Properties

Label 799.1.h.b.93.2
Level 799799
Weight 11
Character 799.93
Analytic conductor 0.3990.399
Analytic rank 00
Dimension 1616
Projective image D40D_{40}
CM discriminant -47
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [799,1,Mod(93,799)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(799, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([5, 4]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("799.93");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 799=1747 799 = 17 \cdot 47
Weight: k k == 1 1
Character orbit: [χ][\chi] == 799.h (of order 88, degree 44, 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: 0.3987529450940.398752945094
Analytic rank: 00
Dimension: 1616
Relative dimension: 44 over Q(ζ8)\Q(\zeta_{8})
Coefficient field: Q(ζ40)\Q(\zeta_{40})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16x12+x8x4+1 x^{16} - x^{12} + x^{8} - x^{4} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D40D_{40}
Projective field: Galois closure of Q[x]/(x40+)\mathbb{Q}[x]/(x^{40} + \cdots)

Embedding invariants

Embedding label 93.2
Root 0.987688+0.156434i-0.987688 + 0.156434i of defining polynomial
Character χ\chi == 799.93
Dual form 799.1.h.b.610.2

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+(0.831254+0.831254i)q2+(0.7630071.84206i)q30.381966iq4+(0.896969+2.16547i)q6+(0.4313510.178671i)q7+(0.5137430.513743i)q8+(2.103912.10391i)q9+(0.7036050.291443i)q12+(0.210041+0.507083i)q14+1.23607q16+(0.3090170.951057i)q17+3.49777q180.930903iq21+(1.33834+0.554357i)q24+(0.707107+0.707107i)q25+(3.63877+1.50723i)q27+(0.06824640.164761i)q28+(0.513743+0.513743i)q32+(1.04744+0.533698i)q34+(0.803622+0.803622i)q36+(0.0600500+0.144974i)q37+(0.773817+0.773817i)q421.00000iq47+(0.9431292.27692i)q48+(0.552967+0.552967i)q491.17557q50+(1.987690.156434i)q51+(1.396801.39680i)q53+(1.771854.27763i)q54+(0.3133950.129812i)q56+(1.14412+1.14412i)q59+(0.9654510.399903i)q61+(1.283430.531615i)q63+0.381966iq64+(0.363271+0.118034i)q68+(0.581990+1.40505i)q71+2.16174iq72+(0.07059300.170427i)q74+(1.842060.763007i)q75+(0.5819901.40505i)q79+4.87749iq81+(1.00000+1.00000i)q830.355573q84+1.17557iq89+(0.831254+0.831254i)q94+(0.554357+1.33834i)q96+(1.57547+0.652583i)q970.919311iq98+O(q100)q+(-0.831254 + 0.831254i) q^{2} +(0.763007 - 1.84206i) q^{3} -0.381966i q^{4} +(0.896969 + 2.16547i) q^{6} +(0.431351 - 0.178671i) q^{7} +(-0.513743 - 0.513743i) q^{8} +(-2.10391 - 2.10391i) q^{9} +(-0.703605 - 0.291443i) q^{12} +(-0.210041 + 0.507083i) q^{14} +1.23607 q^{16} +(-0.309017 - 0.951057i) q^{17} +3.49777 q^{18} -0.930903i q^{21} +(-1.33834 + 0.554357i) q^{24} +(0.707107 + 0.707107i) q^{25} +(-3.63877 + 1.50723i) q^{27} +(-0.0682464 - 0.164761i) q^{28} +(-0.513743 + 0.513743i) q^{32} +(1.04744 + 0.533698i) q^{34} +(-0.803622 + 0.803622i) q^{36} +(-0.0600500 + 0.144974i) q^{37} +(0.773817 + 0.773817i) q^{42} -1.00000i q^{47} +(0.943129 - 2.27692i) q^{48} +(-0.552967 + 0.552967i) q^{49} -1.17557 q^{50} +(-1.98769 - 0.156434i) q^{51} +(1.39680 - 1.39680i) q^{53} +(1.77185 - 4.27763i) q^{54} +(-0.313395 - 0.129812i) q^{56} +(1.14412 + 1.14412i) q^{59} +(0.965451 - 0.399903i) q^{61} +(-1.28343 - 0.531615i) q^{63} +0.381966i q^{64} +(-0.363271 + 0.118034i) q^{68} +(-0.581990 + 1.40505i) q^{71} +2.16174i q^{72} +(-0.0705930 - 0.170427i) q^{74} +(1.84206 - 0.763007i) q^{75} +(-0.581990 - 1.40505i) q^{79} +4.87749i q^{81} +(-1.00000 + 1.00000i) q^{83} -0.355573 q^{84} +1.17557i q^{89} +(0.831254 + 0.831254i) q^{94} +(0.554357 + 1.33834i) q^{96} +(1.57547 + 0.652583i) q^{97} -0.919311i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q4q34q916q16+4q1720q244q274q28+4q3620q42+24q48+4q4916q51+4q53+20q54+20q56+4q614q634q71++32q84+O(q100) 16 q - 4 q^{3} - 4 q^{9} - 16 q^{16} + 4 q^{17} - 20 q^{24} - 4 q^{27} - 4 q^{28} + 4 q^{36} - 20 q^{42} + 24 q^{48} + 4 q^{49} - 16 q^{51} + 4 q^{53} + 20 q^{54} + 20 q^{56} + 4 q^{61} - 4 q^{63} - 4 q^{71}+ \cdots + 32 q^{84}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/799Z)×\left(\mathbb{Z}/799\mathbb{Z}\right)^\times.

