Properties

Label 504.2.bk.a.451.1
Level 504504
Weight 22
Character 504.451
Analytic conductor 4.0244.024
Analytic rank 00
Dimension 1212
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(19,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 504=23327 504 = 2^{3} \cdot 3^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 504.bk (of order 66, degree 22, 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: 4.024460261874.02446026187
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: 22 2^{2}
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 451.1
Root 2.002330.854000i2.00233 - 0.854000i of defining polynomial
Character χ\chi == 504.451
Dual form 504.2.bk.a.19.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.130900.849154i)q2+(0.557875+1.92062i)q4+(1.59713+2.76632i)q5+(0.694153+2.55307i)q7+(1.000002.64575i)q8+(0.5428294.48465i)q10+(0.800840+1.38709i)q11+1.38831q13+(2.952972.29782i)q14+(3.37755+2.14293i)q16+(3.486052.01267i)q17+(4.56957+2.63824i)q19+(4.42204+4.61075i)q20+(2.083530.888631i)q22+(3.83044+2.21151i)q23+(2.60168+4.50624i)q25+(1.570041.17889i)q26+(5.29072+0.0910883i)q285.10613iq29+(0.05798090.100426i)q31+(5.63935+0.444621i)q32+(2.23331+5.23632i)q34+(8.17125+2.15734i)q35+(4.630872.67363i)q37+(7.40801+0.896678i)q38+(8.916131.45930i)q40+4.21689iq41+(3.110850.764282i)q44+(6.20976+0.751640i)q46+(5.05821+8.76108i)q47+(6.036303.54444i)q49+(6.768732.88689i)q50+(0.774501+2.66641i)q52+(6.13514+3.54212i)q535.11619q55+(6.06063+4.38962i)q56+(4.33589+5.77453i)q58+(4.38856+2.53374i)q59+(4.21321+7.29750i)q61+(0.150848+0.0643370i)q62+(6.000005.29150i)q64+(2.21731+3.84050i)q65+(5.018158.69169i)q67+(1.920797.81818i)q68+(11.0728+4.49891i)q70+5.29150iq71+(9.30504+5.37227i)q73+(7.507380.908707i)q74+(7.616317.30460i)q76+(2.985443.00745i)q77+(10.3349+5.96688i)q79+(11.32245.92084i)q80+(3.580794.76889i)q8214.9789iq8312.8580iq85+(2.86907+3.50592i)q88+(1.50000+0.866025i)q89+(0.963697+3.54444i)q91+(6.384376.12307i)q92+(1.7191714.2031i)q94+(14.59658.42726i)q952.87198iq97+(3.81669+9.13416i)q98+O(q100)q+(-1.13090 - 0.849154i) q^{2} +(0.557875 + 1.92062i) q^{4} +(1.59713 + 2.76632i) q^{5} +(-0.694153 + 2.55307i) q^{7} +(1.00000 - 2.64575i) q^{8} +(0.542829 - 4.48465i) q^{10} +(-0.800840 + 1.38709i) q^{11} +1.38831 q^{13} +(2.95297 - 2.29782i) q^{14} +(-3.37755 + 2.14293i) q^{16} +(-3.48605 - 2.01267i) q^{17} +(-4.56957 + 2.63824i) q^{19} +(-4.42204 + 4.61075i) q^{20} +(2.08353 - 0.888631i) q^{22} +(-3.83044 + 2.21151i) q^{23} +(-2.60168 + 4.50624i) q^{25} +(-1.57004 - 1.17889i) q^{26} +(-5.29072 + 0.0910883i) q^{28} -5.10613i q^{29} +(0.0579809 - 0.100426i) q^{31} +(5.63935 + 0.444621i) q^{32} +(2.23331 + 5.23632i) q^{34} +(-8.17125 + 2.15734i) q^{35} +(4.63087 - 2.67363i) q^{37} +(7.40801 + 0.896678i) q^{38} +(8.91613 - 1.45930i) q^{40} +4.21689i q^{41} +(-3.11085 - 0.764282i) q^{44} +(6.20976 + 0.751640i) q^{46} +(5.05821 + 8.76108i) q^{47} +(-6.03630 - 3.54444i) q^{49} +(6.76873 - 2.88689i) q^{50} +(0.774501 + 2.66641i) q^{52} +(6.13514 + 3.54212i) q^{53} -5.11619 q^{55} +(6.06063 + 4.38962i) q^{56} +(-4.33589 + 5.77453i) q^{58} +(4.38856 + 2.53374i) q^{59} +(4.21321 + 7.29750i) q^{61} +(-0.150848 + 0.0643370i) q^{62} +(-6.00000 - 5.29150i) q^{64} +(2.21731 + 3.84050i) q^{65} +(5.01815 - 8.69169i) q^{67} +(1.92079 - 7.81818i) q^{68} +(11.0728 + 4.49891i) q^{70} +5.29150i q^{71} +(9.30504 + 5.37227i) q^{73} +(-7.50738 - 0.908707i) q^{74} +(-7.61631 - 7.30460i) q^{76} +(-2.98544 - 3.00745i) q^{77} +(-10.3349 + 5.96688i) q^{79} +(-11.3224 - 5.92084i) q^{80} +(3.58079 - 4.76889i) q^{82} -14.9789i q^{83} -12.8580i q^{85} +(2.86907 + 3.50592i) q^{88} +(-1.50000 + 0.866025i) q^{89} +(-0.963697 + 3.54444i) q^{91} +(-6.38437 - 6.12307i) q^{92} +(1.71917 - 14.2031i) q^{94} +(-14.5965 - 8.42726i) q^{95} -2.87198i q^{97} +(3.81669 + 9.13416i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+12q8+6q10+6q116q14+6q176q19+24q226q26+6q2818q35+24q38+42q406q4418q4612q49+48q5024q52+18q58++6q98+O(q100) 12 q + 12 q^{8} + 6 q^{10} + 6 q^{11} - 6 q^{14} + 6 q^{17} - 6 q^{19} + 24 q^{22} - 6 q^{26} + 6 q^{28} - 18 q^{35} + 24 q^{38} + 42 q^{40} - 6 q^{44} - 18 q^{46} - 12 q^{49} + 48 q^{50} - 24 q^{52} + 18 q^{58}+ \cdots + 6 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/504Z)×\left(\mathbb{Z}/504\mathbb{Z}\right)^\times.

