Properties

Label 2646.2.f.r.1765.1
Level 26462646
Weight 22
Character 2646.1765
Analytic conductor 21.12821.128
Analytic rank 00
Dimension 88
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2646,2,Mod(883,2646)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2646.883");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 2646=23372 2646 = 2 \cdot 3^{3} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 2646.f (of order 33, degree 22, not 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: 21.128416374821.1284163748
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(ζ24)\Q(\zeta_{24})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8x4+1 x^{8} - x^{4} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 32 3^{2}
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 1765.1
Root 0.965926+0.258819i0.965926 + 0.258819i of defining polynomial
Character χ\chi == 2646.1765
Dual form 2646.2.f.r.883.1

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+(0.500000+0.866025i)q2+(0.500000+0.866025i)q4+(1.93185+3.34607i)q51.00000q83.86370q10+(1.866033.23205i)q11+(3.346075.79555i)q13+(0.5000000.866025i)q16+5.41662q17+2.96713q19+(1.931853.34607i)q20+(1.866033.23205i)q22+(0.732051+1.26795i)q23+(4.964108.59808i)q25+6.69213q26+(2.000003.46410i)q29+(0.8965751.55291i)q31+(0.5000000.866025i)q32+(2.70831+4.69093i)q34+0.535898q37+(1.48356+2.56961i)q38+(1.931853.34607i)q40+(0.6377561.10463i)q41+(1.866033.23205i)q43+3.73205q441.46410q46+(5.277929.14162i)q47+(4.964108.59808i)q50+(3.34607+5.79555i)q52+2.92820q53+14.4195q55+(2.000003.46410i)q58+(4.311997.46859i)q59+(3.48477+6.03579i)q61+1.79315q62+1.00000q64+(12.9282+22.3923i)q65+(2.76795+4.79423i)q67+(2.70831+4.69093i)q682.53590q71+6.83083q73+(0.267949+0.464102i)q74+(1.48356+2.56961i)q76+(2.46410+4.26795i)q79+3.86370q80+1.27551q82+(8.95215+15.5056i)q83+(10.4641+18.1244i)q85+(1.866033.23205i)q86+(1.86603+3.23205i)q88+7.07107q89+(0.7320511.26795i)q92+(5.277929.14162i)q94+(5.73205+9.92820i)q95+(2.948555.10703i)q97+O(q100)q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.93185 + 3.34607i) q^{5} -1.00000 q^{8} -3.86370 q^{10} +(-1.86603 - 3.23205i) q^{11} +(3.34607 - 5.79555i) q^{13} +(-0.500000 - 0.866025i) q^{16} +5.41662 q^{17} +2.96713 q^{19} +(-1.93185 - 3.34607i) q^{20} +(1.86603 - 3.23205i) q^{22} +(-0.732051 + 1.26795i) q^{23} +(-4.96410 - 8.59808i) q^{25} +6.69213 q^{26} +(-2.00000 - 3.46410i) q^{29} +(0.896575 - 1.55291i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.70831 + 4.69093i) q^{34} +0.535898 q^{37} +(1.48356 + 2.56961i) q^{38} +(1.93185 - 3.34607i) q^{40} +(0.637756 - 1.10463i) q^{41} +(-1.86603 - 3.23205i) q^{43} +3.73205 q^{44} -1.46410 q^{46} +(-5.27792 - 9.14162i) q^{47} +(4.96410 - 8.59808i) q^{50} +(3.34607 + 5.79555i) q^{52} +2.92820 q^{53} +14.4195 q^{55} +(2.00000 - 3.46410i) q^{58} +(4.31199 - 7.46859i) q^{59} +(3.48477 + 6.03579i) q^{61} +1.79315 q^{62} +1.00000 q^{64} +(12.9282 + 22.3923i) q^{65} +(-2.76795 + 4.79423i) q^{67} +(-2.70831 + 4.69093i) q^{68} -2.53590 q^{71} +6.83083 q^{73} +(0.267949 + 0.464102i) q^{74} +(-1.48356 + 2.56961i) q^{76} +(2.46410 + 4.26795i) q^{79} +3.86370 q^{80} +1.27551 q^{82} +(8.95215 + 15.5056i) q^{83} +(-10.4641 + 18.1244i) q^{85} +(1.86603 - 3.23205i) q^{86} +(1.86603 + 3.23205i) q^{88} +7.07107 q^{89} +(-0.732051 - 1.26795i) q^{92} +(5.27792 - 9.14162i) q^{94} +(-5.73205 + 9.92820i) q^{95} +(-2.94855 - 5.10703i) q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+4q24q48q88q114q16+8q22+8q2312q2516q29+4q32+32q378q43+16q44+16q46+12q5032q53+16q58+8q64+32q95+O(q100) 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 8 q^{11} - 4 q^{16} + 8 q^{22} + 8 q^{23} - 12 q^{25} - 16 q^{29} + 4 q^{32} + 32 q^{37} - 8 q^{43} + 16 q^{44} + 16 q^{46} + 12 q^{50} - 32 q^{53} + 16 q^{58} + 8 q^{64}+ \cdots - 32 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/2646Z)×\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times.

nn 785785 10811081
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) 11

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 0.500000 + 0.866025i 0.353553 + 0.612372i
33 0 0
44 −0.500000 + 0.866025i −0.250000 + 0.433013i
55 −1.93185 + 3.34607i −0.863950 + 1.49641i 0.00413535 + 0.999991i 0.498684π0.498684\pi
−0.868086 + 0.496414i 0.834650π0.834650\pi
66 0 0
77 0 0
88 −1.00000 −0.353553
99 0 0
1010 −3.86370 −1.22181
1111 −1.86603 3.23205i −0.562628 0.974500i −0.997266 0.0738948i 0.976457π-0.976457\pi
0.434638 0.900605i 0.356876π-0.356876\pi
1212 0 0
1313 3.34607 5.79555i 0.928032 1.60740i 0.141420 0.989950i 0.454833π-0.454833\pi
0.786612 0.617448i 0.211833π-0.211833\pi
1414 0 0
1515 0 0
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 5.41662 1.31372 0.656861 0.754011i 0.271884π-0.271884\pi
0.656861 + 0.754011i 0.271884π0.271884\pi
1818 0 0
1919 2.96713 0.680706 0.340353 0.940298i 0.389453π-0.389453\pi
0.340353 + 0.940298i 0.389453π0.389453\pi
2020 −1.93185 3.34607i −0.431975 0.748203i
2121 0 0
2222 1.86603 3.23205i 0.397838 0.689076i
2323 −0.732051 + 1.26795i −0.152643 + 0.264386i −0.932198 0.361948i 0.882112π-0.882112\pi
0.779555 + 0.626334i 0.215445π0.215445\pi
2424 0 0
2525 −4.96410 8.59808i −0.992820 1.71962i
2626 6.69213 1.31243
2727 0 0
2828 0 0
2929 −2.00000 3.46410i −0.371391 0.643268i 0.618389 0.785872i 0.287786π-0.287786\pi
−0.989780 + 0.142605i 0.954452π0.954452\pi
3030 0 0
3131 0.896575 1.55291i 0.161030 0.278912i −0.774209 0.632931i 0.781852π-0.781852\pi
0.935238 + 0.354019i 0.115185π0.115185\pi
3232 0.500000 0.866025i 0.0883883 0.153093i
3333 0 0
3434 2.70831 + 4.69093i 0.464471 + 0.804488i
3535 0 0
3636 0 0
3737 0.535898 0.0881012 0.0440506 0.999029i 0.485974π-0.485974\pi
0.0440506 + 0.999029i 0.485974π0.485974\pi
3838 1.48356 + 2.56961i 0.240666 + 0.416845i
3939 0 0
4040 1.93185 3.34607i 0.305453 0.529059i
