Properties

Label 1020.1.cl.a.719.1
Level 10201020
Weight 11
Character 1020.719
Analytic conductor 0.5090.509
Analytic rank 00
Dimension 1616
Projective image D16D_{16}
CM discriminant -15
Inner twists 88

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1020,1,Mod(299,1020)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1020, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 8, 3])) N = Newforms(chi, 1, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1020.299"); S:= CuspForms(chi, 1); N := Newforms(S);
 
Level: N N == 1020=223517 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17
Weight: k k == 1 1
Character orbit: [χ][\chi] == 1020.cl (of order 1616, degree 88, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(24)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 0.5090463128860.509046312886
Analytic rank: 00
Dimension: 1616
Relative dimension: 22 over Q(ζ16)\Q(\zeta_{16})
Coefficient field: Q(ζ32)\Q(\zeta_{32})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x16+1 x^{16} + 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: D16D_{16}
Projective field: Galois closure of Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)

Embedding invariants

Embedding label 719.1
Root 0.831470+0.555570i0.831470 + 0.555570i of defining polynomial
Character χ\chi == 1020.719
Dual form 1020.1.cl.a.959.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.9807850.195090i)q2+(0.8314700.555570i)q3+(0.923880+0.382683i)q4+(0.1950900.980785i)q5+(0.923880+0.382683i)q6+(0.8314700.555570i)q8+(0.3826830.923880i)q9+(0.382683+0.923880i)q10+(0.9807850.195090i)q12+(0.3826830.923880i)q15+(0.707107+0.707107i)q16+(0.5555700.831470i)q17+(0.555570+0.831470i)q18+(0.707107+0.292893i)q19+(0.5555700.831470i)q20+(1.17588+0.785695i)q231.00000q24+(0.9238800.382683i)q25+(0.1950900.980785i)q27+(0.195090+0.980785i)q30+(0.216773+0.324423i)q31+(0.5555700.831470i)q32+(0.382683+0.923880i)q34+(0.7071070.707107i)q36+(0.7506610.149316i)q38+(0.707107+0.707107i)q40+(0.8314700.555570i)q45+(1.000001.00000i)q46+(1.38704+1.38704i)q47+(0.980785+0.195090i)q48+(0.9238800.382683i)q49+(0.831470+0.555570i)q50+(0.9238800.382683i)q51+(0.636379+1.53636i)q53+1.00000iq54+(0.425215+0.636379i)q571.00000iq60+(0.3826830.0761205i)q61+(0.1493160.360480i)q62+(0.382683+0.923880i)q64+(0.1950900.980785i)q68+1.41421q69+(0.831470+0.555570i)q72+(0.980785+0.195090i)q750.765367q76+(1.089791.63099i)q79+(0.8314700.555570i)q80+(0.7071070.707107i)q81+(0.4252151.02656i)q83+(0.923880+0.382683i)q85+(0.707107+0.707107i)q90+(0.785695+1.17588i)q92+(0.360480+0.149316i)q93+(1.630991.08979i)q94+(0.149316+0.750661i)q95+(0.9238800.382683i)q96+(0.980785+0.195090i)q98+O(q100)q+(-0.980785 - 0.195090i) q^{2} +(0.831470 - 0.555570i) q^{3} +(0.923880 + 0.382683i) q^{4} +(0.195090 - 0.980785i) q^{5} +(-0.923880 + 0.382683i) q^{6} +(-0.831470 - 0.555570i) q^{8} +(0.382683 - 0.923880i) q^{9} +(-0.382683 + 0.923880i) q^{10} +(0.980785 - 0.195090i) q^{12} +(-0.382683 - 0.923880i) q^{15} +(0.707107 + 0.707107i) q^{16} +(-0.555570 - 0.831470i) q^{17} +(-0.555570 + 0.831470i) q^{18} +(-0.707107 + 0.292893i) q^{19} +(0.555570 - 0.831470i) q^{20} +(1.17588 + 0.785695i) q^{23} -1.00000 q^{24} +(-0.923880 - 0.382683i) q^{25} +(-0.195090 - 0.980785i) q^{27} +(0.195090 + 0.980785i) q^{30} +(0.216773 + 0.324423i) q^{31} +(-0.555570 - 0.831470i) q^{32} +(0.382683 + 0.923880i) q^{34} +(0.707107 - 0.707107i) q^{36} +(0.750661 - 0.149316i) q^{38} +(-0.707107 + 0.707107i) q^{40} +(-0.831470 - 0.555570i) q^{45} +(-1.00000 - 1.00000i) q^{46} +(-1.38704 + 1.38704i) q^{47} +(0.980785 + 0.195090i) q^{48} +(0.923880 - 0.382683i) q^{49} +(0.831470 + 0.555570i) q^{50} +(-0.923880 - 0.382683i) q^{51} +(0.636379 + 1.53636i) q^{53} +1.00000i q^{54} +(-0.425215 + 0.636379i) q^{57} -1.00000i q^{60} +(0.382683 - 0.0761205i) q^{61} +(-0.149316 - 0.360480i) q^{62} +(0.382683 + 0.923880i) q^{64} +(-0.195090 - 0.980785i) q^{68} +1.41421 q^{69} +(-0.831470 + 0.555570i) q^{72} +(-0.980785 + 0.195090i) q^{75} -0.765367 q^{76} +(1.08979 - 1.63099i) q^{79} +(0.831470 - 0.555570i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(-0.425215 - 1.02656i) q^{83} +(-0.923880 + 0.382683i) q^{85} +(0.707107 + 0.707107i) q^{90} +(0.785695 + 1.17588i) q^{92} +(0.360480 + 0.149316i) q^{93} +(1.63099 - 1.08979i) q^{94} +(0.149316 + 0.750661i) q^{95} +(-0.923880 - 0.382683i) q^{96} +(-0.980785 + 0.195090i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q16q2416q46+O(q100) 16 q - 16 q^{24} - 16 q^{46}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1020Z)×\left(\mathbb{Z}/1020\mathbb{Z}\right)^\times.