nn 5252 377377
χ(n)\chi(n) 1-1 e(58)e\left(\frac{5}{8}\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 −0.831254 + 0.831254i −0.831254 + 0.831254i −0.987688 0.156434i 0.950000π-0.950000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
33 0.763007 1.84206i 0.763007 1.84206i 0.309017 0.951057i 0.400000π-0.400000\pi
0.453990 0.891007i 0.350000π-0.350000\pi
44 0.381966i 0.381966i
55 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
66 0.896969 + 2.16547i 0.896969 + 2.16547i
77 0.431351 0.178671i 0.431351 0.178671i −0.156434 0.987688i 0.550000π-0.550000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
88 −0.513743 0.513743i −0.513743 0.513743i
99 −2.10391 2.10391i −2.10391 2.10391i
1010 0 0
1111 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
1212 −0.703605 0.291443i −0.703605 0.291443i
1313 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
1414 −0.210041 + 0.507083i −0.210041 + 0.507083i
1515 0 0
1616 1.23607 1.23607
1717 −0.309017 0.951057i −0.309017 0.951057i
1818 3.49777 3.49777
1919 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
2020 0 0
2121 0.930903i 0.930903i
2222 0 0
2323 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
2424 −1.33834 + 0.554357i −1.33834 + 0.554357i
2525 0.707107 + 0.707107i 0.707107 + 0.707107i
2626 0 0
2727 −3.63877 + 1.50723i −3.63877 + 1.50723i
2828 −0.0682464 0.164761i −0.0682464 0.164761i
2929 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
3030 0 0
3131 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
3232 −0.513743 + 0.513743i −0.513743 + 0.513743i
3333 0 0
3434 1.04744 + 0.533698i 1.04744 + 0.533698i
3535 0 0
3636 −0.803622 + 0.803622i −0.803622 + 0.803622i
3737 −0.0600500 + 0.144974i −0.0600500 + 0.144974i −0.951057 0.309017i 0.900000π-0.900000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
3838 0 0
3939 0 0
4040 0 0
4141 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
4242 0.773817 + 0.773817i 0.773817 + 0.773817i
4343 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
4444 0 0
4545 0 0
4646 0 0
4747 1.00000i 1.00000i
4848 0.943129 2.27692i 0.943129 2.27692i
4949 −0.552967 + 0.552967i −0.552967 + 0.552967i
5050 −1.17557 −1.17557
5151 −1.98769 0.156434i −1.98769 0.156434i
5252 0 0
5353 1.39680 1.39680i 1.39680 1.39680i 0.587785 0.809017i 0.300000π-0.300000\pi
0.809017 0.587785i 0.200000π-0.200000\pi
5454 1.77185 4.27763i 1.77185 4.27763i
5555 0 0
5656 −0.313395 0.129812i −0.313395 0.129812i
5757 0 0
5858 0 0
5959 1.14412 + 1.14412i 1.14412 + 1.14412i 0.987688 + 0.156434i 0.0500000π0.0500000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
6060 0 0
6161 0.965451 0.399903i 0.965451 0.399903i 0.156434 0.987688i 0.450000π-0.450000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
6262 0 0
6363 −1.28343 0.531615i −1.28343 0.531615i
6464 0.381966i 0.381966i
6565 0 0
6666 0 0
6767 0 0 1.00000 00
−1.00000 π\pi
6868 −0.363271 + 0.118034i −0.363271 + 0.118034i
6969 0 0
7070 0 0
7171 −0.581990 + 1.40505i −0.581990 + 1.40505i 0.309017 + 0.951057i 0.400000π0.400000\pi
−0.891007 + 0.453990i 0.850000π0.850000\pi
7272 2.16174i 2.16174i
7373 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
7474 −0.0705930 0.170427i −0.0705930 0.170427i
7575 1.84206 0.763007i 1.84206 0.763007i
7676 0 0
7777 0 0
7878 0 0
7979 −0.581990 1.40505i −0.581990 1.40505i −0.891007 0.453990i 0.850000π-0.850000\pi
0.309017 0.951057i 0.400000π-0.400000\pi
8080 0 0
8181 4.87749i 4.87749i
8282 0 0
8383 −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i 0.5π0.5\pi
−1.00000 π\pi
8484 −0.355573 −0.355573
8585 0 0
8686 0 0
8787 0 0
8888 0 0
8989 1.17557i 1.17557i 0.809017 + 0.587785i 0.200000π0.200000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
9090 0 0
9191 0 0
9292 0 0
9393 0 0
9494 0.831254 + 0.831254i 0.831254 + 0.831254i
9595 0 0
9696 0.554357 + 1.33834i 0.554357 + 1.33834i
9797 1.57547 + 0.652583i 1.57547 + 0.652583i 0.987688 0.156434i 0.0500000π-0.0500000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
9898 0.919311i 0.919311i
9999 0 0
100100 0.270091 0.270091i 0.270091 0.270091i
101101 0.907981 0.907981 0.453990 0.891007i 0.350000π-0.350000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
102102 1.78231 1.52224i 1.78231 1.52224i
103103 1.78201 1.78201 0.891007 0.453990i 0.150000π-0.150000\pi
0.891007 + 0.453990i 0.150000π0.150000\pi
104104 0 0
105105 0 0
106106 2.32219i 2.32219i
107107 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
108108 0.575710 + 1.38989i 0.575710 + 1.38989i
109109 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
110110 0 0
111111 0.221232 + 0.221232i 0.221232 + 0.221232i
112112 0.533179 0.220850i 0.533179 0.220850i
113113 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
114114 0 0
115115 0 0
116116 0 0
117117 0 0
118118 −1.90211 −1.90211
