Properties

Label 2888.1.bb.a.2395.1
Level 28882888
Weight 11
Character 2888.2395
Analytic conductor 1.4411.441
Analytic rank 00
Dimension 1818
Projective image D19D_{19}
CM discriminant -8
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2888,1,Mod(115,2888)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2888, base_ring=CyclotomicField(38))
 
chi = DirichletCharacter(H, H._module([19, 19, 4]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2888.115");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 2888=23192 2888 = 2^{3} \cdot 19^{2}
Weight: k k == 1 1
Character orbit: [χ][\chi] == 2888.bb (of order 3838, degree 1818, 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: 1.441299756481.44129975648
Analytic rank: 00
Dimension: 1818
Coefficient field: Q(ζ38)\Q(\zeta_{38})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x18x17+x16x15+x14x13+x12x11+x10x9+x8++1 x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D19D_{19}
Projective field: Galois closure of Q[x]/(x19)\mathbb{Q}[x]/(x^{19} - \cdots)

Embedding invariants

Embedding label 2395.1
Root 0.6772820.735724i0.677282 - 0.735724i of defining polynomial
Character χ\chi == 2888.2395
Dual form 2888.1.bb.a.1939.1

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+(0.789141+0.614213i)q2+(0.917421+0.996584i)q3+(0.245485+0.969400i)q4+(0.111859+1.34994i)q6+(0.401695+0.915773i)q8+(0.0689406+0.831990i)q9+(0.04054410.489294i)q11+(0.740876+1.13399i)q12+(0.879474+0.475947i)q16+(0.431796+1.70512i)q17+(0.565423+0.614213i)q18+(0.7891410.614213i)q19+(0.2685360.411024i)q22+(1.28117+0.439826i)q24+(0.5469480.837166i)q25+(0.1765450.137410i)q27+(0.9863610.164595i)q32+(0.4504270.489294i)q33+(1.38806+1.08037i)q34+(0.823455+0.137410i)q36+1.00000q38+(1.281170.439826i)q41+(1.55676+0.259777i)q43+(0.4643690.159418i)q44+(1.281170.439826i)q48+(0.8794740.475947i)q49+(0.9458170.324699i)q50+(2.09544+1.13399i)q51+0.223718q54+(1.33609+0.222954i)q57+(1.49277+0.512467i)q59+(0.6772820.735724i)q64+(0.6559810.109464i)q66+(0.06634350.151248i)q671.75895q68+(0.7342210.397341i)q72+(0.4643691.83375i)q73+(1.336090.222954i)q75+(0.789141+0.614213i)q76+(1.12236+0.187289i)q81+(0.7408761.13399i)q82+(1.54695+0.837166i)q83+(1.388060.751179i)q86+(0.464369+0.159418i)q88+(0.4317961.70512i)q89+(0.7408761.13399i)q96+(0.8033911.83155i)q97+(0.4016950.915773i)q98+0.409883q99+O(q100)q+(0.789141 + 0.614213i) q^{2} +(0.917421 + 0.996584i) q^{3} +(0.245485 + 0.969400i) q^{4} +(0.111859 + 1.34994i) q^{6} +(-0.401695 + 0.915773i) q^{8} +(-0.0689406 + 0.831990i) q^{9} +(-0.0405441 - 0.489294i) q^{11} +(-0.740876 + 1.13399i) q^{12} +(-0.879474 + 0.475947i) q^{16} +(-0.431796 + 1.70512i) q^{17} +(-0.565423 + 0.614213i) q^{18} +(0.789141 - 0.614213i) q^{19} +(0.268536 - 0.411024i) q^{22} +(-1.28117 + 0.439826i) q^{24} +(0.546948 - 0.837166i) q^{25} +(0.176545 - 0.137410i) q^{27} +(-0.986361 - 0.164595i) q^{32} +(0.450427 - 0.489294i) q^{33} +(-1.38806 + 1.08037i) q^{34} +(-0.823455 + 0.137410i) q^{36} +1.00000 q^{38} +(-1.28117 - 0.439826i) q^{41} +(-1.55676 + 0.259777i) q^{43} +(0.464369 - 0.159418i) q^{44} +(-1.28117 - 0.439826i) q^{48} +(-0.879474 - 0.475947i) q^{49} +(0.945817 - 0.324699i) q^{50} +(-2.09544 + 1.13399i) q^{51} +0.223718 q^{54} +(1.33609 + 0.222954i) q^{57} +(1.49277 + 0.512467i) q^{59} +(-0.677282 - 0.735724i) q^{64} +(0.655981 - 0.109464i) q^{66} +(0.0663435 - 0.151248i) q^{67} -1.75895 q^{68} +(-0.734221 - 0.397341i) q^{72} +(0.464369 - 1.83375i) q^{73} +(1.33609 - 0.222954i) q^{75} +(0.789141 + 0.614213i) q^{76} +(1.12236 + 0.187289i) q^{81} +(-0.740876 - 1.13399i) q^{82} +(1.54695 + 0.837166i) q^{83} +(-1.38806 - 0.751179i) q^{86} +(0.464369 + 0.159418i) q^{88} +(-0.431796 - 1.70512i) q^{89} +(-0.740876 - 1.13399i) q^{96} +(-0.803391 - 1.83155i) q^{97} +(-0.401695 - 0.915773i) q^{98} +0.409883 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 18qq2+17q3q42q6q8+16q92q112q12q162q173q18q192q222q24q25+15q27q324q332q34+6q99+O(q100) 18 q - q^{2} + 17 q^{3} - q^{4} - 2 q^{6} - q^{8} + 16 q^{9} - 2 q^{11} - 2 q^{12} - q^{16} - 2 q^{17} - 3 q^{18} - q^{19} - 2 q^{22} - 2 q^{24} - q^{25} + 15 q^{27} - q^{32} - 4 q^{33} - 2 q^{34}+ \cdots - 6 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2888Z)×\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times.