nn 241241 341341 511511 817817
χ(n)\chi(n) e(516)e\left(\frac{5}{16}\right) 1-1 1-1 1-1

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 −0.980785 0.195090i −0.980785 0.195090i
33 0.831470 0.555570i 0.831470 0.555570i
44 0.923880 + 0.382683i 0.923880 + 0.382683i
55 0.195090 0.980785i 0.195090 0.980785i
66 −0.923880 + 0.382683i −0.923880 + 0.382683i
77 0 0 0.980785 0.195090i 0.0625000π-0.0625000\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
88 −0.831470 0.555570i −0.831470 0.555570i
99 0.382683 0.923880i 0.382683 0.923880i
1010 −0.382683 + 0.923880i −0.382683 + 0.923880i
1111 0 0 0.555570 0.831470i 0.312500π-0.312500\pi
−0.555570 + 0.831470i 0.687500π0.687500\pi
1212 0.980785 0.195090i 0.980785 0.195090i
1313 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
1414 0 0
1515 −0.382683 0.923880i −0.382683 0.923880i
1616 0.707107 + 0.707107i 0.707107 + 0.707107i
1717 −0.555570 0.831470i −0.555570 0.831470i
1818 −0.555570 + 0.831470i −0.555570 + 0.831470i
1919 −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i 0.750000π-0.750000\pi
1.00000i 0.5π0.5\pi
2020 0.555570 0.831470i 0.555570 0.831470i
2121 0 0
2222 0 0
2323 1.17588 + 0.785695i 1.17588 + 0.785695i 0.980785 0.195090i 0.0625000π-0.0625000\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
2424 −1.00000 −1.00000
2525 −0.923880 0.382683i −0.923880 0.382683i
2626 0 0
2727 −0.195090 0.980785i −0.195090 0.980785i
2828 0 0
2929 0 0 −0.980785 0.195090i 0.937500π-0.937500\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
3030 0.195090 + 0.980785i 0.195090 + 0.980785i
3131 0.216773 + 0.324423i 0.216773 + 0.324423i 0.923880 0.382683i 0.125000π-0.125000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
3232 −0.555570 0.831470i −0.555570 0.831470i
3333 0 0
3434 0.382683 + 0.923880i 0.382683 + 0.923880i
3535 0 0
3636 0.707107 0.707107i 0.707107 0.707107i
3737 0 0 −0.555570 0.831470i 0.687500π-0.687500\pi
0.555570 + 0.831470i 0.312500π0.312500\pi
3838 0.750661 0.149316i 0.750661 0.149316i
3939 0 0
4040 −0.707107 + 0.707107i −0.707107 + 0.707107i
4141 0 0 −0.195090 0.980785i 0.562500π-0.562500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
4242 0 0
4343 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
4444 0 0
4545 −0.831470 0.555570i −0.831470 0.555570i
4646 −1.00000 1.00000i −1.00000 1.00000i
4747 −1.38704 + 1.38704i −1.38704 + 1.38704i −0.555570 + 0.831470i 0.687500π0.687500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
4848 0.980785 + 0.195090i 0.980785 + 0.195090i
4949 0.923880 0.382683i 0.923880 0.382683i
5050 0.831470 + 0.555570i 0.831470 + 0.555570i
5151 −0.923880 0.382683i −0.923880 0.382683i
5252 0 0
5353 0.636379 + 1.53636i 0.636379 + 1.53636i 0.831470 + 0.555570i 0.187500π0.187500\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
5454 1.00000i 1.00000i
5555 0 0
5656 0 0
5757 −0.425215 + 0.636379i −0.425215 + 0.636379i
5858 0 0
5959 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
6060 1.00000i 1.00000i
6161 0.382683 0.0761205i 0.382683 0.0761205i 1.00000i 0.5π-0.5\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
6262 −0.149316 0.360480i −0.149316 0.360480i
6363 0 0
6464 0.382683 + 0.923880i 0.382683 + 0.923880i
6565 0 0
6666 0 0
6767 0 0 1.00000 00
−1.00000 π\pi
6868 −0.195090 0.980785i −0.195090 0.980785i
6969 1.41421 1.41421
7070 0 0
7171 0 0 0.831470 0.555570i 0.187500π-0.187500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
7272 −0.831470 + 0.555570i −0.831470 + 0.555570i
7373 0 0 0.195090 0.980785i 0.437500π-0.437500\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
7474 0 0
7575 −0.980785 + 0.195090i −0.980785 + 0.195090i
7676 −0.765367 −0.765367
7777 0 0
7878 0 0
7979 1.08979 1.63099i 1.08979 1.63099i 0.382683 0.923880i 0.375000π-0.375000\pi
0.707107 0.707107i 0.250000π-0.250000\pi
8080 0.831470 0.555570i 0.831470 0.555570i
8181 −0.707107 0.707107i −0.707107 0.707107i
8282 0 0
8383 −0.425215 1.02656i −0.425215 1.02656i −0.980785 0.195090i 0.937500π-0.937500\pi
0.555570 0.831470i 0.312500π-0.312500\pi
8484 0 0
8585 −0.923880 + 0.382683i −0.923880 + 0.382683i
8686 0 0
8787 0 0
8888 0 0
8989 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
9090 0.707107 + 0.707107i 0.707107 + 0.707107i
9191 0 0
9292 0.785695 + 1.17588i 0.785695 + 1.17588i
9393 0.360480 + 0.149316i 0.360480 + 0.149316i
9494 1.63099 1.08979i 1.63099 1.08979i
9595 0.149316 + 0.750661i 0.149316 + 0.750661i
9696 −0.923880 0.382683i −0.923880 0.382683i
9797 0 0 −0.980785 0.195090i 0.937500π-0.937500\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
9898 −0.980785 + 0.195090i −0.980785 + 0.195090i
9999 0 0
100100 −0.707107 0.707107i −0.707107 0.707107i
101101 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
102102 0.831470 + 0.555570i 0.831470 + 0.555570i
103103 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
104104 0 0
105105 0 0
106106 −0.324423 1.63099i −0.324423 1.63099i
107107 −1.81225 0.360480i −1.81225 0.360480i −0.831470 0.555570i 0.812500π-0.812500\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
108108 0.195090 0.980785i 0.195090 0.980785i
109109 0.216773 + 1.08979i 0.216773 + 1.08979i 0.923880 + 0.382683i 0.125000π0.125000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
110110 0 0
111111 0 0
112112 0 0
113113 1.53636 + 1.02656i 1.53636 + 1.02656i 0.980785 + 0.195090i 0.0625000π0.0625000\pi
0.555570 + 0.831470i 0.312500π0.312500\pi
114114 0.541196 0.541196i 0.541196 0.541196i
115115 1.00000 1.00000i 1.00000 1.00000i
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 −0.195090 + 0.980785i −0.195090 + 0.980785i