119119 −0.303221 0.355026i −0.303221 0.355026i
120120 0 0
121121 −0.707107 + 0.707107i −0.707107 + 0.707107i
122122 −0.470114 + 1.13496i −0.470114 + 1.13496i
123123 0 0
124124 0 0
125125 0 0
126126 1.50876 0.624950i 1.50876 0.624950i
127127 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
128128 −0.831254 0.831254i −0.831254 0.831254i
129129 0 0
130130 0 0
131131 −1.57547 0.652583i −1.57547 0.652583i −0.587785 0.809017i 0.700000π-0.700000\pi
−0.987688 + 0.156434i 0.950000π0.950000\pi
132132 0 0
133133 0 0
134134 0 0
135135 0 0
136136 −0.329843 + 0.647354i −0.329843 + 0.647354i
137137 0 0 1.00000 00
−1.00000 π\pi
138138 0 0
139139 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
140140 0 0
141141 −1.84206 0.763007i −1.84206 0.763007i
142142 −0.684170 1.65173i −0.684170 1.65173i
143143 0 0
144144 −2.60057 2.60057i −2.60057 2.60057i
145145 0 0
146146 0 0
147147 0.596682 + 1.44052i 0.596682 + 1.44052i
148148 0.0553750 + 0.0229371i 0.0553750 + 0.0229371i
149149 1.78201i 1.78201i 0.453990 + 0.891007i 0.350000π0.350000\pi
−0.453990 + 0.891007i 0.650000π0.650000\pi
150150 −0.896969 + 2.16547i −0.896969 + 2.16547i
151151 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
152152 0 0
153153 −1.35079 + 2.65108i −1.35079 + 2.65108i
154154 0 0
155155 0 0
156156 0 0
157157 0.312869i 0.312869i 0.987688 + 0.156434i 0.0500000π0.0500000\pi
−0.987688 + 0.156434i 0.950000π0.950000\pi
158158 1.65173 + 0.684170i 1.65173 + 0.684170i
159159 −1.50723 3.63877i −1.50723 3.63877i
160160 0 0
161161 0 0
162162 −4.05443 4.05443i −4.05443 4.05443i
163163 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
164164 0 0
165165 0 0
166166 1.66251i 1.66251i
167167 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
168168 −0.478245 + 0.478245i −0.478245 + 0.478245i
169169 −1.00000 −1.00000
170170 0 0
171171 0 0
172172 0 0
173173 −0.744220 + 1.79671i −0.744220 + 1.79671i −0.156434 + 0.987688i 0.550000π0.550000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
174174 0 0
175175 0.431351 + 0.178671i 0.431351 + 0.178671i
176176 0 0
177177 2.98052 1.23457i 2.98052 1.23457i
178178 −0.977198 0.977198i −0.977198 0.977198i
179179 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
180180 0 0
181181 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
182182 0 0
183183 2.08355i 2.08355i
184184 0 0
185185 0 0
186186 0 0
187187 0 0
188188 −0.381966 −0.381966
189189 −1.30029 + 1.30029i −1.30029 + 1.30029i
190190 0 0
191191 1.41421i 1.41421i −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 0.707107i 0.250000π-0.250000\pi
192192 0.703605 + 0.291443i 0.703605 + 0.291443i
193193 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
194194 −1.85208 + 0.767157i −1.85208 + 0.767157i
195195 0 0
196196 0.211214 + 0.211214i 0.211214 + 0.211214i
197197 1.70711 0.707107i 1.70711 0.707107i 0.707107 0.707107i 0.250000π-0.250000\pi
1.00000 00
198198 0 0
199199 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
200200 0.726543i 0.726543i
201201 0 0
202202 −0.754763 + 0.754763i −0.754763 + 0.754763i
203203 0 0
204204 −0.0597526 + 0.759229i −0.0597526 + 0.759229i
205205 0 0
206206 −1.48131 + 1.48131i −1.48131 + 1.48131i
207207 0 0
208208 0 0
209209 0 0
210210 0 0
211211 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
212212 −0.533531 0.533531i −0.533531 0.533531i
213213 2.14412 + 2.14412i 2.14412 + 2.14412i
214214 0 0
215215 0 0
216216 2.64372 + 1.09506i 2.64372 + 1.09506i
217217 0 0
218218 0 0
219219 0 0
220220 0 0
221221 0 0
222222 −0.367799 −0.367799
223223 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
224224 −0.129812 + 0.313395i −0.129812 + 0.313395i
225225 2.97538i 2.97538i
226226 0 0
227227 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
228228 0 0
229229 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
230230 0 0
231231 0 0
232232 0 0
233233 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
234234 0 0
235235 0 0
236236 0.437016 0.437016i 0.437016 0.437016i
237237 −3.03225 −3.03225
238238 0.547171 + 0.0430633i 0.547171 + 0.0430633i
239239 1.90211 1.90211 0.951057 0.309017i 0.100000π-0.100000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
240240 0 0
241241 0.0600500 0.144974i 0.0600500 0.144974i −0.891007 0.453990i 0.850000π-0.850000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
242242 1.17557i 1.17557i
243243 5.34588 + 2.21433i 5.34588 + 2.21433i
244244 −0.152749 0.368770i −0.152749 0.368770i
245245 0 0
246246 0 0
247247 0 0
248248 0 0
249249 1.07906 + 2.60507i 1.07906 + 2.60507i
250250 0 0
251251 0.907981i 0.907981i 0.891007 + 0.453990i 0.150000π0.150000\pi
−0.891007 + 0.453990i 0.850000π0.850000\pi
252252 −0.203059 + 0.490227i −0.203059 + 0.490227i
253253 0 0
254254 0 0
255255 0 0
256256 1.00000 1.00000
257257 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
258258 0 0
