LMFDB - Embedded newform 1110.2.l.b.697.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 3]))

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			697.3
Character	$\chi$	$=$	1110.697
Dual form			1110.2.l.b.43.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.248996 + 2.22216i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.88943 - 2.88943i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.248996 + 2.22216i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.88943 - 2.88943i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-2.22216 + 0.248996i) q^{10} -4.93091i q^{11} +(0.707107 + 0.707107i) q^{12} +1.83135i q^{13} +(2.88943 - 2.88943i) q^{14} +(1.39524 - 1.74737i) q^{15} +1.00000 q^{16} +2.74310 q^{17} -1.00000 q^{18} +(5.44485 + 5.44485i) q^{19} +(-0.248996 - 2.22216i) q^{20} +4.08627i q^{21} +4.93091 q^{22} +8.34738i q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.87600 + 1.10662i) q^{25} -1.83135 q^{26} +(0.707107 - 0.707107i) q^{27} +(2.88943 + 2.88943i) q^{28} +(-0.469514 + 0.469514i) q^{29} +(1.74737 + 1.39524i) q^{30} +(2.48079 + 2.48079i) q^{31} +1.00000i q^{32} +(-3.48668 + 3.48668i) q^{33} +2.74310i q^{34} +(5.70132 - 7.14024i) q^{35} -1.00000i q^{36} +(-2.83501 + 5.38170i) q^{37} +(-5.44485 + 5.44485i) q^{38} +(1.29496 - 1.29496i) q^{39} +(2.22216 - 0.248996i) q^{40} -4.25710i q^{41} -4.08627 q^{42} +5.61051i q^{43} +4.93091i q^{44} +(-2.22216 + 0.248996i) q^{45} -8.34738 q^{46} +(-0.544094 - 0.544094i) q^{47} +(-0.707107 - 0.707107i) q^{48} +9.69763i q^{49} +(-1.10662 - 4.87600i) q^{50} +(-1.93966 - 1.93966i) q^{51} -1.83135i q^{52} +(-7.02831 + 7.02831i) q^{53} +(0.707107 + 0.707107i) q^{54} +(10.9573 - 1.22778i) q^{55} +(-2.88943 + 2.88943i) q^{56} -7.70018i q^{57} +(-0.469514 - 0.469514i) q^{58} +(-7.44209 - 7.44209i) q^{59} +(-1.39524 + 1.74737i) q^{60} +(1.23325 + 1.23325i) q^{61} +(-2.48079 + 2.48079i) q^{62} +(2.88943 - 2.88943i) q^{63} -1.00000 q^{64} +(-4.06955 + 0.455999i) q^{65} +(-3.48668 - 3.48668i) q^{66} +(5.74859 - 5.74859i) q^{67} -2.74310 q^{68} +(5.90249 - 5.90249i) q^{69} +(7.14024 + 5.70132i) q^{70} +13.0269 q^{71} +1.00000 q^{72} +(5.94865 + 5.94865i) q^{73} +(-5.38170 - 2.83501i) q^{74} +(4.23035 + 2.66535i) q^{75} +(-5.44485 - 5.44485i) q^{76} +(-14.2475 + 14.2475i) q^{77} +(1.29496 + 1.29496i) q^{78} +(4.75210 + 4.75210i) q^{79} +(0.248996 + 2.22216i) q^{80} -1.00000 q^{81} +4.25710 q^{82} +(-0.579710 + 0.579710i) q^{83} -4.08627i q^{84} +(0.683022 + 6.09560i) q^{85} -5.61051 q^{86} +0.663993 q^{87} -4.93091 q^{88} +(-2.52805 + 2.52805i) q^{89} +(-0.248996 - 2.22216i) q^{90} +(5.29155 - 5.29155i) q^{91} -8.34738i q^{92} -3.50837i q^{93} +(0.544094 - 0.544094i) q^{94} +(-10.7436 + 13.4551i) q^{95} +(0.707107 - 0.707107i) q^{96} -17.4278 q^{97} -9.69763 q^{98} +4.93091 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) $ 40 * q - 40 * q^4 - 4 * q^7	$ 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	0.248996	+	2.22216i	0.111355	+	0.993781i
$5$	0.248996	+	2.22216i	0.111355	+	0.993781i
$6$	0.707107	−	0.707107i	0.288675	−	0.288675i
$7$	−2.88943	−	2.88943i	−1.09210	−	1.09210i	−0.995304	−	0.0967984i	$-0.969140\pi$
$7$	−2.88943	−	2.88943i	−1.09210	−	1.09210i	−0.0967984	−	0.995304i	$-0.530860\pi$
$8$		−	1.00000i		−	0.353553i
$9$			1.00000i			0.333333i
$10$	−2.22216	+	0.248996i	−0.702709	+	0.0787396i
$11$		−	4.93091i		−	1.48672i	−0.668889	−	0.743362i	$-0.733230\pi$
$11$		−	4.93091i		−	1.48672i	0.668889	−	0.743362i	$-0.266770\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$			1.83135i			0.507924i	0.967214	+	0.253962i	$0.0817339\pi$
$13$			1.83135i			0.507924i	−0.967214	+	0.253962i	$0.918266\pi$
$14$	2.88943	−	2.88943i	0.772233	−	0.772233i
$15$	1.39524	−	1.74737i	0.360249	−	0.451170i
$16$	1.00000			0.250000
$17$	2.74310			0.665299			0.332649	−	0.943051i	$-0.392057\pi$
$17$	2.74310			0.665299			0.332649	+	0.943051i	$0.392057\pi$
$18$	−1.00000			−0.235702
$19$	5.44485	+	5.44485i	1.24913	+	1.24913i	0.956103	+	0.293030i	$0.0946637\pi$
$19$	5.44485	+	5.44485i	1.24913	+	1.24913i	0.293030	+	0.956103i	$0.405336\pi$
$20$	−0.248996	−	2.22216i	−0.0556773	−	0.496890i
$21$			4.08627i			0.891698i
$22$	4.93091			1.05127
$23$			8.34738i			1.74055i	0.492567	+	0.870275i	$0.336059\pi$
$23$			8.34738i			1.74055i	−0.492567	+	0.870275i	$0.663941\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−4.87600	+	1.10662i	−0.975200	+	0.221324i
$26$	−1.83135			−0.359157
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.88943	+	2.88943i	0.546051	+	0.546051i
$29$	−0.469514	+	0.469514i	−0.0871866	+	0.0871866i	−0.749355	−	0.662168i	$-0.769636\pi$
$29$	−0.469514	+	0.469514i	−0.0871866	+	0.0871866i	0.662168	+	0.749355i	$0.269636\pi$
$30$	1.74737	+	1.39524i	0.319025	+	0.254734i
$31$	2.48079	+	2.48079i	0.445564	+	0.445564i	0.893877	−	0.448313i	$-0.147975\pi$
$31$	2.48079	+	2.48079i	0.445564	+	0.445564i	−0.448313	+	0.893877i	$0.647975\pi$
$32$			1.00000i			0.176777i
$33$	−3.48668	+	3.48668i	−0.606952	+	0.606952i
$34$			2.74310i			0.470437i
$35$	5.70132	−	7.14024i	0.963700	−	1.20692i
$36$		−	1.00000i		−	0.166667i
$37$	−2.83501	+	5.38170i	−0.466073	+	0.884747i
$37$	−2.83501	+	5.38170i	−0.466073	+	0.884747i
$38$	−5.44485	+	5.44485i	−0.883271	+	0.883271i
$39$	1.29496	−	1.29496i	0.207359	−	0.207359i
$40$	2.22216	−	0.248996i	0.351355	−	0.0393698i
$41$		−	4.25710i		−	0.664848i	−0.943130	−	0.332424i	$-0.892134\pi$
$41$		−	4.25710i		−	0.664848i	0.943130	−	0.332424i	$-0.107866\pi$
$42$	−4.08627			−0.630526
$43$			5.61051i			0.855595i	0.903875	+	0.427798i	$0.140710\pi$
$43$			5.61051i			0.855595i	−0.903875	+	0.427798i	$0.859290\pi$
$44$			4.93091i			0.743362i
$45$	−2.22216	+	0.248996i	−0.331260	+	0.0371182i
$46$	−8.34738			−1.23075
$47$	−0.544094	−	0.544094i	−0.0793643	−	0.0793643i	0.666310	−	0.745675i	$-0.267873\pi$
$47$	−0.544094	−	0.544094i	−0.0793643	−	0.0793643i	−0.745675	+	0.666310i	$0.767873\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$			9.69763i			1.38538i
$50$	−1.10662	−	4.87600i	−0.156500	−	0.689571i
$51$	−1.93966	−	1.93966i	−0.271607	−	0.271607i
$52$		−	1.83135i		−	0.253962i
$53$	−7.02831	+	7.02831i	−0.965413	+	0.965413i	−0.999422	−	0.0340086i	$-0.989173\pi$
$53$	−7.02831	+	7.02831i	−0.965413	+	0.965413i	0.0340086	+	0.999422i	$0.489173\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	10.9573	−	1.22778i	1.47748	−	0.165554i
$56$	−2.88943	+	2.88943i	−0.386117	+	0.386117i
$57$		−	7.70018i		−	1.01991i
$58$	−0.469514	−	0.469514i	−0.0616502	−	0.0616502i
$59$	−7.44209	−	7.44209i	−0.968878	−	0.968878i	0.0306521	−	0.999530i	$-0.490242\pi$
$59$	−7.44209	−	7.44209i	−0.968878	−	0.968878i	−0.999530	+	0.0306521i	$0.990242\pi$
$60$	−1.39524	+	1.74737i	−0.180124	+	0.225585i
$61$	1.23325	+	1.23325i	0.157902	+	0.157902i	0.781636	−	0.623734i	$-0.214385\pi$
$61$	1.23325	+	1.23325i	0.157902	+	0.157902i	−0.623734	+	0.781636i	$0.714385\pi$
$62$	−2.48079	+	2.48079i	−0.315061	+	0.315061i
$63$	2.88943	−	2.88943i	0.364034	−	0.364034i
$64$	−1.00000			−0.125000
$65$	−4.06955	+	0.455999i	−0.504766	+	0.0565597i
$66$	−3.48668	−	3.48668i	−0.429180	−	0.429180i
$67$	5.74859	−	5.74859i	0.702302	−	0.702302i	−0.262602	−	0.964904i	$-0.584581\pi$
$67$	5.74859	−	5.74859i	0.702302	−	0.702302i	0.964904	+	0.262602i	$0.0845807\pi$
$68$	−2.74310			−0.332649
$69$	5.90249	−	5.90249i	0.710576	−	0.710576i
$70$	7.14024	+	5.70132i	0.853422	+	0.681439i
$71$	13.0269			1.54601			0.773007	−	0.634398i	$-0.218752\pi$
$71$	13.0269			1.54601			0.773007	+	0.634398i	$0.218752\pi$
$72$	1.00000			0.117851
$73$	5.94865	+	5.94865i	0.696237	+	0.696237i	0.963597	−	0.267360i	$-0.0861513\pi$
$73$	5.94865	+	5.94865i	0.696237	+	0.696237i	−0.267360	+	0.963597i	$0.586151\pi$
$74$	−5.38170	−	2.83501i	−0.625610	−	0.329563i
$75$	4.23035	+	2.66535i	0.488479	+	0.307769i
$76$	−5.44485	−	5.44485i	−0.624567	−	0.624567i
$77$	−14.2475	+	14.2475i	−1.62365	+	1.62365i
$78$	1.29496	+	1.29496i	0.146625	+	0.146625i
$79$	4.75210	+	4.75210i	0.534652	+	0.534652i	0.921953	−	0.387301i	$-0.126593\pi$
$79$	4.75210	+	4.75210i	0.534652	+	0.534652i	−0.387301	+	0.921953i	$0.626593\pi$
$80$	0.248996	+	2.22216i	0.0278387	+	0.248445i
$81$	−1.00000			−0.111111
$82$	4.25710			0.470118
$83$	−0.579710	+	0.579710i	−0.0636314	+	0.0636314i	−0.738206	−	0.674575i	$-0.764327\pi$