nn 14451445 21672167 25292529
χ(n)\chi(n) 1-1 1-1 e(419)e\left(\frac{4}{19}\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 0.789141 + 0.614213i 0.789141 + 0.614213i
33 0.917421 + 0.996584i 0.917421 + 0.996584i 1.00000 00
−0.0825793 + 0.996584i 0.526316π0.526316\pi
44 0.245485 + 0.969400i 0.245485 + 0.969400i
55 0 0 0.879474 0.475947i 0.157895π-0.157895\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
66 0.111859 + 1.34994i 0.111859 + 1.34994i
77 0 0 0.245485 0.969400i 0.421053π-0.421053\pi
−0.245485 + 0.969400i 0.578947π0.578947\pi
88 −0.401695 + 0.915773i −0.401695 + 0.915773i
99 −0.0689406 + 0.831990i −0.0689406 + 0.831990i
1010 0 0
1111 −0.0405441 0.489294i −0.0405441 0.489294i −0.986361 0.164595i 0.947368π-0.947368\pi
0.945817 0.324699i 0.105263π-0.105263\pi
1212 −0.740876 + 1.13399i −0.740876 + 1.13399i
1313 0 0 −0.677282 0.735724i 0.736842π-0.736842\pi
0.677282 + 0.735724i 0.263158π0.263158\pi
1414 0 0
1515 0 0
1616 −0.879474 + 0.475947i −0.879474 + 0.475947i
1717 −0.431796 + 1.70512i −0.431796 + 1.70512i 0.245485 + 0.969400i 0.421053π0.421053\pi
−0.677282 + 0.735724i 0.736842π0.736842\pi
1818 −0.565423 + 0.614213i −0.565423 + 0.614213i
1919 0.789141 0.614213i 0.789141 0.614213i
2020 0 0
2121 0 0
2222 0.268536 0.411024i 0.268536 0.411024i
2323 0 0 0.677282 0.735724i 0.263158π-0.263158\pi
−0.677282 + 0.735724i 0.736842π0.736842\pi
2424 −1.28117 + 0.439826i −1.28117 + 0.439826i
2525 0.546948 0.837166i 0.546948 0.837166i
2626 0 0
2727 0.176545 0.137410i 0.176545 0.137410i
2828 0 0
2929 0 0 0.245485 0.969400i 0.421053π-0.421053\pi
−0.245485 + 0.969400i 0.578947π0.578947\pi
3030 0 0
3131 0 0 0.789141 0.614213i 0.210526π-0.210526\pi
−0.789141 + 0.614213i 0.789474π0.789474\pi
3232 −0.986361 0.164595i −0.986361 0.164595i
3333 0.450427 0.489294i 0.450427 0.489294i
3434 −1.38806 + 1.08037i −1.38806 + 1.08037i
3535 0 0
3636 −0.823455 + 0.137410i −0.823455 + 0.137410i
3737 0 0 −0.0825793 0.996584i 0.526316π-0.526316\pi
0.0825793 + 0.996584i 0.473684π0.473684\pi
3838 1.00000 1.00000
3939 0 0
4040 0 0
4141 −1.28117 0.439826i −1.28117 0.439826i −0.401695 0.915773i 0.631579π-0.631579\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
4242 0 0
4343 −1.55676 + 0.259777i −1.55676 + 0.259777i −0.879474 0.475947i 0.842105π-0.842105\pi
−0.677282 + 0.735724i 0.736842π0.736842\pi
4444 0.464369 0.159418i 0.464369 0.159418i
4545 0 0
4646 0 0
4747 0 0 −0.0825793 0.996584i 0.526316π-0.526316\pi
0.0825793 + 0.996584i 0.473684π0.473684\pi
4848 −1.28117 0.439826i −1.28117 0.439826i
4949 −0.879474 0.475947i −0.879474 0.475947i
5050 0.945817 0.324699i 0.945817 0.324699i
5151 −2.09544 + 1.13399i −2.09544 + 1.13399i
5252 0 0
5353 0 0 −0.0825793 0.996584i 0.526316π-0.526316\pi
0.0825793 + 0.996584i 0.473684π0.473684\pi
5454 0.223718 0.223718
5555 0 0
5656 0 0
5757 1.33609 + 0.222954i 1.33609 + 0.222954i
5858 0 0
5959 1.49277 + 0.512467i 1.49277 + 0.512467i 0.945817 0.324699i 0.105263π-0.105263\pi
0.546948 + 0.837166i 0.315789π0.315789\pi
6060 0 0
6161 0 0 −0.401695 0.915773i 0.631579π-0.631579\pi
0.401695 + 0.915773i 0.368421π0.368421\pi
6262 0 0
6363 0 0
6464 −0.677282 0.735724i −0.677282 0.735724i
6565 0 0
6666 0.655981 0.109464i 0.655981 0.109464i
6767 0.0663435 0.151248i 0.0663435 0.151248i −0.879474 0.475947i 0.842105π-0.842105\pi
0.945817 + 0.324699i 0.105263π0.105263\pi
6868 −1.75895 −1.75895
6969 0 0
7070 0 0
7171 0 0 0.401695 0.915773i 0.368421π-0.368421\pi
−0.401695 + 0.915773i 0.631579π0.631579\pi
7272 −0.734221 0.397341i −0.734221 0.397341i
7373 0.464369 1.83375i 0.464369 1.83375i −0.0825793 0.996584i 0.526316π-0.526316\pi
0.546948 0.837166i 0.315789π-0.315789\pi
7474 0 0
7575 1.33609 0.222954i 1.33609 0.222954i
7676 0.789141 + 0.614213i 0.789141 + 0.614213i
7777 0 0
7878 0 0
7979 0 0 0.986361 0.164595i 0.0526316π-0.0526316\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
8080 0 0
8181 1.12236 + 0.187289i 1.12236 + 0.187289i
8282 −0.740876 1.13399i −0.740876 1.13399i
8383 1.54695 + 0.837166i 1.54695 + 0.837166i 1.00000 00
0.546948 + 0.837166i 0.315789π0.315789\pi
8484 0 0
8585 0 0
8686 −1.38806 0.751179i −1.38806 0.751179i
8787 0 0
8888 0.464369 + 0.159418i 0.464369 + 0.159418i
8989 −0.431796 1.70512i −0.431796 1.70512i −0.677282 0.735724i 0.736842π-0.736842\pi
0.245485 0.969400i 0.421053π-0.421053\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0 0
9595 0 0
9696 −0.740876 1.13399i −0.740876 1.13399i
9797 −0.803391 1.83155i −0.803391 1.83155i −0.401695 0.915773i 0.631579π-0.631579\pi
−0.401695 0.915773i 0.631579π-0.631579\pi
9898 −0.401695 0.915773i −0.401695 0.915773i
9999 0.409883 0.409883
100100 0.945817 + 0.324699i 0.945817 + 0.324699i
101101 0 0 0.0825793 0.996584i 0.473684π-0.473684\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
102102 −2.35011 0.392164i −2.35011 0.392164i
103103 0 0 −0.245485 0.969400i 0.578947π-0.578947\pi
0.245485 + 0.969400i 0.421053π0.421053\pi
104104 0 0
105105 0 0
106106 0 0
107107 1.49277 + 1.16187i 1.49277 + 1.16187i 0.945817 + 0.324699i 0.105263π0.105263\pi
0.546948 + 0.837166i 0.315789π0.315789\pi
108108 0.176545 + 0.137410i 0.176545 + 0.137410i
109109 0 0 0.0825793 0.996584i 0.473684π-0.473684\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
110110 0 0
111111 0 0
112112 0 0
113113 0.387445 + 1.52999i 0.387445 + 1.52999i 0.789141 + 0.614213i 0.210526π0.210526\pi
−0.401695 + 0.915773i 0.631579π0.631579\pi
114114 0.917421 + 0.996584i 0.917421 + 0.996584i
115115 0 0
116116 0 0