259259 0.0732636i 0.0732636i
260260 0 0
261261 0 0
262262 1.85208 0.767157i 1.85208 0.767157i
263263 −1.14412 1.14412i −1.14412 1.14412i −0.987688 0.156434i 0.950000π-0.950000\pi
−0.156434 0.987688i 0.550000π-0.550000\pi
264264 0 0
265265 0 0
266266 0 0
267267 2.16547 + 0.896969i 2.16547 + 0.896969i
268268 0 0
269269 −0.292893 + 0.707107i −0.292893 + 0.707107i 0.707107 + 0.707107i 0.250000π0.250000\pi
−1.00000 π\pi
270270 0 0
271271 −0.907981 −0.907981 −0.453990 0.891007i 0.650000π-0.650000\pi
−0.453990 + 0.891007i 0.650000π0.650000\pi
272272 −0.381966 1.17557i −0.381966 1.17557i
273273 0 0
274274 0 0
275275 0 0
276276 0 0
277277 −1.40505 0.581990i −1.40505 0.581990i −0.453990 0.891007i 0.650000π-0.650000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
278278 0 0
279279 0 0
280280 0 0
281281 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
282282 2.16547 0.896969i 2.16547 0.896969i
283283 0.178671 + 0.431351i 0.178671 + 0.431351i 0.987688 0.156434i 0.0500000π-0.0500000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
284284 0.536680 + 0.222300i 0.536680 + 0.222300i
285285 0 0
286286 0 0
287287 0 0
288288 2.16174 2.16174
289289 −0.809017 + 0.587785i −0.809017 + 0.587785i
290290 0 0
291291 2.40420 2.40420i 2.40420 2.40420i
292292 0 0
293293 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
294294 −1.69343 0.701442i −1.69343 0.701442i
295295 0 0
296296 0.105329 0.0436289i 0.105329 0.0436289i
297297 0 0
298298 −1.48131 1.48131i −1.48131 1.48131i
299299 0 0
300300 −0.291443 0.703605i −0.291443 0.703605i
301301 0 0
302302 0 0
303303 0.692796 1.67256i 0.692796 1.67256i
304304 0 0
305305 0 0
306306 −1.08087 3.32657i −1.08087 3.32657i
307307 −0.907981 −0.907981 −0.453990 0.891007i 0.650000π-0.650000\pi
−0.453990 + 0.891007i 0.650000π0.650000\pi
308308 0 0
309309 1.35969 3.28258i 1.35969 3.28258i
310310 0 0
311311 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
312312 0 0
313313 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
314314 −0.260074 0.260074i −0.260074 0.260074i
315315 0 0
316316 −0.536680 + 0.222300i −0.536680 + 0.222300i
317317 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
318318 4.27763 + 1.77185i 4.27763 + 1.77185i
319319 0 0
320320 0 0
321321 0 0
322322 0 0
323323 0 0
324324 1.86304 1.86304
325325 0 0
326326 0 0
327327 0 0
328328 0 0
329329 −0.178671 0.431351i −0.178671 0.431351i
330330 0 0
331331 −0.831254 0.831254i −0.831254 0.831254i 0.156434 0.987688i 0.450000π-0.450000\pi
−0.987688 + 0.156434i 0.950000π0.950000\pi
332332 0.381966 + 0.381966i 0.381966 + 0.381966i
333333 0.431351 0.178671i 0.431351 0.178671i
334334 0 0
335335 0 0
336336 1.15066i 1.15066i
337337 0.744220 1.79671i 0.744220 1.79671i 0.156434 0.987688i 0.450000π-0.450000\pi
0.587785 0.809017i 0.300000π-0.300000\pi
338338 0.831254 0.831254i 0.831254 0.831254i
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 −0.318395 + 0.768673i −0.318395 + 0.768673i
344344 0 0
345345 0 0
346346 −0.874883 2.11215i −0.874883 2.11215i
347347 −1.84206 + 0.763007i −1.84206 + 0.763007i −0.891007 + 0.453990i 0.850000π0.850000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
348348 0 0
349349 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
350350 −0.507083 + 0.210041i −0.507083 + 0.210041i
351351 0 0
352352 0 0
353353 0.312869i 0.312869i −0.987688 0.156434i 0.950000π-0.950000\pi
0.987688 0.156434i 0.0500000π-0.0500000\pi
354354 −1.45133 + 3.50381i −1.45133 + 3.50381i
355355 0 0
356356 0.449028 0.449028
357357 −0.885341 + 0.287665i −0.885341 + 0.287665i
358358 0 0
359359 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
360360 0 0
361361 1.00000i 1.00000i
362362 0 0
363363 0.763007 + 1.84206i 0.763007 + 1.84206i
364364 0 0
365365 0 0
366366 1.73196 + 1.73196i 1.73196 + 1.73196i
367367 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
368368 0 0
369369 0 0
370370 0 0
371371 0.352943 0.852080i 0.352943 0.852080i
372372 0 0
373373 0 0 1.00000 00
−1.00000 π\pi
374374 0 0
375375 0 0
376376 −0.513743 + 0.513743i −0.513743 + 0.513743i
377377 0 0
378378 2.16174i 2.16174i
379379 −1.79671 0.744220i −1.79671 0.744220i −0.987688 0.156434i 0.950000π-0.950000\pi
−0.809017 0.587785i 0.800000π-0.800000\pi
380380 0 0
381381 0 0
382382 1.17557 + 1.17557i 1.17557 + 1.17557i
383383 1.26007 + 1.26007i 1.26007 + 1.26007i 0.951057 + 0.309017i 0.100000π0.100000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
384384 −2.16547 + 0.896969i −2.16547 + 0.896969i
385385 0 0
386386 0 0
387387 0 0
388388 0.249264 0.601777i 0.249264 0.601777i
389389 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
390390 0 0
391391 0 0
392392 0.568166 0.568166
393393 −2.40420 + 2.40420i −2.40420 + 2.40420i
394394 −0.831254 + 2.00682i −0.831254 + 2.00682i
395395 0 0
396396 0 0
397397 −0.497066 1.20002i −0.497066 1.20002i −0.951057 0.309017i 0.900000π-0.900000\pi
