LMFDB - Embedded newform 280.2.b.d.141.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(141,280)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("280.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.b (of order $2$, degree $1$, 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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.8272021826830336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 4x^{9} + 4x^{8} - 12x^{7} + 10x^{6} - 24x^{5} + 16x^{4} - 32x^{3} + 48x^{2} + 64 $ x^12 + 3x^10 - 4x^9 + 4x^8 - 12x^7 + 10x^6 - 24x^5 + 16x^4 - 32x^3 + 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			141.9
Root			$-0.722588 + 1.21568i$ of defining polynomial
Character	$\chi$	$=$	280.141
Dual form			280.2.b.d.141.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21568 - 0.722588i) q^{2} +1.52755i q^{3} +(0.955734 - 1.75686i) q^{4} +1.00000i q^{5} +(1.10379 + 1.85701i) q^{6} +1.00000 q^{7} +(-0.107626 - 2.82638i) q^{8} +0.666582 q^{9} +O(q^{10})$	\(q+(1.21568 - 0.722588i) q^{2} +1.52755i q^{3} +(0.955734 - 1.75686i) q^{4} +1.00000i q^{5} +(1.10379 + 1.85701i) q^{6} +1.00000 q^{7} +(-0.107626 - 2.82638i) q^{8} +0.666582 q^{9} +(0.722588 + 1.21568i) q^{10} +1.22377i q^{11} +(2.68370 + 1.45993i) q^{12} +1.21525i q^{13} +(1.21568 - 0.722588i) q^{14} -1.52755 q^{15} +(-2.17314 - 3.35819i) q^{16} +2.59497 q^{17} +(0.810347 - 0.481664i) q^{18} -0.616085i q^{19} +(1.75686 + 0.955734i) q^{20} +1.52755i q^{21} +(0.884280 + 1.48771i) q^{22} -8.36914 q^{23} +(4.31744 - 0.164405i) q^{24} -1.00000 q^{25} +(0.878126 + 1.47735i) q^{26} +5.60090i q^{27} +(0.955734 - 1.75686i) q^{28} -9.00634i q^{29} +(-1.85701 + 1.10379i) q^{30} -1.50644 q^{31} +(-5.06843 - 2.51218i) q^{32} -1.86937 q^{33} +(3.15464 - 1.87509i) q^{34} +1.00000i q^{35} +(0.637075 - 1.17109i) q^{36} -4.36914i q^{37} +(-0.445175 - 0.748959i) q^{38} -1.85636 q^{39} +(2.82638 - 0.107626i) q^{40} -4.58844 q^{41} +(1.10379 + 1.85701i) q^{42} -0.301914i q^{43} +(2.15000 + 1.16960i) q^{44} +0.666582i q^{45} +(-10.1742 + 6.04744i) q^{46} -10.6855 q^{47} +(5.12981 - 3.31959i) q^{48} +1.00000 q^{49} +(-1.21568 + 0.722588i) q^{50} +3.96395i q^{51} +(2.13503 + 1.16146i) q^{52} +4.62460i q^{53} +(4.04714 + 6.80887i) q^{54} -1.22377 q^{55} +(-0.107626 - 2.82638i) q^{56} +0.941102 q^{57} +(-6.50787 - 10.9488i) q^{58} -5.34775i q^{59} +(-1.45993 + 2.68370i) q^{60} -3.54867i q^{61} +(-1.83134 + 1.08853i) q^{62} +0.666582 q^{63} +(-7.97683 + 0.608384i) q^{64} -1.21525 q^{65} +(-2.27255 + 1.35079i) q^{66} +9.16229i q^{67} +(2.48010 - 4.55901i) q^{68} -12.7843i q^{69} +(0.722588 + 1.21568i) q^{70} +13.3881 q^{71} +(-0.0717416 - 1.88401i) q^{72} +15.3881 q^{73} +(-3.15709 - 5.31145i) q^{74} -1.52755i q^{75} +(-1.08238 - 0.588813i) q^{76} +1.22377i q^{77} +(-2.25673 + 1.34138i) q^{78} -6.69217 q^{79} +(3.35819 - 2.17314i) q^{80} -6.55592 q^{81} +(-5.57805 + 3.31555i) q^{82} +9.02746i q^{83} +(2.68370 + 1.45993i) q^{84} +2.59497i q^{85} +(-0.218160 - 0.367030i) q^{86} +13.7577 q^{87} +(3.45883 - 0.131709i) q^{88} -12.5124 q^{89} +(0.481664 + 0.810347i) q^{90} +1.21525i q^{91} +(-7.99867 + 14.7034i) q^{92} -2.30116i q^{93} +(-12.9901 + 7.72123i) q^{94} +0.616085 q^{95} +(3.83749 - 7.74229i) q^{96} +2.91526 q^{97} +(1.21568 - 0.722588i) q^{98} +0.815742i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9	$ 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9} + 16 q^{12} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{20} + 12 q^{22} + 8 q^{23} - 24 q^{24} - 12 q^{25} + 6 q^{28} + 12 q^{30} + 24 q^{31} - 2 q^{32} - 24 q^{33} - 20 q^{34} - 18 q^{36} + 12 q^{38} - 48 q^{39} + 12 q^{40} - 16 q^{41} + 16 q^{44} - 48 q^{46} - 16 q^{47} + 20 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{52} + 44 q^{54} - 8 q^{55} + 10 q^{56} + 40 q^{57} + 4 q^{58} - 8 q^{60} + 8 q^{62} - 20 q^{63} - 6 q^{64} + 8 q^{65} + 64 q^{66} - 56 q^{68} - 32 q^{71} - 46 q^{72} - 8 q^{73} - 32 q^{74} - 12 q^{76} - 24 q^{78} + 8 q^{80} + 60 q^{81} - 28 q^{82} + 16 q^{84} - 76 q^{86} + 48 q^{87} - 40 q^{88} - 48 q^{89} + 24 q^{90} + 12 q^{94} + 28 q^{96} + 32 q^{97} - 2 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9 + 16 * q^12 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^20 + 12 * q^22 + 8 * q^23 - 24 * q^24 - 12 * q^25 + 6 * q^28 + 12 * q^30 + 24 * q^31 - 2 * q^32 - 24 * q^33 - 20 * q^34 - 18 * q^36 + 12 * q^38 - 48 * q^39 + 12 * q^40 - 16 * q^41 + 16 * q^44 - 48 * q^46 - 16 * q^47 + 20 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^52 + 44 * q^54 - 8 * q^55 + 10 * q^56 + 40 * q^57 + 4 * q^58 - 8 * q^60 + 8 * q^62 - 20 * q^63 - 6 * q^64 + 8 * q^65 + 64 * q^66 - 56 * q^68 - 32 * q^71 - 46 * q^72 - 8 * q^73 - 32 * q^74 - 12 * q^76 - 24 * q^78 + 8 * q^80 + 60 * q^81 - 28 * q^82 + 16 * q^84 - 76 * q^86 + 48 * q^87 - 40 * q^88 - 48 * q^89 + 24 * q^90 + 12 * q^94 + 28 * q^96 + 32 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.21568	−	0.722588i	0.859612	−	0.510947i
$2$	1.21568	−	0.722588i	0.859612	−	0.510947i
$3$			1.52755i			0.881933i	0.897524	+	0.440967i	$0.145364\pi$
$3$			1.52755i			0.881933i	−0.897524	+	0.440967i	$0.854636\pi$
$4$	0.955734	−	1.75686i	0.477867	−	0.878432i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	1.10379	+	1.85701i	0.450621	+	0.758121i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−0.107626	−	2.82638i	−0.0380516	−	0.999276i
$9$	0.666582			0.222194
$10$	0.722588	+	1.21568i	0.228502	+	0.384430i
$11$			1.22377i			0.368980i	0.982834	+	0.184490i	$0.0590634\pi$
$11$			1.22377i			0.368980i	−0.982834	+	0.184490i	$0.940937\pi$
$12$	2.68370	+	1.45993i	0.774718	+	0.421447i
$13$			1.21525i			0.337050i	0.985697	+	0.168525i	$0.0539004\pi$
$13$			1.21525i			0.337050i	−0.985697	+	0.168525i	$0.946100\pi$
$14$	1.21568	−	0.722588i	0.324903	−	0.193120i
$15$	−1.52755			−0.394412
$16$	−2.17314	−	3.35819i	−0.543286	−	0.839548i
$17$	2.59497			0.629372			0.314686	−	0.949196i	$-0.398101\pi$
$17$	2.59497			0.629372			0.314686	+	0.949196i	$0.398101\pi$
$18$	0.810347	−	0.481664i	0.191001	−	0.113529i
$19$		−	0.616085i		−	0.141340i	−0.997500	−	0.0706698i	$-0.977486\pi$
$19$		−	0.616085i		−	0.141340i	0.997500	−	0.0706698i	$-0.0225137\pi$
$20$	1.75686	+	0.955734i	0.392847	+	0.213709i
$21$			1.52755i			0.333339i
$22$	0.884280	+	1.48771i	0.188529	+	0.317180i
$23$	−8.36914			−1.74509			−0.872543	−	0.488537i	$-0.837531\pi$
$23$	−8.36914			−1.74509			−0.872543	+	0.488537i	$0.837531\pi$
$24$	4.31744	−	0.164405i	0.881294	−	0.0335589i
$25$	−1.00000			−0.200000
$26$	0.878126	+	1.47735i	0.172215	+	0.289733i
$27$			5.60090i			1.07789i
$28$	0.955734	−	1.75686i	0.180617	−	0.332016i
$29$		−	9.00634i		−	1.67244i	−0.548398	−	0.836218i	$-0.684762\pi$
$29$		−	9.00634i		−	1.67244i	0.548398	−	0.836218i	$-0.315238\pi$
$30$	−1.85701	+	1.10379i	−0.339042	+	0.201524i
$31$	−1.50644			−0.270564			−0.135282	−	0.990807i	$-0.543194\pi$
$31$	−1.50644			−0.270564			−0.135282	+	0.990807i	$0.543194\pi$
$32$	−5.06843	−	2.51218i	−0.895980	−	0.444095i
$33$	−1.86937			−0.325416
$34$	3.15464	−	1.87509i	0.541016	−	0.321576i
$35$			1.00000i			0.169031i
$36$	0.637075	−	1.17109i	0.106179	−	0.195182i
$37$		−	4.36914i		−	0.718282i	−0.933283	−	0.359141i	$-0.883070\pi$
$37$		−	4.36914i		−	0.718282i	0.933283	−	0.359141i	$-0.116930\pi$
$38$	−0.445175	−	0.748959i	−0.0722170	−	0.121497i
$39$	−1.85636			−0.297256
$40$	2.82638	−	0.107626i	0.446890	−	0.0170172i
$41$	−4.58844			−0.716593			−0.358297	−	0.933608i	$-0.616642\pi$
$41$	−4.58844			−0.716593			−0.358297	+	0.933608i	$0.616642\pi$
$42$	1.10379	+	1.85701i	0.170319	+	0.286543i
$43$		−	0.301914i		−	0.0460415i	−0.999735	−	0.0230208i	$-0.992672\pi$
$43$		−	0.301914i		−	0.0460415i	0.999735	−	0.0230208i	$-0.00732838\pi$
$44$	2.15000	+	1.16960i	0.324124	+	0.176323i
$45$			0.666582i			0.0993681i
$46$	−10.1742	+	6.04744i	−1.50010	+	0.891646i
$47$	−10.6855			−1.55864			−0.779322	−	0.626624i	$-0.784436\pi$
$47$	−10.6855			−1.55864			−0.779322	+	0.626624i	$0.784436\pi$
$48$	5.12981	−	3.31959i	0.740425	−	0.479142i
$49$	1.00000			0.142857
$50$	−1.21568	+	0.722588i	−0.171922	+	0.102189i
$51$			3.96395i			0.555064i
$52$	2.13503	+	1.16146i	0.296076	+	0.161065i