$83$	−0.579710	+	0.579710i	−0.0636314	+	0.0636314i	0.674575	+	0.738206i	$0.264327\pi$
$84$		−	4.08627i		−	0.445849i
$85$	0.683022	+	6.09560i	0.0740841	+	0.661161i
$86$	−5.61051			−0.604997
$87$	0.663993			0.0711875
$88$	−4.93091			−0.525636
$89$	−2.52805	+	2.52805i	−0.267972	+	0.267972i	−0.828283	−	0.560310i	$-0.810682\pi$
$89$	−2.52805	+	2.52805i	−0.267972	+	0.267972i	0.560310	+	0.828283i	$0.310682\pi$
$90$	−0.248996	−	2.22216i	−0.0262465	−	0.234236i
$91$	5.29155	−	5.29155i	0.554706	−	0.554706i
$92$		−	8.34738i		−	0.870275i
$93$		−	3.50837i		−	0.363801i
$94$	0.544094	−	0.544094i	0.0561191	−	0.0561191i
$95$	−10.7436	+	13.4551i	−1.10227	+	1.38046i
$96$	0.707107	−	0.707107i	0.0721688	−	0.0721688i
$97$	−17.4278			−1.76952			−0.884761	−	0.466045i	$-0.845679\pi$
$97$	−17.4278			−1.76952			−0.884761	+	0.466045i	$0.845679\pi$
$98$	−9.69763			−0.979608
$99$	4.93091			0.495575
$100$	4.87600	−	1.10662i	0.487600	−	0.110662i
$101$			13.9975i			1.39281i	0.717650	+	0.696404i	$0.245218\pi$
$101$			13.9975i			1.39281i	−0.717650	+	0.696404i	$0.754782\pi$
$102$	1.93966	−	1.93966i	0.192055	−	0.192055i
$103$	12.0104			1.18342			0.591709	−	0.806151i	$-0.298453\pi$
$103$	12.0104			1.18342			0.591709	+	0.806151i	$0.298453\pi$
$104$	1.83135			0.179578
$105$	−9.08036	+	1.01747i	−0.886152	+	0.0992947i
$106$	−7.02831	−	7.02831i	−0.682650	−	0.682650i
$107$	10.6057	+	10.6057i	1.02529	+	1.02529i	0.999672	+	0.0256174i	$0.00815516\pi$
$107$	10.6057	+	10.6057i	1.02529	+	1.02529i	0.0256174	+	0.999672i	$0.491845\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	11.8333	+	11.8333i	1.13343	+	1.13343i	0.989603	+	0.143824i	$0.0459398\pi$
$109$	11.8333	+	11.8333i	1.13343	+	1.13343i	0.143824	+	0.989603i	$0.454060\pi$
$110$	1.22778	+	10.9573i	0.117064	+	1.04473i
$111$	5.81009	−	1.80078i	0.551470	−	0.170923i
$112$	−2.88943	−	2.88943i	−0.273026	−	0.273026i
$113$	6.01525			0.565867			0.282934	−	0.959139i	$-0.408692\pi$
$113$	6.01525			0.565867			0.282934	+	0.959139i	$0.408692\pi$
$114$	7.70018			0.721188
$115$	−18.5492	+	2.07847i	−1.72972	+	0.193818i
$116$	0.469514	−	0.469514i	0.0435933	−	0.0435933i
$117$	−1.83135			−0.169308
$118$	7.44209	−	7.44209i	0.685100	−	0.685100i
$119$	−7.92599	−	7.92599i	−0.726574	−	0.726574i
$120$	−1.74737	−	1.39524i	−0.159513	−	0.127367i
$121$	−13.3138			−1.21035
$122$	−1.23325	+	1.23325i	−0.111654	+	0.111654i
$123$	−3.01023	+	3.01023i	−0.271423	+	0.271423i
$124$	−2.48079	−	2.48079i	−0.222782	−	0.222782i
$125$	−3.67320	−	10.5597i	−0.328541	−	0.944490i
$126$	2.88943	+	2.88943i	0.257411	+	0.257411i
$127$	−3.19427	−	3.19427i	−0.283446	−	0.283446i	0.551036	−	0.834482i	$-0.314233\pi$
$127$	−3.19427	−	3.19427i	−0.283446	−	0.283446i	−0.834482	+	0.551036i	$0.814233\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	3.96723	−	3.96723i	0.349295	−	0.349295i
$130$	−0.455999	−	4.06955i	−0.0399938	−	0.356923i
$131$	−1.15532	−	1.15532i	−0.100941	−	0.100941i	0.654833	−	0.755774i	$-0.272739\pi$
$131$	−1.15532	−	1.15532i	−0.100941	−	0.100941i	−0.755774	+	0.654833i	$0.772739\pi$
$132$	3.48668	−	3.48668i	0.303476	−	0.303476i
$133$		−	31.4650i		−	2.72836i
$134$	5.74859	+	5.74859i	0.496602	+	0.496602i
$135$	1.74737	+	1.39524i	0.150390	+	0.120083i
$136$		−	2.74310i		−	0.235219i
$137$	7.63981	+	7.63981i	0.652713	+	0.652713i	0.953646	−	0.300932i	$-0.0972978\pi$
$137$	7.63981	+	7.63981i	0.652713	+	0.652713i	−0.300932	+	0.953646i	$0.597298\pi$
$138$	5.90249	+	5.90249i	0.502453	+	0.502453i
$139$	6.69829			0.568142			0.284071	−	0.958803i	$-0.408315\pi$
$139$	6.69829			0.568142			0.284071	+	0.958803i	$0.408315\pi$
$140$	−5.70132	+	7.14024i	−0.481850	+	0.603460i
$141$			0.769466i			0.0648007i
$142$			13.0269i			1.09320i
$143$	9.03020			0.755143
$144$			1.00000i			0.0833333i
$145$	−1.16024	−	0.926429i	−0.0963530	−	0.0769357i
$146$	−5.94865	+	5.94865i	−0.492314	+	0.492314i
$147$	6.85726	−	6.85726i	0.565577	−	0.565577i
$148$	2.83501	−	5.38170i	0.233036	−	0.442373i
$149$			2.09937i			0.171987i	0.996296	+	0.0859934i	$0.0274064\pi$
$149$			2.09937i			0.171987i	−0.996296	+	0.0859934i	$0.972594\pi$
$150$	−2.66535	+	4.23035i	−0.217625	+	0.345407i
$151$		−	16.4484i		−	1.33855i	−0.743013	−	0.669276i	$-0.766604\pi$
$151$		−	16.4484i		−	1.33855i	0.743013	−	0.669276i	$-0.233396\pi$
$152$	5.44485	−	5.44485i	0.441635	−	0.441635i
$153$			2.74310i			0.221766i
$154$	−14.2475	−	14.2475i	−1.14810	−	1.14810i
$155$	−4.89501	+	6.13043i	−0.393177	+	0.492408i
$156$	−1.29496	+	1.29496i	−0.103680	+	0.103680i
$157$	13.6581	+	13.6581i	1.09003	+	1.09003i	0.995524	+	0.0945109i	$0.0301287\pi$
$157$	13.6581	+	13.6581i	1.09003	+	1.09003i	0.0945109	+	0.995524i	$0.469871\pi$
$158$	−4.75210	+	4.75210i	−0.378056	+	0.378056i
$159$	9.93953			0.788256
$160$	−2.22216	+	0.248996i	−0.175677	+	0.0196849i
$161$	24.1192	−	24.1192i	1.90086	−	1.90086i
$162$		−	1.00000i		−	0.0785674i
$163$	−16.1683			−1.26640			−0.633200	−	0.773988i	$-0.718259\pi$
$163$	−16.1683			−1.26640			−0.633200	+	0.773988i	$0.718259\pi$
$164$			4.25710i			0.332424i
$165$	−8.61613	−	6.87979i	−0.670765	−	0.535591i
$166$	−0.579710	−	0.579710i	−0.0449942	−	0.0449942i
$167$	0.266278			0.0206052			0.0103026	−	0.999947i	$-0.496721\pi$
$167$	0.266278			0.0206052			0.0103026	+	0.999947i	$0.496721\pi$
$168$	4.08627			0.315263
$169$	9.64617			0.742013
$170$	−6.09560	+	0.683022i	−0.467511	+	0.0523854i
$171$	−5.44485	+	5.44485i	−0.416378	+	0.416378i
$172$		−	5.61051i		−	0.427798i
$173$	−18.1556	−	18.1556i	−1.38034	−	1.38034i	−0.843997	−	0.536348i	$-0.819803\pi$
$173$	−18.1556	−	18.1556i	−1.38034	−	1.38034i	−0.536348	−	0.843997i	$-0.680197\pi$
$174$			0.663993i			0.0503372i
$175$	17.2864	+	10.8914i	1.30673	+	0.823310i
$176$		−	4.93091i		−	0.371681i
$177$			10.5247i			0.791086i
$178$	−2.52805	−	2.52805i	−0.189485	−	0.189485i
$179$	−8.43042	+	8.43042i	−0.630119	+	0.630119i	−0.948098	−	0.317979i	$-0.896996\pi$
$179$	−8.43042	+	8.43042i	−0.630119	+	0.630119i	0.317979	+	0.948098i	$0.396996\pi$
$180$	2.22216	−	0.248996i	0.165630	−	0.0185591i
$181$	14.9316			1.10985			0.554927	−	0.831899i	$-0.312746\pi$
$181$	14.9316			1.10985			0.554927	+	0.831899i	$0.312746\pi$
$182$	5.29155	+	5.29155i	0.392236	+	0.392236i
$183$		−	1.74408i		−	0.128926i
$184$	8.34738			0.615377
$185$	−12.6649	−	4.95982i	−0.931143	−	0.364653i
$186$	3.50837			0.257246
$187$		−	13.5260i		−	0.989116i
$188$	0.544094	+	0.544094i	0.0396822	+	0.0396822i
$189$	−4.08627			−0.297233
$190$	−13.4551	−	10.7436i	−0.976134	−	0.779421i
$191$	−3.66128	+	3.66128i	−0.264921	+	0.264921i	−0.827050	−	0.562129i	$-0.809983\pi$
$191$	−3.66128	+	3.66128i	−0.264921	+	0.264921i	0.562129	+	0.827050i	$0.309983\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$		−	7.43122i		−	0.534911i	−0.963570	−	0.267455i	$-0.913817\pi$
$193$		−	7.43122i		−	0.534911i	0.963570	−	0.267455i	$-0.0861828\pi$
$194$		−	17.4278i		−	1.25124i
$195$	3.20005	+	2.55517i	0.229160	+	0.182979i
$196$		−	9.69763i		−	0.692688i
$197$	−13.1030	−	13.1030i	−0.933552	−	0.933552i	0.0643735	−	0.997926i	$-0.479495\pi$
$197$	−13.1030	−	13.1030i	−0.933552	−	0.933552i	−0.997926	+	0.0643735i	$0.979495\pi$
$198$			4.93091i			0.350424i
$199$	10.2425	−	10.2425i	0.726071	−	0.726071i	−0.243764	−	0.969835i	$-0.578382\pi$
$199$	10.2425	−	10.2425i	0.726071	−	0.726071i	0.969835	+	0.243764i	$0.0783823\pi$
$200$	1.10662	+	4.87600i	0.0782499	+	0.344785i
$201$	−8.12973			−0.573427
$202$	−13.9975			−0.984863
$203$	2.71326			0.190433
$204$	1.93966	+	1.93966i	0.135804	+	0.135804i
$205$	9.45997	−	1.06000i	0.660713	−	0.0740338i
$206$			12.0104i			0.836803i
$207$	−8.34738			−0.580183
$208$			1.83135i			0.126981i
$209$	26.8480	−	26.8480i	1.85712	−	1.85712i
$210$	−1.01747	−	9.08036i	−0.0702119	−	0.626604i
$211$	8.47994			0.583783			0.291892	−	0.956451i	$-0.405715\pi$
$211$	8.47994			0.583783			0.291892	+	0.956451i	$0.405715\pi$
$212$	7.02831	−	7.02831i	0.482706	−	0.482706i
$213$	−9.21144	−	9.21144i	−0.631157	−	0.631157i
$214$	−10.6057	+	10.6057i	−0.724989	+	0.724989i
$215$	−12.4675	+	1.39700i	−0.850274	+	0.0952745i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$		−	14.3362i		−	0.973202i
$218$	−11.8333	+	11.8333i	−0.801454	+	0.801454i
$219$		−	8.41266i		−	0.568475i
$220$	−10.9573	+	1.22778i	−0.738739	+	0.0827768i
