LMFDB - Embedded newform 574.2.f.a.337.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(155,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("574.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 40 x^{18} + 666 x^{16} + 6052 x^{14} + 33033 x^{12} + 112020 x^{10} + 235396 x^{8} + \cdots + 8464 $ x^20 + 40x^18 + 666x^16 + 6052x^14 + 33033x^12 + 112020x^10 + 235396x^8 + 296360x^6 + 208336x^4 + 71168*x^2 + 8464
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.10
Root			$-3.31217i$ of defining polynomial
Character	$\chi$	$=$	574.337
Dual form			574.2.f.a.155.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(2.34205 + 2.34205i) q^{3} -1.00000 q^{4} +2.35731i q^{5} +(-2.34205 + 2.34205i) q^{6} +(-0.707107 - 0.707107i) q^{7} -1.00000i q^{8} +7.97044i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(2.34205 + 2.34205i) q^{3} -1.00000 q^{4} +2.35731i q^{5} +(-2.34205 + 2.34205i) q^{6} +(-0.707107 - 0.707107i) q^{7} -1.00000i q^{8} +7.97044i q^{9} -2.35731 q^{10} +(1.67518 + 1.67518i) q^{11} +(-2.34205 - 2.34205i) q^{12} +(-4.42004 - 4.42004i) q^{13} +(0.707107 - 0.707107i) q^{14} +(-5.52095 + 5.52095i) q^{15} +1.00000 q^{16} +(3.75627 - 3.75627i) q^{17} -7.97044 q^{18} +(3.52259 - 3.52259i) q^{19} -2.35731i q^{20} -3.31217i q^{21} +(-1.67518 + 1.67518i) q^{22} -1.71869 q^{23} +(2.34205 - 2.34205i) q^{24} -0.556923 q^{25} +(4.42004 - 4.42004i) q^{26} +(-11.6410 + 11.6410i) q^{27} +(0.707107 + 0.707107i) q^{28} +(5.42613 + 5.42613i) q^{29} +(-5.52095 - 5.52095i) q^{30} +2.57310 q^{31} +1.00000i q^{32} +7.84674i q^{33} +(3.75627 + 3.75627i) q^{34} +(1.66687 - 1.66687i) q^{35} -7.97044i q^{36} -5.09991 q^{37} +(3.52259 + 3.52259i) q^{38} -20.7040i q^{39} +2.35731 q^{40} +(0.943192 + 6.33328i) q^{41} +3.31217 q^{42} -5.89724i q^{43} +(-1.67518 - 1.67518i) q^{44} -18.7888 q^{45} -1.71869i q^{46} +(-0.679779 + 0.679779i) q^{47} +(2.34205 + 2.34205i) q^{48} +1.00000i q^{49} -0.556923i q^{50} +17.5948 q^{51} +(4.42004 + 4.42004i) q^{52} +(-4.33950 - 4.33950i) q^{53} +(-11.6410 - 11.6410i) q^{54} +(-3.94893 + 3.94893i) q^{55} +(-0.707107 + 0.707107i) q^{56} +16.5002 q^{57} +(-5.42613 + 5.42613i) q^{58} +10.5692 q^{59} +(5.52095 - 5.52095i) q^{60} +7.85529i q^{61} +2.57310i q^{62} +(5.63595 - 5.63595i) q^{63} -1.00000 q^{64} +(10.4194 - 10.4194i) q^{65} -7.84674 q^{66} +(-3.96328 + 3.96328i) q^{67} +(-3.75627 + 3.75627i) q^{68} +(-4.02526 - 4.02526i) q^{69} +(1.66687 + 1.66687i) q^{70} +(-6.54439 - 6.54439i) q^{71} +7.97044 q^{72} -0.118582i q^{73} -5.09991i q^{74} +(-1.30434 - 1.30434i) q^{75} +(-3.52259 + 3.52259i) q^{76} -2.36907i q^{77} +20.7040 q^{78} +(-5.91431 - 5.91431i) q^{79} +2.35731i q^{80} -30.6166 q^{81} +(-6.33328 + 0.943192i) q^{82} -5.14412 q^{83} +3.31217i q^{84} +(8.85470 + 8.85470i) q^{85} +5.89724 q^{86} +25.4166i q^{87} +(1.67518 - 1.67518i) q^{88} +(-4.61120 - 4.61120i) q^{89} -18.7888i q^{90} +6.25089i q^{91} +1.71869 q^{92} +(6.02635 + 6.02635i) q^{93} +(-0.679779 - 0.679779i) q^{94} +(8.30386 + 8.30386i) q^{95} +(-2.34205 + 2.34205i) q^{96} +(8.67715 - 8.67715i) q^{97} -1.00000 q^{98} +(-13.3519 + 13.3519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} - 20 q^{4} + 4 q^{6}+O(q^{10}) $ 20 * q - 4 * q^3 - 20 * q^4 + 4 * q^6	$ 20 q - 4 q^{3} - 20 q^{4} + 4 q^{6} + 16 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{15} + 20 q^{16} - 4 q^{17} - 20 q^{18} + 12 q^{19} - 16 q^{22} + 8 q^{23} - 4 q^{24} - 20 q^{25} + 20 q^{26} - 16 q^{27} + 12 q^{29} + 4 q^{30} - 8 q^{31} - 4 q^{34} - 32 q^{37} + 12 q^{38} - 12 q^{41} - 16 q^{44} - 72 q^{45} + 12 q^{47} - 4 q^{48} + 80 q^{51} + 20 q^{52} - 16 q^{54} - 20 q^{55} + 48 q^{57} - 12 q^{58} - 8 q^{59} - 4 q^{60} + 16 q^{63} - 20 q^{64} + 20 q^{65} - 40 q^{66} - 4 q^{67} + 4 q^{68} - 8 q^{69} - 8 q^{71} + 20 q^{72} + 20 q^{75} - 12 q^{76} + 24 q^{78} + 24 q^{79} + 4 q^{81} + 12 q^{82} - 4 q^{85} + 8 q^{86} + 16 q^{88} - 48 q^{89} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 28 q^{95} + 4 q^{96} + 16 q^{97} - 20 q^{98} - 8 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 - 20 * q^4 + 4 * q^6 + 16 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^15 + 20 * q^16 - 4 * q^17 - 20 * q^18 + 12 * q^19 - 16 * q^22 + 8 * q^23 - 4 * q^24 - 20 * q^25 + 20 * q^26 - 16 * q^27 + 12 * q^29 + 4 * q^30 - 8 * q^31 - 4 * q^34 - 32 * q^37 + 12 * q^38 - 12 * q^41 - 16 * q^44 - 72 * q^45 + 12 * q^47 - 4 * q^48 + 80 * q^51 + 20 * q^52 - 16 * q^54 - 20 * q^55 + 48 * q^57 - 12 * q^58 - 8 * q^59 - 4 * q^60 + 16 * q^63 - 20 * q^64 + 20 * q^65 - 40 * q^66 - 4 * q^67 + 4 * q^68 - 8 * q^69 - 8 * q^71 + 20 * q^72 + 20 * q^75 - 12 * q^76 + 24 * q^78 + 24 * q^79 + 4 * q^81 + 12 * q^82 - 4 * q^85 + 8 * q^86 + 16 * q^88 - 48 * q^89 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 28 * q^95 + 4 * q^96 + 16 * q^97 - 20 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	2.34205	+	2.34205i	1.35219	+	1.35219i	0.883212	+	0.468974i	$0.155376\pi$
$3$	2.34205	+	2.34205i	1.35219	+	1.35219i	0.468974	+	0.883212i	$0.344624\pi$
$4$	−1.00000			−0.500000
$5$			2.35731i			1.05422i	0.849796	+	0.527111i	$0.176725\pi$
$5$			2.35731i			1.05422i	−0.849796	+	0.527111i	$0.823275\pi$
$6$	−2.34205	+	2.34205i	−0.956140	+	0.956140i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		−	1.00000i		−	0.353553i
$9$			7.97044i			2.65681i
$10$	−2.35731			−0.745448
$11$	1.67518	+	1.67518i	0.505087	+	0.505087i	0.913014	−	0.407928i	$-0.133748\pi$
$11$	1.67518	+	1.67518i	0.505087	+	0.505087i	−0.407928	+	0.913014i	$0.633748\pi$
$12$	−2.34205	−	2.34205i	−0.676093	−	0.676093i
$13$	−4.42004	−	4.42004i	−1.22590	−	1.22590i	−0.965501	−	0.260398i	$-0.916146\pi$
$13$	−4.42004	−	4.42004i	−1.22590	−	1.22590i	−0.260398	−	0.965501i	$-0.583854\pi$
$14$	0.707107	−	0.707107i	0.188982	−	0.188982i
$15$	−5.52095	+	5.52095i	−1.42550	+	1.42550i
$16$	1.00000			0.250000
$17$	3.75627	−	3.75627i	0.911029	−	0.911029i	−0.0853244	−	0.996353i	$-0.527193\pi$
$17$	3.75627	−	3.75627i	0.911029	−	0.911029i	0.996353	+	0.0853244i	$0.0271927\pi$
$18$	−7.97044			−1.87865
$19$	3.52259	−	3.52259i	0.808139	−	0.808139i	−0.176213	−	0.984352i	$-0.556385\pi$
$19$	3.52259	−	3.52259i	0.808139	−	0.808139i	0.984352	+	0.176213i	$0.0563848\pi$
$20$		−	2.35731i		−	0.527111i
$21$		−	3.31217i		−	0.722774i
$22$	−1.67518	+	1.67518i	−0.357150	+	0.357150i
$23$	−1.71869			−0.358371			−0.179186	−	0.983815i	$-0.557346\pi$
$23$	−1.71869			−0.358371			−0.179186	+	0.983815i	$0.557346\pi$
$24$	2.34205	−	2.34205i	0.478070	−	0.478070i
$25$	−0.556923			−0.111385
$26$	4.42004	−	4.42004i	0.866842	−	0.866842i
$27$	−11.6410	+	11.6410i	−2.24032	+	2.24032i
$28$	0.707107	+	0.707107i	0.133631	+	0.133631i
$29$	5.42613	+	5.42613i	1.00761	+	1.00761i	0.999971	+	0.00763659i	$0.00243082\pi$
$29$	5.42613	+	5.42613i	1.00761	+	1.00761i	0.00763659	+	0.999971i	$0.497569\pi$
$30$	−5.52095	−	5.52095i	−1.00798	−	1.00798i
$31$	2.57310			0.462143			0.231072	−	0.972937i	$-0.425777\pi$
$31$	2.57310			0.462143			0.231072	+	0.972937i	$0.425777\pi$
$32$			1.00000i			0.176777i
$33$			7.84674i			1.36594i
$34$	3.75627	+	3.75627i	0.644195	+	0.644195i
$35$	1.66687	−	1.66687i	0.281753	−	0.281753i
$36$		−	7.97044i		−	1.32841i
$37$	−5.09991			−0.838420			−0.419210	−	0.907889i	$-0.637693\pi$
$37$	−5.09991			−0.838420			−0.419210	+	0.907889i	$0.637693\pi$
$38$	3.52259	+	3.52259i	0.571440	+	0.571440i
$39$		−	20.7040i		−	3.31529i
$40$	2.35731			0.372724
$41$	0.943192	+	6.33328i	0.147302	+	0.989092i
$41$	0.943192	+	6.33328i	0.147302	+	0.989092i
$42$	3.31217			0.511078
$43$		−	5.89724i		−	0.899321i	−0.893200	−	0.449661i	$-0.851545\pi$
$43$		−	5.89724i		−	0.899321i	0.893200	−	0.449661i	$-0.148455\pi$
$44$	−1.67518	−	1.67518i	−0.252543	−	0.252543i
$45$	−18.7888			−2.80087
$46$		−	1.71869i		−	0.253407i
$47$	−0.679779	+	0.679779i	−0.0991560	+	0.0991560i	−0.754945	−	0.655789i	$-0.772336\pi$
$47$	−0.679779	+	0.679779i	−0.0991560	+	0.0991560i	0.655789	+	0.754945i	$0.272336\pi$
$48$	2.34205	+	2.34205i	0.338046	+	0.338046i
$49$			1.00000i			0.142857i
$50$		−	0.556923i		−	0.0787608i
$51$	17.5948			2.46376
$52$	4.42004	+	4.42004i	0.612950	+	0.612950i
$53$	−4.33950	−	4.33950i	−0.596076	−	0.596076i	0.343190	−	0.939266i	$-0.388493\pi$
$53$	−4.33950	−	4.33950i	−0.596076	−	0.596076i	−0.939266	+	0.343190i	$0.888493\pi$