$53$			4.62460i			0.635238i	0.948218	+	0.317619i	$0.102883\pi$
$53$			4.62460i			0.635238i	−0.948218	+	0.317619i	$0.897117\pi$
$54$	4.04714	+	6.80887i	0.550746	+	0.926570i
$55$	−1.22377			−0.165013
$56$	−0.107626	−	2.82638i	−0.0143821	−	0.377691i
$57$	0.941102			0.124652
$58$	−6.50787	−	10.9488i	−0.854525	−	1.43765i
$59$		−	5.34775i		−	0.696218i	−0.937454	−	0.348109i	$-0.886824\pi$
$59$		−	5.34775i		−	0.696218i	0.937454	−	0.348109i	$-0.113176\pi$
$60$	−1.45993	+	2.68370i	−0.188477	+	0.346465i
$61$		−	3.54867i		−	0.454361i	−0.973853	−	0.227180i	$-0.927049\pi$
$61$		−	3.54867i		−	0.454361i	0.973853	−	0.227180i	$-0.0729507\pi$
$62$	−1.83134	+	1.08853i	−0.232580	+	0.138244i
$63$	0.666582			0.0839814
$64$	−7.97683	+	0.608384i	−0.997104	+	0.0760480i
$65$	−1.21525			−0.150733
$66$	−2.27255	+	1.35079i	−0.279732	+	0.166270i
$67$			9.16229i			1.11935i	0.828712	+	0.559676i	$0.189074\pi$
$67$			9.16229i			1.11935i	−0.828712	+	0.559676i	$0.810926\pi$
$68$	2.48010	−	4.55901i	0.300756	−	0.552861i
$69$		−	12.7843i		−	1.53905i
$70$	0.722588	+	1.21568i	0.0863657	+	0.145301i
$71$	13.3881			1.58887			0.794436	−	0.607347i	$-0.207766\pi$
$71$	13.3881			1.58887			0.794436	+	0.607347i	$0.207766\pi$
$72$	−0.0717416	−	1.88401i	−0.00845482	−	0.222033i
$73$	15.3881			1.80104			0.900519	−	0.434816i	$-0.143187\pi$
$73$	15.3881			1.80104			0.900519	+	0.434816i	$0.143187\pi$
$74$	−3.15709	−	5.31145i	−0.367004	−	0.617444i
$75$		−	1.52755i		−	0.176387i
$76$	−1.08238	−	0.588813i	−0.124157	−	0.0675415i
$77$			1.22377i			0.139461i
$78$	−2.25673	+	1.34138i	−0.255525	+	0.151882i
$79$	−6.69217			−0.752928			−0.376464	−	0.926431i	$-0.622860\pi$
$79$	−6.69217			−0.752928			−0.376464	+	0.926431i	$0.622860\pi$
$80$	3.35819	−	2.17314i	0.375457	−	0.242965i
$81$	−6.55592			−0.728436
$82$	−5.57805	+	3.31555i	−0.615993	+	0.366141i
$83$			9.02746i			0.990892i	0.868639	+	0.495446i	$0.164995\pi$
$83$			9.02746i			0.990892i	−0.868639	+	0.495446i	$0.835005\pi$
$84$	2.68370	+	1.45993i	0.292816	+	0.159292i
$85$			2.59497i			0.281464i
$86$	−0.218160	−	0.367030i	−0.0235248	−	0.0395779i
$87$	13.7577			1.47498
$88$	3.45883	−	0.131709i	0.368713	−	0.0140403i
$89$	−12.5124			−1.32631			−0.663154	−	0.748483i	$-0.730783\pi$
$89$	−12.5124			−1.32631			−0.663154	+	0.748483i	$0.730783\pi$
$90$	0.481664	+	0.810347i	0.0507718	+	0.0854181i
$91$			1.21525i			0.127393i
$92$	−7.99867	+	14.7034i	−0.833919	+	1.53294i
$93$		−	2.30116i		−	0.238619i
$94$	−12.9901	+	7.72123i	−1.33983	+	0.796384i
$95$	0.616085			0.0632090
$96$	3.83749	−	7.74229i	0.391662	−	0.790194i
$97$	2.91526			0.296000			0.148000	−	0.988987i	$-0.452716\pi$
$97$	2.91526			0.296000			0.148000	+	0.988987i	$0.452716\pi$
$98$	1.21568	−	0.722588i	0.122802	−	0.0729924i
$99$			0.815742i			0.0819852i
$100$	−0.955734	+	1.75686i	−0.0955734	+	0.175686i
$101$			12.0587i			1.19989i	0.800043	+	0.599943i	$0.204810\pi$
$101$			12.0587i			1.19989i	−0.800043	+	0.599943i	$0.795190\pi$
$102$	2.86430	+	4.81888i	0.283608	+	0.477140i
$103$	1.23059			0.121254			0.0606269	−	0.998160i	$-0.480690\pi$
$103$	1.23059			0.121254			0.0606269	+	0.998160i	$0.480690\pi$
$104$	3.43476	−	0.130793i	0.336806	−	0.0128253i
$105$	−1.52755			−0.149074
$106$	3.34168	+	5.62202i	0.324573	+	0.546058i
$107$			10.9852i			1.06198i	0.847378	+	0.530991i	$0.178180\pi$
$107$			10.9852i			1.06198i	−0.847378	+	0.530991i	$0.821820\pi$
$108$	9.84002	+	5.35297i	0.946856	+	0.515090i
$109$		−	11.1496i		−	1.06793i	−0.845505	−	0.533967i	$-0.820700\pi$
$109$		−	11.1496i		−	1.06793i	0.845505	−	0.533967i	$-0.179300\pi$
$110$	−1.48771	+	0.884280i	−0.141847	+	0.0843128i
$111$	6.67409			0.633477
$112$	−2.17314	−	3.35819i	−0.205343	−	0.317319i
$113$	15.7046			1.47736			0.738681	−	0.674055i	$-0.235449\pi$
$113$	15.7046			1.47736			0.738681	+	0.674055i	$0.235449\pi$
$114$	1.14408	−	0.680029i	0.107152	−	0.0636906i
$115$		−	8.36914i		−	0.780426i
$116$	−15.8229	−	8.60767i	−1.46912	−	0.799202i
$117$			0.810065i			0.0748905i
$118$	−3.86422	−	6.50113i	−0.355730	−	0.598477i
$119$	2.59497			0.237880
$120$	0.164405	+	4.31744i	0.0150080	+	0.394127i
$121$	9.50239			0.863854
$122$	−2.56423	−	4.31403i	−0.232154	−	0.390574i
$123$		−	7.00908i		−	0.631987i
$124$	−1.43975	+	2.64660i	−0.129294	+	0.237672i
$125$		−	1.00000i		−	0.0894427i
$126$	0.810347	−	0.481664i	0.0721915	−	0.0429100i
$127$	8.55227			0.758891			0.379446	−	0.925214i	$-0.376115\pi$
$127$	8.55227			0.758891			0.379446	+	0.925214i	$0.376115\pi$
$128$	−9.25763	+	6.50356i	−0.818267	+	0.574839i
$129$	0.461190			0.0406055
$130$	−1.47735	+	0.878126i	−0.129572	+	0.0770168i
$131$		−	10.9491i		−	0.956624i	−0.878190	−	0.478312i	$-0.841249\pi$
$131$		−	10.9491i		−	0.956624i	0.878190	−	0.478312i	$-0.158751\pi$
$132$	−1.78662	+	3.28423i	−0.155506	+	0.285856i
$133$		−	0.616085i		−	0.0534213i
$134$	6.62056	+	11.1384i	0.571929	+	0.962208i
$135$	−5.60090			−0.482049
$136$	−0.279286	−	7.33436i	−0.0239486	−	0.628916i
$137$	−12.9668			−1.10783			−0.553916	−	0.832572i	$-0.686867\pi$
$137$	−12.9668			−1.10783			−0.553916	+	0.832572i	$0.686867\pi$
$138$	−9.23778	−	15.5416i	−0.786372	−	1.32299i
$139$		−	10.5377i		−	0.893795i	−0.894585	−	0.446897i	$-0.852529\pi$
$139$		−	10.5377i		−	0.893795i	0.894585	−	0.446897i	$-0.147471\pi$
$140$	1.75686	+	0.955734i	0.148482	+	0.0807743i
$141$		−	16.3227i		−	1.37462i
$142$	16.2756	−	9.67406i	1.36581	−	0.811829i
$143$	−1.48719			−0.124365
$144$	−1.44858	−	2.23851i	−0.120715	−	0.186542i
$145$	9.00634			0.747936
$146$	18.7069	−	11.1192i	1.54819	−	0.920235i
$147$			1.52755i			0.125990i
$148$	−7.67598	−	4.17573i	−0.630962	−	0.343243i
$149$			4.27806i			0.350472i	0.984526	+	0.175236i	$0.0560689\pi$
$149$			4.27806i			0.350472i	−0.984526	+	0.175236i	$0.943931\pi$
$150$	−1.10379	−	1.85701i	−0.0901242	−	0.151624i
$151$	18.3166			1.49058			0.745291	−	0.666739i	$-0.232311\pi$
$151$	18.3166			1.49058			0.745291	+	0.666739i	$0.232311\pi$
$152$	−1.74129	+	0.0663068i	−0.141237	+	0.00537819i
$153$	1.72976			0.139843
$154$	0.884280	+	1.48771i	0.0712573	+	0.119883i
$155$		−	1.50644i		−	0.121000i
$156$	−1.77419	+	3.26138i	−0.142049	+	0.261119i
$157$		−	6.32577i		−	0.504852i	−0.967616	−	0.252426i	$-0.918772\pi$
$157$		−	6.32577i		−	0.504852i	0.967616	−	0.252426i	$-0.0812283\pi$
$158$	−8.13551	+	4.83568i	−0.647226	+	0.384706i
$159$	−7.06432			−0.560237
$160$	2.51218	−	5.06843i	0.198605	−	0.400694i
$161$	−8.36914			−0.659580
$162$	−7.96988	+	4.73723i	−0.626173	+	0.372192i
$163$		−	2.52500i		−	0.197774i	−0.995099	−	0.0988868i	$-0.968472\pi$
$163$		−	2.52500i		−	0.197774i	0.995099	−	0.0988868i	$-0.0315282\pi$
$164$	−4.38532	+	8.06126i	−0.342436	+	0.629479i
$165$		−	1.86937i		−	0.145530i
$166$	6.52313	+	10.9745i	0.506293	+	0.851783i
$167$	−5.19991			−0.402381			−0.201191	−	0.979552i	$-0.564481\pi$
$167$	−5.19991			−0.402381			−0.201191	+	0.979552i	$0.564481\pi$
$168$	4.31744	−	0.164405i	0.333098	−	0.0126841i
$169$	11.5232			0.886397
$170$	1.87509	+	3.15464i	0.143813	+	0.241950i
$171$		−	0.410671i		−	0.0314048i
$172$	−0.530423	−	0.288550i	−0.0404444	−	0.0220017i
$173$			22.4890i			1.70981i	0.518787	+	0.854903i	$0.326384\pi$
$173$			22.4890i			1.70981i	−0.518787	+	0.854903i	$0.673616\pi$
$174$	16.7249	−	9.94112i	1.26791	−	0.753634i
$175$	−1.00000			−0.0755929
$176$	4.10965	−	2.65943i	0.309776	−	0.200462i
$177$	8.16897			0.614017
$178$	−15.2110	+	9.04128i	−1.14011	+	0.677673i
$179$		−	18.5336i		−	1.38526i	−0.721291	−	0.692632i	$-0.756451\pi$
$179$		−	18.5336i		−	1.38526i	0.721291	−	0.692632i	$-0.243549\pi$
$180$	1.17109	+	0.637075i	0.0872882	+	0.0474848i
$181$			6.92786i			0.514944i	0.966286	+	0.257472i	$0.0828895\pi$
$181$			6.92786i			0.514944i	−0.966286	+	0.257472i	$0.917111\pi$
$182$	0.878126	+	1.47735i	0.0650910	+	0.109509i
$183$	5.42078			0.400716
$184$	0.900737	+	23.6544i	0.0664032	+	1.74382i
$185$	4.36914			0.321225
$186$	−1.66279	−	2.79746i	−0.121922	−	0.205120i
$187$			3.17564i			0.232226i
$188$	−10.2125	+	18.7730i	−0.744824	+	1.36916i
$189$			5.60090i			0.407405i
$190$	0.748959	−	0.445175i	0.0543352	−	0.0322964i
$191$	−2.49777			−0.180732			−0.0903660	−	0.995909i	$-0.528804\pi$