$221$			5.02356i			0.337922i
$222$	1.80078	+	5.81009i	0.120861	+	0.389948i
$223$	−16.2856	+	16.2856i	−1.09056	+	1.09056i	−0.0950945	+	0.995468i	$0.530315\pi$
$223$	−16.2856	+	16.2856i	−1.09056	+	1.09056i	−0.995468	+	0.0950945i	$0.969685\pi$
$224$	2.88943	−	2.88943i	0.193058	−	0.193058i
$225$	−1.10662	−	4.87600i	−0.0737747	−	0.325067i
$226$			6.01525i			0.400129i
$227$	−6.39016			−0.424130			−0.212065	−	0.977256i	$-0.568019\pi$
$227$	−6.39016			−0.424130			−0.212065	+	0.977256i	$0.568019\pi$
$228$			7.70018i			0.509957i
$229$			15.3620i			1.01515i	0.861608	+	0.507574i	$0.169458\pi$
$229$			15.3620i			1.01515i	−0.861608	+	0.507574i	$0.830542\pi$
$230$	−2.07847	−	18.5492i	−0.137050	−	1.22310i
$231$	20.1490			1.32571
$232$	0.469514	+	0.469514i	0.0308251	+	0.0308251i
$233$	−14.9071	−	14.9071i	−0.976598	−	0.976598i	0.0231339	−	0.999732i	$-0.492636\pi$
$233$	−14.9071	−	14.9071i	−0.976598	−	0.976598i	−0.999732	+	0.0231339i	$0.992636\pi$
$234$		−	1.83135i		−	0.119719i
$235$	1.07359	−	1.34454i	0.0700332	−	0.0877083i
$236$	7.44209	+	7.44209i	0.484439	+	0.484439i
$237$		−	6.72048i		−	0.436542i
$238$	7.92599	−	7.92599i	0.513766	−	0.513766i
$239$	8.66507	+	8.66507i	0.560497	+	0.560497i	0.929449	−	0.368952i	$-0.120283\pi$
$239$	8.66507	+	8.66507i	0.560497	+	0.560497i	−0.368952	+	0.929449i	$0.620283\pi$
$240$	1.39524	−	1.74737i	0.0900622	−	0.112792i
$241$	11.1430	−	11.1430i	0.717782	−	0.717782i	−0.250369	−	0.968151i	$-0.580552\pi$
$241$	11.1430	−	11.1430i	0.717782	−	0.717782i	0.968151	+	0.250369i	$0.0805519\pi$
$242$		−	13.3138i		−	0.855845i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−1.23325	−	1.23325i	−0.0789510	−	0.0789510i
$245$	−21.5497	+	2.41468i	−1.37676	+	0.154268i
$246$	−3.01023	−	3.01023i	−0.191925	−	0.191925i
$247$	−9.97141	+	9.97141i	−0.634466	+	0.634466i
$248$	2.48079	−	2.48079i	0.157531	−	0.157531i
$249$	0.819833			0.0519548
$250$	10.5597	−	3.67320i	0.667855	−	0.232313i
$251$	−9.10789	−	9.10789i	−0.574885	−	0.574885i	0.358604	−	0.933490i	$-0.383253\pi$
$251$	−9.10789	−	9.10789i	−0.574885	−	0.574885i	−0.933490	+	0.358604i	$0.883253\pi$
$252$	−2.88943	+	2.88943i	−0.182017	+	0.182017i
$253$	41.1601			2.58772
$254$	3.19427	−	3.19427i	0.200427	−	0.200427i
$255$	3.82727	−	4.79321i	0.239673	−	0.300163i
$256$	1.00000			0.0625000
$257$	−20.8722			−1.30197			−0.650986	−	0.759090i	$-0.725644\pi$
$257$	−20.8722			−1.30197			−0.650986	+	0.759090i	$0.725644\pi$
$258$	3.96723	+	3.96723i	0.246989	+	0.246989i
$259$	23.7416	−	7.35850i	1.47523	−	0.457235i
$260$	4.06955	−	0.455999i	0.252383	−	0.0282799i
$261$	−0.469514	−	0.469514i	−0.0290622	−	0.0290622i
$262$	1.15532	−	1.15532i	0.0713757	−	0.0713757i
$263$	−0.897695	−	0.897695i	−0.0553543	−	0.0553543i	0.678888	−	0.734242i	$-0.262462\pi$
$263$	−0.897695	−	0.897695i	−0.0553543	−	0.0553543i	−0.734242	+	0.678888i	$0.762462\pi$
$264$	3.48668	+	3.48668i	0.214590	+	0.214590i
$265$	−17.3681	−	13.8680i	−1.06691	−	0.851906i
$266$	31.4650			1.92924
$267$	3.57520			0.218799
$268$	−5.74859	+	5.74859i	−0.351151	+	0.351151i
$269$			10.6873i			0.651619i	0.945435	+	0.325810i	$0.105637\pi$
$269$			10.6873i			0.651619i	−0.945435	+	0.325810i	$0.894363\pi$
$270$	−1.39524	+	1.74737i	−0.0849115	+	0.106342i
$271$	−21.1698			−1.28597			−0.642986	−	0.765878i	$-0.722305\pi$
$271$	−21.1698			−1.28597			−0.642986	+	0.765878i	$0.722305\pi$
$272$	2.74310			0.166325
$273$	−7.48339			−0.452915
$274$	−7.63981	+	7.63981i	−0.461538	+	0.461538i
$275$	5.45664	+	24.0431i	0.329048	+	1.44985i
$276$	−5.90249	+	5.90249i	−0.355288	+	0.355288i
$277$			27.0099i			1.62287i	0.584443	+	0.811435i	$0.301313\pi$
$277$			27.0099i			1.62287i	−0.584443	+	0.811435i	$0.698687\pi$
$278$			6.69829i			0.401737i
$279$	−2.48079	+	2.48079i	−0.148521	+	0.148521i
$280$	−7.14024	−	5.70132i	−0.426711	−	0.340719i
$281$	6.59580	−	6.59580i	0.393473	−	0.393473i	−0.482451	−	0.875923i	$-0.660253\pi$
$281$	6.59580	−	6.59580i	0.393473	−	0.393473i	0.875923	+	0.482451i	$0.160253\pi$
$282$	−0.769466			−0.0458210
$283$	7.61412			0.452613			0.226306	−	0.974056i	$-0.427335\pi$
$283$	7.61412			0.452613			0.226306	+	0.974056i	$0.427335\pi$
$284$	−13.0269			−0.773007
$285$	17.1110	−	1.91732i	1.01357	−	0.113572i
$286$			9.03020i			0.533967i
$287$	−12.3006	+	12.3006i	−0.726082	+	0.726082i
$288$	−1.00000			−0.0589256
$289$	−9.47542			−0.557378
$290$	0.926429	−	1.16024i	0.0544018	−	0.0681318i
$291$	12.3233	+	12.3233i	0.722404	+	0.722404i
$292$	−5.94865	−	5.94865i	−0.348118	−	0.348118i
$293$	3.86863	−	3.86863i	0.226008	−	0.226008i	−0.585015	−	0.811023i	$-0.698911\pi$
$293$	3.86863	−	3.86863i	0.226008	−	0.226008i	0.811023	+	0.585015i	$0.198911\pi$
$294$	6.85726	+	6.85726i	0.399923	+	0.399923i
$295$	14.6845	−	18.3906i	0.854963	−	1.07074i
$296$	5.38170	+	2.83501i	0.312805	+	0.164782i
$297$	−3.48668	−	3.48668i	−0.202317	−	0.202317i
$298$	−2.09937			−0.121613
$299$	−15.2870			−0.884068
$300$	−4.23035	−	2.66535i	−0.244240	−	0.153884i
$301$	16.2112	−	16.2112i	0.934398	−	0.934398i
$302$	16.4484			0.946500
$303$	9.89776	−	9.89776i	0.568611	−	0.568611i
$304$	5.44485	+	5.44485i	0.312283	+	0.312283i
$305$	−2.43341	+	3.04756i	−0.139337	+	0.174503i
$306$	−2.74310			−0.156812
$307$	11.5991	−	11.5991i	0.661998	−	0.661998i	−0.293853	−	0.955851i	$-0.594937\pi$
$307$	11.5991	−	11.5991i	0.661998	−	0.661998i	0.955851	+	0.293853i	$0.0949375\pi$
$308$	14.2475	−	14.2475i	0.811827	−	0.811827i
$309$	−8.49263	−	8.49263i	−0.483129	−	0.483129i
$310$	−6.13043	−	4.89501i	−0.348185	−	0.278018i
$311$	−10.3616	−	10.3616i	−0.587555	−	0.587555i	0.349414	−	0.936969i	$-0.386381\pi$
$311$	−10.3616	−	10.3616i	−0.587555	−	0.587555i	−0.936969	+	0.349414i	$0.886381\pi$
$312$	−1.29496	−	1.29496i	−0.0733126	−	0.0733126i
$313$			22.6679i			1.28126i	0.767848	+	0.640632i	$0.221327\pi$
$313$			22.6679i			1.28126i	−0.767848	+	0.640632i	$0.778673\pi$
$314$	−13.6581	+	13.6581i	−0.770771	+	0.770771i
$315$	7.14024	+	5.70132i	0.402307	+	0.321233i
$316$	−4.75210	−	4.75210i	−0.267326	−	0.267326i
$317$	18.8950	−	18.8950i	1.06125	−	1.06125i	0.0632489	−	0.997998i	$-0.479854\pi$
$317$	18.8950	−	18.8950i	1.06125	−	1.06125i	0.997998	−	0.0632489i	$-0.0201462\pi$
$318$			9.93953i			0.557381i
$319$	2.31513	+	2.31513i	0.129622	+	0.129622i
$320$	−0.248996	−	2.22216i	−0.0139193	−	0.124223i
$321$		−	14.9987i		−	0.837145i
$322$	24.1192	+	24.1192i	1.34411	+	1.34411i
$323$	14.9357	+	14.9357i	0.831047	+	0.831047i
$324$	1.00000			0.0555556
$325$	−2.02661	−	8.92965i	−0.112416	−	0.495328i
$326$		−	16.1683i		−	0.895480i
$327$		−	16.7348i		−	0.925439i
$328$	−4.25710			−0.235059
$329$			3.14425i			0.173348i
$330$	6.87979	−	8.61613i	0.378720	−	0.474302i
$331$	−7.58835	+	7.58835i	−0.417093	+	0.417093i	−0.884201	−	0.467107i	$-0.845296\pi$
$331$	−7.58835	+	7.58835i	−0.417093	+	0.417093i	0.467107	+	0.884201i	$0.345296\pi$
$332$	0.579710	−	0.579710i	0.0318157	−	0.0318157i
$333$	−5.38170	−	2.83501i	−0.294916	−	0.155358i
$334$			0.266278i			0.0145701i
$335$	14.2057	+	11.3429i	0.776139	+	0.619730i
$336$			4.08627i			0.222924i
$337$	−15.6272	+	15.6272i	−0.851266	+	0.851266i	−0.990289	−	0.139023i	$-0.955604\pi$
$337$	−15.6272	+	15.6272i	−0.851266	+	0.851266i	0.139023	+	0.990289i	$0.455604\pi$
$338$			9.64617i			0.524682i
$339$	−4.25343	−	4.25343i	−0.231014	−	0.231014i
$340$	−0.683022	−	6.09560i	−0.0370420	−	0.330581i
$341$	12.2326	−	12.2326i	0.662430	−	0.662430i
$342$	−5.44485	−	5.44485i	−0.294424	−	0.294424i
$343$	7.79461	−	7.79461i	0.420869	−	0.420869i
$344$	5.61051			0.302499
$345$	14.5860	+	11.6466i	0.785283	+	0.627031i
$346$	18.1556	−	18.1556i	0.976051	−	0.976051i
$347$		−	7.97256i		−	0.427990i	−0.976835	−	0.213995i	$-0.931352\pi$
$347$		−	7.97256i		−	0.427990i	0.976835	−	0.213995i	$-0.0686476\pi$
$348$	−0.663993			−0.0355938
$349$		−	1.39367i		−	0.0746015i	−0.999304	−	0.0373008i	$-0.988124\pi$
$349$		−	1.39367i		−	0.0746015i	0.999304	−	0.0373008i	$-0.0118760\pi$
$350$	−10.8914	+	17.2864i	−0.582168	+	0.923996i
$351$	1.29496	+	1.29496i	0.0691198	+	0.0691198i
$352$	4.93091			0.262818
$353$	8.13118			0.432779			0.216390	−	0.976307i	$-0.430572\pi$
$353$	8.13118			0.432779			0.216390	+	0.976307i	$0.430572\pi$
$354$	−10.5247			−0.559382
$355$	3.24366	+	28.9480i	0.172156	+	1.53640i
$356$	2.52805	−	2.52805i	0.133986	−	0.133986i
