Properties

Label 3840.1.dy.a.149.1
Level 38403840
Weight 11
Character 3840.149
Analytic conductor 1.9161.916
Analytic rank 00
Dimension 6464
Projective image D64D_{64}
CM discriminant -15
Inner twists 88

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3840,1,Mod(29,3840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3840, base_ring=CyclotomicField(64))
 
chi = DirichletCharacter(H, H._module([0, 59, 32, 32]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3840.29");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 3840=2835 3840 = 2^{8} \cdot 3 \cdot 5
Weight: k k == 1 1
Character orbit: [χ][\chi] == 3840.dy (of order 6464, degree 3232, 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: 1.916409648511.91640964851
Analytic rank: 00
Dimension: 6464
Relative dimension: 22 over Q(ζ64)\Q(\zeta_{64})
Coefficient field: Q(ζ128)\Q(\zeta_{128})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x64+1 x^{64} + 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: D64D_{64}
Projective field: Galois closure of Q[x]/(x64+)\mathbb{Q}[x]/(x^{64} + \cdots)

Embedding invariants

Embedding label 149.1
Root 0.9415440.336890i-0.941544 - 0.336890i of defining polynomial
Character χ\chi == 3840.149
Dual form 3840.1.dy.a.1469.1

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+(0.8577290.514103i)q2+(0.941544+0.336890i)q3+(0.471397+0.881921i)q4+(0.8032080.595699i)q5+(0.6343930.773010i)q6+(0.04906770.998795i)q8+(0.773010+0.634393i)q9+(0.382683+0.923880i)q10+(0.146730+0.989177i)q12+(0.5555700.831470i)q15+(0.555570+0.831470i)q16+(1.09911+1.64494i)q17+(0.3368900.941544i)q18+(0.05045170.0841735i)q19+(0.1467300.989177i)q20+(1.71098+0.914539i)q23+(0.3826830.923880i)q24+(0.290285+0.956940i)q25+(0.514103+0.857729i)q27+(0.0490677+0.998795i)q30+(0.674993+1.62958i)q31+(0.9039890.427555i)q32+(1.788410.845855i)q34+(0.195090+0.980785i)q36+(0.0865477+0.0462607i)q38+(0.634393+0.773010i)q40+(0.2429800.970031i)q45+(1.93773+0.0951944i)q46+(1.773240.352719i)q47+(0.803208+0.595699i)q48+(0.980785+0.195090i)q49+(0.2429800.970031i)q50+(1.58903+1.17850i)q51+(0.1957980.00961895i)q531.00000iq54+(0.07585970.0622564i)q57+(0.4713970.881921i)q60+(1.21416+0.574257i)q61+(1.416731.05072i)q62+(0.9951850.0980171i)q64+(1.968830.193913i)q68+(1.91906+0.284666i)q69+(0.6715590.740951i)q72+(0.0490677+0.998795i)q75+(0.0980171+0.00481527i)q76+(0.2167731.08979i)q79+(0.9415440.336890i)q80+(0.195090+0.980785i)q81+(1.499690.375652i)q83+(1.862710.666487i)q85+(0.290285+0.956940i)q90+(1.613101.07784i)q92+(1.18452+1.30692i)q93+(1.702290.609090i)q94+(0.0906652+0.0375548i)q95+(0.9951850.0980171i)q96+(0.7409510.671559i)q98+O(q100)q+(-0.857729 - 0.514103i) q^{2} +(0.941544 + 0.336890i) q^{3} +(0.471397 + 0.881921i) q^{4} +(-0.803208 - 0.595699i) q^{5} +(-0.634393 - 0.773010i) q^{6} +(0.0490677 - 0.998795i) q^{8} +(0.773010 + 0.634393i) q^{9} +(0.382683 + 0.923880i) q^{10} +(0.146730 + 0.989177i) q^{12} +(-0.555570 - 0.831470i) q^{15} +(-0.555570 + 0.831470i) q^{16} +(-1.09911 + 1.64494i) q^{17} +(-0.336890 - 0.941544i) q^{18} +(0.0504517 - 0.0841735i) q^{19} +(0.146730 - 0.989177i) q^{20} +(-1.71098 + 0.914539i) q^{23} +(0.382683 - 0.923880i) q^{24} +(0.290285 + 0.956940i) q^{25} +(0.514103 + 0.857729i) q^{27} +(0.0490677 + 0.998795i) q^{30} +(-0.674993 + 1.62958i) q^{31} +(0.903989 - 0.427555i) q^{32} +(1.78841 - 0.845855i) q^{34} +(-0.195090 + 0.980785i) q^{36} +(-0.0865477 + 0.0462607i) q^{38} +(-0.634393 + 0.773010i) q^{40} +(-0.242980 - 0.970031i) q^{45} +(1.93773 + 0.0951944i) q^{46} +(1.77324 - 0.352719i) q^{47} +(-0.803208 + 0.595699i) q^{48} +(0.980785 + 0.195090i) q^{49} +(0.242980 - 0.970031i) q^{50} +(-1.58903 + 1.17850i) q^{51} +(-0.195798 - 0.00961895i) q^{53} -1.00000i q^{54} +(0.0758597 - 0.0622564i) q^{57} +(0.471397 - 0.881921i) q^{60} +(-1.21416 + 0.574257i) q^{61} +(1.41673 - 1.05072i) q^{62} +(-0.995185 - 0.0980171i) q^{64} +(-1.96883 - 0.193913i) q^{68} +(-1.91906 + 0.284666i) q^{69} +(0.671559 - 0.740951i) q^{72} +(-0.0490677 + 0.998795i) q^{75} +(0.0980171 + 0.00481527i) q^{76} +(0.216773 - 1.08979i) q^{79} +(0.941544 - 0.336890i) q^{80} +(0.195090 + 0.980785i) q^{81} +(1.49969 - 0.375652i) q^{83} +(1.86271 - 0.666487i) q^{85} +(-0.290285 + 0.956940i) q^{90} +(-1.61310 - 1.07784i) q^{92} +(-1.18452 + 1.30692i) q^{93} +(-1.70229 - 0.609090i) q^{94} +(-0.0906652 + 0.0375548i) q^{95} +(0.995185 - 0.0980171i) q^{96} +(-0.740951 - 0.671559i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 64q+O(q100) 64 q+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/3840Z)×\left(\mathbb{Z}/3840\mathbb{Z}\right)^\times.

