Properties

Label 959.1.r.a.552.1
Level 959959
Weight 11
Character 959.552
Analytic conductor 0.4790.479
Analytic rank 00
Dimension 1616
Projective image D34D_{34}
CM discriminant -7
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [959,1,Mod(202,959)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(959, base_ring=CyclotomicField(34))
 
chi = DirichletCharacter(H, H._module([17, 25]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("959.202");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: N N == 959=7137 959 = 7 \cdot 137
Weight: k k == 1 1
Character orbit: [χ][\chi] == 959.r (of order 3434, degree 1616, 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: 0.4786033471150.478603347115
Analytic rank: 00
Dimension: 1616
Coefficient field: Q(ζ34)\Q(\zeta_{34})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x16x15+x14x13+x12x11+x10x9+x8x7+x6x5++1 x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + \cdots + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a4]\Z[a_1, \ldots, a_{4}]
Coefficient ring index: 1 1
Twist minimal: yes
Projective image: D34D_{34}
Projective field: Galois closure of Q[x]/(x34)\mathbb{Q}[x]/(x^{34} - \cdots)

Embedding invariants

Embedding label 552.1
Root 0.9324720.361242i-0.932472 - 0.361242i of defining polynomial
Character χ\chi == 959.552
Dual form 959.1.r.a.377.1

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+(0.1112081.20013i)q2+(0.444966+0.0831786i)q4+(0.850217+0.526432i)q7+(0.1805290.634493i)q8+(0.602635+0.798017i)q9+(0.1813950.0339085i)q11+(0.5372351.07891i)q14+(1.16350+0.450743i)q16+(0.8907050.811985i)q18+(0.06086710.213926i)q22+(0.260991+0.673696i)q23+(0.982973+0.183750i)q25+(0.4221060.163525i)q28+(0.7194011.85699i)q29+(0.376298+0.755708i)q32+(0.3345300.304965i)q361.96595q37+(0.4867340.533922i)q43+(0.0778940+0.0301763i)q44+(0.7794970.388143i)q46+(0.445738+0.895163i)q49+(0.1112081.20013i)q50+(1.206141.32307i)q53+(0.1805290.634493i)q56+(2.14862+1.06989i)q58+(0.0922684+0.995734i)q63+(0.195769+0.121215i)q64+(0.840204+1.35698i)q67+(0.0675278+0.361242i)q71+(0.3975430.526432i)q72+(0.218629+2.35939i)q74+(0.172075+0.0666624i)q77+(1.206140.600584i)q79+(0.273663+0.961826i)q81+(0.586645+0.643519i)q86+(0.05426160.108972i)q88+(0.1721690.278063i)q92+(1.024740.634493i)q98+(0.136374+0.124322i)q99+O(q100)q+(-0.111208 - 1.20013i) q^{2} +(-0.444966 + 0.0831786i) q^{4} +(0.850217 + 0.526432i) q^{7} +(-0.180529 - 0.634493i) q^{8} +(0.602635 + 0.798017i) q^{9} +(0.181395 - 0.0339085i) q^{11} +(0.537235 - 1.07891i) q^{14} +(-1.16350 + 0.450743i) q^{16} +(0.890705 - 0.811985i) q^{18} +(-0.0608671 - 0.213926i) q^{22} +(0.260991 + 0.673696i) q^{23} +(0.982973 + 0.183750i) q^{25} +(-0.422106 - 0.163525i) q^{28} +(-0.719401 - 1.85699i) q^{29} +(0.376298 + 0.755708i) q^{32} +(-0.334530 - 0.304965i) q^{36} -1.96595 q^{37} +(-0.486734 - 0.533922i) q^{43} +(-0.0778940 + 0.0301763i) q^{44} +(0.779497 - 0.388143i) q^{46} +(0.445738 + 0.895163i) q^{49} +(0.111208 - 1.20013i) q^{50} +(-1.20614 - 1.32307i) q^{53} +(0.180529 - 0.634493i) q^{56} +(-2.14862 + 1.06989i) q^{58} +(0.0922684 + 0.995734i) q^{63} +(-0.195769 + 0.121215i) q^{64} +(-0.840204 + 1.35698i) q^{67} +(-0.0675278 + 0.361242i) q^{71} +(0.397543 - 0.526432i) q^{72} +(0.218629 + 2.35939i) q^{74} +(0.172075 + 0.0666624i) q^{77} +(1.20614 - 0.600584i) q^{79} +(-0.273663 + 0.961826i) q^{81} +(-0.586645 + 0.643519i) q^{86} +(-0.0542616 - 0.108972i) q^{88} +(-0.172169 - 0.278063i) q^{92} +(1.02474 - 0.634493i) q^{98} +(0.136374 + 0.124322i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q2q23q4+q74q8+q9+2q11+2q145q16+2q18+4q22+17q23+q25+3q286q32+3q362q3711q44q49+2q50+2q99+O(q100) 16 q - 2 q^{2} - 3 q^{4} + q^{7} - 4 q^{8} + q^{9} + 2 q^{11} + 2 q^{14} - 5 q^{16} + 2 q^{18} + 4 q^{22} + 17 q^{23} + q^{25} + 3 q^{28} - 6 q^{32} + 3 q^{36} - 2 q^{37} - 11 q^{44} - q^{49} + 2 q^{50}+ \cdots - 2 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/959Z)×\left(\mathbb{Z}/959\mathbb{Z}\right)^\times.