nn 7373 127127 253253 281281
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) 1-1 1-1 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 −1.13090 0.849154i −0.799668 0.600443i
33 0 0
44 0.557875 + 1.92062i 0.278937 + 0.960309i
55 1.59713 + 2.76632i 0.714260 + 1.23714i 0.963244 + 0.268628i 0.0865701π0.0865701\pi
−0.248984 + 0.968508i 0.580097π0.580097\pi
66 0 0
77 −0.694153 + 2.55307i −0.262365 + 0.964969i
88 1.00000 2.64575i 0.353553 0.935414i
99 0 0
1010 0.542829 4.48465i 0.171658 1.41817i
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 2.95297 2.29782i 0.789213 0.614119i
1515 0 0
1616 −3.37755 + 2.14293i −0.844388 + 0.535732i
1717 −3.48605 2.01267i −0.845490 0.488144i 0.0136363 0.999907i 0.495659π-0.495659\pi
−0.859127 + 0.511763i 0.828993π0.828993\pi
1818 0 0
1919 −4.56957 + 2.63824i −1.04833 + 0.605255i −0.922182 0.386756i 0.873595π-0.873595\pi
−0.126150 + 0.992011i 0.540262π0.540262\pi
2020 −4.42204 + 4.61075i −0.988799 + 1.03099i
2121 0 0
2222 2.08353 0.888631i 0.444210 0.189457i
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 −1.57004 1.17889i −0.307910 0.231199i
2727 0 0
2828 −5.29072 + 0.0910883i −0.999852 + 0.0172141i
2929 5.10613i 0.948185i −0.880475 0.474093i 0.842776π-0.842776\pi
0.880475 0.474093i 0.157224π-0.157224\pi
3030 0 0
3131 0.0579809 0.100426i 0.0104137 0.0180370i −0.860772 0.508991i 0.830018π-0.830018\pi
0.871185 + 0.490954i 0.163352π0.163352\pi
3232 5.63935 + 0.444621i 0.996906 + 0.0785986i
3333 0 0
3434 2.23331 + 5.23632i 0.383009 + 0.898022i
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 7.40801 + 0.896678i 1.20174 + 0.145460i
3939 0 0
4040 8.91613 1.45930i 1.40976 0.230736i
4141 4.21689i 0.658568i 0.944231 + 0.329284i 0.106807π0.106807\pi
−0.944231 + 0.329284i 0.893193π0.893193\pi
4242 0 0
4343 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
4444 −3.11085 0.764282i −0.468978 0.115220i
4545 0 0
4646 6.20976 + 0.751640i 0.915579 + 0.110823i
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 6.76873 2.88689i 0.957244 0.408267i
5151 0 0
5252 0.774501 + 2.66641i 0.107404 + 0.369764i
5353 6.13514 + 3.54212i 0.842726 + 0.486548i 0.858190 0.513332i 0.171589π-0.171589\pi
−0.0154638 + 0.999880i 0.504922π0.504922\pi
5454 0 0
5555 −5.11619 −0.689868
5656 6.06063 + 4.38962i 0.809885 + 0.586588i
5757 0 0
5858 −4.33589 + 5.77453i −0.569331 + 0.758233i
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 −0.150848 + 0.0643370i −0.0191577 + 0.00817081i
6363 0 0
6464 −6.00000 5.29150i −0.750000 0.661438i
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 0.623270π-0.623270\pi
0.990721 0.135913i 0.0433969π-0.0433969\pi
6868 1.92079 7.81818i 0.232930 0.948094i
6969 0 0
7070 11.0728 + 4.49891i 1.32345 + 0.537723i
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 −7.50738 0.908707i −0.872716 0.105635i
7575 0 0
7676 −7.61631 7.30460i −0.873651 0.837895i
7777 −2.98544 3.00745i −0.340223 0.342731i
7878 0 0
7979 −10.3349 + 5.96688i −1.16277 + 0.671327i −0.951967 0.306201i 0.900942π-0.900942\pi
−0.210805 + 0.977528i 0.567609π0.567609\pi
8080 −11.3224 5.92084i −1.26589 0.661970i
8181 0 0
8282 3.58079 4.76889i 0.395432 0.526636i
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 0 0
8888 2.86907 + 3.50592i 0.305844 + 0.373732i
8989 −1.50000 + 0.866025i −0.159000 + 0.0917985i −0.577389 0.816469i 0.695928π-0.695928\pi
0.418389 + 0.908268i 0.362595π0.362595\pi
9090 0 0
9191 −0.963697 + 3.54444i −0.101023 + 0.371558i
9292 −6.38437 6.12307i −0.665616 0.638375i
9393 0 0
9494 1.71917 14.2031i 0.177319 1.46494i
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 3.81669 + 9.13416i 0.385544 + 0.922690i
9999 0 0
100100 −10.1062 2.48292i −1.01062 0.248292i
101101 −3.40310 + 5.89434i −0.338621 + 0.586509i −0.984174 0.177207i 0.943294π-0.943294\pi
0.645553 + 0.763716i 0.276627π0.276627\pi
102102 0 0
103103 7.02471 + 12.1672i 0.692165 + 1.19887i 0.971127 + 0.238563i 0.0766765π0.0766765\pi
−0.278962 + 0.960302i 0.589990π0.589990\pi
104104 1.38831 3.67311i 0.136135 0.360178i
105105 0 0
106106 −3.93043 9.21547i −0.381757 0.895086i
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 5.78591 + 4.34444i 0.551665 + 0.414226i
111111 0 0
112112 −3.12650 10.1106i −0.295427 0.955365i
113113 1.43695 0.135177 0.0675887 0.997713i 0.478469π-0.478469\pi
0.0675887 + 0.997713i 0.478469π0.478469\pi
114114 0 0
115115 −12.2355 7.06415i −1.14096 0.658735i
116116 9.80694 2.84858i 0.910551 0.264484i
117117 0 0
118118 −2.81150 6.59198i −0.258819 0.606841i
119119 7.55833 7.50301i 0.692871 0.687800i
120120 0 0
121121 4.21731 + 7.30460i 0.383392 + 0.664054i
122122 1.43197 11.8304i 0.129645 1.07108i
123123 0 0
124124 0.225226 + 0.0553342i 0.0202259 + 0.00496916i
125125 −0.649581 −0.0581003
126126 0 0
127127 4.92077i 0.436647i 0.975876 + 0.218324i 0.0700589π0.0700589\pi
−0.975876 + 0.218324i 0.929941π0.929941\pi
128128 2.29211 + 11.0791i 0.202595 + 0.979263i
129129 0 0
130130 0.753613 6.22606i 0.0660962 0.546062i
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 −13.0556 + 5.56826i −1.12783 + 0.481025i
135135 0 0
136136 −8.81107 + 7.21054i −0.755543 + 0.618299i
137137 −0.0514223 + 0.0890661i −0.00439331 + 0.00760943i −0.868214 0.496190i 0.834732π-0.834732\pi
0.863820 + 0.503800i 0.168065π0.168065\pi
138138 0 0
139139 14.9789i 1.27049i −0.772310 0.635246i 0.780899π-0.780899\pi
0.772310 0.635246i 0.219101π-0.219101\pi
140140 −8.70197 14.4903i −0.735451 1.22466i
141141 0 0
142142 4.49330 5.98417i 0.377069 0.502180i
143143 −1.11181 + 1.92571i −0.0929743 + 0.161036i
144144 0 0
