Properties

Label 2695.1.ck.c.2034.2
Level 26952695
Weight 11
Character 2695.2034
Analytic conductor 1.3451.345
Analytic rank 00
Dimension 2424
Projective image D42D_{42}
CM discriminant -55
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] = [2695,1,Mod(109,2695)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2695, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([21, 40, 21])) 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("2695.109"); S:= CuspForms(chi, 1); N := Newforms(S);
 
Level: N N == 2695=57211 2695 = 5 \cdot 7^{2} \cdot 11
Weight: k k == 1 1
Character orbit: [χ][\chi] == 2695.ck (of order 4242, degree 1212, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 1.344980209051.34498020905
Analytic rank: 00
Dimension: 2424
Relative dimension: 22 over Q(ζ42)\Q(\zeta_{42})
Coefficient field: Q(ζ84)\Q(\zeta_{84})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x24+x22x18x16+x12x8x6+x2+1 x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a4]\Z[a_1, \ldots, a_{4}]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D42D_{42}
Projective field: Galois closure of Q[x]/(x42)\mathbb{Q}[x]/(x^{42} - \cdots)

Embedding invariants

Embedding label 2034.2
Root 0.149042+0.988831i-0.149042 + 0.988831i of defining polynomial
Character χ\chi == 2695.2034
Dual form 2695.1.ck.c.1374.2

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+(1.076590.332083i)q2+(0.2225210.151712i)q4+(0.988831+0.149042i)q5+(0.974928+0.222521i)q7+(0.513267+0.643616i)q8+(0.733052+0.680173i)q9+(1.114060.167917i)q10+(0.733052+0.680173i)q11+(0.302705+1.32624i)q13+(0.975699+0.563320i)q14+(0.437235+1.11406i)q16+(0.1168531.55929i)q17+(0.563320+0.975699i)q18+(0.2426470.116853i)q20+(1.01507+0.488831i)q22+(0.955573+0.294755i)q25+(0.114533+1.52833i)q26+(0.183183+0.197424i)q28+(0.500000+0.866025i)q31+(0.0392431+0.523663i)q32+(0.3920121.71752i)q34+(0.997204+0.0747301i)q35+(0.0599289+0.262566i)q36+(0.603460+0.559929i)q40+(0.367554+0.460898i)q43+(0.266310+0.0401398i)q44+(0.826239+0.563320i)q45+(0.9009690.433884i)q49+1.12664q50+(0.133848+0.341040i)q52+(0.623490+0.781831i)q55+(0.3571800.741692i)q56+(1.449730.218511i)q59+(0.250701+1.09839i)q62+(0.5633200.826239i)q63+(0.1346590.589980i)q64+(0.496990+1.26631i)q65+(0.2105610.364703i)q68+(1.04876+0.411608i)q70+(1.488830.716983i)q71+(0.06151900.820914i)q72+(1.77904+0.548760i)q73+(0.8660250.500000i)q77+(0.598393+1.03645i)q80+(0.07473010.997204i)q81+(0.3854181.68862i)q83+(0.3479481.52446i)q85+(0.548760+0.374138i)q86+(0.814021+0.122694i)q88+(1.400971.29991i)q89+(0.702449+0.880843i)q901.36035iq91+(0.8258860.766310i)q981.00000q99+O(q100)q+(1.07659 - 0.332083i) q^{2} +(0.222521 - 0.151712i) q^{4} +(0.988831 + 0.149042i) q^{5} +(-0.974928 + 0.222521i) q^{7} +(-0.513267 + 0.643616i) q^{8} +(-0.733052 + 0.680173i) q^{9} +(1.11406 - 0.167917i) q^{10} +(0.733052 + 0.680173i) q^{11} +(-0.302705 + 1.32624i) q^{13} +(-0.975699 + 0.563320i) q^{14} +(-0.437235 + 1.11406i) q^{16} +(0.116853 - 1.55929i) q^{17} +(-0.563320 + 0.975699i) q^{18} +(0.242647 - 0.116853i) q^{20} +(1.01507 + 0.488831i) q^{22} +(0.955573 + 0.294755i) q^{25} +(0.114533 + 1.52833i) q^{26} +(-0.183183 + 0.197424i) q^{28} +(-0.500000 + 0.866025i) q^{31} +(-0.0392431 + 0.523663i) q^{32} +(-0.392012 - 1.71752i) q^{34} +(-0.997204 + 0.0747301i) q^{35} +(-0.0599289 + 0.262566i) q^{36} +(-0.603460 + 0.559929i) q^{40} +(0.367554 + 0.460898i) q^{43} +(0.266310 + 0.0401398i) q^{44} +(-0.826239 + 0.563320i) q^{45} +(0.900969 - 0.433884i) q^{49} +1.12664 q^{50} +(0.133848 + 0.341040i) q^{52} +(0.623490 + 0.781831i) q^{55} +(0.357180 - 0.741692i) q^{56} +(1.44973 - 0.218511i) q^{59} +(-0.250701 + 1.09839i) q^{62} +(0.563320 - 0.826239i) q^{63} +(-0.134659 - 0.589980i) q^{64} +(-0.496990 + 1.26631i) q^{65} +(-0.210561 - 0.364703i) q^{68} +(-1.04876 + 0.411608i) q^{70} +(-1.48883 - 0.716983i) q^{71} +(-0.0615190 - 0.820914i) q^{72} +(1.77904 + 0.548760i) q^{73} +(-0.866025 - 0.500000i) q^{77} +(-0.598393 + 1.03645i) q^{80} +(0.0747301 - 0.997204i) q^{81} +(-0.385418 - 1.68862i) q^{83} +(0.347948 - 1.52446i) q^{85} +(0.548760 + 0.374138i) q^{86} +(-0.814021 + 0.122694i) q^{88} +(1.40097 - 1.29991i) q^{89} +(-0.702449 + 0.880843i) q^{90} -1.36035i q^{91} +(0.825886 - 0.766310i) q^{98} -1.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+4q42q5+2q92q116q1426q16+8q20+2q25+6q2612q3114q348q3618q442q45+4q494q55+14q562q59+24q99+O(q100) 24 q + 4 q^{4} - 2 q^{5} + 2 q^{9} - 2 q^{11} - 6 q^{14} - 26 q^{16} + 8 q^{20} + 2 q^{25} + 6 q^{26} - 12 q^{31} - 14 q^{34} - 8 q^{36} - 18 q^{44} - 2 q^{45} + 4 q^{49} - 4 q^{55} + 14 q^{56} - 2 q^{59}+ \cdots - 24 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2695Z)×\left(\mathbb{Z}/2695\mathbb{Z}\right)^\times.