$191$	−2.49777			−0.180732			−0.0903660	+	0.995909i	$0.528804\pi$
$192$	−0.929339	−	12.1850i	−0.0670692	−	0.879379i
$193$	7.13085			0.513290			0.256645	−	0.966506i	$-0.417383\pi$
$193$	7.13085			0.513290			0.256645	+	0.966506i	$0.417383\pi$
$194$	3.54401	−	2.10653i	0.254445	−	0.151240i
$195$		−	1.85636i		−	0.132937i
$196$	0.955734	−	1.75686i	0.0682667	−	0.125490i
$197$			9.55907i			0.681056i	0.940234	+	0.340528i	$0.110606\pi$
$197$			9.55907i			0.681056i	−0.940234	+	0.340528i	$0.889394\pi$
$198$	0.589445	+	0.991678i	0.0418900	+	0.0704755i
$199$	−1.51023			−0.107057			−0.0535286	−	0.998566i	$-0.517047\pi$
$199$	−1.51023			−0.107057			−0.0535286	+	0.998566i	$0.517047\pi$
$200$	0.107626	+	2.82638i	0.00761031	+	0.199855i
$201$	−13.9959			−0.987193
$202$	8.71347	+	14.6595i	0.613078	+	1.03144i
$203$		−	9.00634i		−	0.632121i
$204$	6.96412	+	3.78848i	0.487586	+	0.265247i
$205$		−	4.58844i		−	0.320470i
$206$	1.49600	−	0.889211i	0.104231	−	0.0619543i
$207$	−5.57871			−0.387747
$208$	4.08105	−	2.64092i	0.282970	−	0.183115i
$209$	0.753946			0.0521515
$210$	−1.85701	+	1.10379i	−0.128146	+	0.0761688i
$211$			3.63666i			0.250358i	0.992134	+	0.125179i	$0.0399505\pi$
$211$			3.63666i			0.250358i	−0.992134	+	0.125179i	$0.960050\pi$
$212$	8.12480	+	4.41989i	0.558013	+	0.303559i
$213$			20.4510i			1.40128i
$214$	7.93779	+	13.3545i	0.542616	+	0.912893i
$215$	0.301914			0.0205904
$216$	15.8303	−	0.602803i	1.07711	−	0.0410155i
$217$	−1.50644			−0.102264
$218$	−8.05654	−	13.5543i	−0.545658	−	0.918010i
$219$			23.5061i			1.58840i
$220$	−1.16960	+	2.15000i	−0.0788543	+	0.144953i
$221$			3.15354i			0.212130i
$222$	8.11353	−	4.82262i	0.544544	−	0.323673i
$223$	−11.1788			−0.748585			−0.374292	−	0.927311i	$-0.622114\pi$
$223$	−11.1788			−0.748585			−0.374292	+	0.927311i	$0.622114\pi$
$224$	−5.06843	−	2.51218i	−0.338648	−	0.167852i
$225$	−0.666582			−0.0444388
$226$	19.0917	−	11.3479i	1.26996	−	0.754853i
$227$		−	28.6749i		−	1.90322i	−0.307311	−	0.951609i	$-0.599429\pi$
$227$		−	28.6749i		−	1.90322i	0.307311	−	0.951609i	$-0.400571\pi$
$228$	0.899444	−	1.65339i	0.0595671	−	0.109498i
$229$			25.7972i			1.70473i	0.522951	+	0.852363i	$0.324831\pi$
$229$			25.7972i			1.70473i	−0.522951	+	0.852363i	$0.675169\pi$
$230$	−6.04744	−	10.1742i	−0.398756	−	0.670864i
$231$	−1.86937			−0.122996
$232$	−25.4553	+	0.969317i	−1.67122	+	0.0636388i
$233$	1.67971			0.110041			0.0550207	−	0.998485i	$-0.482478\pi$
$233$	1.67971			0.110041			0.0550207	+	0.998485i	$0.482478\pi$
$234$	0.585343	+	0.984776i	0.0382651	+	0.0643768i
$235$		−	10.6855i		−	0.697047i
$236$	−9.39527	−	5.11103i	−0.611580	−	0.332699i
$237$		−	10.2226i		−	0.664032i
$238$	3.15464	−	1.87509i	0.204485	−	0.121544i
$239$	7.35061			0.475471			0.237736	−	0.971330i	$-0.423595\pi$
$239$	7.35061			0.475471			0.237736	+	0.971330i	$0.423595\pi$
$240$	3.31959	+	5.12981i	0.214279	+	0.331128i
$241$	−9.47954			−0.610631			−0.305315	−	0.952251i	$-0.598762\pi$
$241$	−9.47954			−0.610631			−0.305315	+	0.952251i	$0.598762\pi$
$242$	11.5518	−	6.86631i	0.742579	−	0.441383i
$243$			6.78817i			0.435462i
$244$	−6.23453	−	3.39159i	−0.399125	−	0.217124i
$245$			1.00000i			0.0638877i
$246$	−5.06467	−	8.52077i	−0.322912	−	0.543264i
$247$	0.748699			0.0476385
$248$	0.162132	+	4.25776i	0.0102954	+	0.270368i
$249$	−13.7899			−0.873901
$250$	−0.722588	−	1.21568i	−0.0457005	−	0.0768861i
$251$			26.4286i			1.66816i	0.551645	+	0.834079i	$0.314000\pi$
$251$			26.4286i			1.66816i	−0.551645	+	0.834079i	$0.686000\pi$
$252$	0.637075	−	1.17109i	0.0401319	−	0.0737720i
$253$		−	10.2419i		−	0.643902i
$254$	10.3968	−	6.17977i	0.652352	−	0.387753i
$255$	−3.96395			−0.248232
$256$	−6.55488	+	14.5957i	−0.409680	+	0.912229i
$257$	−30.0639			−1.87533			−0.937666	−	0.347538i	$-0.887018\pi$
$257$	−30.0639			−1.87533			−0.937666	+	0.347538i	$0.887018\pi$
$258$	0.560658	−	0.333250i	0.0349050	−	0.0207473i
$259$		−	4.36914i		−	0.271485i
$260$	−1.16146	+	2.13503i	−0.0720306	+	0.132409i
$261$		−	6.00346i		−	0.371605i
$262$	−7.91165	−	13.3105i	−0.488784	−	0.822326i
$263$	−10.0971			−0.622617			−0.311308	−	0.950309i	$-0.600767\pi$
$263$	−10.0971			−0.622617			−0.311308	+	0.950309i	$0.600767\pi$
$264$	0.201193	+	5.28355i	0.0123826	+	0.325180i
$265$	−4.62460			−0.284087
$266$	−0.445175	−	0.748959i	−0.0272955	−	0.0459216i
$267$		−	19.1133i		−	1.16972i
$268$	16.0969	+	8.75671i	0.983274	+	0.534901i
$269$		−	3.89504i		−	0.237484i	−0.992925	−	0.118742i	$-0.962114\pi$
$269$		−	3.89504i		−	0.237484i	0.992925	−	0.118742i	$-0.0378862\pi$
$270$	−6.80887	+	4.04714i	−0.414375	+	0.246301i
$271$	4.59538			0.279149			0.139575	−	0.990212i	$-0.455426\pi$
$271$	4.59538			0.279149			0.139575	+	0.990212i	$0.455426\pi$
$272$	−5.63924	−	8.71439i	−0.341929	−	0.528388i
$273$	−1.85636			−0.112352
$274$	−15.7635	+	9.36968i	−0.952306	+	0.566043i
$275$		−	1.22377i		−	0.0737960i
$276$	−22.4603	−	12.2184i	−1.35195	−	0.735461i
$277$			23.8524i			1.43315i	0.697509	+	0.716576i	$0.254292\pi$
$277$			23.8524i			1.43315i	−0.697509	+	0.716576i	$0.745708\pi$
$278$	−7.61440	−	12.8104i	−0.456681	−	0.768317i
$279$	−1.00416			−0.0601176
$280$	2.82638	−	0.107626i	0.168908	−	0.00643189i
$281$	−18.5743			−1.10805			−0.554026	−	0.832499i	$-0.686909\pi$
$281$	−18.5743			−1.10805			−0.554026	+	0.832499i	$0.686909\pi$
$282$	−11.7946	−	19.8431i	−0.702357	−	1.18164i
$283$		−	26.2412i		−	1.55988i	−0.625855	−	0.779939i	$-0.715250\pi$
$283$		−	26.2412i		−	1.55988i	0.625855	−	0.779939i	$-0.284750\pi$
$284$	12.7954	−	23.5210i	0.759270	−	1.39572i
$285$			0.941102i			0.0557461i
$286$	−1.80794	+	1.07462i	−0.106906	+	0.0635438i
$287$	−4.58844			−0.270847
$288$	−3.37852	−	1.67457i	−0.199081	−	0.0986753i
$289$	−10.2661			−0.603891
$290$	10.9488	−	6.50787i	0.642935	−	0.382155i
$291$			4.45321i			0.261052i
$292$	14.7069	−	27.0348i	0.860657	−	1.58209i
$293$			32.6791i			1.90913i	0.297995	+	0.954567i	$0.403682\pi$
$293$			32.6791i			1.90913i	−0.297995	+	0.954567i	$0.596318\pi$
$294$	1.10379	+	1.85701i	0.0643744	+	0.108303i
$295$	5.34775			0.311358
$296$	−12.3488	+	0.470233i	−0.717762	+	0.0273317i
$297$	−6.85421			−0.397721
$298$	3.09127	+	5.20073i	0.179073	+	0.301270i
$299$		−	10.1706i		−	0.588182i
$300$	−2.68370	−	1.45993i	−0.154944	−	0.0842894i
$301$		−	0.301914i		−	0.0174021i
$302$	22.2670	−	13.2353i	1.28132	−	0.761608i
$303$	−18.4203			−1.05822
$304$	−2.06893	+	1.33884i	−0.118661	+	0.0767878i
$305$	3.54867			0.203196
$306$	2.10282	−	1.24990i	0.120210	−	0.0714521i
$307$			14.6454i			0.835857i	0.908480	+	0.417928i	$0.137244\pi$
$307$			14.6454i			0.835857i	−0.908480	+	0.417928i	$0.862756\pi$
$308$	2.15000	+	1.16960i	0.122507	+	0.0666440i
$309$			1.87979i			0.106938i
$310$	−1.08853	−	1.83134i	−0.0618245	−	0.104013i
$311$	−7.95771			−0.451240			−0.225620	−	0.974215i	$-0.572441\pi$
$311$	−7.95771			−0.451240			−0.225620	+	0.974215i	$0.572441\pi$
$312$	0.199793	+	5.24678i	0.0113110	+	0.297041i
$313$	22.7593			1.28643			0.643215	−	0.765685i	$-0.277600\pi$
$313$	22.7593			1.28643			0.643215	+	0.765685i	$0.277600\pi$
$314$	−4.57092	−	7.69009i	−0.257952	−	0.433977i
$315$			0.666582i			0.0375576i
$316$	−6.39593	+	11.7572i	−0.359799	+	0.661396i
$317$		−	24.6960i		−	1.38707i	−0.720424	−	0.693534i	$-0.756053\pi$
$317$		−	24.6960i		−	1.38707i	0.720424	−	0.693534i	$-0.243947\pi$
$318$	−8.58793	+	5.10459i	−0.481587	+	0.286251i
$319$	11.0217			0.617096
$320$	−0.608384	−	7.97683i	−0.0340097	−	0.445919i
$321$	−16.7805			−0.936597
$322$	−10.1742	+	6.04744i	−0.566984	+	0.337010i
$323$		−	1.59872i		−	0.0889552i
$324$	−6.26572	+	11.5179i	−0.348096	+	0.639882i
$325$		−	1.21525i		−	0.0674101i
$326$	−1.82454	−	3.06959i	−0.101052	−	0.170009i
$327$	17.0316			0.941847
$328$	0.493835	+	12.9687i	0.0272675	+	0.716074i
$329$	−10.6855			−0.589112
$330$	−1.35079	−	2.27255i	−0.0743583	−	0.125100i
$331$			21.9090i			1.20423i	0.798411	+	0.602113i	$0.205674\pi$
$331$			21.9090i			1.20423i	−0.798411	+	0.602113i	$0.794326\pi$
$332$	15.8600	+	8.62785i	0.870432	+	0.473515i
$333$		−	2.91239i		−	0.159598i
$334$	−6.32141	+	3.75739i	−0.345892	+	0.205595i
$335$	−9.16229			−0.500589
$336$	5.12981	−	3.31959i	0.279854	−	0.181099i
