Properties

Label 63.2.o.a.41.2
Level 6363
Weight 22
Character 63.41
Analytic conductor 0.5030.503
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] = [63,2,Mod(20,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.20");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 63=327 63 = 3^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 63.o (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: 0.5030575327340.503057532734
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x127x10+37x878x6+123x436x2+9 x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 3 3
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 41.2
Root 1.295890.748185i1.29589 - 0.748185i of defining polynomial
Character χ\chi == 63.41
Dual form 63.2.o.a.20.2

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+(1.97141+1.13819i)q2+(0.578751+1.63250i)q3+(1.590972.75564i)q4+(0.717144+1.24213i)q5+(2.999052.55959i)q6+(2.40147+1.11037i)q7+2.69056iq8+(2.33009+1.88962i)q93.26499iq10+(2.801501.61745i)q11+(5.41936+1.00243i)q12+(4.43334+2.55959i)q13+(3.470464.92235i)q14+(2.442820.451852i)q15+(0.119562+0.207087i)q16+1.09132q17+(2.442826.37731i)q184.48911iq19+(2.28191+3.95238i)q20+(3.202543.27777i)q21+(3.68194+6.37731i)q22+(3.47141+2.00422i)q23+(4.39234+1.55716i)q24+(1.47141+2.54856i)q2511.6532q26+(4.433342.71026i)q27+(0.760877+8.38418i)q28+(1.028590.593857i)q29+(5.330091.88962i)q30+(3.242751.87220i)q31+(5.131602.96273i)q32+(4.26186+3.63735i)q33+(2.15143+1.24213i)q34+(0.3429713.77924i)q35+(1.50000+9.42724i)q360.239123q37+(5.10948+8.84988i)q38+(1.61273+8.71878i)q39+(3.342031.92952i)q40+(3.716206.43664i)q41+(10.0442+2.81671i)q42+(3.823266.62208i)q4310.2933iq44+(0.6761374.24941i)q459.12476q46+(2.110423.65536i)q47+(0.268872+0.315036i)q48+(4.534145.33307i)q49+(5.801503.34950i)q50+(0.631600+1.78157i)q51+(14.10668.14447i)q52+7.01414iq53+(11.8247+0.297022i)q54+4.63977iq55+(2.987536.46131i)q56+(7.328462.59808i)q57+(1.35185+2.34147i)q58+(4.73531+8.20179i)q59+(5.13160+6.01266i)q60+(2.82757+1.63250i)q61+8.52371q62+(3.497477.12514i)q63+13.0104q64+(6.35868+3.67119i)q65+(12.54192.31989i)q66+(0.330095+0.571741i)q67+(1.736253.00728i)q68+(1.26280+6.82701i)q69+(3.62537+7.84079i)q70+3.82347iq71+(5.084146.26926i)q727.31073iq73+(0.4714100.272169i)q74+(3.30893+3.87705i)q75+(12.37047.14205i)q76+(4.93176+6.99498i)q77+(6.7443319.0239i)q78+(1.830093.16982i)q790.342971q80+(1.858688.80598i)q81+16.9190iq82+(5.452459.44392i)q83+(14.1275+3.61022i)q84+(0.782630+1.35556i)q85+(15.0744+8.70322i)q86+(1.56477+1.33548i)q87+(4.35185+7.53762i)q88+13.6915q89+(6.16959+7.60775i)q90+(13.48871.22412i)q91+(11.04586.37731i)q92+(1.179626.37731i)q93+(8.32102+4.80415i)q94+(5.57605+3.21934i)q95+(1.8667310.0920i)q96+(2.697091.55716i)q97+(2.86857+15.6744i)q98+(3.47141+9.06259i)q99+O(q100)q+(-1.97141 + 1.13819i) q^{2} +(0.578751 + 1.63250i) q^{3} +(1.59097 - 2.75564i) q^{4} +(-0.717144 + 1.24213i) q^{5} +(-2.99905 - 2.55959i) q^{6} +(-2.40147 + 1.11037i) q^{7} +2.69056i q^{8} +(-2.33009 + 1.88962i) q^{9} -3.26499i q^{10} +(2.80150 - 1.61745i) q^{11} +(5.41936 + 1.00243i) q^{12} +(4.43334 + 2.55959i) q^{13} +(3.47046 - 4.92235i) q^{14} +(-2.44282 - 0.451852i) q^{15} +(0.119562 + 0.207087i) q^{16} +1.09132 q^{17} +(2.44282 - 6.37731i) q^{18} -4.48911i q^{19} +(2.28191 + 3.95238i) q^{20} +(-3.20254 - 3.27777i) q^{21} +(-3.68194 + 6.37731i) q^{22} +(3.47141 + 2.00422i) q^{23} +(-4.39234 + 1.55716i) q^{24} +(1.47141 + 2.54856i) q^{25} -11.6532 q^{26} +(-4.43334 - 2.71026i) q^{27} +(-0.760877 + 8.38418i) q^{28} +(1.02859 - 0.593857i) q^{29} +(5.33009 - 1.88962i) q^{30} +(-3.24275 - 1.87220i) q^{31} +(-5.13160 - 2.96273i) q^{32} +(4.26186 + 3.63735i) q^{33} +(-2.15143 + 1.24213i) q^{34} +(0.342971 - 3.77924i) q^{35} +(1.50000 + 9.42724i) q^{36} -0.239123 q^{37} +(5.10948 + 8.84988i) q^{38} +(-1.61273 + 8.71878i) q^{39} +(-3.34203 - 1.92952i) q^{40} +(3.71620 - 6.43664i) q^{41} +(10.0442 + 2.81671i) q^{42} +(-3.82326 - 6.62208i) q^{43} -10.2933i q^{44} +(-0.676137 - 4.24941i) q^{45} -9.12476 q^{46} +(-2.11042 - 3.65536i) q^{47} +(-0.268872 + 0.315036i) q^{48} +(4.53414 - 5.33307i) q^{49} +(-5.80150 - 3.34950i) q^{50} +(0.631600 + 1.78157i) q^{51} +(14.1066 - 8.14447i) q^{52} +7.01414i q^{53} +(11.8247 + 0.297022i) q^{54} +4.63977i q^{55} +(-2.98753 - 6.46131i) q^{56} +(7.32846 - 2.59808i) q^{57} +(-1.35185 + 2.34147i) q^{58} +(-4.73531 + 8.20179i) q^{59} +(-5.13160 + 6.01266i) q^{60} +(-2.82757 + 1.63250i) q^{61} +8.52371 q^{62} +(3.49747 - 7.12514i) q^{63} +13.0104 q^{64} +(-6.35868 + 3.67119i) q^{65} +(-12.5419 - 2.31989i) q^{66} +(-0.330095 + 0.571741i) q^{67} +(1.73625 - 3.00728i) q^{68} +(-1.26280 + 6.82701i) q^{69} +(3.62537 + 7.84079i) q^{70} +3.82347i q^{71} +(-5.08414 - 6.26926i) q^{72} -7.31073i q^{73} +(0.471410 - 0.272169i) q^{74} +(-3.30893 + 3.87705i) q^{75} +(-12.3704 - 7.14205i) q^{76} +(-4.93176 + 6.99498i) q^{77} +(-6.74433 - 19.0239i) q^{78} +(-1.83009 - 3.16982i) q^{79} -0.342971 q^{80} +(1.85868 - 8.80598i) q^{81} +16.9190i q^{82} +(-5.45245 - 9.44392i) q^{83} +(-14.1275 + 3.61022i) q^{84} +(-0.782630 + 1.35556i) q^{85} +(15.0744 + 8.70322i) q^{86} +(1.56477 + 1.33548i) q^{87} +(4.35185 + 7.53762i) q^{88} +13.6915 q^{89} +(6.16959 + 7.60775i) q^{90} +(-13.4887 - 1.22412i) q^{91} +(11.0458 - 6.37731i) q^{92} +(1.17962 - 6.37731i) q^{93} +(8.32102 + 4.80415i) q^{94} +(5.57605 + 3.21934i) q^{95} +(1.86673 - 10.0920i) q^{96} +(2.69709 - 1.55716i) q^{97} +(-2.86857 + 15.6744i) q^{98} +(-3.47141 + 9.06259i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q6q2+2q42q712q912q14+6q15+2q166q1824q2110q22+24q238q28+30q29+48q3012q32+18q364q37+36q42+24q99+O(q100) 12 q - 6 q^{2} + 2 q^{4} - 2 q^{7} - 12 q^{9} - 12 q^{14} + 6 q^{15} + 2 q^{16} - 6 q^{18} - 24 q^{21} - 10 q^{22} + 24 q^{23} - 8 q^{28} + 30 q^{29} + 48 q^{30} - 12 q^{32} + 18 q^{36} - 4 q^{37} + 36 q^{42}+ \cdots - 24 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/63Z)×\left(\mathbb{Z}/63\mathbb{Z}\right)^\times.