117117 0 0
118118 0.863238 + 1.32128i 0.863238 + 1.32128i
119119 0 0
120120 0 0
121121 0.748596 0.124919i 0.748596 0.124919i
122122 0 0
123123 −0.737047 1.68030i −0.737047 1.68030i
124124 0 0
125125 0 0
126126 0 0
127127 0 0 1.00000 00
−1.00000 π\pi
128128 −0.0825793 0.996584i −0.0825793 0.996584i
129129 −1.68709 1.31311i −1.68709 1.31311i
130130 0 0
131131 −1.38806 + 1.08037i −1.38806 + 1.08037i −0.401695 + 0.915773i 0.631579π0.631579\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
132132 0.584895 + 0.316529i 0.584895 + 0.316529i
133133 0 0
134134 0.145253 0.0786068i 0.145253 0.0786068i
135135 0 0
136136 −1.38806 1.08037i −1.38806 1.08037i
137137 0.792434 1.80657i 0.792434 1.80657i 0.245485 0.969400i 0.421053π-0.421053\pi
0.546948 0.837166i 0.315789π-0.315789\pi
138138 0 0
139139 −1.07898 + 0.180049i −1.07898 + 0.180049i −0.677282 0.735724i 0.736842π-0.736842\pi
−0.401695 + 0.915773i 0.631579π0.631579\pi
140140 0 0
141141 0 0
142142 0 0
143143 0 0
144144 −0.335352 0.764525i −0.335352 0.764525i
145145 0 0
146146 1.49277 1.16187i 1.49277 1.16187i
147147 −0.332526 1.31311i −0.332526 1.31311i
148148 0 0
149149 0 0 0.945817 0.324699i 0.105263π-0.105263\pi
−0.945817 + 0.324699i 0.894737π0.894737\pi
150150 1.19130 + 0.644701i 1.19130 + 0.644701i
151151 0 0 0.945817 0.324699i 0.105263π-0.105263\pi
−0.945817 + 0.324699i 0.894737π0.894737\pi
152152 0.245485 + 0.969400i 0.245485 + 0.969400i
153153 −1.38888 0.476802i −1.38888 0.476802i
154154 0 0
155155 0 0
156156 0 0
157157 0 0 −0.677282 0.735724i 0.736842π-0.736842\pi
0.677282 + 0.735724i 0.263158π0.263158\pi
158158 0 0
159159 0 0
160160 0 0
161161 0 0
162162 0.770666 + 0.837166i 0.770666 + 0.837166i
163163 0.863238 + 0.671885i 0.863238 + 0.671885i 0.945817 0.324699i 0.105263π-0.105263\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
164164 0.111859 1.34994i 0.111859 1.34994i
165165 0 0
166166 0.706561 + 1.61080i 0.706561 + 1.61080i
167167 0 0 0.245485 0.969400i 0.421053π-0.421053\pi
−0.245485 + 0.969400i 0.578947π0.578947\pi
168168 0 0
169169 −0.0825793 + 0.996584i −0.0825793 + 0.996584i
170170 0 0
171171 0.456615 + 0.698901i 0.456615 + 0.698901i
172172 −0.633988 1.44535i −0.633988 1.44535i
173173 0 0 0.945817 0.324699i 0.105263π-0.105263\pi
−0.945817 + 0.324699i 0.894737π0.894737\pi
174174 0 0
175175 0 0
176176 0.268536 + 0.411024i 0.268536 + 0.411024i
177177 0.858777 + 1.95781i 0.858777 + 1.95781i
178178 0.706561 1.61080i 0.706561 1.61080i
179179 −1.55676 0.259777i −1.55676 0.259777i −0.677282 0.735724i 0.736842π-0.736842\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
180180 0 0
181181 0 0 0.789141 0.614213i 0.210526π-0.210526\pi
−0.789141 + 0.614213i 0.789474π0.789474\pi
182182 0 0
183183 0 0
184184 0 0
185185 0 0
186186 0 0
187187 0.851814 + 0.142143i 0.851814 + 0.142143i
188188 0 0
189189 0 0
190190 0 0
191191 0 0 0.401695 0.915773i 0.368421π-0.368421\pi
−0.401695 + 0.915773i 0.631579π0.631579\pi
192192 0.111859 1.34994i 0.111859 1.34994i
193193 0.0136387 + 0.164595i 0.0136387 + 0.164595i 1.00000 00
−0.986361 + 0.164595i 0.947368π0.947368\pi
194194 0.490971 1.93880i 0.490971 1.93880i
195195 0 0
196196 0.245485 0.969400i 0.245485 0.969400i
197197 0 0 0.0825793 0.996584i 0.473684π-0.473684\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
198198 0.323455 + 0.251755i 0.323455 + 0.251755i
199199 0 0 −0.677282 0.735724i 0.736842π-0.736842\pi
0.677282 + 0.735724i 0.263158π0.263158\pi
200200 0.546948 + 0.837166i 0.546948 + 0.837166i
201201 0.211596 0.0726411i 0.211596 0.0726411i
202202 0 0
203203 0 0
204204 −1.61369 1.75294i −1.61369 1.75294i
205205 0 0
206206 0 0
207207 0 0
208208 0 0
209209 −0.332526 0.361219i −0.332526 0.361219i
210210 0 0
211211 0.706561 + 0.382372i 0.706561 + 0.382372i 0.789141 0.614213i 0.210526π-0.210526\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
212212 0 0
213213 0 0
214214 0.464369 + 1.83375i 0.464369 + 1.83375i
215215 0 0
216216 0.0549195 + 0.216872i 0.0549195 + 0.216872i
217217 0 0
218218 0 0
219219 2.25351 1.21954i 2.25351 1.21954i
220220 0 0
221221 0 0
222222 0 0
223223 0 0 −0.789141 0.614213i 0.789474π-0.789474\pi
0.789141 + 0.614213i 0.210526π0.210526\pi
224224 0 0
225225 0.658807 + 0.512770i 0.658807 + 0.512770i
226226 −0.633988 + 1.44535i −0.633988 + 1.44535i
227227 0.706561 0.382372i 0.706561 0.382372i −0.0825793 0.996584i 0.526316π-0.526316\pi
0.789141 + 0.614213i 0.210526π0.210526\pi
228228 0.111859 + 1.34994i 0.111859 + 1.34994i
229229 0 0 −0.879474 0.475947i 0.842105π-0.842105\pi
0.879474 + 0.475947i 0.157895π0.157895\pi
230230 0 0
231231 0 0
232232 0 0
233233 −0.165159 1.99317i −0.165159 1.99317i −0.0825793 0.996584i 0.526316π-0.526316\pi
−0.0825793 0.996584i 0.526316π-0.526316\pi
234234 0 0
235235 0 0
236236 −0.130333 + 1.57289i −0.130333 + 1.57289i
237237 0 0
238238 0 0
239239 0 0 0.245485 0.969400i 0.421053π-0.421053\pi
−0.245485 + 0.969400i 0.578947π0.578947\pi
240240 0 0
241241 −1.28117 + 1.39172i −1.28117 + 1.39172i −0.401695 + 0.915773i 0.631579π0.631579\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
242242 0.667474 + 0.361219i 0.667474 + 0.361219i
243243 0.720667 + 1.10306i 0.720667 + 1.10306i
244244 0 0
245245 0 0
246246 0.450427 1.77870i 0.450427 1.77870i
247247 0 0
248248 0 0
249249 0.584895 + 2.30970i 0.584895 + 2.30970i
250250 0 0
251251 −0.0405441 + 0.489294i −0.0405441 + 0.489294i 0.945817 + 0.324699i 0.105263π0.105263\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
252252 0 0
253253 0 0