nn 414414 549549
χ(n)\chi(n) e(534)e\left(\frac{5}{34}\right) 1-1

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.111208 1.20013i −0.111208 1.20013i −0.850217 0.526432i 0.823529π-0.823529\pi
0.739009 0.673696i 0.235294π-0.235294\pi
33 0 0 −0.895163 0.445738i 0.852941π-0.852941\pi
0.895163 + 0.445738i 0.147059π0.147059\pi
44 −0.444966 + 0.0831786i −0.444966 + 0.0831786i
55 0 0 −0.995734 0.0922684i 0.970588π-0.970588\pi
0.995734 + 0.0922684i 0.0294118π0.0294118\pi
66 0 0
77 0.850217 + 0.526432i 0.850217 + 0.526432i
88 −0.180529 0.634493i −0.180529 0.634493i
99 0.602635 + 0.798017i 0.602635 + 0.798017i
1010 0 0
1111 0.181395 0.0339085i 0.181395 0.0339085i −0.0922684 0.995734i 0.529412π-0.529412\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
1212 0 0
1313 0 0 0.526432 0.850217i 0.323529π-0.323529\pi
−0.526432 + 0.850217i 0.676471π0.676471\pi
1414 0.537235 1.07891i 0.537235 1.07891i
1515 0 0
1616 −1.16350 + 0.450743i −1.16350 + 0.450743i
1717 0 0 0.273663 0.961826i 0.411765π-0.411765\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
1818 0.890705 0.811985i 0.890705 0.811985i
1919 0 0 0.739009 0.673696i 0.235294π-0.235294\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
2020 0 0
2121 0 0
2222 −0.0608671 0.213926i −0.0608671 0.213926i
2323 0.260991 + 0.673696i 0.260991 + 0.673696i 1.00000 00
−0.739009 + 0.673696i 0.764706π0.764706\pi
2424 0 0
2525 0.982973 + 0.183750i 0.982973 + 0.183750i
2626 0 0
2727 0 0
2828 −0.422106 0.163525i −0.422106 0.163525i
2929 −0.719401 1.85699i −0.719401 1.85699i −0.445738 0.895163i 0.647059π-0.647059\pi
−0.273663 0.961826i 0.588235π-0.588235\pi
3030 0 0
3131 0 0 0.673696 0.739009i 0.264706π-0.264706\pi
−0.673696 + 0.739009i 0.735294π0.735294\pi
3232 0.376298 + 0.755708i 0.376298 + 0.755708i
3333 0 0
3434 0 0
3535 0 0
3636 −0.334530 0.304965i −0.334530 0.304965i
3737 −1.96595 −1.96595 −0.982973 0.183750i 0.941176π-0.941176\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
3838 0 0
3939 0 0
4040 0 0
4141 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4242 0 0
4343 −0.486734 0.533922i −0.486734 0.533922i 0.445738 0.895163i 0.352941π-0.352941\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
4444 −0.0778940 + 0.0301763i −0.0778940 + 0.0301763i
4545 0 0
4646 0.779497 0.388143i 0.779497 0.388143i
4747 0 0 0.798017 0.602635i 0.205882π-0.205882\pi
−0.798017 + 0.602635i 0.794118π0.794118\pi
4848 0 0
4949 0.445738 + 0.895163i 0.445738 + 0.895163i
5050 0.111208 1.20013i 0.111208 1.20013i
5151 0 0
5252 0 0
5353 −1.20614 1.32307i −1.20614 1.32307i −0.932472 0.361242i 0.882353π-0.882353\pi
−0.273663 0.961826i 0.588235π-0.588235\pi
5454 0 0
5555 0 0
5656 0.180529 0.634493i 0.180529 0.634493i
5757 0 0
5858 −2.14862 + 1.06989i −2.14862 + 1.06989i
5959 0 0 −0.602635 0.798017i 0.705882π-0.705882\pi
0.602635 + 0.798017i 0.294118π0.294118\pi
6060 0 0
6161 0 0 0.602635 0.798017i 0.294118π-0.294118\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
6262 0 0
6363 0.0922684 + 0.995734i 0.0922684 + 0.995734i
6464 −0.195769 + 0.121215i −0.195769 + 0.121215i
6565 0 0
6666 0 0
6767 −0.840204 + 1.35698i −0.840204 + 1.35698i 0.0922684 + 0.995734i 0.470588π0.470588\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
6868 0 0
6969 0 0
7070 0 0
7171 −0.0675278 + 0.361242i −0.0675278 + 0.361242i 0.932472 + 0.361242i 0.117647π0.117647\pi
−1.00000 π\pi
7272 0.397543 0.526432i 0.397543 0.526432i
7373 0 0 0.850217 0.526432i 0.176471π-0.176471\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
7474 0.218629 + 2.35939i 0.218629 + 2.35939i
7575 0 0
7676 0 0
7777 0.172075 + 0.0666624i 0.172075 + 0.0666624i
7878 0 0
7979 1.20614 0.600584i 1.20614 0.600584i 0.273663 0.961826i 0.411765π-0.411765\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
8080 0 0
8181 −0.273663 + 0.961826i −0.273663 + 0.961826i
8282 0 0
8383 0 0 0.961826 0.273663i 0.0882353π-0.0882353\pi
−0.961826 + 0.273663i 0.911765π0.911765\pi
8484 0 0
8585 0 0
8686 −0.586645 + 0.643519i −0.586645 + 0.643519i
8787 0 0
8888 −0.0542616 0.108972i −0.0542616 0.108972i
8989 0 0 −0.995734 0.0922684i 0.970588π-0.970588\pi
0.995734 + 0.0922684i 0.0294118π0.0294118\pi
9090 0 0
9191 0 0
9292 −0.172169 0.278063i −0.172169 0.278063i
9393 0 0
9494 0 0
9595 0 0
9696 0 0
9797 0 0 −0.183750 0.982973i 0.558824π-0.558824\pi
0.183750 + 0.982973i 0.441176π0.441176\pi
9898 1.02474 0.634493i 1.02474 0.634493i
9999 0.136374 + 0.124322i 0.136374 + 0.124322i
100100 −0.452674 −0.452674
101101 0 0 −0.739009 0.673696i 0.764706π-0.764706\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
102102 0 0
103103 0 0 −0.982973 0.183750i 0.941176π-0.941176\pi
0.982973 + 0.183750i 0.0588235π0.0588235\pi
104104 0 0
105105 0 0
106106 −1.45372 + 1.59465i −1.45372 + 1.59465i
107107 −0.831277 + 1.66943i −0.831277 + 1.66943i −0.0922684 + 0.995734i 0.529412π0.529412\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
108108 0 0
109109 1.12388 + 0.435393i 1.12388 + 0.435393i 0.850217 0.526432i 0.176471π-0.176471\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
110110 0 0
111111 0 0
112112 −1.22651 0.229275i −1.22651 0.229275i
113113 0.193463 1.03494i 0.193463 1.03494i −0.739009 0.673696i 0.764706π-0.764706\pi