nn 511511 15371537 25612561 28212821
χ(n)\chi(n) 11 1-1 1-1 e(1364)e\left(\frac{13}{64}\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 −0.857729 0.514103i −0.857729 0.514103i
33 0.941544 + 0.336890i 0.941544 + 0.336890i
44 0.471397 + 0.881921i 0.471397 + 0.881921i
55 −0.803208 0.595699i −0.803208 0.595699i
66 −0.634393 0.773010i −0.634393 0.773010i
77 0 0 −0.995185 0.0980171i 0.968750π-0.968750\pi
0.995185 + 0.0980171i 0.0312500π0.0312500\pi
88 0.0490677 0.998795i 0.0490677 0.998795i
99 0.773010 + 0.634393i 0.773010 + 0.634393i
1010 0.382683 + 0.923880i 0.382683 + 0.923880i
1111 0 0 −0.671559 0.740951i 0.734375π-0.734375\pi
0.671559 + 0.740951i 0.265625π0.265625\pi
1212 0.146730 + 0.989177i 0.146730 + 0.989177i
1313 0 0 0.146730 0.989177i 0.453125π-0.453125\pi
−0.146730 + 0.989177i 0.546875π0.546875\pi
1414 0 0
1515 −0.555570 0.831470i −0.555570 0.831470i
1616 −0.555570 + 0.831470i −0.555570 + 0.831470i
1717 −1.09911 + 1.64494i −1.09911 + 1.64494i −0.427555 + 0.903989i 0.640625π0.640625\pi
−0.671559 + 0.740951i 0.734375π0.734375\pi
1818 −0.336890 0.941544i −0.336890 0.941544i
1919 0.0504517 0.0841735i 0.0504517 0.0841735i −0.831470 0.555570i 0.812500π-0.812500\pi
0.881921 + 0.471397i 0.156250π0.156250\pi
2020 0.146730 0.989177i 0.146730 0.989177i
2121 0 0
2222 0 0
2323 −1.71098 + 0.914539i −1.71098 + 0.914539i −0.740951 + 0.671559i 0.765625π0.765625\pi
−0.970031 + 0.242980i 0.921875π0.921875\pi
2424 0.382683 0.923880i 0.382683 0.923880i
2525 0.290285 + 0.956940i 0.290285 + 0.956940i
2626 0 0
2727 0.514103 + 0.857729i 0.514103 + 0.857729i
2828 0 0
2929 0 0 0.998795 0.0490677i 0.0156250π-0.0156250\pi
−0.998795 + 0.0490677i 0.984375π0.984375\pi
3030 0.0490677 + 0.998795i 0.0490677 + 0.998795i
3131 −0.674993 + 1.62958i −0.674993 + 1.62958i 0.0980171 + 0.995185i 0.468750π0.468750\pi
−0.773010 + 0.634393i 0.781250π0.781250\pi
3232 0.903989 0.427555i 0.903989 0.427555i
3333 0 0
3434 1.78841 0.845855i 1.78841 0.845855i
3535 0 0
3636 −0.195090 + 0.980785i −0.195090 + 0.980785i
3737 0 0 −0.970031 0.242980i 0.921875π-0.921875\pi
0.970031 + 0.242980i 0.0781250π0.0781250\pi
3838 −0.0865477 + 0.0462607i −0.0865477 + 0.0462607i
3939 0 0
4040 −0.634393 + 0.773010i −0.634393 + 0.773010i
4141 0 0 0.290285 0.956940i 0.406250π-0.406250\pi
−0.290285 + 0.956940i 0.593750π0.593750\pi
4242 0 0
4343 0 0 −0.336890 0.941544i 0.609375π-0.609375\pi
0.336890 + 0.941544i 0.390625π0.390625\pi
4444 0 0
4545 −0.242980 0.970031i −0.242980 0.970031i
4646 1.93773 + 0.0951944i 1.93773 + 0.0951944i
4747 1.77324 0.352719i 1.77324 0.352719i 0.803208 0.595699i 0.203125π-0.203125\pi
0.970031 + 0.242980i 0.0781250π0.0781250\pi
4848 −0.803208 + 0.595699i −0.803208 + 0.595699i
4949 0.980785 + 0.195090i 0.980785 + 0.195090i
5050 0.242980 0.970031i 0.242980 0.970031i
5151 −1.58903 + 1.17850i −1.58903 + 1.17850i
5252 0 0
5353 −0.195798 0.00961895i −0.195798 0.00961895i −0.0490677 0.998795i 0.515625π-0.515625\pi
−0.146730 + 0.989177i 0.546875π0.546875\pi
5454 1.00000i 1.00000i
5555 0 0
5656 0 0
5757 0.0758597 0.0622564i 0.0758597 0.0622564i
5858 0 0
5959 0 0 −0.146730 0.989177i 0.546875π-0.546875\pi
0.146730 + 0.989177i 0.453125π0.453125\pi
6060 0.471397 0.881921i 0.471397 0.881921i
6161 −1.21416 + 0.574257i −1.21416 + 0.574257i −0.923880 0.382683i 0.875000π-0.875000\pi
−0.290285 + 0.956940i 0.593750π0.593750\pi
6262 1.41673 1.05072i 1.41673 1.05072i
6363 0 0
6464 −0.995185 0.0980171i −0.995185 0.0980171i
6565 0 0
6666 0 0
6767 0 0 −0.427555 0.903989i 0.640625π-0.640625\pi
0.427555 + 0.903989i 0.359375π0.359375\pi
6868 −1.96883 0.193913i −1.96883 0.193913i
6969 −1.91906 + 0.284666i −1.91906 + 0.284666i
7070 0 0
7171 0 0 −0.634393 0.773010i 0.718750π-0.718750\pi
0.634393 + 0.773010i 0.281250π0.281250\pi
7272 0.671559 0.740951i 0.671559 0.740951i
7373 0 0 0.995185 0.0980171i 0.0312500π-0.0312500\pi
−0.995185 + 0.0980171i 0.968750π0.968750\pi
7474 0 0
7575 −0.0490677 + 0.998795i −0.0490677 + 0.998795i
7676 0.0980171 + 0.00481527i 0.0980171 + 0.00481527i
7777 0 0
7878 0 0
7979 0.216773 1.08979i 0.216773 1.08979i −0.707107 0.707107i 0.750000π-0.750000\pi
0.923880 0.382683i 0.125000π-0.125000\pi
8080 0.941544 0.336890i 0.941544 0.336890i
8181 0.195090 + 0.980785i 0.195090 + 0.980785i
8282 0 0
8383 1.49969 0.375652i 1.49969 0.375652i 0.595699 0.803208i 0.296875π-0.296875\pi
0.903989 + 0.427555i 0.140625π0.140625\pi
8484 0 0
8585 1.86271 0.666487i 1.86271 0.666487i
8686 0 0
8787 0 0
8888 0 0
8989 0 0 −0.881921 0.471397i 0.843750π-0.843750\pi
0.881921 + 0.471397i 0.156250π0.156250\pi
9090 −0.290285 + 0.956940i −0.290285 + 0.956940i
9191 0 0
9292 −1.61310 1.07784i −1.61310 1.07784i
9393 −1.18452 + 1.30692i −1.18452 + 1.30692i
9494 −1.70229 0.609090i −1.70229 0.609090i
9595 −0.0906652 + 0.0375548i −0.0906652 + 0.0375548i
9696 0.995185 0.0980171i 0.995185 0.0980171i
9797 0 0 −0.923880 0.382683i 0.875000π-0.875000\pi
0.923880 + 0.382683i 0.125000π0.125000\pi
9898 −0.740951 0.671559i −0.740951 0.671559i
9999 0 0
100100 −0.707107 + 0.707107i −0.707107 + 0.707107i
101101 0 0 0.857729 0.514103i 0.171875π-0.171875\pi
−0.857729 + 0.514103i 0.828125π0.828125\pi
102102 1.96883 0.193913i 1.96883 0.193913i
103103 0 0 0.956940 0.290285i 0.0937500π-0.0937500\pi
−0.956940 + 0.290285i 0.906250π0.906250\pi
104104 0 0
105105 0 0
106106 0.162997 + 0.108911i 0.162997 + 0.108911i
107107 −0.248225 + 0.524828i −0.248225 + 0.524828i −0.989177 0.146730i 0.953125π-0.953125\pi
0.740951 + 0.671559i 0.234375π0.234375\pi
108108 −0.514103 + 0.857729i −0.514103 + 0.857729i
109109 0.577920 + 0.346392i 0.577920 + 0.346392i 0.773010 0.634393i 0.218750π-0.218750\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
110110 0 0
111111 0 0
112112 0 0
113113 0.710998 0.475074i 0.710998 0.475074i −0.146730 0.989177i 0.546875π-0.546875\pi
0.857729 + 0.514103i 0.171875π0.171875\pi
114114 −0.0970732 + 0.0143994i −0.0970732 + 0.0143994i