0.453990 0.891007i 0.350000π-0.350000\pi
398398 0 0
399399 0 0
400400 0.874032 + 0.874032i 0.874032 + 0.874032i
401401 1.84206 0.763007i 1.84206 0.763007i 0.891007 0.453990i 0.150000π-0.150000\pi
0.951057 0.309017i 0.100000π-0.100000\pi
402402 0 0
403403 0 0
404404 0.346818i 0.346818i
405405 0 0
406406 0 0
407407 0 0
408408 0.940794 + 1.10153i 0.940794 + 1.10153i
409409 0 0 1.00000 00
−1.00000 π\pi
410410 0 0
411411 0 0
412412 0.680668i 0.680668i
413413 0.697940 + 0.289096i 0.697940 + 0.289096i
414414 0 0
415415 0 0
416416 0 0
417417 0 0
418418 0 0
419419 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
420420 0 0
421421 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
422422 0 0
423423 −2.10391 + 2.10391i −2.10391 + 2.10391i
424424 −1.43520 −1.43520
425425 0.453990 0.891007i 0.453990 0.891007i
426426 −3.56462 −3.56462
427427 0.344997 0.344997i 0.344997 0.344997i
428428 0 0
429429 0 0
430430 0 0
431431 −0.652583 1.57547i −0.652583 1.57547i −0.809017 0.587785i 0.800000π-0.800000\pi
0.156434 0.987688i 0.450000π-0.450000\pi
432432 −4.49777 + 1.86304i −4.49777 + 1.86304i
433433 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
434434 0 0
435435 0 0
436436 0 0
437437 0 0
438438 0 0
439439 0.707107 1.70711i 0.707107 1.70711i 1.00000i 0.5π-0.5\pi
0.707107 0.707107i 0.250000π-0.250000\pi
440440 0 0
441441 2.32678 2.32678
442442 0 0
443443 0 0 1.00000 00
−1.00000 π\pi
444444 0.0845030 0.0845030i 0.0845030 0.0845030i
445445 0 0
446446 0 0
447447 3.28258 + 1.35969i 3.28258 + 1.35969i
448448 0.0682464 + 0.164761i 0.0682464 + 0.164761i
449449 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
450450 2.47329 + 2.47329i 2.47329 + 2.47329i
451451 0 0
452452 0 0
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 0.642040 0.642040i 0.642040 0.642040i −0.309017 0.951057i 0.600000π-0.600000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
458458 0 0
459459 2.55790 + 2.99492i 2.55790 + 2.99492i
460460 0 0
461461 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
462462 0 0
463463 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
464464 0 0
465465 0 0
466466 0 0
467467 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
468468 0 0
469469 0 0
470470 0 0
471471 0.576324 + 0.238721i 0.576324 + 0.238721i
472472 1.17557i 1.17557i
473473 0 0
474474 2.52057 2.52057i 2.52057 2.52057i
475475 0 0
476476 −0.135608 + 0.115820i −0.135608 + 0.115820i
477477 −5.87749 −5.87749
478478 −1.58114 + 1.58114i −1.58114 + 1.58114i
479479 −0.178671 + 0.431351i −0.178671 + 0.431351i −0.987688 0.156434i 0.950000π-0.950000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
480480 0 0
481481 0 0
482482 0.0705930 + 0.170427i 0.0705930 + 0.170427i
483483 0 0
484484 0.270091 + 0.270091i 0.270091 + 0.270091i
485485 0 0
486486 −6.28445 + 2.60311i −6.28445 + 2.60311i
487487 −0.707107 1.70711i −0.707107 1.70711i −0.707107 0.707107i 0.750000π-0.750000\pi
1.00000i 0.5π-0.5\pi
488488 −0.701442 0.290547i −0.701442 0.290547i
489489 0 0
490490 0 0
491491 −0.221232 + 0.221232i −0.221232 + 0.221232i −0.809017 0.587785i 0.800000π-0.800000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 0.710053i 0.710053i
498498 −3.06244 1.26851i −3.06244 1.26851i
499499 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
500500 0 0
501501 0 0
502502 −0.754763 0.754763i −0.754763 0.754763i
503503 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
504504 0.386241 + 0.932467i 0.386241 + 0.932467i
505505 0 0
506506 0 0
507507 −0.763007 + 1.84206i −0.763007 + 1.84206i
508508 0 0
509509 0 0 1.00000 00
−1.00000 π\pi
510510 0 0
511511 0 0
512512 0 0
513513 0 0
514514 0 0
515515 0 0
516516 0 0
517517 0 0
518518 −0.0609007 0.0609007i −0.0609007 0.0609007i
519519 2.74180 + 2.74180i 2.74180 + 2.74180i
520520 0 0
521521 −0.744220 1.79671i −0.744220 1.79671i −0.587785 0.809017i 0.700000π-0.700000\pi
−0.156434 0.987688i 0.550000π-0.550000\pi
522522 0 0
523523 0 0 1.00000 00
−1.00000 π\pi
524524 −0.249264 + 0.601777i −0.249264 + 0.601777i
525525 0.658248 0.658248i 0.658248 0.658248i
526526 1.90211 1.90211
527527 0 0
528528 0 0
529529 −0.707107 + 0.707107i −0.707107 + 0.707107i
530530 0 0
531531 4.81426i 4.81426i
532532 0 0
533533 0 0
534534 −2.54567 + 1.05445i −2.54567 + 1.05445i
535535 0 0
536536 0 0
537537 0 0
538538 −0.344317 0.831254i −0.344317 0.831254i
539539 0 0
540540 0 0
541541 −0.744220 + 1.79671i −0.744220 + 1.79671i −0.156434 + 0.987688i 0.550000π0.550000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
542542 0.754763 0.754763i 0.754763 0.754763i
543543 0 0
544544 0.647354 + 0.329843i 0.647354 + 0.329843i
545545 0 0
546546 0 0
547547 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
548548 0 0
549549 −2.87258 1.18986i −2.87258 1.18986i
550550 0 0
551551 0 0
552552 0 0