4141 0.637756 1.10463i 0.0996008 0.172514i −0.811919 0.583771i 0.801577π-0.801577\pi
0.911519 + 0.411257i 0.134910π0.134910\pi
4242 0 0
4343 −1.86603 3.23205i −0.284566 0.492883i 0.687938 0.725770i 0.258516π-0.258516\pi
−0.972504 + 0.232887i 0.925183π0.925183\pi
4444 3.73205 0.562628
4545 0 0
4646 −1.46410 −0.215870
4747 −5.27792 9.14162i −0.769863 1.33344i −0.937637 0.347617i 0.886991π-0.886991\pi
0.167773 0.985826i 0.446342π-0.446342\pi
4848 0 0
4949 0 0
5050 4.96410 8.59808i 0.702030 1.21595i
5151 0 0
5252 3.34607 + 5.79555i 0.464016 + 0.803699i
5353 2.92820 0.402220 0.201110 0.979569i 0.435545π-0.435545\pi
0.201110 + 0.979569i 0.435545π0.435545\pi
5454 0 0
5555 14.4195 1.94433
5656 0 0
5757 0 0
5858 2.00000 3.46410i 0.262613 0.454859i
5959 4.31199 7.46859i 0.561373 0.972327i −0.436004 0.899945i 0.643606π-0.643606\pi
0.997377 0.0723823i 0.0230602π-0.0230602\pi
6060 0 0
6161 3.48477 + 6.03579i 0.446179 + 0.772804i 0.998133 0.0610700i 0.0194513π-0.0194513\pi
−0.551955 + 0.833874i 0.686118π0.686118\pi
6262 1.79315 0.227730
6363 0 0
6464 1.00000 0.125000
6565 12.9282 + 22.3923i 1.60355 + 2.77742i
6666 0 0
6767 −2.76795 + 4.79423i −0.338159 + 0.585708i −0.984086 0.177690i 0.943137π-0.943137\pi
0.645928 + 0.763399i 0.276471π0.276471\pi
6868 −2.70831 + 4.69093i −0.328431 + 0.568859i
6969 0 0
7070 0 0
7171 −2.53590 −0.300956 −0.150478 0.988613i 0.548081π-0.548081\pi
−0.150478 + 0.988613i 0.548081π0.548081\pi
7272 0 0
7373 6.83083 0.799488 0.399744 0.916627i 0.369099π-0.369099\pi
0.399744 + 0.916627i 0.369099π0.369099\pi
7474 0.267949 + 0.464102i 0.0311485 + 0.0539507i
7575 0 0
7676 −1.48356 + 2.56961i −0.170176 + 0.294754i
7777 0 0
7878 0 0
7979 2.46410 + 4.26795i 0.277233 + 0.480182i 0.970696 0.240310i 0.0772492π-0.0772492\pi
−0.693463 + 0.720492i 0.743916π0.743916\pi
8080 3.86370 0.431975
8181 0 0
8282 1.27551 0.140857
8383 8.95215 + 15.5056i 0.982626 + 1.70196i 0.652043 + 0.758182i 0.273912π0.273912\pi
0.330583 + 0.943777i 0.392755π0.392755\pi
8484 0 0
8585 −10.4641 + 18.1244i −1.13499 + 1.96586i
8686 1.86603 3.23205i 0.201219 0.348521i
8787 0 0
8888 1.86603 + 3.23205i 0.198919 + 0.344538i
8989 7.07107 0.749532 0.374766 0.927119i 0.377723π-0.377723\pi
0.374766 + 0.927119i 0.377723π0.377723\pi
9090 0 0
9191 0 0
9292 −0.732051 1.26795i −0.0763216 0.132193i
9393 0 0
9494 5.27792 9.14162i 0.544376 0.942886i
9595 −5.73205 + 9.92820i −0.588096 + 1.01861i
9696 0 0
9797 −2.94855 5.10703i −0.299379 0.518540i 0.676615 0.736337i 0.263446π-0.263446\pi
−0.975994 + 0.217797i 0.930113π0.930113\pi
9898 0 0
9999 0 0
100100 9.92820 0.992820
101101 −2.44949 4.24264i −0.243733 0.422159i 0.718041 0.696000i 0.245039π-0.245039\pi
−0.961775 + 0.273842i 0.911706π0.911706\pi
102102 0 0
103103 3.72500 6.45189i 0.367035 0.635724i −0.622065 0.782965i 0.713706π-0.713706\pi
0.989101 + 0.147241i 0.0470394π0.0470394\pi
104104 −3.34607 + 5.79555i −0.328109 + 0.568301i
105105 0 0
106106 1.46410 + 2.53590i 0.142206 + 0.246308i
107107 −3.39230 −0.327946 −0.163973 0.986465i 0.552431π-0.552431\pi
−0.163973 + 0.986465i 0.552431π0.552431\pi
108108 0 0
109109 −8.92820 −0.855167 −0.427583 0.903976i 0.640635π-0.640635\pi
−0.427583 + 0.903976i 0.640635π0.640635\pi
110110 7.20977 + 12.4877i 0.687424 + 1.19065i
111111 0 0
112112 0 0
113113 3.46410 6.00000i 0.325875 0.564433i −0.655814 0.754923i 0.727674π-0.727674\pi
0.981689 + 0.190490i 0.0610077π0.0610077\pi
114114 0 0
115115 −2.82843 4.89898i −0.263752 0.456832i
116116 4.00000 0.371391
117117 0 0
118118 8.62398 0.793902
119119 0 0
120120 0 0
121121 −1.46410 + 2.53590i −0.133100 + 0.230536i
122122 −3.48477 + 6.03579i −0.315496 + 0.546455i
123123 0 0
124124 0.896575 + 1.55291i 0.0805149 + 0.139456i
125125 19.0411 1.70309
126126 0 0
127127 6.53590 0.579967 0.289984 0.957032i 0.406350π-0.406350\pi
0.289984 + 0.957032i 0.406350π0.406350\pi
128128 0.500000 + 0.866025i 0.0441942 + 0.0765466i
129129 0 0
130130 −12.9282 + 22.3923i −1.13388 + 1.96394i
131131 −3.01790 + 5.22715i −0.263675 + 0.456698i −0.967216 0.253957i 0.918268π-0.918268\pi
0.703541 + 0.710655i 0.251601π0.251601\pi
132132 0 0
133133 0 0
134134 −5.53590 −0.478229
135135 0 0
136136 −5.41662 −0.464471
137137 −4.33013 7.50000i −0.369948 0.640768i 0.619609 0.784910i 0.287291π-0.287291\pi
−0.989557 + 0.144142i 0.953958π0.953958\pi
138138 0 0
139139 −8.17569 + 14.1607i −0.693453 + 1.20110i 0.277246 + 0.960799i 0.410578π0.410578\pi
−0.970699 + 0.240297i 0.922755π0.922755\pi
140140 0 0
141141 0 0
142142 −1.26795 2.19615i −0.106404 0.184297i
143143 −24.9754 −2.08855
144144 0 0
145145 15.4548 1.28345
146146 3.41542 + 5.91567i 0.282662 + 0.489585i
147147 0 0
148148 −0.267949 + 0.464102i −0.0220253 + 0.0381489i
149149 4.53590 7.85641i 0.371595 0.643622i −0.618216 0.786008i 0.712144π-0.712144\pi
0.989811 + 0.142386i 0.0454776π0.0454776\pi
150150 0 0
151151 1.19615 + 2.07180i 0.0973415 + 0.168600i 0.910583 0.413325i 0.135633π-0.135633\pi
−0.813242 + 0.581926i 0.802299π0.802299\pi
152152 −2.96713 −0.240666
153153 0 0
154154 0 0
155155 3.46410 + 6.00000i 0.278243 + 0.481932i
156156 0 0
157157 2.31079 4.00240i 0.184421 0.319427i −0.758960 0.651137i 0.774292π-0.774292\pi
0.943381 + 0.331710i 0.107626π0.107626\pi
158158 −2.46410 + 4.26795i −0.196033 + 0.339540i
159159 0 0
160160 1.93185 + 3.34607i 0.152726 + 0.264530i
161161 0 0
162162 0 0
163163 21.3205 1.66995 0.834976 0.550287i 0.185482π-0.185482\pi
0.834976 + 0.550287i 0.185482π0.185482\pi
164164 0.637756 + 1.10463i 0.0498004 + 0.0862568i
165165 0 0
166166 −8.95215 + 15.5056i −0.694822 + 1.20347i
167167 −10.5558 + 18.2832i −0.816835 + 1.41480i 0.0911679 + 0.995836i 0.470940π0.470940\pi
−0.908003 + 0.418964i 0.862393π0.862393\pi
168168 0 0
169169 −15.8923 27.5263i −1.22248 2.11741i
170170 −20.9282 −1.60512
171171 0 0
172172 3.73205 0.284566
173173 −0.896575 1.55291i −0.0681654 0.118066i 0.829928 0.557870i 0.188381π-0.188381\pi
−0.898094 + 0.439804i 0.855048π0.855048\pi
