Properties

Label 224.2.q.a.143.3
Level 224224
Weight 22
Character 224.143
Analytic conductor 1.7891.789
Analytic rank 00
Dimension 1212
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [224,2,Mod(47,224)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(224, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("224.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 224=257 224 = 2^{5} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 224.q (of order 66, 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: 1.788649005281.78864900528
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: 12.0.144054149089536.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x123x11+x9+48x8189x7+431x6654x5+624x4340x3+96x212x+4 x^{12} - 3x^{11} + x^{9} + 48x^{8} - 189x^{7} + 431x^{6} - 654x^{5} + 624x^{4} - 340x^{3} + 96x^{2} - 12x + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 26 2^{6}
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 143.3
Root 2.37165+1.78079i-2.37165 + 1.78079i of defining polynomial
Character χ\chi == 224.143
Dual form 224.2.q.a.47.3

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+(0.416472+0.240450i)q3+(1.597132.76632i)q5+(0.6941532.55307i)q7+(1.384372.39779i)q9+(0.800840+1.38709i)q11+1.38831q131.53613iq15+(3.48605+2.01267i)q17+(4.569572.63824i)q19+(0.9029820.896373i)q21+(3.83044+2.21151i)q23+(2.60168+4.50624i)q252.77419iq27+5.10613iq29+(0.0579809+0.100426i)q31+(0.667055+0.385124i)q33+(8.17125+2.15734i)q35+(4.630872.67363i)q37+(0.578191+0.333819i)q394.21689iq41+(4.42204+7.65920i)q45+(5.05821+8.76108i)q47+(6.036303.54444i)q49+(0.967895+1.67644i)q51+(6.135143.54212i)q53+5.11619q55+2.53747q57+(4.38856+2.53374i)q59+(4.21321+7.29750i)q61+(7.08269+1.86995i)q63+(2.217313.84050i)q65+(5.01815+8.69169i)q672.12703q69+5.29150iq71+(9.30504+5.37227i)q73+(2.16706+1.25115i)q75+(2.98544+3.00745i)q77+(10.33495.96688i)q79+(3.48605+6.03801i)q8114.9789iq8312.8580iq85+(1.22777+2.12656i)q87+(1.500000.866025i)q89+(0.9636973.54444i)q91+(0.0482949+0.0278831i)q93+(14.59658.42726i)q952.87198iq97+4.43462q99+O(q100)q+(0.416472 + 0.240450i) q^{3} +(-1.59713 - 2.76632i) q^{5} +(0.694153 - 2.55307i) q^{7} +(-1.38437 - 2.39779i) q^{9} +(-0.800840 + 1.38709i) q^{11} +1.38831 q^{13} -1.53613i q^{15} +(3.48605 + 2.01267i) q^{17} +(4.56957 - 2.63824i) q^{19} +(0.902982 - 0.896373i) q^{21} +(-3.83044 + 2.21151i) q^{23} +(-2.60168 + 4.50624i) q^{25} -2.77419i q^{27} +5.10613i q^{29} +(-0.0579809 + 0.100426i) q^{31} +(-0.667055 + 0.385124i) q^{33} +(-8.17125 + 2.15734i) q^{35} +(4.63087 - 2.67363i) q^{37} +(0.578191 + 0.333819i) q^{39} -4.21689i q^{41} +(-4.42204 + 7.65920i) q^{45} +(5.05821 + 8.76108i) q^{47} +(-6.03630 - 3.54444i) q^{49} +(0.967895 + 1.67644i) q^{51} +(-6.13514 - 3.54212i) q^{53} +5.11619 q^{55} +2.53747 q^{57} +(4.38856 + 2.53374i) q^{59} +(4.21321 + 7.29750i) q^{61} +(-7.08269 + 1.86995i) q^{63} +(-2.21731 - 3.84050i) q^{65} +(-5.01815 + 8.69169i) q^{67} -2.12703 q^{69} +5.29150i q^{71} +(9.30504 + 5.37227i) q^{73} +(-2.16706 + 1.25115i) q^{75} +(2.98544 + 3.00745i) q^{77} +(10.3349 - 5.96688i) q^{79} +(-3.48605 + 6.03801i) q^{81} -14.9789i q^{83} -12.8580i q^{85} +(-1.22777 + 2.12656i) q^{87} +(1.50000 - 0.866025i) q^{89} +(0.963697 - 3.54444i) q^{91} +(-0.0482949 + 0.0278831i) q^{93} +(-14.5965 - 8.42726i) q^{95} -2.87198i q^{97} +4.43462 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+6q3+6q116q17+6q196q3318q3512q496q5136q5742q5912q6530q67+18q7324q75+6q81+18q89+72q91+24q99+O(q100) 12 q + 6 q^{3} + 6 q^{11} - 6 q^{17} + 6 q^{19} - 6 q^{33} - 18 q^{35} - 12 q^{49} - 6 q^{51} - 36 q^{57} - 42 q^{59} - 12 q^{65} - 30 q^{67} + 18 q^{73} - 24 q^{75} + 6 q^{81} + 18 q^{89} + 72 q^{91} + 24 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/224Z)×\left(\mathbb{Z}/224\mathbb{Z}\right)^\times.

nn 127127 129129 197197
χ(n)\chi(n) 1-1 e(16)e\left(\frac{1}{6}\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 0
33 0.416472 + 0.240450i 0.240450 + 0.138824i 0.615384 0.788228i 0.289001π-0.289001\pi
−0.374933 + 0.927052i 0.622334π0.622334\pi
44 0 0
55 −1.59713 2.76632i −0.714260 1.23714i −0.963244 0.268628i 0.913430π-0.913430\pi
0.248984 0.968508i 0.419903π-0.419903\pi
66 0 0
77 0.694153 2.55307i 0.262365 0.964969i
88 0 0
99 −1.38437 2.39779i −0.461456 0.799265i
1010 0 0
1111 −0.800840 + 1.38709i −0.241462 + 0.418225i −0.961131 0.276093i 0.910960π-0.910960\pi
0.719669 + 0.694318i 0.244294π0.244294\pi
1212 0 0
1313 1.38831 0.385047 0.192523 0.981292i 0.438333π-0.438333\pi
0.192523 + 0.981292i 0.438333π0.438333\pi
1414 0 0
1515 1.53613i 0.396626i
1616 0 0
1717 3.48605 + 2.01267i 0.845490 + 0.488144i 0.859127 0.511763i 0.171007π-0.171007\pi
−0.0136363 + 0.999907i 0.504341π0.504341\pi
1818 0 0
1919 4.56957 2.63824i 1.04833 0.605255i 0.126150 0.992011i 0.459738π-0.459738\pi
0.922182 + 0.386756i 0.126405π0.126405\pi
2020 0 0
2121 0.902982 0.896373i 0.197047 0.195605i
2222 0 0
2323 −3.83044 + 2.21151i −0.798702 + 0.461131i −0.843017 0.537887i 0.819223π-0.819223\pi
0.0443149 + 0.999018i 0.485890π0.485890\pi
2424 0 0
2525 −2.60168 + 4.50624i −0.520336 + 0.901248i
2626 0 0
2727 2.77419i 0.533893i
2828 0 0
2929 5.10613i 0.948185i 0.880475 + 0.474093i 0.157224π0.157224\pi
−0.880475 + 0.474093i 0.842776π0.842776\pi
3030 0 0
3131 −0.0579809 + 0.100426i −0.0104137 + 0.0180370i −0.871185 0.490954i 0.836648π-0.836648\pi
0.860772 + 0.508991i 0.169982π0.169982\pi
3232 0 0
3333 −0.667055 + 0.385124i −0.116119 + 0.0670416i
3434 0 0
3535 −8.17125 + 2.15734i −1.38119 + 0.364658i
3636 0 0
3737 4.63087 2.67363i 0.761310 0.439543i −0.0684556 0.997654i 0.521807π-0.521807\pi
0.829766 + 0.558111i 0.188474π0.188474\pi
3838 0 0
3939 0.578191 + 0.333819i 0.0925847 + 0.0534538i