$357$			11.2090i			0.593246i
$358$	−8.43042	−	8.43042i	−0.445561	−	0.445561i
$359$		−	7.41829i		−	0.391523i	−0.980652	−	0.195761i	$-0.937282\pi$
$359$		−	7.41829i		−	0.391523i	0.980652	−	0.195761i	$-0.0627178\pi$
$360$	0.248996	+	2.22216i	0.0131233	+	0.117118i
$361$			40.2927i			2.12067i
$362$			14.9316i			0.784785i
$363$	9.41430	+	9.41430i	0.494122	+	0.494122i
$364$	−5.29155	+	5.29155i	−0.277353	+	0.277353i
$365$	−11.7377	+	14.7000i	−0.614377	+	0.769436i
$366$	1.74408			0.0911648
$367$	−24.4204	−	24.4204i	−1.27474	−	1.27474i	−0.943574	−	0.331162i	$-0.892559\pi$
$367$	−24.4204	−	24.4204i	−1.27474	−	1.27474i	−0.331162	−	0.943574i	$-0.607441\pi$
$368$			8.34738i			0.435137i
$369$	4.25710			0.221616
$370$	4.95982	−	12.6649i	0.257849	−	0.658418i
$371$	40.6157			2.10866
$372$			3.50837i			0.181901i
$373$	25.6268	+	25.6268i	1.32690	+	1.32690i	0.908057	+	0.418847i	$0.137566\pi$
$373$	25.6268	+	25.6268i	1.32690	+	1.32690i	0.418847	+	0.908057i	$0.362434\pi$
$374$	13.5260			0.699410
$375$	−4.86950	+	10.0642i	−0.251460	+	0.519713i
$376$	−0.544094	+	0.544094i	−0.0280595	+	0.0280595i
$377$	−0.859844	−	0.859844i	−0.0442842	−	0.0442842i
$378$		−	4.08627i		−	0.210175i
$379$			1.27584i			0.0655357i	0.999463	+	0.0327678i	$0.0104322\pi$
$379$			1.27584i			0.0655357i	−0.999463	+	0.0327678i	$0.989568\pi$
$380$	10.7436	−	13.4551i	0.551134	−	0.690231i
$381$			4.51738i			0.231433i
$382$	−3.66128	−	3.66128i	−0.187327	−	0.187327i
$383$		−	20.0723i		−	1.02565i	−0.858494	−	0.512823i	$-0.828600\pi$
$383$		−	20.0723i		−	1.02565i	0.858494	−	0.512823i	$-0.171400\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−35.2079	−	28.1127i	−1.79436	−	1.43276i
$386$	7.43122			0.378239
$387$	−5.61051			−0.285198
$388$	17.4278			0.884761
$389$	−8.42098	−	8.42098i	−0.426961	−	0.426961i	0.460631	−	0.887592i	$-0.347623\pi$
$389$	−8.42098	−	8.42098i	−0.426961	−	0.426961i	−0.887592	+	0.460631i	$0.847623\pi$
$390$	−2.55517	+	3.20005i	−0.129386	+	0.162041i
$391$			22.8977i			1.15799i
$392$	9.69763			0.489804
$393$			1.63387i			0.0824176i
$394$	13.1030	−	13.1030i	0.660121	−	0.660121i
$395$	−9.37667	+	11.7432i	−0.471791	+	0.590863i
$396$	−4.93091			−0.247787
$397$	4.91456	−	4.91456i	0.246655	−	0.246655i	−0.572942	−	0.819596i	$-0.694198\pi$
$397$	4.91456	−	4.91456i	0.246655	−	0.246655i	0.819596	+	0.572942i	$0.194198\pi$
$398$	10.2425	+	10.2425i	0.513409	+	0.513409i
$399$	−22.2491	+	22.2491i	−1.11385	+	1.11385i
$400$	−4.87600	+	1.10662i	−0.243800	+	0.0553310i
$401$	−9.79743	−	9.79743i	−0.489260	−	0.489260i	0.418812	−	0.908073i	$-0.362446\pi$
$401$	−9.79743	−	9.79743i	−0.489260	−	0.489260i	−0.908073	+	0.418812i	$0.862446\pi$
$402$		−	8.12973i		−	0.405474i
$403$	−4.54320	+	4.54320i	−0.226313	+	0.226313i
$404$		−	13.9975i		−	0.696404i
$405$	−0.248996	−	2.22216i	−0.0123727	−	0.110420i
$406$			2.71326i			0.134657i
$407$	26.5367	+	13.9792i	1.31537	+	0.692921i
$408$	−1.93966	+	1.93966i	−0.0960276	+	0.0960276i
$409$	−1.43202	+	1.43202i	−0.0708087	+	0.0708087i	−0.741624	−	0.670816i	$-0.765944\pi$
$409$	−1.43202	+	1.43202i	−0.0708087	+	0.0708087i	0.670816	+	0.741624i	$0.265944\pi$
$410$	1.06000	+	9.45997i	0.0523498	+	0.467194i
$411$		−	10.8043i		−	0.532938i
$412$	−12.0104			−0.591709
$413$			43.0068i			2.11623i
$414$		−	8.34738i		−	0.410251i
$415$	−1.43255	−	1.14386i	−0.0703213	−	0.0561500i
$416$	−1.83135			−0.0897892
$417$	−4.73641	−	4.73641i	−0.231943	−	0.231943i
$418$	26.8480	+	26.8480i	1.31318	+	1.31318i
$419$		−	23.3375i		−	1.14011i	−0.821605	−	0.570057i	$-0.806921\pi$
$419$		−	23.3375i		−	1.14011i	0.821605	−	0.570057i	$-0.193079\pi$
$420$	9.08036	−	1.01747i	0.443076	−	0.0496473i
$421$	−12.1830	−	12.1830i	−0.593762	−	0.593762i	0.344884	−	0.938645i	$-0.387918\pi$
$421$	−12.1830	−	12.1830i	−0.593762	−	0.593762i	−0.938645	+	0.344884i	$0.887918\pi$
$422$			8.47994i			0.412797i
$423$	0.544094	−	0.544094i	0.0264548	−	0.0264548i
$424$	7.02831	+	7.02831i	0.341325	+	0.341325i
$425$	−13.3753	+	3.03557i	−0.648800	+	0.147247i
$426$	9.21144	−	9.21144i	0.446296	−	0.446296i
$427$		−	7.12681i		−	0.344890i
$428$	−10.6057	−	10.6057i	−0.512645	−	0.512645i
$429$	−6.38532	−	6.38532i	−0.308286	−	0.308286i
$430$	−1.39700	−	12.4675i	−0.0673692	−	0.601235i
$431$	−22.3232	−	22.3232i	−1.07527	−	1.07527i	−0.996927	−	0.0783421i	$-0.975037\pi$
$431$	−22.3232	−	22.3232i	−1.07527	−	1.07527i	−0.0783421	−	0.996927i	$-0.524963\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−1.25239	+	1.25239i	−0.0601862	+	0.0601862i	−0.736559	−	0.676373i	$-0.763551\pi$
$433$	−1.25239	+	1.25239i	−0.0601862	+	0.0601862i	0.676373	+	0.736559i	$0.263551\pi$
$434$	14.3362			0.688158
$435$	0.165332	+	1.47550i	0.00792706	+	0.0707448i
$436$	−11.8333	−	11.8333i	−0.566714	−	0.566714i
$437$	−45.4502	+	45.4502i	−2.17418	+	2.17418i
$438$	8.41266			0.401972
$439$	−0.852686	+	0.852686i	−0.0406965	+	0.0406965i	−0.727162	−	0.686466i	$-0.759161\pi$
$439$	−0.852686	+	0.852686i	−0.0406965	+	0.0406965i	0.686466	+	0.727162i	$0.259161\pi$
$440$	−1.22778	−	10.9573i	−0.0585320	−	0.522367i
$441$	−9.69763			−0.461792
$442$	−5.02356			−0.238947
$443$	−13.9950	−	13.9950i	−0.664922	−	0.664922i	0.291614	−	0.956536i	$-0.405808\pi$
$443$	−13.9950	−	13.9950i	−0.664922	−	0.664922i	−0.956536	+	0.291614i	$0.905808\pi$
$444$	−5.81009	+	1.80078i	−0.275735	+	0.0854615i
$445$	−6.24720	−	4.98825i	−0.296146	−	0.236466i
$446$	−16.2856	−	16.2856i	−0.771144	−	0.771144i
$447$	1.48448	−	1.48448i	0.0702133	−	0.0702133i
$448$	2.88943	+	2.88943i	0.136513	+	0.136513i
$449$	2.16577	+	2.16577i	0.102209	+	0.102209i	0.756362	−	0.654153i	$-0.226975\pi$
$449$	2.16577	+	2.16577i	0.102209	+	0.102209i	−0.654153	+	0.756362i	$0.726975\pi$
$450$	4.87600	−	1.10662i	0.229857	−	0.0521666i
$451$	−20.9914			−0.988445
$452$	−6.01525			−0.282934
$453$	−11.6308	+	11.6308i	−0.546462	+	0.546462i
$454$		−	6.39016i		−	0.299905i
$455$	13.0763	+	10.4411i	0.613025	+	0.489487i
$456$	−7.70018			−0.360594
$457$	15.2516			0.713439			0.356720	−	0.934212i	$-0.383895\pi$
$457$	15.2516			0.713439			0.356720	+	0.934212i	$0.383895\pi$
$458$	−15.3620			−0.717818
$459$	1.93966	−	1.93966i	0.0905357	−	0.0905357i
$460$	18.5492	−	2.07847i	0.864862	−	0.0969091i
$461$	14.4647	−	14.4647i	0.673686	−	0.673686i	−0.284878	−	0.958564i	$-0.591953\pi$
$461$	14.4647	−	14.4647i	0.673686	−	0.673686i	0.958564	+	0.284878i	$0.0919530\pi$
$462$			20.1490i			0.937418i
$463$		−	17.5203i		−	0.814237i	−0.913375	−	0.407118i	$-0.866534\pi$
$463$		−	17.5203i		−	0.814237i	0.913375	−	0.407118i	$-0.133466\pi$
$464$	−0.469514	+	0.469514i	−0.0217966	+	0.0217966i
$465$	7.79617	−	0.873572i	0.361539	−	0.0405109i
$466$	14.9071	−	14.9071i	0.690559	−	0.690559i
$467$	17.1724			0.794646			0.397323	−	0.917679i	$-0.369939\pi$
$467$	17.1724			0.794646			0.397323	+	0.917679i	$0.369939\pi$
$468$	1.83135			0.0846541
$469$	−33.2203			−1.53397
$470$	1.34454	+	1.07359i	0.0620191	+	0.0495209i
$471$		−	19.3155i		−	0.890010i
$472$	−7.44209	+	7.44209i	−0.342550	+	0.342550i
$473$	27.6649			1.27203
$474$	6.72048			0.308682
$475$	−32.5745	−	20.5237i	−1.49462	−	0.941692i
$476$	7.92599	+	7.92599i	0.363287	+	0.363287i
$477$	−7.02831	−	7.02831i	−0.321804	−	0.321804i
$478$	−8.66507	+	8.66507i	−0.396331	+	0.396331i
$479$	16.4237	+	16.4237i	0.750419	+	0.750419i	0.974557	−	0.224139i	$-0.0719569\pi$
$479$	16.4237	+	16.4237i	0.750419	+	0.750419i	−0.224139	+	0.974557i	$0.571957\pi$
$480$	1.74737	+	1.39524i	0.0797563	+	0.0636836i
$481$	−9.85577	−	5.19189i	−0.449384	−	0.236730i
$482$	11.1430	+	11.1430i	0.507548	+	0.507548i
$483$	−34.1097			−1.55204
$484$	13.3138			0.605174
$485$	−4.33945	−	38.7273i	−0.197044	−	1.75852i
$486$	−0.707107	+	0.707107i	−0.0320750	+	0.0320750i
$487$	−17.8636			−0.809478			−0.404739	−	0.914432i	$-0.632638\pi$
$487$	−17.8636			−0.809478			−0.404739	+	0.914432i	$0.632638\pi$
$488$	1.23325	−	1.23325i	0.0558268	−	0.0558268i
$489$	11.4327	+	11.4327i	0.517006	+	0.517006i
$490$	−2.41468	−	21.5497i	−0.109084	−	0.973516i
$491$	−38.7653			−1.74945			−0.874726	−	0.484618i	$-0.838958\pi$
$491$	−38.7653			−1.74945			−0.874726	+	0.484618i	$0.838958\pi$
$492$	3.01023	−	3.01023i	0.135711	−	0.135711i
$493$	−1.28792	+	1.28792i	−0.0580051	+	0.0580051i
$494$	−9.97141	−	9.97141i	−0.448635	−	0.448635i