121121 −0.382683 0.923880i −0.382683 0.923880i
122122 −0.390181 −0.390181
123123 0 0
124124 0.0761205 + 0.382683i 0.0761205 + 0.382683i
125125 −0.555570 + 0.831470i −0.555570 + 0.831470i
126126 0 0
127127 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
128128 −0.195090 0.980785i −0.195090 0.980785i
129129 0 0
130130 0 0
131131 0 0 0.195090 0.980785i 0.437500π-0.437500\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
132132 0 0
133133 0 0
134134 0 0
135135 −1.00000 −1.00000
136136 1.00000i 1.00000i
137137 1.96157 1.96157 0.980785 0.195090i 0.0625000π-0.0625000\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
138138 −1.38704 0.275899i −1.38704 0.275899i
139139 −1.38268 + 0.923880i −1.38268 + 0.923880i −0.382683 + 0.923880i 0.625000π0.625000\pi
−1.00000 π\pi
140140 0 0
141141 −0.382683 + 1.92388i −0.382683 + 1.92388i
142142 0 0
143143 0 0
144144 0.923880 0.382683i 0.923880 0.382683i
145145 0 0
146146 0 0
147147 0.555570 0.831470i 0.555570 0.831470i
148148 0 0
149149 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
150150 1.00000 1.00000
151151 0.541196 + 1.30656i 0.541196 + 1.30656i 0.923880 + 0.382683i 0.125000π0.125000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
152152 0.750661 + 0.149316i 0.750661 + 0.149316i
153153 −0.980785 + 0.195090i −0.980785 + 0.195090i
154154 0 0
155155 0.360480 0.149316i 0.360480 0.149316i
156156 0 0
157157 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
158158 −1.38704 + 1.38704i −1.38704 + 1.38704i
159159 1.38268 + 0.923880i 1.38268 + 0.923880i
160160 −0.923880 + 0.382683i −0.923880 + 0.382683i
161161 0 0
162162 0.555570 + 0.831470i 0.555570 + 0.831470i
163163 0 0 −0.195090 0.980785i 0.562500π-0.562500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
164164 0 0
165165 0 0
166166 0.216773 + 1.08979i 0.216773 + 1.08979i
167167 1.02656 + 1.53636i 1.02656 + 1.53636i 0.831470 + 0.555570i 0.187500π0.187500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
168168 0 0
169169 1.00000i 1.00000i
170170 0.980785 0.195090i 0.980785 0.195090i
171171 0.765367i 0.765367i
172172 0 0
173173 1.02656 + 1.53636i 1.02656 + 1.53636i 0.831470 + 0.555570i 0.187500π0.187500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
180180 −0.555570 0.831470i −0.555570 0.831470i
181181 −1.38268 0.923880i −1.38268 0.923880i −0.382683 0.923880i 0.625000π-0.625000\pi
−1.00000 π\pi
182182 0 0
183183 0.275899 0.275899i 0.275899 0.275899i
184184 −0.541196 1.30656i −0.541196 1.30656i
185185 0 0
186186 −0.324423 0.216773i −0.324423 0.216773i
187187 0 0
188188 −1.81225 + 0.750661i −1.81225 + 0.750661i
189189 0 0
190190 0.765367i 0.765367i
191191 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
192192 0.831470 + 0.555570i 0.831470 + 0.555570i
193193 0 0 0.555570 0.831470i 0.312500π-0.312500\pi
−0.555570 + 0.831470i 0.687500π0.687500\pi
194194 0 0
195195 0 0
196196 1.00000 1.00000
197197 −1.38704 + 0.275899i −1.38704 + 0.275899i −0.831470 0.555570i 0.812500π-0.812500\pi
−0.555570 + 0.831470i 0.687500π0.687500\pi
198198 0 0
199199 −0.216773 + 1.08979i −0.216773 + 1.08979i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
200200 0.555570 + 0.831470i 0.555570 + 0.831470i
201201 0 0
202202 0 0
203203 0 0
204204 −0.707107 0.707107i −0.707107 0.707107i
205205 0 0
206206 0 0
207207 1.17588 0.785695i 1.17588 0.785695i
208208 0 0
209209 0 0
210210 0 0
211211 1.08979 0.216773i 1.08979 0.216773i 0.382683 0.923880i 0.375000π-0.375000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
212212 1.66294i 1.66294i
213213 0 0
214214 1.70711 + 0.707107i 1.70711 + 0.707107i
215215 0 0
216216 −0.382683 + 0.923880i −0.382683 + 0.923880i
217217 0 0
218218 1.11114i 1.11114i
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
224224 0 0
225225 −0.707107 + 0.707107i −0.707107 + 0.707107i
226226 −1.30656 1.30656i −1.30656 1.30656i
227227 0.636379 + 0.425215i 0.636379 + 0.425215i 0.831470 0.555570i 0.187500π-0.187500\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
228228 −0.636379 + 0.425215i −0.636379 + 0.425215i
229229 −1.70711 0.707107i −1.70711 0.707107i −0.707107 0.707107i 0.750000π-0.750000\pi
−1.00000 π\pi
230230 −1.17588 + 0.785695i −1.17588 + 0.785695i
231231 0 0
232232 0 0
233233 −1.38704 0.275899i −1.38704 0.275899i −0.555570 0.831470i 0.687500π-0.687500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
234234 0 0
235235 1.08979 + 1.63099i 1.08979 + 1.63099i
236236 0 0
237237 1.96157i 1.96157i
238238 0 0
239239 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
240240 0.382683 0.923880i 0.382683 0.923880i
241241 1.08979 + 1.63099i 1.08979 + 1.63099i 0.707107 + 0.707107i 0.250000π0.250000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
242242 0.195090 + 0.980785i 0.195090 + 0.980785i
243243 −0.980785 0.195090i −0.980785 0.195090i
244244 0.382683 + 0.0761205i 0.382683 + 0.0761205i
245245 −0.195090 0.980785i −0.195090 0.980785i
246246 0 0
247247 0 0
248248 0.390181i 0.390181i
249249 −0.923880 0.617317i −0.923880 0.617317i
250250 0.707107 0.707107i 0.707107 0.707107i
251251 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
252252 0 0
253253 0 0
254254 0 0
255255 −0.555570 + 0.831470i −0.555570 + 0.831470i
256256 1.00000i 1.00000i
257257 −0.149316 0.360480i −0.149316 0.360480i 0.831470 0.555570i 0.187500π-0.187500\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 0.425215 1.02656i 0.425215 1.02656i −0.555570 0.831470i 0.687500π-0.687500\pi
0.980785 0.195090i 0.0625000π-0.0625000\pi
264264 0 0