145145 14.1252 8.15518i 1.17303 0.677251i
146146 −5.96120 13.9769i −0.493352 1.15674i
147147 0 0
148148 7.71848 + 7.40258i 0.634455 + 0.608489i
149149 9.79164 5.65320i 0.802162 0.463129i −0.0420645 0.999115i 0.513393π-0.513393\pi
0.844227 + 0.535986i 0.180060π0.180060\pi
150150 0 0
151151 −12.8351 7.41032i −1.04450 0.603044i −0.123397 0.992357i 0.539379π-0.539379\pi
−0.921105 + 0.389314i 0.872712π0.872712\pi
152152 2.41057 + 14.7282i 0.195523 + 1.19461i
153153 0 0
154154 0.822447 + 5.93623i 0.0662747 + 0.478355i
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 16.7546 + 2.02801i 1.33292 + 0.161339i
159159 0 0
160160 7.77685 + 16.3104i 0.614814 + 1.28945i
161161 −2.98721 11.3145i −0.235425 0.891707i
162162 0 0
163163 4.35226 + 7.53834i 0.340895 + 0.590448i 0.984599 0.174826i 0.0559364π-0.0559364\pi
−0.643704 + 0.765275i 0.722603π0.722603\pi
164164 −8.09904 + 2.35250i −0.632429 + 0.183699i
165165 0 0
166166 −12.7194 + 16.9396i −0.987215 + 1.31477i
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 −10.9184 + 14.5411i −0.837406 + 1.11526i
171171 0 0
172172 0 0
173173 0.485324 + 0.840606i 0.0368985 + 0.0639101i 0.883885 0.467704i 0.154919π-0.154919\pi
−0.846986 + 0.531615i 0.821586π0.821586\pi
174174 0 0
175175 −9.69877 9.77028i −0.733158 0.738564i
176176 −0.267569 6.40113i −0.0201688 0.482503i
177177 0 0
178178 2.43174 + 0.294342i 0.182267 + 0.0220619i
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 4.09962 3.19008i 0.303884 0.236465i
183183 0 0
184184 2.02065 + 12.3459i 0.148965 + 0.910152i
185185 14.7922 + 8.54031i 1.08755 + 0.627896i
186186 0 0
187187 5.58353 3.22365i 0.408308 0.235737i
188188 −14.0049 + 14.6025i −1.02141 + 1.06500i
189189 0 0
190190 9.35110 + 21.9250i 0.678400 + 1.59061i
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 −2.43876 + 3.24793i −0.175093 + 0.233188i
195195 0 0
196196 3.44001 13.5708i 0.245715 0.969342i
197197 15.6891i 1.11780i −0.829233 0.558902i 0.811223π-0.811223\pi
0.829233 0.558902i 0.188777π-0.188777\pi
198198 0 0
199199 5.91290 10.2414i 0.419154 0.725997i −0.576700 0.816956i 0.695660π-0.695660\pi
0.995855 + 0.0909591i 0.0289933π0.0289933\pi
200200 9.32071 + 11.3896i 0.659074 + 0.805369i
201201 0 0
202202 8.85377 3.77616i 0.622949 0.265690i
203203 13.0363 + 3.54444i 0.914969 + 0.248771i
204204 0 0
205205 −11.6653 + 6.73495i −0.814738 + 0.470389i
206206 2.38754 19.7249i 0.166348 1.37430i
207207 0 0
208208 −4.68908 + 2.97504i −0.325129 + 0.206282i
209209 8.45124i 0.584585i
210210 0 0
211211 10.0726 0.693427 0.346713 0.937971i 0.387298π-0.387298\pi
0.346713 + 0.937971i 0.387298π0.387298\pi
212212 −3.38043 + 13.7593i −0.232169 + 0.944994i
213213 0 0
214214 −0.873339 + 7.21519i −0.0597002 + 0.493220i
215215 0 0
216216 0 0
217217 0.216146 + 0.217740i 0.0146730 + 0.0147812i
218218 −1.57074 3.68283i −0.106384 0.249433i
219219 0 0
220220 −2.85420 9.82626i −0.192430 0.662486i
221221 −4.83970 2.79420i −0.325553 0.187958i
222222 0 0
223223 24.3086 1.62783 0.813913 0.580987i 0.197333π-0.197333\pi
0.813913 + 0.580987i 0.197333π0.197333\pi
224224 −5.04972 + 14.0890i −0.337399 + 0.941362i
225225 0 0
226226 −1.62505 1.22020i −0.108097 0.0811662i
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 7.83855 + 18.3786i 0.516859 + 1.21185i
231231 0 0
232232 −13.5096 5.10613i −0.886946 0.335234i
233233 −0.318991 0.552509i −0.0208978 0.0361961i 0.855387 0.517989i 0.173319π-0.173319\pi
−0.876285 + 0.481793i 0.839986π0.839986\pi
234234 0 0
235235 −16.1573 + 27.9853i −1.05399 + 1.82556i
236236 −2.41808 + 9.84227i −0.157403 + 0.640677i
237237 0 0
238238 −14.9189 + 2.06697i −0.967051 + 0.133982i
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 1.43337 11.8419i 0.0921403 0.761228i
243243 0 0
244244 −11.6653 + 12.1631i −0.746792 + 0.778661i
245245 0.164257 22.3593i 0.0104940 1.42848i
246246 0 0
247247 −6.34397 + 3.66269i −0.403657 + 0.233051i
248248 −0.207721 0.253829i −0.0131903 0.0161182i
249249 0 0
250250 0.734612 + 0.551594i 0.0464609 + 0.0348859i
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 4.17849 5.56490i 0.262182 0.349173i
255255 0 0
256256 6.81571 14.4757i 0.425982 0.904732i
257257 20.4302 11.7954i 1.27440 0.735777i 0.298589 0.954382i 0.403484π-0.403484\pi
0.975813 + 0.218605i 0.0701506π0.0701506\pi
258258 0 0
259259 3.61144 + 13.6788i 0.224404 + 0.849961i
260260 −6.13915 + 6.40113i −0.380734 + 0.396981i
261261 0 0
262262 −5.53865 0.670408i −0.342179 0.0414179i
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 −7.43157 + 18.2907i −0.455659 + 1.12148i
267267 0 0
268268 19.4929 + 4.78908i 1.19072 + 0.292540i
269269 −11.6690 + 20.2113i −0.711471 + 1.23230i 0.252834 + 0.967510i 0.418637π0.418637\pi
−0.964305 + 0.264794i 0.914696π0.914696\pi
270270 0 0
271271 −6.81961 11.8119i −0.414262 0.717522i 0.581089 0.813840i 0.302627π-0.302627\pi
−0.995351 + 0.0963179i 0.969293π0.969293\pi
272272 16.0873 0.672454i 0.975436 0.0407735i
273273 0 0
274274 0.133784 0.0570595i 0.00808221 0.00344709i
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 −12.7194 + 16.9396i −0.762858 + 1.01597i
279279 0 0
280280 −2.46346 + 23.7764i −0.147220 + 1.42091i
281281 −1.43695 −0.0857215 −0.0428608 0.999081i 0.513647π-0.513647\pi
−0.0428608 + 0.999081i 0.513647π0.513647\pi
282282 0 0
283283 27.0428 + 15.6132i 1.60753 + 0.928108i 0.989921 + 0.141622i 0.0452318π0.0452318\pi
0.617609 + 0.786486i 0.288102π0.288102\pi
284284 −10.1630 + 2.95200i −0.603061 + 0.175169i
285285 0 0
286286 2.89257 1.23369i 0.171041 0.0729497i
287287 −10.7660 2.92717i −0.635497 0.172785i
