Properties

Label 580.1.y.a.419.1
Level 580580
Weight 11
Character 580.419
Analytic conductor 0.2890.289
Analytic rank 00
Dimension 66
Projective image D14D_{14}
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] = [580,1,Mod(179,580)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(580, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 7, 11]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("580.179");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 580=22529 580 = 2^{2} \cdot 5 \cdot 29
Weight: k k == 1 1
Character orbit: [χ][\chi] == 580.y (of order 1414, degree 66, 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: 0.2894577073270.289457707327
Analytic rank: 00
Dimension: 66
Coefficient field: Q(ζ14)\Q(\zeta_{14})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6x5+x4x3+x2x+1 x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 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: D14D_{14}
Projective field: Galois closure of Q[x]/(x14)\mathbb{Q}[x]/(x^{14} - \cdots)

Embedding invariants

Embedding label 419.1
Root 0.900969+0.433884i0.900969 + 0.433884i of defining polynomial
Character χ\chi == 580.419
Dual form 580.1.y.a.299.1

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+(0.9009690.433884i)q2+(0.623490+0.781831i)q4+(0.2225210.974928i)q5+(0.2225210.974928i)q8+(0.2225210.974928i)q9+(0.623490+0.781831i)q10+(1.524460.347948i)q13+(0.222521+0.974928i)q16+1.80194q17+(0.222521+0.974928i)q18+(0.9009690.433884i)q20+(0.9009690.433884i)q25+(1.22252+0.974928i)q26+(0.2225210.974928i)q29+(0.6234900.781831i)q32+(1.623490.781831i)q34+(0.6234900.781831i)q36+(0.277479+1.21572i)q371.00000q401.56366iq411.00000q45+(0.222521+0.974928i)q49+(0.623490+0.781831i)q50+(0.6784481.40881i)q52+(0.376510+0.781831i)q53+(0.623490+0.781831i)q58+(0.678448+0.541044i)q61+(0.900969+0.433884i)q64+(0.678448+1.40881i)q65+(1.12349+1.40881i)q68+(0.900969+0.433884i)q72+(1.623490.781831i)q73+(0.2774791.21572i)q74+(0.900969+0.433884i)q80+(0.900969+0.433884i)q81+(0.678448+1.40881i)q82+(0.4009691.75676i)q85+(0.846011+1.75676i)q89+(0.900969+0.433884i)q90+(0.777479+0.974928i)q97+(0.2225210.974928i)q98+O(q100)q+(-0.900969 - 0.433884i) q^{2} +(0.623490 + 0.781831i) q^{4} +(0.222521 - 0.974928i) q^{5} +(-0.222521 - 0.974928i) q^{8} +(-0.222521 - 0.974928i) q^{9} +(-0.623490 + 0.781831i) q^{10} +(-1.52446 - 0.347948i) q^{13} +(-0.222521 + 0.974928i) q^{16} +1.80194 q^{17} +(-0.222521 + 0.974928i) q^{18} +(0.900969 - 0.433884i) q^{20} +(-0.900969 - 0.433884i) q^{25} +(1.22252 + 0.974928i) q^{26} +(0.222521 - 0.974928i) q^{29} +(0.623490 - 0.781831i) q^{32} +(-1.62349 - 0.781831i) q^{34} +(0.623490 - 0.781831i) q^{36} +(0.277479 + 1.21572i) q^{37} -1.00000 q^{40} -1.56366i q^{41} -1.00000 q^{45} +(0.222521 + 0.974928i) q^{49} +(0.623490 + 0.781831i) q^{50} +(-0.678448 - 1.40881i) q^{52} +(-0.376510 + 0.781831i) q^{53} +(-0.623490 + 0.781831i) q^{58} +(0.678448 + 0.541044i) q^{61} +(-0.900969 + 0.433884i) q^{64} +(-0.678448 + 1.40881i) q^{65} +(1.12349 + 1.40881i) q^{68} +(-0.900969 + 0.433884i) q^{72} +(1.62349 - 0.781831i) q^{73} +(0.277479 - 1.21572i) q^{74} +(0.900969 + 0.433884i) q^{80} +(-0.900969 + 0.433884i) q^{81} +(-0.678448 + 1.40881i) q^{82} +(0.400969 - 1.75676i) q^{85} +(-0.846011 + 1.75676i) q^{89} +(0.900969 + 0.433884i) q^{90} +(0.777479 + 0.974928i) q^{97} +(0.222521 - 0.974928i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6qq2q4+q5q8q9+q10q16+2q17q18+q20q25+7q26+q29q325q34q36+2q376q406q45+q49++q98+O(q100) 6 q - q^{2} - q^{4} + q^{5} - q^{8} - q^{9} + q^{10} - q^{16} + 2 q^{17} - q^{18} + q^{20} - q^{25} + 7 q^{26} + q^{29} - q^{32} - 5 q^{34} - q^{36} + 2 q^{37} - 6 q^{40} - 6 q^{45} + q^{49}+ \cdots + q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/580Z)×\left(\mathbb{Z}/580\mathbb{Z}\right)^\times.