265265 1.63099 0.324423i 1.63099 0.324423i
266266 0 0
267267 0 0
268268 0 0
269269 0 0 0.831470 0.555570i 0.187500π-0.187500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
270270 0.980785 + 0.195090i 0.980785 + 0.195090i
271271 −1.84776 −1.84776 −0.923880 0.382683i 0.875000π-0.875000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
272272 0.195090 0.980785i 0.195090 0.980785i
273273 0 0
274274 −1.92388 0.382683i −1.92388 0.382683i
275275 0 0
276276 1.30656 + 0.541196i 1.30656 + 0.541196i
277277 0 0 0.195090 0.980785i 0.437500π-0.437500\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
278278 1.53636 0.636379i 1.53636 0.636379i
279279 0.382683 0.0761205i 0.382683 0.0761205i
280280 0 0
281281 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
282282 0.750661 1.81225i 0.750661 1.81225i
283283 0 0 0.555570 0.831470i 0.312500π-0.312500\pi
−0.555570 + 0.831470i 0.687500π0.687500\pi
284284 0 0
285285 0.541196 + 0.541196i 0.541196 + 0.541196i
286286 0 0
287287 0 0
288288 −0.980785 + 0.195090i −0.980785 + 0.195090i
289289 −0.382683 + 0.923880i −0.382683 + 0.923880i
290290 0 0
291291 0 0
292292 0 0
293293 1.38704 1.38704i 1.38704 1.38704i 0.555570 0.831470i 0.312500π-0.312500\pi
0.831470 0.555570i 0.187500π-0.187500\pi
294294 −0.707107 + 0.707107i −0.707107 + 0.707107i
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 −0.980785 0.195090i −0.980785 0.195090i
301301 0 0
302302 −0.275899 1.38704i −0.275899 1.38704i
303303 0 0
304304 −0.707107 0.292893i −0.707107 0.292893i
305305 0.390181i 0.390181i
306306 1.00000 1.00000
307307 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
308308 0 0
309309 0 0
310310 −0.382683 + 0.0761205i −0.382683 + 0.0761205i
311311 0 0 −0.980785 0.195090i 0.937500π-0.937500\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
312312 0 0
313313 0 0 −0.195090 0.980785i 0.562500π-0.562500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
314314 0 0
315315 0 0
316316 1.63099 1.08979i 1.63099 1.08979i
317317 −0.636379 0.425215i −0.636379 0.425215i 0.195090 0.980785i 0.437500π-0.437500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
318318 −1.17588 1.17588i −1.17588 1.17588i
319319 0 0
320320 0.980785 0.195090i 0.980785 0.195090i
321321 −1.70711 + 0.707107i −1.70711 + 0.707107i
322322 0 0
323323 0.636379 + 0.425215i 0.636379 + 0.425215i
324324 −0.382683 0.923880i −0.382683 0.923880i
325325 0 0
326326 0 0
327327 0.785695 + 0.785695i 0.785695 + 0.785695i
328328 0 0
329329 0 0
330330 0 0
331331 0.707107 1.70711i 0.707107 1.70711i 1.00000i 0.5π-0.5\pi
0.707107 0.707107i 0.250000π-0.250000\pi
332332 1.11114i 1.11114i
333333 0 0
334334 −0.707107 1.70711i −0.707107 1.70711i
335335 0 0
336336 0 0
337337 0 0 0.831470 0.555570i 0.187500π-0.187500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
338338 0.195090 0.980785i 0.195090 0.980785i
339339 1.84776 1.84776
340340 −1.00000 −1.00000
341341 0 0
342342 0.149316 0.750661i 0.149316 0.750661i
343343 0 0
344344 0 0
345345 0.275899 1.38704i 0.275899 1.38704i
346346 −0.707107 1.70711i −0.707107 1.70711i
347347 0.750661 0.149316i 0.750661 0.149316i 0.195090 0.980785i 0.437500π-0.437500\pi
0.555570 + 0.831470i 0.312500π0.312500\pi
348348 0 0
349349 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
350350 0 0
351351 0 0
352352 0 0
353353 −1.17588 1.17588i −1.17588 1.17588i −0.980785 0.195090i 0.937500π-0.937500\pi
−0.195090 0.980785i 0.562500π-0.562500\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
360360 0.382683 + 0.923880i 0.382683 + 0.923880i
361361 −0.292893 + 0.292893i −0.292893 + 0.292893i
362362 1.17588 + 1.17588i 1.17588 + 1.17588i
363363 −0.831470 0.555570i −0.831470 0.555570i
364364 0 0
365365 0 0
366366 −0.324423 + 0.216773i −0.324423 + 0.216773i
367367 0 0 −0.195090 0.980785i 0.562500π-0.562500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
368368 0.275899 + 1.38704i 0.275899 + 1.38704i
369369 0 0
370370 0 0
371371 0 0
372372 0.275899 + 0.275899i 0.275899 + 0.275899i
373373 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
374374 0 0
375375 1.00000i 1.00000i
376376 1.92388 0.382683i 1.92388 0.382683i
377377 0 0
378378 0 0
379379 −1.08979 0.216773i −1.08979 0.216773i −0.382683 0.923880i 0.625000π-0.625000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
380380 −0.149316 + 0.750661i −0.149316 + 0.750661i
381381 0 0
382382 0 0
383383 −0.360480 0.149316i −0.360480 0.149316i 0.195090 0.980785i 0.437500π-0.437500\pi
−0.555570 + 0.831470i 0.687500π0.687500\pi
384384 −0.707107 0.707107i −0.707107 0.707107i
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
390390 0 0
391391 1.41421i 1.41421i
392392 −0.980785 0.195090i −0.980785 0.195090i
393393 0 0
394394 1.41421 1.41421
395395 −1.38704 1.38704i −1.38704 1.38704i
396396 0 0
397397 0 0 0.555570 0.831470i 0.312500π-0.312500\pi
−0.555570 + 0.831470i 0.687500π0.687500\pi
398398 0.425215 1.02656i 0.425215 1.02656i
399399 0 0
400400 −0.382683 0.923880i −0.382683 0.923880i
401401 0 0 0.980785 0.195090i 0.0625000π-0.0625000\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
402402 0 0
403403 0 0
404404 0 0
405405 −0.831470 + 0.555570i −0.831470 + 0.555570i
406406 0 0
407407 0 0
408408 0.555570 + 0.831470i 0.555570 + 0.831470i
409409 −0.765367 −0.765367 −0.382683 0.923880i 0.625000π-0.625000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
410410 0 0
411411 1.63099 1.08979i 1.63099 1.08979i
412412 0 0
413413 0 0
414414 −1.30656 + 0.541196i −1.30656 + 0.541196i
415415 −1.08979 + 0.216773i −1.08979 + 0.216773i
416416 0 0
417417 −0.636379 + 1.53636i −0.636379 + 1.53636i