0.932472 0.361242i 0.117647π-0.117647\pi
114114 0 0
115115 0 0
116116 0.474571 + 0.766459i 0.474571 + 0.766459i
117117 0 0
118118 0 0
119119 0 0
120120 0 0
121121 −0.900718 + 0.348940i −0.900718 + 0.348940i
122122 0 0
123123 0 0
124124 0 0
125125 0 0
126126 1.18475 0.221468i 1.18475 0.221468i
127127 1.59603i 1.59603i −0.602635 0.798017i 0.705882π-0.705882\pi
0.602635 0.798017i 0.294118π-0.294118\pi
128128 0.675996 + 0.895163i 0.675996 + 0.895163i
129129 0 0
130130 0 0
131131 0 0 0.361242 0.932472i 0.382353π-0.382353\pi
−0.361242 + 0.932472i 0.617647π0.617647\pi
132132 0 0
133133 0 0
134134 1.72198 + 0.857445i 1.72198 + 0.857445i
135135 0 0
136136 0 0
137137 −1.00000 −1.00000
138138 0 0
139139 0 0 −0.0922684 0.995734i 0.529412π-0.529412\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
140140 0 0
141141 0 0
142142 0.441046 + 0.0408689i 0.441046 + 0.0408689i
143143 0 0
144144 −1.06087 0.656861i −1.06087 0.656861i
145145 0 0
146146 0 0
147147 0 0
148148 0.874780 0.163525i 0.874780 0.163525i
149149 1.72198 + 0.489946i 1.72198 + 0.489946i 0.982973 0.183750i 0.0588235π-0.0588235\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
150150 0 0
151151 −0.891477 + 1.79033i −0.891477 + 1.79033i −0.445738 + 0.895163i 0.647059π0.647059\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
152152 0 0
153153 0 0
154154 0.0608671 0.213926i 0.0608671 0.213926i
155155 0 0
156156 0 0
157157 0 0 0.995734 0.0922684i 0.0294118π-0.0294118\pi
−0.995734 + 0.0922684i 0.970588π0.970588\pi
158158 −0.854910 1.38073i −0.854910 1.38073i
159159 0 0
160160 0 0
161161 −0.132756 + 0.710182i −0.132756 + 0.710182i
162162 1.18475 + 0.221468i 1.18475 + 0.221468i
163163 1.72198 + 0.857445i 1.72198 + 0.857445i 0.982973 + 0.183750i 0.0588235π0.0588235\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
164164 0 0
165165 0 0
166166 0 0
167167 0 0 0.445738 0.895163i 0.352941π-0.352941\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
168168 0 0
169169 −0.445738 0.895163i −0.445738 0.895163i
170170 0 0
171171 0 0
172172 0.260991 + 0.197091i 0.260991 + 0.197091i
173173 0 0 −0.739009 0.673696i 0.764706π-0.764706\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
174174 0 0
175175 0.739009 + 0.673696i 0.739009 + 0.673696i
176176 −0.195769 + 0.121215i −0.195769 + 0.121215i
177177 0 0
178178 0 0
179179 0 0 −0.602635 0.798017i 0.705882π-0.705882\pi
0.602635 + 0.798017i 0.294118π0.294118\pi
180180 0 0
181181 0 0 0.932472 0.361242i 0.117647π-0.117647\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
182182 0 0
183183 0 0
184184 0.380338 0.287218i 0.380338 0.287218i
185185 0 0
186186 0 0
187187 0 0
188188 0 0
189189 0 0
190190 0 0
191191 −1.53511 + 0.436776i −1.53511 + 0.436776i −0.932472 0.361242i 0.882353π-0.882353\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
192192 0 0
193193 0.329838 1.15926i 0.329838 1.15926i −0.602635 0.798017i 0.705882π-0.705882\pi
0.932472 0.361242i 0.117647π-0.117647\pi
194194 0 0
195195 0 0
196196 −0.272797 0.361242i −0.272797 0.361242i
197197 0.510366 + 0.197717i 0.510366 + 0.197717i 0.602635 0.798017i 0.294118π-0.294118\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
198198 0.134036 0.177492i 0.134036 0.177492i
199199 0 0 −0.798017 0.602635i 0.794118π-0.794118\pi
0.798017 + 0.602635i 0.205882π0.205882\pi
200200 −0.0608671 0.656861i −0.0608671 0.656861i
201201 0 0
202202 0 0
203203 0.365931 1.95756i 0.365931 1.95756i
204204 0 0
205205 0 0
206206 0 0
207207 −0.380338 + 0.614268i −0.380338 + 0.614268i
208208 0 0
209209 0 0
210210 0 0
211211 0.0822551 + 0.887674i 0.0822551 + 0.887674i 0.932472 + 0.361242i 0.117647π0.117647\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
212212 0.646741 + 0.488396i 0.646741 + 0.488396i
213213 0 0
214214 2.09597 + 0.811985i 2.09597 + 0.811985i
215215 0 0
216216 0 0
217217 0 0
218218 0.397543 1.39722i 0.397543 1.39722i
219219 0 0
220220 0 0
221221 0 0
222222 0 0
223223 0 0 0.673696 0.739009i 0.264706π-0.264706\pi
−0.673696 + 0.739009i 0.735294π0.735294\pi
224224 −0.0778940 + 0.840611i −0.0778940 + 0.840611i
225225 0.445738 + 0.895163i 0.445738 + 0.895163i
226226 −1.26357 0.117087i −1.26357 0.117087i
227227 0 0 0.798017 0.602635i 0.205882π-0.205882\pi
−0.798017 + 0.602635i 0.794118π0.794118\pi
228228 0 0
229229 0 0 −0.526432 0.850217i 0.676471π-0.676471\pi
0.526432 + 0.850217i 0.323529π0.323529\pi
230230 0 0
231231 0 0
232232 −1.04837 + 0.791695i −1.04837 + 0.791695i
233233 1.34739i 1.34739i −0.739009 0.673696i 0.764706π-0.764706\pi
0.739009 0.673696i 0.235294π-0.235294\pi
234234 0 0
235235 0 0
236236 0 0
237237 0 0
238238 0 0
239239 1.07524 + 0.811985i 1.07524 + 0.811985i 0.982973 0.183750i 0.0588235π-0.0588235\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
240240 0 0
241241 0 0 −0.961826 0.273663i 0.911765π-0.911765\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
242242 0.518940 + 1.04217i 0.518940 + 1.04217i
243243 0 0
244244 0 0
245245 0 0
246246 0 0
247247 0 0
248248 0 0
249249 0 0
250250 0 0
251251 0 0 −0.361242 0.932472i 0.617647π-0.617647\pi
0.361242 + 0.932472i 0.382353π0.382353\pi
252252 −0.123880 0.435393i −0.123880 0.435393i
253253 0.0701864 + 0.113355i 0.0701864 + 0.113355i