$337$	−8.11255			−0.441919			−0.220959	−	0.975283i	$-0.570919\pi$
$337$	−8.11255			−0.441919			−0.220959	+	0.975283i	$0.570919\pi$
$338$	14.0084	−	8.32650i	0.761958	−	0.452902i
$339$			23.9896i			1.30293i
$340$	4.55901	+	2.48010i	0.247247	+	0.134502i
$341$		−	1.84353i		−	0.0998327i
$342$	−0.296746	−	0.499243i	−0.0160462	−	0.0269959i
$343$	1.00000			0.0539949
$344$	−0.853325	+	0.0324939i	−0.0460082	+	0.00175195i
$345$	12.7843			0.688284
$346$	16.2503	+	27.3393i	0.873620	+	1.46977i
$347$		−	16.4019i		−	0.880502i	−0.897875	−	0.440251i	$-0.854889\pi$
$347$		−	16.4019i		−	0.880502i	0.897875	−	0.440251i	$-0.145111\pi$
$348$	13.1487	−	24.1703i	0.704842	−	1.29567i
$349$		−	6.10529i		−	0.326809i	−0.986559	−	0.163404i	$-0.947752\pi$
$349$		−	6.10529i		−	0.326809i	0.986559	−	0.163404i	$-0.0522476\pi$
$350$	−1.21568	+	0.722588i	−0.0649806	+	0.0386239i
$351$	−6.80650			−0.363304
$352$	3.07433	−	6.20258i	0.163862	−	0.330599i
$353$	−32.8495			−1.74840			−0.874202	−	0.485562i	$-0.838615\pi$
$353$	−32.8495			−1.74840			−0.874202	+	0.485562i	$0.838615\pi$
$354$	9.93082	−	5.90280i	0.527817	−	0.313730i
$355$			13.3881i			0.710565i
$356$	−11.9585	+	21.9825i	−0.633799	+	1.16507i
$357$			3.96395i			0.209795i
$358$	−13.3921	−	22.5308i	−0.707796	−	1.19079i
$359$	5.79226			0.305704			0.152852	−	0.988249i	$-0.451154\pi$
$359$	5.79226			0.305704			0.152852	+	0.988249i	$0.451154\pi$
$360$	1.88401	−	0.0717416i	0.0992962	−	0.00378111i
$361$	18.6204			0.980023
$362$	5.00599	+	8.42203i	0.263109	+	0.442652i
$363$			14.5154i			0.761861i
$364$	2.13503	+	1.16146i	0.111906	+	0.0608769i
$365$			15.3881i			0.805449i
$366$	6.58991	−	3.91699i	0.344460	−	0.204744i
$367$	34.3223			1.79161			0.895806	−	0.444446i	$-0.146599\pi$
$367$	34.3223			1.79161			0.895806	+	0.444446i	$0.146599\pi$
$368$	18.1873	+	28.1052i	0.948081	+	1.46508i
$369$	−3.05857			−0.159223
$370$	5.31145	−	3.15709i	0.276129	−	0.164129i
$371$			4.62460i			0.240097i
$372$	−4.04283	−	2.19930i	−0.209611	−	0.114028i
$373$		−	25.7019i		−	1.33079i	−0.746489	−	0.665397i	$-0.768262\pi$
$373$		−	25.7019i		−	1.33079i	0.746489	−	0.665397i	$-0.231738\pi$
$374$	2.29468	+	3.86055i	0.118655	+	0.199624i
$375$	1.52755			0.0788825
$376$	1.15004	+	30.2013i	0.0593088	+	1.55751i
$377$	10.9450			0.563695
$378$	4.04714	+	6.80887i	0.208162	+	0.350211i
$379$			21.1070i			1.08419i	0.840316	+	0.542097i	$0.182369\pi$
$379$			21.1070i			1.08419i	−0.840316	+	0.542097i	$0.817631\pi$
$380$	0.588813	−	1.08238i	0.0302055	−	0.0555248i
$381$			13.0640i			0.669291i
$382$	−3.03647	+	1.80485i	−0.155359	+	0.0923444i
$383$	16.1690			0.826196			0.413098	−	0.910687i	$-0.364447\pi$
$383$	16.1690			0.826196			0.413098	+	0.910687i	$0.364447\pi$
$384$	−9.93453	−	14.1415i	−0.506969	−	0.721656i
$385$	−1.22377			−0.0623690
$386$	8.66880	−	5.15266i	0.441230	−	0.262264i
$387$		−	0.201251i		−	0.0102301i
$388$	2.78621	−	5.12172i	0.141449	−	0.260016i
$389$			15.6258i			0.792258i	0.918195	+	0.396129i	$0.129647\pi$
$389$			15.6258i			0.792258i	−0.918195	+	0.396129i	$0.870353\pi$
$390$	−1.34138	−	2.25673i	−0.0679236	−	0.114274i
$391$	−21.7176			−1.09831
$392$	−0.107626	−	2.82638i	−0.00543594	−	0.142754i
$393$	16.7253			0.843678
$394$	6.90727	+	11.6207i	0.347983	+	0.585444i
$395$		−	6.69217i		−	0.336720i
$396$	1.43315	+	0.779632i	0.0720184	+	0.0391780i
$397$		−	25.6663i		−	1.28815i	−0.764961	−	0.644076i	$-0.777242\pi$
$397$		−	25.6663i		−	1.28815i	0.764961	−	0.644076i	$-0.222758\pi$
$398$	−1.83595	+	1.09127i	−0.0920277	+	0.0547005i
$399$	0.941102			0.0471140
$400$	2.17314	+	3.35819i	0.108657	+	0.167910i
$401$	4.29958			0.214711			0.107355	−	0.994221i	$-0.465762\pi$
$401$	4.29958			0.214711			0.107355	+	0.994221i	$0.465762\pi$
$402$	−17.0144	+	10.1132i	−0.848604	+	0.504403i
$403$		−	1.83070i		−	0.0911936i
$404$	21.1855	+	11.5249i	1.05402	+	0.573386i
$405$		−	6.55592i		−	0.325766i
$406$	−6.50787	−	10.9488i	−0.322980	−	0.543379i
$407$	5.34682			0.265032
$408$	11.2036	−	0.426624i	0.554662	−	0.0211211i
$409$	−18.1383			−0.896881			−0.448440	−	0.893813i	$-0.648020\pi$
$409$	−18.1383			−0.896881			−0.448440	+	0.893813i	$0.648020\pi$
$410$	−3.31555	−	5.57805i	−0.163743	−	0.275480i
$411$		−	19.8075i		−	0.977034i
$412$	1.17612	−	2.16198i	0.0579432	−	0.106513i
$413$		−	5.34775i		−	0.263146i
$414$	−6.78191	+	4.03111i	−0.333313	+	0.198118i
$415$	−9.02746			−0.443140
$416$	3.05293	−	6.15942i	0.149682	−	0.301990i
$417$	16.0969			0.788267
$418$	0.916553	−	0.544792i	0.0448301	−	0.0266466i
$419$		−	33.4913i		−	1.63616i	−0.575107	−	0.818078i	$-0.695040\pi$
$419$		−	33.4913i		−	1.63616i	0.575107	−	0.818078i	$-0.304960\pi$
$420$	−1.45993	+	2.68370i	−0.0712375	+	0.130951i
$421$		−	24.4624i		−	1.19222i	−0.802901	−	0.596112i	$-0.796711\pi$
$421$		−	24.4624i		−	1.19222i	0.802901	−	0.596112i	$-0.203289\pi$
$422$	2.62780	+	4.42099i	0.127919	+	0.215211i
$423$	−7.12277			−0.346321
$424$	13.0709	−	0.497728i	0.634778	−	0.0241718i
$425$	−2.59497			−0.125874
$426$	14.7776	+	24.8618i	0.715979	+	1.20456i
$427$		−	3.54867i		−	0.171732i
$428$	19.2995	+	10.4990i	0.932879	+	0.507486i
$429$		−	2.27176i		−	0.109682i
$430$	0.367030	−	0.218160i	0.0176998	−	0.0105206i
$431$	40.9753			1.97371			0.986856	−	0.161602i	$-0.0516662\pi$
$431$	40.9753			1.97371			0.986856	+	0.161602i	$0.0516662\pi$
$432$	18.8089	−	12.1716i	0.904943	−	0.585605i
$433$	16.8063			0.807657			0.403828	−	0.914835i	$-0.367679\pi$
$433$	16.8063			0.807657			0.403828	+	0.914835i	$0.367679\pi$
$434$	−1.83134	+	1.08853i	−0.0879070	+	0.0522512i
$435$			13.7577i			0.659629i
$436$	−19.5883	−	10.6560i	−0.938108	−	0.510331i
$437$			5.15610i			0.246650i
$438$	16.9852	+	28.5758i	0.811585	+	1.36540i
$439$	11.0244			0.526167			0.263084	−	0.964773i	$-0.415261\pi$
$439$	11.0244			0.526167			0.263084	+	0.964773i	$0.415261\pi$
$440$	0.131709	+	3.45883i	0.00627900	+	0.164893i
$441$	0.666582			0.0317420
$442$	2.27871	+	3.83368i	0.108387	+	0.182350i
$443$		−	16.7121i		−	0.794015i	−0.917815	−	0.397008i	$-0.870049\pi$
$443$		−	16.7121i		−	0.794015i	0.917815	−	0.397008i	$-0.129951\pi$
$444$	6.37865	−	11.7255i	0.302718	−	0.556466i
$445$		−	12.5124i		−	0.593143i
$446$	−13.5897	+	8.07763i	−0.643493	+	0.382487i
$447$	−6.53496			−0.309093
$448$	−7.97683	+	0.608384i	−0.376870	+	0.0287434i
$449$	31.8563			1.50339			0.751696	−	0.659509i	$-0.229236\pi$
$449$	31.8563			1.50339			0.751696	+	0.659509i	$0.229236\pi$
$450$	−0.810347	+	0.481664i	−0.0382001	+	0.0227058i
$451$		−	5.61519i		−	0.264409i
$452$	15.0094	−	27.5908i	0.705983	−	1.29776i
$453$			27.9795i			1.31459i
$454$	−20.7201	−	34.8593i	−0.972443	−	1.63603i
$455$	−1.21525			−0.0569719
$456$	−0.101287	−	2.65991i	−0.00474320	−	0.124562i
$457$	−7.35361			−0.343987			−0.171994	−	0.985098i	$-0.555021\pi$
$457$	−7.35361			−0.343987			−0.171994	+	0.985098i	$0.555021\pi$
$458$	18.6407	+	31.3610i	0.871024	+	1.46540i
$459$			14.5341i			0.678396i
$460$	−14.7034	−	7.99867i	−0.685551	−	0.372940i
$461$		−	25.7173i		−	1.19777i	−0.800833	−	0.598887i	$-0.795610\pi$
$461$		−	25.7173i		−	1.19777i	0.800833	−	0.598887i	$-0.204390\pi$
$462$	−2.27255	+	1.35079i	−0.105729	+	0.0628442i
$463$	−26.1530			−1.21543			−0.607716	−	0.794154i	$-0.707914\pi$
$463$	−26.1530			−1.21543			−0.607716	+	0.794154i	$0.707914\pi$
$464$	−30.2450	+	19.5721i	−1.40409	+	0.908611i
$465$	2.30116			0.106714
$466$	2.04198	−	1.21374i	0.0945929	−	0.0562252i
$467$		−	7.89518i		−	0.365345i	−0.983174	−	0.182673i	$-0.941525\pi$
$467$		−	7.89518i		−	0.365345i	0.983174	−	0.182673i	$-0.0584748\pi$
$468$	1.42317	+	0.774207i	0.0657862	+	0.0357877i
$469$			9.16229i			0.423075i
$470$	−7.72123	−	12.9901i	−0.356154	−	0.599190i
$471$	9.66295			0.445245
$472$	−15.1148	+	0.575557i	−0.695713	+	0.0264922i
$473$	0.369474			0.0169884
$474$	−7.38676	−	12.4274i	−0.339285	−	0.570810i
$475$			0.616085i			0.0282679i
$476$	2.48010	−	4.55901i	0.113675	−	0.208962i
$477$			3.08268i			0.141146i
$478$	8.93595	−	5.31146i	0.408721	−	0.242940i
$479$	24.6752			1.12744			0.563720	−	0.825966i	$-0.309370\pi$
$479$	24.6752			1.12744			0.563720	+	0.825966i	$0.309370\pi$
$480$	7.74229	+	3.83749i	0.353386	+	0.175157i
$481$	5.30960			0.242097
$482$	−11.5240	+	6.84980i	−0.524906	+	0.312000i