254254 0 0
255255 0 0
256256 0.546948 0.837166i 0.546948 0.837166i
257257 −0.156210 + 0.0536269i −0.156210 + 0.0536269i −0.401695 0.915773i 0.631579π-0.631579\pi
0.245485 + 0.969400i 0.421053π0.421053\pi
258258 −0.524819 2.07246i −0.524819 2.07246i
259259 0 0
260260 0 0
261261 0 0
262262 −1.75895 −1.75895
263263 0 0 −0.401695 0.915773i 0.631579π-0.631579\pi
0.401695 + 0.915773i 0.368421π0.368421\pi
264264 0.267148 + 0.609036i 0.267148 + 0.609036i
265265 0 0
266266 0 0
267267 1.30316 1.99464i 1.30316 1.99464i
268268 0.162906 + 0.0271842i 0.162906 + 0.0271842i
269269 0 0 −0.879474 0.475947i 0.842105π-0.842105\pi
0.879474 + 0.475947i 0.157895π0.157895\pi
270270 0 0
271271 0 0 0.245485 0.969400i 0.421053π-0.421053\pi
−0.245485 + 0.969400i 0.578947π0.578947\pi
272272 −0.431796 1.70512i −0.431796 1.70512i
273273 0 0
274274 1.73496 0.938912i 1.73496 0.938912i
275275 −0.431796 0.233676i −0.431796 0.233676i
276276 0 0
277277 0 0 −0.677282 0.735724i 0.736842π-0.736842\pi
0.677282 + 0.735724i 0.263158π0.263158\pi
278278 −0.962053 0.520637i −0.962053 0.520637i
279279 0 0
280280 0 0
281281 −0.439413 + 0.672572i −0.439413 + 0.672572i −0.986361 0.164595i 0.947368π-0.947368\pi
0.546948 + 0.837166i 0.315789π0.315789\pi
282282 0 0
283283 −1.35456 + 1.47145i −1.35456 + 1.47145i −0.677282 + 0.735724i 0.736842π0.736842\pi
−0.677282 + 0.735724i 0.736842π0.736842\pi
284284 0 0
285285 0 0
286286 0 0
287287 0 0
288288 0.204941 0.809295i 0.204941 0.809295i
289289 −1.84153 0.996584i −1.84153 0.996584i
290290 0 0
291291 1.08824 2.48095i 1.08824 2.48095i
292292 1.89163 1.89163
293293 0 0 1.00000 00
−1.00000 π\pi
294294 0.544122 1.24047i 0.544122 1.24047i
295295 0 0
296296 0 0
297297 −0.0743919 0.0808112i −0.0743919 0.0808112i
298298 0 0
299299 0 0
300300 0.544122 + 1.24047i 0.544122 + 1.24047i
301301 0 0
302302 0 0
303303 0 0
304304 −0.401695 + 0.915773i −0.401695 + 0.915773i
305305 0 0
306306 −0.803162 1.22933i −0.803162 1.22933i
307307 −1.35456 −1.35456 −0.677282 0.735724i 0.736842π-0.736842\pi
−0.677282 + 0.735724i 0.736842π0.736842\pi
308308 0 0
309309 0 0
310310 0 0
311311 0 0 0.945817 0.324699i 0.105263π-0.105263\pi
−0.945817 + 0.324699i 0.894737π0.894737\pi
312312 0 0
313313 −1.86584 0.640542i −1.86584 0.640542i −0.986361 0.164595i 0.947368π-0.947368\pi
−0.879474 0.475947i 0.842105π-0.842105\pi
314314 0 0
315315 0 0
316316 0 0
317317 0 0 0.945817 0.324699i 0.105263π-0.105263\pi
−0.945817 + 0.324699i 0.894737π0.894737\pi
318318 0 0
319319 0 0
320320 0 0
321321 0.211596 + 2.55359i 0.211596 + 2.55359i
322322 0 0
323323 0.706561 + 1.61080i 0.706561 + 1.61080i
324324 0.0939655 + 1.13399i 0.0939655 + 1.13399i
325325 0 0
326326 0.268536 + 1.06042i 0.268536 + 1.06042i
327327 0 0
328328 0.917421 0.996584i 0.917421 0.996584i
329329 0 0
330330 0 0
331331 −0.439413 0.672572i −0.439413 0.672572i 0.546948 0.837166i 0.315789π-0.315789\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
332332 −0.431796 + 1.70512i −0.431796 + 1.70512i
333333 0 0
334334 0 0
335335 0 0
336336 0 0
337337 1.03463 0.355188i 1.03463 0.355188i 0.245485 0.969400i 0.421053π-0.421053\pi
0.789141 + 0.614213i 0.210526π0.210526\pi
338338 −0.677282 + 0.735724i −0.677282 + 0.735724i
339339 −1.16931 + 1.78976i −1.16931 + 1.78976i
340340 0 0
341341 0 0
342342 −0.0689406 + 0.831990i −0.0689406 + 0.831990i
343343 0 0
344344 0.387445 1.52999i 0.387445 1.52999i
345345 0 0
346346 0 0
347347 0.387445 0.301561i 0.387445 0.301561i −0.401695 0.915773i 0.631579π-0.631579\pi
0.789141 + 0.614213i 0.210526π0.210526\pi
348348 0 0
349349 0 0 0.546948 0.837166i 0.315789π-0.315789\pi
−0.546948 + 0.837166i 0.684211π0.684211\pi
350350 0 0
351351 0 0
352352 −0.0405441 + 0.489294i −0.0405441 + 0.489294i
353353 −0.439413 + 1.00176i −0.439413 + 1.00176i 0.546948 + 0.837166i 0.315789π0.315789\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
354354 −0.524819 + 2.07246i −0.524819 + 2.07246i
355355 0 0
356356 1.54695 0.837166i 1.54695 0.837166i
357357 0 0
358358 −1.06894 1.16118i −1.06894 1.16118i
359359 0 0 −0.789141 0.614213i 0.789474π-0.789474\pi
0.789141 + 0.614213i 0.210526π0.210526\pi
360360 0 0
361361 0.245485 0.969400i 0.245485 0.969400i
362362 0 0
363363 0.811270 + 0.631437i 0.811270 + 0.631437i
364364 0 0
365365 0 0
366366 0 0
367367 0 0 −0.0825793 0.996584i 0.526316π-0.526316\pi
0.0825793 + 0.996584i 0.473684π0.473684\pi
368368 0 0
369369 0.454255 1.03560i 0.454255 1.03560i
370370 0 0
371371 0 0
372372 0 0
373373 0 0 0.546948 0.837166i 0.315789π-0.315789\pi
−0.546948 + 0.837166i 0.684211π0.684211\pi
374374 0.584895 + 0.635365i 0.584895 + 0.635365i
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 0.111859 0.121511i 0.111859 0.121511i −0.677282 0.735724i 0.736842π-0.736842\pi
0.789141 + 0.614213i 0.210526π0.210526\pi
380380 0 0
381381 0 0
382382 0 0
383383 0 0 0.546948 0.837166i 0.315789π-0.315789\pi
−0.546948 + 0.837166i 0.684211π0.684211\pi
384384 0.917421 0.996584i 0.917421 0.996584i
385385 0 0
386386 −0.0903332 + 0.138265i −0.0903332 + 0.138265i
387387 −0.108808 1.31311i −0.108808 1.31311i
388388 1.57828 1.22843i 1.57828 1.22843i
389389 0 0 1.00000 00
−1.00000 π\pi
390390 0 0
391391 0 0
392392 0.789141 0.614213i 0.789141 0.614213i
393393 −2.35011 0.392164i −2.35011 0.392164i
394394 0 0
395395 0 0
396396 0.100620 + 0.397341i 0.100620 + 0.397341i
397397 0 0 0.986361 0.164595i 0.0526316π-0.0526316\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
398398 0 0
399399 0 0
400400 −0.0825793 + 0.996584i −0.0825793 + 0.996584i