nn 1010 2929
χ(n)\chi(n) 1-1 e(56)e\left(\frac{5}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.97141 + 1.13819i −1.39400 + 0.804825i −0.993755 0.111585i 0.964407π-0.964407\pi
−0.400242 + 0.916409i 0.631074π0.631074\pi
33 0.578751 + 1.63250i 0.334142 + 0.942523i
44 1.59097 2.75564i 0.795486 1.37782i
55 −0.717144 + 1.24213i −0.320716 + 0.555497i −0.980636 0.195839i 0.937257π-0.937257\pi
0.659920 + 0.751336i 0.270590π0.270590\pi
66 −2.99905 2.55959i −1.22436 1.04495i
77 −2.40147 + 1.11037i −0.907671 + 0.419682i
88 2.69056i 0.951257i
99 −2.33009 + 1.88962i −0.776698 + 0.629873i
1010 3.26499i 1.03248i
1111 2.80150 1.61745i 0.844686 0.487679i −0.0141686 0.999900i 0.504510π-0.504510\pi
0.858854 + 0.512220i 0.171177π0.171177\pi
1212 5.41936 + 1.00243i 1.56443 + 0.289375i
1313 4.43334 + 2.55959i 1.22959 + 0.709903i 0.966944 0.254990i 0.0820722π-0.0820722\pi
0.262644 + 0.964893i 0.415406π0.415406\pi
1414 3.47046 4.92235i 0.927521 1.31555i
1515 −2.44282 0.451852i −0.630733 0.116668i
1616 0.119562 + 0.207087i 0.0298904 + 0.0517717i
1717 1.09132 0.264683 0.132341 0.991204i 0.457750π-0.457750\pi
0.132341 + 0.991204i 0.457750π0.457750\pi
1818 2.44282 6.37731i 0.575778 1.50315i
1919 4.48911i 1.02987i −0.857228 0.514936i 0.827816π-0.827816\pi
0.857228 0.514936i 0.172184π-0.172184\pi
2020 2.28191 + 3.95238i 0.510251 + 0.883780i
2121 −3.20254 3.27777i −0.698851 0.715267i
2222 −3.68194 + 6.37731i −0.784993 + 1.35965i
2323 3.47141 + 2.00422i 0.723839 + 0.417909i 0.816164 0.577820i 0.196097π-0.196097\pi
−0.0923250 + 0.995729i 0.529430π0.529430\pi
2424 −4.39234 + 1.55716i −0.896582 + 0.317855i
2525 1.47141 + 2.54856i 0.294282 + 0.509711i
2626 −11.6532 −2.28539
2727 −4.43334 2.71026i −0.853197 0.521589i
2828 −0.760877 + 8.38418i −0.143792 + 1.58446i
2929 1.02859 0.593857i 0.191004 0.110276i −0.401448 0.915882i 0.631493π-0.631493\pi
0.592453 + 0.805605i 0.298160π0.298160\pi
3030 5.33009 1.88962i 0.973138 0.344996i
3131 −3.24275 1.87220i −0.582414 0.336257i 0.179678 0.983726i 0.442494π-0.442494\pi
−0.762092 + 0.647468i 0.775828π0.775828\pi
3232 −5.13160 2.96273i −0.907147 0.523742i
3333 4.26186 + 3.63735i 0.741894 + 0.633181i
3434 −2.15143 + 1.24213i −0.368967 + 0.213023i
3535 0.342971 3.77924i 0.0579728 0.638808i
3636 1.50000 + 9.42724i 0.250000 + 1.57121i
3737 −0.239123 −0.0393116 −0.0196558 0.999807i 0.506257π-0.506257\pi
−0.0196558 + 0.999807i 0.506257π0.506257\pi
3838 5.10948 + 8.84988i 0.828867 + 1.43564i
3939 −1.61273 + 8.71878i −0.258243 + 1.39612i
4040 −3.34203 1.92952i −0.528421 0.305084i
4141 3.71620 6.43664i 0.580373 1.00523i −0.415062 0.909793i 0.636240π-0.636240\pi
0.995435 0.0954418i 0.0304264π-0.0304264\pi
4242 10.0442 + 2.81671i 1.54986 + 0.434628i
4343 −3.82326 6.62208i −0.583041 1.00986i −0.995116 0.0987075i 0.968529π-0.968529\pi
0.412075 0.911150i 0.364804π-0.364804\pi
4444 10.2933i 1.55177i
4545 −0.676137 4.24941i −0.100793 0.633464i
4646 −9.12476 −1.34537
4747 −2.11042 3.65536i −0.307837 0.533189i 0.670052 0.742314i 0.266272π-0.266272\pi
−0.977889 + 0.209125i 0.932939π0.932939\pi
4848 −0.268872 + 0.315036i −0.0388084 + 0.0454715i
4949 4.53414 5.33307i 0.647734 0.761867i
5050 −5.80150 3.34950i −0.820457 0.473691i
5151 0.631600 + 1.78157i 0.0884417 + 0.249470i
5252 14.1066 8.14447i 1.95624 1.12944i
5353 7.01414i 0.963466i 0.876318 + 0.481733i 0.159992π0.159992\pi
−0.876318 + 0.481733i 0.840008π0.840008\pi
5454 11.8247 + 0.297022i 1.60914 + 0.0404196i
5555 4.63977i 0.625627i
5656 −2.98753 6.46131i −0.399226 0.863429i
5757 7.32846 2.59808i 0.970678 0.344124i
5858 −1.35185 + 2.34147i −0.177506 + 0.307450i
5959 −4.73531 + 8.20179i −0.616484 + 1.06778i 0.373638 + 0.927575i 0.378110π0.378110\pi
−0.990122 + 0.140208i 0.955223π0.955223\pi
6060 −5.13160 + 6.01266i −0.662487 + 0.776231i
6161 −2.82757 + 1.63250i −0.362033 + 0.209020i −0.669972 0.742386i 0.733694π-0.733694\pi
0.307939 + 0.951406i 0.400361π0.400361\pi
6262 8.52371 1.08251
6363 3.49747 7.12514i 0.440640 0.897684i
6464 13.0104 1.62630
6565 −6.35868 + 3.67119i −0.788698 + 0.455355i
6666 −12.5419 2.31989i −1.54380 0.285558i
6767 −0.330095 + 0.571741i −0.0403275 + 0.0698493i −0.885485 0.464669i 0.846173π-0.846173\pi
0.845157 + 0.534518i 0.179507π0.179507\pi
6868 1.73625 3.00728i 0.210552 0.364686i
6969 −1.26280 + 6.82701i −0.152023 + 0.821876i
7070 3.62537 + 7.84079i 0.433314 + 0.937154i
7171 3.82347i 0.453762i 0.973922 + 0.226881i 0.0728529π0.0728529\pi
−0.973922 + 0.226881i 0.927147π0.927147\pi
7272 −5.08414 6.26926i −0.599171 0.738840i
7373 7.31073i 0.855656i −0.903860 0.427828i 0.859279π-0.859279\pi
0.903860 0.427828i 0.140721π-0.140721\pi
7474 0.471410 0.272169i 0.0548003 0.0316390i
7575 −3.30893 + 3.87705i −0.382083 + 0.447683i
7676 −12.3704 7.14205i −1.41898 0.819249i
7777 −4.93176 + 6.99498i −0.562026 + 0.797152i
7878 −6.74433 19.0239i −0.763644 2.15403i
7979 −1.83009 3.16982i −0.205902 0.356632i 0.744518 0.667602i 0.232679π-0.232679\pi
−0.950420 + 0.310970i 0.899346π0.899346\pi
8080 −0.342971 −0.0383454
8181 1.85868 8.80598i 0.206521 0.978442i
8282 16.9190i 1.86839i
8383 −5.45245 9.44392i −0.598484 1.03660i −0.993045 0.117735i 0.962437π-0.962437\pi
0.394561 0.918870i 0.370897π-0.370897\pi
8484 −14.1275 + 3.61022i −1.54144 + 0.393907i
8585 −0.782630 + 1.35556i −0.0848882 + 0.147031i
8686 15.0744 + 8.70322i 1.62552 + 0.938492i
8787 1.56477 + 1.33548i 0.167761 + 0.143178i
8888 4.35185 + 7.53762i 0.463909 + 0.803513i
8989 13.6915 1.45129 0.725646 0.688068i 0.241541π-0.241541\pi
0.725646 + 0.688068i 0.241541π0.241541\pi
9090 6.16959 + 7.60775i 0.650332 + 0.801927i
9191 −13.4887 1.22412i −1.41399 0.128322i
9292 11.0458 6.37731i 1.15161 0.664881i
9393 1.17962 6.37731i 0.122321 0.661297i
9494 8.32102 + 4.80415i 0.858248 + 0.495510i
9595 5.57605 + 3.21934i 0.572091 + 0.330297i
9696 1.86673 10.0920i 0.190523 1.03001i
9797 2.69709 1.55716i 0.273848 0.158106i −0.356787 0.934186i 0.616128π-0.616128\pi
0.630635 + 0.776080i 0.282795π0.282795\pi
9898 −2.86857 + 15.6744i −0.289770 + 1.58335i
9999 −3.47141 + 9.06259i −0.348890 + 0.910824i
100100 9.36389 0.936389
101101 3.54471 + 6.13962i 0.352712 + 0.610915i 0.986724 0.162408i 0.0519262π-0.0519262\pi
−0.634012 + 0.773324i 0.718593π0.718593\pi
102102 −3.27292 2.79332i −0.324067 0.276580i
103103 1.47529 + 0.851761i 0.145365 + 0.0839265i 0.570918 0.821007i 0.306587π-0.306587\pi
−0.425553 + 0.904933i 0.639921π0.639921\pi
104104 −6.88674 + 11.9282i −0.675300 + 1.16965i
105105 6.36809 1.62734i 0.621462 0.158812i
106106 −7.98345 13.8277i −0.775421 1.34307i
107107 4.93582i 0.477164i −0.971122 0.238582i 0.923317π-0.923317\pi
0.971122 0.238582i 0.0766826π-0.0766826\pi
108108 −14.5218 + 7.90477i −1.39736 + 0.760637i
109109 8.13844 0.779521 0.389760 0.920916i 0.372558π-0.372558\pi
0.389760 + 0.920916i 0.372558π0.372558\pi
110110 −5.28096 9.14690i −0.503520 0.872123i
111111 −0.138393 0.390368i −0.0131357 0.0370521i
112112 −0.517068 0.364555i −0.0488583 0.0344472i
113113 −3.39699 1.96125i −0.319562 0.184499i 0.331635 0.943408i 0.392400π-0.392400\pi
−0.651197 + 0.758908i 0.725733π0.725733\pi
114114 −11.4903 + 13.4631i −1.07616 + 1.26093i
115115 −4.97900 + 2.87463i −0.464294 + 0.268060i
116116 3.77924i 0.350893i
117117 −15.1668 + 2.41323i −1.40217 + 0.223104i
118118 21.5588i 1.98465i
119119 −2.62076 + 1.21177i −0.240245 + 0.111083i
120120 1.21574 6.57256i 0.110981 0.599990i
121121 −0.267713 + 0.463693i −0.0243376 + 0.0421539i
122122 3.71620 6.43664i 0.336449 0.582746i
123123 12.6586 + 2.34147i 1.14138 + 0.211123i
124124 −10.3182 + 5.95724i −0.926605 + 0.534976i
125125 −11.3923 −1.01896
126126 1.21484 + 18.0274i 0.108227 + 1.60601i
127127 6.16827 0.547345 0.273673 0.961823i 0.411761π-0.411761\pi
0.273673 + 0.961823i 0.411761π0.411761\pi
128128 −15.3856 + 8.88290i −1.35991 + 0.785145i
129129 8.59781 10.0740i 0.756995 0.886966i
130130 8.35705 14.4748i 0.732962 1.26953i
131131 4.13138 7.15575i 0.360960 0.625201i −0.627159 0.778891i 0.715782π-0.715782\pi
0.988119 + 0.153690i 0.0491158π0.0491158\pi
132132 16.8037 5.95724i 1.46258 0.518511i
133133 4.98459 + 10.7805i 0.432219 + 0.934786i
134134 1.50285i 0.129826i
135135 6.54583 3.56314i 0.563375 0.306666i
136136 2.93625i 0.251782i
137137 −8.96169 + 5.17404i −0.765649 + 0.442048i −0.831320 0.555794i 0.812415π-0.812415\pi
0.0656711 + 0.997841i 0.479081π0.479081\pi
138138 −5.28096 14.8962i −0.449546 1.26804i
139139 15.4589 + 8.92521i 1.31121 + 0.757026i 0.982296 0.187334i 0.0599848π-0.0599848\pi