115115 1.91906 + 0.284666i 1.91906 + 0.284666i
116116 0 0
117117 0 0
118118 0 0
119119 0 0
120120 −0.857729 + 0.514103i −0.857729 + 0.514103i
121121 −0.0980171 + 0.995185i −0.0980171 + 0.995185i
122122 1.33665 + 0.131649i 1.33665 + 0.131649i
123123 0 0
124124 −1.75535 + 0.172887i −1.75535 + 0.172887i
125125 0.336890 0.941544i 0.336890 0.941544i
126126 0 0
127127 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
128128 0.803208 + 0.595699i 0.803208 + 0.595699i
129129 0 0
130130 0 0
131131 0 0 0.336890 0.941544i 0.390625π-0.390625\pi
−0.336890 + 0.941544i 0.609375π0.609375\pi
132132 0 0
133133 0 0
134134 0 0
135135 0.0980171 0.995185i 0.0980171 0.995185i
136136 1.58903 + 1.17850i 1.58903 + 1.17850i
137137 −1.19462 + 1.45565i −1.19462 + 1.45565i −0.336890 + 0.941544i 0.609375π0.609375\pi
−0.857729 + 0.514103i 0.828125π0.828125\pi
138138 1.79238 + 0.742430i 1.79238 + 0.742430i
139139 0.761850 0.690501i 0.761850 0.690501i −0.195090 0.980785i 0.562500π-0.562500\pi
0.956940 + 0.290285i 0.0937500π0.0937500\pi
140140 0 0
141141 1.78841 + 0.265286i 1.78841 + 0.265286i
142142 0 0
143143 0 0
144144 −0.956940 + 0.290285i −0.956940 + 0.290285i
145145 0 0
146146 0 0
147147 0.857729 + 0.514103i 0.857729 + 0.514103i
148148 0 0
149149 0 0 0.427555 0.903989i 0.359375π-0.359375\pi
−0.427555 + 0.903989i 0.640625π0.640625\pi
150150 0.555570 0.831470i 0.555570 0.831470i
151151 −0.598102 1.11897i −0.598102 1.11897i −0.980785 0.195090i 0.937500π-0.937500\pi
0.382683 0.923880i 0.375000π-0.375000\pi
152152 −0.0815966 0.0545211i −0.0815966 0.0545211i
153153 −1.89317 + 0.574286i −1.89317 + 0.574286i
154154 0 0
155155 1.51290 0.906796i 1.51290 0.906796i
156156 0 0
157157 0 0 −0.0490677 0.998795i 0.515625π-0.515625\pi
0.0490677 + 0.998795i 0.484375π0.484375\pi
158158 −0.746196 + 0.823301i −0.746196 + 0.823301i
159159 −0.181112 0.0750191i −0.181112 0.0750191i
160160 −0.980785 0.195090i −0.980785 0.195090i
161161 0 0
162162 0.336890 0.941544i 0.336890 0.941544i
163163 0 0 0.671559 0.740951i 0.265625π-0.265625\pi
−0.671559 + 0.740951i 0.734375π0.734375\pi
164164 0 0
165165 0 0
166166 −1.47945 0.448786i −1.47945 0.448786i
167167 −1.05072 0.561621i −1.05072 0.561621i −0.146730 0.989177i 0.546875π-0.546875\pi
−0.903989 + 0.427555i 0.859375π0.859375\pi
168168 0 0
169169 −0.956940 0.290285i −0.956940 0.290285i
170170 −1.94034 0.385958i −1.94034 0.385958i
171171 0.0923988 0.0330608i 0.0923988 0.0330608i
172172 0 0
173173 1.85652 0.465035i 1.85652 0.465035i 0.857729 0.514103i 0.171875π-0.171875\pi
0.998795 + 0.0490677i 0.0156250π0.0156250\pi
174174 0 0
175175 0 0
176176 0 0
177177 0 0
178178 0 0
179179 0 0 −0.595699 0.803208i 0.703125π-0.703125\pi
0.595699 + 0.803208i 0.296875π0.296875\pi
180180 0.740951 0.671559i 0.740951 0.671559i
181181 −0.0788231 + 1.60448i −0.0788231 + 1.60448i 0.555570 + 0.831470i 0.312500π0.312500\pi
−0.634393 + 0.773010i 0.718750π0.718750\pi
182182 0 0
183183 −1.33665 + 0.131649i −1.33665 + 0.131649i
184184 0.829484 + 1.75380i 0.829484 + 1.75380i
185185 0 0
186186 1.68789 0.512016i 1.68789 0.512016i
187187 0 0
188188 1.14697 + 1.39759i 1.14697 + 1.39759i
189189 0 0
190190 0.0970732 + 0.0143994i 0.0970732 + 0.0143994i
191191 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
192192 −0.903989 0.427555i −0.903989 0.427555i
193193 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
194194 0 0
195195 0 0
196196 0.290285 + 0.956940i 0.290285 + 0.956940i
197197 0.287822 + 1.94034i 0.287822 + 1.94034i 0.336890 + 0.941544i 0.390625π0.390625\pi
−0.0490677 + 0.998795i 0.515625π0.515625\pi
198198 0 0
199199 −0.301614 + 0.247528i −0.301614 + 0.247528i −0.773010 0.634393i 0.781250π-0.781250\pi
0.471397 + 0.881921i 0.343750π0.343750\pi
200200 0.970031 0.242980i 0.970031 0.242980i
201201 0 0
202202 0 0
203203 0 0
204204 −1.78841 0.845855i −1.78841 0.845855i
205205 0 0
206206 0 0
207207 −1.90278 0.378487i −1.90278 0.378487i
208208 0 0
209209 0 0
210210 0 0
211211 0.163715 + 0.653587i 0.163715 + 0.653587i 0.995185 + 0.0980171i 0.0312500π0.0312500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
212212 −0.0838155 0.177213i −0.0838155 0.177213i
213213 0 0
214214 0.482726 0.322547i 0.482726 0.322547i
215215 0 0
216216 0.881921 0.471397i 0.881921 0.471397i
217217 0 0
218218 −0.317618 0.594221i −0.317618 0.594221i
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
224224 0 0
225225 −0.382683 + 0.923880i −0.382683 + 0.923880i
226226 −0.854080 + 0.0419583i −0.854080 + 0.0419583i
227227 −1.98797 + 0.0976628i −1.98797 + 0.0976628i −0.998795 0.0490677i 0.984375π-0.984375\pi
−0.989177 + 0.146730i 0.953125π0.953125\pi
228228 0.0906652 + 0.0375548i 0.0906652 + 0.0375548i
229229 −0.881921 1.47140i −0.881921 1.47140i −0.881921 0.471397i 0.843750π-0.843750\pi
1.00000i 0.5π-0.5\pi
230230 −1.49969 1.23076i −1.49969 1.23076i
231231 0 0
232232 0 0
233233 −1.51290 + 0.808661i −1.51290 + 0.808661i −0.998795 0.0490677i 0.984375π-0.984375\pi
−0.514103 + 0.857729i 0.671875π0.671875\pi
234234 0 0
235235 −1.63439 0.773010i −1.63439 0.773010i
236236 0 0
237237 0.571240 0.953057i 0.571240 0.953057i
238238 0 0
239239 0 0 0.555570 0.831470i 0.312500π-0.312500\pi
−0.555570 + 0.831470i 0.687500π0.687500\pi
240240 1.00000 1.00000
241241 −0.523788 0.783904i −0.523788 0.783904i 0.471397 0.881921i 0.343750π-0.343750\pi
−0.995185 + 0.0980171i 0.968750π0.968750\pi
242242 0.595699 0.803208i 0.595699 0.803208i
243243 −0.146730 + 0.989177i −0.146730 + 0.989177i
244244 −1.07880 0.800094i −1.07880 0.800094i
245245 −0.671559 0.740951i −0.671559 0.740951i
246246 0 0
247247 0 0
248248 1.59449 + 0.754140i 1.59449 + 0.754140i
249249 1.53858 + 0.151537i 1.53858 + 0.151537i
250250 −0.773010 + 0.634393i −0.773010 + 0.634393i
251251 0 0 −0.803208 0.595699i 0.796875π-0.796875\pi
0.803208 + 0.595699i 0.203125π0.203125\pi
252252 0 0
253253 0 0
254254 0 0
255255 1.97835 1.97835
256256 −0.382683 0.923880i −0.382683 0.923880i
257257 0.485960 0.485960 0.242980 0.970031i 0.421875π-0.421875\pi