401401 0.162906 + 1.96598i 0.162906 + 1.96598i 0.245485 + 0.969400i 0.421053π0.421053\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
402402 0.211596 + 0.0726411i 0.211596 + 0.0726411i
403403 0 0
404404 0 0
405405 0 0
406406 0 0
407407 0 0
408408 −0.196754 2.37447i −0.196754 2.37447i
409409 −0.759861 0.260861i −0.759861 0.260861i −0.0825793 0.996584i 0.526316π-0.526316\pi
−0.677282 + 0.735724i 0.736842π0.736842\pi
410410 0 0
411411 2.52739 0.867655i 2.52739 0.867655i
412412 0 0
413413 0 0
414414 0 0
415415 0 0
416416 0 0
417417 −1.16931 0.910111i −1.16931 0.910111i
418418 −0.0405441 0.489294i −0.0405441 0.489294i
419419 0.387445 0.301561i 0.387445 0.301561i −0.401695 0.915773i 0.631579π-0.631579\pi
0.789141 + 0.614213i 0.210526π0.210526\pi
420420 0 0
421421 0 0 0.0825793 0.996584i 0.473684π-0.473684\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
422422 0.322718 + 0.735724i 0.322718 + 0.735724i
423423 0 0
424424 0 0
425425 1.19130 + 1.29410i 1.19130 + 1.29410i
426426 0 0
427427 0 0
428428 −0.759861 + 1.73231i −0.759861 + 1.73231i
429429 0 0
430430 0 0
431431 0 0 0.401695 0.915773i 0.368421π-0.368421\pi
−0.401695 + 0.915773i 0.631579π0.631579\pi
432432 −0.0898664 + 0.204875i −0.0898664 + 0.204875i
433433 1.19130 + 0.644701i 1.19130 + 0.644701i 0.945817 0.324699i 0.105263π-0.105263\pi
0.245485 + 0.969400i 0.421053π0.421053\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
438438 2.52739 + 0.421747i 2.52739 + 0.421747i
439439 0 0 0.677282 0.735724i 0.263158π-0.263158\pi
−0.677282 + 0.735724i 0.736842π0.736842\pi
440440 0 0
441441 0.456615 0.698901i 0.456615 0.698901i
442442 0 0
443443 0.863238 + 1.32128i 0.863238 + 1.32128i 0.945817 + 0.324699i 0.105263π0.105263\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 −1.28117 0.439826i −1.28117 0.439826i −0.401695 0.915773i 0.631579π-0.631579\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
450450 0.204941 + 0.809295i 0.204941 + 0.809295i
451451 −0.163260 + 0.644701i −0.163260 + 0.644701i
452452 −1.38806 + 0.751179i −1.38806 + 0.751179i
453453 0 0
454454 0.792434 + 0.132234i 0.792434 + 0.132234i
455455 0 0
456456 −0.740876 + 1.13399i −0.740876 + 1.13399i
457457 −0.439413 0.672572i −0.439413 0.672572i 0.546948 0.837166i 0.315789π-0.315789\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
458458 0 0
459459 0.158070 + 0.360364i 0.158070 + 0.360364i
460460 0 0
461461 0 0 −0.945817 0.324699i 0.894737π-0.894737\pi
0.945817 + 0.324699i 0.105263π0.105263\pi
462462 0 0
463463 0 0 −0.986361 0.164595i 0.947368π-0.947368\pi
0.986361 + 0.164595i 0.0526316π0.0526316\pi
464464 0 0
465465 0 0
466466 1.09390 1.67433i 1.09390 1.67433i
467467 1.03463 1.58361i 1.03463 1.58361i 0.245485 0.969400i 0.421053π-0.421053\pi
0.789141 0.614213i 0.210526π-0.210526\pi
468468 0 0
469469 0 0
470470 0 0
471471 0 0
472472 −1.06894 + 1.16118i −1.06894 + 1.16118i
473473 0.190224 + 0.751179i 0.190224 + 0.751179i
474474 0 0
475475 −0.0825793 0.996584i −0.0825793 0.996584i
476476 0 0
477477 0 0
478478 0 0
479479 0 0 −0.546948 0.837166i 0.684211π-0.684211\pi
0.546948 + 0.837166i 0.315789π0.315789\pi
480480 0 0
481481 0 0
482482 −1.86584 + 0.311353i −1.86584 + 0.311353i
483483 0 0
484484 0.304866 + 0.695024i 0.304866 + 0.695024i
485485 0 0
486486 −0.108808 + 1.31311i −0.108808 + 1.31311i
487487 0 0 −0.546948 0.837166i 0.684211π-0.684211\pi
0.546948 + 0.837166i 0.315789π0.315789\pi
488488 0 0
489489 0.122362 + 1.47669i 0.122362 + 1.47669i
490490 0 0
491491 −1.07898 1.65150i −1.07898 1.65150i −0.677282 0.735724i 0.736842π-0.736842\pi
−0.401695 0.915773i 0.631579π-0.631579\pi
492492 1.44795 1.12698i 1.44795 1.12698i
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 0 0
498498 −0.957082 + 2.18193i −0.957082 + 2.18193i
499499 −0.633988 0.493453i −0.633988 0.493453i 0.245485 0.969400i 0.421053π-0.421053\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
500500 0 0
501501 0 0
502502 −0.332526 + 0.361219i −0.332526 + 0.361219i
503503 0 0 0.879474 0.475947i 0.157895π-0.157895\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
504504 0 0
505505 0 0
506506 0 0
507507 −1.06894 + 0.831990i −1.06894 + 0.831990i
508508 0 0
509509 0 0 0.945817 0.324699i 0.105263π-0.105263\pi
−0.945817 + 0.324699i 0.894737π0.894737\pi
510510 0 0
511511 0 0
512512 0.945817 0.324699i 0.945817 0.324699i
513513 0.0549195 0.216872i 0.0549195 0.216872i
514514 −0.156210 0.0536269i −0.156210 0.0536269i
515515 0 0
516516 0.858777 1.95781i 0.858777 1.95781i
517517 0 0
518518 0 0
519519 0 0
520520 0 0
521521 0.464369 0.159418i 0.464369 0.159418i −0.0825793 0.996584i 0.526316π-0.526316\pi
0.546948 + 0.837166i 0.315789π0.315789\pi
522522 0 0
523523 1.19130 + 1.29410i 1.19130 + 1.29410i 0.945817 + 0.324699i 0.105263π0.105263\pi
0.245485 + 0.969400i 0.421053π0.421053\pi
524524 −1.38806 1.08037i −1.38806 1.08037i
525525 0 0
526526 0 0
527527 0 0
528528 −0.163260 + 0.644701i −0.163260 + 0.644701i
529529 −0.0825793 0.996584i −0.0825793 0.996584i
530530 0 0
531531 −0.529280 + 1.20664i −0.529280 + 1.20664i
532532 0 0
533533 0 0
534534 2.25351 0.773631i 2.25351 0.773631i
535535 0 0
536536 0.111859 + 0.121511i 0.111859 + 0.121511i
537537 −1.16931 1.78976i −1.16931 1.78976i
538538 0 0
539539 −0.197221 + 0.449618i −0.197221 + 0.449618i
540540 0 0
541541 0 0 0.789141 0.614213i 0.210526π-0.210526\pi
−0.789141 + 0.614213i 0.789474π0.789474\pi
542542 0 0
543543 0 0
544544 0.706561 1.61080i 0.706561 1.61080i
545545 0 0
546546 0 0