174174 0 0
175175 0 0
176176 −1.86603 + 3.23205i −0.140657 + 0.243625i
177177 0 0
178178 3.53553 + 6.12372i 0.264999 + 0.458993i
179179 −18.9282 −1.41476 −0.707380 0.706833i 0.750123π-0.750123\pi
−0.707380 + 0.706833i 0.750123π0.750123\pi
180180 0 0
181181 16.9706 1.26141 0.630706 0.776022i 0.282765π-0.282765\pi
0.630706 + 0.776022i 0.282765π0.282765\pi
182182 0 0
183183 0 0
184184 0.732051 1.26795i 0.0539675 0.0934745i
185185 −1.03528 + 1.79315i −0.0761150 + 0.131835i
186186 0 0
187187 −10.1075 17.5068i −0.739137 1.28022i
188188 10.5558 0.769863
189189 0 0
190190 −11.4641 −0.831693
191191 0.535898 + 0.928203i 0.0387762 + 0.0671624i 0.884762 0.466043i 0.154321π-0.154321\pi
−0.845986 + 0.533205i 0.820987π0.820987\pi
192192 0 0
193193 11.5263 19.9641i 0.829680 1.43705i −0.0686098 0.997644i 0.521856π-0.521856\pi
0.898290 0.439404i 0.144810π-0.144810\pi
194194 2.94855 5.10703i 0.211693 0.366663i
195195 0 0
196196 0 0
197197 3.07180 0.218856 0.109428 0.993995i 0.465098π-0.465098\pi
0.109428 + 0.993995i 0.465098π0.465098\pi
198198 0 0
199199 17.8028 1.26200 0.631002 0.775781i 0.282644π-0.282644\pi
0.631002 + 0.775781i 0.282644π0.282644\pi
200200 4.96410 + 8.59808i 0.351015 + 0.607976i
201201 0 0
202202 2.44949 4.24264i 0.172345 0.298511i
203203 0 0
204204 0 0
205205 2.46410 + 4.26795i 0.172100 + 0.298087i
206206 7.45001 0.519066
207207 0 0
208208 −6.69213 −0.464016
209209 −5.53674 9.58991i −0.382984 0.663348i
210210 0 0
211211 −2.53590 + 4.39230i −0.174578 + 0.302379i −0.940015 0.341132i 0.889190π-0.889190\pi
0.765437 + 0.643511i 0.222523π0.222523\pi
212212 −1.46410 + 2.53590i −0.100555 + 0.174166i
213213 0 0
214214 −1.69615 2.93782i −0.115947 0.200825i
215215 14.4195 0.983404
216216 0 0
217217 0 0
218218 −4.46410 7.73205i −0.302347 0.523681i
219219 0 0
220220 −7.20977 + 12.4877i −0.486082 + 0.841920i
221221 18.1244 31.3923i 1.21918 2.11167i
222222 0 0
223223 −13.3843 23.1822i −0.896276 1.55240i −0.832217 0.554450i 0.812929π-0.812929\pi
−0.0640595 0.997946i 0.520405π-0.520405\pi
224224 0 0
225225 0 0
226226 6.92820 0.460857
227227 5.25933 + 9.10943i 0.349074 + 0.604614i 0.986085 0.166240i 0.0531627π-0.0531627\pi
−0.637011 + 0.770855i 0.719829π0.719829\pi
228228 0 0
229229 12.4877 21.6293i 0.825209 1.42930i −0.0765496 0.997066i 0.524390π-0.524390\pi
0.901759 0.432239i 0.142276π-0.142276\pi
230230 2.82843 4.89898i 0.186501 0.323029i
231231 0 0
232232 2.00000 + 3.46410i 0.131306 + 0.227429i
233233 24.1244 1.58044 0.790220 0.612824i 0.209966π-0.209966\pi
0.790220 + 0.612824i 0.209966π0.209966\pi
234234 0 0
235235 40.7846 2.66049
236236 4.31199 + 7.46859i 0.280687 + 0.486164i
237237 0 0
238238 0 0
239239 −6.46410 + 11.1962i −0.418128 + 0.724219i −0.995751 0.0920846i 0.970647π-0.970647\pi
0.577623 + 0.816304i 0.303980π0.303980\pi
240240 0 0
241241 11.7112 + 20.2844i 0.754387 + 1.30664i 0.945679 + 0.325103i 0.105399π0.105399\pi
−0.191292 + 0.981533i 0.561268π0.561268\pi
242242 −2.92820 −0.188232
243243 0 0
244244 −6.96953 −0.446179
245245 0 0
246246 0 0
247247 9.92820 17.1962i 0.631716 1.09416i
248248 −0.896575 + 1.55291i −0.0569326 + 0.0986102i
249249 0 0
250250 9.52056 + 16.4901i 0.602133 + 1.04292i
251251 −16.3514 −1.03209 −0.516045 0.856561i 0.672596π-0.672596\pi
−0.516045 + 0.856561i 0.672596π0.672596\pi
252252 0 0
253253 5.46410 0.343525
254254 3.26795 + 5.66025i 0.205049 + 0.355156i
255255 0 0
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 −1.34486 + 2.32937i −0.0838903 + 0.145302i −0.904918 0.425586i 0.860068π-0.860068\pi
0.821028 + 0.570889i 0.193401π0.193401\pi
258258 0 0
259259 0 0
260260 −25.8564 −1.60355
261261 0 0
262262 −6.03579 −0.372892
263263 −7.73205 13.3923i −0.476779 0.825805i 0.522867 0.852414i 0.324862π-0.324862\pi
−0.999646 + 0.0266092i 0.991529π0.991529\pi
264264 0 0
265265 −5.65685 + 9.79796i −0.347498 + 0.601884i
266266 0 0
267267 0 0
268268 −2.76795 4.79423i −0.169079 0.292854i
269269 −5.65685 −0.344904 −0.172452 0.985018i 0.555169π-0.555169\pi
−0.172452 + 0.985018i 0.555169π0.555169\pi
270270 0 0
271271 −18.0058 −1.09378 −0.546888 0.837206i 0.684188π-0.684188\pi
−0.546888 + 0.837206i 0.684188π0.684188\pi
272272 −2.70831 4.69093i −0.164215 0.284429i
273273 0 0
274274 4.33013 7.50000i 0.261593 0.453092i
275275 −18.5263 + 32.0885i −1.11718 + 1.93501i
276276 0 0
277277 −12.2679 21.2487i −0.737110 1.27671i −0.953792 0.300469i 0.902857π-0.902857\pi
0.216682 0.976242i 0.430477π-0.430477\pi
278278 −16.3514 −0.980691
279279 0 0
280280 0 0
281281 −4.92820 8.53590i −0.293992 0.509209i 0.680758 0.732508i 0.261651π-0.261651\pi
−0.974750 + 0.223299i 0.928317π0.928317\pi
282282 0 0
283283 4.70951 8.15711i 0.279951 0.484890i −0.691421 0.722452i 0.743015π-0.743015\pi
0.971372 + 0.237562i 0.0763483π0.0763483\pi
284284 1.26795 2.19615i 0.0752389 0.130318i
285285 0 0
286286 −12.4877 21.6293i −0.738412 1.27897i
287287 0 0
288288 0 0
289289 12.3397 0.725867
290290 7.72741 + 13.3843i 0.453769 + 0.785951i
291291 0 0
292292 −3.41542 + 5.91567i −0.199872 + 0.346189i
293293 9.52056 16.4901i 0.556197 0.963361i −0.441612 0.897206i 0.645593π-0.645593\pi
0.997809 0.0661554i 0.0210733π-0.0210733\pi
294294 0 0
295295 16.6603 + 28.8564i 0.969997 + 1.68008i
296296 −0.535898 −0.0311485
297297 0 0
298298 9.07180 0.525515
299299 4.89898 + 8.48528i 0.283315 + 0.490716i
300300 0 0
301301 0 0
302302 −1.19615 + 2.07180i −0.0688308 + 0.119219i
303303 0 0
304304 −1.48356 2.56961i −0.0850882 0.147377i
305305 −26.9282 −1.54190
306306 0 0
307307 11.0735 0.631996 0.315998 0.948760i 0.397661π-0.397661\pi
0.315998 + 0.948760i 0.397661π0.397661\pi
308308 0 0
309309 0 0
310310 −3.46410 + 6.00000i −0.196748 + 0.340777i
311311 6.17449 10.6945i 0.350123 0.606431i −0.636147 0.771568i 0.719473π-0.719473\pi
0.986271 + 0.165136i 0.0528063π0.0528063\pi
312312 0 0
313313 11.7112 + 20.2844i 0.661958 + 1.14654i 0.980101 + 0.198502i 0.0636075π0.0636075\pi