288288 0 0
289289 −0.398321 0.689912i −0.0234306 0.0405831i
290290 −22.8992 2.77176i −1.34469 0.162763i
291291 0 0
292292 −5.12703 + 20.8685i −0.300037 + 1.22124i
293293 31.3006 1.82860 0.914299 0.405040i 0.132742π-0.132742\pi
0.914299 + 0.405040i 0.132742π0.132742\pi
294294 0 0
295295 16.1869i 0.942437i
296296 −2.44290 14.9258i −0.141991 0.867543i
297297 0 0
298298 −15.8738 1.92139i −0.919545 0.111303i
299299 −5.31783 + 3.07025i −0.307538 + 0.177557i
300300 0 0
301301 0 0
302302 8.22268 + 19.2793i 0.473162 + 1.10940i
303303 0 0
304304 9.78040 18.7031i 0.560944 1.07270i
305305 −13.4581 + 23.3102i −0.770611 + 1.33474i
306306 0 0
307307 14.7215i 0.840202i −0.907477 0.420101i 0.861995π-0.861995\pi
0.907477 0.420101i 0.138005π-0.138005\pi
308308 4.11067 7.41168i 0.234227 0.422319i
309309 0 0
310310 −0.418901 0.314538i −0.0237920 0.0178646i
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 −0.960963 + 0.409854i −0.0542303 + 0.0231294i
315315 0 0
316316 −17.2257 16.5207i −0.969022 0.929363i
317317 −20.3971 + 11.7763i −1.14562 + 0.661422i −0.947815 0.318821i 0.896713π-0.896713\pi
−0.197801 + 0.980242i 0.563380π0.563380\pi
318318 0 0
319319 7.08269 + 4.08919i 0.396555 + 0.228951i
320320 5.05517 25.0492i 0.282593 1.40029i
321321 0 0
322322 −6.22951 + 15.3322i −0.347157 + 0.854429i
323323 21.2397 1.18181
324324 0 0
325325 −3.61193 + 6.25604i −0.200354 + 0.347023i
326326 1.47923 12.2209i 0.0819272 0.676851i
327327 0 0
328328 11.1568 + 4.21689i 0.616034 + 0.232839i
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 0.803937π-0.803937\pi
−0.0922207 0.995739i 0.529397π-0.529397\pi
332332 28.7687 8.35634i 1.57889 0.458614i
333333 0 0
334334 1.57004 + 1.17889i 0.0859086 + 0.0645058i
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 12.5220 + 9.40235i 0.681108 + 0.511420i
339339 0 0
340340 24.6954 7.17316i 1.33929 0.389019i
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 0 0
346346 0.164951 1.36276i 0.00886780 0.0732623i
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 2.67188 + 19.2850i 0.142818 + 1.03083i
351351 0 0
352352 −5.13295 + 7.46625i −0.273587 + 0.397952i
353353 8.29108 + 4.78686i 0.441290 + 0.254779i 0.704145 0.710057i 0.251331π-0.251331\pi
−0.262855 + 0.964835i 0.584664π0.584664\pi
354354 0 0
355355 −14.6380 + 8.45124i −0.776903 + 0.448545i
356356 −2.50012 2.39779i −0.132506 0.127083i
357357 0 0
358358 18.5629 7.91711i 0.981077 0.418432i
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 −17.3274 13.0105i −0.910708 0.683819i
363363 0 0
364364 −7.34514 + 0.126458i −0.384990 + 0.00662822i
365365 34.3209i 1.79644i
366366 0 0
367367 −8.41302 + 14.5718i −0.439156 + 0.760640i −0.997625 0.0688852i 0.978056π-0.978056\pi
0.558469 + 0.829526i 0.311389π0.311389\pi
368368 8.19841 15.6778i 0.427372 0.817264i
369369 0 0
370370 −9.47653 22.2191i −0.492661 1.15512i
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 −9.05179 1.09564i −0.468057 0.0566544i
375375 0 0
376376 28.2379 4.62169i 1.45626 0.238346i
377377 7.08888i 0.365096i
378378 0 0
379379 25.5822 1.31407 0.657034 0.753861i 0.271811π-0.271811\pi
0.657034 + 0.753861i 0.271811π0.271811\pi
380380 8.04257 32.7356i 0.412575 1.67930i
381381 0 0
382382 −3.51085 0.424959i −0.179631 0.0217428i
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 −4.03327 + 1.72020i −0.205288 + 0.0875560i
387387 0 0
388388 5.51599 1.60221i 0.280032 0.0813398i
389389 −27.7043 15.9951i −1.40466 0.810983i −0.409796 0.912177i 0.634400π-0.634400\pi
−0.994867 + 0.101195i 0.967734π0.967734\pi
390390 0 0
391391 17.8041 0.900394
392392 −15.4140 + 12.4261i −0.778525 + 0.627614i
393393 0 0
394394 −13.3225 + 17.7429i −0.671178 + 0.893873i
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 −15.3835 + 6.56110i −0.771104 + 0.328878i
399399 0 0
400400 −0.869248 20.7953i −0.0434624 1.03976i
401401 −2.94858 5.10709i −0.147245 0.255036i 0.782963 0.622068i 0.213707π-0.213707\pi
−0.930208 + 0.367032i 0.880374π0.880374\pi
402402 0 0
403403 0.0804953 0.139422i 0.00400976 0.00694510i
404404 −13.2193 3.24775i −0.657684 0.161582i
405405 0 0
406406 −11.7330 15.0782i −0.582299 0.748320i
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 18.9113 + 2.28905i 0.933961 + 0.113048i
411411 0 0
412412 −19.4496 + 20.2795i −0.958211 + 0.999101i
413413 −9.51514 + 9.44550i −0.468210 + 0.464783i
414414 0 0
415415 41.4364 23.9233i 2.03403 1.17435i
416416 7.82915 + 0.617270i 0.383856 + 0.0302641i
417417 0 0
418418 −7.17641 + 9.55752i −0.351010 + 0.467474i
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 −11.3911 8.55319i −0.554511 0.416363i
423423 0 0
424424 15.5067 12.6899i 0.753073 0.616277i
425425 18.1391 10.4726i 0.879878 0.507998i
426426 0 0
427427 −21.5556 + 5.69103i −1.04315 + 0.275408i
428428 7.11447 7.41807i 0.343891 0.358566i
429429 0 0
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 −0.0595453 0.429784i −0.00285827 0.0206303i
435435 0 0
436436 −1.35094 + 5.49872i −0.0646984 + 0.263341i
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 0.972915π-0.972915\pi
0.424590 0.905386i 0.360418π-0.360418\pi
440440 −5.11619 + 13.5362i −0.243905 + 0.645312i
441441 0 0
442442 3.10051 + 7.26962i 0.147476 + 0.345780i
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 −27.4907 20.6418i −1.30172 0.977416i
447447 0 0
448448 17.6745 11.6453i 0.835041 0.550188i
449449 −11.5096 −0.543170 −0.271585 0.962414i 0.587548π-0.587548\pi
−0.271585 + 0.962414i 0.587548π0.587548\pi
450450 0 0
451451 −5.84923 3.37705i −0.275429 0.159019i
452452 0.801641 + 2.75984i 0.0377060 + 0.129812i