$54$	−11.6410	−	11.6410i	−1.58415	−	1.58415i
$55$	−3.94893	+	3.94893i	−0.532474	+	0.532474i
$56$	−0.707107	+	0.707107i	−0.0944911	+	0.0944911i
$57$	16.5002			2.18551
$58$	−5.42613	+	5.42613i	−0.712486	+	0.712486i
$59$	10.5692			1.37599			0.687997	−	0.725714i	$-0.258490\pi$
$59$	10.5692			1.37599			0.687997	+	0.725714i	$0.258490\pi$
$60$	5.52095	−	5.52095i	0.712752	−	0.712752i
$61$			7.85529i			1.00577i	0.864354	+	0.502883i	$0.167727\pi$
$61$			7.85529i			1.00577i	−0.864354	+	0.502883i	$0.832273\pi$
$62$			2.57310i			0.326785i
$63$	5.63595	−	5.63595i	0.710063	−	0.710063i
$64$	−1.00000			−0.125000
$65$	10.4194	−	10.4194i	1.29237	−	1.29237i
$66$	−7.84674			−0.965867
$67$	−3.96328	+	3.96328i	−0.484191	+	0.484191i	−0.906467	−	0.422276i	$-0.861231\pi$
$67$	−3.96328	+	3.96328i	−0.484191	+	0.484191i	0.422276	+	0.906467i	$0.361231\pi$
$68$	−3.75627	+	3.75627i	−0.455514	+	0.455514i
$69$	−4.02526	−	4.02526i	−0.484584	−	0.484584i
$70$	1.66687	+	1.66687i	0.199229	+	0.199229i
$71$	−6.54439	−	6.54439i	−0.776676	−	0.776676i	0.202588	−	0.979264i	$-0.435065\pi$
$71$	−6.54439	−	6.54439i	−0.776676	−	0.776676i	−0.979264	+	0.202588i	$0.935065\pi$
$72$	7.97044			0.939325
$73$		−	0.118582i		−	0.0138790i	−0.999976	−	0.00693948i	$-0.997791\pi$
$73$		−	0.118582i		−	0.0138790i	0.999976	−	0.00693948i	$-0.00220892\pi$
$74$		−	5.09991i		−	0.592852i
$75$	−1.30434	−	1.30434i	−0.150613	−	0.150613i
$76$	−3.52259	+	3.52259i	−0.404069	+	0.404069i
$77$		−	2.36907i		−	0.269980i
$78$	20.7040			2.34426
$79$	−5.91431	−	5.91431i	−0.665412	−	0.665412i	0.291238	−	0.956651i	$-0.405933\pi$
$79$	−5.91431	−	5.91431i	−0.665412	−	0.665412i	−0.956651	+	0.291238i	$0.905933\pi$
$80$			2.35731i			0.263556i
$81$	−30.6166			−3.40184
$82$	−6.33328	+	0.943192i	−0.699393	+	0.104158i
$83$	−5.14412			−0.564641			−0.282320	−	0.959320i	$-0.591104\pi$
$83$	−5.14412			−0.564641			−0.282320	+	0.959320i	$0.591104\pi$
$84$			3.31217i			0.361387i
$85$	8.85470	+	8.85470i	0.960427	+	0.960427i
$86$	5.89724			0.635916
$87$			25.4166i			2.72495i
$88$	1.67518	−	1.67518i	0.178575	−	0.178575i
$89$	−4.61120	−	4.61120i	−0.488786	−	0.488786i	0.419137	−	0.907923i	$-0.362333\pi$
$89$	−4.61120	−	4.61120i	−0.488786	−	0.488786i	−0.907923	+	0.419137i	$0.862333\pi$
$90$		−	18.7888i		−	1.98052i
$91$			6.25089i			0.655271i
$92$	1.71869			0.179186
$93$	6.02635	+	6.02635i	0.624904	+	0.624904i
$94$	−0.679779	−	0.679779i	−0.0701138	−	0.0701138i
$95$	8.30386	+	8.30386i	0.851958	+	0.851958i
$96$	−2.34205	+	2.34205i	−0.239035	+	0.239035i
$97$	8.67715	−	8.67715i	0.881031	−	0.881031i	−0.112608	−	0.993639i	$-0.535921\pi$
$97$	8.67715	−	8.67715i	0.881031	−	0.881031i	0.993639	+	0.112608i	$0.0359205\pi$
$98$	−1.00000			−0.101015
$99$	−13.3519	+	13.3519i	−1.34192	+	1.34192i
$100$	0.556923			0.0556923
$101$	4.71955	−	4.71955i	0.469613	−	0.469613i	−0.432176	−	0.901789i	$-0.642254\pi$
$101$	4.71955	−	4.71955i	0.469613	−	0.469613i	0.901789	+	0.432176i	$0.142254\pi$
$102$			17.5948i			1.74214i
$103$			12.7473i			1.25603i	0.778202	+	0.628014i	$0.216132\pi$
$103$			12.7473i			1.25603i	−0.778202	+	0.628014i	$0.783868\pi$
$104$	−4.42004	+	4.42004i	−0.433421	+	0.433421i
$105$	7.80781			0.761964
$106$	4.33950	−	4.33950i	0.421490	−	0.421490i
$107$	−11.0852			−1.07165			−0.535826	−	0.844329i	$-0.680000\pi$
$107$	−11.0852			−1.07165			−0.535826	+	0.844329i	$0.680000\pi$
$108$	11.6410	−	11.6410i	1.12016	−	1.12016i
$109$	−5.41578	+	5.41578i	−0.518738	+	0.518738i	−0.917189	−	0.398451i	$-0.869548\pi$
$109$	−5.41578	+	5.41578i	−0.518738	+	0.518738i	0.398451	+	0.917189i	$0.369548\pi$
$110$	−3.94893	−	3.94893i	−0.376516	−	0.376516i
$111$	−11.9443	−	11.9443i	−1.13370	−	1.13370i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	0.000169098	0		1.59074e−5	0		7.95369e−6	−	1.00000i	$-0.499997\pi$
$113$	0.000169098	0		1.59074e−5	0		7.95369e−6		1.00000i	$0.499997\pi$
$114$			16.5002i			1.54539i
$115$		−	4.05148i		−	0.377803i
$116$	−5.42613	−	5.42613i	−0.503804	−	0.503804i
$117$	35.2297	−	35.2297i	3.25699	−	3.25699i
$118$			10.5692i			0.972974i
$119$	−5.31217			−0.486965
$120$	5.52095	+	5.52095i	0.503992	+	0.503992i
$121$		−	5.38752i		−	0.489775i
$122$	−7.85529			−0.711184
$123$	−12.6239	+	17.0419i	−1.13826	+	1.53662i
$124$	−2.57310			−0.231072
$125$			10.4737i			0.936798i
$126$	5.63595	+	5.63595i	0.502091	+	0.502091i
$127$	18.4768			1.63955			0.819777	−	0.572683i	$-0.194097\pi$
$127$	18.4768			1.63955			0.819777	+	0.572683i	$0.194097\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	13.8117	−	13.8117i	1.21605	−	1.21605i
$130$	10.4194	+	10.4194i	0.913844	+	0.913844i
$131$			11.2520i			0.983089i	0.870852	+	0.491545i	$0.163568\pi$
$131$			11.2520i			0.983089i	−0.870852	+	0.491545i	$0.836432\pi$
$132$		−	7.84674i		−	0.682971i
$133$	−4.98170			−0.431968
$134$	−3.96328	−	3.96328i	−0.342375	−	0.342375i
$135$	−27.4416	−	27.4416i	−2.36179	−	2.36179i
$136$	−3.75627	−	3.75627i	−0.322097	−	0.322097i
$137$	14.5869	−	14.5869i	1.24625	−	1.24625i	0.288882	−	0.957365i	$-0.406717\pi$
$137$	14.5869	−	14.5869i	1.24625	−	1.24625i	0.957365	−	0.288882i	$-0.0932835\pi$
$138$	4.02526	−	4.02526i	0.342653	−	0.342653i
$139$	15.3497			1.30195			0.650973	−	0.759101i	$-0.274361\pi$
$139$	15.3497			1.30195			0.650973	+	0.759101i	$0.274361\pi$
$140$	−1.66687	+	1.66687i	−0.140876	+	0.140876i
$141$	−3.18416			−0.268155
$142$	6.54439	−	6.54439i	0.549193	−	0.549193i
$143$		−	14.8088i		−	1.23837i
$144$			7.97044i			0.664203i
$145$	−12.7911	+	12.7911i	−1.06224	+	1.06224i
$146$	0.118582			0.00981391
$147$	−2.34205	+	2.34205i	−0.193169	+	0.193169i
$148$	5.09991			0.419210
$149$	12.0801	−	12.0801i	0.989639	−	0.989639i	−0.0103078	−	0.999947i	$-0.503281\pi$
$149$	12.0801	−	12.0801i	0.989639	−	0.989639i	0.999947	+	0.0103078i	$0.00328112\pi$
$150$	1.30434	−	1.30434i	0.106499	−	0.106499i
$151$	−1.36000	−	1.36000i	−0.110675	−	0.110675i	0.649600	−	0.760276i	$-0.274936\pi$
$151$	−1.36000	−	1.36000i	−0.110675	−	0.110675i	−0.760276	+	0.649600i	$0.774936\pi$
$152$	−3.52259	−	3.52259i	−0.285720	−	0.285720i
$153$	29.9391	+	29.9391i	2.42043	+	2.42043i
$154$	2.36907			0.190905
$155$			6.06561i			0.487202i
$156$			20.7040i			1.65764i
$157$	−5.51651	−	5.51651i	−0.440265	−	0.440265i	0.451836	−	0.892101i	$-0.350769\pi$
$157$	−5.51651	−	5.51651i	−0.440265	−	0.440265i	−0.892101	+	0.451836i	$0.850769\pi$
$158$	5.91431	−	5.91431i	0.470518	−	0.470518i
$159$		−	20.3267i		−	1.61201i
$160$	−2.35731			−0.186362
$161$	1.21530	+	1.21530i	0.0957787	+	0.0957787i
$162$		−	30.6166i		−	2.40547i
$163$	−1.13951			−0.0892533			−0.0446266	−	0.999004i	$-0.514210\pi$
$163$	−1.13951			−0.0892533			−0.0446266	+	0.999004i	$0.514210\pi$
$164$	−0.943192	−	6.33328i	−0.0736509	−	0.494546i
$165$	−18.4972			−1.44001
$166$		−	5.14412i		−	0.399261i
$167$	5.88635	+	5.88635i	0.455500	+	0.455500i	0.897175	−	0.441675i	$-0.145616\pi$
$167$	5.88635	+	5.88635i	0.455500	+	0.455500i	−0.441675	+	0.897175i	$0.645616\pi$
$168$	−3.31217			−0.255539
$169$			26.0736i			2.00566i
$170$	−8.85470	+	8.85470i	−0.679124	+	0.679124i
$171$	28.0766	+	28.0766i	2.14707	+	2.14707i
$172$			5.89724i			0.449661i
$173$			8.08562i			0.614739i	0.951590	+	0.307369i	$0.0994487\pi$
$173$			8.08562i			0.614739i	−0.951590	+	0.307369i	$0.900551\pi$
$174$	−25.4166			−1.92683
$175$	0.393804	+	0.393804i	0.0297688	+	0.0297688i
$176$	1.67518	+	1.67518i	0.126272	+	0.126272i
$177$	24.7537	+	24.7537i	1.86060	+	1.86060i
$178$	4.61120	−	4.61120i	0.345624	−	0.345624i
$179$	13.4722	−	13.4722i	1.00696	−	1.00696i	0.00698608	−	0.999976i	$-0.497776\pi$
$179$	13.4722	−	13.4722i	1.00696	−	1.00696i	0.999976	−	0.00698608i	$-0.00222376\pi$
$180$	18.7888			1.40044
$181$	9.70528	−	9.70528i	0.721388	−	0.721388i	−0.247500	−	0.968888i	$-0.579609\pi$
$181$	9.70528	−	9.70528i	0.721388	−	0.721388i	0.968888	+	0.247500i	$0.0796090\pi$
$182$	−6.25089			−0.463347
$183$	−18.3975	+	18.3975i	−1.35998	+	1.35998i
$184$			1.71869i			0.126703i
$185$		−	12.0221i		−	0.883881i
$186$	−6.02635	+	6.02635i	−0.441874	+	0.441874i
$187$	12.5849			0.920297
$188$	0.679779	−	0.679779i	0.0495780	−	0.0495780i
$189$	16.4629			1.19750
$190$	−8.30386	+	8.30386i	−0.602425	+	0.602425i
$191$	−5.17631	+	5.17631i	−0.374544	+	0.374544i	−0.869129	−	0.494585i	$-0.835320\pi$