0.328912 + 0.944361i 0.393318π0.393318\pi
140140 −9.86857 6.95777i −0.834047 0.588039i
141141 4.74596 5.56081i 0.399682 0.468304i
142142 −4.35185 7.53762i −0.365199 0.632543i
143143 16.5600 1.38482
144144 −0.669905 0.256606i −0.0558254 0.0213838i
145145 1.70352i 0.141470i
146146 8.32102 + 14.4124i 0.688653 + 1.19278i
147147 11.3304 + 4.31545i 0.934512 + 0.355932i
148148 −0.380438 + 0.658939i −0.0312718 + 0.0541644i
149149 −15.1758 8.76175i −1.24325 0.717790i −0.273495 0.961873i 0.588180π-0.588180\pi
−0.969754 + 0.244083i 0.921513π0.921513\pi
150150 2.11042 11.4095i 0.172315 0.931579i
151151 −0.550343 0.953223i −0.0447863 0.0775722i 0.842763 0.538284i 0.180927π-0.180927\pi
−0.887550 + 0.460712i 0.847594π0.847594\pi
152152 12.0782 0.979674
153153 −2.54287 + 2.06217i −0.205579 + 0.166717i
154154 1.76088 19.4033i 0.141895 1.56356i
155155 4.65103 2.68527i 0.373580 0.215686i
156156 21.4601 + 18.3154i 1.71818 + 1.46641i
157157 −8.45150 4.87948i −0.674503 0.389425i 0.123277 0.992372i 0.460660π-0.460660\pi
−0.797781 + 0.602947i 0.793993π0.793993\pi
158158 7.21574 + 4.16601i 0.574053 + 0.331430i
159159 −11.4506 + 4.05944i −0.908088 + 0.321934i
160160 7.36019 4.24941i 0.581874 0.335945i
161161 −10.5619 0.958511i −0.832397 0.0755413i
162162 6.35868 + 19.4757i 0.499585 + 1.53016i
163163 −7.22545 −0.565941 −0.282970 0.959129i 0.591320π-0.591320\pi
−0.282970 + 0.959129i 0.591320π0.591320\pi
164164 −11.8247 20.4810i −0.923356 1.59930i
165165 −7.57442 + 2.68527i −0.589668 + 0.209048i
166166 21.4980 + 12.4119i 1.66857 + 0.963350i
167167 −8.65419 + 14.9895i −0.669681 + 1.15992i 0.308312 + 0.951285i 0.400236π0.400236\pi
−0.977993 + 0.208637i 0.933097π0.933097\pi
168168 8.81903 8.61663i 0.680403 0.664787i
169169 6.60301 + 11.4367i 0.507924 + 0.879750i
170170 3.56314i 0.273280i
171171 8.48270 + 10.4601i 0.648689 + 0.799900i
172172 −24.3308 −1.85520
173173 0.978103 + 1.69412i 0.0743638 + 0.128802i 0.900809 0.434215i 0.142974π-0.142974\pi
−0.826446 + 0.563017i 0.809641π0.809641\pi
174174 −4.60483 0.851761i −0.349091 0.0645718i
175175 −6.36340 4.48647i −0.481028 0.339145i
176176 0.669905 + 0.386770i 0.0504960 + 0.0291539i
177177 −16.1300 2.98358i −1.21240 0.224260i
178178 −26.9915 + 15.5835i −2.02310 + 1.16804i
179179 23.2017i 1.73418i −0.498152 0.867090i 0.665988π-0.665988\pi
0.498152 0.867090i 0.334012π-0.334012\pi
180180 −12.7856 4.89749i −0.952980 0.365037i
181181 10.2744i 0.763689i 0.924226 + 0.381845i 0.124711π0.124711\pi
−0.924226 + 0.381845i 0.875289π0.875289\pi
182182 27.9849 12.9395i 2.07438 0.959137i
183183 −4.30150 3.67119i −0.317976 0.271382i
184184 −5.39248 + 9.34004i −0.397539 + 0.688557i
185185 0.171486 0.297022i 0.0126079 0.0218375i
186186 4.93310 + 13.9149i 0.361713 + 1.02029i
187187 3.05733 1.76515i 0.223574 0.129080i
188188 −13.4305 −0.979520
189189 13.6559 + 1.58593i 0.993324 + 0.115360i
190190 −14.6569 −1.06332
191191 19.6758 11.3598i 1.42369 0.821968i 0.427079 0.904215i 0.359543π-0.359543\pi
0.996612 + 0.0822464i 0.0262094π0.0262094\pi
192192 7.52978 + 21.2394i 0.543415 + 1.53283i
193193 −8.43598 + 14.6116i −0.607235 + 1.05176i 0.384459 + 0.923142i 0.374388π0.374388\pi
−0.991694 + 0.128620i 0.958945π0.958945\pi
194194 −3.54471 + 6.13962i −0.254495 + 0.440799i
195195 −9.67330 8.25583i −0.692719 0.591212i
196196 −7.48235 20.9792i −0.534454 1.49852i
197197 8.94426i 0.637252i 0.947880 + 0.318626i 0.103221π0.103221\pi
−0.947880 + 0.318626i 0.896779π0.896779\pi
198198 −3.47141 21.8172i −0.246702 1.55048i
199199 5.78528i 0.410108i 0.978751 + 0.205054i 0.0657369π0.0657369\pi
−0.978751 + 0.205054i 0.934263π0.934263\pi
200200 −6.85705 + 3.95892i −0.484867 + 0.279938i
201201 −1.12441 0.207983i −0.0793097 0.0146700i
202202 −13.9762 8.06914i −0.983359 0.567743i
203203 −1.81073 + 2.56825i −0.127088 + 0.180256i
204204 5.91423 + 1.09396i 0.414079 + 0.0765927i
205205 5.33009 + 9.23200i 0.372270 + 0.644791i
206206 −3.87788 −0.270185
207207 −11.8759 + 1.88962i −0.825434 + 0.131338i
208208 1.22412i 0.0848771i
209209 −7.26091 12.5763i −0.502248 0.869918i
210210 −10.7019 + 10.4563i −0.738501 + 0.721551i
211211 −12.9451 + 22.4216i −0.891180 + 1.54357i −0.0527186 + 0.998609i 0.516789π0.516789\pi
−0.838462 + 0.544960i 0.816545π0.816545\pi
212212 19.3285 + 11.1593i 1.32748 + 0.766423i
213213 −6.24180 + 2.21284i −0.427681 + 0.151621i
214214 5.61793 + 9.73053i 0.384034 + 0.665166i
215215 10.9673 0.747964
216216 7.29211 11.9282i 0.496165 0.811610i
217217 9.86621 + 0.895374i 0.669762 + 0.0607819i
218218 −16.0442 + 9.26312i −1.08665 + 0.627378i
219219 11.9347 4.23109i 0.806475 0.285910i
220220 12.7856 + 7.38175i 0.862003 + 0.497678i
221221 4.83818 + 2.79332i 0.325451 + 0.187899i
222222 0.717144 + 0.612058i 0.0481315 + 0.0410786i
223223 15.4827 8.93892i 1.03680 0.598594i 0.117871 0.993029i 0.462393π-0.462393\pi
0.918924 + 0.394435i 0.129060π0.129060\pi
224224 15.6131 + 1.41692i 1.04320 + 0.0946717i
225225 −8.24433 3.15798i −0.549622 0.210532i
226226 8.92915 0.593958
227227 −5.48365 9.49796i −0.363963 0.630402i 0.624646 0.780908i 0.285243π-0.285243\pi
−0.988609 + 0.150506i 0.951910π0.951910\pi
228228 4.50000 24.3281i 0.298020 1.61117i
229229 −16.8349 9.71965i −1.11248 0.642293i −0.173012 0.984920i 0.555350π-0.555350\pi
−0.939471 + 0.342627i 0.888683π0.888683\pi
230230 6.54377 11.3341i 0.431483 0.747351i
231231 −14.2735 4.00274i −0.939130 0.263361i
232232 1.59781 + 2.76748i 0.104901 + 0.181694i
233233 2.94031i 0.192626i −0.995351 0.0963131i 0.969295π-0.969295\pi
0.995351 0.0963131i 0.0307050π-0.0307050\pi
234234 27.1532 22.0202i 1.77506 1.43950i
235235 6.05391 0.394914
236236 15.0675 + 26.0976i 0.980809 + 1.69881i
237237 4.11555 4.82216i 0.267334 0.313233i
238238 3.78737 5.37183i 0.245499 0.348204i
239239 −10.7255 6.19234i −0.693772 0.400549i 0.111252 0.993792i 0.464514π-0.464514\pi
−0.805023 + 0.593243i 0.797847π0.797847\pi
240240 −0.198495 0.559900i −0.0128128 0.0361414i
241241 11.6943 6.75168i 0.753293 0.434914i −0.0735896 0.997289i 0.523445π-0.523445\pi
0.826882 + 0.562375i 0.190112π0.190112\pi
242242 1.21884i 0.0783499i
243243 15.4515 2.06217i 0.991211 0.132288i
244244 10.3890i 0.665089i
245245 3.37273 + 9.45656i 0.215476 + 0.604157i
246246 −27.6202 + 9.79190i −1.76100 + 0.624308i
247247 11.4903 19.9018i 0.731109 1.26632i
248248 5.03727 8.72481i 0.319867 0.554026i
249249 12.2616 14.3668i 0.777045 0.910458i
250250 22.4589 12.9666i 1.42042 0.820082i
251251 7.51441 0.474305 0.237153 0.971472i 0.423786π-0.423786\pi
0.237153 + 0.971472i 0.423786π0.423786\pi
252252 −14.0700 20.9737i −0.886325 1.32122i
253253 12.9669 0.815222
254254 −12.1602 + 7.02069i −0.762998 + 0.440517i
255255 −2.66589 0.493113i −0.166944 0.0308799i
256256 7.21053 12.4890i 0.450658 0.780563i
257257 3.87788 6.71668i 0.241895 0.418975i −0.719359 0.694639i 0.755564π-0.755564\pi
0.961254 + 0.275664i 0.0888976π0.0888976\pi
258258 −5.48365 + 29.6459i −0.341397 + 1.84568i
259259 0.574248 0.265516i 0.0356820 0.0164984i
260260 23.3630i 1.44891i
261261 −1.27455 + 3.32738i −0.0788927 + 0.205960i
262262 18.8092i 1.16204i
263263 −12.1127 + 6.99329i −0.746903 + 0.431224i −0.824574 0.565755i 0.808585π-0.808585\pi
0.0776710 + 0.996979i 0.475252π0.475252\pi
264264 −9.78651 + 11.4668i −0.602318 + 0.705732i
265265 −8.71246 5.03014i −0.535202 0.308999i
266266 −22.0969 15.5793i −1.35485 0.955228i
267267 7.92395 + 22.3513i 0.484938 + 1.36788i
268268 1.05034 + 1.81925i 0.0641599 + 0.111128i
269269 −25.8321 −1.57501 −0.787505 0.616308i 0.788628π-0.788628\pi
−0.787505 + 0.616308i 0.788628π0.788628\pi
270270 −8.84897 + 14.4748i −0.538531 + 0.880910i
271271 16.6537i 1.01164i −0.862639 0.505821i 0.831190π-0.831190\pi
0.862639 0.505821i 0.168810π-0.168810\pi
272272 0.130480 + 0.225997i 0.00791148 + 0.0137031i
273273 −5.80820 22.7286i −0.351528 1.37560i
274274 11.7781 20.4003i 0.711542 1.23243i
275275 8.24433 + 4.75986i 0.497152 + 0.287031i
276276 16.8037 + 14.3414i 1.01147 + 0.863252i
277277 −15.7044 27.2008i −0.943585 1.63434i −0.758560 0.651603i 0.774097π-0.774097\pi
−0.185025 0.982734i 0.559237π-0.559237\pi
278278 −40.6345 −2.43709
279279 11.0937 1.76515i 0.664160 0.105677i
280280 10.1683 + 0.922786i 0.607670 + 0.0551470i
281281 8.10464 4.67922i 0.483483 0.279139i −0.238384 0.971171i 0.576618π-0.576618\pi
0.721867 + 0.692032i 0.243284π0.243284\pi
282282 −3.02696 + 16.3645i −0.180253 + 0.974489i
283283 −13.6603 7.88676i −0.812018 0.468819i 0.0356380 0.999365i 0.488654π-0.488654\pi