254254 −1.91545 + 0.177492i −1.91545 + 0.177492i
255255 0 0
256256 0.828972 0.755708i 0.828972 0.755708i
257257 0 0 0.273663 0.961826i 0.411765π-0.411765\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
258258 0 0
259259 −1.67148 1.03494i −1.67148 1.03494i
260260 0 0
261261 1.04837 1.69318i 1.04837 1.69318i
262262 0 0
263263 −1.45285 + 0.271585i −1.45285 + 0.271585i −0.850217 0.526432i 0.823529π-0.823529\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
264264 0 0
265265 0 0
266266 0 0
267267 0 0
268268 0.260991 0.673696i 0.260991 0.673696i
269269 0 0 −0.995734 0.0922684i 0.970588π-0.970588\pi
0.995734 + 0.0922684i 0.0294118π0.0294118\pi
270270 0 0
271271 0 0 −0.895163 0.445738i 0.852941π-0.852941\pi
0.895163 + 0.445738i 0.147059π0.147059\pi
272272 0 0
273273 0 0
274274 0.111208 + 1.20013i 0.111208 + 1.20013i
275275 0.184537 0.184537
276276 0 0
277277 −1.78269 0.887674i −1.78269 0.887674i −0.932472 0.361242i 0.882353π-0.882353\pi
−0.850217 0.526432i 0.823529π-0.823529\pi
278278 0 0
279279 0 0
280280 0 0
281281 −0.757949 0.469302i −0.757949 0.469302i 0.0922684 0.995734i 0.470588π-0.470588\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
282282 0 0
283283 0 0 −0.602635 0.798017i 0.705882π-0.705882\pi
0.602635 + 0.798017i 0.294118π0.294118\pi
284284 0.166357i 0.166357i
285285 0 0
286286 0 0
287287 0 0
288288 −0.376298 + 0.755708i −0.376298 + 0.755708i
289289 −0.850217 0.526432i −0.850217 0.526432i
290290 0 0
291291 0 0
292292 0 0
293293 0 0 0.739009 0.673696i 0.235294π-0.235294\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
294294 0 0
295295 0 0
296296 0.354910 + 1.24738i 0.354910 + 1.24738i
297297 0 0
298298 0.396499 2.12108i 0.396499 2.12108i
299299 0 0
300300 0 0
301301 −0.132756 0.710182i −0.132756 0.710182i
302302 2.24776 + 0.870787i 2.24776 + 0.870787i
303303 0 0
304304 0 0
305305 0 0
306306 0 0
307307 0 0 −0.961826 0.273663i 0.911765π-0.911765\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
308308 −0.0821126 0.0153495i −0.0821126 0.0153495i
309309 0 0
310310 0 0
311311 0 0 1.00000 00
−1.00000 π\pi
312312 0 0
313313 0 0 0.850217 0.526432i 0.176471π-0.176471\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
314314 0 0
315315 0 0
316316 −0.486734 + 0.367564i −0.486734 + 0.367564i
317317 0.247582 + 0.271585i 0.247582 + 0.271585i 0.850217 0.526432i 0.176471π-0.176471\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
318318 0 0
319319 −0.193463 0.312454i −0.193463 0.312454i
320320 0 0
321321 0 0
322322 0.867072 + 0.0803461i 0.867072 + 0.0803461i
323323 0 0
324324 0.0417675 0.450743i 0.0417675 0.450743i
325325 0 0
326326 0.837545 2.16195i 0.837545 2.16195i
327327 0 0
328328 0 0
329329 0 0
330330 0 0
331331 0.353470 0.100571i 0.353470 0.100571i −0.0922684 0.995734i 0.529412π-0.529412\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
332332 0 0
333333 −1.18475 1.56886i −1.18475 1.56886i
334334 0 0
335335 0 0
336336 0 0
337337 −0.0170269 0.183750i −0.0170269 0.183750i 0.982973 0.183750i 0.0588235π-0.0588235\pi
−1.00000 π\pi
338338 −1.02474 + 0.634493i −1.02474 + 0.634493i
339339 0 0
340340 0 0
341341 0 0
342342 0 0
343343 −0.0922684 + 0.995734i −0.0922684 + 0.995734i
344344 −0.250900 + 0.405217i −0.250900 + 0.405217i
345345 0 0
346346 0 0
347347 −1.44574 + 0.895163i −1.44574 + 0.895163i −0.445738 + 0.895163i 0.647059π0.647059\pi
−1.00000 1.00000π1.00000\pi
348348 0 0
349349 0 0 −0.798017 0.602635i 0.794118π-0.794118\pi
0.798017 + 0.602635i 0.205882π0.205882\pi
350350 0.726337 0.961826i 0.726337 0.961826i
351351 0 0
352352 0.0938833 + 0.124322i 0.0938833 + 0.124322i
353353 0 0 0.895163 0.445738i 0.147059π-0.147059\pi
−0.895163 + 0.445738i 0.852941π0.852941\pi
354354 0 0
355355 0 0
356356 0 0
357357 0 0
358358 0 0
359359 0.719401 1.85699i 0.719401 1.85699i 0.273663 0.961826i 0.411765π-0.411765\pi
0.445738 0.895163i 0.352941π-0.352941\pi
360360 0 0
361361 0.0922684 0.995734i 0.0922684 0.995734i
362362 0 0
363363 0 0
364364 0 0
365365 0 0
366366 0 0
367367 0 0 0.932472 0.361242i 0.117647π-0.117647\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
368368 −0.607327 0.666206i −0.607327 0.666206i
369369 0 0
370370 0 0
371371 −0.328972 1.75984i −0.328972 1.75984i
372372 0 0
373373 −1.25664 1.14558i −1.25664 1.14558i −0.982973 0.183750i 0.941176π-0.941176\pi
−0.273663 0.961826i 0.588235π-0.588235\pi
374374 0 0
375375 0 0
376376 0 0
377377 0 0
378378 0 0
379379 0.397365 + 0.798017i 0.397365 + 0.798017i 1.00000 00
−0.602635 + 0.798017i 0.705882π0.705882\pi
380380 0 0
381381 0 0
382382 0.694903 + 1.79375i 0.694903 + 1.79375i
383383 0 0 −0.932472 0.361242i 0.882353π-0.882353\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
384384 0 0
385385 0 0
386386 −1.42794 0.266928i −1.42794 0.266928i
387387 0.132756 0.710182i 0.132756 0.710182i
388388 0 0
389389 −0.465346 1.63552i −0.465346 1.63552i −0.739009 0.673696i 0.764706π-0.764706\pi
0.273663 0.961826i 0.411765π-0.411765\pi
390390 0 0
391391 0 0
392392 0.487506 0.444420i 0.487506 0.444420i
393393 0 0
394394 0.180529 0.634493i 0.180529 0.634493i
395395 0 0
396396 −0.0710229 0.0439755i −0.0710229 0.0439755i
397397 0 0 0.445738 0.895163i 0.352941π-0.352941\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