4040 0 0
4141 4.21689i 0.658568i −0.944231 0.329284i 0.893193π-0.893193\pi
0.944231 0.329284i 0.106807π-0.106807\pi
4242 0 0
4343 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4444 0 0
4545 −4.42204 + 7.65920i −0.659199 + 1.14177i
4646 0 0
4747 5.05821 + 8.76108i 0.737816 + 1.27794i 0.953477 + 0.301467i 0.0974763π0.0974763\pi
−0.215660 + 0.976468i 0.569190π0.569190\pi
4848 0 0
4949 −6.03630 3.54444i −0.862329 0.506348i
5050 0 0
5151 0.967895 + 1.67644i 0.135532 + 0.234749i
5252 0 0
5353 −6.13514 3.54212i −0.842726 0.486548i 0.0154638 0.999880i 0.495078π-0.495078\pi
−0.858190 + 0.513332i 0.828411π0.828411\pi
5454 0 0
5555 5.11619 0.689868
5656 0 0
5757 2.53747 0.336096
5858 0 0
5959 4.38856 + 2.53374i 0.571342 + 0.329865i 0.757685 0.652620i 0.226330π-0.226330\pi
−0.186343 + 0.982485i 0.559664π0.559664\pi
6060 0 0
6161 4.21321 + 7.29750i 0.539447 + 0.934349i 0.998934 + 0.0461646i 0.0146999π0.0146999\pi
−0.459487 + 0.888184i 0.651967π0.651967\pi
6262 0 0
6363 −7.08269 + 1.86995i −0.892335 + 0.235591i
6464 0 0
6565 −2.21731 3.84050i −0.275024 0.476355i
6666 0 0
6767 −5.01815 + 8.69169i −0.613065 + 1.06186i 0.377656 + 0.925946i 0.376730π0.376730\pi
−0.990721 + 0.135913i 0.956603π0.956603\pi
6868 0 0
6969 −2.12703 −0.256064
7070 0 0
7171 5.29150i 0.627986i 0.949425 + 0.313993i 0.101667π0.101667\pi
−0.949425 + 0.313993i 0.898333π0.898333\pi
7272 0 0
7373 9.30504 + 5.37227i 1.08907 + 0.628776i 0.933329 0.359021i 0.116890π-0.116890\pi
0.155743 + 0.987798i 0.450223π0.450223\pi
7474 0 0
7575 −2.16706 + 1.25115i −0.250230 + 0.144470i
7676 0 0
7777 2.98544 + 3.00745i 0.340223 + 0.342731i
7878 0 0
7979 10.3349 5.96688i 1.16277 0.671327i 0.210805 0.977528i 0.432391π-0.432391\pi
0.951967 + 0.306201i 0.0990581π0.0990581\pi
8080 0 0
8181 −3.48605 + 6.03801i −0.387338 + 0.670890i
8282 0 0
8383 14.9789i 1.64415i −0.569382 0.822073i 0.692818π-0.692818\pi
0.569382 0.822073i 0.307182π-0.307182\pi
8484 0 0
8585 12.8580i 1.39465i
8686 0 0
8787 −1.22777 + 2.12656i −0.131631 + 0.227992i
8888 0 0
8989 1.50000 0.866025i 0.159000 0.0917985i −0.418389 0.908268i 0.637405π-0.637405\pi
0.577389 + 0.816469i 0.304072π0.304072\pi
9090 0 0
9191 0.963697 3.54444i 0.101023 0.371558i
9292 0 0
9393 −0.0482949 + 0.0278831i −0.00500795 + 0.00289134i
9494 0 0
9595 −14.5965 8.42726i −1.49756 0.864619i
9696 0 0
9797 2.87198i 0.291606i −0.989314 0.145803i 0.953423π-0.953423\pi
0.989314 0.145803i 0.0465765π-0.0465765\pi
9898 0 0
9999 4.43462 0.445696
100100 0 0
101101 3.40310 5.89434i 0.338621 0.586509i −0.645553 0.763716i 0.723373π-0.723373\pi
0.984174 + 0.177207i 0.0567062π0.0567062\pi
102102 0 0
103103 −7.02471 12.1672i −0.692165 1.19887i −0.971127 0.238563i 0.923324π-0.923324\pi
0.278962 0.960302i 0.410010π-0.410010\pi
104104 0 0
105105 −3.92184 1.06631i −0.382732 0.104061i
106106 0 0
107107 −2.56957 4.45063i −0.248410 0.430259i 0.714675 0.699457i 0.246575π-0.246575\pi
−0.963085 + 0.269198i 0.913241π0.913241\pi
108108 0 0
109109 2.45182 + 1.41556i 0.234842 + 0.135586i 0.612804 0.790235i 0.290042π-0.290042\pi
−0.377962 + 0.925821i 0.623375π0.623375\pi
110110 0 0
111111 2.57151 0.244077
112112 0 0
113113 −1.43695 −0.135177 −0.0675887 0.997713i 0.521531π-0.521531\pi
−0.0675887 + 0.997713i 0.521531π0.521531\pi
114114 0 0
115115 12.2355 + 7.06415i 1.14096 + 0.658735i
116116 0 0
117117 −1.92193 3.32887i −0.177682 0.307754i
118118 0 0
119119 7.55833 7.50301i 0.692871 0.687800i
120120 0 0
121121 4.21731 + 7.30460i 0.383392 + 0.664054i
122122 0 0
123123 1.01395 1.75622i 0.0914251 0.158353i
124124 0 0
125125 0.649581 0.0581003
126126 0 0
127127 4.92077i 0.436647i −0.975876 0.218324i 0.929941π-0.929941\pi
0.975876 0.218324i 0.0700589π-0.0700589\pi
128128 0 0
129129 0 0
130130 0 0
131131 3.41647 1.97250i 0.298499 0.172338i −0.343270 0.939237i 0.611534π-0.611534\pi
0.641768 + 0.766899i 0.278201π0.278201\pi
132132 0 0
133133 −3.56363 13.4978i −0.309006 1.17041i
134134 0 0
135135 −7.67429 + 4.43075i −0.660498 + 0.381339i
136136 0 0
137137 0.0514223 0.0890661i 0.00439331 0.00760943i −0.863820 0.503800i 0.831935π-0.831935\pi
0.868214 + 0.496190i 0.165268π0.165268\pi
138138 0 0
139139 14.9789i 1.27049i 0.772310 + 0.635246i 0.219101π0.219101\pi
−0.772310 + 0.635246i 0.780899π0.780899\pi
140140 0 0
141141 4.86500i 0.409707i
142142 0 0
143143 −1.11181 + 1.92571i −0.0929743 + 0.161036i
144144 0 0
145145 14.1252 8.15518i 1.17303 0.677251i
146146 0 0
147147 −1.66169 2.92759i −0.137054 0.241464i
148148 0 0
149149 −9.79164 + 5.65320i −0.802162 + 0.463129i −0.844227 0.535986i 0.819940π-0.819940\pi
0.0420645 + 0.999115i 0.486607π0.486607\pi
150150 0 0
151151 12.8351 + 7.41032i 1.04450 + 0.603044i 0.921105 0.389314i 0.127288π-0.127288\pi
0.123397 + 0.992357i 0.460621π0.460621\pi
152152 0 0
153153 11.1451i 0.901028i
154154 0 0
155155 0.370413 0.0297523
156156 0 0
157157 0.369362 0.639755i 0.0294783 0.0510580i −0.850910 0.525312i 0.823949π-0.823949\pi
0.880388 + 0.474254i 0.157282π0.157282\pi
158158 0 0
159159 −1.70341 2.95039i −0.135089 0.233981i
160160 0 0
161161 2.98721 + 11.3145i 0.235425 + 0.891707i
162162 0 0
163163 −4.35226 7.53834i −0.340895 0.590448i 0.643704 0.765275i 0.277397π-0.277397\pi
−0.984599 + 0.174826i 0.944064π0.944064\pi
164164 0 0
165165 2.13075 + 1.23019i 0.165879 + 0.0957703i
166166 0 0
167167 −1.38831 −0.107430 −0.0537152 0.998556i 0.517106π-0.517106\pi
−0.0537152 + 0.998556i 0.517106π0.517106\pi
168168 0 0
169169 −11.0726 −0.851739
170170 0 0
171171 −12.6519 7.30460i −0.967518 0.558597i
172172 0 0
173173 −0.485324 0.840606i −0.0368985 0.0639101i 0.846986 0.531615i 0.178414π-0.178414\pi
−0.883885 + 0.467704i 0.845081π0.845081\pi
174174 0 0
175175 9.69877 + 9.77028i 0.733158 + 0.738564i