nn 981981 18161816 21572157
χ(n)\chi(n) 1-1 e(821)e\left(\frac{8}{21}\right) 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 1.07659 0.332083i 1.07659 0.332083i 0.294755 0.955573i 0.404762π-0.404762\pi
0.781831 + 0.623490i 0.214286π0.214286\pi
33 0 0 −0.365341 0.930874i 0.619048π-0.619048\pi
0.365341 + 0.930874i 0.380952π0.380952\pi
44 0.222521 0.151712i 0.222521 0.151712i
55 0.988831 + 0.149042i 0.988831 + 0.149042i
66 0 0
77 −0.974928 + 0.222521i −0.974928 + 0.222521i
88 −0.513267 + 0.643616i −0.513267 + 0.643616i
99 −0.733052 + 0.680173i −0.733052 + 0.680173i
1010 1.11406 0.167917i 1.11406 0.167917i
1111 0.733052 + 0.680173i 0.733052 + 0.680173i
1212 0 0
1313 −0.302705 + 1.32624i −0.302705 + 1.32624i 0.563320 + 0.826239i 0.309524π0.309524\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
1414 −0.975699 + 0.563320i −0.975699 + 0.563320i
1515 0 0
1616 −0.437235 + 1.11406i −0.437235 + 1.11406i
1717 0.116853 1.55929i 0.116853 1.55929i −0.563320 0.826239i 0.690476π-0.690476\pi
0.680173 0.733052i 0.261905π-0.261905\pi
1818 −0.563320 + 0.975699i −0.563320 + 0.975699i
1919 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
2020 0.242647 0.116853i 0.242647 0.116853i
2121 0 0
2222 1.01507 + 0.488831i 1.01507 + 0.488831i
2323 0 0 −0.0747301 0.997204i 0.523810π-0.523810\pi
0.0747301 + 0.997204i 0.476190π0.476190\pi
2424 0 0
2525 0.955573 + 0.294755i 0.955573 + 0.294755i
2626 0.114533 + 1.52833i 0.114533 + 1.52833i
2727 0 0
2828 −0.183183 + 0.197424i −0.183183 + 0.197424i
2929 0 0 0.900969 0.433884i 0.142857π-0.142857\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
3030 0 0
3131 −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
3232 −0.0392431 + 0.523663i −0.0392431 + 0.523663i
3333 0 0
3434 −0.392012 1.71752i −0.392012 1.71752i
3535 −0.997204 + 0.0747301i −0.997204 + 0.0747301i
3636 −0.0599289 + 0.262566i −0.0599289 + 0.262566i
3737 0 0 −0.826239 0.563320i 0.809524π-0.809524\pi
0.826239 + 0.563320i 0.190476π0.190476\pi
3838 0 0
3939 0 0
4040 −0.603460 + 0.559929i −0.603460 + 0.559929i
4141 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
4242 0 0
4343 0.367554 + 0.460898i 0.367554 + 0.460898i 0.930874 0.365341i 0.119048π-0.119048\pi
−0.563320 + 0.826239i 0.690476π0.690476\pi
4444 0.266310 + 0.0401398i 0.266310 + 0.0401398i
4545 −0.826239 + 0.563320i −0.826239 + 0.563320i
4646 0 0
4747 0 0 0.955573 0.294755i 0.0952381π-0.0952381\pi
−0.955573 + 0.294755i 0.904762π0.904762\pi
4848 0 0
4949 0.900969 0.433884i 0.900969 0.433884i
5050 1.12664 1.12664
5151 0 0
5252 0.133848 + 0.341040i 0.133848 + 0.341040i
5353 0 0 0.826239 0.563320i 0.190476π-0.190476\pi
−0.826239 + 0.563320i 0.809524π0.809524\pi
5454 0 0
5555 0.623490 + 0.781831i 0.623490 + 0.781831i
5656 0.357180 0.741692i 0.357180 0.741692i
5757 0 0
5858 0 0
5959 1.44973 0.218511i 1.44973 0.218511i 0.623490 0.781831i 0.285714π-0.285714\pi
0.826239 + 0.563320i 0.190476π0.190476\pi
6060 0 0
6161 0 0 −0.826239 0.563320i 0.809524π-0.809524\pi
0.826239 + 0.563320i 0.190476π0.190476\pi
6262 −0.250701 + 1.09839i −0.250701 + 1.09839i
6363 0.563320 0.826239i 0.563320 0.826239i
6464 −0.134659 0.589980i −0.134659 0.589980i
6565 −0.496990 + 1.26631i −0.496990 + 1.26631i
6666 0 0
6767 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
6868 −0.210561 0.364703i −0.210561 0.364703i
6969 0 0
7070 −1.04876 + 0.411608i −1.04876 + 0.411608i
7171 −1.48883 0.716983i −1.48883 0.716983i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.988831 + 0.149042i 0.952381π0.952381\pi
7272 −0.0615190 0.820914i −0.0615190 0.820914i
7373 1.77904 + 0.548760i 1.77904 + 0.548760i 0.997204 0.0747301i 0.0238095π-0.0238095\pi
0.781831 + 0.623490i 0.214286π0.214286\pi
7474 0 0
7575 0 0
7676 0 0
7777 −0.866025 0.500000i −0.866025 0.500000i
7878 0 0
7979 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
8080 −0.598393 + 1.03645i −0.598393 + 1.03645i
8181 0.0747301 0.997204i 0.0747301 0.997204i
8282 0 0
8383 −0.385418 1.68862i −0.385418 1.68862i −0.680173 0.733052i 0.738095π-0.738095\pi
0.294755 0.955573i 0.404762π-0.404762\pi
8484 0 0
8585 0.347948 1.52446i 0.347948 1.52446i
8686 0.548760 + 0.374138i 0.548760 + 0.374138i
8787 0 0
8888 −0.814021 + 0.122694i −0.814021 + 0.122694i
8989 1.40097 1.29991i 1.40097 1.29991i 0.500000 0.866025i 0.333333π-0.333333\pi
0.900969 0.433884i 0.142857π-0.142857\pi
9090 −0.702449 + 0.880843i −0.702449 + 0.880843i
9191 1.36035i 1.36035i
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 0 0 1.00000 00
−1.00000 π\pi
9898 0.825886 0.766310i 0.825886 0.766310i
9999 −1.00000 −1.00000
100100 0.257353 0.0793829i 0.257353 0.0793829i
101101 0 0 −0.365341 0.930874i 0.619048π-0.619048\pi
0.365341 + 0.930874i 0.380952π0.380952\pi
102102 0 0
103103 0 0 −0.988831 0.149042i 0.952381π-0.952381\pi
0.988831 + 0.149042i 0.0476190π0.0476190\pi
104104 −0.698220 0.875540i −0.698220 0.875540i
105105 0 0
106106 0 0
107107 −0.636119 + 0.590232i −0.636119 + 0.590232i −0.930874 0.365341i 0.880952π-0.880952\pi
0.294755 + 0.955573i 0.404762π0.404762\pi
108108 0 0
109109 0 0 −0.733052 0.680173i 0.761905π-0.761905\pi
0.733052 + 0.680173i 0.238095π0.238095\pi
110110 0.930874 + 0.634659i 0.930874 + 0.634659i
111111 0 0
112112 0.178372 1.18342i 0.178372 1.18342i
113113 0 0 −0.222521 0.974928i 0.571429π-0.571429\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
114114 0 0
115115 0 0
116116 0 0
117117 −0.680173 1.17809i −0.680173 1.17809i
118118 1.48819 0.716677i 1.48819 0.716677i
119119 0.233052 + 1.54620i 0.233052 + 1.54620i
120120 0 0
121121 0.0747301 + 0.997204i 0.0747301 + 0.997204i
122122 0 0
123123 0 0