0.242980 + 0.970031i 0.421875π0.421875\pi
258258 0 0
259259 0 0
260260 0 0
261261 0 0
262262 0 0
263263 −0.292048 0.0287642i −0.292048 0.0287642i −0.0490677 0.998795i 0.515625π-0.515625\pi
−0.242980 + 0.970031i 0.578125π0.578125\pi
264264 0 0
265265 0.151537 + 0.124363i 0.151537 + 0.124363i
266266 0 0
267267 0 0
268268 0 0
269269 0 0 0.146730 0.989177i 0.453125π-0.453125\pi
−0.146730 + 0.989177i 0.546875π0.546875\pi
270270 −0.595699 + 0.803208i −0.595699 + 0.803208i
271271 −0.425215 0.636379i −0.425215 0.636379i 0.555570 0.831470i 0.312500π-0.312500\pi
−0.980785 + 0.195090i 0.937500π0.937500\pi
272272 −0.757083 1.82776i −0.757083 1.82776i
273273 0 0
274274 1.77301 0.634393i 1.77301 0.634393i
275275 0 0
276276 −1.15569 1.55827i −1.15569 1.55827i
277277 0 0 −0.903989 0.427555i 0.859375π-0.859375\pi
0.903989 + 0.427555i 0.140625π0.140625\pi
278278 −1.00845 + 0.200593i −1.00845 + 0.200593i
279279 −1.55557 + 0.831470i −1.55557 + 0.831470i
280280 0 0
281281 0 0 −0.290285 0.956940i 0.593750π-0.593750\pi
0.290285 + 0.956940i 0.406250π0.406250\pi
282282 −1.39759 1.14697i −1.39759 1.14697i
283283 0 0 −0.514103 0.857729i 0.671875π-0.671875\pi
0.514103 + 0.857729i 0.328125π0.328125\pi
284284 0 0
285285 −0.0980171 + 0.00481527i −0.0980171 + 0.00481527i
286286 0 0
287287 0 0
288288 0.970031 + 0.242980i 0.970031 + 0.242980i
289289 −1.11509 2.69207i −1.11509 2.69207i
290290 0 0
291291 0 0
292292 0 0
293293 1.49969 + 0.375652i 1.49969 + 0.375652i 0.903989 0.427555i 0.140625π-0.140625\pi
0.595699 + 0.803208i 0.296875π0.296875\pi
294294 −0.471397 0.881921i −0.471397 0.881921i
295295 0 0
296296 0 0
297297 0 0
298298 0 0
299299 0 0
300300 −0.903989 + 0.427555i −0.903989 + 0.427555i
301301 0 0
302302 −0.0622564 + 1.26726i −0.0622564 + 1.26726i
303303 0 0
304304 0.0419583 + 0.0887133i 0.0419583 + 0.0887133i
305305 1.31731 + 0.262029i 1.31731 + 0.262029i
306306 1.91906 + 0.480701i 1.91906 + 0.480701i
307307 0 0 0.803208 0.595699i 0.203125π-0.203125\pi
−0.803208 + 0.595699i 0.796875π0.796875\pi
308308 0 0
309309 0 0
310310 −1.76384 −1.76384
311311 0 0 −0.0980171 0.995185i 0.531250π-0.531250\pi
0.0980171 + 0.995185i 0.468750π0.468750\pi
312312 0 0
313313 0 0 0.773010 0.634393i 0.218750π-0.218750\pi
−0.773010 + 0.634393i 0.781250π0.781250\pi
314314 0 0
315315 0 0
316316 1.06330 0.322547i 1.06330 0.322547i
317317 1.50328 0.710998i 1.50328 0.710998i 0.514103 0.857729i 0.328125π-0.328125\pi
0.989177 + 0.146730i 0.0468750π0.0468750\pi
318318 0.116777 + 0.157456i 0.116777 + 0.157456i
319319 0 0
320320 0.740951 + 0.671559i 0.740951 + 0.671559i
321321 −0.410525 + 0.410525i −0.410525 + 0.410525i
322322 0 0
323323 0.0830083 + 0.175506i 0.0830083 + 0.175506i
324324 −0.773010 + 0.634393i −0.773010 + 0.634393i
325325 0 0
326326 0 0
327327 0.427441 + 0.520839i 0.427441 + 0.520839i
328328 0 0
329329 0 0
330330 0 0
331331 0.0584592 1.18996i 0.0584592 1.18996i −0.773010 0.634393i 0.781250π-0.781250\pi
0.831470 0.555570i 0.187500π-0.187500\pi
332332 1.03824 + 1.14553i 1.03824 + 1.14553i
333333 0 0
334334 0.612501 + 1.02190i 0.612501 + 1.02190i
335335 0 0
336336 0 0
337337 0 0 −0.195090 0.980785i 0.562500π-0.562500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
338338 0.671559 + 0.740951i 0.671559 + 0.740951i
339339 0.829484 0.207775i 0.829484 0.207775i
340340 1.46586 + 1.32858i 1.46586 + 1.32858i
341341 0 0
342342 −0.0962497 0.0191453i −0.0962497 0.0191453i
343343 0 0
344344 0 0
345345 1.71098 + 0.914539i 1.71098 + 0.914539i
346346 −1.83147 0.555570i −1.83147 0.555570i
347347 0.404061 1.61310i 0.404061 1.61310i −0.336890 0.941544i 0.609375π-0.609375\pi
0.740951 0.671559i 0.234375π-0.234375\pi
348348 0 0
349349 1.34150 1.48012i 1.34150 1.48012i 0.634393 0.773010i 0.281250π-0.281250\pi
0.707107 0.707107i 0.250000π-0.250000\pi
350350 0 0
351351 0 0
352352 0 0
353353 1.36910 + 0.567099i 1.36910 + 0.567099i 0.941544 0.336890i 0.109375π-0.109375\pi
0.427555 + 0.903989i 0.359375π0.359375\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 0 0 0.956940 0.290285i 0.0937500π-0.0937500\pi
−0.956940 + 0.290285i 0.906250π0.906250\pi
360360 −0.980785 + 0.195090i −0.980785 + 0.195090i
361361 0.466857 + 0.873428i 0.466857 + 0.873428i
362362 0.892476 1.33569i 0.892476 1.33569i
363363 −0.427555 + 0.903989i −0.427555 + 0.903989i
364364 0 0
365365 0 0
366366 1.21416 + 0.574257i 1.21416 + 0.574257i
367367 0 0 −0.831470 0.555570i 0.812500π-0.812500\pi
0.831470 + 0.555570i 0.187500π0.187500\pi
368368 0.190159 1.93072i 0.190159 1.93072i
369369 0 0
370370 0 0
371371 0 0
372372 −1.71098 0.428579i −1.71098 0.428579i
373373 0 0 0.740951 0.671559i 0.234375π-0.234375\pi
−0.740951 + 0.671559i 0.765625π0.765625\pi
374374 0 0
375375 0.634393 0.773010i 0.634393 0.773010i
376376 −0.265286 1.78841i −0.265286 1.78841i
377377 0 0
378378 0 0
379379 −0.956940 + 1.29028i −0.956940 + 1.29028i 1.00000i 0.5π0.5\pi
−0.956940 + 0.290285i 0.906250π0.906250\pi
380380 −0.0758597 0.0622564i −0.0758597 0.0622564i
381381 0 0
382382 0 0
383383 1.48190i 1.48190i 0.671559 + 0.740951i 0.265625π0.265625\pi
−0.671559 + 0.740951i 0.734375π0.734375\pi
384384 0.555570 + 0.831470i 0.555570 + 0.831470i
385385 0 0
386386 0 0
387387 0 0
388388 0 0
389389 0 0 0.595699 0.803208i 0.296875π-0.296875\pi
−0.595699 + 0.803208i 0.703125π0.703125\pi
390390 0 0
391391 0.376202 3.81965i 0.376202 3.81965i
392392 0.242980 0.970031i 0.242980 0.970031i
393393 0 0
394394 0.750661 1.81225i 0.750661 1.81225i
395395 −0.823301 + 0.746196i −0.823301 + 0.746196i
396396 0 0
397397 0 0 −0.989177 0.146730i 0.953125π-0.953125\pi
0.989177 + 0.146730i 0.0468750π0.0468750\pi
398398 0.385958 0.0572514i 0.385958 0.0572514i
399399 0 0
400400 −0.956940 0.290285i −0.956940 0.290285i
401401 0 0 −0.831470 0.555570i 0.812500π-0.812500\pi
0.831470 + 0.555570i 0.187500π0.187500\pi
402402 0 0
403403 0 0
404404 0 0
405405 0.427555 0.903989i 0.427555 0.903989i
406406 0 0