453453 0 0
454454 −7.94707 18.6331i −0.372974 0.874494i
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 1.80985 14.9523i 0.0845689 0.698675i
459459 0 0
460460 6.74168 27.4406i 0.314332 1.27942i
461461 −17.3671 −0.808866 −0.404433 0.914568i 0.632531π-0.632531\pi
−0.404433 + 0.914568i 0.632531π0.632531\pi
462462 0 0
463463 21.7288i 1.00983i −0.863171 0.504913i 0.831525π-0.831525\pi
0.863171 0.504913i 0.168475π-0.168475\pi
464464 10.9421 + 17.2462i 0.507973 + 0.800636i
465465 0 0
466466 −0.108418 + 0.895705i −0.00502235 + 0.0414928i
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 42.0361 17.9285i 1.93898 0.826981i
471471 0 0
472472 11.0922 9.07731i 0.510560 0.417817i
473473 0 0
474474 0 0
475475 27.4555i 1.25974i
476476 18.6270 + 10.3309i 0.853768 + 0.473517i
477477 0 0
478478 4.02108 5.35527i 0.183920 0.244944i
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 6.49482 + 15.2281i 0.295831 + 0.693619i
483483 0 0
484484 −11.6766 + 12.1749i −0.530755 + 0.553404i
485485 7.94483 4.58695i 0.360756 0.208283i
486486 0 0
487487 −1.58745 0.916514i −0.0719342 0.0415312i 0.463602 0.886044i 0.346557π-0.346557\pi
−0.535536 + 0.844513i 0.679890π0.679890\pi
488488 23.5206 3.84962i 1.06473 0.174264i
489489 0 0
490490 −19.1722 + 25.1467i −0.866113 + 1.13601i
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 10.2846 + 1.24486i 0.462726 + 0.0560091i
495495 0 0
496496 0.0193720 + 0.463443i 0.000869830 + 0.0208092i
497497 −13.5096 3.67311i −0.605987 0.164762i
498498 0 0
499499 5.68404 + 9.84505i 0.254453 + 0.440725i 0.964747 0.263180i 0.0847714π-0.0847714\pi
−0.710294 + 0.703905i 0.751438π0.751438\pi
500500 −0.362385 1.24760i −0.0162063 0.0557943i
501501 0 0
502502 9.81887 13.0767i 0.438238 0.583644i
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 −6.01562 + 8.01158i −0.267427 + 0.356158i
507507 0 0
508508 −9.45091 + 2.74517i −0.419317 + 0.121797i
509509 13.2178 + 22.8940i 0.585870 + 1.01476i 0.994766 + 0.102176i 0.0325804π0.0325804\pi
−0.408896 + 0.912581i 0.634086π0.634086\pi
510510 0 0
511511 −20.1749 + 20.0272i −0.892484 + 0.885952i
512512 −20.0000 + 10.5830i −0.883883 + 0.467707i
513513 0 0
514514 −33.1207 4.00898i −1.46089 0.176829i
515515 −22.4388 + 38.8652i −0.988773 + 1.71260i
516516 0 0
517517 −16.2033 −0.712619
518518 7.53126 18.5361i 0.330905 0.814428i
519519 0 0
520520 12.3783 2.02596i 0.542825 0.0888442i
521521 10.4163 + 6.01384i 0.456345 + 0.263471i 0.710506 0.703691i 0.248466π-0.248466\pi
−0.254161 + 0.967162i 0.581799π0.581799\pi
522522 0 0
523523 2.43276 1.40455i 0.106377 0.0614168i −0.445868 0.895099i 0.647105π-0.647105\pi
0.552245 + 0.833682i 0.313771π0.313771\pi
524524 5.69439 + 5.46133i 0.248760 + 0.238579i
525525 0 0
526526 5.92487 + 13.8917i 0.258337 + 0.605708i
527527 −0.404248 + 0.233393i −0.0176093 + 0.0101668i
528528 0 0
529529 −1.71848 + 2.97649i −0.0747164 + 0.129413i
530530 19.2155 25.5912i 0.834668 1.11161i
531531 0 0
532532 23.9360 14.3744i 1.03776 0.623211i
533533 5.85434i 0.253580i
534534 0 0
535535 8.20791 14.2165i 0.354859 0.614634i
536536 −17.9779 21.9685i −0.776527 0.948894i
537537 0 0
538538 30.3590 12.9482i 1.30887 0.558236i
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 −2.31783 + 19.1490i −0.0995592 + 0.822520i
543543 0 0
544544 −18.7642 12.9001i −0.804507 0.553088i
545545 9.04336i 0.387375i
546546 0 0
547547 28.4561 1.21669 0.608347 0.793671i 0.291833π-0.291833\pi
0.608347 + 0.793671i 0.291833π0.291833\pi
548548 −0.199749 0.0490750i −0.00853286 0.00209638i
549549 0 0
550550 −1.41629 + 11.7008i −0.0603906 + 0.498924i
551551 13.4712 + 23.3329i 0.573894 + 0.994013i
552552 0 0
553553 −8.05982 30.5277i −0.342738 1.29817i
554554 −0.253810 0.595095i −0.0107833 0.0252832i
555555 0 0
556556 28.7687 8.35634i 1.22007 0.354388i
557557 −7.96630 4.59935i −0.337543 0.194881i 0.321642 0.946861i 0.395765π-0.395765\pi
−0.659185 + 0.751981i 0.729099π0.729099\pi
558558 0 0
559559 0 0
560560 22.9758 24.7970i 0.970905 1.04786i
561561 0 0
562562 1.62505 + 1.22020i 0.0685488 + 0.0514709i
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 −17.3248 40.6205i −0.728214 1.70741i
567567 0 0
568568 14.0000 + 5.29150i 0.587427 + 0.222027i
569569 −11.7699 20.3861i −0.493420 0.854628i 0.506551 0.862210i 0.330920π-0.330920\pi
−0.999971 + 0.00758149i 0.997587π0.997587\pi
570570 0 0
571571 −15.1713 + 26.2774i −0.634897 + 1.09967i 0.351640 + 0.936135i 0.385624π0.385624\pi
−0.986537 + 0.163539i 0.947709π0.947709\pi
572572 −4.31881 1.06106i −0.180579 0.0443651i
573573 0 0
574574 9.68967 + 12.4523i 0.404439 + 0.519751i
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 −0.135380 + 1.11846i −0.00563107 + 0.0465217i
579579 0 0
580580 23.5431 + 22.5795i 0.977574 + 0.937564i
581581 38.2421 + 10.3976i 1.58655 + 0.431367i
582582 0 0
583583 −9.82652 + 5.67335i −0.406973 + 0.234966i
584584 23.5187 19.2465i 0.973211 0.796428i
585585 0 0
586586 −35.3978 26.5790i −1.46227 1.09797i
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 13.7452 18.3058i 0.565880 0.753637i
591591 0 0
592592 −9.91160 + 18.9540i −0.407364 + 0.779003i
593593 −18.2934 + 10.5617i −0.751221 + 0.433717i −0.826135 0.563473i 0.809465π-0.809465\pi
0.0749142 + 0.997190i 0.476132π0.476132\pi
594594 0 0
595595 32.8274 + 8.92543i 1.34579 + 0.365907i
596596 16.3202 + 15.6522i 0.668500 + 0.641140i
597597 0 0
598598 8.62105 + 1.04351i 0.352541 + 0.0426721i
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 0 0
604604 7.07205 28.7853i 0.287758 1.17126i
605605 −13.4712 + 23.3329i −0.547683 + 0.948616i