124124 0.0201262 + 0.268565i 0.0201262 + 0.268565i
125125 0.900969 + 0.433884i 0.900969 + 0.433884i
126126 0.332083 1.07659i 0.332083 1.07659i
127127 0.781831 0.376510i 0.781831 0.376510i 1.00000i 0.5π-0.5\pi
0.781831 + 0.623490i 0.214286π0.214286\pi
128128 −0.603460 1.04522i −0.603460 1.04522i
129129 0 0
130130 −0.114533 + 1.52833i −0.114533 + 1.52833i
131131 0 0 0.365341 0.930874i 0.380952π-0.380952\pi
−0.365341 + 0.930874i 0.619048π0.619048\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 0.943608 + 0.875540i 0.943608 + 0.875540i
137137 0 0 0.988831 0.149042i 0.0476190π-0.0476190\pi
−0.988831 + 0.149042i 0.952381π0.952381\pi
138138 0 0
139139 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
140140 −0.210561 + 0.167917i −0.210561 + 0.167917i
141141 0 0
142142 −1.84095 0.277479i −1.84095 0.277479i
143143 −1.12397 + 0.766310i −1.12397 + 0.766310i
144144 −0.437235 1.11406i −0.437235 1.11406i
145145 0 0
146146 2.09752 2.09752
147147 0 0
148148 0 0
149149 0 0 0.955573 0.294755i 0.0952381π-0.0952381\pi
−0.955573 + 0.294755i 0.904762π0.904762\pi
150150 0 0
151151 0 0 0.826239 0.563320i 0.190476π-0.190476\pi
−0.826239 + 0.563320i 0.809524π0.809524\pi
152152 0 0
153153 0.974928 + 1.22252i 0.974928 + 1.22252i
154154 −1.09839 0.250701i −1.09839 0.250701i
155155 −0.623490 + 0.781831i −0.623490 + 0.781831i
156156 0 0
157157 0 0 0.988831 0.149042i 0.0476190π-0.0476190\pi
−0.988831 + 0.149042i 0.952381π0.952381\pi
158158 0 0
159159 0 0
160160 −0.116853 + 0.511965i −0.116853 + 0.511965i
161161 0 0
162162 −0.250701 1.09839i −0.250701 1.09839i
163163 0 0 0.365341 0.930874i 0.380952π-0.380952\pi
−0.365341 + 0.930874i 0.619048π0.619048\pi
164164 0 0
165165 0 0
166166 −0.975699 1.68996i −0.975699 1.68996i
167167 0 0 −0.433884 0.900969i 0.642857π-0.642857\pi
0.433884 + 0.900969i 0.357143π0.357143\pi
168168 0 0
169169 −0.766310 0.369035i −0.766310 0.369035i
170170 −0.131651 1.75676i −0.131651 1.75676i
171171 0 0
172172 0.151712 + 0.0467970i 0.151712 + 0.0467970i
173173 −0.149042 1.98883i −0.149042 1.98883i −0.149042 0.988831i 0.547619π-0.547619\pi
1.00000i 0.5π-0.5\pi
174174 0 0
175175 −0.997204 0.0747301i −0.997204 0.0747301i
176176 −1.07827 + 0.519266i −1.07827 + 0.519266i
177177 0 0
178178 1.07659 1.86470i 1.07659 1.86470i
179179 −0.123490 + 1.64786i −0.123490 + 1.64786i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
180180 −0.0983929 + 0.250701i −0.0983929 + 0.250701i
181181 0.162592 + 0.712362i 0.162592 + 0.712362i 0.988831 + 0.149042i 0.0476190π0.0476190\pi
−0.826239 + 0.563320i 0.809524π0.809524\pi
182182 −0.451748 1.46453i −0.451748 1.46453i
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 1.14625 1.06356i 1.14625 1.06356i
188188 0 0
189189 0 0
190190 0 0
191191 −0.988831 0.149042i −0.988831 0.149042i −0.365341 0.930874i 0.619048π-0.619048\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
192192 0 0
193193 0.571270 + 1.45557i 0.571270 + 1.45557i 0.866025 + 0.500000i 0.166667π0.166667\pi
−0.294755 + 0.955573i 0.595238π0.595238\pi
194194 0 0
195195 0 0
196196 0.134659 0.233236i 0.134659 0.233236i
197197 −1.99441 −1.99441 −0.997204 0.0747301i 0.976190π-0.976190\pi
−0.997204 + 0.0747301i 0.976190π0.976190\pi
198198 −1.07659 + 0.332083i −1.07659 + 0.332083i
199199 0.0546039 + 0.139129i 0.0546039 + 0.139129i 0.955573 0.294755i 0.0952381π-0.0952381\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
200200 −0.680173 + 0.463734i −0.680173 + 0.463734i
201201 0 0
202202 0 0
203203 0 0
204204 0 0
205205 0 0
206206 0 0
207207 0 0
208208 −1.34515 0.917109i −1.34515 0.917109i
209209 0 0
210210 0 0
211211 0 0 −0.222521 0.974928i 0.571429π-0.571429\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
212212 0 0
213213 0 0
214214 −0.488831 + 0.846680i −0.488831 + 0.846680i
215215 0.294755 + 0.510531i 0.294755 + 0.510531i
216216 0 0
217217 0.294755 0.955573i 0.294755 0.955573i
218218 0 0
219219 0 0
220220 0.257353 + 0.0793829i 0.257353 + 0.0793829i
221221 2.03262 + 0.626980i 2.03262 + 0.626980i
222222 0 0
223223 0 0 −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
224224 −0.0782667 0.519266i −0.0782667 0.519266i
225225 −0.900969 + 0.433884i −0.900969 + 0.433884i
226226 0 0
227227 0.149042 0.258149i 0.149042 0.258149i −0.781831 0.623490i 0.785714π-0.785714\pi
0.930874 + 0.365341i 0.119048π0.119048\pi
228228 0 0
229229 0.603718 1.53825i 0.603718 1.53825i −0.222521 0.974928i 0.571429π-0.571429\pi
0.826239 0.563320i 0.190476π-0.190476\pi
230230 0 0
231231 0 0
232232 0 0
233233 0 0 0.563320 0.826239i 0.309524π-0.309524\pi
−0.563320 + 0.826239i 0.690476π0.690476\pi
234234 −1.12349 1.04245i −1.12349 1.04245i
235235 0 0
236236 0.289444 0.268565i 0.289444 0.268565i
237237 0 0
238238 0.764367 + 1.58722i 0.764367 + 1.58722i
239239 0 0 −0.623490 0.781831i 0.714286π-0.714286\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
240240 0 0
241241 0 0 0.826239 0.563320i 0.190476π-0.190476\pi
−0.826239 + 0.563320i 0.809524π0.809524\pi
242242 0.411608 + 1.04876i 0.411608 + 1.04876i
243243 0 0
244244 0 0
245245 0.955573 0.294755i 0.955573 0.294755i
246246 0 0
247247 0 0
248248 −0.300754 0.766310i −0.300754 0.766310i
249249 0 0
250250 1.11406 + 0.167917i 1.11406 + 0.167917i
251251 −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
252252 0.269318i 0.269318i
253253 0 0
254254 0.716677 0.664979i 0.716677 0.664979i
255255 0 0
256256 −0.553170 0.513267i −0.553170 0.513267i
257257 0 0 −0.826239 0.563320i 0.809524π-0.809524\pi
0.826239 + 0.563320i 0.190476π0.190476\pi
258258 0 0
259259 0 0
260260 0.0815240 + 0.357180i 0.0815240 + 0.357180i
261261 0 0
262262 0 0