547547 0.111859 + 0.121511i 0.111859 + 0.121511i 0.789141 0.614213i 0.210526π-0.210526\pi
−0.677282 + 0.735724i 0.736842π0.736842\pi
548548 1.94582 + 0.324699i 1.94582 + 0.324699i
549549 0 0
550550 −0.197221 0.449618i −0.197221 0.449618i
551551 0 0
552552 0 0
553553 0 0
554554 0 0
555555 0 0
556556 −0.439413 1.00176i −0.439413 1.00176i
557557 0 0 0.245485 0.969400i 0.421053π-0.421053\pi
−0.245485 + 0.969400i 0.578947π0.578947\pi
558558 0 0
559559 0 0
560560 0 0
561561 0.639815 + 0.979309i 0.639815 + 0.979309i
562562 −0.759861 + 0.260861i −0.759861 + 0.260861i
563563 −1.28117 + 1.39172i −1.28117 + 1.39172i −0.401695 + 0.915773i 0.631579π0.631579\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
564564 0 0
565565 0 0
566566 −1.97272 + 0.329189i −1.97272 + 0.329189i
567567 0 0
568568 0 0
569569 −1.86584 0.640542i −1.86584 0.640542i −0.986361 0.164595i 0.947368π-0.947368\pi
−0.879474 0.475947i 0.842105π-0.842105\pi
570570 0 0
571571 1.78914 0.614213i 1.78914 0.614213i 0.789141 0.614213i 0.210526π-0.210526\pi
1.00000 00
572572 0 0
573573 0 0
574574 0 0
575575 0 0
576576 0.658807 0.512770i 0.658807 0.512770i
577577 −0.332526 1.31311i −0.332526 1.31311i −0.879474 0.475947i 0.842105π-0.842105\pi
0.546948 0.837166i 0.315789π-0.315789\pi
578578 −0.841109 1.91753i −0.841109 1.91753i
579579 −0.151520 + 0.164595i −0.151520 + 0.164595i
580580 0 0
581581 0 0
582582 2.38261 1.28940i 2.38261 1.28940i
583583 0 0
584584 1.49277 + 1.16187i 1.49277 + 1.16187i
585585 0 0
586586 0 0
587587 −0.197221 + 0.449618i −0.197221 + 0.449618i −0.986361 0.164595i 0.947368π-0.947368\pi
0.789141 + 0.614213i 0.210526π0.210526\pi
588588 1.19130 0.644701i 1.19130 0.644701i
589589 0 0
590590 0 0
591591 0 0
592592 0 0
593593 0.863238 + 0.671885i 0.863238 + 0.671885i 0.945817 0.324699i 0.105263π-0.105263\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
594594 −0.00907043 0.109464i −0.00907043 0.109464i
595595 0 0
596596 0 0
597597 0 0
598598 0 0
599599 0 0 −0.401695 0.915773i 0.631579π-0.631579\pi
0.401695 + 0.915773i 0.368421π0.368421\pi
600600 −0.332526 + 1.31311i −0.332526 + 1.31311i
601601 −1.97272 + 0.329189i −1.97272 + 0.329189i −0.986361 + 0.164595i 0.947368π0.947368\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
602602 0 0
603603 0.121263 + 0.0656242i 0.121263 + 0.0656242i
604604 0 0
605605 0 0
606606 0 0
607607 0 0 0.245485 0.969400i 0.421053π-0.421053\pi
−0.245485 + 0.969400i 0.578947π0.578947\pi
608608 −0.879474 + 0.475947i −0.879474 + 0.475947i
609609 0 0
610610 0 0
611611 0 0
612612 0.121263 1.46343i 0.121263 1.46343i
613613 0 0 0.0825793 0.996584i 0.473684π-0.473684\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
614614 −1.06894 0.831990i −1.06894 0.831990i
615615 0 0
616616 0 0
617617 −0.962053 + 1.47253i −0.962053 + 1.47253i −0.0825793 + 0.996584i 0.526316π0.526316\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
618618 0 0
619619 −0.197221 0.778807i −0.197221 0.778807i −0.986361 0.164595i 0.947368π-0.947368\pi
0.789141 0.614213i 0.210526π-0.210526\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 −0.401695 0.915773i −0.401695 0.915773i
626626 −1.07898 1.65150i −1.07898 1.65150i
627627 0.0549195 0.662780i 0.0549195 0.662780i
628628 0 0
629629 0 0
630630 0 0
631631 0 0 0.879474 0.475947i 0.157895π-0.157895\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
632632 0 0
633633 0.267148 + 1.05494i 0.267148 + 1.05494i
634634 0 0
635635 0 0
636636 0 0
637637 0 0
638638 0 0
639639 0 0
640640 0 0
641641 −1.55676 0.259777i −1.55676 0.259777i −0.677282 0.735724i 0.736842π-0.736842\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
642642 −1.40147 + 2.14510i −1.40147 + 2.14510i
643643 −1.86584 + 0.311353i −1.86584 + 0.311353i −0.986361 0.164595i 0.947368π-0.947368\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
644644 0 0
645645 0 0
646646 −0.431796 + 1.70512i −0.431796 + 1.70512i
647647 0 0 0.986361 0.164595i 0.0526316π-0.0526316\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
648648 −0.622362 + 0.952596i −0.622362 + 0.952596i
649649 0.190224 0.751179i 0.190224 0.751179i
650650 0 0
651651 0 0
652652 −0.439413 + 1.00176i −0.439413 + 1.00176i
653653 0 0 1.00000 00
−1.00000 π\pi
654654 0 0
655655 0 0
656656 1.33609 0.222954i 1.33609 0.222954i
657657 1.49365 + 0.512770i 1.49365 + 0.512770i
658658 0 0
659659 0.464369 + 0.159418i 0.464369 + 0.159418i 0.546948 0.837166i 0.315789π-0.315789\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
660660 0 0
661661 0 0 −0.401695 0.915773i 0.631579π-0.631579\pi
0.401695 + 0.915773i 0.368421π0.368421\pi
662662 0.0663435 0.800647i 0.0663435 0.800647i
663663 0 0
664664 −1.38806 + 1.08037i −1.38806 + 1.08037i
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 1.19130 + 0.644701i 1.19130 + 0.644701i 0.945817 0.324699i 0.105263π-0.105263\pi
0.245485 + 0.969400i 0.421053π0.421053\pi
674674 1.03463 + 0.355188i 1.03463 + 0.355188i
675675 −0.0184745 0.222954i −0.0184745 0.222954i
676676 −0.986361 + 0.164595i −0.986361 + 0.164595i
677677 0 0 −0.401695 0.915773i 0.631579π-0.631579\pi
0.401695 + 0.915773i 0.368421π0.368421\pi
678678 −2.02204 + 0.694169i −2.02204 + 0.694169i
679679 0 0
680680 0 0
681681 1.02928 + 0.353352i 1.02928 + 0.353352i
682682 0 0
683683 0.111859 1.34994i 0.111859 1.34994i −0.677282 0.735724i 0.736842π-0.736842\pi
0.789141 0.614213i 0.210526π-0.210526\pi
684684 −0.565423 + 0.614213i −0.565423 + 0.614213i
685685 0 0
686686 0 0
687687 0 0
688688 1.24549 0.969400i 1.24549 0.969400i
