Properties

Label 1740.1.v.a.1043.1
Level 17401740
Weight 11
Character 1740.1043
Analytic conductor 0.8680.868
Analytic rank 00
Dimension 44
Projective image D4D_{4}
CM discriminant -116
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] = [1740,1,Mod(347,1740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1740, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 1, 2])) 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("1740.347"); S:= CuspForms(chi, 1); N := Newforms(S);
 
Level: N N == 1740=223529 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29
Weight: k k == 1 1
Character orbit: [χ][\chi] == 1740.v (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 0.8683731219810.868373121981
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(i)\Q(i)
Coefficient field: Q(ζ8)\Q(\zeta_{8})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4+1 x^{4} + 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: D4D_{4}
Projective field: Galois closure of 4.2.3784500.2

Embedding invariants

Embedding label 1043.1
Root 0.7071070.707107i-0.707107 - 0.707107i of defining polynomial
Character χ\chi == 1740.1043
Dual form 1740.1.v.a.347.1

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+(0.7071070.707107i)q2+(0.707107+0.707107i)q3+1.00000iq41.00000q51.00000iq6+(0.7071070.707107i)q8+1.00000iq9+(0.707107+0.707107i)q10+1.41421iq11+(0.707107+0.707107i)q12+(1.000001.00000i)q13+(0.7071070.707107i)q151.00000q16+(0.7071070.707107i)q18+1.41421iq191.00000iq20+(1.000001.00000i)q22+1.00000q24+1.00000q25+1.41421iq26+(0.707107+0.707107i)q271.00000q29+1.00000iq301.41421q31+(0.707107+0.707107i)q32+(1.00000+1.00000i)q331.00000q36+(1.000001.00000i)q381.41421iq39+(0.707107+0.707107i)q401.41421q441.00000iq45+(1.41421+1.41421i)q47+(0.7071070.707107i)q481.00000iq49+(0.7071070.707107i)q50+(1.000001.00000i)q52+(1.00000+1.00000i)q53+1.00000q541.41421iq55+(1.00000+1.00000i)q57+(0.707107+0.707107i)q58+(0.7071070.707107i)q60+(1.00000+1.00000i)q621.00000iq64+(1.00000+1.00000i)q65+1.41421q66+(0.707107+0.707107i)q72+(0.707107+0.707107i)q751.41421q76+(1.00000+1.00000i)q78+1.41421iq79+1.00000q801.00000q81+(0.7071070.707107i)q87+(1.00000+1.00000i)q88+(0.707107+0.707107i)q90+(1.000001.00000i)q932.00000iq941.41421iq95+1.00000iq96+(0.707107+0.707107i)q981.41421q99+O(q100)q+(-0.707107 - 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} +1.00000i q^{4} -1.00000 q^{5} -1.00000i q^{6} +(0.707107 - 0.707107i) q^{8} +1.00000i q^{9} +(0.707107 + 0.707107i) q^{10} +1.41421i q^{11} +(-0.707107 + 0.707107i) q^{12} +(-1.00000 - 1.00000i) q^{13} +(-0.707107 - 0.707107i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{18} +1.41421i q^{19} -1.00000i q^{20} +(1.00000 - 1.00000i) q^{22} +1.00000 q^{24} +1.00000 q^{25} +1.41421i q^{26} +(-0.707107 + 0.707107i) q^{27} -1.00000 q^{29} +1.00000i q^{30} -1.41421 q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.00000 + 1.00000i) q^{33} -1.00000 q^{36} +(1.00000 - 1.00000i) q^{38} -1.41421i q^{39} +(-0.707107 + 0.707107i) q^{40} -1.41421 q^{44} -1.00000i q^{45} +(1.41421 + 1.41421i) q^{47} +(-0.707107 - 0.707107i) q^{48} -1.00000i q^{49} +(-0.707107 - 0.707107i) q^{50} +(1.00000 - 1.00000i) q^{52} +(-1.00000 + 1.00000i) q^{53} +1.00000 q^{54} -1.41421i q^{55} +(-1.00000 + 1.00000i) q^{57} +(0.707107 + 0.707107i) q^{58} +(0.707107 - 0.707107i) q^{60} +(1.00000 + 1.00000i) q^{62} -1.00000i q^{64} +(1.00000 + 1.00000i) q^{65} +1.41421 q^{66} +(0.707107 + 0.707107i) q^{72} +(0.707107 + 0.707107i) q^{75} -1.41421 q^{76} +(-1.00000 + 1.00000i) q^{78} +1.41421i q^{79} +1.00000 q^{80} -1.00000 q^{81} +(-0.707107 - 0.707107i) q^{87} +(1.00000 + 1.00000i) q^{88} +(-0.707107 + 0.707107i) q^{90} +(-1.00000 - 1.00000i) q^{93} -2.00000i q^{94} -1.41421i q^{95} +1.00000i q^{96} +(-0.707107 + 0.707107i) q^{98} -1.41421 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q4q54q134q16+4q22+4q24+4q254q294q334q36+4q38+4q524q53+4q544q57+4q62+4q654q78+4q804q81+4q93+O(q100) 4 q - 4 q^{5} - 4 q^{13} - 4 q^{16} + 4 q^{22} + 4 q^{24} + 4 q^{25} - 4 q^{29} - 4 q^{33} - 4 q^{36} + 4 q^{38} + 4 q^{52} - 4 q^{53} + 4 q^{54} - 4 q^{57} + 4 q^{62} + 4 q^{65} - 4 q^{78} + 4 q^{80} - 4 q^{81}+ \cdots - 4 q^{93}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1740Z)×\left(\mathbb{Z}/1740\mathbb{Z}\right)^\times.