$191$	−5.17631	+	5.17631i	−0.374544	+	0.374544i	0.494585	+	0.869129i	$0.335320\pi$
$192$	−2.34205	−	2.34205i	−0.169023	−	0.169023i
$193$	−17.5844	−	17.5844i	−1.26575	−	1.26575i	−0.948261	−	0.317492i	$-0.897159\pi$
$193$	−17.5844	−	17.5844i	−1.26575	−	1.26575i	−0.317492	−	0.948261i	$-0.602841\pi$
$194$	8.67715	+	8.67715i	0.622983	+	0.622983i
$195$	48.8057			3.49505
$196$		−	1.00000i		−	0.0714286i
$197$		−	21.8173i		−	1.55442i	−0.629244	−	0.777208i	$-0.716635\pi$
$197$		−	21.8173i		−	1.55442i	0.629244	−	0.777208i	$-0.283365\pi$
$198$	−13.3519	−	13.3519i	−0.948881	−	0.948881i
$199$	−16.0664	+	16.0664i	−1.13891	+	1.13891i	−0.150270	+	0.988645i	$0.548014\pi$
$199$	−16.0664	+	16.0664i	−1.13891	+	1.13891i	−0.988645	+	0.150270i	$0.951986\pi$
$200$			0.556923i			0.0393804i
$201$	−18.5644			−1.30943
$202$	4.71955	+	4.71955i	0.332066	+	0.332066i
$203$		−	7.67371i		−	0.538589i
$204$	−17.5948			−1.23188
$205$	−14.9295	+	2.22340i	−1.04272	+	0.155289i
$206$	−12.7473			−0.888146
$207$		−	13.6987i		−	0.952125i
$208$	−4.42004	−	4.42004i	−0.306475	−	0.306475i
$209$	11.8020			0.816360
$210$			7.80781i			0.538790i
$211$	−3.30054	+	3.30054i	−0.227219	+	0.227219i	−0.811530	−	0.584311i	$-0.801365\pi$
$211$	−3.30054	+	3.30054i	−0.227219	+	0.227219i	0.584311	+	0.811530i	$0.301365\pi$
$212$	4.33950	+	4.33950i	0.298038	+	0.298038i
$213$		−	30.6546i		−	2.10042i
$214$		−	11.0852i		−	0.757772i
$215$	13.9016			0.948084
$216$	11.6410	+	11.6410i	0.792073	+	0.792073i
$217$	−1.81946	−	1.81946i	−0.123513	−	0.123513i
$218$	−5.41578	−	5.41578i	−0.366803	−	0.366803i
$219$	0.277725	−	0.277725i	0.0187669	−	0.0187669i
$220$	3.94893	−	3.94893i	0.266237	−	0.266237i
$221$	−33.2057			−2.23366
$222$	11.9443	−	11.9443i	0.801647	−	0.801647i
$223$	−5.76975			−0.386371			−0.193186	−	0.981162i	$-0.561882\pi$
$223$	−5.76975			−0.386371			−0.193186	+	0.981162i	$0.561882\pi$
$224$	0.707107	−	0.707107i	0.0472456	−	0.0472456i
$225$		−	4.43892i		−	0.295928i
$226$		0	0.000169098i		0	1.12482e-5i
$227$	7.60640	−	7.60640i	0.504855	−	0.504855i	−0.408088	−	0.912943i	$-0.633804\pi$
$227$	7.60640	−	7.60640i	0.504855	−	0.504855i	0.912943	+	0.408088i	$0.133804\pi$
$228$	−16.5002			−1.09275
$229$	19.3861	−	19.3861i	1.28107	−	1.28107i	0.341013	−	0.940058i	$-0.389230\pi$
$229$	19.3861	−	19.3861i	1.28107	−	1.28107i	0.940058	−	0.341013i	$-0.110770\pi$
$230$	4.05148			0.267147
$231$	5.54848	−	5.54848i	0.365063	−	0.365063i
$232$	5.42613	−	5.42613i	0.356243	−	0.356243i
$233$	−14.8028	−	14.8028i	−0.969764	−	0.969764i	0.0297925	−	0.999556i	$-0.490515\pi$
$233$	−14.8028	−	14.8028i	−0.969764	−	0.969764i	−0.999556	+	0.0297925i	$0.990515\pi$
$234$	35.2297	+	35.2297i	2.30304	+	2.30304i
$235$	−1.60245	−	1.60245i	−0.104532	−	0.104532i
$236$	−10.5692			−0.687997
$237$		−	27.7033i		−	1.79952i
$238$		−	5.31217i		−	0.344337i
$239$	−2.51316	−	2.51316i	−0.162563	−	0.162563i	0.621138	−	0.783701i	$-0.286671\pi$
$239$	−2.51316	−	2.51316i	−0.162563	−	0.162563i	−0.783701	+	0.621138i	$0.786671\pi$
$240$	−5.52095	+	5.52095i	−0.356376	+	0.356376i
$241$			4.77168i			0.307371i	0.988120	+	0.153685i	$0.0491142\pi$
$241$			4.77168i			0.307371i	−0.988120	+	0.153685i	$0.950886\pi$
$242$	5.38752			0.346323
$243$	−36.7826	−	36.7826i	−2.35961	−	2.35961i
$244$		−	7.85529i		−	0.502883i
$245$	−2.35731			−0.150603
$246$	−17.0419	−	12.6239i	−1.08655	−	0.804869i
$247$	−31.1401			−1.98139
$248$		−	2.57310i		−	0.163392i
$249$	−12.0478	−	12.0478i	−0.763500	−	0.763500i
$250$	−10.4737			−0.662416
$251$			23.1506i			1.46125i	0.682779	+	0.730625i	$0.260771\pi$
$251$			23.1506i			1.46125i	−0.682779	+	0.730625i	$0.739229\pi$
$252$	−5.63595	+	5.63595i	−0.355032	+	0.355032i
$253$	−2.87912	−	2.87912i	−0.181008	−	0.181008i
$254$			18.4768i			1.15934i
$255$			41.4764i			2.59735i
$256$	1.00000			0.0625000
$257$	−21.8073	−	21.8073i	−1.36030	−	1.36030i	−0.873530	−	0.486769i	$-0.838175\pi$
$257$	−21.8073	−	21.8073i	−1.36030	−	1.36030i	−0.486769	−	0.873530i	$-0.661825\pi$
$258$	13.8117	+	13.8117i	0.859877	+	0.859877i
$259$	3.60618	+	3.60618i	0.224077	+	0.224077i
$260$	−10.4194	+	10.4194i	−0.646185	+	0.646185i
$261$	−43.2487	+	43.2487i	−2.67702	+	2.67702i
$262$	−11.2520			−0.695149
$263$	2.15774	−	2.15774i	0.133052	−	0.133052i	−0.637444	−	0.770496i	$-0.720008\pi$
$263$	2.15774	−	2.15774i	0.133052	−	0.133052i	0.770496	+	0.637444i	$0.220008\pi$
$264$	7.84674			0.482933
$265$	10.2296	−	10.2296i	0.628397	−	0.628397i
$266$		−	4.98170i		−	0.305448i
$267$		−	21.5994i		−	1.32186i
$268$	3.96328	−	3.96328i	0.242096	−	0.242096i
$269$	13.0247			0.794131			0.397065	−	0.917790i	$-0.370029\pi$
$269$	13.0247			0.794131			0.397065	+	0.917790i	$0.370029\pi$
$270$	27.4416	−	27.4416i	1.67004	−	1.67004i
$271$	−14.3920			−0.874254			−0.437127	−	0.899400i	$-0.644004\pi$
$271$	−14.3920			−0.874254			−0.437127	+	0.899400i	$0.644004\pi$
$272$	3.75627	−	3.75627i	0.227757	−	0.227757i
$273$	−14.6399	+	14.6399i	−0.886048	+	0.886048i
$274$	14.5869	+	14.5869i	0.881229	+	0.881229i
$275$	−0.932948	−	0.932948i	−0.0562589	−	0.0562589i
$276$	4.02526	+	4.02526i	0.242292	+	0.242292i
$277$	28.7062			1.72479			0.862393	−	0.506239i	$-0.168965\pi$
$277$	28.7062			1.72479			0.862393	+	0.506239i	$0.168965\pi$
$278$			15.3497i			0.920615i
$279$			20.5088i			1.22783i
$280$	−1.66687	−	1.66687i	−0.0996146	−	0.0996146i
$281$	−12.2428	+	12.2428i	−0.730345	+	0.730345i	−0.970688	−	0.240343i	$-0.922740\pi$
$281$	−12.2428	+	12.2428i	−0.730345	+	0.730345i	0.240343	+	0.970688i	$0.422740\pi$
$282$		−	3.18416i		−	0.189614i
$283$	−11.6869			−0.694717			−0.347358	−	0.937732i	$-0.612921\pi$
$283$	−11.6869			−0.694717			−0.347358	+	0.937732i	$0.612921\pi$
$284$	6.54439	+	6.54439i	0.388338	+	0.388338i
$285$			38.8962i			2.30401i
$286$	14.8088			0.875661
$287$	3.81136	−	5.14524i	0.224978	−	0.303714i
$288$	−7.97044			−0.469663
$289$		−	11.2191i		−	0.659947i
$290$	−12.7911	−	12.7911i	−0.751119	−	0.751119i
$291$	40.6447			2.38264
$292$			0.118582i			0.00693948i
$293$	−6.02747	+	6.02747i	−0.352128	+	0.352128i	−0.860901	−	0.508773i	$-0.830099\pi$
$293$	−6.02747	+	6.02747i	−0.352128	+	0.352128i	0.508773	+	0.860901i	$0.330099\pi$
$294$	−2.34205	−	2.34205i	−0.136591	−	0.136591i
$295$			24.9149i			1.45060i
$296$			5.09991i			0.296426i
$297$	−39.0017			−2.26311
$298$	12.0801	+	12.0801i	0.699781	+	0.699781i
$299$	7.59667	+	7.59667i	0.439327	+	0.439327i
$300$	1.30434	+	1.30434i	0.0753063	+	0.0753063i
$301$	−4.16998	+	4.16998i	−0.240354	+	0.240354i
$302$	1.36000	−	1.36000i	0.0782592	−	0.0782592i
$303$	22.1069			1.27001
$304$	3.52259	−	3.52259i	0.202035	−	0.202035i
$305$	−18.5174			−1.06030
$306$	−29.9391	+	29.9391i	−1.71150	+	1.71150i
$307$			19.2720i			1.09991i	0.835193	+	0.549957i	$0.185356\pi$
$307$			19.2720i			1.09991i	−0.835193	+	0.549957i	$0.814644\pi$
$308$			2.36907i			0.134990i
$309$	−29.8549	+	29.8549i	−1.69838	+	1.69838i
$310$	−6.06561			−0.344504
$311$	6.75243	−	6.75243i	0.382895	−	0.382895i	−0.489249	−	0.872144i	$-0.662729\pi$
$311$	6.75243	−	6.75243i	0.382895	−	0.382895i	0.872144	+	0.489249i	$0.162729\pi$
$312$	−20.7040			−1.17213
$313$	−17.7319	+	17.7319i	−1.00227	+	1.00227i	−0.00226940	+	0.999997i	$0.500722\pi$
$313$	−17.7319	+	17.7319i	−1.00227	+	1.00227i	−0.999997	+	0.00226940i	$0.999278\pi$
$314$	5.51651	−	5.51651i	0.311315	−	0.311315i
$315$	13.2857	+	13.2857i	0.748564	+	0.748564i
$316$	5.91431	+	5.91431i	0.332706	+	0.332706i
$317$	−1.30927	−	1.30927i	−0.0735361	−	0.0735361i	0.669382	−	0.742918i	$-0.266559\pi$
$317$	−1.30927	−	1.30927i	−0.0735361	−	0.0735361i	−0.742918	+	0.669382i	$0.766559\pi$
$318$	20.3267			1.13986
$319$			18.1795i			1.01786i
$320$		−	2.35731i		−	0.131778i
$321$	−25.9623	−	25.9623i	−1.44907	−	1.44907i
$322$	−1.21530	+	1.21530i	−0.0677258	+	0.0677258i
$323$		−	26.4636i		−	1.47248i
$324$	30.6166			1.70092
$325$	2.46162	+	2.46162i	0.136546	+	0.136546i
$326$		−	1.13951i		−	0.0631116i
$327$	−25.3681			−1.40286
$328$	6.33328	−	0.943192i	0.349697	−	0.0520791i
$329$	0.961353			0.0530011
$330$		−	18.4972i		−	1.01824i
$331$	−1.74874	−	1.74874i	−0.0961192	−	0.0961192i	0.657412	−	0.753531i	$-0.271651\pi$
$331$	−1.74874	−	1.74874i	−0.0961192	−	0.0961192i	−0.753531	+	0.657412i	$0.771651\pi$
$332$	5.14412			0.282320
$333$		−	40.6485i		−	2.22753i
$334$	−5.88635	+	5.88635i	−0.322087	+	0.322087i