553553 −0.502083 0.502083i −0.502083 0.502083i
554554 1.65173 0.684170i 1.65173 0.684170i
555555 0 0
556556 0 0
557557 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 0 0
563563 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
564564 −0.291443 + 0.703605i −0.291443 + 0.703605i
565565 0 0
566566 −0.507083 0.210041i −0.507083 0.210041i
567567 0.871468 + 2.10391i 0.871468 + 2.10391i
568568 1.02083 0.422840i 1.02083 0.422840i
569569 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
570570 0 0
571571 −1.20002 + 0.497066i −1.20002 + 0.497066i −0.891007 0.453990i 0.850000π-0.850000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
572572 0 0
573573 −2.60507 1.07906i −2.60507 1.07906i
574574 0 0
575575 0 0
576576 0.803622 0.803622i 0.803622 0.803622i
577577 0 0 1.00000 00
−1.00000 π\pi
578578 0.183900 1.16110i 0.183900 1.16110i
579579 0 0
580580 0 0
581581 −0.252679 + 0.610022i −0.252679 + 0.610022i
582582 3.99700i 3.99700i
583583 0 0
584584 0 0
585585 0 0
586586 0 0
587587 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
588588 0.550229 0.227912i 0.550229 0.227912i
589589 0 0
590590 0 0
591591 3.68413i 3.68413i
592592 −0.0742259 + 0.179197i −0.0742259 + 0.179197i
593593 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
594594 0 0
595595 0 0
596596 0.680668 0.680668
597597 0 0
598598 0 0
599599 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
600600 −1.33834 0.554357i −1.33834 0.554357i
601601 0.399903 + 0.965451i 0.399903 + 0.965451i 0.987688 + 0.156434i 0.0500000π0.0500000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
602602 0 0
603603 0 0
604604 0 0
605605 0 0
606606 0.814431 + 1.96621i 0.814431 + 1.96621i
607607 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 1.01262 + 0.515957i 1.01262 + 0.515957i
613613 −1.17557 −1.17557 −0.587785 0.809017i 0.700000π-0.700000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
614614 0.754763 0.754763i 0.754763 0.754763i
615615 0 0
616616 0 0
617617 1.20002 + 0.497066i 1.20002 + 0.497066i 0.891007 0.453990i 0.150000π-0.150000\pi
0.309017 + 0.951057i 0.400000π0.400000\pi
618618 1.59841 + 3.85890i 1.59841 + 3.85890i
619619 −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i 0.750000π-0.750000\pi
1.00000i 0.5π0.5\pi
620620 0 0
621621 0 0
622622 0 0
623623 0.210041 + 0.507083i 0.210041 + 0.507083i
624624 0 0
625625 1.00000i 1.00000i
626626 0 0
627627 0 0
628628 0.119505 0.119505
629629 0.156434 + 0.0123117i 0.156434 + 0.0123117i
630630 0 0
631631 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
632632 −0.422840 + 1.02083i −0.422840 + 1.02083i
633633 0 0
634634 0 0
635635 0 0
636636 −1.38989 + 0.575710i −1.38989 + 0.575710i
637637 0 0
638638 0 0
639639 4.18054 1.73164i 4.18054 1.73164i
640640 0 0
641641 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
642642 0 0
643643 −0.399903 + 0.965451i −0.399903 + 0.965451i 0.587785 + 0.809017i 0.300000π0.300000\pi
−0.987688 + 0.156434i 0.950000π0.950000\pi
644644 0 0
645645 0 0
646646 0 0
647647 0.312869 0.312869 0.156434 0.987688i 0.450000π-0.450000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
648648 2.50578 2.50578i 2.50578 2.50578i
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 0.144974 0.0600500i 0.144974 0.0600500i −0.309017 0.951057i 0.600000π-0.600000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0.507083 + 0.210041i 0.507083 + 0.210041i
659659 0.618034i 0.618034i 0.951057 + 0.309017i 0.100000π0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
660660 0 0
661661 −1.34500 + 1.34500i −1.34500 + 1.34500i −0.453990 + 0.891007i 0.650000π0.650000\pi
−0.891007 + 0.453990i 0.850000π0.850000\pi
662662 1.38197 1.38197
663663 0 0
664664 1.02749 1.02749
665665 0 0
666666 −0.210041 + 0.507083i −0.210041 + 0.507083i
667667 0 0
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0.478245 + 0.478245i 0.478245 + 0.478245i
673673 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
674674 0.874883 + 2.11215i 0.874883 + 2.11215i
675675 −3.63877 1.50723i −3.63877 1.50723i
676676 0.381966i 0.381966i
677677 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
678678 0 0
679679 0.796180 0.796180
680680 0 0
681681 0 0
682682 0 0
683683 0.399903 0.965451i 0.399903 0.965451i −0.587785 0.809017i 0.700000π-0.700000\pi
0.987688 0.156434i 0.0500000π-0.0500000\pi
684684 0 0
685685 0 0
686686 −0.374295 0.903629i −0.374295 0.903629i
687687 0 0
688688 0 0
689689 0 0
690690 0 0
691691 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
692692 0.686280 + 0.284267i 0.686280 + 0.284267i
693693 0 0
694694 0.896969 2.16547i 0.896969 2.16547i
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 0.0682464 0.164761i 0.0682464 0.164761i
701701 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
702702 0 0
703703 0 0
704704 0 0
705705 0 0