$483$		−	12.7843i		−	0.581706i
$484$	9.08176	−	16.6944i	0.412807	−	0.758837i
$485$			2.91526i			0.132375i
$486$	4.90505	+	8.25222i	0.222498	+	0.374328i
$487$	−14.2369			−0.645138			−0.322569	−	0.946546i	$-0.604546\pi$
$487$	−14.2369			−0.645138			−0.322569	+	0.946546i	$0.604546\pi$
$488$	−10.0299	+	0.381929i	−0.454032	+	0.0172891i
$489$	3.85708			0.174423
$490$	0.722588	+	1.21568i	0.0326432	+	0.0549186i
$491$			14.6003i			0.658902i	0.944173	+	0.329451i	$0.106864\pi$
$491$			14.6003i			0.658902i	−0.944173	+	0.329451i	$0.893136\pi$
$492$	−12.3140	−	6.69882i	−0.555158	−	0.302006i
$493$		−	23.3712i		−	1.05258i
$494$	0.910174	−	0.541000i	0.0409507	−	0.0243408i
$495$	−0.815742			−0.0366649
$496$	3.27370	+	5.05890i	0.146994	+	0.227151i
$497$	13.3881			0.600537
$498$	−16.7641	+	9.96443i	−0.751216	+	0.446517i
$499$			22.9361i			1.02676i	0.858161	+	0.513381i	$0.171607\pi$
$499$			22.9361i			1.02676i	−0.858161	+	0.513381i	$0.828393\pi$
$500$	−1.75686	−	0.955734i	−0.0785694	−	0.0427417i
$501$		−	7.94314i		−	0.354873i
$502$	19.0970	+	32.1286i	0.852340	+	1.43397i
$503$	−11.5344			−0.514293			−0.257147	−	0.966372i	$-0.582782\pi$
$503$	−11.5344			−0.514293			−0.257147	+	0.966372i	$0.582782\pi$
$504$	−0.0717416	−	1.88401i	−0.00319562	−	0.0839206i
$505$	−12.0587			−0.536605
$506$	−7.40066	−	12.4508i	−0.329000	−	0.553506i
$507$			17.6022i			0.781743i
$508$	8.17370	−	15.0252i	0.362649	−	0.666635i
$509$			10.7973i			0.478582i	0.970948	+	0.239291i	$0.0769151\pi$
$509$			10.7973i			0.478582i	−0.970948	+	0.239291i	$0.923085\pi$
$510$	−4.81888	+	2.86430i	−0.213383	+	0.126833i
$511$	15.3881			0.680729
$512$	2.57804	+	22.4801i	0.113934	+	0.993488i
$513$	3.45063			0.152349
$514$	−36.5479	+	21.7238i	−1.61206	+	0.958195i
$515$			1.23059i			0.0542264i
$516$	0.440775	−	0.810249i	0.0194040	−	0.0356692i
$517$		−	13.0766i		−	0.575109i
$518$	−3.15709	−	5.31145i	−0.138714	−	0.233372i
$519$	−34.3531			−1.50794
$520$	0.130793	+	3.43476i	0.00573564	+	0.150624i
$521$	44.2258			1.93757			0.968784	−	0.247904i	$-0.0797419\pi$
$521$	44.2258			1.93757			0.968784	+	0.247904i	$0.0797419\pi$
$522$	−4.33803	−	7.29826i	−0.189870	−	0.319436i
$523$		−	11.9059i		−	0.520608i	−0.965527	−	0.260304i	$-0.916177\pi$
$523$		−	11.9059i		−	0.520608i	0.965527	−	0.260304i	$-0.0838228\pi$
$524$	−19.2360	−	10.4644i	−0.840329	−	0.457139i
$525$		−	1.52755i		−	0.0666679i
$526$	−12.2749	+	7.29608i	−0.535209	+	0.318124i
$527$	−3.90915			−0.170285
$528$	4.06242	+	6.27771i	0.176794	+	0.273202i
$529$	47.0425			2.04532
$530$	−5.62202	+	3.34168i	−0.244205	+	0.145153i
$531$		−	3.56471i		−	0.154695i
$532$	−1.08238	−	0.588813i	−0.0469270	−	0.0255283i
$533$		−	5.57611i		−	0.241528i
$534$	−13.8110	−	23.2356i	−0.597662	−	1.00550i
$535$	−10.9852			−0.474933
$536$	25.8961	−	0.986101i	1.11854	−	0.0425931i
$537$	28.3110			1.22171
$538$	−2.81450	−	4.73510i	−0.121342	−	0.204145i
$539$			1.22377i			0.0527115i
$540$	−5.35297	+	9.84002i	−0.230355	+	0.423447i
$541$		−	24.9088i		−	1.07091i	−0.844563	−	0.535457i	$-0.820140\pi$
$541$		−	24.9088i		−	1.07091i	0.844563	−	0.535457i	$-0.179860\pi$
$542$	5.58649	−	3.32056i	0.239960	−	0.142630i
$543$	−10.5827			−0.454146
$544$	−13.1524	−	6.51903i	−0.563905	−	0.279501i
$545$	11.1496			0.477595
$546$	−2.25673	+	1.34138i	−0.0965793	+	0.0574060i
$547$		−	22.2892i		−	0.953016i	−0.879170	−	0.476508i	$-0.841902\pi$
$547$		−	22.2892i		−	0.953016i	0.879170	−	0.476508i	$-0.158098\pi$
$548$	−12.3929	+	22.7810i	−0.529397	+	0.973156i
$549$		−	2.36548i		−	0.100956i
$550$	−0.884280	−	1.48771i	−0.0377058	−	0.0634360i
$551$	−5.54867			−0.236381
$552$	−36.1333	+	1.37592i	−1.53793	+	0.0585632i
$553$	−6.69217			−0.284580
$554$	17.2355	+	28.9968i	0.732265	+	1.23196i
$555$			6.67409i			0.283299i
$556$	−18.5133	−	10.0712i	−0.785138	−	0.427115i
$557$			36.4724i			1.54538i	0.634781	+	0.772692i	$0.281090\pi$
$557$			36.4724i			1.54538i	−0.634781	+	0.772692i	$0.718910\pi$
$558$	−1.22074	+	0.725595i	−0.0516779	+	0.0307169i
$559$	0.366902			0.0155183
$560$	3.35819	−	2.17314i	0.141909	−	0.0918321i
$561$	−4.85096			−0.204808
$562$	−22.5804	+	13.4216i	−0.952495	+	0.566156i
$563$			36.8169i			1.55165i	0.630951	+	0.775823i	$0.282665\pi$
$563$			36.8169i			1.55165i	−0.630951	+	0.775823i	$0.717335\pi$
$564$	−28.6768	−	15.6002i	−1.20751	−	0.656885i
$565$			15.7046i			0.660697i
$566$	−18.9616	−	31.9008i	−0.797015	−	1.34089i
$567$	−6.55592			−0.275323
$568$	−1.44091	−	37.8398i	−0.0604591	−	1.58772i
$569$	−5.01521			−0.210248			−0.105124	−	0.994459i	$-0.533524\pi$
$569$	−5.01521			−0.210248			−0.105124	+	0.994459i	$0.533524\pi$
$570$	0.680029	+	1.14408i	0.0284833	+	0.0479200i
$571$			14.0744i			0.588995i	0.955652	+	0.294498i	$0.0951523\pi$
$571$			14.0744i			0.588995i	−0.955652	+	0.294498i	$0.904848\pi$
$572$	−1.42136	+	2.61279i	−0.0594299	+	0.109246i
$573$		−	3.81547i		−	0.159394i
$574$	−5.57805	+	3.31555i	−0.232823	+	0.138388i
$575$	8.36914			0.349017
$576$	−5.31721	+	0.405538i	−0.221550	+	0.0168974i
$577$	−44.3287			−1.84543			−0.922714	−	0.385485i	$-0.874034\pi$
$577$	−44.3287			−1.84543			−0.922714	+	0.385485i	$0.874034\pi$
$578$	−12.4803	+	7.41819i	−0.519112	+	0.308556i
$579$			10.8927i			0.452687i
$580$	8.60767	−	15.8229i	0.357414	−	0.657011i
$581$			9.02746i			0.374522i
$582$	3.21784	+	5.41366i	0.133384	+	0.224404i
$583$	−5.65944			−0.234390
$584$	−1.65616	−	43.4925i	−0.0685323	−	1.79973i
$585$	−0.810065			−0.0334921
$586$	23.6135	+	39.7272i	0.975466	+	1.64112i
$587$		−	7.17908i		−	0.296313i	−0.988964	−	0.148156i	$-0.952666\pi$
$587$		−	7.17908i		−	0.296313i	0.988964	−	0.148156i	$-0.0473339\pi$
$588$	2.68370	+	1.45993i	0.110674	+	0.0602067i
$589$			0.928092i			0.0382414i
$590$	6.50113	−	3.86422i	0.267647	−	0.159087i
$591$	−14.6020			−0.600646
$592$	−14.6724	+	9.49477i	−0.603032	+	0.390233i
$593$	−13.2728			−0.545051			−0.272525	−	0.962149i	$-0.587859\pi$
$593$	−13.2728			−0.545051			−0.272525	+	0.962149i	$0.587859\pi$
$594$	−8.33249	+	4.95276i	−0.341886	+	0.203214i
$595$			2.59497i			0.106383i
$596$	7.51597	+	4.08869i	0.307866	+	0.167479i
$597$		−	2.30695i		−	0.0944173i
$598$	−7.34916	−	12.3642i	−0.300529	−	0.505608i
$599$	−9.23655			−0.377395			−0.188698	−	0.982035i	$-0.560427\pi$
$599$	−9.23655			−0.377395			−0.188698	+	0.982035i	$0.560427\pi$
$600$	−4.31744	+	0.164405i	−0.176259	+	0.00671179i
$601$	−22.0644			−0.900027			−0.450014	−	0.893022i	$-0.648581\pi$
$601$	−22.0644			−0.900027			−0.450014	+	0.893022i	$0.648581\pi$
$602$	−0.218160	−	0.367030i	−0.00889152	−	0.0149590i
$603$			6.10741i			0.248713i
$604$	17.5058	−	32.1797i	0.712300	−	1.30938i
$605$			9.50239i			0.386327i
$606$	−22.3931	+	13.3103i	−0.909659	+	0.540694i
$607$	12.1921			0.494864			0.247432	−	0.968905i	$-0.420413\pi$
$607$	12.1921			0.494864			0.247432	+	0.968905i	$0.420413\pi$
$608$	−1.54772	+	3.12258i	−0.0627682	+	0.126637i
$609$	13.7577			0.557489
$610$	4.31403	−	2.56423i	0.174670	−	0.103822i
$611$		−	12.9856i		−	0.525341i
$612$	1.65319	−	3.03895i	0.0668262	−	0.122842i
$613$		−	13.6108i		−	0.549737i	−0.961482	−	0.274868i	$-0.911366\pi$
$613$		−	13.6108i		−	0.549737i	0.961482	−	0.274868i	$-0.0886343\pi$
$614$	10.5826	+	17.8040i	0.427078	+	0.718513i
$615$	7.00908			0.282633
$616$	3.45883	−	0.131709i	0.139360	−	0.00530672i
$617$	8.92315			0.359233			0.179616	−	0.983737i	$-0.442514\pi$
$617$	8.92315			0.359233			0.179616	+	0.983737i	$0.442514\pi$
$618$	1.35832	+	2.28522i	0.0546395	+	0.0919251i
$619$		−	18.4729i		−	0.742487i	−0.928536	−	0.371243i	$-0.878932\pi$
$619$		−	18.4729i		−	0.742487i	0.928536	−	0.371243i	$-0.121068\pi$
$620$	−2.64660	−	1.43975i	−0.106290	−	0.0578218i
$621$		−	46.8747i		−	1.88102i
$622$	−9.67400	+	5.75015i	−0.387892	+	0.230560i
$623$	−12.5124			−0.501297
$624$	4.03414	+	6.23402i	0.161495	+	0.249560i
$625$	1.00000			0.0400000
$626$	27.6679	−	16.4456i	1.10583	−	0.657297i
$627$			1.15169i			0.0459941i
$628$	−11.1135	−	6.04576i	−0.443478	−	0.241252i
$629$		−	11.3378i		−	0.452067i
$630$	0.481664	+	0.810347i	0.0191899	+	0.0322850i
$631$	−31.4140			−1.25057			−0.625286	−	0.780396i	$-0.715018\pi$
$631$	−31.4140			−1.25057			−0.625286	+	0.780396i	$0.715018\pi$
$632$	0.720252	+	18.9146i	0.0286501	+	0.752383i