−0.318143 + 0.948043i 0.603059π0.603059\pi
314314 4.62158 0.260811
315315 0 0
316316 −4.92820 −0.277233
317317 −13.0000 22.5167i −0.730153 1.26466i −0.956818 0.290689i 0.906116π-0.906116\pi
0.226665 0.973973i 0.427218π-0.427218\pi
318318 0 0
319319 −7.46410 + 12.9282i −0.417909 + 0.723840i
320320 −1.93185 + 3.34607i −0.107994 + 0.187051i
321321 0 0
322322 0 0
323323 16.0718 0.894259
324324 0 0
325325 −66.4408 −3.68547
326326 10.6603 + 18.4641i 0.590417 + 1.02263i
327327 0 0
328328 −0.637756 + 1.10463i −0.0352142 + 0.0609928i
329329 0 0
330330 0 0
331331 2.26795 + 3.92820i 0.124658 + 0.215914i 0.921599 0.388143i 0.126883π-0.126883\pi
−0.796941 + 0.604057i 0.793550π0.793550\pi
332332 −17.9043 −0.982626
333333 0 0
334334 −21.1117 −1.15518
335335 −10.6945 18.5235i −0.584305 1.01205i
336336 0 0
337337 3.50000 6.06218i 0.190657 0.330228i −0.754811 0.655942i 0.772271π-0.772271\pi
0.945468 + 0.325714i 0.105605π0.105605\pi
338338 15.8923 27.5263i 0.864427 1.49723i
339339 0 0
340340 −10.4641 18.1244i −0.567496 0.982931i
341341 −6.69213 −0.362399
342342 0 0
343343 0 0
344344 1.86603 + 3.23205i 0.100609 + 0.174261i
345345 0 0
346346 0.896575 1.55291i 0.0482002 0.0834852i
347347 10.7942 18.6962i 0.579465 1.00366i −0.416076 0.909330i 0.636595π-0.636595\pi
0.995541 0.0943323i 0.0300716π-0.0300716\pi
348348 0 0
349349 8.24504 + 14.2808i 0.441347 + 0.764436i 0.997790 0.0664504i 0.0211674π-0.0211674\pi
−0.556443 + 0.830886i 0.687834π0.687834\pi
350350 0 0
351351 0 0
352352 −3.73205 −0.198919
353353 13.2134 + 22.8862i 0.703277 + 1.21811i 0.967310 + 0.253598i 0.0816139π0.0816139\pi
−0.264033 + 0.964514i 0.585053π0.585053\pi
354354 0 0
355355 4.89898 8.48528i 0.260011 0.450352i
356356 −3.53553 + 6.12372i −0.187383 + 0.324557i
357357 0 0
358358 −9.46410 16.3923i −0.500193 0.866360i
359359 −0.535898 −0.0282836 −0.0141418 0.999900i 0.504502π-0.504502\pi
−0.0141418 + 0.999900i 0.504502π0.504502\pi
360360 0 0
361361 −10.1962 −0.536640
362362 8.48528 + 14.6969i 0.445976 + 0.772454i
363363 0 0
364364 0 0
365365 −13.1962 + 22.8564i −0.690718 + 1.19636i
366366 0 0
367367 −7.86611 13.6245i −0.410607 0.711193i 0.584349 0.811503i 0.301350π-0.301350\pi
−0.994956 + 0.100310i 0.968017π0.968017\pi
368368 1.46410 0.0763216
369369 0 0
370370 −2.07055 −0.107643
371371 0 0
372372 0 0
373373 −15.3923 + 26.6603i −0.796983 + 1.38042i 0.124589 + 0.992208i 0.460239π0.460239\pi
−0.921572 + 0.388207i 0.873095π0.873095\pi
374374 10.1075 17.5068i 0.522649 0.905254i
375375 0 0
376376 5.27792 + 9.14162i 0.272188 + 0.471443i
377377 −26.7685 −1.37865
378378 0 0
379379 −17.5885 −0.903458 −0.451729 0.892155i 0.649193π-0.649193\pi
−0.451729 + 0.892155i 0.649193π0.649193\pi
380380 −5.73205 9.92820i −0.294048 0.509306i
381381 0 0
382382 −0.535898 + 0.928203i −0.0274189 + 0.0474910i
383383 10.8332 18.7637i 0.553552 0.958781i −0.444462 0.895798i 0.646605π-0.646605\pi
0.998015 0.0629833i 0.0200615π-0.0200615\pi
384384 0 0
385385 0 0
386386 23.0526 1.17334
387387 0 0
388388 5.89709 0.299379
389389 4.00000 + 6.92820i 0.202808 + 0.351274i 0.949432 0.313972i 0.101660π-0.101660\pi
−0.746624 + 0.665246i 0.768327π0.768327\pi
390390 0 0
391391 −3.96524 + 6.86800i −0.200531 + 0.347329i
392392 0 0
393393 0 0
394394 1.53590 + 2.66025i 0.0773774 + 0.134022i
395395 −19.0411 −0.958062
396396 0 0
397397 −18.0058 −0.903687 −0.451844 0.892097i 0.649233π-0.649233\pi
−0.451844 + 0.892097i 0.649233π0.649233\pi
398398 8.90138 + 15.4176i 0.446186 + 0.772817i
399399 0 0
400400 −4.96410 + 8.59808i −0.248205 + 0.429904i
401401 8.89230 15.4019i 0.444061 0.769135i −0.553926 0.832566i 0.686871π-0.686871\pi
0.997986 + 0.0634307i 0.0202042π0.0202042\pi
402402 0 0
403403 −6.00000 10.3923i −0.298881 0.517678i
404404 4.89898 0.243733
405405 0 0
406406 0 0
407407 −1.00000 1.73205i −0.0495682 0.0858546i
408408 0 0
409409 8.36516 14.4889i 0.413631 0.716429i −0.581653 0.813437i 0.697594π-0.697594\pi
0.995284 + 0.0970077i 0.0309271π0.0309271\pi
410410 −2.46410 + 4.26795i −0.121693 + 0.210779i
411411 0 0
412412 3.72500 + 6.45189i 0.183518 + 0.317862i
413413 0 0
414414 0 0
415415 −69.1769 −3.39576
416416 −3.34607 5.79555i −0.164054 0.284150i
417417 0 0
418418 5.53674 9.58991i 0.270811 0.469058i
419419 3.95164 6.84443i 0.193050 0.334373i −0.753209 0.657781i 0.771495π-0.771495\pi
0.946260 + 0.323408i 0.104829π0.104829\pi
420420 0 0
421421 −14.1962 24.5885i −0.691878 1.19837i −0.971222 0.238177i 0.923450π-0.923450\pi
0.279344 0.960191i 0.409883π-0.409883\pi
422422 −5.07180 −0.246891
423423 0 0
424424 −2.92820 −0.142206
425425 −26.8886 46.5725i −1.30429 2.25910i
426426 0 0
427427 0 0
428428 1.69615 2.93782i 0.0819866 0.142005i
429429 0 0
430430 7.20977 + 12.4877i 0.347686 + 0.602210i
431431 37.8564 1.82348 0.911739 0.410769i 0.134740π-0.134740\pi
0.911739 + 0.410769i 0.134740π0.134740\pi
432432 0 0
433433 −7.10823 −0.341600 −0.170800 0.985306i 0.554635π-0.554635\pi
−0.170800 + 0.985306i 0.554635π0.554635\pi
434434 0 0
435435 0 0
436436 4.46410 7.73205i 0.213792 0.370298i
437437 −2.17209 + 3.76217i −0.103905 + 0.179969i
438438 0 0
439439 −9.79796 16.9706i −0.467631 0.809961i 0.531685 0.846942i 0.321559π-0.321559\pi
−0.999316 + 0.0369815i 0.988226π0.988226\pi
440440 −14.4195 −0.687424
441441 0 0
442442 36.2487 1.72418
443443 −9.16025 15.8660i −0.435217 0.753818i 0.562097 0.827072i 0.309995π-0.309995\pi
−0.997313 + 0.0732540i 0.976662π0.976662\pi
444444 0 0
445445 −13.6603 + 23.6603i −0.647558 + 1.12160i
446446 13.3843 23.1822i 0.633763 1.09771i
447447 0 0
448448 0 0
449449 17.7846 0.839308 0.419654 0.907684i 0.362151π-0.362151\pi
0.419654 + 0.907684i 0.362151π0.362151\pi
450450 0 0
451451 −4.76028 −0.224153
452452 3.46410 + 6.00000i 0.162938 + 0.282216i
453453 0 0
454454 −5.25933 + 9.10943i −0.246833 + 0.427527i
455455 0 0
456456 0 0
457457 −3.52628 6.10770i −0.164952 0.285706i 0.771686 0.636004i 0.219414π-0.219414\pi