407407 0 0
408408 1.09911 + 1.64494i 1.09911 + 1.64494i
409409 1.21415 0.368309i 1.21415 0.368309i 0.382683 0.923880i 0.375000π-0.375000\pi
0.831470 + 0.555570i 0.187500π0.187500\pi
410410 0 0
411411 −1.61518 + 0.968101i −1.61518 + 0.968101i
412412 0 0
413413 0 0
414414 1.43749 + 1.30287i 1.43749 + 1.30287i
415415 −1.42834 0.591637i −1.42834 0.591637i
416416 0 0
417417 0.949938 0.393477i 0.949938 0.393477i
418418 0 0
419419 0 0 0.671559 0.740951i 0.265625π-0.265625\pi
−0.671559 + 0.740951i 0.734375π0.734375\pi
420420 0 0
421421 −0.249834 + 0.997391i −0.249834 + 0.997391i 0.707107 + 0.707107i 0.250000π0.250000\pi
−0.956940 + 0.290285i 0.906250π0.906250\pi
422422 0.195588 0.644767i 0.195588 0.644767i
423423 1.59449 + 0.852275i 1.59449 + 0.852275i
424424 −0.0192147 + 0.195090i −0.0192147 + 0.195090i
425425 −1.89317 0.574286i −1.89317 0.574286i
426426 0 0
427427 0 0
428428 −0.579870 + 0.0284872i −0.579870 + 0.0284872i
429429 0 0
430430 0 0
431431 0 0 −0.195090 0.980785i 0.562500π-0.562500\pi
0.195090 + 0.980785i 0.437500π0.437500\pi
432432 −0.998795 0.0490677i −0.998795 0.0490677i
433433 0 0 0.195090 0.980785i 0.437500π-0.437500\pi
−0.195090 + 0.980785i 0.562500π0.562500\pi
434434 0 0
435435 0 0
436436 −0.0330608 + 0.672968i −0.0330608 + 0.672968i
437437 −0.00934193 + 0.190159i −0.00934193 + 0.190159i
438438 0 0
439439 1.95213 0.192268i 1.95213 0.192268i 0.956940 0.290285i 0.0937500π-0.0937500\pi
0.995185 + 0.0980171i 0.0312500π0.0312500\pi
440440 0 0
441441 0.634393 + 0.773010i 0.634393 + 0.773010i
442442 0 0
443443 −0.932589 + 0.138337i −0.932589 + 0.138337i −0.595699 0.803208i 0.703125π-0.703125\pi
−0.336890 + 0.941544i 0.609375π0.609375\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 0 0
449449 0 0 −0.707107 0.707107i 0.750000π-0.750000\pi
0.707107 + 0.707107i 0.250000π0.250000\pi
450450 0.803208 0.595699i 0.803208 0.595699i
451451 0 0
452452 0.754140 + 0.403096i 0.754140 + 0.403096i
453453 −0.186170 1.25505i −0.186170 1.25505i
454454 1.75535 + 0.938254i 1.75535 + 0.938254i
455455 0 0
456456 −0.0584592 0.0788231i −0.0584592 0.0788231i
457457 0 0 −0.0980171 0.995185i 0.531250π-0.531250\pi
0.0980171 + 0.995185i 0.468750π0.468750\pi
458458 1.71546i 1.71546i
459459 −1.97597 0.0970732i −1.97597 0.0970732i
460460 0.653587 + 1.82665i 0.653587 + 1.82665i
461461 0 0 0.803208 0.595699i 0.203125π-0.203125\pi
−0.803208 + 0.595699i 0.796875π0.796875\pi
462462 0 0
463463 0 0 −0.980785 0.195090i 0.937500π-0.937500\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
464464 0 0
465465 1.72995 0.344109i 1.72995 0.344109i
466466 1.71339 + 0.0841735i 1.71339 + 0.0841735i
467467 0.476623 + 1.90278i 0.476623 + 1.90278i 0.427555 + 0.903989i 0.359375π0.359375\pi
0.0490677 + 0.998795i 0.484375π0.484375\pi
468468 0 0
469469 0 0
470470 1.00446 + 1.50328i 1.00446 + 1.50328i
471471 0 0
472472 0 0
473473 0 0
474474 −0.979938 + 0.523788i −0.979938 + 0.523788i
475475 0.0951944 + 0.0238449i 0.0951944 + 0.0238449i
476476 0 0
477477 −0.145252 0.131649i −0.145252 0.131649i
478478 0 0
479479 0 0 −0.382683 0.923880i 0.625000π-0.625000\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
480480 −0.857729 0.514103i −0.857729 0.514103i
481481 0 0
482482 0.0462607 + 0.941658i 0.0462607 + 0.941658i
483483 0 0
484484 −0.923880 + 0.382683i −0.923880 + 0.382683i
485485 0 0
486486 0.634393 0.773010i 0.634393 0.773010i
487487 0 0 −0.290285 0.956940i 0.593750π-0.593750\pi
0.290285 + 0.956940i 0.406250π0.406250\pi
488488 0.513989 + 1.24088i 0.513989 + 1.24088i
489489 0 0
490490 0.195090 + 0.980785i 0.195090 + 0.980785i
491491 0 0 −0.903989 0.427555i 0.859375π-0.859375\pi
0.903989 + 0.427555i 0.140625π0.140625\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 −0.979938 1.46658i −0.979938 1.46658i
497497 0 0
498498 −1.24178 0.920964i −1.24178 0.920964i
499499 0.251710 1.69689i 0.251710 1.69689i −0.382683 0.923880i 0.625000π-0.625000\pi
0.634393 0.773010i 0.281250π-0.281250\pi
500500 0.989177 0.146730i 0.989177 0.146730i
501501 −0.800094 0.882768i −0.800094 0.882768i
502502 0 0
503503 −1.45565 1.19462i −1.45565 1.19462i −0.941544 0.336890i 0.890625π-0.890625\pi
−0.514103 0.857729i 0.671875π-0.671875\pi
504504 0 0
505505 0 0
506506 0 0
507507 −0.803208 0.595699i −0.803208 0.595699i
508508 0 0
509509 0 0 −0.941544 0.336890i 0.890625π-0.890625\pi
0.941544 + 0.336890i 0.109375π0.109375\pi
510510 −1.69689 1.01708i −1.69689 1.01708i
511511 0 0
512512 −0.146730 + 0.989177i −0.146730 + 0.989177i
513513 0.0981353 0.0981353
514514 −0.416822 0.249834i −0.416822 0.249834i
515515 0 0
516516 0 0
517517 0 0
518518 0 0
519519 1.90466 + 0.187593i 1.90466 + 0.187593i
520520 0 0
521521 0 0 −0.773010 0.634393i 0.781250π-0.781250\pi
0.773010 + 0.634393i 0.218750π0.218750\pi
522522 0 0
523523 0 0 −0.671559 0.740951i 0.734375π-0.734375\pi
0.671559 + 0.740951i 0.265625π0.265625\pi
524524 0 0
525525 0 0
526526 0.235710 + 0.174814i 0.235710 + 0.174814i
527527 −1.93866 2.90142i −1.93866 2.90142i
528528 0 0
529529 1.53551 2.29805i 1.53551 2.29805i
530530 −0.0660420 0.184575i −0.0660420 0.184575i
531531 0 0
532532 0 0
533533 0 0
534534 0 0
535535 0.512016 0.273678i 0.512016 0.273678i
536536 0 0
537537 0 0
538538 0 0
539539 0 0
540540 0.923880 0.382683i 0.923880 0.382683i
541541 1.18996 0.0584592i 1.18996 0.0584592i 0.555570 0.831470i 0.312500π-0.312500\pi
0.634393 + 0.773010i 0.281250π0.281250\pi
542542 0.0375548 + 0.764445i 0.0375548 + 0.764445i
543543 −0.614748 + 1.48413i −0.614748 + 1.48413i
544544 −0.290285 + 1.95694i −0.290285 + 1.95694i
545545 −0.257844 0.622491i −0.257844 0.622491i
546546 0 0
547547 0 0 −0.740951 0.671559i 0.765625π-0.765625\pi
0.740951 + 0.671559i 0.234375π0.234375\pi
548548 −1.84691 0.367372i −1.84691 0.367372i
549549 −1.30287 0.326351i −1.30287 0.326351i
550550 0 0
551551 0 0
552552 0.190159 + 1.93072i 0.190159 + 1.93072i
553553 0 0
554554 0 0
555555 0 0
556556 0.968101 + 0.346392i 0.968101 + 0.346392i