176176 0 0
177177 1.21848 + 2.11046i 0.0915864 + 0.158632i
178178 0 0
179179 −7.13495 + 12.3581i −0.533291 + 0.923687i 0.465953 + 0.884810i 0.345712π0.345712\pi
−0.999244 + 0.0388779i 0.987622π0.987622\pi
180180 0 0
181181 15.3218 1.13886 0.569429 0.822041i 0.307164π-0.307164\pi
0.569429 + 0.822041i 0.307164π0.307164\pi
182182 0 0
183183 4.05228i 0.299553i
184184 0 0
185185 −14.7922 8.54031i −1.08755 0.627896i
186186 0 0
187187 −5.58353 + 3.22365i −0.408308 + 0.235737i
188188 0 0
189189 −7.08269 1.92571i −0.515190 0.140075i
190190 0 0
191191 2.16564 1.25033i 0.156700 0.0904709i −0.419599 0.907709i 0.637829π-0.637829\pi
0.576300 + 0.817238i 0.304496π0.304496\pi
192192 0 0
193193 1.55026 2.68512i 0.111590 0.193279i −0.804822 0.593517i 0.797739π-0.797739\pi
0.916411 + 0.400237i 0.131072π0.131072\pi
194194 0 0
195195 2.13261i 0.152720i
196196 0 0
197197 15.6891i 1.11780i 0.829233 + 0.558902i 0.188777π0.188777\pi
−0.829233 + 0.558902i 0.811223π0.811223\pi
198198 0 0
199199 −5.91290 + 10.2414i −0.419154 + 0.725997i −0.995855 0.0909591i 0.971007π-0.971007\pi
0.576700 + 0.816956i 0.304340π0.304340\pi
200200 0 0
201201 −4.17984 + 2.41323i −0.294823 + 0.170216i
202202 0 0
203203 13.0363 + 3.54444i 0.914969 + 0.248771i
204204 0 0
205205 −11.6653 + 6.73495i −0.814738 + 0.470389i
206206 0 0
207207 10.6055 + 6.12307i 0.737131 + 0.425583i
208208 0 0
209209 8.45124i 0.584585i
210210 0 0
211211 −10.0726 −0.693427 −0.346713 0.937971i 0.612702π-0.612702\pi
−0.346713 + 0.937971i 0.612702π0.612702\pi
212212 0 0
213213 −1.27234 + 2.20376i −0.0871796 + 0.150999i
214214 0 0
215215 0 0
216216 0 0
217217 0.216146 + 0.217740i 0.0146730 + 0.0147812i
218218 0 0
219219 2.58353 + 4.47480i 0.174579 + 0.302379i
220220 0 0
221221 4.83970 + 2.79420i 0.325553 + 0.187958i
222222 0 0
223223 −24.3086 −1.62783 −0.813913 0.580987i 0.802667π-0.802667\pi
−0.813913 + 0.580987i 0.802667π0.802667\pi
224224 0 0
225225 14.4067 0.960448
226226 0 0
227227 12.4048 + 7.16194i 0.823339 + 0.475355i 0.851566 0.524247i 0.175653π-0.175653\pi
−0.0282277 + 0.999602i 0.508986π0.508986\pi
228228 0 0
229229 5.32502 + 9.22321i 0.351887 + 0.609487i 0.986580 0.163278i 0.0522066π-0.0522066\pi
−0.634693 + 0.772765i 0.718873π0.718873\pi
230230 0 0
231231 0.520210 + 1.97037i 0.0342273 + 0.129641i
232232 0 0
233233 0.318991 + 0.552509i 0.0208978 + 0.0361961i 0.876285 0.481793i 0.160014π-0.160014\pi
−0.855387 + 0.517989i 0.826681π0.826681\pi
234234 0 0
235235 16.1573 27.9853i 1.05399 1.82556i
236236 0 0
237237 5.73896 0.372785
238238 0 0
239239 4.73540i 0.306307i 0.988202 + 0.153154i 0.0489430π0.0489430\pi
−0.988202 + 0.153154i 0.951057π0.951057\pi
240240 0 0
241241 −10.1380 5.85317i −0.653045 0.377036i 0.136577 0.990629i 0.456390π-0.456390\pi
−0.789622 + 0.613594i 0.789723π0.789723\pi
242242 0 0
243243 −10.1112 + 5.83773i −0.648636 + 0.374490i
244244 0 0
245245 −0.164257 + 22.3593i −0.0104940 + 1.42848i
246246 0 0
247247 6.34397 3.66269i 0.403657 0.233051i
248248 0 0
249249 3.60168 6.23829i 0.228247 0.395336i
250250 0 0
251251 11.5631i 0.729858i 0.931035 + 0.364929i 0.118907π0.118907\pi
−0.931035 + 0.364929i 0.881093π0.881093\pi
252252 0 0
253253 7.08425i 0.445383i
254254 0 0
255255 3.09172 5.35501i 0.193611 0.335344i
256256 0 0
257257 −20.4302 + 11.7954i −1.27440 + 0.735777i −0.975813 0.218605i 0.929849π-0.929849\pi
−0.298589 + 0.954382i 0.596516π0.596516\pi
258258 0 0
259259 −3.61144 13.6788i −0.224404 0.849961i
260260 0 0
261261 12.2435 7.06876i 0.757851 0.437546i
262262 0 0
263263 −9.24833 5.33953i −0.570277 0.329249i 0.186983 0.982363i 0.440129π-0.440129\pi
−0.757260 + 0.653114i 0.773462π0.773462\pi
264264 0 0
265265 22.6290i 1.39009i
266266 0 0
267267 0.832945 0.0509754
268268 0 0
269269 11.6690 20.2113i 0.711471 1.23230i −0.252834 0.967510i 0.581363π-0.581363\pi
0.964305 0.264794i 0.0853040π-0.0853040\pi
270270 0 0
271271 6.81961 + 11.8119i 0.414262 + 0.717522i 0.995351 0.0963179i 0.0307066π-0.0307066\pi
−0.581089 + 0.813840i 0.697373π0.697373\pi
272272 0 0
273273 1.25362 1.24444i 0.0758722 0.0753169i
274274 0 0
275275 −4.16706 7.21755i −0.251283 0.435235i
276276 0 0
277277 0.396180 + 0.228735i 0.0238042 + 0.0137433i 0.511855 0.859072i 0.328959π-0.328959\pi
−0.488051 + 0.872815i 0.662292π0.662292\pi
278278 0 0
279279 0.321068 0.0192218
280280 0 0
281281 1.43695 0.0857215 0.0428608 0.999081i 0.486353π-0.486353\pi
0.0428608 + 0.999081i 0.486353π0.486353\pi
282282 0 0
283283 −27.0428 15.6132i −1.60753 0.928108i −0.989921 0.141622i 0.954768π-0.954768\pi
−0.617609 0.786486i 0.711898π-0.711898\pi
284284 0 0
285285 −4.05268 7.01945i −0.240060 0.415796i
286286 0 0
287287 −10.7660 2.92717i −0.635497 0.172785i
288288 0 0
289289 −0.398321 0.689912i −0.0234306 0.0405831i
290290 0 0
291291 0.690570 1.19610i 0.0404819 0.0701168i
292292 0 0
293293 −31.3006 −1.82860 −0.914299 0.405040i 0.867258π-0.867258\pi
−0.914299 + 0.405040i 0.867258π0.867258\pi
294294 0 0
295295 16.1869i 0.942437i
296296 0 0
297297 3.84806 + 2.22168i 0.223287 + 0.128915i
298298 0 0
299299 −5.31783 + 3.07025i −0.307538 + 0.177557i
300300 0 0
301301 0 0
302302 0 0
303303 2.83459 1.63655i 0.162843 0.0940175i
304304 0 0
305305 13.4581 23.3102i 0.770611 1.33474i
306306 0 0
307307 14.7215i 0.840202i 0.907477 + 0.420101i 0.138005π0.138005\pi
−0.907477 + 0.420101i 0.861995π0.861995\pi
308308 0 0
309309 6.75638i 0.384357i
310310 0 0
311311 7.79025 13.4931i 0.441745 0.765124i −0.556074 0.831133i 0.687693π-0.687693\pi
0.997819 + 0.0660082i 0.0210263π0.0210263\pi
312312 0 0
313313 11.3329 6.54308i 0.640576 0.369837i −0.144260 0.989540i 0.546080π-0.546080\pi
0.784836 + 0.619703i 0.212747π0.212747\pi
314314 0 0
315315 16.4849 + 16.6064i 0.928818 + 0.935666i