−0.936638 + 0.350298i 0.886080π0.886080\pi
458458 24.9754 1.16702
459459 0 0
460460 5.65685 0.263752
461461 12.8666 + 22.2856i 0.599258 + 1.03795i 0.992931 + 0.118695i 0.0378711π0.0378711\pi
−0.393672 + 0.919251i 0.628796π0.628796\pi
462462 0 0
463463 −19.3205 + 33.4641i −0.897900 + 1.55521i −0.0677264 + 0.997704i 0.521575π0.521575\pi
−0.830174 + 0.557505i 0.811759π0.811759\pi
464464 −2.00000 + 3.46410i −0.0928477 + 0.160817i
465465 0 0
466466 12.0622 + 20.8923i 0.558770 + 0.967817i
467467 −27.5636 −1.27549 −0.637745 0.770248i 0.720133π-0.720133\pi
−0.637745 + 0.770248i 0.720133π0.720133\pi
468468 0 0
469469 0 0
470470 20.3923 + 35.3205i 0.940627 + 1.62921i
471471 0 0
472472 −4.31199 + 7.46859i −0.198475 + 0.343770i
473473 −6.96410 + 12.0622i −0.320210 + 0.554620i
474474 0 0
475475 −14.7291 25.5116i −0.675819 1.17055i
476476 0 0
477477 0 0
478478 −12.9282 −0.591322
479479 −7.72741 13.3843i −0.353074 0.611542i 0.633712 0.773569i 0.281530π-0.281530\pi
−0.986786 + 0.162026i 0.948197π0.948197\pi
480480 0 0
481481 1.79315 3.10583i 0.0817606 0.141614i
482482 −11.7112 + 20.2844i −0.533432 + 0.923931i
483483 0 0
484484 −1.46410 2.53590i −0.0665501 0.115268i
485485 22.7846 1.03460
486486 0 0
487487 38.7846 1.75750 0.878749 0.477284i 0.158379π-0.158379\pi
0.878749 + 0.477284i 0.158379π0.158379\pi
488488 −3.48477 6.03579i −0.157748 0.273227i
489489 0 0
490490 0 0
491491 −0.696152 + 1.20577i −0.0314169 + 0.0544157i −0.881306 0.472545i 0.843335π-0.843335\pi
0.849889 + 0.526961i 0.176669π0.176669\pi
492492 0 0
493493 −10.8332 18.7637i −0.487904 0.845075i
494494 19.8564 0.893382
495495 0 0
496496 −1.79315 −0.0805149
497497 0 0
498498 0 0
499499 −6.30385 + 10.9186i −0.282199 + 0.488783i −0.971926 0.235286i 0.924397π-0.924397\pi
0.689727 + 0.724069i 0.257731π0.257731\pi
500500 −9.52056 + 16.4901i −0.425772 + 0.737459i
501501 0 0
502502 −8.17569 14.1607i −0.364899 0.632024i
503503 −7.45001 −0.332179 −0.166090 0.986111i 0.553114π-0.553114\pi
−0.166090 + 0.986111i 0.553114π0.553114\pi
504504 0 0
505505 18.9282 0.842294
506506 2.73205 + 4.73205i 0.121454 + 0.210365i
507507 0 0
508508 −3.26795 + 5.66025i −0.144992 + 0.251133i
509509 −13.2456 + 22.9420i −0.587099 + 1.01689i 0.407511 + 0.913200i 0.366397π0.366397\pi
−0.994610 + 0.103685i 0.966937π0.966937\pi
510510 0 0
511511 0 0
512512 −1.00000 −0.0441942
513513 0 0
514514 −2.68973 −0.118639
515515 14.3923 + 24.9282i 0.634201 + 1.09847i
516516 0 0
517517 −19.6975 + 34.1170i −0.866293 + 1.50046i
518518 0 0
519519 0 0
520520 −12.9282 22.3923i −0.566939 0.981968i
521521 32.3610 1.41776 0.708881 0.705328i 0.249200π-0.249200\pi
0.708881 + 0.705328i 0.249200π0.249200\pi
522522 0 0
523523 3.76217 0.164508 0.0822540 0.996611i 0.473788π-0.473788\pi
0.0822540 + 0.996611i 0.473788π0.473788\pi
524524 −3.01790 5.22715i −0.131837 0.228349i
525525 0 0
526526 7.73205 13.3923i 0.337133 0.583932i
527527 4.85641 8.41154i 0.211548 0.366413i
528528 0 0
529529 10.4282 + 18.0622i 0.453400 + 0.785312i
530530 −11.3137 −0.491436
531531 0 0
532532 0 0
533533 −4.26795 7.39230i −0.184865 0.320196i
534534 0 0
535535 6.55343 11.3509i 0.283329 0.490741i
536536 2.76795 4.79423i 0.119557 0.207079i
537537 0 0
538538 −2.82843 4.89898i −0.121942 0.211210i
539539 0 0
540540 0 0
541541 −19.3205 −0.830654 −0.415327 0.909672i 0.636333π-0.636333\pi
−0.415327 + 0.909672i 0.636333π0.636333\pi
542542 −9.00292 15.5935i −0.386709 0.669799i
543543 0 0
544544 2.70831 4.69093i 0.116118 0.201122i
545545 17.2480 29.8744i 0.738822 1.27968i
546546 0 0
547547 19.1865 + 33.2321i 0.820357 + 1.42090i 0.905417 + 0.424524i 0.139559π0.139559\pi
−0.0850597 + 0.996376i 0.527108π0.527108\pi
548548 8.66025 0.369948
549549 0 0
550550 −37.0526 −1.57993
551551 −5.93426 10.2784i −0.252808 0.437876i
552552 0 0
553553 0 0
554554 12.2679 21.2487i 0.521215 0.902771i
555555 0 0
556556 −8.17569 14.1607i −0.346727 0.600548i
557557 −6.92820 −0.293557 −0.146779 0.989169i 0.546891π-0.546891\pi
−0.146779 + 0.989169i 0.546891π0.546891\pi
558558 0 0
559559 −24.9754 −1.05635
560560 0 0
561561 0 0
562562 4.92820 8.53590i 0.207884 0.360065i
563563 12.7973 22.1655i 0.539341 0.934166i −0.459599 0.888127i 0.652007π-0.652007\pi
0.998940 0.0460390i 0.0146598π-0.0146598\pi
564564 0 0
565565 13.3843 + 23.1822i 0.563080 + 0.975283i
566566 9.41902 0.395911
567567 0 0
568568 2.53590 0.106404
569569 7.89230 + 13.6699i 0.330863 + 0.573071i 0.982681 0.185304i 0.0593270π-0.0593270\pi
−0.651819 + 0.758375i 0.725994π0.725994\pi
570570 0 0
571571 −2.52628 + 4.37564i −0.105722 + 0.183115i −0.914033 0.405640i 0.867049π-0.867049\pi
0.808311 + 0.588755i 0.200382π0.200382\pi
572572 12.4877 21.6293i 0.522136 0.904367i
573573 0 0
574574 0 0
575575 14.5359 0.606189
576576 0 0
577577 44.6357 1.85821 0.929103 0.369820i 0.120581π-0.120581\pi
0.929103 + 0.369820i 0.120581π0.120581\pi
578578 6.16987 + 10.6865i 0.256633 + 0.444501i
579579 0 0
580580 −7.72741 + 13.3843i −0.320863 + 0.555751i
581581 0 0
582582 0 0
583583 −5.46410 9.46410i −0.226300 0.391963i
584584 −6.83083 −0.282662
585585 0 0
586586 19.0411 0.786581
587587 −14.5768 25.2478i −0.601650 1.04209i −0.992571 0.121664i 0.961177π-0.961177\pi
0.390922 0.920424i 0.372156π-0.372156\pi
588588 0 0
589589 2.66025 4.60770i 0.109614 0.189857i
590590 −16.6603 + 28.8564i −0.685892 + 1.18800i
591591 0 0
592592 −0.267949 0.464102i −0.0110126 0.0190745i
593593 −2.72689 −0.111980 −0.0559900 0.998431i 0.517831π-0.517831\pi
−0.0559900 + 0.998431i 0.517831π0.517831\pi
594594 0 0
595595 0 0
596596 4.53590 + 7.85641i 0.185798 + 0.321811i
597597 0 0
598598 −4.89898 + 8.48528i −0.200334 + 0.346989i
599599 −18.3923 + 31.8564i −0.751489 + 1.30162i 0.195612 + 0.980681i 0.437331π0.437331\pi
−0.947101 + 0.320936i 0.896003π0.896003\pi
600600 0 0
601601 −0.448288 0.776457i −0.0182860 0.0316723i 0.856738 0.515753i 0.172488π-0.172488\pi