263263 −0.866025 + 1.50000i −0.866025 + 1.50000i 1.00000i 0.5π0.5\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 0 0
269269 1.19158 + 0.367554i 1.19158 + 0.367554i 0.826239 0.563320i 0.190476π-0.190476\pi
0.365341 + 0.930874i 0.380952π0.380952\pi
270270 0 0
271271 0 0 −0.0747301 0.997204i 0.523810π-0.523810\pi
0.0747301 + 0.997204i 0.476190π0.476190\pi
272272 1.68605 + 0.811957i 1.68605 + 0.811957i
273273 0 0
274274 0 0
275275 0.500000 + 0.866025i 0.500000 + 0.866025i
276276 0 0
277277 0.139129 1.85654i 0.139129 1.85654i −0.294755 0.955573i 0.595238π-0.595238\pi
0.433884 0.900969i 0.357143π-0.357143\pi
278278 0 0
279279 −0.222521 0.974928i −0.222521 0.974928i
280280 0.463734 0.680173i 0.463734 0.680173i
281281 0 0 0.222521 0.974928i 0.428571π-0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
282282 0 0
283283 1.42935 + 1.32624i 1.42935 + 1.32624i 0.866025 + 0.500000i 0.166667π0.166667\pi
0.563320 + 0.826239i 0.309524π0.309524\pi
284284 −0.440071 + 0.0663300i −0.440071 + 0.0663300i
285285 0 0
286286 −0.955573 + 1.19825i −0.955573 + 1.19825i
287287 0 0
288288 −0.327414 0.410564i −0.327414 0.410564i
289289 −1.42890 0.215372i −1.42890 0.215372i
290290 0 0
291291 0 0
292292 0.479126 0.147791i 0.479126 0.147791i
293293 0.298085 0.298085 0.149042 0.988831i 0.452381π-0.452381\pi
0.149042 + 0.988831i 0.452381π0.452381\pi
294294 0 0
295295 1.46610 1.46610
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 0 0
301301 −0.460898 0.367554i −0.460898 0.367554i
302302 0 0
303303 0 0
304304 0 0
305305 0 0
306306 1.45557 + 0.992393i 1.45557 + 0.992393i
307307 −0.250701 + 1.09839i −0.250701 + 1.09839i 0.680173 + 0.733052i 0.261905π0.261905\pi
−0.930874 + 0.365341i 0.880952π0.880952\pi
308308 −0.268565 + 0.0201262i −0.268565 + 0.0201262i
309309 0 0
310310 −0.411608 + 1.04876i −0.411608 + 1.04876i
311311 −0.147791 + 1.97213i −0.147791 + 1.97213i 0.0747301 + 0.997204i 0.476190π0.476190\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
312312 0 0
313313 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
314314 0 0
315315 0.680173 0.733052i 0.680173 0.733052i
316316 0 0
317317 0 0 −0.0747301 0.997204i 0.523810π-0.523810\pi
0.0747301 + 0.997204i 0.476190π0.476190\pi
318318 0 0
319319 0 0
320320 −0.0452231 0.603460i −0.0452231 0.603460i
321321 0 0
322322 0 0
323323 0 0
324324 −0.134659 0.233236i −0.134659 0.233236i
325325 −0.680173 + 1.17809i −0.680173 + 1.17809i
326326 0 0
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 −1.57906 1.07659i −1.57906 1.07659i −0.955573 0.294755i 0.904762π-0.904762\pi
−0.623490 0.781831i 0.714286π-0.714286\pi
332332 −0.341948 0.317282i −0.341948 0.317282i
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 0.848162 + 1.06356i 0.848162 + 1.06356i 0.997204 + 0.0747301i 0.0238095π0.0238095\pi
−0.149042 + 0.988831i 0.547619π0.547619\pi
338338 −0.947549 0.142820i −0.947549 0.142820i
339339 0 0
340340 −0.153853 0.392012i −0.153853 0.392012i
341341 −0.955573 + 0.294755i −0.955573 + 0.294755i
342342 0 0
343343 −0.781831 + 0.623490i −0.781831 + 0.623490i
344344 −0.485294 −0.485294
345345 0 0
346346 −0.820914 2.09165i −0.820914 2.09165i
347347 1.64786 1.12349i 1.64786 1.12349i 0.781831 0.623490i 0.214286π-0.214286\pi
0.866025 0.500000i 0.166667π-0.166667\pi
348348 0 0
349349 0 0 −0.623490 0.781831i 0.714286π-0.714286\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
350350 −1.09839 + 0.250701i −1.09839 + 0.250701i
351351 0 0
352352 −0.384948 + 0.357180i −0.384948 + 0.357180i
353353 0 0 0.988831 0.149042i 0.0476190π-0.0476190\pi
−0.988831 + 0.149042i 0.952381π0.952381\pi
354354 0 0
355355 −1.36534 0.930874i −1.36534 0.930874i
356356 0.114533 0.501801i 0.114533 0.501801i
357357 0 0
358358 0.414278 + 1.81507i 0.414278 + 1.81507i
359359 0 0 0.365341 0.930874i 0.380952π-0.380952\pi
−0.365341 + 0.930874i 0.619048π0.619048\pi
360360 0.0615190 0.820914i 0.0615190 0.820914i
361361 −0.500000 + 0.866025i −0.500000 + 0.866025i
362362 0.411608 + 0.712926i 0.411608 + 0.712926i
363363 0 0
364364 −0.206381 0.302705i −0.206381 0.302705i
365365 1.67738 + 0.807782i 1.67738 + 0.807782i
366366 0 0
367367 0 0 −0.955573 0.294755i 0.904762π-0.904762\pi
0.955573 + 0.294755i 0.0952381π0.0952381\pi
368368 0 0
369369 0 0
370370 0 0
371371 0 0
372372 0 0
373373 0.149042 + 0.258149i 0.149042 + 0.258149i 0.930874 0.365341i 0.119048π-0.119048\pi
−0.781831 + 0.623490i 0.785714π0.785714\pi
374374 0.880843 1.52566i 0.880843 1.52566i
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 0.440071 1.92808i 0.440071 1.92808i 0.0747301 0.997204i 0.476190π-0.476190\pi
0.365341 0.930874i 0.380952π-0.380952\pi
380380 0 0
381381 0 0
382382 −1.11406 + 0.167917i −1.11406 + 0.167917i
383383 0 0 0.733052 0.680173i 0.238095π-0.238095\pi
−0.733052 + 0.680173i 0.761905π0.761905\pi
384384 0 0
385385 −0.781831 0.623490i −0.781831 0.623490i
386386 1.09839 + 1.37734i 1.09839 + 1.37734i
387387 −0.582926 0.0878620i −0.582926 0.0878620i
388388 0 0
389389 −0.722521 1.84095i −0.722521 1.84095i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.222521 0.974928i 0.571429π-0.571429\pi
390390 0 0
391391 0 0
392392 −0.183183 + 0.802576i −0.183183 + 0.802576i
393393 0 0
394394 −2.14715 + 0.662309i −2.14715 + 0.662309i
395395 0 0
396396 −0.222521 + 0.151712i −0.222521 + 0.151712i
397397 0 0 −0.988831 0.149042i 0.952381π-0.952381\pi
0.988831 + 0.149042i 0.0476190π0.0476190\pi
398398 0.104988 + 0.131651i 0.104988 + 0.131651i
399399 0 0
400400 −0.746184 + 0.935685i −0.746184 + 0.935685i
401401 1.40097 1.29991i 1.40097 1.29991i 0.500000 0.866025i 0.333333π-0.333333\pi
0.900969 0.433884i 0.142857π-0.142857\pi
402402 0 0