606606 0 0
607607 4.08757 + 7.07987i 0.165909 + 0.287363i 0.936978 0.349389i 0.113611π-0.113611\pi
−0.771069 + 0.636752i 0.780277π0.780277\pi
608608 −26.9425 + 12.8463i −1.09266 + 0.520985i
609609 0 0
610610 35.0138 14.9335i 1.41767 0.604639i
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 −12.5009 + 16.6486i −0.504493 + 0.671883i
615615 0 0
616616 −10.9424 + 4.89128i −0.440882 + 0.197075i
617617 −39.6548 −1.59644 −0.798221 0.602365i 0.794225π-0.794225\pi
−0.798221 + 0.602365i 0.794225π0.794225\pi
618618 0 0
619619 −12.4719 7.20065i −0.501288 0.289419i 0.227957 0.973671i 0.426795π-0.426795\pi
−0.729245 + 0.684252i 0.760129π0.760129\pi
620620 0.206644 + 0.711423i 0.00829903 + 0.0285714i
621621 0 0
622622 −20.2677 + 8.64425i −0.812662 + 0.346603i
623623 −1.16979 4.43075i −0.0468667 0.177514i
624624 0 0
625625 11.9709 + 20.7343i 0.478837 + 0.829370i
626626 −18.3725 2.22384i −0.734314 0.0888826i
627627 0 0
628628 1.43478 + 0.352502i 0.0572541 + 0.0140663i
629629 −21.5246 −0.858241
630630 0 0
631631 36.6698i 1.45980i 0.683553 + 0.729900i 0.260434π0.260434\pi
−0.683553 + 0.729900i 0.739566π0.739566\pi
632632 5.45194 + 33.3106i 0.216867 + 1.32502i
633633 0 0
634634 33.0670 + 4.00248i 1.31326 + 0.158959i
635635 −13.6124 + 7.85913i −0.540192 + 0.311880i
636636 0 0
637637 −8.38024 4.92077i −0.332037 0.194968i
638638 −4.53747 10.6388i −0.179640 0.421193i
639639 0 0
640640 −26.9875 + 24.0355i −1.06677 + 0.950086i
641641 9.13798 15.8274i 0.360929 0.625147i −0.627185 0.778870i 0.715793π-0.715793\pi
0.988114 + 0.153723i 0.0491265π0.0491265\pi
642642 0 0
643643 13.6340i 0.537671i 0.963186 + 0.268836i 0.0866389π0.0866389\pi
−0.963186 + 0.268836i 0.913361π0.913361\pi
644644 20.0643 12.0494i 0.790646 0.474812i
645645 0 0
646646 −24.0200 18.0357i −0.945053 0.709607i
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 9.39708 4.00788i 0.368584 0.157202i
651651 0 0
652652 −12.0503 + 12.5645i −0.471924 + 0.492063i
653653 −8.40495 + 4.85260i −0.328911 + 0.189897i −0.655358 0.755319i 0.727482π-0.727482\pi
0.326446 + 0.945216i 0.394149π0.394149\pi
654654 0 0
655655 10.9131 + 6.30070i 0.426411 + 0.246189i
656656 −9.03650 14.2428i −0.352816 0.556087i
657657 0 0
658658 35.0682 + 14.2483i 1.36710 + 0.555456i
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 −5.61739 + 46.4087i −0.218326 + 1.80373i
663663 0 0
664664 −39.6304 14.9789i −1.53796 0.581293i
665665 31.6475 31.4159i 1.22724 1.21826i
666666 0 0
667667 11.2922 + 19.5587i 0.437238 + 0.757318i
668668 −0.774501 2.66641i −0.0299663 0.103166i
669669 0 0
670670 −36.2552 27.2227i −1.40066 1.05171i
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 17.5398 + 13.1700i 0.675607 + 0.507290i
675675 0 0
676676 −6.17713 21.2663i −0.237582 0.817933i
677677 −1.80224 3.12157i −0.0692657 0.119972i 0.829313 0.558785i 0.188732π-0.188732\pi
−0.898578 + 0.438813i 0.855399π0.855399\pi
678678 0 0
679679 7.33237 + 1.99360i 0.281391 + 0.0765072i
680680 −34.0191 12.8580i −1.30457 0.493083i
681681 0 0
682682 0.0315633 0.260764i 0.00120862 0.00998516i
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 −25.9695 + 3.40375i −0.991520 + 0.129956i
687687 0 0
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 0.783381π0.783381\pi
−0.933526 + 0.358509i 0.883285π0.883285\pi
692692 −1.34373 + 1.40108i −0.0510811 + 0.0532609i
693693 0 0
694694 −29.2674 + 12.4826i −1.11097 + 0.473834i
695695 41.4364 23.9233i 1.57177 0.907462i
696696 0 0
697697 8.48721 14.7003i 0.321476 0.556813i
698698 32.2008 + 24.1784i 1.21882 + 0.915167i
699699 0 0
700700 13.3543 24.0782i 0.504745 0.910072i
701701 0.741474i 0.0280051i 0.999902 + 0.0140025i 0.00445729π0.00445729\pi
−0.999902 + 0.0140025i 0.995543π0.995543\pi
702702 0 0
703703 −14.1074 + 24.4347i −0.532071 + 0.921574i
704704 12.1449 4.08492i 0.457726 0.153956i
705705 0 0
706706 −5.31161 12.4539i −0.199905 0.468708i
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 23.7305 + 2.87238i 0.890590 + 0.107799i
711711 0 0
712712 0.791288 + 4.83465i 0.0296548 + 0.181186i
713713 0.512901i 0.0192083i
714714 0 0
715715 −7.10284 −0.265631
716716 −27.7156 6.80925i −1.03578 0.254474i
717717 0 0
718718 −5.27242 0.638183i −0.196765 0.0238168i
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 −11.5012 + 4.90528i −0.428029 + 0.182556i
723723 0 0
724724 8.54763 + 29.4273i 0.317670 + 1.09366i
725725 23.0095 + 13.2845i 0.854550 + 0.493375i
726726 0 0
727727 13.2022 0.489642 0.244821 0.969568i 0.421271π-0.421271\pi
0.244821 + 0.969568i 0.421271π0.421271\pi
728728 8.41401 + 6.09414i 0.311844 + 0.225864i
729729 0 0
730730 29.1438 38.8136i 1.07866 1.43656i
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 21.8880 9.33529i 0.807900 0.344572i
735735 0 0
736736 −22.5845 + 10.7684i −0.832476 + 0.396928i
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 0.598710π-0.598710\pi
0.977297 0.211875i 0.0679571π-0.0679571\pi
740740 −8.15045 + 33.1747i −0.299617 + 1.21953i
741741 0 0
742742 26.2560 3.63770i 0.963889 0.133544i
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 18.0522 + 2.18507i 0.660939 + 0.0800012i
747747 0 0
748748 9.30631 + 8.92543i 0.340273 + 0.326346i
749749 13.1464 3.47087i 0.480360 0.126823i
750750 0 0
751751 11.9997 6.92806i 0.437877 0.252808i −0.264820 0.964298i 0.585312π-0.585312\pi
0.702697 + 0.711490i 0.251979π0.251979\pi
752752 −35.8588 18.7516i −1.30763 0.683801i
753753 0 0
754754 −6.01955 + 8.01682i −0.219219 + 0.291955i
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 −28.9309 21.7232i −1.05082 0.789022i
759759 0 0