−0.847656 + 0.530546i 0.821987π0.821987\pi
284284 10.5361 + 6.08303i 0.625203 + 0.360961i
285285 −2.02841 + 10.9661i −0.120153 + 0.649575i
286286 −32.6466 + 18.8485i −1.93044 + 1.11454i
287287 −1.77726 + 19.5838i −0.104908 + 1.15599i
288288 17.5555 2.79332i 1.03447 0.164598i
289289 −15.8090 −0.929943
290290 −1.93894 3.35834i −0.113858 0.197209i
291291 4.10301 + 3.50178i 0.240523 + 0.205278i
292292 −20.1458 11.6312i −1.17894 0.680662i
293293 12.4287 21.5271i 0.726090 1.25762i −0.232434 0.972612i 0.574669π-0.574669\pi
0.958524 0.285013i 0.0919978π-0.0919978\pi
294294 −27.2486 + 4.38863i −1.58917 + 0.255950i
295295 −6.79179 11.7637i −0.395433 0.684911i
296296 0.643376i 0.0373955i
297297 −16.8037 0.422088i −0.975051 0.0244920i
298298 39.8903 2.31078
299299 10.2600 + 17.7708i 0.593349 + 1.02771i
300300 5.41936 + 15.2865i 0.312887 + 0.882568i
301301 16.5344 + 11.6575i 0.953029 + 0.671926i
302302 2.16991 + 1.25280i 0.124864 + 0.0720903i
303303 −7.97141 + 9.34004i −0.457946 + 0.536571i
304304 0.929636 0.536725i 0.0533183 0.0307833i
305305 4.68294i 0.268144i
306306 2.66589 6.95966i 0.152399 0.397857i
307307 18.8878i 1.07799i 0.842310 + 0.538993i 0.181195π0.181195\pi
−0.842310 + 0.538993i 0.818805π0.818805\pi
308308 11.4294 + 24.7190i 0.651250 + 1.40850i
309309 −0.536670 + 2.90137i −0.0305301 + 0.165053i
310310 −6.11273 + 10.5876i −0.347179 + 0.601332i
311311 3.97716 6.88864i 0.225524 0.390619i −0.730953 0.682428i 0.760924π-0.760924\pi
0.956476 + 0.291809i 0.0942573π0.0942573\pi
312312 −23.4584 4.33914i −1.32807 0.245655i
313313 9.64210 5.56687i 0.545004 0.314658i −0.202101 0.979365i 0.564777π-0.564777\pi
0.747104 + 0.664707i 0.231444π0.231444\pi
314314 22.2152 1.25367
315315 6.34216 + 9.45407i 0.357340 + 0.532676i
316316 −11.6465 −0.655168
317317 −20.1380 + 11.6267i −1.13107 + 0.653021i −0.944203 0.329365i 0.893165π-0.893165\pi
−0.186863 + 0.982386i 0.559832π0.559832\pi
318318 17.9533 21.0358i 1.00677 1.17963i
319319 1.92107 3.32738i 0.107559 0.186298i
320320 −9.33033 + 16.1606i −0.521581 + 0.903405i
321321 8.05772 2.85661i 0.449738 0.159441i
322322 21.9129 10.1319i 1.22116 0.564629i
323323 4.89904i 0.272590i
324324 −21.3090 19.1319i −1.18383 1.06289i
325325 15.0648i 0.835646i
326326 14.2443 8.22396i 0.788920 0.455483i
327327 4.71013 + 13.2860i 0.260471 + 0.734716i
328328 17.3182 + 9.99866i 0.956237 + 0.552084i
329329 9.12695 + 6.43489i 0.503185 + 0.354767i
330330 11.8759 13.9149i 0.653748 0.765992i
331331 9.57962 + 16.5924i 0.526544 + 0.912000i 0.999522 + 0.0309261i 0.00984566π0.00984566\pi
−0.472978 + 0.881074i 0.656821π0.656821\pi
332332 −34.6988 −1.90434
333333 0.557180 0.451852i 0.0305333 0.0247613i
334334 39.4006i 2.15590i
335335 −0.473451 0.820041i −0.0258674 0.0448036i
336336 0.295882 1.05510i 0.0161417 0.0575603i
337337 14.2781 24.7304i 0.777779 1.34715i −0.155441 0.987845i 0.549680π-0.549680\pi
0.933219 0.359307i 0.116987π-0.116987\pi
338338 −26.0345 15.0310i −1.41609 0.817579i
339339 1.23573 6.68065i 0.0671156 0.362843i
340340 2.49028 + 4.31330i 0.135055 + 0.233922i
341341 −12.1128 −0.655943
342342 −28.6285 10.9661i −1.54805 0.592978i
343343 −4.96690 + 17.8418i −0.268187 + 0.963367i
344344 17.8171 10.2867i 0.960634 0.554622i
345345 −7.57442 6.46451i −0.407793 0.348038i
346346 −3.85648 2.22654i −0.207326 0.119700i
347347 2.56690 + 1.48200i 0.137798 + 0.0795578i 0.567314 0.823501i 0.307983π-0.307983\pi
−0.429516 + 0.903059i 0.641316π0.641316\pi
348348 6.16959 2.18724i 0.330725 0.117248i
349349 −23.3885 + 13.5034i −1.25196 + 0.722818i −0.971498 0.237048i 0.923820π-0.923820\pi
−0.280460 + 0.959866i 0.590487π0.590487\pi
350350 17.6514 + 1.60189i 0.943504 + 0.0856245i
351351 −12.7174 23.3630i −0.678803 1.24703i
352352 −19.1683 −1.02167
353353 14.8238 + 25.6755i 0.788990 + 1.36657i 0.926586 + 0.376083i 0.122729π0.122729\pi
−0.137596 + 0.990488i 0.543937π0.543937\pi
354354 35.1947 12.4772i 1.87058 0.663154i
355355 −4.74924 2.74198i −0.252064 0.145529i
356356 21.7827 37.7288i 1.15448 1.99962i
357357 −3.49498 3.57708i −0.184974 0.189319i
358358 26.4081 + 45.7401i 1.39571 + 2.41744i
359359 24.6261i 1.29972i 0.760056 + 0.649858i 0.225172π0.225172\pi
−0.760056 + 0.649858i 0.774828π0.774828\pi
360360 11.4333 1.81919i 0.602587 0.0958797i
361361 −1.15211 −0.0606373
362362 −11.6943 20.2550i −0.614636 1.06458i
363363 −0.911917 0.168678i −0.0478632 0.00885332i
364364 −24.8333 + 35.2224i −1.30162 + 1.84615i
365365 9.08087 + 5.24284i 0.475314 + 0.274423i
366366 12.6586 + 2.34147i 0.661673 + 0.122391i
367367 −4.85598 + 2.80360i −0.253480 + 0.146347i −0.621357 0.783528i 0.713418π-0.713418\pi
0.367877 + 0.929875i 0.380085π0.380085\pi
368368 0.958511i 0.0499658i
369369 3.50371 + 22.0202i 0.182396 + 1.14633i
370370 0.780736i 0.0405885i
371371 −7.78832 16.8443i −0.404349 0.874510i
372372 −15.6969 13.3967i −0.813844 0.694588i
373373 1.86677 3.23333i 0.0966574 0.167416i −0.813642 0.581367i 0.802518π-0.802518\pi
0.910299 + 0.413951i 0.135852π0.135852\pi
374374 −4.01816 + 6.95966i −0.207774 + 0.359876i
375375 −6.59329 18.5979i −0.340476 0.960390i
376376 9.83498 5.67823i 0.507200 0.292832i
377377 6.08012 0.313142
378378 −28.7266 + 12.4166i −1.47754 + 0.638641i
379379 −30.4419 −1.56369 −0.781847 0.623470i 0.785722π-0.785722\pi
−0.781847 + 0.623470i 0.785722π0.785722\pi
380380 17.7427 10.2437i 0.910181 0.525493i
381381 3.56989 + 10.0697i 0.182891 + 0.515886i
382382 −25.8594 + 44.7897i −1.32308 + 2.29164i
383383 −8.49251 + 14.7095i −0.433947 + 0.751618i −0.997209 0.0746601i 0.976213π-0.976213\pi
0.563262 + 0.826278i 0.309546π0.309546\pi
384384 −23.4058 19.9760i −1.19442 1.01940i
385385 −5.15189 11.1423i −0.262565 0.567864i
386386 38.4071i 1.95487i
387387 21.4218 + 8.20557i 1.08893 + 0.417113i
388388 9.90962i 0.503085i
389389 9.43310 5.44621i 0.478277 0.276134i −0.241421 0.970420i 0.577613π-0.577613\pi
0.719698 + 0.694287i 0.244280π0.244280\pi
390390 28.4668 + 5.26554i 1.44147 + 0.266631i
391391 3.78840 + 2.18724i 0.191588 + 0.110613i
392392 14.3489 + 12.1994i 0.724731 + 0.616161i
393393 14.0728 + 2.60306i 0.709878 + 0.131307i
394394 −10.1803 17.6328i −0.512877 0.888328i
395395 5.24976 0.264144
396396 19.4503 + 23.9843i 0.977417 + 1.20526i
397397 22.3035i 1.11938i −0.828702 0.559690i 0.810920π-0.810920\pi
0.828702 0.559690i 0.189080π-0.189080\pi
398398 −6.58477 11.4052i −0.330065 0.571689i
399399 −14.7143 + 14.3765i −0.736634 + 0.719727i
400400 −0.351848 + 0.609419i −0.0175924 + 0.0304710i
401401 20.8554 + 12.0409i 1.04147 + 0.601293i 0.920249 0.391333i 0.127986π-0.127986\pi
0.121221 + 0.992626i 0.461319π0.461319\pi
402402 2.45340 0.869775i 0.122364 0.0433804i
403403 −9.58414 16.6002i −0.477420 0.826915i
404404 22.5581 1.12231
405405 9.60522 + 8.62388i 0.477287 + 0.428524i
406406 0.646517 7.12403i 0.0320861 0.353560i
407407 −0.669905 + 0.386770i −0.0332060 + 0.0191715i
408408 −4.79342 + 1.69936i −0.237310 + 0.0841308i
409409 22.8191 + 13.1746i 1.12833 + 0.651443i 0.943515 0.331330i 0.107497π-0.107497\pi
0.184817 + 0.982773i 0.440831π0.440831\pi
410410 −21.0156 12.1334i −1.03789 0.599224i
411411 −13.6332 11.6355i −0.672476 0.573935i
412412 4.69430 2.71026i 0.231272 0.133525i
413413 2.26464 24.9543i 0.111436 1.22792i
414414 21.2616 17.2423i 1.04495 0.847414i
415415 15.6408 0.767775
416416 −15.1668 26.2696i −0.743611 1.28797i
417417 −5.62352 + 30.4021i −0.275385 + 1.48880i
418418 28.6285 + 16.5286i 1.40026 + 0.808443i
419419 −16.1761 + 28.0178i −0.790252 + 1.36876i 0.135558 + 0.990769i 0.456717π0.456717\pi
−0.925811 + 0.377988i 0.876616π0.876616\pi
420420 5.64709 20.1372i 0.275550 0.982596i
421421 −5.54746 9.60849i −0.270367 0.468289i 0.698589 0.715523i 0.253812π-0.253812\pi
−0.968956 + 0.247234i 0.920478π0.920478\pi
422422 58.9363i 2.86898i
423423 11.8247 + 4.52945i 0.574938 + 0.220229i
424424 −18.8720 −0.916504
425425 1.60577 + 2.78128i 0.0778914 + 0.134912i
426426 9.78651 11.4668i 0.474158 0.555568i
427427 4.97764 7.06006i 0.240885 0.341660i
428428 −13.6014 7.85276i −0.657447 0.379577i
429429 9.58414 + 27.0342i 0.462726 + 1.30522i
430430 −21.6210 + 12.4829i −1.04266 + 0.601980i
431431 16.3047i 0.785368i 0.919673 + 0.392684i 0.128453π0.128453\pi
−0.919673 + 0.392684i 0.871547π0.871547\pi
432432 0.0312007 1.24213i 0.00150114 0.0597620i
433433 12.5359i 0.602438i −0.953555 0.301219i 0.902606π-0.902606\pi
0.953555 0.301219i 0.0973936π-0.0973936\pi
434434 −20.4695 + 9.46451i −0.982565 + 0.454311i