316316 0 0
317317 20.3971 11.7763i 1.14562 0.661422i 0.197801 0.980242i 0.436620π-0.436620\pi
0.947815 + 0.318821i 0.103287π0.103287\pi
318318 0 0
319319 −7.08269 4.08919i −0.396555 0.228951i
320320 0 0
321321 2.47142i 0.137941i
322322 0 0
323323 21.2397 1.18181
324324 0 0
325325 −3.61193 + 6.25604i −0.200354 + 0.347023i
326326 0 0
327327 0.680744 + 1.17908i 0.0376452 + 0.0652035i
328328 0 0
329329 25.8788 6.83243i 1.42674 0.376684i
330330 0 0
331331 16.5277 + 28.6268i 0.908445 + 1.57347i 0.816225 + 0.577735i 0.196063π0.196063\pi
0.0922207 + 0.995739i 0.470603π0.470603\pi
332332 0 0
333333 −12.8217 7.40258i −0.702622 0.405659i
334334 0 0
335335 32.0587 1.75155
336336 0 0
337337 −15.5096 −0.844860 −0.422430 0.906396i 0.638823π-0.638823\pi
−0.422430 + 0.906396i 0.638823π0.638823\pi
338338 0 0
339339 −0.598452 0.345516i −0.0325035 0.0187659i
340340 0 0
341341 −0.0928668 0.160850i −0.00502902 0.00871052i
342342 0 0
343343 −13.2393 + 12.9507i −0.714855 + 0.699272i
344344 0 0
345345 3.39716 + 5.88405i 0.182897 + 0.316786i
346346 0 0
347347 11.2494 19.4846i 0.603900 1.04599i −0.388324 0.921523i 0.626946π-0.626946\pi
0.992224 0.124463i 0.0397209π-0.0397209\pi
348348 0 0
349349 −28.4735 −1.52415 −0.762077 0.647486i 0.775820π-0.775820\pi
−0.762077 + 0.647486i 0.775820π0.775820\pi
350350 0 0
351351 3.85142i 0.205574i
352352 0 0
353353 −8.29108 4.78686i −0.441290 0.254779i 0.262855 0.964835i 0.415336π-0.415336\pi
−0.704145 + 0.710057i 0.748669π0.748669\pi
354354 0 0
355355 14.6380 8.45124i 0.776903 0.448545i
356356 0 0
357357 4.95194 1.30739i 0.262084 0.0691945i
358358 0 0
359359 3.25225 1.87769i 0.171647 0.0991006i −0.411715 0.911313i 0.635070π-0.635070\pi
0.583362 + 0.812212i 0.301737π0.301737\pi
360360 0 0
361361 4.42067 7.65683i 0.232667 0.402991i
362362 0 0
363363 4.05622i 0.212896i
364364 0 0
365365 34.3209i 1.79644i
366366 0 0
367367 8.41302 14.5718i 0.439156 0.760640i −0.558469 0.829526i 0.688611π-0.688611\pi
0.997625 + 0.0688852i 0.0219442π0.0219442\pi
368368 0 0
369369 −10.1112 + 5.83773i −0.526370 + 0.303900i
370370 0 0
371371 −13.3020 + 13.2046i −0.690606 + 0.685551i
372372 0 0
373373 −11.1354 + 6.42901i −0.576568 + 0.332882i −0.759768 0.650194i 0.774688π-0.774688\pi
0.183200 + 0.983076i 0.441354π0.441354\pi
374374 0 0
375375 0.270533 + 0.156192i 0.0139702 + 0.00806572i
376376 0 0
377377 7.08888i 0.365096i
378378 0 0
379379 −25.5822 −1.31407 −0.657034 0.753861i 0.728189π-0.728189\pi
−0.657034 + 0.753861i 0.728189π0.728189\pi
380380 0 0
381381 1.18320 2.04936i 0.0606172 0.104992i
382382 0 0
383383 −13.4846 23.3561i −0.689033 1.19344i −0.972151 0.234355i 0.924702π-0.924702\pi
0.283118 0.959085i 0.408631π-0.408631\pi
384384 0 0
385385 3.55142 13.0620i 0.180997 0.665701i
386386 0 0
387387 0 0
388388 0 0
389389 27.7043 + 15.9951i 1.40466 + 0.810983i 0.994867 0.101195i 0.0322665π-0.0322665\pi
0.409796 + 0.912177i 0.365600π0.365600\pi
390390 0 0
391391 −17.8041 −0.900394
392392 0 0
393393 1.89716 0.0956988
394394 0 0
395395 −33.0126 19.0598i −1.66104 0.959004i
396396 0 0
397397 −8.51929 14.7558i −0.427571 0.740575i 0.569086 0.822278i 0.307297π-0.307297\pi
−0.996657 + 0.0817035i 0.973964π0.973964\pi
398398 0 0
399399 1.76139 6.47833i 0.0881799 0.324322i
400400 0 0
401401 2.94858 + 5.10709i 0.147245 + 0.255036i 0.930208 0.367032i 0.119626π-0.119626\pi
−0.782963 + 0.622068i 0.786293π0.786293\pi
402402 0 0
403403 −0.0804953 + 0.139422i −0.00400976 + 0.00694510i
404404 0 0
405405 22.2707 1.10664
406406 0 0
407407 8.56461i 0.424532i
408408 0 0
409409 −0.207751 0.119945i −0.0102726 0.00593090i 0.494855 0.868976i 0.335221π-0.335221\pi
−0.505128 + 0.863045i 0.668555π0.668555\pi
410410 0 0
411411 0.0428320 0.0247290i 0.00211274 0.00121979i
412412 0 0
413413 9.51514 9.44550i 0.468210 0.464783i
414414 0 0
415415 −41.4364 + 23.9233i −2.03403 + 1.17435i
416416 0 0
417417 −3.60168 + 6.23829i −0.176375 + 0.305490i
418418 0 0
419419 29.4140i 1.43697i −0.695544 0.718484i 0.744837π-0.744837\pi
0.695544 0.718484i 0.255163π-0.255163\pi
420420 0 0
421421 32.1265i 1.56575i 0.622180 + 0.782874i 0.286247π0.286247\pi
−0.622180 + 0.782874i 0.713753π0.713753\pi
422422 0 0
423423 14.0049 24.2571i 0.680939 1.17942i
424424 0 0
425425 −18.1391 + 10.4726i −0.879878 + 0.507998i
426426 0 0
427427 21.5556 5.69103i 1.04315 0.275408i
428428 0 0
429429 −0.926077 + 0.534671i −0.0447114 + 0.0258141i
430430 0 0
431431 32.7662 + 18.9176i 1.57829 + 0.911228i 0.995098 + 0.0988962i 0.0315312π0.0315312\pi
0.583196 + 0.812332i 0.301802π0.301802\pi
432432 0 0
433433 25.4835i 1.22466i 0.790602 + 0.612330i 0.209768π0.209768\pi
−0.790602 + 0.612330i 0.790232π0.790232\pi
434434 0 0
435435 7.84367 0.376075
436436 0 0
437437 −11.6690 + 20.2113i −0.558204 + 0.966837i
438438 0 0
439439 11.9804 + 20.7506i 0.571792 + 0.990373i 0.996382 + 0.0849871i 0.0270849π0.0270849\pi
−0.424590 + 0.905386i 0.639582π0.639582\pi
440440 0 0
441441 −0.142375 + 19.3806i −0.00677975 + 0.922887i
442442 0 0
443443 5.13495 + 8.89399i 0.243969 + 0.422566i 0.961841 0.273608i 0.0882172π-0.0882172\pi
−0.717872 + 0.696175i 0.754884π0.754884\pi
444444 0 0
445445 −4.79140 2.76632i −0.227134 0.131136i
446446 0 0
447447 −5.43726 −0.257174
448448 0 0
449449 11.5096 0.543170 0.271585 0.962414i 0.412452π-0.412452\pi
0.271585 + 0.962414i 0.412452π0.412452\pi
450450 0 0
451451 5.84923 + 3.37705i 0.275429 + 0.159019i
452452 0 0
453453 3.56363 + 6.17239i 0.167434 + 0.290004i
454454 0 0
455455 −11.3442 + 2.99505i −0.531824 + 0.140410i
456456 0 0
457457 −15.3050 26.5091i −0.715939 1.24004i −0.962596 0.270941i 0.912665π-0.912665\pi
0.246657 0.969103i 0.420668π-0.420668\pi
458458 0 0
459459 5.58353 9.67095i 0.260617 0.451401i
460460 0 0