$495$	1.22778	+	10.9573i	0.0551845	+	0.492493i
$496$	2.48079	+	2.48079i	0.111391	+	0.111391i
$497$	−37.6404	−	37.6404i	−1.68840	−	1.68840i
$498$			0.819833i			0.0367376i
$499$	−7.54787	+	7.54787i	−0.337889	+	0.337889i	−0.855572	−	0.517683i	$-0.826795\pi$
$499$	−7.54787	+	7.54787i	−0.337889	+	0.337889i	0.517683	+	0.855572i	$0.326795\pi$
$500$	3.67320	+	10.5597i	0.164270	+	0.472245i
$501$	−0.188287	−	0.188287i	−0.00841205	−	0.00841205i
$502$	9.10789	−	9.10789i	0.406505	−	0.406505i
$503$			17.9380i			0.799816i	0.916555	+	0.399908i	$0.130958\pi$
$503$			17.9380i			0.799816i	−0.916555	+	0.399908i	$0.869042\pi$
$504$	−2.88943	−	2.88943i	−0.128706	−	0.128706i
$505$	−31.1048	+	3.48534i	−1.38415	+	0.155096i
$506$			41.1601i			1.82979i
$507$	−6.82087	−	6.82087i	−0.302925	−	0.302925i
$508$	3.19427	+	3.19427i	0.141723	+	0.141723i
$509$	−14.1696			−0.628055			−0.314028	−	0.949414i	$-0.601678\pi$
$509$	−14.1696			−0.628055			−0.314028	+	0.949414i	$0.601678\pi$
$510$	4.79321	+	3.82727i	0.212247	+	0.169475i
$511$		−	34.3764i		−	1.52072i
$512$			1.00000i			0.0441942i
$513$	7.70018			0.339971
$514$		−	20.8722i		−	0.920633i
$515$	2.99054	+	26.6890i	0.131779	+	1.17606i
$516$	−3.96723	+	3.96723i	−0.174648	+	0.174648i
$517$	−2.68288	+	2.68288i	−0.117993	+	0.117993i
$518$	7.35850	+	23.7416i	0.323314	+	1.04315i
$519$			25.6759i			1.12705i
$520$	0.455999	+	4.06955i	0.0199969	+	0.178462i
$521$			14.0818i			0.616936i	0.951235	+	0.308468i	$0.0998162\pi$
$521$			14.0818i			0.616936i	−0.951235	+	0.308468i	$0.900184\pi$
$522$	0.469514	−	0.469514i	0.0205501	−	0.0205501i
$523$		−	9.57199i		−	0.418554i	−0.977856	−	0.209277i	$-0.932889\pi$
$523$		−	9.57199i		−	0.418554i	0.977856	−	0.209277i	$-0.0671110\pi$
$524$	1.15532	+	1.15532i	0.0504703	+	0.0504703i
$525$	−4.52195	−	19.9247i	−0.197354	−	0.869584i
$526$	0.897695	−	0.897695i	0.0391414	−	0.0391414i
$527$	6.80506	+	6.80506i	0.296433	+	0.296433i
$528$	−3.48668	+	3.48668i	−0.151738	+	0.151738i
$529$	−46.6788			−2.02951
$530$	13.8680	−	17.3681i	0.602388	−	0.754421i
$531$	7.44209	−	7.44209i	0.322959	−	0.322959i
$532$			31.4650i			1.36418i
$533$	7.79623			0.337692
$534$			3.57520i			0.154714i
$535$	−20.9267	+	26.2083i	−0.904742	+	1.13308i
$536$	−5.74859	−	5.74859i	−0.248301	−	0.248301i
$537$	11.9224			0.514490
$538$	−10.6873			−0.460764
$539$	47.8181			2.05967
$540$	−1.74737	−	1.39524i	−0.0751949	−	0.0600415i
$541$	−7.51447	+	7.51447i	−0.323072	+	0.323072i	−0.849944	−	0.526872i	$-0.823365\pi$
$541$	−7.51447	+	7.51447i	−0.323072	+	0.323072i	0.526872	+	0.849944i	$0.323365\pi$
$542$		−	21.1698i		−	0.909320i
$543$	−10.5582	−	10.5582i	−0.453096	−	0.453096i
$544$			2.74310i			0.117609i
$545$	−23.3491	+	29.2420i	−1.00017	+	1.25259i
$546$		−	7.48339i		−	0.320259i
$547$			12.8110i			0.547759i	0.961764	+	0.273880i	$0.0883070\pi$
$547$			12.8110i			0.547759i	−0.961764	+	0.273880i	$0.911693\pi$
$548$	−7.63981	−	7.63981i	−0.326357	−	0.326357i
$549$	−1.23325	+	1.23325i	−0.0526340	+	0.0526340i
$550$	−24.0431	+	5.45664i	−1.02520	+	0.232672i
$551$	−5.11286			−0.217815
$552$	−5.90249	−	5.90249i	−0.251227	−	0.251227i
$553$		−	27.4617i		−	1.16779i
$554$	−27.0099			−1.14754
$555$	5.44833	+	12.4626i	0.231269	+	0.529007i
$556$	−6.69829			−0.284071
$557$		−	5.34895i		−	0.226642i	−0.993558	−	0.113321i	$-0.963851\pi$
$557$		−	5.34895i		−	0.226642i	0.993558	−	0.113321i	$-0.0361489\pi$
$558$	−2.48079	−	2.48079i	−0.105020	−	0.105020i
$559$	−10.2748			−0.434578
$560$	5.70132	−	7.14024i	0.240925	−	0.301730i
$561$	−9.56429	+	9.56429i	−0.403805	+	0.403805i
$562$	6.59580	+	6.59580i	0.278227	+	0.278227i
$563$			39.3536i			1.65856i	0.558836	+	0.829279i	$0.311248\pi$
$563$			39.3536i			1.65856i	−0.558836	+	0.829279i	$0.688752\pi$
$564$		−	0.769466i		−	0.0324003i
$565$	1.49778	+	13.3669i	0.0630119	+	0.562348i
$566$			7.61412i			0.320046i
$567$	2.88943	+	2.88943i	0.121345	+	0.121345i
$568$		−	13.0269i		−	0.546598i
$569$	17.8957	−	17.8957i	0.750226	−	0.750226i	−0.224296	−	0.974521i	$-0.572008\pi$
$569$	17.8957	−	17.8957i	0.750226	−	0.750226i	0.974521	+	0.224296i	$0.0720081\pi$
$570$	1.91732	+	17.1110i	0.0803076	+	0.716702i
$571$	14.1071			0.590362			0.295181	−	0.955441i	$-0.404620\pi$
$571$	14.1071			0.590362			0.295181	+	0.955441i	$0.404620\pi$
$572$	−9.03020			−0.377572
$573$	5.17783			0.216307
$574$	−12.3006	−	12.3006i	−0.513417	−	0.513417i
$575$	−9.23738	−	40.7018i	−0.385226	−	1.69738i
$576$		−	1.00000i		−	0.0416667i
$577$	8.43655			0.351218			0.175609	−	0.984460i	$-0.443811\pi$
$577$	8.43655			0.351218			0.175609	+	0.984460i	$0.443811\pi$
$578$		−	9.47542i		−	0.394125i
$579$	−5.25466	+	5.25466i	−0.218376	+	0.218376i
$580$	1.16024	+	0.926429i	0.0481765	+	0.0384679i
$581$	3.35006			0.138984
$582$	−12.3233	+	12.3233i	−0.510817	+	0.510817i
$583$	34.6559	+	34.6559i	1.43530	+	1.43530i
$584$	5.94865	−	5.94865i	0.246157	−	0.246157i
$585$	−0.455999	−	4.06955i	−0.0188532	−	0.168255i
$586$	3.86863	+	3.86863i	0.159812	+	0.159812i
$587$		−	23.4466i		−	0.967743i	−0.875139	−	0.483872i	$-0.839230\pi$
$587$		−	23.4466i		−	0.967743i	0.875139	−	0.483872i	$-0.160770\pi$
$588$	−6.85726	+	6.85726i	−0.282789	+	0.282789i
$589$			27.0151i			1.11314i
$590$	18.3906	+	14.6845i	0.757128	+	0.604550i
$591$			18.5305i			0.762242i
$592$	−2.83501	+	5.38170i	−0.116518	+	0.221187i
$593$	−20.7079	+	20.7079i	−0.850371	+	0.850371i	−0.990179	−	0.139807i	$-0.955352\pi$
$593$	−20.7079	+	20.7079i	−0.850371	+	0.850371i	0.139807	+	0.990179i	$0.455352\pi$
$594$	3.48668	−	3.48668i	0.143060	−	0.143060i
$595$	15.6393	−	19.5864i	0.641148	−	0.802963i
$596$		−	2.09937i		−	0.0859934i
$597$	−14.4851			−0.592834
$598$		−	15.2870i		−	0.625130i
$599$			35.8882i			1.46635i	0.680038	+	0.733177i	$0.261963\pi$
$599$			35.8882i			1.46635i	−0.680038	+	0.733177i	$0.738037\pi$
$600$	2.66535	−	4.23035i	0.108813	−	0.172703i
$601$	−2.20315			−0.0898682			−0.0449341	−	0.998990i	$-0.514308\pi$
$601$	−2.20315			−0.0898682			−0.0449341	+	0.998990i	$0.514308\pi$
$602$	16.2112	+	16.2112i	0.660719	+	0.660719i
$603$	5.74859	+	5.74859i	0.234101	+	0.234101i
$604$			16.4484i			0.669276i
$605$	−3.31510	−	29.5855i	−0.134778	−	1.20282i
$606$	9.89776	+	9.89776i	0.402069	+	0.402069i
$607$			37.3445i			1.51577i	0.652391	+	0.757883i	$0.273766\pi$
$607$			37.3445i			1.51577i	−0.652391	+	0.757883i	$0.726234\pi$
$608$	−5.44485	+	5.44485i	−0.220818	+	0.220818i
$609$	−1.91856	−	1.91856i	−0.0777441	−	0.0777441i
$610$	−3.04756	−	2.43341i	−0.123392	−	0.0985260i
$611$	0.996426	−	0.996426i	0.0403111	−	0.0403111i
$612$		−	2.74310i		−	0.110883i
$613$	6.97292	+	6.97292i	0.281634	+	0.281634i	0.833760	−	0.552127i	$-0.186183\pi$
$613$	6.97292	+	6.97292i	0.281634	+	0.281634i	−0.552127	+	0.833760i	$0.686183\pi$
$614$	11.5991	+	11.5991i	0.468103	+	0.468103i
$615$	−7.43874	−	5.93967i	−0.299959	−	0.239511i
$616$	14.2475	+	14.2475i	0.574049	+	0.574049i
$617$	8.33189	−	8.33189i	0.335429	−	0.335429i	−0.519215	−	0.854644i	$-0.673775\pi$
$617$	8.33189	−	8.33189i	0.335429	−	0.335429i	0.854644	+	0.519215i	$0.173775\pi$
$618$	8.49263	−	8.49263i	0.341623	−	0.341623i
$619$	24.7413			0.994437			0.497218	−	0.867625i	$-0.334355\pi$
$619$	24.7413			0.994437			0.497218	+	0.867625i	$0.334355\pi$
$620$	4.89501	−	6.13043i	0.196589	−	0.246204i
$621$	5.90249	+	5.90249i	0.236859	+	0.236859i
$622$	10.3616	−	10.3616i	0.415464	−	0.415464i
$623$	14.6092			0.585307
$624$	1.29496	−	1.29496i	0.0518398	−	0.0518398i
$625$	22.5508	−	10.7918i	0.902031	−	0.431671i
$626$	−22.6679			−0.905990
$627$	−37.9688			−1.51633
$628$	−13.6581	−	13.6581i	−0.545017	−	0.545017i
$629$	−7.77670	+	14.7625i	−0.310077	+	0.588621i
$630$	−5.70132	+	7.14024i	−0.227146	+	0.284474i
$631$	0.137530	+	0.137530i	0.00547496	+	0.00547496i	0.709839	−	0.704364i	$-0.248768\pi$
$631$	0.137530	+	0.137530i	0.00547496	+	0.00547496i	−0.704364	+	0.709839i	$0.748768\pi$
$632$	4.75210	−	4.75210i	0.189028	−	0.189028i
$633$	−5.99623	−	5.99623i	−0.238329	−	0.238329i
$634$	18.8950	+	18.8950i	0.750415	+	0.750415i
$635$	6.30283	−	7.89355i	0.250120	−	0.313246i
$636$	−9.93953			−0.394128
$637$	−17.7597			−0.703666
$638$	−2.31513	+	2.31513i	−0.0916569	+	0.0916569i
$639$			13.0269i			0.515338i
$640$	2.22216	−	0.248996i	0.0878386	−	0.00984245i
$641$	34.7424			1.37224			0.686121	−	0.727487i	$-0.259312\pi$