760760 −36.8929 + 30.1913i −1.33825 + 1.09515i
761761 −40.7899 + 23.5501i −1.47863 + 0.853689i −0.999708 0.0241662i 0.992307π-0.992307\pi
−0.478925 + 0.877856i 0.658974π0.658974\pi
762762 0 0
763763 −5.31596 + 5.27705i −0.192451 + 0.191042i
764764 3.60957 + 3.46184i 0.130590 + 0.125245i
765765 0 0
766766 −4.58312 + 37.8640i −0.165595 + 1.36808i
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 −15.1079 + 11.7561i −0.544453 + 0.423661i
771771 0 0
772772 6.02195 + 1.47949i 0.216735 + 0.0532480i
773773 13.5389 23.4501i 0.486960 0.843440i −0.512927 0.858432i 0.671439π-0.671439\pi
0.999888 + 0.0149920i 0.00477229π0.00477229\pi
774774 0 0
775775 0.301696 + 0.522552i 0.0108372 + 0.0187706i
776776 −7.59856 2.87198i −0.272772 0.103098i
777777 0 0
778778 17.7485 + 41.6141i 0.636315 + 1.49194i
779779 −11.1252 19.2694i −0.398601 0.690398i
780780 0 0
781781 −7.33982 4.23764i −0.262639 0.151635i
782782 −20.1347 15.1184i −0.720016 0.540635i
783783 0 0
784784 27.9834 0.963845i 0.999407 0.0344230i
785785 2.35969 0.0842208
786786 0 0
787787 −46.9684 27.1172i −1.67424 0.966624i −0.965220 0.261439i 0.915803π-0.915803\pi
−0.709023 0.705186i 0.750864π-0.750864\pi
788788 30.1329 8.75257i 1.07344 0.311798i
789789 0 0
790790 21.1492 + 49.5876i 0.752456 + 1.76425i
791791 −0.997467 + 3.66864i −0.0354658 + 0.130442i
792792 0 0
793793 5.84923 + 10.1312i 0.207712 + 0.359768i
794794 −2.89551 + 23.9216i −0.102758 + 0.848946i
795795 0 0
796796 22.9686 + 5.64298i 0.814099 + 0.200010i
797797 −20.1437 −0.713527 −0.356763 0.934195i 0.616120π-0.616120\pi
−0.356763 + 0.934195i 0.616120π0.616120\pi
798798 0 0
799799 40.7221i 1.44064i
800800 −16.6754 + 24.2555i −0.589563 + 0.857562i
801801 0 0
802802 −1.00215 + 8.27941i −0.0353873 + 0.292356i
803803 −14.9037 + 8.60465i −0.525940 + 0.303651i
804804 0 0
805805 26.5285 26.3344i 0.935008 0.928164i
806806 −0.209423 + 0.0893195i −0.00737661 + 0.00314615i
807807 0 0
808808 12.1919 + 14.8981i 0.428908 + 0.524113i
809809 17.2771 29.9249i 0.607432 1.05210i −0.384231 0.923237i 0.625533π-0.625533\pi
0.991662 0.128865i 0.0411334π-0.0411334\pi
810810 0 0
811811 13.6340i 0.478754i −0.970927 0.239377i 0.923057π-0.923057\pi
0.970927 0.239377i 0.0769431π-0.0769431\pi
812812 0.465109 + 27.0151i 0.0163221 + 0.948045i
813813 0 0
814814 7.27267 9.68573i 0.254907 0.339485i
815815 −13.9023 + 24.0795i −0.486976 + 0.843468i
816816 0 0
817817 0 0
818818 0.133094 + 0.312058i 0.00465352 + 0.0109109i
819819 0 0
820820 −19.4430 18.6473i −0.678980 0.651191i
821821 27.7311 16.0106i 0.967822 0.558772i 0.0692505 0.997599i 0.477939π-0.477939\pi
0.898572 + 0.438827i 0.144606π0.144606\pi
822822 0 0
823823 −26.8399 15.4960i −0.935580 0.540158i −0.0470083 0.998894i 0.514969π-0.514969\pi
−0.888572 + 0.458737i 0.848302π0.848302\pi
824824 39.2160 6.41848i 1.36615 0.223598i
825825 0 0
826826 18.7814 2.60210i 0.653487 0.0905387i
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 −67.1750 8.13097i −2.33168 0.282230i
831831 0 0
832832 −8.32984 7.34623i −0.288785 0.254685i
833833 13.9090 + 24.5052i 0.481920 + 0.849054i
834834 0 0
835835 −2.21731 3.84050i −0.0767332 0.132906i
836836 16.2316 4.71473i 0.561382 0.163063i
837837 0 0
838838 −24.9770 + 33.2643i −0.862816 + 1.14910i
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 27.2803 36.3319i 0.940142 1.25208i
843843 0 0
844844 5.61925 + 19.3456i 0.193423 + 0.665904i
845845 −17.6844 30.6304i −0.608363 1.05372i
846846 0 0
847847 −21.5766 + 5.69657i −0.741380 + 0.195736i
848848 −28.3123 + 1.18346i −0.972247 + 0.0406402i
849849 0 0
850850 −29.4065 3.55941i −1.00863 0.122087i
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 29.2098 + 11.8680i 0.999540 + 0.406116i
855855 0 0
856856 −14.3448 + 2.34782i −0.490297 + 0.0802469i
857857 −1.91744 1.10704i −0.0654986 0.0378156i 0.466893 0.884314i 0.345373π-0.345373\pi
−0.532392 + 0.846498i 0.678707π0.678707\pi
858858 0 0
859859 5.26337 3.03881i 0.179584 0.103683i −0.407513 0.913199i 0.633604π-0.633604\pi
0.587097 + 0.809516i 0.300271π0.300271\pi
860860 0 0
861861 0 0
862862 −20.9914 49.2175i −0.714970 1.67635i
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 21.6394 28.8193i 0.735338 0.979321i
867867 0 0
868868 −0.297613 + 0.536607i −0.0101016 + 0.0182136i
869869 19.1141i 0.648400i
870870 0 0
871871 6.96673 12.0667i 0.236059 0.408866i
872872 6.19704 5.07135i 0.209858 0.171738i
873873 0 0
874874 −30.3590 + 12.9482i −1.02691 + 0.437979i
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 −4.07185 + 33.6401i −0.137418 + 1.13530i
879879 0 0
880880 17.2802 10.9636i 0.582516 0.369584i
881881 53.9142i 1.81642i 0.418519 + 0.908208i 0.362549π0.362549\pi
−0.418519 + 0.908208i 0.637451π0.637451\pi
882882 0 0
883883 11.1987 0.376866 0.188433 0.982086i 0.439659π-0.439659\pi
0.188433 + 0.982086i 0.439659π0.439659\pi
884884 2.66665 10.8540i 0.0896891 0.365061i
885885 0 0
886886 1.74525 14.4186i 0.0586328 0.484402i
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 3.06957 + 7.19707i 0.102892 + 0.241246i
891891 0 0
892892 13.5612 + 46.6876i 0.454062 + 1.56322i
893893 −46.2278 26.6896i −1.54695 0.893134i
894894 0 0
895895 −45.5819 −1.52364
896896 −29.8767 1.83868i −0.998112 0.0614262i
897897 0 0
898898 13.0162 + 9.77339i 0.434355 + 0.326142i
899899 −0.512788 0.296058i −0.0171024 0.00987410i
900900 0 0
901901 −14.2583 24.6960i −0.475011 0.822744i
902902 3.74726 + 8.78601i 0.124770 + 0.292542i
903903 0 0
904904 1.43695 3.80183i 0.0477924 0.126447i
905905 24.4709 + 42.3849i 0.813441 + 1.40892i
906906 0 0