398398 0 0
399399 0 0
400400 −1.22651 + 0.229275i −1.22651 + 0.229275i
401401 1.05286i 1.05286i 0.850217 + 0.526432i 0.176471π0.176471\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
402402 0 0
403403 0 0
404404 0 0
405405 0 0
406406 −2.39002 0.221468i −2.39002 0.221468i
407407 −0.356612 + 0.0666624i −0.356612 + 0.0666624i
408408 0 0
409409 0 0 −0.0922684 0.995734i 0.529412π-0.529412\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
410410 0 0
411411 0 0
412412 0 0
413413 0 0
414414 0.779497 + 0.388143i 0.779497 + 0.388143i
415415 0 0
416416 0 0
417417 0 0
418418 0 0
419419 0 0 −0.273663 0.961826i 0.588235π-0.588235\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
420420 0 0
421421 0.367499i 0.367499i 0.982973 + 0.183750i 0.0588235π0.0588235\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
422422 1.05617 0.197433i 1.05617 0.197433i
423423 0 0
424424 −0.621734 + 1.00414i −0.621734 + 1.00414i
425425 0 0
426426 0 0
427427 0 0
428428 0.231030 0.811985i 0.231030 0.811985i
429429 0 0
430430 0 0
431431 1.58923 0.147263i 1.58923 0.147263i 0.739009 0.673696i 0.235294π-0.235294\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
432432 0 0
433433 0 0 −0.273663 0.961826i 0.588235π-0.588235\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
434434 0 0
435435 0 0
436436 −0.536304 0.100253i −0.536304 0.100253i
437437 0 0
438438 0 0
439439 0 0 −0.932472 0.361242i 0.882353π-0.882353\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
440440 0 0
441441 −0.445738 + 0.895163i −0.445738 + 0.895163i
442442 0 0
443443 0.757949 + 1.52217i 0.757949 + 1.52217i 0.850217 + 0.526432i 0.176471π0.176471\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
444444 0 0
445445 0 0
446446 0 0
447447 0 0
448448 −0.230258 −0.230258
449449 0.658809 + 0.600584i 0.658809 + 0.600584i 0.932472 0.361242i 0.117647π-0.117647\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
450450 1.02474 0.634493i 1.02474 0.634493i
451451 0 0
452452 0.476604i 0.476604i
453453 0 0
454454 0 0
455455 0 0
456456 0 0
457457 0 0 −0.445738 0.895163i 0.647059π-0.647059\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
458458 0 0
459459 0 0
460460 0 0
461461 0 0 0.0922684 0.995734i 0.470588π-0.470588\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
462462 0 0
463463 0.694903 1.79375i 0.694903 1.79375i 0.0922684 0.995734i 0.470588π-0.470588\pi
0.602635 0.798017i 0.294118π-0.294118\pi
464464 1.67405 + 1.83634i 1.67405 + 1.83634i
465465 0 0
466466 −1.61704 + 0.149841i −1.61704 + 0.149841i
467467 0 0 0.273663 0.961826i 0.411765π-0.411765\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
468468 0 0
469469 −1.42871 + 0.711414i −1.42871 + 0.711414i
470470 0 0
471471 0 0
472472 0 0
473473 −0.106395 0.0803461i −0.106395 0.0803461i
474474 0 0
475475 0 0
476476 0 0
477477 0.328972 1.75984i 0.328972 1.75984i
478478 0.854910 1.38073i 0.854910 1.38073i
479479 0 0 0.0922684 0.995734i 0.470588π-0.470588\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
480480 0 0
481481 0 0
482482 0 0
483483 0 0
484484 0.371765 0.230187i 0.371765 0.230187i
485485 0 0
486486 0 0
487487 0.890705 1.17948i 0.890705 1.17948i −0.0922684 0.995734i 0.529412π-0.529412\pi
0.982973 0.183750i 0.0588235π-0.0588235\pi
488488 0 0
489489 0 0
490490 0 0
491491 1.91545 0.544991i 1.91545 0.544991i 0.932472 0.361242i 0.117647π-0.117647\pi
0.982973 0.183750i 0.0588235π-0.0588235\pi
492492 0 0
493493 0 0
494494 0 0
495495 0 0
496496 0 0
497497 −0.247582 + 0.271585i −0.247582 + 0.271585i
498498 0 0
499499 −0.397365 0.798017i −0.397365 0.798017i 0.602635 0.798017i 0.294118π-0.294118\pi
−1.00000 π\pi
500500 0 0
501501 0 0
502502 0 0
503503 0 0 −0.526432 0.850217i 0.676471π-0.676471\pi
0.526432 + 0.850217i 0.323529π0.323529\pi
504504 0.615129 0.238302i 0.615129 0.238302i
505505 0 0
506506 0.128235 0.0968387i 0.128235 0.0968387i
507507 0 0
508508 0.132756 + 0.710182i 0.132756 + 0.710182i
509509 0 0 0.850217 0.526432i 0.176471π-0.176471\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
510510 0 0
511511 0 0
512512 −0.170162 0.155124i −0.170162 0.155124i
513513 0 0
514514 0 0
515515 0 0
516516 0 0
517517 0 0
518518 −1.05617 + 2.12108i −1.05617 + 2.12108i
519519 0 0
520520 0 0
521521 0 0 −0.183750 0.982973i 0.558824π-0.558824\pi
0.183750 + 0.982973i 0.441176π0.441176\pi
522522 −2.14862 1.06989i −2.14862 1.06989i
523523 0 0 −0.982973 0.183750i 0.941176π-0.941176\pi
0.982973 + 0.183750i 0.0588235π0.0588235\pi
524524 0 0
525525 0 0
526526 0.487506 + 1.71341i 0.487506 + 1.71341i
527527 0 0
528528 0 0
529529 0.353259 0.322039i 0.353259 0.322039i
530530 0 0
531531 0 0
532532 0 0
533533 0 0
534534 0 0
535535 0 0
536536 1.01267 + 0.288130i 1.01267 + 0.288130i
537537 0 0
538538 0 0
539539 0.111208 + 0.147263i 0.111208 + 0.147263i
540540 0 0
541541 0.465346 + 0.288130i 0.465346 + 0.288130i 0.739009 0.673696i 0.235294π-0.235294\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
542542 0 0
543543 0 0
544544 0 0
545545 0 0
546546 0 0
547547 1.47802 1.47802 0.739009 0.673696i 0.235294π-0.235294\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
548548 0.444966 0.0831786i 0.444966 0.0831786i
549549 0 0
550550 −0.0205220 0.221468i −0.0205220 0.221468i