nn 117117 291291 321321
χ(n)\chi(n) 1-1 1-1 e(914)e\left(\frac{9}{14}\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 −0.900969 0.433884i −0.900969 0.433884i
33 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
44 0.623490 + 0.781831i 0.623490 + 0.781831i
55 0.222521 0.974928i 0.222521 0.974928i
66 0 0
77 0 0 −0.781831 0.623490i 0.785714π-0.785714\pi
0.781831 + 0.623490i 0.214286π0.214286\pi
88 −0.222521 0.974928i −0.222521 0.974928i
99 −0.222521 0.974928i −0.222521 0.974928i
1010 −0.623490 + 0.781831i −0.623490 + 0.781831i
1111 0 0 −0.974928 0.222521i 0.928571π-0.928571\pi
0.974928 + 0.222521i 0.0714286π0.0714286\pi
1212 0 0
1313 −1.52446 0.347948i −1.52446 0.347948i −0.623490 0.781831i 0.714286π-0.714286\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
1414 0 0
1515 0 0
1616 −0.222521 + 0.974928i −0.222521 + 0.974928i
1717 1.80194 1.80194 0.900969 0.433884i 0.142857π-0.142857\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
1818 −0.222521 + 0.974928i −0.222521 + 0.974928i
1919 0 0 0.781831 0.623490i 0.214286π-0.214286\pi
−0.781831 + 0.623490i 0.785714π0.785714\pi
2020 0.900969 0.433884i 0.900969 0.433884i
2121 0 0
2222 0 0
2323 0 0 −0.433884 0.900969i 0.642857π-0.642857\pi
0.433884 + 0.900969i 0.357143π0.357143\pi
2424 0 0
2525 −0.900969 0.433884i −0.900969 0.433884i
2626 1.22252 + 0.974928i 1.22252 + 0.974928i
2727 0 0
2828 0 0
2929 0.222521 0.974928i 0.222521 0.974928i
3030 0 0
3131 0 0 0.433884 0.900969i 0.357143π-0.357143\pi
−0.433884 + 0.900969i 0.642857π0.642857\pi
3232 0.623490 0.781831i 0.623490 0.781831i
3333 0 0
3434 −1.62349 0.781831i −1.62349 0.781831i
3535 0 0
3636 0.623490 0.781831i 0.623490 0.781831i
3737 0.277479 + 1.21572i 0.277479 + 1.21572i 0.900969 + 0.433884i 0.142857π0.142857\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
3838 0 0
3939 0 0
4040 −1.00000 −1.00000
4141 1.56366i 1.56366i −0.623490 0.781831i 0.714286π-0.714286\pi
0.623490 0.781831i 0.285714π-0.285714\pi
4242 0 0
4343 0 0 0.900969 0.433884i 0.142857π-0.142857\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
4444 0 0
4545 −1.00000 −1.00000
4646 0 0
4747 0 0 0.222521 0.974928i 0.428571π-0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
4848 0 0
4949 0.222521 + 0.974928i 0.222521 + 0.974928i
5050 0.623490 + 0.781831i 0.623490 + 0.781831i
5151 0 0
5252 −0.678448 1.40881i −0.678448 1.40881i
5353 −0.376510 + 0.781831i −0.376510 + 0.781831i 0.623490 + 0.781831i 0.285714π0.285714\pi
−1.00000 π\pi
5454 0 0
5555 0 0
5656 0 0
5757 0 0
5858 −0.623490 + 0.781831i −0.623490 + 0.781831i
5959 0 0 1.00000 00
−1.00000 π\pi
6060 0 0
6161 0.678448 + 0.541044i 0.678448 + 0.541044i 0.900969 0.433884i 0.142857π-0.142857\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
6262 0 0
6363 0 0
6464 −0.900969 + 0.433884i −0.900969 + 0.433884i
6565 −0.678448 + 1.40881i −0.678448 + 1.40881i
6666 0 0
6767 0 0 0.974928 0.222521i 0.0714286π-0.0714286\pi
−0.974928 + 0.222521i 0.928571π0.928571\pi
6868 1.12349 + 1.40881i 1.12349 + 1.40881i
6969 0 0
7070 0 0
7171 0 0 0.222521 0.974928i 0.428571π-0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
7272 −0.900969 + 0.433884i −0.900969 + 0.433884i
7373 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i 0.285714π-0.285714\pi
1.00000 00
7474 0.277479 1.21572i 0.277479 1.21572i
7575 0 0
7676 0 0
7777 0 0
7878 0 0
7979 0 0 0.974928 0.222521i 0.0714286π-0.0714286\pi
−0.974928 + 0.222521i 0.928571π0.928571\pi
8080 0.900969 + 0.433884i 0.900969 + 0.433884i
8181 −0.900969 + 0.433884i −0.900969 + 0.433884i
8282 −0.678448 + 1.40881i −0.678448 + 1.40881i
8383 0 0 0.781831 0.623490i 0.214286π-0.214286\pi
−0.781831 + 0.623490i 0.785714π0.785714\pi
8484 0 0
8585 0.400969 1.75676i 0.400969 1.75676i
8686 0 0
8787 0 0
8888 0 0
8989 −0.846011 + 1.75676i −0.846011 + 1.75676i −0.222521 + 0.974928i 0.571429π0.571429\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
9090 0.900969 + 0.433884i 0.900969 + 0.433884i
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 00
−0.222521 + 0.974928i 0.571429π0.571429\pi
9898 0.222521 0.974928i 0.222521 0.974928i
9999 0 0
100100 −0.222521 0.974928i −0.222521 0.974928i
101101 0.846011 + 1.75676i 0.846011 + 1.75676i 0.623490 + 0.781831i 0.285714π0.285714\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
102102 0 0
103103 0 0 −0.974928 0.222521i 0.928571π-0.928571\pi
0.974928 + 0.222521i 0.0714286π0.0714286\pi
104104 1.56366i 1.56366i
105105 0 0
106106 0.678448 0.541044i 0.678448 0.541044i
107107 0 0 0.974928 0.222521i 0.0714286π-0.0714286\pi
−0.974928 + 0.222521i 0.928571π0.928571\pi
108108 0 0
109109 −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i 0.428571π0.428571\pi
−1.00000 π\pi
110110 0 0
111111 0 0
112112 0 0
113113 −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i 0.857143π-0.857143\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
114114 0 0
115115 0 0
116116 0.900969 0.433884i 0.900969 0.433884i
117117 1.56366i 1.56366i
118118 0 0
119119 0 0
120120 0 0