$641$	34.7424			1.37224			0.686121	+	0.727487i	$0.259312\pi$
$642$	14.9987			0.591951
$643$	−10.3530			−0.408282			−0.204141	−	0.978942i	$-0.565440\pi$
$643$	−10.3530			−0.408282			−0.204141	+	0.978942i	$0.565440\pi$
$644$	−24.1192	+	24.1192i	−0.950429	+	0.950429i
$645$	9.80366	+	7.82800i	0.386019	+	0.308227i
$646$	−14.9357	+	14.9357i	−0.587639	+	0.587639i
$647$		−	21.7902i		−	0.856663i	−0.903622	−	0.428331i	$-0.859102\pi$
$647$		−	21.7902i		−	0.856663i	0.903622	−	0.428331i	$-0.140898\pi$
$648$			1.00000i			0.0392837i
$649$	−36.6963	+	36.6963i	−1.44045	+	1.44045i
$650$	8.92965	−	2.02661i	0.350250	−	0.0794901i
$651$	−10.1372	+	10.1372i	−0.397308	+	0.397308i
$652$	16.1683			0.633200
$653$	42.4982			1.66308			0.831541	−	0.555464i	$-0.187459\pi$
$653$	42.4982			1.66308			0.831541	+	0.555464i	$0.187459\pi$
$654$	16.7348			0.654384
$655$	2.27963	−	2.85497i	0.0890726	−	0.111553i
$656$		−	4.25710i		−	0.166212i
$657$	−5.94865	+	5.94865i	−0.232079	+	0.232079i
$658$	−3.14425			−0.122576
$659$	17.1397			0.667669			0.333835	−	0.942632i	$-0.391657\pi$
$659$	17.1397			0.667669			0.333835	+	0.942632i	$0.391657\pi$
$660$	8.61613	+	6.87979i	0.335382	+	0.267795i
$661$	20.1373	+	20.1373i	0.783252	+	0.783252i	0.980378	−	0.197126i	$-0.0631609\pi$
$661$	20.1373	+	20.1373i	0.783252	+	0.783252i	−0.197126	+	0.980378i	$0.563161\pi$
$662$	−7.58835	−	7.58835i	−0.294930	−	0.294930i
$663$	3.55220	−	3.55220i	0.137956	−	0.137956i
$664$	0.579710	+	0.579710i	0.0224971	+	0.0224971i
$665$	69.9204	−	7.83468i	2.71140	−	0.303816i
$666$	2.83501	−	5.38170i	0.109854	−	0.208537i
$667$	−3.91921	−	3.91921i	−0.151753	−	0.151753i
$668$	−0.266278			−0.0103026
$669$	23.0313			0.890441
$670$	−11.3429	+	14.2057i	−0.438215	+	0.548813i
$671$	6.08106	−	6.08106i	0.234757	−	0.234757i
$672$	−4.08627			−0.157631
$673$	26.9868	−	26.9868i	1.04027	−	1.04027i	0.0411115	−	0.999155i	$-0.486910\pi$
$673$	26.9868	−	26.9868i	1.04027	−	1.04027i	0.999155	−	0.0411115i	$-0.0130899\pi$
$674$	−15.6272	−	15.6272i	−0.601936	−	0.601936i
$675$	−2.66535	+	4.23035i	−0.102590	+	0.162826i
$676$	−9.64617			−0.371006
$677$	−5.05044	+	5.05044i	−0.194104	+	0.194104i	−0.797467	−	0.603363i	$-0.793827\pi$
$677$	−5.05044	+	5.05044i	−0.194104	+	0.194104i	0.603363	+	0.797467i	$0.293827\pi$
$678$	4.25343	−	4.25343i	0.163352	−	0.163352i
$679$	50.3564	+	50.3564i	1.93250	+	1.93250i
$680$	6.09560	−	0.683022i	0.233756	−	0.0261927i
$681$	4.51853	+	4.51853i	0.173150	+	0.173150i
$682$	12.2326	+	12.2326i	0.468409	+	0.468409i
$683$		−	33.7252i		−	1.29046i	−0.763990	−	0.645229i	$-0.776762\pi$
$683$		−	33.7252i		−	1.29046i	0.763990	−	0.645229i	$-0.223238\pi$
$684$	5.44485	−	5.44485i	0.208189	−	0.208189i
$685$	−15.0746	+	18.8792i	−0.575971	+	0.721337i
$686$	7.79461	+	7.79461i	0.297600	+	0.297600i
$687$	10.8626	−	10.8626i	0.414433	−	0.414433i
$688$			5.61051i			0.213899i
$689$	−12.8713	−	12.8713i	−0.490357	−	0.490357i
$690$	−11.6466	+	14.5860i	−0.443378	+	0.555279i
$691$			38.3015i			1.45706i	0.685015	+	0.728529i	$0.259796\pi$
$691$			38.3015i			1.45706i	−0.685015	+	0.728529i	$0.740204\pi$
$692$	18.1556	+	18.1556i	0.690172	+	0.690172i
$693$	−14.2475	−	14.2475i	−0.541218	−	0.541218i
$694$	7.97256			0.302634
$695$	1.66785	+	14.8847i	0.0632652	+	0.564608i
$696$		−	0.663993i		−	0.0251686i
$697$		−	11.6776i		−	0.442322i
$698$	1.39367			0.0527513
$699$			21.0819i			0.797389i
$700$	−17.2864	−	10.8914i	−0.653364	−	0.411655i
$701$	−3.16581	+	3.16581i	−0.119571	+	0.119571i	−0.764360	−	0.644789i	$-0.776945\pi$
$701$	−3.16581	+	3.16581i	−0.119571	+	0.119571i	0.644789	+	0.764360i	$0.276945\pi$
$702$	−1.29496	+	1.29496i	−0.0488751	+	0.0488751i
$703$	−44.7387	+	13.8664i	−1.68735	+	0.522980i
$704$			4.93091i			0.185840i
$705$	−1.70988	+	0.191594i	−0.0643977	+	0.00721586i
$706$			8.13118i			0.306021i
$707$	40.4449	−	40.4449i	1.52109	−	1.52109i
$708$		−	10.5247i		−	0.395543i
$709$	−3.37894	−	3.37894i	−0.126899	−	0.126899i	0.640805	−	0.767704i	$-0.278601\pi$
$709$	−3.37894	−	3.37894i	−0.126899	−	0.126899i	−0.767704	+	0.640805i	$0.778601\pi$
$710$	−28.9480	+	3.24366i	−1.08640	+	0.121732i
$711$	−4.75210	+	4.75210i	−0.178217	+	0.178217i
$712$	2.52805	+	2.52805i	0.0947426	+	0.0947426i
$713$	−20.7081	+	20.7081i	−0.775526	+	0.775526i
$714$	−11.2090			−0.419488
$715$	2.24849	+	20.0666i	0.0840887	+	0.750447i
$716$	8.43042	−	8.43042i	0.315059	−	0.315059i
$717$		−	12.2543i		−	0.457644i
$718$	7.41829			0.276848
$719$			33.2657i			1.24060i	0.784364	+	0.620301i	$0.212989\pi$
$719$			33.2657i			1.24060i	−0.784364	+	0.620301i	$0.787011\pi$
$720$	−2.22216	+	0.248996i	−0.0828151	+	0.00927955i
$721$	−34.7032	−	34.7032i	−1.29241	−	1.29241i
$722$	−40.2927			−1.49954
$723$	−15.7585			−0.586066
$724$	−14.9316			−0.554927
$725$	1.76978	−	2.80893i	0.0657279	−	0.104321i
$726$	−9.41430	+	9.41430i	−0.349397	+	0.349397i
$727$		−	0.0260774i		−	0.000967156i	−1.00000		0.000483578i	$-0.999846\pi$
$727$		−	0.0260774i		−	0.000967156i	1.00000		0.000483578i	$-0.000153928\pi$
$728$	−5.29155	−	5.29155i	−0.196118	−	0.196118i
$729$		−	1.00000i		−	0.0370370i
$730$	−14.7000	−	11.7377i	−0.544073	−	0.434430i
$731$			15.3902i			0.569226i
$732$			1.74408i			0.0644632i
$733$	−4.32418	−	4.32418i	−0.159717	−	0.159717i	0.622724	−	0.782441i	$-0.286026\pi$
$733$	−4.32418	−	4.32418i	−0.159717	−	0.159717i	−0.782441	+	0.622724i	$0.786026\pi$
$734$	24.4204	−	24.4204i	0.901374	−	0.901374i
$735$	16.9454	+	13.5305i	0.625039	+	0.499080i
$736$	−8.34738			−0.307689
$737$	−28.3457	−	28.3457i	−1.04413	−	1.04413i
$738$			4.25710i			0.156706i
$739$	−4.68946			−0.172505			−0.0862523	−	0.996273i	$-0.527489\pi$
$739$	−4.68946			−0.172505			−0.0862523	+	0.996273i	$0.527489\pi$
$740$	12.6649	+	4.95982i	0.465572	+	0.182327i
$741$	14.1017			0.518039
$742$			40.6157i			1.49105i
$743$	−22.9763	−	22.9763i	−0.842918	−	0.842918i	0.146320	−	0.989237i	$-0.453257\pi$
$743$	−22.9763	−	22.9763i	−0.842918	−	0.842918i	−0.989237	+	0.146320i	$0.953257\pi$
$744$	−3.50837			−0.128623
$745$	−4.66513	+	0.522735i	−0.170917	+	0.0191515i
$746$	−25.6268	+	25.6268i	−0.938263	+	0.938263i
$747$	−0.579710	−	0.579710i	−0.0212105	−	0.0212105i
$748$			13.5260i			0.494558i
$749$		−	61.2887i		−	2.23944i
$750$	−10.0642	−	4.86950i	−0.367492	−	0.177809i
$751$		−	22.7491i		−	0.830126i	−0.909793	−	0.415063i	$-0.863759\pi$
$751$		−	22.7491i		−	0.830126i	0.909793	−	0.415063i	$-0.136241\pi$
$752$	−0.544094	−	0.544094i	−0.0198411	−	0.0198411i
$753$			12.8805i			0.469392i
$754$	0.859844	−	0.859844i	0.0313137	−	0.0313137i
$755$	36.5510	−	4.09560i	1.33023	−	0.149054i
$756$	4.08627			0.148616
$757$	18.9847			0.690010			0.345005	−	0.938601i	$-0.387877\pi$
$757$	18.9847			0.690010			0.345005	+	0.938601i	$0.387877\pi$
$758$	−1.27584			−0.0463407
$759$	−29.1046	−	29.1046i	−1.05643	−	1.05643i
$760$	13.4551	+	10.7436i	0.488067	+	0.389711i
$761$		−	5.29007i		−	0.191765i	−0.995393	−	0.0958825i	$-0.969433\pi$
$761$		−	5.29007i		−	0.191765i	0.995393	−	0.0958825i	$-0.0305673\pi$
$762$	−4.51738			−0.163648
$763$		−	68.3832i		−	2.47564i
$764$	3.66128	−	3.66128i	0.132461	−	0.132461i
$765$	−6.09560	+	0.683022i	−0.220387	+	0.0246947i
$766$	20.0723			0.725242
$767$	13.6291	−	13.6291i	0.492117	−	0.492117i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	2.00119	−	2.00119i	0.0721646	−	0.0721646i	−0.670103	−	0.742268i	$-0.733750\pi$
$769$	2.00119	−	2.00119i	0.0721646	−	0.0721646i	0.742268	+	0.670103i	$0.233750\pi$
$770$	28.1127	−	35.2079i	1.01311	−	1.26880i
$771$	14.7589	+	14.7589i	0.531528	+	0.531528i
$772$			7.43122i			0.267455i
$773$	−12.7879	+	12.7879i	−0.459948	+	0.459948i	−0.898638	−	0.438690i	$-0.855443\pi$
$773$	−12.7879	+	12.7879i	−0.459948	+	0.459948i	0.438690	+	0.898638i	$0.355443\pi$
$774$		−	5.61051i		−	0.201666i
$775$	−14.8417	−	9.35106i	−0.533128	−	0.335900i
$776$			17.4278i			0.625621i
$777$	−21.9911	−	11.5846i	−0.788927	−	0.415596i
$778$	8.42098	−	8.42098i	0.301907	−	0.301907i
$779$	23.1793	−	23.1793i	0.830483	−	0.830483i
$780$	−3.20005	−	2.55517i	−0.114580	−	0.0914896i
$781$		−	64.2346i		−	2.29849i
$782$	−22.8977			−0.818819
$783$			0.663993i			0.0237292i
$784$			9.69763i			0.346344i
$785$	−26.9497	+	33.7513i	−0.961875	+	1.20464i
$786$	−1.63387			−0.0582780
$787$	−14.1647	−	14.1647i	−0.504915	−	0.504915i	0.408046	−	0.912961i	$-0.366210\pi$