nn 581581 697697 871871 901901
χ(n)\chi(n) 1-1 e(34)e\left(\frac{3}{4}\right) 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 −0.707107 0.707107i −0.707107 0.707107i
33 0.707107 + 0.707107i 0.707107 + 0.707107i
44 1.00000i 1.00000i
55 −1.00000 −1.00000
66 1.00000i 1.00000i
77 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
88 0.707107 0.707107i 0.707107 0.707107i
99 1.00000i 1.00000i
1010 0.707107 + 0.707107i 0.707107 + 0.707107i
1111 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
1212 −0.707107 + 0.707107i −0.707107 + 0.707107i
1313 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
1414 0 0
1515 −0.707107 0.707107i −0.707107 0.707107i
1616 −1.00000 −1.00000
1717 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
1818 0.707107 0.707107i 0.707107 0.707107i
1919 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
2020 1.00000i 1.00000i
2121 0 0
2222 1.00000 1.00000i 1.00000 1.00000i
2323 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
2424 1.00000 1.00000
2525 1.00000 1.00000
2626 1.41421i 1.41421i
2727 −0.707107 + 0.707107i −0.707107 + 0.707107i
2828 0 0
2929 −1.00000 −1.00000
3030 1.00000i 1.00000i
3131 −1.41421 −1.41421 −0.707107 0.707107i 0.750000π-0.750000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
3232 0.707107 + 0.707107i 0.707107 + 0.707107i
3333 −1.00000 + 1.00000i −1.00000 + 1.00000i
3434 0 0
3535 0 0
3636 −1.00000 −1.00000
3737 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
3838 1.00000 1.00000i 1.00000 1.00000i
3939 1.41421i 1.41421i
4040 −0.707107 + 0.707107i −0.707107 + 0.707107i
4141 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4242 0 0
4343 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
4444 −1.41421 −1.41421
4545 1.00000i 1.00000i
4646 0 0
4747 1.41421 + 1.41421i 1.41421 + 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
4848 −0.707107 0.707107i −0.707107 0.707107i
4949 1.00000i 1.00000i
5050 −0.707107 0.707107i −0.707107 0.707107i
5151 0 0
5252 1.00000 1.00000i 1.00000 1.00000i
5353 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
5454 1.00000 1.00000
5555 1.41421i 1.41421i
5656 0 0
5757 −1.00000 + 1.00000i −1.00000 + 1.00000i
5858 0.707107 + 0.707107i 0.707107 + 0.707107i
5959 0 0 1.00000 00
−1.00000 π\pi
6060 0.707107 0.707107i 0.707107 0.707107i
6161 0 0 1.00000 00
−1.00000 π\pi
6262 1.00000 + 1.00000i 1.00000 + 1.00000i
6363 0 0
6464 1.00000i 1.00000i
6565 1.00000 + 1.00000i 1.00000 + 1.00000i
6666 1.41421 1.41421
6767 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
6868 0 0
6969 0 0
7070 0 0
7171 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
7272 0.707107 + 0.707107i 0.707107 + 0.707107i
7373 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
7474 0 0
7575 0.707107 + 0.707107i 0.707107 + 0.707107i
7676 −1.41421 −1.41421
7777 0 0
7878 −1.00000 + 1.00000i −1.00000 + 1.00000i
7979 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
8080 1.00000 1.00000
8181 −1.00000 −1.00000
8282 0 0
8383 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
8484 0 0
8585 0 0
8686 0 0
8787 −0.707107 0.707107i −0.707107 0.707107i
8888 1.00000 + 1.00000i 1.00000 + 1.00000i
8989 0 0 1.00000 00
−1.00000 π\pi
9090 −0.707107 + 0.707107i −0.707107 + 0.707107i
9191 0 0
9292 0 0
9393 −1.00000 1.00000i −1.00000 1.00000i
9494 2.00000i 2.00000i
9595 1.41421i 1.41421i
9696 1.00000i 1.00000i
9797 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
9898 −0.707107 + 0.707107i −0.707107 + 0.707107i
9999 −1.41421 −1.41421
100100 1.00000i 1.00000i
101101 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
102102 0 0
103103 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
104104 −1.41421 −1.41421
105105 0 0
106106 1.41421 1.41421
107107 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
108108 −0.707107 0.707107i −0.707107 0.707107i
109109 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
110110 −1.00000 + 1.00000i −1.00000 + 1.00000i
111111 0 0
112112 0 0
113113 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
114114 1.41421 1.41421
115115 0 0
116116 1.00000i 1.00000i
117117 1.00000 1.00000i 1.00000 1.00000i
118118 0 0
119119 0 0
120120 −1.00000 −1.00000
121121 −1.00000 −1.00000
122122 0 0