121121 0.900969 + 0.433884i 0.900969 + 0.433884i
122122 −0.376510 0.781831i −0.376510 0.781831i
123123 0 0
124124 0 0
125125 −0.623490 + 0.781831i −0.623490 + 0.781831i
126126 0 0
127127 0 0 0.222521 0.974928i 0.428571π-0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
128128 1.00000 1.00000
129129 0 0
130130 1.22252 0.974928i 1.22252 0.974928i
131131 0 0 −0.433884 0.900969i 0.642857π-0.642857\pi
0.433884 + 0.900969i 0.357143π0.357143\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 −0.400969 1.75676i −0.400969 1.75676i
137137 −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i 0.142857π-0.142857\pi
−1.00000 π\pi
138138 0 0
139139 0 0 0.900969 0.433884i 0.142857π-0.142857\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 1.00000 1.00000
145145 −0.900969 0.433884i −0.900969 0.433884i
146146 −1.80194 −1.80194
147147 0 0
148148 −0.777479 + 0.974928i −0.777479 + 0.974928i
149149 −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i 0.857143π-0.857143\pi
−0.222521 0.974928i 0.571429π-0.571429\pi
150150 0 0
151151 0 0 0.900969 0.433884i 0.142857π-0.142857\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
152152 0 0
153153 −0.400969 1.75676i −0.400969 1.75676i
154154 0 0
155155 0 0
156156 0 0
157157 −0.445042 −0.445042 −0.222521 0.974928i 0.571429π-0.571429\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
158158 0 0
159159 0 0
160160 −0.623490 0.781831i −0.623490 0.781831i
161161 0 0
162162 1.00000 1.00000
163163 0 0 0.222521 0.974928i 0.428571π-0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
164164 1.22252 0.974928i 1.22252 0.974928i
165165 0 0
166166 0 0
167167 0 0 −0.781831 0.623490i 0.785714π-0.785714\pi
0.781831 + 0.623490i 0.214286π0.214286\pi
168168 0 0
169169 1.30194 + 0.626980i 1.30194 + 0.626980i
170170 −1.12349 + 1.40881i −1.12349 + 1.40881i
171171 0 0
172172 0 0
173173 0.867767i 0.867767i −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 0.433884i 0.142857π-0.142857\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 1.52446 1.21572i 1.52446 1.21572i
179179 0 0 −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
180180 −0.623490 0.781831i −0.623490 0.781831i
181181 −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i 0.857143π-0.857143\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
182182 0 0
183183 0 0
184184 0 0
185185 1.24698 1.24698
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
192192 0 0
193193 0.277479 + 0.347948i 0.277479 + 0.347948i 0.900969 0.433884i 0.142857π-0.142857\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
194194 −0.277479 1.21572i −0.277479 1.21572i
195195 0 0
196196 −0.623490 + 0.781831i −0.623490 + 0.781831i
197197 −0.846011 1.75676i −0.846011 1.75676i −0.623490 0.781831i 0.714286π-0.714286\pi
−0.222521 0.974928i 0.571429π-0.571429\pi
198198 0 0
199199 0 0 −0.623490 0.781831i 0.714286π-0.714286\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
200200 −0.222521 + 0.974928i −0.222521 + 0.974928i
201201 0 0
202202 1.94986i 1.94986i
203203 0 0
204204 0 0
205205 −1.52446 0.347948i −1.52446 0.347948i
206206 0 0
207207 0 0
208208 0.678448 1.40881i 0.678448 1.40881i
209209 0 0
210210 0 0
211211 0 0 0.974928 0.222521i 0.0714286π-0.0714286\pi
−0.974928 + 0.222521i 0.928571π0.928571\pi
212212 −0.846011 + 0.193096i −0.846011 + 0.193096i
213213 0 0
214214 0 0
215215 0 0
216216 0 0
217217 0 0
218218 1.12349 0.541044i 1.12349 0.541044i
219219 0 0
220220 0 0
221221 −2.74698 0.626980i −2.74698 0.626980i
222222 0 0
223223 0 0 0.974928 0.222521i 0.0714286π-0.0714286\pi
−0.974928 + 0.222521i 0.928571π0.928571\pi
224224 0 0
225225 −0.222521 + 0.974928i −0.222521 + 0.974928i
226226 0.400969 0.193096i 0.400969 0.193096i
227227 0 0 0.433884 0.900969i 0.357143π-0.357143\pi
−0.433884 + 0.900969i 0.642857π0.642857\pi
228228 0 0
229229 −0.678448 0.541044i −0.678448 0.541044i 0.222521 0.974928i 0.428571π-0.428571\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
230230 0 0
231231 0 0
232232 −1.00000 −1.00000
233233 1.94986i 1.94986i 0.222521 + 0.974928i 0.428571π0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
234234 0.678448 1.40881i 0.678448 1.40881i
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
240240 0 0
241241 −0.400969 1.75676i −0.400969 1.75676i −0.623490 0.781831i 0.714286π-0.714286\pi
0.222521 0.974928i 0.428571π-0.428571\pi
242242 −0.623490 0.781831i −0.623490 0.781831i
243243 0 0
244244 0.867767i 0.867767i
245245 1.00000 1.00000
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 0.900969 0.433884i 0.900969 0.433884i
251251 0 0 0.781831 0.623490i 0.214286π-0.214286\pi
−0.781831 + 0.623490i 0.785714π0.785714\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 −0.900969 0.433884i −0.900969 0.433884i
257257 1.22252 0.974928i 1.22252 0.974928i 0.222521 0.974928i 0.428571π-0.428571\pi
1.00000 00
258258 0 0
259259 0 0
260260 −1.52446 + 0.347948i −1.52446 + 0.347948i
261261 −1.00000 −1.00000
262262 0 0
263263 0 0 −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
264264 0 0