461461 17.3671 0.808866 0.404433 0.914568i 0.367469π-0.367469\pi
0.404433 + 0.914568i 0.367469π0.367469\pi
462462 0 0
463463 21.7288i 1.00983i 0.863171 + 0.504913i 0.168475π0.168475\pi
−0.863171 + 0.504913i 0.831525π0.831525\pi
464464 0 0
465465 0.154267 + 0.0890661i 0.00715396 + 0.00413034i
466466 0 0
467467 0.585859 0.338246i 0.0271103 0.0156521i −0.486384 0.873745i 0.661684π-0.661684\pi
0.513494 + 0.858093i 0.328351π0.328351\pi
468468 0 0
469469 18.7071 + 18.8450i 0.863814 + 0.870183i
470470 0 0
471471 0.307659 0.177627i 0.0141762 0.00818461i
472472 0 0
473473 0 0
474474 0 0
475475 27.4555i 1.25974i
476476 0 0
477477 19.6144i 0.898082i
478478 0 0
479479 −14.3839 + 24.9136i −0.657217 + 1.13833i 0.324116 + 0.946017i 0.394933π0.394933\pi
−0.981333 + 0.192316i 0.938400π0.938400\pi
480480 0 0
481481 6.42907 3.71182i 0.293140 0.169245i
482482 0 0
483483 −1.47649 + 5.43045i −0.0671824 + 0.247094i
484484 0 0
485485 −7.94483 + 4.58695i −0.360756 + 0.208283i
486486 0 0
487487 1.58745 + 0.916514i 0.0719342 + 0.0415312i 0.535536 0.844513i 0.320110π-0.320110\pi
−0.463602 + 0.886044i 0.653443π0.653443\pi
488488 0 0
489489 4.18601i 0.189298i
490490 0 0
491491 −13.4370 −0.606401 −0.303201 0.952927i 0.598055π-0.598055\pi
−0.303201 + 0.952927i 0.598055π0.598055\pi
492492 0 0
493493 −10.2770 + 17.8002i −0.462851 + 0.801682i
494494 0 0
495495 −7.08269 12.2676i −0.318343 0.551387i
496496 0 0
497497 13.5096 + 3.67311i 0.605987 + 0.164762i
498498 0 0
499499 −5.68404 9.84505i −0.254453 0.440725i 0.710294 0.703905i 0.248562π-0.248562\pi
−0.964747 + 0.263180i 0.915229π0.915229\pi
500500 0 0
501501 −0.578191 0.333819i −0.0258317 0.0149139i
502502 0 0
503503 13.2022 0.588656 0.294328 0.955704i 0.404904π-0.404904\pi
0.294328 + 0.955704i 0.404904π0.404904\pi
504504 0 0
505505 −21.7408 −0.967454
506506 0 0
507507 −4.61144 2.66241i −0.204801 0.118242i
508508 0 0
509509 −13.2178 22.8940i −0.585870 1.01476i −0.994766 0.102176i 0.967420π-0.967420\pi
0.408896 0.912581i 0.365914π-0.365914\pi
510510 0 0
511511 20.1749 20.0272i 0.892484 0.885952i
512512 0 0
513513 −7.31899 12.6769i −0.323141 0.559697i
514514 0 0
515515 −22.4388 + 38.8652i −0.988773 + 1.71260i
516516 0 0
517517 −16.2033 −0.712619
518518 0 0
519519 0.466786i 0.0204896i
520520 0 0
521521 −10.4163 6.01384i −0.456345 0.263471i 0.254161 0.967162i 0.418201π-0.418201\pi
−0.710506 + 0.703691i 0.751534π0.751534\pi
522522 0 0
523523 −2.43276 + 1.40455i −0.106377 + 0.0614168i −0.552245 0.833682i 0.686229π-0.686229\pi
0.445868 + 0.895099i 0.352895π0.352895\pi
524524 0 0
525525 1.69000 + 6.40113i 0.0737577 + 0.279368i
526526 0 0
527527 −0.404248 + 0.233393i −0.0176093 + 0.0101668i
528528 0 0
529529 −1.71848 + 2.97649i −0.0747164 + 0.129413i
530530 0 0
531531 14.0305i 0.608872i
532532 0 0
533533 5.85434i 0.253580i
534534 0 0
535535 −8.20791 + 14.2165i −0.354859 + 0.614634i
536536 0 0
537537 −5.94302 + 3.43120i −0.256460 + 0.148067i
538538 0 0
539539 9.75058 5.53440i 0.419987 0.238383i
540540 0 0
541541 1.68628 0.973573i 0.0724988 0.0418572i −0.463312 0.886195i 0.653339π-0.653339\pi
0.535811 + 0.844338i 0.320006π0.320006\pi
542542 0 0
543543 6.38109 + 3.68413i 0.273839 + 0.158101i
544544 0 0
545545 9.04336i 0.387375i
546546 0 0
547547 −28.4561 −1.21669 −0.608347 0.793671i 0.708167π-0.708167\pi
−0.608347 + 0.793671i 0.708167π0.708167\pi
548548 0 0
549549 11.6653 20.2048i 0.497862 0.862321i
550550 0 0
551551 13.4712 + 23.3329i 0.573894 + 0.994013i
552552 0 0
553553 −8.05982 30.5277i −0.342738 1.29817i
554554 0 0
555555 −4.10704 7.11361i −0.174334 0.301956i
556556 0 0
557557 7.96630 + 4.59935i 0.337543 + 0.194881i 0.659185 0.751981i 0.270901π-0.270901\pi
−0.321642 + 0.946861i 0.604235π0.604235\pi
558558 0 0
559559 0 0
560560 0 0
561561 −3.10051 −0.130904
562562 0 0
563563 23.5533 + 13.5985i 0.992653 + 0.573108i 0.906066 0.423136i 0.139071π-0.139071\pi
0.0865866 + 0.996244i 0.472404π0.472404\pi
564564 0 0
565565 2.29501 + 3.97508i 0.0965518 + 0.167233i
566566 0 0
567567 12.9956 + 13.0914i 0.545764 + 0.549788i
568568 0 0
569569 11.7699 + 20.3861i 0.493420 + 0.854628i 0.999971 0.00758149i 0.00241329π-0.00241329\pi
−0.506551 + 0.862210i 0.669080π0.669080\pi
570570 0 0
571571 15.1713 26.2774i 0.634897 1.09967i −0.351640 0.936135i 0.614376π-0.614376\pi
0.986537 0.163539i 0.0522909π-0.0522909\pi
572572 0 0
573573 1.20257 0.0502382
574574 0 0
575575 23.0145i 0.959772i
576576 0 0
577577 24.7760 + 14.3044i 1.03144 + 0.595500i 0.917396 0.397976i 0.130287π-0.130287\pi
0.114041 + 0.993476i 0.463620π0.463620\pi
578578 0 0
579579 1.29128 0.745520i 0.0536637 0.0309828i
580580 0 0
581581 −38.2421 10.3976i −1.58655 0.431367i
582582 0 0
583583 9.82652 5.67335i 0.406973 0.234966i
584584 0 0
585585 −6.13915 + 10.6333i −0.253823 + 0.439634i
586586 0 0
587587 15.2362i 0.628867i 0.949280 + 0.314433i 0.101814π0.101814\pi
−0.949280 + 0.314433i 0.898186π0.898186\pi
588588 0 0
589589 0.611872i 0.0252117i
590590 0 0
591591 −3.77246 + 6.53409i −0.155178 + 0.268777i
592592 0 0
593593 18.2934 10.5617i 0.751221 0.433717i −0.0749142 0.997190i 0.523868π-0.523868\pi
0.826135 + 0.563473i 0.190535π0.190535\pi
594594 0 0
595595 −32.8274 8.92543i −1.34579 0.365907i
596596 0 0
597597 −4.92512 + 2.84352i −0.201572 + 0.116378i
598598 0 0
599599 −29.1795 16.8468i −1.19224 0.688341i −0.233427 0.972374i 0.574994π-0.574994\pi
−0.958814 + 0.284033i 0.908327π0.908327\pi
600600 0 0
601601 24.3960i 0.995132i −0.867426 0.497566i 0.834227π-0.834227\pi
0.867426 0.497566i 0.165773π-0.165773\pi
602602 0 0
603603 27.7879 1.13161
604604 0 0
605605 13.4712 23.3329i 0.547683 0.948616i
606606 0 0
607607 −4.08757 7.07987i −0.165909 0.287363i 0.771069 0.636752i 0.219723π-0.219723\pi