$335$	−9.34268	−	9.34268i	−0.510445	−	0.510445i
$336$		−	3.31217i		−	0.180693i
$337$			11.5912i			0.631412i	0.948857	+	0.315706i	$0.102241\pi$
$337$			11.5912i			0.631412i	−0.948857	+	0.315706i	$0.897759\pi$
$338$	−26.0736			−1.41822
$339$	0.000396036	0	0.000396036i	2.15097e−5	0	2.15097e-5i
$340$	−8.85470	−	8.85470i	−0.480213	−	0.480213i
$341$	4.31042	+	4.31042i	0.233422	+	0.233422i
$342$	−28.0766	+	28.0766i	−1.51821	+	1.51821i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−5.89724			−0.317958
$345$	9.48879	−	9.48879i	0.510860	−	0.510860i
$346$	−8.08562			−0.434686
$347$	10.3609	−	10.3609i	0.556202	−	0.556202i	−0.372022	−	0.928224i	$-0.621335\pi$
$347$	10.3609	−	10.3609i	0.556202	−	0.556202i	0.928224	+	0.372022i	$0.121335\pi$
$348$		−	25.4166i		−	1.36247i
$349$		−	25.0526i		−	1.34103i	−0.741894	−	0.670517i	$-0.766072\pi$
$349$		−	25.0526i		−	1.34103i	0.741894	−	0.670517i	$-0.233928\pi$
$350$	−0.393804	+	0.393804i	−0.0210497	+	0.0210497i
$351$	102.908			5.49281
$352$	−1.67518	+	1.67518i	−0.0892875	+	0.0892875i
$353$	−20.9592			−1.11555			−0.557773	−	0.829993i	$-0.688344\pi$
$353$	−20.9592			−1.11555			−0.557773	+	0.829993i	$0.688344\pi$
$354$	−24.7537	+	24.7537i	−1.31564	+	1.31564i
$355$	15.4272	−	15.4272i	0.818790	−	0.818790i
$356$	4.61120	+	4.61120i	0.244393	+	0.244393i
$357$	−12.4414	−	12.4414i	−0.658468	−	0.658468i
$358$	13.4722	+	13.4722i	0.712029	+	0.712029i
$359$	−18.8935			−0.997161			−0.498580	−	0.866843i	$-0.666145\pi$
$359$	−18.8935			−0.997161			−0.498580	+	0.866843i	$0.666145\pi$
$360$			18.7888i			0.990258i
$361$		−	5.81735i		−	0.306176i
$362$	9.70528	+	9.70528i	0.510098	+	0.510098i
$363$	12.6179	−	12.6179i	0.662267	−	0.662267i
$364$		−	6.25089i		−	0.327635i
$365$	0.279535			0.0146315
$366$	−18.3975	−	18.3975i	−0.961653	−	0.961653i
$367$		−	8.64663i		−	0.451350i	−0.974203	−	0.225675i	$-0.927541\pi$
$367$		−	8.64663i		−	0.451350i	0.974203	−	0.225675i	$-0.0724588\pi$
$368$	−1.71869			−0.0895928
$369$	−50.4790	+	7.51766i	−2.62783	+	0.391354i
$370$	12.0221			0.624998
$371$			6.13698i			0.318616i
$372$	−6.02635	−	6.02635i	−0.312452	−	0.312452i
$373$	5.15540			0.266936			0.133468	−	0.991053i	$-0.457389\pi$
$373$	5.15540			0.266936			0.133468	+	0.991053i	$0.457389\pi$
$374$			12.5849i			0.650748i
$375$	−24.5300	+	24.5300i	−1.26673	+	1.26673i
$376$	0.679779	+	0.679779i	0.0350569	+	0.0350569i
$377$		−	47.9675i		−	2.47045i
$378$			16.4629i			0.846761i
$379$	−37.0858			−1.90497			−0.952486	−	0.304584i	$-0.901483\pi$
$379$	−37.0858			−1.90497			−0.952486	+	0.304584i	$0.901483\pi$
$380$	−8.30386	−	8.30386i	−0.425979	−	0.425979i
$381$	43.2738	+	43.2738i	2.21698	+	2.21698i
$382$	−5.17631	−	5.17631i	−0.264843	−	0.264843i
$383$	−24.9805	+	24.9805i	−1.27644	+	1.27644i	−0.333798	+	0.942645i	$0.608330\pi$
$383$	−24.9805	+	24.9805i	−1.27644	+	1.27644i	−0.942645	+	0.333798i	$0.891670\pi$
$384$	2.34205	−	2.34205i	0.119517	−	0.119517i
$385$	5.58463			0.284619
$386$	17.5844	−	17.5844i	0.895023	−	0.895023i
$387$	47.0036			2.38933
$388$	−8.67715	+	8.67715i	−0.440516	+	0.440516i
$389$			8.06824i			0.409076i	0.978859	+	0.204538i	$0.0655692\pi$
$389$			8.06824i			0.409076i	−0.978859	+	0.204538i	$0.934431\pi$
$390$			48.8057i			2.47137i
$391$	−6.45585	+	6.45585i	−0.326486	+	0.326486i
$392$	1.00000			0.0505076
$393$	−26.3527	+	26.3527i	−1.32932	+	1.32932i
$394$	21.8173			1.09914
$395$	13.9419	−	13.9419i	0.701493	−	0.701493i
$396$	13.3519	−	13.3519i	0.670960	−	0.670960i
$397$	3.41244	+	3.41244i	0.171265	+	0.171265i	0.787535	−	0.616270i	$-0.211357\pi$
$397$	3.41244	+	3.41244i	0.171265	+	0.171265i	−0.616270	+	0.787535i	$0.711357\pi$
$398$	−16.0664	−	16.0664i	−0.805334	−	0.805334i
$399$	−11.6674	−	11.6674i	−0.584101	−	0.584101i
$400$	−0.556923			−0.0278461
$401$		−	31.9751i		−	1.59676i	−0.602154	−	0.798380i	$-0.705691\pi$
$401$		−	31.9751i		−	1.59676i	0.602154	−	0.798380i	$-0.294309\pi$
$402$		−	18.5644i		−	0.925909i
$403$	−11.3732	−	11.3732i	−0.566541	−	0.566541i
$404$	−4.71955	+	4.71955i	−0.234806	+	0.234806i
$405$		−	72.1729i		−	3.58630i
$406$	7.67371			0.380840
$407$	−8.54328	−	8.54328i	−0.423475	−	0.423475i
$408$		−	17.5948i		−	0.871071i
$409$	0.0693173			0.00342752			0.00171376	−	0.999999i	$-0.499454\pi$
$409$	0.0693173			0.00342752			0.00171376	+	0.999999i	$0.499454\pi$
$410$	−2.22340	−	14.9295i	−0.109806	−	0.737316i
$411$	68.3268			3.37031
$412$		−	12.7473i		−	0.628014i
$413$	−7.47356	−	7.47356i	−0.367750	−	0.367750i
$414$	13.6987			0.673254
$415$		−	12.1263i		−	0.595257i
$416$	4.42004	−	4.42004i	0.216711	−	0.216711i
$417$	35.9499	+	35.9499i	1.76047	+	1.76047i
$418$			11.8020i			0.577254i
$419$		−	1.41309i		−	0.0690337i	−0.999404	−	0.0345169i	$-0.989011\pi$
$419$		−	1.41309i		−	0.0690337i	0.999404	−	0.0345169i	$-0.0109892\pi$
$420$	−7.80781			−0.380982
$421$	−16.5163	−	16.5163i	−0.804956	−	0.804956i	0.178909	−	0.983866i	$-0.442743\pi$
$421$	−16.5163	−	16.5163i	−0.804956	−	0.804956i	−0.983866	+	0.178909i	$0.942743\pi$
$422$	−3.30054	−	3.30054i	−0.160668	−	0.160668i
$423$	−5.41814	−	5.41814i	−0.263439	−	0.263439i
$424$	−4.33950	+	4.33950i	−0.210745	+	0.210745i
$425$	−2.09195	+	2.09195i	−0.101475	+	0.101475i
$426$	30.6546			1.48522
$427$	5.55453	−	5.55453i	0.268802	−	0.268802i
$428$	11.0852			0.535826
$429$	34.6829	−	34.6829i	1.67451	−	1.67451i
$430$			13.9016i			0.670397i
$431$		−	2.55453i		−	0.123047i	−0.998106	−	0.0615236i	$-0.980404\pi$
$431$		−	2.55453i		−	0.123047i	0.998106	−	0.0615236i	$-0.0195960\pi$
$432$	−11.6410	+	11.6410i	−0.560080	+	0.560080i
$433$	20.6943			0.994502			0.497251	−	0.867607i	$-0.334343\pi$
$433$	20.6943			0.994502			0.497251	+	0.867607i	$0.334343\pi$
$434$	1.81946	−	1.81946i	0.0873369	−	0.0873369i
$435$	−59.9149			−2.87270
$436$	5.41578	−	5.41578i	0.259369	−	0.259369i
$437$	−6.05424	+	6.05424i	−0.289614	+	0.289614i
$438$	0.277725	+	0.277725i	0.0132702	+	0.0132702i
$439$	3.71523	+	3.71523i	0.177318	+	0.177318i	0.790186	−	0.612867i	$-0.209984\pi$
$439$	3.71523	+	3.71523i	0.177318	+	0.177318i	−0.612867	+	0.790186i	$0.709984\pi$
$440$	3.94893	+	3.94893i	0.188258	+	0.188258i
$441$	−7.97044			−0.379545
$442$		−	33.2057i		−	1.57944i
$443$			6.82700i			0.324361i	0.986761	+	0.162180i	$0.0518526\pi$
$443$			6.82700i			0.324361i	−0.986761	+	0.162180i	$0.948147\pi$
$444$	11.9443	+	11.9443i	0.566850	+	0.566850i
$445$	10.8700	−	10.8700i	0.515289	−	0.515289i
$446$		−	5.76975i		−	0.273206i
$447$	56.5844			2.67635
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$			5.65511i			0.266881i	0.991057	+	0.133441i	$0.0426025\pi$
$449$			5.65511i			0.266881i	−0.991057	+	0.133441i	$0.957397\pi$
$450$	4.43892			0.209253
$451$	−9.02938	+	12.1894i	−0.425177	+	0.573977i
$452$	−0.000169098	0		−7.95369e−6	0
$453$		−	6.37039i		−	0.299307i
$454$	7.60640	+	7.60640i	0.356986	+	0.356986i
$455$	−14.7353			−0.690801
$456$		−	16.5002i		−	0.772694i
$457$	1.76819	−	1.76819i	0.0827124	−	0.0827124i	−0.664540	−	0.747253i	$-0.731373\pi$
$457$	1.76819	−	1.76819i	0.0827124	−	0.0827124i	0.747253	+	0.664540i	$0.231373\pi$
$458$	19.3861	+	19.3861i	0.905855	+	0.905855i
$459$			87.4537i			4.08199i
$460$			4.05148i			0.188901i
$461$	−6.54562			−0.304860			−0.152430	−	0.988314i	$-0.548710\pi$
$461$	−6.54562			−0.304860			−0.152430	+	0.988314i	$0.548710\pi$
$462$	5.54848	+	5.54848i	0.258139	+	0.258139i
$463$	−1.48077	−	1.48077i	−0.0688173	−	0.0688173i	0.671860	−	0.740678i	$-0.265495\pi$
$463$	−1.48077	−	1.48077i	−0.0688173	−	0.0688173i	−0.740678	+	0.671860i	$0.765495\pi$
$464$	5.42613	+	5.42613i	0.251902	+	0.251902i
$465$	−14.2060	+	14.2060i	−0.658787	+	0.658787i
$466$	14.8028	−	14.8028i	0.685726	−	0.685726i
$467$	5.44742			0.252077			0.126038	−	0.992025i	$-0.459774\pi$
$467$	5.44742			0.252077			0.126038	+	0.992025i	$0.459774\pi$
$468$	−35.2297	+	35.2297i	−1.62849	+	1.62849i
$469$	5.60492			0.258811
$470$	1.60245	−	1.60245i	0.0739156	−	0.0739156i
$471$		−	25.8399i		−	1.19064i
$472$		−	10.5692i		−	0.486487i
$473$	9.87896	−	9.87896i	0.454235	−	0.454235i
$474$	27.7033			1.27245
$475$	−1.96181	+	1.96181i	−0.0900142	+	0.0900142i
$476$	5.31217			0.243483
$477$	34.5877	−	34.5877i	1.58366	−	1.58366i
$478$	2.51316	−	2.51316i	0.114949	−	0.114949i
$479$	−3.63744	−	3.63744i	−0.166199	−	0.166199i	0.619107	−	0.785306i	$-0.287495\pi$