265265 0.678448 + 0.541044i 0.678448 + 0.541044i
266266 0 0
267267 0 0
268268 0 0
269269 1.90097 0.433884i 1.90097 0.433884i 0.900969 0.433884i 0.142857π-0.142857\pi
1.00000 00
270270 0 0
271271 0 0 0.781831 0.623490i 0.214286π-0.214286\pi
−0.781831 + 0.623490i 0.785714π0.785714\pi
272272 −0.400969 + 1.75676i −0.400969 + 1.75676i
273273 0 0
274274 −0.0990311 + 0.433884i −0.0990311 + 0.433884i
275275 0 0
276276 0 0
277277 0.846011 + 0.193096i 0.846011 + 0.193096i 0.623490 0.781831i 0.285714π-0.285714\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
278278 0 0
279279 0 0
280280 0 0
281281 0.277479 + 1.21572i 0.277479 + 1.21572i 0.900969 + 0.433884i 0.142857π0.142857\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
282282 0 0
283283 0 0 −0.781831 0.623490i 0.785714π-0.785714\pi
0.781831 + 0.623490i 0.214286π0.214286\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 −0.900969 0.433884i −0.900969 0.433884i
289289 2.24698 2.24698
290290 0.623490 + 0.781831i 0.623490 + 0.781831i
291291 0 0
292292 1.62349 + 0.781831i 1.62349 + 0.781831i
293293 0.777479 0.974928i 0.777479 0.974928i −0.222521 0.974928i 0.571429π-0.571429\pi
1.00000 00
294294 0 0
295295 0 0
296296 1.12349 0.541044i 1.12349 0.541044i
297297 0 0
298298 0.400969 + 1.75676i 0.400969 + 1.75676i
299299 0 0
300300 0 0
301301 0 0
302302 0 0
303303 0 0
304304 0 0
305305 0.678448 0.541044i 0.678448 0.541044i
306306 −0.400969 + 1.75676i −0.400969 + 1.75676i
307307 0 0 1.00000 00
−1.00000 π\pi
308308 0 0
309309 0 0
310310 0 0
311311 0 0 0.974928 0.222521i 0.0714286π-0.0714286\pi
−0.974928 + 0.222521i 0.928571π0.928571\pi
312312 0 0
313313 −0.376510 0.781831i −0.376510 0.781831i 0.623490 0.781831i 0.285714π-0.285714\pi
−1.00000 π\pi
314314 0.400969 + 0.193096i 0.400969 + 0.193096i
315315 0 0
316316 0 0
317317 −1.62349 0.781831i −1.62349 0.781831i −0.623490 0.781831i 0.714286π-0.714286\pi
−1.00000 π\pi
318318 0 0
319319 0 0
320320 0.222521 + 0.974928i 0.222521 + 0.974928i
321321 0 0
322322 0 0
323323 0 0
324324 −0.900969 0.433884i −0.900969 0.433884i
325325 1.22252 + 0.974928i 1.22252 + 0.974928i
326326 0 0
327327 0 0
328328 −1.52446 + 0.347948i −1.52446 + 0.347948i
329329 0 0
330330 0 0
331331 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
332332 0 0
333333 1.12349 0.541044i 1.12349 0.541044i
334334 0 0
335335 0 0
336336 0 0
337337 −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i 0.285714π0.285714\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
338338 −0.900969 1.12978i −0.900969 1.12978i
339339 0 0
340340 1.62349 0.781831i 1.62349 0.781831i
341341 0 0
342342 0 0
343343 0 0
344344 0 0
345345 0 0
346346 −0.376510 + 0.781831i −0.376510 + 0.781831i
347347 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
348348 0 0
349349 1.80194 1.80194 0.900969 0.433884i 0.142857π-0.142857\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
350350 0 0
351351 0 0
352352 0 0
353353 −0.678448 + 1.40881i −0.678448 + 1.40881i 0.222521 + 0.974928i 0.428571π0.428571\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
354354 0 0
355355 0 0
356356 −1.90097 + 0.433884i −1.90097 + 0.433884i
357357 0 0
358358 0 0
359359 0 0 −0.974928 0.222521i 0.928571π-0.928571\pi
0.974928 + 0.222521i 0.0714286π0.0714286\pi
360360 0.222521 + 0.974928i 0.222521 + 0.974928i
361361 0.222521 0.974928i 0.222521 0.974928i
362362 0.400969 0.193096i 0.400969 0.193096i
363363 0 0
364364 0 0
365365 −0.400969 1.75676i −0.400969 1.75676i
366366 0 0
367367 0 0 −0.623490 0.781831i 0.714286π-0.714286\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
368368 0 0
369369 −1.52446 + 0.347948i −1.52446 + 0.347948i
370370 −1.12349 0.541044i −1.12349 0.541044i
371371 0 0
372372 0 0
373373 −1.52446 + 1.21572i −1.52446 + 1.21572i −0.623490 + 0.781831i 0.714286π0.714286\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
374374 0 0
375375 0 0
376376 0 0
377377 −0.678448 + 1.40881i −0.678448 + 1.40881i
378378 0 0
379379 0 0 0.433884 0.900969i 0.357143π-0.357143\pi
−0.433884 + 0.900969i 0.642857π0.642857\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 −0.433884 0.900969i 0.642857π-0.642857\pi
0.433884 + 0.900969i 0.357143π0.357143\pi
384384 0 0
385385 0 0
386386 −0.0990311 0.433884i −0.0990311 0.433884i
387387 0 0
388388 −0.277479 + 1.21572i −0.277479 + 1.21572i
389389 0.867767i 0.867767i 0.900969 + 0.433884i 0.142857π0.142857\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
390390 0 0
391391 0 0
392392 0.900969 0.433884i 0.900969 0.433884i
393393 0 0
394394 1.94986i 1.94986i
395395 0 0
396396 0 0
397397 0.846011 0.193096i 0.846011 0.193096i 0.222521 0.974928i 0.428571π-0.428571\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
398398 0 0
399399 0 0
400400 0.623490 0.781831i 0.623490 0.781831i
401401 −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i 0.571429π-0.571429\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
402402 0 0
403403 0 0
404404 −0.846011 + 1.75676i −0.846011 + 1.75676i
405405 0.222521 + 0.974928i 0.222521 + 0.974928i