557557 0.308290 + 1.23076i 0.308290 + 1.23076i 0.903989 + 0.427555i 0.140625π0.140625\pi
−0.595699 + 0.803208i 0.703125π0.703125\pi
558558 1.76172 + 0.0865477i 1.76172 + 0.0865477i
559559 0 0
560560 0 0
561561 0 0
562562 0 0
563563 1.57555 1.16851i 1.57555 1.16851i 0.671559 0.740951i 0.265625π-0.265625\pi
0.903989 0.427555i 0.140625π-0.140625\pi
564564 0.609090 + 1.70229i 0.609090 + 1.70229i
565565 −0.854080 0.0419583i −0.854080 0.0419583i
566566 0 0
567567 0 0
568568 0 0
569569 0 0 0.773010 0.634393i 0.218750π-0.218750\pi
−0.773010 + 0.634393i 0.781250π0.781250\pi
570570 0.0865477 + 0.0462607i 0.0865477 + 0.0462607i
571571 −0.0713052 0.480701i −0.0713052 0.480701i −0.995185 0.0980171i 0.968750π-0.968750\pi
0.923880 0.382683i 0.125000π-0.125000\pi
572572 0 0
573573 0 0
574574 0 0
575575 −1.37183 1.37183i −1.37183 1.37183i
576576 −0.707107 0.707107i −0.707107 0.707107i
577577 0 0 0.707107 0.707107i 0.250000π-0.250000\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
578578 −0.427555 + 2.88234i −0.427555 + 2.88234i
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 0 0
584584 0 0
585585 0 0
586586 −1.09320 1.09320i −1.09320 1.09320i
587587 0.0939097 1.91158i 0.0939097 1.91158i −0.242980 0.970031i 0.578125π-0.578125\pi
0.336890 0.941544i 0.390625π-0.390625\pi
588588 −0.0490677 + 0.998795i −0.0490677 + 0.998795i
589589 0.103113 + 0.139031i 0.103113 + 0.139031i
590590 0 0
591591 −0.382683 + 1.92388i −0.382683 + 1.92388i
592592 0 0
593593 0.200593 + 1.00845i 0.200593 + 1.00845i 0.941544 + 0.336890i 0.109375π0.109375\pi
−0.740951 + 0.671559i 0.765625π0.765625\pi
594594 0 0
595595 0 0
596596 0 0
597597 −0.367372 + 0.131448i −0.367372 + 0.131448i
598598 0 0
599599 0 0 −0.956940 0.290285i 0.906250π-0.906250\pi
0.956940 + 0.290285i 0.0937500π0.0937500\pi
600600 0.995185 + 0.0980171i 0.995185 + 0.0980171i
601601 −1.11897 0.598102i −1.11897 0.598102i −0.195090 0.980785i 0.562500π-0.562500\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
602602 0 0
603603 0 0
604604 0.704900 1.05496i 0.704900 1.05496i
605605 0.671559 0.740951i 0.671559 0.740951i
606606 0 0
607607 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
608608 0.00961895 0.0976628i 0.00961895 0.0976628i
609609 0 0
610610 −0.995185 0.901983i −0.995185 0.901983i
611611 0 0
612612 −1.39891 1.39891i −1.39891 1.39891i
613613 0 0 0.857729 0.514103i 0.171875π-0.171875\pi
−0.857729 + 0.514103i 0.828125π0.828125\pi
614614 0 0
615615 0 0
616616 0 0
617617 0.852275 + 1.59449i 0.852275 + 1.59449i 0.803208 + 0.595699i 0.203125π0.203125\pi
0.0490677 + 0.998795i 0.484375π0.484375\pi
618618 0 0
619619 0.805124 1.70229i 0.805124 1.70229i 0.0980171 0.995185i 0.468750π-0.468750\pi
0.707107 0.707107i 0.250000π-0.250000\pi
620620 1.51290 + 0.906796i 1.51290 + 0.906796i
621621 −1.66405 0.997391i −1.66405 0.997391i
622622 0 0
623623 0 0
624624 0 0
625625 −0.831470 + 0.555570i −0.831470 + 0.555570i
626626 0 0
627627 0 0
628628 0 0
629629 0 0
630630 0 0
631631 −1.17221 + 1.42834i −1.17221 + 1.42834i −0.290285 + 0.956940i 0.593750π0.593750\pi
−0.881921 + 0.471397i 0.843750π0.843750\pi
632632 −1.07784 0.269985i −1.07784 0.269985i
633633 −0.0660420 + 0.670535i −0.0660420 + 0.670535i
634634 −1.65493 0.162997i −1.65493 0.162997i
635635 0 0
636636 −0.0192147 0.195090i −0.0192147 0.195090i
637637 0 0
638638 0 0
639639 0 0
640640 −0.290285 0.956940i −0.290285 0.956940i
641641 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
642642 0.563170 0.141067i 0.563170 0.141067i
643643 0 0 0.336890 0.941544i 0.390625π-0.390625\pi
−0.336890 + 0.941544i 0.609375π0.609375\pi
644644 0 0
645645 0 0
646646 0.0190297 0.193211i 0.0190297 0.193211i
647647 0.195798 1.98797i 0.195798 1.98797i 0.0490677 0.998795i 0.484375π-0.484375\pi
0.146730 0.989177i 0.453125π-0.453125\pi
648648 0.989177 0.146730i 0.989177 0.146730i
649649 0 0
650650 0 0
651651 0 0
652652 0 0
653653 0.574286 + 0.0851872i 0.574286 + 0.0851872i 0.427555 0.903989i 0.359375π-0.359375\pi
0.146730 + 0.989177i 0.453125π0.453125\pi
654654 −0.0988640 0.666487i −0.0988640 0.666487i
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 0 0 −0.857729 0.514103i 0.828125π-0.828125\pi
0.857729 + 0.514103i 0.171875π0.171875\pi
660660 0 0
661661 −0.805124 + 1.70229i −0.805124 + 1.70229i −0.0980171 + 0.995185i 0.531250π0.531250\pi
−0.707107 + 0.707107i 0.750000π0.750000\pi
662662 −0.661906 + 0.990612i −0.661906 + 0.990612i
663663 0 0
664664 −0.301614 1.51631i −0.301614 1.51631i
665665 0 0
666666 0 0
667667 0 0
668668 1.19140i 1.19140i
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
674674 0 0
675675 −0.671559 + 0.740951i −0.671559 + 0.740951i
676676 −0.195090 0.980785i −0.195090 0.980785i
677677 0.229080 0.914539i 0.229080 0.914539i −0.740951 0.671559i 0.765625π-0.765625\pi
0.970031 0.242980i 0.0781250π-0.0781250\pi
678678 −0.818289 0.248225i −0.818289 0.248225i
679679 0 0
680680 −0.574286 1.89317i −0.574286 1.89317i
681681 −1.90466 0.577774i −1.90466 0.577774i
682682 0 0
683683 1.04619 0.374332i 1.04619 0.374332i 0.242980 0.970031i 0.421875π-0.421875\pi
0.803208 + 0.595699i 0.203125π0.203125\pi
684684 0.0727135 + 0.0659037i 0.0727135 + 0.0659037i
685685 1.82665 0.457553i 1.82665 0.457553i
686686 0 0
687687 −0.334669 1.68250i −0.334669 1.68250i
688688 0 0
689689 0 0
690690 −0.997391 1.66405i −0.997391 1.66405i
691691 −0.956940 1.29028i −0.956940 1.29028i −0.956940 0.290285i 0.906250π-0.906250\pi
1.00000i 0.5π-0.5\pi
692692 1.28528 + 1.41809i 1.28528 + 1.41809i
693693 0 0
694694 −1.17588 + 1.17588i −1.17588 + 1.17588i
695695 −1.02325 + 0.100782i −1.02325 + 0.100782i
696696 0 0
697697 0 0
698698 −1.91158 + 0.579870i −1.91158 + 0.579870i
699699 −1.69689 + 0.251710i −1.69689 + 0.251710i
700700 0 0
701701 0 0 −0.427555 0.903989i 0.640625π-0.640625\pi
0.427555 + 0.903989i 0.359375π0.359375\pi
702702 0 0
703703 0 0
704704 0 0
705705 −1.27843 1.27843i −1.27843 1.27843i
706706 −0.882768 1.19028i −0.882768 1.19028i