435435 −2.78100 + 0.985915i −0.133339 + 0.0472710i
436436 12.9480 22.4266i 0.620098 1.07404i
437437 8.99716 15.5835i 0.430393 0.745462i
438438 −18.7125 + 21.9253i −0.894116 + 1.04763i
439439 −16.1276 + 9.31127i −0.769728 + 0.444403i −0.832778 0.553608i 0.813251π-0.813251\pi
0.0630496 + 0.998010i 0.479917π0.479917\pi
440440 −12.4836 −0.595132
441441 −0.487504 + 20.9943i −0.0232145 + 0.999731i
442442 −12.7174 −0.604904
443443 4.11436 2.37543i 0.195479 0.112860i −0.399066 0.916922i 0.630666π-0.630666\pi
0.594545 + 0.804062i 0.297332π0.297332\pi
444444 −1.29589 0.239703i −0.0615004 0.0113758i
445445 −9.81875 + 17.0066i −0.465453 + 0.806189i
446446 −20.3484 + 35.2445i −0.963527 + 1.66888i
447447 5.52053 29.8453i 0.261112 1.41163i
448448 −31.2441 + 14.4464i −1.47615 + 0.682529i
449449 16.2393i 0.766379i 0.923670 + 0.383189i 0.125174π0.125174\pi
−0.923670 + 0.383189i 0.874826π0.874826\pi
450450 19.8473 3.15798i 0.935612 0.148868i
451451 24.0431i 1.13214i
452452 −10.8090 + 6.24060i −0.508414 + 0.293533i
453453 1.23762 1.45011i 0.0581485 0.0681322i
454454 21.6210 + 12.4829i 1.01473 + 0.585852i
455455 11.1938 15.8768i 0.524774 0.744315i
456456 6.99028 + 19.7177i 0.327350 + 0.923365i
457457 2.87360 + 4.97722i 0.134421 + 0.232825i 0.925376 0.379050i 0.123749π-0.123749\pi
−0.790955 + 0.611874i 0.790416π0.790416\pi
458458 44.2514 2.06773
459459 −4.83818 2.95774i −0.225827 0.138056i
460460 18.2938i 0.852953i
461461 18.1346 + 31.4101i 0.844613 + 1.46291i 0.885957 + 0.463768i 0.153503π0.153503\pi
−0.0413440 + 0.999145i 0.513164π0.513164\pi
462462 32.6949 8.35504i 1.52110 0.388711i
463463 14.6202 25.3230i 0.679461 1.17686i −0.295683 0.955286i 0.595547π-0.595547\pi
0.975144 0.221574i 0.0711195π-0.0711195\pi
464464 0.245960 + 0.142005i 0.0114184 + 0.00659241i
465465 7.07549 + 6.03869i 0.328118 + 0.280038i
466466 3.34665 + 5.79656i 0.155030 + 0.268521i
467467 2.64215 0.122264 0.0611320 0.998130i 0.480529π-0.480529\pi
0.0611320 + 0.998130i 0.480529π0.480529\pi
468468 −17.4799 + 45.6336i −0.808007 + 2.10941i
469469 0.157867 1.73955i 0.00728961 0.0803249i
470470 −11.9347 + 6.89053i −0.550508 + 0.317836i
471471 3.07442 16.6211i 0.141662 0.765858i
472472 −22.0674 12.7406i −1.01574 0.586435i
473473 −21.4218 12.3679i −0.984973 0.568675i
474474 −2.62488 + 14.1907i −0.120565 + 0.651803i
475475 11.4408 6.60532i 0.524938 0.303073i
476476 −0.830357 + 9.14978i −0.0380593 + 0.419380i
477477 −13.2540 16.3436i −0.606861 0.748322i
478478 28.1923 1.28949
479479 −15.5409 26.9177i −0.710083 1.22990i −0.964826 0.262891i 0.915324π-0.915324\pi
0.254742 0.967009i 0.418009π-0.418009\pi
480480 11.1969 + 9.55614i 0.511064 + 0.436176i
481481 −1.06012 0.612058i −0.0483371 0.0279074i
482482 −15.3694 + 26.6207i −0.700059 + 1.21254i
483483 −4.54796 17.7971i −0.206939 0.809794i
484484 0.851848 + 1.47544i 0.0387204 + 0.0670657i
485485 4.46684i 0.202829i
486486 −28.1140 + 21.6521i −1.27528 + 0.982161i
487487 34.8720 1.58020 0.790100 0.612978i 0.210029π-0.210029\pi
0.790100 + 0.612978i 0.210029π0.210029\pi
488488 −4.39234 7.60775i −0.198832 0.344387i
489489 −4.18174 11.7955i −0.189105 0.533412i
490490 −17.4124 14.8039i −0.786614 0.668773i
491491 −22.6758 13.0919i −1.02334 0.590828i −0.108273 0.994121i 0.534532π-0.534532\pi
−0.915071 + 0.403293i 0.867866π0.867866\pi
492492 26.5917 31.1573i 1.19884 1.40468i
493493 1.12252 0.648085i 0.0505556 0.0291883i
494494 52.3127i 2.35366i
495495 −8.76740 10.8111i −0.394065 0.485924i
496496 0.895374i 0.0402035i
497497 −4.24548 9.18195i −0.190436 0.411867i
498498 −7.82038 + 42.2789i −0.350440 + 1.89456i
499499 −6.23912 + 10.8065i −0.279302 + 0.483764i −0.971211 0.238220i 0.923436π-0.923436\pi
0.691910 + 0.721984i 0.256770π0.256770\pi
500500 −18.1248 + 31.3931i −0.810566 + 1.40394i
501501 −29.4789 5.45276i −1.31702 0.243611i
502502 −14.8140 + 8.55285i −0.661180 + 0.381733i
503503 −37.8479 −1.68756 −0.843778 0.536693i 0.819673π-0.819673\pi
−0.843778 + 0.536693i 0.819673π0.819673\pi
504504 19.1706 + 9.41017i 0.853928 + 0.419162i
505505 −10.1683 −0.452482
506506 −25.5631 + 14.7588i −1.13642 + 0.656111i
507507 −14.8490 + 17.3984i −0.659466 + 0.772691i
508508 9.81354 16.9976i 0.435406 0.754145i
509509 17.6924 30.6441i 0.784200 1.35827i −0.145276 0.989391i 0.546407π-0.546407\pi
0.929476 0.368883i 0.120260π-0.120260\pi
510510 5.81682 2.06217i 0.257573 0.0913144i
511511 8.11764 + 17.5565i 0.359103 + 0.776654i
512512 2.70367i 0.119486i
513513 −12.1666 + 19.9018i −0.537170 + 0.878684i
514514 17.6551i 0.778734i
515515 −2.11599 + 1.22167i −0.0932419 + 0.0538332i
516516 −14.0815 39.7199i −0.619902 1.74857i
517517 −11.8247 6.82701i −0.520051 0.300252i
518518 −0.829869 + 1.17705i −0.0364623 + 0.0517165i
519519 −2.19957 + 2.57723i −0.0965506 + 0.113128i
520520 −9.87756 17.1084i −0.433160 0.750255i
521521 −2.31879 −0.101588 −0.0507940 0.998709i 0.516175π-0.516175\pi
−0.0507940 + 0.998709i 0.516175π0.516175\pi
522522 −1.27455 8.01033i −0.0557855 0.350602i
523523 20.1840i 0.882585i 0.897363 + 0.441293i 0.145480π0.145480\pi
−0.897363 + 0.441293i 0.854520π0.854520\pi
524524 −13.1458 22.7692i −0.574277 0.994677i
525525 3.64133 12.9848i 0.158921 0.566703i
526526 15.9194 27.5733i 0.694120 1.20225i
527527 −3.53886 2.04316i −0.154155 0.0890015i
528528 −0.243693 + 1.31746i −0.0106054 + 0.0573352i
529529 −3.46621 6.00365i −0.150705 0.261028i
530530 22.9011 0.994761
531531 −4.46454 28.0589i −0.193745 1.21765i
532532 37.6375 + 3.41566i 1.63179 + 0.148088i
533533 32.9503 19.0239i 1.42724 0.824016i
534534 −41.0614 35.0445i −1.77690 1.51653i
535535 6.13093 + 3.53970i 0.265063 + 0.153034i
536536 −1.53831 0.888141i −0.0664447 0.0383618i
537537 37.8768 13.4280i 1.63450 0.579462i
538538 50.9256 29.4019i 2.19556 1.26761i
539539 4.07644 22.2744i 0.175585 0.959424i
540540 0.595485 23.7068i 0.0256256 1.02018i
541541 −22.7713 −0.979014 −0.489507 0.871999i 0.662823π-0.662823\pi
−0.489507 + 0.871999i 0.662823π0.662823\pi
542542 18.9552 + 32.8313i 0.814194 + 1.41023i
543543 −16.7729 + 5.94631i −0.719795 + 0.255181i
544544 −5.60020 3.23327i −0.240106 0.138626i
545545 −5.83643 + 10.1090i −0.250005 + 0.433022i
546546 37.3200 + 38.1966i 1.59715 + 1.63466i
547547 14.7918 + 25.6201i 0.632451 + 1.09544i 0.987049 + 0.160419i 0.0512845π0.0512845\pi
−0.354598 + 0.935019i 0.615382π0.615382\pi
548548 32.9270i 1.40657i
549549 3.50371 9.14690i 0.149535 0.390380i
550550 −21.6706 −0.924037
551551 −2.66589 4.61745i −0.113571 0.196710i
552552 −18.3685 3.39765i −0.781815 0.144613i
553553 7.91461 + 5.58014i 0.336563 + 0.237292i
554554 61.9196 + 35.7493i 2.63071 + 1.51884i
555555 0.584135 + 0.108048i 0.0247952 + 0.00458639i
556556 49.1894 28.3995i 2.08609 1.20441i
557557 4.71407i 0.199741i −0.995000 0.0998707i 0.968157π-0.968157\pi
0.995000 0.0998707i 0.0318429π-0.0318429\pi
558558 −19.8611 + 16.1066i −0.840786 + 0.681845i
559559 39.1439i 1.65561i
560560 0.823636 0.380827i 0.0348050 0.0160929i
561561 4.65103 + 3.96950i 0.196367 + 0.167592i
562562 −10.6517 + 18.4493i −0.449316 + 0.778238i
563563 13.6742 23.6844i 0.576299 0.998179i −0.419601 0.907709i 0.637830π-0.637830\pi
0.995899 0.0904697i 0.0288368π-0.0288368\pi
564564 −7.77292 21.9253i −0.327299 0.923220i
565565 4.87226 2.81300i 0.204977 0.118344i
566566 35.9066 1.50927
567567 5.31436 + 23.2112i 0.223182 + 0.974777i
568568 −10.2873 −0.431645
569569 20.4018 11.7790i 0.855288 0.493801i −0.00714355 0.999974i 0.502274π-0.502274\pi
0.862432 + 0.506174i 0.168941π0.168941\pi
570570 −8.48270 23.9274i −0.355301 1.00221i
571571 −9.59385 + 16.6170i −0.401490 + 0.695401i −0.993906 0.110231i 0.964841π-0.964841\pi
0.592416 + 0.805632i 0.298174π0.298174\pi
572572 26.3465 45.6336i 1.10160 1.90804i
573573 29.9323 + 25.5462i 1.25044 + 1.06721i
574574 −18.7864 40.6305i −0.784131 1.69589i
575575 11.7961i 0.491932i
576576 −30.3155 + 24.5847i −1.26314 + 1.02436i
577577 2.23413i 0.0930079i 0.998918 + 0.0465039i 0.0148080π0.0148080\pi
−0.998918 + 0.0465039i 0.985192π0.985192\pi
578578 31.1661 17.9937i 1.29634 0.748441i
579579 −28.7357 5.31527i −1.19421 0.220895i
580580 4.69430 + 2.71026i 0.194920 + 0.112537i
581581 23.5802 + 16.6250i 0.978271 + 0.689723i
582582 −12.0744 2.23342i −0.500501 0.0925783i
583583 11.3450 + 19.6501i 0.469862 + 0.813826i
584584 19.6700 0.813949
585585 7.87919 20.5697i 0.325765 0.850453i
586586 56.5849i 2.33750i
587587 12.9883 + 22.4963i 0.536083 + 0.928522i 0.999110 + 0.0421784i 0.0134298π0.0134298\pi