$479$	−3.63744	−	3.63744i	−0.166199	−	0.166199i	−0.785306	+	0.619107i	$0.787495\pi$
$480$	−5.52095	−	5.52095i	−0.251996	−	0.251996i
$481$	22.5418	+	22.5418i	1.02782	+	1.02782i
$482$	−4.77168			−0.217344
$483$			5.69258i			0.259021i
$484$			5.38752i			0.244887i
$485$	20.4548	+	20.4548i	0.928803	+	0.928803i
$486$	36.7826	−	36.7826i	1.66849	−	1.66849i
$487$			12.2821i			0.556557i	0.960500	+	0.278278i	$0.0897638\pi$
$487$			12.2821i			0.556557i	−0.960500	+	0.278278i	$0.910236\pi$
$488$	7.85529			0.355592
$489$	−2.66879	−	2.66879i	−0.120687	−	0.120687i
$490$		−	2.35731i		−	0.106493i
$491$	−1.50592			−0.0679610			−0.0339805	−	0.999422i	$-0.510818\pi$
$491$	−1.50592			−0.0679610			−0.0339805	+	0.999422i	$0.510818\pi$
$492$	12.6239	−	17.0419i	0.569128	−	0.768308i
$493$	40.7640			1.83592
$494$		−	31.1401i		−	1.40106i
$495$	−31.4747	−	31.4747i	−1.41468	−	1.41468i
$496$	2.57310			0.115536
$497$			9.25517i			0.415151i
$498$	12.0478	−	12.0478i	0.539876	−	0.539876i
$499$	12.6594	+	12.6594i	0.566714	+	0.566714i	0.931206	−	0.364492i	$-0.118757\pi$
$499$	12.6594	+	12.6594i	0.566714	+	0.566714i	−0.364492	+	0.931206i	$0.618757\pi$
$500$		−	10.4737i		−	0.468399i
$501$			27.5723i			1.23184i
$502$	−23.1506			−1.03326
$503$	4.59784	+	4.59784i	0.205007	+	0.205007i	0.802141	−	0.597134i	$-0.203694\pi$
$503$	4.59784	+	4.59784i	0.205007	+	0.205007i	−0.597134	+	0.802141i	$0.703694\pi$
$504$	−5.63595	−	5.63595i	−0.251045	−	0.251045i
$505$	11.1255	+	11.1255i	0.495076	+	0.495076i
$506$	2.87912	−	2.87912i	0.127992	−	0.127992i
$507$	−61.0658	+	61.0658i	−2.71203	+	2.71203i
$508$	−18.4768			−0.819777
$509$	−0.141229	+	0.141229i	−0.00625987	+	0.00625987i	−0.710230	−	0.703970i	$-0.751409\pi$
$509$	−0.141229	+	0.141229i	−0.00625987	+	0.00625987i	0.703970	+	0.710230i	$0.251409\pi$
$510$	−41.4764			−1.83660
$511$	−0.0838500	+	0.0838500i	−0.00370931	+	0.00370931i
$512$			1.00000i			0.0441942i
$513$			82.0133i			3.62098i
$514$	21.8073	−	21.8073i	0.961877	−	0.961877i
$515$	−30.0494			−1.32413
$516$	−13.8117	+	13.8117i	−0.608025	+	0.608025i
$517$	−2.27751			−0.100165
$518$	−3.60618	+	3.60618i	−0.158446	+	0.158446i
$519$	−18.9370	+	18.9370i	−0.831241	+	0.831241i
$520$	−10.4194	−	10.4194i	−0.456922	−	0.456922i
$521$	−18.4433	−	18.4433i	−0.808018	−	0.808018i	0.176316	−	0.984334i	$-0.443582\pi$
$521$	−18.4433	−	18.4433i	−0.808018	−	0.808018i	−0.984334	+	0.176316i	$0.943582\pi$
$522$	−43.2487	−	43.2487i	−1.89294	−	1.89294i
$523$	−18.7348			−0.819216			−0.409608	−	0.912262i	$-0.634335\pi$
$523$	−18.7348			−0.819216			−0.409608	+	0.912262i	$0.634335\pi$
$524$		−	11.2520i		−	0.491545i
$525$			1.84462i			0.0805058i
$526$	2.15774	+	2.15774i	0.0940821	+	0.0940821i
$527$	9.66527	−	9.66527i	0.421026	−	0.421026i
$528$			7.84674i			0.341486i
$529$	−20.0461			−0.871570
$530$	10.2296	+	10.2296i	0.444344	+	0.444344i
$531$			84.2412i			3.65576i
$532$	4.98170			0.215984
$533$	23.8244	−	32.1623i	1.03195	−	1.39310i
$534$	21.5994			0.934696
$535$		−	26.1314i		−	1.12976i
$536$	3.96328	+	3.96328i	0.171187	+	0.171187i
$537$	63.1054			2.72320
$538$			13.0247i			0.561535i
$539$	−1.67518	+	1.67518i	−0.0721552	+	0.0721552i
$540$	27.4416	+	27.4416i	1.18090	+	1.18090i
$541$		−	38.4372i		−	1.65254i	−0.563272	−	0.826271i	$-0.690458\pi$
$541$		−	38.4372i		−	1.65254i	0.563272	−	0.826271i	$-0.309542\pi$
$542$		−	14.3920i		−	0.618191i
$543$	45.4606			1.95090
$544$	3.75627	+	3.75627i	0.161049	+	0.161049i
$545$	−12.7667	−	12.7667i	−0.546865	−	0.546865i
$546$	−14.6399	−	14.6399i	−0.626531	−	0.626531i
$547$	−11.0135	+	11.0135i	−0.470903	+	0.470903i	−0.902207	−	0.431303i	$-0.858054\pi$
$547$	−11.0135	+	11.0135i	−0.470903	+	0.470903i	0.431303	+	0.902207i	$0.358054\pi$
$548$	−14.5869	+	14.5869i	−0.623123	+	0.623123i
$549$	−62.6101			−2.67213
$550$	0.932948	−	0.932948i	0.0397810	−	0.0397810i
$551$	38.2281			1.62857
$552$	−4.02526	+	4.02526i	−0.171326	+	0.171326i
$553$			8.36410i			0.355678i
$554$			28.7062i			1.21961i
$555$	28.1564	−	28.1564i	1.19517	−	1.19517i
$556$	−15.3497			−0.650973
$557$	−2.53056	+	2.53056i	−0.107223	+	0.107223i	−0.758683	−	0.651460i	$-0.774157\pi$
$557$	−2.53056	+	2.53056i	−0.107223	+	0.107223i	0.651460	+	0.758683i	$0.274157\pi$
$558$	−20.5088			−0.868206
$559$	−26.0661	+	26.0661i	−1.10248	+	1.10248i
$560$	1.66687	−	1.66687i	0.0704382	−	0.0704382i
$561$	29.4745	+	29.4745i	1.24441	+	1.24441i
$562$	−12.2428	−	12.2428i	−0.516432	−	0.516432i
$563$	−1.37321	−	1.37321i	−0.0578738	−	0.0578738i	0.677578	−	0.735451i	$-0.263030\pi$
$563$	−1.37321	−	1.37321i	−0.0578738	−	0.0578738i	−0.735451	+	0.677578i	$0.763030\pi$
$564$	3.18416			0.134077
$565$		0	0.000398616i		0	1.67699e-5i
$566$		−	11.6869i		−	0.491239i
$567$	21.6492	+	21.6492i	0.909181	+	0.909181i
$568$	−6.54439	+	6.54439i	−0.274597	+	0.274597i
$569$			19.9807i			0.837634i	0.908071	+	0.418817i	$0.137555\pi$
$569$			19.9807i			0.837634i	−0.908071	+	0.418817i	$0.862445\pi$
$570$	−38.8962			−1.62918
$571$	−28.9607	−	28.9607i	−1.21197	−	1.21197i	−0.970378	−	0.241591i	$-0.922331\pi$
$571$	−28.9607	−	28.9607i	−1.21197	−	1.21197i	−0.241591	−	0.970378i	$-0.577669\pi$
$572$			14.8088i			0.619186i
$573$	−24.2464			−1.01291
$574$	5.14524	+	3.81136i	0.214758	+	0.159083i
$575$	0.957176			0.0399170
$576$		−	7.97044i		−	0.332102i
$577$	8.39619	+	8.39619i	0.349538	+	0.349538i	0.859937	−	0.510400i	$-0.170502\pi$
$577$	8.39619	+	8.39619i	0.349538	+	0.349538i	−0.510400	+	0.859937i	$0.670502\pi$
$578$	11.2191			0.466653
$579$		−	82.3673i		−	3.42307i
$580$	12.7911	−	12.7911i	0.531121	−	0.531121i
$581$	3.63744	+	3.63744i	0.150907	+	0.150907i
$582$			40.6447i			1.68478i
$583$		−	14.5389i		−	0.602140i
$584$	−0.118582			−0.00490695
$585$	83.0474	+	83.0474i	3.43359	+	3.43359i
$586$	−6.02747	−	6.02747i	−0.248992	−	0.248992i
$587$	20.5735	+	20.5735i	0.849158	+	0.849158i	0.990028	−	0.140870i	$-0.0449900\pi$
$587$	20.5735	+	20.5735i	0.849158	+	0.849158i	−0.140870	+	0.990028i	$0.544990\pi$
$588$	2.34205	−	2.34205i	0.0965847	−	0.0965847i
$589$	9.06401	−	9.06401i	0.373476	−	0.373476i
$590$	−24.9149			−1.02573
$591$	51.0972	−	51.0972i	2.10186	−	2.10186i
$592$	−5.09991			−0.209605
$593$	28.3648	−	28.3648i	1.16480	−	1.16480i	0.181390	−	0.983411i	$-0.441940\pi$
$593$	28.3648	−	28.3648i	1.16480	−	1.16480i	0.983411	−	0.181390i	$-0.0580597\pi$
$594$		−	39.0017i		−	1.60026i
$595$		−	12.5224i		−	0.513370i
$596$	−12.0801	+	12.0801i	−0.494820	+	0.494820i
$597$	−75.2566			−3.08005
$598$	−7.59667	+	7.59667i	−0.310651	+	0.310651i
$599$	22.6005			0.923430			0.461715	−	0.887028i	$-0.347234\pi$
$599$	22.6005			0.923430			0.461715	+	0.887028i	$0.347234\pi$
$600$	−1.30434	+	1.30434i	−0.0532496	+	0.0532496i
$601$	−27.9125	+	27.9125i	−1.13857	+	1.13857i	−0.149868	+	0.988706i	$0.547885\pi$
$601$	−27.9125	+	27.9125i	−1.13857	+	1.13857i	−0.988706	+	0.149868i	$0.952115\pi$
$602$	−4.16998	−	4.16998i	−0.169956	−	0.169956i
$603$	−31.5891	−	31.5891i	−1.28641	−	1.28641i
$604$	1.36000	+	1.36000i	0.0553376	+	0.0553376i
$605$	12.7001			0.516332
$606$			22.1069i			0.898031i
$607$		−	27.3502i		−	1.11011i	−0.831814	−	0.555054i	$-0.812697\pi$
$607$		−	27.3502i		−	1.11011i	0.831814	−	0.555054i	$-0.187303\pi$
$608$	3.52259	+	3.52259i	0.142860	+	0.142860i
$609$	17.9722	−	17.9722i	0.728272	−	0.728272i
$610$		−	18.5174i		−	0.749746i
$611$	6.00931			0.243111
$612$	−29.9391	−	29.9391i	−1.21022	−	1.21022i
$613$		−	6.28710i		−	0.253934i	−0.991907	−	0.126967i	$-0.959476\pi$
$613$		−	6.28710i		−	0.253934i	0.991907	−	0.126967i	$-0.0405242\pi$
$614$	−19.2720			−0.777756
$615$	−40.1731	−	29.7584i	−1.61993	−	1.19997i
$616$	−2.36907			−0.0954524
$617$			14.1283i			0.568783i	0.958708	+	0.284392i	$0.0917916\pi$
$617$			14.1283i			0.568783i	−0.958708	+	0.284392i	$0.908208\pi$
$618$	−29.8549	−	29.8549i	−1.20094	−	1.20094i
$619$	10.5017			0.422099			0.211049	−	0.977475i	$-0.432312\pi$
$619$	10.5017			0.422099			0.211049	+	0.977475i	$0.432312\pi$
$620$		−	6.06561i		−	0.243601i
$621$	20.0073	−	20.0073i	0.802866	−	0.802866i
$622$	6.75243	+	6.75243i	0.270748	+	0.270748i
$623$			6.52122i			0.261267i
$624$		−	20.7040i		−	0.828822i
$625$	−27.4745			−1.09898
$626$	−17.7319	−	17.7319i	−0.708710	−	0.708710i
$627$	27.6409	+	27.6409i	1.10387	+	1.10387i
$628$	5.51651	+	5.51651i	0.220133	+	0.220133i