551551 0 0
552552 0 0
553553 1.34164 + 0.124322i 1.34164 + 0.124322i
554554 −0.867072 + 2.23817i −0.867072 + 2.23817i
555555 0 0
556556 0 0
557557 0.890705 + 1.17948i 0.890705 + 1.17948i 0.982973 + 0.183750i 0.0588235π0.0588235\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
558558 0 0
559559 0 0
560560 0 0
561561 0 0
562562 −0.478932 + 0.961826i −0.478932 + 0.961826i
563563 0 0 −0.850217 0.526432i 0.823529π-0.823529\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
564564 0 0
565565 0 0
566566 0 0
567567 −0.739009 + 0.673696i −0.739009 + 0.673696i
568568 0.241396 0.0223686i 0.241396 0.0223686i
569569 0.554262 + 0.895163i 0.554262 + 0.895163i 1.00000 00
−0.445738 + 0.895163i 0.647059π0.647059\pi
570570 0 0
571571 0.486734 + 1.25640i 0.486734 + 1.25640i 0.932472 + 0.361242i 0.117647π0.117647\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
572572 0 0
573573 0 0
574574 0 0
575575 0.132756 + 0.710182i 0.132756 + 0.710182i
576576 −0.214709 0.0831786i −0.214709 0.0831786i
577577 0 0 −0.361242 0.932472i 0.617647π-0.617647\pi
0.361242 + 0.932472i 0.382353π0.382353\pi
578578 −0.537235 + 1.07891i −0.537235 + 1.07891i
579579 0 0
580580 0 0
581581 0 0
582582 0 0
583583 −0.263650 0.199099i −0.263650 0.199099i
584584 0 0
585585 0 0
586586 0 0
587587 0 0 0.850217 0.526432i 0.176471π-0.176471\pi
−0.850217 + 0.526432i 0.823529π0.823529\pi
588588 0 0
589589 0 0
590590 0 0
591591 0 0
592592 2.28738 0.886136i 2.28738 0.886136i
593593 0 0 −0.526432 0.850217i 0.676471π-0.676471\pi
0.526432 + 0.850217i 0.323529π0.323529\pi
594594 0 0
595595 0 0
596596 −0.806977 0.0747774i −0.806977 0.0747774i
597597 0 0
598598 0 0
599599 −1.20614 + 1.32307i −1.20614 + 1.32307i −0.273663 + 0.961826i 0.588235π0.588235\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
600600 0 0
601601 0 0 −0.673696 0.739009i 0.735294π-0.735294\pi
0.673696 + 0.739009i 0.264706π0.264706\pi
602602 −0.837545 + 0.238302i −0.837545 + 0.238302i
603603 −1.58923 + 0.147263i −1.58923 + 0.147263i
604604 0.247760 0.870787i 0.247760 0.870787i
605605 0 0
606606 0 0
607607 0 0 −0.602635 0.798017i 0.705882π-0.705882\pi
0.602635 + 0.798017i 0.294118π0.294118\pi
608608 0 0
609609 0 0
610610 0 0
611611 0 0
612612 0 0
613613 1.12388 1.48826i 1.12388 1.48826i 0.273663 0.961826i 0.411765π-0.411765\pi
0.850217 0.526432i 0.176471π-0.176471\pi
614614 0 0
615615 0 0
616616 0.0112322 0.121215i 0.0112322 0.121215i
617617 −0.136374 + 1.47171i −0.136374 + 1.47171i 0.602635 + 0.798017i 0.294118π0.294118\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
618618 0 0
619619 0 0 0.183750 0.982973i 0.441176π-0.441176\pi
−0.183750 + 0.982973i 0.558824π0.558824\pi
620620 0 0
621621 0 0
622622 0 0
623623 0 0
624624 0 0
625625 0.932472 + 0.361242i 0.932472 + 0.361242i
626626 0 0
627627 0 0
628628 0 0
629629 0 0
630630 0 0
631631 0.353470 0.100571i 0.353470 0.100571i −0.0922684 0.995734i 0.529412π-0.529412\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
632632 −0.598808 0.656861i −0.598808 0.656861i
633633 0 0
634634 0.298404 0.327333i 0.298404 0.327333i
635635 0 0
636636 0 0
637637 0 0
638638 −0.353470 + 0.266928i −0.353470 + 0.266928i
639639 −0.328972 + 0.163808i −0.328972 + 0.163808i
640640 0 0
641641 0.831277 0.322039i 0.831277 0.322039i 0.0922684 0.995734i 0.470588π-0.470588\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
642642 0 0
643643 0 0 0.798017 0.602635i 0.205882π-0.205882\pi
−0.798017 + 0.602635i 0.794118π0.794118\pi
644644 0.327049i 0.327049i
645645 0 0
646646 0 0
647647 0 0 −0.739009 0.673696i 0.764706π-0.764706\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
648648 0.659675 0.659675
649649 0 0
650650 0 0
651651 0 0
652652 −0.837545 0.238302i −0.837545 0.238302i
653653 −0.397365 0.798017i −0.397365 0.798017i 0.602635 0.798017i 0.294118π-0.294118\pi
−1.00000 π\pi
654654 0 0
655655 0 0
656656 0 0
657657 0 0
658658 0 0
659659 −1.72198 0.857445i −1.72198 0.857445i −0.982973 0.183750i 0.941176π-0.941176\pi
−0.739009 0.673696i 0.764706π-0.764706\pi
660660 0 0
661661 0 0 0.183750 0.982973i 0.441176π-0.441176\pi
−0.183750 + 0.982973i 0.558824π0.558824\pi
662662 −0.160007 0.413025i −0.160007 0.413025i
663663 0 0
664664 0 0
665665 0 0
666666 −1.75108 + 1.59632i −1.75108 + 1.59632i
667667 1.06329 0.969315i 1.06329 0.969315i
668668 0 0
669669 0 0
670670 0 0
671671 0 0
672672 0 0
673673 1.91545 + 0.544991i 1.91545 + 0.544991i 0.982973 + 0.183750i 0.0588235π0.0588235\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
674674 −0.218629 + 0.0408689i −0.218629 + 0.0408689i
675675 0 0
676676 0.272797 + 0.361242i 0.272797 + 0.361242i
677677 0 0 −0.273663 0.961826i 0.588235π-0.588235\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
678678 0 0
679679 0 0
680680 0 0
681681 0 0
682682 0 0
683683 0.172075 + 1.85699i 0.172075 + 1.85699i 0.445738 + 0.895163i 0.352941π0.352941\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
684684 0 0
685685 0 0
686686 1.20527 1.20527
687687 0 0
688688 0.806977 + 0.401827i 0.806977 + 0.401827i
689689 0 0
690690 0 0
691691 0 0 0.361242 0.932472i 0.382353π-0.382353\pi
−0.361242 + 0.932472i 0.617647π0.617647\pi
692692 0 0
693693 0.0505009 + 0.177492i 0.0505009 + 0.177492i