706706 0.260074 + 0.260074i 0.260074 + 0.260074i
707707 0.391658 0.162230i 0.391658 0.162230i
708708 −0.471565 1.13846i −0.471565 1.13846i
709709 0.431351 + 0.178671i 0.431351 + 0.178671i 0.587785 0.809017i 0.300000π-0.300000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
710710 0 0
711711 −1.73164 + 4.18054i −1.73164 + 4.18054i
712712 0.603941 0.603941i 0.603941 0.603941i
713713 0 0
714714 0.496821 0.975066i 0.496821 0.975066i
715715 0 0
716716 0 0
717717 1.45133 3.50381i 1.45133 3.50381i
718718 0 0
719719 −0.965451 0.399903i −0.965451 0.399903i −0.156434 0.987688i 0.550000π-0.550000\pi
−0.809017 + 0.587785i 0.800000π0.800000\pi
720720 0 0
721721 0.768673 0.318395i 0.768673 0.318395i
722722 0.831254 + 0.831254i 0.831254 + 0.831254i
723723 −0.221232 0.221232i −0.221232 0.221232i
724724 0 0
725725 0 0
726726 −2.16547 0.896969i −2.16547 0.896969i
727727 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
728728 0 0
729729 4.70898 4.70898i 4.70898 4.70898i
730730 0 0
731731 0 0
732732 −0.795846 −0.795846
733733 −1.34500 + 1.34500i −1.34500 + 1.34500i −0.453990 + 0.891007i 0.650000π0.650000\pi
−0.891007 + 0.453990i 0.850000π0.850000\pi
734734 0 0
735735 0 0
736736 0 0
737737 0 0
738738 0 0
739739 0.221232 + 0.221232i 0.221232 + 0.221232i 0.809017 0.587785i 0.200000π-0.200000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
740740 0 0
741741 0 0
742742 0.414910 + 1.00168i 0.414910 + 1.00168i
743743 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
744744 0 0
745745 0 0
746746 0 0
747747 4.20782 4.20782
748748 0 0
749749 0 0
750750 0 0
751751 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
752752 1.23607i 1.23607i
753753 1.67256 + 0.692796i 1.67256 + 0.692796i
754754 0 0
755755 0 0
756756 0.496666 + 0.496666i 0.496666 + 0.496666i
757757 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
758758 2.11215 0.874883i 2.11215 0.874883i
759759 0 0
760760 0 0
761761 1.41421i 1.41421i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
762762 0 0
763763 0 0
764764 −0.540182 −0.540182
765765 0 0
766766 −2.09488 −2.09488
767767 0 0
768768 0.763007 1.84206i 0.763007 1.84206i
769769 1.90211i 1.90211i 0.309017 + 0.951057i 0.400000π0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
770770 0 0
771771 0 0
772772 0 0
773773 1.34500 + 1.34500i 1.34500 + 1.34500i 0.891007 + 0.453990i 0.150000π0.150000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
774774 0 0
775775 0 0
776776 −0.474129 1.14465i −0.474129 1.14465i
777777 0.134956 + 0.0559007i 0.134956 + 0.0559007i
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 0 0
783783 0 0
784784 −0.683504 + 0.683504i −0.683504 + 0.683504i
785785 0 0
786786 3.99700i 3.99700i
787787 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
788788 −0.270091 0.652057i −0.270091 0.652057i
789789 −2.98052 + 1.23457i −2.98052 + 1.23457i
790790 0 0
791791 0 0
792792 0 0
793793 0 0
794794 1.41071 + 0.584336i 1.41071 + 0.584336i
795795 0 0
796796 0 0
797797 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
798798 0 0
799799 −0.951057 + 0.309017i −0.951057 + 0.309017i
800800 −0.726543 −0.726543
801801 2.47329 2.47329i 2.47329 2.47329i
802802 −0.896969 + 2.16547i −0.896969 + 2.16547i
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 1.07906 + 1.07906i 1.07906 + 1.07906i
808808 −0.466469 0.466469i −0.466469 0.466469i
809809 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
810810 0 0
811811 1.40505 + 0.581990i 1.40505 + 0.581990i 0.951057 0.309017i 0.100000π-0.100000\pi
0.453990 + 0.891007i 0.350000π0.350000\pi
812812 0 0
813813 −0.692796 + 1.67256i −0.692796 + 1.67256i
814814 0 0
815815 0 0
816816 −2.45692 0.193364i −2.45692 0.193364i
817817 0 0
818818 0 0
819819 0 0
820820 0 0
821821 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
822822 0 0
823823 −0.707107 + 0.292893i −0.707107 + 0.292893i −0.707107 0.707107i 0.750000π-0.750000\pi
1.00000i 0.5π0.5\pi
824824 −0.915497 0.915497i −0.915497 0.915497i
825825 0 0
826826 −0.820478 + 0.339853i −0.820478 + 0.339853i
827827 0.399903 + 0.965451i 0.399903 + 0.965451i 0.987688 + 0.156434i 0.0500000π0.0500000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
828828 0 0
829829 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
830830 0 0
831831 −2.14412 + 2.14412i −2.14412 + 2.14412i
832832 0 0
833833 0.696779 + 0.355026i 0.696779 + 0.355026i
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
840840 0 0
841841 0.707107 + 0.707107i 0.707107 + 0.707107i
842842 0 0
843843 0 0
844844 0 0
845845 0 0
846846 3.49777i 3.49777i
847847 −0.178671 + 0.431351i −0.178671 + 0.431351i
848848 1.72654 1.72654i 1.72654 1.72654i
849849 0.930903 0.930903
850850 0.363271 + 1.11803i 0.363271 + 1.11803i
851851 0 0
852852 0.818982 0.818982i 0.818982 0.818982i
853853 0.497066 1.20002i 0.497066 1.20002i −0.453990 0.891007i 0.650000π-0.650000\pi