−0.875024 + 0.484080i 0.839154π0.839154\pi
602602 0 0
603603 0 0
604604 −2.39230 −0.0973415
605605 −5.65685 9.79796i −0.229984 0.398344i
606606 0 0
607607 −15.8338 + 27.4249i −0.642672 + 1.11314i 0.342162 + 0.939641i 0.388841π0.388841\pi
−0.984834 + 0.173500i 0.944492π0.944492\pi
608608 1.48356 2.56961i 0.0601665 0.104211i
609609 0 0
610610 −13.4641 23.3205i −0.545146 0.944220i
611611 −70.6410 −2.85783
612612 0 0
613613 11.0718 0.447186 0.223593 0.974683i 0.428221π-0.428221\pi
0.223593 + 0.974683i 0.428221π0.428221\pi
614614 5.53674 + 9.58991i 0.223444 + 0.387017i
615615 0 0
616616 0 0
617617 −15.4282 + 26.7224i −0.621116 + 1.07580i 0.368162 + 0.929762i 0.379987π0.379987\pi
−0.989278 + 0.146043i 0.953346π0.953346\pi
618618 0 0
619619 12.3168 + 21.3333i 0.495054 + 0.857459i 0.999984 0.00570182i 0.00181496π-0.00181496\pi
−0.504930 + 0.863160i 0.668482π0.668482\pi
620620 −6.92820 −0.278243
621621 0 0
622622 12.3490 0.495149
623623 0 0
624624 0 0
625625 −11.9641 + 20.7224i −0.478564 + 0.828897i
626626 −11.7112 + 20.2844i −0.468075 + 0.810729i
627627 0 0
628628 2.31079 + 4.00240i 0.0922105 + 0.159713i
629629 2.90276 0.115740
630630 0 0
631631 35.7128 1.42170 0.710852 0.703341i 0.248309π-0.248309\pi
0.710852 + 0.703341i 0.248309π0.248309\pi
632632 −2.46410 4.26795i −0.0980167 0.169770i
633633 0 0
634634 13.0000 22.5167i 0.516296 0.894251i
635635 −12.6264 + 21.8695i −0.501063 + 0.867866i
636636 0 0
637637 0 0
638638 −14.9282 −0.591013
639639 0 0
640640 −3.86370 −0.152726
641641 8.96410 + 15.5263i 0.354061 + 0.613251i 0.986957 0.160986i 0.0514673π-0.0514673\pi
−0.632896 + 0.774237i 0.718134π0.718134\pi
642642 0 0
643643 −6.53485 + 11.3187i −0.257709 + 0.446365i −0.965628 0.259929i 0.916301π-0.916301\pi
0.707919 + 0.706294i 0.249634π0.249634\pi
644644 0 0
645645 0 0
646646 8.03590 + 13.9186i 0.316168 + 0.547619i
647647 12.0716 0.474583 0.237291 0.971439i 0.423740π-0.423740\pi
0.237291 + 0.971439i 0.423740π0.423740\pi
648648 0 0
649649 −32.1851 −1.26338
650650 −33.2204 57.5394i −1.30301 2.25688i
651651 0 0
652652 −10.6603 + 18.4641i −0.417488 + 0.723110i
653653 3.00000 5.19615i 0.117399 0.203341i −0.801337 0.598213i 0.795878π-0.795878\pi
0.918736 + 0.394872i 0.129211π0.129211\pi
654654 0 0
655655 −11.6603 20.1962i −0.455604 0.789129i
656656 −1.27551 −0.0498004
657657 0 0
658658 0 0
659659 0.124356 + 0.215390i 0.00484421 + 0.00839042i 0.868437 0.495799i 0.165125π-0.165125\pi
−0.863593 + 0.504189i 0.831791π0.831791\pi
660660 0 0
661661 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
662662 −2.26795 + 3.92820i −0.0881463 + 0.152674i
663663 0 0
664664 −8.95215 15.5056i −0.347411 0.601733i
665665 0 0
666666 0 0
667667 5.85641 0.226761
668668 −10.5558 18.2832i −0.408417 0.707400i
669669 0 0
670670 10.6945 18.5235i 0.413166 0.715624i
671671 13.0053 22.5259i 0.502065 0.869602i
672672 0 0
673673 20.7846 + 36.0000i 0.801188 + 1.38770i 0.918835 + 0.394643i 0.129132π0.129132\pi
−0.117647 + 0.993055i 0.537535π0.537535\pi
674674 7.00000 0.269630
675675 0 0
676676 31.7846 1.22248
677677 10.0382 + 17.3867i 0.385799 + 0.668224i 0.991880 0.127179i 0.0405924π-0.0405924\pi
−0.606081 + 0.795403i 0.707259π0.707259\pi
678678 0 0
679679 0 0
680680 10.4641 18.1244i 0.401280 0.695037i
681681 0 0
682682 −3.34607 5.79555i −0.128127 0.221923i
683683 3.67949 0.140792 0.0703959 0.997519i 0.477574π-0.477574\pi
0.0703959 + 0.997519i 0.477574π0.477574\pi
684684 0 0
685685 33.4607 1.27847
686686 0 0
687687 0 0
688688 −1.86603 + 3.23205i −0.0711416 + 0.123221i
689689 9.79796 16.9706i 0.373273 0.646527i
690690 0 0
691691 4.81105 + 8.33298i 0.183021 + 0.317001i 0.942908 0.333054i 0.108079π-0.108079\pi
−0.759887 + 0.650055i 0.774746π0.774746\pi
692692 1.79315 0.0681654
693693 0 0
694694 21.5885 0.819487
695695 −31.5885 54.7128i −1.19822 2.07538i
696696 0 0
697697 3.45448 5.98334i 0.130848 0.226635i
698698 −8.24504 + 14.2808i −0.312080 + 0.540538i
699699 0 0
700700 0 0
701701 −20.7846 −0.785024 −0.392512 0.919747i 0.628394π-0.628394\pi
−0.392512 + 0.919747i 0.628394π0.628394\pi
702702 0 0
703703 1.59008 0.0599710
704704 −1.86603 3.23205i −0.0703285 0.121812i
705705 0 0
706706 −13.2134 + 22.8862i −0.497292 + 0.861335i
707707 0 0
708708 0 0
709709 −4.19615 7.26795i −0.157590 0.272954i 0.776409 0.630229i 0.217039π-0.217039\pi
−0.933999 + 0.357276i 0.883706π0.883706\pi
710710 9.79796 0.367711
711711 0 0
712712 −7.07107 −0.264999
713713 1.31268 + 2.27362i 0.0491602 + 0.0851479i
714714 0 0
715715 48.2487 83.5692i 1.80440 3.12531i
716716 9.46410 16.3923i 0.353690 0.612609i
717717 0 0
718718 −0.267949 0.464102i −0.00999978 0.0173201i
719719 −15.3805 −0.573595 −0.286798 0.957991i 0.592591π-0.592591\pi
−0.286798 + 0.957991i 0.592591π0.592591\pi
720720 0 0
721721 0 0
722722 −5.09808 8.83013i −0.189731 0.328623i
723723 0 0
724724 −8.48528 + 14.6969i −0.315353 + 0.546207i
725725 −19.8564 + 34.3923i −0.737448 + 1.27730i
726726 0 0
727727 −0.795040 1.37705i −0.0294864 0.0510719i 0.850906 0.525319i 0.176054π-0.176054\pi
−0.880392 + 0.474247i 0.842721π0.842721\pi
728728 0 0
729729 0 0
730730 −26.3923 −0.976823
731731 −10.1075 17.5068i −0.373841 0.647512i
732732 0 0
733733 −8.24504 + 14.2808i −0.304538 + 0.527475i −0.977158 0.212513i 0.931835π-0.931835\pi
0.672621 + 0.739988i 0.265169π0.265169\pi
734734 7.86611 13.6245i 0.290343 0.502889i
735735 0 0
736736 0.732051 + 1.26795i 0.0269838 + 0.0467372i
737737 20.6603 0.761030
738738 0 0
739739 −18.1244 −0.666715 −0.333358 0.942800i 0.608182π-0.608182\pi
−0.333358 + 0.942800i 0.608182π0.608182\pi
740740 −1.03528 1.79315i −0.0380575 0.0659175i
741741 0 0
742742 0 0
743743 25.7846 44.6603i 0.945946 1.63843i 0.192099 0.981376i 0.438471π-0.438471\pi
0.753847 0.657050i 0.228196π-0.228196\pi
744744 0 0
745745 17.5254 + 30.3548i 0.642080 + 1.11211i
746746 −30.7846 −1.12710
747747 0 0
748748 20.2151 0.739137
749749 0 0