$633$	−5.55518			−0.220799
$634$	−17.8451	−	30.0224i	−0.708718	−	1.19234i
$635$			8.55227i			0.339387i
$636$	−6.75162	+	12.4111i	−0.267719	+	0.492131i
$637$			1.21525i			0.0481500i
$638$	13.3988	−	7.96413i	0.530463	−	0.315303i
$639$	8.92425			0.353038
$640$	−6.50356	−	9.25763i	−0.257076	−	0.365940i
$641$	−1.35417			−0.0534864			−0.0267432	−	0.999642i	$-0.508514\pi$
$641$	−1.35417			−0.0534864			−0.0267432	+	0.999642i	$0.508514\pi$
$642$	−20.3997	+	12.1254i	−0.805110	+	0.478551i
$643$		−	1.55217i		−	0.0612116i	−0.999532	−	0.0306058i	$-0.990256\pi$
$643$		−	1.55217i		−	0.0612116i	0.999532	−	0.0306058i	$-0.00974365\pi$
$644$	−7.99867	+	14.7034i	−0.315192	+	0.579397i
$645$			0.461190i			0.0181594i
$646$	−1.15522	−	1.94353i	−0.0454514	−	0.0764670i
$647$	14.9269			0.586837			0.293418	−	0.955984i	$-0.405207\pi$
$647$	14.9269			0.586837			0.293418	+	0.955984i	$0.405207\pi$
$648$	0.705588	+	18.5295i	0.0277181	+	0.727908i
$649$	6.54441			0.256891
$650$	−0.878126	−	1.47735i	−0.0344429	−	0.0579465i
$651$		−	2.30116i		−	0.0901896i
$652$	−4.43609	−	2.41323i	−0.173731	−	0.0945095i
$653$		−	43.8373i		−	1.71549i	−0.514078	−	0.857744i	$-0.671866\pi$
$653$		−	43.8373i		−	1.71549i	0.514078	−	0.857744i	$-0.328134\pi$
$654$	20.7048	−	12.3068i	0.809624	−	0.481234i
$655$	10.9491			0.427815
$656$	9.97134	+	15.4088i	0.389315	+	0.601614i
$657$	10.2574			0.400180
$658$	−12.9901	+	7.72123i	−0.506408	+	0.301005i
$659$			21.8689i			0.851893i	0.904748	+	0.425946i	$0.140059\pi$
$659$			21.8689i			0.851893i	−0.904748	+	0.425946i	$0.859941\pi$
$660$	−3.28423	−	1.78662i	−0.127839	−	0.0695442i
$661$			13.0207i			0.506446i	0.967408	+	0.253223i	$0.0814906\pi$
$661$			13.0207i			0.506446i	−0.967408	+	0.253223i	$0.918509\pi$
$662$	15.8311	+	26.6342i	0.615295	+	1.03517i
$663$	−4.81720			−0.187085
$664$	25.5150	−	0.971590i	0.990175	−	0.0377050i
$665$	0.616085			0.0238907
$666$	−2.10446	−	3.54052i	−0.0815460	−	0.137192i
$667$			75.3753i			2.91854i
$668$	−4.96973	+	9.13554i	−0.192285	+	0.353465i
$669$		−	17.0761i		−	0.660202i
$670$	−11.1384	+	6.62056i	−0.430313	+	0.255774i
$671$	4.34275			0.167650
$672$	3.83749	−	7.74229i	0.148034	−	0.298665i
$673$	−23.1308			−0.891629			−0.445814	−	0.895125i	$-0.647086\pi$
$673$	−23.1308			−0.891629			−0.445814	+	0.895125i	$0.647086\pi$
$674$	−9.86223	+	5.86203i	−0.379879	+	0.225797i
$675$		−	5.60090i		−	0.215579i
$676$	11.0131	−	20.2446i	0.423580	−	0.778640i
$677$		−	23.4736i		−	0.902162i	−0.892483	−	0.451081i	$-0.851039\pi$
$677$		−	23.4736i		−	0.902162i	0.892483	−	0.451081i	$-0.148961\pi$
$678$	17.3346	+	29.1635i	0.665730	+	1.12002i
$679$	2.91526			0.111877
$680$	7.33436	−	0.279286i	0.281260	−	0.0107101i
$681$	43.8024			1.67851
$682$	−1.33211	−	2.24113i	−0.0510092	−	0.0858174i
$683$		−	33.0062i		−	1.26295i	−0.775397	−	0.631475i	$-0.782450\pi$
$683$		−	33.0062i		−	1.26295i	0.775397	−	0.631475i	$-0.217550\pi$
$684$	−0.721493	−	0.392492i	−0.0275870	−	0.0150073i
$685$		−	12.9668i		−	0.495438i
$686$	1.21568	−	0.722588i	0.0464147	−	0.0275885i
$687$	−39.4066			−1.50345
$688$	−1.01389	+	0.656104i	−0.0386540	+	0.0250137i
$689$	−5.62006			−0.214107
$690$	15.5416	−	9.23778i	0.591657	−	0.351676i
$691$		−	25.0583i		−	0.953263i	−0.879103	−	0.476631i	$-0.841858\pi$
$691$		−	25.0583i		−	0.953263i	0.879103	−	0.476631i	$-0.158142\pi$
$692$	39.5101	+	21.4935i	1.50195	+	0.817060i
$693$			0.815742i			0.0309875i
$694$	−11.8518	−	19.9394i	−0.449890	−	0.756891i
$695$	10.5377			0.399717
$696$	−1.48068	−	38.8844i	−0.0561251	−	1.47391i
$697$	−11.9068			−0.451004
$698$	−4.41161	−	7.42206i	−0.166982	−	0.280929i
$699$			2.56584i			0.0970491i
$700$	−0.955734	+	1.75686i	−0.0361234	+	0.0664032i
$701$			2.91899i			0.110249i	0.998479	+	0.0551244i	$0.0175555\pi$
$701$			2.91899i			0.110249i	−0.998479	+	0.0551244i	$0.982444\pi$
$702$	−8.27450	+	4.91830i	−0.312301	+	0.185629i
$703$	−2.69176			−0.101522
$704$	−0.744521	−	9.76180i	−0.0280602	−	0.367912i
$705$	16.3227			0.614749
$706$	−39.9344	+	23.7367i	−1.50295	+	0.893341i
$707$			12.0587i			0.453514i
$708$	7.80736	−	14.3518i	0.293419	−	0.539373i
$709$			27.0827i			1.01711i	0.861029	+	0.508556i	$0.169821\pi$
$709$			27.0827i			1.01711i	−0.861029	+	0.508556i	$0.830179\pi$
$710$	9.67406	+	16.2756i	0.363061	+	0.610811i
$711$	−4.46088			−0.167296
$712$	1.34666	+	35.3647i	0.0504681	+	1.32535i
$713$	12.6076			0.472157
$714$	2.86430	+	4.81888i	0.107194	+	0.180342i
$715$		−	1.48719i		−	0.0556177i
$716$	−32.5610	−	17.7132i	−1.21686	−	0.661972i
$717$			11.2284i			0.419334i
$718$	7.04150	−	4.18541i	0.262787	−	0.156198i
$719$	33.3718			1.24456			0.622280	−	0.782795i	$-0.286207\pi$
$719$	33.3718			1.24456			0.622280	+	0.782795i	$0.286207\pi$
$720$	2.23851	−	1.44858i	0.0834243	−	0.0539853i
$721$	1.23059			0.0458296
$722$	22.6364	−	13.4549i	0.842440	−	0.500740i
$723$		−	14.4805i		−	0.538536i
$724$	12.1713	+	6.62119i	0.452343	+	0.246075i
$725$			9.00634i			0.334487i
$726$	10.4887	+	17.6460i	0.389270	+	0.654905i
$727$	−24.7727			−0.918768			−0.459384	−	0.888238i	$-0.651930\pi$
$727$	−24.7727			−0.918768			−0.459384	+	0.888238i	$0.651930\pi$
$728$	3.43476	−	0.130793i	0.127301	−	0.00484750i
$729$	−30.0371			−1.11248
$730$	11.1192	+	18.7069i	0.411541	+	0.692374i
$731$		−	0.783458i		−	0.0289772i
$732$	5.18083	−	9.52358i	0.191489	−	0.352002i
$733$		−	9.77137i		−	0.360914i	−0.983583	−	0.180457i	$-0.942242\pi$
$733$		−	9.77137i		−	0.360914i	0.983583	−	0.180457i	$-0.0577576\pi$
$734$	41.7248	−	24.8009i	1.54009	−	0.915418i
$735$	−1.52755			−0.0563446
$736$	42.4184	+	21.0248i	1.56356	+	0.774984i
$737$	−11.2125			−0.413019
$738$	−3.71823	+	2.21008i	−0.136870	+	0.0813543i
$739$			8.19838i			0.301582i	0.988566	+	0.150791i	$0.0481821\pi$
$739$			8.19838i			0.301582i	−0.988566	+	0.150791i	$0.951818\pi$
$740$	4.17573	−	7.67598i	0.153503	−	0.282175i
$741$			1.14368i			0.0420140i
$742$	3.34168	+	5.62202i	0.122677	+	0.206391i
$743$	16.1936			0.594085			0.297043	−	0.954864i	$-0.404000\pi$
$743$	16.1936			0.594085			0.297043	+	0.954864i	$0.404000\pi$
$744$	−6.50395	+	0.247665i	−0.238446	+	0.00907983i
$745$	−4.27806			−0.156736
$746$	−18.5719	−	31.2452i	−0.679965	−	1.14397i
$747$			6.01754i			0.220170i
$748$	5.57917	+	3.03507i	0.203995	+	0.110973i
$749$			10.9852i			0.401391i
$750$	1.85701	−	1.10379i	0.0678084	−	0.0403047i
$751$	−27.1393			−0.990328			−0.495164	−	0.868800i	$-0.664892\pi$
$751$	−27.1393			−0.990328			−0.495164	+	0.868800i	$0.664892\pi$
$752$	23.2212	+	35.8840i	0.846790	+	1.30856i
$753$	−40.3711			−1.47120
$754$	13.3055	−	7.90870i	0.484559	−	0.288018i
$755$			18.3166i			0.666609i
$756$	9.84002	+	5.35297i	0.357878	+	0.194686i
$757$			41.8750i			1.52197i	0.648768	+	0.760986i	$0.275285\pi$
$757$			41.8750i			1.52197i	−0.648768	+	0.760986i	$0.724715\pi$
$758$	15.2517	+	25.6593i	0.553965	+	0.931986i
$759$	15.6450			0.567879
$760$	−0.0663068	−	1.74129i	−0.00240520	−	0.0631632i
$761$	−22.8830			−0.829509			−0.414754	−	0.909933i	$-0.636132\pi$
$761$	−22.8830			−0.829509			−0.414754	+	0.909933i	$0.636132\pi$
$762$	9.43992	+	15.8816i	0.341972	+	0.575331i
$763$		−	11.1496i		−	0.403641i
$764$	−2.38720	+	4.38824i	−0.0863658	+	0.158761i
$765$			1.72976i			0.0625395i
$766$	19.6562	−	11.6835i	0.710208	−	0.422142i
$767$	6.49886			0.234660
$768$	−22.2957	−	10.0129i	−0.804525	−	0.361311i
$769$	19.1315			0.689899			0.344949	−	0.938621i	$-0.387896\pi$
$769$	19.1315			0.689899			0.344949	+	0.938621i	$0.387896\pi$
$770$	−1.48771	+	0.884280i	−0.0536132	+	0.0318673i
$771$		−	45.9241i		−	1.65392i
$772$	6.81519	−	12.5279i	0.245284	−	0.450890i
$773$		−	31.7796i		−	1.14303i	−0.820590	−	0.571517i	$-0.806355\pi$
$773$		−	31.7796i		−	1.14303i	0.820590	−	0.571517i	$-0.193645\pi$
$774$	−0.145421	−	0.244655i	−0.00522706	−	0.00879396i
$775$	1.50644			0.0541128
$776$	−0.313758	−	8.23963i	−0.0112633	−	0.295785i
$777$	6.67409			0.239432
$778$	11.2910	+	18.9959i	0.404802	+	0.681035i
$779$			2.82687i			0.101283i
$780$	−3.26138	−	1.77419i	−0.116776	−	0.0635261i
$781$			16.3839i			0.586263i
$782$	−26.4016	+	15.6929i	−0.944119	+	0.561177i
$783$	50.4436			1.80271
$784$	−2.17314	−	3.35819i	−0.0776123	−	0.119935i
$785$	6.32577			0.225776