418418 0 0
419419 0 0 0.555570 0.831470i 0.312500π-0.312500\pi
−0.555570 + 0.831470i 0.687500π0.687500\pi
420420 0 0
421421 −0.541196 0.541196i −0.541196 0.541196i 0.382683 0.923880i 0.375000π-0.375000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
422422 −1.11114 −1.11114
423423 0.750661 + 1.81225i 0.750661 + 1.81225i
424424 0.324423 1.63099i 0.324423 1.63099i
425425 0.195090 + 0.980785i 0.195090 + 0.980785i
426426 0 0
427427 0 0
428428 −1.53636 1.02656i −1.53636 1.02656i
429429 0 0
430430 0 0
431431 0 0 −0.831470 0.555570i 0.812500π-0.812500\pi
0.831470 + 0.555570i 0.187500π0.187500\pi
432432 0.555570 0.831470i 0.555570 0.831470i
433433 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
434434 0 0
435435 0 0
436436 −0.216773 + 1.08979i −0.216773 + 1.08979i
437437 −1.06159 0.211164i −1.06159 0.211164i
438438 0 0
439439 −0.923880 1.38268i −0.923880 1.38268i −0.923880 0.382683i 0.875000π-0.875000\pi
1.00000i 0.5π-0.5\pi
440440 0 0
441441 1.00000i 1.00000i
442442 0 0
443443 1.96157i 1.96157i −0.195090 0.980785i 0.562500π-0.562500\pi
0.195090 0.980785i 0.437500π-0.437500\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 0 0 −0.195090 0.980785i 0.562500π-0.562500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
450450 0.831470 0.555570i 0.831470 0.555570i
451451 0 0
452452 1.02656 + 1.53636i 1.02656 + 1.53636i
453453 1.17588 + 0.785695i 1.17588 + 0.785695i
454454 −0.541196 0.541196i −0.541196 0.541196i
455455 0 0
456456 0.707107 0.292893i 0.707107 0.292893i
457457 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
458458 1.53636 + 1.02656i 1.53636 + 1.02656i
459459 −0.707107 + 0.707107i −0.707107 + 0.707107i
460460 1.30656 0.541196i 1.30656 0.541196i
461461 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
462462 0 0
463463 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
464464 0 0
465465 0.216773 0.324423i 0.216773 0.324423i
466466 1.30656 + 0.541196i 1.30656 + 0.541196i
467467 −0.149316 + 0.360480i −0.149316 + 0.360480i −0.980785 0.195090i 0.937500π-0.937500\pi
0.831470 + 0.555570i 0.187500π0.187500\pi
468468 0 0
469469 0 0
470470 −0.750661 1.81225i −0.750661 1.81225i
471471 0 0
472472 0 0
473473 0 0
474474 −0.382683 + 1.92388i −0.382683 + 1.92388i
475475 0.765367 0.765367
476476 0 0
477477 1.66294 1.66294
478478 0 0
479479 0 0 0.831470 0.555570i 0.187500π-0.187500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
480480 −0.555570 + 0.831470i −0.555570 + 0.831470i
481481 0 0
482482 −0.750661 1.81225i −0.750661 1.81225i
483483 0 0
484484 1.00000i 1.00000i
485485 0 0
486486 0.923880 + 0.382683i 0.923880 + 0.382683i
487487 0 0 0.555570 0.831470i 0.312500π-0.312500\pi
−0.555570 + 0.831470i 0.687500π0.687500\pi
488488 −0.360480 0.149316i −0.360480 0.149316i
489489 0 0
490490 1.00000i 1.00000i
491491 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 −0.0761205 + 0.382683i −0.0761205 + 0.382683i
497497 0 0
498498 0.785695 + 0.785695i 0.785695 + 0.785695i
499499 −1.38268 0.923880i −1.38268 0.923880i −0.382683 0.923880i 0.625000π-0.625000\pi
−1.00000 π\pi
500500 −0.831470 + 0.555570i −0.831470 + 0.555570i
501501 1.70711 + 0.707107i 1.70711 + 0.707107i
502502 0 0
503503 0.360480 + 1.81225i 0.360480 + 1.81225i 0.555570 + 0.831470i 0.312500π0.312500\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
504504 0 0
505505 0 0
506506 0 0
507507 0.555570 + 0.831470i 0.555570 + 0.831470i
508508 0 0
509509 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
510510 0.707107 0.707107i 0.707107 0.707107i
511511 0 0
512512 0.195090 0.980785i 0.195090 0.980785i
513513 0.425215 + 0.636379i 0.425215 + 0.636379i
514514 0.0761205 + 0.382683i 0.0761205 + 0.382683i
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 1.70711 + 0.707107i 1.70711 + 0.707107i
520520 0 0
521521 0 0 −0.831470 0.555570i 0.812500π-0.812500\pi
0.831470 + 0.555570i 0.187500π0.187500\pi
522522 0 0
523523 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
524524 0 0
525525 0 0
526526 −0.617317 + 0.923880i −0.617317 + 0.923880i
527527 0.149316 0.360480i 0.149316 0.360480i
528528 0 0
529529 0.382683 + 0.923880i 0.382683 + 0.923880i
530530 −1.66294 −1.66294
531531 0 0
532532 0 0
533533 0 0
534534 0 0
535535 −0.707107 + 1.70711i −0.707107 + 1.70711i
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 −0.923880 0.382683i −0.923880 0.382683i
541541 1.38268 0.923880i 1.38268 0.923880i 0.382683 0.923880i 0.375000π-0.375000\pi
1.00000 00
542542 1.81225 + 0.360480i 1.81225 + 0.360480i
543543 −1.66294 −1.66294
544544 −0.382683 + 0.923880i −0.382683 + 0.923880i
545545 1.11114 1.11114
546546 0 0
547547 0 0 0.831470 0.555570i 0.187500π-0.187500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
548548 1.81225 + 0.750661i 1.81225 + 0.750661i
549549 0.0761205 0.382683i 0.0761205 0.382683i
550550 0 0
551551 0 0
552552 −1.17588 0.785695i −1.17588 0.785695i
553553 0 0
554554 0 0
555555 0 0
556556 −1.63099 + 0.324423i −1.63099 + 0.324423i
557557 0.785695 + 0.785695i 0.785695 + 0.785695i 0.980785 0.195090i 0.0625000π-0.0625000\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
558558 −0.390181 −0.390181
559559 0 0
560560 0 0
561561 0 0
562562 0 0
563563 1.53636 0.636379i 1.53636 0.636379i 0.555570 0.831470i 0.312500π-0.312500\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
564564 −1.08979 + 1.63099i −1.08979 + 1.63099i
565565 1.30656 1.30656i 1.30656 1.30656i
566566 0 0
567567 0 0
568568 0 0
569569 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
570570 −0.425215 0.636379i −0.425215 0.636379i