123123 0 0
124124 1.41421i 1.41421i
125125 −1.00000 −1.00000
126126 0 0
127127 1.41421 1.41421i 1.41421 1.41421i 0.707107 0.707107i 0.250000π-0.250000\pi
0.707107 0.707107i 0.250000π-0.250000\pi
128128 −0.707107 + 0.707107i −0.707107 + 0.707107i
129129 0 0
130130 1.41421i 1.41421i
131131 1.41421i 1.41421i −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 0.707107i 0.250000π-0.250000\pi
132132 −1.00000 1.00000i −1.00000 1.00000i
133133 0 0
134134 0 0
135135 0.707107 0.707107i 0.707107 0.707107i
136136 0 0
137137 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
138138 0 0
139139 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
140140 0 0
141141 2.00000i 2.00000i
142142 0 0
143143 1.41421 1.41421i 1.41421 1.41421i
144144 1.00000i 1.00000i
145145 1.00000 1.00000
146146 0 0
147147 0.707107 0.707107i 0.707107 0.707107i
148148 0 0
149149 2.00000 2.00000 1.00000 00
1.00000 00
150150 1.00000i 1.00000i
151151 0 0 1.00000 00
−1.00000 π\pi
152152 1.00000 + 1.00000i 1.00000 + 1.00000i
153153 0 0
154154 0 0
155155 1.41421 1.41421
156156 1.41421 1.41421
157157 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
158158 1.00000 1.00000i 1.00000 1.00000i
159159 −1.41421 −1.41421
160160 −0.707107 0.707107i −0.707107 0.707107i
161161 0 0
162162 0.707107 + 0.707107i 0.707107 + 0.707107i
163163 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
164164 0 0
165165 1.00000 1.00000i 1.00000 1.00000i
166166 0 0
167167 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
168168 0 0
169169 1.00000i 1.00000i
170170 0 0
171171 −1.41421 −1.41421
172172 0 0
173173 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
174174 1.00000i 1.00000i
175175 0 0
176176 1.41421i 1.41421i
177177 0 0
178178 0 0
179179 0 0 1.00000 00
−1.00000 π\pi
180180 1.00000 1.00000
181181 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
182182 0 0
183183 0 0
184184 0 0
185185 0 0
186186 1.41421i 1.41421i
187187 0 0
188188 −1.41421 + 1.41421i −1.41421 + 1.41421i
189189 0 0
190190 −1.00000 + 1.00000i −1.00000 + 1.00000i
191191 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
192192 0.707107 0.707107i 0.707107 0.707107i
193193 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
194194 0 0
195195 1.41421i 1.41421i
196196 1.00000 1.00000
197197 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
198198 1.00000 + 1.00000i 1.00000 + 1.00000i
199199 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
200200 0.707107 0.707107i 0.707107 0.707107i
201201 0 0
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 1.00000 + 1.00000i 1.00000 + 1.00000i
209209 −2.00000 −2.00000
210210 0 0
211211 1.41421 1.41421 0.707107 0.707107i 0.250000π-0.250000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
212212 −1.00000 1.00000i −1.00000 1.00000i
213213 0 0
214214 0 0
215215 0 0
216216 1.00000i 1.00000i
217217 0 0
218218 1.41421 1.41421i 1.41421 1.41421i
219219 0 0
220220 1.41421 1.41421
221221 0 0
222222 0 0
223223 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
224224 0 0
225225 1.00000i 1.00000i
226226 0 0
227227 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
228228 −1.00000 1.00000i −1.00000 1.00000i
229229 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
230230 0 0
231231 0 0
232232 −0.707107 + 0.707107i −0.707107 + 0.707107i
233233 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
234234 −1.41421 −1.41421
235235 −1.41421 1.41421i −1.41421 1.41421i
236236 0 0
237237 −1.00000 + 1.00000i −1.00000 + 1.00000i
238238 0 0
239239 0 0 1.00000 00
−1.00000 π\pi
240240 0.707107 + 0.707107i 0.707107 + 0.707107i
241241 2.00000 2.00000 1.00000 00
1.00000 00
242242 0.707107 + 0.707107i 0.707107 + 0.707107i
243243 −0.707107 0.707107i −0.707107 0.707107i
244244 0 0
245245 1.00000i 1.00000i
246246 0 0
247247 1.41421 1.41421i 1.41421 1.41421i
248248 −1.00000 + 1.00000i −1.00000 + 1.00000i
249249 0 0
250250 0.707107 + 0.707107i 0.707107 + 0.707107i
251251 1.41421i 1.41421i −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 0.707107i 0.250000π-0.250000\pi
252252 0 0
253253 0 0
254254 −2.00000 −2.00000
255255 0 0
256256 1.00000 1.00000
257257 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
258258 0 0