$629$	−19.1566	+	19.1566i	−0.763825	+	0.763825i
$630$	−13.2857	+	13.2857i	−0.529315	+	0.529315i
$631$	−32.2755			−1.28487			−0.642433	−	0.766342i	$-0.722075\pi$
$631$	−32.2755			−1.28487			−0.642433	+	0.766342i	$0.722075\pi$
$632$	−5.91431	+	5.91431i	−0.235259	+	0.235259i
$633$	−15.4601			−0.614483
$634$	1.30927	−	1.30927i	0.0519979	−	0.0519979i
$635$			43.5557i			1.72845i
$636$			20.3267i			0.806006i
$637$	4.42004	−	4.42004i	0.175129	−	0.175129i
$638$	−18.1795			−0.719734
$639$	52.1617	−	52.1617i	2.06348	−	2.06348i
$640$	2.35731			0.0931810
$641$	8.97612	−	8.97612i	0.354535	−	0.354535i	−0.507259	−	0.861794i	$-0.669341\pi$
$641$	8.97612	−	8.97612i	0.354535	−	0.354535i	0.861794	+	0.507259i	$0.169341\pi$
$642$	25.9623	−	25.9623i	1.02465	−	1.02465i
$643$	2.57918	+	2.57918i	0.101713	+	0.101713i	0.756132	−	0.654419i	$-0.227087\pi$
$643$	2.57918	+	2.57918i	0.101713	+	0.101713i	−0.654419	+	0.756132i	$0.727087\pi$
$644$	−1.21530	−	1.21530i	−0.0478893	−	0.0478893i
$645$	32.5584	+	32.5584i	1.28199	+	1.28199i
$646$	26.4636			1.04120
$647$			22.3354i			0.878094i	0.898464	+	0.439047i	$0.144684\pi$
$647$			22.3354i			0.878094i	−0.898464	+	0.439047i	$0.855316\pi$
$648$			30.6166i			1.20273i
$649$	17.7054	+	17.7054i	0.694996	+	0.694996i
$650$	−2.46162	+	2.46162i	−0.0965528	+	0.0965528i
$651$		−	8.52255i		−	0.334025i
$652$	1.13951			0.0446266
$653$	33.0407	+	33.0407i	1.29298	+	1.29298i	0.932932	+	0.360052i	$0.117241\pi$
$653$	33.0407	+	33.0407i	1.29298	+	1.29298i	0.360052	+	0.932932i	$0.382759\pi$
$654$		−	25.3681i		−	0.991972i
$655$	−26.5244			−1.03639
$656$	0.943192	+	6.33328i	0.0368255	+	0.247273i
$657$	0.945150			0.0368738
$658$			0.961353i			0.0374774i
$659$	25.4736	+	25.4736i	0.992312	+	0.992312i	0.999971	−	0.00765899i	$-0.00243796\pi$
$659$	25.4736	+	25.4736i	0.992312	+	0.992312i	−0.00765899	+	0.999971i	$0.502438\pi$
$660$	18.4972			0.720003
$661$			4.30656i			0.167506i	0.996487	+	0.0837529i	$0.0266906\pi$
$661$			4.30656i			0.167506i	−0.996487	+	0.0837529i	$0.973309\pi$
$662$	1.74874	−	1.74874i	0.0679665	−	0.0679665i
$663$	−77.7697	−	77.7697i	−3.02032	−	3.02032i
$664$			5.14412i			0.199631i
$665$		−	11.7434i		−	0.455391i
$666$	40.6485			1.57510
$667$	−9.32582	−	9.32582i	−0.361097	−	0.361097i
$668$	−5.88635	−	5.88635i	−0.227750	−	0.227750i
$669$	−13.5131	−	13.5131i	−0.522446	−	0.522446i
$670$	9.34268	−	9.34268i	0.360939	−	0.360939i
$671$	−13.1590	+	13.1590i	−0.507999	+	0.507999i
$672$	3.31217			0.127770
$673$	−23.5787	+	23.5787i	−0.908891	+	0.908891i	−0.996183	−	0.0872917i	$-0.972179\pi$
$673$	−23.5787	+	23.5787i	−0.908891	+	0.908891i	0.0872917	+	0.996183i	$0.472179\pi$
$674$	−11.5912			−0.446476
$675$	6.48316	−	6.48316i	0.249537	−	0.249537i
$676$		−	26.0736i		−	1.00283i
$677$			43.7002i			1.67954i	0.542945	+	0.839769i	$0.317309\pi$
$677$			43.7002i			1.67954i	−0.542945	+	0.839769i	$0.682691\pi$
$678$	−0.000396036	0	0.000396036i	−1.52097e−5	0	1.52097e-5i
$679$	−12.2713			−0.470931
$680$	8.85470	−	8.85470i	0.339562	−	0.339562i
$681$	35.6292			1.36531
$682$	−4.31042	+	4.31042i	−0.165055	+	0.165055i
$683$	−9.53515	+	9.53515i	−0.364852	+	0.364852i	−0.865596	−	0.500743i	$-0.833060\pi$
$683$	−9.53515	+	9.53515i	−0.364852	+	0.364852i	0.500743	+	0.865596i	$0.333060\pi$
$684$	−28.0766	−	28.0766i	−1.07354	−	1.07354i
$685$	34.3860	+	34.3860i	1.31382	+	1.31382i
$686$	0.707107	+	0.707107i	0.0269975	+	0.0269975i
$687$	90.8068			3.46449
$688$		−	5.89724i		−	0.224830i
$689$			38.3616i			1.46146i
$690$	9.48879	+	9.48879i	0.361232	+	0.361232i
$691$	−29.8806	+	29.8806i	−1.13671	+	1.13671i	−0.147676	+	0.989036i	$0.547179\pi$
$691$	−29.8806	+	29.8806i	−1.13671	+	1.13671i	−0.989036	+	0.147676i	$0.952821\pi$
$692$		−	8.08562i		−	0.307369i
$693$	18.8825			0.717287
$694$	10.3609	+	10.3609i	0.393294	+	0.393294i
$695$			36.1841i			1.37254i
$696$	25.4166			0.963414
$697$	27.3324	+	20.2466i	1.03529	+	0.766895i
$698$	25.0526			0.948254
$699$		−	69.3379i		−	2.62260i
$700$	−0.393804	−	0.393804i	−0.0148844	−	0.0148844i
$701$	−11.2577			−0.425198			−0.212599	−	0.977140i	$-0.568193\pi$
$701$	−11.2577			−0.425198			−0.212599	+	0.977140i	$0.568193\pi$
$702$			102.908i			3.88401i
$703$	−17.9649	+	17.9649i	−0.677560	+	0.677560i
$704$	−1.67518	−	1.67518i	−0.0631358	−	0.0631358i
$705$		−	7.50606i		−	0.282695i
$706$		−	20.9592i		−	0.788811i
$707$	−6.67445			−0.251019
$708$	−24.7537	−	24.7537i	−0.930299	−	0.930299i
$709$	8.69216	+	8.69216i	0.326441	+	0.326441i	0.851231	−	0.524790i	$-0.175856\pi$
$709$	8.69216	+	8.69216i	0.326441	+	0.326441i	−0.524790	+	0.851231i	$0.675856\pi$
$710$	15.4272	+	15.4272i	0.578972	+	0.578972i
$711$	47.1397	−	47.1397i	1.76788	−	1.76788i
$712$	−4.61120	+	4.61120i	−0.172812	+	0.172812i
$713$	−4.42236			−0.165619
$714$	12.4414	−	12.4414i	0.465607	−	0.465607i
$715$	34.9089			1.30552
$716$	−13.4722	+	13.4722i	−0.503481	+	0.503481i
$717$		−	11.7719i		−	0.439630i
$718$		−	18.8935i		−	0.705099i
$719$	11.8503	−	11.8503i	0.441941	−	0.441941i	−0.450723	−	0.892664i	$-0.648834\pi$
$719$	11.8503	−	11.8503i	0.441941	−	0.441941i	0.892664	+	0.450723i	$0.148834\pi$
$720$	−18.7888			−0.700218
$721$	9.01370	−	9.01370i	0.335688	−	0.335688i
$722$	5.81735			0.216499
$723$	−11.1755	+	11.1755i	−0.415622	+	0.415622i
$724$	−9.70528	+	9.70528i	−0.360694	+	0.360694i
$725$	−3.02194	−	3.02194i	−0.112232	−	0.112232i
$726$	12.6179	+	12.6179i	0.468293	+	0.468293i
$727$	3.77947	+	3.77947i	0.140173	+	0.140173i	0.773711	−	0.633538i	$-0.218398\pi$
$727$	3.77947	+	3.77947i	0.140173	+	0.140173i	−0.633538	+	0.773711i	$0.718398\pi$
$728$	6.25089			0.231673
$729$		−	80.4440i		−	2.97941i
$730$			0.279535i			0.0103460i
$731$	−22.1516	−	22.1516i	−0.819307	−	0.819307i
$732$	18.3975	−	18.3975i	0.679992	−	0.679992i
$733$		−	29.8721i		−	1.10335i	−0.834059	−	0.551675i	$-0.813989\pi$
$733$		−	29.8721i		−	1.10335i	0.834059	−	0.551675i	$-0.186011\pi$
$734$	8.64663			0.319153
$735$	−5.52095	−	5.52095i	−0.203643	−	0.203643i
$736$		−	1.71869i		−	0.0633517i
$737$	−13.2784			−0.489117
$738$	−7.51766	−	50.4790i	−0.276729	−	1.85816i
$739$	−27.0349			−0.994495			−0.497248	−	0.867609i	$-0.665656\pi$
$739$	−27.0349			−0.994495			−0.497248	+	0.867609i	$0.665656\pi$
$740$			12.0221i			0.441940i
$741$	−72.9317	−	72.9317i	−2.67921	−	2.67921i
$742$	−6.13698			−0.225296
$743$		−	12.7706i		−	0.468509i	−0.972175	−	0.234254i	$-0.924735\pi$
$743$		−	12.7706i		−	0.468509i	0.972175	−	0.234254i	$-0.0752648\pi$
$744$	6.02635	−	6.02635i	0.220937	−	0.220937i
$745$	28.4765	+	28.4765i	1.04330	+	1.04330i
$746$			5.15540i			0.188753i
$747$		−	41.0009i		−	1.50015i
$748$	−12.5849			−0.460149
$749$	7.83845	+	7.83845i	0.286411	+	0.286411i
$750$	−24.5300	−	24.5300i	−0.895710	−	0.895710i
$751$	19.7644	+	19.7644i	0.721214	+	0.721214i	0.968852	−	0.247639i	$-0.0796546\pi$
$751$	19.7644	+	19.7644i	0.721214	+	0.721214i	−0.247639	+	0.968852i	$0.579655\pi$
$752$	−0.679779	+	0.679779i	−0.0247890	+	0.0247890i
$753$	−54.2199	+	54.2199i	−1.97588	+	1.97588i
$754$	47.9675			1.74687
$755$	3.20595	−	3.20595i	0.116676	−	0.116676i
$756$	−16.4629			−0.598751
$757$	−19.4173	+	19.4173i	−0.705732	+	0.705732i	−0.965635	−	0.259903i	$-0.916310\pi$
$757$	−19.4173	+	19.4173i	−0.705732	+	0.705732i	0.259903	+	0.965635i	$0.416310\pi$
$758$		−	37.0858i		−	1.34702i
$759$		−	13.4861i		−	0.489514i
$760$	8.30386	−	8.30386i	0.301213	−	0.301213i
$761$	29.2041			1.05865			0.529324	−	0.848420i	$-0.322446\pi$
$761$	29.2041			1.05865			0.529324	+	0.848420i	$0.322446\pi$
$762$	−43.2738	+	43.2738i	−1.56764	+	1.56764i
$763$	7.65908			0.277277
$764$	5.17631	−	5.17631i	0.187272	−	0.187272i
$765$	−70.5758	+	70.5758i	−2.55167	+	2.55167i
$766$	−24.9805	−	24.9805i	−0.902581	−	0.902581i
$767$	−46.7164	−	46.7164i	−1.68683	−	1.68683i
$768$	2.34205	+	2.34205i	0.0845116	+	0.0845116i
$769$	−2.16827			−0.0781897			−0.0390948	−	0.999236i	$-0.512447\pi$
$769$	−2.16827			−0.0781897			−0.0390948	+	0.999236i	$0.512447\pi$
$770$			5.58463i			0.201256i
$771$		−	102.148i		−	3.67876i
$772$	17.5844	+	17.5844i	0.632877	+	0.632877i
$773$	5.77522	−	5.77522i	0.207720	−	0.207720i	−0.595578	−	0.803298i	$-0.703077\pi$
$773$	5.77522	−	5.77522i	0.207720	−	0.207720i	0.803298	+	0.595578i	$0.203077\pi$
$774$			47.0036i			1.68951i
$775$	−1.43302			−0.0514756
$776$	−8.67715	−	8.67715i	−0.311492	−	0.311492i