707707 0 0
708708 0 0
709709 0.293107 + 1.97597i 0.293107 + 1.97597i 0.195090 + 0.980785i 0.437500π0.437500\pi
0.0980171 + 0.995185i 0.468750π0.468750\pi
710710 0 0
711711 0.858923 0.704900i 0.858923 0.704900i
712712 0 0
713713 −0.335411 3.40549i −0.335411 3.40549i
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 0 0
719719 0 0 −0.980785 0.195090i 0.937500π-0.937500\pi
0.980785 + 0.195090i 0.0625000π0.0625000\pi
720720 0.941544 + 0.336890i 0.941544 + 0.336890i
721721 0 0
722722 0.0485951 0.989177i 0.0485951 0.989177i
723723 −0.229080 0.914539i −0.229080 0.914539i
724724 −1.45218 + 0.686831i −1.45218 + 0.686831i
725725 0 0
726726 0.831470 0.555570i 0.831470 0.555570i
727727 0 0 0.290285 0.956940i 0.406250π-0.406250\pi
−0.290285 + 0.956940i 0.593750π0.593750\pi
728728 0 0
729729 −0.471397 + 0.881921i −0.471397 + 0.881921i
730730 0 0
731731 0 0
732732 −0.746196 1.11676i −0.746196 1.11676i
733733 0 0 −0.740951 0.671559i 0.765625π-0.765625\pi
0.740951 + 0.671559i 0.234375π0.234375\pi
734734 0 0
735735 −0.382683 0.923880i −0.382683 0.923880i
736736 −1.15569 + 1.55827i −1.15569 + 1.55827i
737737 0 0
738738 0 0
739739 −0.854080 + 0.0419583i −0.854080 + 0.0419583i −0.471397 0.881921i 0.656250π-0.656250\pi
−0.382683 + 0.923880i 0.625000π0.625000\pi
740740 0 0
741741 0 0
742742 0 0
743743 −0.430174 1.41809i −0.430174 1.41809i −0.857729 0.514103i 0.828125π-0.828125\pi
0.427555 0.903989i 0.359375π-0.359375\pi
744744 1.24723 + 1.24723i 1.24723 + 1.24723i
745745 0 0
746746 0 0
747747 1.39759 + 0.661009i 1.39759 + 0.661009i
748748 0 0
749749 0 0
750750 −0.941544 + 0.336890i −0.941544 + 0.336890i
751751 −0.322547 + 0.482726i −0.322547 + 0.482726i −0.956940 0.290285i 0.906250π-0.906250\pi
0.634393 + 0.773010i 0.281250π0.281250\pi
752752 −0.691883 + 1.67035i −0.691883 + 1.67035i
753753 0 0
754754 0 0
755755 −0.186170 + 1.25505i −0.186170 + 1.25505i
756756 0 0
757757 0 0 −0.671559 0.740951i 0.734375π-0.734375\pi
0.671559 + 0.740951i 0.265625π0.265625\pi
758758 1.48413 0.614748i 1.48413 0.614748i
759759 0 0
760760 0.0330608 + 0.0923988i 0.0330608 + 0.0923988i
761761 0 0 −0.995185 0.0980171i 0.968750π-0.968750\pi
0.995185 + 0.0980171i 0.0312500π0.0312500\pi
762762 0 0
763763 0 0
764764 0 0
765765 1.86271 + 0.666487i 1.86271 + 0.666487i
766766 0.761850 1.27107i 0.761850 1.27107i
767767 0 0
768768 −0.0490677 0.998795i −0.0490677 0.998795i
769769 −0.580569 −0.580569 −0.290285 0.956940i 0.593750π-0.593750\pi
−0.290285 + 0.956940i 0.593750π0.593750\pi
770770 0 0
771771 0.457553 + 0.163715i 0.457553 + 0.163715i
772772 0 0
773773 1.48413 + 1.10071i 1.48413 + 1.10071i 0.970031 + 0.242980i 0.0781250π0.0781250\pi
0.514103 + 0.857729i 0.328125π0.328125\pi
774774 0 0
775775 −1.75535 0.172887i −1.75535 0.172887i
776776 0 0
777777 0 0
778778 0 0
779779 0 0
780780 0 0
781781 0 0
782782 −2.28637 + 3.08281i −2.28637 + 3.08281i
783783 0 0
784784 −0.707107 + 0.707107i −0.707107 + 0.707107i
785785 0 0
786786 0 0
787787 0 0 0.514103 0.857729i 0.328125π-0.328125\pi
−0.514103 + 0.857729i 0.671875π0.671875\pi
788788 −1.57555 + 1.16851i −1.57555 + 1.16851i
789789 −0.265286 0.125471i −0.265286 0.125471i
790790 1.08979 0.216773i 1.08979 0.216773i
791791 0 0
792792 0 0
793793 0 0
794794 0 0
795795 0.100782 + 0.168144i 0.100782 + 0.168144i
796796 −0.360480 0.149316i −0.360480 0.149316i
797797 −1.66094 + 0.0815966i −1.66094 + 0.0815966i −0.857729 0.514103i 0.828125π-0.828125\pi
−0.803208 + 0.595699i 0.796875π0.796875\pi
798798 0 0
799799 −1.36879 + 3.30455i −1.36879 + 3.30455i
800800 0.671559 + 0.740951i 0.671559 + 0.740951i
801801 0 0
802802 0 0
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 0 0 0.290285 0.956940i 0.406250π-0.406250\pi
−0.290285 + 0.956940i 0.593750π0.593750\pi
810810 −0.831470 + 0.555570i −0.831470 + 0.555570i
811811 −0.499238 1.39528i −0.499238 1.39528i −0.881921 0.471397i 0.843750π-0.843750\pi
0.382683 0.923880i 0.375000π-0.375000\pi
812812 0 0
813813 −0.185969 0.742430i −0.185969 0.742430i
814814 0 0
815815 0 0
816816 −0.0970732 1.97597i −0.0970732 1.97597i
817817 0 0
818818 −1.23076 0.308290i −1.23076 0.308290i
819819 0 0
820820 0 0
821821 0 0 −0.998795 0.0490677i 0.984375π-0.984375\pi
0.998795 + 0.0490677i 0.0156250π0.0156250\pi
822822 1.88309 1.88309
823823 0 0 −0.0980171 0.995185i 0.531250π-0.531250\pi
0.0980171 + 0.995185i 0.468750π0.468750\pi
824824 0 0
825825 0 0
826826 0 0
827827 −0.244004 1.64494i −0.244004 1.64494i −0.671559 0.740951i 0.734375π-0.734375\pi
0.427555 0.903989i 0.359375π-0.359375\pi
828828 −0.563170 1.85652i −0.563170 1.85652i
829829 −0.265286 + 0.125471i −0.265286 + 0.125471i −0.555570 0.831470i 0.687500π-0.687500\pi
0.290285 + 0.956940i 0.406250π0.406250\pi
830830 0.920964 + 1.24178i 0.920964 + 1.24178i
831831 0 0
832832 0 0
833833 −1.39891 + 1.39891i −1.39891 + 1.39891i
834834 −1.01708 0.150869i −1.01708 0.150869i
835835 0.509389 + 1.07701i 0.509389 + 1.07701i
836836 0 0
837837 −1.74475 + 0.258809i −1.74475 + 0.258809i
838838 0 0
839839 0 0 −0.634393 0.773010i 0.718750π-0.718750\pi
0.634393 + 0.773010i 0.281250π0.281250\pi
840840 0 0
841841 0.995185 0.0980171i 0.995185 0.0980171i
842842 0.727051 0.727051i 0.727051 0.727051i
843843 0 0
844844 −0.499238 + 0.452483i −0.499238 + 0.452483i
845845 0.595699 + 0.803208i 0.595699 + 0.803208i
846846 −0.929487 1.55075i −0.929487 1.55075i
847847 0 0
848848 0.116777 0.157456i 0.116777 0.157456i
849849 0 0
850850 1.32858 + 1.46586i 1.32858 + 1.46586i
851851 0 0
852852 0 0
853853 0 0 0.941544 0.336890i 0.109375π-0.109375\pi
−0.941544 + 0.336890i 0.890625π0.890625\pi
854854 0 0
855855 −0.0939097 0.0284872i −0.0939097 0.0284872i
856856 0.512016 + 0.273678i 0.512016 + 0.273678i
857857 1.18452 + 0.633141i 1.18452 + 0.633141i 0.941544 0.336890i 0.109375π-0.109375\pi
0.242980 + 0.970031i 0.421875π0.421875\pi
858858 0 0
859859 0.326351 1.30287i 0.326351 1.30287i −0.555570 0.831470i 0.687500π-0.687500\pi