$786$	20.3325	−	12.0855i	0.725236	−	0.431074i
$787$			48.3246i			1.72259i	0.508109	+	0.861293i	$0.330345\pi$
$787$			48.3246i			1.72259i	−0.508109	+	0.861293i	$0.669655\pi$
$788$	16.7940	+	9.13593i	0.598261	+	0.325454i
$789$		−	15.4239i		−	0.549107i
$790$	−4.83568	−	8.13551i	−0.172046	−	0.289448i
$791$	15.7046			0.558391
$792$	2.30560	−	0.0877951i	0.0819258	−	0.00311966i
$793$	4.31253			0.153142
$794$	−18.5461	−	31.2018i	−0.658177	−	1.10731i
$795$		−	7.06432i		−	0.250546i
$796$	−1.44338	+	2.65326i	−0.0511591	+	0.0940425i
$797$		−	4.83126i		−	0.171132i	−0.996332	−	0.0855661i	$-0.972730\pi$
$797$		−	4.83126i		−	0.171132i	0.996332	−	0.0855661i	$-0.0272699\pi$
$798$	1.14408	−	0.680029i	0.0404998	−	0.0240728i
$799$	−27.7286			−0.980967
$800$	5.06843	+	2.51218i	0.179196	+	0.0888190i
$801$	−8.34051			−0.294698
$802$	5.22690	−	3.10683i	0.184568	−	0.109706i
$803$			18.8315i			0.664548i
$804$	−13.3763	+	24.5889i	−0.471747	+	0.867182i
$805$		−	8.36914i		−	0.294973i
$806$	−1.32284	−	2.22554i	−0.0465951	−	0.0783912i
$807$	5.94987			0.209445
$808$	34.0825	−	1.29783i	1.19902	−	0.0456575i
$809$	−26.9745			−0.948374			−0.474187	−	0.880424i	$-0.657258\pi$
$809$	−26.9745			−0.948374			−0.474187	+	0.880424i	$0.657258\pi$
$810$	−4.73723	−	7.96988i	−0.166449	−	0.280033i
$811$			8.63552i			0.303234i	0.988439	+	0.151617i	$0.0484481\pi$
$811$			8.63552i			0.303234i	−0.988439	+	0.151617i	$0.951552\pi$
$812$	−15.8229	−	8.60767i	−0.555276	−	0.302070i
$813$			7.01968i			0.246191i
$814$	6.49999	−	3.86354i	0.227825	−	0.135417i
$815$	2.52500			0.0884470
$816$	13.3117	−	8.61424i	0.466003	−	0.301559i
$817$	−0.186005			−0.00650749
$818$	−22.0503	+	13.1065i	−0.770970	+	0.458258i
$819$			0.810065i			0.0283060i
$820$	−8.06126	−	4.38532i	−0.281511	−	0.153142i
$821$			49.4882i			1.72715i	0.504221	+	0.863575i	$0.331780\pi$
$821$			49.4882i			1.72715i	−0.504221	+	0.863575i	$0.668220\pi$
$822$	−14.3127	−	24.0795i	−0.499212	−	0.839871i
$823$	−10.1490			−0.353773			−0.176886	−	0.984231i	$-0.556602\pi$
$823$	−10.1490			−0.353773			−0.176886	+	0.984231i	$0.556602\pi$
$824$	−0.132444	−	3.47812i	−0.00461390	−	0.121166i
$825$	1.86937			0.0650832
$826$	−3.86422	−	6.50113i	−0.134453	−	0.226203i
$827$		−	23.3610i		−	0.812341i	−0.913797	−	0.406170i	$-0.866864\pi$
$827$		−	23.3610i		−	0.812341i	0.913797	−	0.406170i	$-0.133136\pi$
$828$	−5.33177	+	9.80104i	−0.185292	+	0.340610i
$829$		−	7.55731i		−	0.262476i	−0.991351	−	0.131238i	$-0.958105\pi$
$829$		−	7.55731i		−	0.262476i	0.991351	−	0.131238i	$-0.0418952\pi$
$830$	−10.9745	+	6.52313i	−0.380929	+	0.226421i
$831$	−36.4358			−1.26395
$832$	−0.739340	−	9.69386i	−0.0256320	−	0.336074i
$833$	2.59497			0.0899103
$834$	19.5686	−	11.6314i	0.677604	−	0.402763i
$835$		−	5.19991i		−	0.179950i
$836$	0.720572	−	1.32458i	0.0249215	−	0.0458116i
$837$		−	8.43739i		−	0.291639i
$838$	−24.2004	−	40.7145i	−0.835989	−	1.40646i
$839$	5.56944			0.192279			0.0961393	−	0.995368i	$-0.469351\pi$
$839$	5.56944			0.192279			0.0961393	+	0.995368i	$0.469351\pi$
$840$	0.164405	+	4.31744i	0.00567249	+	0.148966i
$841$	−52.1142			−1.79704
$842$	−17.6762	−	29.7383i	−0.609163	−	1.02485i
$843$		−	28.3733i		−	0.977228i
$844$	6.38911	+	3.47568i	0.219922	+	0.119638i
$845$			11.5232i			0.396409i
$846$	−8.65898	+	5.14683i	−0.297702	+	0.176952i
$847$	9.50239			0.326506
$848$	15.5303	−	10.0499i	0.533312	−	0.345116i
$849$	40.0848			1.37571
$850$	−3.15464	+	1.87509i	−0.108203	+	0.0643151i
$851$			36.5659i			1.25346i
$852$	35.9296	+	19.5457i	1.23093	+	0.669625i
$853$			8.90694i			0.304968i	0.988306	+	0.152484i	$0.0487272\pi$
$853$			8.90694i			0.304968i	−0.988306	+	0.152484i	$0.951273\pi$
$854$	−2.56423	−	4.31403i	−0.0877460	−	0.147623i
$855$	0.410671			0.0140447
$856$	31.0484	−	1.18230i	1.06121	−	0.0404101i
$857$	−25.2236			−0.861622			−0.430811	−	0.902442i	$-0.641773\pi$
$857$	−25.2236			−0.861622			−0.430811	+	0.902442i	$0.641773\pi$
$858$	−1.64154	−	2.76172i	−0.0560414	−	0.0942836i
$859$		−	29.6267i		−	1.01085i	−0.862871	−	0.505424i	$-0.831336\pi$
$859$		−	29.6267i		−	1.01085i	0.862871	−	0.505424i	$-0.168664\pi$
$860$	0.288550	−	0.530423i	0.00983947	−	0.0180873i
$861$		−	7.00908i		−	0.238869i
$862$	49.8127	−	29.6083i	1.69663	−	1.00846i
$863$	49.8219			1.69596			0.847978	−	0.530031i	$-0.177820\pi$
$863$	49.8219			1.69596			0.847978	+	0.530031i	$0.177820\pi$
$864$	14.0705	−	28.3877i	0.478687	−	0.965770i
$865$	−22.4890			−0.764649
$866$	20.4310	−	12.1440i	0.694272	−	0.412670i
$867$		−	15.6821i		−	0.532591i
$868$	−1.43975	+	2.64660i	−0.0488684	+	0.0898316i
$869$		−	8.18967i		−	0.277816i
$870$	9.94112	+	16.7249i	0.337035	+	0.567026i
$871$	−11.1345			−0.377278
$872$	−31.5129	+	1.19998i	−1.06716	+	0.0406366i
$873$	1.94326			0.0657693
$874$	3.72573	+	6.26814i	0.126025	+	0.212023i
$875$		−	1.00000i		−	0.0338062i
$876$	41.2970	+	22.4656i	1.39530	+	0.759042i
$877$			5.95625i			0.201128i	0.994931	+	0.100564i	$0.0320648\pi$
$877$			5.95625i			0.201128i	−0.994931	+	0.100564i	$0.967935\pi$
$878$	13.4021	−	7.96611i	0.452300	−	0.268843i
$879$	−49.9191			−1.68373
$880$	2.65943	+	4.10965i	0.0896493	+	0.138536i
$881$	23.9797			0.807895			0.403948	−	0.914782i	$-0.367638\pi$
$881$	23.9797			0.807895			0.403948	+	0.914782i	$0.367638\pi$
$882$	0.810347	−	0.481664i	0.0272858	−	0.0162185i
$883$			34.2431i			1.15237i	0.817319	+	0.576186i	$0.195459\pi$
$883$			34.2431i			1.15237i	−0.817319	+	0.576186i	$0.804541\pi$
$884$	5.54034	+	3.01395i	0.186342	+	0.101370i
$885$			8.16897i			0.274597i
$886$	−12.0759	−	20.3165i	−0.405699	−	0.682545i
$887$	−46.8360			−1.57260			−0.786300	−	0.617845i	$-0.788006\pi$
$887$	−46.8360			−1.57260			−0.786300	+	0.617845i	$0.788006\pi$
$888$	−0.718306	−	18.8635i	−0.0241048	−	0.633018i
$889$	8.55227			0.286834
$890$	−9.04128	−	15.2110i	−0.303064	−	0.509873i
$891$		−	8.02294i		−	0.268778i
$892$	−10.6839	+	19.6396i	−0.357724	+	0.657581i
$893$			6.58319i			0.220298i
$894$	−7.94439	+	4.72208i	−0.265700	+	0.157930i
$895$	18.5336			0.619509
$896$	−9.25763	+	6.50356i	−0.309276	+	0.217269i
$897$	15.5361			0.518737
$898$	38.7270	−	23.0190i	1.29234	−	0.768154i
$899$			13.5675i			0.452501i
$900$	−0.637075	+	1.17109i	−0.0212358	+	0.0390365i
$901$			12.0007i			0.399801i
$902$	−4.05746	−	6.82624i	−0.135099	−	0.227289i
$903$	0.461190			0.0153475
$904$	−1.69022	−	44.3871i	−0.0562159	−	1.47629i
$905$	−6.92786			−0.230290
$906$	20.2177	+	34.0141i	0.671687	+	1.13004i
$907$			11.4406i			0.379879i	0.981796	+	0.189939i	$0.0608292\pi$
$907$			11.4406i			0.379879i	−0.981796	+	0.189939i	$0.939171\pi$
$908$	−50.3779	−	27.4056i	−1.67185	−	0.909485i
$909$			8.03811i			0.266607i
$910$	−1.47735	+	0.878126i	−0.0489738	+	0.0291096i
$911$	35.7370			1.18402			0.592010	−	0.805930i	$-0.298334\pi$
$911$	35.7370			1.18402			0.592010	+	0.805930i	$0.298334\pi$
$912$	−2.04515	−	3.16040i	−0.0677217	−	0.104651i
$913$	−11.0475			−0.365620
$914$	−8.93960	+	5.31363i	−0.295696	+	0.175759i
$915$			5.42078i			0.179206i
$916$	45.3221	+	24.6552i	1.49749	+	0.814632i
$917$		−	10.9491i		−	0.361570i
$918$	10.5022	+	17.6688i	0.346624	+	0.583158i
$919$	4.15619			0.137100			0.0685500	−	0.997648i	$-0.478163\pi$
$919$	4.15619			0.137100			0.0685500	+	0.997648i	$0.478163\pi$
$920$	−23.6544	+	0.900737i	−0.779861	+	0.0296964i
$921$	−22.3716			−0.737170
$922$	−18.5830	−	31.2639i	−0.611999	−	1.02962i
$923$			16.2699i			0.535530i
$924$	−1.78662	+	3.28423i	−0.0587756	+	0.108043i
$925$			4.36914i			0.143656i
$926$	−31.7936	+	18.8978i	−1.04480	+	0.621021i
$927$	0.820290			0.0269419
$928$	−22.6256	+	45.6480i	−0.742721	+	1.49847i
$929$	−24.1240			−0.791483			−0.395742	−	0.918362i	$-0.629512\pi$
$929$	−24.1240			−0.791483			−0.395742	+	0.918362i	$0.629512\pi$
$930$	2.79746	−	1.66279i	0.0917325	−	0.0545250i
$931$		−	0.616085i		−	0.0201914i
$932$	1.60535	−	2.95102i	0.0525851	−	0.0966638i
$933$		−	12.1558i		−	0.397964i
$934$	−5.70496	−	9.59797i	−0.186672	−	0.314055i
$935$	−3.17564			−0.103855
$936$	2.28955	−	0.0871841i	0.0748363	−	0.00284970i
$937$	21.6990			0.708875			0.354438	−	0.935080i	$-0.384672\pi$
$937$	21.6990			0.708875			0.354438	+	0.935080i	$0.384672\pi$
$938$	6.62056	+	11.1384i	0.216169	+	0.363681i