−0.936978 + 0.349389i 0.886389π0.886389\pi
608608 0 0
609609 4.57700 + 4.61075i 0.185469 + 0.186837i
610610 0 0
611611 7.02235 + 12.1631i 0.284094 + 0.492065i
612612 0 0
613613 −14.7221 8.49981i −0.594620 0.343304i 0.172302 0.985044i 0.444879π-0.444879\pi
−0.766922 + 0.641740i 0.778213π0.778213\pi
614614 0 0
615615 −6.47768 −0.261205
616616 0 0
617617 39.6548 1.59644 0.798221 0.602365i 0.205775π-0.205775\pi
0.798221 + 0.602365i 0.205775π0.205775\pi
618618 0 0
619619 12.4719 + 7.20065i 0.501288 + 0.289419i 0.729245 0.684252i 0.239871π-0.239871\pi
−0.227957 + 0.973671i 0.573205π0.573205\pi
620620 0 0
621621 6.13514 + 10.6264i 0.246195 + 0.426422i
622622 0 0
623623 −1.16979 4.43075i −0.0468667 0.177514i
624624 0 0
625625 11.9709 + 20.7343i 0.478837 + 0.829370i
626626 0 0
627627 −2.03211 + 3.51971i −0.0811545 + 0.140564i
628628 0 0
629629 21.5246 0.858241
630630 0 0
631631 36.6698i 1.45980i −0.683553 0.729900i 0.739566π-0.739566\pi
0.683553 0.729900i 0.260434π-0.260434\pi
632632 0 0
633633 −4.19496 2.42196i −0.166735 0.0962644i
634634 0 0
635635 −13.6124 + 7.85913i −0.540192 + 0.311880i
636636 0 0
637637 −8.38024 4.92077i −0.332037 0.194968i
638638 0 0
639639 12.6879 7.32538i 0.501927 0.289788i
640640 0 0
641641 −9.13798 + 15.8274i −0.360929 + 0.625147i −0.988114 0.153723i 0.950874π-0.950874\pi
0.627185 + 0.778870i 0.284207π0.284207\pi
642642 0 0
643643 13.6340i 0.537671i −0.963186 0.268836i 0.913361π-0.913361\pi
0.963186 0.268836i 0.0866389π-0.0866389\pi
644644 0 0
645645 0 0
646646 0 0
647647 −8.74153 + 15.1408i −0.343665 + 0.595245i −0.985110 0.171923i 0.945002π-0.945002\pi
0.641445 + 0.767169i 0.278335π0.278335\pi
648648 0 0
649649 −7.02907 + 4.05824i −0.275915 + 0.159300i
650650 0 0
651651 0.0376633 + 0.142655i 0.00147614 + 0.00559110i
652652 0 0
653653 8.40495 4.85260i 0.328911 0.189897i −0.326446 0.945216i 0.605851π-0.605851\pi
0.655358 + 0.755319i 0.272518π0.272518\pi
654654 0 0
655655 −10.9131 6.30070i −0.426411 0.246189i
656656 0 0
657657 29.7488i 1.16061i
658658 0 0
659659 28.9465 1.12760 0.563798 0.825913i 0.309340π-0.309340\pi
0.563798 + 0.825913i 0.309340π0.309340\pi
660660 0 0
661661 6.43683 11.1489i 0.250364 0.433643i −0.713262 0.700897i 0.752783π-0.752783\pi
0.963626 + 0.267254i 0.0861164π0.0861164\pi
662662 0 0
663663 1.34373 + 2.32742i 0.0521863 + 0.0903893i
664664 0 0
665665 −31.6475 + 31.4159i −1.22724 + 1.21826i
666666 0 0
667667 −11.2922 19.5587i −0.437238 0.757318i
668668 0 0
669669 −10.1239 5.84502i −0.391412 0.225982i
670670 0 0
671671 −13.4964 −0.521024
672672 0 0
673673 −23.6548 −0.911825 −0.455912 0.890025i 0.650687π-0.650687\pi
−0.455912 + 0.890025i 0.650687π0.650687\pi
674674 0 0
675675 12.5012 + 7.21755i 0.481170 + 0.277804i
676676 0 0
677677 1.80224 + 3.12157i 0.0692657 + 0.119972i 0.898578 0.438813i 0.144601π-0.144601\pi
−0.829313 + 0.558785i 0.811268π0.811268\pi
678678 0 0
679679 −7.33237 1.99360i −0.281391 0.0765072i
680680 0 0
681681 3.44419 + 5.96550i 0.131981 + 0.228599i
682682 0 0
683683 −3.80924 + 6.59779i −0.145756 + 0.252457i −0.929655 0.368432i 0.879895π-0.879895\pi
0.783899 + 0.620889i 0.213228π0.213228\pi
684684 0 0
685685 −0.328514 −0.0125519
686686 0 0
687687 5.12162i 0.195402i
688688 0 0
689689 −8.51745 4.91755i −0.324489 0.187344i
690690 0 0
691691 44.9707 25.9639i 1.71077 0.987712i 0.777241 0.629203i 0.216619π-0.216619\pi
0.933526 0.358509i 0.116715π-0.116715\pi
692692 0 0
693693 3.07831 11.3219i 0.116935 0.430083i
694694 0 0
695695 41.4364 23.9233i 1.57177 0.907462i
696696 0 0
697697 8.48721 14.7003i 0.321476 0.556813i
698698 0 0
699699 0.306806i 0.0116045i
700700 0 0
701701 0.741474i 0.0280051i −0.999902 0.0140025i 0.995543π-0.995543\pi
0.999902 0.0140025i 0.00445729π-0.00445729\pi
702702 0 0
703703 14.1074 24.4347i 0.532071 0.921574i
704704 0 0
705705 13.4581 7.77006i 0.506863 0.292637i
706706 0 0
707707 −12.6864 12.7799i −0.477120 0.480638i
708708 0 0
709709 35.6491 20.5820i 1.33883 0.772974i 0.352196 0.935926i 0.385435π-0.385435\pi
0.986634 + 0.162952i 0.0521016π0.0521016\pi
710710 0 0
711711 −28.6147 16.5207i −1.07314 0.619575i
712712 0 0
713713 0.512901i 0.0192083i
714714 0 0
715715 7.10284 0.265631
716716 0 0
717717 −1.13863 + 1.97216i −0.0425229 + 0.0736518i
718718 0 0
719719 −7.02471 12.1672i −0.261978 0.453758i 0.704790 0.709416i 0.251041π-0.251041\pi
−0.966767 + 0.255658i 0.917708π0.917708\pi
720720 0 0
721721 −35.9398 + 9.48869i −1.33847 + 0.353377i
722722 0 0
723723 −2.81479 4.87536i −0.104683 0.181317i
724724 0 0
725725 −23.0095 13.2845i −0.854550 0.493375i
726726 0 0
727727 −13.2022 −0.489642 −0.244821 0.969568i 0.578729π-0.578729\pi
−0.244821 + 0.969568i 0.578729π0.578729\pi
728728 0 0
729729 15.3015 0.566724
730730 0 0
731731 0 0
732732 0 0
733733 24.9797 + 43.2661i 0.922646 + 1.59807i 0.795304 + 0.606211i 0.207311π0.207311\pi
0.127342 + 0.991859i 0.459356π0.459356\pi
734734 0 0
735735 −5.44471 + 9.27253i −0.200831 + 0.342022i
736736 0 0
737737 −8.03747 13.9213i −0.296064 0.512798i
738738 0 0
739739 −18.2718 + 31.6476i −0.672138 + 1.16418i 0.305159 + 0.952301i 0.401290π0.401290\pi
−0.977297 + 0.211875i 0.932043π0.932043\pi
740740 0 0
741741 3.52278 0.129413
742742 0 0
743743 15.1330i 0.555177i 0.960700 + 0.277589i 0.0895352π0.0895352\pi
−0.960700 + 0.277589i 0.910465π0.910465\pi
744744 0 0
745745 31.2771 + 18.0579i 1.14591 + 0.661589i
746746 0 0
747747 −35.9163 + 20.7363i −1.31411 + 0.758701i
748748 0 0
749749 −13.1464 + 3.47087i −0.480360 + 0.126823i
750750 0 0
751751 −11.9997 + 6.92806i −0.437877 + 0.252808i −0.702697 0.711490i 0.748021π-0.748021\pi
0.264820 + 0.964298i 0.414688π0.414688\pi
752752 0 0
753753 −2.78036 + 4.81572i −0.101322 + 0.175495i
754754 0 0
755755 47.3412i 1.72292i