0.881921 0.471397i 0.156250π-0.156250\pi
860860 0 0
861861 0 0
862862 0 0
863863 0.949938 0.393477i 0.949938 0.393477i 0.146730 0.989177i 0.453125π-0.453125\pi
0.803208 + 0.595699i 0.203125π0.203125\pi
864864 0.831470 + 0.555570i 0.831470 + 0.555570i
865865 −1.76820 0.732410i −1.76820 0.732410i
866866 0 0
867867 −0.142977 2.91037i −0.142977 2.91037i
868868 0 0
869869 0 0
870870 0 0
871871 0 0
872872 0.374332 0.560227i 0.374332 0.560227i
873873 0 0
874874 0.105774 0.158302i 0.105774 0.158302i
875875 0 0
876876 0 0
877877 0 0 −0.857729 0.514103i 0.828125π-0.828125\pi
0.857729 + 0.514103i 0.171875π0.171875\pi
878878 −1.77324 0.838679i −1.77324 0.838679i
879879 1.28547 + 0.858923i 1.28547 + 0.858923i
880880 0 0
881881 0 0 0.831470 0.555570i 0.187500π-0.187500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
882882 −0.146730 0.989177i −0.146730 0.989177i
883883 0 0 −0.989177 0.146730i 0.953125π-0.953125\pi
0.989177 + 0.146730i 0.0468750π0.0468750\pi
884884 0 0
885885 0 0
886886 0.871028 + 0.360791i 0.871028 + 0.360791i
887887 −1.08827 + 1.32607i −1.08827 + 1.32607i −0.146730 + 0.989177i 0.546875π0.546875\pi
−0.941544 + 0.336890i 0.890625π0.890625\pi
888888 0 0
889889 0 0
890890 0 0
891891 0 0
892892 0 0
893893 0.0597732 0.167055i 0.0597732 0.167055i
894894 0 0
895895 0 0
896896 0 0
897897 0 0
898898 0 0
899899 0 0
900900 −0.995185 + 0.0980171i −0.995185 + 0.0980171i
901901 0.231027 0.311504i 0.231027 0.311504i
902902 0 0
903903 0 0
904904 −0.439614 0.733452i −0.439614 0.733452i
905905 1.01910 1.24178i 1.01910 1.24178i
906906 −0.485544 + 1.17221i −0.485544 + 1.17221i
907907 0 0 0.740951 0.671559i 0.234375π-0.234375\pi
−0.740951 + 0.671559i 0.765625π0.765625\pi
908908 −1.02325 1.70720i −1.02325 1.70720i
909909 0 0
910910 0 0
911911 0 0 0.831470 0.555570i 0.187500π-0.187500\pi
−0.831470 + 0.555570i 0.812500π0.812500\pi
912912 0.00961895 + 0.0976628i 0.00961895 + 0.0976628i
913913 0 0
914914 0 0
915915 1.15203 + 0.690501i 1.15203 + 0.690501i
916916 0.881921 1.47140i 0.881921 1.47140i
917917 0 0
918918 1.64494 + 1.09911i 1.64494 + 1.09911i
919919 0.938254 + 1.75535i 0.938254 + 1.75535i 0.555570 + 0.831470i 0.312500π0.312500\pi
0.382683 + 0.923880i 0.375000π0.375000\pi
920920 0.378487 1.90278i 0.378487 1.90278i
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 0 0
926926 0 0
927927 0 0
928928 0 0
929929 0 0 0.923880 0.382683i 0.125000π-0.125000\pi
−0.923880 + 0.382683i 0.875000π0.875000\pi
930930 −1.66074 0.594221i −1.66074 0.594221i
931931 0.0659037 0.0727135i 0.0659037 0.0727135i
932932 −1.42635 0.953057i −1.42635 0.953057i
933933 0 0
934934 0.569414 1.87711i 0.569414 1.87711i
935935 0 0
936936 0 0
937937 0 0 −0.956940 0.290285i 0.906250π-0.906250\pi
0.956940 + 0.290285i 0.0937500π0.0937500\pi
938938 0 0
939939 0 0
940940 −0.0887133 1.80580i −0.0887133 1.80580i
941941 0 0 0.970031 0.242980i 0.0781250π-0.0781250\pi
−0.970031 + 0.242980i 0.921875π0.921875\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 0 0
947947 0.755815 + 1.01910i 0.755815 + 1.01910i 0.998795 + 0.0490677i 0.0156250π0.0156250\pi
−0.242980 + 0.970031i 0.578125π0.578125\pi
948948 1.10980 + 0.0545211i 1.10980 + 0.0545211i
949949 0 0
950950 −0.0693922 0.0693922i −0.0693922 0.0693922i
951951 1.65493 0.162997i 1.65493 0.162997i
952952 0 0
953953 −0.755815 0.920964i −0.755815 0.920964i 0.242980 0.970031i 0.421875π-0.421875\pi
−0.998795 + 0.0490677i 0.984375π0.984375\pi
954954 0.0569057 + 0.187593i 0.0569057 + 0.187593i
955955 0 0
956956 0 0
957957 0 0
958958 0 0
959959 0 0
960960 0.471397 + 0.881921i 0.471397 + 0.881921i
961961 −1.49280 1.49280i −1.49280 1.49280i
962962 0 0
963963 −0.524828 + 0.248225i −0.524828 + 0.248225i
964964 0.444430 0.831470i 0.444430 0.831470i
965965 0 0
966966 0 0
967967 0 0 0.773010 0.634393i 0.218750π-0.218750\pi
−0.773010 + 0.634393i 0.781250π0.781250\pi
968968 0.989177 + 0.146730i 0.989177 + 0.146730i
969969 0.0190297 + 0.193211i 0.0190297 + 0.193211i
970970 0 0
971971 0 0 −0.998795 0.0490677i 0.984375π-0.984375\pi
0.998795 + 0.0490677i 0.0156250π0.0156250\pi
972972 −0.941544 + 0.336890i −0.941544 + 0.336890i
973973 0 0
974974 0 0
975975 0 0
976976 0.197076 1.32858i 0.197076 1.32858i
977977 −0.476623 + 0.0948062i −0.476623 + 0.0948062i −0.427555 0.903989i 0.640625π-0.640625\pi
−0.0490677 + 0.998795i 0.515625π0.515625\pi
978978 0 0
979979 0 0
980980 0.336890 0.941544i 0.336890 0.941544i
981981 0.226990 + 0.634393i 0.226990 + 0.634393i
982982 0 0
983983 0.0851872 0.280825i 0.0851872 0.280825i −0.903989 0.427555i 0.859375π-0.859375\pi
0.989177 + 0.146730i 0.0468750π0.0468750\pi
984984 0 0
985985 0.924678 1.72995i 0.924678 1.72995i
986986 0 0
987987 0 0
988988 0 0
989989 0 0
990990 0 0
991991 0.292893 + 0.707107i 0.292893 + 0.707107i 1.00000 00
−0.707107 + 0.707107i 0.750000π0.750000\pi
992992 0.0865477 + 1.76172i 0.0865477 + 1.76172i
993993 0.455929 1.10071i 0.455929 1.10071i
994994 0 0
995995 0.389711 0.0191453i 0.389711 0.0191453i
996996 0.591637 + 1.42834i 0.591637 + 1.42834i
997997 0 0 −0.514103 0.857729i 0.671875π-0.671875\pi
0.514103 + 0.857729i 0.328125π0.328125\pi
998998 −1.08827 + 1.32607i −1.08827 + 1.32607i
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 3840.1.dy.a.149.1 64
3.2 odd 2 inner 3840.1.dy.a.149.2 yes 64
5.4 even 2 inner 3840.1.dy.a.149.2 yes 64
15.14 odd 2 CM 3840.1.dy.a.149.1 64
256.189 even 64 inner 3840.1.dy.a.1469.1 yes 64
768.701 odd 64 inner 3840.1.dy.a.1469.2 yes 64
1280.189 even 64 inner 3840.1.dy.a.1469.2 yes 64
3840.1469 odd 64 inner 3840.1.dy.a.1469.1 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3840.1.dy.a.149.1 64 1.1 even 1 trivial
3840.1.dy.a.149.1 64 15.14 odd 2 CM
3840.1.dy.a.149.2 yes 64 3.2 odd 2 inner
3840.1.dy.a.149.2 yes 64 5.4 even 2 inner
3840.1.dy.a.1469.1 yes 64 256.189 even 64 inner
3840.1.dy.a.1469.1 yes 64 3840.1469 odd 64 inner
3840.1.dy.a.1469.2 yes 64 768.701 odd 64 inner
3840.1.dy.a.1469.2 yes 64 1280.189 even 64 inner