571571 0.0761205 + 0.382683i 0.0761205 + 0.382683i 1.00000 00
−0.923880 + 0.382683i 0.875000π0.875000\pi
572572 0 0
573573 0 0
574574 0 0
575575 −0.785695 1.17588i −0.785695 1.17588i
576576 1.00000 1.00000
577577 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
578578 0.555570 0.831470i 0.555570 0.831470i
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 −1.63099 + 1.08979i −1.63099 + 1.08979i
587587 −1.53636 0.636379i −1.53636 0.636379i −0.555570 0.831470i 0.687500π-0.687500\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
588588 0.831470 0.555570i 0.831470 0.555570i
589589 −0.248303 0.165911i −0.248303 0.165911i
590590 0 0
591591 −1.00000 + 1.00000i −1.00000 + 1.00000i
592592 0 0
593593 −1.81225 + 0.750661i −1.81225 + 0.750661i −0.831470 + 0.555570i 0.812500π0.812500\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
594594 0 0
595595 0 0
596596 0 0
597597 0.425215 + 1.02656i 0.425215 + 1.02656i
598598 0 0
599599 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
600600 0.923880 + 0.382683i 0.923880 + 0.382683i
601601 −0.216773 + 0.324423i −0.216773 + 0.324423i −0.923880 0.382683i 0.875000π-0.875000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
602602 0 0
603603 0 0
604604 1.41421i 1.41421i
605605 −0.980785 + 0.195090i −0.980785 + 0.195090i
606606 0 0
607607 0 0 0.195090 0.980785i 0.437500π-0.437500\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
608608 0.636379 + 0.425215i 0.636379 + 0.425215i
609609 0 0
610610 −0.0761205 + 0.382683i −0.0761205 + 0.382683i
611611 0 0
612612 −0.980785 0.195090i −0.980785 0.195090i
613613 0 0 1.00000 00
−1.00000 π\pi
614614 0 0
615615 0 0
616616 0 0
617617 0.360480 1.81225i 0.360480 1.81225i −0.195090 0.980785i 0.562500π-0.562500\pi
0.555570 0.831470i 0.312500π-0.312500\pi
618618 0 0
619619 −0.382683 + 0.0761205i −0.382683 + 0.0761205i −0.382683 0.923880i 0.625000π-0.625000\pi
1.00000i 0.5π0.5\pi
620620 0.390181 0.390181
621621 0.541196 1.30656i 0.541196 1.30656i
622622 0 0
623623 0 0
624624 0 0
625625 0.707107 + 0.707107i 0.707107 + 0.707107i
626626 0 0
627627 0 0
628628 0 0
629629 0 0
630630 0 0
631631 1.30656 0.541196i 1.30656 0.541196i 0.382683 0.923880i 0.375000π-0.375000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
632632 −1.81225 + 0.750661i −1.81225 + 0.750661i
633633 0.785695 0.785695i 0.785695 0.785695i
634634 0.541196 + 0.541196i 0.541196 + 0.541196i
635635 0 0
636636 0.923880 + 1.38268i 0.923880 + 1.38268i
637637 0 0
638638 0 0
639639 0 0
640640 −1.00000 −1.00000
641641 0 0 −0.980785 0.195090i 0.937500π-0.937500\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
642642 1.81225 0.360480i 1.81225 0.360480i
643643 0 0 −0.555570 0.831470i 0.687500π-0.687500\pi
0.555570 + 0.831470i 0.312500π0.312500\pi
644644 0 0
645645 0 0
646646 −0.541196 0.541196i −0.541196 0.541196i
647647 1.66294i 1.66294i −0.555570 0.831470i 0.687500π-0.687500\pi
0.555570 0.831470i 0.312500π-0.312500\pi
648648 0.195090 + 0.980785i 0.195090 + 0.980785i
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 −0.149316 0.750661i −0.149316 0.750661i −0.980785 0.195090i 0.937500π-0.937500\pi
0.831470 0.555570i 0.187500π-0.187500\pi
654654 −0.617317 0.923880i −0.617317 0.923880i
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 −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i 0.750000π-0.750000\pi
1.00000i 0.5π0.5\pi
662662 −1.02656 + 1.53636i −1.02656 + 1.53636i
663663 0 0
664664 −0.216773 + 1.08979i −0.216773 + 1.08979i
665665 0 0
666666 0 0
667667 0 0
668668 0.360480 + 1.81225i 0.360480 + 1.81225i
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 0 0 0.980785 0.195090i 0.0625000π-0.0625000\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
674674 0 0
675675 −0.195090 + 0.980785i −0.195090 + 0.980785i
676676 −0.382683 + 0.923880i −0.382683 + 0.923880i
677677 −1.17588 + 0.785695i −1.17588 + 0.785695i −0.980785 0.195090i 0.937500π-0.937500\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
678678 −1.81225 0.360480i −1.81225 0.360480i
679679 0 0
680680 0.980785 + 0.195090i 0.980785 + 0.195090i
681681 0.765367 0.765367
682682 0 0
683683 −1.53636 + 1.02656i −1.53636 + 1.02656i −0.555570 + 0.831470i 0.687500π0.687500\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
684684 −0.292893 + 0.707107i −0.292893 + 0.707107i
685685 0.382683 1.92388i 0.382683 1.92388i
686686 0 0
687687 −1.81225 + 0.360480i −1.81225 + 0.360480i
688688 0 0
689689 0 0
690690 −0.541196 + 1.30656i −0.541196 + 1.30656i
691691 −1.08979 + 1.63099i −1.08979 + 1.63099i −0.382683 + 0.923880i 0.625000π0.625000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
692692 0.360480 + 1.81225i 0.360480 + 1.81225i
693693 0 0
694694 −0.765367 −0.765367
695695 0.636379 + 1.53636i 0.636379 + 1.53636i
696696 0 0
697697 0 0
698698 0 0
699699 −1.30656 + 0.541196i −1.30656 + 0.541196i
700700 0 0
701701 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
702702 0 0
703703 0 0
704704 0 0
705705 1.81225 + 0.750661i 1.81225 + 0.750661i
706706 0.923880 + 1.38268i 0.923880 + 1.38268i
707707 0 0
708708 0 0
709709 −1.08979 0.216773i −1.08979 0.216773i −0.382683 0.923880i 0.625000π-0.625000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
710710 0 0
711711 −1.08979 1.63099i −1.08979 1.63099i
712712 0 0
713713 0.551799i 0.551799i
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 −0.980785 0.195090i 0.937500π-0.937500\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
720720 −0.195090 0.980785i −0.195090 0.980785i
721721 0 0
722722 0.344406 0.230125i 0.344406 0.230125i