689689 0 0
690690 0 0
691691 −0.130333 + 0.101443i −0.130333 + 0.101443i −0.677282 0.735724i 0.736842π-0.736842\pi
0.546948 + 0.837166i 0.315789π0.315789\pi
692692 0 0
693693 0 0
694694 0.490971 0.490971
695695 0 0
696696 0 0
697697 1.30316 1.99464i 1.30316 1.99464i
698698 0 0
699699 1.83484 1.99317i 1.83484 1.99317i
700700 0 0
701701 0 0 0.879474 0.475947i 0.157895π-0.157895\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
702702 0 0
703703 0 0
704704 −0.332526 + 0.361219i −0.332526 + 0.361219i
705705 0 0
706706 −0.962053 + 0.520637i −0.962053 + 0.520637i
707707 0 0
708708 −1.68709 + 1.31311i −1.68709 + 1.31311i
709709 0 0 −0.677282 0.735724i 0.736842π-0.736842\pi
0.677282 + 0.735724i 0.263158π0.263158\pi
710710 0 0
711711 0 0
712712 1.73496 + 0.289513i 1.73496 + 0.289513i
713713 0 0
714714 0 0
715715 0 0
716716 −0.130333 1.57289i −0.130333 1.57289i
717717 0 0
718718 0 0
719719 0 0 −0.677282 0.735724i 0.736842π-0.736842\pi
0.677282 + 0.735724i 0.263158π0.263158\pi
720720 0 0
721721 0 0
722722 0.789141 0.614213i 0.789141 0.614213i
723723 −2.56234 −2.56234
724724 0 0
725725 0 0
726726 0.252369 + 0.996584i 0.252369 + 0.996584i
727727 0 0 0.879474 0.475947i 0.157895π-0.157895\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
728728 0 0
729729 −0.158807 + 0.627115i −0.158807 + 0.627115i
730730 0 0
731731 0.229250 2.76663i 0.229250 2.76663i
732732 0 0
733733 0 0 −0.0825793 0.996584i 0.526316π-0.526316\pi
0.0825793 + 0.996584i 0.473684π0.473684\pi
734734 0 0
735735 0 0
736736 0 0
737737 −0.0766945 0.0263293i −0.0766945 0.0263293i
738738 0.994549 0.538223i 0.994549 0.538223i
739739 0.268536 1.06042i 0.268536 1.06042i −0.677282 0.735724i 0.736842π-0.736842\pi
0.945817 0.324699i 0.105263π-0.105263\pi
740740 0 0
741741 0 0
742742 0 0
743743 0 0 0.879474 0.475947i 0.157895π-0.157895\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
744744 0 0
745745 0 0
746746 0 0
747747 −0.803162 + 1.22933i −0.803162 + 1.22933i
748748 0.0713149 + 0.860643i 0.0713149 + 0.860643i
749749 0 0
750750 0 0
751751 0 0 0.245485 0.969400i 0.421053π-0.421053\pi
−0.245485 + 0.969400i 0.578947π0.578947\pi
752752 0 0
753753 −0.524819 + 0.408483i −0.524819 + 0.408483i
754754 0 0
755755 0 0
756756 0 0
757757 0 0 −0.245485 0.969400i 0.578947π-0.578947\pi
0.245485 + 0.969400i 0.421053π0.421053\pi
758758 0.162906 0.0271842i 0.162906 0.0271842i
759759 0 0
760760 0 0
761761 −0.156210 + 1.88517i −0.156210 + 1.88517i 0.245485 + 0.969400i 0.421053π0.421053\pi
−0.401695 + 0.915773i 0.631579π0.631579\pi
762762 0 0
763763 0 0
764764 0 0
765765 0 0
766766 0 0
767767 0 0
768768 1.33609 0.222954i 1.33609 0.222954i
769769 0.0136387 + 0.164595i 0.0136387 + 0.164595i 1.00000 00
−0.986361 + 0.164595i 0.947368π0.947368\pi
770770 0 0
771771 −0.196754 0.106478i −0.196754 0.106478i
772772 −0.156210 + 0.0536269i −0.156210 + 0.0536269i
773773 0 0 0.879474 0.475947i 0.157895π-0.157895\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
774774 0.720667 1.10306i 0.720667 1.10306i
775775 0 0
776776 2.00000 2.00000
777777 0 0
778778 0 0
779779 −1.28117 + 0.439826i −1.28117 + 0.439826i
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 1.00000 1.00000
785785 0 0
786786 −1.61369 1.75294i −1.61369 1.75294i
787787 −0.156210 0.0536269i −0.156210 0.0536269i 0.245485 0.969400i 0.421053π-0.421053\pi
−0.401695 + 0.915773i 0.631579π0.631579\pi
788788 0 0
789789 0 0
790790 0 0
791791 0 0
792792 −0.164648 + 0.375360i −0.164648 + 0.375360i
793793 0 0
794794 0 0
795795 0 0
796796 0 0
797797 0 0 0.986361 0.164595i 0.0526316π-0.0526316\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
798798 0 0
799799 0 0
800800 −0.677282 + 0.735724i −0.677282 + 0.735724i
801801 1.44841 0.241698i 1.44841 0.241698i
802802 −1.07898 + 1.65150i −1.07898 + 1.65150i
803803 −0.916071 0.152865i −0.916071 0.152865i
804804 0.122362 + 0.187289i 0.122362 + 0.187289i
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 1.19130 0.644701i 1.19130 0.644701i 0.245485 0.969400i 0.421053π-0.421053\pi
0.945817 + 0.324699i 0.105263π0.105263\pi
810810 0 0
811811 0.464369 + 1.83375i 0.464369 + 1.83375i 0.546948 + 0.837166i 0.315789π0.315789\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
812812 0 0
813813 0 0
814814 0 0
815815 0 0
816816 1.30316 1.99464i 1.30316 1.99464i
817817 −1.06894 + 1.16118i −1.06894 + 1.16118i
818818 −0.439413 0.672572i −0.439413 0.672572i
819819 0 0
820820 0 0
821821 0 0 1.00000 00
−1.00000 π\pi
822822 2.52739 + 0.867655i 2.52739 + 0.867655i
823823 0 0 0.0825793 0.996584i 0.473684π-0.473684\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
824824 0 0
825825 −0.163260 0.644701i −0.163260 0.644701i
826826 0 0
827827 −0.740876 + 1.13399i −0.740876 + 1.13399i 0.245485 + 0.969400i 0.421053π0.421053\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
828828 0 0
829829 0 0 −0.789141 0.614213i 0.789474π-0.789474\pi
0.789141 + 0.614213i 0.210526π0.210526\pi
830830 0 0
831831 0 0
832832 0 0
833833 1.19130 1.29410i 1.19130 1.29410i
834834 −0.363749 1.43641i −0.363749 1.43641i
835835 0 0
836836 0.268536 0.411024i 0.268536 0.411024i
837837 0 0
838838 0.490971 0.490971
839839 0 0 0.789141 0.614213i 0.210526π-0.210526\pi
−0.789141 + 0.614213i 0.789474π0.789474\pi
840840 0 0
841841 −0.879474 0.475947i −0.879474 0.475947i
842842 0 0
843843 −1.07340 + 0.179119i −1.07340 + 0.179119i
844844 −0.197221 + 0.778807i −0.197221 + 0.778807i
845845 0 0
846846 0 0
847847 0 0
848848 0 0
849849 −2.70913 −2.70913