403403 −0.997204 0.925270i −0.997204 0.925270i
404404 0 0
405405 0.222521 0.974928i 0.222521 0.974928i
406406 0 0
407407 0 0
408408 0 0
409409 0 0 0.0747301 0.997204i 0.476190π-0.476190\pi
−0.0747301 + 0.997204i 0.523810π0.523810\pi
410410 0 0
411411 0 0
412412 0 0
413413 −1.36476 + 0.535628i −1.36476 + 0.535628i
414414 0 0
415415 −0.129436 1.72721i −0.129436 1.72721i
416416 −0.682623 0.210561i −0.682623 0.210561i
417417 0 0
418418 0 0
419419 −1.32091 0.636119i −1.32091 0.636119i −0.365341 0.930874i 0.619048π-0.619048\pi
−0.955573 + 0.294755i 0.904762π0.904762\pi
420420 0 0
421421 1.12349 0.541044i 1.12349 0.541044i 0.222521 0.974928i 0.428571π-0.428571\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
422422 0 0
423423 0 0
424424 0 0
425425 0.571270 1.45557i 0.571270 1.45557i
426426 0 0
427427 0 0
428428 −0.0520043 + 0.227846i −0.0520043 + 0.227846i
429429 0 0
430430 0.486868 + 0.451748i 0.486868 + 0.451748i
431431 0 0 0.988831 0.149042i 0.0476190π-0.0476190\pi
−0.988831 + 0.149042i 0.952381π0.952381\pi
432432 0 0
433433 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
434434 1.12664i 1.12664i
435435 0 0
436436 0 0
437437 0 0
438438 0 0
439439 0 0 0.955573 0.294755i 0.0952381π-0.0952381\pi
−0.955573 + 0.294755i 0.904762π0.904762\pi
440440 −0.823216 −0.823216
441441 −0.365341 + 0.930874i −0.365341 + 0.930874i
442442 2.39650 2.39650
443443 0 0 0.955573 0.294755i 0.0952381π-0.0952381\pi
−0.955573 + 0.294755i 0.904762π0.904762\pi
444444 0 0
445445 1.57906 1.07659i 1.57906 1.07659i
446446 0 0
447447 0 0
448448 0.262566 + 0.545223i 0.262566 + 0.545223i
449449 0.914101 1.14625i 0.914101 1.14625i −0.0747301 0.997204i 0.523810π-0.523810\pi
0.988831 0.149042i 0.0476190π-0.0476190\pi
450450 −0.825886 + 0.766310i −0.825886 + 0.766310i
451451 0 0
452452 0 0
453453 0 0
454454 0.0747301 0.327414i 0.0747301 0.327414i
455455 0.202749 1.34515i 0.202749 1.34515i
456456 0 0
457457 −0.632789 + 1.61232i −0.632789 + 1.61232i 0.149042 + 0.988831i 0.452381π0.452381\pi
−0.781831 + 0.623490i 0.785714π0.785714\pi
458458 0.139129 1.85654i 0.139129 1.85654i
459459 0 0
460460 0 0
461461 0 0 0.900969 0.433884i 0.142857π-0.142857\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
462462 0 0
463463 0 0 −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
464464 0 0
465465 0 0
466466 0 0
467467 0 0 −0.0747301 0.997204i 0.523810π-0.523810\pi
0.0747301 + 0.997204i 0.476190π0.476190\pi
468468 −0.330084 0.158960i −0.330084 0.158960i
469469 0 0
470470 0 0
471471 0 0
472472 −0.603460 + 1.04522i −0.603460 + 1.04522i
473473 −0.0440542 + 0.587862i −0.0440542 + 0.587862i
474474 0 0
475475 0 0
476476 0.286436 + 0.308705i 0.286436 + 0.308705i
477477 0 0
478478 0 0
479479 0 0 −0.733052 0.680173i 0.761905π-0.761905\pi
0.733052 + 0.680173i 0.238095π0.238095\pi
480480 0 0
481481 0 0
482482 0 0
483483 0 0
484484 0.167917 + 0.210561i 0.167917 + 0.210561i
485485 0 0
486486 0 0
487487 0 0 −0.365341 0.930874i 0.619048π-0.619048\pi
0.365341 + 0.930874i 0.380952π0.380952\pi
488488 0 0
489489 0 0
490490 0.930874 0.634659i 0.930874 0.634659i
491491 0 0 1.00000 00
−1.00000 π\pi
492492 0 0
493493 0 0
494494 0 0
495495 −0.988831 0.149042i −0.988831 0.149042i
496496 −0.746184 0.935685i −0.746184 0.935685i
497497 1.61105 + 0.367711i 1.61105 + 0.367711i
498498 0 0
499499 −1.40097 + 1.29991i −1.40097 + 1.29991i −0.500000 + 0.866025i 0.666667π0.666667\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
500500 0.266310 0.0401398i 0.266310 0.0401398i
501501 0 0
502502 −1.67738 1.14362i −1.67738 1.14362i
503503 0.385418 1.68862i 0.385418 1.68862i −0.294755 0.955573i 0.595238π-0.595238\pi
0.680173 0.733052i 0.261905π-0.261905\pi
504504 0.242647 + 0.786643i 0.242647 + 0.786643i
505505 0 0
506506 0 0
507507 0 0
508508 0.116853 0.202395i 0.116853 0.202395i
509509 0.988831 + 1.71271i 0.988831 + 1.71271i 0.623490 + 0.781831i 0.285714π0.285714\pi
0.365341 + 0.930874i 0.380952π0.380952\pi
510510 0 0
511511 −1.85654 0.139129i −1.85654 0.139129i
512512 0.321415 + 0.154785i 0.321415 + 0.154785i
513513 0 0
514514 0 0
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 0 0
520520 −0.559929 0.969825i −0.559929 0.969825i
521521 0.826239 1.43109i 0.826239 1.43109i −0.0747301 0.997204i 0.523810π-0.523810\pi
0.900969 0.433884i 0.142857π-0.142857\pi
522522 0 0
523523 0.215372 0.548760i 0.215372 0.548760i −0.781831 0.623490i 0.785714π-0.785714\pi
0.997204 + 0.0747301i 0.0238095π0.0238095\pi
524524 0 0
525525 0 0
526526 −0.434227 + 1.90247i −0.434227 + 1.90247i
527527 1.29196 + 0.880843i 1.29196 + 0.880843i
528528 0 0
529529 −0.988831 + 0.149042i −0.988831 + 0.149042i
530530 0 0
531531 −0.914101 + 1.14625i −0.914101 + 1.14625i
532532 0 0
533533 0 0
534534 0 0
535535 −0.716983 + 0.488831i −0.716983 + 0.488831i
536536 0 0
537537 0 0
538538 1.40490 1.40490
539539 0.955573 + 0.294755i 0.955573 + 0.294755i
540540 0 0
541541 0 0 0.955573 0.294755i 0.0952381π-0.0952381\pi
−0.955573 + 0.294755i 0.904762π0.904762\pi
542542 0 0
543543 0 0
544544 0.811957 + 0.122383i 0.811957 + 0.122383i
545545 0 0
546546 0 0
547547 −1.16078 + 1.45557i −1.16078 + 1.45557i −0.294755 + 0.955573i 0.595238π0.595238\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
548548 0 0
549549 0 0
550550 0.825886 + 0.766310i 0.825886 + 0.766310i
551551 0 0
552552 0 0
553553 0 0
554554 −0.466742 2.04493i −0.466742 2.04493i
555555 0 0
556556 0 0
557557 −0.974928 + 1.68862i −0.974928 + 1.68862i −0.294755 + 0.955573i 0.595238π0.595238\pi
−0.680173 + 0.733052i 0.738095π0.738095\pi
558558 −0.563320 0.975699i −0.563320 0.975699i
559559 −0.722521 + 0.347948i −0.722521 + 0.347948i