$939$			34.7660i			1.13455i
$940$	−18.7730	−	10.2125i	−0.612308	−	0.333096i
$941$			51.1661i			1.66797i	0.551789	+	0.833984i	$0.313945\pi$
$941$			51.1661i			1.66797i	−0.551789	+	0.833984i	$0.686055\pi$
$942$	11.7470	−	6.98233i	0.382738	−	0.227497i
$943$	38.4013			1.25052
$944$	−17.9588	+	11.6214i	−0.584508	+	0.378245i
$945$	−5.60090			−0.182197
$946$	0.449160	−	0.266977i	0.0146034	−	0.00868017i
$947$		−	23.5083i		−	0.763916i	−0.924180	−	0.381958i	$-0.875250\pi$
$947$		−	23.5083i		−	0.763916i	0.924180	−	0.381958i	$-0.124750\pi$
$948$	−17.9598	−	9.77013i	−0.583307	−	0.317319i
$949$			18.7004i			0.607040i
$950$	0.445175	+	0.748959i	0.0144434	+	0.0242995i
$951$	37.7245			1.22330
$952$	−0.279286	−	7.33436i	−0.00905171	−	0.237708i
$953$	22.8816			0.741208			0.370604	−	0.928791i	$-0.379151\pi$
$953$	22.8816			0.741208			0.370604	+	0.928791i	$0.379151\pi$
$954$	2.22750	+	3.74753i	0.0721181	+	0.121331i
$955$		−	2.49777i		−	0.0808258i
$956$	7.02523	−	12.9140i	0.227212	−	0.417669i
$957$			16.8362i			0.544237i
$958$	29.9971	−	17.8300i	0.969161	−	0.576061i
$959$	−12.9668			−0.418721
$960$	12.1850	−	0.929339i	0.393270	−	0.0299943i
$961$	−28.7307			−0.926795
$962$	6.45476	−	3.83665i	0.208110	−	0.123699i
$963$			7.32255i			0.235966i
$964$	−9.05992	+	16.6543i	−0.291800	+	0.536398i
$965$			7.13085i			0.229550i
$966$	−9.23778	−	15.5416i	−0.297221	−	0.500042i
$967$	−16.0161			−0.515043			−0.257522	−	0.966273i	$-0.582906\pi$
$967$	−16.0161			−0.515043			−0.257522	+	0.966273i	$0.582906\pi$
$968$	−1.02270	−	26.8574i	−0.0328710	−	0.863228i
$969$	2.44213			0.0784525
$970$	2.10653	+	3.54401i	0.0676366	+	0.113791i
$971$		−	56.1089i		−	1.80062i	−0.435248	−	0.900311i	$-0.643339\pi$
$971$		−	56.1089i		−	1.80062i	0.435248	−	0.900311i	$-0.356661\pi$
$972$	11.9259	+	6.48769i	0.382523	+	0.208093i
$973$		−	10.5377i		−	0.337823i
$974$	−17.3075	+	10.2874i	−0.554568	+	0.329631i
$975$	1.85636			0.0594512
$976$	−11.9171	+	7.71177i	−0.381457	+	0.246848i
$977$	31.2207			0.998839			0.499420	−	0.866360i	$-0.333547\pi$
$977$	31.2207			0.998839			0.499420	+	0.866360i	$0.333547\pi$
$978$	4.68896	−	2.78708i	0.149936	−	0.0891209i
$979$		−	15.3122i		−	0.489382i
$980$	1.75686	+	0.955734i	0.0561210	+	0.0305298i
$981$		−	7.43210i		−	0.237289i
$982$	10.5500	+	17.7492i	0.336664	+	0.566400i
$983$	−1.55847			−0.0497074			−0.0248537	−	0.999691i	$-0.507912\pi$
$983$	−1.55847			−0.0497074			−0.0248537	+	0.999691i	$0.507912\pi$
$984$	−19.8103	+	0.754360i	−0.631530	+	0.0240481i
$985$	−9.55907			−0.304577
$986$	−16.8877	−	28.4117i	−0.537814	−	0.904814i
$987$		−	16.3227i		−	0.519557i
$988$	0.715557	−	1.31536i	0.0227649	−	0.0418472i
$989$			2.52676i			0.0803464i
$990$	−0.991678	+	0.589445i	−0.0315176	+	0.0187338i
$991$	−23.8733			−0.758360			−0.379180	−	0.925323i	$-0.623794\pi$
$991$	−23.8733			−0.758360			−0.379180	+	0.925323i	$0.623794\pi$
$992$	7.63526	+	3.78444i	0.242420	+	0.120156i
$993$	−33.4671			−1.06205
$994$	16.2756	−	9.67406i	0.516229	−	0.306843i
$995$		−	1.51023i		−	0.0478774i
$996$	−13.1795	+	24.2270i	−0.417608	+	0.767662i
$997$			16.1965i			0.512949i	0.966551	+	0.256474i	$0.0825609\pi$
$997$			16.1965i			0.512949i	−0.966551	+	0.256474i	$0.917439\pi$
$998$	16.5734	+	27.8829i	0.524620	+	0.882617i
$999$	24.4711			0.774231

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.b.d.141.9	✓	12
4.3	odd	2		1120.2.b.d.561.4		12
8.3	odd	2		1120.2.b.d.561.9		12
8.5	even	2	inner	280.2.b.d.141.10	yes	12
16.3	odd	4		8960.2.a.cg.1.5		6
16.5	even	4		8960.2.a.ca.1.5		6
16.11	odd	4		8960.2.a.cd.1.2		6
16.13	even	4		8960.2.a.cf.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.b.d.141.9	✓	12	1.1	even	1	trivial
280.2.b.d.141.10	yes	12	8.5	even	2	inner
1120.2.b.d.561.4		12	4.3	odd	2
1120.2.b.d.561.9		12	8.3	odd	2
8960.2.a.ca.1.5		6	16.5	even	4
8960.2.a.cd.1.2		6	16.11	odd	4
8960.2.a.cf.1.2		6	16.13	even	4
8960.2.a.cg.1.5		6	16.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21568 - 0.722588i) q^{2} +1.52755i q^{3} +(0.955734 - 1.75686i) q^{4} +1.00000i q^{5} +(1.10379 + 1.85701i) q^{6} +1.00000 q^{7} +(-0.107626 - 2.82638i) q^{8} +0.666582 q^{9} +O(q^{10})\)	\(q+(1.21568 - 0.722588i) q^{2} +1.52755i q^{3} +(0.955734 - 1.75686i) q^{4} +1.00000i q^{5} +(1.10379 + 1.85701i) q^{6} +1.00000 q^{7} +(-0.107626 - 2.82638i) q^{8} +0.666582 q^{9} +(0.722588 + 1.21568i) q^{10} +1.22377i q^{11} +(2.68370 + 1.45993i) q^{12} +1.21525i q^{13} +(1.21568 - 0.722588i) q^{14} -1.52755 q^{15} +(-2.17314 - 3.35819i) q^{16} +2.59497 q^{17} +(0.810347 - 0.481664i) q^{18} -0.616085i q^{19} +(1.75686 + 0.955734i) q^{20} +1.52755i q^{21} +(0.884280 + 1.48771i) q^{22} -8.36914 q^{23} +(4.31744 - 0.164405i) q^{24} -1.00000 q^{25} +(0.878126 + 1.47735i) q^{26} +5.60090i q^{27} +(0.955734 - 1.75686i) q^{28} -9.00634i q^{29} +(-1.85701 + 1.10379i) q^{30} -1.50644 q^{31} +(-5.06843 - 2.51218i) q^{32} -1.86937 q^{33} +(3.15464 - 1.87509i) q^{34} +1.00000i q^{35} +(0.637075 - 1.17109i) q^{36} -4.36914i q^{37} +(-0.445175 - 0.748959i) q^{38} -1.85636 q^{39} +(2.82638 - 0.107626i) q^{40} -4.58844 q^{41} +(1.10379 + 1.85701i) q^{42} -0.301914i q^{43} +(2.15000 + 1.16960i) q^{44} +0.666582i q^{45} +(-10.1742 + 6.04744i) q^{46} -10.6855 q^{47} +(5.12981 - 3.31959i) q^{48} +1.00000 q^{49} +(-1.21568 + 0.722588i) q^{50} +3.96395i q^{51} +(2.13503 + 1.16146i) q^{52} +4.62460i q^{53} +(4.04714 + 6.80887i) q^{54} -1.22377 q^{55} +(-0.107626 - 2.82638i) q^{56} +0.941102 q^{57} +(-6.50787 - 10.9488i) q^{58} -5.34775i q^{59} +(-1.45993 + 2.68370i) q^{60} -3.54867i q^{61} +(-1.83134 + 1.08853i) q^{62} +0.666582 q^{63} +(-7.97683 + 0.608384i) q^{64} -1.21525 q^{65} +(-2.27255 + 1.35079i) q^{66} +9.16229i q^{67} +(2.48010 - 4.55901i) q^{68} -12.7843i q^{69} +(0.722588 + 1.21568i) q^{70} +13.3881 q^{71} +(-0.0717416 - 1.88401i) q^{72} +15.3881 q^{73} +(-3.15709 - 5.31145i) q^{74} -1.52755i q^{75} +(-1.08238 - 0.588813i) q^{76} +1.22377i q^{77} +(-2.25673 + 1.34138i) q^{78} -6.69217 q^{79} +(3.35819 - 2.17314i) q^{80} -6.55592 q^{81} +(-5.57805 + 3.31555i) q^{82} +9.02746i q^{83} +(2.68370 + 1.45993i) q^{84} +2.59497i q^{85} +(-0.218160 - 0.367030i) q^{86} +13.7577 q^{87} +(3.45883 - 0.131709i) q^{88} -12.5124 q^{89} +(0.481664 + 0.810347i) q^{90} +1.21525i q^{91} +(-7.99867 + 14.7034i) q^{92} -2.30116i q^{93} +(-12.9901 + 7.72123i) q^{94} +0.616085 q^{95} +(3.83749 - 7.74229i) q^{96} +2.91526 q^{97} +(1.21568 - 0.722588i) q^{98} +0.815742i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9	\( 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9} + 16 q^{12} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{20} + 12 q^{22} + 8 q^{23} - 24 q^{24} - 12 q^{25} + 6 q^{28} + 12 q^{30} + 24 q^{31} - 2 q^{32} - 24 q^{33} - 20 q^{34} - 18 q^{36} + 12 q^{38} - 48 q^{39} + 12 q^{40} - 16 q^{41} + 16 q^{44} - 48 q^{46} - 16 q^{47} + 20 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{52} + 44 q^{54} - 8 q^{55} + 10 q^{56} + 40 q^{57} + 4 q^{58} - 8 q^{60} + 8 q^{62} - 20 q^{63} - 6 q^{64} + 8 q^{65} + 64 q^{66} - 56 q^{68} - 32 q^{71} - 46 q^{72} - 8 q^{73} - 32 q^{74} - 12 q^{76} - 24 q^{78} + 8 q^{80} + 60 q^{81} - 28 q^{82} + 16 q^{84} - 76 q^{86} + 48 q^{87} - 40 q^{88} - 48 q^{89} + 24 q^{90} + 12 q^{94} + 28 q^{96} + 32 q^{97} - 2 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9 + 16 * q^12 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^20 + 12 * q^22 + 8 * q^23 - 24 * q^24 - 12 * q^25 + 6 * q^28 + 12 * q^30 + 24 * q^31 - 2 * q^32 - 24 * q^33 - 20 * q^34 - 18 * q^36 + 12 * q^38 - 48 * q^39 + 12 * q^40 - 16 * q^41 + 16 * q^44 - 48 * q^46 - 16 * q^47 + 20 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^52 + 44 * q^54 - 8 * q^55 + 10 * q^56 + 40 * q^57 + 4 * q^58 - 8 * q^60 + 8 * q^62 - 20 * q^63 - 6 * q^64 + 8 * q^65 + 64 * q^66 - 56 * q^68 - 32 * q^71 - 46 * q^72 - 8 * q^73 - 32 * q^74 - 12 * q^76 - 24 * q^78 + 8 * q^80 + 60 * q^81 - 28 * q^82 + 16 * q^84 - 76 * q^86 + 48 * q^87 - 40 * q^88 - 48 * q^89 + 24 * q^90 + 12 * q^94 + 28 * q^96 + 32 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

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