756756 0 0
757757 46.6967i 1.69722i −0.529019 0.848610i 0.677440π-0.677440\pi
0.529019 0.848610i 0.322560π-0.322560\pi
758758 0 0
759759 1.70341 2.95039i 0.0618299 0.107093i
760760 0 0
761761 40.7899 23.5501i 1.47863 0.853689i 0.478925 0.877856i 0.341026π-0.341026\pi
0.999708 + 0.0241662i 0.00769309π0.00769309\pi
762762 0 0
763763 5.31596 5.27705i 0.192451 0.191042i
764764 0 0
765765 −30.8309 + 17.8002i −1.11469 + 0.643568i
766766 0 0
767767 6.09267 + 3.51761i 0.219994 + 0.127013i
768768 0 0
769769 17.3071i 0.624110i 0.950064 + 0.312055i 0.101017π0.101017\pi
−0.950064 + 0.312055i 0.898983π0.898983\pi
770770 0 0
771771 −11.3448 −0.408574
772772 0 0
773773 −13.5389 + 23.4501i −0.486960 + 0.843440i −0.999888 0.0149920i 0.995228π-0.995228\pi
0.512927 + 0.858432i 0.328561π0.328561\pi
774774 0 0
775775 −0.301696 0.522552i −0.0108372 0.0187706i
776776 0 0
777777 1.78502 6.56523i 0.0640372 0.235526i
778778 0 0
779779 −11.1252 19.2694i −0.398601 0.690398i
780780 0 0
781781 −7.33982 4.23764i −0.262639 0.151635i
782782 0 0
783783 14.1654 0.506230
784784 0 0
785785 −2.35969 −0.0842208
786786 0 0
787787 46.9684 + 27.1172i 1.67424 + 0.966624i 0.965220 + 0.261439i 0.0841969π0.0841969\pi
0.709023 + 0.705186i 0.249136π0.249136\pi
788788 0 0
789789 −2.56778 4.44753i −0.0914155 0.158336i
790790 0 0
791791 −0.997467 + 3.66864i −0.0354658 + 0.130442i
792792 0 0
793793 5.84923 + 10.1312i 0.207712 + 0.359768i
794794 0 0
795795 −5.44115 + 9.42435i −0.192978 + 0.334247i
796796 0 0
797797 20.1437 0.713527 0.356763 0.934195i 0.383880π-0.383880\pi
0.356763 + 0.934195i 0.383880π0.383880\pi
798798 0 0
799799 40.7221i 1.44064i
800800 0 0
801801 −4.15310 2.39779i −0.146743 0.0847219i
802802 0 0
803803 −14.9037 + 8.60465i −0.525940 + 0.303651i
804804 0 0
805805 26.5285 26.3344i 0.935008 0.928164i
806806 0 0
807807 9.71963 5.61163i 0.342147 0.197539i
808808 0 0
809809 −17.2771 + 29.9249i −0.607432 + 1.05210i 0.384231 + 0.923237i 0.374467π0.374467\pi
−0.991662 + 0.128865i 0.958867π0.958867\pi
810810 0 0
811811 13.6340i 0.478754i 0.970927 + 0.239377i 0.0769431π0.0769431\pi
−0.970927 + 0.239377i 0.923057π0.923057\pi
812812 0 0
813813 6.55911i 0.230038i
814814 0 0
815815 −13.9023 + 24.0795i −0.486976 + 0.843468i
816816 0 0
817817 0 0
818818 0 0
819819 −9.83294 + 2.59606i −0.343591 + 0.0907136i
820820 0 0
821821 −27.7311 + 16.0106i −0.967822 + 0.558772i −0.898572 0.438827i 0.855394π-0.855394\pi
−0.0692505 + 0.997599i 0.522061π0.522061\pi
822822 0 0
823823 26.8399 + 15.4960i 0.935580 + 0.540158i 0.888572 0.458737i 0.151698π-0.151698\pi
0.0470083 + 0.998894i 0.485031π0.485031\pi
824824 0 0
825825 4.00788i 0.139537i
826826 0 0
827827 11.0191 0.383172 0.191586 0.981476i 0.438637π-0.438637\pi
0.191586 + 0.981476i 0.438637π0.438637\pi
828828 0 0
829829 −18.9836 + 32.8806i −0.659328 + 1.14199i 0.321462 + 0.946922i 0.395826π0.395826\pi
−0.980790 + 0.195067i 0.937508π0.937508\pi
830830 0 0
831831 0.109999 + 0.190524i 0.00381582 + 0.00660919i
832832 0 0
833833 −13.9090 24.5052i −0.481920 0.849054i
834834 0 0
835835 2.21731 + 3.84050i 0.0767332 + 0.132906i
836836 0 0
837837 0.278601 + 0.160850i 0.00962984 + 0.00555979i
838838 0 0
839839 8.32984 0.287578 0.143789 0.989608i 0.454071π-0.454071\pi
0.143789 + 0.989608i 0.454071π0.454071\pi
840840 0 0
841841 2.92739 0.100945
842842 0 0
843843 0.598452 + 0.345516i 0.0206118 + 0.0119002i
844844 0 0
845845 17.6844 + 30.6304i 0.608363 + 1.05372i
846846 0 0
847847 21.5766 5.69657i 0.741380 0.195736i
848848 0 0
849849 −7.50840 13.0049i −0.257687 0.446328i
850850 0 0
851851 −11.8255 + 20.4824i −0.405374 + 0.702128i
852852 0 0
853853 −6.94153 −0.237673 −0.118837 0.992914i 0.537917π-0.537917\pi
−0.118837 + 0.992914i 0.537917π0.537917\pi
854854 0 0
855855 46.6657i 1.59593i
856856 0 0
857857 1.91744 + 1.10704i 0.0654986 + 0.0378156i 0.532392 0.846498i 0.321293π-0.321293\pi
−0.466893 + 0.884314i 0.654627π0.654627\pi
858858 0 0
859859 −5.26337 + 3.03881i −0.179584 + 0.103683i −0.587097 0.809516i 0.699729π-0.699729\pi
0.407513 + 0.913199i 0.366396π0.366396\pi
860860 0 0
861861 −3.77991 3.80778i −0.128819 0.129769i
862862 0 0
863863 7.64747 4.41527i 0.260323 0.150298i −0.364159 0.931337i 0.618643π-0.618643\pi
0.624482 + 0.781039i 0.285310π0.285310\pi
864864 0 0
865865 −1.55026 + 2.68512i −0.0527103 + 0.0912969i
866866 0 0
867867 0.383106i 0.0130110i
868868 0 0
869869 19.1141i 0.648400i
870870 0 0
871871 −6.96673 + 12.0667i −0.236059 + 0.408866i
872872 0 0
873873 −6.88643 + 3.97588i −0.233070 + 0.134563i
874874 0 0
875875 0.450909 1.65842i 0.0152435 0.0560650i
876876 0 0
877877 −10.3059 + 5.95011i −0.348005 + 0.200921i −0.663806 0.747905i 0.731060π-0.731060\pi
0.315801 + 0.948825i 0.397727π0.397727\pi
878878 0 0
879879 −13.0358 7.52623i −0.439687 0.253854i
880880 0 0
881881 53.9142i 1.81642i −0.418519 0.908208i 0.637451π-0.637451\pi
0.418519 0.908208i 0.362549π-0.362549\pi
882882 0 0
883883 −11.1987 −0.376866 −0.188433 0.982086i 0.560341π-0.560341\pi
−0.188433 + 0.982086i 0.560341π0.560341\pi
884884 0 0
885885 3.89215 6.74139i 0.130833 0.226609i
886886 0 0
887887 −18.1832 31.4942i −0.610531 1.05747i −0.991151 0.132740i 0.957623π-0.957623\pi
0.380620 0.924732i 0.375711π-0.375711\pi
888888 0 0
889889 −12.5630 3.41576i −0.421351 0.114561i
890890 0 0
891891 −5.58353 9.67095i −0.187055 0.323989i
892892 0 0
893893 46.2278 + 26.6896i 1.54695 + 0.893134i
894894 0 0
895895 45.5819 1.52364
896896 0 0
897897 −2.95297 −0.0985968
898898 0 0
899899 −0.512788 0.296058i −0.0171024 0.00987410i
900900 0 0
901901 −14.2583 24.6960i −0.475011 0.822744i
902902 0 0
903903 0 0
904904 0 0
905905 −24.4709 42.3849i −0.813441 1.40892i
906906 0 0
907907 −8.92370 + 15.4563i −0.296307 + 0.513218i −0.975288 0.220937i 0.929088π-0.929088\pi