723723 1.81225 + 0.750661i 1.81225 + 0.750661i
724724 −0.923880 1.38268i −0.923880 1.38268i
725725 0 0
726726 0.707107 + 0.707107i 0.707107 + 0.707107i
727727 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
728728 0 0
729729 −0.923880 + 0.382683i −0.923880 + 0.382683i
730730 0 0
731731 0 0
732732 0.360480 0.149316i 0.360480 0.149316i
733733 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
734734 0 0
735735 −0.707107 0.707107i −0.707107 0.707107i
736736 1.41421i 1.41421i
737737 0 0
738738 0 0
739739 0.541196 1.30656i 0.541196 1.30656i −0.382683 0.923880i 0.625000π-0.625000\pi
0.923880 0.382683i 0.125000π-0.125000\pi
740740 0 0
741741 0 0
742742 0 0
743743 −0.149316 + 0.750661i −0.149316 + 0.750661i 0.831470 + 0.555570i 0.187500π0.187500\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
744744 −0.216773 0.324423i −0.216773 0.324423i
745745 0 0
746746 0 0
747747 −1.11114 −1.11114
748748 0 0
749749 0 0
750750 0.195090 0.980785i 0.195090 0.980785i
751751 −0.923880 + 0.617317i −0.923880 + 0.617317i −0.923880 0.382683i 0.875000π-0.875000\pi
1.00000i 0.5π0.5\pi
752752 −1.96157 −1.96157
753753 0 0
754754 0 0
755755 1.38704 0.275899i 1.38704 0.275899i
756756 0 0
757757 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
758758 1.02656 + 0.425215i 1.02656 + 0.425215i
759759 0 0
760760 0.292893 0.707107i 0.292893 0.707107i
761761 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
762762 0 0
763763 0 0
764764 0 0
765765 1.00000i 1.00000i
766766 0.324423 + 0.216773i 0.324423 + 0.216773i
767767 0 0
768768 0.555570 + 0.831470i 0.555570 + 0.831470i
769769 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
770770 0 0
771771 −0.324423 0.216773i −0.324423 0.216773i
772772 0 0
773773 −1.02656 0.425215i −1.02656 0.425215i −0.195090 0.980785i 0.562500π-0.562500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
774774 0 0
775775 −0.0761205 0.382683i −0.0761205 0.382683i
776776 0 0
777777 0 0
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 −0.275899 + 1.38704i −0.275899 + 1.38704i
783783 0 0
784784 0.923880 + 0.382683i 0.923880 + 0.382683i
785785 0 0
786786 0 0
787787 0 0 −0.980785 0.195090i 0.937500π-0.937500\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
788788 −1.38704 0.275899i −1.38704 0.275899i
789789 −0.216773 1.08979i −0.216773 1.08979i
790790 1.08979 + 1.63099i 1.08979 + 1.63099i
791791 0 0
792792 0 0
793793 0 0
794794 0 0
795795 1.17588 1.17588i 1.17588 1.17588i
796796 −0.617317 + 0.923880i −0.617317 + 0.923880i
797797 0.360480 0.149316i 0.360480 0.149316i −0.195090 0.980785i 0.562500π-0.562500\pi
0.555570 + 0.831470i 0.312500π0.312500\pi
798798 0 0
799799 1.92388 + 0.382683i 1.92388 + 0.382683i
800800 0.195090 + 0.980785i 0.195090 + 0.980785i
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 0.980785 0.195090i 0.0625000π-0.0625000\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
810810 0.923880 0.382683i 0.923880 0.382683i
811811 0.216773 1.08979i 0.216773 1.08979i −0.707107 0.707107i 0.750000π-0.750000\pi
0.923880 0.382683i 0.125000π-0.125000\pi
812812 0 0
813813 −1.53636 + 1.02656i −1.53636 + 1.02656i
814814 0 0
815815 0 0
816816 −0.382683 0.923880i −0.382683 0.923880i
817817 0 0
818818 0.750661 + 0.149316i 0.750661 + 0.149316i
819819 0 0
820820 0 0
821821 0 0 0.195090 0.980785i 0.437500π-0.437500\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
822822 −1.81225 + 0.750661i −1.81225 + 0.750661i
823823 0 0 0.980785 0.195090i 0.0625000π-0.0625000\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
824824 0 0
825825 0 0
826826 0 0
827827 0.785695 1.17588i 0.785695 1.17588i −0.195090 0.980785i 0.562500π-0.562500\pi
0.980785 0.195090i 0.0625000π-0.0625000\pi
828828 1.38704 0.275899i 1.38704 0.275899i
829829 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
830830 1.11114 1.11114
831831 0 0
832832 0 0
833833 −0.831470 0.555570i −0.831470 0.555570i
834834 0.923880 1.38268i 0.923880 1.38268i
835835 1.70711 0.707107i 1.70711 0.707107i
836836 0 0
837837 0.275899 0.275899i 0.275899 0.275899i
838838 0 0
839839 0 0 −0.831470 0.555570i 0.812500π-0.812500\pi
0.831470 + 0.555570i 0.187500π0.187500\pi
840840 0 0
841841 0.923880 + 0.382683i 0.923880 + 0.382683i
842842 0.425215 + 0.636379i 0.425215 + 0.636379i
843843 0 0
844844 1.08979 + 0.216773i 1.08979 + 0.216773i
845845 0.980785 + 0.195090i 0.980785 + 0.195090i
846846 −0.382683 1.92388i −0.382683 1.92388i
847847 0 0
848848 −0.636379 + 1.53636i −0.636379 + 1.53636i
849849 0 0
850850 1.00000i 1.00000i
851851 0 0
852852 0 0
853853 0 0 −0.555570 0.831470i 0.687500π-0.687500\pi
0.555570 + 0.831470i 0.312500π0.312500\pi
854854 0 0
855855 0.750661 + 0.149316i 0.750661 + 0.149316i
856856 1.30656 + 1.30656i 1.30656 + 1.30656i
857857 0.275899 + 1.38704i 0.275899 + 1.38704i 0.831470 + 0.555570i 0.187500π0.187500\pi
−0.555570 + 0.831470i 0.687500π0.687500\pi
858858 0 0
859859 −1.70711 0.707107i −1.70711 0.707107i −0.707107 0.707107i 0.750000π-0.750000\pi
−1.00000 π\pi
860860 0 0
861861 0 0
862862 0 0
863863 0.785695 0.785695i 0.785695 0.785695i −0.195090 0.980785i 0.562500π-0.562500\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
864864 −0.707107 + 0.707107i −0.707107 + 0.707107i
865865 1.70711 0.707107i 1.70711 0.707107i
866866 0 0
867867 0.195090 + 0.980785i 0.195090 + 0.980785i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0.425215 1.02656i 0.425215 1.02656i
873873 0 0
874874 1.00000 + 0.414214i 1.00000 + 0.414214i
875875 0 0
876876 0 0
877877 0 0 0.980785 0.195090i 0.0625000π-0.0625000\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