$777$			16.8917i			0.605988i
$778$	−8.06824			−0.289260
$779$	25.6321	+	18.9871i	0.918364	+	0.680283i
$780$	−48.8057			−1.74753
$781$		−	21.9261i		−	0.784578i
$782$	−6.45585	−	6.45585i	−0.230861	−	0.230861i
$783$	−126.332			−4.51473
$784$			1.00000i			0.0357143i
$785$	13.0041	−	13.0041i	0.464138	−	0.464138i
$786$	−26.3527	−	26.3527i	−0.939971	−	0.939971i
$787$			5.98684i			0.213408i	0.994291	+	0.106704i	$0.0340297\pi$
$787$			5.98684i			0.213408i	−0.994291	+	0.106704i	$0.965970\pi$
$788$			21.8173i			0.777208i
$789$	10.1071			0.359823
$790$	13.9419	+	13.9419i	0.496030	+	0.496030i
$791$	−0.000119570	0	0.000119570i	−4.25142e−6	0	4.25142e-6i
$792$	13.3519	+	13.3519i	0.474441	+	0.474441i
$793$	34.7207	−	34.7207i	1.23297	−	1.23297i
$794$	−3.41244	+	3.41244i	−0.121103	+	0.121103i
$795$	47.9164			1.69942
$796$	16.0664	−	16.0664i	0.569457	−	0.569457i
$797$	−43.8575			−1.55351			−0.776756	−	0.629801i	$-0.783136\pi$
$797$	−43.8575			−1.55351			−0.776756	+	0.629801i	$0.783136\pi$
$798$	11.6674	−	11.6674i	0.413022	−	0.413022i
$799$			5.10686i			0.180668i
$800$		−	0.556923i		−	0.0196902i
$801$	36.7533	−	36.7533i	1.29861	−	1.29861i
$802$	31.9751			1.12908
$803$	0.198646	−	0.198646i	0.00701008	−	0.00701008i
$804$	18.5644			0.654717
$805$	−2.86483	+	2.86483i	−0.100972	+	0.100972i
$806$	11.3732	−	11.3732i	0.400605	−	0.400605i
$807$	30.5046	+	30.5046i	1.07381	+	1.07381i
$808$	−4.71955	−	4.71955i	−0.166033	−	0.166033i
$809$	22.4032	+	22.4032i	0.787655	+	0.787655i	0.981109	−	0.193454i	$-0.0619691\pi$
$809$	22.4032	+	22.4032i	0.787655	+	0.787655i	−0.193454	+	0.981109i	$0.561969\pi$
$810$	72.1729			2.53590
$811$			19.2952i			0.677545i	0.940868	+	0.338773i	$0.110012\pi$
$811$			19.2952i			0.677545i	−0.940868	+	0.338773i	$0.889988\pi$
$812$			7.67371i			0.269294i
$813$	−33.7069	−	33.7069i	−1.18215	−	1.18215i
$814$	8.54328	−	8.54328i	0.299442	−	0.299442i
$815$		−	2.68618i		−	0.0940928i
$816$	17.5948			0.615940
$817$	−20.7736	−	20.7736i	−0.726776	−	0.726776i
$818$			0.0693173i			0.00242362i
$819$	−49.8223			−1.74093
$820$	14.9295	−	2.22340i	0.521361	−	0.0776445i
$821$	7.15897			0.249850			0.124925	−	0.992166i	$-0.460131\pi$
$821$	7.15897			0.249850			0.124925	+	0.992166i	$0.460131\pi$
$822$			68.3268i			2.38317i
$823$	6.59163	+	6.59163i	0.229770	+	0.229770i	0.812596	−	0.582827i	$-0.198053\pi$
$823$	6.59163	+	6.59163i	0.229770	+	0.229770i	−0.582827	+	0.812596i	$0.698053\pi$
$824$	12.7473			0.444073
$825$		−	4.37003i		−	0.152145i
$826$	7.47356	−	7.47356i	0.260038	−	0.260038i
$827$	4.46257	+	4.46257i	0.155179	+	0.155179i	0.780426	−	0.625248i	$-0.215002\pi$
$827$	4.46257	+	4.46257i	0.155179	+	0.155179i	−0.625248	+	0.780426i	$0.715002\pi$
$828$			13.6987i			0.476063i
$829$		−	39.7899i		−	1.38196i	−0.722874	−	0.690980i	$-0.757179\pi$
$829$		−	39.7899i		−	1.38196i	0.722874	−	0.690980i	$-0.242821\pi$
$830$	12.1263			0.420910
$831$	67.2314	+	67.2314i	2.33223	+	2.33223i
$832$	4.42004	+	4.42004i	0.153237	+	0.153237i
$833$	3.75627	+	3.75627i	0.130147	+	0.130147i
$834$	−35.9499	+	35.9499i	−1.24484	+	1.24484i
$835$	−13.8760	+	13.8760i	−0.480198	+	0.480198i
$836$	−11.8020			−0.408180
$837$	−29.9536	+	29.9536i	−1.03535	+	1.03535i
$838$	1.41309			0.0488142
$839$	−31.7620	+	31.7620i	−1.09655	+	1.09655i	−0.101734	+	0.994812i	$0.532439\pi$
$839$	−31.7620	+	31.7620i	−1.09655	+	1.09655i	−0.994812	+	0.101734i	$0.967561\pi$
$840$		−	7.80781i		−	0.269395i
$841$			29.8858i			1.03055i
$842$	16.5163	−	16.5163i	0.569190	−	0.569190i
$843$	−57.3467			−1.97513
$844$	3.30054	−	3.30054i	0.113609	−	0.113609i
$845$	−61.4636			−2.11441
$846$	5.41814	−	5.41814i	0.186279	−	0.186279i
$847$	−3.80956	+	3.80956i	−0.130898	+	0.130898i
$848$	−4.33950	−	4.33950i	−0.149019	−	0.149019i
$849$	−27.3715	−	27.3715i	−0.939386	−	0.939386i
$850$	−2.09195	−	2.09195i	−0.0717533	−	0.0717533i
$851$	8.76515			0.300465
$852$			30.6546i			1.05021i
$853$		−	38.0092i		−	1.30141i	−0.759331	−	0.650705i	$-0.774473\pi$
$853$		−	38.0092i		−	1.30141i	0.759331	−	0.650705i	$-0.225527\pi$
$854$	5.55453	+	5.55453i	0.190072	+	0.190072i
$855$	−66.1854	+	66.1854i	−2.26349	+	2.26349i
$856$			11.0852i			0.378886i
$857$	23.7128			0.810016			0.405008	−	0.914313i	$-0.367269\pi$
$857$	23.7128			0.810016			0.405008	+	0.914313i	$0.367269\pi$
$858$	34.6829	+	34.6829i	1.18406	+	1.18406i
$859$			6.83833i			0.233321i	0.993172	+	0.116660i	$0.0372189\pi$
$859$			6.83833i			0.233321i	−0.993172	+	0.116660i	$0.962781\pi$
$860$	−13.9016			−0.474042
$861$	20.9769	−	3.12401i	0.714889	−	0.106466i
$862$	2.55453			0.0870075
$863$			19.9099i			0.677742i	0.940833	+	0.338871i	$0.110045\pi$
$863$			19.9099i			0.677742i	−0.940833	+	0.338871i	$0.889955\pi$
$864$	−11.6410	−	11.6410i	−0.396036	−	0.396036i
$865$	−19.0603			−0.648071
$866$			20.6943i			0.703219i
$867$	26.2757	−	26.2757i	0.892371	−	0.892371i
$868$	1.81946	+	1.81946i	0.0617565	+	0.0617565i
$869$		−	19.8151i		−	0.672182i
$870$		−	59.9149i		−	2.03130i
$871$	35.0357			1.18714
$872$	5.41578	+	5.41578i	0.183402	+	0.183402i
$873$	69.1607	+	69.1607i	2.34074	+	2.34074i
$874$	−6.05424	−	6.05424i	−0.204788	−	0.204788i
$875$	7.40604	−	7.40604i	0.250370	−	0.250370i
$876$	−0.277725	+	0.277725i	−0.00938347	+	0.00938347i
$877$	21.4335			0.723759			0.361879	−	0.932225i	$-0.382135\pi$
$877$	21.4335			0.723759			0.361879	+	0.932225i	$0.382135\pi$
$878$	−3.71523	+	3.71523i	−0.125383	+	0.125383i
$879$	−28.2333			−0.952286
$880$	−3.94893	+	3.94893i	−0.133118	+	0.133118i
$881$		−	5.60848i		−	0.188955i	−0.995527	−	0.0944773i	$-0.969882\pi$
$881$		−	5.60848i		−	0.188955i	0.995527	−	0.0944773i	$-0.0301180\pi$
$882$		−	7.97044i		−	0.268379i
$883$	−9.52109	+	9.52109i	−0.320410	+	0.320410i	−0.848924	−	0.528514i	$-0.822749\pi$
$883$	−9.52109	+	9.52109i	−0.320410	+	0.320410i	0.528514	+	0.848924i	$0.322749\pi$
$884$	33.2057			1.11683
$885$	−58.3521	+	58.3521i	−1.96148	+	1.96148i
$886$	−6.82700			−0.229358
$887$	−11.3727	+	11.3727i	−0.381858	+	0.381858i	−0.871771	−	0.489913i	$-0.837028\pi$
$887$	−11.3727	+	11.3727i	−0.381858	+	0.381858i	0.489913	+	0.871771i	$0.337028\pi$
$888$	−11.9443	+	11.9443i	−0.400823	+	0.400823i
$889$	−13.0651	−	13.0651i	−0.438189	−	0.438189i
$890$	10.8700	+	10.8700i	0.364365	+	0.364365i
$891$	−51.2884	−	51.2884i	−1.71823	−	1.71823i
$892$	5.76975			0.193186
$893$			4.78917i			0.160264i
$894$			56.5844i			1.89247i
$895$	31.7583	+	31.7583i	1.06156	+	1.06156i
$896$	−0.707107	+	0.707107i	−0.0236228	+	0.0236228i
$897$			35.5836i			1.18810i
$898$	−5.65511			−0.188713
$899$	13.9620	+	13.9620i	0.465659	+	0.465659i
$900$			4.43892i			0.147964i
$901$	−32.6007			−1.08609
$902$	−12.1894	−	9.02938i	−0.405863	−	0.300645i
$903$	−19.5326			−0.650006
$904$		0	0.000169098i		0	5.62411e-6i
$905$	22.8784	+	22.8784i	0.760503	+	0.760503i
$906$	6.37039			0.211642
$907$			32.8515i			1.09082i	0.838170	+	0.545409i	$0.183626\pi$
$907$			32.8515i			1.09082i	−0.838170	+	0.545409i	$0.816374\pi$
$908$	−7.60640	+	7.60640i	−0.252427	+	0.252427i
$909$	37.6169	+	37.6169i	1.24767	+	1.24767i
$910$		−	14.7353i		−	0.488470i
$911$			23.7055i			0.785399i	0.919667	+	0.392700i	$0.128459\pi$
$911$			23.7055i			0.785399i	−0.919667	+	0.392700i	$0.871541\pi$
$912$	16.5002			0.546377
$913$	−8.61735	−	8.61735i	−0.285193	−	0.285193i
$914$	1.76819	+	1.76819i	0.0584865	+	0.0584865i
$915$	−43.3687	−	43.3687i	−1.43372	−	1.43372i
$916$	−19.3861	+	19.3861i	−0.640536	+	0.640536i
$917$	7.95634	−	7.95634i	0.262742	−	0.262742i
$918$	−87.4537			−2.88640
$919$	−16.0869	+	16.0869i	−0.530659	+	0.530659i	−0.920769	−	0.390109i	$-0.872437\pi$
$919$	−16.0869	+	16.0869i	−0.530659	+	0.530659i	0.390109	+	0.920769i	$0.372437\pi$
$920$	−4.05148			−0.133573
$921$	−45.1362	+	45.1362i	−1.48729	+	1.48729i
$922$		−	6.54562i		−	0.215568i
$923$			57.8530i			1.90425i
$924$	−5.54848	+	5.54848i	−0.182532	+	0.182532i
$925$	2.84026			0.0933870
$926$	1.48077	−	1.48077i	0.0486612	−	0.0486612i
$927$	−101.602			−3.33703
$928$	−5.42613	+	5.42613i	−0.178122	+	0.178122i
$929$	6.29638	−	6.29638i	0.206577	−	0.206577i	−0.596234	−	0.802811i	$-0.703337\pi$
$929$	6.29638	−	6.29638i	0.206577	−	0.206577i	0.802811	+	0.596234i	$0.203337\pi$
$930$	−14.2060	−	14.2060i	−0.465833	−	0.465833i
$931$	3.52259	+	3.52259i	0.115448	+	0.115448i