0.951057 0.309017i 0.100000π-0.100000\pi
854854 0.573560i 0.573560i
855855 0 0
856856 0 0
857857 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
858858 0 0
859859 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
860860 0 0
861861 0 0
862862 1.85208 + 0.767157i 1.85208 + 0.767157i
863863 0.618034i 0.618034i −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 0.309017i 0.100000π-0.100000\pi
864864 1.09506 2.64372i 1.09506 2.64372i
865865 0 0
866866 0 0
867867 0.465451 + 1.93874i 0.465451 + 1.93874i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0 0
873873 −1.94168 4.68763i −1.94168 4.68763i
874874 0 0
875875 0 0
876876 0 0
877877 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
878878 0.831254 + 2.00682i 0.831254 + 2.00682i
879879 0 0
880880 0 0
881881 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
882882 −1.93415 + 1.93415i −1.93415 + 1.93415i
883883 0.312869 0.312869 0.156434 0.987688i 0.450000π-0.450000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
884884 0 0
885885 0 0
886886 0 0
887887 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
888888 0.227313i 0.227313i
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 0 0
894894 −3.85890 + 1.59841i −3.85890 + 1.59841i
895895 0 0
896896 −0.507083 0.210041i −0.507083 0.210041i
897897 0 0
898898 0 0
899899 0 0
900900 −1.13649 −1.13649
901901 −1.76007 0.896802i −1.76007 0.896802i
902902 0 0
903903 0 0
904904 0 0
905905 0 0
906906 0 0
907907 0.292893 + 0.707107i 0.292893 + 0.707107i 1.00000 00
−0.707107 + 0.707107i 0.750000π0.750000\pi
908908 0 0
909909 −1.91031 1.91031i −1.91031 1.91031i
910910 0 0
911911 −0.965451 + 0.399903i −0.965451 + 0.399903i −0.809017 0.587785i 0.800000π-0.800000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
912912 0 0
913913 0 0
914914 1.06740i 1.06740i
915915 0 0
916916 0 0
917917 −0.796180 −0.796180
918918 −4.61580 0.363271i −4.61580 0.363271i
919919 0 0 1.00000 00
−1.00000 π\pi
920920 0 0
921921 −0.692796 + 1.67256i −0.692796 + 1.67256i
922922 0 0
923923 0 0
924924 0 0
925925 −0.144974 + 0.0600500i −0.144974 + 0.0600500i
926926 0 0
927927 −3.74919 3.74919i −3.74919 3.74919i
928928 0 0
929929 −0.0600500 0.144974i −0.0600500 0.144974i 0.891007 0.453990i 0.150000π-0.150000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
930930 0 0
931931 0 0
932932 0 0
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
938938 0 0
939939 0 0
940940 0 0
941941 0.652583 + 1.57547i 0.652583 + 1.57547i 0.809017 + 0.587785i 0.200000π0.200000\pi
−0.156434 + 0.987688i 0.550000π0.550000\pi
942942 −0.677510 + 0.280634i −0.677510 + 0.280634i
943943 0 0
944944 1.41421 + 1.41421i 1.41421 + 1.41421i
945945 0 0
946946 0 0
947947 −0.707107 0.292893i −0.707107 0.292893i 1.00000i 0.5π-0.5\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
948948 1.15822i 1.15822i
949949 0 0
950950 0 0
951951 0 0
952952 −0.0266146 + 0.338170i −0.0266146 + 0.338170i
953953 0 0 1.00000 00
−1.00000 π\pi
954954 4.88569 4.88569i 4.88569 4.88569i
955955 0 0
956956 0.726543i 0.726543i
957957 0 0
958958 −0.210041 0.507083i −0.210041 0.507083i
959959 0 0
960960 0 0
961961 −0.707107 0.707107i −0.707107 0.707107i
962962 0 0
963963 0 0
964964 −0.0553750 0.0229371i −0.0553750 0.0229371i
965965 0 0
966966 0 0
967967 0.221232 0.221232i 0.221232 0.221232i −0.587785 0.809017i 0.700000π-0.700000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
968968 0.726543 0.726543
969969 0 0
970970 0 0
971971 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
972972 0.845800 2.04194i 0.845800 2.04194i
973973 0 0
974974 2.00682 + 0.831254i 2.00682 + 0.831254i
975975 0 0
976976 1.19336 0.494307i 1.19336 0.494307i
977977 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
978978 0 0
979979 0 0
980980 0 0
981981 0 0
982982 0.367799i 0.367799i
983983 0 0 0.382683 0.923880i 0.375000π-0.375000\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
984984 0 0
985985 0 0
986986 0 0
987987 −0.930903 −0.930903
988988 0 0
989989 0 0
990990 0 0
991991 0.965451 + 0.399903i 0.965451 + 0.399903i 0.809017 0.587785i 0.200000π-0.200000\pi
0.156434 + 0.987688i 0.450000π0.450000\pi
992992 0 0
993993 −2.16547 + 0.896969i −2.16547 + 0.896969i
994994 −0.590234 0.590234i −0.590234 0.590234i
995995 0 0
996996 0.995048 0.412163i 0.995048 0.412163i
997997 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
998998 0 0
999999 0.618034i 0.618034i
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 799.1.h.b.93.2 16
17.15 even 8 inner 799.1.h.b.610.2 yes 16
47.46 odd 2 CM 799.1.h.b.93.2 16
799.610 odd 8 inner 799.1.h.b.610.2 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
799.1.h.b.93.2 16 1.1 even 1 trivial
799.1.h.b.93.2 16 47.46 odd 2 CM
799.1.h.b.610.2 yes 16 17.15 even 8 inner
799.1.h.b.610.2 yes 16 799.610 odd 8 inner