−0.463028 + 0.886344i 0.653237π0.653237\pi
588588 29.9181 24.3567i 1.23380 1.00445i
589589 −8.40451 + 14.5570i −0.346302 + 0.599813i
590590 26.7788 + 15.4608i 1.10247 + 0.636509i
591591 −14.6015 + 5.17650i −0.600625 + 0.212933i
592592 −0.0285900 0.0495193i −0.00117504 0.00203523i
593593 −5.71754 −0.234791 −0.117396 0.993085i 0.537455π-0.537455\pi
−0.117396 + 0.993085i 0.537455π0.537455\pi
594594 33.6075 18.2938i 1.37893 0.750604i
595595 0.374290 4.12434i 0.0153444 0.169081i
596596 −48.2885 + 27.8794i −1.97797 + 1.14198i
597597 −9.44445 + 3.34824i −0.386536 + 0.137034i
598598 −40.4532 23.3557i −1.65425 0.955084i
599599 21.8662 + 12.6245i 0.893429 + 0.515822i 0.875063 0.484010i 0.160820π-0.160820\pi
0.0183665 + 0.999831i 0.494153π0.494153\pi
600600 −10.4314 8.90289i −0.425862 0.363459i
601601 −40.2546 + 23.2410i −1.64202 + 0.948021i −0.661907 + 0.749586i 0.730252π0.730252\pi
−0.980114 + 0.198435i 0.936414π0.936414\pi
602602 −45.8646 4.16229i −1.86930 0.169642i
603603 −0.311220 1.95596i −0.0126739 0.0796530i
604604 −3.50232 −0.142508
605605 −0.383978 0.665069i −0.0156109 0.0270389i
606606 5.08414 27.4861i 0.206529 1.11655i
607607 6.09405 + 3.51840i 0.247350 + 0.142808i 0.618550 0.785745i 0.287720π-0.287720\pi
−0.371200 + 0.928553i 0.621054π0.621054\pi
608608 −13.3000 + 23.0363i −0.539387 + 0.934246i
609609 −5.24062 1.46963i −0.212361 0.0595524i
610610 5.33009 + 9.23200i 0.215809 + 0.373793i
611611 21.6073i 0.874138i
612612 1.63697 + 10.2881i 0.0661707 + 0.415872i
613613 6.54256 0.264252 0.132126 0.991233i 0.457820π-0.457820\pi
0.132126 + 0.991233i 0.457820π0.457820\pi
614614 −21.4980 37.2357i −0.867590 1.50271i
615615 −11.9864 + 14.0444i −0.483339 + 0.566324i
616616 −18.8204 13.2692i −0.758297 0.534632i
617617 −30.0043 17.3230i −1.20793 0.697396i −0.245620 0.969366i 0.578992π-0.578992\pi
−0.962306 + 0.271970i 0.912325π0.912325\pi
618618 −2.24433 6.33063i −0.0902800 0.254655i
619619 −14.7072 + 8.49123i −0.591134 + 0.341291i −0.765546 0.643381i 0.777531π-0.777531\pi
0.174412 + 0.984673i 0.444198π0.444198\pi
620620 17.0888i 0.686302i
621621 −9.95800 18.2938i −0.399601 0.734105i
622622 18.1071i 0.726029i
623623 −32.8797 + 15.2027i −1.31730 + 0.609081i
624624 −1.99837 + 0.708458i −0.0799986 + 0.0283610i
625625 0.812855 1.40791i 0.0325142 0.0563162i
626626 −12.6724 + 21.9492i −0.506489 + 0.877265i
627627 16.3285 19.1319i 0.652096 0.764056i
628628 −26.8922 + 15.5262i −1.07312 + 0.619564i
629629 −0.260959 −0.0104051
630630 −23.2636 11.4192i −0.926842 0.454953i
631631 26.2438 1.04475 0.522374 0.852716i 0.325047π-0.325047\pi
0.522374 + 0.852716i 0.325047π0.325047\pi
632632 8.52859 4.92398i 0.339249 0.195866i
633633 −44.0953 8.15637i −1.75263 0.324186i
634634 26.4669 45.8420i 1.05113 1.82062i
635635 −4.42354 + 7.66179i −0.175543 + 0.304049i
636636 −7.03115 + 38.0121i −0.278803 + 1.50728i
637637 33.7518 12.0378i 1.33730 0.476954i
638638 8.74619i 0.346265i
639639 −7.22489 8.90904i −0.285812 0.352436i
640640 25.4813i 1.00724i
641641 16.5092 9.53157i 0.652073 0.376474i −0.137177 0.990547i 0.543803π-0.543803\pi
0.789250 + 0.614072i 0.210470π0.210470\pi
642642 −12.6337 + 14.8028i −0.498612 + 0.584220i
643643 −15.3447 8.85928i −0.605136 0.349376i 0.165923 0.986139i 0.446940π-0.446940\pi
−0.771060 + 0.636763i 0.780273π0.780273\pi
644644 −19.4450 + 27.5799i −0.766242 + 1.08680i
645645 6.34733 + 17.9041i 0.249926 + 0.704973i
646646 5.57605 + 9.65801i 0.219387 + 0.379989i
647647 21.7902 0.856661 0.428330 0.903622i 0.359102π-0.359102\pi
0.428330 + 0.903622i 0.359102π0.359102\pi
648648 23.6930 + 5.00091i 0.930750 + 0.196454i
649649 30.6365i 1.20259i
650650 −17.1467 29.6990i −0.672549 1.16489i
651651 4.24838 + 16.6248i 0.166507 + 0.651576i
652652 −11.4955 + 19.9108i −0.450198 + 0.779766i
653653 −13.0852 7.55475i −0.512064 0.295640i 0.221618 0.975134i 0.428866π-0.428866\pi
−0.733682 + 0.679493i 0.762200π0.762200\pi
654654 −24.4076 20.8311i −0.954413 0.814559i
655655 5.92558 + 10.2634i 0.231532 + 0.401024i
656656 1.77726 0.0693903
657657 13.8145 + 17.0347i 0.538954 + 0.664586i
658658 −25.3171 2.29757i −0.986964 0.0895685i
659659 −27.1850 + 15.6952i −1.05898 + 0.611400i −0.925149 0.379605i 0.876060π-0.876060\pi
−0.133827 + 0.991005i 0.542727π0.542727\pi
660660 −4.65103 + 25.1446i −0.181041 + 0.978752i
661661 37.8554 + 21.8558i 1.47240 + 0.850093i 0.999518 0.0310314i 0.00987918π-0.00987918\pi
0.472885 + 0.881124i 0.343213π0.343213\pi
662662 −37.7707 21.8069i −1.46800 0.847551i
663663 −1.75999 + 9.51495i −0.0683524 + 0.369530i
664664 25.4095 14.6702i 0.986078 0.569312i
665665 −16.9654 1.53964i −0.657890 0.0597046i
666666 −0.584135 + 1.52496i −0.0226348 + 0.0590912i
667667 4.76088 0.184342
668668 27.5371 + 47.6957i 1.06544 + 1.84540i
669669 23.5534 + 20.1020i 0.910625 + 0.777188i
670670 1.86673 + 1.07776i 0.0721181 + 0.0416374i
671671 −5.28096 + 9.14690i −0.203869 + 0.353112i
672672 6.72300 + 26.3084i 0.259346 + 1.01487i
673673 −4.60589 7.97763i −0.177544 0.307515i 0.763495 0.645814i 0.223482π-0.223482\pi
−0.941039 + 0.338299i 0.890149π0.890149\pi
674674 65.0051i 2.50390i
675675 0.383978 15.2865i 0.0147793 0.588378i
676676 42.0208 1.61618
677677 11.4194 + 19.7789i 0.438882 + 0.760165i 0.997604 0.0691899i 0.0220414π-0.0220414\pi
−0.558722 + 0.829355i 0.688708π0.688708\pi
678678 5.16775 + 14.5768i 0.198466 + 0.559819i
679679 −4.74795 + 6.73427i −0.182209 + 0.258437i
680680 −3.64721 2.10571i −0.139864 0.0807505i
681681 12.3317 14.4490i 0.472553 0.553687i
682682 23.8792 13.7867i 0.914383 0.527919i
683683 34.1826i 1.30796i −0.756511 0.653981i 0.773098π-0.773098\pi
0.756511 0.653981i 0.226902π-0.226902\pi
684684 42.3199 6.73367i 1.61814 0.257468i
685685 14.8421i 0.567088i
686686 −10.5156 40.8268i −0.401489 1.55877i
687687 6.12408 33.1082i 0.233648 1.26316i
688688 0.914230 1.58349i 0.0348547 0.0603701i
689689 −17.9533 + 31.0961i −0.683967 + 1.18467i
690690 22.2902 + 4.12304i 0.848572 + 0.156961i
691691 0.224082 0.129374i 0.00852446 0.00492160i −0.495732 0.868476i 0.665100π-0.665100\pi
0.504256 + 0.863554i 0.331767π0.331767\pi
692692 6.22453 0.236621
693693 −1.72637 25.6181i −0.0655795 0.973152i
694694 −6.74720 −0.256120
695695 −22.1725 + 12.8013i −0.841052 + 0.485582i
696696 −3.59318 + 4.21010i −0.136199 + 0.159583i
697697 4.05555 7.02441i 0.153615 0.266069i
698698 30.7389 53.2413i 1.16348 2.01521i
699699 4.80005 1.70171i 0.181555 0.0643645i
700700 −22.4871 + 10.3974i −0.849933 + 0.392986i
701701 5.16189i 0.194962i −0.995237 0.0974810i 0.968921π-0.968921\pi
0.995237 0.0974810i 0.0310785π-0.0310785\pi
702702 51.6628 + 31.5833i 1.94989 + 1.19203i
703703 1.07345i 0.0404860i
704704 36.4487 21.0437i 1.37371 0.793113i
705705 3.50371 + 9.88299i 0.131957 + 0.372215i
706706 −58.4475 33.7447i −2.19970 1.27000i
707707 −15.3298 10.8082i −0.576537 0.406483i
708708 −33.8840 + 39.7016i −1.27344 + 1.49208i
709709 −11.7472 20.3468i −0.441175 0.764138i 0.556602 0.830780i 0.312105π-0.312105\pi
−0.997777 + 0.0666412i 0.978772π0.978772\pi
710710 12.4836 0.468501
711711 10.2540 + 3.92779i 0.384557 + 0.147304i
712712 36.8377i 1.38055i
713713 −7.50460 12.9984i −0.281050 0.486792i
714714 10.9614 + 3.07392i 0.410222 + 0.115039i
715715 −11.8759 + 20.5697i −0.444134 + 0.769263i
716716 −63.9357 36.9133i −2.38939 1.37952i
717717 3.90162 21.0931i 0.145709 0.787736i
718718 −28.0293 48.5481i −1.04604 1.81180i
719719 10.1566 0.378776 0.189388 0.981902i 0.439350π-0.439350\pi
0.189388 + 0.981902i 0.439350π0.439350\pi
720720 0.799156 0.648085i 0.0297828 0.0241527i
721721 −4.48865 0.407352i −0.167166 0.0151706i
722722 2.27128 1.31132i 0.0845283 0.0488024i
723723 17.7902 + 15.1833i 0.661623 + 0.564673i
724724 28.3126 + 16.3463i 1.05223 + 0.607504i
725725 3.02696 + 1.74761i 0.112418 + 0.0649047i
726726 1.98975 0.705404i 0.0738466 0.0261800i
727727 5.74874 3.31904i 0.213209 0.123096i −0.389593 0.920987i 0.627384π-0.627384\pi
0.602802 + 0.797891i 0.294051π0.294051\pi
728728 3.29356 36.2920i 0.122067 1.34507i
729729 12.3090 + 24.0310i 0.455890 + 0.890036i
730730 −23.8695 −0.883449
731731 −4.17238 7.22678i −0.154321 0.267292i
732732 −16.9601 + 6.01266i −0.626862 + 0.222234i
733733 −5.20130 3.00297i −0.192114 0.110917i 0.400858 0.916140i 0.368712π-0.368712\pi
−0.592972 + 0.805223i 0.702046π0.702046\pi
734734 6.38209 11.0541i 0.235567 0.408014i
735735 −13.4858 + 10.9790i −0.497432 + 0.404965i
736736 −11.8759 20.5697i −0.437752 0.758209i
737737 2.13565i 0.0786676i
738738 −31.9705 39.4229i −1.17685 1.45118i