$932$	14.8028	+	14.8028i	0.484882	+	0.484882i
$933$	31.6291			1.03549
$934$			5.44742i			0.178245i
$935$			29.6665i			0.970198i
$936$	−35.2297	−	35.2297i	−1.15152	−	1.15152i
$937$	24.5474	−	24.5474i	0.801930	−	0.801930i	−0.181467	−	0.983397i	$-0.558085\pi$
$937$	24.5474	−	24.5474i	0.801930	−	0.801930i	0.983397	+	0.181467i	$0.0580847\pi$
$938$			5.60492i			0.183007i
$939$	−83.0582			−2.71050
$940$	1.60245	+	1.60245i	0.0522662	+	0.0522662i
$941$		−	5.33509i		−	0.173919i	−0.996212	−	0.0869595i	$-0.972285\pi$
$941$		−	5.33509i		−	0.173919i	0.996212	−	0.0869595i	$-0.0277151\pi$
$942$	25.8399			0.841911
$943$	−1.62105	−	10.8849i	−0.0527887	−	0.354462i
$944$	10.5692			0.343998
$945$			38.8082i			1.26243i
$946$	9.87896	+	9.87896i	0.321193	+	0.321193i
$947$	−7.80965			−0.253779			−0.126890	−	0.991917i	$-0.540499\pi$
$947$	−7.80965			−0.253779			−0.126890	+	0.991917i	$0.540499\pi$
$948$			27.7033i			0.899761i
$949$	−0.524137	+	0.524137i	−0.0170142	+	0.0170142i
$950$	−1.96181	−	1.96181i	−0.0636496	−	0.0636496i
$951$		−	6.13278i		−	0.198869i
$952$			5.31217i			0.172168i
$953$	4.39853			0.142482			0.0712412	−	0.997459i	$-0.477304\pi$
$953$	4.39853			0.142482			0.0712412	+	0.997459i	$0.477304\pi$
$954$	34.5877	+	34.5877i	1.11982	+	1.11982i
$955$	−12.2022	−	12.2022i	−0.394853	−	0.394853i
$956$	2.51316	+	2.51316i	0.0812814	+	0.0812814i
$957$	−42.5774	+	42.5774i	−1.37633	+	1.37633i
$958$	3.63744	−	3.63744i	0.117520	−	0.117520i
$959$	−20.6291			−0.666147
$960$	5.52095	−	5.52095i	0.178188	−	0.178188i
$961$	−24.3791			−0.786424
$962$	−22.5418	+	22.5418i	−0.726778	+	0.726778i
$963$		−	88.3543i		−	2.84718i
$964$		−	4.77168i		−	0.153685i
$965$	41.4519	−	41.4519i	1.33439	−	1.33439i
$966$	−5.69258			−0.183156
$967$	38.1819	−	38.1819i	1.22785	−	1.22785i	0.263071	−	0.964776i	$-0.415265\pi$
$967$	38.1819	−	38.1819i	1.22785	−	1.22785i	0.964776	−	0.263071i	$-0.0847354\pi$
$968$	−5.38752			−0.173162
$969$	61.9792	−	61.9792i	1.99106	−	1.99106i
$970$	−20.4548	+	20.4548i	−0.656763	+	0.656763i
$971$	4.41028	+	4.41028i	0.141533	+	0.141533i	0.774323	−	0.632790i	$-0.218091\pi$
$971$	4.41028	+	4.41028i	0.141533	+	0.141533i	−0.632790	+	0.774323i	$0.718091\pi$
$972$	36.7826	+	36.7826i	1.17980	+	1.17980i
$973$	−10.8539	−	10.8539i	−0.347960	−	0.347960i
$974$	−12.2821			−0.393545
$975$			11.5305i			0.369272i
$976$			7.85529i			0.251442i
$977$	−9.13535	−	9.13535i	−0.292266	−	0.292266i	0.545709	−	0.837975i	$-0.316260\pi$
$977$	−9.13535	−	9.13535i	−0.292266	−	0.292266i	−0.837975	+	0.545709i	$0.816260\pi$
$978$	2.66879	−	2.66879i	0.0853386	−	0.0853386i
$979$		−	15.4492i		−	0.493759i
$980$	2.35731			0.0753016
$981$	−43.1662	−	43.1662i	−1.37819	−	1.37819i
$982$		−	1.50592i		−	0.0480557i
$983$	15.9151			0.507614			0.253807	−	0.967255i	$-0.418317\pi$
$983$	15.9151			0.507614			0.253807	+	0.967255i	$0.418317\pi$
$984$	17.0419	+	12.6239i	0.543276	+	0.402434i
$985$	51.4301			1.63870
$986$			40.7640i			1.29819i
$987$	2.25154	+	2.25154i	0.0716673	+	0.0716673i
$988$	31.1401			0.990697
$989$			10.1355i			0.322291i
$990$	31.4747	−	31.4747i	1.00033	−	1.00033i
$991$	−36.9034	−	36.9034i	−1.17227	−	1.17227i	−0.981666	−	0.190607i	$-0.938954\pi$
$991$	−36.9034	−	36.9034i	−1.17227	−	1.17227i	−0.190607	−	0.981666i	$-0.561046\pi$
$992$			2.57310i			0.0816962i
$993$		−	8.19127i		−	0.259942i
$994$	−9.25517			−0.293556
$995$	−37.8735	−	37.8735i	−1.20067	−	1.20067i
$996$	12.0478	+	12.0478i	0.381750	+	0.381750i
$997$	13.7132	+	13.7132i	0.434301	+	0.434301i	0.890089	−	0.455788i	$-0.150642\pi$
$997$	13.7132	+	13.7132i	0.434301	+	0.434301i	−0.455788	+	0.890089i	$0.650642\pi$
$998$	−12.6594	+	12.6594i	−0.400728	+	0.400728i
$999$	59.3683	−	59.3683i	1.87833	−	1.87833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.f.a.337.10	yes	20
41.32	even	4	inner	574.2.f.a.155.10	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.f.a.155.10	✓	20	41.32	even	4	inner
574.2.f.a.337.10	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(2.34205 + 2.34205i) q^{3} -1.00000 q^{4} +2.35731i q^{5} +(-2.34205 + 2.34205i) q^{6} +(-0.707107 - 0.707107i) q^{7} -1.00000i q^{8} +7.97044i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(2.34205 + 2.34205i) q^{3} -1.00000 q^{4} +2.35731i q^{5} +(-2.34205 + 2.34205i) q^{6} +(-0.707107 - 0.707107i) q^{7} -1.00000i q^{8} +7.97044i q^{9} -2.35731 q^{10} +(1.67518 + 1.67518i) q^{11} +(-2.34205 - 2.34205i) q^{12} +(-4.42004 - 4.42004i) q^{13} +(0.707107 - 0.707107i) q^{14} +(-5.52095 + 5.52095i) q^{15} +1.00000 q^{16} +(3.75627 - 3.75627i) q^{17} -7.97044 q^{18} +(3.52259 - 3.52259i) q^{19} -2.35731i q^{20} -3.31217i q^{21} +(-1.67518 + 1.67518i) q^{22} -1.71869 q^{23} +(2.34205 - 2.34205i) q^{24} -0.556923 q^{25} +(4.42004 - 4.42004i) q^{26} +(-11.6410 + 11.6410i) q^{27} +(0.707107 + 0.707107i) q^{28} +(5.42613 + 5.42613i) q^{29} +(-5.52095 - 5.52095i) q^{30} +2.57310 q^{31} +1.00000i q^{32} +7.84674i q^{33} +(3.75627 + 3.75627i) q^{34} +(1.66687 - 1.66687i) q^{35} -7.97044i q^{36} -5.09991 q^{37} +(3.52259 + 3.52259i) q^{38} -20.7040i q^{39} +2.35731 q^{40} +(0.943192 + 6.33328i) q^{41} +3.31217 q^{42} -5.89724i q^{43} +(-1.67518 - 1.67518i) q^{44} -18.7888 q^{45} -1.71869i q^{46} +(-0.679779 + 0.679779i) q^{47} +(2.34205 + 2.34205i) q^{48} +1.00000i q^{49} -0.556923i q^{50} +17.5948 q^{51} +(4.42004 + 4.42004i) q^{52} +(-4.33950 - 4.33950i) q^{53} +(-11.6410 - 11.6410i) q^{54} +(-3.94893 + 3.94893i) q^{55} +(-0.707107 + 0.707107i) q^{56} +16.5002 q^{57} +(-5.42613 + 5.42613i) q^{58} +10.5692 q^{59} +(5.52095 - 5.52095i) q^{60} +7.85529i q^{61} +2.57310i q^{62} +(5.63595 - 5.63595i) q^{63} -1.00000 q^{64} +(10.4194 - 10.4194i) q^{65} -7.84674 q^{66} +(-3.96328 + 3.96328i) q^{67} +(-3.75627 + 3.75627i) q^{68} +(-4.02526 - 4.02526i) q^{69} +(1.66687 + 1.66687i) q^{70} +(-6.54439 - 6.54439i) q^{71} +7.97044 q^{72} -0.118582i q^{73} -5.09991i q^{74} +(-1.30434 - 1.30434i) q^{75} +(-3.52259 + 3.52259i) q^{76} -2.36907i q^{77} +20.7040 q^{78} +(-5.91431 - 5.91431i) q^{79} +2.35731i q^{80} -30.6166 q^{81} +(-6.33328 + 0.943192i) q^{82} -5.14412 q^{83} +3.31217i q^{84} +(8.85470 + 8.85470i) q^{85} +5.89724 q^{86} +25.4166i q^{87} +(1.67518 - 1.67518i) q^{88} +(-4.61120 - 4.61120i) q^{89} -18.7888i q^{90} +6.25089i q^{91} +1.71869 q^{92} +(6.02635 + 6.02635i) q^{93} +(-0.679779 - 0.679779i) q^{94} +(8.30386 + 8.30386i) q^{95} +(-2.34205 + 2.34205i) q^{96} +(8.67715 - 8.67715i) q^{97} -1.00000 q^{98} +(-13.3519 + 13.3519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 20 q^{4} + 4 q^{6}+O(q^{10}) \) 20 * q - 4 * q^3 - 20 * q^4 + 4 * q^6	\( 20 q - 4 q^{3} - 20 q^{4} + 4 q^{6} + 16 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{15} + 20 q^{16} - 4 q^{17} - 20 q^{18} + 12 q^{19} - 16 q^{22} + 8 q^{23} - 4 q^{24} - 20 q^{25} + 20 q^{26} - 16 q^{27} + 12 q^{29} + 4 q^{30} - 8 q^{31} - 4 q^{34} - 32 q^{37} + 12 q^{38} - 12 q^{41} - 16 q^{44} - 72 q^{45} + 12 q^{47} - 4 q^{48} + 80 q^{51} + 20 q^{52} - 16 q^{54} - 20 q^{55} + 48 q^{57} - 12 q^{58} - 8 q^{59} - 4 q^{60} + 16 q^{63} - 20 q^{64} + 20 q^{65} - 40 q^{66} - 4 q^{67} + 4 q^{68} - 8 q^{69} - 8 q^{71} + 20 q^{72} + 20 q^{75} - 12 q^{76} + 24 q^{78} + 24 q^{79} + 4 q^{81} + 12 q^{82} - 4 q^{85} + 8 q^{86} + 16 q^{88} - 48 q^{89} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 28 q^{95} + 4 q^{96} + 16 q^{97} - 20 q^{98} - 8 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 - 20 * q^4 + 4 * q^6 + 16 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^15 + 20 * q^16 - 4 * q^17 - 20 * q^18 + 12 * q^19 - 16 * q^22 + 8 * q^23 - 4 * q^24 - 20 * q^25 + 20 * q^26 - 16 * q^27 + 12 * q^29 + 4 * q^30 - 8 * q^31 - 4 * q^34 - 32 * q^37 + 12 * q^38 - 12 * q^41 - 16 * q^44 - 72 * q^45 + 12 * q^47 - 4 * q^48 + 80 * q^51 + 20 * q^52 - 16 * q^54 - 20 * q^55 + 48 * q^57 - 12 * q^58 - 8 * q^59 - 4 * q^60 + 16 * q^63 - 20 * q^64 + 20 * q^65 - 40 * q^66 - 4 * q^67 + 4 * q^68 - 8 * q^69 - 8 * q^71 + 20 * q^72 + 20 * q^75 - 12 * q^76 + 24 * q^78 + 24 * q^79 + 4 * q^81 + 12 * q^82 - 4 * q^85 + 8 * q^86 + 16 * q^88 - 48 * q^89 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 28 * q^95 + 4 * q^96 + 16 * q^97 - 20 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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