750750 0 0
751751 3.39230 5.87564i 0.123787 0.214405i −0.797471 0.603357i 0.793829π-0.793829\pi
0.921258 + 0.388952i 0.127163π0.127163\pi
752752 −5.27792 + 9.14162i −0.192466 + 0.333361i
753753 0 0
754754 −13.3843 23.1822i −0.487426 0.844247i
755755 −9.24316 −0.336393
756756 0 0
757757 −15.3205 −0.556833 −0.278417 0.960460i 0.589810π-0.589810\pi
−0.278417 + 0.960460i 0.589810π0.589810\pi
758758 −8.79423 15.2321i −0.319421 0.553253i
759759 0 0
760760 5.73205 9.92820i 0.207923 0.360134i
761761 15.2282 26.3760i 0.552021 0.956129i −0.446108 0.894979i 0.647190π-0.647190\pi
0.998129 0.0611492i 0.0194765π-0.0194765\pi
762762 0 0
763763 0 0
764764 −1.07180 −0.0387762
765765 0 0
766766 21.6665 0.782841
767767 −28.8564 49.9808i −1.04194 1.80470i
768768 0 0
769769 19.0919 33.0681i 0.688471 1.19247i −0.283862 0.958865i 0.591616π-0.591616\pi
0.972332 0.233601i 0.0750511π-0.0750511\pi
770770 0 0
771771 0 0
772772 11.5263 + 19.9641i 0.414840 + 0.718524i
773773 0.203072 0.00730399 0.00365199 0.999993i 0.498838π-0.498838\pi
0.00365199 + 0.999993i 0.498838π0.498838\pi
774774 0 0
775775 −17.8028 −0.639494
776776 2.94855 + 5.10703i 0.105847 + 0.183332i
777777 0 0
778778 −4.00000 + 6.92820i −0.143407 + 0.248388i
779779 1.89230 3.27757i 0.0677989 0.117431i
780780 0 0
781781 4.73205 + 8.19615i 0.169326 + 0.293281i
782782 −7.93048 −0.283593
783783 0 0
784784 0 0
785785 8.92820 + 15.4641i 0.318661 + 0.551937i
786786 0 0
787787 −23.3717 + 40.4810i −0.833111 + 1.44299i 0.0624487 + 0.998048i 0.480109π0.480109\pi
−0.895559 + 0.444942i 0.853224π0.853224\pi
788788 −1.53590 + 2.66025i −0.0547141 + 0.0947676i
789789 0 0
790790 −9.52056 16.4901i −0.338726 0.586691i
791791 0 0
792792 0 0
793793 46.6410 1.65627
794794 −9.00292 15.5935i −0.319502 0.553393i
795795 0 0
796796 −8.90138 + 15.4176i −0.315501 + 0.546464i
797797 −10.4543 + 18.1074i −0.370310 + 0.641396i −0.989613 0.143756i 0.954082π-0.954082\pi
0.619303 + 0.785152i 0.287415π0.287415\pi
798798 0 0
799799 −28.5885 49.5167i −1.01139 1.75177i
800800 −9.92820 −0.351015
801801 0 0
802802 17.7846 0.627996
803803 −12.7465 22.0776i −0.449814 0.779101i
804804 0 0
805805 0 0
806806 6.00000 10.3923i 0.211341 0.366053i
807807 0 0
808808 2.44949 + 4.24264i 0.0861727 + 0.149256i
809809 26.2679 0.923532 0.461766 0.887002i 0.347216π-0.347216\pi
0.461766 + 0.887002i 0.347216π0.347216\pi
810810 0 0
811811 −46.1242 −1.61964 −0.809820 0.586679i 0.800435π-0.800435\pi
−0.809820 + 0.586679i 0.800435π0.800435\pi
812812 0 0
813813 0 0
814814 1.00000 1.73205i 0.0350500 0.0607083i
815815 −41.1881 + 71.3398i −1.44275 + 2.49892i
816816 0 0
817817 −5.53674 9.58991i −0.193706 0.335508i
818818 16.7303 0.584962
819819 0 0
820820 −4.92820 −0.172100
821821 −5.19615 9.00000i −0.181347 0.314102i 0.760993 0.648761i 0.224712π-0.224712\pi
−0.942339 + 0.334659i 0.891379π0.891379\pi
822822 0 0
823823 −15.3923 + 26.6603i −0.536542 + 0.929318i 0.462545 + 0.886596i 0.346936π0.346936\pi
−0.999087 + 0.0427222i 0.986397π0.986397\pi
824824 −3.72500 + 6.45189i −0.129767 + 0.224762i
825825 0 0
826826 0 0
827827 12.0000 0.417281 0.208640 0.977992i 0.433096π-0.433096\pi
0.208640 + 0.977992i 0.433096π0.433096\pi
828828 0 0
829829 −37.3244 −1.29633 −0.648164 0.761501i 0.724463π-0.724463\pi
−0.648164 + 0.761501i 0.724463π0.724463\pi
830830 −34.5885 59.9090i −1.20058 2.07947i
831831 0 0
832832 3.34607 5.79555i 0.116004 0.200925i
833833 0 0
834834 0 0
835835 −40.7846 70.6410i −1.41141 2.44463i
836836 11.0735 0.382984
837837 0 0
838838 7.90327 0.273014
839839 −11.3137 19.5959i −0.390593 0.676526i 0.601935 0.798545i 0.294397π-0.294397\pi
−0.992528 + 0.122019i 0.961063π0.961063\pi
840840 0 0
841841 6.50000 11.2583i 0.224138 0.388218i
842842 14.1962 24.5885i 0.489232 0.847374i
843843 0 0
844844 −2.53590 4.39230i −0.0872892 0.151189i
845845 122.806 4.22467
846846 0 0
847847 0 0
848848 −1.46410 2.53590i −0.0502775 0.0870831i
849849 0 0
850850 26.8886 46.5725i 0.922273 1.59742i
851851 −0.392305 + 0.679492i −0.0134480 + 0.0232927i
852852 0 0
853853 −8.00481 13.8647i −0.274079 0.474719i 0.695823 0.718213i 0.255040π-0.255040\pi
−0.969902 + 0.243494i 0.921706π0.921706\pi
854854 0 0
855855 0 0
856856 3.39230 0.115947
857857 −4.19187 7.26054i −0.143192 0.248015i 0.785505 0.618855i 0.212403π-0.212403\pi
−0.928697 + 0.370840i 0.879070π0.879070\pi
858858 0 0
859859 7.36705 12.7601i 0.251361 0.435369i −0.712540 0.701631i 0.752455π-0.752455\pi
0.963901 + 0.266262i 0.0857887π0.0857887\pi
860860 −7.20977 + 12.4877i −0.245851 + 0.425827i
861861 0 0
862862 18.9282 + 32.7846i 0.644697 + 1.11665i
863863 −22.1051 −0.752467 −0.376233 0.926525i 0.622781π-0.622781\pi
−0.376233 + 0.926525i 0.622781π0.622781\pi
864864 0 0
865865 6.92820 0.235566
866866 −3.55412 6.15591i −0.120774 0.209186i
867867 0 0
868868 0 0
869869 9.19615 15.9282i 0.311958 0.540327i
870870 0 0
871871 18.5235 + 32.0836i 0.627644 + 1.08711i
872872 8.92820 0.302347
873873 0 0
874874 −4.34418 −0.146944
875875 0 0
876876 0 0
877877 −16.5885 + 28.7321i −0.560152 + 0.970212i 0.437330 + 0.899301i 0.355924π0.355924\pi
−0.997483 + 0.0709114i 0.977409π0.977409\pi
878878 9.79796 16.9706i 0.330665 0.572729i
879879 0 0
880880 −7.20977 12.4877i −0.243041 0.420960i
881881 −12.7279 −0.428815 −0.214407 0.976744i 0.568782π-0.568782\pi
−0.214407 + 0.976744i 0.568782π0.568782\pi
882882 0 0
883883 7.53590 0.253603 0.126802 0.991928i 0.459529π-0.459529\pi
0.126802 + 0.991928i 0.459529π0.459529\pi
884884 18.1244 + 31.3923i 0.609588 + 1.05584i
885885 0 0
886886 9.16025 15.8660i 0.307745 0.533030i
887887 −14.3824 + 24.9110i −0.482913 + 0.836430i −0.999808 0.0196195i 0.993755π-0.993755\pi
0.516895 + 0.856049i 0.327088π0.327088\pi
888888 0 0
889889 0 0
890890 −27.3205 −0.915786
891891 0 0
892892 26.7685 0.896276
893893 −15.6603 27.1244i −0.524050 0.907682i
894894 0 0
895895 36.5665 63.3350i 1.22228 2.11706i
896896 0 0
897897 0 0