560560 0.352759 1.14362i 0.352759 1.14362i
561561 0 0
562562 0 0
563563 1.90580 + 0.587862i 1.90580 + 0.587862i 0.974928 + 0.222521i 0.0714286π0.0714286\pi
0.930874 + 0.365341i 0.119048π0.119048\pi
564564 0 0
565565 0 0
566566 1.97924 + 0.953150i 1.97924 + 0.953150i
567567 0.149042 + 0.988831i 0.149042 + 0.988831i
568568 1.22563 0.590232i 1.22563 0.590232i
569569 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
570570 0 0
571571 0 0 0.0747301 0.997204i 0.476190π-0.476190\pi
−0.0747301 + 0.997204i 0.523810π0.523810\pi
572572 −0.133848 + 0.341040i −0.133848 + 0.341040i
573573 0 0
574574 0 0
575575 0 0
576576 0.500000 + 0.340894i 0.500000 + 0.340894i
577577 0 0 −0.733052 0.680173i 0.761905π-0.761905\pi
0.733052 + 0.680173i 0.238095π0.238095\pi
578578 −1.60986 + 0.242647i −1.60986 + 0.242647i
579579 0 0
580580 0 0
581581 0.751509 + 1.56052i 0.751509 + 1.56052i
582582 0 0
583583 0 0
584584 −1.26631 + 0.863355i −1.26631 + 0.863355i
585585 −0.496990 1.26631i −0.496990 1.26631i
586586 0.320914 0.0989888i 0.320914 0.0989888i
587587 0 0 1.00000 00
−1.00000 π\pi
588588 0 0
589589 0 0
590590 1.57839 0.486868i 1.57839 0.486868i
591591 0 0
592592 0 0
593593 −0.582926 0.0878620i −0.582926 0.0878620i −0.149042 0.988831i 0.547619π-0.547619\pi
−0.433884 + 0.900969i 0.642857π0.642857\pi
594594 0 0
595595 1.56366i 1.56366i
596596 0 0
597597 0 0
598598 0 0
599599 −1.44973 1.34515i −1.44973 1.34515i −0.826239 0.563320i 0.809524π-0.809524\pi
−0.623490 0.781831i 0.714286π-0.714286\pi
600600 0 0
601601 0 0 0.222521 0.974928i 0.428571π-0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
602602 −0.618255 0.242647i −0.618255 0.242647i
603603 0 0
604604 0 0
605605 −0.0747301 + 0.997204i −0.0747301 + 0.997204i
606606 0 0
607607 −0.149042 0.258149i −0.149042 0.258149i 0.781831 0.623490i 0.214286π-0.214286\pi
−0.930874 + 0.365341i 0.880952π0.880952\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0.402413 + 0.124128i 0.402413 + 0.124128i
613613 1.90580 + 0.587862i 1.90580 + 0.587862i 0.974928 + 0.222521i 0.0714286π0.0714286\pi
0.930874 + 0.365341i 0.119048π0.119048\pi
614614 0.0948562 + 1.26577i 0.0948562 + 1.26577i
615615 0 0
616616 0.766310 0.300754i 0.766310 0.300754i
617617 0 0 0.900969 0.433884i 0.142857π-0.142857\pi
−0.900969 + 0.433884i 0.857143π0.857143\pi
618618 0 0
619619 −0.222521 + 0.385418i −0.222521 + 0.385418i −0.955573 0.294755i 0.904762π-0.904762\pi
0.733052 + 0.680173i 0.238095π0.238095\pi
620620 −0.0201262 + 0.268565i −0.0201262 + 0.268565i
621621 0 0
622622 0.495802 + 2.17225i 0.495802 + 2.17225i
623623 −1.07659 + 1.57906i −1.07659 + 1.57906i
624624 0 0
625625 0.826239 + 0.563320i 0.826239 + 0.563320i
626626 0 0
627627 0 0
628628 0 0
629629 0 0
630630 0.488831 1.01507i 0.488831 1.01507i
631631 0.0931869 + 0.116853i 0.0931869 + 0.116853i 0.826239 0.563320i 0.190476π-0.190476\pi
−0.733052 + 0.680173i 0.761905π0.761905\pi
632632 0 0
633633 0 0
634634 0 0
635635 0.829215 0.255779i 0.829215 0.255779i
636636 0 0
637637 0.302705 + 1.32624i 0.302705 + 1.32624i
638638 0 0
639639 1.57906 0.487076i 1.57906 0.487076i
640640 −0.440937 1.12349i −0.440937 1.12349i
641641 1.48883 1.01507i 1.48883 1.01507i 0.500000 0.866025i 0.333333π-0.333333\pi
0.988831 0.149042i 0.0476190π-0.0476190\pi
642642 0 0
643643 0 0 −0.623490 0.781831i 0.714286π-0.714286\pi
0.623490 + 0.781831i 0.285714π0.285714\pi
644644 0 0
645645 0 0
646646 0 0
647647 0 0 0.988831 0.149042i 0.0476190π-0.0476190\pi
−0.988831 + 0.149042i 0.952381π0.952381\pi
648648 0.603460 + 0.559929i 0.603460 + 0.559929i
649649 1.21135 + 0.825886i 1.21135 + 0.825886i
650650 −0.341040 + 1.49419i −0.341040 + 1.49419i
651651 0 0
652652 0 0
653653 0 0 0.365341 0.930874i 0.380952π-0.380952\pi
−0.365341 + 0.930874i 0.619048π0.619048\pi
654654 0 0
655655 0 0
656656 0 0
657657 −1.67738 + 0.807782i −1.67738 + 0.807782i
658658 0 0
659659 0 0 −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
660660 0 0
661661 −1.72188 0.531130i −1.72188 0.531130i −0.733052 0.680173i 0.761905π-0.761905\pi
−0.988831 + 0.149042i 0.952381π0.952381\pi
662662 −2.05751 0.634659i −2.05751 0.634659i
663663 0 0
664664 1.28465 + 0.618654i 1.28465 + 0.618654i
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 −0.385418 + 1.68862i −0.385418 + 1.68862i 0.294755 + 0.955573i 0.404762π0.404762\pi
−0.680173 + 0.733052i 0.738095π0.738095\pi
674674 1.26631 + 0.863355i 1.26631 + 0.863355i
675675 0 0
676676 −0.226507 + 0.0341405i −0.226507 + 0.0341405i
677677 1.42935 1.32624i 1.42935 1.32624i 0.563320 0.826239i 0.309524π-0.309524\pi
0.866025 0.500000i 0.166667π-0.166667\pi
678678 0 0
679679 0 0
680680 0.802576 + 1.00640i 0.802576 + 1.00640i
681681 0 0
682682 −0.930874 + 0.634659i −0.930874 + 0.634659i
683683 0 0 −0.365341 0.930874i 0.619048π-0.619048\pi
0.365341 + 0.930874i 0.380952π0.380952\pi
684684 0 0
685685 0 0
686686 −0.634659 + 0.930874i −0.634659 + 0.930874i
687687 0 0
688688 −0.674173 + 0.207955i −0.674173 + 0.207955i
689689 0 0
690690 0 0
691691 −1.23305 0.185853i −1.23305 0.185853i −0.500000 0.866025i 0.666667π-0.666667\pi
−0.733052 + 0.680173i 0.761905π0.761905\pi
692692 −0.334895 0.419945i −0.334895 0.419945i
693693 0.974928 0.222521i 0.974928 0.222521i
694694 1.40097 1.75676i 1.40097 1.75676i
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 −0.233236 + 0.134659i −0.233236 + 0.134659i
701701 0 0 −0.222521 0.974928i 0.571429π-0.571429\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
702702 0 0
703703 0 0
704704 0.302576 0.524077i 0.302576 0.524077i
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 0.0747301 + 0.997204i 0.0747301 + 0.997204i 0.900969 + 0.433884i 0.142857π0.142857\pi