878878 0.636379 + 1.53636i 0.636379 + 1.53636i
879879 0.382683 1.92388i 0.382683 1.92388i
880880 0 0
881881 0 0 0.831470 0.555570i 0.187500π-0.187500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
882882 −0.195090 + 0.980785i −0.195090 + 0.980785i
883883 0 0 1.00000 00
−1.00000 π\pi
884884 0 0
885885 0 0
886886 −0.382683 + 1.92388i −0.382683 + 1.92388i
887887 0 0 −0.555570 0.831470i 0.687500π-0.687500\pi
0.555570 + 0.831470i 0.312500π0.312500\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 0.574531 1.38704i 0.574531 1.38704i
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 −0.923880 + 0.382683i −0.923880 + 0.382683i
901901 0.923880 1.38268i 0.923880 1.38268i
902902 0 0
903903 0 0
904904 −0.707107 1.70711i −0.707107 1.70711i
905905 −1.17588 + 1.17588i −1.17588 + 1.17588i
906906 −1.00000 1.00000i −1.00000 1.00000i
907907 0 0 −0.831470 0.555570i 0.812500π-0.812500\pi
0.831470 + 0.555570i 0.187500π0.187500\pi
908908 0.425215 + 0.636379i 0.425215 + 0.636379i
909909 0 0
910910 0 0
911911 0 0 −0.195090 0.980785i 0.562500π-0.562500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
912912 −0.750661 + 0.149316i −0.750661 + 0.149316i
913913 0 0
914914 0 0
915915 −0.216773 0.324423i −0.216773 0.324423i
916916 −1.30656 1.30656i −1.30656 1.30656i
917917 0 0
918918 0.831470 0.555570i 0.831470 0.555570i
919919 0.765367i 0.765367i −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 0.382683i 0.125000π-0.125000\pi
920920 −1.38704 + 0.275899i −1.38704 + 0.275899i
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 −0.831470 0.555570i 0.812500π-0.812500\pi
0.831470 + 0.555570i 0.187500π0.187500\pi
930930 −0.275899 + 0.275899i −0.275899 + 0.275899i
931931 −0.541196 + 0.541196i −0.541196 + 0.541196i
932932 −1.17588 0.785695i −1.17588 0.785695i
933933 0 0
934934 0.216773 0.324423i 0.216773 0.324423i
935935 0 0
936936 0 0
937937 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
938938 0 0
939939 0 0
940940 0.382683 + 1.92388i 0.382683 + 1.92388i
941941 0 0 0.555570 0.831470i 0.312500π-0.312500\pi
−0.555570 + 0.831470i 0.687500π0.687500\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 −0.980785 0.195090i 0.937500π-0.937500\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
948948 0.750661 1.81225i 0.750661 1.81225i
949949 0 0
950950 −0.750661 0.149316i −0.750661 0.149316i
951951 −0.765367 −0.765367
952952 0 0
953953 0.390181 0.390181 0.195090 0.980785i 0.437500π-0.437500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
954954 −1.63099 0.324423i −1.63099 0.324423i
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0.707107 0.707107i 0.707107 0.707107i
961961 0.324423 0.783227i 0.324423 0.783227i
962962 0 0
963963 −1.02656 + 1.53636i −1.02656 + 1.53636i
964964 0.382683 + 1.92388i 0.382683 + 1.92388i
965965 0 0
966966 0 0
967967 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
968968 −0.195090 + 0.980785i −0.195090 + 0.980785i
969969 0.765367 0.765367
970970 0 0
971971 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
972972 −0.831470 0.555570i −0.831470 0.555570i
973973 0 0
974974 0 0
975975 0 0
976976 0.324423 + 0.216773i 0.324423 + 0.216773i
977977 1.02656 + 0.425215i 1.02656 + 0.425215i 0.831470 0.555570i 0.187500π-0.187500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
978978 0 0
979979 0 0
980980 0.195090 0.980785i 0.195090 0.980785i
981981 1.08979 + 0.216773i 1.08979 + 0.216773i
982982 0 0
983983 −0.425215 0.636379i −0.425215 0.636379i 0.555570 0.831470i 0.312500π-0.312500\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
984984 0 0
985985 1.41421i 1.41421i
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 1.63099 + 0.324423i 1.63099 + 0.324423i 0.923880 0.382683i 0.125000π-0.125000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
992992 0.149316 0.360480i 0.149316 0.360480i
993993 −0.360480 1.81225i −0.360480 1.81225i
994994 0 0
995995 1.02656 + 0.425215i 1.02656 + 0.425215i
996996 −0.617317 0.923880i −0.617317 0.923880i
997997 0 0 −0.831470 0.555570i 0.812500π-0.812500\pi
0.831470 + 0.555570i 0.187500π0.187500\pi
998998 1.17588 + 1.17588i 1.17588 + 1.17588i
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 1020.1.cl.a.719.1 16
3.2 odd 2 inner 1020.1.cl.a.719.2 yes 16
4.3 odd 2 1020.1.cl.b.719.2 yes 16
5.4 even 2 inner 1020.1.cl.a.719.2 yes 16
12.11 even 2 1020.1.cl.b.719.1 yes 16
15.14 odd 2 CM 1020.1.cl.a.719.1 16
17.7 odd 16 1020.1.cl.b.959.2 yes 16
20.19 odd 2 1020.1.cl.b.719.1 yes 16
51.41 even 16 1020.1.cl.b.959.1 yes 16
60.59 even 2 1020.1.cl.b.719.2 yes 16
68.7 even 16 inner 1020.1.cl.a.959.1 yes 16
85.24 odd 16 1020.1.cl.b.959.1 yes 16
204.143 odd 16 inner 1020.1.cl.a.959.2 yes 16
255.194 even 16 1020.1.cl.b.959.2 yes 16
340.279 even 16 inner 1020.1.cl.a.959.2 yes 16
1020.959 odd 16 inner 1020.1.cl.a.959.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1020.1.cl.a.719.1 16 1.1 even 1 trivial
1020.1.cl.a.719.1 16 15.14 odd 2 CM
1020.1.cl.a.719.2 yes 16 3.2 odd 2 inner
1020.1.cl.a.719.2 yes 16 5.4 even 2 inner
1020.1.cl.a.959.1 yes 16 68.7 even 16 inner
1020.1.cl.a.959.1 yes 16 1020.959 odd 16 inner
1020.1.cl.a.959.2 yes 16 204.143 odd 16 inner
1020.1.cl.a.959.2 yes 16 340.279 even 16 inner
1020.1.cl.b.719.1 yes 16 12.11 even 2
1020.1.cl.b.719.1 yes 16 20.19 odd 2
1020.1.cl.b.719.2 yes 16 4.3 odd 2
1020.1.cl.b.719.2 yes 16 60.59 even 2
1020.1.cl.b.959.1 yes 16 51.41 even 16
1020.1.cl.b.959.1 yes 16 85.24 odd 16
1020.1.cl.b.959.2 yes 16 17.7 odd 16
1020.1.cl.b.959.2 yes 16 255.194 even 16