259259 0 0
260260 −1.00000 + 1.00000i −1.00000 + 1.00000i
261261 1.00000i 1.00000i
262262 −1.00000 + 1.00000i −1.00000 + 1.00000i
263263 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
264264 1.41421i 1.41421i
265265 1.00000 1.00000i 1.00000 1.00000i
266266 0 0
267267 0 0
268268 0 0
269269 0 0 1.00000 00
−1.00000 π\pi
270270 −1.00000 −1.00000
271271 1.41421 1.41421 0.707107 0.707107i 0.250000π-0.250000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
272272 0 0
273273 0 0
274274 0 0
275275 1.41421i 1.41421i
276276 0 0
277277 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
278278 0 0
279279 1.41421i 1.41421i
280280 0 0
281281 2.00000i 2.00000i 1.00000i 0.5π-0.5\pi
1.00000i 0.5π-0.5\pi
282282 1.41421 1.41421i 1.41421 1.41421i
283283 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
284284 0 0
285285 1.00000 1.00000i 1.00000 1.00000i
286286 −2.00000 −2.00000
287287 0 0
288288 −0.707107 + 0.707107i −0.707107 + 0.707107i
289289 1.00000i 1.00000i
290290 −0.707107 0.707107i −0.707107 0.707107i
291291 0 0
292292 0 0
293293 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
294294 −1.00000 −1.00000
295295 0 0
296296 0 0
297297 −1.00000 1.00000i −1.00000 1.00000i
298298 −1.41421 1.41421i −1.41421 1.41421i
299299 0 0
300300 −0.707107 + 0.707107i −0.707107 + 0.707107i
301301 0 0
302302 0 0
303303 0 0
304304 1.41421i 1.41421i
305305 0 0
306306 0 0
307307 −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i 0.750000π0.750000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
308308 0 0
309309 0 0
310310 −1.00000 1.00000i −1.00000 1.00000i
311311 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
312312 −1.00000 1.00000i −1.00000 1.00000i
313313 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
314314 0 0
315315 0 0
316316 −1.41421 −1.41421
317317 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
318318 1.00000 + 1.00000i 1.00000 + 1.00000i
319319 1.41421i 1.41421i
320320 1.00000i 1.00000i
321321 0 0
322322 0 0
323323 0 0
324324 1.00000i 1.00000i
325325 −1.00000 1.00000i −1.00000 1.00000i
326326 0 0
327327 −1.41421 + 1.41421i −1.41421 + 1.41421i
328328 0 0
329329 0 0
330330 −1.41421 −1.41421
331331 −1.41421 −1.41421 −0.707107 0.707107i 0.750000π-0.750000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
332332 0 0
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
338338 0.707107 0.707107i 0.707107 0.707107i
339339 0 0
340340 0 0
341341 2.00000i 2.00000i
342342 1.00000 + 1.00000i 1.00000 + 1.00000i
343343 0 0
344344 0 0
345345 0 0
346346 −1.41421 −1.41421
347347 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
348348 0.707107 0.707107i 0.707107 0.707107i
349349 0 0 1.00000 00
−1.00000 π\pi
350350 0 0
351351 1.41421 1.41421
352352 −1.00000 + 1.00000i −1.00000 + 1.00000i
353353 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 −1.41421 −1.41421 −0.707107 0.707107i 0.750000π-0.750000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
360360 −0.707107 0.707107i −0.707107 0.707107i
361361 −1.00000 −1.00000
362362 0 0
363363 −0.707107 0.707107i −0.707107 0.707107i
364364 0 0
365365 0 0
366366 0 0
367367 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 1.00000 1.00000i 1.00000 1.00000i
373373 −1.00000 1.00000i −1.00000 1.00000i 1.00000i 0.5π-0.5\pi
−1.00000 π\pi
374374 0 0
375375 −0.707107 0.707107i −0.707107 0.707107i
376376 2.00000 2.00000
377377 1.00000 + 1.00000i 1.00000 + 1.00000i
378378 0 0
379379 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
380380 1.41421 1.41421
381381 2.00000 2.00000
382382 1.00000 1.00000i 1.00000 1.00000i
383383 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
384384 −1.00000 −1.00000
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 0 0 1.00000 00
−1.00000 π\pi
390390 1.00000 1.00000i 1.00000 1.00000i
391391 0 0
392392 −0.707107 0.707107i −0.707107 0.707107i
393393 1.00000 1.00000i 1.00000 1.00000i
394394 1.41421i 1.41421i
395395 1.41421i 1.41421i
396396 1.41421i 1.41421i
397397 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
398398 0 0
399399 0 0
400400 −1.00000 −1.00000
401401 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
402402 0 0
403403 1.41421 + 1.41421i 1.41421 + 1.41421i
404404 0 0