$787$	−14.1647	−	14.1647i	−0.504915	−	0.504915i	−0.912961	+	0.408046i	$0.866210\pi$
$788$	13.1030	+	13.1030i	0.466776	+	0.466776i
$789$			1.26953i			0.0451966i
$790$	−11.7432	−	9.37667i	−0.417803	−	0.333607i
$791$	−17.3807	−	17.3807i	−0.617985	−	0.617985i
$792$		−	4.93091i		−	0.175212i
$793$	−2.25852	+	2.25852i	−0.0802023	+	0.0802023i
$794$	4.91456	+	4.91456i	0.174411	+	0.174411i
$795$	2.47491	+	22.0872i	0.0877760	+	0.783354i
$796$	−10.2425	+	10.2425i	−0.363035	+	0.363035i
$797$			7.22178i			0.255809i	0.991787	+	0.127904i	$0.0408251\pi$
$797$			7.22178i			0.255809i	−0.991787	+	0.127904i	$0.959175\pi$
$798$	−22.2491	−	22.2491i	−0.787611	−	0.787611i
$799$	−1.49250	−	1.49250i	−0.0528010	−	0.0528010i
$800$	−1.10662	−	4.87600i	−0.0391250	−	0.172393i
$801$	−2.52805	−	2.52805i	−0.0893241	−	0.0893241i
$802$	9.79743	−	9.79743i	0.345959	−	0.345959i
$803$	29.3322	−	29.3322i	1.03511	−	1.03511i
$804$	8.12973			0.286714
$805$	59.6023	+	47.5911i	2.10071	+	1.67737i
$806$	−4.54320	−	4.54320i	−0.160027	−	0.160027i
$807$	7.55710	−	7.55710i	0.266022	−	0.266022i
$808$	13.9975			0.492432
$809$	−19.0001	+	19.0001i	−0.668008	+	0.668008i	−0.957255	−	0.289247i	$-0.906595\pi$
$809$	−19.0001	+	19.0001i	−0.668008	+	0.668008i	0.289247	+	0.957255i	$0.406595\pi$
$810$	2.22216	−	0.248996i	0.0780788	−	0.00874885i
$811$	24.8813			0.873702			0.436851	−	0.899534i	$-0.356094\pi$
$811$	24.8813			0.873702			0.436851	+	0.899534i	$0.356094\pi$
$812$	−2.71326			−0.0952167
$813$	14.9693	+	14.9693i	0.524996	+	0.524996i
$814$	−13.9792	+	26.5367i	−0.489969	+	0.930110i
$815$	−4.02585	−	35.9286i	−0.141020	−	1.25852i
$816$	−1.93966	−	1.93966i	−0.0679018	−	0.0679018i
$817$	−30.5484	+	30.5484i	−1.06875	+	1.06875i
$818$	−1.43202	−	1.43202i	−0.0500693	−	0.0500693i
$819$	5.29155	+	5.29155i	0.184902	+	0.184902i
$820$	−9.45997	+	1.06000i	−0.330356	+	0.0370169i
$821$	20.4258			0.712865			0.356433	−	0.934321i	$-0.383993\pi$
$821$	20.4258			0.712865			0.356433	+	0.934321i	$0.383993\pi$
$822$	10.8043			0.376844
$823$	39.9531	−	39.9531i	1.39268	−	1.39268i	0.573403	−	0.819274i	$-0.305623\pi$
$823$	39.9531	−	39.9531i	1.39268	−	1.39268i	0.819274	−	0.573403i	$-0.194377\pi$
$824$		−	12.0104i		−	0.418402i
$825$	13.1426	−	20.8595i	0.457567	−	0.726233i
$826$	−43.0068			−1.49640
$827$	23.3248			0.811081			0.405541	−	0.914077i	$-0.367083\pi$
$827$	23.3248			0.811081			0.405541	+	0.914077i	$0.367083\pi$
$828$	8.34738			0.290092
$829$	5.39568	−	5.39568i	0.187400	−	0.187400i	−0.607171	−	0.794571i	$-0.707696\pi$
$829$	5.39568	−	5.39568i	0.187400	−	0.187400i	0.794571	+	0.607171i	$0.207696\pi$
$830$	1.14386	−	1.43255i	0.0397040	−	0.0497247i
$831$	19.0989	−	19.0989i	0.662534	−	0.662534i
$832$		−	1.83135i		−	0.0634906i
$833$			26.6015i			0.921689i
$834$	4.73641	−	4.73641i	0.164008	−	0.164008i
$835$	0.0663023	+	0.591713i	0.00229449	+	0.0204771i
$836$	−26.8480	+	26.8480i	−0.928558	+	0.928558i
$837$	3.50837			0.121267
$838$	23.3375			0.806182
$839$	−21.8465			−0.754225			−0.377112	−	0.926167i	$-0.623083\pi$
$839$	−21.8465			−0.754225			−0.377112	+	0.926167i	$0.623083\pi$
$840$	1.01747	+	9.08036i	0.0351060	+	0.313302i
$841$			28.5591i			0.984797i
$842$	12.1830	−	12.1830i	0.419853	−	0.419853i
$843$	−9.32787			−0.321269
$844$	−8.47994			−0.291892
$845$	2.40186	+	21.4353i	0.0826265	+	0.737398i
$846$	0.544094	+	0.544094i	0.0187064	+	0.0187064i
$847$	38.4694	+	38.4694i	1.32182	+	1.32182i
$848$	−7.02831	+	7.02831i	−0.241353	+	0.241353i
$849$	−5.38400	−	5.38400i	−0.184778	−	0.184778i
$850$	−3.03557	−	13.3753i	−0.104119	−	0.458771i
$851$	−44.9231	−	23.6649i	−1.53994	−	0.811222i
$852$	9.21144	+	9.21144i	0.315579	+	0.315579i
$853$	−26.7385			−0.915510			−0.457755	−	0.889078i	$-0.651346\pi$
$853$	−26.7385			−0.915510			−0.457755	+	0.889078i	$0.651346\pi$
$854$	7.12681			0.243874
$855$	−13.4551	−	10.7436i	−0.460154	−	0.367423i
$856$	10.6057	−	10.6057i	0.362494	−	0.362494i
$857$	29.7105			1.01489			0.507446	−	0.861684i	$-0.330590\pi$
$857$	29.7105			1.01489			0.507446	+	0.861684i	$0.330590\pi$
$858$	6.38532	−	6.38532i	0.217991	−	0.217991i
$859$	−31.7210	−	31.7210i	−1.08231	−	1.08231i	−0.996294	−	0.0860136i	$-0.972587\pi$
$859$	−31.7210	−	31.7210i	−1.08231	−	1.08231i	−0.0860136	−	0.996294i	$-0.527413\pi$
$860$	12.4675	−	1.39700i	0.425137	−	0.0476372i
$861$	17.3957			0.592843
$862$	22.3232	−	22.3232i	0.760330	−	0.760330i
$863$	−38.1491	+	38.1491i	−1.29861	+	1.29861i	−0.369302	+	0.929309i	$0.620403\pi$
$863$	−38.1491	+	38.1491i	−1.29861	+	1.29861i	−0.929309	+	0.369302i	$0.879597\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	35.8240	−	44.8654i	1.21805	−	1.52547i
$866$	−1.25239	−	1.25239i	−0.0425581	−	0.0425581i
$867$	6.70013	+	6.70013i	0.227548	+	0.227548i
$868$			14.3362i			0.486601i
$869$	23.4321	−	23.4321i	0.794881	−	0.794881i
$870$	−1.47550	+	0.165332i	−0.0500241	+	0.00560528i
$871$	10.5277	+	10.5277i	0.356716	+	0.356716i
$872$	11.8333	−	11.8333i	0.400727	−	0.400727i
$873$		−	17.4278i		−	0.589841i
$874$	−45.4502	−	45.4502i	−1.53738	−	1.53738i
$875$	−19.8981	+	41.1250i	−0.672679	+	1.39028i
$876$			8.41266i			0.284237i
$877$	30.8709	+	30.8709i	1.04244	+	1.04244i	0.999059	+	0.0433789i	$0.0138123\pi$
$877$	30.8709	+	30.8709i	1.04244	+	1.04244i	0.0433789	+	0.999059i	$0.486188\pi$
$878$	−0.852686	−	0.852686i	−0.0287768	−	0.0287768i
$879$	−5.47107			−0.184535
$880$	10.9573	−	1.22778i	0.369369	−	0.0413884i
$881$			27.7954i			0.936451i	0.883609	+	0.468226i	$0.155107\pi$
$881$			27.7954i			0.936451i	−0.883609	+	0.468226i	$0.844893\pi$
$882$		−	9.69763i		−	0.326536i
$883$	34.7761			1.17031			0.585154	−	0.810922i	$-0.301034\pi$
$883$	34.7761			1.17031			0.585154	+	0.810922i	$0.301034\pi$
$884$		−	5.02356i		−	0.168961i
$885$	−23.3876	+	2.62062i	−0.786166	+	0.0880910i
$886$	13.9950	−	13.9950i	0.470171	−	0.470171i
$887$	−0.453518	+	0.453518i	−0.0152276	+	0.0152276i	−0.714680	−	0.699452i	$-0.753427\pi$
$887$	−0.453518	+	0.453518i	−0.0152276	+	0.0152276i	0.699452	+	0.714680i	$0.253427\pi$
$888$	−1.80078	−	5.81009i	−0.0604304	−	0.194974i
$889$			18.4593i			0.619104i
$890$	4.98825	−	6.24720i	0.167207	−	0.209407i
$891$			4.93091i			0.165192i
$892$	16.2856	−	16.2856i	0.545281	−	0.545281i
$893$		−	5.92502i		−	0.198273i
$894$	1.48448	+	1.48448i	0.0496483	+	0.0496483i
$895$	−20.8329	−	16.6346i	−0.696367	−	0.556033i
$896$	−2.88943	+	2.88943i	−0.0965291	+	0.0965291i
$897$	10.8095	+	10.8095i	0.360919	+	0.360919i
$898$	−2.16577	+	2.16577i	−0.0722726	+	0.0722726i
$899$	−2.32954			−0.0776944
$900$	1.10662	+	4.87600i	0.0368874	+	0.162533i
$901$	−19.2793	+	19.2793i	−0.642288	+	0.642288i
$902$		−	20.9914i		−	0.698936i
$903$	−22.9261			−0.762932
$904$		−	6.01525i		−	0.200064i
$905$	3.71790	+	33.1803i	0.123587	+	1.10295i
$906$	−11.6308	−	11.6308i	−0.386407	−	0.386407i
$907$	39.3372			1.30617			0.653086	−	0.757284i	$-0.273474\pi$
$907$	39.3372			1.30617			0.653086	+	0.757284i	$0.273474\pi$
$908$	6.39016			0.212065
$909$	−13.9975			−0.464269
$910$	−10.4411	+	13.0763i	−0.346119	+	0.433474i
$911$	9.39778	−	9.39778i	0.311362	−	0.311362i	−0.534075	−	0.845437i	$-0.679340\pi$
$911$	9.39778	−	9.39778i	0.311362	−	0.311362i	0.845437	+	0.534075i	$0.179340\pi$
$912$		−	7.70018i		−	0.254978i
$913$	2.85849	+	2.85849i	0.0946023	+	0.0946023i
$914$			15.2516i			0.504478i
$915$	3.87564	−	0.434271i	0.128125	−	0.0143566i
$916$		−	15.3620i		−	0.507574i
$917$			6.67642i			0.220475i
$918$	1.93966	+	1.93966i	0.0640184	+	0.0640184i
$919$	−8.13901	+	8.13901i	−0.268481	+	0.268481i	−0.828488	−	0.560007i	$-0.810799\pi$
$919$	−8.13901	+	8.13901i	−0.268481	+	0.268481i	0.560007	+	0.828488i	$0.310799\pi$
$920$	2.07847	+	18.5492i	0.0685251	+	0.611550i
$921$	−16.4037			−0.540519
$922$	14.4647	+	14.4647i	0.476368	+	0.476368i
$923$			23.8569i			0.785258i
$924$	−20.1490			−0.662854
$925$	7.86800	−	29.3785i	0.258698	−	0.965958i
$926$	17.5203			0.575752
$927$			12.0104i			0.394473i
$928$	−0.469514	−	0.469514i	−0.0154126	−	0.0154126i
$929$	37.2885			1.22339			0.611697	−	0.791092i	$-0.290487\pi$
$929$	37.2885			1.22339			0.611697	+	0.791092i	$0.290487\pi$
$930$	0.873572	+	7.79617i	0.0286456	+	0.255646i
$931$	−52.8021	+	52.8021i	−1.73052	+	1.73052i
$932$	14.9071	+	14.9071i	0.488299	+	0.488299i
$933$			14.6536i			0.479736i
$934$			17.1724i			0.561900i