406406 0 0
407407 0 0
408408 0 0
409409 −1.52446 1.21572i −1.52446 1.21572i −0.900969 0.433884i 0.857143π-0.857143\pi
−0.623490 0.781831i 0.714286π-0.714286\pi
410410 1.22252 + 0.974928i 1.22252 + 0.974928i
411411 0 0
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 −1.22252 + 0.974928i −1.22252 + 0.974928i
417417 0 0
418418 0 0
419419 0 0 0.222521 0.974928i 0.428571π-0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
420420 0 0
421421 0 0 0.900969 0.433884i 0.142857π-0.142857\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
422422 0 0
423423 0 0
424424 0.846011 + 0.193096i 0.846011 + 0.193096i
425425 −1.62349 0.781831i −1.62349 0.781831i
426426 0 0
427427 0 0
428428 0 0
429429 0 0
430430 0 0
431431 0 0 −0.623490 0.781831i 0.714286π-0.714286\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
432432 0 0
433433 1.80194 + 0.867767i 1.80194 + 0.867767i 0.900969 + 0.433884i 0.142857π0.142857\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
434434 0 0
435435 0 0
436436 −1.24698 −1.24698
437437 0 0
438438 0 0
439439 0 0 −0.623490 0.781831i 0.714286π-0.714286\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
440440 0 0
441441 0.900969 0.433884i 0.900969 0.433884i
442442 2.20291 + 1.75676i 2.20291 + 1.75676i
443443 0 0 −0.222521 0.974928i 0.571429π-0.571429\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
444444 0 0
445445 1.52446 + 1.21572i 1.52446 + 1.21572i
446446 0 0
447447 0 0
448448 0 0
449449 −0.376510 0.781831i −0.376510 0.781831i 0.623490 0.781831i 0.285714π-0.285714\pi
−1.00000 π\pi
450450 0.623490 0.781831i 0.623490 0.781831i
451451 0 0
452452 −0.445042 −0.445042
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 −1.52446 1.21572i −1.52446 1.21572i −0.900969 0.433884i 0.857143π-0.857143\pi
−0.623490 0.781831i 0.714286π-0.714286\pi
458458 0.376510 + 0.781831i 0.376510 + 0.781831i
459459 0 0
460460 0 0
461461 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
462462 0 0
463463 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
464464 0.900969 + 0.433884i 0.900969 + 0.433884i
465465 0 0
466466 0.846011 1.75676i 0.846011 1.75676i
467467 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
468468 −1.22252 + 0.974928i −1.22252 + 0.974928i
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 0.846011 + 0.193096i 0.846011 + 0.193096i
478478 0 0
479479 0 0 −0.433884 0.900969i 0.642857π-0.642857\pi
0.433884 + 0.900969i 0.357143π0.357143\pi
480480 0 0
481481 1.94986i 1.94986i
482482 −0.400969 + 1.75676i −0.400969 + 1.75676i
483483 0 0
484484 0.222521 + 0.974928i 0.222521 + 0.974928i
485485 1.12349 0.541044i 1.12349 0.541044i
486486 0 0
487487 0 0 −0.433884 0.900969i 0.642857π-0.642857\pi
0.433884 + 0.900969i 0.357143π0.357143\pi
488488 0.376510 0.781831i 0.376510 0.781831i
489489 0 0
490490 −0.900969 0.433884i −0.900969 0.433884i
491491 0 0 0.433884 0.900969i 0.357143π-0.357143\pi
−0.433884 + 0.900969i 0.642857π0.642857\pi
492492 0 0
493493 0.400969 1.75676i 0.400969 1.75676i
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 0 0
499499 0 0 0.900969 0.433884i 0.142857π-0.142857\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
500500 −1.00000 −1.00000
501501 0 0
502502 0 0
503503 0 0 −0.623490 0.781831i 0.714286π-0.714286\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
504504 0 0
505505 1.90097 0.433884i 1.90097 0.433884i
506506 0 0
507507 0 0
508508 0 0
509509 0.277479 1.21572i 0.277479 1.21572i −0.623490 0.781831i 0.714286π-0.714286\pi
0.900969 0.433884i 0.142857π-0.142857\pi
510510 0 0
511511 0 0
512512 0.623490 + 0.781831i 0.623490 + 0.781831i
513513 0 0
514514 −1.52446 + 0.347948i −1.52446 + 0.347948i
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 1.52446 + 0.347948i 1.52446 + 0.347948i
521521 0.445042 0.445042 0.222521 0.974928i 0.428571π-0.428571\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
522522 0.900969 + 0.433884i 0.900969 + 0.433884i
523523 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
524524 0 0
525525 0 0
526526 0 0
527527 0 0
528528 0 0
529529 −0.623490 + 0.781831i −0.623490 + 0.781831i
530530 −0.376510 0.781831i −0.376510 0.781831i
531531 0 0
532532 0 0
533533 −0.544073 + 2.38374i −0.544073 + 2.38374i
534534 0 0
535535 0 0
536536 0 0
537537 0 0
538538 −1.90097 0.433884i −1.90097 0.433884i
539539 0 0
540540 0 0
541541 −1.22252 + 0.974928i −1.22252 + 0.974928i −0.222521 + 0.974928i 0.571429π0.571429\pi
−1.00000 π\pi
542542 0 0
543543 0 0
544544 1.12349 1.40881i 1.12349 1.40881i
545545 0.777479 + 0.974928i 0.777479 + 0.974928i
546546 0 0
547547 0 0 0.781831 0.623490i 0.214286π-0.214286\pi
−0.781831 + 0.623490i 0.785714π0.785714\pi
548548 0.277479 0.347948i 0.277479 0.347948i
549549 0.376510 0.781831i 0.376510 0.781831i
550550 0 0
551551 0 0
552552 0 0
553553 0 0
554554 −0.678448 0.541044i −0.678448 0.541044i
555555 0 0
556556 0 0
557557 −0.678448 1.40881i −0.678448 1.40881i −0.900969 0.433884i 0.857143π-0.857143\pi
0.222521 0.974928i 0.428571π-0.428571\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 0.277479 1.21572i 0.277479 1.21572i