−0.826239 + 0.563320i 0.809524π0.809524\pi
710710 −1.77904 0.548760i −1.77904 0.548760i
711711 0 0
712712 0.117572 + 1.56889i 0.117572 + 1.56889i
713713 0 0
714714 0 0
715715 −1.22563 + 0.590232i −1.22563 + 0.590232i
716716 0.222521 + 0.385418i 0.222521 + 0.385418i
717717 0 0
718718 0 0
719719 −0.455573 + 1.16078i −0.455573 + 1.16078i 0.500000 + 0.866025i 0.333333π0.333333\pi
−0.955573 + 0.294755i 0.904762π0.904762\pi
720720 −0.266310 1.16678i −0.266310 1.16678i
721721 0 0
722722 −0.250701 + 1.09839i −0.250701 + 1.09839i
723723 0 0
724724 0.144254 + 0.133848i 0.144254 + 0.133848i
725725 0 0
726726 0 0
727727 0 0 0.623490 0.781831i 0.285714π-0.285714\pi
−0.623490 + 0.781831i 0.714286π0.714286\pi
728728 0.875540 + 0.698220i 0.875540 + 0.698220i
729729 0.623490 + 0.781831i 0.623490 + 0.781831i
730730 2.07409 + 0.312619i 2.07409 + 0.312619i
731731 0.761623 0.519266i 0.761623 0.519266i
732732 0 0
733733 −0.829215 + 0.255779i −0.829215 + 0.255779i −0.680173 0.733052i 0.738095π-0.738095\pi
−0.149042 + 0.988831i 0.547619π0.547619\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 0 0 0.826239 0.563320i 0.190476π-0.190476\pi
−0.826239 + 0.563320i 0.809524π0.809524\pi
740740 0 0
741741 0 0
742742 0 0
743743 0.848162 1.06356i 0.848162 1.06356i −0.149042 0.988831i 0.547619π-0.547619\pi
0.997204 0.0747301i 0.0238095π-0.0238095\pi
744744 0 0
745745 0 0
746746 0.246184 + 0.228425i 0.246184 + 0.228425i
747747 1.43109 + 0.975699i 1.43109 + 0.975699i
748748 0.0937086 0.410564i 0.0937086 0.410564i
749749 0.488831 0.716983i 0.488831 0.716983i
750750 0 0
751751 0.266948 0.680173i 0.266948 0.680173i −0.733052 0.680173i 0.761905π-0.761905\pi
1.00000 00
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 0 0 −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
758758 −0.166507 2.22188i −0.166507 2.22188i
759759 0 0
760760 0 0
761761 0 0 −0.0747301 0.997204i 0.523810π-0.523810\pi
0.0747301 + 0.997204i 0.476190π0.476190\pi
762762 0 0
763763 0 0
764764 −0.242647 + 0.116853i −0.242647 + 0.116853i
765765 0.781831 + 1.35417i 0.781831 + 1.35417i
766766 0 0
767767 −0.149042 + 1.98883i −0.149042 + 1.98883i
768768 0 0
769769 0 0 −0.222521 0.974928i 0.571429π-0.571429\pi
0.222521 + 0.974928i 0.428571π0.428571\pi
770770 −1.04876 0.411608i −1.04876 0.411608i
771771 0 0
772772 0.347948 + 0.237227i 0.347948 + 0.237227i
773773 0 0 −0.733052 0.680173i 0.761905π-0.761905\pi
0.733052 + 0.680173i 0.238095π0.238095\pi
774774 −0.656748 + 0.0989888i −0.656748 + 0.0989888i
775775 −0.733052 + 0.680173i −0.733052 + 0.680173i
776776 0 0
777777 0 0
778778 −1.38921 1.74201i −1.38921 1.74201i
779779 0 0
780780 0 0
781781 −0.603718 1.53825i −0.603718 1.53825i
782782 0 0
783783 0 0
784784 0.0894359 + 1.19344i 0.0894359 + 1.19344i
785785 0 0
786786 0 0
787787 −0.728639 1.85654i −0.728639 1.85654i −0.433884 0.900969i 0.642857π-0.642857\pi
−0.294755 0.955573i 0.595238π-0.595238\pi
788788 −0.443797 + 0.302576i −0.443797 + 0.302576i
789789 0 0
790790 0 0
791791 0 0
792792 0.513267 0.643616i 0.513267 0.643616i
793793 0 0
794794 0 0
795795 0 0
796796 0.0332580 + 0.0226749i 0.0332580 + 0.0226749i
797797 0 0 0.222521 0.974928i 0.428571π-0.428571\pi
−0.222521 + 0.974928i 0.571429π0.571429\pi
798798 0 0
799799 0 0
800800 −0.191852 + 0.488831i −0.191852 + 0.488831i
801801 −0.142820 + 1.90580i −0.142820 + 1.90580i
802802 1.07659 1.86470i 1.07659 1.86470i
803803 0.930874 + 1.61232i 0.930874 + 1.61232i
804804 0 0
805805 0 0
806806 −1.38084 0.664979i −1.38084 0.664979i
807807 0 0
808808 0 0
809809 0 0 −0.955573 0.294755i 0.904762π-0.904762\pi
0.955573 + 0.294755i 0.0952381π0.0952381\pi
810810 −0.0841939 1.12349i −0.0841939 1.12349i
811811 0 0 −0.900969 0.433884i 0.857143π-0.857143\pi
0.900969 + 0.433884i 0.142857π0.142857\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 0 0
817817 0 0
818818 0 0
819819 0.925270 + 0.997204i 0.925270 + 0.997204i
820820 0 0
821821 0 0 −0.826239 0.563320i 0.809524π-0.809524\pi
0.826239 + 0.563320i 0.190476π0.190476\pi
822822 0 0
823823 0 0 0.988831 0.149042i 0.0476190π-0.0476190\pi
−0.988831 + 0.149042i 0.952381π0.952381\pi
824824 0 0
825825 0 0
826826 −1.29141 + 1.02986i −1.29141 + 1.02986i
827827 0.974928 + 1.22252i 0.974928 + 1.22252i 0.974928 + 0.222521i 0.0714286π0.0714286\pi
1.00000i 0.5π0.5\pi
828828 0 0
829829 1.21135 0.825886i 1.21135 0.825886i 0.222521 0.974928i 0.428571π-0.428571\pi
0.988831 + 0.149042i 0.0476190π0.0476190\pi
830830 −0.712926 1.81651i −0.712926 1.81651i
831831 0 0
832832 0.823216 0.823216
833833 −0.571270 1.45557i −0.571270 1.45557i
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 −1.63332 0.246184i −1.63332 0.246184i
839839 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 00
−0.222521 + 0.974928i 0.571429π0.571429\pi
840840 0 0
841841 0.623490 0.781831i 0.623490 0.781831i
842842 1.02986 0.955573i 1.02986 0.955573i
843843 0 0
844844 0 0
845845 −0.702749 0.479126i −0.702749 0.479126i
846846 0 0
847847 −0.294755 0.955573i −0.294755 0.955573i
848848 0 0
849849 0 0
850850 0.131651 1.75676i 0.131651 1.75676i
851851 0 0
852852 0 0
853853 −0.781831 + 0.376510i −0.781831 + 0.376510i −0.781831 0.623490i 0.785714π-0.785714\pi
1.00000i 0.5π0.5\pi
854854 0 0
855855 0 0
856856 −0.0533842 0.712362i −0.0533842 0.712362i
857857 1.07659 + 0.332083i 1.07659 + 0.332083i 0.781831 0.623490i 0.214286π-0.214286\pi
0.294755 + 0.955573i 0.404762π0.404762\pi
858858 0 0
859859 −0.0931869 1.24349i −0.0931869 1.24349i −0.826239 0.563320i 0.809524π-0.809524\pi
0.733052 0.680173i 0.238095π-0.238095\pi
860860 0.143043 + 0.0688859i 0.143043 + 0.0688859i