739739 −15.6386 −0.575275 −0.287638 0.957739i 0.592870π-0.592870\pi
−0.287638 + 0.957739i 0.592870π0.592870\pi
740740 −0.545658 0.945107i −0.0200588 0.0347428i
741741 39.1396 + 7.23970i 1.43783 + 0.265957i
742742 34.5260 + 24.3423i 1.26749 + 0.893634i
743743 27.3807 + 15.8083i 1.00450 + 0.579949i 0.909577 0.415535i 0.136406π-0.136406\pi
0.0949246 + 0.995484i 0.469739π0.469739\pi
744744 17.1586 + 3.17384i 0.629063 + 0.116359i
745745 21.7664 12.5669i 0.797461 0.460414i
746746 8.49897i 0.311169i
747747 30.5501 + 11.7022i 1.11777 + 0.428160i
748748 11.2332i 0.410727i
749749 5.48062 + 11.8532i 0.200257 + 0.433108i
750750 34.1661 + 29.1596i 1.24757 + 1.06476i
751751 7.13680 12.3613i 0.260426 0.451070i −0.705929 0.708282i 0.749470π-0.749470\pi
0.966355 + 0.257212i 0.0828038π0.0828038\pi
752752 0.504652 0.874082i 0.0184028 0.0318745i
753753 4.34897 + 12.2673i 0.158485 + 0.447043i
754754 −11.9864 + 6.92036i −0.436519 + 0.252025i
755755 1.57870 0.0574548
756756 26.0965 35.1077i 0.949120 1.27686i
757757 −10.8227 −0.393358 −0.196679 0.980468i 0.563016π-0.563016\pi
−0.196679 + 0.980468i 0.563016π0.563016\pi
758758 60.0134 34.6488i 2.17979 1.25850i
759759 7.50460 + 21.1684i 0.272400 + 0.768365i
760760 −8.66182 + 15.0027i −0.314197 + 0.544206i
761761 −2.93098 + 5.07660i −0.106248 + 0.184027i −0.914247 0.405157i 0.867217π-0.867217\pi
0.808000 + 0.589183i 0.200550π0.200550\pi
762762 −18.4990 15.7882i −0.670147 0.571948i
763763 −19.5442 + 9.03671i −0.707549 + 0.327151i
764764 72.2926i 2.61546i
765765 −0.737879 4.63744i −0.0266781 0.167667i
766766 38.6645i 1.39701i
767767 −41.9865 + 24.2409i −1.51604 + 0.875288i
768768 24.5614 + 4.54315i 0.886282 + 0.163937i
769769 −27.5683 15.9166i −0.994140 0.573967i −0.0876307 0.996153i 0.527930π-0.527930\pi
−0.906509 + 0.422186i 0.861263π0.861263\pi
770770 22.8386 + 16.1022i 0.823045 + 0.580282i
771771 13.2093 + 2.44334i 0.475721 + 0.0879947i
772772 26.8428 + 46.4931i 0.966094 + 1.67332i
773773 −19.0382 −0.684755 −0.342378 0.939562i 0.611232π-0.611232\pi
−0.342378 + 0.939562i 0.611232π0.611232\pi
774774 −51.5706 + 8.20557i −1.85367 + 0.294943i
775775 11.0191i 0.395818i
776776 4.18965 + 7.25668i 0.150400 + 0.260500i
777777 0.765801 + 0.783790i 0.0274730 + 0.0281183i
778778 −12.3977 + 21.4734i −0.444478 + 0.769859i
779779 −28.8948 16.6824i −1.03526 0.597710i
780780 −38.1401 + 13.5214i −1.36563 + 0.484143i
781781 6.18427 + 10.7115i 0.221290 + 0.383286i
782782 −9.95800 −0.356097
783783 −6.16959 0.154972i −0.220483 0.00553826i
784784 1.64652 + 0.301330i 0.0588042 + 0.0107618i
785785 12.1219 6.99857i 0.432649 0.249790i
786786 −30.7060 + 10.8859i −1.09525 + 0.388286i
787787 16.4123 + 9.47564i 0.585035 + 0.337770i 0.763132 0.646243i 0.223661π-0.223661\pi
−0.178097 + 0.984013i 0.556994π0.556994\pi
788788 24.6472 + 14.2301i 0.878020 + 0.506925i
789789 −18.4268 15.7266i −0.656010 0.559883i
790790 −10.3494 + 5.97525i −0.368216 + 0.212590i
791791 10.3355 + 0.937963i 0.367488 + 0.0333501i
792792 −24.3834 9.34004i −0.866428 0.331884i
793793 −16.7141 −0.593535
794794 25.3857 + 43.9693i 0.900905 + 1.56041i
795795 3.16935 17.1343i 0.112405 0.607690i
796796 15.9422 + 9.20422i 0.565055 + 0.326235i
797797 26.7207 46.2816i 0.946497 1.63938i 0.193770 0.981047i 0.437929π-0.437929\pi
0.752727 0.658333i 0.228738π-0.228738\pi
798798 12.6445 45.0897i 0.447611 1.59616i
799799 −2.30314 3.98916i −0.0814792 0.141126i
800800 17.4376i 0.616511i
801801 −31.9024 + 25.8716i −1.12722 + 0.914129i
802802 −54.8194 −1.93574
803803 −11.8247 20.4810i −0.417286 0.722760i
804804 −2.36203 + 2.76757i −0.0833024 + 0.0976048i
805805 8.76501 12.4319i 0.308926 0.438167i
806806 37.7885 + 21.8172i 1.33104 + 0.768479i
807807 −14.9503 42.1708i −0.526277 1.48448i
808808 −16.5190 + 9.53727i −0.581137 + 0.335520i
809809 2.58095i 0.0907413i 0.998970 + 0.0453706i 0.0144469π0.0144469\pi
−0.998970 + 0.0453706i 0.985553π0.985553\pi
810810 −28.7515 6.06860i −1.01022 0.213229i
811811 6.06938i 0.213125i 0.994306 + 0.106562i 0.0339844π0.0339844\pi
−0.994306 + 0.106562i 0.966016π0.966016\pi
812812 4.19637 + 9.07573i 0.147264 + 0.318496i
813813 27.1871 9.63835i 0.953495 0.338032i
814814 0.880438 1.52496i 0.0308593 0.0534500i
815815 5.18169 8.97494i 0.181507 0.314379i
816816 −0.293425 + 0.343803i −0.0102719 + 0.0120355i
817817 −29.7272 + 17.1630i −1.04002 + 0.600458i
818818 −59.9811 −2.09719
819819 33.7429 22.6361i 1.17907 0.790969i
820820 33.9201 1.18454
821821 8.03938 4.64154i 0.280576 0.161991i −0.353108 0.935583i 0.614875π-0.614875\pi
0.633684 + 0.773592i 0.281542π0.281542\pi
822822 40.1200 + 7.42106i 1.39935 + 0.258839i
823823 −9.03448 + 15.6482i −0.314922 + 0.545461i −0.979421 0.201828i 0.935312π-0.935312\pi
0.664499 + 0.747289i 0.268645π0.268645\pi
824824 −2.29172 + 3.96937i −0.0798357 + 0.138280i
825825 −2.99905 + 16.2136i −0.104414 + 0.564486i
826826 23.9383 + 51.7728i 0.832921 + 1.80141i
827827 48.5440i 1.68804i 0.536310 + 0.844021i 0.319818π0.319818\pi
−0.536310 + 0.844021i 0.680182π0.680182\pi
828828 −13.6871 + 35.7321i −0.475661 + 1.24178i
829829 5.44792i 0.189214i −0.995515 0.0946071i 0.969841π-0.969841\pi
0.995515 0.0946071i 0.0301595π-0.0301595\pi
830830 −30.8344 + 17.8022i −1.07028 + 0.617924i
831831 35.3163 41.3798i 1.22511 1.43545i
832832 57.6796 + 33.3013i 1.99968 + 1.15452i
833833 4.94817 5.82006i 0.171444 0.201653i
834834 −23.5172 66.3357i −0.814335 2.29702i
835835 −12.4126 21.4992i −0.429556 0.744012i
836836 −46.2076 −1.59812
837837 9.30206 + 17.0888i 0.321526 + 0.590675i
838838 73.6460i 2.54406i
839839 24.2673 + 42.0322i 0.837801 + 1.45111i 0.891729 + 0.452569i 0.149492π0.149492\pi
−0.0539281 + 0.998545i 0.517174π0.517174\pi
840840 4.37845 + 17.1337i 0.151071 + 0.591170i
841841 −13.7947 + 23.8931i −0.475678 + 0.823899i
842842 21.8727 + 12.6282i 0.753781 + 0.435196i
843843 12.3294 + 10.5227i 0.424646 + 0.362421i
844844 41.1907 + 71.3444i 1.41784 + 2.45578i
845845 −18.9412 −0.651598
846846 −28.4668 + 4.52945i −0.978708 + 0.155726i
847847 0.128033 1.41081i 0.00439926 0.0484759i
848848 −1.45254 + 0.838622i −0.0498803 + 0.0287984i
849849 4.96922 26.8648i 0.170543 0.921998i
850850 −6.33127 3.65536i −0.217161 0.125378i
851851 −0.830095 0.479256i −0.0284553 0.0164287i
852852 −3.83274 + 20.7207i −0.131308 + 0.709881i
853853 10.7703 6.21823i 0.368768 0.212908i −0.304152 0.952623i 0.598373π-0.598373\pi
0.672920 + 0.739715i 0.265040π0.265040\pi
854854 −1.77726 + 19.5838i −0.0608165 + 0.670144i
855855 −19.0761 + 3.03526i −0.652387 + 0.103804i
856856 13.2801 0.453906
857857 −5.29077 9.16388i −0.180729 0.313032i 0.761400 0.648283i 0.224512π-0.224512\pi
−0.942129 + 0.335250i 0.891179π0.891179\pi
858858 −49.6644 42.3869i −1.69552 1.44707i
859859 28.1452 + 16.2496i 0.960302 + 0.554431i 0.896266 0.443517i 0.146269π-0.146269\pi
0.0640360 + 0.997948i 0.479603π0.479603\pi
860860 17.4487 30.2220i 0.594995 1.03056i
861861 −32.9991 + 8.43276i −1.12461 + 0.287388i
862862 −18.5579 32.1432i −0.632084 1.09480i
863863 25.2203i 0.858510i 0.903183 + 0.429255i 0.141224π0.141224\pi
−0.903183 + 0.429255i 0.858776π0.858776\pi
864864 14.7204 + 27.0427i 0.500797 + 0.920013i
865865 −2.80576 −0.0953987
866866 14.2683 + 24.7135i 0.484857 + 0.839797i
867867 −9.14949 25.8082i −0.310733 0.876492i
868868 18.1642 25.7632i 0.616533 0.874462i
869869 −10.2540 5.92017i −0.347844 0.200828i
870870 4.36032 5.10896i 0.147829 0.173210i
871871 −2.92685 + 1.68982i −0.0991724 + 0.0572572i
872872 21.8970i 0.741525i
873873 −3.34203 + 8.72481i −0.113110 + 0.295290i
874874 40.9621i 1.38556i
875875 27.3583 12.6497i 0.924878 0.427638i
876876 7.32846 39.6194i 0.247606 1.33862i
877877 7.47893 12.9539i 0.252546 0.437422i −0.711680 0.702503i 0.752066π-0.752066\pi
0.964226 + 0.265082i 0.0853989π0.0853989\pi
878878 21.1961 36.7127i 0.715333 1.23899i
879879 42.3360 + 7.83094i 1.42796 + 0.264131i
880880 −0.960836 + 0.554739i −0.0323898 + 0.0187003i
881881 36.4482 1.22797 0.613985 0.789318i 0.289566π-0.289566\pi
0.613985 + 0.789318i 0.289566π0.289566\pi
882882 −22.9346 41.9433i −0.772247 1.41231i
883883 15.9831 0.537873 0.268936 0.963158i 0.413328π-0.413328\pi
0.268936 + 0.963158i 0.413328π0.413328\pi
884884 15.3948 8.88819i 0.517783 0.298942i
885885 15.2735 17.8958i 0.513413 0.601562i
886886 −5.40739 + 9.36588i −0.181665 + 0.314653i
887887 −24.5208 + 42.4713i −0.823329 + 1.42605i 0.0798613 + 0.996806i 0.474552π0.474552\pi
−0.903190 + 0.429241i 0.858781π0.858781\pi