563563 0 0 1.00000 00
−1.00000 π\pi
564564 0 0
565565 0.277479 + 0.347948i 0.277479 + 0.347948i
566566 0 0
567567 0 0
568568 0 0
569569 −1.52446 0.347948i −1.52446 0.347948i −0.623490 0.781831i 0.714286π-0.714286\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
570570 0 0
571571 0 0 −0.222521 0.974928i 0.571429π-0.571429\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 0.623490 + 0.781831i 0.623490 + 0.781831i
577577 −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i 0.428571π0.428571\pi
−1.00000 π\pi
578578 −2.02446 0.974928i −2.02446 0.974928i
579579 0 0
580580 −0.222521 0.974928i −0.222521 0.974928i
581581 0 0
582582 0 0
583583 0 0
584584 −1.12349 1.40881i −1.12349 1.40881i
585585 1.52446 + 0.347948i 1.52446 + 0.347948i
586586 −1.12349 + 0.541044i −1.12349 + 0.541044i
587587 0 0 −0.781831 0.623490i 0.785714π-0.785714\pi
0.781831 + 0.623490i 0.214286π0.214286\pi
588588 0 0
589589 0 0
590590 0 0
591591 0 0
592592 −1.24698 −1.24698
593593 −0.846011 0.193096i −0.846011 0.193096i −0.222521 0.974928i 0.571429π-0.571429\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
594594 0 0
595595 0 0
596596 0.400969 1.75676i 0.400969 1.75676i
597597 0 0
598598 0 0
599599 0 0 0.781831 0.623490i 0.214286π-0.214286\pi
−0.781831 + 0.623490i 0.785714π0.785714\pi
600600 0 0
601601 0 0 −0.222521 0.974928i 0.571429π-0.571429\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
602602 0 0
603603 0 0
604604 0 0
605605 0.623490 0.781831i 0.623490 0.781831i
606606 0 0
607607 0 0 −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
608608 0 0
609609 0 0
610610 −0.846011 + 0.193096i −0.846011 + 0.193096i
611611 0 0
612612 1.12349 1.40881i 1.12349 1.40881i
613613 1.22252 0.974928i 1.22252 0.974928i 0.222521 0.974928i 0.428571π-0.428571\pi
1.00000 00
614614 0 0
615615 0 0
616616 0 0
617617 0.0990311 + 0.433884i 0.0990311 + 0.433884i 1.00000 00
−0.900969 + 0.433884i 0.857143π0.857143\pi
618618 0 0
619619 0 0 0.781831 0.623490i 0.214286π-0.214286\pi
−0.781831 + 0.623490i 0.785714π0.785714\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 0.623490 + 0.781831i 0.623490 + 0.781831i
626626 0.867767i 0.867767i
627627 0 0
628628 −0.277479 0.347948i −0.277479 0.347948i
629629 0.500000 + 2.19064i 0.500000 + 2.19064i
630630 0 0
631631 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
632632 0 0
633633 0 0
634634 1.12349 + 1.40881i 1.12349 + 1.40881i
635635 0 0
636636 0 0
637637 1.56366i 1.56366i
638638 0 0
639639 0 0
640640 0.222521 0.974928i 0.222521 0.974928i
641641 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
642642 0 0
643643 0 0 0.433884 0.900969i 0.357143π-0.357143\pi
−0.433884 + 0.900969i 0.642857π0.642857\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 0.974928 0.222521i 0.0714286π-0.0714286\pi
−0.974928 + 0.222521i 0.928571π0.928571\pi
648648 0.623490 + 0.781831i 0.623490 + 0.781831i
649649 0 0
650650 −0.678448 1.40881i −0.678448 1.40881i
651651 0 0
652652 0 0
653653 −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i 0.857143π-0.857143\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
654654 0 0
655655 0 0
656656 1.52446 + 0.347948i 1.52446 + 0.347948i
657657 −1.12349 1.40881i −1.12349 1.40881i
658658 0 0
659659 0 0 0.974928 0.222521i 0.0714286π-0.0714286\pi
−0.974928 + 0.222521i 0.928571π0.928571\pi
660660 0 0
661661 −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i 0.857143π-0.857143\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
662662 0 0
663663 0 0
664664 0 0
665665 0 0
666666 −1.24698 −1.24698
667667 0 0
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 −0.846011 1.75676i −0.846011 1.75676i −0.623490 0.781831i 0.714286π-0.714286\pi
−0.222521 0.974928i 0.571429π-0.571429\pi
674674 0.777479 0.974928i 0.777479 0.974928i
675675 0 0
676676 0.321552 + 1.40881i 0.321552 + 1.40881i
677677 −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i 0.285714π-0.285714\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
678678 0 0
679679 0 0
680680 −1.80194 −1.80194
681681 0 0
682682 0 0
683683 0 0 −0.974928 0.222521i 0.928571π-0.928571\pi
0.974928 + 0.222521i 0.0714286π0.0714286\pi
684684 0 0
685685 −0.445042 −0.445042
686686 0 0
687687 0 0
688688 0 0
689689 0.846011 1.06086i 0.846011 1.06086i
690690 0 0
691691 0 0 −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
692692 0.678448 0.541044i 0.678448 0.541044i
693693 0 0
694694 0 0
695695 0 0
696696 0 0
697697 2.81762i 2.81762i
698698 −1.62349 0.781831i −1.62349 0.781831i
699699 0 0
700700 0 0
701701 1.62349 + 0.781831i 1.62349 + 0.781831i 1.00000 00
0.623490 + 0.781831i 0.285714π0.285714\pi
702702 0 0
703703 0 0
704704 0 0
705705 0 0
706706 1.22252 0.974928i 1.22252 0.974928i
707707 0 0
708708 0 0
709709 −0.0990311 + 0.433884i −0.0990311 + 0.433884i 0.900969 + 0.433884i 0.142857π0.142857\pi
−1.00000 π\pi
710710 0 0
711711 0 0
712712 1.90097 + 0.433884i 1.90097 + 0.433884i