405405 1.00000 1.00000
406406 0 0
407407 0 0
408408 0 0
409409 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
410410 0 0
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 1.41421i 1.41421i
417417 0 0
418418 1.41421 + 1.41421i 1.41421 + 1.41421i
419419 0 0 1.00000 00
−1.00000 π\pi
420420 0 0
421421 0 0 1.00000 00
−1.00000 π\pi
422422 −1.00000 1.00000i −1.00000 1.00000i
423423 −1.41421 + 1.41421i −1.41421 + 1.41421i
424424 1.41421i 1.41421i
425425 0 0
426426 0 0
427427 0 0
428428 0 0
429429 2.00000 2.00000
430430 0 0
431431 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
432432 0.707107 0.707107i 0.707107 0.707107i
433433 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
434434 0 0
435435 0.707107 + 0.707107i 0.707107 + 0.707107i
436436 −2.00000 −2.00000
437437 0 0
438438 0 0
439439 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
440440 −1.00000 1.00000i −1.00000 1.00000i
441441 1.00000 1.00000
442442 0 0
443443 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
444444 0 0
445445 0 0
446446 0 0
447447 1.41421 + 1.41421i 1.41421 + 1.41421i
448448 0 0
449449 0 0 1.00000 00
−1.00000 π\pi
450450 0.707107 0.707107i 0.707107 0.707107i
451451 0 0
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 1.41421i 1.41421i
457457 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
458458 0 0
459459 0 0
460460 0 0
461461 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\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 1.00000 1.00000
465465 1.00000 + 1.00000i 1.00000 + 1.00000i
466466 −1.41421 −1.41421
467467 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
468468 1.00000 + 1.00000i 1.00000 + 1.00000i
469469 0 0
470470 2.00000i 2.00000i
471471 0 0
472472 0 0
473473 0 0
474474 1.41421 1.41421
475475 1.41421i 1.41421i
476476 0 0
477477 −1.00000 1.00000i −1.00000 1.00000i
478478 0 0
479479 1.41421 1.41421 0.707107 0.707107i 0.250000π-0.250000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
480480 1.00000i 1.00000i
481481 0 0
482482 −1.41421 1.41421i −1.41421 1.41421i
483483 0 0
484484 1.00000i 1.00000i
485485 0 0
486486 1.00000i 1.00000i
487487 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
488488 0 0
489489 0 0
490490 0.707107 0.707107i 0.707107 0.707107i
491491 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
492492 0 0
493493 0 0
494494 −2.00000 −2.00000
495495 1.41421 1.41421
496496 1.41421 1.41421
497497 0 0
498498 0 0
499499 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
500500 1.00000i 1.00000i
501501 0 0
502502 −1.00000 + 1.00000i −1.00000 + 1.00000i
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 0
506506 0 0
507507 −0.707107 + 0.707107i −0.707107 + 0.707107i
508508 1.41421 + 1.41421i 1.41421 + 1.41421i
509509 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
510510 0 0
511511 0 0
512512 −0.707107 0.707107i −0.707107 0.707107i
513513 −1.00000 1.00000i −1.00000 1.00000i
514514 1.41421i 1.41421i
515515 0 0
516516 0 0
517517 −2.00000 + 2.00000i −2.00000 + 2.00000i
518518 0 0
519519 1.41421 1.41421
520520 1.41421 1.41421
521521 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
522522 −0.707107 + 0.707107i −0.707107 + 0.707107i
523523 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
524524 1.41421 1.41421
525525 0 0
526526 0 0
527527 0 0
528528 1.00000 1.00000i 1.00000 1.00000i
529529 1.00000i 1.00000i
530530 −1.41421 −1.41421
531531 0 0
532532 0 0
533533 0 0
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 0 0
539539 1.41421 1.41421
540540 0.707107 + 0.707107i 0.707107 + 0.707107i
541541 0 0 1.00000 00
−1.00000 π\pi
542542 −1.00000 1.00000i −1.00000 1.00000i
543543 0 0
544544 0 0
545545 2.00000i 2.00000i
546546 0 0
547547 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
548548 0 0
549549 0 0
550550 1.00000 1.00000i 1.00000 1.00000i
551551 1.41421i 1.41421i
552552 0 0
553553 0 0
554554 −1.41421 −1.41421
555555 0 0
556556 0 0
557557 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
558558 −1.00000 + 1.00000i −1.00000 + 1.00000i
559559 0 0
560560 0 0
561561 0 0
562562 −1.41421 + 1.41421i −1.41421 + 1.41421i
563563 −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i 0.750000π0.750000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