907907 8.92370 15.4563i 0.296307 0.513218i −0.678981 0.734156i 0.737578π-0.737578\pi
0.975288 + 0.220937i 0.0709116π0.0709116\pi
908908 −6.83501 + 27.8205i −0.226828 + 0.923254i
909909 0 0
910910 15.3724 + 6.24586i 0.509591 + 0.207048i
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 −5.20183 + 42.9755i −0.172061 + 1.42150i
915915 0 0
916916 −14.7436 + 15.3727i −0.487141 + 0.507929i
917917 2.66437 + 10.0917i 0.0879854 + 0.333257i
918918 0 0
919919 28.2802 16.3276i 0.932879 0.538598i 0.0451579 0.998980i 0.485621π-0.485621\pi
0.887721 + 0.460382i 0.152288π0.152288\pi
920920 −30.9254 + 25.3078i −1.01958 + 0.834375i
921921 0 0
922922 19.6405 + 14.7473i 0.646825 + 0.485678i
923923 7.34623i 0.241804i
924924 0 0
925925 27.8238i 0.914839i
926926 −18.4511 + 24.5732i −0.606342 + 0.807525i
927927 0 0
928928 2.27029 28.7953i 0.0745260 0.945252i
929929 23.3027 13.4538i 0.764537 0.441406i −0.0663853 0.997794i 0.521147π-0.521147\pi
0.830922 + 0.556388i 0.187813π0.187813\pi
930930 0 0
931931 36.9344 + 0.271329i 1.21048 + 0.00889246i
932932 0.883202 0.920891i 0.0289302 0.0301648i
933933 0 0
934934 −0.949771 0.114962i −0.0310775 0.00376167i
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 −5.15355 37.1971i −0.168269 1.21453i
939939 0 0
940940 −62.7628 15.4197i −2.04710 0.502936i
941941 6.32087 10.9481i 0.206055 0.356897i −0.744414 0.667719i 0.767271π-0.767271\pi
0.950468 + 0.310822i 0.100604π0.100604\pi
942942 0 0
943943 −9.32569 16.1526i −0.303686 0.526000i
944944 −20.2522 + 0.846548i −0.659154 + 0.0275528i
945945 0 0
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 −23.3139 + 31.0494i −0.756403 + 1.00738i
951951 0 0
952952 −12.2928 27.5005i −0.398411 0.891295i
953953 44.4561 1.44007 0.720037 0.693936i 0.244125π-0.244125\pi
0.720037 + 0.693936i 0.244125π0.244125\pi
954954 0 0
955955 6.91764 + 3.99390i 0.223850 + 0.129240i
956956 −9.09489 + 2.64176i −0.294150 + 0.0854406i
957957 0 0
958958 37.4223 15.9607i 1.20906 0.515668i
959959 −0.191697 0.193110i −0.00619021 0.00623585i
960960 0 0
961961 15.4933 + 26.8351i 0.499783 + 0.865650i
962962 −10.4225 1.26156i −0.336036 0.0406744i
963963 0 0
964964 5.58598 22.7365i 0.179912 0.732294i
965965 9.90388 0.318817
966966 0 0
967967 25.7160i 0.826972i 0.910510 + 0.413486i 0.135689π0.135689\pi
−0.910510 + 0.413486i 0.864311π0.864311\pi
968968 23.5435 3.85336i 0.756716 0.123852i
969969 0 0
970970 −12.8798 1.55900i −0.413547 0.0500564i
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 1.01699 + 2.38448i 0.0325863 + 0.0764035i
975975 0 0
976976 −29.8684 15.6191i −0.956063 0.499954i
977977 17.1348 29.6783i 0.548189 0.949492i −0.450209 0.892923i 0.648651π-0.648651\pi
0.998399 0.0565688i 0.0180160π-0.0180160\pi
978978 0 0
979979 2.77419i 0.0886635i
980980 43.0353 12.1582i 1.37471 0.388380i
981981 0 0
982982 15.1959 + 11.4100i 0.484920 + 0.364109i
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 26.7374 11.4036i 0.851491 0.363163i
987987 0 0
988988 −10.5738 10.1410i −0.336396 0.322629i
989989 0 0
990990 0 0
991991 22.6482 + 13.0759i 0.719443 + 0.415371i 0.814548 0.580097i 0.196985π-0.196985\pi
−0.0951047 + 0.995467i 0.530319π0.530319\pi
992992 0.371626 0.540558i 0.0117992 0.0171627i
993993 0 0
994994 12.1589 + 15.6256i 0.385658 + 0.495615i
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 1.93187 15.9604i 0.0611524 0.505218i
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 504.2.bk.a.451.1 12
3.2 odd 2 56.2.m.a.3.6 yes 12
4.3 odd 2 2016.2.bs.a.1711.6 12
7.5 odd 6 inner 504.2.bk.a.19.4 12
8.3 odd 2 inner 504.2.bk.a.451.3 12
8.5 even 2 2016.2.bs.a.1711.1 12
12.11 even 2 224.2.q.a.143.3 12
21.2 odd 6 392.2.m.g.19.3 12
21.5 even 6 56.2.m.a.19.3 yes 12
21.11 odd 6 392.2.e.e.195.4 12
21.17 even 6 392.2.e.e.195.3 12
21.20 even 2 392.2.m.g.227.6 12
24.5 odd 2 224.2.q.a.143.4 12
24.11 even 2 56.2.m.a.3.4 12
28.19 even 6 2016.2.bs.a.271.1 12
56.5 odd 6 2016.2.bs.a.271.6 12
56.19 even 6 inner 504.2.bk.a.19.2 12
84.11 even 6 1568.2.e.e.783.6 12
84.23 even 6 1568.2.q.g.1391.3 12
84.47 odd 6 224.2.q.a.47.4 12
84.59 odd 6 1568.2.e.e.783.7 12
84.83 odd 2 1568.2.q.g.815.4 12
168.5 even 6 224.2.q.a.47.3 12
168.11 even 6 392.2.e.e.195.2 12
168.53 odd 6 1568.2.e.e.783.5 12
168.59 odd 6 392.2.e.e.195.1 12
168.83 odd 2 392.2.m.g.227.4 12
168.101 even 6 1568.2.e.e.783.8 12
168.107 even 6 392.2.m.g.19.5 12
168.125 even 2 1568.2.q.g.815.3 12
168.131 odd 6 56.2.m.a.19.5 yes 12
168.149 odd 6 1568.2.q.g.1391.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.2.m.a.3.4 12 24.11 even 2
56.2.m.a.3.6 yes 12 3.2 odd 2
56.2.m.a.19.3 yes 12 21.5 even 6
56.2.m.a.19.5 yes 12 168.131 odd 6
224.2.q.a.47.3 12 168.5 even 6
224.2.q.a.47.4 12 84.47 odd 6
224.2.q.a.143.3 12 12.11 even 2
224.2.q.a.143.4 12 24.5 odd 2
392.2.e.e.195.1 12 168.59 odd 6
392.2.e.e.195.2 12 168.11 even 6
392.2.e.e.195.3 12 21.17 even 6
392.2.e.e.195.4 12 21.11 odd 6
392.2.m.g.19.3 12 21.2 odd 6
392.2.m.g.19.5 12 168.107 even 6
392.2.m.g.227.4 12 168.83 odd 2
392.2.m.g.227.6 12 21.20 even 2
504.2.bk.a.19.2 12 56.19 even 6 inner
504.2.bk.a.19.4 12 7.5 odd 6 inner
504.2.bk.a.451.1 12 1.1 even 1 trivial
504.2.bk.a.451.3 12 8.3 odd 2 inner
1568.2.e.e.783.5 12 168.53 odd 6
1568.2.e.e.783.6 12 84.11 even 6
1568.2.e.e.783.7 12 84.59 odd 6
1568.2.e.e.783.8 12 168.101 even 6
1568.2.q.g.815.3 12 168.125 even 2
1568.2.q.g.815.4 12 84.83 odd 2
1568.2.q.g.1391.3 12 84.23 even 6
1568.2.q.g.1391.4 12 168.149 odd 6
2016.2.bs.a.271.1 12 28.19 even 6
2016.2.bs.a.271.6 12 56.5 odd 6
2016.2.bs.a.1711.1 12 8.5 even 2
2016.2.bs.a.1711.6 12 4.3 odd 2