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 0.900969 0.433884i 0.142857π-0.142857\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
720720 0.222521 0.974928i 0.222521 0.974928i
721721 0 0
722722 −0.623490 + 0.781831i −0.623490 + 0.781831i
723723 0 0
724724 −0.445042 −0.445042
725725 −0.623490 + 0.781831i −0.623490 + 0.781831i
726726 0 0
727727 0 0 −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
728728 0 0
729729 0.623490 + 0.781831i 0.623490 + 0.781831i
730730 −0.400969 + 1.75676i −0.400969 + 1.75676i
731731 0 0
732732 0 0
733733 0.445042 + 1.94986i 0.445042 + 1.94986i 0.222521 + 0.974928i 0.428571π0.428571\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 1.52446 + 0.347948i 1.52446 + 0.347948i
739739 0 0 −0.433884 0.900969i 0.642857π-0.642857\pi
0.433884 + 0.900969i 0.357143π0.357143\pi
740740 0.777479 + 0.974928i 0.777479 + 0.974928i
741741 0 0
742742 0 0
743743 0 0 0.222521 0.974928i 0.428571π-0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
744744 0 0
745745 −1.62349 + 0.781831i −1.62349 + 0.781831i
746746 1.90097 0.433884i 1.90097 0.433884i
747747 0 0
748748 0 0
749749 0 0
750750 0 0
751751 0 0 −0.781831 0.623490i 0.785714π-0.785714\pi
0.781831 + 0.623490i 0.214286π0.214286\pi
752752 0 0
753753 0 0
754754 1.22252 0.974928i 1.22252 0.974928i
755755 0 0
756756 0 0
757757 −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i 0.857143π-0.857143\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
758758 0 0
759759 0 0
760760 0 0
761761 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i 0.714286π-0.714286\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
762762 0 0
763763 0 0
764764 0 0
765765 −1.80194 −1.80194
766766 0 0
767767 0 0
768768 0 0
769769 0.846011 + 1.75676i 0.846011 + 1.75676i 0.623490 + 0.781831i 0.285714π0.285714\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
770770 0 0
771771 0 0
772772 −0.0990311 + 0.433884i −0.0990311 + 0.433884i
773773 0.277479 + 0.347948i 0.277479 + 0.347948i 0.900969 0.433884i 0.142857π-0.142857\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
774774 0 0
775775 0 0
776776 0.777479 0.974928i 0.777479 0.974928i
777777 0 0
778778 0.376510 0.781831i 0.376510 0.781831i
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −1.00000 −1.00000
785785 −0.0990311 + 0.433884i −0.0990311 + 0.433884i
786786 0 0
787787 0 0 0.781831 0.623490i 0.214286π-0.214286\pi
−0.781831 + 0.623490i 0.785714π0.785714\pi
788788 0.846011 1.75676i 0.846011 1.75676i
789789 0 0
790790 0 0
791791 0 0
792792 0 0
793793 −0.846011 1.06086i −0.846011 1.06086i
794794 −0.846011 0.193096i −0.846011 0.193096i
795795 0 0
796796 0 0
797797 −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i 0.857143π-0.857143\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
798798 0 0
799799 0 0
800800 −0.900969 + 0.433884i −0.900969 + 0.433884i
801801 1.90097 + 0.433884i 1.90097 + 0.433884i
802802 0.777479 + 0.974928i 0.777479 + 0.974928i
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 1.52446 1.21572i 1.52446 1.21572i
809809 −1.22252 0.974928i −1.22252 0.974928i −0.222521 0.974928i 0.571429π-0.571429\pi
−1.00000 π\pi
810810 0.222521 0.974928i 0.222521 0.974928i
811811 0 0 1.00000 00
−1.00000 π\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 0 0
818818 0.846011 + 1.75676i 0.846011 + 1.75676i
819819 0 0
820820 −0.678448 1.40881i −0.678448 1.40881i
821821 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i 0.285714π0.285714\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
822822 0 0
823823 0 0 0.222521 0.974928i 0.428571π-0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
824824 0 0
825825 0 0
826826 0 0
827827 0 0 0.900969 0.433884i 0.142857π-0.142857\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
828828 0 0
829829 1.56366i 1.56366i 0.623490 + 0.781831i 0.285714π0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
830830 0 0
831831 0 0
832832 1.52446 0.347948i 1.52446 0.347948i
833833 0.400969 + 1.75676i 0.400969 + 1.75676i
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 0 0 0.433884 0.900969i 0.357143π-0.357143\pi
−0.433884 + 0.900969i 0.642857π0.642857\pi
840840 0 0
841841 −0.900969 0.433884i −0.900969 0.433884i
842842 0 0
843843 0 0
844844 0 0
845845 0.900969 1.12978i 0.900969 1.12978i
846846 0 0
847847 0 0
848848 −0.678448 0.541044i −0.678448 0.541044i
849849 0 0
850850 1.12349 + 1.40881i 1.12349 + 1.40881i
851851 0 0
852852 0 0
853853 0.445042 0.445042 0.222521 0.974928i 0.428571π-0.428571\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
854854 0 0
855855 0 0
856856 0 0
857857 0 0 0.222521 0.974928i 0.428571π-0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
858858 0 0
859859 0 0 −0.974928 0.222521i 0.928571π-0.928571\pi
0.974928 + 0.222521i 0.0714286π0.0714286\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 −0.781831 0.623490i 0.785714π-0.785714\pi
0.781831 + 0.623490i 0.214286π0.214286\pi
864864 0 0
865865 −0.846011 0.193096i −0.846011 0.193096i
866866 −1.24698 1.56366i −1.24698 1.56366i
867867 0 0