564564 −2.00000 −2.00000
565565 0 0
566566 0 0
567567 0 0
568568 0 0
569569 0 0 1.00000 00
−1.00000 π\pi
570570 −1.41421 −1.41421
571571 0 0 1.00000 00
−1.00000 π\pi
572572 1.41421 + 1.41421i 1.41421 + 1.41421i
573573 −1.00000 + 1.00000i −1.00000 + 1.00000i
574574 0 0
575575 0 0
576576 1.00000 1.00000
577577 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
578578 0.707107 0.707107i 0.707107 0.707107i
579579 0 0
580580 1.00000i 1.00000i
581581 0 0
582582 0 0
583583 −1.41421 1.41421i −1.41421 1.41421i
584584 0 0
585585 −1.00000 + 1.00000i −1.00000 + 1.00000i
586586 0 0
587587 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
588588 0.707107 + 0.707107i 0.707107 + 0.707107i
589589 2.00000i 2.00000i
590590 0 0
591591 1.41421i 1.41421i
592592 0 0
593593 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
594594 1.41421i 1.41421i
595595 0 0
596596 2.00000i 2.00000i
597597 0 0
598598 0 0
599599 −1.41421 −1.41421 −0.707107 0.707107i 0.750000π-0.750000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
600600 1.00000 1.00000
601601 0 0 1.00000 00
−1.00000 π\pi
602602 0 0
603603 0 0
604604 0 0
605605 1.00000 1.00000
606606 0 0
607607 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
608608 −1.00000 + 1.00000i −1.00000 + 1.00000i
609609 0 0
610610 0 0
611611 2.82843i 2.82843i
612612 0 0
613613 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
614614 2.00000 2.00000
615615 0 0
616616 0 0
617617 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
618618 0 0
619619 1.41421i 1.41421i −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 0.707107i 0.250000π-0.250000\pi
620620 1.41421i 1.41421i
621621 0 0
622622 1.00000 1.00000i 1.00000 1.00000i
623623 0 0
624624 1.41421i 1.41421i
625625 1.00000 1.00000
626626 1.41421i 1.41421i
627627 −1.41421 1.41421i −1.41421 1.41421i
628628 0 0
629629 0 0
630630 0 0
631631 0 0 1.00000 00
−1.00000 π\pi
632632 1.00000 + 1.00000i 1.00000 + 1.00000i
633633 1.00000 + 1.00000i 1.00000 + 1.00000i
634634 0 0
635635 −1.41421 + 1.41421i −1.41421 + 1.41421i
636636 1.41421i 1.41421i
637637 −1.00000 + 1.00000i −1.00000 + 1.00000i
638638 −1.00000 + 1.00000i −1.00000 + 1.00000i
639639 0 0
640640 0.707107 0.707107i 0.707107 0.707107i
641641 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
642642 0 0
643643 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
648648 −0.707107 + 0.707107i −0.707107 + 0.707107i
649649 0 0
650650 1.41421i 1.41421i
651651 0 0
652652 0 0
653653 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
654654 2.00000 2.00000
655655 1.41421i 1.41421i
656656 0 0
657657 0 0
658658 0 0
659659 1.41421 1.41421 0.707107 0.707107i 0.250000π-0.250000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
660660 1.00000 + 1.00000i 1.00000 + 1.00000i
661661 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
662662 1.00000 + 1.00000i 1.00000 + 1.00000i
663663 0 0
664664 0 0
665665 0 0
666666 0 0
667667 0 0
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
674674 0 0
675675 −0.707107 + 0.707107i −0.707107 + 0.707107i
676676 −1.00000 −1.00000
677677 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 −1.41421 + 1.41421i −1.41421 + 1.41421i
683683 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
684684 1.41421i 1.41421i
685685 0 0
686686 0 0
687687 0 0
688688 0 0
689689 2.00000 2.00000
690690 0 0
691691 0 0 1.00000 00
−1.00000 π\pi
692692 1.00000 + 1.00000i 1.00000 + 1.00000i
693693 0 0
694694 0 0
695695 0 0
696696 −1.00000 −1.00000
697697 0 0
698698 0 0
699699 1.41421 1.41421
700700 0 0
701701 2.00000i 2.00000i 1.00000i 0.5π-0.5\pi
1.00000i 0.5π-0.5\pi
702702 −1.00000 1.00000i −1.00000 1.00000i
703703 0 0
704704 1.41421 1.41421
705705 2.00000i 2.00000i
706706 −1.41421 −1.41421
707707 0 0
708708 0 0
709709 2.00000i 2.00000i 1.00000i 0.5π0.5\pi
1.00000i 0.5π0.5\pi
710710 0 0
711711 −1.41421 −1.41421
712712 0 0
713713 0 0
714714 0 0
715715 −1.41421 + 1.41421i −1.41421 + 1.41421i
716716 0 0
717717 0 0
718718 1.00000 + 1.00000i 1.00000 + 1.00000i
719719 0 0 1.00000 00
−1.00000 π\pi
720720 1.00000i 1.00000i
721721 0 0
722722 0.707107 + 0.707107i 0.707107 + 0.707107i
723723 1.41421 + 1.41421i 1.41421 + 1.41421i