888888 1.05031 0.372354i 0.0352461 0.0124954i
889889 −14.8129 + 6.84909i −0.496810 + 0.229711i
890890 44.7026i 1.49843i
891891 −9.03611 27.6763i −0.302721 0.927192i
892892 56.8862i 1.90469i
893893 −16.4093 + 9.47393i −0.549117 + 0.317033i
894894 23.0865 + 65.1208i 0.772129 + 2.17796i
895895 28.8196 + 16.6390i 0.963332 + 0.556180i
896896 27.0848 38.4159i 0.904841 1.28338i
897897 −23.0728 + 27.0342i −0.770378 + 0.902646i
898898 −18.4834 32.0143i −0.616801 1.06833i
899899 −4.44728 −0.148325
900900 −21.8187 + 17.6942i −0.727292 + 0.589806i
901901 7.65464i 0.255013i
902902 27.3657 + 47.3987i 0.911177 + 1.57820i
903903 −9.46149 + 33.7392i −0.314859 + 1.12277i
904904 5.27687 9.13981i 0.175506 0.303986i
905905 −12.7621 7.36821i −0.424227 0.244928i
906906 −0.789351 + 4.26742i −0.0262244 + 0.141776i
907907 2.42915 + 4.20741i 0.0806585 + 0.139705i 0.903533 0.428519i 0.140964π-0.140964\pi
−0.822874 + 0.568223i 0.807631π0.807631\pi
908908 −34.8973 −1.15811
909909 −19.8611 7.60775i −0.658750 0.252333i
910910 −3.99673 + 44.0404i −0.132490 + 1.45992i
911911 14.4945 8.36843i 0.480226 0.277258i −0.240285 0.970702i 0.577241π-0.577241\pi
0.720510 + 0.693444i 0.243908π0.243908\pi
912912 1.41423 + 1.20700i 0.0468298 + 0.0399677i
913913 −30.5501 17.6381i −1.01106 0.583737i
914914 −11.3301 6.54143i −0.374766 0.216371i
915915 7.64489 2.71026i 0.252732 0.0895983i
916916 −53.5678 + 30.9274i −1.76993 + 1.02187i
917917 −1.97582 + 21.7717i −0.0652472 + 0.718965i
918918 12.9045 + 0.324145i 0.425912 + 0.0106984i
919919 30.6400 1.01072 0.505360 0.862909i 0.331360π-0.331360\pi
0.505360 + 0.862909i 0.331360π0.331360\pi
920920 −7.73436 13.3963i −0.254994 0.441663i
921921 −30.8344 + 10.9314i −1.01603 + 0.360200i
922922 −71.5015 41.2814i −2.35478 1.35953i
923923 −9.78651 + 16.9507i −0.322127 + 0.557940i
924924 −33.7389 + 32.9646i −1.10993 + 1.08445i
925925 −0.351848 0.609419i −0.0115687 0.0200376i
926926 66.5627i 2.18739i
927927 −5.04708 + 0.803057i −0.165768 + 0.0263759i
928928 −7.03775 −0.231025
929929 −14.8723 25.7595i −0.487943 0.845142i 0.511961 0.859009i 0.328919π-0.328919\pi
−0.999904 + 0.0138670i 0.995586π0.995586\pi
930930 −20.8219 3.85145i −0.682777 0.126294i
931931 −23.9407 20.3542i −0.784626 0.667083i
932932 −8.10245 4.67795i −0.265405 0.153231i
933933 13.5475 + 2.50589i 0.443524 + 0.0820393i
934934 −5.20876 + 3.00728i −0.170436 + 0.0984011i
935935 5.06346i 0.165593i
936936 −6.49295 40.8071i −0.212229 1.33382i
937937 4.03712i 0.131887i 0.997823 + 0.0659434i 0.0210057π0.0210057\pi
−0.997823 + 0.0659434i 0.978994π0.978994\pi
938938 1.66873 + 3.60905i 0.0544858 + 0.117840i
939939 14.6683 + 12.5189i 0.478681 + 0.408538i
940940 9.63160 16.6824i 0.314148 0.544121i
941941 −7.20264 + 12.4753i −0.234799 + 0.406684i −0.959214 0.282680i 0.908777π-0.908777\pi
0.724415 + 0.689364i 0.242110π0.242110\pi
942942 12.8571 + 36.2662i 0.418905 + 1.18162i
943943 25.8009 14.8962i 0.840193 0.485085i
944944 −2.26464 −0.0737079
945945 −11.7632 + 15.8251i −0.382657 + 0.514791i
946946 56.3081 1.83073
947947 27.0334 15.6077i 0.878467 0.507183i 0.00831468 0.999965i 0.497353π-0.497353\pi
0.870153 + 0.492782i 0.164020π0.164020\pi
948948 −6.74043 19.0129i −0.218919 0.617511i
949949 18.7125 32.4109i 0.607432 1.05210i
950950 −15.0363 + 26.0436i −0.487841 + 0.844966i
951951 −30.6355 26.1463i −0.993423 0.847853i
952952 −3.26034 7.05133i −0.105668 0.228535i
953953 8.55869i 0.277243i −0.990345 0.138622i 0.955733π-0.955733\pi
0.990345 0.138622i 0.0442672π-0.0442672\pi
954954 44.7313 + 17.1343i 1.44823 + 0.554743i
955955 32.5865i 1.05447i
956956 −34.1278 + 19.7037i −1.10377 + 0.637263i
957957 6.54377 + 1.21041i 0.211530 + 0.0391270i
958958 61.2751 + 35.3772i 1.97971 + 1.14298i
959959 15.7761 22.3761i 0.509438 0.722563i
960960 −31.7821 5.87877i −1.02576 0.189737i
961961 −8.48973 14.7046i −0.273862 0.474343i
962962 2.78656 0.0898424
963963 9.32683 + 11.5009i 0.300553 + 0.370613i
964964 42.9669i 1.38387i
965965 −12.0996 20.9572i −0.389501 0.674635i
966966 29.2224 + 29.9088i 0.940215 + 0.962301i
967967 16.0280 27.7614i 0.515427 0.892745i −0.484413 0.874840i 0.660967π-0.660967\pi
0.999840 0.0179059i 0.00569994π-0.00569994\pi
968968 −1.24759 0.720299i −0.0400992 0.0231513i
969969 7.99766 2.83532i 0.256922 0.0910837i
970970 −5.08414 8.80598i −0.163242 0.282743i
971971 −33.2366 −1.06661 −0.533307 0.845922i 0.679051π-0.679051\pi
−0.533307 + 0.845922i 0.679051π0.679051\pi
972972 18.9002 45.8596i 0.606225 1.47095i
973973 −47.0345 4.26845i −1.50786 0.136840i
974974 −68.7469 + 39.6911i −2.20279 + 1.27178i
975975 −24.5933 + 8.71878i −0.787616 + 0.279225i
976976 −0.676137 0.390368i −0.0216426 0.0124954i
977977 45.1558 + 26.0707i 1.44466 + 0.834076i 0.998156 0.0607042i 0.0193346π-0.0193346\pi
0.446507 + 0.894780i 0.352668π0.352668\pi
978978 21.6695 + 18.4942i 0.692915 + 0.591379i
979979 38.3567 22.1453i 1.22589 0.707765i
980980 31.4248 + 5.75107i 1.00383 + 0.183711i
981981 −18.9633 + 15.3785i −0.605453 + 0.490999i
982982 59.6044 1.90205
983983 12.1192 + 20.9911i 0.386544 + 0.669513i 0.991982 0.126379i 0.0403356π-0.0403356\pi
−0.605438 + 0.795892i 0.707002π0.707002\pi
984984 −6.29987 + 34.0586i −0.200833 + 1.08575i
985985 −11.1099 6.41432i −0.353992 0.204377i
986986 −1.47529 + 2.55528i −0.0469829 + 0.0813768i
987987 −5.22271 + 18.6239i −0.166241 + 0.592806i
988988 −36.5614 63.3263i −1.16317 2.01468i
989989 30.6506i 0.974632i
990990 29.5893 + 11.3341i 0.940410 + 0.360222i
991991 −24.1981 −0.768678 −0.384339 0.923192i 0.625571π-0.625571\pi
−0.384339 + 0.923192i 0.625571π0.625571\pi
992992 11.0937 + 19.2148i 0.352224 + 0.610070i
993993 −21.5428 + 25.2416i −0.683641 + 0.801017i
994994 18.8204 + 13.2692i 0.596948 + 0.420874i
995995 −7.18607 4.14888i −0.227814 0.131528i
996996 −20.0819 56.6457i −0.636321 1.79489i
997997 −8.81920 + 5.09177i −0.279307 + 0.161258i −0.633110 0.774062i 0.718222π-0.718222\pi
0.353803 + 0.935320i 0.384888π0.384888\pi
998998 28.4053i 0.899155i
999999 1.06012 + 0.648085i 0.0335406 + 0.0205045i
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 63.2.o.a.41.2 yes 12
3.2 odd 2 189.2.o.a.125.6 12
4.3 odd 2 1008.2.cc.a.545.2 12
7.2 even 3 441.2.s.c.374.5 12
7.3 odd 6 441.2.i.c.68.1 12
7.4 even 3 441.2.i.c.68.2 12
7.5 odd 6 441.2.s.c.374.6 12
7.6 odd 2 inner 63.2.o.a.41.1 yes 12
9.2 odd 6 inner 63.2.o.a.20.1 12
9.4 even 3 567.2.c.c.566.2 12
9.5 odd 6 567.2.c.c.566.11 12
9.7 even 3 189.2.o.a.62.5 12
12.11 even 2 3024.2.cc.a.881.4 12
21.2 odd 6 1323.2.s.c.962.1 12
21.5 even 6 1323.2.s.c.962.2 12
21.11 odd 6 1323.2.i.c.1097.6 12
21.17 even 6 1323.2.i.c.1097.5 12
21.20 even 2 189.2.o.a.125.5 12
28.27 even 2 1008.2.cc.a.545.5 12
36.7 odd 6 3024.2.cc.a.2897.3 12
36.11 even 6 1008.2.cc.a.209.5 12
63.2 odd 6 441.2.i.c.227.5 12
63.11 odd 6 441.2.s.c.362.6 12
63.13 odd 6 567.2.c.c.566.1 12
63.16 even 3 1323.2.i.c.521.1 12
63.20 even 6 inner 63.2.o.a.20.2 yes 12
63.25 even 3 1323.2.s.c.656.2 12
63.34 odd 6 189.2.o.a.62.6 12
63.38 even 6 441.2.s.c.362.5 12
63.41 even 6 567.2.c.c.566.12 12
63.47 even 6 441.2.i.c.227.6 12
63.52 odd 6 1323.2.s.c.656.1 12
63.61 odd 6 1323.2.i.c.521.2 12
84.83 odd 2 3024.2.cc.a.881.3 12
252.83 odd 6 1008.2.cc.a.209.2 12
252.223 even 6 3024.2.cc.a.2897.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.o.a.20.1 12 9.2 odd 6 inner
63.2.o.a.20.2 yes 12 63.20 even 6 inner
63.2.o.a.41.1 yes 12 7.6 odd 2 inner
63.2.o.a.41.2 yes 12 1.1 even 1 trivial
189.2.o.a.62.5 12 9.7 even 3
189.2.o.a.62.6 12 63.34 odd 6
189.2.o.a.125.5 12 21.20 even 2
189.2.o.a.125.6 12 3.2 odd 2
441.2.i.c.68.1 12 7.3 odd 6
441.2.i.c.68.2 12 7.4 even 3
441.2.i.c.227.5 12 63.2 odd 6
441.2.i.c.227.6 12 63.47 even 6
441.2.s.c.362.5 12 63.38 even 6
441.2.s.c.362.6 12 63.11 odd 6
441.2.s.c.374.5 12 7.2 even 3
441.2.s.c.374.6 12 7.5 odd 6
567.2.c.c.566.1 12 63.13 odd 6
567.2.c.c.566.2 12 9.4 even 3
567.2.c.c.566.11 12 9.5 odd 6
567.2.c.c.566.12 12 63.41 even 6
1008.2.cc.a.209.2 12 252.83 odd 6
1008.2.cc.a.209.5 12 36.11 even 6
1008.2.cc.a.545.2 12 4.3 odd 2
1008.2.cc.a.545.5 12 28.27 even 2
1323.2.i.c.521.1 12 63.16 even 3
1323.2.i.c.521.2 12 63.61 odd 6
1323.2.i.c.1097.5 12 21.17 even 6
1323.2.i.c.1097.6 12 21.11 odd 6
1323.2.s.c.656.1 12 63.52 odd 6
1323.2.s.c.656.2 12 63.25 even 3
1323.2.s.c.962.1 12 21.2 odd 6
1323.2.s.c.962.2 12 21.5 even 6
3024.2.cc.a.881.3 12 84.83 odd 2
3024.2.cc.a.881.4 12 12.11 even 2
3024.2.cc.a.2897.3 12 36.7 odd 6
3024.2.cc.a.2897.4 12 252.223 even 6