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 1.12349 + 0.541044i 1.12349 + 0.541044i
873873 0.777479 0.974928i 0.777479 0.974928i
874874 0 0
875875 0 0
876876 0 0
877877 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
878878 0 0
879879 0 0
880880 0 0
881881 0.846011 + 0.193096i 0.846011 + 0.193096i 0.623490 0.781831i 0.285714π-0.285714\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
882882 −1.00000 −1.00000
883883 0 0 −0.974928 0.222521i 0.928571π-0.928571\pi
0.974928 + 0.222521i 0.0714286π0.0714286\pi
884884 −1.22252 2.53859i −1.22252 2.53859i
885885 0 0
886886 0 0
887887 0 0 1.00000 00
−1.00000 π\pi
888888 0 0
889889 0 0
890890 −0.846011 1.75676i −0.846011 1.75676i
891891 0 0
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0.867767i 0.867767i
899899 0 0
900900 −0.900969 + 0.433884i −0.900969 + 0.433884i
901901 −0.678448 + 1.40881i −0.678448 + 1.40881i
902902 0 0
903903 0 0
904904 0.400969 + 0.193096i 0.400969 + 0.193096i
905905 0.277479 + 0.347948i 0.277479 + 0.347948i
906906 0 0
907907 0 0 −0.222521 0.974928i 0.571429π-0.571429\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
908908 0 0
909909 1.52446 1.21572i 1.52446 1.21572i
910910 0 0
911911 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
912912 0 0
913913 0 0
914914 0.846011 + 1.75676i 0.846011 + 1.75676i
915915 0 0
916916 0.867767i 0.867767i
917917 0 0
918918 0 0
919919 0 0 −0.222521 0.974928i 0.571429π-0.571429\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
920920 0 0
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 0.277479 1.21572i 0.277479 1.21572i
926926 0 0
927927 0 0
928928 −0.623490 0.781831i −0.623490 0.781831i
929929 1.24698 1.24698 0.623490 0.781831i 0.285714π-0.285714\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
930930 0 0
931931 0 0
932932 −1.52446 + 1.21572i −1.52446 + 1.21572i
933933 0 0
934934 0 0
935935 0 0
936936 1.52446 0.347948i 1.52446 0.347948i
937937 −1.90097 + 0.433884i −1.90097 + 0.433884i −0.900969 + 0.433884i 0.857143π0.857143\pi
−1.00000 π\pi
938938 0 0
939939 0 0
940940 0 0
941941 −0.445042 + 1.94986i −0.445042 + 1.94986i −0.222521 + 0.974928i 0.571429π0.571429\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0 0 −0.623490 0.781831i 0.714286π-0.714286\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
948948 0 0
949949 −2.74698 + 0.626980i −2.74698 + 0.626980i
950950 0 0
951951 0 0
952952 0 0
953953 −1.22252 + 0.974928i −1.22252 + 0.974928i −0.222521 + 0.974928i 0.571429π0.571429\pi
−1.00000 π\pi
954954 −0.678448 0.541044i −0.678448 0.541044i
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 −0.623490 0.781831i −0.623490 0.781831i
962962 −0.846011 + 1.75676i −0.846011 + 1.75676i
963963 0 0
964964 1.12349 1.40881i 1.12349 1.40881i
965965 0.400969 0.193096i 0.400969 0.193096i
966966 0 0
967967 0 0 −0.623490 0.781831i 0.714286π-0.714286\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
968968 0.222521 0.974928i 0.222521 0.974928i
969969 0 0
970970 −1.24698 −1.24698
971971 0 0 −0.433884 0.900969i 0.642857π-0.642857\pi
0.433884 + 0.900969i 0.357143π0.357143\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 −0.678448 + 0.541044i −0.678448 + 0.541044i
977977 −1.90097 + 0.433884i −1.90097 + 0.433884i −0.900969 + 0.433884i 0.857143π0.857143\pi
−1.00000 π\pi
978978 0 0
979979 0 0
980980 0.623490 + 0.781831i 0.623490 + 0.781831i
981981 1.12349 + 0.541044i 1.12349 + 0.541044i
982982 0 0
983983 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
984984 0 0
985985 −1.90097 + 0.433884i −1.90097 + 0.433884i
986986 −1.12349 + 1.40881i −1.12349 + 1.40881i
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
992992 0 0
993993 0 0
994994 0 0
995995 0 0
996996 0 0
997997 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i 0.857143π-0.857143\pi
1.00000 00
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 580.1.y.a.419.1 yes 6
4.3 odd 2 CM 580.1.y.a.419.1 yes 6
5.2 odd 4 2900.1.be.c.651.2 12
5.3 odd 4 2900.1.be.c.651.1 12
5.4 even 2 580.1.y.b.419.1 yes 6
20.3 even 4 2900.1.be.c.651.1 12
20.7 even 4 2900.1.be.c.651.2 12
20.19 odd 2 580.1.y.b.419.1 yes 6
29.9 even 14 580.1.y.b.299.1 yes 6
116.67 odd 14 580.1.y.b.299.1 yes 6
145.9 even 14 inner 580.1.y.a.299.1 6
145.38 odd 28 2900.1.be.c.2851.1 12
145.67 odd 28 2900.1.be.c.2851.2 12
580.67 even 28 2900.1.be.c.2851.2 12
580.183 even 28 2900.1.be.c.2851.1 12
580.299 odd 14 inner 580.1.y.a.299.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
580.1.y.a.299.1 6 145.9 even 14 inner
580.1.y.a.299.1 6 580.299 odd 14 inner
580.1.y.a.419.1 yes 6 1.1 even 1 trivial
580.1.y.a.419.1 yes 6 4.3 odd 2 CM
580.1.y.b.299.1 yes 6 29.9 even 14
580.1.y.b.299.1 yes 6 116.67 odd 14
580.1.y.b.419.1 yes 6 5.4 even 2
580.1.y.b.419.1 yes 6 20.19 odd 2
2900.1.be.c.651.1 12 5.3 odd 4
2900.1.be.c.651.1 12 20.3 even 4
2900.1.be.c.651.2 12 5.2 odd 4
2900.1.be.c.651.2 12 20.7 even 4
2900.1.be.c.2851.1 12 145.38 odd 28
2900.1.be.c.2851.1 12 580.183 even 28
2900.1.be.c.2851.2 12 145.67 odd 28
2900.1.be.c.2851.2 12 580.67 even 28