850850 0.145253 + 1.75294i 0.145253 + 1.75294i
851851 0 0
852852 0 0
853853 0 0 0.789141 0.614213i 0.210526π-0.210526\pi
−0.789141 + 0.614213i 0.789474π0.789474\pi
854854 0 0
855855 0 0
856856 −1.66364 + 0.900319i −1.66364 + 0.900319i
857857 0.322718 0.735724i 0.322718 0.735724i −0.677282 0.735724i 0.736842π-0.736842\pi
1.00000 00
858858 0 0
859859 0.706561 1.61080i 0.706561 1.61080i −0.0825793 0.996584i 0.526316π-0.526316\pi
0.789141 0.614213i 0.210526π-0.210526\pi
860860 0 0
861861 0 0
862862 0 0
863863 0 0 0.677282 0.735724i 0.263158π-0.263158\pi
−0.677282 + 0.735724i 0.736842π0.736842\pi
864864 −0.196754 + 0.106478i −0.196754 + 0.106478i
865865 0 0
866866 0.544122 + 1.24047i 0.544122 + 1.24047i
867867 −0.696274 2.74952i −0.696274 2.74952i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 1.57921 0.542145i 1.57921 0.542145i
874874 0 0
875875 0 0
876876 1.73542 + 1.88517i 1.73542 + 1.88517i
877877 0 0 0.401695 0.915773i 0.368421π-0.368421\pi
−0.401695 + 0.915773i 0.631579π0.631579\pi
878878 0 0
879879 0 0
880880 0 0
881881 −1.06894 + 1.16118i −1.06894 + 1.16118i −0.0825793 + 0.996584i 0.526316π0.526316\pi
−0.986361 + 0.164595i 0.947368π0.947368\pi
882882 0.789607 0.271073i 0.789607 0.271073i
883883 −0.962053 1.47253i −0.962053 1.47253i −0.879474 0.475947i 0.842105π-0.842105\pi
−0.0825793 0.996584i 0.526316π-0.526316\pi
884884 0 0
885885 0 0
886886 −0.130333 + 1.57289i −0.130333 + 1.57289i
887887 0 0 0.245485 0.969400i 0.421053π-0.421053\pi
−0.245485 + 0.969400i 0.578947π0.578947\pi
888888 0 0
889889 0 0
890890 0 0
891891 0.0461343 0.556759i 0.0461343 0.556759i
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 −0.740876 1.13399i −0.740876 1.13399i
899899 0 0
900900 −0.335352 + 0.764525i −0.335352 + 0.764525i
901901 0 0
902902 −0.524819 + 0.408483i −0.524819 + 0.408483i
903903 0 0
904904 −1.55676 0.259777i −1.55676 0.259777i
905905 0 0
906906 0 0
907907 0.598305 + 0.915773i 0.598305 + 0.915773i 1.00000 00
−0.401695 + 0.915773i 0.631579π0.631579\pi
908908 0.544122 + 0.591074i 0.544122 + 0.591074i
909909 0 0
910910 0 0
911911 0 0 −0.401695 0.915773i 0.631579π-0.631579\pi
0.401695 + 0.915773i 0.368421π0.368421\pi
912912 −1.28117 + 0.439826i −1.28117 + 0.439826i
913913 0.346901 0.790855i 0.346901 0.790855i
914914 0.0663435 0.800647i 0.0663435 0.800647i
915915 0 0
916916 0 0
917917 0 0
918918 −0.0966005 + 0.381467i −0.0966005 + 0.381467i
919919 0 0 0.0825793 0.996584i 0.473684π-0.473684\pi
−0.0825793 + 0.996584i 0.526316π0.526316\pi
920920 0 0
921921 −1.24270 1.34994i −1.24270 1.34994i
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 1.33609 + 1.45138i 1.33609 + 1.45138i 0.789141 + 0.614213i 0.210526π0.210526\pi
0.546948 + 0.837166i 0.315789π0.315789\pi
930930 0 0
931931 −0.986361 + 0.164595i −0.986361 + 0.164595i
932932 1.89163 0.649399i 1.89163 0.649399i
933933 0 0
934934 1.78914 0.614213i 1.78914 0.614213i
935935 0 0
936936 0 0
937937 1.24549 0.969400i 1.24549 0.969400i 0.245485 0.969400i 0.421053π-0.421053\pi
1.00000 00
938938 0 0
939939 −1.07340 2.44711i −1.07340 2.44711i
940940 0 0
941941 0 0 0.879474 0.475947i 0.157895π-0.157895\pi
−0.879474 + 0.475947i 0.842105π0.842105\pi
942942 0 0
943943 0 0
944944 −1.55676 + 0.259777i −1.55676 + 0.259777i
945945 0 0
946946 −0.311270 + 0.709624i −0.311270 + 0.709624i
947947 1.24549 + 0.969400i 1.24549 + 0.969400i 1.00000 00
0.245485 + 0.969400i 0.421053π0.421053\pi
948948 0 0
949949 0 0
950950 0.546948 0.837166i 0.546948 0.837166i
951951 0 0
952952 0 0
953953 0.598305 + 0.915773i 0.598305 + 0.915773i 1.00000 00
−0.401695 + 0.915773i 0.631579π0.631579\pi
954954 0 0
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0 0
961961 0.245485 0.969400i 0.245485 0.969400i
962962 0 0
963963 −1.06957 + 1.16187i −1.06957 + 1.16187i
964964 −1.66364 0.900319i −1.66364 0.900319i
965965 0 0
966966 0 0
967967 0 0 1.00000 00
−1.00000 π\pi
968968 −0.186311 + 0.735724i −0.186311 + 0.735724i
969969 −0.957082 + 2.18193i −0.957082 + 2.18193i
970970 0 0
971971 0.490971 + 1.93880i 0.490971 + 1.93880i 0.245485 + 0.969400i 0.421053π0.421053\pi
0.245485 + 0.969400i 0.421053π0.421053\pi
972972 −0.892396 + 0.969400i −0.892396 + 0.969400i
973973 0 0
974974 0 0
975975 0 0
976976 0 0
977977 −1.07898 + 1.65150i −1.07898 + 1.65150i −0.401695 + 0.915773i 0.631579π0.631579\pi
−0.677282 + 0.735724i 0.736842π0.736842\pi
978978 −0.810441 + 1.24047i −0.810441 + 1.24047i
979979 −0.816800 + 0.280408i −0.816800 + 0.280408i
980980 0 0
981981 0 0
982982 0.162906 1.96598i 0.162906 1.96598i
983983 0 0 −0.945817 0.324699i 0.894737π-0.894737\pi
0.945817 + 0.324699i 0.105263π0.105263\pi
984984 1.83484 1.83484
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0 0 −0.879474 0.475947i 0.842105π-0.842105\pi
0.879474 + 0.475947i 0.157895π0.157895\pi
992992 0 0
993993 0.267148 1.05494i 0.267148 1.05494i
994994 0 0
995995 0 0
996996 −2.09544 + 1.13399i −2.09544 + 1.13399i
997997 0 0 −0.879474 0.475947i 0.842105π-0.842105\pi
0.879474 + 0.475947i 0.157895π0.157895\pi
998998 −0.197221 0.778807i −0.197221 0.778807i
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 2888.1.bb.a.2395.1 yes 18
8.3 odd 2 CM 2888.1.bb.a.2395.1 yes 18
361.134 even 19 inner 2888.1.bb.a.1939.1 18
2888.1939 odd 38 inner 2888.1.bb.a.1939.1 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2888.1.bb.a.1939.1 18 361.134 even 19 inner
2888.1.bb.a.1939.1 18 2888.1939 odd 38 inner
2888.1.bb.a.2395.1 yes 18 1.1 even 1 trivial
2888.1.bb.a.2395.1 yes 18 8.3 odd 2 CM