694694 1.23509 + 1.63552i 1.23509 + 1.63552i
695695 0 0
696696 0 0
697697 0 0
698698 0 0
699699 0 0
700700 −0.384871 0.238302i −0.384871 0.238302i
701701 1.83319 0.710182i 1.83319 0.710182i 0.850217 0.526432i 0.176471π-0.176471\pi
0.982973 0.183750i 0.0588235π-0.0588235\pi
702702 0 0
703703 0 0
704704 −0.0314012 + 0.0286260i −0.0314012 + 0.0286260i
705705 0 0
706706 0 0
707707 0 0
708708 0 0
709709 −0.365931 + 1.95756i −0.365931 + 1.95756i −0.0922684 + 0.995734i 0.529412π0.529412\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
710710 0 0
711711 1.20614 + 0.600584i 1.20614 + 0.600584i
712712 0 0
713713 0 0
714714 0 0
715715 0 0
716716 0 0
717717 0 0
718718 −2.30863 0.656861i −2.30863 0.656861i
719719 0 0 −0.982973 0.183750i 0.941176π-0.941176\pi
0.982973 + 0.183750i 0.0588235π0.0588235\pi
720720 0 0
721721 0 0
722722 −1.20527 −1.20527
723723 0 0
724724 0 0
725725 −0.365931 1.95756i −0.365931 1.95756i
726726 0 0
727727 0 0 0.798017 0.602635i 0.205882π-0.205882\pi
−0.798017 + 0.602635i 0.794118π0.794118\pi
728728 0 0
729729 −0.932472 + 0.361242i −0.932472 + 0.361242i
730730 0 0
731731 0 0
732732 0 0
733733 0 0 −0.995734 0.0922684i 0.970588π-0.970588\pi
0.995734 + 0.0922684i 0.0294118π0.0294118\pi
734734 0 0
735735 0 0
736736 −0.410907 + 0.450743i −0.410907 + 0.450743i
737737 −0.106395 + 0.274638i −0.106395 + 0.274638i
738738 0 0
739739 1.29596 0.368731i 1.29596 0.368731i 0.445738 0.895163i 0.352941π-0.352941\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
740740 0 0
741741 0 0
742742 −2.07545 + 0.590517i −2.07545 + 0.590517i
743743 −1.72198 + 0.857445i −1.72198 + 0.857445i −0.739009 + 0.673696i 0.764706π0.764706\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
744744 0 0
745745 0 0
746746 −1.23509 + 1.63552i −1.23509 + 1.63552i
747747 0 0
748748 0 0
749749 −1.58561 + 0.981767i −1.58561 + 0.981767i
750750 0 0
751751 0.193463 1.03494i 0.193463 1.03494i −0.739009 0.673696i 0.764706π-0.764706\pi
0.932472 0.361242i 0.117647π-0.117647\pi
752752 0 0
753753 0 0
754754 0 0
755755 0 0
756756 0 0
757757 1.18475 1.56886i 1.18475 1.56886i 0.445738 0.895163i 0.352941π-0.352941\pi
0.739009 0.673696i 0.235294π-0.235294\pi
758758 0.913532 0.565635i 0.913532 0.565635i
759759 0 0
760760 0 0
761761 0 0 0.602635 0.798017i 0.294118π-0.294118\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
762762 0 0
763763 0.726337 + 0.961826i 0.726337 + 0.961826i
764764 0.646741 0.322039i 0.646741 0.322039i
765765 0 0
766766 0 0
767767 0 0
768768 0 0
769769 0 0 −0.673696 0.739009i 0.735294π-0.735294\pi
0.673696 + 0.739009i 0.264706π0.264706\pi
770770 0 0
771771 0 0
772772 −0.0503411 + 0.543267i −0.0503411 + 0.543267i
773773 0 0 −0.445738 0.895163i 0.647059π-0.647059\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
774774 −0.867072 0.0803461i −0.867072 0.0803461i
775775 0 0
776776 0 0
777777 0 0
778778 −1.91108 + 0.740358i −1.91108 + 0.740358i
779779 0 0
780780 0 0
781781 0.0678171i 0.0678171i
782782 0 0
783783 0 0
784784 −0.922106 0.840611i −0.922106 0.840611i
785785 0 0
786786 0 0
787787 0 0 −0.798017 0.602635i 0.794118π-0.794118\pi
0.798017 + 0.602635i 0.205882π0.205882\pi
788788 −0.243542 0.0455258i −0.243542 0.0455258i
789789 0 0
790790 0 0
791791 0.709310 0.778076i 0.709310 0.778076i
792792 0.0542616 0.108972i 0.0542616 0.108972i
793793 0 0
794794 0 0
795795 0 0
796796 0 0
797797 0 0 −0.982973 0.183750i 0.941176π-0.941176\pi
0.982973 + 0.183750i 0.0588235π0.0588235\pi
798798 0 0
799799 0 0
800800 0.231030 + 0.811985i 0.231030 + 0.811985i
801801 0 0
802802 1.26357 0.117087i 1.26357 0.117087i
803803 0 0
804804 0 0
805805 0 0
806806 0 0
807807 0 0
808808 0 0
809809 −1.01267 + 1.63552i −1.01267 + 1.63552i −0.273663 + 0.961826i 0.588235π0.588235\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
810810 0 0
811811 0 0 0.982973 0.183750i 0.0588235π-0.0588235\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
812812 0.901486i 0.901486i
813813 0 0
814814 0.119662 + 0.420567i 0.119662 + 0.420567i
815815 0 0
816816 0 0
817817 0 0
818818 0 0
819819 0 0
820820 0 0
821821 −0.891477 −0.891477 −0.445738 0.895163i 0.647059π-0.647059\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
822822 0 0
823823 0.891477 0.891477 0.445738 0.895163i 0.352941π-0.352941\pi
0.445738 + 0.895163i 0.352941π0.352941\pi
824824 0 0
825825 0 0
826826 0 0
827827 −0.719401 0.0666624i −0.719401 0.0666624i −0.273663 0.961826i 0.588235π-0.588235\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
828828 0.118144 0.304965i 0.118144 0.304965i
829829 0 0 −0.850217 0.526432i 0.823529π-0.823529\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
830830 0 0
831831 0 0
832832 0 0
833833 0 0
834834 0 0
835835 0 0
836836 0 0
837837 0 0
838838 0 0
839839 0 0 0.273663 0.961826i 0.411765π-0.411765\pi
−0.273663 + 0.961826i 0.588235π0.588235\pi
840840 0 0
841841 −2.19186 + 1.99815i −2.19186 + 1.99815i
842842 0.441046 0.0408689i 0.441046 0.0408689i
843843 0 0
844844 −0.110436 0.388143i −0.110436 0.388143i
845845 0 0
846846 0 0
847847 −0.949499 0.177492i −0.949499 0.177492i
848848 1.99970 + 0.995734i 1.99970 + 0.995734i
849849 0 0
850850 0 0
851851 −0.513094 1.32445i −0.513094 1.32445i
852852 0 0
853853 0 0 0.673696 0.739009i 0.264706π-0.264706\pi