724724 0 0
725725 −1.00000 −1.00000
726726 1.00000i 1.00000i
727727 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
728728 0 0
729729 1.00000i 1.00000i
730730 0 0
731731 0 0
732732 0 0
733733 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
734734 0 0
735735 −0.707107 + 0.707107i −0.707107 + 0.707107i
736736 0 0
737737 0 0
738738 0 0
739739 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
740740 0 0
741741 2.00000 2.00000
742742 0 0
743743 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
744744 −1.41421 −1.41421
745745 −2.00000 −2.00000
746746 1.41421i 1.41421i
747747 0 0
748748 0 0
749749 0 0
750750 1.00000i 1.00000i
751751 1.41421 1.41421 0.707107 0.707107i 0.250000π-0.250000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
752752 −1.41421 1.41421i −1.41421 1.41421i
753753 1.00000 1.00000i 1.00000 1.00000i
754754 1.41421i 1.41421i
755755 0 0
756756 0 0
757757 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
758758 1.00000 1.00000i 1.00000 1.00000i
759759 0 0
760760 −1.00000 1.00000i −1.00000 1.00000i
761761 0 0 1.00000 00
−1.00000 π\pi
762762 −1.41421 1.41421i −1.41421 1.41421i
763763 0 0
764764 −1.41421 −1.41421
765765 0 0
766766 0 0
767767 0 0
768768 0.707107 + 0.707107i 0.707107 + 0.707107i
769769 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
770770 0 0
771771 1.41421i 1.41421i
772772 0 0
773773 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
774774 0 0
775775 −1.41421 −1.41421
776776 0 0
777777 0 0
778778 0 0
779779 0 0
780780 −1.41421 −1.41421
781781 0 0
782782 0 0
783783 0.707107 0.707107i 0.707107 0.707107i
784784 1.00000i 1.00000i
785785 0 0
786786 −1.41421 −1.41421
787787 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
788788 −1.00000 + 1.00000i −1.00000 + 1.00000i
789789 0 0
790790 −1.00000 + 1.00000i −1.00000 + 1.00000i
791791 0 0
792792 −1.00000 + 1.00000i −1.00000 + 1.00000i
793793 0 0
794794 1.41421 1.41421
795795 1.41421 1.41421
796796 0 0
797797 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
798798 0 0
799799 0 0
800800 0.707107 + 0.707107i 0.707107 + 0.707107i
801801 0 0
802802 1.41421 1.41421i 1.41421 1.41421i
803803 0 0
804804 0 0
805805 0 0
806806 2.00000i 2.00000i
807807 0 0
808808 0 0
809809 0 0 1.00000 00
−1.00000 π\pi
810810 −0.707107 0.707107i −0.707107 0.707107i
811811 0 0 1.00000 00
−1.00000 π\pi
812812 0 0
813813 1.00000 + 1.00000i 1.00000 + 1.00000i
814814 0 0
815815 0 0
816816 0 0
817817 0 0
818818 0 0
819819 0 0
820820 0 0
821821 0 0 1.00000 00
−1.00000 π\pi
822822 0 0
823823 −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i 0.750000π-0.750000\pi
−0.707107 0.707107i 0.750000π-0.750000\pi
824824 0 0
825825 −1.00000 + 1.00000i −1.00000 + 1.00000i
826826 0 0
827827 −1.41421 1.41421i −1.41421 1.41421i −0.707107 0.707107i 0.750000π-0.750000\pi
−0.707107 0.707107i 0.750000π-0.750000\pi
828828 0 0
829829 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
830830 0 0
831831 1.41421 1.41421
832832 −1.00000 + 1.00000i −1.00000 + 1.00000i
833833 0 0
834834 0 0
835835 0 0
836836 2.00000i 2.00000i
837837 1.00000 1.00000i 1.00000 1.00000i
838838 0 0
839839 −1.41421 −1.41421 −0.707107 0.707107i 0.750000π-0.750000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
840840 0 0
841841 1.00000 1.00000
842842 0 0
843843 1.41421 1.41421i 1.41421 1.41421i
844844 1.41421i 1.41421i
845845 1.00000i 1.00000i
846846 2.00000 2.00000
847847 0 0
848848 1.00000 1.00000i 1.00000 1.00000i
849849 0 0
850850 0 0
851851 0 0
852852 0 0
853853 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
854854 0 0
855855 1.41421 1.41421
856856 0 0
857857 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
858858 −1.41421 1.41421i −1.41421 1.41421i
859859 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
864864 −1.00000 −1.00000
865865 −1.00000 + 1.00000i −1.00000 + 1.00000i
866866 0 0
867867 −0.707107 + 0.707107i −0.707107 + 0.707107i
868868 0 0
869869 −2.00000 −2.00000
870870 1.00000i 1.00000i
871871 0 0
872872 1.41421 + 1.41421i 1.41421 + 1.41421i
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
878878 0 0
879879 0 0
880880 1.41421i 1.41421i
881881 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
