 0.100571i
843843 0 0
844844 0 0
845845 −0.212904 0.0296988i −0.212904 0.0296988i
846846 0 0
847847 0 0
848848 −1.20614 + 1.32307i −1.20614 + 1.32307i
849849 0 0
850850 2.16060 + 1.96965i 2.16060 + 1.96965i
851851 0 0
852852 0 0
853853 1.03397 1.50941i 1.03397 1.50941i 0.183750 0.982973i 0.441176π-0.441176\pi
0.850217 0.526432i 0.176471π-0.176471\pi
854854 0 0
855855 0 0
856856 0 0
857857 −0.516087 + 0.621500i −0.516087 + 0.621500i −0.961826 0.273663i 0.911765π-0.911765\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
858858 0 0
859859 0 0 0.798017 0.602635i 0.205882π-0.205882\pi
−0.798017 + 0.602635i 0.794118π0.794118\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 0.0922684 0.995734i 0.470588π-0.470588\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
864864 0 0
865865 0.848166 + 0.930394i 0.848166 + 0.930394i
866866 1.20527 1.20527
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0.0127611 + 0.0914812i 0.0127611 + 0.0914812i
873873 −0.488975 + 1.45890i −0.488975 + 1.45890i
874874 0 0
875875 0 0
876876 0 0
877877 −1.24376 + 1.49780i −1.24376 + 1.49780i −0.445738 + 0.895163i 0.647059π0.647059\pi
−0.798017 + 0.602635i 0.794118π0.794118\pi
878878 0 0
879879 0 0
880880 0 0
881881 −0.869557 + 1.26940i −0.869557 + 1.26940i 0.0922684 + 0.995734i 0.470588π0.470588\pi
−0.961826 + 0.273663i 0.911765π0.911765\pi
882882 −0.798017 + 0.602635i −0.798017 + 0.602635i
883883 0 0 −0.982973 0.183750i 0.941176π-0.941176\pi
0.982973 + 0.183750i 0.0588235π0.0588235\pi
884884 0.981767 0.380338i 0.981767 0.380338i
885885 0 0
886886 0 0
887887 0 0 0.998933 0.0461835i 0.0147059π-0.0147059\pi
−0.998933 + 0.0461835i 0.985294π0.985294\pi
888888 0 0
889889 0 0
890890 −0.611055 2.59805i −0.611055 2.59805i
891891 0 0
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 1.87814 + 0.261989i 1.87814 + 0.261989i
899899 0 0
900900 2.72622 + 1.05614i 2.72622 + 1.05614i
901901 1.20614 1.32307i 1.20614 1.32307i
902902 0 0
903903 0 0
904904 0.571231 1.29371i 0.571231 1.29371i
905905 −1.92775 −1.92775
906906 0 0
907907 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
908908 0 0
909909 −0.365931 0.0339085i −0.365931 0.0339085i
910910 0 0
911911 0 0 −0.565136 0.824997i 0.691176π-0.691176\pi
0.565136 + 0.824997i 0.308824π0.308824\pi
912912 0 0
913913 0 0
914914 −1.67148 + 1.03494i −1.67148 + 1.03494i
915915 0 0
916916 1.66943 0.831277i 1.66943 0.831277i
917917 0 0
918918 0 0
919919 0 0 0.850217 0.526432i 0.176471π-0.176471\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
920920 0 0
921921 0 0
922922 1.47171 + 1.34164i 1.47171 + 1.34164i
923923 0 0
924924 0 0
925925 0.806980 5.78505i 0.806980 5.78505i
926926 0 0
927927 0 0
928928 −0.145517 + 0.434164i −0.145517 + 0.434164i
929929 0.722071 + 1.05409i 0.722071 + 1.05409i 0.995734 + 0.0922684i 0.0294118π0.0294118\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
930930 0 0
931931 0 0
932932 −0.799224 + 0.799224i −0.799224 + 0.799224i
933933 0 0
934934 0 0
935935 0 0
936936 0.778076 0.709310i 0.778076 0.709310i
937937 −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
938938 0 0
939939 0 0
940940 0 0
941941 −1.21146 + 0.406040i −1.21146 + 0.406040i −0.850217 0.526432i 0.823529π-0.823529\pi
−0.361242 + 0.932472i 0.617647π0.617647\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 0.0461835 0.998933i 0.485294π-0.485294\pi
−0.0461835 + 0.998933i 0.514706π0.514706\pi
948948 0 0
949949 −1.94354 0.651408i −1.94354 0.651408i
950950 0 0
951951 0 0
952952 0 0
953953 −0.811985 + 1.07524i −0.811985 + 1.07524i 0.183750 + 0.982973i 0.441176π0.441176\pi
−0.995734 + 0.0922684i 0.970588π0.970588\pi
954954 0.646741 1.66943i 0.646741 1.66943i
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 0.961826 + 0.273663i 0.961826 + 0.273663i
962962 −1.73537 1.18875i −1.73537 1.18875i
963963 0 0
964964 0.947359 0.222817i 0.947359 0.222817i
965965 3.50262 + 1.35692i 3.50262 + 1.35692i
966966 0 0
967967 0 0 −0.183750 0.982973i 0.558824π-0.558824\pi
0.183750 + 0.982973i 0.441176π0.441176\pi
968968 −0.445738 0.895163i −0.445738 0.895163i
969969 0 0
970970 1.35853 2.72830i 1.35853 2.72830i
971971 0 0 −0.961826 0.273663i 0.911765π-0.911765\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0.850217 1.52643i 0.850217 1.52643i
977977 0.722483i 0.722483i −0.932472 0.361242i 0.882353π-0.882353\pi
0.932472 0.361242i 0.117647π-0.117647\pi
978978 0 0
979979 0 0
980980 1.73049 0.963876i 1.73049 0.963876i
981981 −0.0449462 0.0806938i −0.0449462 0.0806938i
982982 0 0
983983 0 0 0.824997 0.565136i 0.191176π-0.191176\pi
−0.824997 + 0.565136i 0.808824π0.808824\pi
984984 0 0
985985 0.612695 + 2.15340i 0.612695 + 2.15340i
986986 0.145517 0.434164i 0.145517 0.434164i
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 0.228951 0.973438i 0.426471π-0.426471\pi
−0.228951 + 0.973438i 0.573529π0.573529\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 1.89430 + 0.0875787i 1.89430 + 0.0875787i 0.961826 0.273663i 0.0882353π-0.0882353\pi
0.932472 + 0.361242i 0.117647π0.117647\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.o.a.191.1 yes 32
4.3 odd 2 CM 1156.1.o.a.191.1 yes 32
289.115 even 68 inner 1156.1.o.a.115.1 32
1156.115 odd 68 inner 1156.1.o.a.115.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1156.1.o.a.115.1 32 289.115 even 68 inner
1156.1.o.a.115.1 32 1156.115 odd 68 inner
1156.1.o.a.191.1 yes 32 1.1 even 1 trivial
1156.1.o.a.191.1 yes 32 4.3 odd 2 CM