861861 0 0
862862 0 0
863863 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
864864 0 0
865865 0.149042 1.98883i 0.149042 1.98883i
866866 0 0
867867 0 0
868868 −0.0793829 0.257353i −0.0793829 0.257353i
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 0 0
874874 0 0
875875 −0.974928 0.222521i −0.974928 0.222521i
876876 0 0
877877 −1.71271 0.258149i −1.71271 0.258149i −0.781831 0.623490i 0.785714π-0.785714\pi
−0.930874 + 0.365341i 0.880952π0.880952\pi
878878 0 0
879879 0 0
880880 −1.14362 + 0.352759i −1.14362 + 0.352759i
881881 0.149460 0.149460 0.0747301 0.997204i 0.476190π-0.476190\pi
0.0747301 + 0.997204i 0.476190π0.476190\pi
882882 −0.0841939 + 1.12349i −0.0841939 + 1.12349i
883883 0 0 1.00000 00
−1.00000 π\pi
884884 0.547421 0.168857i 0.547421 0.168857i
885885 0 0
886886 0 0
887887 1.84095 + 0.277479i 1.84095 + 0.277479i 0.974928 0.222521i 0.0714286π-0.0714286\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
888888 0 0
889889 −0.678448 + 0.541044i −0.678448 + 0.541044i
890890 1.34248 1.68342i 1.34248 1.68342i
891891 0.733052 0.680173i 0.733052 0.680173i
892892 0 0
893893 0 0
894894 0 0
895895 −0.367711 + 1.61105i −0.367711 + 1.61105i
896896 0.820914 + 0.884735i 0.820914 + 0.884735i
897897 0 0
898898 0.603460 1.53759i 0.603460 1.53759i
899899 0 0
900900 −0.134659 + 0.233236i −0.134659 + 0.233236i
901901 0 0
902902 0 0
903903 0 0
904904 0 0
905905 0.0546039 + 0.728639i 0.0546039 + 0.728639i
906906 0 0
907907 0 0 −0.955573 0.294755i 0.904762π-0.904762\pi
0.955573 + 0.294755i 0.0952381π0.0952381\pi
908908 −0.00599930 0.0800550i −0.00599930 0.0800550i
909909 0 0
910910 −0.228425 1.51550i −0.228425 1.51550i
911911 0.134659 0.0648483i 0.134659 0.0648483i −0.365341 0.930874i 0.619048π-0.619048\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
912912 0 0
913913 0.866025 1.50000i 0.866025 1.50000i
914914 −0.145828 + 1.94594i −0.145828 + 1.94594i
915915 0 0
916916 −0.0990311 0.433884i −0.0990311 0.433884i
917917 0 0
918918 0 0
919919 0 0 −0.826239 0.563320i 0.809524π-0.809524\pi
0.826239 + 0.563320i 0.190476π0.190476\pi
920920 0 0
921921 0 0
922922 0 0
923923 1.40157 1.75751i 1.40157 1.75751i
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 −1.72188 + 0.531130i −1.72188 + 0.531130i −0.988831 0.149042i 0.952381π-0.952381\pi
−0.733052 + 0.680173i 0.761905π0.761905\pi
930930 0 0
931931 0 0
932932 0 0
933933 0 0
934934 0 0
935935 1.29196 0.880843i 1.29196 0.880843i
936936 1.10735 + 0.166906i 1.10735 + 0.166906i
937937 −0.848162 1.06356i −0.848162 1.06356i −0.997204 0.0747301i 0.976190π-0.976190\pi
0.149042 0.988831i 0.452381π-0.452381\pi
938938 0 0
939939 0 0
940940 0 0
941941 0 0 0.988831 0.149042i 0.0476190π-0.0476190\pi
−0.988831 + 0.149042i 0.952381π0.952381\pi
942942 0 0
943943 0 0
944944 −0.390438 + 1.71062i −0.390438 + 1.71062i
945945 0 0
946946 0.147791 + 0.647514i 0.147791 + 0.647514i
947947 0 0 0.365341 0.930874i 0.380952π-0.380952\pi
−0.365341 + 0.930874i 0.619048π0.619048\pi
948948 0 0
949949 −1.26631 + 2.19331i −1.26631 + 2.19331i
950950 0 0
951951 0 0
952952 −1.11478 0.643616i −1.11478 0.643616i
953953 −1.75676 0.846011i −1.75676 0.846011i −0.974928 0.222521i 0.928571π-0.928571\pi
−0.781831 0.623490i 0.785714π-0.785714\pi
954954 0 0
955955 −0.955573 0.294755i −0.955573 0.294755i
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 0 0
962962 0 0
963963 0.0648483 0.865341i 0.0648483 0.865341i
964964 0 0
965965 0.347948 + 1.52446i 0.347948 + 1.52446i
966966 0 0
967967 0.414278 1.81507i 0.414278 1.81507i −0.149042 0.988831i 0.547619π-0.547619\pi
0.563320 0.826239i 0.309524π-0.309524\pi
968968 −0.680173 0.463734i −0.680173 0.463734i
969969 0 0
970970 0 0
971971 0.109562 0.101659i 0.109562 0.101659i −0.623490 0.781831i 0.714286π-0.714286\pi
0.733052 + 0.680173i 0.238095π0.238095\pi
972972 0 0
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 0 0 −0.365341 0.930874i 0.619048π-0.619048\pi
0.365341 + 0.930874i 0.380952π0.380952\pi
978978 0 0
979979 1.91115 1.91115
980980 0.167917 0.210561i 0.167917 0.210561i
981981 0 0
982982 0 0
983983 0 0 −0.365341 0.930874i 0.619048π-0.619048\pi
0.365341 + 0.930874i 0.380952π0.380952\pi
984984 0 0
985985 −1.97213 0.297251i −1.97213 0.297251i
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 −1.11406 + 0.167917i −1.11406 + 0.167917i
991991 0.914101 + 0.848162i 0.914101 + 0.848162i 0.988831 0.149042i 0.0476190π-0.0476190\pi
−0.0747301 + 0.997204i 0.523810π0.523810\pi
992992 −0.433884 0.295817i −0.433884 0.295817i
993993 0 0
994994 1.85654 0.139129i 1.85654 0.139129i
995995 0.0332580 + 0.145713i 0.0332580 + 0.145713i
996996 0 0
997997 0.0440542 0.587862i 0.0440542 0.587862i −0.930874 0.365341i 0.880952π-0.880952\pi
0.974928 0.222521i 0.0714286π-0.0714286\pi
998998 −1.07659 + 1.86470i −1.07659 + 1.86470i
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 2695.1.ck.c.2034.2 yes 24
5.4 even 2 inner 2695.1.ck.c.2034.1 yes 24
11.10 odd 2 inner 2695.1.ck.c.2034.1 yes 24
49.2 even 21 inner 2695.1.ck.c.1374.2 yes 24
55.54 odd 2 CM 2695.1.ck.c.2034.2 yes 24
245.149 even 42 inner 2695.1.ck.c.1374.1 24
539.296 odd 42 inner 2695.1.ck.c.1374.1 24
2695.1374 odd 42 inner 2695.1.ck.c.1374.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2695.1.ck.c.1374.1 24 245.149 even 42 inner
2695.1.ck.c.1374.1 24 539.296 odd 42 inner
2695.1.ck.c.1374.2 yes 24 49.2 even 21 inner
2695.1.ck.c.1374.2 yes 24 2695.1374 odd 42 inner
2695.1.ck.c.2034.1 yes 24 5.4 even 2 inner
2695.1.ck.c.2034.1 yes 24 11.10 odd 2 inner
2695.1.ck.c.2034.2 yes 24 1.1 even 1 trivial
2695.1.ck.c.2034.2 yes 24 55.54 odd 2 CM