882882 −0.707107 0.707107i −0.707107 0.707107i
883883 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
884884 0 0
885885 0 0
886886 0 0
887887 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
888888 0 0
889889 0 0
890890 0 0
891891 1.41421i 1.41421i
892892 0 0
893893 −2.00000 + 2.00000i −2.00000 + 2.00000i
894894 2.00000i 2.00000i
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 1.41421 1.41421
900900 −1.00000 −1.00000
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 0 0
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 0
910910 0 0
911911 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
912912 1.00000 1.00000i 1.00000 1.00000i
913913 0 0
914914 1.41421 1.41421
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
920920 0 0
921921 −2.00000 −2.00000
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 −0.707107 0.707107i −0.707107 0.707107i
929929 −2.00000 −2.00000 −1.00000 π\pi
−1.00000 π\pi
930930 1.41421i 1.41421i
931931 1.41421 1.41421
932932 1.00000 + 1.00000i 1.00000 + 1.00000i
933933 −1.00000 + 1.00000i −1.00000 + 1.00000i
934934 0 0
935935 0 0
936936 1.41421i 1.41421i
937937 1.00000 1.00000i 1.00000 1.00000i 1.00000i 0.5π-0.5\pi
1.00000 00
938938 0 0
939939 1.41421i 1.41421i
940940 1.41421 1.41421i 1.41421 1.41421i
941941 0 0 1.00000 00
−1.00000 π\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
948948 −1.00000 1.00000i −1.00000 1.00000i
949949 0 0
950950 1.00000 1.00000i 1.00000 1.00000i
951951 0 0
952952 0 0
953953 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
954954 1.41421i 1.41421i
955955 1.41421i 1.41421i
956956 0 0
957957 1.00000 1.00000i 1.00000 1.00000i
958958 −1.00000 1.00000i −1.00000 1.00000i
959959 0 0
960960 −0.707107 + 0.707107i −0.707107 + 0.707107i
961961 1.00000 1.00000
962962 0 0
963963 0 0
964964 2.00000i 2.00000i
965965 0 0
966966 0 0
967967 −1.41421 + 1.41421i −1.41421 + 1.41421i −0.707107 + 0.707107i 0.750000π0.750000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
968968 −0.707107 + 0.707107i −0.707107 + 0.707107i
969969 0 0
970970 0 0
971971 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
972972 0.707107 0.707107i 0.707107 0.707107i
973973 0 0
974974 0 0
975975 1.41421i 1.41421i
976976 0 0
977977 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
978978 0 0
979979 0 0
980980 −1.00000 −1.00000
981981 −2.00000 −2.00000
982982 1.00000 1.00000i 1.00000 1.00000i
983983 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
984984 0 0
985985 −1.00000 1.00000i −1.00000 1.00000i
986986 0 0
987987 0 0
988988 1.41421 + 1.41421i 1.41421 + 1.41421i
989989 0 0
990990 −1.00000 1.00000i −1.00000 1.00000i
991991 0 0 1.00000 00
−1.00000 π\pi
992992 −1.00000 1.00000i −1.00000 1.00000i
993993 −1.00000 1.00000i −1.00000 1.00000i
994994 0 0
995995 0 0
996996 0 0
997997 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\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 1740.1.v.a.1043.1 yes 4
3.2 odd 2 1740.1.v.b.1043.2 yes 4
4.3 odd 2 inner 1740.1.v.a.1043.2 yes 4
5.2 odd 4 1740.1.v.b.347.2 yes 4
12.11 even 2 1740.1.v.b.1043.1 yes 4
15.2 even 4 inner 1740.1.v.a.347.1 4
20.7 even 4 1740.1.v.b.347.1 yes 4
29.28 even 2 inner 1740.1.v.a.1043.2 yes 4
60.47 odd 4 inner 1740.1.v.a.347.2 yes 4
87.86 odd 2 1740.1.v.b.1043.1 yes 4
116.115 odd 2 CM 1740.1.v.a.1043.1 yes 4
145.57 odd 4 1740.1.v.b.347.1 yes 4
348.347 even 2 1740.1.v.b.1043.2 yes 4
435.347 even 4 inner 1740.1.v.a.347.2 yes 4
580.347 even 4 1740.1.v.b.347.2 yes 4
1740.347 odd 4 inner 1740.1.v.a.347.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1740.1.v.a.347.1 4 15.2 even 4 inner
1740.1.v.a.347.1 4 1740.347 odd 4 inner
1740.1.v.a.347.2 yes 4 60.47 odd 4 inner
1740.1.v.a.347.2 yes 4 435.347 even 4 inner
1740.1.v.a.1043.1 yes 4 1.1 even 1 trivial
1740.1.v.a.1043.1 yes 4 116.115 odd 2 CM
1740.1.v.a.1043.2 yes 4 4.3 odd 2 inner
1740.1.v.a.1043.2 yes 4 29.28 even 2 inner
1740.1.v.b.347.1 yes 4 20.7 even 4
1740.1.v.b.347.1 yes 4 145.57 odd 4
1740.1.v.b.347.2 yes 4 5.2 odd 4
1740.1.v.b.347.2 yes 4 580.347 even 4
1740.1.v.b.1043.1 yes 4 12.11 even 2
1740.1.v.b.1043.1 yes 4 87.86 odd 2
1740.1.v.b.1043.2 yes 4 3.2 odd 2
1740.1.v.b.1043.2 yes 4 348.347 even 2