898898 8.89230 + 15.4019i 0.296740 + 0.513969i
899899 −7.17260 −0.239220
900900 0 0
901901 15.8610 0.528405
902902 −2.38014 4.12252i −0.0792500 0.137265i
903903 0 0
904904 −3.46410 + 6.00000i −0.115214 + 0.199557i
905905 −32.7846 + 56.7846i −1.08980 + 1.88758i
906906 0 0
907907 −21.6244 37.4545i −0.718025 1.24366i −0.961781 0.273819i 0.911713π-0.911713\pi
0.243756 0.969837i 0.421620π-0.421620\pi
908908 −10.5187 −0.349074
909909 0 0
910910 0 0
911911 −23.4641 40.6410i −0.777400 1.34650i −0.933435 0.358745i 0.883205π-0.883205\pi
0.156035 0.987752i 0.450129π-0.450129\pi
912912 0 0
913913 33.4099 57.8676i 1.10571 1.91514i
914914 3.52628 6.10770i 0.116639 0.202025i
915915 0 0
916916 12.4877 + 21.6293i 0.412605 + 0.714652i
917917 0 0
918918 0 0
919919 22.9282 0.756332 0.378166 0.925738i 0.376555π-0.376555\pi
0.378166 + 0.925738i 0.376555π0.376555\pi
920920 2.82843 + 4.89898i 0.0932505 + 0.161515i
921921 0 0
922922 −12.8666 + 22.2856i −0.423740 + 0.733939i
923923 −8.48528 + 14.6969i −0.279296 + 0.483756i
924924 0 0
925925 −2.66025 4.60770i −0.0874686 0.151500i
926926 −38.6410 −1.26982
927927 0 0
928928 −4.00000 −0.131306
929929 13.9898 + 24.2311i 0.458991 + 0.794997i 0.998908 0.0467220i 0.0148775π-0.0148775\pi
−0.539916 + 0.841719i 0.681544π0.681544\pi
930930 0 0
931931 0 0
932932 −12.0622 + 20.8923i −0.395110 + 0.684350i
933933 0 0
934934 −13.7818 23.8707i −0.450954 0.781075i
935935 78.1051 2.55431
936936 0 0
937937 9.89949 0.323402 0.161701 0.986840i 0.448302π-0.448302\pi
0.161701 + 0.986840i 0.448302π0.448302\pi
938938 0 0
939939 0 0
940940 −20.3923 + 35.3205i −0.665124 + 1.15203i
941941 4.34418 7.52433i 0.141616 0.245286i −0.786489 0.617604i 0.788103π-0.788103\pi
0.928105 + 0.372318i 0.121437π0.121437\pi
942942 0 0
943943 0.933740 + 1.61729i 0.0304068 + 0.0526661i
944944 −8.62398 −0.280687
945945 0 0
946946 −13.9282 −0.452845
947947 3.06218 + 5.30385i 0.0995074 + 0.172352i 0.911481 0.411342i 0.134940π-0.134940\pi
−0.811973 + 0.583694i 0.801607π0.801607\pi
948948 0 0
949949 22.8564 39.5885i 0.741950 1.28510i
950950 14.7291 25.5116i 0.477876 0.827705i
951951 0 0
952952 0 0
953953 −19.0000 −0.615470 −0.307735 0.951472i 0.599571π-0.599571\pi
−0.307735 + 0.951472i 0.599571π0.599571\pi
954954 0 0
955955 −4.14110 −0.134003
956956 −6.46410 11.1962i −0.209064 0.362109i
957957 0 0
958958 7.72741 13.3843i 0.249661 0.432426i
959959 0 0
960960 0 0
961961 13.8923 + 24.0622i 0.448139 + 0.776199i
962962 3.58630 0.115627
963963 0 0
964964 −23.4225 −0.754387
965965 44.5341 + 77.1354i 1.43360 + 2.48308i
966966 0 0
967967 −17.7846 + 30.8038i −0.571914 + 0.990585i 0.424455 + 0.905449i 0.360466π0.360466\pi
−0.996369 + 0.0851359i 0.972868π0.972868\pi
968968 1.46410 2.53590i 0.0470580 0.0815069i
969969 0 0
970970 11.3923 + 19.7321i 0.365785 + 0.633558i
971971 −3.00429 −0.0964123 −0.0482062 0.998837i 0.515350π-0.515350\pi
−0.0482062 + 0.998837i 0.515350π0.515350\pi
972972 0 0
973973 0 0
974974 19.3923 + 33.5885i 0.621370 + 1.07624i
975975 0 0
976976 3.48477 6.03579i 0.111545 0.193201i
977977 −24.9904 + 43.2846i −0.799513 + 1.38480i 0.120420 + 0.992723i 0.461576π0.461576\pi
−0.919934 + 0.392074i 0.871758π0.871758\pi
978978 0 0
979979 −13.1948 22.8541i −0.421707 0.730419i
980980 0 0
981981 0 0
982982 −1.39230 −0.0444302
983983 3.48477 + 6.03579i 0.111147 + 0.192512i 0.916233 0.400646i 0.131214π-0.131214\pi
−0.805086 + 0.593158i 0.797881π0.797881\pi
984984 0 0
985985 −5.93426 + 10.2784i −0.189081 + 0.327498i
986986 10.8332 18.7637i 0.345000 0.597558i
987987 0 0
988988 9.92820 + 17.1962i 0.315858 + 0.547082i
989989 5.46410 0.173748
990990 0 0
991991 1.75129 0.0556315 0.0278158 0.999613i 0.491145π-0.491145\pi
0.0278158 + 0.999613i 0.491145π0.491145\pi
992992 −0.896575 1.55291i −0.0284663 0.0493051i
993993 0 0
994994 0 0
995995 −34.3923 + 59.5692i −1.09031 + 1.88847i
996996 0 0
997997 3.24453 + 5.61969i 0.102755 + 0.177977i 0.912819 0.408365i 0.133901π-0.133901\pi
−0.810064 + 0.586342i 0.800567π0.800567\pi
998998 −12.6077 −0.399090
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 2646.2.f.r.1765.1 8
3.2 odd 2 882.2.f.q.589.3 yes 8
7.2 even 3 2646.2.h.t.361.4 8
7.3 odd 6 2646.2.e.q.1549.4 8
7.4 even 3 2646.2.e.q.1549.1 8
7.5 odd 6 2646.2.h.t.361.1 8
7.6 odd 2 inner 2646.2.f.r.1765.4 8
9.2 odd 6 882.2.f.q.295.3 yes 8
9.4 even 3 7938.2.a.ci.1.4 4
9.5 odd 6 7938.2.a.cp.1.1 4
9.7 even 3 inner 2646.2.f.r.883.1 8
21.2 odd 6 882.2.h.q.67.4 8
21.5 even 6 882.2.h.q.67.1 8
21.11 odd 6 882.2.e.s.373.1 8
21.17 even 6 882.2.e.s.373.4 8
21.20 even 2 882.2.f.q.589.2 yes 8
63.2 odd 6 882.2.e.s.655.1 8
63.11 odd 6 882.2.h.q.79.3 8
63.13 odd 6 7938.2.a.ci.1.1 4
63.16 even 3 2646.2.e.q.2125.1 8
63.20 even 6 882.2.f.q.295.2 8
63.25 even 3 2646.2.h.t.667.4 8
63.34 odd 6 inner 2646.2.f.r.883.4 8
63.38 even 6 882.2.h.q.79.2 8
63.41 even 6 7938.2.a.cp.1.4 4
63.47 even 6 882.2.e.s.655.4 8
63.52 odd 6 2646.2.h.t.667.1 8
63.61 odd 6 2646.2.e.q.2125.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
882.2.e.s.373.1 8 21.11 odd 6
882.2.e.s.373.4 8 21.17 even 6
882.2.e.s.655.1 8 63.2 odd 6
882.2.e.s.655.4 8 63.47 even 6
882.2.f.q.295.2 8 63.20 even 6
882.2.f.q.295.3 yes 8 9.2 odd 6
882.2.f.q.589.2 yes 8 21.20 even 2
882.2.f.q.589.3 yes 8 3.2 odd 2
882.2.h.q.67.1 8 21.5 even 6
882.2.h.q.67.4 8 21.2 odd 6
882.2.h.q.79.2 8 63.38 even 6
882.2.h.q.79.3 8 63.11 odd 6
2646.2.e.q.1549.1 8 7.4 even 3
2646.2.e.q.1549.4 8 7.3 odd 6
2646.2.e.q.2125.1 8 63.16 even 3
2646.2.e.q.2125.4 8 63.61 odd 6
2646.2.f.r.883.1 8 9.7 even 3 inner
2646.2.f.r.883.4 8 63.34 odd 6 inner
2646.2.f.r.1765.1 8 1.1 even 1 trivial
2646.2.f.r.1765.4 8 7.6 odd 2 inner
2646.2.h.t.361.1 8 7.5 odd 6
2646.2.h.t.361.4 8 7.2 even 3
2646.2.h.t.667.1 8 63.52 odd 6
2646.2.h.t.667.4 8 63.25 even 3
7938.2.a.ci.1.1 4 63.13 odd 6
7938.2.a.ci.1.4 4 9.4 even 3
7938.2.a.cp.1.1 4 9.5 odd 6
7938.2.a.cp.1.4 4 63.41 even 6