0.678981 + 0.734156i 0.262422π0.262422\pi
908908 0 0
909909 −18.8446 −0.625034
910910 0 0
911911 11.1458i 0.369278i −0.982806 0.184639i 0.940888π-0.940888\pi
0.982806 0.184639i 0.0591116π-0.0591116\pi
912912 0 0
913913 20.7771 + 11.9957i 0.687623 + 0.396999i
914914 0 0
915915 11.2099 6.47203i 0.370587 0.213959i
916916 0 0
917917 −2.66437 10.0917i −0.0879854 0.333257i
918918 0 0
919919 −28.2802 + 16.3276i −0.932879 + 0.538598i −0.887721 0.460382i 0.847712π-0.847712\pi
−0.0451579 + 0.998980i 0.514379π0.514379\pi
920920 0 0
921921 −3.53980 + 6.13111i −0.116640 + 0.202027i
922922 0 0
923923 7.34623i 0.241804i
924924 0 0
925925 27.8238i 0.914839i
926926 0 0
927927 −19.4496 + 33.6876i −0.638807 + 1.10645i
928928 0 0
929929 −23.3027 + 13.4538i −0.764537 + 0.441406i −0.830922 0.556388i 0.812187π-0.812187\pi
0.0663853 + 0.997794i 0.478853π0.478853\pi
930930 0 0
931931 −36.9344 0.271329i −1.21048 0.00889246i
932932 0 0
933933 6.48885 3.74634i 0.212435 0.122650i
934934 0 0
935935 17.8353 + 10.2972i 0.583276 + 0.336755i
936936 0 0
937937 32.6476i 1.06655i 0.845942 + 0.533275i 0.179039π0.179039\pi
−0.845942 + 0.533275i 0.820961π0.820961\pi
938938 0 0
939939 6.29315 0.205369
940940 0 0
941941 −6.32087 + 10.9481i −0.206055 + 0.356897i −0.950468 0.310822i 0.899396π-0.899396\pi
0.744414 + 0.667719i 0.232729π0.232729\pi
942942 0 0
943943 9.32569 + 16.1526i 0.303686 + 0.526000i
944944 0 0
945945 5.98488 + 22.6686i 0.194688 + 0.737410i
946946 0 0
947947 −21.1271 36.5931i −0.686537 1.18912i −0.972951 0.231011i 0.925797π-0.925797\pi
0.286414 0.958106i 0.407537π-0.407537\pi
948948 0 0
949949 12.9182 + 7.45835i 0.419344 + 0.242108i
950950 0 0
951951 11.3264 0.367285
952952 0 0
953953 −44.4561 −1.44007 −0.720037 0.693936i 0.755875π-0.755875\pi
−0.720037 + 0.693936i 0.755875π0.755875\pi
954954 0 0
955955 −6.91764 3.99390i −0.223850 0.129240i
956956 0 0
957957 −1.96650 3.40607i −0.0635678 0.110103i
958958 0 0
959959 −0.191697 0.193110i −0.00619021 0.00623585i
960960 0 0
961961 15.4933 + 26.8351i 0.499783 + 0.865650i
962962 0 0
963963 −7.11447 + 12.3226i −0.229261 + 0.397091i
964964 0 0
965965 −9.90388 −0.318817
966966 0 0
967967 25.7160i 0.826972i −0.910510 0.413486i 0.864311π-0.864311\pi
0.910510 0.413486i 0.135689π-0.135689\pi
968968 0 0
969969 8.84573 + 5.10709i 0.284166 + 0.164063i
970970 0 0
971971 40.2746 23.2526i 1.29247 0.746210i 0.313381 0.949627i 0.398538π-0.398538\pi
0.979092 + 0.203417i 0.0652048π0.0652048\pi
972972 0 0
973973 38.2421 + 10.3976i 1.22599 + 0.333333i
974974 0 0
975975 −3.00854 + 1.73698i −0.0963503 + 0.0556278i
976976 0 0
977977 −17.1348 + 29.6783i −0.548189 + 0.949492i 0.450209 + 0.892923i 0.351349π0.351349\pi
−0.998399 + 0.0565688i 0.981984π0.981984\pi
978978 0 0
979979 2.77419i 0.0886635i
980980 0 0
981981 7.83862i 0.250268i
982982 0 0
983983 0.777334 1.34638i 0.0247931 0.0429429i −0.853363 0.521318i 0.825441π-0.825441\pi
0.878156 + 0.478375i 0.158774π0.158774\pi
984984 0 0
985985 43.4012 25.0577i 1.38288 0.798404i
986986 0 0
987987 12.4207 + 3.37705i 0.395354 + 0.107493i
988988 0 0
989989 0 0
990990 0 0
991991 −22.6482 13.0759i −0.719443 0.415371i 0.0951047 0.995467i 0.469681π-0.469681\pi
−0.814548 + 0.580097i 0.803015π0.803015\pi
992992 0 0
993993 15.8964i 0.504457i
994994 0 0
995995 37.7748 1.19754
996996 0 0
997997 18.1467 31.4310i 0.574711 0.995429i −0.421362 0.906893i 0.638448π-0.638448\pi
0.996073 0.0885360i 0.0282188π-0.0282188\pi
998998 0 0
999999 −7.41717 12.8469i −0.234669 0.406458i
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 224.2.q.a.143.3 12
3.2 odd 2 2016.2.bs.a.1711.6 12
4.3 odd 2 56.2.m.a.3.6 yes 12
7.2 even 3 1568.2.q.g.1391.3 12
7.3 odd 6 1568.2.e.e.783.7 12
7.4 even 3 1568.2.e.e.783.6 12
7.5 odd 6 inner 224.2.q.a.47.4 12
7.6 odd 2 1568.2.q.g.815.4 12
8.3 odd 2 inner 224.2.q.a.143.4 12
8.5 even 2 56.2.m.a.3.4 12
12.11 even 2 504.2.bk.a.451.1 12
21.5 even 6 2016.2.bs.a.271.1 12
24.5 odd 2 504.2.bk.a.451.3 12
24.11 even 2 2016.2.bs.a.1711.1 12
28.3 even 6 392.2.e.e.195.3 12
28.11 odd 6 392.2.e.e.195.4 12
28.19 even 6 56.2.m.a.19.3 yes 12
28.23 odd 6 392.2.m.g.19.3 12
28.27 even 2 392.2.m.g.227.6 12
56.3 even 6 1568.2.e.e.783.8 12
56.5 odd 6 56.2.m.a.19.5 yes 12
56.11 odd 6 1568.2.e.e.783.5 12
56.13 odd 2 392.2.m.g.227.4 12
56.19 even 6 inner 224.2.q.a.47.3 12
56.27 even 2 1568.2.q.g.815.3 12
56.37 even 6 392.2.m.g.19.5 12
56.45 odd 6 392.2.e.e.195.1 12
56.51 odd 6 1568.2.q.g.1391.4 12
56.53 even 6 392.2.e.e.195.2 12
84.47 odd 6 504.2.bk.a.19.4 12
168.5 even 6 504.2.bk.a.19.2 12
168.131 odd 6 2016.2.bs.a.271.6 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.2.m.a.3.4 12 8.5 even 2
56.2.m.a.3.6 yes 12 4.3 odd 2
56.2.m.a.19.3 yes 12 28.19 even 6
56.2.m.a.19.5 yes 12 56.5 odd 6
224.2.q.a.47.3 12 56.19 even 6 inner
224.2.q.a.47.4 12 7.5 odd 6 inner
224.2.q.a.143.3 12 1.1 even 1 trivial
224.2.q.a.143.4 12 8.3 odd 2 inner
392.2.e.e.195.1 12 56.45 odd 6
392.2.e.e.195.2 12 56.53 even 6
392.2.e.e.195.3 12 28.3 even 6
392.2.e.e.195.4 12 28.11 odd 6
392.2.m.g.19.3 12 28.23 odd 6
392.2.m.g.19.5 12 56.37 even 6
392.2.m.g.227.4 12 56.13 odd 2
392.2.m.g.227.6 12 28.27 even 2
504.2.bk.a.19.2 12 168.5 even 6
504.2.bk.a.19.4 12 84.47 odd 6
504.2.bk.a.451.1 12 12.11 even 2
504.2.bk.a.451.3 12 24.5 odd 2
1568.2.e.e.783.5 12 56.11 odd 6
1568.2.e.e.783.6 12 7.4 even 3
1568.2.e.e.783.7 12 7.3 odd 6
1568.2.e.e.783.8 12 56.3 even 6
1568.2.q.g.815.3 12 56.27 even 2
1568.2.q.g.815.4 12 7.6 odd 2
1568.2.q.g.1391.3 12 7.2 even 3
1568.2.q.g.1391.4 12 56.51 odd 6
2016.2.bs.a.271.1 12 21.5 even 6
2016.2.bs.a.271.6 12 168.131 odd 6
2016.2.bs.a.1711.1 12 24.11 even 2
2016.2.bs.a.1711.6 12 3.2 odd 2