−0.673696 + 0.739009i 0.735294π0.735294\pi
854854 0 0
855855 0 0
856856 1.20931 + 0.226059i 1.20931 + 0.226059i
857857 0 0 −0.798017 0.602635i 0.794118π-0.794118\pi
0.798017 + 0.602635i 0.205882π0.205882\pi
858858 0 0
859859 0 0 1.00000 00
−1.00000 π\pi
860860 0 0
861861 0 0
862862 −0.353470 1.89090i −0.353470 1.89090i
863863 1.34739i 1.34739i −0.739009 0.673696i 0.764706π-0.764706\pi
0.739009 0.673696i 0.235294π-0.235294\pi
864864 0 0
865865 0 0
866866 0 0
867867 0 0
868868 0 0
869869 0.198422 0.149841i 0.198422 0.149841i
870870 0 0
871871 0 0
872872 0.0733613 0.791695i 0.0733613 0.791695i
873873 0 0
874874 0 0
875875 0 0
876876 0 0
877877 0 0 −0.0922684 0.995734i 0.529412π-0.529412\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
878878 0 0
879879 0 0
880880 0 0
881881 0 0 −0.602635 0.798017i 0.705882π-0.705882\pi
0.602635 + 0.798017i 0.294118π0.294118\pi
882882 1.12388 + 0.435393i 1.12388 + 0.435393i
883883 1.12388 1.48826i 1.12388 1.48826i 0.273663 0.961826i 0.411765π-0.411765\pi
0.850217 0.526432i 0.176471π-0.176471\pi
884884 0 0
885885 0 0
886886 1.74250 1.07891i 1.74250 1.07891i
887887 0 0 0.602635 0.798017i 0.294118π-0.294118\pi
−0.602635 + 0.798017i 0.705882π0.705882\pi
888888 0 0
889889 0.840204 1.35698i 0.840204 1.35698i
890890 0 0
891891 −0.0170269 + 0.183750i −0.0170269 + 0.183750i
892892 0 0
893893 0 0
894894 0 0
895895 0 0
896896 0.103501 + 1.11695i 0.103501 + 1.11695i
897897 0 0
898898 0.647513 0.857445i 0.647513 0.857445i
899899 0 0
900900 −0.272797 0.361242i −0.272797 0.361242i
901901 0 0
902902 0 0
903903 0 0
904904 −0.691586 + 0.0640848i −0.691586 + 0.0640848i
905905 0 0
906906 0 0
907907 −0.380338 + 0.981767i −0.380338 + 0.981767i 0.602635 + 0.798017i 0.294118π0.294118\pi
−0.982973 + 0.183750i 0.941176π0.941176\pi
908908 0 0
909909 0 0
910910 0 0
911911 −1.78269 0.165190i −1.78269 0.165190i −0.850217 0.526432i 0.823529π-0.823529\pi
−0.932472 + 0.361242i 0.882353π0.882353\pi
912912 0 0
913913 0 0
914914 0 0
915915 0 0
916916 0 0
917917 0 0
918918 0 0
919919 −0.353470 1.89090i −0.353470 1.89090i −0.445738 0.895163i 0.647059π-0.647059\pi
0.0922684 0.995734i 0.470588π-0.470588\pi
920920 0 0
921921 0 0
922922 0 0
923923 0 0
924924 0 0
925925 −1.93247 0.361242i −1.93247 0.361242i
926926 −2.23001 0.634493i −2.23001 0.634493i
927927 0 0
928928 1.13263 1.24244i 1.13263 1.24244i
929929 0 0 0.445738 0.895163i 0.352941π-0.352941\pi
−0.445738 + 0.895163i 0.647059π0.647059\pi
930930 0 0
931931 0 0
932932 0.112074 + 0.599544i 0.112074 + 0.599544i
933933 0 0
934934 0 0
935935 0 0
936936 0 0
937937 0 0 −0.273663 0.961826i 0.588235π-0.588235\pi
0.273663 + 0.961826i 0.411765π0.411765\pi
938938 1.01267 + 1.63552i 1.01267 + 1.63552i
939939 0 0
940940 0 0
941941 0 0 0.739009 0.673696i 0.235294π-0.235294\pi
−0.739009 + 0.673696i 0.764706π0.764706\pi
942942 0 0
943943 0 0
944944 0 0
945945 0 0
946946 −0.0845935 + 0.136623i −0.0845935 + 0.136623i
947947 0.694903 + 0.197717i 0.694903 + 0.197717i 0.602635 0.798017i 0.294118π-0.294118\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
948948 0 0
949949 0 0
950950 0 0
951951 0 0
952952 0 0
953953 0 0 −0.932472 0.361242i 0.882353π-0.882353\pi
0.932472 + 0.361242i 0.117647π0.117647\pi
954954 −2.14862 0.199099i −2.14862 0.199099i
955955 0 0
956956 −0.545986 0.271869i −0.545986 0.271869i
957957 0 0
958958 0 0
959959 −0.850217 0.526432i −0.850217 0.526432i
960960 0 0
961961 −0.0922684 0.995734i −0.0922684 0.995734i
962962 0 0
963963 −1.83319 + 0.342683i −1.83319 + 0.342683i
964964 0 0
965965 0 0
966966 0 0
967967 0.510366 + 1.79375i 0.510366 + 1.79375i 0.602635 + 0.798017i 0.294118π0.294118\pi
−0.0922684 + 0.995734i 0.529412π0.529412\pi
968968 0.384005 + 0.508505i 0.384005 + 0.508505i
969969 0 0
970970 0 0
971971 0 0 −0.961826 0.273663i 0.911765π-0.911765\pi
0.961826 + 0.273663i 0.0882353π0.0882353\pi
972972 0 0
973973 0 0
974974 −1.51458 0.937791i −1.51458 0.937791i
975975 0 0
976976 0 0
977977 0.404479 0.368731i 0.404479 0.368731i −0.445738 0.895163i 0.647059π-0.647059\pi
0.850217 + 0.526432i 0.176471π0.176471\pi
978978 0 0
979979 0 0
980980 0 0
981981 0.329838 + 1.15926i 0.329838 + 1.15926i
982982 −0.867072 2.23817i −0.867072 2.23817i
983983 0 0 0.183750 0.982973i 0.441176π-0.441176\pi
−0.183750 + 0.982973i 0.558824π0.558824\pi
984984 0 0
985985 0 0
986986 0 0
987987 0 0
988988 0 0
989989 0.232667 0.467259i 0.232667 0.467259i
990990 0 0
991991 0.831277 + 1.66943i 0.831277 + 1.66943i 0.739009 + 0.673696i 0.235294π0.235294\pi
0.0922684 + 0.995734i 0.470588π0.470588\pi
992992 0 0
993993 0 0
994994 0.353470 + 0.266928i 0.353470 + 0.266928i
995995 0 0
996996 0 0
997997 0 0 −0.739009 0.673696i 0.764706π-0.764706\pi
0.739009 + 0.673696i 0.235294π0.235294\pi
998998 −0.913532 + 0.565635i −0.913532 + 0.565635i
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 959.1.r.a.552.1 yes 16
7.6 odd 2 CM 959.1.r.a.552.1 yes 16
137.103 even 34 inner 959.1.r.a.377.1 16
959.377 odd 34 inner 959.1.r.a.377.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
959.1.r.a.377.1 16 137.103 even 34 inner
959.1.r.a.377.1 16 959.377 odd 34 inner
959.1.r.a.552.1 yes 16 1.1 even 1 trivial
959.1.r.a.552.1 yes 16 7.6 odd 2 CM