$935$	30.0568	−	3.36791i	0.982964	−	0.110143i
$936$			1.83135i			0.0598595i
$937$	13.1402	+	13.1402i	0.429272	+	0.429272i	0.888380	−	0.459108i	$-0.151831\pi$
$937$	13.1402	+	13.1402i	0.429272	+	0.429272i	−0.459108	+	0.888380i	$0.651831\pi$
$938$		−	33.2203i		−	1.08468i
$939$	16.0286	−	16.0286i	0.523074	−	0.523074i
$940$	−1.07359	+	1.34454i	−0.0350166	+	0.0438542i
$941$	25.4378			0.829248			0.414624	−	0.909993i	$-0.363913\pi$
$941$	25.4378			0.829248			0.414624	+	0.909993i	$0.363913\pi$
$942$	19.3155			0.629332
$943$	35.5356			1.15720
$944$	−7.44209	−	7.44209i	−0.242219	−	0.242219i
$945$	−1.01747	−	9.08036i	−0.0330982	−	0.295384i
$946$			27.6649i			0.899464i
$947$	15.8796			0.516019			0.258009	−	0.966142i	$-0.416933\pi$
$947$	15.8796			0.516019			0.258009	+	0.966142i	$0.416933\pi$
$948$			6.72048i			0.218271i
$949$	−10.8940	+	10.8940i	−0.353636	+	0.353636i
$950$	20.5237	−	32.5745i	0.665877	−	1.05686i
$951$	−26.7215			−0.866504
$952$	−7.92599	+	7.92599i	−0.256883	+	0.256883i
$953$	−21.5090	−	21.5090i	−0.696745	−	0.696745i	0.266962	−	0.963707i	$-0.413980\pi$
$953$	−21.5090	−	21.5090i	−0.696745	−	0.696745i	−0.963707	+	0.266962i	$0.913980\pi$
$954$	7.02831	−	7.02831i	0.227550	−	0.227550i
$955$	−9.04760	−	7.22431i	−0.292774	−	0.233773i
$956$	−8.66507	−	8.66507i	−0.280248	−	0.280248i
$957$		−	3.27409i		−	0.105836i
$958$	−16.4237	+	16.4237i	−0.530626	+	0.530626i
$959$		−	44.1494i		−	1.42566i
$960$	−1.39524	+	1.74737i	−0.0450311	+	0.0563962i
$961$		−	18.6913i		−	0.602946i
$962$	5.19189	−	9.85577i	0.167393	−	0.317763i
$963$	−10.6057	+	10.6057i	−0.341763	+	0.341763i
$964$	−11.1430	+	11.1430i	−0.358891	+	0.358891i
$965$	16.5134	−	1.85035i	0.531584	−	0.0595648i
$966$		−	34.1097i		−	1.09746i
$967$	17.3334			0.557403			0.278702	−	0.960378i	$-0.410096\pi$
$967$	17.3334			0.557403			0.278702	+	0.960378i	$0.410096\pi$
$968$			13.3138i			0.427923i
$969$		−	21.1223i		−	0.678547i
$970$	38.7273	−	4.33945i	1.24346	−	0.139331i
$971$	37.2252			1.19461			0.597307	−	0.802013i	$-0.296238\pi$
$971$	37.2252			1.19461			0.597307	+	0.802013i	$0.296238\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−19.3543	−	19.3543i	−0.620469	−	0.620469i
$974$		−	17.8636i		−	0.572387i
$975$	−4.88119	+	7.74725i	−0.156323	+	0.248110i
$976$	1.23325	+	1.23325i	0.0394755	+	0.0394755i
$977$		−	48.3802i		−	1.54782i	−0.633296	−	0.773910i	$-0.718298\pi$
$977$		−	48.3802i		−	1.54782i	0.633296	−	0.773910i	$-0.281702\pi$
$978$	−11.4327	+	11.4327i	−0.365578	+	0.365578i
$979$	12.4656	+	12.4656i	0.398401	+	0.398401i
$980$	21.5497	−	2.41468i	0.688380	−	0.0771340i
$981$	−11.8333	+	11.8333i	−0.377809	+	0.377809i
$982$		−	38.7653i		−	1.23705i
$983$	20.0257	+	20.0257i	0.638721	+	0.638721i	0.950240	−	0.311519i	$-0.100838\pi$
$983$	20.0257	+	20.0257i	0.638721	+	0.638721i	−0.311519	+	0.950240i	$0.600838\pi$
$984$	3.01023	+	3.01023i	0.0959625	+	0.0959625i
$985$	25.8544	−	32.3797i	0.823791	−	1.03170i
$986$	−1.28792	−	1.28792i	−0.0410158	−	0.0410158i
$987$	2.22332	−	2.22332i	0.0707690	−	0.0707690i
$988$	9.97141	−	9.97141i	0.317233	−	0.317233i
$989$	−46.8331			−1.48921
$990$	−10.9573	+	1.22778i	−0.348245	+	0.0390214i
$991$	−6.78432	−	6.78432i	−0.215511	−	0.215511i	0.591093	−	0.806604i	$-0.298697\pi$
$991$	−6.78432	−	6.78432i	−0.215511	−	0.215511i	−0.806604	+	0.591093i	$0.798697\pi$
$992$	−2.48079	+	2.48079i	−0.0787653	+	0.0787653i
$993$	10.7315			0.340555
$994$	37.6404	−	37.6404i	1.19388	−	1.19388i
$995$	25.3108	+	20.2101i	0.802406	+	0.640704i
$996$	−0.819833			−0.0259774
$997$	−7.43038			−0.235323			−0.117661	−	0.993054i	$-0.537540\pi$
$997$	−7.43038			−0.235323			−0.117661	+	0.993054i	$0.537540\pi$
$998$	−7.54787	−	7.54787i	−0.238924	−	0.238924i
$999$	1.80078	+	5.81009i	0.0569743	+	0.183823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.l.b.697.3	yes	40
5.3	odd	4		1110.2.o.b.253.18	yes	40
37.6	odd	4		1110.2.o.b.487.18	yes	40
185.43	even	4	inner	1110.2.l.b.43.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.b.43.3	✓	40	185.43	even	4	inner
1110.2.l.b.697.3	yes	40	1.1	even	1	trivial
1110.2.o.b.253.18	yes	40	5.3	odd	4
1110.2.o.b.487.18	yes	40	37.6	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.248996 + 2.22216i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.88943 - 2.88943i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(0.248996 + 2.22216i) q^{5} +(0.707107 - 0.707107i) q^{6} +(-2.88943 - 2.88943i) q^{7} -1.00000i q^{8} +1.00000i q^{9} +(-2.22216 + 0.248996i) q^{10} -4.93091i q^{11} +(0.707107 + 0.707107i) q^{12} +1.83135i q^{13} +(2.88943 - 2.88943i) q^{14} +(1.39524 - 1.74737i) q^{15} +1.00000 q^{16} +2.74310 q^{17} -1.00000 q^{18} +(5.44485 + 5.44485i) q^{19} +(-0.248996 - 2.22216i) q^{20} +4.08627i q^{21} +4.93091 q^{22} +8.34738i q^{23} +(-0.707107 + 0.707107i) q^{24} +(-4.87600 + 1.10662i) q^{25} -1.83135 q^{26} +(0.707107 - 0.707107i) q^{27} +(2.88943 + 2.88943i) q^{28} +(-0.469514 + 0.469514i) q^{29} +(1.74737 + 1.39524i) q^{30} +(2.48079 + 2.48079i) q^{31} +1.00000i q^{32} +(-3.48668 + 3.48668i) q^{33} +2.74310i q^{34} +(5.70132 - 7.14024i) q^{35} -1.00000i q^{36} +(-2.83501 + 5.38170i) q^{37} +(-5.44485 + 5.44485i) q^{38} +(1.29496 - 1.29496i) q^{39} +(2.22216 - 0.248996i) q^{40} -4.25710i q^{41} -4.08627 q^{42} +5.61051i q^{43} +4.93091i q^{44} +(-2.22216 + 0.248996i) q^{45} -8.34738 q^{46} +(-0.544094 - 0.544094i) q^{47} +(-0.707107 - 0.707107i) q^{48} +9.69763i q^{49} +(-1.10662 - 4.87600i) q^{50} +(-1.93966 - 1.93966i) q^{51} -1.83135i q^{52} +(-7.02831 + 7.02831i) q^{53} +(0.707107 + 0.707107i) q^{54} +(10.9573 - 1.22778i) q^{55} +(-2.88943 + 2.88943i) q^{56} -7.70018i q^{57} +(-0.469514 - 0.469514i) q^{58} +(-7.44209 - 7.44209i) q^{59} +(-1.39524 + 1.74737i) q^{60} +(1.23325 + 1.23325i) q^{61} +(-2.48079 + 2.48079i) q^{62} +(2.88943 - 2.88943i) q^{63} -1.00000 q^{64} +(-4.06955 + 0.455999i) q^{65} +(-3.48668 - 3.48668i) q^{66} +(5.74859 - 5.74859i) q^{67} -2.74310 q^{68} +(5.90249 - 5.90249i) q^{69} +(7.14024 + 5.70132i) q^{70} +13.0269 q^{71} +1.00000 q^{72} +(5.94865 + 5.94865i) q^{73} +(-5.38170 - 2.83501i) q^{74} +(4.23035 + 2.66535i) q^{75} +(-5.44485 - 5.44485i) q^{76} +(-14.2475 + 14.2475i) q^{77} +(1.29496 + 1.29496i) q^{78} +(4.75210 + 4.75210i) q^{79} +(0.248996 + 2.22216i) q^{80} -1.00000 q^{81} +4.25710 q^{82} +(-0.579710 + 0.579710i) q^{83} -4.08627i q^{84} +(0.683022 + 6.09560i) q^{85} -5.61051 q^{86} +0.663993 q^{87} -4.93091 q^{88} +(-2.52805 + 2.52805i) q^{89} +(-0.248996 - 2.22216i) q^{90} +(5.29155 - 5.29155i) q^{91} -8.34738i q^{92} -3.50837i q^{93} +(0.544094 - 0.544094i) q^{94} +(-10.7436 + 13.4551i) q^{95} +(0.707107 - 0.707107i) q^{96} -17.4278 q^{97} -9.69763 q^{98} +4.93091 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} - 4 q^{7}+O(q^{10}) \) 40 * q - 40 * q^4 - 4 * q^7	\( 40 q - 40 q^{4} - 4 q^{7} + 4 q^{14} + 40 q^{16} + 24 q^{17} - 40 q^{18} + 4 q^{19} + 8 q^{22} + 8 q^{25} + 8 q^{26} + 4 q^{28} + 28 q^{31} - 4 q^{33} + 20 q^{35} + 20 q^{37} - 4 q^{38} + 4 q^{39} + 16 q^{42} - 16 q^{47} + 16 q^{51} + 20 q^{53} + 16 q^{55} - 4 q^{56} - 4 q^{59} - 8 q^{61} - 28 q^{62} + 4 q^{63} - 40 q^{64} - 4 q^{65} - 4 q^{66} + 16 q^{67} - 24 q^{68} - 8 q^{69} + 12 q^{70} + 40 q^{71} + 40 q^{72} + 8 q^{73} - 8 q^{74} + 16 q^{75} - 4 q^{76} - 24 q^{77} + 4 q^{78} - 12 q^{79} - 40 q^{81} - 24 q^{82} - 8 q^{83} - 8 q^{85} + 8 q^{87} - 8 q^{88} + 12 q^{89} - 24 q^{91} + 16 q^{94} - 28 q^{95} + 40 q^{97} - 56 q^{98} + 8 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 - 4 * q^7 + 4 * q^14 + 40 * q^16 + 24 * q^17 - 40 * q^18 + 4 * q^19 + 8 * q^22 + 8 * q^25 + 8 * q^26 + 4 * q^28 + 28 * q^31 - 4 * q^33 + 20 * q^35 + 20 * q^37 - 4 * q^38 + 4 * q^39 + 16 * q^42 - 16 * q^47 + 16 * q^51 + 20 * q^53 + 16 * q^55 - 4 * q^56 - 4 * q^59 - 8 * q^61 - 28 * q^62 + 4 * q^63 - 40 * q^64 - 4 * q^65 - 4 * q^66 + 16 * q^67 - 24 * q^68 - 8 * q^69 + 12 * q^70 + 40 * q^71 + 40 * q^72 + 8 * q^73 - 8 * q^74 + 16 * q^75 - 4 * q^76 - 24 * q^77 + 4 * q^78 - 12 * q^79 - 40 * q^81 - 24 * q^82 - 8 * q^83 - 8 * q^85 + 8 * q^87 - 8 * q^88 + 12 * q^89 - 24 * q^91 + 16 * q^94 - 28 * q^95 + 40 * q^97 - 56 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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